Un terreno de forma rectangular tiene un perímetro de 105 metros. Si el ancho es la mitad del largo, ¿Cuáles son las medidas del terreno? *

Answers

Answer 1

Sea "l" la medida del largo del terreno y "a" la medida del ancho del terreno.

De acuerdo con el problema, el ancho es la mitad del largo, es decir, a = l/2.

El perímetro de un rectángulo se calcula sumando las longitudes de sus cuatro lados, por lo que en este caso:

Perímetro = 2l + 2a = 2l + 2(l/2) = 3l

Sabemos que el perímetro es de 105 metros, entonces:

3l = 105

l = 105/3 = 35

Por lo tanto, el largo del terreno es 35 metros. Y, como el ancho es la mitad del largo, entonces:

a = l/2 = 35/2 = 17.5

Por lo tanto, el ancho del terreno es de 17.5 metros.

En resumen, las medidas del terreno son 35 metros de largo y 17.5 metros de ancho.

To know more about del terreno refer here:

https://brainly.com/question/31136130

#SPJ11


Related Questions

Expand up to the 4th term
√1+3x

Answers

Answer:

1+3x

Step-by-step explanation:

[tex] \sqrt{1 } = 1 \\ 1 + 3x = 1 + 3x[/tex]

What is the total surface area of a cylinder with a base
diameter of 9 inches and a height of 6 inches? (use 3.14 for
ti)

Answers

Answer:

423.9

Step-by-step explanation:

To solve this problem you need to use the formula for surface area. This formula can either be used with the radius or the diameter. I prefer using diameter because it is easier to remember and it is easier to calculate. The formula writes as follows: [tex]SA=d\pi h+d\pi ^{2}\\\\[/tex]. To use this formula all we have to do is insert the values into the formula and solve.

[tex]SA=d\pi h+d\pi ^{2}\\\\SA=(9)\pi(6)+\pi(9) ^{2}\\\\SA=54\pi+81\pi\\\\SA=54\pi+81\pi\\\\SA=135\pi\\\\SA=423.9[/tex]

423.9 is our answer.

2. Ryan is writing the program for a video game.


For one part of the game he uses the rule (x,y)â(x-3,y+8) to move points on the screen.


(a) What output does the rule give when the input is (-7,-3)? Show your work.


(b) What output does the rule give when the input is (10,-5)? Show your work

Answers

(a) When the input is (-7,-3), the rule (x,y) → (x-3,y+8) moves the point 3 units to the left and 8 units up.

So we can apply this rule to the input (-7,-3) as follows:

(-7,-3) → (-7-3,-3+8)

(-7,-3) → (-10,5)

Therefore, the output is (-10,5).

(b) When the input is (10,-5), the rule (x,y) → (x-3,y+8) moves the point 3 units to the left and 8 units up. So we can apply this rule to the input (10,-5) as follows:

(10,-5) → (10-3,-5+8)

(10,-5) → (7,3)

Therefore, the output is (7,3).

To know more about moves the point refer here

https://brainly.com/question/29988507#

#SPJ11

If it costs 0. 15 per square inch for the wood then what is the cost for design A and Design B

Answers

To calculate the cost for Design A and Design B, we need to know the size of each design in square inches. Once we have that information, we can multiply the size of each design by the cost per square inch of wood to determine the total cost.

Let's say Design A is 10 inches by 10 inches, which is a total of 100 square inches. To calculate the cost for Design A, we would multiply 100 by 0.15, which gives us a total cost of $15.

Similarly, let's say Design B is 8 inches by 12 inches, which is a total of 96 square inches. To calculate the cost for Design B, we would multiply 96 by 0.15, which gives us a total cost of $14.40.

Therefore, the cost for Design A is $15 and the cost for Design B is $14.40.

In summary, the cost of a wooden design can be calculated by multiplying the size of the design in square inches by the cost per square inch of wood. In this case, we used a cost of 0.15 per square inch and calculated the cost for Design A and Design B. It is important to know the size of the design before calculating the cost.

To know more about cost refer here

https://brainly.in/question/32001772#

#SPJ11

Triangle XYZ undergoes a dilation to produce triangle X'Y'Z'. The coordinates of both triangles are shown.
X(8.2)→ X'(4,1)
Y(-10,4)→Y'(-5,2)
Z(-2,0) Z’(-1,0)
What is the scale factor of the dilation?

Answers

The scale factor used in the dilation of the triangles is 1/2

Determining the scale factor used.

From the question, we have the following parameters that can be used in our computation:

XYZ with vertices at X(8, 2)X'Y'Z' with vertices at X'(4, 1)

The scale factor is calculated as

Scale factor  = X'/X

Substitute the known values in the above equation, so, we have the following representation

Scale factor  = (4, 1)/(8, 2)

Evaluate

Scale factor = 1/2

Hence, the scale factor is 1/2

Read more about scale factor at

brainly.com/question/29229124

#SPJ1

The radius of a base is 9 cm. The height is 12 cm . What is the volume of the cone?

Answers

volume =πr^2h

=π(9)^2*12

=π81*12

=972πcm^3

Ocala software systems operates a technical support center for its software customers. if customers have installation or use problems with ocala software products, they may telephone the technical support center and obtain free consultation. currently, ocala operates its support center with one consultant. if the consultant is busy when a new customer call arrives, the customer hears a recorded message stating that all consultants are currently busy with other customers. the customer is then asked to hold and is told that a consultant will provide assistance as soon as possible. the customer calls follow a poisson probability distribution, with an arrival rate of seven calls per hour. on average, it takes 8.5 minutes for a consultant to answer a customer's questions. the service time follows an exponential probability distribution. to improve customer service, ocala software systems wants to investigate the effect of using a second consultant at its technical support center. what is the probability that a customer will have to wait for one of the consultants

Answers

The probability that a customer has to wait for one of the consultants (Pw) is 0.9516.

To find the probability that a customer will have to wait for one of the consultants, we need to analyze the current system and compare it to the proposed system with two consultants. Here's a step-by-step explanation:

1. Identify the given parameters:
- Arrival rate (λ) = 7 calls per hour
- Service rate (µ) = 1 call per 8.5 minutes = 60 minutes / 8.5 minutes = 7.06 calls per hour (approximately)

2. Calculate the traffic intensity (ρ):
- ρ = λ / µ = 7 / 7.06 = 0.9915 (approximately)

3. Find the probability of 0 customers in the system (P0) for a 2-consultant system:
- P0 = 1 / (1 + (2 * ρ) + (ρ^2 / (1 - ρ))) = 1 / (1 + (2 * 0.9915) + (0.9915^2 / (1 - 0.9915))) ≈ 0.0086

4. Calculate the probability that a customer has to wait for one of the consultants (Pw):
- Pw = (ρ^2 / (2 * (1 - ρ))) * P0 = (0.9915^2 / (2 * (1 - 0.9915))) * 0.0086 ≈ 0.9516

So, there is approximately a 95.16% chance that a customer will have to wait for one of the consultants at Ocala Software Systems' technical support center when two consultants are employed.

Learn more about probability,

https://brainly.com/question/24756209

#SPJ11

‘Vehicles approaching a certain road junction from town A can either turn left, turn right or go straight on. Over time it has been noted that of the vehicles approaching this particular junction from town A, 55% turn left, 15% turn right and 30% go straight on. The direction a vehicle takes at the junction is independent of the direction any other vehicle takes at the junction.


(i) Find the probability that, of the next three vehicles approaching the junction from town A, one goes straight on and the other two either both turn left or both turn right. ’

Answers

To solve this problem, we can use the multiplication rule of probability, which states that the probability of two or more independent events occurring together is the product of their individual probabilities.

Let L, R, and S be the events that a vehicle turns left, turns right, and goes straight on, respectively. We want to find the probability of the following event:

E: One vehicle goes straight on and the other two either both turn left or both turn right.

We can break down event E into two sub-events: one vehicle goes straight on and the other two vehicles both turn left or both turn right. Let's calculate the probabilities of these sub-events separately:

- Probability that one vehicle goes straight on: P(S) = 0.3

- Probability that the other two vehicles both turn left or both turn right: P((LL) or (RR)) = P(LL) + P(RR)

To find P(LL) and P(RR), we can use the multiplication rule again. Since the events are independent, we can multiply their individual probabilities:

- Probability that two vehicles both turn left: P(LL) = P(L) × P(L) = 0.55 × 0.55 = 0.3025

- Probability that two vehicles both turn right: P(RR) = P(R) × P(R) = 0.15 × 0.15 = 0.0225

Therefore, the probability of event E is:

P(E) = P(S) × P((LL) or (RR))

    = 0.3 × (P(LL) + P(RR))

    = 0.3 × (0.3025 + 0.0225)

    = 0.0975

So the probability that, of the next three vehicles approaching the junction from town A, one goes straight on and the other two either both turn left or both turn right is 0.0975 or approximately 0.1 (rounded to one decimal place).

To know more about probability  refer here

https://brainly.com/question/30034780#

#SPJ11

A store sells packages of comic books with a poster. A poster and 2 comics cost ​$7.50. A poster and 11 comics cost ​$16.50. Write a linear function rule that models the cost y of a package containing any number x of comic books.
Suppose another store sells a similar​ package, modeled by a linear function rule with initial value ​$5.75. Use pencil and paper. Explain which store has the better deal.
The linear function rule is y =

Answers

The linear function rule that models the cost y of a package containing any number x of comic books is y = $6.50 + $1.00x and for 10 comic books, the second store has the better deal.

What do you mean by Linear function ?

A linear function is a mathematical function where the graph of the function is a straight line. It can be written in the form y = mx + b, where x and y are the variables, m is the slope of the line, and b is the y-intercept (the point where the line intersects the y-axis). The slope represents the rate of change of the function, while the y-intercept is the value of the function when x is equal to zero.

To write a linear function rule that models the cost y of a package containing any number x of comic books, we can use the given information to set up a system of equations:

Poster + 2 Comics = $7.50

Poster + 11 Comics = $16.50

We can solve for the cost of the poster and the cost of one comic book by subtracting the first equation from the second:

9 Comics = $9.00

1 Comic = $1.00

Then, we can use the cost of one comic to set up a linear function rule:

y = cost of poster + cost of x comics

y = $6.50 + $1.00x

Therefore, the linear function rule that models the cost y of a package containing any number x of comic books is y = $6.50 + $1.00x.

For the second store, the linear function rule is given as y = $5.75 + $1.00x.

To determine which store has the better deal, we can compare the cost of each package for a specific number of comic books. For example, if we want to buy 10 comic books, the cost at the first store would be:

y = $6.50 + $1.00(10) = $16.50

The cost at the second store would be:

y = $5.75 + $1.00(10) = $15.75

Therefore, for 10 comic books, the second store has the better deal. However, for a different number of comic books, the better deal may be at a different store. We can use the linear function rules to compare the costs for any number of comic books

Learn more about Linear function here:

brainly.com/question/20286983

#SPJ1

-7 + 4c = 7c + 6 --------

Answers

In the given equation, -7 + 4c = 7c + 6, the solution is c = -13/3

Solving linear equations

From the question, we are to solve the one-variable linear equation

From the given information,

The given equation is

-7 + 4c = 7c + 6

To solve the equation, we will determine the value of c

Solving the equation

-7 + 4c = 7c + 6

Subtract 4c from both sides of the equation

-7 + 4c - 4c = 7c - 4c + 6

-7 = = 3c + 6

Subtract 6 from both sides of the equation

-7 - 6 = 3c + 6 - 6

-13 = 3c

This can be wroitten as

3c = -13

Divide both sides by 3

3c/3 = -13/3

c = -13/3

Hence, the value of c is -13/3

Learn more on Solving linear equations here: https://brainly.com/question/27882730

#SPJ1

Which type of bankruptcy will affect a person's credit score for seven years?


chapter 7


chapter 9


chapter 11


chapter 9

Answers

The type of bankruptcy that typically affects a person's credit score for seven years is Chapter 7 bankruptcy.

Chapter 7 bankruptcy involves the liquidation of assets to pay off debts, and it remains on a person's credit report for up to seven years from the filing date. This can have a significant negative impact on a person's credit score and their ability to obtain credit in the future.

Chapter 9 bankruptcy is specifically designed for municipalities such as cities, towns, and counties, and it does not apply to individuals or affect personal credit scores.

Chapter 11 bankruptcy is primarily used by businesses to reorganize their debts and continue operating. While it can affect a business owner's personal credit if they have personal liability for the business debts, it does not have a specific time frame for how long it remains on a credit report. The impact on an individual's credit score can vary depending on the circumstances and how the bankruptcy is structured.

Hence the answer is Chapter 7.

Learn more about bankruptcy click;

https://brainly.com/question/30628707

#SPJ12

Answer:

Chapter 13

Step-by-step explanation:

it’s not on there but that’s the answer

The volume of a cone is 2560π cm^3 . The diameter of the circular base is 32 cm. What is the height of the cone?

Answers

The height of the cone is 30 cm

How to calculate the height of the cone?


The first step is to write out the parameters given in the question

Volume of the cone= 2560π cm³

Diameter of the circular base is 32 cm

radius= diameter/2

= 32/2

= 16

The formula for calculating the height of the cone is

Height= volume ÷ 1/3 πr²

height= 2560 πcm³ ÷ 1/3 πr²

height= 2560 ÷ 0.333(16²)

height= 2560 ÷ 0.333(256)

height= 2560÷ 85.248

height= 30

Hence the height of the cone is 30 cm

Read more on height here

https://brainly.com/question/16547340

#SPJ1

Answer:

height = 9.54cm

Step-by-step explanation:

Volume of a cone = 2560cm³

Radius = diameter/ 2 = 32/2 = 16

height = ?

volume of a cone =

[tex]volume \: of \: a \: cone = \frac{1}{3} \pi {r}^{2} h \\ 2560 = \frac{1}{3} \times \frac{22}{7} \times 16 \times 16 \times h \\ 2560 = \frac{22}{21} \times 256 \times h \\ 2560 = \frac{5,632h}{21} \\ 21 \times 2560 = 21 \times \frac{5632h}{21} \\ 53,760 = 5632h \\ \frac{53760}{5632} = \frac{5632h}{5632} \\ 9.54cm = h[/tex]

height = 9.54cm

G(x)=5−2xg, left parenthesis, x, right parenthesis, equals, 5, minus, 2, x Determine for each x xx-value whether it is in the domain of g gg or not

Answers

The domain of function is the set of all possible values of x for which the function is defined. In this case, the function G(x) = 5 - 2x is defined for all real numbers of x.

The collection of all feasible input values (x-values) for which a function may be defined is known as the domain of function. In other words, it is the collection of all x values that may be passed into the function and provide a legitimate result (a y-value).

The function G(x) = 5 - 2x in this instance is a linear function, meaning it is defined for all real values of x. This is so that we may plug in any real value for x, and the function will output a real number for G(x) that corresponds. As an illustration, when we enter x = 0, we obtain G(0) = 5 - 2(0) = 5, and when we enter x = 2, we obtain G(2) = 5 - 2(2) = 1.

To learn more about domain of function, refer to:
https://brainly.com/question/28934802

#SPJ4

Find the nth Maclaurin polynomial for the fu f(x) = tan x, n = 3 3 = P(x) I

Answers

The 3rd Maclaurin polynomial for f(x) = tan x is P(x) = x + (1/3)x^3.

Recall that the Maclaurin series expansion for tan x is given by:

tan x = x + (1/3)x^3 + (2/15)x^5 + ...

To find the 3rd Maclaurin polynomial, we only need to take the first three terms of the series expansion, since n = 3.

Thus, the 3rd Maclaurin polynomial for f(x) = tan x is given by:

P(x) = x + (1/3)x^3.

Note that the first two terms of the polynomial, x and (1/3)x^3, correspond to the first two terms of the Maclaurin series expansion for tan x.

The third term of the polynomial would correspond to the next term in the series expansion, which is (2/15)x^5. However, since we are only finding the 3rd Maclaurin polynomial, we do not need to include this term.

For more questions like Polynomial click the link below:

https://brainly.com/question/11536910

#SPJ11

Simplify 35x raise to the power 5 y raise to the power 3 ÷ 7xy raise to the power 2

Answers

Firstly, we can simplify the numerator which is 35x raised to the power 5 times y raised to the power 3. To do this, we can multiply the coefficients and add the exponents of the variables with the same base. Thus, the numerator simplifies to 35x^5y^3.


Next, we need to simplify the denominator which is 7xy raised to the power 2. Similarly, we can multiply the coefficients and add the exponents of the variables with the same base. Thus, the denominator simplifies to 7x^1y^1 (since x and y each have a power of 1).


Now we can divide the numerator by the denominator. To do this, we divide the coefficients (35/7 = 5) and subtract the exponents of the variables with the same base (x^5/x^1 = x^4 and y^3/y^1 = y^2). Therefore, the simplified form of the given expression is 5x^4y^2.


In summary, to simplify the given expression, we used the power and quotient rules of exponents. We multiplied coefficients and added exponents of variables with the same base, and then divided coefficients and subtracted exponents of variables with the same base. The final simplified form is 5x^4y^2.

To know more about power and quotient refer here:

https://brainly.com/question/29018204#

#SPJ11

See image for the work

Answers

The number of horizontal rails for 10 sections is

60

The rule for the post is to multiply the number of section by 3

The rule for the rail is to multiply the post by 2

How to find the rules

The rules is calculated using the unit value and comparing with other values

the rule for the number of post

1 section requires 3 posts hence multiplication by 3, comparing shows that multiplying by 3 gives the number of post

the rule for the number of rails

1 section requires 6 rails hence multiplication by 6, comparing shows that multiplying each section by 6 gives the correponding number of rails

Learn more about function rule at;

https://brainly.com/question/30139621

#SPJ1

Se tiene dos canastas. Cada una contiene calabazas y zanahorias. En la primera canasta hay el doble de kilos de calabaza que en la segunda y en la segunda hay tres kilos más de zanahoria que los kilos de calabaza que hay en la primera. La primera canasta tiene 4 kilos menos de zanahoria que la segunda.

¿Cuantos kilos pesan ambas canastas en conjunto?

Representarlo de manera algebraica

Answers

The algebraic expression for the weigh of both baskets where each one contains pumpkins and carrots in kilos is equals to the 7x + 2, in kilos.

We have two baskets where each one contains pumpkins and carrots. We have to determine the both baskets weigh together in kilos. Let's assume that

The number of pumpkins in second basket = x kilos

Now, according to first scenario, first basket contains the pumpkins twice as many kilos of pumpkin as in the second basket. That is the number of pumpkins in first basket = 2x kilos

In second case, the second basket there are three more kilos of carrots than there are kilos of pumpkin in the first. So, the number of carrots in second basket

= (3 + 2x ) kilos

In third case, the first basket has 4 kilos less carrot than the second, that is x

=( ( 3 + 2x) - 4 ) kg

Now, weigh of first basket = carrots + pumpkins = (2x + 2x - 1) kilos

= (4x - 1 ) kilos

Weigh of second basket = carrots + pumpkins = (3 + 2x) kilos + x kilos

= (3 + 3x) kilos

So, weigh of both baskets together

= (4x - 1 ) kilos + (3 + 3x) kilos

=( 7x + 2 ) kilos.

Hence, required expression is 7x + 2.

For more information about algebraic expression,

https://brainly.com/question/4344214

#SPJ4

Complete question:

You have two baskets. Each contains pumpkins and carrots. In the first basket there are twice as many kilos of pumpkin as in the second, and in the second there are three more kilos of carrots than there are kilos of pumpkin in the first. The first basket has 4 kilos less carrot than the second. How many kilos do both baskets weigh together? Represent it algebraically

In a recent​ poll, 813 adults were asked to identify their favorite seat when they​ fly, and 520 of them chose a window seat. Use a 0. 01 significance level to test the claim that the majority of adults prefer window seats when they fly. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, conclusion about the null​ hypothesis, and final conclusion that addresses the original claim. Use the​ P-value method and the normal distribution as an approximation to the binomial distribution

Answers

The P-value is less than the significance level of 0.01, we reject the null hypothesis.

Null Hypothesis: The proportion of adults who prefer window seats when they fly is 0.5 or less.

Alternative Hypothesis: The proportion of adults who prefer window seats when they fly is greater than 0.5.

Let p be the true proportion of adults who prefer window seats when they fly.

The sample proportion of adults who prefer window seats is:

= 520/813 = 0.639

The standard error of the sample proportion is:

SE = sqrt((1-)/n) = sqrt(0.639(1-0.639)/813) = 0.022

The test statistic is:

z = ( - 0.5)/SE = (0.639 - 0.5)/0.022 = 6.32

Using a normal distribution, the P-value is P(Z > 6.32) < 0.0001.

Since the P-value is less than the significance level of 0.01, we reject the null hypothesis.

Therefore, we conclude that there is sufficient evidence to support the claim that the majority of adults prefer window seats when they fly.

To learn more about window visit:

https://brainly.com/question/276025

#SPJ11

Find the sum of the series. [infinity] 5(−1)nπ2n + 1 32n + 1(2n + 1)! n = 0

Answers

The sum of the series is 1/16. The given series is: ∑ [infinity] 5(−1)nπ2n + 1 / 32n + 1(2n + 1)!

To find the sum of the series, we can use the ratio test to check the convergence of the series. First, let's take the ratio of the (n+1)th term to the nth term: | a(n+1) / a(n) | = 5π2 / 32(2n + 3)(2n + 2)(2n + 1)

As n approaches infinity, the denominator of the ratio tends to infinity, making the ratio go to zero. Therefore, by the ratio test, the series converges.

Now, we need to find the sum of the series. To do this, we can use the formula for the sum of an infinite series: S = lim [n → ∞] Sn, where Sn is the nth partial sum of the series.

Using partial fractions, we can write the series as: 5π2 / 32n + 1 (2n + 1)! = 1 / 64 [ 1 / (n!) - 1 / (2n + 1)! ] - 5π2 / 32(2n + 3)(2n + 2)(2n + 1)

Substituting this expression into Sn and simplifying, we get: Sn = (1 - cos(π/4n+1)) / 32

Taking the limit as n approaches infinity, we get: S = lim [n → ∞] Sn = 1 / 16 Therefore, the sum of the series is 1/16.

To know more about ratio test, refer here:

https://brainly.com/question/15586862#

#SPJ11

Find the exact values of sin 2. cos2u. and tan 2u using the double angle formulas Cos u =- 4/5 π/2 < u < π sin 2u = cos 2u= tan 2u =

Answers

The probability of drawing either a two or a ten from a standard deck of 52 cards is the sum of the probabilities of drawing a two and drawing a ten.

There are four twos and four tens in the deck, so the probability of drawing a two is 4/52 and the probability of drawing a ten is 4/52. Therefore, the probability of drawing either a two or a ten is:

4/52 + 4/52 = 8/52 = 2/13

The probability of drawing either a two or a club from a standard deck of 52 cards is the sum of the probabilities of drawing a two and drawing a club, minus the probability of drawing the two of clubs (since we have already counted it). There are four twos and 13 clubs in the deck, including the two of clubs. Therefore, the probability of drawing a two is 4/52, the probability of drawing a club is 13/52, and the probability of drawing the two of clubs is 1/52. Therefore, the probability of drawing either a two or a club is:

4/52 + 13/52 - 1/52 = 16/52 = 4/13

For more similar questions on topic  Probability

https://brainly.com/question/13604758

#SPJ11

Find the maximum volume of a box inscribed in the tetrahedron bounded by the coordinate planes and the plane x + 1/7y + 1/6z = 1. (Use symbolic notation and fractions where needed.) the maximum volume of the box: ...

Answers

The maximum volume of the box is 5/49, which occurs at vertex 3.

How to find the maximum volume of a box inscribed in the tetrahedron bounded by the coordinate planes?

Let the length, width, and height of the box be x, y, and z respectively. Then the volume of the box is given by V = xyz.

The tetrahedron is bounded by the coordinate planes and the plane x + 1/7y + 1/6z = 1. We can find the vertices of the tetrahedron as follows:

(0, 0, 0)

(7, 0, 0)

(0, 6, 0)

(0, 0, 6)

We can see that the maximum values of x, y, and z occur at different vertices of the tetrahedron.

Therefore, we need to find the coordinates of the vertices of the box at each vertex of the tetrahedron.

At vertex 1, we have x = 0, y = 0, and z = 0. The distance from this vertex to the plane is 1, so the maximum value of x is 1.

Therefore, we set x = 1 and solve for y and z:

1 + 1/7y + 1/6z = 1

y = 0

z = 0

At vertex 2, we have x = 7, y = 0, and z = 0. The distance from this vertex to the plane is 6/7, so the maximum value of y is 6/7.

Therefore, we set y = 6/7 and solve for x and z:

x + 1/7(6/7) + 1/6z = 1

x = 5/6

z = 1/7

At vertex 3, we have x = 0, y = 6, and z = 0. The distance from this vertex to the plane is 5/6, so the maximum value of z is 5/6.

Therefore, we set z = 5/6 and solve for x and y:

x + 1/7y + 1/6(5/6) = 1

x = 4/7

y = 3/7

At vertex 4, we have x = 0, y = 0, and z = 6. The distance from this vertex to the plane is 1/7, so the maximum value of x is 7.

Therefore, we set x = 7 and solve for y and z:

7 + 1/7y + 1/6(6) = 1

y = -42/7

z = 1/6

Now we can calculate the volume of the box at each vertex of the tetrahedron:

V1 = 1(0)(0) = 0

V2 = 5/6(6/7)(1/7) = 5/294

V3 = 4/7(3/7)(5/6) = 5/49

V4 = 7(-42/7)(1/6) = -49/6

Therefore, the maximum volume of the box is 5/49, which occurs at vertex 3.

Learn more about volume of a box

brainly.com/question/23952628

#SPJ11

Find the inverse of the function

Answers

The inverse of the function f(x) = √(x+1) is [tex]f^-1[/tex](x) = x² - 1.

What is inverse function?

Given a function f(x), its inverse function, denoted as [tex]f^-1[/tex](x), is a function that takes the output of f(x) and returns the original input. In other words, if y = f(x), then x = [tex]f^-1[/tex](y).

According to question:

To find the inverse of the function f(x), we follow these steps:

Step 1: Replace f(x) with y:

   y = √(x+1)

Step 2: Interchange x and y:

   x = √(y+1)

Step 3: Solve for y:

   x² = y+1

   y = x² - 1

Step 4: Replace y with f^-1(x):

   f^-1(x) = x² - 1

Therefore, the inverse of the function f(x) = √(x+1) is [tex]f^-1[/tex](x) = x² - 1.

To verify this, we can check that ([tex]f^-1[/tex] o f)(x) = x and (f o [tex]f^-1[/tex])(x) = x for all x in the domain of the functions:

([tex]f^-1[/tex] o f)(x) = [tex]f^-1[/tex](f(x)) = (√(x+1))² - 1 = x

(f o [tex]f^-1[/tex])(x) = f([tex]f^-1[/tex](x)) = √((x² - 1) + 1) = √(x²) = |x| + 1

Since the range of f(x) is [0, infinity), we restrict the domain of [tex]f^-1[/tex](x) to [1, infinity) to ensure that the inverse is a function.

To know more about inverse function visit:

https://brainly.com/question/30350743

#SPJ1

Solve (t^2 + 4) dx/dt = (x^2 + 36), using separation of variables, given the inital condition 2(0) = 6.

Answers

To solve this differential equation using separation of variables, we can rearrange it as:

dx/(x^2 + 36) = (t^2 + 4)/dt

Now we can integrate both sides:

∫ dx/(x^2 + 36) = ∫ (t^2 + 4)/dt

To integrate the left side, we can use the substitution u = x/6, du/dx = 1/6 dx, and dx = 6 du:

∫ dx/(x^2 + 36) = ∫ du/u^2 + 1

= arctan(x/6) + C1

To integrate the right side, we can use the power rule:

∫ (t^2 + 4)/dt = (1/3)t^3 + 4t + C2

Putting these together, we have:

arctan(x/6) = (1/3)t^3 + 4t + C

Where C = C2 - C1 is the constant of integration.

Now we can solve for x:

x/6 = 6 tan((1/3)t^3 + 4t + C)

x = 36 tan((1/3)t^3 + 4t + C)

Using the initial condition 2(0) = 6, we have:

x(0) = 36 tan(C) = 6

tan(C) = 1/6

C = arctan(1/6)

Therefore, the solution to the differential equation with the given initial condition is:

x = 36 tan((1/3)t^3 + 4t + arctan(1/6))

First, let's rewrite the equation using the given terms and separating the variables:

(t^2 + 4) dx/dt = (x^2 + 36)

Now, separate the variables:

dx/x^2 + 36 = dt/t^2 + 4

Next, we'll integrate both sides:

∫(1/(x^2 + 36)) dx = ∫(1/(t^2 + 4)) dt

Using the substitution method, we find:

(1/6) arctan(x/6) = (1/2) arctan(t/2) + C

Now, we'll use the initial condition 2(0) = 6 to find the value of C. Since 2(0) = 0, we have:

(1/6) arctan(6/6) = (1/2) arctan(0/2) + C

This simplifies to:

(1/6) arctan(1) = C

Therefore, the solution to the differential equation is:

(1/6) arctan(x/6) = (1/2) arctan(t/2) + (1/6) arctan(1)

Learn more about differential equation here: brainly.com/question/14620493

#SPJ11

A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, can the company build 10 child bikes and 12 adult bikes in a week

Answers

Step-by-step explanation:

we only need to calculate directly the work hours needed for 10 child bikes and 12 adult bikes.

as a child bikes needs 4 hours to build and 4 hours to test, for 10 child bikes that means 10×4 = 40 hours to build and 40 hours to test

an adult bike needs 6 hours to build and 4 his to test.

so, for 12 bikes that are 12×6 = 72 hours to build and 12×4 = 48 hours to test.

together that means we need

40 + 72 = 112 hours to build

40 + 48 = 88 hours to test

the limits of the company are 120 build hours and 100 test hours per week.

as 112 < 120 and 88 < 100, yes, the company can build 10 child bikes and 12 adult bikes in one week.

in fact, with that they still have 8 work hours (120 - 112) and 12 test hours (100 - 88) left and could therefore build either 2 additional child bikes (8 build hours, 8 test hours) or one additional adult bike (6 build hours, 4 test hours).

QUESTION 4
This spinner is divided into eight equal-sized sections. Each section is labeled with a number.
Write the events below in the correct
order from least likely to most likely.

A) Arrow lands on a section labeled with an odd number.
B) Arrow lands on a section labeled
with the number 1.
C) Arrow lands on a section labeled
with a number less than 4.

Answers

Ranking of the events below in the correct order from least likely to most likely are:

Event B

Event A

Event C

What is the probability of Occurrence?

The probability of an event is defined as a number that describes the chance that the event will eventually happen. An event that is sure to happen has a probability of 1. An event that can never possibly happen has a probability of zero. Finally, If there is a chance that an event will happen, then it will have a probability that is between zero and 1.

i) Arrow lands on a section labeled with an odd number: The odd numbers here are 1 and 3.

There are a total of four 1's, and two 3's. This tells us that there are 6 odd numbers on the spinner.

There are 8 numbers in total on the spinner. Thus, 6 out of the 8 numbers are seen as odd numbers. Therefore, the probability that the arrow lands on an odd number would be:

P(odd number) = 6/8 =  75%

ii) Arrow lands on a section labeled with the number 1: There are four 1's on the spinner, and there are seen to be 8 numbers in total on the spinner. Thus, the probability of the arrow landing on a 1 is:

P(Number 1) = 4/8 = 50%.

iii) Arrow lands on a section labeled with a number less than 4:

The numbers that are less than 4 are 3, 2, and 1.

There are two 3's.

There is one 2.

There are four 1's.

2 + 1 + 4 = 7.

The probability of the arrow landing on a number less than 4 is 7/8, which is 88.5%.

Read more about Probability of Occurrence at: https://brainly.com/question/28151602

#SPJ1

Ozone (O3) is a major component of air pollution in many cities. Atmospheric ozone levels are influenced by many factors, including weather. In one study, the mean percent relative humidity (x) and the mean ozone levels (y) were measured for 120 days in a western city. Mean ozone levels were measured in ppb. The following output (from MINITAB) describes the fit of a linear model to these data. Assume that assumptions 1 through 4 for errors in linear models hold.




The regression equation is


Ozone = 88. 8 - 0. 752 Humidity



Predictor Coef SE Coef T P


Constant 88. 761 7. 288 12. 18 0


Humidity -0. 7524 0. 13024 -5. 78 0


S = 11. 43 R-Sq = 22. 0% R-Sq(adj) = 21. 4%


Predicted Values for New Observations


New Obs Fit SE Fit 95. 0% CI 95. 0% PI


1 43. 62 1. 2 (41. 23 46. 00) (20. 86, 66. 37)


Values of Predictors for New Observations


New Obs Humidity


1 60



Required:


a. What are the slope and intercept of the least-squares line?


b. Is the linear model useful for predicting ozone levels from relative humidity? Explain.


c. Predict the ozone level for a day when the relative humidity is 50%.


d. What is the correlation between relative humidity and ozone level?


e. The output provides a 95% confidence interval for the mean ozone level for days where the relative humidity is 60%. There are n = 120 observations in this data set. Using the value "SE Fit," find a 90% confidence interval.


f. Upon learning that the relative humidity on a certain day is 60%, someone predicts that the ozone level that day will be 80ppb. Is this a reasonable prediction? If so, explain why. If not, give a reasonable range of predicted values

Answers

a. The slope and intercept of the least-squares line are -0.752 and 88.761, respectively.

b. The linear model may be useful for predicting ozone levels from relative humidity, but only to a limited extent. The R-squared value of 0.22 indicates that only 22% of the variation in ozone levels can be explained by relative humidity.

Additionally, the 95% prediction interval for a new observation (20.86, 66.37) is relatively wide, which suggests that the model may not be very precise in its predictions.

c. To predict the ozone level for a day when the relative humidity is 50%, we plug in x = 50 into the regression equation: Ozone = 88.8 - 0.752(50) = 53.8 ppb.

d. The correlation between relative humidity and ozone level can be found by taking the square root of the R-squared value, which gives us a correlation coefficient of 0.47.

This indicates a moderate positive correlation between relative humidity and ozone levels.

e. To find a 90% confidence interval for the mean ozone level for days where the relative humidity is 60%, we use the formula:

Mean ozone level ± (t-value)*(SE Fit)/sqrt(n), where the t-value is obtained from a t-distribution with n-2 degrees of freedom and a 90% confidence level.

For n = 120 and a 90% confidence level, the t-value is approximately 1.66. Plugging in the values, we get: 43.62 ± 1.66*(1.2)/sqrt(120), which simplifies to (42.39, 44.85).

f. To determine if a predicted ozone level of 80 ppb is reasonable when the relative humidity is 60%, we can calculate the 95% prediction interval for a new observation with x = 60: 43.62 ± 2.064*(11.43) = (21.18, 66.06).

Since the predicted value of 80 ppb falls outside of this range, it is not a reasonable prediction.

A more reasonable range of predicted values would be the 95% prediction interval, which gives us a range of (21.18, 66.06).

To know more about intercept refer here

https://brainly.com/question/14180189#

#SPJ11

A cistern in the form of an inverted circular cone is being filled with water at the rate of 65 liters per minute. if the cistern is 5 meters deep, and the radius of its opening is 2 meters, find the rate at which the water level is rising in the cistern 30 minutes after the filling process began.

Answers

Let's start by finding the volume of the cistern at any given time t. Since the cistern is in the form of an inverted circular cone, its volume can be expressed as:

V = (1/3)πr^2h

where r is the radius of the circular opening, h is the height of the cone (which is also the depth of the cistern), and π is the constant pi.

We are given that the cistern is 5 meters deep, and the radius of its opening is 2 meters. Therefore, we can plug these values into the equation above to get:

V = (1/3)π(2^2)(5)

V = 20/3 π

Now, we need to find the rate at which the water level is rising in the cistern after 30 minutes. Let's call this rate dh/dt (the change in height with respect to time).

We know that the water is being added to the cistern at a rate of 65 liters per minute. Since 1 liter is equal to 0.001 cubic meters, the volume of water being added per minute is:

(65 liters/minute) × (0.001 m^3/liter) = 0.065 m^3/minute

Therefore, the rate at which the height of the water in the cistern is changing is:

dh/dt = (0.065 m^3/minute) / (20/3 π m^3) = 3.87/π meters/minute

After 30 minutes, the height of the water in the cistern will have risen by:

h = (65 liters/minute) × (0.001 m^3/liter) × (30 minutes) / (20/3 π m^3) = 0.2925 meters

Therefore, the rate at which the water level is rising in the cistern 30 minutes after the filling process began is:

dh/dt = 3.87/π meters/minute

To know more about cistern refer here

https://brainly.com/question/19698275#

#SPJ11

You are conducting a poll to determine what proportion of Americans favor a government-run, single-payer healthcare system in the United States. You want your poll to be accurate to within 2% of the population proportion with 99% confidence. What is the minimum sample size required if a previous poll indicated that 21% of Americans favor a government-run, single-payer healthcare system?

Answers

The minimum sample size required is approximately 2507 individuals to accurately poll the proportion of Americans favoring a government-run, single-payer healthcare system within a 2% margin of error and with 99% confidence.

To determine the minimum sample size required for your poll on the proportion of Americans favoring a government-run, single-payer healthcare system, you need to consider the desired margin of error (2%), the confidence level (99%), and the estimated proportion from a previous poll (21%).

Step 1: Identify the critical value (Z-score) for a 99% confidence level. You can use a Z-score table or calculator for this. The critical value is approximately 2.576.

Step 2: Determine the margin of error (E). In this case, the margin of error is 2%, or 0.02.

Step 3: Use the estimated proportion (p) from the previous poll, which is 21%, or 0.21. Calculate the estimated proportion for not favoring the single-payer system (q), which is 1 - p, or 0.79.

Step 4: Apply the formula for the minimum sample size (n):

n = (Z^2 * p * q) / E^2

n = (2.576^2 * 0.21 * 0.79) / 0.02^2

n ≈ 2506.73

Since you cannot have a fraction of a person, round up to the nearest whole number. The minimum sample size required is approximately 2507 individuals to accurately poll the proportion of Americans favoring a government-run, single-payer healthcare system within a 2% margin of error and with 99% confidence.

To know more about poll, visit:

https://brainly.com/question/28844387#

#SPJ11

Jhon bought a rectangular door mat that was 1/2 meter long and 3/10 meter wide. What is the area of the door mat ?

Answers

Jhon bought a rectangular door mat that was 1/2 meter long and 3/10 meter wide. The area of the rectangular door mat is 3/20 square meters.

Find the area of John's rectangular door mat that is 1/2 meter long and 3/10 meter wide, you'll need to multiply the length by the width.
Identify the length and width.
Length = 1/2 meter
Width = 3/10 meter
Multiply the length and width to find the area.
Area = Length × Width
Area = (1/2) × (3/10)
Calculate the multiplication.
Area = 3/20 square meters
The area of the rectangular door mat is 3/20 square meters.

Read more about  rectangular.

https://brainly.com/question/21308574

#SPJ11

Frets are small metal bars positioned across the neck of a guitar so that the guitar can produce notes of a


specific scale. To find the distance a fret should be placed from the bridge, multiply the


string length by 2 " where nis the number of notes higher than the string 's root note.


Determine where to place a fret to produce an A note on a C string (5 notes higher) that is 70 cm long. Round


your answer to the nearest hundredth.


a. 52. 44 cm


C. 58. 33 cm


b. 93. 44 cm


d. 74. 92 cm

Answers

To produce an A note on a C string (5 notes higher) that is 70 cm long we should place a fret at a distance of 74.92cm from bridge.

To find where to place the fret, we use the formula:

distance from bridge = (string length) x [tex]2^{(n/12)[/tex]

In this case, the string length is 70 cm and we want to produce an A note on a C string, which is 5 notes higher.         So n = 5.

distance from bridge = [tex]70 * 2^{(5/12)[/tex]

Using a calculator, we get:

distance from bridge ≈ 74.92 cm

Therefore, the answer is d. 74.92 cm, rounded to the nearest hundredth.

To know more about fret refer here:

https://brainly.com/question/11667033

#SPJ11

Other Questions
1. A gas takes up a volume of 10 ml, has a pressure of 6 atm, and a temperature of 100 K. What is the new volume of the gas at stp?2. The gas in an aerosol can is under a pressure of 8 atm at a temperature of 45 C. It is dangerous to dispose of an aerosol can by incineration. (V constant)What would the pressure in the aerosol can be at a temperature of 60 C ?3. A sample of nitrogen occupies a volume of 600mL at 20 C. What volume will it occupy at STP?(P constant) Who can detect a batter who enters the batter box with an illegal bat or is discovered having used an illegal bat Twenty people each choose a number from a choice of, 1,2,3,4 or 5. the mode is larger than the median. the median is larger than the meanfill in a set of possible frequency Oshi, a principal, lets his past teacher friends break rules, while fining others who do the same. Yoshi is failing to meet which ethical challenge of leadership?a. The challenge of consistencyb. The challenge of power 2.for the reaction c + 2h2 - ch4, how many grams of hydrogen are requiredto produce 0.6 moles of methane, ch4 ?cannu help em do the whole paper Law if sines math question Mr. Larson, a math teacher, assigned his students a project to do in pairs. He recorded thegrade each pair earned. Math project grades92 77 97 70 96 7573847187808610095Which box plot represents the data?Math project grades5060708090100Math project grades5060708090100 In order to calculate the line voltage of a wye-connected three-phase system you must multiply 1. 73 by the ________________ ________ is the earliest recorded Greek play right Estimating Estimate to as many decimal places as your calculator will display by using Newton's method to solve the equation tan(x) = 0 with xo 3. Based on the following code segment, what is the value of variable z?var x = "hello";var y= "world!";var z = y.length 2 x.length + (3); What kind of message do the two composers of calle 13 have? Ben's Barbershop has a rectangular logo for their measuresb 7 1/5 feet long with an area that is exactly the maximum area allowed by thr building owner. Create an equation that could be used to determine M, the unknown side length of the logo For/fun/as/ping-pong/a/friendly/started/game/played Randy divides (2x4 3x3 3x2 7x 3) by (x2 2x 1) as shown below. what error does randy make? x squared minus 2 x 1 startlongdivisionsymbol 2 x superscript 4 baseline minus 3 x cubed minus 3 x squared 7 x minus 3 endlongdivisionsymbol. minus 2 x superscript 4 baseline minus 4 x cubed 2 x squared to get a remainder of x cubed minus 5 x squared 7 x. minus x cubed minus 2 x squared x to get a remainder of negative 3 x squared 6 x minus 3. minus negative 3 x squared 6 x minus 3 to get a remainder of 0 and a quotient of 2 x squared x 3. he makes a subtraction error. he makes an error writing the constant term in the quotient. he makes an error choosing the x-term in the quotient. he makes an error rewriting the problem in long division. .who is your favourite nepali musician? write his/her biography in about 300 words . Read the sentence. The drought-ridden ground gratefully drank in the rain. Which type of figurative language does this sentence contain? personification hyperbole meiosis onomatopoeia The building of the Berlin Wall And what type of workers were the East Germans scared of losing Discuss drought prevention and drought preparation strategies The Instant Paper Clip Office Supply Company sells and delivers office supplies to companies, schools, and agencies within a 50-mile radius of its warehouse. The office supply business is competitive, and the ability to deliver orders promptly is a big factor in getting new customers and maintaining old ones. The manager of the company wants to be certain that enough drivers and vehicles are available to deliver orders promptly and that they have adequate inventory in stock. Therefore, the manager wants to be able to forecast the demand for deliveries during the next month. From the records of previous orders, management has accumulated the following data for the past 10 months:Month Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sept Oct. Orders 120 90 100 75 110 50 75 130 110 90Required:a. Compute the monthly demand forecast for February through November using the naive method. b. Compute the monthly demand forecast for April through November using a 3- month moving average. c. Compute the monthly demand forecast for June through November using a 5- month moving average. d. Compute the monthly demand forecast for April through November using a 3- month weighted moving average. Use weights of 0. 5, 0. 33, and 0. 17, with the heavier weights on the more recent months. e. Compute the mean absolute deviation for June through October for each of the methods used. Which method would you use to forecast demand for November?