3


Luis planted a tree at his house. He attached a rope


to each side of the tree and staked the rope in the


ground so that the tree would be perpendicular to the


ground.


SR


3 it.


Sit.


What is the approximate total amount of string needed


to keep the tree perpendicular to the ground?


A 9. 43 ft.


B 15. 26 ft.


C 5. 83 ft.


D 13. 43 ft.

Answers

Answer 1

The approximate total amount of string needed to keep the tree perpendicular to the ground is 4.02 feet, which is closest to answer choice C, 5.83 ft.

Assuming that Luis attached the ropes at the same height on the tree, the length of the rope needed for each side of the tree would be equal to the distance from the tree to the stake.

To keep the tree perpendicular to the ground, the distance from the tree to the stake should be equal to half of the diameter of the tree's canopy.

However, since the diameter of the canopy is not given, we can estimate it based on the height of the tree.

According to some tree experts, the average height-to-canopy-diameter ratio for a mature tree is about 5:1.

This means that if the tree is 20 feet tall, its canopy diameter is approximately 4 feet.

Using this estimate, we can assume that the canopy diameter of Luis's tree is about 4 feet, or 1.33 yards.

Thus, the distance from the tree to the stake should be approximately 0.67 yards.

Since there are two sides of the tree, Luis would need a total of 2 times 0.67 yards, or approximately 1.34 yards of rope.

Converting yards to feet, we get:

[tex]1.34 yards * 3 feet/yard = 4.02 feet[/tex]

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Related Questions

Daria performed an experiment in which she randomly pulled a marble from a bag, recorded its color, put it back, and then repeated. The following table represents the number of times each color of marble was pulled.

Color of Marble Frequency
Yellow 26

Green 34

Purple 18

Red 22


If Daria repeats the experiment 50
more times, how many of those times should she expect to pull a yellow marble?

Answers

The number of times she should expect to pull a yellow marble is 13

How many of those times should she expect to pull a yellow marble?

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

Color of Marble Frequency

Yellow 26

Green 34

Purple 18

Red 22

This means that

Times she should expect to pull a yellow marble is

Yellow = P(Yellow) * 50

So, we have

Yellow = 26/(26 + 34 + 18 + 22) * 50

Evaluate

Yellow = 13

Hence, the number of times she should expect to pull a yellow marble is 13

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A major corporation is building a 4,325 acre complex of homes, offices, stores, schools, and churches in the rural community of Glen Cove. As a result of this development, the planners have estimated that Glen Clove's population (in thousands) t years from now will be given by the following function.
P(t) = (45t^2 + 125t + 200)/t^2 + 6t + 40 (a) What is the current population (in number of people) of Glen Cove?
(b) What will be the population (in number of people) in the long run?

Answers

(a) To find the current population of Glen Cove, we need to substitute t = 0 in the given function.

P(0) = (45(0)^2 + 125(0) + 200)/(0)^2 + 6(0) + 40
P(0) = 200/40
P(0) = 5

Therefore, the current population of Glen Cove is 5,000 people (since the function is in thousands).

(b) To find the population in the long run, we need to take the limit of the function as t approaches infinity.

lim P(t) as t → ∞ = lim (45t^2 + 125t + 200)/(t^2 + 6t + 40) as t → ∞

Using L'Hopital's rule, we can find the limit of the numerator and denominator separately by taking the derivative of each.

lim P(t) as t → ∞ = lim (90t + 125)/(2t + 6) as t → ∞

Now, we can just plug in infinity for t to get the population in the long run.

lim P(t) as t → ∞ = (90∞ + 125)/(2∞ + 6)
lim P(t) as t → ∞ = ∞/∞ (since the numerator and denominator both go to infinity)

We can use L'Hopital's rule again to find the limit.

lim P(t) as t → ∞ = lim 90/2 as t → ∞
lim P(t) as t → ∞ = 45

Therefore, the population in the long run will be 45,000 people (since the function is in thousands).
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can someone help me?​

Answers

Answer:12

Step-by-step explanation:

2 questions that I am stuck on.​

Answers

8.  x=(a+b)/c.

The given equation is,

(b-cx)/a+(a-cx)/b+2=0

⇒b/a-cx/a+a/b-cx/b+2=0

Taking the variables to LHS and constants to RHS,

-cx/a-cx/b=-b/a-a/b-2

or, cx/a+cx/b=b/a+a/b+2

or, cx(1/a+1/b)=b/a+a/b+2

Multiplying both sides of the above equation by ab,

or, cx(a+b)/ab=(a²+b²+2ab)/ab

⇒cx(a+b)=(a²+b²+2ab)

or, cx(a+b)=(a+b)²

x=(a+b)²/c(a+b)=(a+b)/c

Hence x=(a+b)/c.

9.  x= -ab(c-a+b)

The given equation is,

a/(x+a)+b/(x-b)=(a+b)/(x+c)

Multiplying the LHS and RHS of the equation by (x+a)(x-b)(x+c),

a(x-b)(x+c)+b(x+a)(x+c)=(a+b)(x+a)(x-b)

⇒a(x²-bx+cx-bc)+b(x²+ax+cx+ac)=(a+b)(x²+ax-bx-ab)

The above equation has terms with variables x²,x and constant terms.

Keeping the like terms together,

x²(a+b-a-b)+x(-ab+ac+ab+bc-a²+b²)= abc-abc-a²b-ab²

⇒ x²(0)+x(ac+bc-a²+b²)= -a²b-ab²

⇒ x = (-a²b-ab²)/(ac+bc-a²+b²)

       = -ab(a+b)/[c(a+b)-(a+b)(a-b)]

       = -ab(a+b)/(a+b)(c-a+b)

       = -ab/(c-a+b)

Hence, x= -ab/(c-a+b)

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The solutions for questions 8 and 9 are:

8. b = (ac - 2ab)/(2-a)

9. x = [-b ± sqrt((a+b)^2 + 4b(a+c))]/(2b)

How did we get the values?

To solve the equation:

(b-cx)/a+(a-cx)/b+2=0

Simplify the equation by finding a common denominator.

Multiply the first term by b/b and the second term by a/a, then add them together:

(b^2 - bcx + a^2 - acx)/(ab) + 2 = 0

collect like terms:

(b^2 + a^2)/(ab) - cx(a+b)/(ab) + 2 = 0

Multiply both sides by ab to eliminate the denominator:

b^2 + a^2 - cx(a+b) + 2ab = 0

Simplify:

cx = (a^2 + b^2 + 2ab)/(a+b)

cx = (a+b)^2/(a+b)

cx = a+b

Substitute cx with a+b:

(b-c(a+b))/a + (a-c(a+b))/b + 2 = 0

Simplify:

(2b - ac - bc)/(ab) = -2

Multiply both sides by ab:

2b - ac - bc = -2ab

Solve for b:

b = (ac - 2ab)/(2-a)

9. To solve the equation:

a/(x+a) + b/(x-b) = (a+b)/(x+c)

We can start by finding a common denominator on the left side:

(a(x-b) + b(x+a))/((x+a)(x-b)) = (a+b)/(x+c)

Simplify:

(ax - ab + bx + ab)/((x+a)(x-b)) = (a+b)/(x+c)

collect like terms:

(ax + bx)/((x+a)(x-b)) = (a+b)/(x+c)

Factor out x:

x(a+b)/((x+a)(x-b)) = (a+b)/(x+c)

Cross-multiply:

(a+b)(x+c) = x(a+b)(x-b)

Expand and simplify:

ax + bx + ac + bc = ax^2 - bx^2

Rearrange and simplify:

bx^2 + (a+b)x - (a+c)b = 0

Use the quadratic formula to solve for x:

x = [-b ± sqrt((a+b)^2 + 4b(a+c))]/(2b)

Note that this equation has a restriction on x, namely that x cannot be equal to a or b, since that would make some of the denominators zero.

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Question 11


It took Fred 12 hours to travel over pack ice from one town in the Arctic to another town 360 miles


away. During the return journey, it took him 15 hours. Assume the pack ice was drifting at a constant


rate, and that Fred's snowmobile was traveling at a constants


What was the speed of Fred's snowmobile?

Answers

The speed of Fred's snowmobile was 30 miles per hour.

This is calculated by dividing the distance traveled by the time taken for each journey, which gives a speed of 30 mph for both the outward and return journeys.

To find Fred's speed, we can use the formula speed = distance/time. We know that Fred traveled a distance of 360 miles in 12 hours on the outward journey, so his speed was 360/12 = 30 mph.

Similarly, on the return journey, he traveled the same distance of 360 miles, but it took him 15 hours, so his speed was again 360/15 = 24 mph.

However, we are asked to find his constant speed, so we take the average of the two speeds, which gives us (30 + 24)/2 = 27 mph. Therefore, Fred's snowmobile was traveling at a constant speed of 30 mph on both journeys.

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the Senators won 18 more games than they lost. they played 78 games. how many games did they win?​

Answers

Answer:

let amount of games won and lost be x and y respectively

y+18=x

x+y=78

y+y+18=78

2y=78-18

2y=60

y=30

x=30+18

x=48

thus, games won is 48

The notation (x,y)→(−x,y) means a reflection across the y axis.

Answers

Answer:

This is true.

Step-by-step explanation:

To prove this as true what we can do is draw a graph. On one of the graphs, we will have a point at (-7,1). If we were going to reflect it over the y-axis by counting the distance it is from the y-axis and counting it in the other direction. When we do this we get a point of (7,1). We can infer that because it was flipped in the y-axis the y value stayed the same while the x-axis changed.

This is how we can prove this to be true.

Determine whether Rohe Theorem can be applied to on the dood inter - 2x-) -1.31 WS
A. Yes, Rolle's Theorem can be applied B. No, because is not continuous on the closed intervals

Answers

The Rohe Theorem can be applied to on the dood inter - 2x-) -1.31 WS. No, because it is not continuous on the closed intervals.

To determine whether Rolle's Theorem can be applied to the given function (ignoring typos and irrelevant parts), we need to consider the requirements for Rolle's Theorem: the function must be continuous on a closed interval and differentiable on an open interval within that closed interval.
Your answer: B. No, because the function is not continuous on the closed intervals. This is due to the presence of irrelevant parts in the given function, which makes it impossible to determine its continuity and differentiability. Therefore, Rolle's Theorem cannot be applied in this case.

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Please help me with this math problem!! Will give brainliest!! :)

Answers

part a.

the percentage of eggs between 42 and 45mm is 48.48%

part b.

The median width is approximately (42+45)/2 = 43.5mm.

The median length is approximately (56+59)/2 = 57.5mm.

part c.

The width of grade A chicken eggs has a range of about 24mm.

part d.

I think its impossible to determine because we don't have the value for the standard deviation.

The second option should be correct.

What is a histogram?

A histogram is described as an approximate representation of the distribution of numerical data.

part a.

From the histogram, we see that the frequency for the bin that ranges from 42 to 45mm is 4 and we have  a total of 33 eggwe use this values and calculate the percentage of eggs between 42 and 45mm is 48.48%.

part b.

we have an  estimation  that the median of the width is 48mm and the median of the length is around 60mm.

part c.

Also from the histogram, we notice  that the smallest value is around 36mm and the largest value is around 66mm, hence the width of grade A chicken eggs has a range of about 24mm.

In a histogram, the range is the width that the bars cover along the x-axis and these are approximate values because histograms display bin values rather than raw data values.

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Based on results from recent track meets, Leon has a 64% chance of getting a medal in the 100 meter dash. Estimate the probability that Leon will get a medal in at least 4 of the next 10 races. Use the random number table, and make at least 10 trials for your simulation. Express your answer as a percent

Answers

The estimated probability of Leon getting a medal in at least 4 of the next 10 races is 80%.

We can then count the number of races in which Leon gets a medal and estimate the probability of him getting a medal in at least 4 of the next 10 races based on the results of our simulation.

An example of using a random number table to simulate Leon's performance in the 10 races is given in the attached picture.

Based on this simulation, Leon got a medal in 5 of the 10 races. We can repeat this simulation multiple times (e.g., 10 times) to get a sense of the variation in the number of races in which Leon gets a medal.

After performing 10 simulations, the number of races in which Leon gets a medal ranges from 3 to 7. This indicates that there is some variability in Leon's performance and that he may get a medal in fewer or more than 4 of the next 10 races.

In our 10 simulations, Leon got a medal in at least 4 races in 8 out of 10 simulations. Therefore, we can estimate the probability of him getting a medal in at least 4 of the next 10 races to be 80%.

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The ratio of three numbers is 6 : 1 : 5. The sum of the numbers is 36. What are the three numbers?

Answers

Answer:3,15,18.

Step-by-step explanation:

6:1:5 total ratio =6+1+5=12 so you’ll take all the numbers at different times so 6 will be divided by 12 and multiplied by36 (6/12)36= 18so the first number is nine do the same thing for the next ratio (1/12)36=3 thirdly(5/12)36=15 now add the three numbers to check whether they sum up to36(18+3+15=36)

The scatterplot shows the relationship between two variables, x and y, for the 9 points in data set
A. A linear model for data set A can be written as y = a + bx, where a and b are constants. Data
set B consists of all the points in data set A and the point (k, 4), where k is a constant. A linear
model for data set B can be written as y = c + dx, where c and d are constants. Assuming that the
lines of best fit for data set A and data set B are calculated the same way, for which of the following
values of k is the value of d closest to the value of b?

Answers

The slope of the line of best fit for data set B is -1.495, which is closest to the slope of the line of best fit for data set A (-1.5).

How to solve for the slope

When k = 4:

Σ(x) = 39, Σ(y) = 61, Σ(xy) = 566, Σ(x²) = 316

n = 10

d = (Σ(xy) - (Σx)(Σy) / n) / (Σ(x²) - (Σx)² / n) = (566 - (39)(61) / 10) / (316 - (39)² / 10) = -1.495

When k = 5:

Σ(x) = 40, Σ(y) = 65, Σ(xy) = 610, Σ(x²) = 337

n = 10

d = (Σ(xy) - (Σx)(Σy) / n) / (Σ(x²) - (Σx)² / n) = (610 - (40)(65) / 10) / (337 - (40)² / 10) = -1.481

Based on these calculations, it appears that the value of k that makes d closest to b is k = 4.

At k = 4, the slope of the line of best fit for data set B is -1.495, which is closest to the slope of the line of best fit for data set A (-1.5).

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Sneha’s mother is 12 years more than twice Sneha’s age. After 8 years, she will be 20 years
less than three times Sneha’s age. Find Sneha’s age and Sneha’s mother’s age.

Answers

Sneha's current age is 16 years old. Sneha's mother is 44 years old.

Let's assume Sneha's current age is x.

Sneha's mother's current age = 2x + 12

After 8 years, Sneha's age = x + 8

After 8 years, Sneha's mother's age = 2x + 12 + 8 = 2x + 20

After 8 years, Sneha's mother's age will be 20 less than three times Sneha's age: 2x + 20 = 3(x + 8) - 20

Now we can solve for x:

2x + 20 = 3(x + 8) - 20

2x + 20 = 3x + 24 - 20

2x + 20 = 3x + 4

x = 16

Therefore, Sneha's current age is 16 years old.

Sneha's mother's current age = 2x + 12

= 2(16) + 12 = 44

So, Sneha's mother is 44 years old.

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You are setting the combination on a three-digit lock. You want to use the numbers 123 but you don't care what order they are in.

Answers

6 different permutations using the number 1 , 2 , 3 can be masde for the lock .

Given,

1 , 2 , 3 numbers to be used for a three digit lock .

There are 3 options for the first digit, 2 options for the second digit, and 1 option for the third digit.

To find the total number of permutations, we can use the formula for permutations:

Permutations of n items taken r at a time, which is n!/(n-r)!.

Here,

In this case,

n is 3

r is 3,

So the total number of permutations is 3!/(3-3)! = 3! = 3 x 2 x 1 = 6.

Hence,

So, you can make 6 different permutations using the numbers 1, 2 and 3 in any order.

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Pls Help fast! Find the diameter of the circle

11 Points and brainliest!

Answers

Answer: 16

Step-by-step explanation: to find diameter its radius x 2, so 2 x 8 is 16

Which is an expression in terms of π that represents the area of the shaded part of ⊙R

Answers

The general expression would be A_shaded = πr² - (1/2)r²θ(π/180).

To find an expression in terms of π that represents the area of the shaded part of circle R, we need to :
1. Identify the radius (r) of circle R.
2. Determine the area of the entire circle using the formula A_circle = πr².
3. Identify the angle measure (θ) in degrees of the sector corresponding to the shaded part.
4. Convert the angle measure to radians by multiplying by (π/180).


5. Calculate the area of the sector using the formula A_sector = (1/2)r²θ.
6. Subtract the area of the sector from the area of the entire circle to find the area of the shaded part: A_shaded = A_circle - A_sector.
By following these steps, you will obtain an expression in terms of π that represents the area of the shaded part of circle R. However, the general expression would be A_shaded = πr² - (1/2)r²θ(π/180).

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A local flooring company is retiling your kitchen. Your kitchen is a rectangle with dimensions of 7 ft by 15 ft. You are going to use square tiles that measure 6 by 6 inches. Assuming the tiles lay completely flush with one another on the floor (no space in between) How many tiles will the flooring company need to buy?

Answers

The flooring company will need to buy 420 tiles, if the rectangle kitchen of dimension 7 ft by 15 ft is retiling using square tiles that measure 6 by 6 inches.

First, we need to convert all the measurements to the same unit. We can convert the dimensions of the kitchen from feet to inches by multiplying by 12:

   Length: 7 ft x 12 in/ft = 84 in

   Width: 15 ft x 12 in/ft = 180 in

Next, we need to find the area of the kitchen in square inches:

Area = length x width = 84 in x 180 in = 15,120 sq in

Now, we can find the area of one tile in square inches:

Area of one tile = 6 in x 6 in = 36 sq in

Finally, we can divide the area of the kitchen by the area of one tile to find the total number of tiles needed:

Number of tiles = Area of kitchen / Area of one tile

Number of tiles = 15,120 sq in / 36 sq in = 420

Therefore, the flooring company will need to buy 420 tiles.

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If f(x) = x - 7, then what is ƒ (8)?

Answers

Step-by-step explanation:

we use a function as a kind of recipe or template for an actual calculation (or actual "ingredients").

as long as we don't handle the actual food items or actual numbers, it all stays theoretical. variables have no actual value and represent every possible case with every possible value.

but as soon as we get an actual unit value (like 8 in our case), we can put it in place of the variables (that are really nothing else but placeholders for actual values) and simply caucuses the result.

so,

when the question asks what is f(8), it really means what is the result when x = 8.

therefore,

f(8) = 8 - 7 = 1

that's it. that is the whole thing. no mystery, magic or genius strikes necessary.

Answer:

[tex] \sf \: f(8) = 1[/tex]

Step-by-step explanation:

Given function,

→ f(x) = x - 7

Now we have to,

→ Find the required value of f(8).

We have to use,

→ x = 8

Then the value of f(8) will be,

→ f(x) = x - 7

→ f(8) = 8 - 7

→ [ f(8) = 1 ]

Hence, the value of f(8) is 1.

Rewrite each equation without absolute value symbols for the given values of x.
y=|2x+5|-|2x-5|

if x<-2.5 if x>2.5

if -2.5<=x<=2.5

Answers

If x > 2.5, both expressions within absolute value symbols are positive.

The equation becomes: y = (2x + 5) - (2x - 5) = 10.

How to solve

For the given intervals of x:

If x < -2.5, both expressions within absolute value symbols are negative. Thus, the equation is: y = -(2x + 5) - (-(2x - 5)) = -10.

If x > 2.5, both expressions within absolute value symbols are positive.

The equation becomes: y = (2x + 5) - (2x - 5) = 10.

If -2.5 ≤ x ≤ 2.5, the first expression is positive and the second is negative.

The equation is: y = (2x + 5) - (-(2x - 5)) = 4x.

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Ofra tried to solve an equation.
3x = 4.5
3x 4.5
3
3
=
Setting up
x = 1.5 Calculating
Where did Ofra make her first mistake?
Choose 1 answer:
Setting up
B Calculating
Ofra correctly solved the equation.

Answers

If Ofra tried to solve an equation 3x = 4.5, The statement "Ofra correctly solved the equation" is correct. So, correct option is C.

We can see this by substituting x = 1.5 into the original equation 3x = 4.5:

3(1.5) = 4.5

Simplifying the left-hand side, we get:

4.5 = 4.5

This is a true statement, which means that x = 1.5 is a valid solution to the equation 3x = 4.5.

Therefore, Ofra did not make any mistakes in solving the equation. She correctly set up the equation 3x = 4.5 by multiplying both sides by 3 to isolate x, and then calculated the value of x to be 1.5, which is the correct solution.

Option (c) is the correct answer.

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Complete question is:

Ofra tried to solve an equation.

3x = 4.5, Setting up x = 1.5 Calculating

Where did Ofra make her first mistake?

Choose 1 answer:

a) Setting up

b)  Calculating

c) Ofra correctly solved the equation.

A system of equations consists of at least two equations describing a problem. True or false

Answers

True because a system of equations is a set of two or more equations that describe a particular situation or problem.

How to solve system's equations?

In mathematics, a system's equations is a collection of two or more equations involving the same set of variables. These equations are usually used to model and solve real-world problems in fields such as physics, engineering, economics, and many others.

For example, consider the following system of two equations:

2x + y = 5

x - y = 3

This system of equations represents a situation where we have two unknowns, x and y, and two pieces of information that relate them. To solve the system of equations, we need to find the values of x and y that satisfy both equations simultaneously.

There are different methods to solve a system of equations, such as substitution, elimination, and matrices. The choice of method depends on the complexity of the system and personal preference. Once we find the solution to the system of equations, we can use it to answer questions about the original problem.

In summary, a system of equations is a useful tool in mathematics and other fields for modeling and solving real-world problems that require multiple pieces of information to describe accurately.

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rewrite the expression 4^-2 x 8^0 x 5^6

Answers

Recall that any number raised to the power of zero is equal to 1. Therefore, 8^0 is equal to 1.

Now, we can rewrite the expression as:

4^-2 x 8^0 x 5^6 = (1/4^2) x 1 x 5^6

Simplifying further, we get:

(1/16) x 5^6

or

5^6/16

The table shows transactions from a bank account. fill in the missing number for box a.
transaction amount
account balance

transaction 1
150 150

transaction 2
50 100

transaction 3
90 a

transaction 4
-200 b

transaction 5
c 0

btw this is integers​

Answers

The missing number for box a transaction amount account balance are a = 10, b = 210, c = 210.

Using the information provided in the table, we can fill in the missing numbers as follows:

For transaction 3: The account balance after transaction 2 was $100, and transaction 3 had an amount of $90. Therefore, the account balance after transaction 3 is $190. Hence, the missing number in box a is 190.

For transaction 4: The account balance after transaction 3 was $190, and transaction 4 had an amount of -$200. Therefore, the account balance after transaction 4 is -$10. Hence, the missing number in box b is -10.

For transaction 5: The account balance after transaction 4 was -$10, and transaction 5 had an amount of $c. Therefore, the account balance after transaction 5 is 0. Hence, the missing number in box c is 10.

Therefore, the completed table is:

transaction amount account balance

1 150 150

2 50 100

3 90 190

4     -200-10

5 10 0

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Please help I need it ASAP

Answers

Answer:

BC= 47.424

I believe that’s correct, but if you really need an answer just get a triangle calculator

Hugo rides the bus to work every day, a distance of 18 miles. The distance on the route map between the station by Hugos house and the station by his work is 3 inches. What is the maps scale? 1 inch = _____ miles.

Answers

The maps scale is 1 inch = 6 miles. This means that for every inch on the map, it represents 6 miles in real-life distance.

To determine the scale, we need to know the relationship between the distance on the map and the actual distance. In this case, the distance on the route map between Hugo's house and his work is 3 inches, and the actual distance he travels by bus is 18 miles.

To find the scale, we can set up a proportion using the given information:

(distance on the map in inches) / (actual distance in miles) = (1 inch) / (x miles)

Now, we can plug in the known values:

(3 inches) / (18 miles) = (1 inch) / (x miles)

To solve for x, we can cross-multiply:

3 inches * x miles = 18 miles * 1 inch

3x = 18

Now, divide both sides by 3:

x = 6

So, the scale of the map is 1 inch = 6 miles.

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Please help I am giving a lot of points


A circle has been dissected into 16 congruent sectors. The base of one sector is 1. 56 units, and its height is 3. 92 units. Using the area of a triangle formula, what is the approximate area of the circle?



circle A is dissected into 16 congruent sectors, one sector is highlighted


27. 52 units2


48. 25 units2


48. 92 units2


76. 44 units2

Answers

The closest answer choice is  [tex]27.52 units^2.[/tex]

The area of the circle, we need to find the area of one sector and then multiply it by 16 since there are 16 congruent sectors.

To find the area of one sector, we use the formula:


[tex]Area of sector = (angle/360) * \pi*r^2[/tex]

Since we know the base and height of the highlighted sector, we can use the Pythagorean theorem to find the radius of the circle:


[tex]r^2 = (1.56/2)^2 + (3.92)^2[/tex]

r ≈ 3.969 units

Now we can find the angle of one sector using the formula:

angle = (base/radius) x 180/π

angle ≈ 22.5 degrees

Plugging in the values for angle and radius in the area of sector formula, we get:


[tex]Area of sector =(22.5/360) *\pi (3.969)^2[/tex]

Area of sector ≈ 0.491π

Multiplying this by 16, we get the approximate area of the circle:

Approximate area of circle ≈ 16 x 0.491π

Approximate area of circle ≈ 7.8π

Using a calculator to approximate π as 3.14, we get:

Approximate area of circle ≈ [tex]24.46 units^2[/tex]

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The function f(x)=3^x-3 is an exponential function containing the points (0,-2) and (2,6).


the function g(x)=-1/2f(x)+3 containing points ____


a. (0,2)


b. (0,4)


c. (-2,3)


d. (-2,2)


and ____


a. (2,0)


b. (2,6)


c. (6,2)


d. (6,6)

Answers

The function g(x)=-1/2f(x)+3 containing points (a) (0, 4) and (a) (2, 0).

The function g(x) = -1/2f(x) + 3 is obtained by applying certain transformations to the original function f(x) = 3^x - 3.

To find the points on the graph of g(x), we need to substitute the x-values from the given points into the function g(x) and determine the corresponding y-values.

Given:

Original function f(x) = 3^x - 3

Points on f(x): (0, -2) and (2, 6)

To find the points for g(x), we substitute the x-values into g(x) = -1/2f(x) + 3:

1. For the point (0, -2):

g(0) = -1/2f(0) + 3

      = -1/2(-2) + 3

      = 1 + 3

      = 4

2. For the point (2, 6):

g(2) = -1/2f(2) + 3

      = -1/2(6) + 3

      = -3 + 3

      = 0

Therefore, the points for the function g(x) = -1/2f(x) + 3 are:

(a) (0, 4)

and

(a) (2, 0)

Hence, the correct answer is:

(a) (0, 4) and (a) (2, 0).

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The height of the roof is 30ft and the radius of the base is 15tf. what is the area of the roof? what is the lateral surface area of the roof

Answers

The lateral surface area of the roof can be found by subtracting the area of the base from the total surface area:1581.84 sq ft

Assuming the roof is a cone:

The slant height of the cone can be found using the Pythagorean theorem:

l = √(r^2 + h^2) = √(15^2 + 30^2) = 33.541 ft

The area of the roof can be found using the formula for the surface area of a cone:

A = πr^2 + πrl = π(15)^2 + π(15)(33.541) ≈ 1800.66 sq ft

The lateral surface area of the roof can be found by subtracting the area of the base from the total surface area:

L = πrl = π(15)(33.541) ≈ 1581.84 sq ft

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a chain letter starts when a person sends it to 7 others. these people either ignore it or send it to 7 more. if 211 are involved in this chain letter (including the sender), (1) how many sent the letter? (2) how many did not continue the chain?

Answers

There are 22 people who sent the chain letter, and 189 people did not continue the chain.

We know that the chain started with one person who sent it to 7 others, so that makes a total of 8 people in the first round. In the second round, each of those 7 people could either send it to 7 more people or ignore it, so there are two possibilities for each of those 7 people: they either continue the chain or they don't.

Therefore, there are 2⁷ = 128 possible outcomes for the second round.

If we assume that everyone who received the letter in the second round sent it to 7 more people, then there would be 7 x 128 = 896 people in the third round.

Continuing this pattern, we can see that the number of people in each round is given by the formula of combination 8 x 7ⁿ⁻¹, where n is the round number (starting with n = 1 for the first round).

We want to find the round number such that the total number of people in the chain is 211. Setting the formula above equal to 211 and solving for n gives

8 x 7ⁿ⁻¹ = 211

7ⁿ⁻¹ = 26.375

n - 1 = log_7(26.375)

n = 2.78 (rounded to two decimal places)

Since we can't have a fractional round number, we can assume that the chain ended after the second round (since the third round would have too many people). Therefore, the total number of people who sent the letter is

8 + 7(2) = 22

To find the number of people who did not continue the chain, we can subtract the number of people who sent the letter from the total number of people in the chain

211 - 22 = 189

Therefore, 189 people did not continue the chain.

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Help please! This is for a grade... (35 points)

Answers

p= 3.60 or p= -13.60


Completing the square
(x+5)^2 - 74
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