The parametric equations for the tangent line to curve C at point P are: x = -t y = 6t - 1 z = 8t + 6
To find the parametric equations for the tangent line to curve C at point P, we need to first find the derivative of the curve at P.
Taking the derivative of each component of the curve, we get:
dx/dt = -1
dy/dt = -6t
dz/dt = 8
At point P = (0, -1, 6), t = -1.
Plugging this into the derivative, we get:
dx/dt = -1
dy/dt = 6
dz/dt = 8
So, the tangent vector to curve C at point P is < -1, 6, 8 >.
To get the parametric equations for the tangent line, we can use the point-slope form: r(t) = P + t< -1, 6, 8 > Plugging in the coordinates of point P, we get: r(t) = <0, -1, 6> + t< -1, 6, 8 > Expanding this out, we get: r(t) = <-t, 6t - 1, 8t + 6>
So, the parametric equations for the tangent line to curve C at point P are: x = -t y = 6t - 1 z = 8t + 6
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4 Gabriela is building a wooden box with a rectangular base that is 18 in. By 15 in.
and is 15 in. Tall.
Part A
If she wants an open box without a top, how much wood will Gabriela use?
Strow your work
Gabriela will use 1620 square inches of wood to build the open box.
The amount of wood Gabriela will use depends on the surface area of the box, which is the sum of the areas of its six faces. Since the box is open on top, it will have five faces: four sides and a bottom.
The area of the bottom is the area of a rectangle with length 18 in. and width 15 in., which is:
Area of bottom = length x width = 18 in. x 15 in. = 270 in²
The area of each side is the product of the height and the length of the corresponding base, which is:
Area of each side = height x length = 15 in. x 18 in. = 270 in²
So the total surface area of the box is:
Total surface area = 2 x (Area of bottom) + 4 x (Area of each side)
= 2 x 270 in² + 4 x 270 in²
= 1620 in²
Therefore, Gabriela will use 1620 square inches of wood to build the open box.
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Find the missing side
17 cm
1319
a
area = 25 cm²
Answer:
a= 2.9cm
Step-by-step explanation:
area =25 so 17a=50
50/17=2.941176...
Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use C for the constant of integration.)
∫9x√(-x^2 + 9dx)
The substitution is u = -x² + 9 and the evaluated value is -4.5(2/3)(-x² + 9)³/² + C.
To evaluate the given integral ∫9x√(-x² + 9dx),
we can use the substitution u = -x² + 9. This substitution will allow us to simplify the expression under the square root.
First, we can find du/dx by taking the derivative of u with respect to x: du/dx = -2x.
Next, we can solve for dx in terms of du by dividing both sides by -2x: dx = -du/(2x).
Using the substitution and the expression for dx in terms of du, we can rewrite the integral as:
∫9x√(-x² + 9dx) = -4.5∫√udu
Now, we can integrate the simplified expression √u using the power rule of integration:
-4.5∫√udu = -4.5(2/3)u³/² + C
Substituting back for u, we get:
-4.5(2/3)(-x² + 9)³/² + C
Therefore, the solution to the integral ∫9x√(-x^2 + 9dx) using the substitution u = -x^2 + 9 is:
-4.5(2/3)(-x² + 9)³/² + C
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Please help I need all of this in alphabetical order
Answer: Apartment
Confidence
Cooperating
Disrespect
Encode
Forearm
Injustice
Intercontinental
Interplanetary
Mold
Overgrown
Refuel
Repaid
Semi-Sweet
Semicircular
Shield
Subzero
Supermarket
Transportation
Unbelievably
Step-by-step explanation:
Answer:
15
13
6
11
7
1
4
12
17
16
10
8
9
19
3
18
2
5
14
20
The Bullock family is looking to rent a
large truck for their upcoming move. With Heather's Moving, they would pay
$10 for the first day plus $8 per
additional day. With Newton Rent-a-
Truck, in comparison, the family would
pay $80 for the first day plus $1 per
additional day. Before deciding on which
company to use, Mrs. Bullock wants to
find out what number of additional days
would make the two choices equivalent
with regards to cost. What would the
total cost be?
To determine the number of additional days that would make the cost equivalent for both Heather's Moving and Newton Rent-a-Truck, we can set up an equation:
Heather's Moving: 10 + 8x
Newton Rent-a-Truck: 80 + x
To find the point at which the costs are equal, we can set the equations equal to each other:
10 + 8x = 80 + x
Now, we can solve for x (additional days):
7x = 70
x = 10
So, the costs would be equivalent after 10 additional days. To find the total cost, we can plug the value of x back into either equation:
Total cost = 10 + 8(10) = 10 + 80 = $90.
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We will use boosting to predict Salary in the Hitters data set. A) Remove the observations for whom the salary information is unknown, and then log-transform the salaries. B) Create a training set consisting of the first 200 observations, and a test set consisting of the remaining observations. C) Perform boosting on the training set with 1,000 trees. What is the the test set MSE
Using boosting with 1,000 trees on the Hitters data set, after removing observations with unknown salary information and log-transforming salaries, results in a test set MSE (Mean Squared Error) value.
1. Remove observations with unknown salary information from the Hitters data set.
2. Log-transform the remaining salaries.
3. Create a training set with the first 200 observations and a test set with the remaining observations.
4. Apply the boosting algorithm on the training set, using 1,000 trees as the parameter.
5. Evaluate the performance of the boosting model on the test set by calculating the Mean Squared Error (MSE). The test set MSE will give you an indication of the model's accuracy in predicting salary based on the provided data.
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How many terms are to be considered in the series with first term - 3 and common ratio r = -4 for the sum to exceed 1507
,Based on the information, we need to consider 5 terms in the series for the sum to exceed 1507.
How to explain the seriesSubstituting the given values, we get:
1507 < -3(1 - (-4)^n)/(1 - (-4))
Simplifying this inequality, we get:
-4^n < 502
Taking the logarithm of both sides, we get:
n*log(4) > log(502)
n > log(502)/log(4)
n > 4.29
n = 5
Therefore, we need to consider 5 terms in the series for the sum to exceed 1507.
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a farmer made a loss of 28% by selling a gold for1440shillings what percentage profit would have made if he had sold the goat.for.sh 2100
The farmer would have made a profit of 5% if he had sold the goat for 2100 shillings.
Let's use the given terms and find out the percentage profit if the farmer had sold the goat for 2100 shillings.
Calculate the cost price of the goat
We know that the farmer made a loss of 28% by selling the goat for 1440 shillings. Let's represent the cost price as "CP".
We can write the equation:
[tex]CP \times (1 - loss% ) = selling price (SP)[/tex]
[tex]CP \times (1 - 0.28) = 1440[/tex]
Solve for CP
[tex]CP \times 0.72 = 1440[/tex]
CP = 1440 / 0.72
CP = 2000 shillings
Calculate the percentage profit
Now we want to find out the percentage profit if the farmer had sold the goat for 2100 shillings.
We can write the equation:
[tex](SP_{new - CP)} / CP \times 100 = profit[/tex]
[tex](2100 - 2000) / 2000 \times 100 = profit%[/tex]
[tex]100 / 2000 \times 100 = profit%[/tex]
5% = profit%.
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What is the money multiplier when the reserve requirement is:
(Instructions: Enter your responses rounded to three decimal places.)
(a) 0.040?
(b) 0.125?
(c) 0.400?
(d) 0.200?
The money multipliers are:
(a) 25.000
(b) 8.000
(c) 2.500
(d) 5.000
The money multiplier represents the amount of money the banking system can create through the lending process for every dollar of reserves held by the central bank. It is inversely related to the reserve requirement, which is the percentage of deposits that banks are required to hold as reserves.
When the reserve requirement is low, su
The money multiplier is given by the formula:
Money multiplier = 1 / Reserve requirement
(a) When the reserve requirement is 0.040, the money multiplier is:
Money multiplier = 1 / 0.040 = 25.000
(b) When the reserve requirement is 0.125, the money multiplier is:
Money multiplier = 1 / 0.125 = 8.000
(c) When the reserve requirement is 0.400, the money multiplier is:
Money multiplier = 1 / 0.400 = 2.500
(d) When the reserve requirement is 0.200, the money multiplier is:
Money multiplier = 1 / 0.200 = 5.000
Therefore, the money multipliers are:
(a) 25.000
(b) 8.000
(c) 2.500
(d) 5.000
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Y/4=3/2 what is the y and how did you get the answer
y = 6
Sorry for bad handwriting
if i was helpful Brainliests my answer ^_^
The value of Y in the equation Y/4 = 3/2 is 6.
To find the value of Y, we'll use the following steps:
1. We start with the given equation:
Y/4 = 3/2.
2. Our goal is to isolate Y. To do this, we'll multiply both sides of the equation by 4, which is the denominator on the left side.
3. Multiplying both sides by 4 gives us: (Y/4) * 4 = (3/2) * 4.
4. On the left side, the 4s cancel out, leaving just Y: Y = (3/2) * 4.
5. Now, we simplify the right side by multiplying 3/2 by 4. We can think of 4 as 4/1, so the equation becomes: Y = (3/2) * (4/1).
6. Multiply the numerators (3*4) and denominators (2*1) separately: Y = (12/2).
7. Finally, simplify the fraction: Y = 6.
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Anyone who knows how to do this please help answer!! Fill in the correct numbers in both sides of the chart and answer the bottom questions.
WILL MARK BRAINLIEST!!!
a) Here is the chart showing the number of bacteria after 0 to 4 hours:
| Time (hours) | Number of bacteria |
|--------------|--------------------|
| 0 | 50 |
| 1 | 150 |
| 2 | 450 |
| 3 | 1,350 |
| 4 | 4,050 |
b) To write an expression that models the number of bacteria after a number of hours, n, we can use the formula:
Number of bacteria = Initial number of bacteria x Growth factor^nIn this case, the initial number of bacteria is 50, and the growth factor is 3 (since the number of bacteria triples every hour). Therefore, the expression that models the number of bacteria after n hours is:
Number of bacteria = 50 x 3^nc) To determine the number of bacteria that are present after 12 hours using the expression we derived in part b), we can substitute n = 12 into the expression:
Number of bacteria = 50 x 3^12= 26572050
Therefore, there are approximately 2.7 billion bacteria present after 12 hours.In ΔEFG, g = 5. 2 cm, e = 5. 1 cm and ∠F=42°. Find the area of ΔEFG, to the nearest 10th of a square centimeter
The area of ΔEFG is approximately 6.7 square centimeters.
To find the area of ΔEFG with given sides g = 5.2 cm, e = 5.1 cm, and ∠F = 42°, you can use the formula for the area of a triangle when two sides and the included angle are known. This formula is:
Area = (1/2)ab * sin(C)
In this case, a = g, b = e, and C = ∠F. Plug in the values:
Area = (1/2)(5.2 cm)(5.1 cm) * sin(42°)
Area ≈ 6.675 square centimeters
So, the area of ΔEFG is approximately 6.7 square centimeters to the nearest 10th of a square centimeter.
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100%
A DVD player manufacturer shipped 960 DVD players last month. According to the manufacturer's records, 5 out of every 24 players were
repaired during the first year of ownership.
How many of the 960 DVD players were repaired in the first year?
If 5 out of every 24 players were repaired during the first year of ownership, then 200 of the 960 DVD players were repaired in the first year.
Based on the manufacturer's records, we know that 5 out of every 24 players were repaired in the first year of ownership. To find out how many out of the 960 DVD players were repaired in the first year, we can set up a proportion:
5/24 = x/960
To solve for x, we can cross-multiply:
5 * 960 = 24x
4800 = 24x
x = 200
Therefore, 200 of the 960 DVD players were repaired in the first year, which is approximately 20.8% of the total shipped.
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brandy has a rectangular wooden deck that measures 7 feet by 12 feet she builds an addition to the deck that is 4 feet longer. what is the perimeter of the deck now
Answer:
new perimeter of Brandy deck is 46 feet .
Step-by-step explanation:
The new perimeter of Brandy deck is 46 feet.
Perimeter of a rectangleThe entire length of all the sides of a rectangle is called the perimeter. As a result, we can calculate the perimeter of a rectangle by adding all four sides.
How can we find new perimeter of a deck?Using the given information,
Width = 7 Feet
Length = 12 feet
Perimeter = 2 (Width + Length)
[tex]= 2(7+12)[/tex]
[tex]=2(19)[/tex]
[tex]=38[/tex]
Perimeter when deck is 4 feet longer [tex]=38+ 4+4=46[/tex] Feet
Hence, the new perimeter of a deck is 46 feet.
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A recent report states that 55% of U. S. Adults use Netflix to stream shows and movies. An advertising company believes the proportion of California residents who use Netflix is greater than the national proportion, because Netflix headquarters is located in Los Gatos, California. The company selects a random sample of 600 adults from California and finds that 360 of them use Netflix. Is there convincing evidence at the level that more than 55% of California residents use Netflix?
Calculated test statistic of 2.08 is greater than the critical value of 1.645, we reject the null hypothesis and conclude that there is convincing evidence at the 0.05 level that more than 55% of California residents use Netflix.
We can use a hypothesis testing approach to answer this question. The null hypothesis is that the true proportion of California residents who use Netflix is the same as the national proportion, or p = 0.55. The alternative hypothesis is that the true proportion of California residents who use Netflix is greater than 0.55, or p > 0.55.
We can use the sample proportion of Netflix users in California, which is 360/600 = 0.6, as an estimate of the true proportion p. The standard error of the sample proportion is:
SE = √[(p*(1-p))/n] = √[(0.55*(1-0.55))/600] = 0.024
The test statistic is:
z = (p - 0.55)/SE = (0.6 - 0.55)/0.024 = 2.08
Assuming a significance level of 0.05 and a one-tailed test (since the alternative hypothesis is one-sided), the critical z-value is 1.645.
Since our calculated test statistic of 2.08 is greater than the critical value of 1.645, we reject the null hypothesis and conclude that there is convincing evidence at the 0.05 level that more than 55% of California residents use Netflix. However, we should keep in mind that this conclusion is based on a sample of 600 adults from California, and there is always some degree of uncertainty involved in statistical inference based on samples.
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Which expression is equivalent to the given expression?
2x^2-11x-6
Answer:
B
Step-by-step explanation:
using the diamond factoring method:
2x^2-12x+x-6
2x(x-6) + (x-6)
(2x+1)(x-6)
B
Solve system of equations by the substitution method.
Chris has $3.85 in dimes and quarters. There are 25 coins in all. How many of each type of coin does he have?
Solving a system of equations we can see that he has 9 quarters and 16 dimes.
How to solve the system of equations?Let's define the variables:
x = number of dimes
y = number of quarters.
There are 25 coins, so:
x + y = 25
The value is $3.85, so:
x*0.10 + y*0.25 = 3.85
So the system of equations is:
x + y = 25
x*0.10 + y*0.25 = 3.85
We can isolate x on the first equation to get:
x = 25 - y
Replacing that in the other one we get:
(25 -y)*0.10 + y*0.25 = 3.85
2.5 + y*0.15 = 3.85
y = (3.85 - 2.5)/0.15
y = 9
Then the other 16 coins are dimes.
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please help find uv 10 points like ill actually do anything for someone to respond fast please!! im bad at math
Answer:
0.8660
Step-by-step explanation:
sin24=opposite ÷hypotenus
sin24=opposite ÷5
cross multiply
sin24x5=opposite
sin24=0.4067x5
opposite =0.8660
Suppose the area of a square can be represented by the expression 25x^2 + 80x + 64. What is an expression for the length of one side of the square?
The expression for the length of one side of the square is: 5x + 8.
How to find length of one side of the square?To see why, note that the area of a square is given by side squared, so we can set up an equation:
[tex]side^2 = 25x^2 + 80x + 64[/tex]
Taking the square root of both sides, we get:
[tex]side =[/tex] √ [tex](25x^2 + 80x + 64)[/tex]
Simplifying the square root, we get:
side = √[(5x + 8)(5x + 8)]
And finally, we can take the square root of the perfect square to get:
side = 5x + 8.
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The marginal cost function for a company is given by C'(q) = q^2 - 17q + 70 dollars/unit;
where q is the quantity produced. If C(0) = 650, find the total cost of producing 20 units. What is the fixed cost and what is the total variable cost for this quantity? Fixed cost = Variable Cost of producing 20 units =
Total cost of producing 20 units =
The problem involves analyzing the cost of production for a company that produces a certain quantity of units. Specifically, we are given the marginal cost function C'(q) = q^2 - 17q + 70, where q is the quantity produced, and we need to find the total cost of producing 20 units, as well as the fixed cost and variable cost for this quantity. To find the total cost, we need to integrate the marginal cost function from 0 to 20, which will give us the total variable cost. We can then find the fixed cost by subtracting the total variable cost from the initial cost C(0), which is given in the problem. Cost analysis is an important concept in economics and business, and is used to optimize production and pricing decisions for companies. Understanding the relationship between marginal cost, fixed cost, and variable cost is crucial for making informed decisions about production and pricing strategies.
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The marginal cost function for a company is given by C'(q) = [tex]q^2[/tex] - 17q + 70 dollars/unit; where q is the quantity produced. If C(0) = 650, then total cost of producing 20 units = 2,600 dollars. Fixed cost for the quantity = 650 dollars. Variable Cost of producing 20 units = 1,950 dollars
To find the total cost function C(q), integrate the marginal cost function C'(q):
C(q) = ∫[tex](q^2 - 17q + 70)[/tex] dq = [tex](1/3)q^3 - (17/2)q^2 + 70q + K[/tex]
To find the constant K, use the given information: C(0) = 650
650 = [tex](1/3)(0)^3 - (17/2)(0)^2 + 70(0) + K[/tex]
K = 650
So the total cost function is:
C(q) = [tex](1/3)q^3 - (17/2)q^2 + 70q + 650[/tex]
Now, we find the total cost of producing 20 units:
C(20) = [tex](1/3)(20)^3 - (17/2)(20)^2 + 70(20) + 650[/tex]
C(20) = 2,600
Total cost of producing 20 units = 2,600 dollars.
Fixed cost is the cost incurred when producing 0 units, which is given as C(0) = 650 dollars.
To find the total variable cost for producing 20 units, subtract the fixed cost from the total cost:
Variable Cost = Total Cost - Fixed Cost
Variable Cost = 2,600 - 650
Variable Cost = 1,950 dollars
To summarize:
Fixed cost = 650 dollars
Variable cost of producing 20 units = 1,950 dollars
Total cost of producing 20 units = 2,600 dollars
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Express u = (7, -10) as a linear combination u = rv + sw, where v = (2, 1) and w = (1,4).
(Use symbolic notation and fractions where needed.)
To express u = (7, -10) as a linear combination u = rv + sw, where v = (2, 1) and w = (1,4), we need to find the values of r and s such that:
u = rv + sw
Substituting the given values, we get:
(7, -10) = r(2, 1) + s(1,4)
Using the symbolic notation, we can write this as a system of equations:
7 = 2r + s
-10 = r + 4s
We can solve this system of equations by using the elimination method:
Multiply the second equation by 2:
7 = 2r + s
-20 = 2r + 8s
Subtracting the first equation from the second, we get:
-27 = 7s
Dividing both sides by 7, we get:
s = -27/7
Substituting this value of s into the first equation, we get:
7 = 2r - 27/7
Multiplying both sides by 7, we get:
49 = 14r - 27
Adding 27 to both sides, we get:
76 = 14r
Dividing both sides by 14, we get:
r = 38/7
Therefore, u = (7, -10) can be expressed as the linear combination:
u = (38/7)(2,1) + (-27/7)(1,4)
Using fractions where needed, the answer is:
u = (76/7, 38/7) + (-27/7, -108/7)
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An air temperature of 30°C is equal to
1. -1°F
2. 68°F
3. 83°F
4. 86°F
Answer:
86 degrees fahrenheit
Step-by-step explanation:
(30°C × 9/5) + 32 = 86°F
Lucas takes lessons to learn how to play merengue music on his guitar he rides the bus to each lesson and then walks home he attends lessons and each lesson cost $13 which expression represents the total cost for Lucas to attend the lessons if each bus ride costs X dollars.
The expression that represents the total cost for Lucas to attend the lessons if each bus ride costs X dollars is:13n + Xn = (13+X)n
What do you mean by Cost ?Cost is the most significant factor to determine success when you are operating a business. You need to understand different cost factors and how it affects profitability. We define costs as the value of money required to produce a product or deliver goods. In this section, we have explained different cost definitions.
If each lesson costs $13 and Lucas attends "n" lessons, then the total cost for the lessons will be 13n dollars.
Now, let's consider the cost of the bus rides. Lucas takes the bus to each lesson, so he takes "n" bus rides in total. If each bus ride costs X dollars, then the total cost of the bus rides will be Xn dollars.
Finally, Lucas walks home after each lesson, so there is no cost associated with walking.
Therefore, the expression that represents the total cost for Lucas to attend the lessons if each bus ride costs X dollars is:
13n + Xn = (13+X)n
So If each lesson costs $13 and Lucas attends "n" lessons, then the total cost for the lessons will be 13n dollars.
Now, let's consider the cost of the bus rides. Lucas takes the bus to each lesson, so he takes "n" bus rides in total. If each bus ride costs X dollars, then the total cost of the bus rides will be Xn dollars.
Finally, Lucas walks home after each lesson, so there is no cost associated with walking.
Therefore, the expression that represents the total cost for Lucas to attend the lessons if each bus ride costs X dollars is:
13n + Xn = (13+X)n
So the total cost depends on the number of lessons (n) and the cost of each bus ride (X).
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You have decided to purchase a car for $25,625. The credit union requires a 10% down payment and will finance the balance with a 9% annual interest loan for 36 months. The sales tax in your city is 7. 5%, and the license and title charges are $175. 13. What is the total purchase price of the car including tax, license, and title? Round your answer to the nearest cent. A. $24,949. 80 c. $27,722. 01 b. $24,967. 32 d. $27,735. 14.
Answer is 27,529.82
To calculate the total purchase price of the car including tax, license, and title, we need to add the down payment, the financed balance, the sales tax, and the license and title charges.
First, we calculate the down payment:
10% of $25,625 = $2,562.50
Next, we calculate the financed balance:
$25,625 - $2,562.50 = $23,062.50
Then, we calculate the sales tax:
7.5% of $23,062.50 = $1,729.69
Finally, we add the license and title charges:
$1,729.69 + $175.13 = $1,904.82
So the total purchase price of the car including tax, license, and title is:
$2,562.50 + $23,062.50 + $1,904.82 = $27,529.82
Rounded to the nearest cent, the answer is option D: $27,735.14.
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Ellen mixed 1over 4 kg of flour with 2 over 9 kg of sugar. Determine a reasonable estimate for the amount of flour and sugar combined
A reasonable estimate for the amount of flour and sugar combined is approximately 0.36 kg.
To determine a reasonable estimate for the amount of flour and sugar combined, we first need to add the fractions 1/4 and 2/9. To do this, we need to find a common denominator. The least common multiple of 4 and 9 is 36. We can convert 1/4 to 9/36 by multiplying both the numerator and denominator by 9. We can also convert 2/9 to 4/36 by multiplying both the numerator and denominator by 4. Now we can add the fractions:
9/36 + 4/36 = 13/36
So Ellen mixed 13/36 kg of flour and sugar combined. To convert this to a decimal, we can divide the numerator by the denominator:
13 ÷ 36 ≈ 0.36
Therefore, a reasonable estimate for the amount of flour and sugar combined is approximately 0.36 kg.
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What is the volume of a container of 4 moles of gas at 200k with a pressure of 3 atm
The volume of the container is 2216 liters
How to determine the valueUsing the general gas law, we have that;
PV = nRT
Such that the parameters are given as;
P is the pressure of the gas measured in atmV is the volume of gas measured in litersn is the number of molesR is the universal gas constantT is the temperature measured in KelvinFrom the information given, we have that;
Substitute the values
3V = 4 × 8.31 × 200
Multiply the values, we have;
3V = 6648
Divide both sides by the coefficient of V, we get;
V = 2216 liters
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Si un cateto de un triángulo rectángulo y la hipotenusa miden 5 y 13cm, respectivamente, ¿cuánto mide el otro cateto?
The measure of the other side of the right triangle is given as follows:
12 cm.
What is the Pythagorean Theorem?The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
The theorem is expressed as follows:
c² = a² + b².
In which:
c is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.The parameters for this problem are given as follows:
Sides of 5 and x.Hypotenuse of 13.Hence the other side has the length given as follows:
5² + x² = 13²
25 + x² = 169
x² = 144
x = 12.
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I absolutely hate IQR so can someone help
The interquartile range (IQR) of the given data set is 4.
Interquartile range (IQR) is a measure of variability in a data set that measures the spread of the middle 50% of the data. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).
How to fine the interquartile range (IQR)?To find the interquartile range (IQR), we first need to find the median of the data set.
The median is the middle value of the dataset when the data is arranged in order. In this case, the data set is already in order, so the median is the middle value or the average of the two middle values:
Median = (26 + 28) / 2 = 27
Now, we need to find the first quartile (Q1) and the third quartile (Q3) of the data set.
Q1 is the median of the lower half of the data set, and Q3 is the median of the upper half of the data set.
Lower half: 22, 24, 26
Upper half: 28, 30
Q1 = median of the lower half = (24 + 26) / 2 = 25
Q3 = median of the upper half = (28 + 30) / 2 = 29
Now we can find the IQR:
IQR = Q3 - Q1 = 29 - 25 = 4
Therefore, the interquartile range (IQR) of the given data set is 4.
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Triangle TUV, with vertices T(2,-8), U(9,-6), and V(6,-3), is drawn on the coordinate
grid below. what is the area. in square units, of triangle TUV
The area of the triangle TUV, with vertices T(2,-8), U(9,-6), and V(6,-3), is 13.58
How did we arrive at the above?First using distance calculator we derived the length of TV and the length of VU.
Since TV = Height; and
VU = Base
and the triangle is a right triangle,
Then, area is given by 1/2 base x Height
Length of TV usign distance calculator is 6.40312
Lenght of VU using distance calculator is 4.24264
So area = 1/2 * 6.40312 * 4.24264
Area = 13.58
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Find the distance traveled by the top of second hand of a clock in 4 minute if the hand is 8 cm long
The second hand of a clock rotates once around the clock face in 60 seconds or one minute. Therefore, in 4 minutes, the second hand will rotate 4 times around the clock face.
The length of the second hand of a clock is 8 cm. The distance traveled by the top of the second hand in one full rotation is equal to the circumference of a circle with radius 8 cm, which is 2πr = 2π(8) = 16π cm.
The distance traveled by the top of the second hand in 4 rotations (or 4 minutes) is:
4 rotations * 16π cm/rotation = 64π cm
So the distance traveled by the top of the second hand of a clock in 4 minutes if the hand is 8 cm long is approximately 64π cm or about 201.06 cm (when rounded to two decimal places).
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