Solve the right angle trig problem.

Answer:

10 cm

Step-by-step explanation:

V =1/3 x π x r² x h

94.25 =1/3 x π x 3² x h

94.25 ÷ 3π =h

so, h= 10 cm

Answer:

a=y-k/(x-h)^2

It is possible to add another data point that would be reasonable, even though no measurements were made. This data point could be an estimate or a prediction based on the existing data points. For example, if the existing data points show a linear relationship between acceleration and force, it would be reasonable to add a data point that falls along the same line.

One possible data point that could be added is (3m/s2, 4n). This data point falls between the existing data points (2m/s2, 3n) and (5m/s2, 5n), and would be a reasonable estimate based on the existing data.

Another possible data point that could be added is (7m/s2, 6n). This data point falls along the same line as the existing data points, and would be a reasonable prediction based on the existing data.

Overall, it is possible to add another data point that would be reasonable, even though no measurements were made, as long as the data point is based on the existing data and follows the same pattern or relationship.

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The dimensions of the box that minimize the amount of materials used are a base with side length 32 cm and a height of 15.625 cm.

To minimize the amount of material used for the open-top box with a volume of 16,000 cm³, we will use calculus to find the dimensions that result in the smallest surface area. Let the side length of the square base be 'x' cm and the height of the box be 'h' cm. The volume V is given by V = x²h, and we know V = 16,000 cm³.

First, express the height in terms of the base side length:
h = 16,000 / x²

The surface area (A) of the box, including the base and four sides, can be expressed as:
A = x² + 4(xh)

Substitute the expression for 'h' from above:
A = x² + 4(x * 16,000 / x²) = x² + 64,000 / x

Now, find the critical points of 'A' with respect to 'x' by differentiating A with respect to x and setting the derivative to zero:
dA/dx = 2x - 64,000 / x² = 0

Solve for 'x':
x³ = 32,000
x = 32 cm

Now, find the corresponding height 'h':
h = 16,000 / 32² = 16,000 / 1,024 = 15.625 cm

So, the dimensions of the box that minimize the amount of materials used are a base with side length 32 cm and a height of 15.625 cm.

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Answer:

(x-2y-8)(x-2y-4)

Step-by-step explanation:

Let (x-2y) = x

x^2 -12x +32

Then factor the quadratic polynomial by 2 brackets factoring.

(x-8)(x-4)

Then convert x to (x-2y)

(x-2y-8)(x-2y-4)

A 50 percent increase in Earth's albedo, which refers to the reflectivity of its surface, would lead to a decrease in average surface temperatures.

Albedo plays a crucial role in determining how much of the sun's energy is absorbed or reflected by the Earth. The given information states that approximately 30 percent of the sun's energy is currently reflected back into space. If Earth's albedo increases by 50 percent, meaning more energy is reflected, it would result in less energy being absorbed by the Earth's surface and atmosphere.

The increased albedo would cause a higher percentage of the incoming solar radiation to be reflected and scattered back into space. With less energy being absorbed, the average surface temperatures would decrease. This is because less solar energy would be available to warm the Earth's surface and drive atmospheric processes that contribute to temperature regulation. Therefore, a 50 percent increase in Earth's albedo would likely lead to a cooling effect and lower average surface temperatures on our planet.

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In calculating the mean of this data set  Ashrita did the best job.

The  Mean of the data set is the most commonly used measures of central tendency.

It means the average value of the data set.

one doesn't have to arrange the data in order  for finding it.

The data set value  takes is to add them all together and divide that by the number of the data.

It can be written as

\(,(x_1 + x_2 + x_3 + ..... + x_n) / n\)

Where \(x_1 , x_2 , x_3 , ..... ,x_n\)are the values in the data set

Therefore we can conclude that Ashrita did the best job in calculating the mean of this data set.

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(b) No, The branch manager's argument that dispatching buses every 0.5 minutes will reduce the average traveling time (a round trip) to 3.5 minutes is not correct.

To calculate the average time, we need to consider the time it takes for the bus to travel to the airport and back, as well as the time spent waiting for the bus.

If buses are dispatched every 3 minutes, and the average traveling time (a round trip) is 21 minutes, it means that passengers spend 18 minutes waiting for the bus (21 minutes - 3 minutes of traveling time).

If buses are dispatched every 0.5 minutes, the waiting time will be significantly reduced. However, the traveling time remains the same at 21 minutes for a round trip.

Therefore, the average traveling time will not be reduced to 3.5 minutes but will remain at 21 minutes (assuming the traveling time remains constant).

(c) The average traveling time, following the branch manager's suggestion of dispatching buses every 0.5 minutes, would still be 21 minutes.

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Complete question:

The Avis Company is a car rental company and is located three miles from the Los Angeles airport (LAX). Avis is dispatching a bus from its offices to the airport every 3 minutes. The average traveling time (a round trip) is 21 minutes.

(a) The branch manager wants to improve the service and suggests dispatching buses every 0.5 minute. She argues that this will reduce the average traveling time (a round trip) to 3.5 minutes. Is she correct? (Enter "Yes" or "No" in the following blank).

c. Following the branch manager's suggestion (dispatch busses every 0.5 min), what will the average traveling time be? average travelling time ____(mins) (enter the numbers only)

To apply the Mean Value Theorem (MVT), we need to check if the function f(x) = 18x^2 + 12x + 5 satisfies the conditions of the theorem on the interval [-1, 1].

The conditions required for the MVT are as follows:

The function f(x) must be continuous on the closed interval [-1, 1].

The function f(x) must be differentiable on the open interval (-1, 1).

By examining the given equation, we can see that the left-hand side (4x - 4) and the right-hand side (4x + _____) have the same expression, which is 4x. To make the equation true for all values of x, we need the expressions on both sides to be equal.

By adding "0" to the right-hand side, the equation becomes 4x - 4 = 4x + 0. Since the two expressions on both sides are now identical (both equal to 4x), the equation holds true for all values of x.

Adding 0 to an expression does not change its value, so the equation 4x - 4 = 4x + 0 is satisfied for any value of x, making it true for all values of x.

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Answer:

The measurement to be converted is 12 feet 8 inches.

The students need to convert the given measurement into inches. This is because they are trying to find the equivalent length in inches of 12 feet 8 inches.

Stella is incorrect. 12 feet is equal to 144 inches, not 152 inches. To convert feet to inches, we multiply the number of feet by 12.

Vladimir is also incorrect. He is only considering the 8 inches and not the 12 feet. To find the total length in inches, we need to first convert the 12 feet to inches (12 feet x 12 inches/foot = 144 inches) and then add the 8 inches, giving a total of 144 + 8 = 152 inches.

So, the correct answer is 12 feet 8 inches = 152 inches.

Step-by-step explanation:

Answer:

18.5 in approx

Step-by-step explanation:

Given data

aspect ratio of 16: 9

L= 16in

W= 9 in

We want to find the diagonal of the TV

applying Pythagoras theorem

d^2= l^2+w^2

d^2= 16^2+ 9^2

d^2=256+81

d^2= 337

d= √337

d= 18.35 in

Hence the tv is 18.5 in approx

The coordinate of the centroid of the given triangle will be at (-2.33,5).

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The given triangle with vertices has been drawn.

The midpoint of H( – 6, 3) and F(1, 5) will be as,

x = (-6 + 1)/2 = -2.5

y = (3 + 5)/2 = 4 so D(-2.5,4)

The coordinate of the centroid will intersect 2:1 of the median from the vertex side.

Thus by intercept formula,

x = (2 × -2.5 + 1 × -2)/(2 + 1) and y = (2 × 4 + 1 × 7)/(2 + 1)

x = -2.33 and y = 5

So the coordinate of vertices will be (-2.33,5).

Hence "The specified triangle's centroid's coordinate will be at (-2.33,5)".

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Answer:

5*(x+8)-(7*x+38)=0

5 • (x + 8) -  (7x + 38)  = 0

  2 - 2x  =   -2 • (x - 1)

 -2 • (x - 1)  = 0

  -2   =  0

This equation has no solution.

A a non-zero constant never equals zero.

x-1 = 0

 x = 1

The domain of the function is {R} and the range of the function is {R}. where R are all the real numbers.

The range of values that we are permitted to enter into our function is known as the domain of a function.

The x values for a function like f make up this set (x).

A function's range is the collection of values it can take as input. The values in this set

Hence, once we input an x value, the function returns. The y values are those.

The given function is:

f(x) = -log(5 - x) + 5

The domain of the function is the input value or the x-coordinates of the function, and the range of the function are the output values that are obtained when the input value is plugged in the function.

For the function:

f(0) = - log (5 - 0) + 5

f(0) = 4.30

f(1) = 4.39

f(2) = 4.69

The domain is {0, 1, 2, ....} and the range of the function is {4.30, 4.39, 4.69...}.

Hence, the domain of the function is {R} and the range of the function is {R}. where R are all the real numbers.

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The rate of change of the volume of water in the pool is 12 gallons/second.

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

When one quantity increases or declines, the other quantity also rises or falls in direct proportion. On the other hand, in indirect or inverse proportion, if one quantity rises, the other one falls, and vice versa.

When the ratio x:y is constant, two values, x and y, are said to be directly proportional to one another. If we spend Rs. 50 on two pens, as an example. For four pens, it will cost us 100 Rs. When the ratio x:y1 is constant, two values, x and y, are said to be inversely proportional to one another.

The rate of change of the volume of water in the pool is the rate at which the volume is decreasing, which is the same as the rate at which the pool is being drained.

This is given by the number of gallons of water being drained per second, which is 12 gallons/second.

So the rate of change of the volume of water in the pool is 12 gallons/second.

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The rate of change of the volume of water in the pool is 12 gallons/second.What is the Unitary method?The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.What is direct and indirect proportion?When one quantity increases or declines, the other quantity also rises or falls in direct proportion. On the other hand, in indirect or inverse proportion, if one quantity rises, the other one falls, and vice versa.When the ratio x:y is constant, two values, x and y, are said to be directly proportional to one another. If we spend Rs. 50 on two pens, as an example. For four pens, it will cost us 100 Rs. When the ratio x:y1 is constant, two values, x and y, are said to be inversely proportional to one another.The rate of change of the volume of water in the pool is the rate at which the volume is decreasing, which is the same as the rate at which the pool is being drained.This is given by the number of gallons of water being drained per second, which is 12 gallons/second.So the rate of change of the volume of water in the pool is 12 gallons/second. I got the same thing the other person did so they are correct

Answer:

12

Step-by-step explanation:

Step-by-step explanation:

The first term is 6x3

Because he subtracted like terms 8x3 and 2x3

Answer:

6x³

Step-by-step explanation:

2x²y + 8x³ – xy² – 2x³ + 3xy² + 6y³=

6x³+2x²y+2xy²+6y³

Answer:

There is no question showing up so I dont know how to help u

Step-by-step explanation:

Solution :

\($y=x^{3/2}, \ \ y =8, \ \ x=0$\)

\($v=2 \pi \int_0^4 x (8-x^{3/2}) \ dx$\)

 \($= 2\pi \left(\frac{8x^2}{2}-\frac{x^{7/2}}{7/2}\ \left|_0^4\)

 \($=2\pi \left( 4x^2-\frac{2}{7}x^{7/2}\ |_0^4$\)

 \($=2\pi \left( 64-\frac{2}{7} \times 32 \times 4 \right)$\)

  \($=2\pi \left(1-\frac{4}{7} \right) 64$\)

  \($=128 \pi \times \frac{3}{7}$\)

 \($=\frac{384 \pi}{7}$\)

Total Cost = No of Units x Unit cost of refrigerators

Total Cost = 42 x $ 501 = $ 21, 042

Rounding off to the nearest tens,

We have to round down 42 (in $ 21, 042) to 40

Therefore, the total cost will be $ 21, 040

Answer: $21,040

Step-by-step explanation:

Use Pythagorean theorem to find the base of the right triangle

221^2 = 195^2 + b^2

b = 104 km

triangle area = 1/2 base * height =  1/2 * 104 * 195 = 10140 km^2

Now multiply by the height to find volume

10140 km^2  * 15 km  = 152100 km^3

Answer:

I'm have trouble understanding the answer options.    The quadratic equation is x^2 + x = 342

Step-by-step explanation:

Let x be the first integer, so (x+1) becomes the second.  Their product is 342:

(x)(x+1) = 342

x^2 + x = 342

[The consecutive integers are 18 and 19, or -18 and -19]

The quadratic equation is x² + x = 342.

An integer is a positive, negative, or zero integers (not a fraction). Examples of integers are -5, 1, 5, 8, 97, and 3,043. Examples of non-integers are: -1.43, 1 3/4, 3.14 ,. 09 and 5,643.1. Integers include positive numbers, negative numbers, and zeros.

Integermeans whole or undamaged in Latin. That is, integers do not contain fractions or decimals. In this article, learn more about integers, integer definitions, and integer properties. Integer contains all integers and negative numbers. That is, including a negative number along with an integer from a set of integers.

Let x be the first integer, so (x+1) becomes the second.  Their product is 342:

(x)(x+1) = 342

x² + x = 342

[The consecutive integers are 18 and 19, or -18 and -19].

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Answer:

incenter is angle bisectors

altitude orthocenter

centroid perpendicular bisector

circumcenter medians

Answer:

1 1/2

Step-by-step explanation:

Because 4 cups of tomatoes is half of 8, you need to find half of the 3 cups of unions. 3/2=1 1/2.

Answer:

1 1/2

Step-by-step explanation:

she needs one and a half cup of onions

Answer:

i need more info

Step-by-step explanation:

The correct way to solve for the answer is to divide the quantity of potatoes the store bought by the quantity of each bag of potatoes.

Quantity of potatoes the store bought = 250 kilograms

Quantity of each bag of potatoes= 10 pounds

Convert kilograms to pounds:

1 kilogram = 2.20462 pounds

25 kilograms= 551.156 pounds

Number of bags of potatoes= Quantity of potatoes the store bought / Quantity of each bag of potatoes

= 551.156 pounds ÷ 10 pounds

= 55.1156 bags

Approximately,

55 bags

Therefore, the store will pack an approximate number of 55 bags of potatoes.

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Answer: I think it's 30 degrees. Sorry if I'm wrong.

Step-by-step explanation:

Answer:

280 trees on a 1.5 acre plot

Step-by-step explanation:

It has more trees with less acres already without any calculations.

The instantaneous rate of change of g(x) with respect to x at x = 9 is 4.To find the derivative of the function g(x) at x = 9, denoted as g'(9), we can use the equation of the tangent line given as f'(9) = 4.

The derivative of a function represents its rate of change at a specific point. In this case, the derivative g'(x) at x = 9 is given as 4, which means that at that point, the function g(x) has a slope of 4. The tangent line to the graph of g(x) at (9,32) has this slope of 4, indicating the instantaneous rate of change of g(x) with respect to x at x = 9.

This means that for a small change in x around x = 9, the corresponding change in g(x) is approximately 4 times that of x. Thus, the instantaneous rate of change of g(x) with respect to x at x = 9 is 4, indicating how quickly g(x) is changing at that particular point.

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