If the area of the smaller circle is half the area of the larger, the ratio of the radius of the smaller circle to that of the larger circle is?

Answer:

20 1/2

Step-by-step explanation:

because area equals length times width

Answer and Step-by-step explanation:

First, let's split the figure into two common shapes that we know the area formula for.

The top shape can become a triangle, while the bottom shape can become a rectangle.

We know the area of a triangle is

\(A = \frac{bh}{2}\)

and the area of a rectangle is

A = lw

Where:

A = Area

b = Base length (length)

h = Height

l = Longer length of a side

w = Smaller length of a side

Area of a Triangle:

b = 3

h = 3

A = \(\frac{3 * 3}{2}\)

A = 4.5

Area of a Rectangle:

w = 3

l = 8

A = 3 × 8

A = 24

Now we add together the areas to get the area of the figure.

Area of the Figure:

A = 4.5 + 24

A = 28.5

The area of the figure is 28.5 \(units^{2}\).

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We can apply the power rule for differentiation. The derivative of \(\(y = \frac{1}{x^{25}}\)\) with respect to x is: \(\[\frac{dy}{dx} = -25x^{-26}\]\)

To find the derivative of  \(\(y = \frac{1}{x^{25}}\)\) with respect to x, we can apply the power rule for differentiation.

The power rule states that if we have a function \(\(f(x) = x^n\)\), then its derivative with respect to x is given by \(\(\frac{d}{dx}f(x)) = nx^{n-1}\)\).

Using the power rule, let's differentiate y with respect to x:

\(\[\frac{d}{dx} \left(\frac{1}{x^{25}}\right)\]\)

Applying the power rule, we have:

\(\[\frac{d}{dx} \left(x^{-25}\right)\) = \(-25x^{-25-1} = -25x^{-26}\]\)

Therefore, the derivative of \(\(y = \frac{1}{x^{25}}\)\) with respect to x is:

\(\[\frac{dy}{dx} = -25x^{-26}\]\)

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Paul has 40 dimes and 20 quarters in his piggybank.

Given that Paul has a mix of quarters and dimes in his piggybank, and he has twice as many dimes than he has quarters, and he counts all his coins and notices that he has 9.00$ in total, to determine how many quarters does Paul have, the following calculation has to be done:

Therefore, Paul has 40 dimes and 20 quarters in his piggybank.

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Answer:

75%

Step-by-step explanation:

100% ÷ 4 = 25%. 3 questions correct= 75% and one wrong which is 25%. 100-25=75

Answer:

75%

Step-by-step explanation: 100 divided by one fourth is 75 therefore leaving that as your grade.

Answer:

hope this will help you

Step-by-step explanation:

\(b { }^{2} - 81 = 0 \\ b {}^{2} = 81 \\ b = \sqrt{81} \\ b = 9\)

Answer: Heyaa! :D

Your Answer Is... 9

Step-by-step explanation:

Since both terms are perfect squares, factor using the difference of squares formula,

a²−b²=(a + b)(a − b) where a = B and

b = 9.

(B + 9)(B − 9)

Answer:

Note: The full question is attached as picture below

a) Hо : p = 0.71

Ha : p ≠ 0.71

p = x / n

p = 91/110

p = 0.83.

1 - Pо = 1 - 0.71 = 0.29.

b) Test statistic = z

= p - Pо / [√Pо * (1 - Pо ) / n]

= 0.83 - 0.71 / [√(0.71 * 0.29) / 110]

= 0.12 / 0.043265

= 2.77360453

Test statistic = 2.77

c) P-value

P(z > 2.77) = 2 * [1 - P(z < 2.77)] = 2 * 0.0028

P-value = 0.0056

∝ = 0.01

P-value < ∝

Reject the null hypothesis.  There is sufficient evidence to support the researchers claim at the 1% significance level.

Answer:

2,2

Step-by-step explanation:

Equations are all good

The ordered pair (2, 1) satisfies the given equations. Therefore, the answer is option (C).

To solve the system of equations y = 2x - 3 and y = 3x - 6, we need to find an ordered pair (x, y) that satisfies both equations.

We can do this by completing the table of values for each equation and finding the values of x and y that make both equations true.

For the equation y = 2x - 3, we can complete the table as follows:

x: -1, 0, 1, 2, 3

y: -5, -3, -1, 1, 3

For the equation y = 3x - 6, we can complete the table as follows:

x: -1, 0, 1, 2, 3

y: -9, -6, -3, 0, 3

From these tables, we can see that the ordered pair (2, 1) satisfies both equations.

Therefore, the answer is (2, 1).

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The complete question is as follows:

Consider the equations y = 2x - 3 and y = 3x - 6. Solve the system of equations by completing the table to find an ordered pair that satisfies both equations.

A) (0, 3)

B) (1, -1)

C) (2, 1)

D) (2, 2)

hello

we are requested to perform a basic arithmetic of 51 * 37

we can easily solve this by using the multiplication operator in our calculator or following through the basic method manually.

the answer to this question is 1887

Answer:

All the lateral faces in a triangular pyramid are congruent.

Step-by-step explanation:

The statement that is true for all triangular pyramid is given by: Option B: All triangular pyramids have three lateral faces.

Take a traingle. This is a base. Now take 3 triangles such that each of them are connected to one-one side of the first traingle and when they're taken together, they form a closed object, called as a triangular pyramid.

One such triangular pyramid is shown in the image attached below.

The triangle at bottom is called base of the pyramid, and those 3 triangles which are slant, are called lateral faces of the pyramid.

Evaulating truthness of each statement:

It isn't necessary for all triangular pyramid. This is true only for those triangular pyramid in which the base is formed by an equilateral triangle and the peak of the pyramid is exactly above the centroid of the base. This isn't true for all triangular pyramid.

Obviously  true as this is involved in the definition of triangular pyramids to have 3 triangles on its sides, except the base traingle(which isn't called lateral face).

Total faces in a triangular pyramid = 3 lateral faces + 1 base = 4 faces

Thus, its totally incorrect for any triangular pyramid.

False for most of the triangular pyramids. This is only true when the triangular pyramid has all faces congruent to each other, which isn't always true.

Thus, the statement that is true for all triangular pyramid is given by: Option B: All triangular pyramids have three lateral faces.

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We estimate that f(125) is approximately 52. Based on the given information, we can use the linear approximation method to estimate f(125).

Since we know f(130) = 67 and f′(130) = 3, we can create the linear approximation function:
L(x) = f(130) + f′(130) * (x - 130)
Now we can estimate f(125) using L(x):
L(125) = 67 + 3 * (125 - 130)
L(125) = 67 - 15 = 52
So, the estimated value of f(125) is approximately 52.

To estimate f(125), we can use the linear approximation formula:
f(125) ≈ f(130) + f′(130) * (125 - 130)
Substituting in the given values, we get:
f(125) ≈ 67 + 3 * (-5) = 52
Therefore, we estimate that f(125) is approximately 52.

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Answer: undefined

Step-by-step explanation:

Answer:

x=7

Step-by-step explanation:

55=2x+(x+4)+[3(x+3)]

55=2x+x+4+3x+9

55=6x+13

55-13=6x

42=6x

7=x

Answer:

Step-by-step explanation:

Perimeter is the sum of side lengths:

Solve for x:

Answer:

Step-by-step explanation

The number of trees more than 10m tall but not more than 20m tall is 18 trees.

0 < h ≤ 5 = 5

height greater than 0m less than or equal to 5m

5 < h ≤ 10 = 9

height greater than 5m less than or equal to 10m

10 < h ≤ 15 = 13

height greater than 10m less than or equal to 15m

15 < h ≤ 20 = 5

height greater than 15m less than or equal to 20m

20 < h ≤ 25 = 1

height greater than 20m less than or equal to 25m

The number of trees that are more than 10m tall but not more than 20m tall are;

10 < h ≤ 15 = 13

15 < h ≤ 20 = 5

So,

13 + 5 = 18 trees

Therefore, the total number of trees which are 10m tall but not more than 20m tall is 18 trees.

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Answer:

about 29 gallons

Step-by-step explanation:

3.54*36=127.44

3636/127.44 = 28.5 = 29

Answer:

the answer is b)3

Step-by-step explanation:

2=36

?(x)=54

2×54=36x

108/36=x

x=3

Answer:

AC=73

Step-by-step explanation:

Based on the information provided, you have a closed-end lease.

A closed-end lease, also known as a "walk-away" lease or a "non-recourse" lease, is a type of lease where the lessee has no further financial obligations at the end of the lease term. In this case, you intend to turn in the car and not pay any additional amount based on the residual value of the car.

With a closed-end lease, the residual value of the car is predetermined at the beginning of the lease agreement. The residual value represents the estimated worth of the car at the end of the lease term. At the end of the lease, you have the option to return the car to the lessor without any additional payments, as long as you have complied with the terms and conditions of the lease agreement.

Unlike an open-end lease, where the lessee may be responsible for any difference between the actual value and the predetermined residual value, a closed-end lease provides more certainty and financial protection to the lessee.

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Answer: The tree is 27 feet tall.

Step-by-step explanation:

Here's what we know:

6/10 = x/45 (a 6 foot object creating a 10 shadow is equivalent to something else making a 45 shadow)

We need to isolate x. Multiply both sides by 45:

6*45/10 = x

We can factor out a 2:

3*45/5 = x

We can also factor out a 5:

3*9/1 = x

27 = x

The tree is 27 feet tall.

Answer:

x=35

Step-by-step explanation:

because the angles are next to each other they are supplementary, which makes the total of the angle 180 degrees.

the equation would be:

180=x+14 +4x -9

add the like terms

180=5x =5

then subtract 5 from both sides

175=5x

then divide five from both sides

x=35

Answer:

20 units²

Step-by-step explanation:

I have included the answer as well as an explanation and formula above. Note that the formula is only for area of trapeziums/trapezoids

(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)

Is the relation a function:

To determine if the relation is a function, we need to check if there is exactly one output for each input.

Looking at the given set of points, we see that there are two points with an x-coordinate of -1: (-1, 3) and (-1, -2).

This means that there are two outputs for the same input, so the relation is not a function.

Therefore, the correct answer is: "No, because for each input there is not exactly one output."

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Tyler drank a total of 9 2/21 liters of water altogether.  

Tyler drank a fraction of 9 5/21 liters of water altogether. To find the total amount of water Tyler drank, we need to add the 2 3 liters of water he drank before jogging and the 3 7 liters of water he drank after jogging. To add these fractions, we need to find a common denominator, which is 21.

For the first fraction, we need to multiply both the numerator and denominator by 7 to get 14/21. For the second fraction, we need to multiply both the numerator and denominator by 3 to get 9/21. Now, we can add these two fractions:

14/21 + 9/21 = 23/21

This is an improper fraction, so we can simplify it to a mixed number by dividing the numerator by the denominator:

23 ÷ 21 = 1 remainder 2

So, Tyler drank a total of 9 2/21 liters of water altogether.

Drinking enough water is essential for staying hydrated and healthy, especially during exercise. It is recommended to drink at least 8 cups (64 ounces or 1.9 liters) of water per day, but this can vary depending on factors such as age, gender, weight, and physical activity level. Drinking enough water can help prevent dehydration, regulate body temperature, flush out toxins, and improve overall health and well-being.
 

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Answer:

Option D Neither is the answer.

Step-by-step explanation:

Answer:

The correct answer is choice D.

Step-by-step explanation:

If plugged into the equation the ordered pair should make both sides equal each other. If not then it is not correct. Remember that ordered pairs are in the form (x,y).

(1,2)

3.2+3y=-x+5y

Plug in the values.

3.2+3(2)=9.2

-1+5(2)=-9

(2,4)

3.2+3(4)=15.2

-2+5(4)=18

None of these satisfy the given equation. :D

Answer:

\(Side\ B = 6.0\)

\(\alpha = 56.3\)

\(\theta = 93.7\)

Step-by-step explanation:

Given

Let the three sides be represented with A, B, C

Let the angles be represented with \(\alpha, \beta, \theta\)

[See Attachment for Triangle]

\(A = 10cm\)

\(C = 12cm\)

\(\beta = 30\)

What the question is to calculate the third length (Side B) and the other 2 angles (\(\alpha\ and\ \theta\))

Solving for Side B;

When two angles of a triangle are known, the third side is calculated as thus;

\(B^2 = A^2 + C^2 - 2ABCos\beta\)

Substitute: \(A = 10\),  \(C =12\); \(\beta = 30\)

\(B^2 = 10^2 + 12^2 - 2 * 10 * 12 *Cos30\)

\(B^2 = 100 + 144 - 240*0.86602540378\)

\(B^2 = 100 + 144 - 207.846096907\)

\(B^2 = 36.153903093\)

Take Square root of both sides

\(\sqrt{B^2} = \sqrt{36.153903093}\)

\(B = \sqrt{36.153903093}\)

\(B = 6.0128115797\)

\(B = 6.0\) (Approximated)

Calculating Angle \(\alpha\)

\(A^2 = B^2 + C^2 - 2BCCos\alpha\)

Substitute: \(A = 10\),  \(C =12\); \(B = 6\)

\(10^2 = 6^2 + 12^2 - 2 * 6 * 12 *Cos\alpha\)

\(100 = 36 + 144 - 144 *Cos\alpha\)

\(100 = 36 + 144 - 144 *Cos\alpha\)

\(100 = 180 - 144 *Cos\alpha\)

Subtract 180 from both sides

\(100 - 180 = 180 - 180 - 144 *Cos\alpha\)

\(-80 = - 144 *Cos\alpha\)

Divide both sides by -144

\(\frac{-80}{-144} = \frac{- 144 *Cos\alpha}{-144}\)

\(\frac{-80}{-144} = Cos\alpha\)

\(0.5555556 = Cos\alpha\)

Take arccos of both sides

\(Cos^{-1}(0.5555556) = Cos^{-1}(Cos\alpha)\)

\(Cos^{-1}(0.5555556) = \alpha\)

\(56.25098078 = \alpha\)

\(\alpha = 56.3\) (Approximated)

Calculating \(\theta\)

Sum of angles in a triangle = 180

Hence;

\(\alpha + \beta + \theta = 180\)

\(30 + 56.3 + \theta = 180\)

\(86.3 + \theta = 180\)

Make \(\theta\) the subject of formula

\(\theta = 180 - 86.3\)

\(\theta = 93.7\)

The measure of the larger angle (x) is approximately 171.23 degrees.

Let's assume the two supplementary angles are x and y, where x is the larger angle. The given ratio tells us that the larger angle (x) is 47 times the smaller angle (y).

We can set up the following equation based on the given information:

x/y = 47/2

To find the value of x, we can multiply both sides of the equation by y:

x = (47/2) * y

Since the two angles are supplementary, their sum is 180 degrees:

x + y = 180

Now we can substitute the value of x from the first equation into the second equation:

(47/2) * y + y = 180

To solve for y, we can simplify the equation:

(47/2 + 1) * y = 180

(49/2) * y = 180

Now divide both sides by (49/2):

y = (180 * 2) / 49

y = 360/49

Calculating this value, we find that y is approximately 7.35 degrees.

To find the value of x (the larger angle), we can substitute this value of y back into the first equation:

x = (47/2) * y

x = (47/2) * 7.35

x = 342.45/2

x = 171.23 degrees (approximately)

Therefore, the measure of the larger angle (x) is approximately 171.23 degrees.

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Answer:

1.5625

Step-by-step explanation:

2½ = 5/2

(5/2)² = 25/4

25/4 = 6.25

0.5² = 0.25

6.25 x 0.25 = 1.5625

Answer:

A.654 cm

Step-by-step explanation:

V = h times π times Radius