Which of the following statements is TRUE?


The volume of a______________

A. prism is thrice the volume of a pyramid.

B. pyramid is thrice the volume of a prism.

C. cylinder is twice the volume of a cone.

D. cone is twice the volume of a cylinder.

The amount of dry ingredients used in the cake recipe is approximately 7 cups.

To find the total amount of dry ingredients used in the cake recipe, we need to add up the amounts of flour, sugar, and cocoa.

3 ½ cups of flour is equal to 3 cups plus 0.5 cups, or 3 cups and 8 ounces.

2 ⅔ cups of sugar is equal to 2 cups plus 0.67 cups, or 2 cups and 10.72 ounces.

1 ¾ cups of cocoa is equal to 1 cup plus 0.75 cups, or 1 cup and 12 ounces.

Adding these amounts together, we get:

3 cups and 8 ounces + 2 cups and 10.72 ounces + 1 cup and 12 ounces = 6 cups and 14.72 ounces

To the nearest cup, this is equal to 7 cups.

Therefore, the amount of dry ingredients used in the cake recipe is approximately 7 cups.

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Answer: B. (1, 8)

Step-by-step explanation:

Hope this helps! :)

The missing statement and the reason in the two-column proof:

EC = BC; property iof isosceles triangles

The corret answer is an option (A)

A two-column proof to show that AB/AD = BC/DC is:

        Statement                                        Reason

       ∠1 ≅ ∠2                                               given

       ∠1 ≅ ∠5                          alternate interior angles theorem

       ∠3 ≅ ∠4                                vertical angles theorem

ΔABD is similar to ΔCED                  AA similarity

  AB/AD = EC/DC                         property of similar triangles

        ∠2 ≅ ∠5                     substitution property of congruency

         EC = BC                          property iof isosceles triangles

        AB/AD = BC/DC               substitution property of equality

Therefore, the correct answer is an option (A)

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Find the complete question below.

The equation of the axis of symmetry is x = 5/8

The axis of symmetry of a parabola is a vertical line that divides the parabola into two symmetric halves.

The equation of the axis of symmetry for a parabola of the form y = ax² + bx + c is given by:

x = -b/(2a)

In the given equation, a = 4 and b = -5. Substituting these values into the formula, we get:

x = -(-5)/(2×4)

x = 5/8

Therefore, the equation of the axis of symmetry is x = 5/8

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Answer:

(2,2), (4,8), (3,4)

Step-by-step explanation:

Plug in the x-coodinate and it should equal your desired y value

The statement explains how the number cube is fair is The data should be symmetric about a central value.

Julio's simulation results, when graphed on a dot plot, often demonstrate an example of symmetric distribution where every number occurs with roughly the same frequency.

While perfect symmetry may not be witnessed in this particular simulated experiment, which consists of 40 trials that incorporate 8 rolls each, granted its limited range, the data will commonly point to fairness in its results for a fair number cube.

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The correct answers are given below:

D. Multiply/divide both sides by the same non-zero constant

A. Yes

To achieve equity between Equation A and Equation B, one must:

Via combining 1 with the parenthesis of Equation A and conjoining common terms, one begins by distributing the 1 and fusing both sides together to form 5x + 4 = -3.

Afterward, multiplying both sides of the equation by -12 (the same non-zero constant), yields -60x - 48 = 36.

Ultimately, adding 72 to both equities presents the answer to furthering equations, -12x - 48 = -12.

Thus, the resolution rest in choice D- multiply/divide both sides by the same non-zero constant.

By producing Equation B from Equation A through analogous methods on either side of the equation, it is confirmed that the two compilations are equivalent and manifest exact solutions. Therefore, the proper selection for this query is Yes- Choice A.

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A. B. ​ ​ 4 x ​ +1 x+4 ​ =−3 =−12 ​ 1) How can we get Equation BBB from Equation AAA? Choose 1 answer: Choose 1 answer: (Choice A) A Rewrite one side (or both) using the distributive property (Choice B) B Rewrite one side (or both) by combining like terms (Choice C) C Multiply/divide only one side by a non-zero constant (Choice D) D Multiply/divide both sides by the same non-zero constant 2) Based on the previous answer, are the equations equivalent? In other words, do they have the same solution? Choose 1 answer: Choose 1 answer: (Choice A) A Yes (Choice B) B No

Answer:

I believe it is B. always

Because Adding, subtracting or even multiplying will always give you a new polynomial not the same polynomial.

Im sorry if i am wrong

The correct statements from the box plot are given as follows:

A box and whisker plots shows these five features from a data-set, listed as follows:

Hence the correct statements are given as follows:

The false statements are given as follows:

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The appropriate measure of variability for this data set is the IQR, and its value is 2. The mean and median are measures of central tendency, not measures of variability. The range may not be the best measure of variability for this data set because it is influenced by extreme values.

The given data set is:

2, 10, 10, 12, 12, 20

To determine the appropriate measure of variability, we need to consider the spread or dispersion of the data. In this case, we can see that the range,

20 - 2 = 18.

A better measure of variability for this data set is the interquartile range (IQR), which is the range of the middle 50% of the data. To find the IQR, we first need to find the median of the data:

2, 10, 10, 12, 12, 20

The median is the middle value when the data set is arranged in order, which is 11. We can then divide the data set into two halves:

2, 10, 10 and 12, 12, 20

The lower half has a median of 10, and the upper half has a median of 12. The IQR is the difference between these medians:

IQR = 12 - 10 = 2

Therefore, the appropriate measure of variability for this data set is the IQR, and its value is 2. The mean and median are measures of central tendency, not measures of variability. The range may not be the best measure of variability for this data set because it is influenced by extreme values.

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Answer:

[tex]r = \sqrt{ {8.6}^{2} - {5}^{2} } [/tex]

[tex]r = \sqrt{73.96 - 25} = \sqrt{48.96} = 6.997[/tex]

The closest answer is b.

The x-intercepts for the function y = cos x, where 0≤x≤ 2n are

x = π/2, x = 3π/2, and x = 2π

We have,

The cosine function has an x-intercept whenever it crosses the x-axis, which happens at every multiple of π/2 radians (or 90 degrees).

So the x-intercepts for the graph y = cos x, where 0 ≤ x ≤ 2π are at

x = π/2, x = 3π/2, and x = 2π

(corresponding to 90 degrees, 270 degrees, and 360 degrees).

Now,

If we take 2n to be a multiple of 2π (i.e., 2n = k2π for some integer k), then the x-intercepts for the graph y = cos x,

where 0 ≤ x ≤ 2n, will be at x = kπ/2 for k = 0, 1, 2, ..., 4n-1.

The x-intercepts for the graph y = cos x, where 0≤x≤ 2n are

x = π/2, x = 3π/2, and x = 2π

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A linear equation that describe how x and y are related include the following: A. y = -8x.

In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) by using various data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 24/-3 = 16/-2 = 8/-1 = -8/1 = -16/2

Constant of proportionality, k = -8.

Therefore, the required linear equation is given by;

y = kx

y = -8x

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1)  Total time elapsed = 4 hours 59 minutes.

2)  Total time elapsed =  6 hours 12 minutes

3)  Total time elapsed =   6 hours 2 minutes

1) Time difference from 12:00 noon to 4:00 p.m = 4 hours

Time difference from 4:00 p.m to 4:59 p.m. = 59 minutes

So, the total time elapsed = 4 hours 59 minutes.

2) The time difference from 1:23 a.m. to 2:00 a.m. = 37 minutes

The time difference from 2:00 a.m to 7:00 a.m. = 5 hours

The time difference from 7:00 a.m. to 7:35 a.m. = 35 minutes

Here, the minutes elasped = 37 + 35

                                             = 72 minutes

                                             = 1 hour 12 minutes

So, So, the total hours elapsed = 5 + 1

                                                    = 6 hours

Thus, the total time elapsed = 6 hours 12 minutes

3) Time difference from 11:28 p.m. to 12:00 midnight = 32 minutes

Time difference from 12:00 midnight to 5:30 a.m. = 5 hours 30 minutes

Here, the minutes elasped = 32 + 30

                                             = 62 minutes

                                             = 1 hour 2 minutes

So, the total time elapsed =  6 hours 2 minutes

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The calculated value of x in the equation (x + 1) (x - 5) = 16 is 7

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

(x + 1) (x - 5) = 16

The above expression is the product of two factors

(x + 1) and (x - 5)

And the result is 16

Express 16 as 8 * 2

So, we have

(x + 1) (x - 5) = 8 * 2

By comparison, we have

x + 1 = 8 and x - 5 = 2

When evaluated, we have

x = 7 and x = 7

This means that the value of x in the equation is 7

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Answer: 1

Step-by-step explanation:

The formula for the Z-score is:

Z = (X - μ) / σ

where:

- X is Dr. Baker's bowling average

- μ is the mean bowling average of the players in the tournament

- σ is the standard deviation of the bowling averages of the players in the tournament

From the problem, we know that:

- μ = 158

- σ^2 = 121

- X = 169

Therefore, σ = sqrt(121) = 11.

Now we can plug in the values into the Z-score formula:

Z = (169 - 158) / 11 = 1

This means that Dr. Baker's bowling average is 1 standard deviation above the mean bowling average of the players in the tournament.

So the appropriate statistic is the Z-score, which is 1.

Let's start by using the formula:

distance = rate x time

Let d be the distance the boat traveled, in miles.

The time it took Pat and Jeff to walk to the dock is the same as the time it took them to motor to Dillon, so we can write:

d/8 = (13 - d)/2

Simplifying this equation, we get:

d = 8(13 - d)/2

d = 52 - 4d

5d = 52

d = 10.4

Therefore, the boat traveled a distance of 10.4 miles.

Answer:

governmental fund financial statements and government-wide financial statements have different purposes and accounting methods. Governmental fund financial statements focus on the short-term financial performance and accountability of individual funds, using the modified accrual basis of accounting. Government-wide financial statements provide a broader and longer-term perspective of the government's financial position and activities, using the full accrual basis of accounting.

To reconcile between these two types of statements, some adjustments are needed to account for the differences in measurement focus and basis of accounting. Here are the steps to prepare the reconciliations for Part A and Part B:

Part A: Reconciliation between the Governmental Fund Balance Sheet and the Government-wide Statement of Net Position at 12/31/22.

- Start with the total fund balance of the governmental funds as reported in the fund balance sheet ($200,000).

- Add the net value of capital assets (acquisition value minus accumulated depreciation) as reported in the government-wide statement of net position. This is because capital assets are not reported in governmental fund financial statements, but are reported in government-wide financial statements. The net value of capital assets can be calculated as follows:

- Acquisition value of capital assets as of 1/1/22: $10,000,000

- Plus: Purchases of capital assets during 2022: $1,000,000

- Less: Sales of capital assets during 2022: $30,000

- Equals: Acquisition value of capital assets as of 12/31/22: $10,970,000

- Less: Accumulated depreciation as of 1/1/22: $5,200,000

- Less: Depreciation expense for 2022: $500,000

- Equals: Accumulated depreciation as of 12/31/22: $5,700,000

- Net value of capital assets as of 12/31/22: $5,270,000

- Subtract the amount of bonds payable as reported in the government-wide statement of net position. This is because bonds payable are not reported in governmental fund financial statements, but are reported in government-wide financial statements. The amount of bonds payable can be calculated as follows:

- Bonds payable as of 1/1/22: $3,200,000

- Plus: Issuance of bonds payable during 2022: $400,000

- Less: Repayment of bonds payable during 2022: $200,000

- Bonds payable as of 12/31/22: $3,400,000

- Subtract the amount of accrued interest payable on long-term debt as reported in the government-wide statement of net position. This is because accrued interest payable is not reported in governmental fund financial statements, but are reported in government-wide financial statements. The amount of accrued interest payable is given as $180,000.

- Add the amount of property taxes receivable that are not available to pay current liabilities as reported in the governmental fund balance sheet. This is because property taxes receivable that are not available are not recognized as revenues in governmental fund financial statements, but are recognized as revenues in government-wide financial statements. The amount of property taxes receivable that are not available can be calculated as follows:

- Total property taxes receivable as of 12/31/22: $80,000

- Less: Property taxes receivable expected to be collected within 60 days of year-end: $60,000

- Property taxes receivable that are not available as of 12/31/22: $20,000

- The resulting amount is the net position of governmental activities as reported in the government-wide statement of net position.

The reconciliation can be presented in a table format as follows:

| Reconciliation of Total Fund Balance to Net Position | Amount |

| ----------------------------------------------------- | ------ |

| Total fund balance - governmental funds | \$200,000 |

| Capital assets used in governmental activities are not financial resources and therefore are not reported in the funds | \$5,270,000 |

| Long-term liabilities applicable to governmental activities are not due and payable in the current period and therefore are not reported in the funds | \(-\$3,580,000\) |

| Revenues in the statement of activities that do not provide current financial resources are not reported as revenues in the funds | \$20,000 |

| Net position - governmental activities

The height of the planter box is 15 inches.

We have,

The volume of a rectangular prism is given by the formula:

V = l w h

where V is the volume, l is the length, w is the width, and h is the height.

In this case, we know that the length is 12 1/2 inches and the width is 10 inches, and the volume is 1,875 cubic inches.

So we can plug these values into the formula and solve for the height:

[tex]1,875 = (12 \frac{1}{2})\cdot 10 \cdot h[/tex]

Multiplying the length and width, we get:

1,875 = 125h

Dividing both sides by 125, we get:

h = 15

Therefore,

The height of the planter box is 15 inches.

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The coupon rate of the bonds by King of Diamonds Industries would be 7 %.

The formula for the bond price shows the coupon payment and so can be used to find the coupon rate:

= (Coupon payment  x ( 1 - ( 1 + r ) ^ ( - number of years till maturity ) ) ) / r + Face value /  (1  + rate )^ number of years

1,482.01 = (C x (1 - (1 + 0.07 )^ (- 14) ) ) / 0.07 + F / (1 + 0.07 ) ^ 14

103.7407 - 0.07 x (F / (1 + 0.07) ^14 ) = C x  (1 - ( 1 + 0.07) ^ ( - 14) )

Using a calculator, C is $ 70.

This means that the coupon rate is:

= 70 / 1, 000

= 7 %

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1.33 should be multiplied to the cost of the meal to find the total plus tip in one step.

To find the total cost of the meal plus the 33% tip, Gabriel needs to multiply the cost of the meal by a factor of 1.33 (which represents the original cost plus 33% of the original cost).

So the total cost including the tip can be found by multiplying the cost of the meal by 1.33.

For example, if the cost of the meal was $50, the total cost including the tip would be:

Total cost = Cost of the meal + 33% tip

Total cost = $50 + 0.33($50)

Total cost = $50 + $16.50

Total cost = $66.50

Therefore, Gabriel should multiply the cost of the meal by 1.33 to find the total cost including the 33% tip in one step.

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Answer:

it's b to to the angles rotation that is giving 180 each side of the square is 90 degrees now you add them up

The line plot is not symmetric because the numbers of siblings range from 0 to 8.

a. The line plot is not symmetric because the numbers of siblings range from 0 to 8. The number of students with 0 siblings is much greater than the number of students with 8 siblings.

b. The distribution is skewed left, meaning that the majority of students have fewer siblings than the average.

c. Since the distribution is skewed left, the median would be a better measure of the center because it is not affected by the outliers. The median number of siblings is 0. To measure the spread of the distribution, we can use the range, which is 8.

Therefore, the line plot is not symmetric because the numbers of siblings range from 0 to 8.

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Answer:

2(x + 6)

Step-by-step explanation:

If we let the number be "x", then the sum of the number and six is x + 6. To find twice the sum, we multiply this expression by 2:

2(x + 6)

Therefore, the expression that represents twice the sum of a number and six is 2(x + 6)

The number of students in her middle school would be = 729 students

The number of students that was determined by Fatima = 3^6

That is;

Number of students = 3×3×3×3×3×3

= 729students

Therefore the number of students that were actually calculated by Fatima = 729 students.

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The estimate the number of pieces of food collected by mice is 96 and closest estimate to 24 is given by option b. 20.

Number of pieces of food collected by mice every day = 24 pieces

Total number of days mice collects the food = 4 days

To estimate the total number of pieces of food collected,

Now, multiply the number of pieces collected each day by the number of days,

Total number of pieces

= 24 pieces/day × 4 days

= 96 pieces

To estimate the answer closest to 24, we can round 24 to the nearest tens.

The nearest tens to 24 is 20.

Therefore, the estimate of collection of food pieces in 4 days by mice is equal to 96 and the closest estimate to 24 is option b. 20.

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The above question is incomplete , the complete question is:

A family of mice is collecting pieces of food that fall on the floor in a restaurant. If the mice collect 24 pieces of food every day for 4 days, we want to estimate the number of pieces of food they have collected. Which of the following is the closest estimate to 24?

a. 10

b. 20

c. 30

d. 40

It took approximately 151 seconds to decrease 9 ft water in conical tank.

The volume of a conical tank with vertex down and radius 8 ft and height 20 ft is V = (1/3)πr²h

When the water is 9 ft deep

= (1/3) ×3.14×(8)²×(9)

= 602.88 ft³

We know that the rate of change of volume is 4 ft³/sec. So, the rate of change of depth can be calculated as follows:

Rate of change of depth (dh/dt) = Volume of tank/4 ft³ per sec

= 602.88/4

= 150.72 sec

Therefore, it took approximately 151 seconds to decrease 9 ft water in conical tank.

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Answer:r=3cscθ

Step-by-step explanation:The equation y = 3 represents a horizontal line at a distance of 3 units above the x-axis in the Cartesian coordinate system. To convert this equation into polar form, we can use the fact that x = rcos(theta) and y = rsin(theta) in polar coordinates.

Since y = 3 for all values of x, we can say that r*sin(theta) = 3. Solving for r, we get:

r = 3/sin(theta)

This equation represents a family of circles with center at the origin and radius 3/sin(theta), for all values of theta except for multiples of pi. We can simplify this equation by using the identity sin(theta) = 1/csc(theta), giving us:

r = 3csc(theta)