A rectangular prism is shown in the image.

A rectangular prism with dimensions of 5 yards by 5 yards by 3 and one half yard.

What is the volume of the prism?

twenty eight and one half yd3
forty one and one fourth yd3
eighty seven and one half yd3
166 yd3

Solution B has a 100 times greater {H} than Solution A.

The pH of a solution is a measure of the concentration of hydrogen ions in the solution. A higher pH indicates a lower hydrogen ion concentration, and a lower pH indicates a higher hydrogen ion concentration. Therefore, Solution B has a higher hydrogen ion concentration than Solution A. To calculate the ratio of {H} between the two solutions, we must take the inverse of the pH difference. In this case, the difference is 3. Therefore, the ratio of {H} between the two solutions is 1/3, or 100 times greater {H} in Solution B than in Solution A.

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Answer:347

Step-by-step explanation:=

347 ⇔ 347 R 0

8328 divided by 24

=

347 with a remainder of 0

Answer:

50

Step-by-step explanation:

because 5+7+4= 16

and 800/16=50 assignments

hope you understand

Answer:

50

Step-by-step explanation:

5 hours + 7 hours + 4 hours = 16 hours

800 ÷ 16 = 50 assignments/hour

Answer:

y=2x-1

Step-by-step explanation:

Gradient : (7-3) / (4-2) = 2

y=2x+c

substitute one of the points

3=2*2+c

c=-1

y=2x-1

Answer:

This is FALSE.  Choose Option 2

Step-by-step explanation:

Substituting 7 for x, we get

7 + 9(7) > 73, or 70  73.  This is FALSE.  Choose Option 2

For zeroes i.e for value(s) of q and s, the given equations must be equal to 0, so let's start with first equation and then 2nd equation ;

\({:\implies \quad \sf 6q^{2}-17q+12=0}\)

\({:\implies \quad \sf 6q^{2}-9q-8q+12=0}\)

\({:\implies \quad \sf 3q(2q-3)-4(2q-3)=0}\)

\({:\implies \quad \sf (3q-4)(2q-3)=0}\)

\({:\implies \quad \sf Either\:\:3q-4=0\:\:\:or\:\:\: 2q-3=0}\)

\({:\implies \quad \sf Either\:\:3q=4\:\:\:or\:\:\:2q=3}\)

\({:\implies \quad \bf q=\dfrac{3}{2},\dfrac43}\)

Now, turning to the second equation ;

\({:\implies \quad \sf 8s^{2}+2s-15=0}\)

\({:\implies \quad \sf 8s^{2}+12s-10s-15=0}\)

\({:\implies \quad \sf 4s(2s+3)-5(2s+3)=0}\)

\({:\implies \quad \sf (4s-5)(2s+3)=0}\)

\({:\implies \quad \sf Either\:\:4s-5=0\:\:\:or\:\:\: 2s+3=0}\)

\({:\implies \quad \sf Either\:\:4s=5\:\:\:or\:\:\:2s=-3}\)

\({:\implies \quad \bf s=\dfrac{5}{4},-\dfrac32}\)

Answer:

Below in bold.

Step-by-step explanation:

I am assuming you want to factor these expressions.

6q^2 - 17q + 12

We need 2 numbers whose product is (6*12) = 72 and whose sum is -17.

Theses are -9 and -8 so we write:

= 6q^2 - 9q - 8q + 12

= 3q(2q - 3) - 4(2q - 3)

= (3q - 4)(2q - 3)

If you want the solution of this expression = zero they are q = 4/3, 3/2.

8s^2 + 2s - 15

8 * -15 = -120.   -120 = -2 * 2 * 2 * 3 * 5 = +12 * -10 ( to give the +2s)

= 8s^2 + 12s - 10s - 15

= 4s(2s + 3) - 5(2s + 3)

= (4s - 5)(2s + 3)

If you want the solution of this expression = zero they are s = 5/4, -3/2.

Farmer has 5 types of animals in his farm, including cows, goats, horses, sheep, and dogs. He has a database that indicates the number of animals in each category. This can be done using a Python dictionary.

Let us consider the Python code to determine the number of animals in each category.```
animal_dict = {"Cow": 10, "Goat": 20, "Horse": 8, "Sheep": 25, "Dog": 15}
print("Number of Cows in the Farm:", animal_dict["Cow"])
print("Number of Goats in the Farm:", animal_dict["Goat"])
print("Number of Horses in the Farm:", animal_dict["Horse"])
print("Number of Sheeps in the Farm:", animal_dict["Sheep"])
print("Number of Dogs in the Farm:", animal_dict["Dog"])```

In the code, `animal_dict` is the dictionary that contains the number of animals in each category. The `print` statement is used to display the number of animals in each category. The output for the above code will be:```
Number of Cows in the Farm: 10
Number of Goats in the Farm: 20
Number of Horses in the Farm: 8
Number of Sheeps in the Farm: 25
Number of Dogs in the Farm: 15```

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You want to find Pr[-2 < Z < -1].

The table tells you that

• Pr[Z < 0] = 0.5000

• Pr[Z < 1.00] = 0.8412

• Pr[Z < 2.00] = 0.9772

• Pr[Z < 3.00] = 0.9987

We have

Pr[-2 < Z < -1] = Pr[Z < -1] - Pr[Z < -2]

(because the distribution of Z is continuous)

… = Pr[Z > 1] - Pr[Z > 2]

(by symmetry of the distribution about its mean)

… = (1 - Pr[Z < 1]) - (1 - Pr[Z < 2])

(by definition of complement)

… = Pr[Z < 2] - Pr[Z < 1]

… = 0.9772 - 0.8412

… = 0.1360 ≈ 0.14 … … … (B)

Answer:

it's B aka 0.10.14

Step-by-step explanation:

A brownie recipe calls sugar for 1 time = 1 cup

A brownie recipe calls sugar for 12 times = 1*12

= 12

There are two ways to color a cube with two colors so that no two adjacent vertices are the same color. A cube has 8 vertices, and each vertex can be colored either black or white.Therefore, the first vertex can be colored in two ways.

After coloring the first vertex, there are two vertices adjacent to the first vertex. Each of these vertices can be colored in only one way since they cannot be the same color as the first vertex. After coloring the first vertex and the two vertices adjacent to it, there are two pairs of adjacent vertices left.

The second vertex of the first pair can be colored in one way only (since it cannot be the same color as the first vertex or the vertex adjacent to it). The second vertex of the second pair can be colored in one way only, and this will also determine the color of the fourth vertex (since it cannot be the same color as the second vertex of the second pair).

This completes the coloring of the cube. Therefore, there are two ways to color a cube with two colors so that no two adjacent vertices are the same color.  

There are two ways to color a cube with two colors so that no two adjacent vertices are the same color.

We have to paint a cube with two colors so that no two adjacent vertices are of the same color. A cube has 8 vertices, each of which can be painted black or white. Consider the cube with one of its vertices painted black. Then there are three vertices that are adjacent to it, each of which must be painted white.

We have now fixed 4 vertices: one black and three white. There are now two cases to consider. Either the two remaining vertices are opposite each other, in which case they must be painted black, or they are adjacent to one another, in which case they can each be painted black or white. Therefore, we can paint the cube in 2 ways.

Therefore, there are two ways to paint a cube with two colors so that no two adjacent vertices are the same color.

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Answer:

1. P = 14cm; A = 10cm^2

2. P = 24cm; A = 12cm^2

3. P = 32cm; A = 63cm^2

4. P = 36cm; A = 80cm^2

5. P = 32cm; A = 60cm^2

6. P = 36cm; A = 81cm^2

7. P = 26cm: A = 30cm^2

8. P = 28cm; A = 49cm^2

9. P = 26cm: A = 42cm^2

Step-by-step explanation:

Formula to find perimeter for a rectangle:

length + width + length + width

l + w + l + w

Formula to find area for a rectangle:

length × width

l × w

1.

Perimeter (P): 5 + 2 + 5 + 2 = 14

Area (A): 5 × 2 = 10

2.

P: 6 + 2 + 6 + 2 = 24

A: 6 × 2 = 12

3.

P: 7 + 9 + 7 + 9 = 32

A: 7 × 9 = 63

4.

P: 10 + 8 + 10 + 8 = 36

A: 10 × 8 = 80

5.

P: 10 + 6 + 10 + 6 = 32

A: 10 × 6 = 60

6.

P: 9 + 9 + 9 + 9 = 36

A: 9 × 9 = 81

7.

P: 10 + 3 + 10 + 3 = 26

A: 10 × 3 = 30

8.

P: 7 + 7 + 7 + 7 = 28

A: 7 × 7 = 49

9.

P: 6 + 7 + 6 + 7 = 26

A: 6 × 7 = 42

Area will always have its units squared (cm^2) because the formula requires we multiply the numbers and therefore the units: cm × cm = cm^2

The volume of the solid formed by rotating the region enclosed by x = 0, x = 1, y = 0, y = 8 + x⁷ about the c-axis is 8π/9.

To find the volume of the solid, we need to use the method of cylindrical shells. We can slice the region into thin cylindrical shells with radius x and height (8 + x⁷). The circumference of each shell is 2πx and the thickness of each shell is dx.

Therefore, the volume of each shell is (2πx)(8 + x⁷)dx.

Integrating this expression from x=0 to x=1, we get:

V = ∫₀¹ 2πx(8 + x⁷)dx

= 2π ∫₀¹ (8x + x⁸)dx

= 2π [4x² + x⁹/9] from x=0 to x=1

= 2π[(4 + 1/9) - 0]

= 8π/9

Hence, the volume of the solid is 8π/9.

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Since U is continuous, the conditional expectation is given by: E(U−u∣U>u) = ∫[(U−u)f(u|U>u)]du
To determine if the function S(u) satisfies the properties of a survival function, we need to check the following criteria:

1. S(u) is non-negative: The function S(u) is defined as 1−u for 0≤u≤1 and 0 for u>1. Since 1−u and 0 are both non-negative values, S(u) satisfies this criterion.

2. S(u) is non-increasing: For the given function, as u increases within the interval 0≤u≤1, the value of 1−u decreases. Similarly, for u>1, S(u) is defined as 0, which is constant. Therefore, S(u) is non-increasing.

3. S(0) = 1: Substituting u=0 in the function S(u), we get S(0) = 1−0 = 1. Thus, S(0) equals 1, satisfying this condition.

4. S(u) approaches 0 as u approaches positive infinity: For u>1, S(u) is defined as 0. As u tends towards positive infinity, S(u) approaches 0, meeting this requirement.

Based on the above analysis, the function S(u) satisfies the properties of a survival function.

To find the distribution of U, we need to differentiate the survival function S(u). However, since S(u) is defined piecewise, we need to differentiate each segment separately:

For 0≤u≤1:
S'(u) = d/dx(1−u) = -1

For u>1:
S'(u) = d/dx(0) = 0

Therefore, the derivative of S(u) is -1 for 0≤u≤1 and 0 for u>1.

The distribution function h(u) can be obtained by taking the negative derivative of the survival function:

For 0≤u≤1:
h(u) = -S'(u) = -(-1) = 1

For u>1:
h(u) = -S'(u) = -(0) = 0

Thus, the distribution function h(u) is 1 for 0≤u≤1 and 0 for u>1.

Finally, to find E(U−u∣U>u), we need to calculate the conditional expectation of U−u given U>u. Since U is continuous, the conditional expectation is given by:

E(U−u∣U>u) = ∫[(U−u)f(u|U>u)]du

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Answer:

7.5

Step-by-step explanation:

Answer:

47 a

7.5 6

Step-by-step explanation:

The marginal productivity of labor when 19 units of labor and 11 units of capital are invested is approximately 1.0574, and the marginal productivity of capital under the same conditions is approximately 0.6008.

To find the marginal productivity of labor ((PL)) and the marginal productivity of capital (PK)) in the Cobb-Douglas Production function, we need to take the partial derivatives of the function with respect to each input variable.
Given the Cobb-Douglas Production function: \(\(P(L,K) = 20L^{0.5}K^{0.5}\)\)
To find\(PL):
\(\(\frac{\partial P}{\partial L} = 10L^{-0.5}K^{0.5}\)\)
To find \(PK\):
\(\(\frac{\partial P}{\partial K} = 10L^{0.5}K^{-0.5}\)\)
Substituting the values (L = 19) and (K = 11) into the respective derivative formulas, we can calculate the marginal productivity of labor and capital.
\(\(PL(19,11) = 10(19^{-0.5})(11^{0.5})\)\\\(PK(19,11) = 10(19^{0.5})(11^{-0.5})\)\)
Calculating these values to at least 4 decimal places:
.\(\(PL(19,11) \approx 1.0574\)\)

\(\(PK(19,11) \approx 0.6008\)\)

Therefore, the marginal productivity of labor when 19 units of labor and 11 units of capital are invested is approximately 1.0574, and the marginal productivity of capital under the same conditions is approximately 0.6008.

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A regular pentagon has side lengths of 7 inches. It is dilated by a scale factor of 2. What is the resulting perimeter of the pentagon?Main Answer:The resulting perimeter of the pentagon is

:Given, A regular pentagon has side lengths of 7 inches and it is dilated by a scale factor of 2.To find: The resulting perimeter of the pentagonSolution:The perimeter of the regular pentagon is given as:P = 5 × s where s is the length of the side of the pentagon.

So, the perimeter of the original pentagon is:P = 5 × 7P = 35 inchesThe scale factor of the dilation is 2.Therefore, the side of the new pentagon is 7 × 2 = 14 inches.So, the perimeter of the new pentagon is:P = 5 × 14P = 70 inchesTherefore, the resulting perimeter of the pentagon is 70 inches.

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The equation, which is used to find any corresponding length and width that fit the pattern in the provided table is,

\(I=\dfrac{k}{w}\)

Area of a rectangle is the product of the length of the rectangle and the width of the rectangle. It can be given as,

\(A=a\times b\)

Here, (a)is the length of rectangle and (b) is the width of the rectangle.

A rectangle with constant area has possible lengths and widths as shown in the table below.

Width vs. Length of a rectangle

In the above table, the length of a rectangle is decreasing with increasing the width of a rectangle.

For such relation, the value of w should be inversely proportional to the length of it. The first option given as,

\(I=\dfrac{k}{w}\)

Here l is the length, w is the width, and k is a constant (w not-equals 0).

In this expression, the length of the rectangle is inversely proportional to the width of the rectangle.

Thus, the equation, which is used to find any corresponding length and width that fit the pattern in the provided table is,

\(I=\dfrac{k}{w}\)

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Answer:

a

Step-by-step explanation:

Answer:

$ 13.20

Step-by-step explanation:

First, it says she bought 4 boxes of cereal for $3 EACH (Keyword) so that means each box was $3:

4 x 3= 12

Now it says she bought a carton of milk for $1.20

12 + 1.20 =

13.20

Hope this helps <P

let's assume the temperature on 5th day be x

We know that :

\( \boxed{mean = \frac{sum \: \: of \: all \: \: observations}{number \: \: of \: \: observations} }\)

So,

\( \hookrightarrow \: 0 = \dfrac{ - 2 + ( - 2) + ( - 2) + ( - 2) + x}{5} \)

\( \hookrightarrow \: 0 \times 5= - 2 - 2 - 2 - 2 + x\)

\( \hookrightarrow \: 0 = - 8 + x\)

\( \hookrightarrow \: x = 8\)

Therefore, temperature on the fifth day was x = 8

Answer:

8

Step-by-step explanation:

The answer is 8 because 1/2 times 1/2 times 1/2 is 1/8, which means that 8 B cubes can fit into cube A.

The area of this house in square meters is 152.24.

To convert square feet to square meters, you can use the conversion factor of 1 square foot = 0.092903 square meters.

A house is advertised as having 1640 square feet under the roof.

So, the area of the house in square meters is:

1640 square feet * 0.092903 square meters/square foot = 152.24 square meters.

Unit Conversion: It is defined as the changing from one quantity unit to another quantity unit followed by the method of division, and multiplication by a conversion factor.

Thus, the area of this house in square meters is 152.24 if the house is advertised as having 1640 square feet under the roof.

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450000- 13000= 32000

32000×(35/100) = 11200

2x - y = 3  =    x=0.5y+1.5

x+2y = -6  =   x=−2y−6

Step-by-step explanation:

\( \frac{15}{35} = \frac{g}{7} \)

\( \frac{3}{7} = \frac{g}{7} \)

\(g = 3\)

Answer:

\(\huge\boxed{(2x)^\frac{1}{2}\times(2x^3)^\frac{3}{2}=4x^5}\)

Step-by-step explanation:

\((2x)^\frac{1}{2}\times(2x^3)^\frac{3}{2}\qquad\text{use}\ (ab)^n=a^nb^m\\\\=2^\frac{1}{2}x^\frac{1}{2}\times2^\frac{3}{2}(x^3)^\frac{3}{2}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=2^\frac{1}{2}x^\frac{1}{2}\times2^\frac{2}{3}x^{(3)(\frac{3}{2})}=2^\frac{1}{2}x^\frac{1}{2}\times2^\frac{2}{3}x^\frac{9}{2}\\\\\text{use the commutative and associative property}\\\\=\left(2^\frac{1}{2}\times2^\frac{3}{2}\right)\left(x^\frac{1}{2}\times x^\frac{9}{2}\right)\qquad\text{use}\ a^n\times a^m=a^{n+m}\)

\(=2^{\frac{1}{2}+\frac{3}{2}}x^{\frac{1}{2}+\frac{9}{2}}=2^\frac{1+3}{2}x^{\frac{1+9}{2}}=2^\frac{4}{2}x^\frac{10}{2}=2^2x^5=4x^5\)

Answer:

\( 4x^5 \)

Step-by-step explanation:

\( (2x)^\frac{1}{2} \times (2x^3)^\frac{3}{2} = \)

\(= (2x)^\frac{1}{2} \times (2x \times x^2)^\frac{3}{2}\)

\(= [(2x)^\frac{1}{2} \times (2x)^\frac{3}{2}] \times (x^2)^\frac{3}{2}\)

\(= (2x)^{\frac{1}{2} + \frac{3}{2}} \times x^{{2} \times \frac{3}{2}}\)

\(= (2x)^{\frac{4}{2}} \times x^{\frac{6}{2}}\)

\( = 2^2x^2 \times x^3 \)

\( = 4x^5 \)

Step-by-step explanation:

option b, e and f are correct!

hope this answer helps you dear...may u have a great day ahead!

Answer:

15.7, 15. 89, 15.472

Step-by-step explanation:

All numbers besides 15.7, 15.472 and 15.89 are less than 15.44, which makes 15.7, 15.472 and 15.89 the only numbers out of the list that make this comparision true.

In the event of shortening the standard error of mean to 15 we have to increase the size to 400. Therefore, the correct answer is Option B.

The  given standard error of the mean for a sample of 100 is 30. So to cut the standard error of the mean to 15, we have to proceed by increasing the sample size to 400.

The  formula for evaluating the standard error of mean
SEM = SD / √(n)
here, SEM = standard error of the mean,
SD = standard deviation
n = sample size
Staging the values
15 = SD / √(100)
15 x √(100) = SD
SD = 150
Now evaluating for the value of n
15 = 150 / √(n)
15 x √(n) = 150
√(n) = 10
n = 100
Now looking at the formula, we need to decrease SEM by half,

So we proceed by increasing the  sample size by a factor of 4.

In the event of shortening the standard error of mean to 15 we have to increase the size to 400. Therefore, the correct answer is Option B.

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Answer: x≤12

Step-by-step explanation: the room holds a max of 12 people, so the number of people will be less than or equal to 12