Which correctly describes a cross section of the right rectangular prism if the base is a rectangle measuring 15 inches by 8 inches? Check all that apply.
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A cross section parallel to the base is a rectangle measuring 15 inches by 8 inches.
A cross section parallel to the base is a rectangle measuring 15 inches by 6 inches.
A cross section perpendicular to the base through the midpoints of the 8-inch sides is a rectangle measuring 6 inches by 15 inches.
A cross section perpendicular to the base through the midpoints of the 8-inch sides is a rectangle measuring 4 inches by 15 inches.
A cross section not parallel to the base that passes through opposite 6-inch edges is a rectangle measuring 6 inches by greater than 15 inches.

Answer:

90 degrees

Step-by-step explanation:

If you got 3 questions wrong on a 12 problem math paper, to figure out how many you got right you must subtract the number you got incorrect (3) from the total number (12).

12-3=9

To figure out your grade, you have to divide how many you got correct (9-see above) by the total number of questions (12).

9/12 = 0.75

If you multiply this decimal by 100, you get the equivalent percentage of 75%.

Therefore, you would have gotten a 75% on the paper.

Hope this helps!

In a collision, both the car and truck experience the same force due to Newton's Third Law. However, due to Newton's Second Law, the car, with its smaller mass, experiences a greater acceleration.

According to Newton's Third Law of Motion, 'for every action, there is an equal and opposite reaction', both the truck and the car would experience the same magnitude of force. However, let's recall Newton's Second Law, 'force equals mass times acceleration' (F=ma). Using these physics principles, we can deduce that the car with the smaller mass would experience a greater acceleration, and the large truck would experience a lesser acceleration. This is because when the same force is applied to both objects, an object with a smaller mass will have a greater acceleration compared to an object with a larger mass. Hence, option B) 'The car has the greater acceleration because it has the smaller mass' would be the correct answer based on Newton's laws of motion.

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The length of the garden is 20 feet and the width is 30 feet.

To solve this problem, we will use the formulas for the perimeter and area of a rectangle. The perimeter (P) of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. The area (A) of a rectangle is given by the formula A = lw.

 Given the perimeter of the garden is 100 feet, we can set up the following equation:

[tex]\[ 2(l + w) = 100 \][/tex]

[tex]\[ l + w = 50 \][/tex]

[tex]\[ w = 50 - l \][/tex]

This equation relates the length and width of the garden.

 Next, we are given that the area of the garden is 600 square feet:

[tex]\[ lw = 600 \][/tex]

Substituting the expression for w from the first equation into the area equation, we get:

[tex]\[ l(50 - l) = 600 \][/tex]

[tex]\[ 50l - l^2 = 600 \][/tex]

Rearranging the terms, we have a quadratic equation:

[tex]\[ l^2 - 50l + 600 = 0 \][/tex]

To solve this quadratic equation, we can factor it:

[tex]\[ (l - 20)(l - 30) = 0 \][/tex]

This gives us two possible solutions for the length: l = 20 feet or l = 30 feet.

 Since we are asked to let the length be the shorter side, if necessary, we choose the smaller value for the length:

[tex]\[ l = 20 \text{ feet} \][/tex]

 Now we can find the width by substituting the length back into the equation for the perimeter:

[tex]\[ w = 50 - l \][/tex]

[tex]\[ w = 50 - 20 \][/tex]

[tex]\[ w = 30 \text{ feet} \][/tex]

 Therefore, the length of the garden is 20 feet and the width is 30 feet.

The length of the pond is 77.4 inches, and the width of the pond is 38.7 inches.

In geometry, a rectangular prism can be defined as a 3-dimensional solid shape that has six faces that are rectangles. A rectangular prism is also a cuboid.

Let,a be the length of the pond and b be the width of the pond.

The volume of the pond is;

[tex]\rm Volume \ of \ the \ pond= Area\ of\ the\ base\times deep\\\\Area\ of\ the\ base=\dfrac{Volume \ of \ the \ pond}{base}\\\\Area\ of\ the\ base=\dfrac{72000}{24}\\\\Area\ of\ the\ base=3000 in^2[/tex]

The length of the pond is two times its width.

a = 2b

The area of the base = a × b

3000 = ab

ab = 3000

Substitute the value of a in equation 2

[tex]\rm ab=3000\\\\2b \times b = 3000\\\\b^2=\dfrac{3000}{2}\\\\b^2=1500\\\\b=38.7[/tex]

Substitute the value of b in equation 1

[tex]\rm a=2b\\\\a=2 \times 38.7\\\\a=77.4[/tex]

Hence, the length of the pond is 77.4 inches, and the width of the pond is 38.7 inches.

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The width of the pond is approximately 38.7 inches and the length is approximately 77.4 inches.

To find the length and width of the pond, we can use the formula for the volume of a rectangular prism: length × width × depth. We are given that the depth is 24 inches and the volume is 72,000 cubic inches.

Let's denote the width as w.

Since the length is two times the width, we can express the width as w and the length as 2w.

Therefore, the equation for the volume becomes:

2w × w × 24 = 72,000

48w^2 = 72,000

w^2 = 1,500

w ≈ 38.7

Therefore, the width is approximately 38.7 inches and the length is approximately 77.4 inches.

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For anyone with the “TRICIA” problem:  $1202.30

Answer with Step-by-step explanation:

We know that volume of a cylinder with radius r and height h is:

πr²h

and  volume of cone with radius r and height h is:

πr²h/3

Volume of cone=Volume of cylinder/3 < Volume of cylinder

Volume of cylinder=84π in² where π=3.14

Volume of cone=84π/3 in²

                          = 84(3.14)/3 in²

Hence, correct options are:

The volume of the cone is 1/3 the volume of the cylinder.

The volume of the cone is less than the volume of the cylinder.

The expression 84(3.14)/3 finds the volume of the cone.

the answer is: A, C, and D

Answer:

The answer is A

Step-by-step explanation:

sadly i dont have the work of it just by looking it up you can get the answer tho. Answer is A

Answer: 57

=====================================================

Explanation:

Convert each raw score to a z score

If x = 63.4, then

z = (x-mu)/sigma

z = (63.4-72.3)/8.9

z = -1

if x = 81.2, then 

z = (x-mu)/sigma

z = (81.2-72.3)/8.9

z = 1

So P(63.4 < x < 81.2) is the same as P(-1 < z < 1)

Through the empirical rule (aka the 68-95-99.7 rule), we know that roughly 68% of the data values are within one standard deviation of the mean. In other words

P(-1 < z < 1) = 0.68 approximately (see note below)

Multiply 0.68 by the total 84 to get

0.68*84 = 57.12

which rounds to 57 people

Note: we can use a calculator to get a more accurate result of 0.68268949; a data table works as well but it won't be as accurate. For the purposes of this problem, the value 0.68 is good enough

By definition the interquartile range or IQR is obtained when the 25th percentile or [tex] Q_{1} [/tex] is subtracted from the 75th percentile or [tex] Q_{3} [/tex].

Thus, from the above definition, the formula for IQR is:

[tex] IQR=Q_{3}-Q_{1} [/tex]

As we can see from the provided options that the definition of IQR matches the expression provided in Option A and thus, Option A is the correct answer.

Quartile 3 (Q3) minus quartile 1 (Q1) is right for apex.

Answer:

  15x^3·y

Step-by-step explanation:

The numbers 60, 45, 75 are all multiples of 15, so 15 is their greatest common factor.

The least power of the factor x is 3; the least power of the factor y is 1, so the GCF is ...

  GCF = 15·x^3·y

The equation that models this relation is y = 70/x. So, option (D) is the correct answer.

The constant of proportionality is the ratio of two proportional values at a constant value. Two variable values have a proportional relationship when either their ratio or their product gives a constant.

For the given situation,

The values are y = 10 and x = 7

y varies inversely with x.

⇒ [tex]y[/tex] ∝ [tex]\frac{1}{x}[/tex]

To remove proportionality we introduce a constant 'k'.

⇒ [tex]y=\frac{k}{x}[/tex]

Substitute the values of x and y,

⇒ [tex]10=\frac{k}{7}[/tex]

⇒ [tex]k=70[/tex]

Now substitute the value of k = 70 in y,

⇒ [tex]y = \frac{70}{x}[/tex]

Hence we can conclude that the equation that models this relation is      y = 70/x. So, option (D) is the correct answer.

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9/37  is the correct answer.

Answer: The waitress works:[tex]\[{6 \frac{7}{8}}[/tex]   hours in the evening


Let us denote the number of hours the waitress works in the evening as E and the number of hours she works in the afternoon as A.

Given that:

[tex]\[A = 5 \frac{1}{8} \text{ hours}\][/tex]

We can convert the mixed number to an improper fraction:

[tex]\[5 \frac{1}{8} = 5 + \frac{1}{8} = \frac{40}{8} + \frac{1}{8} = \frac{41}{8}\][/tex]

So, [tex]\( A = \frac{41}{8} \)[/tex] hours.

The waitress works 1.75 hours less in the afternoon than in the evening. Thus, we have:

[tex]\[A = E - 1.75\][/tex]
[tex]\[\frac{41}{8} = E - 1.75\][/tex]

Converting 1.75 to a fraction:

[tex]\[1.75 = \frac{7}{4} = \frac{14}{8}\][/tex]

Now, the equation becomes:

[tex]\[\frac{41}{8} = E - \frac{14}{8}\][/tex]
[tex]\[E = \frac{41}{8} + \frac{14}{8}\]\[E = \frac{41 + 14}{8} = \frac{55}{8}\][/tex]

Convert the improper fraction back to a mixed number:

[tex]\[\frac{55}{8} = 6 \frac{7}{8}\][/tex]

Therefore, the waitress works:

[tex]\[{6 \frac{7}{8}}[/tex]   hours in the evening