The bench below is a rectangular prism on top of two cubes. The total height of the bench is

8 inches. What is the volume of this bench?

- 25 inches

4 inches

4 inches

4 inches

424 cubic inches

464 cubic inches

228 cubic inches

528 cubic inches


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The Total number of students at the school is 1240.

The given ratio is 11 boys : 9 girls,

Let 11x = boys and

9x = girls.

As 124 more boys are there than girls, so

11x - 9x = 124.

2x = 124

x = 62

The actual number of boys = 11x = 11 × 62 = 682

The actual number of girls = 9x = 9 × 62 = 558

Total number of students at the school = 682 boys + 558 girls = 1240 students

Answer:

3x

Step-by-step explanation:

2x--x is the same thing as 2x+x which equals 3x. Hope that helped. ;P

2x minus negative x simplifies to 2x + x, which further simplifies to 3x.

To simplify 2x - (-x), we can apply the concept of subtracting a negative number, which is equivalent to adding its positive counterpart.

The expression -(-x) can be rewritten as +x, since double negation cancels out. Therefore, the expression becomes 2x + x.

Combining like terms, we have 2x + x = 3x.

So, 2x - (-x) simplifies to 3x.

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Final answer:

To determine the original price of the shirt, divide the sale price of $27.20 by 85% (0.85 in decimal form) because Ben paid this amount after a 15% discount. The original price was $32.00.

Explanation:

To find the original price of the shirt before the 15% off sale, we can follow these steps:

Therefore, the original price of the shirt was $32.00 before the 15% discount was applied.

Answer:

Step 1: 14x − 21 = 1; Step 2: 14x = 22

Explanation:

7(2x−3)=1

Step 1: Simplify both sides of the equation

7(2x−3)=1

(7)(2x)+(7)(−3)=1(Distribute)

14x+−21=1

14x−21=1

Step 2: Add 21 to both sides

14x−21+21=1+21

14x=22

Step 3: Divide both sides by 14

14x / 14 = 22 / 14

x = 22 / 14: x = 11/7

Answer:

The last option.

Step-by-step explanation:

When distributed, 7 times 2x becomes 14x and 7 times -3 is -21.

Once you add -21 to both sides, 14x is left alone on one side while 22 is on the other

Answer:

Remember, perimeter means addition. And area means multiplying. I see 16 and 12, so do you want me to add 16 and 12 because I see x in. But, 16 plus 12 equal 28. So, 28 in.

Final answer:

Prime numbers are numbers that are only divisible by 1 and themselves. The prime numbers in the list are 19, 29, 17, and 23.

Explanation:

In mathematics, prime numbers are numbers that are only divisible by 1 and themselves. They have exactly two distinct positive divisors. To determine if a number is prime, you can check if it is divisible by any number less than itself.

Using the list of numbers given, we can determine which ones are prime:

19 - Prime

29 - Prime

17 - Prime

23 - Prime

25 - Not prime (divisible by 5)

Therefore, the prime numbers in the list are: 19, 29, 17, and 23. The correct statement is: none of the above.

Answer: 54.4°

Step-by-step explanation:

If the spotlight is mounted 7.3 meters high, its height will be 7.3meters.

If A is 10.2 meters from the base of the pole, the base of the pole to the parking area will be 10.2meters

The angle of the depression will be facing the base directly therefore, the base will be the opposite of the triangle formed and the height of 7.3m will be the adjacent.

To get the depression angle, we use the trigonometry identity SOH, CAH, TOA

Since we have opposite and adjacent, we will use "TOA" which means

Tan theta = Opposite/Adjacent

Opposite = 10.2m Adjacent = 7.3

Tan theta = 10.2/7.3

Tan theta = 1.39

theta = arctan 1.39

Theta = 54.4°

The angle of depression that the spotlight should aim at is 54.4°

To find the angle of depression for the spotlight to illuminate point A, one takes the inverse tangent of the ratio of the height of the pole to the distance from the pole to point A (7.3 meters / 10.2 meters).

The student has asked to determine the angle of depression that a spotlight should be aimed at to illuminate a specific point on the ground. To find this angle, we use trigonometry, specifically the tangent function, which relates the opposite side (the height of the pole) to the adjacent side (the distance from the base of the pole to point A).

The tangent of the angle of depression (θ) is equal to the opposite side divided by the adjacent side. That is, tan(θ) = height / distance = 7.3 meters / 10.2 meters.

Using a calculator, the angle of depression θ can be found by taking the inverse tangent (or arctan) of 7.3/10.2. Therefore, θ = arctan(7.3/10.2).

Once you calculate this value, you will have the angle of depression at which to aim the spotlight to illuminate point A.

Answer:

Yes

Step-by-step explanation:

The tablecloth is large enough as when you multiply 4×8=32 square feet. Thus meaning a 56 square foot table cloth would be enough.

4×8=32

34% of the scores lie between 433 and 523.

Solution:

Given data:

Mean (μ) = 433

Standard deviation (σ) = 90

Empirical rule to determine the percent:

(1) About 68% of all the values lie within 1 standard deviation of the mean.

(2) About 95% of all the values lie within 2 standard deviations of the mean.

(3) About 99.7% of all the values lie within 3 standard deviations of the mean.

[tex]$Z(X)=\frac{x-\mu}{\sigma}[/tex]

[tex]$Z(433)=\frac{433-\ 433}{90}=0[/tex]

[tex]$Z(523)=\frac{523-\ 433}{90}=1[/tex]

Z lies between o and 1.

P(433 < x < 523) = P(0 < Z < 1)

μ = 433 and μ + σ = 433 + 90 = 523

Using empirical rule, about 68% of all the values lie within 1 standard deviation of the mean.

i. e. [tex]((\mu-\sigma) \ \text{to} \ (\mu+\sigma))=68\%[/tex]

Here μ to μ + σ = [tex]\frac{68\%}{2} =34\%[/tex]

Hence 34% of the scores lie between 433 and 523.

Using the Empirical Rule for normally distributed scores, about 34% of SAT verbal scores lie between 433 (mean) and 523 (mean plus one standard deviation).

The Empirical Rule, also known as the 68-95-99.7 rule, applies to a normally distributed set, as we have here with SAT verbal scores. This rule states that approximately 68% of the data falls within one standard deviation from the mean in a normal distribution.

In this scenario, the mean (average) SAT verbal score is 433, the standard deviation is 90. We're going to find what percent of the scores lie between 433 (mean) and 523 (mean plus one standard deviation).

According to the Empirical Rule, approximately 68% of the scores fall within one standard deviation of the mean (both above and below). So about 34% of the scores fall between the mean and one standard deviation above the mean. Thus, about 34% of the students scored between 433 and 523 on the SAT verbal section.

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Answer:

x=21

Step-by-step explanation:

Each measurment is multiplied by three, so 7 multiplied by 3 is 21

Answer:

294.71

Step-by-step explanation:

298.8-4.09=294.71

Combine the whole number and the decimal parts to get the final answer: 294.71.

Answer:

What Do You Mean

Step-by-step explanation:

Answer:75

Step-by-step explanation: 50 + 25

The value of x is 81

Step-by-step explanation:

The sum of the interior angles of any quadrilateral is 360°

∵ The figure have 4 sides

∴ The figure is a quadrilateral

∵ The sum of the measures of the interior angles of a

    quadrilateral is 360°

- Add the four angles and equate the sum by 360

∴ m∠1 + m∠2 + m∠3 + x = 360

∵ m∠1 = 40% of the sum of the angle measures of the quadrilateral

∴ m∠1 = 40% × 360 = [tex]\frac{40}{100}[/tex] × 360 = 144°

∵ m∠2 = 12.5% of the sum of the angle measures of the quadrilateral

∴ m∠2 = 12.5% × 360 = [tex]\frac{12.5}{100}[/tex] × 360 = 45°

∵ m∠3 = 25% of the sum of the angle measures of the quadrilateral

∴ m∠3 = 25% × 360 = [tex]\frac{25}{100}[/tex] × 360 = 90°

- Substitute these values in the equation above

∴ 144 + 45 + 90 + x = 360

- Add the like terms in the left hand side

∴ 279 + x = 360

- Subtract 279 from both sides

∴ x = 81°

The value of x is 81

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Answer:

b= 8.5

Step-by-step explanation:

To find b, subtract 4.1 to both sides.

12.6= b+4.1

- 4.1      -4.1

8.5= b

Answer:

7.5 = b

Step-by-step explanation:

12.6 - 4.1 = b + 4.1 - 4.1

8.5 = b

Option C: -4, -2, 3 are the roots of the polynomial.

Explanation:

The equation is [tex]x^{3} -10x=-3x^{2} +24[/tex]

Now, Adding [tex]3x^{2}[/tex] on both sides, we have,

[tex]x^{3} +3x^{2} -10x=24[/tex]

Subtracting 24 from both sides of the equation, we have,

[tex]x^{3} +3x^{2} -10x-24=0[/tex]

Solving the equation using synthetic division, we have,

[tex](x-2)(x^{2} +x-12)=0[/tex]

Now, we shall factor [tex](x^{2} +x-12)[/tex], we have,

[tex](x+4)(x-3)[/tex]

Thus, we have,

[tex](x+2)(x-3)(x+4)=0[/tex]

Solving each factor, we have,

[tex]$\begin{aligned} x+2 &=0 \\ x &=-2 \end{aligned}$[/tex]  and  [tex]\begin{array}{r}{x-3=0} \\{x=3}\end{array}[/tex]  and  [tex]\begin{aligned}x+4 &=0 \\x &=-4\end{aligned}[/tex]

Thus, the roots are -2,3 and 4.

Answer:

[tex] 3^{-2} = \dfrac{1}{9} [/tex]

Step-by-step explanation:

Definition of negative exponent:

[tex] a^{-n} = \dfrac{1}{a^n} [/tex]

In our case, a = 3 and -n = -2.

[tex] 3^{-2} = \dfrac{1}{3^2} [/tex]

Now we just evaluate the power in the denominator.

[tex] 3^{-2} = \dfrac{1}{3^2} = \dfrac{1}{9} [/tex]

The combination is solved and the number of ways of choosing the contestants is 10

The number of ways of selecting r objects from n unlike objects is given by combinations

ⁿCₓ = n! / ( ( n - x )! x! )

where

n = total number of objects

x = number of choosing objects from the set

Given data ,

Out of the 7 people in the front row, we need to choose 3 people to be contestants, and we want to count the number of ways that both you and your friend are chosen.

Since we are choosing 3 people, there are 3 positions to be filled. We can think of this as a combination problem, where we need to choose 2 people out of the 5 remaining people in the front row, to fill the two remaining positions after you and your friend are chosen.

The number of ways to choose 2 people out of 5 is given by the combination formula:

C(5, 2) = 5! / (2! (5 - 2)!) = 10

Hence , there are 10 ways to choose you and your friend, and then choose two additional people to fill the remaining positions

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Answer:

1/4  4/16 8/32 16/64

Step-by-step explanation:

Answer:

a simplified fraction is 1/4

Step-by-step explanation:

2/8 (divided by) 2/2= 1/4

Step-by-step explanation:

let’s start with the positive number because it’s easier :

84x12 = 1 008

84×24 = (84×12)×2 = 1008×2 = 2 016

-84x12 = -(84x12) = -1 008

-84x24 = -(84x24) = -2016

Final answer:

The product of the given expressions is found by multiplying the numbers together. The product of -84x12 is -1008, -84x24 is -2016, 84x12 is 1008, and 84x24 is 2016.

Explanation:

The product of -84x12 is -1008. To find the product, simply multiply the two numbers together. In this case, -84 multiplied by 12 gives us -1008.

The product of -84x24 is -2016. Similarly, multiplying -84 by 24 gives us -2016.

The product of 84x12 is 1008. When multiplying a positive number and a negative number, the product will be negative. In this case, 84 multiplied by -12 gives us -1008.

Finally, the product of 84x24 is 2016. When multiplying two positive numbers, the product will also be positive. Therefore, 84 multiplied by 24 equals 2016.

Answer:

x=5

Step-by-step explanation:

15÷5=3

that is the right answer

Answer:

  5

Step-by-step explanation:

Put 3 where x is, and do the arithmetic.

  [tex]\dfrac{15}{x}=\dfrac{15}{3}=5[/tex]

Answer: 27

Step-by-step explanation:

Answer:

Helicopter have traveled  5.55 units of distance approximately  if it went directly from one location to the other.

Step-by-step explanation:

We are given the following in the question:

A traffic helicopter travels due north and then due east to get to the location at (-3,4) to the location at (7,13).

The attached image shows the path of helicopter.

Distance Formula:

[tex](x_1,y_1), (x_2,y_2)\\\\d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]

Distance traveled by helicopter =

[tex]d((-3,4),(-3,13)) + d((-3,13),(7,13))\\\\=\sqrt{(-3+3)^2 + (13-4)^2} + \sqrt{(7+3)^2 + (13-13)^2}\\= 9+10\\= 19 \text{ units}[/tex]

If the helicopter goes directly:

[tex]d((-3,4),(7,13))\\\\=\sqrt{(7+3)^2+(13-4)^2}\\\approx 13.45 \text{ units}[/tex]

Difference in distances =

[tex]19 - 13.45 = 5.55\text{ units}[/tex]

Thus, helicopter have traveled  5.55 units of distance approximately  if it went directly from one location to the other.

Answer:

i had this question in a quiz on edge and got a 100% on the quiz

here is your answer

Step-by-step explanation:

The slope of the line that passes through two points is

(the difference in 'y') divided by (the difference in 'x').

The two points are:  (3, -4) and (5, -7)

The difference in 'y' is . . . (-7) - (-4) = -3

The difference in 'x' is . . . (5) - (3) = 2

The slope of the line through those two points is (-3) / (2) .

That's the 3rd choice on the list.

Answer:

The slope of the line that passes through two points is

(the difference in 'y') divided by (the difference in 'x').

The two points are:  (3, -4) and (5, -7)

The difference in 'y' is . . . (-7) - (-4) = -3

The difference in 'x' is . . . (5) - (3) = 2

The slope of the line through those two points is (-3) / (2) .

That's the 3rd choice on the list.

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Answer: x = 75

Step-by-step explanation: The first thing to note is that what we have here is a quadrilateral. In other words, all the internal angles sum up to 360°. Also take note that the figure is a parallelogram, which means two sides are parallel to each other. Line AD is parallel to BC, and line DC is parallel to AB. That makes angle D equal to angle B (alternate angles), and angle A equals Angle C.

If the sum of the interior angles of a quadrilateral equals 360, then

x + (x + 30) + x + (x + 30) = 360

x + x + 30 + x + x + 30 = 360

Collecting like terms, we have

x + x + x + x + 30 + 30 = 360

4x + 60 = 360

Subtract 60 from both sides of the equation

4x = 300

Divide both sides of the equation by 4

x = 75.

Answer: y = 3/4 + 8.25

Step-by-step explanation:

1. You already know the slope, 3/4, and the coordinates (-7,3). We could plug these into a y=mx+b equation: 3=3/4(-7) + b

2. Next you need to solve for b. Then you get your answer of 8.25. (I attached my work for that)

3. You plug in 8.25 as your y-intercept or b: y=3/4 + 8.25

Answer:

x^2-25

Step-by-step explanation:

rewrite 25 as 5^2

x^2-5^2

since both terms are perfect squares, factor using the difference of square s formula, a^2-b^2=(a+b)(a-b) where a=x and b=5

(x+5)(x-5)

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Answer:

[tex]\[(x+5)*(x-5)\][/tex]

Step-by-step explanation:

Given polynomial expression is [tex]\[x^{2}-25\][/tex]

[tex]\[=> x^{2}-5^{2}\][/tex]

This is of the form [tex]\[a^{2}-b^{2}\][/tex]

An expression of this form can be factorized as [tex]\[(a+b)*(a-b)\][/tex]

Here, a = x and b = 5.

Hence the factorized form of the given polynomial expression can be represented as the following product:

[tex]\[(x+5)*(x-5)\][/tex]

Answer:

117.3 feet per second.

Step-by-step explanation:

Velocity is the speed of an object in a definite direction. In mechanics, velocity is a vector quantity. It requires magnitude and direction to make any sense. Velocities are expressed per unit time.

The SI unit of time is the second.

Now, suppose we need the velocity in feet per second. A simple calculation will help:

feet per second = miles per hour × 1.466667 [ in other words, one mile per hour equals 1.466667 feet per second]

For a space capsule moving at 80 miles per hour, the velocity is given by

                           = 80 × 1.466667

                           = 117. 3 ft/s [feet per second]

Answer:

80 miles

Step-by-step explanation:

it is 80 miles bc it asked for its speed and  that is 80 also i did this on iready a while ago :)