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Using the formula of volume of rectangular prism;

1. The volume of the rectangular prism is 3672cm³

2. The volume of the rectangular prism is 630in³

3. The volume of the rectangular prism is  3744ft³

The volume of a rectangular prism can be calculated by multiplying its length (l), width (w), and height (h). The formula for the volume of a rectangular prism is:

Volume = length × width × height

V = l × w × h

By substituting the given values for the length, width, and height into the formula, you can calculate the volume of the rectangular prism.

1. To find the volume of the rectangular prism, we have to substitute the value into the formula;

v = 9 * 24 * 17

v = 3672cm³

2. The volume of the rectangular prism is given as;

v = 4.5 * 14 * 10

v = 630in³

3. The volume of the rectangular prism is given as;

v = 8 * 12 * 39

v = 3744ft³

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The solution to -4.5 x (-2) is 9.

What is the arithmetic calculation?

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

The reason for this is that when two negative numbers are multiplied together, the result is positive.

This is because the negative sign on a number is similar to a "minus" sign, indicating that the number is less than zero.

When you have two "minus" signs together (in this case, one on -4.5 and one on -2),

they cancel each other out, leaving the positive product of 4.5 and 2, which is 9.

-4.5 is a negative decimal number, and -2 is also a negative integer number. When multiplied, it results in a positive number, which is 9.

Hence, the solution to -4.5 x (-2) is 9.

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The probability of both rice and carrots being served with dinner is 23.4%.

The probability of Alvin's mother serving rice with dinner can be expressed using the formula P(Rice) = 0.78. This means that the probability of Alvin's mother serving rice with dinner is 78%. The probability of Alvin's mother serving carrots with dinner can be expressed using the formula P(Carrots) = 0.30. This means that the probability of Alvin's mother serving carrots with dinner is 30%. To calculate the combined probability of both rice and carrots being served with dinner, we can use the formula P(Rice and Carrots) = P(Rice) * P(Carrots) = 0.78 * 0.30 = 0.2340. This means that the probability of both rice and carrots being served with dinner is 23.4%.

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\(a(1) = 240 \\ a(2) = a(1) + d = 240 + 24 = 264 \\ a(3) = a(2) + d = 264 + 24 = 288 \\ a(4) = a(3) + d = 288 + 24 = 312 \\ a(5) = a(4) + d = 312 + 24 = 336 \\ a(6) = a(5) + d = 336 + 24 = 360\)

Answer: P = 0.5 *(12)^3 = 864 kW

Step-by-step explanation:

We calculate the power as follows:

P=C*v^3,

where C = constant and v is the velocity,

lets find the C first, from the given conditions

P = C*v^3

500= C(10)^3

C=500/(10)^3 = 0.5

If a turbine generates 500 kW in a 10 m/s wind, then 864 KW power does it generate in a 12 m/s wind

Power is the amount of energy transferred or converted per unit time.

Given,

The power P (in kilowatts) generated by a wind turbine varies directly as the cube of the wind speed v

P = kv³

Where k is the proportionality constant.

If a turbine generates 500kW in a 10m/s wind, we need to find how much power does it generate in 12m/s wind

first solve the proportionality constant k

500 = k (10³)

k = 500 / 10³= 0.5

so when v = 12 m/s

P = 0.5(12³)

p = 864 kW

Hence 864 kW  is the power generated by a 12 m/s wind.

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Step-by-step explanation:

A o option

-(-45)

hope it helps

To find the total amount of money in the account at the end of 8 years with simple interest , we can use the formula:

A = P * (1 + r * t

where A = total amount P = principal (initial amount) r = interest rate per year (as a decimal) t = time (in years)

In this case, P = $300 r = 6.5% = 0.065 t = 8 years

Substituting these values in the formula:

A = $300 * (1 + 0.065 * 8) A = $300 * 1.52 A = $456

Therefore, the total amount of money in the account at the end of 8 years is $456 with simple interest.

Note that this assumes that the interest is compounded annually , and that there are no other deposits or withdrawals made during the 8-year period. If the interest is compounded more frequently, or if there are additional deposits or withdrawals, the calculation would be different.

F(3) is equal to 9, based on the given table and the corresponding values of x and f(x). Option D.

To find the value of F(3) based on the given table, we look at the corresponding x-value of 3 and find its corresponding f(x) value.

From the table, we see that when x = 3, f(x) = 9. Therefore, F(3) = 9.

The table shows the values of x and their corresponding f(x) values. We can see that when x increases by 1, f(x) also increases by 3. This indicates that the function has a constant rate of change, where the change in f(x) is always 3 units for every 1 unit change in x.

Given that F(3) represents the value of the function when x = 3, we look at the x-values in the table and find the corresponding f(x) value. In this case, when x = 3, f(x) = 9.

Therefore, the value of F(3) is 9. Option D is correct.

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Answer: The answer is b

Step-by-step explanation:

Answer:

y = - \(\frac{1}{6}\) x + 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 6x + 3 ← is in slope- intercept form

with slope m = 6

given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{6}\) , then

y = - \(\frac{1}{6}\) x + c ← is the partial equation of the perpendicular line

to find c substitute (- 6, 4 ) into the partial equation

4 = 1 + c ⇒ c = 4 - 1 = 3

y = - \(\frac{1}{6}\) x + 3 ← equation of perpendicular line

Using the vertical asymptote concept, it is found that the tangent function is undefined when \(\theta = \frac{\pi}{2}\).

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.

In this problem, we have that:

\(\theta = \frac{\pi}{2}\), which means that \(\cos{\theta} = 0\).

Since \(\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}\), the tangent function is undefined when \(\theta = \frac{\pi}{2}\).

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Answer:

d: tan 0

Step-by-step explanation:

Answer:

It would be the square root of 36.

Step-by-step explanation:

Answer: B

Step-by-step explanation:

Answer:

seeing as no one is answering I will

Since the relationship is proportional, the line will pass through the origin (0, 0). This means that if there is a bag with zero weight, it would have zero cost.

To graph the proportional relationship between the weight and total cost of the bags of lemons, follow these steps:

1. Identify the independent variable and the dependent variable. In this case, the weight of the bag (in pounds) is the independent variable, and the total cost of the bag (in dollars) is the dependent variable.

2. Create a coordinate plane. Label the x-axis as "Weight (pounds)" and the y-axis as "Total Cost (dollars)".

3. Plot the data points. For the first bag, with a weight of 2.4 pounds and a cost of $5.28, plot a point at (2.4, 5.28) on the coordinate plane. For the second bag, with a weight of 2.7 pounds and a cost of $5.94, plot a point at (2.7, 5.94) on the coordinate plane.

4. Draw a straight line passing through the two plotted points. This line represents the proportional relationship between the weight and total cost of the bags of lemons.

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Answer:

(3, - 1 )

Step-by-step explanation:

Given the 2 equations

3x + y = 8 → (1)

7x - 4y = 25 → (2)

Multiplying (1) by 4 and adding to (2) will eliminate the y- term

12x + 4y = 32 → (3)

Add (2) and (3)  term by term to eliminate y

19x + 0 = 57

19x = 57 ( divide both sides by 19 )

x = 3

Substitute x = 3 into either of the 2 equations and solve for y

Substituting into (1)

3(3) + y = 8

9 + y = 8 ( subtract 9 from both sides )

y = - 1

solution is (3, - 1 )

Answer:

Since the spinners have been spun simultaneously, every side on each of the spinner carries equal probability of landing. In order for there to be only 10 possible outcomes, no more no less, the spinners cannot be identical. One of the spinner in two sided while the other spinner must then be a five sided spinner. Choosing this particular pair of spinners gives Nathan 10 possibilities of combinations.

Hope that answers the question, have a great day!

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

Hi! The answer to your question is B. 30 Trees

Step-by-step explanation:

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Arithmetic SequenceAn arithmetic sequence is an ordered list of numbers where the difference between consecutive numbers remains constant. For example, the following numbers are an arithmetic sequence: 2, 4, 6, 8, 10, 12.

The difference between consecutive terms is 2; this is the common difference. We can determine the nth term of an arithmetic sequence using the following formula:an = a1 + (n – 1)dwhere an is the nth term, a1 is the first term, n is the term number, and d is the common difference. Formula for the general term (the nth term) of the arithmetic sequence:

We are given

a₁ = 4 and an = an-1 + 5For the 1st term (n = 1)

:a₁ = 4and for the 2nd term (n = 2):a₂ = a₁ + 5 = 4 + 5 = 9For the

3rd term (n = 3):a₃ = a₂ + 5 = 9 + 5 = 14

For the 4th term (n = 4):a₄ = a₃ + 5 = 14 + 5 = 19

Thus, we can see that the common difference is 5. Hence, the nth term of the arithmetic sequence is given by:

an = a₁ + (n – 1)d = 4 + (n – 1)5 = 5n – 1Therefore, the formula for the general term (the nth term) of the arithmetic sequence is: an = 5n – 1.

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Answer:

D. 37.68

Step-by-step explanation:

Circumference of a circle is 2 x pi x radius

your radius is 6 bc its half of your diameter is 12

when you multify them together, it gives you ab 37.68

Answer:

No, because as the x-values are increasing by a constant amount, the y-values are not being multiplied by a constant amount.

Step-by-step explanation:

We have a set of ordered pairs of the form (x, y)

If a function is exponential then the ratio between the consecutive values of y, is always equal to a constant.

This means that:

\frac{y_2}{y_1}=\frac{y_3}{y_2}=\frac{y_4}{y_3}=by1y2=y2y3=y3y4=b

This is: y_2=by_1y2=by1

Now we have this set of points {(-1, -5), (0, -3), (1, -1), (2, 1)}

Observe that:

\begin{gathered}\frac{y_2}{y_1}=\frac{-3}{-5}=\frac{3}{5}\\\\\frac{y_3}{y_2}=\frac{-1}{-3}=\frac{1}{3}\\\\\frac{3}{5}\neq \frac{1}{3}\end{gathered}y1y2=−5−3=53y2y3=−3−1=3153=31

Then the values of y are not multiplied by a constant amount "b"

Answer:

\(\left[\begin{array}{cc}-230&380\\-170&60\end{array}\right]\)

Step-by-step explanation:

Notice that you are being asked to perform the product of a scalar (the number "-10" times a 2 by 2 matrix.

Such type of product requires the multiplication of each element of the matrix by the scalar "-10"

That means that the element 23 gets transformed into "-230"

The element -38 gets transformed into "380"

The element 17 gets transformed into "-170"

and lastly, the element -6 gets transformed into "60"

\(\left[\begin{array}{cc}1-230&380\\-170&60\\end{array}\right]\)\(\left[\begin{array}{cc}-230&380\\-170&60\end{array}\right]\)

Such modification gets reflected in the second matrix listed among the possible answers.

Answer:

( 2, - 1 )

Step-by-step explanation:

( x - h )² + ( y - k )² = r²

( h, k ) are coordinates of the center of a circle with radius r

~~~~~~~~~

x² + y² - 4x + 2y - 11 = 0

( x² - 4x + 4 ) - 4 + ( y² + 2y  + 1 ) - 1 - 11 = 0

( x - 2 )² + ( y + 1 )² = 4²

Coordinates of the center of a circle are ( 2, - 1 )