At Denver international airport, 85% of recent flights have arrived in time. A sample of 11 flights is studied.

Step-by-step explanation:

it seems you solved the tricky part yourself already.

just to be sure, let's do the first derivative here again.

the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...

f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =

= 3t⁴ + 18t³ + 24t² + 18t + 21

f'(t) = 12t³ + 54t² + 48t + 18

and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).

we simply put the input number (2) at every place of the input variable (t).

so,

f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =

= 426

Answer:

Step-by-step explanation:

bring 5 to the left hand side and the equation will becomes x^2-4x-5=0

then lets see for common factors and -5 and +1 are suitable since when you multiply them you get -5 and if you add them it becomes -4 so

x^2+x-5x-5=0

x(x+1)-5(x+1)=0

take (x+1) common

(x-5)(x+1)=0

x-5=0

x=0+5

x=+5

x+1=0

x=0-1

x=-1

so here are the two solutions

The length of arc RS on circle X is 17.99 centimeters.

To find the length of arc RS on circle X, we need to calculate the circumference of the entire circle and then determine what portion of the circumference is represented by the central angle of 110 degrees.

The circumference of a circle is given by the formula C = 2πr, where r is the radius. In this case, the radius of circle X is 9 centimeters, so the circumference is C = 2π(9) = 18π centimeters.

To find the length of arc RS, we need to determine what fraction of the entire circumference is represented by the central angle of 110 degrees. A full circle has 360 degrees, so the fraction of the circumference represented by the central angle is 110/360.

To find the length of arc RS, we multiply the fraction of the circumference by the total circumference of the circle. Therefore, the length of arc RS is (110/360) * 18π.

Simplifying the expression, we have (110/360) * 18π = (11/36) * 18π.

Canceling out the common factors, (11/36) * 18π = (11/2)π.

Now, we can approximate the value of π as 3.14. Therefore, the length of arc RS is (11/2) * 3.14.

Calculating the approximate value, we have (11/2) * 3.14 ≈ 17.99 centimeters.

Therefore, the approximate length of arc RS on circle X is approximately 17.99 centimeters.

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1. The solution to the system 0.6x + 0.7y = 2 and 0.4x + 0.3y = 1 is x = 1.2857 and y = 1.4286.

2. The solution to the system 2x + 3y + z = 10, 7x + 2y + z = 20, and x + 5y + 8z = 30 is x = 2.4286, y = 0.0952, and z = 3.7730.

3. The solution to the system 4y + 3z = 8, 2x - z = 2, and 3x + 2y = 5 is x = 1, y = 2.5, and z = 4/3.

4. The solution to the system 10x2 + 4x32x4 = -4, -3x1 - 17x2 + x3 + 2x4 = 2, x1 + x2 + x3 = 6, and 8x134x2 + 16x3 - 10x4 = 4 is x = -8/10, y = 2, z = 4/7, and w can take any value.

Sure, let's solve each linear system using Gaussian elimination and row echelon form.

The augmented matrix for the system is:

| 0.6 0.7 | 2 |

| 0.4 0.3 | 1 |

To perform Gaussian elimination, we'll use row operations to eliminate the x-coefficient in the second equation.

Multiply the first equation by 0.4 and subtract it from the second equation.

| 0.6 0.7 | 2 |

| 0 -0.14 | -0.2 |

Now, divide the second row by -0.14 to get a leading coefficient of 1.

| 0.6 0.7 | 2 |

| 0 1 | 1.4286 |

Next, we'll eliminate the x-coefficient in the first equation by multiplying the second equation by -0.6 and adding it to the first equation.

| 0.6 0 | 0.7714 |

| 0 1 | 1.4286 |

The system is now in row echelon form. To solve for x and y, back-substitution can be applied.

From the second equation, y = 1.4286.

Substituting y into the first equation, 0.6x = 0.7714, which gives x = 1.2857.

Therefore, the solution to the system is x = 1.2857 and y = 1.4286.

The augmented matrix for the system is:

| 2 3 1 | 10 |

| 7 2 1 | 20 |

| 1 5 8 | 30 |

We'll start by eliminating the x-coefficient in the second and third equations.

Multiply the first equation by -3.5 and add it to the second equation.

Multiply the first equation by -0.5 and add it to the third equation.

| 2 3 1 | 10 |

| 0 -10.5 -2.5 | -5 |

| 0 3.5 7.5 | 25 |

Now, divide the second row by -10.5 to get a leading coefficient of 1.

| 2 3 1 | 10 |

| 0 1 0.2381| 0.4762 |

| 0 3.5 7.5 | 25 |

Next, eliminate the x-coefficient in the third equation by multiplying the second equation by -3.5 and adding it to the third equation.

| 2 3 1 | 10 |

| 0 1 0.2381| 0.4762 |

| 0 0 6.1905| 23.3333 |

The system is now in row echelon form. To solve for x, y, and z, back-substitution can be applied.

From the third equation, z = 3.7730.

Substituting z into the second equation, y + 0.2381z = 0.4762, which gives y = 0.0952.

Substituting y and z into the first equation, 2x + 3y + z = 10, we find x = 2.4286.

Therefore, the solution to the system is x = 2.4286, y = 0.0952, and z = 3.7730.

The augmented matrix for the system is:

| 0 4 3 | 8 |

| 2 0 -1| 2 |

| 3 2 0 | 5 |

To eliminate the x-coefficient in the second and third equations, multiply the first equation by 2 and subtract it from the second equation.

Multiply the first equation by 3 and subtract it from the third equation.

| 0 4 3 | 8 |

| 2 0 -1| 2 |

| 3 2 0 | 5 |

The system is already in row echelon form. Let's solve for x, y, and z.

From the third equation, 2y = 5, which gives y = 2.5.

Substituting y into the second equation, 2x - z = 2, we find 2x - z = 2.

Substituting y and z into the first equation, 4 + 3z = 8, we get 3z = 4, which gives z = 4/3.

Therefore, the solution to the system is x = 1, y = 2.5, and z = 4/3.

The augmented matrix for the system is:

| 10 2 32 | -4 |

| -3 -17 1 | 2 |

| 1 1 1 | 6 |

| 8 13 -10| 4 |

We'll use row operations to convert the matrix into row echelon form.

| 10 2 32 | -4 |

| 0 -173 -32 | -2 |

| 0 0 -7 | -4 |

| 0 0 0 | 0 |

The system is now in row echelon form. To solve for x, y, z, and w, back-substitution can be applied.

From the third equation, -7z = -4, which gives z = 4/7.

Substituting z into the second equation, -173y - 32z = -2, we find -173y - 32(4/7) = -2, which gives y = 14/7.

Substituting y and z into the first equation, 10x + 2y + 32z = -4, we get 10x + 2(14/7) + 32(4/7) = -4, which simplifies to 10x = -8.

Therefore, the solution to the system is x = -8/10, y = 2, z = 4/7, and w can take any value.

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Sally's average annual percentage gain is approximately 5.26%.

To calculate Sally's average annual percentage gain, we can use the formula:

Average Annual Percentage Gain = (Profit / Initial Investment) * (1 / Time) * 100

Profit = $2500

Initial Investment = $19000

Time = 2.5 years

Substituting the values into the formula:

Average Annual Percentage Gain = (2500 / 19000) * (1 / 2.5) * 100

= (0.1316) * (0.4) * 100

= 5.26

Therefore, Sally's average annual percentage gain is approximately 5.26%.

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Cliff pays a total interest of approximately $679.90 on his $5,000 loan.

To calculate the total interest paid on the loan, we need to use the formula for compound interest:

[tex]A = P(1 + r/n)^{(nt)}[/tex]

Where:

A is the final amount (loan amount + interest)

P is the principal (loan amount)

r is the annual interest rate (in decimal form)

n is the number of times interest is compounded per year

t is the number of years

Given that Cliff takes out a $5,000 loan with a fixed annual interest rate of 7% compounded monthly, we can substitute the values into the formula:

P = $5,000

r = 7% = 0.07

n = 12 (monthly compounding)

t = 2 years

[tex]A = 5000(1 + 0.07/12)^{(12 \times 2)[/tex]

Calculating this expression:

A ≈ 5000[tex](1.00583)^{(24)[/tex]

A ≈ 5000(1.13598)

A ≈ 5679.90

The final amount (A) is the loan amount plus the total interest paid. Therefore, to find the total interest paid, we subtract the principal (P) from the final amount (A):

Total Interest = A - P

Total Interest = 5679.90 - 5000

Total Interest ≈ $679.90

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The investment with compound interest earns a greater amount of interest by $486.12 compared to the investment with simple interest.

To determine which investment earns a greater amount of interest, we need to calculate the interest earned in both scenarios and compare the results.

1. Simple Interest:

The formula for simple interest is given by: I = P * r * t, where I is the interest, P is the principal amount, r is the interest rate, and t is the time period.

Using this formula, we can calculate the interest earned with simple interest:

I = 100,000 * 0.03 * 4

I = $12,000

2. Compound Interest:

The formula for compound interest is given by: A = P * (1 + r/n)^(n*t), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the time period.

In this case, the interest is compounded annually, so n = 1. Let's calculate the amount earned:

A = 100,000 * (1 + 0.03/1)^(1*4)

A = 100,000 * (1.03)^4

A = $112,486.12

The interest earned in the compound interest scenario is A - P = $112,486.12 - $100,000 = $12,486.12.

The difference between the amounts of interest earned by the two investments is:

$12,486.12 - $12,000 = $486.12.

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The intersection of sets M and F contains the elements "c" and "d".

To find the intersection of sets M and F, we need to identify the elements that are common to both sets.

M = {a, b, c, d}

F = {c, d, e, f}

The intersection of M

and F is denoted by M ∩ F, which represents the set containing elements that are present in both M and F.

Looking at the elements in M and F, we can see that the common elements between the two sets are "c" and "d".

Therefore, the intersection of M and F can be expressed as:

M ∩ F = {c, d}

So, the intersection of sets M and F contains the elements "c" and "d".

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Answer:

Step-by-step explanation:

-4(y+9)

Answer:

a

Step-by-step explanation:

the perimeter (P) of a square is the sum of the 4 congruent sides.

the area of a square is calculated as

area = s² ( s is the length of a side )

here area is 36 , then

s² = 36 ( take square root of both sides )

s = [tex]\sqrt{36}[/tex] = 6

then

P = 4s = 4 × 6 = 24 cm

The volume of the first and second solid shapes are 3014.4m³ and 360ft³ respectively.

The first shape comprises of a cone and a cylinder, and the volume is derived as follows:

volume of the cone = 1/3 × 3.14 × (8m)² × 5m

volume of the cone = 1004.8m³

volume of the cylinder = 3.14 × (8m)² × 0m

volume of the cylinder = 2009.6 m³

volume of the first solid shape = 1004.8m³ + 2009.6 m³

volume of the first solid shape = 3014.4m³

The second solid shape comprises of a trianglular prism and a cuboid

volume of the trianglular prism = base area × height

base area = 1/2 × 6ft × 4ft = 12ft²

volume of the trianglular prism = 12ft² × 6ft

volume of the trianglular prism = 72ft³

volume of the cuboid = 12ft × 6ft × 4ft

volume of the cuboid = 288ft³

volume of the second solid shape = 72ft³ + 288ft³

volume of the second solid shape = 360ft³

Therefore, the volume of the first and second solid shapes are 3014.4m³ and 360ft³ respectively.

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Alexei's monthly payment is approximately $18.56.

Alexei finances her purchase of a $900 television with a one-year loan that has a fixed annual interest rate of 2.5%. To find Alexei's monthly payment, we can use the formula for calculating monthly loan payments.
The formula for calculating monthly loan payments is:
M = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M = monthly payment
P = principal loan amount
r = monthly interest rate (annual interest rate divided by 12)
n =number of monthly payments
In this case, the principal loan amount (P) is $900, the annual interest rate (r) is 2.5% (or 0.025 when expressed as a decimal), and the number of monthly payments (n) is 12 (since it is a one-year loan).
First, we need to calculate the monthly interest rate (r) by dividing the annual interest rate by 12: r = 0.025 / 12 = 0.002083.
Next, we can substitute the values into the formula:
M = (900 * 0.002083 * (1 + 0.002083)^12) / ((1 + 0.002083)^12 - 1)
Simplifying the formula gives us:
M = (900 * 0.002083 * 1.002083^12) / (1.002083^12 - 1)
Calculating the values inside the formula gives us:
M = (900 * 0.002083 * 1.026260) / (1.026260 - 1)
Further simplifying the formula gives us:
M = (900 * 0.002083 * 1.026260) / 0.026260
Finally, calculating the expression gives us:
M ≈ 18.56
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6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

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Answer:

Step-by-step explanation:

3.6*

It is very easy to find the perimeter of a square when its area is given in the question. For that, you only ned to know one fomula. That formula is: Area = side^2

For this particular question, the given value for the area of the square is 36 sq.cm. So, we can solve for the side(s) by substituting the given value in the above mentioned formula.

We get

36 = s^2

Now, we need to get the square root of both sides, which gives us

s = √36 s = 6 cm

Since all the sides of a square are equal in length, the side length is 6 cm. Now to determine the perimeter, we must multiply the side length by 4 (because there are 4 equal sides in a square). That gives us Perimeter = 4 x side length Perimeter = 4 x 6 cm.

Therefore, the perimeter of the square is 24 cm.

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Answer:

Step-by-step explanation:

Well, since the length of a month can vary in the number of days, this answer can also vary.

For example, February is only 28 days long, while December is 31 days long.

That being said, the average length of all 12 months is 30.436875 days, so if Denny left to another country on June 20th, he would most likely be back   July 19th of July 20th.

I hope this helps!

[tex]13 \leqslant 4x - 3 \leqslant 29 \\ 13 + 3 \leqslant 4x \leqslant 29 + 3 \\ 16 \leqslant 4x \leqslant 32 \\ 16 \div 4 \leqslant x \leqslant 32 \div 4 \\ 4 \leqslant x \leqslant 8[/tex]

Answer:

Janna will use 26 marshmallows and 39 graham crackers to make 13

Step-by-step explanation:

S'mores       Marshmallows       Graham Crackers

      4                      8                                12

     13

Look at the first line on the table.

For 4 s'mores, 8 marshmallows are used.

8/4 = 2

2 marshmallows are used per s'more.

For 4 s'mores, 12 graham crackers are used.

12/4 = 3

3 graham crackers are used per s'more.

For 13 s'mores,

13 × 2 = 26

13 × 3 = 39

26 marshmallows and 39 graham crackers are needed.

Complete the table:

S'mores       Marshmallows       Graham Crackers

      4                      8                                12

     13                     26                              39

Answer:

Janna will use 26 marshmallows and 39 graham crackers to make 13

The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.

In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.

The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.

The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.

Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.

First, we need to standardize the value of 60.8 using the formula:

Z = (X - μ) / σ

Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.

In this case, the standardized value is:

Z = (60.8 - 60) / sqrt(0.16)

Z = 0.8 / 0.4

Z = 2

Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.

Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

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Hello!

3x + 4 = 1

3x + 4 - 4 = 1 - 4

3x = -3

3x/3 = -3/3

x = -1

The solution of the equation 3x + 4 = 1 is -1.

The answer is:

C) x = -1

Work/explanation:

To solve this equation, I subtract 4 from each side:

[tex]\sf{3x+4=1}[/tex]

Subtract :

[tex]\sf{3x=-3}[/tex]

Divide each side by 3:

[tex]\sf{x=-1}[/tex]

Hence, C is correct.

The volume of the sphere as shown in the diagram is 4186.67.

volume is the amount of space in a certain 3D object.

To calculate the volume of the sphere, we use the formula below

Formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

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The line passes through the points (0, 3), (1, -2), and (-1, 8), and it extends infinitely in both directions.

To graph the line y = -5x + 3, we can start by plotting a few points and then connecting them to create the line.

We can choose arbitrary values for x and calculate the corresponding y values using the given equation. Let's choose three values of x and calculate the corresponding y values:

When x = 0:

y = -5(0) + 3 = 3

So, we have the point (0, 3).

When x = 1:

y = -5(1) + 3 = -5 + 3 = -2

So, we have the point (1, -2).

When x = -1:

y = -5(-1) + 3 = 5 + 3 = 8

So, we have the point (-1, 8).

Now, we can plot these points on a coordinate plane:

     |

10    +

     |

     |

5    +

     |

     |

0----+----+----+----+----+----+----+----+----+----+

     -2   -1    0    1    2    3    4    5    6    7

Once we have plotted these points, we can connect them to form a straight line:

     |

10    +

     |

     |

5    +                 .

     |               .

     |             .

0----+----+----+----+----+----+----+----+----+----+

     -2   -1    0    1    2    3    4    5    6    7

The line passes through the points (0, 3), (1, -2), and (-1, 8), and it extends infinitely in both directions.

The graph of the line y = -5x + 3 is a straight line with a slope of -5 (indicating that it decreases by 5 units in the y-direction for every 1 unit increase in the x-direction) and a y-intercept of 3 (indicating that the line intersects the y-axis at the point (0, 3)).

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There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.

To determine the total number of color-wheel size combinations for the kickboard scooter, we need to multiply the number of color options by the number of wheel size options.

Given that there are 4 color options (silver, red, blue, and purple) and 2 wheel size options (125mm and 180mm), we can use the multiplication principle to find the total number of combinations:

Total combinations = Number of color options × Number of wheel size options

Total combinations = 4 colors × 2 wheel sizes

Total combinations = 8

There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.

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The discriminant of the quadratic-equation -x^2 + 6x - 6 = 0 is 60.

The discriminant of a quadratic equation of the form ax^2 + bx + c = 0 is given by the expression Δ = b^2 - 4ac.

In the given quadratic equation -x^2 + 6x - 6 = 0, we can identify that a = -1, b = 6, and c = -6.

Substituting these values into the discriminant formula, we have:

Δ = (6)^2 - 4(-1)(-6)

The discriminant plays a crucial role in determining the nature of the solutions of a quadratic equation. If the discriminant is positive (Δ > 0), then the equation has two distinct real solutions. If the discriminant is zero (Δ = 0), then the equation has one real solution (also known as a double root). If the discriminant is negative (Δ < 0), then the equation has no real solutions, but it may have complex solutions involving imaginary numbers.

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Hello!

7x² - 14x + 7

7(x² - 2x + 1)

= 7(x(x - 1) - 1(x - 1))

= 7((x - 1)(x - 1))

= 7(x - 1)²

Answer:

1.5926

Step-by-step explanation:

-We need to first convert the height in feet to inches: Since there are 12 inches in a foot, that means there are 74 inches in a height of 6 foot 2 inches.

-Since the observed height is 74 inches and the mean height is 69.7 inches, we can find the z score by using the following formula:

z = (x-mean) / standard deviation

-We would fill this out like this:

z = (74-69.7) / 2.7

-This equals = 1.592592593

-Rounded to 4 decimal places, this equals 1.5926

The total weight of the five bags of cat food is approximately 66.1386 pounds.

To determine the weight of the cat food in pounds, we can use the conversion factor that 1 kilogram is approximately equal to 2.20462 pounds.

Given that each bag of cat food has a mass of 6 kilograms, we can calculate the weight of one bag in pounds by multiplying 6 by 2.20462.

[tex]6 kg \times 2.20462 lb/kg = 13.22772 lb[/tex]

Now, to find the total weight of the five bags of cat food, we multiply the weight of one bag by the number of bags:

[tex]13.22772 lb/bag \times 5 bags = 66.1386 lb[/tex]

It's important to note that the provided conversion factor of 2.20462 pounds per kilogram is an approximation, as the exact conversion factor is 2.20462262185 pounds per kilogram.

However, for the purpose of this calculation, we are using the rounded value to one decimal place.

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The names of the expressions are;

1) Monomial, quadratic

2) Monomial, constant

3) Binomial, Linear

4) Trinomial, quadratic

An algebraic expression that has one or more terms, each of which is a variable raised to a non-negative integer exponent and multiplied by a coefficient, is referred to as a polynomial. The terms are mixed by adding or removing. A polynomial may include 0 terms or more.

A particular kind of polynomial known as a trinomial has exactly three terms. Trinomials are made up of three different pieces, which are frequently denoted by the formula "ax2 + bx + c," where "a," "b," and "c" are coefficients.

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Step-by-step explanation:

this is physics (not math per se).

the first moves to the left, because the distance to the positive charge on the left is shorter than the distance to the positive charge on the right.

the second moves to the right, because the positive charge is greater there and the distance to the positive charge is shorter too.

the third stays where it is. the -2 charge moves to the left until it hits the first +2 charge. there they neutralize each other, and nothing else is happening. also before -2 and +2 meet, they are neutralizing each other already for an outside observer (like the green ringed +2).

but - it depends how picky your teacher tries to be here.

because when you look at the very fine details, until -2 and the right +2 meet and really neutralize each other, there is a tiny little overhang of positive charges the green ringed +2 charge would "feel". simply because the +2 is a little bit closer than the -2.

and when we consider this, the green ringed +2 would move very little to the left (repelled by the other positive overhanging charge on the right) until -2 and +2 actually meet.

Answer:

24in^3

Step-by-step explanation:

this is a triangular prism and to find the volume of a right prism (a triangular prism in this case) we'll first find the area of cross-section which is basically the base area ( the triangle)

which is 1/2*4in*3in

this equals 6in^2

to find the volume we multiply it by the height of the prism which is 4 (the one on the top) so we multiply our previous answer with 4 to get 24in^3