What is the volume of a right rectangular prism with a length of 4. 8 meters, a width of 2. 3 meters, and a height


of 0. 9 meters?


O4. 968 m3


O9. 936 m3


O 11. 94 m3


O 34. 86 m3




PLS ANSWER FAST I WILL GIVE BRAINIEST!!!!!

Check the picture below.

The approximate length of the base of the triangle is 5 units

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. The area of a triangle is expressed as;

A = 1/2 bh

The hexagon is divided into six equal triangles.

The area of the hexagon is 65 units²

Therefore, the area of the triangle = 65/6

= 10.83

Area of a triangle = 1/2 b h

height = 4.3 units

10.83 = 1/2 × 4.3 × b

4.3b = 10.83 × 2

4.3b = 21.66

divide both side by 4.3

b = 21.66/4.3

b = 5.04

therefore the approximated value of the base is 5 units.

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The total cost of the two tickets is $70.88.

A discount is a reduction in the original price of an item or service. It is often used as a marketing strategy to increase sales by making the product more affordable or attractive to consumers. The amount of the discount is typically expressed as a percentage of the original price.

In the given question,

The cost of one ticket after a 25% discount is:

45 * 0.75 = $33.75

The cost of two tickets is:

2 * 33.75 = $67.50

Adding the 5% sales tax:

67.50 * 1.05 = $70.88

Therefore, the total cost of the two tickets is $70.88.

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The fraction, David used 13/8 cups of blueberries for the pancakes.

Let's solve it step-by-step using the given information.

1. David has 3 1/2 cups of blueberries.
2. He uses 1/4 cup for a breakfast smoothie.
3. He uses 1/2 of the remaining blueberries for pancakes.

Step 1: Calculate the remaining blueberries after making the smoothie.
3 1/2 - 1/4 = (7/2) - (1/4)

To subtract the fractions, they need a common denominator, which in this case is 4.

(7/2) * (2/2) - (1/4) = (14/4) - (1/4) = 13/4 cups

Step 2: Calculate the amount of blueberries used for the pancakes.
David uses 1/2 of the remaining blueberries for the pancakes, so:

(13/4) * (1/2) = 13/8 cups

David uses 13/8 cups of blueberries for the pancakes.

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Answer: 8

Step-by-step explanation:

okay so do 17 x 17 - 15 x 15

then to that result do :

squared root.

it is 16 steps from second base to third base .we can get this answer by

solving the logic given in the question .we need to add up the number of steps

what is  add up  ?

"Add up" means to calculate the total of two or more numbers or quantities by combining them together. It involves the mathematical operation of addition, which is the process of finding the sum of two or more numbers. For example, if you add up the numbers 3, 5, and 7, t

In the given question,

To find out how many steps it is from second base to third base, we need to add up the number of steps Gavin took in each direction.

Starting at second base, he took 18 steps forward to get caught, and then took 7 steps back. This leaves him 11 steps forward from second base.

Next, he took 3 more steps forward, for a total of 14 steps forward from second base. But then he took 5 steps back, leaving him 9 steps forward from second base.

Then he took 11 more steps forward, for a total of 20 steps forward from second base. But then he took 4 steps back, leaving him 16 steps forward from second base.

Finally, he was tagged out halfway between second and third base. Since he was 16 steps forward from second base, and halfway between second and third base, we can assume that third base is 16 steps away from second base.

Therefore, it is 16 steps from second base to third base.

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Sarah wants to attend a private college with a yearly tuition of $31,000. Room and board costs are estimated to be $12,000 per year, and the cost of books and supplies is estimated to be $2,000. To calculate the total cost of her four-year degree, follow these steps:

1. Add the yearly costs together: $31,000 (tuition) + $12,000 (room and board) + $2,000 (books and supplies) = $45,000 per year.
2. Multiply the yearly cost by the number of years in the degree program: $45,000 * 4 = $180,000.

Assuming she receives no financial aid, it will cost Sarah $180,000 to get a four-year degree from this private college.

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The Stafford loan will have a lower balance by $272.54 at the time of repayment.

For the Stafford Loan, the principal is $10,720 and the interest rate is 5.95% compounded monthly, so the monthly interest rate is 0.0595/12 = 0.00495833.

After 12 months, the balance of the loan will be:

$10,720(1 + 0.00495833)¹² = $11,204.60

After the time of six-month grace period, the balance will be:

$11,204.60(1 + 0.00495833)⁶ = $11,689.66

For the PLUS Loan, the principal is $11,443.63 and the interest rate is 6.55% compounded monthly, so the monthly interest rate is 0.0655/12 = 0.00545833.

After 12 months, the balance of the loan will be:

$11,443.63(1 + 0.00545833)¹² = $11,962.20

Therefore, the Stafford Loan will have a lower balance at the time of repayment by:

$11,962.20 - $11,689.66 = $272.54

Hence, the Stafford loan will have a lower balance by $272.54 at the time of repayment.

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Part A: The coefficient of the 4th degree term in the Taylor polynomial for f(x) = sin(4x) centered at x = 0 is -1/3! = -1/6.

Part B: Using a 4th degree Taylor polynomial for sin(x) centered at x = 0, we can write g(x) = sin(0.8) ≈ P4(0.8), where P4(0.8) is the 4th degree Taylor polynomial for sin(x) evaluated at x = 0.8.

Evaluating P4(0.8) using the formula for the Taylor series coefficients of sin(x), we get P4(0.8) = 0.8 - 0.008 + 0.00004 - 0.0000014 ≈ 0.78333. This estimate is very close to 1 because sin(0.8) is close to 1, and the Taylor series for sin(x) converges very rapidly for values of x close to 0.

Part C: The series { (-1)n / (2n + 1) } has a partial sum S when x = 1. To find an interval |S - S5| = R5| for which the actual sum exists, we can use the alternating series test. The alternating series test states that if the terms of a series alternate in sign, decrease in absolute value, and approach zero, then the series converges.

Since the terms of the series { (-1)n / (2n + 1) } alternate in sign and decrease in absolute value, we know that the series converges. To find an interval |S - S5| = R5|, we can use the remainder formula for alternating series, which states that |Rn| ≤ a_n+1, where a_n+1 is the first neglected term in the series.

Since the terms of the series decrease in absolute value, we know that a_n+1 ≤ |a_n|. Therefore, we have |R5| ≤ |a6| = 1/7!, which means that the actual sum of the series exists in the interval S - 1/7! ≤ S5 ≤ S + 1/7!. Therefore, an interval for which the actual sum exists is [S - 1/7!, S + 1/7!].

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Answer:

Step-by-step explanation:

You want the median of the Blue box plot and the IQR of the Pink box plot shown in the figure.

A box plot has 5 vertical lines. From left to right, they are ...

Based on the above, we can see the median is the middle line inside the box of the box plot.

The median of the blue plot is 5.2.

The "Interquartile range" is the difference between the 3rd quartile and the 1st quartile. That is, it is the difference between the two ends of the box, the length of the box.

The IQR of the pink plot is 6.4 -5.6 = 0.8.

__

Additional comment

This is basically an exercise in understanding the terms associated with a box plot, and reading a graph. The only calculation involved is figuring out the missing graph coordinates and finding the difference of the coordinates at the ends of the pink plot.

The solution to the differential equation with the given initial condition is:

[tex]u = -1/2 * ln(-2/9 * e^{(9t)} + 4/9 * e^{(-8)} + 2/9)[/tex]

To solve equation, we can separate the variables and write:

[tex]1/e^{(2u)} du = e^{(9t)} dt[/tex]

Integrating both sides, we get:

[tex]\int 1/e^{(2u)} du = \int e^{(9t)} dt[/tex]

Integrating the left side requires the substitution v = 2u, dv/du = 2, and du = dv/2, which gives:

[tex]\int 1/e^{(2u)} du = \int 1/2 * 1/e^v dv = -1/2 * e^{(-2u)}[/tex]

Integrating the right side gives:

[tex]\int e^{(9t)} dt = 1/9 * e^{(9t)}[/tex]

Substituting these integrals back into the original equation, we get:

[tex]-1/2 * e^{(-2u)} = 1/9 * e^{(9t)} + C[/tex]

where C is the constant of integration.

We can solve for the constant of integration using the initial condition u(0) = 4:

[tex]-1/2 * e^{(-24)} = 1/9 * e^{(90)} + C[/tex]

[tex]-1/2 * e^{(-8)} = 1/9 + C[/tex]

[tex]C = -1/2 * e^{(-8)} - 1/9[/tex]

Therefore, the solution to the differential equation [tex]du/dt = e^{(2u+9t)}[/tex] with initial condition u(0) = 4 is:

[tex]-1/2 * e^{(-2u)} = 1/9 * e^{(9t)} - 1/2 * e^{(-8)} - 1/9[/tex]

Solving for u, we get:

[tex]e^{(-2u)} = -2/9 * e^{(9t)} + 4/9 * e^{(-8)} + 2/9[/tex]

Taking the natural logarithm of both sides, we get:

[tex]-2u = ln(-2/9 * e^{(9t)} + 4/9 * e^{(-8)} + 2/9)[/tex]

Dividing by -2, we get:

[tex]u = -1/2 * ln(-2/9 * e^{(9t)} + 4/9 * e^{(-8)} + 2/9)[/tex]

Therefore, the solution to the differential equation with the given initial condition is:

[tex]u = -1/2 * ln(-2/9 * e^{(9t)} + 4/9 * e^{(-8)} + 2/9)[/tex]

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The difference between the means expressed as a multiple of the mean absolute deviation is 2.3.

To find the difference between the means expressed as a multiple of the mean absolute deviation, we need to calculate the absolute difference between the two means and divide it by the mean absolute deviation.

The absolute difference between the means is:

|30.2 - 25.6| = 4.6

To express this difference as a multiple of the mean absolute deviation, we divide it by the mean absolute deviation:

4.6 / 2 = 2.3

Therefore, the difference between the means expressed as a multiple of the mean absolute deviation is 2.3.

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Answer:

Step-by-step explanation:

4/625 x 625/9 = 4 x 1 / 5 x 5 x 5 x 1 = 4/625. The cross cancellation did not change the result.

Answer: D)-3/4

Step-by-step explanation: Rate of change of y with respect to x implies the following formula...(y2-y1)/(x2-x1)...which is also the gradient of the line, you can substitute the value in accordance with the points already ahown in the grid to get, (7-1)/(-4-4)=-3/4

The measure of arc CAD is either 240 or 260.

Without additional information, it is not possible to determine the measure of arc CAD with certainty. The measure of an arc depends on the central angle that subtends it.

If the central angle is known, the measure of the arc can be calculated using the formula: measure of arc = (central angle / 360) x circumference of the circle. However, without knowing the central angle, we cannot determine the measure of arc CAD.

Therefore, we need to be provided with additional information such as the measure of another angle that is related to the central angle, or the length of a chord that subtends the arc in order to determine the central angle and the measure of arc CAD.

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Yes, any ramp with an angle of 4.8 degrees will have a slope ratio of 1:12.

The slope ratio is the ratio of the vertical rise to the horizontal run of the ramp, and it is equivalent to the tangent of the angle of inclination of the ramp.

The tangent of 4.8 degrees is approximately 0.0084, which means that for every 1 unit of vertical rise, there is 0.0084 units of horizontal run. To convert this to a ratio, we can multiply both sides by 100 to get:

1 unit of rise : 100 x 0.0084 = 0.84 units of run

Simplifying this ratio by dividing both sides by 0.84, we get:

1 unit of rise : 1.19 units of run

which is equivalent to a slope ratio of 1:12 (since 12 = 1/0.084). Therefore, any ramp with an angle of 4.8 degrees will have a slope ratio of 1:12.

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The amount of total and per-unit overhead allocated to each of the three products using overhead rate is equal to,

Total Per Unit Factory Overhead ,  Cost Factory Overhead Cost

Flutes $530   $1,060,000

Clarinets $795    $1,192,500

Oboes $397.5     $695,625

Total $1,722.5    $2,948,125

Budgeted factory overhead cost = $2,948,125

The single plantwide overhead rate

= Dividing the budgeted factory overhead cost by the total budgeted direct labor hours.

For this,

Flutes= 2,000×2

         = 4,000 hours

Clarinets= 1,500×3

              = 4,500 hours

Oboes= 1,750×1.5

          = 2,625 hours

Total direct labor hours = 11,125

Substitute the value we have,

⇒ Single plantwide overhead rate = $2,948,125 / (2,000 x 2.0 + 1,500 x 3.0 + 1,750 x 1.5)

= $2,948,125 / 11,125

= $265 per direct labor hour

To allocate overhead to each product

=Multiply the overhead rate by the budgeted direct labor hours per unit for each product.

Substitute the value we have,

Flutes,

$265 x 2.0 = $530 total overhead cost, $265 per unit

Clarinets,

$265 x 3.0 = $795 total overhead cost, $265 per unit

Oboes,

$265 x 1.5 = $397.5 total overhead cost, $265 per unit

And

Total factory overhead cost allocated = Estimated manufacturing overhead rate×  Actual amount of allocation base

For,

Flutes

= 4,000× 265

= $1,060,000

Clarinets

= 4,500×265

= $1,192,500

Oboes

= 2,625×265

= $695,625

This implies,

The total and per-unit overhead allocated to each product, rounded to the nearest dollar is,

Total Per Unit Factory Overhead ,  Cost Factory Overhead Cost

Flutes $530 $1,060,000

Clarinets $795 $1,192,500

Oboes $397.5  $695,625

Total $1,722.5 $2,948,125

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The above question is incomplete, the complete question is:

Bach Instruments Inc. makes three musical instruments: flutes, clarinets, and oboes. The budgeted factory overhead cost is $2,948,125. Overhead is allocated to the three products on the basis of direct labor hours. The products have the following budgeted production volume and direct labor hours per unit:

Budgeted Production Volume Direct Labor Hours Per Unit

Flutes 2,000 units 2.0

Clarinets 1,500 3.0

Oboes 1,750 1.5

a. Determine the single plantwide overhead rate.

$ per direct labor hour

b. Use the overhead rate in (a) to determine the amount of total and per-unit overhead allocated to each of the three products, rounded to the nearest dollar.

Total Per Unit

Factory Overhead Cost Factory Overhead Cost

Flutes $ $

Clarinets

Oboes

Total $

The surface area of the cone is approximately 793.10 cm².

What is cone?

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (usually circular) to a point called the apex or vertex.

What is area of cone?

The surface area of a cone is given by the formula:

Surface Area = πr² + πrℓ

where r is the radius of the circular base and ℓ is the slant height of the cone.

To find the surface area of a cone, we need to find the area of its base and the area of its lateral surface and then add them together.

The formula for the lateral surface area of a cone is given by:

L = πrℓ

where r is the radius of the base and ℓ is the slant height of the cone.

The formula for the area of the base of a cone is given by:

B = πr²

where r is the radius of the base.

Given the slant height ℓ = 19 and the radius r = 9, we can find the lateral surface area of the cone as follows:

L = πrℓ

= π(9)(19)

≈ 538.63 cm²

Next, we can find the area of the base of the cone as follows:

B = πr²

= π(9)²

≈ 254.47 cm²

Therefore, the surface area of the cone is:

A = B + L

≈ 793.10 cm²

So, the surface area of the cone is approximately 793.10 cm².

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The local maximum is at x = -9 with a value of 2575, and the local minimum is at x = 1 with a value of -17.

To find the local minimum and maximum of the given function, we need to find its critical points, where the derivative is zero or undefined.

[tex]f(x) = 2x^3 + 30x^2 - 54x + 5[/tex]

[tex]f'(x) = 6x^2 + 60x - 54[/tex]

Setting f'(x) = 0, we get:

[tex]6x^2 + 60x - 54 = 0[/tex]

[tex]x^2 + 10x - 9 = 0[/tex]

(x + 9)(x - 1) = 0

x = -9 or x = 1

Now, we need to determine if these critical points correspond to local minimum or maximum.

To do so, we can use the second derivative test. We calculate the second derivative of f(x):

f''(x) = 12x + 60

At x = -9:

f''(-9) = 12(-9) + 60 = -48 < 0

This means that f(x) has a local maximum at x = -9.

At x = 1:

f''(1) = 12(1) + 60 = 72 > 0

This means that f(x) has a local minimum at x = 1.

To find the values of the local minimum and maximum, we plug in the corresponding x-values into the original function:

[tex]f(-9) = 2(-9)^3 + 30(-9)^2 - 54(-9) + 5 = 2575[/tex]

[tex]f(1) = 2(1)^3 + 30(1)^2 - 54(1) + 5 = -17[/tex]

Therefore, the local maximum is at x = -9 with a value of 2575, and the local minimum is at x = 1 with a value of -17.

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The equation is y = x + 3 which shows the relationship of the two activities.

The equation to show the relationship between the number of hours Julie practices her violin each week (y) and the number of hours she studies (x) is:

y = x + 3

This means that the number of hours Julie practices her violin each week is equal to the number of hours she studies, plus three additional hours.

A linear equation is an equation that represents a straight line on a graph. It can be written in the form:

y = mx + b

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y=(x+3)^2-1

have a good day :)

Answer: F(x) = (x + 3)^2 - 1

Step-by-step explanation:

But there seems to be some missing information in your question. Please provide more context or details so that I can assist you accurately.
Hi! I'd be happy to help you evaluate the indefinite integral. Based on the provided terms and information, it seems like you want to evaluate the following integral:

∫x * sin(e * cos(x)) dx
To solve this integral, we can use integration by parts, which is defined as:
∫u dv = u * v - ∫v du
Let's choose u = x and dv = sin(e * cos(x)) dx. Then, we need to find du and v:
du = dx
v = ∫sin(e * cos(x)) dx

Unfortunately, the integral for v does not have a simple closed-form expression. However, you can use numerical methods or software (like Wolfram Alpha) to approximate it. Once you have an approximation for v, you can plug it back into the integration by parts formula to obtain an approximation of the original integral:
∫x * sin(e * cos(x)) dx ≈ x * v - ∫v dx

Keep in mind that this is an indefinite integral, so don't forget to add the constant of integration, C, to your final answer.

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There are different ways a person can make up a story about a word problem. The square root of 81 - 7 is 2. Hence the story is given below.

The hypothetical story goes like this: Mia was trying to figure out the length of the missing side of a square garden bed. She knew that the total area of the garden bed was 81 square feet. She also knew that she had already planted in a section of the garden bed that was 7 feet wide.

So, what will be the length of the missing side of the garden bed if Mia wants to make sure it is completely filled with soil. In order to solve this problem, Mia used the equation: the square root of 81-7=2. She plugged in the values she knew and solved for the missing side length. Therefore, The solution will be:= ✓81 - 7= 9 - 7= 2

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A story for the word problem is that what will be the length of the missing side of a square garden when the total area is 81 feet² and the width was 7 feet wide?

From the information, we are seeking a story problem that has the equation had the square root of 81 - 7 = 2.

This will be written as story for the word problem is that what will be the length of the missing side of a square garden when the total area is 81 feet ² and the width was 7 feet wide?

The length will be calculated thus :

= √ 81 - 7

= 9 - 7

= 2

The length of the missing side is 2 feet.

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The mechanic used 412 - 411.375 = 0.625 gallons of motor oil during the day.

To solve this problem, we need to convert both measurements to the same unit.

1 gallon = 8 pints (since there are 8 pints in a gallon)

So the mechanic started with:

412 gallons * 8 pints/gallon = 3,296 pints

And ended with:

5 pints

To find how much motor oil the mechanic used during the day, we can subtract the ending amount from the starting amount:

3,296 pints - 5 pints = 3,291 pints

To convert this back to gallons, we divide by 8:

3,291 pints / 8 pints/gallon = 411.375 gallons (rounded to three decimal places)

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Answer:

The order from smallest to largest price per package is: December, April, February.

Step-by-step explanation:

For the sale in February:

- Price per package = $4.49 ÷ 3 = $1.50 per package

For the sale in April:

- Price per package = $7.39 ÷ 5 = $1.48 per package

For the sale in December:

- Price per package = $5.88 ÷ 4 = $1.47 per package

A restaurant meal cost $90 and there was a 6% meals tax on the price of the meal. The meal tax was $5.40 and the total price of the meal with the meal tax was $95.40.

Find the meal tax, you need to calculate 6% of the $90 meal cost.
Convert the percentage to a decimal by dividing by 100, so 6% = 0.06.
Multiply the meal cost by the decimal. In this case, $90 × 0.06 = $5.40.
So, the meal tax was $5.40.
Find the total price of the meal with the meal tax, you need to add the meal tax to the original cost of the meal.
Add the meal tax to the original cost, so $90 + $5.40 = $95.40.
The total price of the meal with the meal tax was $95.40.

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If he drives at an average speed of 70 km/h for 45 min, the distance of the journey from Mr. Linden's home to his office is 52.5 km.

To find the distance of Mr. Linden's journey from his home to his office, we can use the formula:

Distance = Speed x Time

Since Mr. Linden drives at an average speed of 70 km/h for 45 minutes, we first need to convert the time to hours:

45 minutes = 0.75 hours

Now, we can plug in the values we have into the formula:

Distance = 70 km/h x 0.75 hours
Distance = 52.5 km

Therefore, the distance of the journey from Mr. Linden's home to his office is 52.5 km.

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The limit is equal to 10. We didn't need to use L'Hospital's rule or any other advanced method, as the limit was easily evaluate through simplification and direct substitution.

We can simplify the expression as follows:

[tex]lim x→5 (x + 5) x = lim x→5 (10) = 10[/tex]

Now, we can directly evaluate the limit by substituting 5 for x:

[tex]lim x→5 (x + 5) x = lim x→5 (10) = 10[/tex]

Therefore, the limit is equal to 10. We didn't need to use L'Hospital's rule or any other advanced method, as the limit was easily evaluatable through simplification and direct substitution.

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The fare for this flight would be: $225.

To determine the fare for the flight that was 350 miles with a residual of -105, we need to use the least-squares regression equation:

ý = 102.50 + 0.65x

where ý is the predicted fare and x is the distance in miles.

We know that the distance for this flight is 350 miles, so we can substitute x = 350 into the equation:

ý = 102.50 + 0.65(350)

ý = 102.50 + 227.50

ý = 330

Therefore, the predicted fare for this flight is $330.

The residual of -105 means that the actual fare for this flight was $105 less than the predicted fare based on the regression line. Therefore, the actual fare for this flight would be:

$330 - $105 = $225

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