activation functions: sigmoid 4 points possible (graded) recall that there are several different possible choices of activation functions . let's get more familiar with them and their gradients. what is the derivative of the sigmoid function, ? please write your answer in terms of and :

Answer:

  x = -4/3 or 3

Step-by-step explanation:

You want the solution to 3x² -5x -12 = 0 using the quadratic formula.

The given equation is written in standard form:

  ax² +bx +c = 0

Comparing the equations, we see that ...

The formula for the solution of the equation is ...

  [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

To find the values of x, use the numerical values of a, b, c in this formula:

  [tex]x=\dfrac{-(-5)\pm\sqrt{(-5)^2-4(3)(-12)}}{2(3)}=\dfrac{5\pm\sqrt{25+144}}{6}\\\\x=\dfrac{5\pm\sqrt{169}}{6}=\dfrac{5\pm13}{6}=\left\{\dfrac{-8}{6},\ \dfrac{18}{6}\right\}\\\\\boxed{x=\left\{-\dfrac{4}{3},\ 3\right\}}[/tex]

The earning of an employee is 8.25 dollars per hour and hourly pay rate is 8.25 dollars.

What is pay rate?

Pay rate refers to the amount of money an employer pays an employee for their work, typically expressed as an hourly, weekly, or monthly rate. It is the rate at which an employee is compensated for their time and labor, and can be influenced by a number of factors, such as job skills, experience, industry, location, and market demand for the particular role. The pay rate may also be subject to deductions for taxes, insurance, and other benefits provided by the employer.

Here,

The hourly pay rate of the employee can be calculated by dividing the earnings by the number of hours worked. Using the given equation, we can rewrite it as E = 8.25h

Dividing both sides by h,

E/h = 8.25

Therefore, the hourly pay rate of the employee is 8.25 dollars per hour.

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Part A: The function s(w) = 15w represents the number of seeds planted by the botanist as a function of the number of weeks w that planting occurs at the garden. The units of measurement for this function are seeds and weeks.

Part B: The function f(s) = 3s + 35 represents the number of flowers that can be expected to bloom as a function of the number of seeds planted by the botanist. The units of measurement for this function are flowers and seeds.

Part C: The composite function that represents the number of flowers the botanist can expect to bloom over a certain number of weeks is f(s(w)) = 3(15w) + 35 = 45w + 35.

Part D: To evaluate the composite function for 36 weeks, we substitute w = 36 into the function: f(s(36)) = 45(36) + 35 = 1635. Therefore, the botanist can expect 1635 flowers to bloom after 36 weeks of planting. The units of measurement for this answer are flowers.

1. Part A: What does the function s(w) = 15w represent in terms of the garden? What are the units of measurement for this function?

ANSWER: The function s(w) = 15w represents the total number of seeds planted by the botanist as a function of the number of weeks (w) that planting occurs at the garden. The units of measurement for this function are seeds.

2. Part B: What does the function f(s) = 3s + 35 represent in the context of the garden? What are the units of measurement for this function?

ANSWER:  The function f(s) = 3s + 35 represents the total cost (in dollars) of supplies needed to plant s seeds in the garden. The units of measurement for this function are dollars.

3. Part C:What composite function represents the number of flowers the botanist can expect to bloom over a certain number of weeks?

ANSWER:   the composite function that represents the number of flowers the botanist can expect to bloom over a certain number of weeks is f(s(w)) = 45w + 35.

4. Part D: Evaluate the composite function in Part C for 36 weeks.

ANSWER: the botanist can expect 1,655 flowers to bloom over 36 weeks.

Answer:

45

Step-by-step explanation:

Since 5 x 3 is 15, 15 x 3 = 45

45sq

Answer:

45 squared units

Step-by-step explanation:

So we know that the width of the rectangle is 3 units, and that the length of the rectangle is 5 times greater than the width. With simply maths we can find that the length we use the equation 3 multipled 5 = 15.

So we now know the length of the triangle is 15 units, so to find the area of a rectangle the equation would be: Length times width

3 units multiped by 15 units = x

x = 45 squared units

In the given Sample Space, there are 80 red gumballs in the entire population of 200 gumballs.

What exactly is a sample space?

In probability theory, a sample space is the set of all possible outcomes or results of an experiment or random process. It is denoted by the symbol "S". The sample space depends on the nature of the experiment or process and consists of all the possible values or events that could occur.

Now,

If the random sample of 25 gumballs contains 10 red gumballs, we can estimate the proportion of red gumballs in the entire population of 200 gumballs by using the formula:

proportion of red gumballs = number of red gumballs in sample / sample size

Substituting the given values, we get:

proportion of red gumballs = 10 / 25

= 0.4

This means that the proportion of red gumballs in the entire population of 200 gumballs is estimated to be 0.4. To find the estimated number of red gumballs in the entire population, we can use the formula:

number of red gumballs in population = proportion of red gumballs x population size

Substituting the given values, we get:

number of red gumballs in population = 0.4 x 200

= 80

Therefore, based on the random sample results, it is estimated that there are 80 red gumballs in the entire population of 200 gumballs.

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The area covered by the label is 188.4cm² and total surface area is 244.92cm².

A cylinder's total surface area is equal to the sum of all of its faces' surface areas. The cylinder's total surface area—the sum of its curved and circular areas—has a radius of "r" and a height of "h."

Here, we have

Given: A can of soup in the shape of a cylinder is 10 centimeters tall and has a diameter of 6 centimeters.

We have to find the total surface area of the can including the top and bottom.

The area covered by the label = πd×height

= π(6)×10

= 3.14×6×10

= 188.4

Total surface area =  πr² +  πr³ + 188.4

= 3.14(3)² +  3.14(3)³ + 188.4

= 244.92

Hence, the area covered by the label is 188.4cm²

and total surface area is 244.92cm².

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Answer:

0.125 in decimal 12.5 in percent

Step-by-step explanation:

in percent it will be 12.5

The critical value for a two-tailed test with a significance level of 0.01 and 13 degrees of freedom is approximately ±0.532.

A critical value is a point on a statistical distribution that is compared to a test statistic to determine whether to reject the null hypothesis

It is based on a significance level, which is the probability of rejecting the null hypothesis when it is actually true.

To find the critical value for a correlation coefficient at a significance level of 0.01 and 13 degrees of freedom, we can use Table A-6 in the textbook or online resources.

To determine if the data set has a statistically significant correlation, we need to calculate the correlation coefficient r and compare it to the critical value. We can use a calculator or spreadsheet software to calculate the correlation coefficient. Using the data from the table, we find that:

The mean of the age variable is 41.47, and the standard deviation is 19.16.

The mean of the resting heart rate variable is 66.73, and the standard deviation is 8.53.

The correlation coefficient between age and resting heart rate is 0.439.

Since the correlation coefficient (r=0.439) is greater than the critical value (±0.532), we can conclude that there is not a statistically significant correlation between age and resting heart rate at the 0.01 level of significance. This means that we cannot reject the null hypothesis that there is no correlation between age and resting heart rate in the population.

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The probability that the exam scores are at least 37 is 0.4013 or 40.13%

The probability that the exam scores are at least 37 can be calculated using the normal distribution function. To calculate the probability, we first need to standardize the variable using the formula z = (x - μ) / σ, where x is the value of interest (in this case, x = 37), μ is the mean, and σ is the standard deviation.

z = (37 - 36.12) / 3.53 = 0.25

Using a standard normal distribution table or a calculator, we can find the probability that a standard normal random variable is greater than or equal to 0.25, which is approximately 0.4013.

Therefore, the probability that the exam scores are at least 37 is 0.4013 or 40.13%

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The 95% confidence interval for the percentage of people with diabetes is equals to the (0.335, 0.1652).

We have, a sample of adults with

Sample size = 1000

Sample proportion, p = 25% = 0.25

We have to determine 95% confidence interval for the percentage of people with diabetes.Confidence interval formula for known value of sample proportion is written as CI = p ± Z ( √(p(1 - p)/n)

Now, for the 95% of confidence level or significance level, α = 1- 0.95 = 0.05 or α/2 = 0.25.

Using the normal distribution table, Z₀.₀₂₅ is 1.96. From above formula, confidence interval, CI = 0.25 ± 1.96( √0.25× 0.75/1000)

= 0.25 ± 1.96 ( 0.0433)

= 0.25 ± 0.0848

= ( 0.335, 0.1652)

Hence, required confidence interval is (0.335, 0.1652) .

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The mean absolute deviation of the data given in the pictograph is found to be 1, as the mean of the data is 3.5. MAD=1

What is MAD?

MAD acronym for mean absolute deviation of a data given in any form is the average magnitue between each data point and the mean of the given data. Stpeps for evaluating the mean absolute deviation:

Step i: Calculate the mean of the observations from the data given.

Step ii: Calculate magnitude between each observation & its mean. These are called absolute deviations.

Step iii: finally find the mean of the absolute deviations found.

The observations or frequency of the data in given pictograph is 2,3,4 and 5

The mean of the given data = (sum of data) ÷ (number of observations)

                                             =[tex]\frac{2+3+4+5}{4}[/tex]

                                              =[tex]\frac{14}{4}[/tex]

                                              =3.5

Absolute Deviations of each observation:

|3.5 - 2| = 1.5

|3.5 - 3| = 0.5

|3.5 - 4| = 0.5

|3.5 - 5| = 1.5

Mean of absolute deviations(MAD)= (sum of data) ÷ (number of observations)

                                                        =[tex]\frac{1.5+0.5+0.5+1.5}{4}[/tex]

                                                        =[tex]\frac{4}{4}[/tex]

                                                        =1

MAD of given data is 1.

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Refer to the attachment for complete question.

The probability that the metal ball lands on green or red is 10/19

In the game of roulette, the roulette wheel has 38 slots, numbered from 1 to 36, as well as a 0 slot and a 00 slot. Of the numbered slots, half are red and half are black, and the 0 and 00 slots are green.

So, the probability of the ball landing on green is 2/38, since there are two green slots out of the total of 38 slots on the wheel.

Similarly, there are 18 red slots and 18 black slots, so the probability of the ball landing on red is 18/38 and the probability of the ball landing on black is also 18/38.

To calculate the probability of the ball landing on green or red, we need to add the probabilities of the ball landing on green and the ball landing on red, since these two events are mutually exclusive (i.e., the ball cannot land on both green and red at the same time).

Thus, the probability of the ball landing on green or red is

2/38 + 18/38 = 20/38 = 10/19

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Answer:

9q + 18

Step-by-step explanation:

Heres each step by step process to simplify:

[tex]9(q+2)[/tex]

[tex]9\times q +9\times 2[/tex]

[tex]9q+18[/tex]

Answer: the corect answer is B

Step-by-step explanation: Please give me brainly

The soil will reach about 27 cm up the pot when it fills 75% of the pot's volume.

To determine how far up the pot the soil will reach, we need to first find the volume of the pot, then find 75% of that volume, and finally calculate the height of soil in the pot.
Step 1: Calculate the volume of the pot
The volume of a pyramid can be calculated using the formula V = (1/3) * B * h,

where V is the volume, B is the area of the base, and h is the height.

Since the base is a square with a side length of 36 cm, the area of the base (B) is 36 cm * 36 cm = 1296 cm².

Now, plug the values into the formula:
V = (1/3) * 1296 cm² * 36 cm = 15552 cm³
Step 2: Calculate 75% of the pot's volume
75% of the pot's volume can be calculated as:
Soil volume = 15552 cm³ * 0.75 = 11664 cm³
Step 3: Calculate the height of the soil in the pot
To find the height of the soil, we can use the same formula for the volume of the pyramid, but we will solve for the height[tex](h_soil)[/tex] this time:
11664 cm³ = (1/3) * 1296 cm² * [tex]h_soil[/tex]
Solve for h_soil:
[tex]h_soil[/tex] = (11664 cm³ * 3) / 1296 cm² ≈ 27 cm.

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Answer: Let's start by finding the dimensions of the original rectangular room.

We know that the area of the room is 60m², so we can write:

length x width = 60

We want to find the length and width of the original room, so let's call them "L" and "W", respectively. Then we can write:

L x W = 60

Now let's consider the modified room, where the length is 25% less and the width is 4m more. If the room is a square, that means the length and width are equal. Let's call this side length "S". Then we can write:

S x S = (L - 0.25L) x (W + 4)

Simplifying, we get:

S² = 0.75LW + 4(L - 0.25L)

Simplifying further, we get:

S² = 0.75LW + 3L

Now we can use the fact that LW = 60 to eliminate one variable. Substituting, we get:

S² = 45 + 3L

We want to find the length of the longest stick that can be put on the floor of the original room. This is the diagonal of the rectangle, which we can find using the Pythagorean theorem:

diagonal² = L² + W²

Substituting LW = 60, we get:

diagonal² = L² + (60/L)²

To maximize the diagonal, we can take the derivative of the right-hand side with respect to L and set it equal to zero:

d/dL (L² + (60/L)²) = 2L - 7200/L³ = 0

Solving for L, we get:

L³ = 3600

L = 15

Therefore, the length of the longest stick that can be put on the floor of the room is the diagonal, which is:

diagonal = sqrt(15² + (60/15)²) = sqrt(225 + 16) = sqrt(241) ≈ 15.52 meters

Step-by-step explanation:

Step-by-step explanation:

h=-16t^2+136t+8        For this quadratic  a = -16     b= 136     c = 8

 will reach max height at t = - b/2a = -  136/ (2*-16) = 4.25 s

Plug in 4.25 into the equation for 't' to find max height = 297 ft

Scarlett was charged $33 when she received her bill at the restaurant. She chose to tip 26% for the service she received. She must multiply the bill amount by 0.26 to determine the tip.

Tip = 0.26 x $33 = $8.58 Thus the total cost of the dinner plus the tip is: Total = $33 + $8.58 = $41.58  before tax for the lunch and tip. It should be noted that tax is not included in this computation. The tip amount may be calculated by multiplying the meal cost by the tip percentage: Tipping rate = 33 * 0.26 = 8.58 Therefore the entire cost of the lunch, including the tip, is: Cost total = 33 + 8.58 = 41.58 As a result, Scarlett's lunch plus tip, before tax, was $41.58.Scarlett was charged $33 when she received her bill at the restaurant. She chose to tip 26% for the service she received. She must multiply the bill amount by 0.26 to determine the tip: Tip = 0.26 x $33 = $8.58 Thus the total cost of the dinner plus the tip is: Total = $33 + $8.58 = $41.58  before tax for the lunch and tip. It should be noted that tax is not included in this computation. The tip amount may be calculated by multiplying the meal cost by the tip percentage: Tipping rate = 33 * 0.26 = 8.58 Therefore the entire cost of the lunch, including the tip, is Cost total = 33 + 8.58 = 41.58 As a result, Scarlett's lunch plus tip, before tax, was $41.58.Scarlett was charged $33 when she received her bill at the restaurant. She chose to tip 26% for the service she received. She must multiply the bill amount by 0.26 to determine the tip. Tip = 0.26 x $33 = $8.58 Thus the total cost of the dinner plus the tip is: Total = $33 + $8.58 = $41.58.

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Based on the IQR values, we can see that Player B is more consistent than Player A. Thus option B is correct.

To find the best measure of variability for the data, we need to compare the range and interquartile range (IQR) for both players.

For Player A:

Range = maximum value - minimum value [tex]= 7 - 1 = 6[/tex]

[tex]IQR = Q3 - Q1 = 3 - 1.5 = 1.5[/tex]

For Player B:

Range = maximum value - minimum value [tex]= 10 - 1 = 9[/tex]

[tex]IQR = Q3 - Q1 = 5 - 1.5 = 3.5[/tex]

The IQR is generally considered a better measure of variability than the range because it is not influenced by extreme values. Therefore, the best measure of variability for this data is the interquartile range (IQR).

Based on the IQR values, we can see that Player B is more consistent than Player A.

Therefore, the correct answer is: Player B is the most consistent, with an IQR of  [tex]3.5[/tex]  .

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The parts of the circle when named are listed below

An inscribed angle is an angle between two chords

So, we have

inscribed angle = Angle GJI

A major arc is an arc with the greater central angle

So, we have

Major arc = AJG

Minor arc = GFH

Next, we have

GH = 55 degrees i.e angle at center = arc

GJI = 180 degrees i.e. semicircle

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Answer:

3 is greater than or equal to value a.

Step-by-step explanation:

The final answer is: 5 quarts, 1 pint, and 0.5 cups based on conversion.

To add these two quantities, we first need to convert all of the measurements to a common unit. Since we are adding pints and cups, we can convert everything to cups, and then convert back to pints and quarts as needed.

5 pints is equal to 5 x 2 = 10 cups (since there are 2 cups in a pint).

2 cups is 2 cups.

3 pints is equal to 3 x 2 = 6 cups.

3 cups is 3 cups.

Now we can add the quantities:

10 cups + 2 cups + 6 cups + 3 cups = 21 cups

To convert 21 cups back to pints and quarts, we can use the fact that there are 2 cups in a pint, and 4 cups in a quart.

First, we can divide 21 by 4 to find the number of quarts:

21 cups ÷ 4 = 5 with a remainder of 1 cup

So we have 5 quarts and 1 cup. To convert the remaining cup to pints, we can divide by 2:

1 cup ÷ 2 = 0.5 pints

Therefore, the final answer is:

5 quarts, 1 pint, and 0.5 cups.

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Assuming the shape of the balloon remains the same, the volume of the balloon is directly proportional to the cube of its height. Therefore, we can use the following proportion:

(air volume)₁ / (height)₁³ = (air volume)₂ / (height)₂³

where:

(air volume)₁ = 108 in.³ (when the height is 4 in.)

(height)₁ = 4 in.

(height)₂ = 8 in.

We can solve for (air volume)₂ as follows:

(air volume)₂ = (air volume)₁ × (height)₂³ / (height)₁³

(air volume)₂ = 108 in.³ × (8 in.)³ / (4 in.)³

(air volume)₂ = 108 in.³ × 64 / 64

(air volume)₂ = 108 in.³

Therefore, the balloon must hold 108 in.³ of air for the clown's face to be 8 in. tall.

With the given values, the surface area of the rectangular prism is 544 square units.

A prism is a three-dimensional geometric shape that consists of two identical parallel polygonal bases and a set of parallelograms connecting the corresponding sides of the two bases.

In general, the area of any prism can be found by adding together the areas of its bases and lateral faces.

To find the surface area of the rectangular prism represented by the given net, we need to calculate the area of each face and add them together. The rectangular prism has six faces, so we need to find the area of each face.

The top and bottom faces are rectangles with dimensions 8 x 6, so each has an area of 8 x 6 = 48 square units. There are two of these faces, so their combined area is 2 x 48 = 96 square units.

The front and back faces are rectangles with dimensions 8 x 16, so each has an area of 8 x 16 = 128 square units. There are two of these faces, so their combined area is 2 x 128 = 256 square units.

The left and right faces are rectangles with dimensions 16 x 6, so each has an area of 16 x 6 = 96 square units. There are two of these faces, so their combined area is 2 x 96 = 192 square units.

Therefore, the total surface area of the rectangular prism represented by the given net is:

96 (top and bottom) + 256 (front and back) + 192 (left and right) = 544 square units.

So, the surface area of the rectangular prism is 544 square units.

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The tree stump is approximately 2.64 feet tall. This is solved using the Tangent Function.

Let's assume that the height of the tree stump is h feet.

Since the roots of the tree extend out from the base of the tree the same distance that the stump is tall, the distance between the end of the roots and the top of the stump is also h feet.

Therefore, the total distance covered by the 2x4's is 2h feet (h feet up to the top of the stump and h feet down to the end of the roots).

We can use the tangent function to find the angle of incline. The tangent of an angle is equal to the opposite side divided by the adjacent side.

In this case, the opposite side is h and the adjacent side is 5 feet. So, we have:

tan θ = h/5

To maximize the angle of incline, we want to maximize the value of θ. This occurs when tan θ is as large as possible.

Since the tangent function is an increasing function, we can find the largest possible value of tan θ by finding the largest possible value of h.

Solving for h in the equation tan θ = h/5, we get:

h = 5 tan θ

Since the length of the boards is 5 feet, we know that:

2h = 5

Substituting for h, we get:

2(5 tan θ) = 5

10 tan θ = 5

tan θ = 0.5

Using a calculator or a table of tangent values, we can find that the angle whose tangent is 0.5 is approximately 26.57 degrees.

Therefore, the height of the tree stump is:

h = 5 tan θ

h = 5 tan 26.57

h ≈ 2.64 feet

So, the tree stump is approximately 2.64 feet tall.

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Based on the calculated z-score of 17.07, and a corresponding p-value, the process would be considered out of control at the 0.05 significance level.

To determine whether the process is in control or out of control, we can use a hypothesis test with a significance level of 0.05. The null hypothesis (H0) is that the process is in control, and the alternative hypothesis (Ha) is that the process is out of control.

We can calculate the z-score as follows:

z = (x - μ) / (σ / sqrt(n))

where x is the observed value (118), μ is the mean (104), σ is the standard deviation (8.2), and n is the sample size (1).

Plugging in the values, we get:

z = (118 - 104) / (8.2 / sqrt(1)) = 17.07

The corresponding p-value for this z-score is virtually zero. Since the p-value is less than 0.05, we reject the null hypothesis and conclude that the process is out of control.

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FIFA created a football with a 21 cm circumference out of leather. If 10% of the leather is wasted, the cost of leather with labour is Rs. 25 per square centimetre. All total, Rs. 31,173.90 worth of leather was purchased to produce one football.

The diameter of the leather used to make the football is 21 cm, so its radius is 10.5 cm (half of the diameter).

The formula for calculating a sphere's surface area can be used to determine how much leather is required to produce a football:

Surface area = [tex]4\pi r^2[/tex]

Surface area = 4π[tex](10.5)^2[/tex]

Surface area = 1385.44 sq. cm

If 10% of the leather is wasted, then the actual amount of leather used is 90% of the total leather bought. So, we need to calculate the cost of 90% of the leather:

Cost of leather = 90% of the total leather cost

Cost of leather = 0.9 x 1385.44 sq.cm x Rs. 25/sq.cm

Cost of leather = Rs. 31,173.90

Therefore, the total cost of the leather bought to make the football, including the labour cost, is Rs. 31,173.90.

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a) It takes 350 cubic centimetres to fill the rectangular prism.

b) The capacity of the rectangular prism is 350 cm³.

c) It takes 340 square centimetres to cover the rectangular prism.

d) The rectangular prism contains 350 cm³.

a) We need to find the volume of the rectangular prism to determine how much it takes to fill it. The following formula provides the volume:

V = l × w × h

where the prism's length, breadth, and height are indicated by l, w, and h, respectively.

Substituting the given values, we get:

V = 5 cm × 7 cm × 10 cm

V = 350 cm³

Therefore, it takes 350 cubic centimetres to fill the rectangular prism.

b) The capacity of the rectangular prism is the same as its volume, which we calculated in part (a) to be 350 cm³.

c) To cover the rectangular prism, we need to find its surface area. The following formula determines a rectangular prism's surface area:

SA = 2lw + 2lh + 2wh

where the prism's length, breadth, and height are indicated by l, w, and h, respectively.

Substituting the given values, we get:

SA = 2(5 cm × 7 cm) + 2(5 cm × 10 cm) + 2(7 cm × 10 cm)

SA = 340 cm²

Therefore, it takes 340 square centimetres to cover the rectangular prism.

d) The rectangular prism contains the same amount of volume as its capacity, which we calculated in part (b) to be 350 cm³.

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