Question 1(Multiple Choice Worth 2 points)
(Circle Graphs MC)

The circle graph describes the distribution of preferred transportation methods from a sample of 400 randomly selected San Francisco residents.

circle graph titled San Francisco Residents' Transportation with five sections labeled walk 40 percent, bicycle 8 percent, streetcar 15 percent, bus 10 percent, and cable car 27 percent

Which of the following conclusions can we draw from the circle graph?

Together, Streetcar and Cable Car are the preferred transportation for 168 residents.
Together, Walk and Streetcar are the preferred transportation for 55 residents.
Bus is the preferred transportation for 45 residents.
Bicycle is the preferred transportation for 50 residents.

Question 2(Multiple Choice Worth 2 points)
(Appropriate Measures MC)

The box plot represents the number of tickets sold for a school dance.

A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.

Which of the following is the appropriate measure of center for the data, and what is its value?

The mean is the best measure of center, and it equals 19.
The median is the best measure of center, and it equals 4.
The median is the best measure of center, and it equals 19.
The mean is the best measure of center, and it equals 4.

Question 3(Multiple Choice Worth 2 points)
(Comparing Data LC)

The histograms display the frequency of temperatures in two different locations in a 30-day period.

A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.

A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.

When comparing the data, which measure of center should be used to determine which location typically has the cooler temperature?

Median, because Desert Landing is symmetric
Mean, because Sunny Town is skewed
Mean, because Desert Landing is symmetric
Median, because Sunny Town is skewed

Question 4(Multiple Choice Worth 2 points)
(Appropriate Measures MC)

A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.

10, 11, 35, 39, 40, 42, 42, 45, 49, 49, 51, 51, 52, 53, 53, 54, 56, 59

A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 10 to 19, up to 2 above 30 to 39, up to 6 above 40 to 49, and up to 8 above 50 to 59. There is no shaded bar above 20 to 29.

Which measure of variability should the charity use to accurately represent the data? Explain your answer.

The range of 13 is the most accurate to use, since the data is skewed.
The IQR of 49 is the most accurate to use to show that they need more money.
The range of 49 is the most accurate to use to show that they have plenty of money.
The IQR of 13 is the most accurate to use, since the data is skewed.

Question 5(Multiple Choice Worth 2 points)
(Making Predictions MC)

A recent conference had 900 people in attendance. In one exhibit room of 80 people, there were 65 teachers and 15 principals. What prediction can you make about the number of principals in attendance at the conference?

There were about 820 principals in attendance.
There were about 731 principals in attendance.
There were about 208 principals in attendance.
There were about 169 principals in attendance.

Question 6(Multiple Choice Worth 2 points)
(Creating Graphical Representations LC)

A teacher was interested in the subject that students preferred in a particular school. He gathered data from a random sample of 100 students in the school and wanted to create an appropriate graphical representation for the data.

Which graphical representation would be best for his data?

Stem-and-leaf plot
Histogram
Circle graph
Box plot

Each number is classified according to its value in the given image.

We are given some numbers and we have to drag each number to the correct location according to its value. The numbers given are 4.2×[tex]10^{-6}[/tex], 2.1×[tex]10^{-3}[/tex],  3.1×[tex]10^{-2}[/tex], 3.2×[tex]10^{-5}[/tex], 3.5×[tex]10^{-4}[/tex], 5.8×[tex]10^{-3}[/tex], 5.2×[tex]10^{-4}[/tex].

We will classify these numbers in the categories given in the table.

(a) Now the numbers which are greater than 3.1×[tex]10^{-3}[/tex] are:

3.1×[tex]10^{-2}[/tex] and  5.8×[tex]10^{-3}[/tex].

(b) Numbers falling between 3.1 × [tex]10^{-3}[/tex]  and 4.3 × [tex]10^{-5}[/tex] are:

2.1×[tex]10^{-3}[/tex], 3.5×[tex]10^{-4}[/tex], and 5.2×[tex]10^{-4}[/tex]

(c) Numbers that are less than 4.3 × [tex]10^{-5}[/tex] are:

4.2×[tex]10^{-6}[/tex]and 3.2×[tex]10^{-5}[/tex]

So, the numbers are classified according to their values in the table given in the image.

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The total revenue over the two days is GH¢305.

We can represent the number of items sold and the cost for each item in matrices as follows:

[tex]\begin{equation}A = \begin{bmatrix} 3 & 4 & 1 \ 4 & 2 & 3 \end{bmatrix}, \quad B = \begin{bmatrix} 10 \ 15 \ 20 \end{bmatrix}\end{equation}[/tex]

Here, matrix A represents the number of items sold on each day, and matrix B represents the cost per item. To find the total revenue, we need to multiply the two matrices and then take the sum of all the elements in the resulting matrix:

[tex]\begin{equation}A \cdot B = \begin{bmatrix} 3 & 4 & 1 \ 4 & 2 & 3 \end{bmatrix} \cdot \begin{bmatrix} 10 \ 15 \ 20 \end{bmatrix} = \begin{bmatrix} 95 \ 140 \end{bmatrix}\end{equation}[/tex]

Therefore, the total revenue over the two days is GH¢(95 + 140) = GH¢305.

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Answer:

see explanation

Step-by-step explanation:

the arc BX is equal to the measure of the central angle BCX

the measure of the inscribed angle BNX is half the measure of its intercepted arc BX

The total weight of the cards inside the box is approximately 217.6 oz.

Each deck of cards weighs 3.4 oz, and there are 64 decks of cards in the box. Therefore, the total weight of the cards inside the box is 3.4 oz/deck x 64 decks = 217.6 oz. As the answer needs to be rounded to the nearest ounce, we round 217.6 to the nearest ounce, which gives us 218 oz.

However, the question asks for the weight of the cards, which is only accurate to one decimal place. Therefore, we round 217.6 to one decimal place, which gives us 217.6 oz. Hence, the total weight of the cards inside the box is approximately 217.6 oz.

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The only critical point of f(x) is x = -2.

a) To find the derivative of f(x), we can use the chain rule and the power rule of differentiation.

f(x) = 3sqrt(x + 2)^2

f'(x) = 3 * 2 * sqrt(x + 2) * (x + 2)^1/2-1 * (1)

Applying the power rule, we simplify the expression as:

f'(x) = 6(x + 2)^1/2

Therefore, the derivative of f(x) is f'(x) = 6(x + 2)^1/2.

b) To solve f'(x) = 0, we set f'(x) equal to zero and solve for x:

f'(x) = 6(x + 2)^1/2 = 0

Dividing both sides by 6, we get:

(x + 2)^1/2 = 0

Squaring both sides, we get:

x + 2 = 0

Subtracting 2 from both sides, we get:

x = -2

Therefore, the only critical point of f(x) is x = -2.

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Answer:

f(2) = 2

Step-by-step explanation:

We are given
f(x) = x² - 7x + 4

To find f(2), just plug in 2 wherever you see an x and simplify

f(2) = 3 · 2² - 7 · 2 + 4

= 3 · 4 - 7 · 2 + 4

= 12 - 14 + 4

= 2

The seconds, is it between the time plunk passes Ms. q and the time that plunk finishes the race is 7.5 seconds..

Flow Distance In the Mathematics or Quants part of any competitive test, time is one of the most well-liked and significant topics. For inquiries about a variety of subjects, including motion in a straight line, circular motion, boats and streams, races, clocks, etc.

The notion of Speed, Time, and Distance is frequently employed. Candidates should make an effort to comprehend how the variables of speed, distance, and time interact.

Ms. q being slow will get a head start for the race so,

3 second head start = 3 x 5 = 15 meters

There difference in speed is 8- 5 = 3 m/s          

Time required for the Plunk to catch up to Ms. q is:

15 / 3 = 5 seconds when P catches Q  

(this is 8 seconds after Q starts the race)

In 5 seconds Plunk runs   5 x 8 = 40 meters   this is when they are at the same point that is at time 8 seconds.

60 meters left in the race will take  Plunk :

60 m / 8 m/s = 7.5 seconds to finish the race.

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The trip will take another 1 hour to complete.

If a trip from Boston to the White Mountains of New Hampshire takes 2 3/4 hours, and you have already traveled 1/11 of the way, then the remaining distance is:

1 - 1/11 = 10/11 of the total distance.

To find how much longer the trip will take, we can use the proportion:

time taken for 10/11 of the trip = x (time taken for the whole trip)

distance traveled for 10/11 of the trip = 1 - 1/11 = 10/11 of the total distance

Since the time taken is proportional to the distance traveled, we can set up the following equation:

2 3/4 hours / (1 - 1/11) = x

where x is the time it will take for the whole trip.

Simplifying the left side of the equation, we get:

2 3/4 hours / (10/11) = x

Multiplying both sides by (11/10), we get:

x = (2 3/4 hours) × (11/10) = 3 1/4 hours

Therefore, the remaining time to complete the trip is:

3 1/4 hours - 2 3/4 hours = 1 hour

So the trip will take another 1 hour to complete.

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Answer:true

Step-by-step explanation:

Answer:

true

Step-by-step explanation

_______________________________

_______________________________

The correct answer is D. 29.50.

To find the wingspan of the actual airplane, we will use the given scale factor and the wingspan of the model airplane.
Given information:
Model airplane wingspan = 11.8 inches
Scale factor = 1 inch to 2.5 feet

Step 1: Convert the model wingspan to feet using the scale factor.
1 inch on the model represents 2.5 feet on the actual airplane. To convert 11.8 inches to feet, multiply by the scale factor.
Step 2: Calculate the actual wingspan.
Actual wingspan = Model wingspan * Scale factor
Actual wingspan = 11.8 inches * 2.5 feet/inch

Step 3: Perform the multiplication.
Actual wingspan = 29.5 feet
So, the wingspan of the actual airplane is 29.5 feet.

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Answer:

17.5 feet

Step-by-step explanation:

The picnic are shortest side is 5 units long on the scale drawing

Since each unit on the scale drawing is 1 inch, the shortest side length on the drawing is 5 inches

Each inch on the drawing corresponds to an actual size of 3.5 feet

Therefore 5 inches corresponds to 5 x 3.5ft = 17.5 feet

Therefore the actual length of the shortest side of the picnic area is 17.5 feet

Step-by-step explanation:

f(x)  =  2x^2 -12x + 16       to get to vertex form you will need to complete the square for 'x'....to do THAT you will need the x^2 coefficient to be '1'

Start like this:

2 (x^2 - 6x)    + 16        now complete the square

2 (x^2 - 6x +9)  - 18    + 16

f(x) =  2 (x-3)^2  - 2        Done.

To construct a square and a regular pentagon with equal side lengths of 0.5 inch, we need to use basic geometric constructions.

To construct a square and a regular pentagon with equal side length of 0.5 inch, follow these steps:

(a) Construct a Square:

Connect the endpoints of the four line segments to form a square.

(b) Construct a Regular Pentagon:

Repeat this process for all five vertices of the circle to form the regular pentagon.

A geometric construction is a method of drawing a figure using only a straightedge (an unmarked ruler) and a compass.

For the square, we start by drawing a horizontal line segment of length 0.5 inch. We then draw two perpendicular lines of length 0.5 inch each, meeting at the endpoints of the original line segment.

These two new line segments represent the adjacent sides of the square. We then repeat this process to create the remaining two sides of the square, and connect all four endpoints to form the complete square.

For the regular pentagon, we need to construct a circle with a radius of 0.5 inch. This will be the circumcircle of the pentagon, meaning that all five vertices of the pentagon will lie on the circle.

We draw a horizontal line through the center of the circle, and mark the points where the line intersects the circle. These five points will be the vertices of the pentagon.

We then draw line segments connecting adjacent vertices, using a compass to copy the length of each line segment from the previous one.

This process will create all five sides of the pentagon, and the figure will be a regular pentagon with equal side lengths of 0.5 inch.

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Option A The diameter and circumference of a circle have a proportional relationship is True .

Diameter

The diameter is the length acrοss the circle at its widest pοint, measured frοm center tο center . The radius, a related measurement, is a line that extends frοm the circle's centre tο its edge. The diameter is equivalent tο twice the radius. (A chοrd is a line that crοsses the circle but is nοt at the widest pοint.)

Circumference

The circle's perimeter, οr the distance arοund it, is knοwn as its circumference. Imagine encircling a circle with a string. Imagine taking the string οut and extending it in a straight line. This string's length, if measured, wοuld represent yοur circle's circumference.

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The advertisement generates the maximum rate of growth of car sales on the first day.

The rate of growth of sales is given by the derivative of N(t) with respect to time t:

dN/dt = 72t

To find the day when the maximum rate of growth of sales occurs, we need to find the value of t that maximizes this expression.

Setting dN/dt = 0, we get:

72t = 0

t = 0

However, since we are interested in finding the day when the maximum rate of growth of sales occurs, we need to consider the second derivative of N(t):

d2N/dt2 = 72

Since this is a positive constant, it tells us that N(t) is a convex function and has a minimum value at t = 0. Therefore, the maximum rate of growth of sales occurs on the day when t = 0, which corresponds to the first day of the advertisement.

Answer: 1. on day 12

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The majority of logs in the pile will have a weight close to the mean of 17 pounds, with a smaller number of logs having a weight that is farther away from the mean.

In statistics, the normal distribution is a commonly used continuous probability distribution.

It is also referred to as a Gaussian distribution, and it has a bell-shaped curve that is symmetrical around the mean.

The mean is the center of the distribution, and the standard deviation describes how spread out the data is around the mean.

In this case, the weights of logs in a wood pile are normally distributed with a mean of 17 pounds and a standard deviation of 3.4 pounds.

This means that the majority of logs in the pile will have a weight close to the mean of 17 pounds, with a smaller number of logs having a weight that is farther away from the mean.

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Answer: 9 x 10^4

Step-by-step explanation:

9 ten thousands in standard form is written like this: 90,000

To convert this into scientific notation, we simply count how many spaces we want to move the decimal point.

So far, our number looks like this with a decimal point: 90000.0

To make this number equal to 9, we have to move the decimal point 4 spaces to the left.

The 4 then becomes our exponent.

So now we have 9 by itself, and all we do is multiply it by 10 with an exponent of 4, to show you are multiplying 10 four times.

Therefore, 9 ten thousands written in scientific notation is 9 x 10^4

Answer:

52.5

Step-by-step explanation:

First, we can see that the base is 14m. The top is 7m, and the height is 5m. Since the formula for a trapezoid is

top + base / 2 ∙ h,

we plug in our numbers to get

7 + 14 / 2 ∙ 5.

We can solve to get

21 / 2 ∙ 5

10.5 ∙ 5

52.5

In the △ABC, the  the difference between bc and ab if ad = 1 is found to be 0.709.

We can use the angle bisector theorem to solve this problem. Let's denote the length of segment BD as x and the length of segment CD as y. Then, we can write,

BD/DC = AB/AC

Using the angle bisector theorem, we know that AB/AC = BD/DC, so we can substitute to get,

x/y = AB/AC

We can solve for AB by multiplying both sides by AC,

AB = x/y * AC

Now, we can use the law of sines to find the length of AC. We have,

sin(20°)/AB = sin(140°)/AC

Solving for AC, we get,

AC = AB * sin(20°) / sin(140°)

Substituting the expression we found for AB, we get,

AC = x/yACsin(20°) / sin(140°)

Simplifying, we get,

y = xsin(140°) / (sin(20°) - sin(140°))

We know that AD = 1, so we can use the Pythagorean theorem to find BC:

BC² = BD² + CD²

Substituting the expressions we found for BD and CD, we get,

BC² = x² + y²

Substituting the expression we found for y, we get,

BC² = x² + (xsin(140°) / (sin(20°) - sin(140°)))²

Simplifying, we get,

BC² = x²(1+sin²(140°)/(sin²(20°)-2sin(20°)sin(140°)+sin²(140°)))

Using the identity sin(140°) = sin(180° - 40°) = sin(40°), we can simplify further.

Now, we can substitute x = AD = 1 and sing a calculator, we can evaluate this expression to get,

BC² ≈ 2.917

Taking the square root, we get,

BC ≈ 1.709

Therefore, the difference between BC and AB is 0.709.

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The quotient is -58x2 + 131x - 234 with a remainder of -5898.To solve this problem, we need to use long division. The dividend is 223 + 3x2 + 5x - 4 and the divisor is 22 + 2 + 1, which simplifies to 25.

We start by dividing 2 into 22, which gives us 11. We then write 11 above the 2 and multiply it by 25, which gives us 275. We subtract 275 from 223, which gives us -52. We bring down the 3, which gives us -523. We then repeat the process by dividing 2 into 52, which gives us 26. We write 26 above the 5 and multiply it by 25, which gives us 650. We subtract 650 from -523, which gives us -1173. We bring down the 1, which gives us -11731. We divide 2 into 117, which gives us 58.

We write 58 above the x and multiply it by 25, which gives us 1450. We subtract 1450 from -1173, which gives us -2623. We bring down the -4, which gives us -26234. We divide 2 into 262, which gives us 131. We write 131 above the 5 and multiply it by 25, which gives us 3275. We subtract 3275 from -2623, which gives us -5898. Therefore, the quotient is -58x2 + 131x - 234 with a remainder of -5898.

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We can also pair 3 and 96, since 3 x 96 = 288. This means that the length of the rectangular prism could be 96 inches and the width could be 3 inches.

To find the dimensions of the rectangular prism, we can use the formula for the volume of a rectangular prism, which is:

V = l x w x h

where V is the volume, l is the length, w is the width, and h is the height.

We know that the volume of the box of tissues is 288 cubic inches. We want to find the length, width, and height.

We can start by listing all the factors of 288:

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288

We can see that some of these factors are repeated, so we can pair them up to find the dimensions of the rectangular prism.

For example, we can pair 2 and 144, since 2 x 144 = 288. This means that the length of the rectangular prism could be 144 inches and the width could be 2 inches.

We can also pair 3 and 96, since 3 x 96 = 288. This means that the length of the rectangular prism could be 96 inches and the width could be 3 inches.

We can continue pairing the factors until we find all the possible combinations. Once we have all the possible combinations, we can choose the one that makes the most sense based on the context of the problem (in this case, the dimensions of a box of tissues).

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The best point estimate is 15 hours. The 95% confidence interval for the population mean is (14.71, 15.29).

The best point estimate of the population mean is the sample mean, which is 15 hours since it was stated in the problem that the average time spent by college students on computer gaming is 15 hours.

To calculate the 95% confidence interval for the population mean, we use the formula:

CI = [tex]\bar{X}[/tex] ± z*(σ/√n)

where [tex]\bar{X}[/tex] is the sample mean, z is the z-score corresponding to the desired level of confidence (in this case, 95% corresponds to a z-score of 1.96), σ is the population standard deviation (given as 3), and n is the sample size (given as 350).

Plugging in the values, we get:

CI = 15 ± 1.96*(3/√350)

Simplifying, we get:

CI = 15 ± 0.29

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Answer:

[tex]y=-\dfrac{8}{x}[/tex]

Step-by-step explanation:

Inverse proportions can be represented by an equation in the form:

[tex]\boxed{y=\dfrac{k}{x}}[/tex]

where:

To write an expression for the graphed function, first input the given point (-2, 4) into the inverse proportion equation and solve for k:

[tex]\implies y=\dfrac{k}{x}[/tex]

[tex]\implies 4=\dfrac{k}{-2}[/tex]

[tex]\implies 4 \cdot (-2)=\dfrac{k}{-2}\cdot (-2)[/tex]

[tex]\implies -8=k[/tex]

[tex]\implies k=-8[/tex]

Therefore, the expression for the graphed function is:

[tex]\boxed{y=-\dfrac{8}{x}}[/tex]

Answer:

Set your calculator to degree mode.

Use the Law of Cosines.

x^2 = 18^2 + 15^2 - 2(18)(15)(cos 105°)

x^2 = 688.7623

x = 26.2 cm

The slope of the curve y = x^3 at point P(2, 8) is 12.

To find the slope of the curve y = x^3 at point P with coordinates (2, 8), we need to determine the derivative of the function and then evaluate it at x = 2.

Step 1: Find the derivative of the function y = x^3.
The derivative, dy/dx, represents the slope of the curve. To find the derivative of y = x^3, apply the power rule: d(x^n)/dx = n * x^(n-1).
So, dy/dx = 3 * x^(3-1) = 3x^2.

Step 2: Evaluate the derivative at the given point P (2, 8).
To find the slope at point P, substitute the x-coordinate (2) into the derivative: 3 * (2)^2 = 3 * 4 = 12.

Thus, the slope of the curve y = x^3 at point P(2, 8) is 12.

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Answer:36

Step-by-step explanation:

3 a minute
18 in 6 minutes
36 in 12
3:1

Therefore, there are 13 possible triangles that can be formed with sides of 7cm, 18cm and a whole number as the third side.

Using the triangle inequality law, Let's denote the sides of the triangle as a, b, and c. In this case, we have:

a = 7 cm

b = 18 cm

c = the third side, a whole number

Now, we apply the triangle inequality theorem to these sides:

a + b > c

=> 7 + 18 > c

=> 25 > c

a + c > b

=> 7 + c > 18

=> c > 11

b + c > a

=> 18 + c > 7

=> c > -11

Since c is a whole number, the third condition is always true, as there are no negative whole numbers. Therefore, we only need to consider the first two conditions:

11 < c < 25

Now, we list the whole numbers that fall within 11 and 25 within this range:

these are listed and counted

12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24

There are 13 whole numbers in this range. So, there are 13 possible triangles with sides of 7 cm and 18 cm, and a third side that is a whole number.

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Step-by-step explanation:

remember the original trigonometric triangle inside the norm circle (radius = 1).

sine is the up/down distance from the triangle baseline or corresponding circle diameter.

cosine is the left/right distance from the center of the circle (and the point of the angle).

for larger triangles and circles all these function results need to be multiplied by the actual radius (which we skipped for the norm circle, as a multiplication by 1 is not changing anything).

when you look at the triangle with K representing the angle, we have 10 a the cosine value, 24 as the sine value and 26 as the radius.

so,

10 = cos(K) × 26

cos(K) = 10/26 = 5/13

The surface area of the right rectangular prism is 880 cm².

Given Top and bottom measurements of the rectangular prism = 15 cm and 11 cm

The front and back measurements of the rectangular prism = 11cm and 11cm

The two sides measurements of the rectangular prism = 11 cm and 14 cm

To find the surface area of the rectangular prism, we have to substitute the above values in the below equation,

Surface area = (top*bottom) + (front*back) + (sides)

Surface area = (15 cm * 11 cm) + (11 cm * 11 cm) + (11 cm * 14 cm)

Surface area = 330 cm² + 242 cm²  + 308 cm²  

Surface area = 880cm²

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