a report on high school graduation stated that 85 percent of high school students graduate. suppose 3 high school students are randomly selected from different schools. what is the probability that exactly one of the three graduates? question 4 options: 0.019 0.003 0.614 0.057 0.850

Therefore, we can be 99% confident that the true difference in mean amount of food Piper eats when she is offered Pick-a-Pair and when she is offered Pickled Peppers is between 0.7 and 5.1 grams.

A confidence interval is a statistical measure used to estimate the range of values within which a true population parameter is likely to fall with a certain level of confidence. It is often used in inferential statistics to assess the precision and reliability of a sample estimate of a population parameter, such as the mean, proportion, or standard deviation.

Here,

To construct a confidence interval for the difference in mean amount of food Piper eats when she is offered Pick-a-Pair and when she is offered Pickled Peppers, we can use a two-sample t-test. The null hypothesis is that there is no difference in mean amount of food Piper eats between the two brands, and the alternative hypothesis is that there is a difference. We can use a 99% confidence level, so our significance level is α = 0.01. First, we can calculate the sample means, sample standard deviations, and sample sizes for each brand:

For Pick-a-Pair:

Sample mean: x1 = 85.2

Sample standard deviation: s1 = 3.45

Sample size: n1 = 31

For Pickled Peppers:

Sample mean: x2 = 82.1

Sample standard deviation: s2 = 4.62

Sample size: n2 = 30

Next, we can calculate the pooled standard deviation, sp, using the formula:

sp = √(((n1 - 1)s1² + (n2 - 1)s2²) / (n1 + n2 - 2))

sp = sqrt(((31 - 1)(3.45)² + (30 - 1)(4.62)²) / (31 + 30 - 2))

sp = 4.019

Then, we can calculate the t-statistic using the formula:

t = (x1 - x2) / (sp * √(1/n1 + 1/n2))

t = (85.2 - 82.1) / (4.019 * √(1/31 + 1/30))

t = 1.864

Using a t-table with degrees of freedom (df) = n1 + n2 - 2 = 59 and a significance level of 0.01, we find the critical values to be ±2.660. Since our t-statistic of 1.864 is within this range, we fail to reject the null hypothesis.

Finally, we can construct the confidence interval using the formula:

CI = (x1 - x2) ± t*(sp * √(1/n1 + 1/n2))

CI = (85.2 - 82.1) ± 2.660*(4.019 * √(1/31 + 1/30))

CI = (0.7, 5.1)

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Answer: well it could be

2/5 or 8/20 or 1/5 or 16/40

Step-by-step explanation:

The Fundamental Pythagorean Identity in trigonomety sin²(x)+cos²(x)=1

Using  the Pythagorean Identity: [tex]\frac{1-2cos^2x}{sinxcosx}=tanx-cotx[/tex] ,

Hence prove.

Trigonometry formulas can be used to address many different kinds of issues. These issues could involve Pythagorean identities, product identities, trigonometric ratios (sin, cos, tan, sec, cosec, and cot), etc. Many formulas, such as those involving co-function identities (shifting angles), sum and difference identities, double angle identities, half-angle identities, etc., as well as the sign of ratios in various quadrants,

We know that the Pythagorean theorem,

sin²(x)+cos²(x)=1

We have

1-2cos²x = sin²(x)+cos²(x) -2cos²x

1-2cos²x = sin²(x)-cos²(x)

[tex]\frac{1-2cos^2x}{sinxcosx}=tanx-cotx[/tex]

To prove this take the right-hand sides

[tex]\frac{sin^2x}{sinxcosx}-\frac{cos^2x}{sinxcosx}\\\\=\frac{sinx}{cosx}-\frac{cosx}{sinx}\\\\= tanx-cotx[/tex]

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Answer:

The median increases to 7

Step-by-step explanation:

List the numbers in chronological order,

5, 5.5, 6, 6.5, 6.5, 7, 7.5, 8, 8, 8.5

As of now, the median is 6.75.

When a shoe size of 9 is added, we have

5, 5.5, 6, 6.5, 6.5, 7, 7.5, 8, 8, 8.5, 9

Now, the median is 7.

The answer is

x1 = -1 + square root 7

x2 = - 1 - square root 7

Answer:

The answer is 41

Step-by-step explanation:

82 / 2

The length of side a is approximately 24.1 units.

As per the given information in question:

side b = 20side c = 12angle A = [tex]42^{0}[/tex]

Here we have to find the Length of side a.

The Law of Cosines is given by the equation: c² = a² + b² - 2ab cos(C) where a, b, and c are the sides of a triangle, and C is the angle opposite side c.

To find the length of side a, given side b = 20, side c = 12, and angle A = 42 degrees, we can use the Law of Sines.

The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is the same for all three sides. In this case, we have:
a / sin(A) = b / sin(B) = c / sin(C)
We are given side b, side c, and angle A, so we can use the formula to find the length of side a.

First, let's find angle B using the given information:
a / sin(42) = 20 / sin(B)
Since we have one angle (A) and the sides opposite to it (a) and another side (b), we can find angle B:
sin(B) = 20 x sin(42) / a
Now we can find angle C using the fact that the sum of angles in a triangle is always 180 degrees:
angle C = 180 - angle A - angle B
angle C = 180 - 42 - angle B
Now we have angle C, and we can use the Law of Sines again to find the length of side a:
a / sin(42) = 12 / sin(angle C)
Solve for a:
a = 12 x sin(42) / sin(angle C)
Now, plug in the values of angle B and angle C that we found earlier and solve for a:
a = 12 x sin(42) / sin(180 - 42 - angle B)
a ≈ 24.1 units.

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On solving the provided question we can say that Therefore, the radius of the circle is 9.

The radius of a circle is a line segment that joins the center of the circle to any point on its circumference. It is essentially half of the diameter of the circle. The radius is denoted by the letter 'r' and is used to calculate many other properties of the circle, such as its area, circumference, and diameter.

The length of the radius is an important characteristic of a circle, as it determines the size and shape of the circle. If two circles have the same radius, they will have the same size and shape. The radius is also used in many real-world applications, such as calculating the distance between two points on a map or the distance between the center of the earth and a satellite in orbit.

The equation [tex](x+8)^{2} +(y-2)^{2} =81[/tex]  represents a circle with center (-8, 2) and radius 9.

[tex](x-h)^{2} +(y-k)^{2} =r^{2}[/tex]

Comparing this to the given equation, we see that [tex]h = -8, k = 2[/tex], and [tex]r^2 = 81, so r = 9.[/tex]

Therefore, the radius of the circle is 9.

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The maximum point of this quadratic function f(t) = -16t² + 80t + 64 is equal to 164.

In this exercise, you are required to determine the maximum value of the given quadratic functions that is written in standard form. In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:

y = a(x - h)² + k

Where:

For the given quadratic function f(t) = -16t² + 80t + 64, the axis of symmetry can be calculated as follows:

Axis of symmetry, Xmax = -b/2a

Axis of symmetry, Xmax = -(80)/2(-16)

Axis of symmetry, Xmax = -80/-32

Axis of symmetry, Xmax = 2.5

For the vertex, we have:

f(t) = -16t² + 80t + 64

f(2.5) = -16(2.5)² + 80(2.5) + 64

f(2.5) = 164.

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Answer:

$512.50

Step-by-step explanation:

500 + (.025 x 500)  2.5% move the decimal two places to the left.

500 + 12.50 = 512.50

Helping in the name of Jesus.

This represents the direction and degree of rotation utilised to make the image, which is 90 degrees anticlockwise.

When an item or form is rotated about a fixed point, generally the origin or a specified point in the plane, the amount of rotation that takes place is referred to as the degree of rotation. Angles are measured in degrees, where one full rotation equals 360 degrees. The amount of angle shift, expressed in degrees, that occurs when an item or shape is rotated is known as the degree of rotation. A shape has been turned a quarter of a full rotation anticlockwise, for instance, if it is rotated 90 degrees in that direction. Similar to this, a form has completed one-half of a full rotation if it is rotated 180 degrees.

given

The graph suggests that the image was rotated 90 degrees anticlockwise and in the other manner to make.

Compare the figure's initial placement (the grey triangle) to its final placement to see this (the red triangle).

One of the vertices on the grey triangle is pointing upward, and the other two are pointing to the right and left.

The red triangle's up-pointing vertex remains after the transformation, but the other two vertices now point down and up-left, respectively.

This represents the direction and degree of rotation utilised to make the image, which is 90 degrees anticlockwise.

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Tt represents the points 3 and 7 on the x-axis, since they are both 2 units away from 5 and equation form is | x - 5 | = 2.

What is equation?

An equation is a mathematical statement that shows that two expressions are equal. It typically contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

An absolute value equation that has a solution set containing the numbers 3 and 7 on the x-axis.

One possible equation is:

| x - 5 | = 2

This equation represents the set of all numbers on the x-axis that are 2 units away from the number 5.

In other words, it represents the points 3 and 7 on the x-axis, since they are both 2 units away from 5.

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Answer:

|x+5|=2 is the equation

Pie chart is the  best to show the percentage of gases on earth's atmosphere.

A pie chart, sometimes known as a circle chart, is a circular statistical visual that shows numerical proportion through slices of data. Each slice's arc length in a pie chart is proportional to the quantity it shows, as are its center angle and area. Although it was given that name because it resembles a slice of pie, there are other ways to serve it.

Nitrogen accounts for 78% of the atmosphere, oxygen 21% and argon 0.9%. Gases like carbon dioxide, nitrous oxides, methane, and ozone are trace gases that account for about a tenth of one percent of the atmosphere.

The Pie chart is the best to show the percentage of gases on earth's atmosphere.

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Answer:

u = 10ft

Step-by-step explanation:

7ft x 8ft = 56. 560 ÷ 56 = 10.
Therefore, u = 10ft

The statement " if we design a study to have no more than a 10% chance of a type 2 error, then the statistical power of the study equals 90%" is true because achieving a 10% chance of a type 2 error, or a 90% power, means that the study has a high probability of detecting a true effect if it exists

Statistical power is defined as the probability of correctly rejecting a false null hypothesis, or in other words, the probability of detecting a true effect if it exists. A type 2 error, on the other hand, occurs when we fail to reject a false null hypothesis, or when we fail to detect a true effect that actually exists.

Therefore, if we design a study to have no more than a 10% chance of a type 2 error (i.e., 90% power), then we are saying that the probability of detecting a true effect, if it exists, is 90%. This is equivalent to saying that the study has 90% power to detect the effect.

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The Poisson distribution is a discrete probability distribution, the probability of getting a value between 5 and infinity is effectively zero.

This problem can be solved using the Poisson distribution, which is a discrete probability distribution that gives the probability of a given number of events occurring in a fixed interval of time or space, if these events occur independently and at a constant average rate.

Let X be the number of births in a minute, then X follows a Poisson distribution with a mean of λ=3.

(a) The probability of exactly 5 births in a minute is:

P(X=5) = (e^(-λ) * λ^5) / 5! = (e^(-3) * 3^5) / 5! = 0.1008 (rounded to four decimal places)

(b) The probability of at least 5 births in a minute is:

P(X>=5) = 1 - P(X<5) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)]

To find the probabilities for X=0,1,2,3,4, we can use the Poisson formula:

P(X=k) = (e^(-λ) * λ^k) / k!

P(X=0) = e^(-3) = 0.0498 (rounded to four decimal places)

P(X=1) = e^(-3) * 3 / 1! = 0.1494 (rounded to four decimal places)

P(X=2) = e^(-3) * 3^2 / 2! = 0.2240 (rounded to four decimal places) P(X=3) = e^(-3) * 3^3 / 3! = 0.2240 (rounded to four decimal places) P(X=4) = e^(-3) * 3^4 / 4! = 0.1680 (rounded to four decimal places)

Therefore,

P(X>=5) = 1 - [0.0498 + 0.1494 + 0.2240 + 0.2240 + 0.1680] = 1 - 0.8152 = 0.1848 (rounded to four decimal places)

(c) The probability of more than 5 births in a minute is:

P(X>5) = 1 - P(X<=5) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)]

To find the probability for X=5, we can use the Poisson formula as in part (a):

P(X=5) = (e^(-λ) * λ^5) / 5! = (e^(-3) * 3^5) / 5! = 0.1008 (rounded to four decimal places)

Therefore,

P(X>5) = 1 - [0.0498 + 0.1494 + 0.2240 + 0.2240 + 0.1680 + 0.1008] = 1 - 1.0160 = 0 (rounded to four decimal places)

Since the Poisson distribution is a discrete probability distribution, the probability of getting a value between 5 and infinity is effectively zero.

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The linear equations are x + y = 679, 4x + 7y = 3370 and  586 non-students attended the play.

What is a linear equation, exactly?

A linear equation is a mathematical equation that describes a straight line when plotted on a graph. It is an equation in which the highest power of the variable is one. Linear equations are commonly written in the form of y = mx + b, where "x" and "y" are variables, "m" is the slope of the line, and "b" is the y-intercept. Linear equations can be used to model many real-world situations, such as distance and speed, cost and revenue, and temperature and time.

Now,

a) Let x = student tickets sold and y = number of non-student tickets sold. Then we have the following system of linear equations:

x + y = 679 (the total number of tickets sold is 679)

4x + 7y = 3370 (the total revenue from ticket sales is $3370)

b) To solve for y, we can use the first equation to get:

y = 679 - x

then,

4x + 7(679 - x) = 3370

Simplifying and solving for x, we get:

3x = 2363

x = 787

So 787 student tickets were sold. To find the number of non-student tickets sold, we can use the equation y = 679 - x:

y = 679 - 787 = -108

Since it doesn't make sense to have a negative number of non-student tickets sold, we made an error somewhere. Looking at the problem again, we realize that the equation should be:

x + y = 679 (the total number of tickets sold is 679)

4x + 7y = 3370 (the total revenue from ticket sales is $3370)

where y represents the number of student tickets sold and x represents the number of non-student tickets sold. With this correction, we get:

y = 679 - x

4(679 - x) + 7x = 3370

Simplifying and solving for x, we get:

3x = 1759

x = 586.33

x = 586

So 586 non-student tickets were sold.

Which means 586 non-students attended the play.

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A random sample of students at a middle school shows that 10 students prefer listening to rock, 15 students prefer listening to hip hop and 25 students prefer no music, while they exercise. the given sample is unbiased.

Ten students at a middle school like to listen to rock, fifteen students prefer to listen to hip-hop, and twenty-five students prefer no music when they exercise.

The given sample is unbiased.

The term "biassed samples" refers to those that were created using biassed sampling methods. A biased sample is most likely not representative of the population. On the other hand, an "unbiased sample" is a sample that was created using a non-biased sampling method. An impartial sample is more likely to produce a representative sample. As was previously stated, a representative sample may not always be produced by an unbiased sampling technique, especially if the sample size is too small.

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Probability is a branch of mathematics that deals with the likelihood or chance of an event occurring, expressed as a number between 0 and 1. It is used to analyze and quantify the uncertainty associated with random events or processes.

To find the probability of choosing a number from the sample space that contains both 5 and 7, we need to count the number of outcomes that satisfy this condition and divide by the total number of possible outcomes in the sample space.

From the tree diagram, we can see that there are four possible two-digit numbers that contain both 5 and 7: 57, 75, 56, and 65.

The total number of possible outcomes in the sample space is the number of ways to arrange the four digits in a two-digit number, which is 4 × 3 = 12 (since there are 4 choices for the first digit and 3 choices for the second digit, once the first digit is chosen).

Therefore, the probability of choosing a number from the sample space that contains both 5 and 7 is:

4/12 = 1/3

So the probability of choosing a number from the sample space that contains both 5 and 7 is 1/3 or approximately 0.33.

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For set A: Mean = 6, Mean absolute deviation = 1 and For set B: Mean = 7, MAD = 1.33 based on deviations.

We must first determine the average or mean of the data points in order to calculate the mean and mean absolute deviation (MAD) of two data sets. The mean is calculated by dividing the total number of data points by their sum. The absolute deviation of each data point from the mean must then be determined, and the average of these deviations is used to get the MAD.

Using set A:

Mean = (4 + 6 + 7 + 8 + 5 + 6) / 6 = 6

MAD = (|4-6| + |6-6| + |7-6| + |8-6| + |5-6| + |6-6|) / 6 = 1

Using set B:

Mean = (5 + 7 + 4 + 8 + 9 + 9) / 6 = 7

MAD = (|5-7| + |7-7| + |4-7| + |8-7| + |9-7| + |9-7|) / 6 = 1.33

It is clear from a comparison of the two sets that set B has a higher mean than set A, indicating that set B's values are generally higher. Moreover, set B's MAD is larger than set A's, suggesting that set B's values are more dispersed or volatile. We can therefore say that set B has larger and more varied values than set A.

It is crucial to keep in mind that the mean and MAD are merely two indicators of central tendency and dispersion, respectively, and that to thoroughly examine and contrast data sets, they should be combined with additional statistical indicators and visualizations.

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Answer:

[tex] \ \frac{1}{2} (5 \frac{1}{4} + 7)(2) = 12 \frac{1}{4} [/tex]

A is correct.

The total amount of juice in 16 servings is 2/3 + 1/3 = 1 cup, so the total amount of juice is 16 x 1 = 16 cups. This means there are 16 cups of fruit punch in 16 servings.

This question shows how to calculate the total quantity of a combination by multiplying the amount of each component by its respective ratio and then combining them together. It also emphasizes the need of understanding ratios and unit conversions while preparing recipes and measuring food.

To determine how many cups of fruit punch are in 16 servings, multiply the total amount of juice in 16 servings by 16.

For each serving, there are 2/3 cup of pineapple juice and 1/3 cup of cranberry juice, so the total amount of juice in each serving is:

2/3 + 1/3 = 1 cup

Therefore, the total amount of juice in 16 servings is:

16 x 1 = 16 cups

So there are 16 cups of fruit punch in 16 servings.

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He received Glhf 25,967.23 as interest at the end of 7 years. The total amount he received at the end of 7 years is GhC 39,067.23.

Simple interest is the interest the lender pays the borrower on the loan. It includes principal only and does not include interest. Simple interest rates are not just for certain loans. This is also the type of interest that banks pay on customers' savings.

a. To find the interest he received at the end of 7 years, we first need to calculate the amount he had at the end of 4 years:

   A = P(1 + r/n) (nt)

⇒ A = 14100 (1+ 0.08)(1× 4)

⇒ A = 19628.61

So, he had GhC 19,628.61 at the end of 4 years. He then transferred this amount to another bank offering 12% compound interest per annum. We can use the same formula to find the amount he will have after 7 years:

 A = P(1 + r/n) (nt)

⇒ A = 19628.61( 1 + 0.12/1) (1×7)

⇒ A = 40067.23

Therefore, the amount he received at the end of 7 years is GhC 40,067.23.

To find the interest he received at the end of 7 years, we subtract the principal amount:

Interest = A - P

Interest = 40067.23 - 14100

Interest = 25,967.23

So, he received GhC 25,967.23 as interest at the end of 7 years.

b. The total amount he received at the end of 7 years is the sum of the principal and the interest:

Total amount = P + Interest

Total amount = 14100 + 25,967.23

Total amount = 39,067.23

Therefore, the total amount he received at the end of 7 years is GhC 39,067.23.

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The correct statement is that "P is above sea level and City R is below sea level True"

To determine the position of the points observe the given picture. Here we can observe that the point which has positive values are placed above the sea level and the points which have negative values are placed below the sea level.

The elevation in Feet of these 3 cities is marked on the number line

The point 0 on the number line represents the sea level.

From the figure,

The point P is above sea level and Q is at sea level  

The point R is below the sea level

Hence,  

The correct statement is that "P is above sea level and City R is below sea level True"

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Complete Question:

The elevation in Feet of these 3 cities is marked on the number line shown below. The point 0 on the number line represents the sea level. Which statement must be true?

Which statement must be true?

A City P and City Q are above sea level.

B City Q and City R are below sea level.

C City P is above sea level and City Q is below sea level.

D City P is above sea level and City R is below sea level.

The scatter plot that shows correlation with causation is (c)

A scatter plot is a type of graph that displays the relationship between two variables. The position of each point on the plot represents the value of both variables.

If there is a strong positive correlation between two variables, it means that as one variable increases, the other variable also tends to increase.

If there is a strong negative correlation, it means that as one variable increases, the other variable tends to decrease.

The scatter plot with the mst positive or negative correlation is c

This is the scatter plot that shows correlation with causation

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The farmer can expect to calculate the surface area of the barn in units of m² or square meters. Thus, option B is correct.

Surface area is a two-dimensional measurement that represents the total area of all the faces or sides of a three-dimensional object. It is the sum of the areas of all the faces or surfaces that make up the object.

The surface area is typically expressed in square units, such as square meters (m²), square feet (ft²), or square centimetres (cm²), depending on the unit system used.

For example, the surface area of a cube with sides of length "s" can be calculated by finding the area of each face (which is s²), and then summing the areas:

Surface area of a cube = 6 x (side length)² = [tex]6s^2[/tex]

The farmer can expect to calculate the surface area of the barn in units of m² or square meters.

Surface area is a two-dimensional measurement that represents the total area of all the faces or sides of a three-dimensional object, such as a barn. The unit of measurement for surface area is always expressed in square units, such as m², ft², cm², etc.

Therefore, options (a) m, (c) ft, and (d) ft³ are incorrect, surface area

the farmer expect to calculate the surface area in [tex]m^2[/tex].

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The radius and volume of the cylinder are 4 cm and 754 cm³ respectively and volume of the cone is 216 cm³.

What the volume of a cone and cylinder?

Volume of cone and cylinder is V = (1/3)πr²h and V = (1/3)πr²h respectively

where r is the radius of the base of the cone, h is the height of the cone, and π is the mathematical constant π (approximately equal to 3.14).

For cone:

To use this formula, we first need to find the radius of the base of the cone. We know that the diameter of the base is 12 cm, so the radius is half of that:

r = d/2 = 12/2 = 6 cm

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

[tex]V = \frac{1}{3} \pi {r}^{2} h \\ V = \frac{1}{3} π( {6}^{2} )(19) \\ V = ( \frac{1}{3} )π(36)(19) \\ V = ( \frac{1}{3} )(3.14)(36)(19) \\ V = 216.24 cm³[/tex]

So, volume of the cone is 216.24 cm³ or 216 cm³ ( approximately)

For cylinder:

We are given the diameter of the cylinder as 8 cm, so we can find the radius as half of that:

r = d/2 = 8/2 = 4 cm

We are also given the height of the cylinder as 15 cm.

Now we can plug in these values into the formula:

[tex]V = π {r}^{2} h\\ V = π( {4}^{2} )(15) \\ V = π(16)(15) \\ V = 240π \\ V ≈ 753.98 \: cubic \: centimeters[/tex]

Therefore, the volume of the cylinder is approximately 753.98 cubic centimeters or 754 cm³ (approximately).

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answer is b) y = - 3/4 * x - 8,The reason for this is that the slope of the line is -3/4 (since it goes down by 3 units for every 4 units to the right), and it passes through the point (-6,-8).

what is slope?

In mathematics, the slope of a line is a measure of how steep it is. It is defined as the ratio of the change in the y-coordinates to the change in the x-coordinates between two points on the line.

In the given question,

Based on the information provided, the equation that represents the straight line passing through -8 on the y-axis and -6 on the x-axis would be:

b) y = - 3/4 * x - 8

The reason for this is that the slope of the line is -3/4 (since it goes down by 3 units for every 4 units to the right), and it passes through the point (-6,-8) which can be verified by substituting these values into the equation.

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