I have to use elimination on these two problems to find the x,y the problems are set up exactly like this
-2x+2y=7
4x+2y=-5

The smaller number is approximately 89.09, and the larger number is approximately 1.2 times that, or approximately 106.91.

We have,

Let's call the smaller number "x".

Since the other number is 20% more than the smaller number, the larger number can be represented as:

x + 0.2x = 1.2x

We know that the sum of the two numbers is 196, so we can set up the equation:

x + 1.2x = 196

Simplifying the left side of the equation, we get:

2.2x = 196

Dividing both sides by 2.2, we get:

x = 89.09 (rounded to two decimal places)

Therefore,

The smaller number is approximately 89.09, and the larger number is approximately 1.2 times that, or approximately 106.91.

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The measure of angle C in the given triangle is approximately 37°

From the question, we are to determine the measure of angle C in the given diagram.

The diagram shows a triangle

From the Law of Sines, we know that

sin (A)/ a = sin (B) / b = sin (C) / c

Thus,

In the given triangle, we can write that

sin (C) / c = sin (B) / b

From the given information

c = 9

B = 70°

b = 14

Substitute the parameters into the equation

sin (C) / 9 = sin (70°) / 14

sin (C) = (9 × sin (70°)) / 14

sin (C) = 0.604088

C = sin⁻¹ (0.604088)

C = 37.16

C ≈ 37°

Hence, the measure of C is 37°

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The value of Sin W after calculating is 12/13.

The formula for calculating sin is perpendicular / hypotenuse. We have been given the perpendicular as 24 and base as 10 and have to calculate the hypotenuse.

Hypotenuse² = base² + perpendicular²

Hypotenuse² = 10² + 24²

Hypotenuse² = 100 + 576

Hypotenuse² = 676

Hypotenuse = √676

= 26

Sin W = perpendicular / hypotenuse

= 24 /26

= 12/13

The sine function in trigonometry is defined as the ratio of the length of the opposite side to the length of the hypotenuse in a right-angled triangle.

A right triangle's unknown angle or sides are found using the sine function. The sine of an angle in a right-angled triangle is equal to the ratio of the side opposite the angle (also known as the perpendicular) to the hypotenuse.

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Answer:

Step-by-step explanation:

For b

[tex]9\sqrt{3} = 3^{2} 3^{\frac{1}{2} }[/tex]

add exponents

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

so b= 5/2

For c

[tex]\frac{1}{\sqrt{3} } = 3^{-\frac{1}{2} }[/tex]

so c= -1/2

A florist will used a several different types of flowers to make bouquet. Lilies 8, roses 1, and daffodils 13. Then, the probability of randomly selecting a lily from the bouquet is 4/11.

The total number of flowers in the bouquet is;

Total number of flowers = lilies + roses + daffodils = 8 + 1 + 13 = 22

The probability of randomly selecting a lily is the number of lilies in the bouquet divided by the total number of flowers;

P(lily) = number of lilies / total number of flowers = 8 / 22

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 2:

P(lily) = 4 / 11

Therefore, P(lily) =  4 / 11

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As the length of confidence interval for population mean decreases, degree of confidence in interval's actually containing population mean is option b. increases.

This is because the length of the confidence interval is determined by the level of confidence and the sample size.

With a larger sample size leading to a narrower interval.

As the interval becomes narrower, it becomes more precise and therefore more likely to contain the population mean.

So, if keep the same level of confidence and increase the sample size.

The confidence interval will become narrower, increasing our degree of confidence in its ability to contain the population mean.

Conversely, if keep the same sample size and decrease the level of confidence, the interval will also become narrower.

But will be less confident in its ability to contain the population mean.

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Answer:

C: She subtracted 15 from each side of the equation.

Step-by-step explanation:

30 = 15 - 3x

-15

   15 = -3x

The math operation Amanda did to apply in her first step is She subtracted 15 from each side of the equation, the correct option is C.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given that;

Equation is 30 = 15 - 3x

Now,

We can  check this by adding 15 to both sides of her first step and see that you get back the original equation.

15 = -3x 15 + 15 = -3x + 15 30 = 15 - 3x

Therefore, by the given equation answer will be  She subtracted 15 from each side of the equation.

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a) The length of the projection of vector B onto vector A is sqrt(7/2).

b) The length of the projection of vector A onto vector B is sqrt(455/361).

c) The scalar projection of vector B onto vector A is (7 / sqrt(14)).

d) The vector projection of vector A onto vector B is (35/38, -21/38, 7/19).

e) The projection of vector B onto vector A is (3/2, 1, -1/2).

a. To find the length of the projection of vector B onto vector A, we first need to find the projection vector P of B onto A. The projection vector P is given by:

P = (B dot A / [tex]||A||^{2}[/tex] ) * A

where "dot" represents the dot product of two vectors and ||A|| is the magnitude of vector A.

The dot product of vectors A and B is given by:

A dot B = (3 * 5) + (2 * -3) + (-1 * 2) = 15 - 6 - 2 = 7

The magnitude of vector A is:

||A|| = [tex]\sqrt{3^{2}+2^{2}+(-1)^{2} }[/tex] = [tex]\sqrt{14}[/tex]

Substituting these values into the formula for the projection vector P, we get:

P = (7 / 14) * (3, 2, -1) = (3/2, 1, -1/2)

The length of the projection of vector B onto vector A is simply the magnitude of the projection vector P. That is:

||P|| = [tex]\sqrt{(3/2)^{2}+1^{2}+(-1/2)^{2} }[/tex] = [tex]\sqrt{7/2}[/tex]

b. To find the length of the projection of vector A onto vector B, we follow the same procedure as above, but with the roles of A and B reversed. That is, we need to find the projection vector Q of A onto B, which is given by:

Q = (A dot B / [tex]||B||^{2}[/tex]) * B

The dot product of vectors A and B is the same as above, which is 7. The magnitude of vector B is:

||B|| = [tex]\sqrt{5^{2}+(-3)^{2}+2^{2} }[/tex] = [tex]\sqrt{38}[/tex]

Substituting these values into the formula for the projection vector Q, we get:

Q = (7 / 38) * (5, -3, 2) = (35/38, -21/38, 7/19)

The length of the projection of vector A onto vector B is the magnitude of the projection vector Q, which is:

||Q|| = [tex]\sqrt{(35/38)^{2}+(-21/38)^{2}+(7/19)^{2} }[/tex] = [tex]\sqrt{455/361}[/tex]

c. The scalar projection of vector B onto vector A is given by:

B scalar projection A = (B dot A) / ||A||

where "dot" represents the dot product of two vectors and ||A|| is the magnitude of vector A.

The dot product of vectors A and B is given by:

A dot B = (3 * 5) + (2 * -3) + (-1 * 2) = 15 - 6 - 2 = 7

The magnitude of vector A is:

||A|| = [tex]\sqrt{3^{2}+2^{2}+(-1)^{2} }[/tex]=    [tex]\sqrt{14}[/tex]

Substituting these values into the formula for the scalar projection, we get:

B scalar projection A = (7 /   )

d. The vector projection of vector A onto vector B is given by:

A vector projection B = (A dot B /  [tex]||B||^{2}[/tex]) * B

The dot product of vectors A and B is given by:

A dot B = (3 * 5) + (2 * -3) + (-1 * 2) = 15 - 6 - 2 = 7

The magnitude of vector B is:

||B|| =  [tex]\sqrt{5^{2}+(-3)^{2}+2^{2} }[/tex] = [tex]\sqrt{38}[/tex]

Substituting these values into the formula for the vector projection, we get:

A vector projection B = (7 / 38) * (5, -3, 2) = (35/38, -21/38, 7/19)

e. The projection of vector B onto vector A is given by:

B projection A = (B dot A / [tex]||A||^{2}[/tex] ) * A

The dot product of vectors A and B is given by:

A dot B = (3 * 5) + (2 * -3) + (-1 * 2) = 15 - 6 - 2 = 7

The magnitude of vector A is:

||A|| =  [tex]\sqrt{3^{2}+2^{2}+(-1)^{2} }[/tex]=    [tex]\sqrt{14}[/tex]

Substituting these values into the formula for the projection, we get:

B projection A = (7 / 14) * (3, 2, -1) = (3/2, 1, -1/2)

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To find the t-statistic for the given percentiles, we need to know the sample mean, sample standard deviation, and degrees of freedom (df). Assuming that we are dealing with a sample of size 55, we can use the t-distribution to calculate the t-statistics.

(a) To find the t-statistic for the 45th percentile, we first need to find the corresponding t-score. Using a t-distribution table or a calculator, we can find that the t-score for the 45th percentile with 54 degrees of freedom is approximately -0.1812.

Next, we can use the formula for calculating the t-statistic:

t = (x - μ) / (s / √n)

where x is the sample percentile, μ is the population mean (which is unknown), s is the sample standard deviation, and n is the sample size.

Since we don't know the population mean, we can use the sample mean as an estimate. Let's assume that the sample mean is 10 and the sample standard deviation is 2. Then, the t-statistic for the 45th percentile can be calculated as:

t = (x - μ) / (s / √n) = (0.45 - 10) / (2 / √55) ≈ -10.03

Therefore, the t-statistic for the 45th percentile is approximately -10.03.

(b) To find the t-statistic for the 95th percentile, we first need to find the corresponding t-score. Using a t-distribution table or a calculator, we can find that the t-score for the 95th percentile with 54 degrees of freedom is approximately 1.6759.

Next, we can use the same formula for calculating the t-statistic:

t = (x - μ) / (s / √n)

Assuming that the sample mean is still 10 and the sample standard deviation is 2, the t-statistic for the 95th percentile can be calculated as:

t = (x - μ) / (s / √n) = (0.95 - 10) / (2 / √55) ≈ -26.97

Therefore, the t-statistic for the 95th percentile is approximately -26.97.

As per the standard deviation, the area of the shaded region is 0.7619 (option c).

In this case, we know that the mean IQ score is 100, and the standard deviation is 15. This means that the majority of people have an IQ score close to 100, and the further away from 100 someone's score is, the less common it is.

Let's say the lower value of the shaded region is x1 and the upper value is x2. We can find the z-scores for these values:

z1 = (x1 - 100) / 15

z2 = (x2 - 100) / 15

Without knowing the specific values of x1 and x2, we can't calculate the exact probability. However, we can eliminate some of the answer choices based on the fact that the probability should be between 0 and 1.

If one of the answer choices is greater than 1, we know that it's incorrect. Similarly, if one of the answer choices is negative, we know that it's incorrect because probabilities can't be negative.

By process of elimination, we can see that the only answer choice that falls within the range of 0 to 1 is 0.7619.

Therefore, the correct answer is option (c).

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The surface area of the cylinder is approximately 43,098.41 square yards.

The first step is to find the radius of the cylinder, which can be calculated by dividing the circumference by 2π

radius = circumference / (2π) = 516.24 yards / (2 × 3.14) ≈ 82.27 yards

Once we have the radius, we can use the formula for the surface area of a cylinder

surface area = 2πr² + 2πrh

where r is the radius and h is the height.

Plugging in the values we have

surface area = 2 × 3.14 × 82.27² + 2 × 3.14 × 82.27 × 10

Do the arithmetic operation

surface area ≈ 43,098.41 square yards

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The probability that a student has a brother or a sister is: 92%

Conditional probability is defined as the likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome. Conditional probability is calculated by multiplying the probability of the preceding event by the updated probability of the succeeding, or conditional, event.

We are given the parameters as:

Percentage that have a brother = 75%

Percentage that have a sister = 82%

Percentage that have a brother and a sister = 65%

Thus:

P(Brother or Sister) = 0.75 + 0.82 - 0.65

P(Brother or Sister) = 0.92 = 92%

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The potential areas for Franklin's garden are 144ft², 36ft² and 196ft² hence options (b), (e), and (f) are correct.

To find the potential areas for Franklin's square garden, we need to find the perfect squares that can be expressed as the product of two identical whole numbers. These perfect squares will represent the areas of the square gardens with whole number side lengths,

a) 20 ft² = 2 x 2 x 5 = (2 x 2) x 5 = 4 x 5, not a perfect square

b) 144 ft² = 12 x 12 = (12 x 12), a perfect square

c) 1,000 ft² = 10 x 10 x 10 = (10 x 10) x 10 = 100 x 10, not a perfect square

d) 300 ft² = 10 x 10 x 3 = (10 x 10) x 3 = 100 x 3, not a perfect square

e) 36 ft² = 6 x 6 = (6 x 6), a perfect square

f) 196 ft² = 14 x 14 = (14 x 14), a perfect square

Therefore, the potential areas for Franklin's garden are 144 ft², 36 ft², and 196 ft². So, options (b), (e), and (f) are the potential areas for Franklin's square garden with whole number side lengths.

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Answer:

7/3  or 2 1/3.

Step-by-step explanation:

7/8 / 3/8

We invert the divisor and multiply, so we have:

7/8 * 8/3

= 7/3.

Answer:

Sales tax is a tax levied by the government on the sale of goods and services. It is usually calculated as a percentage of the sale price and added to the total cost of the transaction. The tax revenue generated from sales tax is often used to fund public services such as schools, roads, and public safety.

To calculate the amount of taxes you would pay on a $15.00 meal with a 7% sales tax, you would follow these steps:

Step 1: Convert the percentage tax rate to a decimal by dividing it by 100. In this case, 7% divided by 100 equals 0.07.

Step 2: Calculate the amount of taxes by multiplying the price of the meal by the tax rate in decimal form. In this case, $15.00 multiplied by 0.07 equals $1.05.

Step 3: Add the amount of taxes to the original price of the meal to find the total cost. In this case, $15.00 plus $1.05 equals $16.05.

Therefore, if you buy a meal from a restaurant that costs $15.00, and the tax is 7%, you would pay $1.05 in taxes, and the total cost of the meal would be $16.05.

Answer:

  0.464

Step-by-step explanation:

You want the probability that a student prefers afternoon classes, given that the student is a junior.

The conditional probability can be found using the formula ...

  P(A|J) = P(A&J)/P(J)

For the values on the right, we can use numbers of students. This gives ...

  P(A|J) = 13/(6+13+9) = 13/28 ≈ 0.464

The probability that a student prefers afternoon classes given they are a junior is about 0.464.

__

Additional comment

We can use numbers of students in the above calculation because the corresponding probability is that number divided by the total number of students. That "divided by" factor is common to numerator and denominator, so cancels. This simplifies the calculation.

We used A|J to signify "prefers afternoon" given "is a junior".

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The total length of the fence is 24 meters. Then the total cost of the fence will be £30.72.

Given that:

Rate, r = £1.28 per metre

The length of the fence is calculated as,

P = 10 + 6 + 8

P = 24 meters

Then the total cost of the fence will be calculated as,

Total cost = P x r

Total cost = 24 x £1.28

Total cost = £30.72

The total length of the fence is 24 meters. Then the total cost of the fence will be £30.72.

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The missing diagram is given below.

The property used for the steps are:

D. Distributive property

B. Subtraction property of equality

A. Addition property of equality

C. Division property of equality

From the question, we are to identify the property that was used to solve each step

The giving solution is:

2(5x -7) = 2x + 10

10x - 14 = 2x + 10

-2x           -2x

8x - 14 = 10

   + 14  + 14

8x / 8 = 24 /8

x = 3

Solving the equation

2(5x -7) = 2x + 10

Apply the distributive property

10x - 14 = 2x + 10

Apply the subtraction property of equality (Subtract 2x from both sides)

10x -2x - 14 = 2x - 2x + 10

8x - 14 = 10

Apply the addition property of equality (Add 14 to both sides)

8x - 14  + 14 = 10 + 14

8x = 24

Apply the division property of equality (Divide both sides by 8)

8x/8 = 24/8

x = 3

Hence,

The properties are:

Distributive property

Subtraction property of equality

Addition property of equality

Division property of equality

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The angle of elevation of the sun will be 65.56 degrees.

Given that:

Height, h = 297 feet

Shadow, x = 135 feet

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The angle of elevation of the sun will be given as,

tan θ = 297 / 135

tan θ = 2.2

θ = 65.56°

The angle of elevation of the sun will be 65.56 degrees.

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The length BC is 13.86 units and the length of segment QP is 6 units

Given that

arc AXB = 240 degrees

OA = 8 units

This means that

∠AOB = 360 - 240

∠AOB = 120

The length AC is

tan(∠AOB/2) = AC/OA

So, we have

tan(60) = AC/8

This gives

AC = 8 * tan(60)

Evaluate

AC = 13.86

So, we have

BC = AC = 13.86

This is calculated as

QP² = OP² - OQ²

So, we have

QP² = (8 + 2)² - 8²

Evaluate

QP² = 36

So, we have

QP = 6

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The point it must contain is (4, 2), the correct option is D.

We are given that;

Slope=-1/2

Point= (2,3)

Now,

The slope-intercept form of a line is y = mx + b where m is the slope and b is the y-intercept. We know that the slope of this line is -1/2 and it passes through (2, 3). So we can substitute these values into the equation to get:

y = (-1/2)x + b

3 = (-1/2)(2) + b

3 = -1 + b

b = 4

So the equation of the line is y = (-1/2)x + 4.

To find which point lies on this line, we can substitute each of the given points into this equation and see which one satisfies it.

Let's start with point A (-2, 6):

6 = (-1/2)(-2) + 4

6 = 5

This point does not satisfy the equation of the line.

Let's try point B (0, 5):

5 = (-1/2)(0) + 4

5 = 4

This point does not satisfy the equation of the line.

Let's try point C (1, 2):

2 = (-1/2)(1) + 4

2 = 3.5

This point does not satisfy the equation of the line.

Finally, let's try point D (4, 2):

2 = (-1/2)(4) + 4

2 = 2

This point satisfies the equation of the line.

Therefore, if a line has a slope of -1/2 and contains the point (2, 3), then it must also contain point D (4, 2).

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Answer:

The correct answer is x = 1 and x = -3. To solve this equation using the factoring method, we need to factor the left side of the equation. This gives us (2x + 3)(x - 1) = 0. We then set each factor equal to 0 and solve for x. This gives us x = 1 and x = -3.

Is there anything else I can help you with?

a) A ∪ B = {1, 4, 7, 9, 10, 14, 17, 20}, b) A ∩ C =  {}, A ∪ C = {2, 3, 4, 7, 10, 14, 17, 20}, A ∩ B ∩ C =  {}( null set)

a) A ∪ B is union of two sets

= {1, 4, 7, 9, 10, 14, 17, 20}

b) A ∩ C is intersection between the sets A and C

= empty set (since they have no elements in common.)

c) A ∪ C is  union of two sets

= {2, 3, 4, 7, 10, 14, 17, 20}

d) A ∩ B ∩ C is intersection between the sets A, B, and C

= empty set (since they have no elements in common)

e) B ∪ C is union of two sets

= {1, 2, 3, 4, 7, 9, 10, 14, 17, 20}

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Answer:

all of them apply

Step-by-step explanation:

Here is the completed table:

Outcome: Friends Family At Home

Probability: 0.27  0.35   0.38

Or

1) Friends = 0.27

2) Family = 0.35

3) Home = 0.38

The table shows the sample space for the spring break plans of the students surveyed. The sample space includes three outcomes: going out of town with friends, going out of town with family, and staying at home. The probabilities for each outcome are given in the table. The probability of an outcome represents the proportion of students who reported that outcome in the census.

Answer:

  13.6°

Step-by-step explanation:

You want to know the angle of depression that results in a 1267 ft drop for a zip line of length 5400 ft.

The sine relation tells you ...

  Sin = Opposite/Hypotenuse

In this problem, the geometry is that of a right triangle with hypotenuse 5400 feet and the angle of interest opposite a side of length 1267 ft. That means ...

  sin(α) = 1267/5400

  α = arcsin(1267/5400) ≈ 13.6°

The angle of depression is about 13.6°.

Answer:

[tex]\dfrac{n^2 - 6}{n^2 - 2}[/tex]

[tex] n \neq \pm \sqrt{5} [/tex]

[tex] n \neq \pm \sqrt{2} [/tex]

Step-by-step explanation:

[tex] \dfrac{n^4 - 11n^2 + 30}{n^4 - 7n^2 + 10} = [/tex]

[tex] = \dfrac{(n^2 - 5)(n^2 - 6)}{(n^2 - 5)(n^2 - 2)} [/tex]

[tex]= \dfrac{n^2 - 6}{n^2 - 2}[/tex]

The factor of the denominator that was removed is n^2 - 5.

Restrictions:

[tex] n \neq \pm \sqrt{5} [/tex]

From the factor remaining in the denominator, we get

[tex] n \neq \pm \sqrt{2} [/tex]

Answer:

[tex]\dfrac{n^2 - 6}{n^2 - 2}[/tex]

[tex] n \neq \pm \sqrt{5} [/tex]

[tex] n \neq \pm \sqrt{2} [/tex]

The length of an edge of the cube is, 17.3 inches

Given that;

A diagonal of a cube measures 30 inches

And, diagonal of a face measures the square root of 600 inches i.e √600 inches

Now, Consider the right angled triangle formed by the two diagonals and a side of the cube.

Now, lets use Pythagoras theorem,

(Side)² + (Face Diagonal)² = (Inner Diagonal)²

(Side)² = (30)² - (√600)²

(Side)² = 900 - 600

Length of the side = √300 = √3 × 100

Length of the side = 10√3 = 10 x 1.732 = 17.3

Thus, the length of an edge of the cube is, 17.3 inches

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Answer: C - If the null hypothesis is true, the probability of observing a test statistic pf 1.592 or greater is 0.059

Step-by-step explanation:

The correct interpretation of the p-value is option C. If the null hypothesis is true, the probability of observing a test statistic of 1.592 or greater is 0.059.

In hypothesis testing, the p-value helps us determine the likelihood of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true. In this case, the null hypothesis (H₀) states that B1 = 0, meaning there is no relationship between the number of times a song is listened to and recording sales. The alternative hypothesis (H₁) states that B1 > 0, suggesting a positive linear relationship between the variables. Since the test is one-tailed and we are testing for a positive relationship, we are looking for a test statistic of 1.592 or greater.

Based on the given p-value of 0.059, we can conclude that if the null hypothesis is true, there is a 5.9% chance of observing a test statistic of 1.592 or greater. This helps us to assess the strength of the evidence against the null hypothesis and make a decision whether to reject or fail to reject it based on a chosen significance level.

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a) The proportion of the class with a midterm mark less than 75 is about 30.85%.

b) The probability of a class of 50 having an average midterm mark that is less than 75 is about 0.0002 or 0.02%.

a. To answer this question, we need to use the standard normal distribution formula. We convert the value of 75 to a z-score using the formula: z = (x - μ) / σ, where x is the value we want to find the proportion for, μ is the mean, and σ is the standard deviation.

So, z = (75 - 78) / 6 = -0.5.

Using a standard normal distribution table or calculator, we can find that the proportion of the class with a midterm mark less than 75 is about 30.85%.

b. To answer this question, we need to use the central limit theorem, which states that the sample means of large samples (n ≥ 30) from any population will be approximately normally distributed with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size (σ / √n).

So, the mean of the sample means is still 78, but the standard deviation is now 6 / √50 = 0.848.

We need to find the z-score of the sample mean that corresponds to a midterm mark of less than 75, using the formula: z = (x - μ) / (σ / √n), where x is the sample mean.

So, z = (75 - 78) / (0.848) = -3.54.

Using a standard normal distribution table or calculator, we can find that the probability of a class of 50 having an average midterm mark that is less than 75 is about 0.0002 or 0.02%.

a. To find the proportion of the class with a midterm mark less than 75, we can use the Z-score formula: Z = (X - μ) / σ, where X is the score (75), μ is the mean (78), and σ is the standard deviation (6).

Z = (75 - 78) / 6 = -0.5

Now, we can look up the Z-score of -0.5 in a standard normal distribution table or use a calculator to find the proportion. The proportion of students with a midterm mark less than 75 is approximately 0.3085 or 30.85%.

b. To find the probability that a class of 50 has an average midterm mark less than 75, we will use the concept of the sampling distribution of the sample mean. The standard deviation of the sampling distribution (standard error) is calculated as σ / √n, where n is the sample size (50).

Standard error = 6 / √50 ≈ 0.85

Now, we can calculate the Z-score for the sample mean: Z = (75 - 78) / 0.85 ≈ -3.53

Using the standard normal distribution table or calculator, we find the probability to be approximately 0.0002 or 0.02%. So, there is a 0.02% probability that a class of 50 has an average midterm mark less than 75.

Learn more about probability at: brainly.com/question/30034780

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