professor elderman has given the same multiple choice final exam in his principles of microeconomics class for many years. after examining his records from the past 10 years, he finds that the scores have a mean of 76 and a standard deviation of 12. what is the probability professor elderman's class of 36 has a class average below 78

The measure of angle 11x+1 is 100°.

According to the question,

We have the following information:

We have a figure where two parallel lines are divided by a line. We know that the vertically opposite angles are equal. And when two parallel lines are cut by another line then the alternate interior opposite angles are equal.

Now, we have 10x+10 as the alternate opposite interior angle to 11x+1.

So, we have the following expression:

10x+10 = 11x+1

11x-10x = 10-1

x = 9

Putting the value of x in 11x+1:

11*9+1

99+1

100°

Hence, the measure of angle 11x+1 is 100°.

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The values of the variables x and y in the triangle are 1.25 and 1.75

The tringle represents the given parameter

On the triangle, we have the following equivalent ratio

5 : 8 = 5 + x : 10

7 : 8 = 7 + y : 10

These are true because the horizontal lines of the triangles are parallel

So, we have

5 : 8 = 5 + x : 10

Express as fraction

5/8 = 5 + x/10

This gives

5 + x = 6.25

Solve for x

x  = 1.25

Similarly, we have

7 : 8 = 7 + y : 10

So, we have

7/8 = 7 + y/10

This gives

7 + y = 10*7/8

Evaluate

7 + y = 8.75

So, we have

y = 1.75

Hence, the values of x and y are 1.25 and 1.75

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The length of the first side of the triangle is 15 feet, the length of the second side of the triangle is 13 feet and the third side is 21 feet.

According to the question,

We have the following information:

The first side of a triangle is 2 feet longer than the second. The third side is 5 feet shorter than twice the second. The perimeter is 49 feet.

Let's take the second side to be x feet.

So, we have the following sides:

First side = (x+2) feet

Third side = (2x-5) feet

Perimeter = 49

x+x+2+2x-5 = 49

4x-3 = 49

Adding 3 on both the sides:

4x = 49+3

4x = 52

Dividing by 4 on both the sides:

x = 52/4

x = 13 feet

First side = 2+13

First side = 15 feet

Third side = 2*13-5

Third side = 26-5

Third side = 21 feet

Hence, the length of the first side of the triangle is 15 feet, the length of the second side of the triangle is 13 feet and the third side is 21 feet.

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By using the trial method we get a total number of trials taken by Charlie to see both sides of both the coins is 4.

Probability is the name of the area of mathematics that deals with the examination of random events. The ratio of favorable occurrences to the total number of events is used to calculate an event's probability.

P(E) = F(E)/T (E)P(E)

It stands for the probability that an event will occur.

F(E) = Amount of favorable occurrences

Total number of trials (T(E))

Given that Charlie has 2 fair coins.

If he tosses the pair of coins simultaneously, then the number of samples can be HH, HT, TH, TT.

So to see both sides of both the coins he should toss the coin four times.

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Answer:

.444....

Step-by-step explanation:

4 out of 9 is   4/9      or   4 ÷ 9 = .444...

There are 336 to select a set of 8 donuts from 3 varieties,  where the donuts of the same variety are indistinguishable.

here the total number of   8 donuts of a set needs to make from a given variety of 3, since here the orders so,  we need to use permutations.A permutation of a set is an arrangement of its individuals into a grouping or direct order, or in the event that the set is as of now ordered, a modification of its elements. It alludes to the act or preparation of changing the direct arrange of a requested set. Permutations vary from combinations, which are determinations of a few individuals of a set in any case of an order.

the formula for permutations is :

P(n,r) = n! /(n-r)! , here n i=8 and r = 3

P(8,3) =  8! /(8-3)!

          =  8* 7*6= 336

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Answer:

Step-by-step explanation:

20=v+9-16

So first, we combine like terms

20=v-7

Then we want to add 7 on each side

20=v-7

+7      +7

Then we are left with

27=v

Step-by-step explanation:

Subtract the numbers

20=v+9-16 =20=v-7

Add 7 to both sides

20=v-7

20+7=v-7+7

Then simplify P.S if you dont know how to comment on the answer

ANSWER v=27

The leading coefficients and parabolic equations, considering the vertices, are given as follows:

1. a = 7/4, y = 7/4(x - 4)² - 1.

2. a = -2, y = -2(x + 1)² + 2.

The equation of a parabola with vertex given by (h,k) is presented as follows:

y = a(x - h)² + k.

In which a is the leading coeffiicent.

For item 1, the coordinates of the vertex is given as follows:

(4,-1).

Hence:

h = 4, k = -1, and the equation is:

y = a(x - 4)² - 1.

When x = 6, y = 6, hence the leading coefficient is calculated as follows:

6 = a(6 - 4)² - 1

4a = 7

a = 7/4.

Thus the equation is:

y = 7/4(x - 4)² - 1.

For item 2, the vertex is:

(-1,2).

Hence:

y = a(x + 1)² + 2.

When x = 0, y = 0, hence the leading coefficient is calculated as follows:

0 = a(0 + 1)² + 2

a = -2.

Hence the equation is:

y = -2(x + 1)² + 2.

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Answer:

c = -5

Step-by-step explanation:

6c + 14 = -5c + 4 + 9c

1) We want to first combine the c values on the right side. This would give us 6c + 14 = 4c + 4.

2) Next, we want to move the c value to one side of the equation. This means we would subtract 4c from the right side. This gives us 2c + 14 = 4.

3) We can then subtract 14 from the left side to isolate the c value. This gives us 2c = -10.

3) We can then divide both sides by 2 and get the answer for c.

This gives us c = -5.

Using a proportional relationship, it is found that:

a) The equation is: y = 63/x.

b) When x = 21, the numeric value is of y = 3.

A proportional relationship is a special case of a linear function, with slope represented by the constant of proportionality of k and intercept of 0.

When the two variables are inversely proportional, we have a inverse proportional relationship, in which the output variable y is obtained by the division of k by the input variable x, as follows:

y = k/x.

For this function, when y = 7, x = 9, hence the constant is obtained as follows:

7 = k/9

k = 9 x 7

k = 63.

Hence the equation is:

y = 63/x.

The numeric value of the function when x = 21 is given as follows:

y = 63/21 = 3.

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The tank with the smallest surface area has dimensions of 6ft.

s = 12ft and h = 6ft.

A(s) = s² + 4 × (V ÷ s)

The rectangular tank has a capacity of 864 feet.

Let the square base's long sides be.

Let h represent the tank's height.

Let A represent the tank's whole area.

A = (Base Area) + (4 × Lateral Area)

Lateral Area = s × h

Lateral Area = s × (V ÷ s²)

Lateral Area = (V ÷ s)

Base Area = s²

Compared to the objective function,

A(s) = s² + 4 × (V ÷ s)

A(s) = s² + 4 × (864 ÷ s)

The area function's derivative,

A'(s) = 2s - (3456 ÷ s²)

The smallest surface area is now.

A'(s) = 0

2s - (3456 ÷ s²) = 0

2 × [tex]s^{3}[/tex] = 3456

[tex]s^{3}[/tex] = 3456

s = [tex]\sqrt[3]{3456}[/tex]

s = 12ft

The volume is,

V = s² × h

864 = 12² × h

h = 6ft

As a result, the tank's height is 6 feet, and the square base's long sides measure 12 feet.

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The question is -

A rectangular tank with a square​ base, an open​ top, and a volume of 864 ft cubed is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area. Let s be the length of one of the sides of the square base and let A be the surface area of the tank. Write the objective function.

Answer: Row: 9 Column: 9

Step-by-step explanation:

Carol wants a square garden that means the amount of plants must be square, which it is so the square root of 81 is 9 so the square is 9 by 9

As a result of using all values in the data set to calculate an average, the mean is the most widely used measure of central tendency.

A measure of central tendency, also known as a measure of center or a measure of central placement, is a summary statistic that seeks to summarize an entire collection of data by using a single number that corresponds to the middle or center of the distribution.

You are probably most familiar with the central tendency measure known as the mean, which is the arithmetic average. It is fairly easy to determine the mean. Simply add up all the values then divide by the dataset's observation count.

The teacher can get a mathematical breakdown of how well the children are doing through measures of central tendency.

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The difference between exponents [tex](a^n)^m = a^{mn}[/tex] and [tex]a^nb^n = (ab)^n[/tex] has been described below

What are exponent?

Exponent tells us how many times a number is multiplied by itself.

For example : In [tex]2^4 = 2 \times 2 \times 2 \times 2[/tex]

Here, 2 is multiplied by itself 4 times.

If [tex]a^m = a \times a \times a \times....... \times a[/tex] (m times), a is the base and m is the index.

The laws of index are-

[tex]a^m \times a^n = a^{m + n}\\a^m \div a^n = a^{m-n}\\a^0 = 1\\a^{-n} = \frac{1}{a^n}\\\\a^m b^m = (ab)^m\\(\frac{a}{b})^n = \frac{a^n}{b^n}[/tex]

In case of  [tex](a^n)^m = a^{mn}[/tex], the base is single but in case of [tex]a^nb^n = (ab)^n[/tex], the base is a product of two numbers

If the base can be expressed as a product of different numbers,

[tex]a^nb^n = (ab)^n[/tex] is used

If the base cannot be expressed as a product, then [tex](a^n)^m = a^{mn}[/tex] is used

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Answer:

Step-by-step explanation:

We know that perpendicular lines have opposite-reciprocal slopes.

Given line:

Its slope is 2 and the perpendicular line has a slope of - 1/2.

Let's find the line with the slope of - 1/2:

Answer:

c

Step-by-step explanation:

Answer: Stacy is 12 years old

Step-by-step explanation:

36/4 = 12

The probability of spinning a 1 is the same for both spinners: False​

The spinners that complete the question are added as an attachment

From the attached figures, we  have

Spinner 1

Number of 1 = 1

Sections = 4

Spinner 2

Number of 1 = 2

Sections = 6

The probability of obtaining 1 is calculated as

P(1) = Number of 1/Sections

So, we  have

Spinner 1

Number of 1 = 1

Sections = 4

P(1) = 1/4

Spinner 2

Number of 1 = 2

Sections = 6

P(1) = 2/6

By comparison

1/4 and 2/6 do not have the same value

Hence. it is false that the probability of spinning a 1 is the same for both spinners

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Answer:

135 degrees

Step-by-step explanation:

a triangle rule is sum of all three angles equal 180

We know one angle of the triangle angle is 45 degrees because of the corresponding angle below it

So we just subtract 45 from 180

180-45=135

hopes this helps please mark brainliest

The subtraction between the functions f(x) = 4 · x - 8 and g(x) = - 3 · x + 1 is equal to (f - g) (x) = 7 · x - 9.

Herein we find f(x) and g(x) defined as linear functions and we are asked to find the subtraction between two functions, which is defined below:

(f - g)(x) = f(x) - g(x)

If we know that f(x) = 4 · x - 8 and g(x) = - 3 · x + 1, then the result of the subtraction of the two functions is:

(f - g) (x) = f(x) - g(x)

(f - g) (x) = (4 · x - 8) - (- 3 · x + 1)

(f - g) (x) = 7 · x - 9

The subtraction between the two functions is (f - g) (x) = 7 · x - 9.

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The sequence has the 10th term of 15625000

The sequence is given as:

8,40,200,...

The above sequence has the following parameters

First term, a = 8

Common ratio, r = 5 i.e. 40/8 = 5

Number of terms , n = 10

This means that the sequence is a geometric sequence

The nth term of an geometric sequence is calculated as

f(n) = ar^(n - 1)

Substitute the known values in the above equation

So, we have the following equation

f(10) = 8 * 5^(10 - 1)

Evaluate

f(10) = 15625000

Hence, the 10th term for the sequence is 15625000

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The cost of a pizza with an 11 inch radius is  $26.86

In this question, the cost of a pizza varies directly as the square of its radius.

Let C be the cost of pizza and r be the radius of Pizza.

We have been given the direct proportionality between the cost of pizza and the radius of Pizza.

C ∝ r²

If a pizza with a 6 inch radius costs $8.00

8 = k * 6^2

where k is the proportionality constant.

8 = k * 36

k = 0.222

We need to find the cost of pizza with an 11 inch radius.

so, we get an equation,

C = k * 11^2

substitute above value of k

C = 0.222 * 11^2

C = 0.222 * 121

C = $26.86

Therefore, the cost of a pizza with an 11 inch radius is  $26.86

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The solution to the points are:

This is the point where the curve or curves of the graph changes direction.

In this case, the turning point in the vertex

The graph has its vertex at (1, -3.2)

This means that

Turning point = (1, -3.2)

This is the point where the curve or curves of the graph touches the x-axis i.e. f(x) = 0

In this case, the points are: (-1, 0) and (3, 0)

This means that

The roots are (-1, 0) and (3, 0)

This is the point where the curve or curves of the graph passes through x = 2.5

In this case, the points are: (2.5, -1.4)

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The required number of ounces of nuts would be 1/2 in each granola bar.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

She will use 12.5 ounces of walnuts to make 25 granola bars which is given in the question.

To determine the number of ounces of nuts in each granola bar

Let the number of ounces of nuts in each granola bar would be x

As per the given situation, we can write a ratio as

12.5 ounces : 25 bars = x ounces : 1 bars

⇒ 12.5 / 25 = x / 1

⇒ 1/2 = x

⇒ x = 1/2

Thus, the required number of ounces of nuts would be 1/2 in each granola bar.

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The loan amount at the end of 2 years is Rs. 12,127 .

In the given question we have, amount Rs. 11500 is borrowed by investor at the interest rate of 6% per annum.

compund interest is defined as the addition of interest to the principal of loan.

principal (P) = 11500

If interest is compunded quarterly then time(t) = 3 years = 12 , rate ( r%) = 6/4% = 2/3 %

Using the formula of Amount ,

Amount = P( 1 + r / 100) ᵗ

= 11500( 1 + 2/ 300)⁸

= 12127.83 ~ 12128

compound interest = Amount - principal =

12128- 11500 = Rs. 628

So, An investor has to pay total Rs. 12128 at the end of 2- year.

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Answer: sure:)

Step-by-step explanation:

The volume of a frustum is equal to 445.3785 cubic units.

Mathematically, the volume of a cone can be calculated by using this formula:

Volume of a cone = 1/3 × πr²h

Where:

For the volume of the large cone, we have the following:

Volume of large cone = 1/3 × πr²h

Volume of large cone = 1/3 × 3.142 × 6² × 12

Volume of large cone = 3.142 × 36 × 4

Volume of large cone = 452.448 cubic units.

Since the height of the small cone is quarter of the height of the large cone, we have:

Height of small cone = 1/4 × 12 = 3 units.

Radius of small cone = 12/18 = 3/2 = 1.5 units (similar triangles by AAA).

For the volume of the small cone, we have the following:

Volume of small cone = 1/3 × πr²h

Volume of small cone = 1/3 × 3.142 × 1.5² × 3

Volume of small cone = 3.142 × 2.25

Volume of small cone = 7.0695 cubic units.

Mathematically, we know that the volume of a frustum is made by subtracting the volume of a small cone from the volume of a similar large cone cone:

Volume of the frustum = Volume of large cone - Volume of small cone

Volume of the frustum = 452.448 - 7.0695

Volume of the frustum = 445.3785 cubic units.

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The slope Using the formula will be h = -100t + 4000

This is a linear function because for every 5 seconds that pass, the height of the plane drops 500 feet, or -500 to be exact. So that's the slope of the line.

If we look at the table we can determine where the graph goes through the h axis. The h axis is the y axis, and the t axis is the x axis. So where the graph goes through the h axis is also the y-intercept.

If your teacher is any good at all, he/she would make sure that you understand beyond a shadow of a doubt that the y-intercept exists where x = 0. Looking at the table, where x (t) is 0, y (h) is 4000 feet.

Writing the linear equation then is super easy. In the form y = mx + b, we already know both the slope (-100) and the y-intercept (4000), so we fill in accordingly:

h = -100t + 4000 which appears to be choice a.

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We are going to use these properties :

1. (a^m)^n = a^mn
2. a^m x a^n = a^(m+n)
3. a^m : a^n = a^(m-n)

Using the first property, (3^6)^5 = 3^(6x5) = 3^30

Using the second property :
9 = 3^2
-> 9 x 3^7 = 3^2 x 3^7 = 3^(2+7) = 3^9

Therefore, it is simplified down to 3^30 : 3^9

Finally, we will use the third property :
3^30 : 3^9 = 3^(30-9) = 3^21

The required value of x is x = [tex]\sqrt{79}[/tex]

Given : A right angled triangle

This right angles triangle is again divided in two parts

the first part has measures 3 , z and the other side can be calculated by using The Pythagoras Theorem

According to this theorem

3² + z² = y²

thus 9 + z² = y² ------------------equation 1

Also 7 + 3 = 10

thus 10²  = z² + x²-----------------equation 2

And 7² + y² = x² --------------- equation 3

from equation 1 we know

9 + z² + 49 = x²

58 + z² = x²

Thus on substituting this in equation 2 we get

100 = 58 + z² + z²

42 = 2z²

21 = z²

z = [tex]\sqrt{21}[/tex]

thus x² = 58 + 21 = 79

x = [tex]\sqrt{79}[/tex]

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The cost of the appointment without insurance is $200. Isaiah has an insurance plan throw his employer with a $50 monthly premium and a $20 copay. then Isaiah will have to pay his doctor $ 20

Insurance co-pay is a pre-determined amount that a person with medical insurance pay every time they use medical services. The co-pay is a dollar amount and usually less than $25. Different insurance companies have varying co-pay amounts for different services, such as doctor visits and prescriptions.

Isaiah will pay $20 for a visit to the doctor, as stated in the policy document. The $50 premium is payable to the insurance company every month to maintain the insurance coverage.  

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