Suppose ACT Reading scores are normally distributed with a mean of 21.4 21.4 and a standard deviation of 5.9 5.9 . A university plans to award scholarships to students whose scores are in the top 9% 9% . What is the minimum score required for the scholarship? Round your answer to the nearest tenth, if necessary.

Answer:

See answers below

Step-by-step explanation:

T59 = a+58d = -61

T4 = a+3d = 64.

Subtract

58d-3d = -61-64

-55d = -125

d =125/55

d = 25/11

Get a;

From 2

a+3d = 64

a+3(25/11) = 64

a = 64-75/11

a = 704-75/11

a = 629/11

T23 = a+22d

T23 = 629/11+22(25/11)

T23 = 1179/11

the insterrest will be $650 after 4 years

Answer:

I have completed the answers and attached them to the explanation.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question asks for a subtraction expression:

length is always a positive number so bigger number first here.

OB = 4-(-1)              >only moves in x direction so subtract x's

AB = 4-(-2)             >only moves in y direction so subtract y's

Answer:

_D__

Step-by-step explanation:

HOPE THIS helpsss you III

Answer:

Step-by-step explanation:

(x - 7)² = x² - 14x + 49

so each side is x - 7 long where x ≠ 7

Answer:  6 * 24 = 144 ways.

Step-by-step explanation:

Solution:

Given word => DANGER.

The condition is that vowels can't occupy odd places so, we will let them occupy even places.

A total number of arrangements will be = 6 * 24 = 144 ways.

Answer: 6x24 = 144 ways.

The three true statements are as follows:

In the list, there are several true statements and some of them include the facts that all triangles are polygons, they are closed figures and they have three straight sides.

A polygon is a shape with two or more sides. Triangles ahve three sides, so we can easily address them as polygons. Also, all triangles are closed figures and they also have three straight sides.

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Answer:

The answer is 32

Step-by-step explanation:

The formula for finding the area of a trapezoid is:

         ((base 1 + base 2)/ 2 )* h

Now all you have to do is substitute the numbers in.

Note: bases will always be the ones like 12 and 4 in this case. We have just named then 1 and 2.

Answer:

32 square units

Step-by-step explanation:

\(\displaystyle A=\frac{1}{2}(b_1+b_2)h=\frac{1}{2}(12+4)(4)=\frac{1}{2}(16)(4)=\frac{1}{2}(64)=32\)

Note that \(b_1\) and \(b_2\) are the lengths of each base of the trapezoid, so it doesn't matter which is which.

Answer:

1) SA = 2(wl + hl + hw) = 2(12*2 + 12*6 + 6*2) = 2(24 + 72 + 12) = 2(108) = 216

2) SA = (6*4)/2 + 6*11 + 2(5*11) = 12 + 66 + 110 = 188

3) SA = 2(6*12 + 14*12 + 6*14) = 648

4) (9*12)/2 + 15*6 + 9*6 + 12*6 = 54 + 90 + 54 + 72 = 270

5) 2(16*9 + 4*9 + 16*4) = 488

6) SA = 2πrh+2πr^2 = 2*3.14*10*16 + 2*3.14*10^2 = 1004.8 + 628 = 1632.8

7) SA = 2(7*7 + 14*7 + 7*14) = 490

8) SA = 2πrh+2πr^2 = 2*3.14*7*11 + 2*3.14*7^2 = 483.56 + 307.72 = 791.28

9) (12*10)/2 + 2(14*13) + 14*10 = 60 + 364 + 140 = 564

Answer:Answer:

1) SA = 2(wl + hl + hw) = 2(12*2 + 12*6 + 6*2) = 2(24 + 72 + 12) = 2(108) = 216

2) SA = (6*4)/2 + 6*11 + 2(5*11) = 12 + 66 + 110 = 188

3) SA = 2(6*12 + 14*12 + 6*14) = 648

4) (9*12)/2 + 15*6 + 9*6 + 12*6 = 54 + 90 + 54 + 72 = 270

5) 2(16*9 + 4*9 + 16*4) = 488

6) SA = 2πrh+2πr^2 = 2*3.14*10*16 + 2*3.14*10^2 = 1004.8 + 628 = 1632.8

7) SA = 2(7*7 + 14*7 + 7*14) = 490

8) SA = 2πrh+2πr^2 = 2*3.14*7*11 + 2*3.14*7^2 = 483.56 + 307.72 = 791.28

9) (12*10)/2 + 2(14*13) + 14*10 = 60 + 364 + 140 = 564

Step-by-step explanation:

Answer:

f(-3)= 1

f(1)= -1

If f(x)= -2 then x = 3

If f(x) = 2 then x = -5

Step-by-step explanation:

f(x) can be replaced with any number. It just means y. For example, let's replace the (x,y) with the (-5,2). For this point, this is f(-5) = 2. When they ask for f(x), they are just asking what y is with a given coordinate x. So when they ask what f(-3) is, they are asking what y is with -3 being the x coordinate.

So, f(-3) = 1

f(1) = -1

For these questions:

If f(x) = -2 then x = ?

If f(x) = 2 then x = ?

They are asking what x is when y is -2 or 2. So here:

If f(x) = -2 then x = 3

If f(x) = 2 then x = -5

if x=hours, the amount of money he needs is 10 +38*x

he can spend at most 200, so:

and now we can solve:

so the answer is: he can rent the canoe at most 5 hours

The given passage provides a proof that the Separation Axioms follow from the Replacement Schema.

The proof involves introducing a set F and showing that {a: e X : O(x)} is equal to F (X) for every X. Therefore, the conclusion is that the Separation Axioms can be derived from the Replacement Schema.In the given passage, the author presents a proof that demonstrates a relationship between the Separation Axioms and the Replacement Schema.

The proof involves the introduction of a set F and establishes that the set {a: e X : O(x)} is equivalent to F (X) for any given set X. This implies that the conditions of the Separation Axioms can be satisfied by applying the Replacement Schema. Essentially, the author is showing that the Replacement Schema can be used to derive or prove the Separation Axioms. By providing this proof, the passage establishes a connection between these two concepts in set theory.

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Answer:

x^3-y^3

Step-by-step explanation:

(x-y)(x^2+xy+y^2)
Multiply the terms,
x^3 + x^2y + xy^2-  x^2y - xy^2 - y^3
Simplify the terms,
x^3 - y^3
This is also the formula for difference of two cubes.

Answer:

d

Step-by-step explanation:

Answer:

it is A

Step-by-step explanation:

x=(x+3)² - 2

what grade are u doing

Answer:

Bc is intersected by segment AD

Answer:

Bc is intersected by segment AD

Step-by-step explanation:

Using the integers −9 to 9 at most one time each, place a digit in each box (1, 3) and (9, 3) or (-9, 3) to create endpoints for the longest possible line segment both numerically and graphically whose midpoint is (1, 3).

To find the endpoints of the longest possible line segment with midpoint (1, 3), we can use the midpoint formula, which states that the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is ((x₁+x₂)/2, (y₁+y₂)/2).

In this case, we know the midpoint is (1, 3), so we can set up two equations using the variables for the endpoints (x and y) and solve for them:

(x₁ + x₂)/2 = 1

(y₁ + y₂)/2 = 3

We also know that the line segment must be as long as possible, so the endpoints should be as far away from each other as possible. To maximize the distance between the endpoints, we can choose one endpoint to be -9 and the other endpoint to be 9. This gives us:

(x₁ + x₂)/2 = 1 => x₁ + x₂ = 2

(y₁ + y₂)/2 = 3 => y₁ + y₂ = 6

Now we can solve for x₁ and y₁, since x₂ and y₂ will be 2-x₁ and 6-y₁ respectively:

x₁ + (2-x₁) = 2 => x₁ = 1

y₁ + (6-y₁) = 6 => y₁ = 3

So the endpoints of the longest possible line segment with midpoint (1, 3) are (1, 3) and (9, 3) or (-9, 3), and its length is 8 units.

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Answer:

I dont know

Step-by-step explanation:

Answer:

1456

Step-by-step explanation:

This question is asking us to find the sum of \(4(3)^{n-1}\) from n = 1 to n = 6. We can find the sum like this:

\(4(3)^{1-1} +4(3)^{2-1} +4(3)^{3-1} +4(3)^{4-1} +4(3)^{5-1} +4(3)^{6-1}\)

Which can be simplified to:

\(4(3)^{0} +4(3)^{1} +4(3)^{2} +4(3)^{3} +4(3)^{4} +4(3)^{5}\)

\(4(1) +4(3) +4(9) +4(27)+4(81) +4(243)\)

\(4 +12 +36 +108+324 +972 = 1456\)

A well formatted table of the distribution is attached below :

Answer:

0.124

0.733

0.408

Step-by-step explanation:

Using the table Given :

1.) P(AP Statistics) = 90 / 725 = 0.124

2.) P(12th grade ; Precalculus or AP Statistics) = (100 + 65) / 225 = 165 /225 = 0.733

3.) P(Algebra 11 | 11th grade) = P(Algebara11 n 11th grade) / P(11th grade) = 100 / 245 = 0.408

Answer:

A. 6.6 ft

Step-by-step explanation:

sinusoidal curve equation 29 sin (\(\pi\)/9 x)-49

Given the graph of a sinusoidal function, we can write its equation in the form y = A·sin(B(x - C)) + D using the following steps. D: To find D, take the average of a local maximum and minimum of the sinusoid. y=D is the "midline," or the line around which the sinusoid is centered.

In the state of Michigan, the lowest average temperature of the year is in January and is about 20 °F.

The highest monthly average temperature occurs in July at 78 °F

Assume the period is 12 months and January is at the origin of the graph of this function.

sinusoidal curve equation that models the data y

Then, Graph the curve using x = 0 for January, and x = 11 for December, so that x = 12 will be the start of the next year, or end of the period.

So, using the property of sinusoidal curve equation we have

=29 sin (\(\pi\)/9 x)-49

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Answer:

  $48.53

Step-by-step explanation:

The purchases can be written in equation form as ...

  4v +5f = 352.65

  2v +4f = 249.12

Doubling the second equation and subtracting the first gives ...

  2(2v +4f) -(4v +5f) = 2(249.12) -(352.65)

  3f = 145.59 . . . . simplify

  f = 48.53 . . . . . . divide by 3

The price of each football was $48.53.

Difference in interest paid = $82,740.52

Total interest paid for 25 year loan interest - Total interest paid for 20 year loan interest

According to the given information

A.

Monthly payment for 20 year mortgage \(& $=$ PMT $\left(6.5 \% / 12,20^* 12,-312500^* 0.8\right)$ & $=$ PMT $($ rate, nper, $-$ pv $)$ \\)\

Monthly payment for 25 year mortgage \(& $=$ PMT $\left(7 \% / 12,25^* 12,-312500^* 0.8\right)$ & $=$ PMT(rate,nper,-pv) \\\)

B

Total cost of interest for 20 year mortgage \(& $=(\mathrm{B} 2 * 20 * 12)-(312500 * 0.8)$ \\\)

Total cost of interest for 25 year mortgage \($=(\mathrm{B} 3 * 25 * 12)-(312500 * 0.8)$ &\)

C.

Difference in interest paid \(& $=\mathrm{B} 7-\mathrm{B} 6$ &\) = Total interest for 25 year loan-total interest for 20 years

A.

Monthly payment for 20 year mortgage \(& $\$ 1,863.93$ & $=$ PMT(rate,nper,-pv) \\\)

Monthly payment for 25 year mortgage \(& $\$ 1,766.95$ & $=$ PMT(rate,nper,-pv) \\\)

B.

Total cost of interest for 20 year mortgage = \(& $\$ 197,343.88$ & $=$\)  total monthly payments-loan taken

Total cost of interest for 25 year mortgage = \(& $\$ 280,084.40$ & $\) = total monthly payments-loan taken

C.

Difference in interest paid = $82,740.52

Total interest paid for 25 year loan interest - Total interest paid for 20 year loan interest

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Answer:

-7

Step-by-step explanation:

Look at picture body :\

The notion of finiteness refers to the idea that something has a definite limit or is not infinite. It is a concept that has been applied in various fields of study, such as mathematics, computer science, and philosophy.

In mathematics, finiteness is a fundamental concept used to define various mathematical objects and structures, such as sets, numbers, and sequences. It is also used to define the properties of functions and to study the properties of mathematical systems.

In computer science, the notion of finiteness is crucial for the design and analysis of algorithms and computer programs. Computer scientists use finite state machines, which are mathematical models that describe the behavior of a system that can be in one of a finite number of states.

This concept is essential to the development of computer programs that are efficient, reliable, and secure.

In philosophy, finiteness is a concept that is often used to reflect on the nature of human existence and the limits of human knowledge. It is also used to examine the concept of time and the nature of reality.

In general, the notion of finiteness is a fundamental concept that has many applications in various fields of study.

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Using the ratio of the sides, we have:$x\sqrt{3} = 12\sqrt{3}$ (opposite the $60^{\circ}$ angle is 12$\sqrt{3}$)$x = 2\sqrt{3}\cdot6$ (the hypotenuse is $2x = 12\sqrt{3}$)Simplifying, we have:$x = 12\sqrt{3}$. Therefore $x=y=12\sqrt{3}$, which is our answer

In a 30-60-90 triangle, the sides have the ratio of $1: \sqrt{3}: 2$. Let's apply this to solve for the variables in the given problem.

Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form. x=y=Let's first find the ratio of the sides in a 30-60-90 triangle.

Since the hypotenuse is always twice as long as the shorter leg, we can let $x$ be the shorter leg and $2x$ be the hypotenuse.

Thus, we have: Shorter leg: $x$Opposite the $60^{\circ}$ angle: $x\sqrt{3}$ Hypotenuse: $2x$

Now, let's apply this ratio to solve for the variables in the given problem. We know that $x = y$ since they are equal in the problem.

Using the ratio of the sides, we have:$x\sqrt{3} = 12\sqrt{3}$ (opposite the $60^{\circ}$ angle is 12$\sqrt{3}$)$x = 2\sqrt{3}\cdot6$ (the hypotenuse is $2x = 12\sqrt{3}$)Simplifying, we have:$x = 12\sqrt{3}$

Therefore, $x=y=12\sqrt{3}$, which is our answer.

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The linear equation 3 · x + 4 = 7 · x - 8 has solution x = 3. (Correct choice: C)

The linear equation 2 · x = 7 · x - 5 has solution x = 1. (Correct choice: E)

The linear equation 5 · x - 8 = 5 · x + 12 has no solution. (Correct choice: D)

In this question we find three linear equations with one variable, whose corresponding solution must be determined by using algebra properties. The complete procedure is summarized below:

Now we proceed to apply the procedure for each case:

Case 1

3 · x + 4 = 7 · x - 8

7 · x - 3 · x = 8 + 4

4 · x = 12

x = 3

The linear equation has an unique solution (x = 3). (Correct choice: C)

Case 2

2 · x = 7 · x - 5

7 · x - 2 · x = 5

5 · x = 5

x = 1

The linear equation has an unique solution (x = 1). (Correct choice: E)

Case 3

5 · x - 8 = 5 · x + 12

5 · x - 5 · x = 8 + 12

0 = 20 (CRASH!)

The linear equation has no solution. (Correct choice: D)

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Answer:c

Step-by-step explanation:300 divided by 4 is 75

The total number of attempts to make a sandwich from white, wheat or rye bread, cheddar or Swiss cheese and ham, turkey or roast beef is 18.

A basic principle of calculus states that if there are m possibilities for one event and n possibilities for another event, then there are m × n possibilities for both events to occur.

The sample space is the set of all possible outcomes of a given experiment.

In this case, the test is to make a sandwich.

There are three choices for bread (white, wheat or rye).

There are two options for cheese (cheddar or Swiss).

There are three options for meat (ham, turkey or roast beef).

Therefore, the total number of sample farms can be calculated according to the basic calculation principle.

In this case, there are 3 × 2 × 3 = 18 sample states.

This means that 18 different combinations of bread, cheese and meat can be used to make a sandwich.

For easier visualization, these 18 sample states can be organized into a chart.

Each row of the chart represents a different combination of bread, cheese and meat that can be used to make a sandwich.

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Answer:

Step-by-step explanation:

Set up an equation:

7x + 10x + 13x = 100000 and solve for x:

30x = 100000 so

x = 3333.33

Anna gets 7(3333.33) = 23333.31

Louise gets 10(3333.33) = 33333.33

Lacey gets 13(3333.33) = 43333.29

Answer:

Step-by-step explanation:

10-5=5