Sally borrows some money at a 15% interest rate. She repays the loan in full after 30 months and pays $1692 in interest. How much did she borrow?

Answers

Answer 1

Answer: $4512 was the amount she borrowed.

Step-by-step explanation:

SI = 1692

R = 15% = 0.15

T = 30 months = 2.5 years

SI = PRT

1692 = P x 0.15 x 2.5

1692 = 0.375P

P = 1692 / 0.375

P = 4512


Related Questions

The whole number which is not a natural number is

Answers

Answer:

All negative numbers

Step-by-step explanation:

They are not whole numbers

Answer:

0

Step-by-step explanation:

Since negative numbers are not considered whole numbers, they are not included here. All natural numbers are whole numbers but not all whole numbers are natural numbers. 0 is a whole number but it doesn't count as a natural number which makes the answer 0

I need help on this please

Answers

Answer:

[tex]y=\frac{5}{6}x+5[/tex]

Step-by-step explanation:

Well this is actually really simple we just have to look at the line and see what attributes it has so we can make an equation.

So slope intercept form is [tex]y=mx+b[/tex].

Like to find the y intercept we know it is the point that the line touches the y axis which is 5.

Now for the slope, the slope is how far each points are from each other on a line so to find the slope we can use the following formula [tex]\frac{y^2-y^1}{x^2-x^1}[/tex].

So to do this we need two points that are on the line we can use (-6,0) and (6,10).

So y2 is 10 and y1 is 0 so 10-0 is 10 and 6 - -6 is 12 so the slope is 10/12 and we have to simplify it to 5/6 so the slope is 5/6 and now we have to put it in slope intercept -> [tex]y=\frac{5}{6}x+5[/tex]

The equations x minus y = 2, x minus 2 y = negative 2, x + y = 2, and x + 2 y = negative 2 are shown on the graph below. On a coordinate plane, there are 4 lines. Green line goes through (0, 2) and (2, 0). Orange line goes through (2, 0) and (0, negative 2). Pink line goes through (2, negative 2), and (0, negative 2). Blue line goes through (0, negative 2) and (2, 2). Which system of equations has a solution of approximately (0.7, –1.4)? x minus y = 2 and x + 2 y = negative 2 x minus 2 y = negative 2 and x + y = 2 x minus y = 2 and x minus 2 y = negative 2 x + y = 2 and x + 2 y = negative 2

Answers

Answer:

  x - y = 2   and   x + 2y = -2

Step-by-step explanation:

Since you have the graph, you can easily see that the point of interest is nearest the intersection of the orange and pink lines.

__

Recognizing that the intercepts of a line in standard form are ...

  ax +by =c

  x-intercept: c/a

  y-intercept: c/b

You can easily determine the corresponding intercepts for the given lines. We can tell from the graph that we only need to know what the y-intercept is in order to match the equation to the line. Here are the y-intercepts:

x -y = 2   ⇒   (0, -2) — orangex -2y = -2   ⇒   (0, 1) — bluex +y = 2   ⇒   (0, 2) — greenx +2y = -2   ⇒   (0, -1) — pink

The system of equations with the desired solution is ...

  x -y = 2  and  x +2y = -2

Answer:

A: x-y= 2 and x+2y= -2

Step-by-step explanation:

I got it right on Edge 2020

Find the solution set. 8x^2-2x-3=0 separate the two values with with a comma.

Answers

Answer:

x = -1/2, 3/4

Step-by-step explanation:

Step 1: Factor

(2x + 1)(4x - 3) = 0

Step 2: Find roots

2x + 1 = 0

2x = -1

x = -1/2

4x - 3 = 0

4x = 3

x = 3/4

Figure ABCD is a rectangle find the value of x

Answers

Answer:

8

Step-by-step explanation:

BD is 32 units.

BE is half of BD

3x - 8 = 32/2

3x - 8 = 16

3x = 16 + 8

3x = 24

3/3x = 24/3

x = 8

Answer:

8

Solution,

Diagonals of rectangle bisects each other.so,

2 BE = BD

2( 3x - 8 ) = 32

6x - 16 = 32

Add 16 on both sides

6x - 16 + 16 = 32 + 16

Simplify

6x = 48

divide both sides of equation by 6

6x/6 = 48/6

calculate

X = 8

Hope this helps...

Good luck on your assignment..

NEED ANSWER ASAP What is the location of point G, which partitions the directed line segment from F to D into an 8:5 ratio?

Answers

Answer:

(A) 1

Step-by-step explanation:

We know that the formula is x = (m/m+n) (x2-x1) + x1.

But the trick to the question which is why everyone is getting it wrong is because it asks for F to D not D to F.

The reason everyone else was getting 4 was because they were using this.

They solved the equation x = (8/8+5) (9-[-4]) -4 where it was D to F. This equation does turn out to be 4 but it is incorrect.

However, the correct equation (because it is supposed to be F to D) is

x = (8/8+5) (-4 -9) +9 which is in fact equal to 1.

I also just took the quiz and got 100%.

PRESS THAT THANKS BUTTON!!!

Solve the system of equations:
y = x-2
y= x2 – 3x+ 2

Answers

Answer:

(2, 0)

Step-by-step explanation:

y = x - 2

y = x² - 3x + 2

Since both equations equal y, you can set the equations equal to each other.

x - 2 = x² - 3x + 2

x = x² - 3x + 4

0 = x² - 4x + 4

0 = (x - 2)(x - 2)

x - 2 = 0

x = 2

Now that you have an x-value, solve for y.

y = x - 2

y = 2 - 2

y = 0

The solution is (2, 0).

prime factor of 841​

Answers

Answer:

the prime factor of 841 is 29

Step-by-step explanation:

841 divided by 29 gives back 29 without any remainder

Can someone help me solve this?

What is side b? Thank you

Answers

Answer:

The answer is

b = 39.32 feet

Step-by-step explanation:

To find side b we use cosine

cos ∅ = adjacent / hypotenuse

From the question

side c is the hypotenuse

side c = 48 feet

side b is the adjacent

∅ = 35°

We have

cos 35 = b/c

cos 35 = b / 48

b = 48 cos 35

b = 39.319

b = 39.32 feet to 2 decimal places

Hope this helps you

Answer:

b ≈ 39.32 ft

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos35° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{b}{c}[/tex] = [tex]\frac{b}{48}[/tex] ( multiply both sides by 48 )

48 × cos35° = b, thus

b ≈ 39.32 ft ( to 2 dec. places )

A magician asks two volunteers to each draw a card from a standard deck of cards. What is the probability that the first card is a heart and the second card is a dimand?

Answers

Answer:

The probability of choosing a heart, P(Heart) = 13/52 = 0.25

Step-by-step explanation:

Kite E F G H is inscribed within a rectangle. Points F and H are midpoints of the sides of the rectangle. Points E and G are parallel to the side of the rectangle.
Kite EFGH is inscribed in a rectangle such that F and H are midpoints and EG is parallel to the side of the rectangle.

Which statement describes how the location of segment EG affects the area of EFGH?

The area of EFGH is One-fourth of the area of the rectangle if E and G are not midpoints.
The area of EFGH is One-half of the area of the rectangle only if E and G are midpoints.
The area of EFGH is always One-half of the area of the rectangle.
The area of EFGH is always One-fourth of the area of the rectangle.

Answers

Answer:

The area of EFGH is always One-half of the area of the rectangle.

Step-by-step explanation:

If F and H are midpoints of sides of rectangle then FH is parallel to the other side of rectangle so FH is perpendicular to the EG. That means the lenght of FH is equal to lenght of rectangle, and the lenght of EG is equal to width of rectangle.

So the area of the rectangle:  [tex]A_{rectangle}=EG\cdot FH[/tex]

FH ⊥ EG so the area of quadrangle EFGH:

[tex]A_{_{EFGH}}=\frac12EG\cdot FH=\frac12A_{rectangle}[/tex]

no matter the location of segment EG

The area of EFGH is always One-half of the area of the rectangle.

What is mean by Rectangle?

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

We have given that;

the kite EFGH is inscribed in a triangle and F and H are midpoints and EG is parallel to the side of rectangle.

The kite consists of 2 triangle that are EFG and EHG.

Now,

In a triangle EFG is,

= 1/2 x EG x h......(1)

where h is the height from F to EG

Also the area of EHG:

= 1/2 x EG x h₁

where is the height from H to EG

We also know that h₁ + h is the width of the rectangle and EG is the length of the rectangles.

Area of Kite = = 1/2 x EG x h + 1/2 x EG x h₁

Also, The area of a rectangle is rectangle length × rectangle width.

Thus, The Kite EFGH is inscribed in a rectangle such that F and H are midpoints and EG is parallel to the side of the rectangle.

Hence, The statement describes how the location of segment EG affects the area of EFGH is the area of EFGH is always One-half of the area of the rectangle.

To learn more about the rectangular kite visit:

brainly.com/question/2292872

#SPJ7

Help urgently please❤️ I’m waiting urgently

Answers

Answer:

1. 3511

2 B= 0.25

Step-by-step explanation:

1. The number of single scoop cone is represented as s while the number of double scoop cone is represented as d. The total number of scoop cone the coach bought is 15 and the total sum is 57 dollars .

Therefore, multiply the number of single scoop cone(s) by each price and also find the product of the number of double cone(d) and the price of each . Then add the result to get 57 dollars. Therefore, A = 3 dollars and B = 5 dollars. The sum of s and d will give 15 . Therefore, C and E is equals to 1.

2. s is the number of small candies while l is the number of big candies. The individual cost of the small candies and the large candies are in cents so we have to convert them to dollars.

Cost of each small candies = 10/100 = 0.1 dollars

Cost of each large candies = 25/100 = 0.25 dollars.

Therefore, using the same principle as number 1

A = 0.1 dollars

B = 0.25 dollars

The value of E = 52

Determine the slope of the line that contains the points of (-9,5) and (6,-5)

Answers

Answer:

                 [tex]\bold{m=-\dfrac23}[/tex]

Step-by-step explanation:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}\\\\(-9,\,5)\ \implies\ x_1=-9\,,\ y_1=5\\(6,\,-5)\ \implies\ x_2=6\,,\ y_2=-5\\\\m=\dfrac{-5-5}{6-(-9)}=\dfrac{-10}{6+9}=-\dfrac{10}{15}=-\dfrac23[/tex]

Lynn is making custom bricks. She combines 39 pounds of water and 48 pounds of brick dust in a mixing bucket. She spills 13 pounds of the mixture while stirring the contents. The mixture is then poured into small dirt holes to make bricks. Each brick requires 7 pounds of mixture, and the leftover mixture is washed out of the mixing bucket.

Answers

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Lynn is making custom bricks. She combines 39 pounds of water and 48 pounds of brick dust in a mixing bucket. She spills 13 pounds of the mixture while stirring the contents. The mixture is then poured into small dirt holes to make bricks. Each brick requires 7 pounds of mixture, and the leftover mixture is washed out of the mixing bucket.

What is the greatest number of bricks Lynn can make?  

How many pounds of mixture will be washed out of the bucket if Lynn makes the greatest  number of bricks?

Answer:

Greatest number of bricks = 70

Washed out mixture = 4 pounds

Therefore, Lynn can make at most 70 bricks and 4 pounds of mixture will be washed out if she makes 70 bricks.

Step-by-step explanation:

She combines 39 pounds of water and 48 pounds of brick dust in a mixing bucket.

Amount of mixture = 39 pounds of water + 48 pounds of brick dust

Amount of mixture = 87 pounds

She spills 13 pounds of the mixture while stirring the contents.

Amount of mixture left = 87 pounds - 13 pounds

Amount of mixture left = 74 pounds

Each brick requires 7 pounds of mixture

What is the greatest number of bricks Lynn can make?  

Greatest number of bricks = 7×10

Greatest number of bricks = 70

How many pounds of mixture will be washed out of the bucket if Lynn makes the greatest  number of bricks?

Washed out mixture = 74 pounds - 70 pounds

Washed out mixture = 4 pounds

Therefore, Lynn can make at most 70 bricks and 4 pounds of mixture will be washed out if she makes 70 bricks.

When using a debit card: Question options: A:There are always fees. b:Identification is always required. c:You still need to record transactions in your checkbook. d:You are not personally liable for more than $50 if it is stolen.

Answers

Answer:

D.

Step-by-step explanation:

Since this isn't a credit card, there are no interests or fees on a debit card, so A is incorrect. B is also incorrect. You only need identification when you are withdrawing or depositing at a bank, but purchases made in stores or online do not need your identification. You also don't need to record transactions in your checkbook (but it is recommend to keep track of purchases). Modern day technology already records transaction history and all you need to do is access it online.

D is correct because if someone steals your PIN for your debit card, they could go to stores and use that money. You can dispute charges and report to the bank if that happens.

can someone help me with the question, please.

Answers

Answer:

x = arcsin 0.591 = 0.632 radian or 36.21 degrees

Step-by-step explanation:

Angle x and the sides 13 and 22 cm are related through the sine function as follows:

            opposite side      13 cm

sin x = ---------------------- = ------------- = 0.591

              hypotenuse         22 cm

Now find x using the inverse sine function:

x = arcsin 0.591 = 0.632 radian or 36.21 degrees

Answer:

36.22°

Solution,

Perpendicular = AB

hypotenuse = AC

we know that,

[tex]sin \: theta = \frac{perpendicular}{hypotenuse} [/tex]

[tex]sin \: x \: = \frac{ab}{ac} [/tex]

[tex]x = {sin}^{ - 1} \frac{13}{22} [/tex]

[tex]x = 36.22[/tex]

Hope this helps...

Monique is factoring the expression 4 x + 16 x y. Her work is shown below. Factors of 4x: 1, 2, 4, x Factors of 16xy: 1, 2, 4, 8, 16, x, y GCF: 4x Factored expression: 4 x (0 + 4 y) Which best describes the accuracy of Monique's solution? Monique's solution is accurate. Monique made an error when listing the factors, which affected the GCF and the factored expression. Monique made an error when determining the GCF from her list of factors. Monique made an error when writing the factored expression.

Answers

Answer:

Monique made an error when writing the factored expression.

Step-by-step explanation:

The factorisation of the expression 4x+16xy is 4x(1+4y).

The given expression is 4x+16xy.

What is factorisation?

In mathematics, factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.

Now, 4x=2×2×x and 16xy=2×2×2×2×x×y

so, the GCF of terms 4x.

Now, 4x(4x/4x+16xy/4x)=4x(1+4y)

Therefore, the factorisation of the expression 4x+16xy is 4x(1+4y).

To learn more about the factorisation visit:

https://brainly.com/question/20293447.

#SPJ2

what is the greatest common factor of the polynomial below? 8x^2-4x

Answers

Answer:

4x

Step-by-step explanation:

8x^2 = 2*2*2 *x*x

4x = 2*2 *x

The greatest common factor is 2*2*x = 4x

Answer:

A

Step-by-step explanation:

8x² - 4x

Factor out the greatest common factor.

4x(2x) - 4x(1)

4x(2x - 1)

The greatest common factor of the polynomial is 4x.

Please show your work! *grade 9 work*

Answers

Answer:

c = 6√2 cm

Step-by-step explanation:

a² + b² = c²

6² + 6² = c²

36 + 36 = c²

108 = c²

c = ± √108 = ± 6√2

Since the side length of a triangle can't be negative, c = -6√2 is an extraneous solution; therefore the answer is c = 6√2.

Answer:

72 cm or 6 square root of 2

Step-by-step explanation:

a^2+b^2=c^2

6^2+6^2=c^2

36+36=72

c= 72 cm.  or 6 square root of 2

hope this helps.

The Lewis family and the Perry family each used their sprinklers last summer. The water output rate for the Lewis family's sprinkler was per hour. The water output rate for the Perry family's sprinkler was per hour. The families used their sprinklers for a combined total of hours, resulting in a total water output of . How long was each sprinkler used

Answers

The Lewis family and the Perry family each used their sprinklers last summer. The water output rate for the Lewis family's sprinkler was 15 L per hour. The water output rate for the Perry family's sprinkler was 40 L per hour. The families used their sprinklers for a combined total of 65 hours, resulting in a total water output of 1850 L . How long was each sprinkler used

Answer:

Hours of use of sprinkler by Lewis family is 30 hours.

Hours of use of sprinkler by Perry family is 35 hours.

Step-by-step explanation:

Let W = hours of use by Lewis family

65 - W = hours of use by Perry family

Then;

15W + 40*(65 - W) = 1850

15W + 2600 - 40W = 1850

(15 - 40)W = 1850 - 2600

-25W = −750

W = 750/25 = 30

Therefore;

W = 30

65 - W = 65 - 30 = 35

Hence,

Hours of use by Lewis family is 30 hours.

Hours of use by Perry family is 35 hours.

Use the graph of the polynomial function to find the factored form of the related
polynomial. Assume it has no constant factor.

A. (x + 2)(x+2)
B. x(x-2)
C. x(x + 2)
D. (x-2)(x + 2)

Answers

Answer:

d

Step-by-step explanation:

the answer would be (x-2)(x+2)

Carlos' hourly wage increased by 30% this year. If his previous salary was $20 an hour, what is his new hourly wage?

Answers

Answer:

$26.

Step-by-step explanation:

His original salary was $20. It increased by 20%. In other words, the total salary he earns is now:

[tex]20+20(.3)=20(1.3)=26[/tex]

His new salary is $26.

Note: For the second step, I used the distributive property.

[tex]20(1)+20(.3)=20(1+.3)=20(1.3)[/tex]

The answer is $26 dollars

Use the function below to find (-2).
f(x) = 3x
O A.
O B. -9
O c.
O D. -6

Answers

answer

f(x)= 3x

= 3×-2 = -6

D. -6

ASAP MATH HELP WITH THIS QUESTIONS

Answers

Answer:

y = - x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 5) and (x₂, y₂ ) = (4, - 1)

m = [tex]\frac{-1-5}{4+2}[/tex] = [tex]\frac{-6}{6}[/tex] = - 1, thus

y = - x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (4, - 1 ), then

- 1 = - 4 + c ⇒ c = - 1 + 4 = 3

y = - x + 3 ← equation of line

Select the correct answer.
A particular strain of a common bacteria replicates itself every 14 minutes. Which of the following does this situation represent

Answers

Answer:

c

Step-by-step explanation:

Answer:

Both a relation and a function

Step-by-step explanation:

Replicates itself every 14 minutes, which is exponential function

Write the slope-intercept form of the equation of the line that has the same y-intercept as the black line shown and passes through the point (4, 4) on the blue line. Explain how you determined your answer.

Answers

Answer:

y = 0.5x + 2

Step-by-step explanation:

the y-intercept is 2, as shown in the graph

the slope is 0.5. this is because while the x-value goes up by 2, the y-value goes up by one (from 0, 2 to 2, 3).

using the slope formula of rise / run, you get 1/2, which is equal to 0.5

help quick plz must get this correct I will make u a brainllest

Answers

Answer:

CPCTC

Step-by-step explanation:

You already proved that triangle BAD is congruent to CAD, this means that all of the corresponding angles and sides with be congruent (CPCTC). That means BD is congruent to CD. Hope this helps!

Help me please as fast as fast as you can 20 points!!

Answers

Answer:

see below

Step-by-step explanation:

4! = 4*3*2*1 = 24

10 C3 = 10 CHOOSE 3 =10! /(3! (10 - 3)!) = 10! / 3! * 7! = 10*9*8 / 3*2*1 = 120

7P3 = permutation = 7! / (7-3)! = 7! /4! = 7*6*5 = 210

Evaluate the following expression using the values given: Find 2r2 + 3s3 − r2 + 4t2 − r2 if r = −2, s = −3, and t = 5.

Answers

Answer:

The evaluated answer to this equation is 19.

Step-by-step explanation:

2r² + 3s³ - r² + 4t² - r²

In the problem, we are given values for the variables in the equation.

r = -2

s = -3

t = 5

Let's plug these numbers into the equation.

2(-2)² + 3(-3)³ - (-2)² + 4(5)² - (-2)²

First, simplify the exponents.

2(4) + 3(-27) - (4) + 4(25) - (4)

Next, multiply the numbers starting from left to right.

8 + (-81) - 4 + 100 - 4

Add 8 and -81 together.

-73 - 4 + 100 - 4

Subtract 4 from -73.

-77 + 100 - 4

Add -77 to 100.

23 - 4

Subtract 4 from 23.

19

So, your final simplified answer to this equation is 19.

marcus receives an inheritance of $13,000. he decides to invest this money in a 10-year certificate of deposit (CD) that pays 3.0% interest compounded monthly. how much money will marcus receive when he redeems the CD at the end of 10 years?

Answers

Answer:

Marcus will receive a total of $17,542.2 when he redeems the certificate of deposit (CD) at the end of 10 years

Step-by-step explanation:

Principal(p)=$13,000

Rate(r)=3.0%

Period(n)=12 months

Time(t)=10 years

A=p(1+r/n)^nt

=13,000(1+0.03/12)^12*10

=13,000(1+0.0025)^120

=13,000(1.0025)^120

=13,000(1.3494)

=17,542.2

A=$17,542.2

Marcus will receive a total of $17,542.2 when he redeems the certificate of deposit (CD) at the end of 10 years

Other Questions
if i have to do 60 hours in 5 weeks how many mintues do i do a day Two cylindrical cans of beef stew sell for the same price. One can has a diameter of 8 inches and a height of 4 inches. The other has a diameter of 6 inches and a height of 7 inches. Which can contains more stew & is , therefore ,a better buy? PLEASE HELP ASAP Brent is driving to a conference in another state. Three hours after leaving his home and beginning his drive, Brent is still 470 miles from his destination. After another 4 hours of driving, Brent is 258 miles from his destination. After 9 hours of driving, Brent plans to stop at a hotel for the night and begin his trip again 12 hours later. If Brents average speed had been faster or slower on his trip, what features of the graph would change and how would they change in each situation. Explain your answers. Type your response here: Brent decided that he needed to reach his destination in 11 hours of driving. What would his average rate of speed, rounded to the nearest hundredth, need to be to accomplish this? Show your work. Ruth has a beaker containing a solution of 800 mL of acid and 200 mL of water. She thinks the solution is a little strong, so she drains 100 mL from the beaker, adds 100 mL of water, and stirs the solution. Ruth thinks the solution is still too strong, so again she drains 100 mL from the beaker, and adds 100 mL of water. How many mL of water are now in the beaker? What is the value ofP(X = 2 or X = 0)Enter your answer in the box How can a state's gerrymandering impact goverment at the national level?a) A state can draw districts favoring votes for one party to the House of Representatives.b) A state can change district numbers to increase the number of representatives it has.c) A state can order people to move to another district to encourage the election of certain parties.d) A state can close or restrict voting for districts that do not align with its preferred policies. 1+1(I want to give points back so i am doing this).Pay it Forward ) Find the average rate of change of the area of a circle with respect to its radius r as r changes from (i) 2 to 3 (ii) 2 to 2.5 (iii) 2 to 2.1 (b) Find the instantaneous rate of change when r 2. (c) Show that the rate of change of the area of a circle with respect to its radius (at any r) is equal to the circumference of the circle. Try to explain geometrically why this is true by drawing a circle whose radius is increased by an amount Dr. How can you approximate the resulting change in area DA if Dr is small? Is the selection below a permutation, a combination, or neither? Explain your reasoning. Upper A group of 5 senators is chosen to be part of a special committee. HELP ASAP PLEASE!!!! SHOW WORK D = childs dosage in milligrams a = age of the child M = adult dosage in milligrams The child weighs 55 lbs. Convert the childs weight in pounds (lbs.) to kilograms (kg). Parallelogram H G J L is shown. Diagonals are drawn from point H to point J and from point G to point L and intersect and point K. In parallelogram HGJL, HK = c 7, JK = 3c 33, and GK = c + 12. What is the length of segment GL? GL = units b(1)=16 b(n)=b(n1)+1 Find the 2 term in the sequence. Write a paragraph summarizing Gandhi's influence. Howshould he be remembered?Gandhi fought against racial discrimination in Need Help Please I'm Out Of Time ;( Find the GCF (greatest common factor) of 84 and 36. Be sure to show your work. Then, using complete sentences, explain what your answer means. Samples of aluminum-alloy channels were tested for stiffness. the following frequency distribution was obtained. The distribution is assumed to be normal.stiffness frequency2480 232440 352400 402360 332320 21a) What is the approximate mean of the population from which the sample were taken?b) What is the approximate standard deviation of the population from which the samples were taken?c) What is the approximate probability that stiffness would be less than 2350 for any given channel section? Personal Trainer, Inc. owns and operates fitness centers in a dozen Midwestern cities. The centers have done well, and the company is planning an international expansion by opening a new "supercenter" in the Toronto area. Personal Trainers president, Cassia Umi, hired an IT consultant, Susan Park, to help develop an information system for the new facility. During the project, Susan will work closely with Gray Lewis, who will manage the new operation.BackgroundSusan and Gray finished their work on user interface, input, and output design. They developed a user-centered design that would be flexible and easy to learn. Now Susan turned her attention to the architecture for the new system. Susan wanted to consider their own organization and culture, enterprise resource planning, total cost of ownership, scalability, Web integration, legacy systems, processing methods, security issues, and corporate portal. She also needed to select a network plan, or topology, that would dictate the physical cabling and network connections, or consider a wireless network. When all these tasks were completed, she would submit a system design specification for approval.Tasks1. What software and hardware infrastructure will be necessary to ensure Personal Trainer can process point of sale transactions?2. Prepare an outline for a system design specification and describe the contents of each section. Study the diagram of circle K, where JL and LM are tangent to circle K at points J and M, respectively. Also, JL=3x+10 and ML=7x6. What is the length of LM? 22 17.6164 What is the probability of getting a number less than 6 on a single throw? What would be the volume of an ice cube if the cube has a mass of 100 grams and its density is determined to be 1g/cm3? The time series graph gives some information about the number of umbrellas sold in the first six months of 2015