A researcher conducted a survey to 50 respondents about what they like among the three online games, namely the mobile legends, the clash of clans, and the player's unknown battlegrounds (PUBG) out of 50 respondents, 15 people chose PUBG, 30 chose mobile legends and 20 chose clash of clans, How many Respondents chose all 3 online games?

Answers

Answer 1

Answer:

15 Respondents

Step-by-step explanation:

Total number of respondents = n (PUBG ∪ M ∪ C) = 50

PUBG = n(PUBG ) = 15 people

Mobile legends = n(M) = 30 people

Clash of clans = n(C) = 20 people

n ( PUBG ∩ M) = Unknown

Step 1

The first step is to find the number of respondents that chose two or the games

a) Number of respondents that chose Mobile legends and PUBG =

n ( M ∩ PUBG)

30 - x = 15 - x + x

30 - 15 = x + x - x

15 = x

b) a) Number of respondents that chose Mobile legends and Clash of clans =

n ( M ∩ C)

n ( M ∩ C) = y

30 - y = 20 - y + y

30 - 20 = y + y - y

10 = y

c) Number of respondents that chose PUBG and Clash of clans =

n ( C ∩ PUBG) = z

20 - z = 15 - z + z

20 - 15 = z + z - z

5 = z

Step 2

How many Respondents chose all 3 online games

= n ( PUBG ∩ M)

n (PUBG ∪ M ∪ C) = n(PUB ) + n ( M ) + n (C) – n ( M ∩ PUBG) – n ( C ∩ PUBG) – n ( M ∩ C) + n (PUBG ∩ M ∩ C)

50 = 30 + 20 + 15 - 15 - 5 - 10 + n (PUBG ∩ M ∩ C)

50 = 65 - 30 + n (PUBG ∩ M ∩ C)

50 = 35 + n (PUBG ∩ M ∩ C)

50 - 35 = n (PUBG ∩ M ∩ C)

n (PUBG ∩ M ∩ C) = 15

Therefore, the number of Respondents chose all 3 online games = 15

Answer 2

Answer:

15

Step-by-step explanation:


Related Questions

the cost of renting a car for one day and driving m miles if the rate is $49 per day plus 5 cents per mile

Answers

Answer:

[tex]Total\ Rent = 49 + 5m[/tex]

Step-by-step explanation:

Given

Rent per day = $49

Addition = 5 cents per mile

Required

Determine the rent for a day and m miles

First, we need to generate a formula from the given parameters;

Let d represent number of days and m represent additional miles;

[tex]Total\ Rent = 49 * d + 5 * m[/tex]

[tex]Total\ Rent = 49 d + 5 m[/tex]

Solving for the rent for a day and m miles

We have that: d = 1 and m = m

Substitute these in the formula above

[tex]Total\ Rent = 49 * 1 + 5 * m[/tex]

[tex]Total\ Rent = 49 + 5m[/tex]

Hence, the total rent is

[tex]Total\ Rent = 49 + 5m[/tex]

Q1: Factor the polynomial 6x4 + 24x3 − 72x2 completely by first factoring out the GCF, and then factoring the rest of the expression. Q2: Consider the polynomial 6x4 + 24x3 − 72x2. What is the greatest common factor (GCF) of the terms of the polynomial?

Answers

Answer:

After factorizing the given polynomial we get 6x^2 (x+6)(x-2)

Step-by-step explanation:

Given Polynomial:  

6x^4+24x^3−72x^2

We need to completely factorize the polynomial.

Consider,

6x^4+24x^3−72x^2

GCF = 6x^2, By taking it common out

= 6x^2 (x^2+4x-12)

= 6x^2 (x^2+6x-2x-12)

= 6x^2 (x(x+6)-2(x+6))

= 6x^2 (x+6)(x-2)

Therefore, After factorizing the given polynomial we get 6x² ( x + 6 ) ( x - 2 )

Please mark me Brainliest.

calculate the total surface area of a cylinder whose radius is 7cm and height is 21cm.
1212
1227
1232
1242

Answers

Answer:

C. 1232

Step-by-step explanation:

A=2πrh+2πr2=2·π·7·21+2·π·72=1232.

Answer:

The answer is 1232cm^2

Step-by-step explanation:

Formula for total surface area of a cylinder is=2[tex]\pi[/tex]r²+2[tex]\pi[/tex]rh

radius=7 cm

height=21 cm

∴TSA= 2 x 3.14 x 7² + 2 x 3.14 x 7 x 21

TSA= 2 x 3.14 x 49 + 2 x 3.14 x 7 x 21

TSA=1232cm².

You can also use 22/7 for pile/[tex]\pi[/tex] instead of 3.14.

It's your choice.

Thanks.

What is the average rate of change over the interval [0.75, 1.125]? Explain the meaning of the average rate of change.

Answers

Answer:

1) The average rte of change = 6

2) The average rate of change over an interval is the ratio of the total change in the determinate variable or function (values of the output of the function) to the change in the indeterminate variable (values of the input of the function)

Step-by-step explanation:

1) The average of change of the function is found as follows;

At x = 0.75, y = -0.5, at x = 1.125, y = 1.75

Therefore, the average rate of change = (1.75 - (-0.5))/(1.125 - 0.75) = 6

2) The average rate of change over an interval on a graph or of a curve is found by dividing the difference between the y-coordinate values of the two points on the graph by the difference of the x-coordinate values of the two points.

LET x=0 x-2y=4 what is the value of y?


Solve for the missing variable: LET y=0: x-2y=4 what is the value of x?



Answers

Answer:

When x = 0, then y = -2

When y = 0, then x = 4

Step-by-step explanation:

We are given with the following equation;

x - 2y = 4

Now, we have to find the respective values of x and y for each value of x = 0 and y = 0.

Firstly, putting the value of x = 0;

x - 2y = 4

0 - 2y = 4

-2y = 4

y = [tex]\frac{4}{-2}[/tex]  = -2

This means that when x = 0, then y = -2.

Similarly, putting the value of y = 0;

x - 2y = 4

[tex]x-(2\times 0)=4[/tex]

x - 0 = 4

x = 4

This means that when y = 0, then x = 4.

Simplify 8x - 3 (x + 1) - 4.

Answers

Answer:

5x-1

Step-by-step explanation:

8x-3(x+1)-4

{open the brackets}3x-3

8x-3x-3-4

5x+(-7), which is 5x-7

The answer would be 5x-7 because -3(x+1) distributed is -3x-3, so when you subtract 3x from 8x you get 5x and when you subtract 3 from -4 you get -7 therefore 5x-7

can someone please help me

Answers

Answer:

m = 20a = 48These are the answers.

Step-by-step explanation:

1. m/-8 = -2.5

*-8 = *-8

m = -2.5*-8

m = 2.5*8

m = 20

2. 7/8a = 42

*8            *8

7a = 336

/7       /7

a = 336/7

a = 48

Hope this helped,

Kavitha

I need help solving these​

Answers

Answer: The first one is 1/2f The second one is 8/f

Step-by-step explanation: You're welcome im 99% sure about this.

What word tells you the relationship that describes a equation?

Answers

Answer:

A linear equation in two variables describes a relationship in which the value of one of the variables depends on the value of the other variable.

Step-by-step explanation:

i think this is the right that you are looking for

hope this will help :)

A term in the algebraic expression 9x6+ 23x3 – 14x is

Answers

Terms = 9*6 is a term

            then, 23*3 isa term

then, 14x is also a term

A simple random sample of 36 men from a normally distributed population results in a standard deviation of 10.1 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal​ range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.10 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute.
Complete parts​ (a) through​ (c) below.
a. Identify the null and alternative hypotheses.
b. Compute the test statistic. χ2 = ___ (round to three decimals)
c. Find the​ P-value. ​P-value=____​(Round to four decimal places as​ needed.)
d. State the conclusion. (reject null/ eccept null)

Answers

Answer:

(a) Null Hypothesis, [tex]H_0[/tex] : [tex]\sigma[/tex] = 10 beats per minute  

     Alternate Hypothesis, [tex]H_A[/tex] : [tex]\sigma\neq[/tex] 10 beats per minute  

(b) The value of chi-square test statistics is 35.704.

(c) P-value = 0.4360.

(d) We conclude that the pulse rates of men have a standard deviation equal to 10 beats per minute.

Step-by-step explanation:

We are given that a simple random sample of 36 men from a normally distributed population results in a standard deviation of 10.1 beats per minute.

If the range rule of thumb is applied to that normal​ range, the result is a standard deviation of 10 beats per minute.

Let [tex]\sigma[/tex] = population standard deviation for the pulse rates of men.

(a) So, Null Hypothesis, [tex]H_0[/tex] : [tex]\sigma[/tex] = 10 beats per minute      {means that the pulse rates of men have a standard deviation equal to 10 beats per minute}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\sigma\neq[/tex] 10 beats per minute      {means that the pulse rates of men have a standard deviation different from 10 beats per minute}

The test statistics that will be used here is One-sample chi-square test for standard deviation;

                             T.S.  =  [tex]\frac{(n-1)\times s^{2} }{\sigma^{2} }[/tex]  ~  [tex]\chi^{2}__n_-_1[/tex]  

where, s = sample standard deviation = 10.1 beats per minute

            n = sample of men = 36

So, the test statistics =  [tex]\frac{(36-1)\times 10.1^{2} }{10^{2} }[/tex]  ~ [tex]\chi^{2}__3_5[/tex]

                                   =  35.70  4

(b) The value of chi-square test statistics is 35.704.

(c) Also, the P-value of the test statistics is given by;

                    P-value = P([tex]\chi^{2}__3_5[/tex] > 35.704) = 0.4360

(d) Since the P-value of our test statistics is more than the level of significance as 0.4360 > 0.10, so we have insufficient evidence to reject our null hypothesis as the test statistics will not fall in the rejection region.

Therefore, we conclude that the pulse rates of men have a standard deviation equal to 10 beats per minute.

Jordan drives to the store at 30 miles per hour. On her way home she averages only 20 miles per hour. If the total driving time takes half an hour how far does she live from the store?

Answers

Answer:

Jordan lives 18 miles away from the store

Step-by-step explanation:

Distance=speed × time

Where,

d= distance

s= speed

t= time

Total driving time takes half an hour

Distance=speed × time

time=Distance/speed

t=1.5

Speed 1=30 mph

Speed 2:=20 mph

t=d/s1 + d/s2

1.5=d/30 + d/20

1.5=20d + 30d / 600

1.5=50d/600

Cross product

1.5×600=50d

900=50d

Divide both sides by 50

900/50=d

18=d

Therefore,

d=18 miles

Jordan lives 18 miles away from the store

1. Write an equation to represent the distance (d) that a person can run in t hours if she runs at a speed of 4 miles per hour. 2. Write an equation to represent the total cost (c) of buying candy bars (b) at a cost of $0.98 per bar. If a teacher wants to buy 20 chocolate bars for her students, how much will she pay? 3. Write an equation to represent the number of lawns (l) mowed in d days by a company that mows 18 lawns per day. How many lawns does the company mow in 5 days?

Answers

Answer:

1. The equation that represent the distance (d) that a person can run in t hours is: d = 4t

2. The equation is: c = $0.98(20)

3. The equation is: L = 18(5)

Step-by-step explanation:

1. The variable d represents the distance over time, and t represents the hour in the equation so if you want to find the distance over time, you would say distance per hour. The per means to multiply, so every distance is equal to 4 miles per hour..

2. If the teacher wants to find out how much she will have to pay for 20 chocolate bar, she has to substitute 20 into the equation to replace b, which means bar. So the equation would be: total cost (c) = $0.98 × chocolate bars (b). Once substituted, the equation will be c = $0.98(20).

3. The problem said "mows 18 lawns per day" and "mow in 5 days", that means that you substitute 5 into the equation to replace the d in days, since you are multiplying 5 × 18.. Your new equation will be: L = 18(5), Total Lawns = 18 (lawns) per 5 (days).

A quadratic function is given as..... Which of the following is a zero of the function?

Answers

Answer:

              The last (7, 0)

Step-by-step explanation:

Zeros are x-axis intercepts therefore y=0, so it's always (x, 0)

{For given function:

(x - 3)² - 16 = 0

(x - 3)² = 16

x - 3 = 4    or    x - 3 = -4

x = 7        or       x = -1

Zeros:  (7, 0) and (-1, 0)}

If a translation of (x, y) + (x +6, y-10) is applied to
figure ABCD, what are the coordinates of D'?
B
O (-5,-2)
O (1, -12)
(4, -15)
O (-9, 6)
6
5
-32
2
3
х
D
с

Answers

If (x,y) is (x+6,y-10)
So, ( -5,-2) is (-5+6, 2-10) will be ur second option

The coordinates of the point D of the rectangle after the translation is given by D' ( 1 , -12 )

What is Translation?

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

A translation in the coordinate plane moves every point on a figure a given distance in a given direction. The position of any point (x, y) on the figure changes to (x + a, y + b), where a and b are real numbers.

Given data ,

Let the coordinates of the rectangle be ABCD

Now , the coordinate of the point D be D ( -5 , -2 )

And , the translation rule is ( x , y ) → ( x + 6 , y - 10 )

So , the point after translation be D'

where D' = D ( -5 + 6 , -2 - 10 )

The coordinates of D' = D' ( 1 , -12 )

Hence , the coordinates after translation is  D' ( 1 , -12 )

To learn more about translation click :

https://brainly.com/question/19007400

#SPJ7

(Please help! :( savvas Realize sucks I don't understand)
_______________________________

Find the coordinates of the point 7/10 of the way from A to B. (see picture for graph).

The coordinates of the point 7/10 of the way from A to B are ________.
(Type an ordered pair.)​

Answers

Answer:

(5.4, 2.7)

Step-by-step explanation:

The coordinates of the point 7/10 of the way from A to B is given by the relation;

(x₁ + m×(x₂ - x₁), y₁ + m×(y₂ - y₁))

Where the coordinate of point A is (-3, -5) and the coordinates of the point B is (9, 6) we have;

x₁  = -3

m = 7/10

x₂ = 9

y₁ = -5

y₂ = 6

Substituting the values into the above equation gives;

-3 + 7/10 × (9 - (-3)), -5 + 7/10 × (6 - (-5)) = (5.4, 2.7)

The coordinate of the point P, 7/10 from A is (5.4, 2.7)

We check the length of the point from A to B to give;

[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex] =

[tex]l_{AB} = \sqrt{\left (6-(-5) \right )^{2}+\left (9-(-5) \right )^{2}} = \sqrt{265}[/tex]

the length of the point from A to B gives

[tex]l_{AB} = \sqrt{\left (2.7-(-5) \right )^{2}+\left (5.4-(-5) \right )^{2}} = \dfrac{7}{10} \times \sqrt{265}[/tex]

The coordinate of the point 7/10 of the way from A to B are (5.4, 2.7).

What number divided by 3 gives 12 as the result? A. -36 B. -4 С. 4 D. 36​

Answers

The answer is 36 all you do is divide the answer choices by 3 to get your answer

74. It's a Little Chilly! The normal high temperature in
Las Vegas, Nevada, on January 20 is 60°F. On January
20, 2008, the temperature was 6°F below normal. Ex-
press the departure from normal as an integer.

Answers

Answer:

si

Step-by-step explanation:

no

freememeskids

(2x2 + 2x + 3) - (x2 + 2x + 1) =
O A. x2 + 4
O B. x2 + 4x + 2
O C. x2 + 4x + 4
O D. x2 + 2

Answers

Answer:

[tex] \boxed{\sf D. \ x^2 + 2} [/tex]

Step-by-step explanation:

[tex] \sf Simplify \ the \ following: [/tex]

[tex] \sf \implies (2 {x}^{2} + 2x + 3) - ( {x}^{2} + 2x + 1)[/tex]

[tex] \sf - ( {x}^{2} + 2x + 1) = - {x}^{2} - 2x - 1 : [/tex]

[tex] \sf \implies (2 {x}^{2} + 2x + 3) - {x}^{2} - 2x - 1[/tex]

[tex] \sf Grouping \ like \ terms: [/tex]

[tex] \sf \implies (2 {x}^{2} - {x}^{2}) + (2x - 2x)+ (3 - 1)[/tex]

[tex] \sf 2 {x}^{2} - {x}^{2} = {x}^{2} : [/tex]

[tex] \sf \implies {x}^{2} + (2x - 2x)+ (3 - 1)[/tex]

[tex] \sf 2x - 2x = 0 : [/tex]

[tex] \sf \implies {x}^{2} + 0+ (3 - 1)[/tex]

[tex] \sf 3 - 1 = 2 : [/tex]

[tex] \sf \implies {x}^{2} +2[/tex]

Which of the following list of side lengths could form a triangle?

a. 10, 12, and 25

b. 5, 6, and 12

c. 2, 2, and 4

d. 4, 5, and 6

Answers

Answer:

d. 4, 5, and 6  

Step-by-step explanation:

The sum of the lengths of the two shorter sides must be greater than that of the longest side.

4 + 5 > 6

a. is wrong. 10 + 12 ≯ 25.

b. is wrong. 5 + 6 ≯ 12.

c. is wrong. 2 + 2 ≯ 4

 

A certain list consists of 3 different numbers. Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers

Answers

Answer:

Yes

Step-by-step explanation:

Let the numbers be p q r such that p>q>r

So p + q + r = 3q

2q = p+ r

And q< p but q> c,

So by Solving this would give

q= (p+ r)/2

so q is the mean of p & r.

Since the only other number that fits is q,

Then q is the mean of the numbers p,q,r

As so q is also the median of this set

Thus proving that the mean is the same as the median.

Help!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

the answer is the blue one (the one your mouse is hovering over)

Answer - Blue; x > 2 and x ≤ -3

Ok so one most to the left shows an arrow going "lesser" and starting at -3. Since the dot covers -3, that means it is equal to or less than -3.

So the on most to the right starts at 2 and the arrow is point "greater"

The circle is hollow, meaning is does not include 2. So that means it's greater than 2.

♡  Hope this helped! ♡

❀ 0ranges ❀

Find the length of the radius.



Answers

Answer:

1

Step-by-step explanation:

The radius is the distance from the center of the circle to any point on the circle. So it  is 1 - 0 = 1,

B
M/N
O/P
WX
YZ
Note: Figure is not drawn to scale.
If the measure of ZW equals 118°, then what is the measure of ZZ?
A.
118°
B.
62°
C. 88°
D. 28°

Answers

Answer = 62 degrees

180 - 118 = 62
I hope this helped :)

Which of the following are irrational numbers?
86
-29
88.80
[tex] \sqrt{46} [/tex]

Answers

Answer:

sqrt 46

Step-by-step explanation:

irrational numbers are numbers cannot be define in a fraction. sqrt of 46 will give you infinite decimal which could not be express in a fraction form.

To estimate your average monthly salary, divide your yearly salary by the number of months in a year. Write and solve an equation to determine your yearly salary when your average monthly salary is $4,559.

Answers

Answer:

yearly salary = $54,708

Step-by-step explanation:

Let monthly salary be x

Let yearly salary be y

Let number of months be n

To estimate your average monthly salary, divide your yearly salary by the number of months in a year. This can be written as

x = y divided by n

[tex]x = \frac{y}{n}[/tex]

Therefore, writing an equation to determine yearly salary is the same as making the yearly salary 'y' the subject of the formula above:

[tex]x = \frac{y}{n}\\cross-multiplying\\n\ \times\ x= y\\y\ =\ nx[/tex]

where y = ???

x = $4,559

n = 12 months

[tex]y = 4,559\ \times\ 12 \\= \$\ 54,708[/tex]

Therefore yearly salary = $54,708

I have a shuffled deck of 52 playing cards. A deck of cards has four different suits, with an even number of cards in each. I pick a card at random. What is the probability of me picking any card which is in the spades suit, as a decimal?

Answers

Answer:

The probability is 0.25

Step-by-step explanation:

Here is a probability question.

We want to know the probability of picking a card which is in the spades suit.

Now, what we know is that there are a total of 52 cards and we have 4 suites.

Each suite have equal number of cards. So definitely the number of cards in the spades suit will be 52/4 = 13 cards

Thus, the probability of picking any card in the spades suit = number of cards in the spades suit/ Total number of cards in the deck

Mathematically that would be 13/52 = 1/4 = 0.25

A company uses the formula below to determine the salary offered to a potential employee, where s is the salary and y is the number of years of experience the potential employee has.

Answers

Answer:

63,565.

Step-by-step explanation:

The question is incomplete. Here is the complete question.

A company uses the formula below to determine the salary offered to a potential employee, where s is the salary and y is the number of years of experience the potential employee has. s = 1,856y + 45,005 What salary would be offered to a potential employee with 10 years of experience?

The modelled equation is expressed as

s = 1,856y + 45,005.

Since we are to get the salary that would be offered to a potential employee with 10 years of experience, we will substitute the variable y = 10 into the formula and calculate the value of s as shown:

s = 1,856y + 45,005

s = 1,856(10) + 45,005

s = 18,560 + 45,005

s = 63,565

Hence the salary that would be offered to a potential employee with 10 years of experience is 63,565.

These triangles are similar Find the value of x


Answers

Answer:

C. 4

Step-by-step explanation:

This is just a common ratio.  These two triangles are alike, just that one is smaller than the other.  You can see that one of the sides of the big traingle is 10.  The same side of the smaller triangle is 5.  That means the big traingle's side is twice as big as the small circle's.  

10 divided by 5= 2

If the big triangle's side got divided by 2 to get the smaller triangle's side. So,  that means the other side of the big triangle, 8 is twice as big as the side on the smaller triangle, x.  

8 divided by 2= x

8 divided by 2= 4, so x= 4.

This is the ratio:

8:10 to x:5

As you can see the 10 got divided by 2 to get the 5.  So 8 must also get divided by 2, which equals 4.

4x-y=5 in slope intercept form solve for y

Answers

Answer:

[tex]y=-5+4x[/tex]     and the slope intercept is [tex]y=4x-5[/tex]

Answer:

Use the slope intercept form, y=mx+b to find the slope m and the y intercept b

slope= -4

y intercept= (0,5)

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what is meant by national referendum ? Zev read 15% of his 56-page book. Kelly read 12% of her 64-page book. Marneisha read 14% of his 68-page book Aleisha read 10% of her 72-page book. what the grastest Write a 250-word essay in which you describe how Chinese and American cultures, cultural values, and historical context contribute to the conflicts between the mother and the narrator in "Two Kinds." Suppose the economy is initially in long-run equilibrium. The Fed enacts a policy to . In the short-run, this expansionary monetary policy will cause: Question 1 of 4A statistics test was taken in Mrs. Everett's class. Some of the students were surveyed for theirscores and here are the results of that survey:25 30 35 40 40 45 45 50 50 5055 55 55 60 60 65 65 70 75 80 What is the average score of the student surveyed? a. 55.5b. 52.5What is the median of the student's surveyed?c. 20.0d. 60.5How many students were surveyed? What were some of the most important jobs that would accompany the settlement of a wild and unsettled frontier region? (Explain in 3-5 Sentences) 100 Points. What are a few challenges that Capt. Smith dealt with in Jamestown. Consider these sentences. Scenario A: Carmen reads an article in Tasty Food magazine stating that eating an apple can help you feel awake and alert. Scenario B: Yuki reads an article in the Professional Journal of Medicine stating that ginger root can help prevent some types of cancer. Which article is more likely to have been peer reviewed? How do you know? Pythagorean Theorema a=24 b=26 c=? A hypothesis is:_______a. a testable prediction about the relationship between variables.b. a simple explanation for a psychological finding.c. an observed relationship between independent and dependent variables.d. an unprovable assumption about psychological processes. why is it important that the real numbers have the property of being complete It is more common to see rewards tied to performance indicators as opposed to seniority or loyalty in companies whose cultures are: What kind of wave is formed (transverse or longitudimal wave, pick one) is formed by ripples on a calm pond? With explanation! Please help, most detailed answer will get brainliest and many points. The equation x + 2 = [tex]\sqrt{3x + 10}[/tex] is of the form x + a = [tex]\sqrt{bx + c}[/tex], where a, b, and c are all positive integers and b > 1. Using this equation as a model, create your own equation that has extraneous solutions. (Hint: Substitute 7 for x, and choose a value for a. Then square both sides so you can choose a, b, and c that will make the equation true.) (I know this is a handful but I'm really in need of help right now, thanks to everyone in advance!) A firm's cost of equity is 22%. Its before-tax cost of debt is 13% and its marginal tax rate is 21%. The firm's capital structure calls for a debt-to-equity ratio of 45%. Calculate the firm's cost of capital The following list is of 4 measurements. Given T(x,y)=(x+5,y+4) and the point P(2,3), what is T(P)? To best determine general forecast weather conditions covering a flight information region, the pilot should refer toA. graphical forecasts for aviation (GFA)B. weather depiction chartsC. satellite maps qbasic write a program to input number of keyboard to purchase and display the total amount to be paid for with dry run and output step by step The shape of the distribution of the time required to get an oil change at a 10 minute oil change facility is unknown. However, records indicate that the mean time is 11.4 minutes and the standard deviation is 4.5 minutes.a) To compute the probabilities regarding the sample mean using the normal model, what size sample would be required?b) What is the probability that a random sample of n = 35 oil changes results in a sample mean time of less than 10 minutes? 1) Choose the required sample size:i) Sample size need to be greater than 30ii) The normal model cannot be used if the shape of the distribution is unknowniii) Any sample size could be used.iv) Sample size needs to be less than 302) The probability is approximately ___________. (round to 4 decimal places as needed)