An article in Fire Technology, 2014 (50.3) studied the effectiveness of sprinklers in fire control by the number of sprinklers that activate correctly. The researchers estimate the probability of a sprinkler to activate correctly to be 0.7. Suppose that you are an inspector hired to write a safety report for a large ballroom with 10 sprinklers. Assume the sprinklers activate correctly or not independently.

Required:
a. What is the probability that all of the sprinklers will operate correctly in a fire?
b. What is the probability that at least 7 of the sprinklers will operate correctly in a fire?

Answers

Answer 1

Answer:

a) 0.0282 = 2.82% probability that all of the sprinklers will operate correctly in a fire

b) 0.6496 = 64.96% probability that at least 7 of the sprinklers will operate correctly in a fire.

Step-by-step explanation:

For each sprinkler, there are only two possible outcomes. Either they will operate correctly, or they will not. The sprinklers activate correctly or not independently, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The researchers estimate the probability of a sprinkler to activate correctly to be 0.7.

This means that [tex]p = 0.7[/tex]

10 sprinklers.

This means that [tex]n = 10[/tex]

a. What is the probability that all of the sprinklers will operate correctly in a fire?

This is [tex]P(X = 10)[/tex]. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 10) = C_{10,10}.(0.7)^{10}.(0.3)^{0} = 0.0282[/tex]

0.0282 = 2.82% probability that all of the sprinklers will operate correctly in a fire.

b. What is the probability that at least 7 of the sprinklers will operate correctly in a fire?

This is:

[tex]P(X \geq 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)[/tex]

So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 7) = C_{10,7}.(0.7)^{7}.(0.3)^{3} = 0.2668[/tex]

[tex]P(X = 8) = C_{10,8}.(0.7)^{8}.(0.3)^{2} = 0.2335[/tex]

[tex]P(X = 9) = C_{10,9}.(0.7)^{9}.(0.3)^{1}= 0.1211[/tex]

[tex]P(X = 10) = C_{10,10}.(0.7)^{10}.(0.3)^{0} = 0.0282[/tex]

Then

[tex]P(X \geq 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.2668 + 0.2335 + 0.1211 + 0.0282 = 0.6496[/tex]

0.6496 = 64.96% probability that at least 7 of the sprinklers will operate correctly in a fire.


Related Questions

y = 95°, find the measure of x

Answers

9514 1404 393

Answer:

  x = 100°

  y = 95°

Step-by-step explanation:

It is probably easier to find y first. Opposite angles of an inscribed quadrilateral are supplementary, so ...

  y = 180° -85° = 95°

The measure of an arc is double the measure of the inscribed angle subtending it. The arc subtended by angle y is ...

  90° +x = 2y

  x = 190° -90° = 100°

_____

Additional comment

The rule cited above regarding opposite angles of an inscribed quadrilateral comes from the theorem regarding inscribed angles. In the given diagram, the diagonal from the bottom vertex to the top one is a chord that divides the circle into two arcs. Their sum is 360°. The inscribed angle theorem tells you ...

  2y +2(85°) = 360°

  y + 85° = 180° . . . . . . . divide by 2; opposite angles are supplementary

Please
Help me asap!!

Answers

Answer:

z -2 = 10

Step-by-step explanation:

11z-9-10z+7 = 10

Combine like terms on the left side

11z -10z     -9+7  =10

z -2 = 10

Answer: z=12

Step-by-step explanation:

[tex]11z-9-10z+7=10\\z-9+7=10\\z-2=10\\z=12[/tex]

Operations and scientific notation math project need to know how to find the scientific notation

Answers

Answer:

how did not orderstan that

6) Frazer cycles the first 20 miles at an average speed of 21mph. The second
part is more uphill, and he only manages 13mph. By what percentage did his
speed decrease?
How to solve

Answers

9514 1404 393

Answer:

  38.1% decrease

Step-by-step explanation:

A percentage change is found from ...

  % change = (change)/(original amount) × 100%

  = (new value - original amount)/(original amount) × 100%

  = (13 -21)/21 × 100% = -8/21 × 100% ≈ -38.1%

Frazer's speed decreased by 38.1% during the second part.

_____

Additional comment

A negative % change represents a decrease; a positive % change represents an increase.

A four digit password is a number that begins with a 3. If digits can be repeated how many possible passwords are there? show and explain your work

Answers

Answer:

The answer is 1,000

SInce the beginning number is 3 and there are ten possible numbers to put in the remaining three slots, there are exactly 1,000 possible combinations for a 3-digit code. The answer is 1,000. There are 3 rows of 10 digits. The number of combinations 10 to the thid power which is 1000 (10 * 10 * 10)

20 POINTS! The answer is x=4 and x= -5, how should I word it, saying how he is wrong?

Answers

Answer:

The student took the numbers for the factors 5, -4 for the zeros  instead of solving the equation

The zeros are -5, 4

Step-by-step explanation:

x^2 +x - 20=0

What 2 number multiply to -20 and add to 1

5*-4 = -20

5+-4 = 1

(x+5)(x-4) =0

Using the zero product property

x+5 = 0  x-4 =0

x=-5  x=4

Answer:

Solution given:

equation is:

x²+x-20=0

doing middle term factorisation

note:we need to get 1 while subtracting factor of the product of constant and coefficient of x².

20*1=20=2*5*2*1

we get 1 while subtracting 5-2*2=5-4

now substitute value 5-4 at coefficient of x

we get

x²+(5-4)x-20=0

now

distribute

x²+5x-4x-20=0

taking common from each two term

x(x+5)-4(x+5)=0

again taking common (x+5) and keeping remaining at another bracket

(x+5)(x-4)=0

either

x+5=0

x=-5

or

x-4=0

x=4

Error is:

x= 4 not -4

x=-5 not 5.

Hello! Please help thanks

Answers

Answer:

A. [tex]\frac{5}{13}[/tex]

Step-by-step explanation:

Hi there!

We are given right triangle PQR, with PR=5, RQ=12, and PQ=13

We want to find the value of sin(Q)

Let's first recall that sine is [tex]\frac{opposite}{hypotenuse}[/tex]

In reference to angle Q, PR is the opposite side, RQ is the adjacent side, and PQ is the hypotenuse

So that means that sin(Q) would be [tex]\frac{PR}{PQ}[/tex]

Substituting the values of PR and PQ gives sin(Q) as [tex]\frac{5}{13}[/tex], which is A

Hope this helps!

Aakash, Bao Ying, Chris and Donna all live on the same street as their school, which
runs from east to west.
• Aakash lives 5 blocks to the west.
• Bao Ying lives 4 blocks to the east.
• Chris lives 2: blocks to the west. .
• Donna lives 61 blocks to the east.
a. Draw a picture that represents the positions of their houses along the street.
b. Find how far is each house from every other house?
c. Represent the relative position of the houses on a number line, with the school at
zero, points to the west represented by negative numbers, and points to the east
represented by positive numbers.
d. How can you see the answers to part (b) on the number line? Using the numbers
(some of which are positive and some negative) that label the positions of houses on
the number line, represent these distances using sums or differences.
ko

Answers

The distance between each of the students' houses are:

Aakash & Bao Ying live 9 blocks away from each other

Aakash & Chris live 3 blocks away from each other

Aakash & Donna live 66 blocks away from each other

Bao Ying & Chris live 6 blocks away from each other

Bao Ying & Donna live 57 blocks away from each other

Chris & Donna live 63 blocks away from each other

To solve this question, we represent each with the first letter of their names.

So, we have:

[tex]A= 5\ west[/tex] --- Aakash

[tex]B= 4\ east[/tex] ---- Bao Ying

[tex]C = 2\ west[/tex] --- Chris

[tex]D = 61\ east[/tex] ---- Donna

I've added the picture and the number line that represent the scenario as an attachment.

To calculate how far each lives from each other's, we start by representing west as negative and east as positive.

So, the representations become:

[tex]A = -5[/tex]

[tex]B = 4[/tex]

[tex]C = -2[/tex]

[tex]D = 61[/tex]

The absolute difference of each represents how far they live from one another.

Aakash & Bao Ying         Aakash & Chris                 Aakash & Donna

[tex]AB = |-5 -4| =9[/tex]          [tex]AC = |-5 --2| =3[/tex]         [tex]AD = |-5 -61| =66[/tex]

Bao Ying & Chris                 Bao Ying & Donna

[tex]BC = |4 --2| =6[/tex]                [tex]BD = |4 -61| =57[/tex]

Chris & Donna

[tex]CD = |-2 -61| =63[/tex]

This means that

Aakash & Bao Ying live 9 blocks away from each other

Aakash & Chris live 3 blocks away from each other

Aakash & Donna live 66 blocks away from each other

Bao Ying & Chris live 6 blocks away from each other

Bao Ying & Donna live 57 blocks away from each other

Chris & Donna live 63 blocks away from each other

To carry out the above computations from the number line, we simply count the numbers from one to the other.

For instance:

There are 3 numbers from Akash to Chris.

This means that: Aakash & Chris live 3 blocks away from each other

Learn more about number line at:

https://brainly.com/question/13189025

Which side of the pentagon on the right corresponds to
side KJ on the pentagon on the left.

Answers

Answer:

side st.

Step-by-step explanation:

st corresponds to kj since a it has five sides.

Issac put $5 in a shoe box every day for the months of april, may, and june. He then spent 75% of the money on baseball cards. How much money is left in his shoe box.

Answers

As of 2021:
April-$150
May-$155
June-$150
Total-$455
Spent 75%=455/100x75
=341.25
455-341.25=$113.75
Round off to 3sf: $114
Have a good day

find x on this special right triangle, 45 is not an option!!!!

Answers

let the line between 2 tria be y

sin 60/8√2 = sin 90/y

y=13.06

sin 45/13.06 = sin 90/x

x=18.46

Answer:

First, find the hypotenuse of the right triangle with the 60° & 30°.

Hypotenuse = hsin(x) = opposite side/hypotenuse

[tex]sin(60) = \frac{8\sqrt{2}}{h} \\\\sin(60)h=8\sqrt{2}\\\\\frac{\sqrt{3}}{2} h=8\sqrt{2}\\\\h=\frac{8\sqrt{2}}{\frac{\sqrt{3}}{2}}=8\sqrt{2}*\frac{2}{\sqrt{3}} =\frac{16\sqrt{2} }{\sqrt{3}} =\frac{16\sqrt{2}(\sqrt{3}) }{\sqrt{3}(\sqrt{3})} =\frac{16\sqrt{6} }{3}[/tex]

Use that side length to find x.

sin(x) = opposite side/hypotenuse

[tex]sin(45)=\frac{\frac{16\sqrt{6}}{3}}{x}\\\\sin(45)x=\frac{16\sqrt{6}}{3} \\\\\frac{\sqrt{2}}{2}x=\frac{16\sqrt{6}}{3} \\\\x=\frac{\frac{16\sqrt{6}}{3}}{\frac{\sqrt{2}}{2}}=\frac{16\sqrt{6}}{3}*\frac{2}{\sqrt{2}}=\frac{16\sqrt{2}\sqrt{3}(2)}{3\sqrt{2} }=\frac{32\sqrt{3} }{3}[/tex]

Execute the following 18/3+2*8-5.

Answers

I got 17 as my answer

what are the answers to the questions below?

Answers

Answer:

You have to follow PEMDAS or parenthesis, exponents, multiplication, division, addition, and subtraction. It's an order to solve equations. I listed the steps and the answers for you below :) I have throughly checked them so they should be correct! yw :D

Step-by-step explanation:

1. 5x + 4x - 6x = 24

9x - 6x = 24

3x = 24

24/3 = 8

x = 8

2. 8y + 5 - 4y + 1 = 46

8y - 4y = 4y

5 + 1 = 6

4y + 6 = 46

4y = 46 - 6

4y = 40

40/4 = 10

y = 10

3. 33 = 5 ( x + 8 ) + 3

33 =  5x + 40 + 3 (because we distributed)

33 = 5x + 43

5x + 43 = 33 (just rewriting it to make it easier)

5x = 33 - 43

5x = -10

-10/5 = -2

so x = - 2

4. 2m + 3 ( m - 8 ) = 1

2m + 3m - 24 = 1

we got 3m - 24 because we distributed the 3

5m - 24 = 1

5m = 25

25/5 = 5

m = 5

5. p + p - 2p + 4p = - 48

2p - 2p + 4p = - 48

4p = - 48

- 48 / 4 = - 12

p = - 12

6. 2 ( y + 5 ) + 3y = 25

2y + 10 + 3y = 25

5y + 10 = 25

5y = 25 - 10

5y = 15

15/5 = 3

y = 3

7. 1/4 h + 3/4 h + 1/2 h + 2 = 5

1/4 h + 3/4 h + 1/2 = 3/2 h

3/2 h + 2 = 5

3/2 h = 5 - 2

3/2 h = 3

h = 2

8. 60 = 4 ( k + 3 ) + 2 ( k - 3 )

60 = 4k + 12 + 2k - 6

4k + 12 + 2k - 6 = 60

6k + 6 = 60

6k = 60 - 6

6k = 54

k = 9

9. - 2 ( d + 1.4 ) - 1.8 = 20.6

-2d + - 2.8 - 1.8 = 20.6

-2d - 2.8 = 22.4

-2d = 25.2

d = - 12.6

10. 8 - 2 ( w + 4 ) = 10

8 + - 2 w + - 8 = 10

-2w + 9 + - 8 = 10

-2w = 10

10 / -2 = -5

w = -5

A polynomial function has real coefficients, a leading coefficient of 1, and the zeros -6, 1, and 1. Write a polynomial function of least degree in standard form.​

Answers

Answer:

[tex]{ \sf{ \underline{ {x}^{2} + 5x - 6 }}}[/tex]

Step-by-step explanation:

[tex](x + 6)(x - 1) \\ = {x}^{2} - x + 6x - 6 \\ = {x}^{2} + 5x - 6[/tex]

On the first day of travel, a driver was going at a speed of 40 mph. The next day, he increased the speed to 60 mph. If he drove 2 more hours on the first day and traveled 20 more miles, find the total distance traveled in the two days.

Answers

The Total mileage is "400" and the further solution can be defined as follows:

Let t become the time he spent commuting on the first day of his vacation.

It is then calculated as [tex]t + 2[/tex].

[tex]\to 40\times(t+2) = 60(t) + 20 \\\\\to 40t+80 = 60t + 20 \\\\\to 80-20 = 60t + 40t \\\\\to 60 = 20t \\\\\to t=\frac{60}{20} \\\\\to t=\frac{6}{2} \\\\\to t= 3\\\\[/tex]

It traveled [tex]40\times (3 + 2) + 20 = 40\times 5 + 20 = 200+20=220[/tex] miles on its first day of operation.

The car traveled [tex]180\ miles[/tex] on the second day, which was [tex]60 \ miles \times 3[/tex].

So,

Total mileage= first day traveled + second day traveled [tex]= 220+ 180= 400 \miles[/tex]

Learn more:

Total distance traveled: brainly.com/question/20670144

How many ways are there to rearrange the letters of the word: COMBINATION?

Answers

Answer: 4,989,600 different ways

Step-by-step explanation:

Simplify the following expression:

Answers

Step-by-step explanation:

[tex]{ \bf{( \frac{ - 10 {a}^{3} {b}^{5} \times 6 {a}^{6} {b}^{2} }{ {12a}^{9} {b}^{5} } ) {}^{3} }} \\ \\ = { \sf{( \frac{ - 60 {a}^{9} {b}^{7} }{12 {a}^{9} {b}^{5} } ) {}^{3} }} \\ \\ = { \sf{(5 {b}^{2}) {}^{3} }} \\ = { \sf{125 {b}^{5} }}[/tex]

i don’t quite get the concept yet and i really don’t wanna bother the teacher again :/ please help

Answers

Answer:

they are asking which claims are true vs false

Step-by-step explanation:

I totally get not wanting to bother our teachers again,... (that is why we're here)

m (AB = 20

m<ABD = 140

m (AD = 60

I think they want to know which ones (based on the "graph") are true,...

Slide 1.
1) The polygons below ore similor. Find the value of y.
8.
10

Answers

Answer:

y =6

Step-by-step explanation:

We can write a ratio to solve

3           y

----- = ----------

4            8

Using cross products

3*8 = 4y

24 = 4y

Divide by 4

24/4 = 4y/4

6 = y

A.Yes, since the slopes are the same and the y-intercepts are the same.
B.No, since the y-intercepts are different.
C.Yes, since the slopes are the same and the y-intercepts are different.
D.No, since the slopes are different.

Answers

Answer:

C

Step-by-step explanation:

one line is

y = 3x/7 + 11

its slope is 3/7

the y-intercept is, of course, when x=0. there y=11

the other is

-3x + 7y = 13

7y = 3x + 13

y = 3x/7 + 13/7

its slope is 3/7 (the same as the other line)

the y-intercept (x=0) is y = 13/7 (different to the other line)

Answer:

C. Yes, since the slopes are the same and the y-intercepts are different.

Step-by-step explanation:

[tex]y=\frac{3}{7} x+11[/tex]  and [tex]-3x+7y=13[/tex]

→ Rearrange the second equation to make y the subject

7y = 3x + 13

→ Divide everything by 7

[tex]y=\frac{3}{7} x+\frac{13}{7}[/tex]

k = 2; f(x) = 2x3 + 3x2 - 4x + 4; Lower bound? (1 point)

Answers

f(x) = 2 x 3 +3 x 2 - 4x + 4
0 = 6 + 6 - 4x + 4
0 = 16 - 4x
4x = 16
x = 4
(sorry if that’s not what you’re looking for)

For the function G defined by G(x) = 5x + 3, find G(2)

Answers

G(x)=5x+3

[tex]\\ \sf\longmapsto G(2)[/tex]

[tex]\\ \sf\longmapsto 5(2)+3[/tex]

[tex]\\ \sf\longmapsto 10+3[/tex]

[tex]\\ \sf\longmapsto 13[/tex]

Option c is correct

13, replace x as 2 and then solve, 5(2)+3 which is 10+3 which equals 13.

y you work from 7 a.m. to 4 p.m. The state you live in requires that you take a 30-minute break during any shift longer than 6 hours. This break does not count towards your hours. How many hours did you work today? Remember 30 minutes is equal .5 hours​

Answers

Answer:

You’ve worked 7 hours and 30 minutes

Step-by-step explanation:

12 workers take 4 hours to complete a job. How long would it take 15 workers to complete the job?

Answers

Answer:

3.2 hours

Step-by-step explanation:

12 workers * 4 hours = 48 worker hours

15 workers  * x hours = 48 worker hours

48 /15 =3.2 hours

Answer:

3 hours and 12 minutes.

Step-by-step explanation:

12 Workers complete a job in 4 hours

1 worker complete a job 12 × 4 = 48

15 workers complete a job = 48/15 = 3³/¹⁵ = 3¹/⁵

= 3 hours + 1/5 × 60  minutes = 3 hours 12 minutes.

A sample of 4 children was drawn from a population of rural Indian children aged 12 to 60 months. The sample mean of mid-upper arm circumference was 150 mm with a standard deviation of 6.73. What is a 95% confidence interval for the mean of mid-upper arm circumference based on your sample

Answers

Answer:

The 95% confidence interval for the mean of mid-upper arm circumference based on your sample is between 139.29 mm and 160.71 mm.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So

df = 4 - 1 = 3

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 3 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 3.1824

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 3.1824\frac{6.73}{\sqrt{4}} = 10.71[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 150 - 10.71 = 139.29 mm

The upper end of the interval is the sample mean added to M. So it is 150 + 10.71 = 160.71 mm

The 95% confidence interval for the mean of mid-upper arm circumference based on your sample is between 139.29 mm and 160.71 mm.

A cement mixture costs $33 a ton. It is composed of Grade A cement at $36 a ton and Grade B cement at
$24 a ton. How were these two cements mixed?

Answers

If we used “a” tons of grade A and “b” tons of grade B we would get a + b tons of mixture.
Converting to costs we get 36a + 24b = 33(a + b)
36a + 24b = 33a + 33b
36a - 33a = 33b - 24b
3a = 9b
a = 3b
This means the mixture contains 3 times as much of grade A than grade B
The ratio of grade A : grade B = 3 : 1

For example if we mixed 3 tons of A with 1 ton of B we would get 4 tons of mixture
The cost would be 3 x 36 + 1 x 24 = 108 + 24 = $132 for 4 tons = $33 per ton

What is the derivative of (x + 1) sin x?

Answers

Answer:

By the Sum Rule, the derivative of 1−sin(x) 1 - sin ( x ) with respect to x x is ddx[1]+ddx[−sin(x)] d d x [ 1 ] + d d x [ - sin ( x ) ] .

Which of the following is the function for the graph below and shows the end behavior of the function as x>-00?

Answers

Answer:

A

Step-by-step explanation:

I just used a graphing calculator.

Just type in all the functions and pick the graph and function pair that match the picture.

I hope this helps!

pls ❤ and mark brainliest pls!

Assuming you want x to approach negative infinity, you have the correct answer. It is choice A.

=====================================================

Explanation:

The root x = -2 leads to the factor x+2. That means the answer is between A and B.

As x approaches negative infinity, i.e. as we move to the left, we're going down the red curve and y = f(x) is going to approach negative infinity as well.

In terms of symbols, we'd write [tex]x \to -\infty, \ f(x) \to -\infty[/tex]

Informally, we could say "it falls to the left" as a way to describe this left end behavior.

How much more area does a large pizza with a 12 in. diameter have than a small pizza with an 8 in. diameter? Round your answer to the nearest square inch.

Answers

Answer: About 63 in²

Step-by-step explanation:

Area of circle = π · r²

r = radius lengthπ ≈ 3.14

Area of large pizza:

[tex]\pi *r^{2} =3.14*6^{2} =3.14*36=113.04[/tex]

Area of small pizza:

[tex]\pi *r^{2} =3.14*4^{2} =3.14*16=50.24[/tex]

Difference in area:

[tex]113.04-50.24=62.8[/tex]

Write each percent as a fraction in simple form 15 3/5%

Answers

Answer:

39/250

Step-by-step explanation:

15 3/5 = 78/5 and percent means per 100, so

(78/5)/100 = (78/5)(1/100)

=78/500 = 39/250

Other Questions
g Light that is incident upon the eye is refracted several times before it reaches the retina. As light passes through the eye, at which boundary does most of the overall refraction occur? Can someone please explain how to do this?(Picture above) I'll give brainliest! help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Determine whether (a) x = -1 or (b) x = 2 is a solution to this equation All of the following might be an indication of social media addiction EXCEPTA. an inability to walk away from social media for any significant period of timeB. checking your social media feed the first thing after waking upC. using social media to share information about causes important to youD. scrolling through social media feed even while watching television If 2/3 of the girls in class have brown eyes and 1/4 of the girls have blue eyes what fraction of the girls in class have neither blue or brown 5. Solve each of the following quadratic equations using the Quadratic Formula (Express all roots as integers or as real numbers rounded to one decimal place)a) 2x2 3x - 10 = 0b) 3x2 - 8x + 4 = 0 (answer pls:) find the LCM of 220,440,660 by common division method Will Give Brainliest!Solve for r.Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.35r - 21 < -35r + 19 Nishi invests 3500 at 4% interest per year. Work out how much she will have altogether after: 2 years Determine whether the ordered pair is a solution of the equation. Show your work to receive credit.9. Is (-1,3) a solution to the equation y = -3x + 10?10. Is (7,-2) a solution to the equation x 4y = 15?Please show work to help me understand. A firm has a beta of 1.3 and a debt-to-equity ratio of .4. The market rate of return is 11.6percent, the tax rate is 32 percent, and the risk-free rate is 3.3 percent. The pretax cost of debtis 7.2 percent. What is the firm's WACC? please help I will mark brainlyest When marginal revenue equals marginal cost, the firm a. should increase the level of production to maximize its profit. b. may be minimizing its losses rather than maximizing its profit. c. must be generating positive economic profits. d. must be generating positive accounting profits. The polynomial p(x) = x3 7x - 6 has a known factor of (x + 1).Rewrite p(x) as a product of linear factors.p(x) What is the slope of the graph of y = -3x?-1/31/3-33 Which primary source document could help a historian understand why the US Civil War started? Margarita y Roberto estn en la clase de Matemticas. Cada da necesitan su libro de Matemticas, una calculadora, una regla y su cuaderno. Roberto no tiene una regla. La profesora le dice que necesita comparar una regla este fin de semana.What happens next?A. Margarita va a comprar un libro de Matemticas.B. La profesora va a trabajar en la tienda.C. Roberto va a comprar una regla.D. Margarita y Roberto van a tomar un examen. Select all that apply Some disadvantages of relying solely on financial measures include that: (Check all that apply.) Multiple select question. they can encourage managers to focus too heavily on short-term goals. they can encourage managers to focus too heavily on long-term goals. some profitable opportunities may be rejected to keep return on investment high. residual income is not as effective when comparing investment centers of different sizes. they require managers to focus on too many perspectives. PLEASE Help! I need this by tomorrow!