Using the information given, select the statement that can deduce the line segments to be parallel. If there are none select none. When m<7=m<4​

Answer:

2.16% probability that he would have done at least this well if he had no ESP

Step-by-step explanation:

For each coin toss, there are only two possible outcomes. Either he predicts the correct outcome, or he does not. The tosses are independent. So we use the binomial probability distribution 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.

Fair coin:

Equally as likely to be heads or tails, so [tex]p = 0.5[/tex]

Coin is flipped 25 times

So [tex]n = 25[/tex]

What is the probability that he would have done at least this well if he had no ESP?

[tex]P(X \geq 18) = P(X = 18) + P(X = 19) + P(X = 20) + P(X = 21) + P(X = 22) + P(X = 23) + P(X = 24) + P(X = 25)[/tex]

In which

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

[tex]P(X = 18) = C_{25,18}.(0.5)^{18}.(0.5)^{7} = 0.0143[/tex]

[tex]P(X = 19) = C_{25,19}.(0.5)^{19}.(0.5)^{6} = 0.0053[/tex]

[tex]P(X = 20) = C_{25,20}.(0.5)^{20}.(0.5)^{5} = 0.0016[/tex]

[tex]P(X = 21) = C_{25,21}.(0.5)^{21}.(0.5)^{4} = 0.0004[/tex]

[tex]P(X = 22) = C_{25,22}.(0.5)^{22}.(0.5)^{3} = 0.0001[/tex]

The others(23, 24 and 25) are close to 0.

[tex]P(X \geq 18) = P(X = 18) + P(X = 19) + P(X = 20) + P(X = 21) + P(X = 22) + P(X = 23) + P(X = 24) + P(X = 25) = 0.0143 + 0.0053 + 0.0016 + 0.0004 = 0.0216[/tex]

2.16% probability that he would have done at least this well if he had no ESP

[tex]\text{Solve:}\\\\4(x-2+y)\\\\\text{Use the distributive property:}\\\\4x-8+4y\\\\\text{Since you can't simplify it any further, that'll be your answer}\\\\\boxed{4x-8+4y}[/tex]

Answer:

4x-8+4y

Explanation:

///

Answer:

10/18

=5/9

pls mark as brainliest

Answer:

5/9

Step-by-step explanation:

6 red cards, 8 green cards and 4 blue cards =  18 total cards

not green cards = 6 red+ 4 blue = 10 cards

P( not green) = number not green / total

                      = 10/18

                      =5/9

Answer:

3,325,140 Joules

Step-by-step explanation:

Work done by the pump = Force applied to pump * distance covered by the water.

Since Force = mass * acceleration due to gravity

Force = (density of water * volume of the tank) * acceleration due to gravity

F =ρVg

Workdone = (ρVg )* d

Given ρ = 1000kg/m³, g = 9.8m/s², d = 3m

[tex]V = \pi r^{2}h\\V = \pi (2)^{2} *9\\V = 36 \pi \\V =113.10m^{3}[/tex]

Workdone by the pump = 1000 * 113.10 * 9.8 * 3

Workdone by the pump  = 3,325,140Joules

Answer:

$24

Step-by-step explanation:

2/5 — dress

3/5 — remainder

1/2 of remainder = 1/2 × 3/5 = 3/10 — doll

rewrite fraction spent on dress: 4/10

dress - doll = $8

4/10 - 3/10 = 1/10

1/10 = $8

fraction of money left = 10/10 - 4/10 - 3/10

= 3/10

amount of money left = $8 × 3

$24

Answer:

what's the question?

it's not showing

Answer:

C.

Step-by-step explanation:

To find the perimeter, we'll use the distance formula

Distance Formula = √(x₂-x₁)²+(y₂-y₁)²

Finding Distance of AB

|AB| = √(-2+5)²+(3+1)²

|AB| = √25

|AB| = 5

Now For BC

|BC| = √(6+2)²+(-3-3)²

|BC| = √(8)²+(-6)²

|BC| = √100

|BC| = 10

FOR CA:

|CA| = √(-5-6)²+(-3+1)²

|CA| = √125

Perimeter of Triangle = 10 + 5 + √125

= 15 + √125

Answer;

1) The t-distribution is most suitable for this problem.

2) Test statistic = 2.356

3) p-value = 0.0214

4) Alpha = 5% = 0.05

5) The p-value is greater than the significance level at which the test was performed, meaning that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that the husbands are happier in dual couple marriages.

Step-by-step Explanation:

Wife's score 2 2 3 3 4 2 1 1 2 4

Husband's score 2 1 2 3 2 1 1 1 2 4

To conduct a hypothesis test at the 5% level to see if the mean difference in the husband's versus the wife's satisfaction level is negative (meaning that, within the partnership, the husband is happier than the wife, we first take the difference in the respomses of wives and husbands

x = (wife's score) - (husband's score)

Wife's score 2 2 3 3 4 2 1 1 2 4

Husband's score 2 1 2 3 2 1 1 1 2 4

Difference | 0 | 1 | 1 | 0 | 2 | 1 | 0 | 0 | 0 | 0

To use the hypothesis test method, we have to make sure that the distribution is a random sample of the population and it is normally distributed.

The question already cleared these two for us that this sample size is randomly selected from the population and each variable is independent from the other.

The question also already explained that the distribution is assumed to be normally distributed.

1) The distribution to use for this test is the t-distribution. This is because the sample size isn't very large and we have no information about the population mean and standard deviation.

For any hypothesis testing, we must first define the null and alternative hypothesis

Since we want to investigate whether the husbands are happier, that the mean difference is negative, that is less than 0,

The null hypothesis, which normally counters the claim to be investigated, would be that there isnt evidence to conclude that the husbands are happier in dual couple marriages. That is, the mean difference in happiness isn't less than 0, that it is equal to or greater than 0.

And the alternative hypothesis, which usually confirms the claim to be tested, is that there is significant evidence to conclude that the husbands are happier in dual couple marriages. That is, the mean difference in happiness is less than 0.

Mathematically, if μ is the mean difference in happiness of wives and husbands,

The null hypothesis is represented as

H₀: μ ≥ 0

The alternative hypothesis is represented as

Hₐ: μ < 0

2) To obtain the test statistic, we need the mean and standard deviation first.

Mean = (sum of variables)/(number of variables) = (5/10) = 0.5

Standard deviation = σ = √[Σ(x - xbar)²/N]

Σ(x - xbar)² = 6(0 - 0.5)² + 3(1 - 0.5)² + (2 - 0.5)² = 1.5 + 0.75 + 2.25 = 4.5

σ = √(4.5/10) = 0.671

we compute the t-test statistic

t = (x - μ)/σₓ

x = sample mean difference = 0.50

μ = 0

σₓ = standard error of the sample mean = (σ/√n)

where n = Sample size = 10,

σ = Sample standard deviation = 0.671

σₓ = (0.671/√10) = 0.2122

t = (0.50 - 0) ÷ 0.2122

t = 2.356

3) checking the tables for the p-value of this t-statistic

Degree of freedom = df = n - 1 = 10 - 1 = 9

Significance level = 5% = 0.05

The hypothesis test uses a one-tailed condition because we're testing only in one direction.

p-value (for t = 2.356, at 0.05 significance level, df = 9, with a one tailed condition) = 0.021441 = 0.0214

4) Alpha = significance level = 5% = 0.05

5) The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.05

p-value = 0.0214

0.0214 < 0.05

Hence,

p-value < significance level

This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that the husbands are happier in dual couple marriages.

Hope this Helps!!

Answer:

The total percentage increase in the country's population over the three year period is 7.6%.

Step-by-step explanation:

Let x be the original population of a country.

It is provided that the population increased by 3%, 2.6%, and 1.8% in three successive years.

Compute the population of the country after three years as follows:

[tex]\text{New Population}=\text{Origibal Population}\times I_{1}\%\times I_{2}\%\times I_{3}\%[/tex]

                         [tex]=x\times [1+\frac{3}{100}]\times [1+\frac{2.6}{100}]\times [1+\frac{1.8}{100}]\\\\=x\times 1.03\times 1.026\times 1.018\\\\=1.07580204\cdot x\\\\\approx 1.076\cdot x[/tex]

The new population after three years is 1.076 x.

Compute the total percentage increase in the country's population over the three year period as follows:

[tex]\text{Total Increase}\%=\frac{\text{New Population}\ -\ \text{Original Population}}{\text{Original Population}}\times 100[/tex]

                         [tex]=\frac{1.076x-x}{x}\times 100\\\\=0.076\times 100\\\\=7.6\%[/tex]

Thus, the total percentage increase in the country's population over the three year period is 7.6%.

Answer:

(a)

(b)Discrete

(c)Ratio Scale and Discrete Variable

(d) Experimental Method

Step-by-step explanation:

The psychologist wants to evaluate the claim that omega-3 fatty acids can help improve memory in normal adult humans.

(a)In the study, the participants in the two groups were given fish extracts containing Omega-3 (500 mg) and no Omega-3 (0 mg).

The memory test involves measuring the number of items each participant remembers from the past three weeks of news.

Therefore:

(b) The dependent variable is discrete since the number of news items remembered can only be whole numbers.

(c)The independent variable is in milligrams of Omega-3 where the placebo is 0 mg. This is a ratio scale since it has an absolute zero.

Since the dosage is given in multiples of 50mg, it is a discrete variable.

(d)Since the psychologist seeks to manipulate the conditions of the study by introducing Omega-3 to some of the participants and placebo to other participants, it is an experimental distribution.

Answer:

Step-by-step explanation: 6z=-2-10

6z= -12

z=-12/6

then z= -2

Answer:

(a)

[tex]\left[\begin{array}{ccc}110\\4\\20\\2\end{array}\right] x+\left[\begin{array}{ccc}130\\3\\18\\5\end{array}\right] y=\left[\begin{array}{ccc}295\\9\\48\\8\end{array}\right][/tex]

(b)

[tex]\left[\begin{array}{ccc}110&130&295\\4&3&9\\20&18&48\\2&5&8\end{array}\right][/tex]

1.5 servings of cheerios and 1 serving of Quaker 100% natural cereal will give the desired mixture.

Step-by-step explanation:

Given the mixture of cereals below:

[tex]\left|\begin{array}{c|c|c}&$General Mills &$Quaker \\$Nutrient&$Cherrios &100\% $Natural Cereal\\----&---&---\\$Calories&110&130\\$Protein (g)&4&3\\$Carbhydrate (g)&20&18\\$Fat (g)&2&5\end{array}\right|[/tex]

Suppose a mixture of these two portions of cereals is to be prepared that contain exactly 295 calories, 9 g of protein, 48 g of carbohydrate, and 8 g of fat.

(a)Let x be the number of servings of Cheerios

Let y be the number of servings of Natural Cereal

From the table above, we have

[tex]110x+130y=295\\4x+3y=9\\20x+18y=48\\2x+5y=8[/tex]

Then a vector equation for this problem is:

[tex]\left[\begin{array}{ccc}110\\4\\20\\2\end{array}\right] x+\left[\begin{array}{ccc}130\\3\\18\\5\end{array}\right] y=\left[\begin{array}{ccc}295\\9\\48\\8\end{array}\right][/tex]

(b) Next, we obtain an equivalent matrix equation of the data

[tex]\left[\begin{array}{ccc}110&130\\4&3\\20&18\\2&5\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}295\\9\\48\\8\end{array}\right][/tex]

This is of the form AX=B. To solve for X we, therefore have an equivalence matrix:

[tex]\left[\begin{array}{ccc}110&130&295\\4&3&9\\20&18&48\\2&5&8\end{array}\right][/tex]

Next, we row reduce the matrix using a calculator to obtain the matrix:

[tex]\left[\begin{array}{ccc}1&0&1.5\\0&1&1\\0&0&0\\0&0&0\end{array}\right][/tex]

Therefore:

1x+0=1.5

0x+y=1

x=1.5 and y=1

To get the required mixture, we use 1.5 servings of cheerios and 1 serving of Quaker 100% natural cereal.

Answer:

A

Step-by-step explanation:

The smaller negative integer is x.

The larger one is x+8, since they are 8 units apart.

The equation would be:

x*(x+8)=308

Let's simplify it by distributing.

x^2+8x=308

Subtract 308 from both sides.

x^2+8x-308=0

Therefore, the answer would be A.

Answer:

  yes, they are parallel; the general form equation differs only in the constant.

Step-by-step explanation:

Subtract y from the first equation and multiply by 2.

  y -y = 1/2x -y +3

  0 = x -2y +6

  x -2y +6 = 0 . . . . . put in general form

Compared to the second equation, we see the only difference is in the constant, +6 vs. -8.

This means the lines are parallel.

Answer:

y=1

Step-by-step explanation:

7-y=6

6+1=7

7-1=6

Hope this helps:)

Stay Safe

Answer:

y =1

Step-by-step explanation:

7 - y = 6

Subtract 7 from each side

7 - y-7 = 6 -7

-y = -1

Multiply each side by -1

-y*-1 = -1 *-1

y = 1

Answer:

100

Step-by-step explanation:

4 tens +  6 tens = 10 tens = 10*10 = 100

Answer:

Option B is correct

Step-by-step explanation:

Original expression is |8 - 1| = 7 = distance between number 1 and number 8

=> Option B is correct

Hope this helps!

The number line model that matches the expression |8 - 1| which is correct option(B)

The graph can be defined as a pictorial representation or a diagram that represents data or values.

The expressions is the defined as mathematical statements that have a minimum of two terms containing variables or numbers.

Given the expression as |8 - 1|,

The value of the expression would give us 7. Meaning that the distance between coordinate 8 and 1 is 7 units.

The graphs given models the expression, |8 - 1|.

Option A, would match |-8 -1| = 5 units

Option B, would match |8 - 1| = 7 units.

Therefore, the answer is option (B).

Learn more about graph here :

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Answer:

11e+5f

Step-by-step explanation:

Combine like terms:

4e+7e+6f-f

11e+5f

Answer:

11e   +5f

Step-by-step explanation:

4e + 6f + 7e - f​

Combine like terms

4e+7e      +6f-f

11e   +5f

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is:

Ten rugby balls are randomly selected from the production line to see if their shape is correct. Over time, the company has found that 89.4% of all their rugby balls have the correct shape. If exactly 6 of the 10 have the right shape, should the company stop the production line?

1)Yes as the probability of six having the correct shape is not unusual

2)NO. as the probability of six having the correct shape is unusual

3)Yes as the probability of six having the correct shape is unusual

4) No. as the probability of six having the correct shape is not unusual

Solution:

If exactly 6 of the 10 have the right shape, it means that the probability of success for the sample is

6/10 = 0.6

Expressing the probability in terms if percentage, it becomes

0.6 × 100 = 60%

Over time, the company has found that 89.4% of all their rugby balls have the correct shape. It means that the probability of success for the population is 89.4%

Comparing both probabilities, the probability of only 6 having the right shape is unusual. Therefore, the correct option is

3)Yes as the probability of six having the correct shape is unusual

Note: The first file attached contains the clear and complete question

Answer:

a) The times at which the graph of A(t) has horizontal tangent are t = 1 and t = 7

A(t) has a local maximum at t=7

A(t) has a local minimum at t=1

b) The times at which the graph of D(t) has horizontal tangent are t = 1.59 and t = 7.74

D(t) has a local maximum at t=1.59

D(t) has a local minimum at t=7.74

c) A(t) = (-t^3) + 8(t^2) -21t + 40

d) The water level in vat A is rising most rapidly at t = 4 hrs

e) 138 gallons

f) 18 gallons per hour

g) 98 gallons

Step-by-step explanation:

For clarity and easiness of expression, the calculations are handwritten and attached as files below.

Each step is neatly expressed and solutions to each part of the question are clearly written

Answer:

8x10^13

Step-by-step explanation:

Answer:

For an overall profit, we need at least 97 people to go mushroom hunting.

Any number of people that is more than the socially optimal number should go mushroom hunting on any given day.

Step-by-step explanation:

The socially optimal number of people that will go mushroom hunting is the number where amount spent to go mushroom hunting equally balances the amount obtained by selling the mushrooms obtained.

If x people go mushroom hunting in a day, the total cost of hunting for that day = 200x

The amount of mushroom obtained is given as

M = (100x - x²) in pounds

The selling price of 1 pound = $60

The cost of M pounds = 60M = 60(100x - x²)

= (6000x - 60x²)

At socially optimal number,

200x = 6000x - 60x²

60x² - 6000x + 200x = 0

60x² - 5800x = 0

x(60x - 5800)

x = 0 or (60x - 5800) = 0

x = 0 or x = (5800/60) = 96.67

Socially optimal number of people = 0 or 96.67

For realistic purposes, we take the socially optimal number of people that went mushroom hunting as 96.67

Any number above this number will result in an overall profit, and any number below it results in an overall loss.

So, for an overall profit, we need at least 97 people to go mushroom hunting.

Hope this Helps!!

Answer:

48 people

Step-by-step explanation:

When allocating resources to a particular task it is important to assign optimal units of resources.

In this scenario if the people hunting mushrooms are too many they will not make profit. But an optimal number will guarantee everyone makes positive profit.

Optimal = (M÷x)Px - 200= 0

Optimal= {(100x -x^2) ÷ x} * 60 = 200

Optimal = 6000 - 60x = 200

x= 96.666~ 97 people

However to maximise profit MTB = MTC

Socially Optimal quantity = 60(100x - x^2) -200

∂(Socially Optimal amount) ÷ ∂ x= 6000 - 120x - 200

x = 48.33~ 48 people

So 48 more people go mushroom hunting than is socially optimal

Answer:

  $18,862.91

Step-by-step explanation:

The appropriate formula is ...

 A = P(1 +r/n)^(nt)

where P is the amount invested (14,000), r is the APR (.05), n is the number of times per year interest is compounded (4), and t is the number of years (6).

Filling in the numbers and doing the arithmetic, we get ...

  A = 14,000(1 +.05/4)^(4·6) = 14,000·1.0125^24 ≈ 18,862.91

The balance after 6 years will be $18,862.91.

Answer:

16

Step-by-step explanation:

[tex]16x^0= \\\\16(-3)^0= \\\\16(1)= \\\\16[/tex]

Hope this helps!

x = -3

[tex]A = 16.(-3)^{0} \\ x^{0} = 1\\A = 16.1 \\A = 16[/tex]

Remember that [tex]x^{0} = 1[/tex] ∀ [tex]x[/tex]

Answer:

StartFraction 4 over 2 EndFraction = StartFraction 5 over x EndFraction

Solve the proportion for x.

After using cross products, the proportion becomes the equation

✔ 4x = 10

.

Isolate the variable by dividing both sides of the equation by

✔ 4

.

x = ✔ 2.5

.

The value of x is 2.5 for the given proportion.

A mathematical assessment of two numbers is called a proportion. If two sets of provided numbers rise or fall in the same relation, then the ratios are said to be directly proportional to each other.

The proportion is given in the question, as follows:

4/2 = 5/x

Using cross-product, the proportion becomes the equation as:

4x = 2 × 5

4x = 10

Divide by 4 into both sides of the above equation,

x = 10/4

x = 2.5

Thus, the value of x is 2.5 for the given proportion.

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Answer:

That can be factored as

(x -1  (1/3) ) * ( x +3) * (x -4/5)

and the zeroes are located at:

x = 1.33333333...   x = -3    and x = .8

Step-by-step explanation:

Answer:

[tex]\boxed{\sf \ \ \ f(x)=(x+3)(5x-4)(3x-4) \ \ \ }[/tex]

Step-by-step explanation:

We need to factorise the following function

[tex]f(x)=15 x^3+13 x^2-80 x+48[/tex]

-3 is a trivial solution, we can notice that f(-3)=0

so we can factorise by (x+3)

let s note a, b and c real and let s write

[tex]f(x)=15 x^3+13 x^2-80 x+48=(x+3)(ax^2+bx+c)[/tex]

[tex](x+3)(ax^2+bx+c) = ax^3+bx^2+cx+3ax^2+3bx+3c=ax^3+(b+3a)x^2+(3b+c)x+3c[/tex]

let s identify...

the terms in [tex]x^3[/tex]

   15 = a

the terms in [tex]x^2[/tex]

   13 = b + 3a

the terms in x

   -80 = 3b+c

the constant terms

   48 = 3c

so it comes, c=48/3=16, a = 15, b = 13-3*15=13-45=-32

so [tex]f(x)=(x+3)(15x^2-32x+16)[/tex]

[tex]\Delta=32^2-4*15*16=64[/tex]

so the roots of [tex](15x^2-32x+16)[/tex] are

[tex]\dfrac{32-8}{15*2}=\dfrac{24}{30}=\dfrac{12}{15}=\dfrac{4}{5}[/tex]

and

[tex]\dfrac{32+8}{15*2}=\dfrac{40}{30}=\dfrac{20}{15}=\dfrac{4}{3}[/tex]

so [tex]f(x)=(x+3)(5x-4)(3x-4)[/tex]

the zeros are -3, 4/5, 4/3

Answer:

[tex]54.6-3.51\frac{9.2}{\sqrt{48}}=49.94[/tex]    

[tex]54.6+3.51\frac{9.2}{\sqrt{48}}=59.26[/tex]    

The confidence interval is given by (49.94, 59.26)

Step-by-step explanation:

Info given

[tex]\bar X=54.6[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

s=9.2 represent the sample standard deviation

n=48 represent the sample size  

Part a

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The degrees of freedom are given by:

[tex]df=n-1=48-1=47[/tex]

The Confidence is 0.999 or 99.9%, and the significance is [tex]\alpha=0.001[/tex] and [tex]\alpha/2 =0.0005[/tex], and the critical value would be [tex]t_{\alpha/2}=3.51[/tex]

And replacing we got:

[tex]54.6-3.51\frac{9.2}{\sqrt{48}}=49.94[/tex]    

[tex]54.6+3.51\frac{9.2}{\sqrt{48}}=59.26[/tex]    

The confidence interval is given by (49.94, 59.26)

Answer:

The age of the pottery bowl is 12,378.7 years

Step-by-step explanation:

The amount of C-14 after t yeas is given by the following equation:

[tex]N(t) = N(0)e^{-kt}[/tex]

In which N(0) is the initial amount and k is the decay rate.

In this question, we have that:

[tex]k = 0.0001[/tex]

So

[tex]N(t) = N(0)e^{-0.0001t}[/tex]

Age of the pottery bowl:

29% of its original amount of C-14. So we have to find t for which N(t) = 0.29N(0). So

[tex]N(t) = N(0)e^{-0.0001t}[/tex]

[tex]0.29N(0) = N(0)e^{-0.0001t}[/tex]

[tex]e^{-0.0001t} = 0.29[/tex]

[tex]\ln{e^{-0.0001t}} = \ln{0.29}[/tex]

[tex]-0.0001t = \ln{0.29}[/tex]

[tex]t = -\frac{\ln{0.29}}{0.0001}[/tex]

[tex]t = 12378.7[/tex]

The age of the pottery bowl is 12,378.7 years

Answer:

The perimeter is 26 yards

Step-by-step explanation:

Area of rectangle = A= l x w

1st rectangle = 6 x 5 = 30 yards squared

2nd rectangle= 10 x 3 = 30 yards squared

perimeter of rectangle = 2l+2w= 10 + 10 + 3 + 3= 26

Answer: -13.37

Explanation: I did it in decimals because I didn’t know if your assignment required fraction or decimal. 5 4/7= 5x7=35+4=39/7 so this means 5 4/7 is equal to 39/7. -2 2/5= -2x5=-10+2=-8/5. So it comes out to 39/7x-8/5.

Answer:

k = P - m - n

Step-by-step explanation:

The question is asking you to rearrange the equation so that k is alone on one side.

P = k + m + n

P - k = (k + m + n) - k

P - k = m + n

(P - k) - P = m + n - P

-k = m + n - P

-1(-k) = -1 (m + n - P)

k = -m - n + P

The equation is completely simplified so this is your answer.