A company establishes a fund of 120 from which it wants to pay an amount,C, to any of its 20 employees who achieve a high-performance level during the coming year. Each employee has a 2% chance of achieving a high-performance level during the coming year, independent of any other employee.
Determine the maximum value of C for which the probability is less than 1% that the fund will be inadequate to cover all payments for high performance.

Answer:

-7/2

Step-by-step explanation:

To find the y coordinate of the midpoint and the y coordinates together and divide by 2

(2+-9)/2

-7/2

Answer:

2 goes in green box

Step-by-step explanation:

(9,2) (-7,-9)

(x1, y1) (x2,y2)

Midpoint is (x1+x2)/2 , (y1+y2)/2

(9-7)/2= 1

(2-9)/2 = -7/2

Answer:

X=12

Step-by-step explanation:

Given that: X:24 = 6:X

Then:

[tex]\dfrac{X}{24}= \dfrac{6}{X}\\$Cross multiply\\X^2=24 \times 6\\X^2=144\\X=\pm\sqrt{144}\\X=\pm 12[/tex]

Since we require the positive value of X

X=12.

Answer:

The large sample size 'n' =  199.6569≅ 200

Step-by-step explanation:

Step(i):-

Given Standard deviation of salary for all baseball players for 2015 is about $5,478,384.55

Standard deviation of  of salary for all baseball players for 2015

  (S.D ) σ =  $5,478,384.55

Given estimate of this average salary for all baseball players for 2015

                          =  $497,000

Given Margin of error of error is  =  $497,000

Level of significance ∝ = 80%

The critical value Z₀.₂₀ = 1.282  

Step(ii):-

Margin of error of error is  determined by

          [tex]M.E = \frac{Z_{0.20} S.D}{\sqrt{n} }[/tex]

         [tex]497,000 = \frac{1.282 X 5,478,384.55}{\sqrt{n} }[/tex]

Cross multiplication , we get

 [tex]\sqrt{n} = \frac{1.282 X 5,478,384.55}{497,000 }[/tex]

On calculation , we get

√n = 14.13

Squaring on both sides, we get

n = 199.6569

Conclusion:-

The large sample size 'n' =  199.6569≅ 200

Answer:

m=(3+f)/(f-4)

Step-by-step explanation:

To make m the subject of the formula, we want to isolate m. That is, we want to move m to one side of the equation.

First, the fractions need to be taken away. Multiply both sides by m-1 to get: f(m-1)=4m+3.

The distributive property of subtraction tells us a(b-c)=ab-ac. Thus, from this equation we have fm-f=4m+3.

Subtracting 4m, we have fm-4m-f=3

Now, we work the distributive property backwards, where we have ab-ac=a(b-c). Rearrange the terms of fm and 4m, to get mf, and m4. Thus, this can be simplified to m(f-4).

Going back to the equation, we have m(f-4)-f=3.

Add f on both sides, so we have m(f-4)=3+f.

Divide by f-4, so we have m=(3+f)/(f-4)

Answer:

[tex]\frac{9}{2}[/tex]

Step-by-step explanation:

[tex]\frac{3}{4}[/tex] ÷ [tex]\frac{1}{6}[/tex]

Multiply and flip

[tex]\frac{3}{4}[/tex] x [tex]\frac{6}{1}[/tex]

= [tex]\frac{18}{4}[/tex]

= [tex]\frac{9}{2}[/tex]

The value of the division of the two numbers 3/4 and 1/6 results in an improper fraction of 9/2.

To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction.

In this case, we want to divide 3/4 by 1/6, so we multiply 3/4 by the reciprocal of 1/6.

The reciprocal of a fraction is obtained by flipping the fraction upside down. The reciprocal of 1/6 is 6/1 or simply 6.

Therefore, to solve 3/4 divided by 1/6, we can multiply 3/4 by 6:

(3/4) x 6

= (3 x 6) / 4

= 18/4

To simplify the result, we can divide the numerator and denominator by their greatest common divisor, which is 2:

18/4

= (18/2) / (4/2)

= 9/2

So, the division of 3/4 by 1/6 is equal to 9/2.

In mixed number form, 9/2 can be expressed as 4 1/2, meaning there are 4 whole units and 1/2 unit remaining.

Therefore, 3/4 divided by 1/6 is equal to 4 1/2.

To learn more about the division;

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Answer:

(-1,5)

Step-by-step explanation:

When a line segment is divided in the ratio m:n, we use the section formula to determine the point P which divides the line segment:

The coordinates of x and y are:

[tex](x,y)=\left(\dfrac{mx_2+nx_1}{m+n}, \dfrac{my_2+ny_1}{m+n}\right)[/tex]

Given:

[tex]A(x_1,y_1)=(-7, 4)\\B(x_2,y_2)=(8, 9)\\AP:PB=m:n=2:3[/tex]

The coordinates of P is:

[tex](x,y)=\left(\dfrac{2*8+3*-7}{2+3}, \dfrac{2*9+3*4}{2+3}\right)\\=\left(\dfrac{-5}{5}, \dfrac{25}{5}\right)\\\\=(-1,5)[/tex]

Answer:

The expected number of adult workers with a high school diploma is 4.

Step-by-step explanation:

This random variable X can be modeled with the binomial distribution, with parameters n=10 (the sample size) and p=0.4 (the probability that a adult worker have a high school diploma).

The expected value of X is then the mean of the binomial distribution with the parameters already mentioned.

This is calculated as:

[tex]E(X)=\mu_b=n\cdot p=10\cdot0.4=4[/tex]

Answer:

[tex] z = \frac{500-520}{\frac{90}{\sqrt{100}}}= -2.22[/tex]

And we can find this probability using the normal standard distribution and we got:

[tex] P(z<-2.22) =0.0132[/tex]

Step-by-step explanation:

For this case we have the foolowing parameters given:

[tex] \mu = 520[/tex] represent the mean

[tex] \sigma =90[/tex] represent the standard deviation

[tex] n = 100[/tex] the sample size selected

And for this case since the sample size is large enough (n>30) we can apply the central limit theorem and the distribution for the sample mean would be given by:

[tex] \bar X \sim N(\mu , \frac{\sigma}{\sqrt{n}}) [/tex]

And we want to find this probability:

[tex] P(\bar X <500)[/tex]

We can use the z score formula given by:

[tex] z = \frac{500-520}{\frac{90}{\sqrt{100}}}= -2.22[/tex]

And we can find this probability using the normal standard distribution and we got:

[tex] P(z<-2.22) =0.0132[/tex]

Answer:

Step-by-step explanation:

Step 1: Consider P(1) that is n = 1

[tex]1^2 = \frac{1(1+1)(2*1+1)}{6}=\frac{6}{6}=1 \checkmark[/tex]

Step 2: Suppose the equation is true up to n. That is

[tex]1^2 + 2^2+3^2+........+n^2 = \dfrac{n(n+1)(2n+1)}{6 }[/tex]

Step 3: Prove that the equation is true up to (n+1). That is

[tex]1^2 + 2^2+3^2+........+n^2 + (n+1)^2 = \dfrac{(n+1)(n+2)(2n+3)}{6 }[/tex]

The easiest way to prove it is to expend the right hand side and prove that the right hand side = the right hand side of step 2 + (n+1)^2

From step 2, add (n+1)^2 both sides. The left hand side will be the left hand side of step 3, now, the right hand side after adding.

[tex]\dfrac{n(n+1)(2n+1)}{6 }+(n+1)^2 = \dfrac{2n^3+3n^2+n}{6}+\dfrac{6n^2+12n+6}{6}[/tex]

[tex]=\dfrac{2n^3+9n^2+13n+6}{6}[/tex]

If you expend the right hand-side of the step 3, you will see they are same.

Proof done

Answer:

see below

Step-by-step explanation:

1^2+2^2+3^2+...+n^2=n(n+1)(2n+1)/6

Step1

Verify it for n=1

1^2= 1(1+1)(2*1+1)/6= 1*2*3/6= 6/6=1 - correct

Step2

Assume it is correct for n=k

1^2+2^2+3+2+...+k^2= k(k+1)(2k+1)/6

Step3

Prove it is correct for n= k+1

1^2+2^2+3^2+...+(k+1)^2= (k+1)(k+2)(2k+2+1)/6

prove the above for k+1

1^2+2^2+3^2+...+k^2+(k+1)^2= k(k+1)(2k+1)/6 + (k+1)^2=

= 1/6(k(k+1)(2k+1)+6(k+1)^2)= 1/6((k+1)(k(2k+1)+6(k+1))=

=1/6((k+1)(2k²+k+6k+6))= 1/6(k+1)(2k²+4k+3k+6))=

= 1/6(k+1)(2k(k+2)+3(k+2))=

=1/6(k+1)(k+2)(2k+3)

Proved for n= k+1 that:

the sum of squares of (k+1) terms equal to  (k+1)(k+2)(2k+3)/6

Answer:

24

Step-by-step explanation:

Use the Pythagorean theorem.

Where the sum of the two legs squared is equal to the hypotenuse squared.

10² + x² = 26²

100 + x² = 676

x² = 576

x = √576

x = 24

The value of x is 24.

Answer:

The probability that the student answers at least seventeen questions correctly is [tex]8.03\times 10^{-10}[/tex].

Step-by-step explanation:

Let the random variable X represent the number of correctly answered questions.

It is provided all the questions have five options with only one correct option.

Then the probability of selecting the correct option is,

[tex]P(X)=p=\frac{1}{5}=0.20[/tex]

There are n = 20 question in the exam.

It is also provided that a student taking the examination answers each of the questions with an independent random guess.

Then the random variable can be modeled by the Binomial distribution with parameters n = 20 and p = 0.20.

The probability mass function of X is:

[tex]P(X=x)={20\choose x}\ 0.20^{x}\ (1-0.20)^{20-x};\ x =0,1,2,3...[/tex]

Compute the probability that the student answers at least seventeen questions correctly as follows:

[tex]P(X\geq 17)=P (X=17)+P (X=18)+P (X=19)+P (X=20)[/tex]

[tex]=\sum\limits^{20}_{x=17}{{20\choose x}\ 0.20^{x}\ (1-0.20)^{20-x}}\\\\=0.00000000077+0.000000000032+0.00000000000084+0.000000000000042\\\\=0.000000000802882\\\\=8.03\times10^{-10}[/tex]

Thus, the probability that the student answers at least seventeen questions correctly is [tex]8.03\times 10^{-10}[/tex].

Answer:

150 / 100 x 500

= 150 x 5

= 750

Answer:

45,000 codes

Step-by-step explanation:

Given:

Code of 5 digits

Condition

Required

Calculate the number of codes available

Digits = {0,1,2....9}

n(Digits) = 10

Let the format of the code be represented as follows;

ABCDE

From the conditions given

A can't be 1;

This means that A can be any of 0,2,3,4....9

This implies that A can be any of the above 9 digits

n(A) = 9

There's no condition attached to BCD;

This means that B can be any of 10 digits

This means that C can be any of 10 digits

This means that D can be any of 10 digits

n(B) = n(C) = n(D) = 10

Lastly, E must be an even number;

This means that E can be any of 0,2,4,6,8

This implies that E can be any of the above 5 digits

n(E) = 5

So,

Number of available codes = n(A) * n(B) * n(C) * n(D) * n(E)

Number of available codes = 9 * 10 * 10 * 10 *5

Number of available codes = 45,000

Hence, there are 45,000 available codes

Answer:

The correct answer is:

r + 0.50 = 10.25: Subtract .50 from both sides. The answer is $9.75.

This is because Juan got a $0.50 raise which means that his new rate will be $0.50 more than his original rate (r).

Answer:

$9.75

Step-by-step explanation:

Answer:

The relative change from Ohio to Indiana is 49.04

Step-by-step explanation:

Answer:

  $106.67

Step-by-step explanation:

Using the example, for 3 hours work, Alex would be paid ...

  (2 hr)($30/hr) +(1 hr)($20/hr) = $60 +$20 = $80

At the same rate of pay, for 4 hours work, the pay would be ...

  pay/(4 hr) = $80/(3 hr)

  pay = $80(4/3) ≈ $106.67

Alex's pay for 4 hours of work is $106.67.

Answer:

We conclude that older people are more likely to be victimized.

Step-by-step explanation:

We are given that a survey shows that 10% of the population is victimized by property crime each year.

A random sample of 527 older citizens (65 years or more of age) shows a victimization rate of 12.35%

Let p = population proportion of people who are victimized.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]p \leq[/tex] 10%      {means that older people are less likely to be victimized or remains same}

Alternate Hypothesis, [tex]H_A[/tex] : p > 10%      {means that older people are more likely to be victimized}

The test statistics that would be used here One-sample z-test for proportions;

                             T.S. =  [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]  ~  N(0,1)

where, [tex]\hat p[/tex] = sample proportion of older people who are victimized = 12.35%

            n = sample of older citizens = 527

So, the test statistics  =  [tex]\frac{0.1235-0.10}{\sqrt{\frac{0.10(1-0.10)}{527} } }[/tex]  

                                       =  1.798

The value of z-test statistics is 1.798.

Since in the question, we are not given with the level of significance so we assume it to be 5%. Now at 5% level of significance, the z table gives a critical value of 1.645 for right-tailed test.

Since our test statistics is more than the critical value of z as 1.798 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that older people are more likely to be victimized.

Answer: the answer is c (the third answer ) ‼️

Step-by-step explanation:

The data in the given residual plot shows that model C has the best fit.

A straight line that minimizes the gap between it and some data is called a line of best fit. In a scatter plot containing various data points, a relationship is expressed using the line of best fit.

Given:

The residual plot of the values in the graph,

The points in the first graph are very far from the x-axis and y-axis so, it is not the best fit,

The points in the second graph are very far from the x-axis and y-axis, and they are symmetric to the y-axis but not the best fit.

Most of the points are close to the x-axis, so it is the best fit,

Thus, the third graph is the best line of fit.

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Answer:

$13564

Step-by-step explanation:

[tex]\left|\begin{array}{c|c|c}$If taxable&& \\$income&&\\$ is over&$but not over&$the tax is\\---&---&---\\$0 &7,825 &$10\% of the amount over 0\\7,825 &31,850 &$782.50 plus $15\% $ of the amount over 7,825$ \end{array}\right|[/tex][tex]\left|\begin{array}{c|c|c}31,850 &77,100 &$4,386.25 plus 25\% of the amount over 31,850 \\77,100 &160,850 &$15,698.75 plus 28\% of the amount over 77,100\end{array}\right|[/tex]

[tex]\left|\begin{array}{c|c|c}160,850 &349,700 &$39,148.75 plus 33\% of the amount over 160,850 \\349,700 &$no limit&$101,469.25 plus 35\% of the amount over 349,700\end{array}\right|[/tex]

Mary’s taxable income= $68,562

From the table, If taxable income is over $31,850 but not over $77,100

The tax = $4386.25 + 25% of the amount over 31,850

Amount over $31,850=$68,562-$31,850

=$36,712

Therefore:

Mary's tax = $4386.25 + (25% of $36,712)

=$4386.25 +9,178

=$13564.25

=$13564 (to the nearest dollar)

Income tax is the tax charged on individual's or entities' income

Mary owes $13564 income tax

Given that the taxable income is $68,562.

Using the table as a guide, $68,562 falls within the income range $31,850 - $77,100

So, the tax is $4386 added to 25% of the excess over $31850

This is calculated as:

[tex]Tax = \$4386 + 25\% \times (Income -\$31850)[/tex]

Substitute $68,562 for income

[tex]Tax = \$4386 + 25\% \times (\$68562 -\$31850)[/tex]

Solve the expression in the bracket

[tex]Tax = \$4386 + 25\% \times \$36712[/tex]

Evaluate the product

[tex]Tax = \$4386 + \$9178[/tex]

Add the terms of the expression

[tex]Tax = \$13564[/tex]

Hence, Mary owes $13564 income tax

Read more about income tax at:

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Answer:

The 95% confidence interval estimate of the true population proportion of U.S. employers that were likely to require higher employee contributions for health care coverage is 0.52 +/- 0.0370

= (0.4830, 0.5570)

The margin of error M.E = 0.0370

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

p+/-z√(p(1-p)/n)

p+/-M.E

Given that;

M.E = margin of error

Proportion p = 52% = 0.52

Number of samples n = 700

Confidence interval = 95%

z value (at 95% confidence) = 1.96

Substituting the values we have;

0.52 +/- 1.96√(0.52(1-0.52)/700)

0.52 +/- 1.96(0.0189)

0.52 +/- 0.0370

( 0.4830, 0.5570)

The 95% confidence interval estimate of the true population proportion of U.S. employers that were likely to require higher employee contributions for health care coverage is 0.52 +/- 0.0370

= (0.4830, 0.5570)

The margin of error M.E = 0.0370

Answer:

[tex]=\frac{-209}{29}y[/tex]

I hope this help you :)

Answer: £192.50

Step-by-step explanation:

550 x 0.35 = 192.50

Answer:

Yes because yes.

Step-by-step explanation:

Y + e + s = Yes

Answer:

B. Length A of Rasheeda’s garden is 27 ft.

C. Length B of the book’s garden is 12 ft.

E. Length A of the book’s garden is 9 ft longer than length A of Rasheeda’s garden.

Step-by-step explanation:

step 1

Find the dimension of the book's garden

we know that

Book scale: 1 inch = 2 feet

That means

1 inch in the drawing represent 2 feet in the actual

To find out the actual dimensions, multiply the dimension in the drawing by 2

so

Length A of the book’s garden

Width B of the book’s garden

step 2

Find the dimension of Rasheeda’s garden

we know that

Rasheeda's Scale: 2 inch = 3 feet

That means

2 inch inches the drawing represent 3 feet in the actual

To find out the actual dimensions, multiply the dimension in the drawing by 3 and divided by 2

so

Length A of Rasheeda's garden

Width B of Rasheeda's garden

Verify each statement

A. Length A of the book’s garden is 18 ft.

The statement is false

Because, Length A of the book’s garden is 36 ft (see the explanation)

B. Length A of Rasheeda’s garden is 27 ft.

The statement is true (see the explanation)

C. Length B of the book’s garden is 12 ft

The statement is true (see the explanation)

D. Length B of Rasheeda’s garden is 6 ft.

The statement is false

Because, Length B of Rasheeda’s garden is 9 ft. (see the explanation)

E. Length A of the book’s garden is 9 ft longer than length A of Rasheeda’s garden.

The statement is true

Because the difference between 36 ft and 27 ft is equal to 9 ft

F. Length B of the book’s garden is 3 ft shorter than length B of Rasheeda’s garden.

The statement is false

Because, Length B of the book’s garden is 3 ft greater than length B of Rasheeda’s garden.

taffy927x2 and 22 more users found this answer helpful

Answer:

B. Length A of Rasheeda’s garden is 27 ft.

C. Length B of the book’s garden is 12 ft.

E. Length A of the book’s garden is 9 ft longer than length A of Rasheeda’s garden.

(second, third, and fifth choices)

Explanation: I did the quiz and got it right.

Hope this Helps!

Answer:

2 is the coefficient

Step-by-step explanation:

2 is the coefficient bc a coefficient is the number next to a variable (such as x)  and 2 is next to x and is the only one in the equation

Answer:

-2

Step-by-step explanation:

Answer:

[tex] \frac{4 {x }^{2} - 17x - 9 }{ {x}^{3} - 7 {x}^{2} + 7x + 15 } [/tex]

Step-by-step explanation:

In the picture.

I hope I am correct

I hope it helps :)

Answer:

they may like it

they may dislike it

Step-by-step explanation:

they amy think ots essentiall

they may think its unescary

Answer:

[tex]\boxed{\sf \ \ \ x = -8 \ or \ x = -4 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

[tex]4x^2+48x+128=0\\<=> 4(x^2+12x+32)=0\\<=> x^2+12x+32=0\\<=> (x+6)^2 - 36 + 32= 0\\\\<=> (x+6)^2-4=0\\<=> (x+6+2)(x+6-2)=0\\<=> (x+8)(x+4) = 0\\<=> x = -8 \ or \ x = -4[/tex]

vouch, i confirm that -8, -4 are the answers

Answer:

52.63% probability that thids intial repair was made by the first technican

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Incomplete repair

Event B: Made by the first technican.

The first technican, who services 40% of the breakdowns, has 5% chance of making incomplete repair.

This means that [tex]P(B) = 0.4, P(A|B) = 0.05[/tex].

Probability of an incomplete repair:

5% of 40%(first technican) or 3% of 60%(second technican). So

[tex]P(A) = 0.05*0.4 + 0.03*0.6 = 0.038[/tex]

Given that there is a problem with the production line due to an incomplete repair, what is the probability that thids intial repair was made by the first technican

[tex]P(B|A) = \frac{0.4*0.05}{0.038} = 0.5263[/tex]

52.63% probability that thids intial repair was made by the first technican