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.

The correct answer is $614

Explanation:

To calculate the total amount Kiki earned during the three days, it is necessary to find out first the money she earned on commissions ( 8% of each item she sold) and then add this to the total of her base salary ($150 per day). To begin, you can find the 8% of any price by dividing the total price by 100 and then multiplying it by 8, considering the total price represents 100% and by dividing by 100 you will get the value of 1%, then if you multiply this by 8 you will know the 8%.

$350 /100 = 3.5 x 8 = $28 (commission of  the sofa chair)

$500/100 = 5 x 8 = $40 (commission of the loveseat)

$1,200/ 100 = 12 x 8 = $96 (commission of the couch)

This means, Kiki earned a total of $164 in commissions (28 + 40 + 96 = 164), and if you add this to the total of her base salary (150 + 150 + 150 =450) during the three days, the total earned is $614 because $ 450 (base salary) + $164 (commissions) equals $614.

Answer:

614. I got the assignment correct!

Step-by-step explanation:

Answer:

Addition

Step-by step explanation:

Let a=5.54 and b=5.566

a+b=5.54+5.566=11.106

Using significant rule of addition

a+b=11.11(4 significant figures)

b-a= 0.026

Using significant rule of  subtraction

b-a=0.03(Two significant figures)

[tex]a\times b=5.54\times 5.566= 30.83564[/tex]

Using significant rule of multiplication

[tex]a\times b=30.8[/tex](3  significant figures)

[tex]\frac{b}{a}=\frac{5.566}{5.54}=1.00469[/tex]

Using significant rule of  division

[tex]\frac{b}{a}=1.00[/tex](Three significant figures)

Addition can produce the greatest number of significant figures

Answer: -1

Step-by-step explanation:

to calculate f(-1), you know that x = -1. so all you have to do is substitute:

f(-1) = (-1)2 + 1

f(-1) = -2 + 1

f(-1) = -1

Answer:

0

Step-by-step explanation:

Answer: the slope is 2

Step-by-step explanation:

2x-y=16

-y=16-2x

y=2x-16

Step-by-step explanation:

1.07×1.25

=1.3375 euros

Answer:

7/6 ton or 1 1/6 ton.

Step-by-step explanation:

Seen this before.

Answer:

A shape with two pairs of parallel lines, perpendicular lines, and two pairs of equal sides can be best described as a rectangle.

Answer:

(a) P(Millennial | Read a Book) = 0.3086

(b) P( Not Millennial | Did Not Read a Book) = 0.8421

(c)

P(Millennial and Read a Book) = P(Read a Book) × P(Millennial)

0.25 = 0.81 × 0.28

0.25 ≠ 0.2268

Since the relation doesn't hold true, therefore, being considered a millennial and having read a book in the past year are not independent events.

Step-by-step explanation:

The probability a person has read a book in the past year is 0.81.

P(Read a Book) = 0.81

The probability a person is considered a millennial is 0.28.

P(Millennial) = 0.28

The probability a person has read a book in the past year and is considered a millennial is 0.25.

P(Millennial and Read a Book) = 0.25

(a) Find P(Millennial | Read a Book)

Recall that Multiplicative law of probability is given by

P(A ∩ B) = P(B | A) × P(A)

P(B | A) = P(A ∩ B) / P(A)

For the given case,

P(Millennial | Read a Book) = P(Millennial and Read a Book) / P(Read a Book)

P(Millennial | Read a Book) = 0.25 / 0.81

P(Millennial | Read a Book) = 0.3086

(b) Find P(Not Millennial | Did Not Read a Book)

P( Not Millennial | Did Not Read a Book) = P(Not Millennial and Did Not Read a Book) / P(Did Not Read a Book)

Where

∵  P(A' and B') = 1 - P(A or B)

P(Not Millennial and Did Not Read a Book) = 1 - P(Millennial or Read a Book)

∵  P(A or B) = P(A) + P(B) - P(A and B)

P(Millennial or Read a Book) = P(Read a Book) + P(Millennial) - P(Millennial and Read a Book)

P(Millennial or Read a Book) = 0.81 + 0.28 - 0.25

P(Millennial or Read a Book) = 0.84

So,

P(Not Millennial and Did Not Read a Book) = 1 - 0.84

P(Not Millennial and Did Not Read a Book) = 0.16

Also,

∵  P(A') = 1 - P(A)

P(Did Not Read a Book) = 1 - P(Read a Book)

P(Did Not Read a Book) = 1 - 0.81

P(Did Not Read a Book) = 0.19

Finally,

P( Not Millennial | Did Not Read a Book) = P(Not Millennial and Did Not Read a Book) / P(Did Not Read a Book)

P( Not Millennial | Did Not Read a Book) = 0.16/0.19

P( Not Millennial | Did Not Read a Book) = 0.8421

(c) Are being considered a millennial and having read a book in the past year independent events? Justify your answer mathematically.

Mathematically, two events are considered to be independent if the following relation holds true,

P(A and B) = P(A) × P(B)

For the given case,

P(Millennial and Read a Book) = P(Read a Book) × P(Millennial)

0.25 = 0.81 × 0.28

0.25 ≠ 0.2268

Since the relation doesn't hold true, therefore, being considered a millennial and having read a book in the past year are not independent events.

Answer:

161 cm

Step-by-step explanation:

The height of each box is 115 / 5 = 23 so that means the height of 7 boxes is 7 * 23 = 161.

Answer:

161 cm

Step-by-step explanation:

(115 ÷ 5) ×7= 23×7= 161 cm

Answer:

$23.64

Step-by-step explanation:

12 * $1.97 = $23.64

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is:

The mean annual tuition and fees for a sample of 15 private colleges was $35,500 with a standard deviation of $6500. A dotplot shows that it is reasonable to assume that the population is approximately normal. You wish to test whether the mean tuition and fees for private colleges is different from $32,500. State the null and alternate hypotheses. A) H0: 4 = 32,500, H:4=35,500 C) H: 4 = 35,500, H7:35,500 B) H: 4 = 32,500, H : 4 # 32,500 D) H0:41 # 32,500, H : 4 = 32,500

Solution

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

H0: µ = 32500

For the alternative hypothesis,

Ha: µ ≠ 32500

This is a two tailed test.

Since the number of samples is small and the population standard deviation is not given, the distribution is a student's t.

Since n = 15,

Degrees of freedom, df = n - 1 = 15 - 1 = 14

t = (x - µ)/(s/√n)

Where

x = sample mean = 35500

µ = population mean = 32500

s = samples standard deviation = 6500

t = (35500 - 32500)/(6500/√15) = 1.79

We would determine the p value using the t test calculator. It becomes

p = 0.095

Assuming alpha = 0.05

Since alpha, 0.05 < than the p value, 0.095, then we would fail to reject the null hypothesis.

Answer:

3/4

Step-by-step explanation:

Convert the fractions into decimals.

5/8 = 0.625

3/4 = 0.75

0.75 is greater than 0.625.

Question:

Suppose the amount of sun block lotion in plastic bottles leaving a filling machine has a normal distribution. The bottles are labeled 300 milliliters (ml) but the actual mean is 302 ml and the standard deviation is 2 ml. If you purchase a package of 6 bottles of lotion, what is closest to the probability that at least one bottle has a content of less than 300 ml?

Answer:

0.645314

Step-by-step explanation:

Given:

Mean, u = 302

Standard deviation [tex] \sigma[/tex] = 2

n = 6

Let's first find P(X>300):

[tex] Z = \frac{X - u}{\sigma} [/tex]

[tex] Z = \frac{300 - 302}{2} [/tex]

[tex] Z = -1 [/tex]

Using the standard normal table,

NORMSDIST(-1) = 0.158655

Thus,

P(Z<-1) = 0.158655

Find the closest to the probability that at least one bottle has a content of less than 300 ml:

Given that 6 bottles were purchased & p = 0.158655

Find:

P(X≥1) = 1 – P(X<1) = 1 – P(X=0)

Use bimonial distribution:

[tex] P(X=x) = ^nC_x*p^x*(1 - p)^(^n^-^x^)[/tex]

[tex] P(X=0) = ^6C_0* 0.158655^0*(1 - 0.158655)^(^6^-^0^)[/tex]

[tex] P(X=0) = 1*1* 0.841345^6 [/tex]

[tex] P(X=0) = 0.354686 [/tex]

Therefore,

P(X≥1) = 1 – P(X<1) = 1 – P(X=0)

= 1 - 0.354686

= 0.645314

The closest to the probability that at least one bottle has a content of less than 300 ml is 0.645314

Answer:

[tex] P(x>7)[/tex]

And for this case we can use the cumulative distribution given by:

[tex] F(x) =\frac{x-a}{b-a}, a \leq x \leq b[/tex]

And if we use the complement rule and the before formula we have:

[tex] P(x>7) = 1- P(x<7) = 1- F(7) = 1 -\frac{7-5}{17-5}= 1- 0.1667 =0.8333[/tex]

Step-by-step explanation:

For this problem we denote the random variable X as  the time, in minutes, it takes a barber to complete a haircut and the distribution for X is given by:

[tex] X \sim Unif (a=5, b=17)[/tex]

And we want to find the following probability:

[tex] P(x>7)[/tex]

And for this case we can use the cumulative distribution given by:

[tex] F(x) =\frac{x-a}{b-a}, a \leq x \leq b[/tex]

And if we use the complement rule and the before formula we have:

[tex] P(x>7) = 1- P(x<7) = 1- F(7) = 1 -\frac{7-5}{17-5}= 1- 0.1667 =0.8333[/tex]

Answer:

D.

Step-by-step explanation:

One slope is positive and one negative, so one line should go up and one down. B or D.

y = 1/2 x - 1 line goes up and y-int. = - 1.  Answer D.

y = - 1/2 x + 3 line goes up and y-int. = 3.  Answer D.

Answer:

29

Step-by-step explanation:

What we must do is calculate the z value for each value and thus find what percentage each represents and the subtraction would be the percentage between those two values.

We have that z is equal to:

z = (x - m) / (sd)

x is the value to evaluate, m the mean, sd the standard deviation

So for 100 copies we have:

z = (100 - 80) / (35)

z = 0.5714

and this value represents 0.7157

Which means, that of those 100 copies it is probable that they could be distributed:

100 * 0.7157 = 71.57

71 copies, so a total of about 29 (100 - 71) were being returned

Answer:

4 study all 3 because the number 4 is in all the sciences at the same time so 4 students study all the sciences.

1 (biology and physics) + 4(just physics) + 8(physics and chemistry) + 4 (study all the sciences) = 1 + 4 + 8 + 4 = 17

17 study physics

Biology has 5 (just biology) + 1 (biology and physics) + 4 (every science) + 3 (biology and chemistry) + 9 (just chemistry) + 8 (physics and chemistry) = 5 + 1 + 4 + 3 + 9 + 8 = 30 students

30 students study biology or chemistry

Total students

Add all the numbers (including the 2 at the side)

5 + 1 + 4 + 3 + 4 + 8 + 9 + 2 = 36 students

Hope this helps

Step-by-step explanation:

Answer:

Brent’s club has more possible team combinations because there are more members to choose from

Step-by-step explanation:

Brents club can be created in C12 6 =12!/6!/6!=7*8*9*10*11*12/(2*3*4*5*6)=

=924 variants

Miguel's  club can be created in C10 6=10!/6!/4!=7*8*9*10/(2*3*4)=210 variants

924>210 so Brent’s club has more possible team combinations because there are more members to choose from

Answer:

B

Step-by-step explanation:

Brent’s club has more possible team combinations because there are more members to choose from.

Answer:

The probability that more than 22 of the women sampled have not been the victim of domestic abuse is P=0.537.

Step-by-step explanation:

This problem can be modeled by a binomial random variable.

The probability p can be calculated as the proportion of women that has not been a victim of domestic abuse at some point in her life:

[tex]p=1-\dfrac{X}{n}=1-\dfrac{1}{10}=1-0.1=0.9[/tex]

The sample size is n=25.

We want to calculate the probability that more than 22 of the women of the sample have not been victim of domestic abuse.

The probability that exactly k women have not been victim of domestic abuse can be calculated as:

[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{25}{k} 0.9^{k} 0.1^{25-k}\\\\\\[/tex]

Then, the probability that more than 22 of the women sampled have not been the victim of domestic abuse is:

[tex]P(x>22)=P(x=23)+P(x=24)+P(x=25)\\\\\\P(x=23) = \dbinom{25}{23} p^{23}(1-p)^{2}=300*0.089*0.01=0.266\\\\\\P(x=24) = \dbinom{25}{24} p^{24}(1-p)^{1}=25*0.08*0.1=0.199\\\\\\P(x=25) = \dbinom{25}{25} p^{25}(1-p)^{0}=1*0.072*1=0.072\\\\\\\\P(x>22)=0.266+0.199+0.072=0.537[/tex]

Answer:

B. x^2 - 64 = 0

Step-by-step explanation:

A. x+10 = 33  

B. x^2 - 64 = 0

C. Y-776

D. y = 4x + 6

A quadratic has an term with a power of two

Answer:

21

Step-by-step explanation:

Since angle ABC is an inscribed angle, its measure is half that of arc AC. Therefore:

[tex]2(3x-1.5)=3x+9 \\\\6x-3=3x+9 \\\\3x-3=9 \\\\3x=12 \\\\x=4 \\\\AC=3(4)+9=12+9=21[/tex]

Hope this helps!

Use the Inscribed Angle theorem to get the measure of AC. The intercepted arc AC is,  21°.

We know that, Inscribed Angle Theorem stated that the measure of an inscribed angle is half the measure of the intercepted arc.

Given that,

The inscribed angle is, (3x - 1.5)

And the Intercepted arc AC is, (3x + 9)

So, We get;

(3x - 1.5) = 1/2 (3x + 9)

2 (3x - 1.5) = (3x + 9)

6x - 3 = 3x + 9

3x =  9 + 3

3x = 12

x = 4

Thus, The Intercepted arc AC is,

(3x + 9) = 3×4 + 9

           = 21°

Learn more about the Inscribed Angle theorem visit:

brainly.com/question/5436956

#SPJ2

Answer:

Brainleist :)

Step-by-step explanation:

120 dollars for 4 hours of labor

120/4 dollars for 1 hour of labor

B) 30 dollars for 1 hour of labor

answe:

B) 30 dollars for 1 hour of labor

Step-by-step explanation:

120 dollars for 4 hours of labor

120/4 dollars for 1 hour of labor

important messagee:

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Answer:

C. No, it is not a dilation because the points of the image are not moved away from the center of dilation proportionally.

Step-by-step explanation:

Dilation is the process in which the size i.e dimensions of a given figure is either increased or decreased by a scale factor, without changing the shape of the figure.

Given that: PA = 2, PB = 3, A[tex]A^{I}[/tex] = 4, B[tex]B^{I}[/tex] = 5.

So that: P[tex]A^{I}[/tex] = 6, P[tex]B^{I}[/tex] = 8.

Therefore, triangle A'B'C' is not an exact dilation of triangle ABC. So that the correct option is; No, it is not a dilation because the points of the image are not moved away from the center of dilation proportionally.

Answer:

the answer is c

Step-by-step explanation:

Answer:

Linearly independent, x = 0

Step-by-step explanation:

- We are given three functions as follows:

                           [tex]f ( x ) = e^4^x\\\\g ( x ) = xe^4^x\\\\h( x ) = x^2e^4^x[/tex]

- We are to determine the linear - independence of the given functions. We will use the theorem of linear independence which states that:

                           [tex]c_1*f(x) + c_2*g(x) + c_3*h(x) = 0[/tex]

Where,

                       c1 , c2 , c3 are all zeroes then for all values of (x),

- The system of function is said to be linearly independent

- We will express are system of equations as such:

                           [tex]c_1*e^4^x + c_2*xe^4^x + c_3*x^2e^4^x = 0\\\\[/tex]

- To express our system of linear equations we will choose three arbitrary  values of ( x ). We will choose, x = 0. then we have:

                          [tex]c_1*( 1 ) + c_2*(0) + c_3*(0 ) = 0\\\\c_1 = 0[/tex]

- Next choose x = 1:

                          [tex]c_2*e^4 + c_3*e^4 = 0\\\\c_2 + c_3 = 0[/tex]

- Next choose x = 2:

                          [tex]2*c_2*e^8 + 4*c_3*e^8 = 0\\\\c_2 + 2c_3 = 0[/tex]

- Solve the last two equations simultaneously we have:

                          [tex]c_1 = c_2 = c_3 = 0[/tex]     .... ( Only trivial solution exist )

Answer: The functions are linearly independent

- The only zero exist is x = 0.

Answer:

En álgebra, el teorema del factor es un teorema que vincula factores y ceros de un polinomio. Es un caso especial del teorema del resto polinómico.

Step-by-step explanation:

Answer:

A 90% confidence interval of the true mean is [$119.86, $123.34].

Step-by-step explanation:

We are given that an irate student complained that the cost of textbooks was too high. He randomly surveyed 36 other students and found that the mean amount of money spent on textbooks was $121.60.

Also, the standard deviation of the population was $6.36.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                              P.Q.  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\bar X[/tex] = sample mean amount of money spent on textbooks = $121.60

            [tex]\sigma[/tex] = population standard deviation = $6.36

            n = sample of students = 36

            [tex]\mu[/tex] = population mean

Here for constructing a 90% confidence interval we have used One-sample z-test statistics as we know about population standard deviation.

So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-1.645 < N(0,1) < 1.645) = 0.90  {As the critical value of z at 5% level

                                                      of significance are -1.645 & 1.645}  

P(-1.645 < [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < 1.645) = 0.90

P( [tex]-1.645 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]1.645 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.90

P( [tex]\bar X-1.645 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.645 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.90

90% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.645 \times {\frac{\sigma}{\sqrt{n} } }[/tex] , [tex]\bar X+1.645 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ]

                                      = [ [tex]121.60-1.645 \times {\frac{6.36}{\sqrt{36} } }[/tex] , [tex]121.60+1.645 \times {\frac{6.36}{\sqrt{36} } }[/tex] ]

                                      = [$119.86, $123.34]

Therefore, a 90% confidence interval of the true mean is [$119.86, $123.34].

Answer:

3/118=0.02 rounded to the nearest hundredth.

Step-by-step explanation:

In total, all the lights flash fro 118 seconds.

Because the yellow light takes up 3 of those 118 seconds, the probability that you come to a yellow light is  3/118 = 0.02542372881 round to the nearest hundredth

= 0.02

P.S. Could you mark this as brainliest it it is okay plz?

Answer:

1) A = 0.79

B = 0.4708

2) CI = (0.7728, 0.8072)

3) CI = (0.4481, 0.4935)

b. It appears that the proportion of adults who feel this way in country A is more than those in country B.

Step-by-step explanation:

1) Sample proportions for both Population A and B

For country A:

Sample size,n = 1500

Sample proportion = [tex] \frac{1185}{1500} = 0.79 [/tex]

For Country B:

Sample size,n = 1302

Sample proportion = [tex] \frac{613}{1302} = 0.4708 [/tex]

2) Confidence interval for country A:

Given:

Mean,x = 1185

Sample size = 1500

Sample proportion, p = 0.79

q = 1 - 0.79 = 0.21

Using z table,

90% confidence interval, [tex] Z _\alpha /2 = 1.64 [/tex]

Confidence interval, CI:

[tex] \frac{p +/- Z_\alpha_/2}{\sqrt{(p * q)/n}} [/tex]

[tex] = \frac{0.79 - 1.64}{\sqrt{(0.79 * 0.21)/1500}}, \frac{0.79 + 1.64}{\sqrt{(0.79 * 0.21)/1500}} [/tex]

[tex] CI = (0.7728, 0.8072) [/tex]

3) Confidence interval for country A:

Given:

Mean,x = 613

Sample size = 1302

Sample proportion, p = 0.4708

q = 1 - 0.4708 = 0.5292

Using z table,

90% confidence interval, [tex] Z _\alpha /2 = 1.64 [/tex]

Confidence interval, CI:

[tex] \frac{p +/- Z_\alpha_/2}{\sqrt{(p * q)/n}} [/tex]

[tex] = \frac{0.4708 - 1.64}{\sqrt{(0.4708 * 0.5292)/1302}}, \frac{0.4708 + 1.64}{\sqrt{(0.4708 * 0.5295)/1302}} [/tex]

[tex] CI = (0.4481, 0.4935) [/tex]

From both confidence interval, we could see that that the proportion of adults who feel this way in country A is more than those in country B.

Option B is correct.

Answer:

Step-by-step explanation:

The relations between length (L) and width (W) are ...

  W +9 = L

  LW = 486

Substituting gives ...

  (W+9)W = 486

  W^2 +9W -486 = 0 . . . put in standard form

  (W +27)(W -18) = 0 . . . . factor

  W = 18 . . . .  the positive solution

The width of the rectangle is 18 inches; the length is 27 inches.

_____

Comment on factoring

There are a number of ways to solve quadratics. Apart from using a graphing calculator, one of the easiest is factoring. Here, we're looking for factors of -486 that have a sum of 9.

486 = 2 × 3^5, so we might guess that the factors of interest are -2·3² = -18 and 3·3² = 27. These turn out to be correct: -18 +27 = 9; (-18)(27) = -486.

Answer:

Step-by-step explanation:

When an integers or a whole number is divided by another integer or whole number the result is a whole number.

Hence [tex]\frac{-15}{2}[/tex] is a rational number

This is  because both -15 and 2 are integer numbers

Answer:

rational

Step-by-step explanation: