Suppose a fair six sided die has been relabeled so that the 6 is replaced with another 5,i.e., the sides read 1,2,3,4,5,5. If the die is rolled five times, what is the probability that we roll five distinct values

Answer:

The mean number of tiebreakers is of 35.2 and the standard deviation is of 5.44.

Step-by-step explanation:

For each set, there are only two possible outcomes. Either it goes to a tiebreak, or it does not. The probability of a set going to a tiebreak is independent of any other set, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

The probability that a tennis set will go to a tiebreaker is 16%.

This means that [tex]p = 0.16[/tex]

220 randomly selected tennis sets

This means that [tex]n = 220[/tex]

What is the mean and the standard deviation of the number of tiebreakers?

[tex]E(X) = np = 220*0.16 = 35.2[/tex]

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{220*0.16*0.84} = 5.44[/tex]

The mean number of tiebreakers is of 35.2 and the standard deviation is of 5.44.

Answer:

0.05 metre

5×10^5 kilometer

1.9685

Answer:

Step-by-step explanation:

We get to use the simple version of the half life equation:

[tex]N=N_0(\frac{1}{2})^{\frac{t}{H}[/tex] where N is the amount of radioactive element left after a specific number of years,

N0 is the initial amount of the element,

t is the number of years (our unknown), and

H is the Half life of the element. For us,

N is 61

N0 is 70,

t is unknown,

H is 24 years. Filling in:

[tex]61=70(.5)^{\frac{t}{24}[/tex]. We begin by dividing both sides by 70 to get:

[tex].8714285=(.5)^{\frac{t}{24}[/tex] and then take the natural log of both sides:

[tex]ln(.8714285=ln(.5)^{\frac{t}{24}[/tex] which allows us to bring down the exponent to the front on the right side:

[tex]ln(.8714285)=\frac{t}{24}ln(.5)[/tex]. We divide both sides by ln(.5) to get:

[tex].1985457976=\frac{t}{24}[/tex] and then multiply both sides by 24 to get:

t = 4.8 years

Step-by-step explanation:

tan 30°= root 3/ 3

r²=x² + y²

r²= 4root3 ² + 12²

r²= 48 +144

r²= 192

ŕ= 8root3

so the bottom is 12...

the other side is 4root3

[tex]4 \sqrt{3} [/tex]

and hypotenuse is 8root3

[tex]8 \sqrt{3} [/tex]

The answer for this question is 6.25

Answer:

$72.70

Step-by-step explanation:

bill was $56.80

tip was 20% so was 56.80/ 5( because 5 of 20% will make 100%)= $11.36

tax was 8% so was 56.80*8/100= $4.54

total money paid

56.80+4.54+11.36 = 72.70

Answer:

Step-by-step explanation:

12/35

Part (a)

The graph is shown below. It's a piecewise function composed of 3 parts: Two flat horizontal segments and a decreasing segment.

Note the use of open holes at points C and E. They tell the reader that the specific point is not part of the function. For example, point C at (8000,0.75) is an open hole since the second piece has x = 8000 excluded. In other words, the domain for the second piece is [tex]8,000 < x \le 20,000[/tex] which says to exclude 8000 but to include 20,000.

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

Part (b)

The flat parts are due to the two first pieces being constant functions. Regardless of what x is on those portions, the cost per unit stays the same. We see that the cost starts off at 35 cents per unit (green segment), then it jumps to 75 cents per unit (blue segment).

So far the costs have been constant, but once we get to the red curve portion, then the costs decrease as x increases. Note that 1/(200,000) = 0.000005 which means the costs are decreasing by 0.000005 dollars per unit. Let's multiply that by 10,000 to get 10,000*0.000005 = 0.05

So for the red portion, the costs are decreasing by $0.05 per 10,000 units, or they are decreasing by 5 cents per 10,000 units. When x > 20000, the lowest we can get the cost is at 62 cents per unit. This is when production is at max capacity (42,000 units).

If you wanted the cost per unit to be as small as possible, and x didn't have to be larger than 20 thousand, then you'd stick to the green line. However, the drawback here is that you can only produce at max 8000 units.

Answer:

Person above was super helpful!

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

because I remember doing this before

Answer:

y= (-6/5)x -2

Step-by-step explanation:

y=mx+b , where m is the slope, and b is the y -intercept

the y -intercept is where the line intersects the y-axis so b = -2

the slope m= y(rise) /x(run)  = 6/-5 = -6/5 ( to find the slope you have to know how to get from any point on the line to another point on the same line; start at point (0,-2) go up 6(y-rise) and to the left 5(x-run) at point (-5,4))

y= (-6/5)x -2

Answer:

-11

Step-by-step explanation:

let f(c) = 4c - 3

f(-2) = 4(-2) - 3 = -8 -3 = -11

Answer:

-11

Step-by-step explanation:

4c - 3

c = -2

4(-2) - 3

-8 - 3

-11

4c - 3 = -11 when c = -2

Answer:

$1,627,579

Step-by-step explanation:

Given that

The account receivable turnover is 4.8 times

And, the net sales is $7,812,379

We need to find out the receivable

So as we know that

accounts receivable turnover = net sales ÷ average accounts receivables

Therefore the accounts receivables is

= ($7,812,379 ÷ 4.8)

= $1,627,578.96

= $1,627,579

Hi there!

[tex]\large\boxed{\text{System G.}}[/tex]

For a system to have an infinite number of solutions, both expressions must be equal. We can go through each system and determine this:

F:

x + 2 = y

4 = 2y - x

If we rearrange so that both are in the same format, we get:

x + 2 = y

x + 4 = 2y

These cannot be equal, so they do not have infinite solutions.

G:

2y + 6 = 4x

-3 = y - 2x

Rearrange:

2y + 6 = 4x

-y - 3 = -2x

We can try to make the bottom equation look like the top equation by multiplying all terms by -2. We get:

2y + 6 = 4x. This is the same as the top, so G has infinite solutions.

Just to be sure, we can go through the others:

H:

y + 3 = 2x

4x = 2y - 3

Rearrange:

y + 3 = 2x

2y - 3 = 4x. Cannot be equal to the other equation.

J:

y = 2x - 5

y = 2x - 2. Not equal.

The correct answer is G.

Answer:

___y141.3cm is the answer

Answer:

60 feet

Step-by-step explanation:

You need to find the midpoint between 0 and 120. (0+120)/2 is 60 feet.

Answer:

100 pi cm^2

or approximately 314 cm^2

Step-by-step explanation:

The surface area of a sphere is given by

SA = 4 pi r^2

The radius is 5

SA = 4 *pi * 5^2

SA = 4*pi(25

SA = 100 pi cm^2

If pi is 3.14

SA = 100 *3.14 = 314 cm^2

[tex]\large\fbox{\underline{Surfαcє αrєα σf sphєrє ís 314 cm ².}}[/tex]

☞ Rαdíus σf sphєrє = 5 cm

☞ Surfαcє αrєα σf sphєrє

☞ Surfαcє αrєα σf sphєrє = 4 π r ²

usíng thє fσrmulα

surfαcє αrєα σf sphєrє = 4 π r ²

suвstítutє thє vαluєs

surfαcє αrєα σf sphєrє = 4 × 3.14 × ( 5×5 ) cm ²

mutíplчíng thє vαluєs

surfαcє αrєα σf sphєrє = 100 cm² × 3.14

Hєncє , Surfαcє αrєα σf sphєrє ís 314cm ².

Answer:

a. Females are more likely to enroll in Online Only courses than males.

Step-by-step explanation:

From the data, we have that:

There are 9,000 students that are online only, of which 2,000 are male and 7,000 are female.

There are 9,000 students that are Online and in the class only, of which 8,000 are male and 1,000 are female.

In total, there are 18,000 students, of which 10,000 are male and 8,000 are female.

a. Females are more likely to enroll in Online Only courses than males.

True, 7,000 females compared to 2,000 males in online only courses. This option is the answer to this question.

b. Females are more likely to enroll in Online and In Class courses than males

False, in online and in the class courses, there are 8,000 males and 1,000 females, so females are less likely.

c. There are more females enrolled at the community college than males.

False, there are 10,000 males and 8,000 females.

d. Females are equally likely as males to enroll in an Online Only course.

False, there are 7,000 females compared to 2,000 males in online only courses, so they are more likely, and not equally likely.

Answer:

2.5 days

Step-by-step explanation:

Answer:1 1/15

Step-by-step explanation:

2/3 x 5= 10/15

2/5 x 3= 6/15

Both denominators have to be the same so you can add them together.

10/15 + 6/15=16/15   or 1 1/15

Answer:

0.2348 = 23.48% probability that four will have used the e-ticket check-in kiosk to obtain boarding passes.

Step-by-step explanation:

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[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]

In this question:

Population of 280, which means that [tex]N = 280[/tex]

112 use e-ticket check-in kiosk, which means that [tex]k = 112[/tex]

Sample of eight passengers means that [tex]n = 8[/tex]

Find the approximate hypergeometric probability that four will have used the e-ticket check-in kiosk to obtain boarding passes.

This is P(X = 4). So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 4) = h(4,280,8,112) = \frac{C_{112,4}*C_{168,4}}{C_{280,4}} = 0.2348[/tex]

0.2348 = 23.48% probability that four will have used the e-ticket check-in kiosk to obtain boarding passes.

Answer:

3x4 = 12 is the most related fact to 12:3 = 4

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

because the price of money is maximum 2,500

Answer:

a) The p-value of the test is 0.0076 < 0.05, which means that there is evidence of a difference between males and females in the proportion who said they prefer window tinting as a luxury upgrade at the 0.05.

b) The null hypothesis is [tex]H_0: \pi_1 - \pi_2 = 0[/tex] and the alternate hypothesis is [tex]H_1: \pi_1 - \pi_2 \neq 0[/tex].

Step-by-step explanation:

Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Females:

49% from a sample of 600. So

[tex]\pi_1 = 0.49, s_{\pi_1} = \sqrt{\frac{0.49*0.51}{600}} = 0.0204[/tex]

Males:

41% from a sample of 500. So

[tex]\pi_2 = 0.41, s_{\pi_2} = \sqrt{\frac{0.41*0.59}{500}} = 0.022[/tex]

Test if there is a difference between males and females in the proportion who said they prefer window tinting as a luxury upgrade.

From here, question b can already be answered.

At the null hypothesis we test if there is no difference, that is, the subtraction of the proportions is 0. So

[tex]H_0: \pi_1 - \pi_2 = 0[/tex]

At the alternate hypothesis, we test if there is a difference, that is, the subtraction of the proportions is different of 0. So

[tex]H_1: \pi_1 - \pi_2 \neq 0[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

From the two samples:

[tex]X = \pi_1 - \pi_2 = 0.49 - 0.41 = 0.08[/tex]

[tex]s = \sqrt{s_{\pi_1}^2 + s_{\pi_2}^2} = \sqrt{0.0204^2 + 0.022^2} = 0.03[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{s}[/tex]

[tex]z = \frac{0.08 - 0}{0.03}[/tex]

[tex]z = 2.67[/tex]

Question a:

P-value of the test and decision:

The p-value of the test is the probability that the sample proportion differs from 0 by at least 0.08, which is P(|Z| > 2.670, which is 2 multiplied by the p-value of Z = -2.67.

Looking at the z-table, Z = -2.67 has a p-value of 0.0038.

2*0.0038 = 0.0076

The p-value of the test is 0.0076 < 0.05, which means that there is evidence of a difference between males and females in the proportion who said they prefer window tinting as a luxury upgrade at the 0.05.

Answer:

A, C and F.

Step-by-step explanation:

Equation of a line:

The equation of a line has two formats:

[tex]y = mx + b[/tex]

Slope-intercept format, in which m is the slope and b is the y-intercept(which is the value of x when y = 0).

And in point-slope form:

[tex]y - y(0) = m(x - x(0))[/tex]

In which (x(0),y(0)) is the point and m is the slope.

Slope:

When we have two points on a line, the slope is given by the change in y divided by the change in x. We have points (-2,4), (1,-2). So

Change in y: -2 - 4 = -6

Change in x: 1 - (-2) = 1 + 2 = 3. So

m = -6/3 = -2.

Equation in slope-intercept:

The y-intercept is y = 0, so b = 0. The equation in slope-intercept formula is:

[tex]y = -2x[/tex], so option A is marked.

Equation if point-slope:

Point (-2,4) means that [tex]x_0 = -2, y_0 = 4[/tex]. So

[tex]y - y(0) = m(x - x(0))[/tex]

[tex]y - 4 = -2(x - (-2))[/tex]

[tex]y - 4 = -2(x + 2)[/tex]

So option C is correct.

Point (1,-2) means that [tex]x_0 = 1, y_0 = -2[/tex]. So

[tex]y - y_0 = m(x - x(0))[/tex]

[tex]y - (-2) = -2(x - 1)[/tex]

[tex]y + 2 = -2(x - 1)[/tex]

So option F is correct.

Answer:

Options A, C and F are correct.

Answer:

8ft is the diameter so the radius would be half of that, so it's 4ft. Now substitute

[tex]\pi4 {}^{2} [/tex]

now solve 4^2=16 now multiply it by 3.14 (pi). 16×3.14= 50.24

Answer: Choice B

Each time we're adding 122 to each term to get the next term

This goes on forever because of the three dots, hence the set is infinitely large.

We say that the common difference is 122. Subtracting any two adjacent terms gets us this value. Eg: 354-232 = 122.

Answer:

Step-by-step explanation:

Part A= 59.11

Part B: i think is B

I hope this helps :))

Answer:

Step-by-step explanation:

Part A : 59.11

Part B: the answer is B. You keep the same amount of decimal places in the problem in your product. we had 2 so we have 2 decimal places in 5911 ---> 591.1 --->59.11

Answer: 282.743 in2

Step-by-step explanation: