What is 3/8 equivalent to

How many ways are there to arrange 7 distinct red and 5 distinct blue balls in a row such that:?

BARSIC [14]

You can change them around up to 144 times.

5 0

3 years ago

1. (5pt) In a recent New York City marathon, 25,221 men finished and 253 dropped out. Also,

gladu [14]

Answer:

(a) Explained below.

(b) The 99% confidence interval for the difference between proportions is (-0.00094, 0.00494).

Step-by-step explanation:

The information provided is:

n (Men who finished the marathon) = 25,221

n (Women who finished the marathon) = 12,883

Compute the proportion of men and women who finished the marathon as follows:

$\hat p_{1}=\frac{25221}{25221 +253}=0.99\\\\\hat p_{2}=\frac{12883 }{12883+163}=0.988$

The combined proportion is:

$\hat P=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}\\\\=\frac{25221+12883}{38520}\\\\=0.989$

(a)

The hypothesis is:

H₀: The rate of those who finish the marathon is the same for men and women, i.e. p₁ - p₂ = 0.

Hₐ: The rate of those who finish the marathon is not same for men and women, i.e. p₁ - p₂ ≠ 0.

Compute the test statistic as follows:

$Z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat P(1-\hat P)\cdot [\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}$

$=\frac{0.99-0.988}{\sqrt{0.989(1-0.989)\times[\frac{1}{25474}+\frac{1}{13046}]}}\\\\=1.78$

Compute the p-value as follows:

$p-value=2\times P(Z>1.78)\\\\=2\times 0.03754\\\\=0.07508\\\\\approx 0.075$

The p-value of the test is more than the significance level. The null hypothesis was failed to be rejected.

Thus, concluding that the rate of those who finish is the same for men and women.

(b)

Compute the 99% confidence interval for the difference between proportions as follows:

The critical value of z for 99% confidence level is 2.58.

$CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}$

$=(0.99-0.988)\pm 2.58\times\sqrt{\frac{0.99(1-0.99)}{25474}+\frac{0.988(1-0.988)}{13046}}\\\\=0.002\pm 0.00294\\\\=(-0.00094, 0.00494)\\\\$

Thu, the 99% confidence interval for the difference between proportions is (-0.00094, 0.00494).

6 0

3 years ago

A gym membership charges $50 new member fee and $24 for every month after. Write an equation for this where y is the total cost

DanielleElmas [232]

It's 202739267166262

6 0

3 years ago

Read 2 more answers

singh works at a restaurant where he is paid by the hour plus time and a half for his hours over 40. last week he worked four ho

padilas [110]

Answer:

$8.5 per hour

Step-by-step explanation:

Number of overtime hours = 4 hours

Since overtime starts after 40 hours, then the number of hours worked = 40 + 4 = 44 hours

Total amount earned = $391

Let Hourly pay = x

Overtime pay = 1 1/2x = 3/2x

Therefore ;

40x + (4*3/2x) = 391

40x + 6x = 391

46x = 391

x = 391 / 46

x = 8.5

Hourly pay = $8.5 per hour

7 0

3 years ago

In tossing four fair dice, what is the probability of tossing, at most, one 3

11Alexandr11 [23.1K]

Answer-

In tossing four fair dice, the probability of getting at most one 3 is 0.86.

Solution-

The probability of getting at most one 3 is, either getting zero 3 or only one 3.

$P(A) =The \ probability \ of \ getting \ zero \ 3 =(\frac{5}{6})(\frac{5}{6})(\frac{5}{6})(\frac{5}{6})=\frac{625}{1296} =0.48$ ( ∵ xxxx )

$P(B) = The \ probability \ of \ getting \ only \ one \ 3 =(4)(\frac{1}{6})(\frac{5}{6})(\frac{5}{6})(\frac{5}{6}) = 0.38$ ( ∵ 3xxx, x3xx, xx3x, xxx3 )

P(Atmost one 3) = P(A) + P(B) = 0.48 + 0.38 = 0.86

7 0

3 years ago