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Nutka1998 [239]
3 years ago
13

The time, t, required to complete a job

Mathematics
1 answer:
tigry1 [53]3 years ago
3 0

Answer:

19 hrs

Step-by-step explanation:

t varies inversely with number of people p

t = k/p

If it takes 7.125 hrs for 8 workers to do the job

K = tp

= 7. 125 x 8

= 57

How many hours will it take if there are 3 workers .

Recall t = k/p

t = 57/3

= 19 hrs

Therefore, It’ll take 19 hrs to Complete the job if there are only three workers.

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Barrett purchased a piece of sandpaper for his electric sander, as shown above. The radius of the sandpaper is 2.5 inches.
Alik [6]

Answer:

A = 19.625 inches

Step-by-step explanation:

formula for a circle is A = Pie * radius squared. 2.5 times 2.5 is 6.25 now multiply that by 3.14 to get 19.625 inches.

8 0
3 years ago
Read 2 more answers
Suppose a bag contains many marbles, 54% of which are purple. You draw 5 marbles from the bag with replacement.
dolphi86 [110]

Part A

Use the binomial probability distribution formula.

p = 0.54 = probability of getting a purple marble

n = 5 = sample size

x = 2 = number of purple we want to get

P(x) = \frac{n!}{x!(n-x)!}*p^x*(1-p)^{n-x}\\\\P(2) = \frac{5!}{2!(5-2)!}*0.54^2*(1-0.54)^{5-2}\\\\P(2) = 10*0.54^2*0.46^3\\\\P(2) = 0.283831776\\\\

The \frac{n!}{x!(n-x)!} portion is from the nCr combination formula. The exclamation marks indicate a factorial.

Alternatively, you could use Pascal's Triangle for that portion.

<h3>Answer: 0.283831776</h3>

This decimal value is exact. Round it however you need to.

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

Part B

To find the expected value, aka the mean, we multiply the sample size and probability of getting a purple marble on any single selection.

n*p = 5*0.54 = 2.7

<h3>Answer: 2.7</h3>
6 0
2 years ago
Xan and Katie are twins. Xan weighs 66 6 6 pounds 99 9 9 ounces, and Katie weighs 88 8 8 pounds 11 1 1 ounce. What is the differ
gtnhenbr [62]

Answer:

264 ounces

Step-by-step explanation:

#Convert Xan weight into ounces:

1lb= 16 \ oz\\\\66\ lb=66\times 16=1056 \ oz\\\\\therefore Xan's=1056 \ oz+ 99 \ oz=1155 \ oz

Convert Katie's 88 pounds 11 ounce to ounces:

1lb= 16 \ oz\\\\88\ lb=88\times 16=1056 \ oz\\\\\therefore Katie's=1408 \ oz+ 11 \ oz=1419\ oz

The difference is calculated by subtracting Xan's from Katie's:

=1419 \ oz-1155 \ oz\\\\=264\ oz

Hence, the difference between the weights is 264 ounces

7 0
3 years ago
A plane that carries mail makes a round trip each day from Chicago to New York. It makes 2 intermediate stops on the way to New
Afina-wow [57]

Answer:

Step-by-step explanation:

7(d)

3 0
3 years ago
You are the engineer in charge of evaluating a new product for potential use in a hydraulic system. The manufacturer has sent 10
Allushta [10]

Answer:

a) The null hypothesis is represented as

H₀: p ≥ 0.08

The alternative hypothesis is represented as

Hₐ: p < 0.08

b) A type I error for this question would be that

we conclude that the proportion of defective products is less than 8% when in reality, the proportion of defective products, is more than or equal to 8%.

c) At most, the number of defective products in the sample for you to agree to use the new product = 7

d) If minimum of 5000 pieces are purchased, 90% confidence interval for minimum number of flawed pieces will be (103, 497)

Step-by-step explanation:

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and is usually stating the opposite of the theory is being tested. It usually maintains that random chance is responsible for the outcome or results of any experimental study/hypothesis testing. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis takes the other side of the hypothesis; that there is indeed a significant difference between two proportions being compared. It usually confirms the the theory being tested by the experimental setup. It usually maintains that other than random chance, there are significant factors affecting the outcome or results of the experimental study/hypothesis testing. It usually contains the signs ≠, < and > depending on the directions of the test

For this question, we want to prove that less than 8% of the products we subsequently purchase will be defective.

So, the null hypothesis will be that there is not enough evidence in the sample to say that less than 8% of the products we subsequently purchase will be defective. That is, the proportion of the sample that are defective is more than or equal to 8%.

And the alternative hypothesis is that there is enough evidence in the sample to say that less than 8% of the products we subsequently purchase will be defective.

Mathematically,

The null hypothesis is represented as

H₀: p ≥ 0.08

The alternative hypothesis is represented as

Hₐ: p < 0.08

b) A type I error involves rejecting the null hypothesis and accepting the alternative hypothesis when in reality, the null hypothesis is true. It involves saying that there is enough evidence in the sample to say that less than 8% of the products we subsequently purchase will be defective when in reality, there isn't enough evidence to arrive at this conclusion.

That is, the proportion of defective products in reality, is more than or equal to 8% and we have concluded that the proportion is less than 8%.

c) Out of the 100 samples provided by the manufacturer, at most how many can be defective for you to agree to use the new product?

The engineer agrees to use the new product when less than 8% of the products we subsequently purchase will be defective.

8% of the product = 0.08 × 100 = 8.

Meaning that the engineer agrees to subsequently purchase the product if less than 8 out of 100 are defective.

So, the maximum number of defective product in the sample that will still let the engineer purchase the products will be 7.

(d) For better or worse, your boss convinces you to go through with the deal. Turns out the minimum order is 5000 pieces. Assuming you purchase that many pieces of the new product, and that you found 6 defective pieces out of the 100, generate a 90% two-sided confidence interval for the number of pieces that will be flawed.

Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample proportion) ± (Margin of error)

Sample proportion = 0.495

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error)

Critical value at 90% confidence interval for sample size of 100 using the t-tables since information on the population standard deviation.

Degree of freedom = n - 1 = 100 - 1 = 99

Significance level = (100-90)/2 = 5% = 0.05

Critical value = t(0.05, 99) = 1.660

Standard error of the mean = σₓ = √[p(1-p)/n]

p = 0.06

n = sample size = 100

σₓ = (0.06/√100) = 0.006

σₓ = √[0.06(0.94)/100] = 0.0237486842 = 0.02375

90% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]

CI = 0.06 ± (1.660 × 0.02375)

CI = 0.06 ± 0.039425

90% CI = (0.020575, 0.099425)

90% Confidence interval = (0.0206, 0.0994)

If minimum of 5000 pieces are purchased, 90% confidence interval for minimum number of flawed pieces will be

5000 × (0.0206, 0.0994) = (103, 497)

Hope this Helps!!!

3 0
2 years ago
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