All categories

3 years ago

It takes 4 people 2 days to build a patio. How long will it take 2 people, working at the same rate, to buid the patio?

Mathematics

1 answer:

kifflom [539]3 years ago

4 0

Answer:

4 days

Step-by-step explanation:

The patio takes 4 people 2 days, so that is 4×2. To get this for 2 people, it's 2×4. This means it takes 4 days.

Think about it, for half the people, it should take double the time.

You might be interested in

Gianna brought seven necklaces for $50.75 and Winnie brought three necklaces for $24.60 who got the better deal

olganol [36]

Gianna paid less per necklace so she got the better deal

Gianna: 50.75 / 7 = 7.25
So she paid $7.25 per necklace
Winnie: 24.60 / 3 = 8.20
So she paid $8.20 per necklace

4 0

3 years ago

What is 3a^9r^-3/-4a-2

Lana71 [14]

Answer:

_ 3a^8-8r^3

4r^3

Step-by-step explanation:

5 0

3 years ago

The ratio of M & M’s to raisins in a bag of trail mix is 3:5. If there are 36 M & M’s, how many raisins are there?

Iteru [2.4K]

The correct answer is 60 raisins. To get this answer you will write a proportion of M & Ms to raisins and create and equivalent ratio using the number 36.

After you have the proportion set up, you will use cross products to solve for the number of raisins.

You can also use equivalent ratios to find the number of raisins.

Both of these strategies are shown in the attached picture.

4 0

3 years ago

Suppose you are working in an insurance company as a statistician. Your manager asked you to check police records of car acciden

pochemuha

Answer:

(a) 95% confidence interval for the percentage of all car accidents that involve teenage drivers is [0.177 , 0.243].

(b) We are 95% confident that the percentage of all car accidents that involve teenage drivers will lie between 17.7% and 24.3%.

(c) We conclude that the the percentage of teenagers has not changed since you join the company.

(d) We conclude that the the percentage of teenagers has changed since you join the company.

Step-by-step explanation:

We are given that your manager asked you to check police records of car accidents and out of 576 accidents you selected randomly, teenagers were at the wheel in 120 of them.

(a) Firstly, the pivotal quantity for 95% confidence interval for the population proportion is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} }}$ ~ N(0,1)

where, $\hat p$ = sample proportion teenage drivers = $\frac{120}{576}$ = 0.21

n = sample of accidents = 576

p = population percentage of all car accidents

Here for constructing 95% confidence interval we have used One-sample z proportion statistics.

So, 95% confidence interval for the population population, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level

of significance are -1.96 & 1.96}

P(-1.96 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} }}$ < 1.96) = 0.95

P( $-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }}$ < ${\hat p-p}$ < $1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }}$ ) = 0.95

P( $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }}$ < p < $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }}$ ) = 0.95

95% confidence interval for p = [ $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }}$ , $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }}$ ]

= [ $0.21-1.96 \times {\sqrt{\frac{0.21(1-0.21)}{576} }}$ , $0.21+1.96 \times {\sqrt{\frac{0.21(1-0.21)}{576} }}$ ]

= [0.177 , 0.243]

Therefore, 95% confidence interval for the percentage of all car accidents that involve teenage drivers is [0.177 , 0.243].

(b) We are 95% confident that the percentage of all car accidents that involve teenage drivers will lie between 17.7% and 24.3%.

(c) We are also provided that before you were hired in the company, the percentage of teenagers who where involved in car accidents was 18%.

The manager wants to see if the percentage of teenagers has changed since you join the company.

Let p = percentage of teenagers who where involved in car accidents

So, Null Hypothesis, $H_0$ : p = 18% {means that the percentage of teenagers has not changed since you join the company}

Alternate Hypothesis, $H_A$ : p $\neq$ 18% {means that the percentage of teenagers has changed since you join the company}

The test statistics that will be used here is One-sample z proportion statistics;

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

where, $\hat p$ = sample proportion teenage drivers = $\frac{120}{576}$ = 0.21

n = sample of accidents = 576

So, test statistics = $\frac{0.21-0.18}{\sqrt{\frac{0.21(1-0.21)}{576} }}$

= 1.768

The value of the sample test statistics is 1.768.

Now at 0.05 significance level, the z table gives critical value of -1.96 and 1.96 for two-tailed test. Since our test statistics lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the the percentage of teenagers has not changed since you join the company.

(d) Now at 0.1 significance level, the z table gives critical value of -1.6449 and 1.6449 for two-tailed test. Since our test statistics does not lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the the percentage of teenagers has changed since you join the company.

4 0

3 years ago

2 circles labeled Set A and Set B overlap. Set A contains 1, set B contains 3, and the overlap of the 2 circles contains 2. The

mezya [45]

The region(s) represent the intersection of Set A and Set B (A∩B) is region II

<h3>How to determine which region(s) represent the intersection of Set A and Set B (A∩B)?</h3>

The complete question is added as an attachment

The universal set is given as:

Set U

While the subsets are:

Set A
Set B

The intersection of set A and set B is the region that is common in set A and set B

From the attached figure, we have the region that is common in set A and set B to be region II

This means that

The intersection of set A and set B is the region II

Hence, the region(s) represent the intersection of Set A and Set B (A∩B) is region II