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sergij07 [2.7K]
3 years ago
13

A container holds 4 gallons 2 quarts of juice another container holds 1 3/4 gallons more than the first container altogether how

much juice can both containers hold
Mathematics
1 answer:
Tanya [424]3 years ago
6 0

Answer:

10\frac{3}{4} gallons of juice altogether [or, 10 gallons 3 quarts]

Step-by-step explanation:

4 quarts = 1 gallon

So 2 quarts would be 1/2 gallon

Thus,

we have:

4  1/2 gallons in first container

Next container holds 1  3/4 MORE, so that container holds:

4\frac{1}{2}+1\frac{3}{4}\\=\frac{9}{2}+\frac{7}{4}\\=\frac{18+7}{4}\\=\frac{25}{4} gallons

In total, the number of gallons is:

4\frac{1}{2}+\frac{25}{4}\\=\frac{9}{2}+\frac{25}{4}\\=\frac{18+25}{4}\\=\frac{43}{4}\\=10\frac{3}{4} gallons

or 10 gallons and 3 quarts

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Read 2 more answers
A doctor released the results of clinical trials for a vaccine to prevent a particular disease. In these clinical​ trials, 200,0
CaHeK987 [17]

Answer:

1) No, there is  not  enough evidence to support the claim that the vaccine was effective (P-value=0.104) .

The null and alternative hypothesis are:

H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0

being the subindex 1 for the experimental group and subindex 2 for the control group.

2) Test statistic z=-1.26

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the vaccine was effective.

Then, the null and alternative hypothesis are:

H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0

The significance level is 0.01.

The sample 1 (experimental group), of size n1=100000 has a proportion of p1=0.0002.

p_1=X_1/n_1=21/100000=0.0002

The sample 2 (control group), of size n2=100000 has a proportion of p2=0.0003.

p_2=X_2/n_2=30/100000=0.0003

The difference between proportions is (p1-p2)=-0.0001.

p_d=p_1-p_2=0.0002-0.0003=-0.0001

The pooled proportion, needed to calculate the standard error, is:

p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{21+30}{100000+100000}=\dfrac{51}{200000}=0.00026

The estimated standard error of the difference between means is computed using the formula:

s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.00026*0.99974}{100000}+\dfrac{0.00026*0.99974}{100000}}\\\\\\s_{p1-p2}=\sqrt{0+0.0000000025}=\sqrt{0.0000000051}=0.000071

Then, we can calculate the z-statistic as:

z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.00009-0}{0.000071}=\dfrac{-0.00009}{0.000071}=-1.26

This test is a left-tailed test, so the P-value for this test is calculated as (using a z-table):

P-value=P(z

As the P-value (0.104) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

There is  not  enough evidence to support the claim that the vaccine was effective.

6 0
2 years ago
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