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3 years ago

Ratio of 18 mins to 1.5 hours

Mathematics

2 answers:

katovenus [111]3 years ago

5 0

1.5 hours=90 minutes

amid [387]3 years ago

4 0

1.5 hours = 90 minutes.

So a ratio of 18:90 is the same as 1:5 since both numbers have a GCF of 18.

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4 Consider the triangle below.

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<h2>=>> <u>Solution (part A</u>) :</h2>

Given :

▪︎Triangle AMG is an isosceles triangle.

▪︎Measure of segment AM = (x+1.4) inches

▪︎Measure of segment MG = (2x+0.1) inches

▪︎Measure of segment AG = (3x-0.4) inches

▪︎segment AG is the base of triangle AMG.

Since AG is the base of the isosceles triangle AMG, segment AM and segment MG will be equal.

Which means :

$= \tt x + 1.4 = 2x + 0.1$

$= \tt x + 1.4 - 0.1 = 2x$

$= \tt \: x + 1.3 = 2x$

$= \tt 1.3 = 2x - x$

$\color{plum} \hookrightarrow \tt x = 1.3$

Thus, the value of x = 1.3

Therefore :

▪︎The value of x = 1.3

<h2>=>> <u>Solution (Part B)</u> :</h2>

We know that :

▪︎The value of x = 1.3

Which means :

The length of the leg AM :

$= \tt x + 1.4$

$= \tt 1.3 + 1.4$

$\color{plum} \tt leg \: AM= 2.7 \: inches$

Thus, the length of the leg AM = 2.7 inches

The length of leg MG :

$= \tt 2x + 0.1$

$= \tt2 \times 1.3 + 0.1$

$= \tt 2.6 + 0.1$

$\color{plum} \tt\: leg \:MG = 2.7 \: inches$

Thus, the length of the leg MG = 2.7 inches

Since the measure of the two legs are equal (2.7=2.7), we can conclude that we have found out the correct length of each leg.

Therefore :

▪︎Measure of leg AM = 2.7 inches

▪︎Measure of leg MG = 2.7 inches

<h2>=>> <u>Solution </u><u>(</u><u>part C</u><u>)</u> :</h2>

We know that :

Value of x = 1.3

Then, measure of the base AG :

$= \tt 3x - 0.4$

$= \tt 3 \times 1.3 - 0.4$

$= \tt 3.9 - 0.4$

$\color{plum}\tt \: Base \: AG = 3.5 \: inches$

Thus, the measure of the base = 3.5 inches

Therefore :

▪︎ the length of base AG = 3.5 inches.

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3 years ago

A doctor released the results of clinical trials for a vaccine to prevent a particular disease. In these clinical trials, 200,0

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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.

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3 years ago