Two sides of an isosceles triangle measure 6 and 10. The perimeter of the triangle could be

1 answer:

4 0

If a triangle is isosceles, then two of the sides must be the same length.

Therefore, the sides can be either:
6+6+10= 22
6+10+10=26

Final answer: D

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Which is the equation of a line that has a slope of 3 and passes through point

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Answer:

y = -2/3x - 3

Step-by-step explanation:

y = -2/3x + b

-1 = -2/3(-3) + b

-1 = 2 + b

-3 = b

y = -2/3x - 3

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Suppose an isotope has a half-life of 10 years. If you start with 50 grams of the isotope, how much of it will you have in 10 ye

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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:

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