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2 years ago

X - 3y - 3 = 0 3x - 9y - 2 = 0

Mathematics

2 answers:

Lina20 [59]2 years ago

7 0

Answer: no solution

x - 3y = 3 --------> (1)

3x - 9y - 2 = 0

3x - 9y = 2 ---------> (2)

Solving (1) and (2)

x - 3y = 3

3x - 9y = 2

Multiply Eqn (1) by 3,

3x - 9y = 9 -------> (3)

3x - 9y = 2 ---------> (4)

Answer provided by Education Point

yan [13]2 years ago

6 0

<h3>no solution</h3>

equation 1 : $\sf x - 3y - 3 = 0$

equation 2 : $\sf 3x - 9y - 2 = 0$

make x the subject in equation 1,

$\sf x = 3+3y$

insert this in equation 2,

$\rightarrow \sf 3(3+3y) - 9y - 2 = 0$

$\rightarrow \sf 9+9y- 9y - 2 = 0$

$\rightarrow \sf 7 = 0$

Thus no solution for x and y in this solution.

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Step-by-step explanation:

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2 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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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.

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2 years ago