What is the factorization of the trinomial below? 14x^2-39x-35

Which graph represents the solution to the given system ? Y=- 6X - 2Y +2=- 6X

Nonamiya [84]

Answer: The graph is attached.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

Given the first equation:

$y=- 6x - 2$

You can identify that:

$m=-6\\b=-2$

By definition, the line intersects the x-axis when $y=0$ . Then, subsituting this value into the equation and solving for "x", you get that the x-intercept is:

$0=- 6x - 2\\\\2=-6x\\\\x=-\frac{1}{3}\\\\x=-0.333$

Now you can graph it.

Solve for "y" from the second equation:

$y +2=- 6x\\\\y=-6x-2$

You can identify that:

$m=-6\\b=-2$

Notice that the slopes and the y-intercepts of the first line and the second line are equal; this means that they are exactly the same line and the System of equations has<u> Infinitely many solutions.</u>

See the graph attached.

4 0

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

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

3 years ago

Find the gradient of the line<br> 2y - 8x = -2

natima [27]

answer:

gradient is 4

Step-by-step explanation:

gradient is another way of saying slope

slope in the math is often used to show the speed of something

it's the m in y= mx+b

make the equation look like

y = mx + b

2y - 8x = -2

2y = 8x - 2

y= (8x-2)/2

y=4x-1

gradient is the number next to x

answer : gradient is 4

8 0

2 years ago

Read 2 more answers

What does the number line above represent?

sattari [20]

It is the last one. A closed circle means less than or equal to, so that crosses out the top two. The third says five is greater and we know that is not true because the line is decreasing in value. It must be the fourth.

8 0

3 years ago

four friends are planning to meet at the local park. Mary and Teresa jog to the park. Kevin rides his bike to the park, and Manu

taurus [48]

Not sure this is a hard one

4 0

4 years ago