Write the expression in exponential form logb c=a

sdas [7]

Parallel lines have the same slope.

To compare the slopes of two different lines, you have to get
both equations into the form of
y = 'm' x + (a number) .

In that form, the 'm' is the slope of the line.
Notice that it's the number next to the 'x' .

The equation given in the question is    y = 3 - 2 x .
Right away, they've done something to confuse you.
You always expect the 'x' term to be right after the 'equals' sign,
but here, they put it at the end. The slope of this line is the -2 .

Go through the choices, one at a time.
Look for another one with a slope of -2 .
Remember, rearrange the equation to read ' y = everything else ',
and then the slope is the number next to the 'x'.

Choice #4: y = 4x - 2 . The slope is 4 . That's not it.

Choice #3: y = 3 - 4x . The slope is -4 . That's not it.

Choice #2).   2x + 4y = 1

Subtract 2x from each side: 4y = 1 - 2x

Divide each side by 4 : y = 1/4 - 1/2 x .

   The slope is -1/2. That's not it.

Choice #1).   4x + 2y = 5

Subtract 4x from each side: 2y = 5 - 4x

Divide each side by 2 :    y = 5/2 - 2 x .

   The slope is -2 .
   This one is it.
This one is parallel to y = 3 - 2x ,
   because they have the same slope.

4 0

3 years ago

Someone please help! I’m very confused on this problem.

weqwewe [10]

If i'm mistaken; he needs to buy 3 sheets?

7 0

3 years ago

If a polyhedron has 5 faces and 7 vertices, then it must have how many edges? Please show step-by-step work

Juli2301 [7.4K]

Answer:

10 edges

Step-by-step explanation:

we know that

The Euler's formula state that: In a polyhedron, the number of vertices, minus the number of edges, plus the number of faces, is equal to two

$V - E + F = 2$

in this problem we have

$V=7\\E=?\\F=5$

substitute the given values

$7 - E + 5 = 2$

solve for E

Combine like terms in the left side

$12 - E = 2$

subtract 12 both sides

$- E = -10$

Multiply by -1 both sides

$E =10$

8 0

3 years ago

If f(x) = 3x2 + 1 and g(x) = 1 – x, what is the value of (f – g)(2)?

Stels [109]

So (f-g)(x) = 3x2 + x, so when x = 2, the function is 14

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