All categories

3 years ago

Find an equation of the line containing the point (2,-5) and parallel to y = – 4x – 2.

Mathematics

1 answer:

katen-ka-za [31]3 years ago

7 0

Answer:

the desired equation is y = – 4x + 3

Step-by-step explanation:

Parallel lines have the same slope and thus similar equations. Thus, the equation of a line parallel to the given line has the form y = – 4x + C. We need only find C.

The new line goes through (2, -5), and so we substitute 2 for x and -5 for y to obtain

-5 = – 4(2) + C. Then -5 + 8 = C, or C = 3.

Then the desired equation is y = – 4x + 3

You might be interested in

A sample of 200 observations from the first population indicated that x1 is 170. A sample of 150 observations from the second po

igor_vitrenko [27]

Answer:

a) For this case the value of the significanceis $\alpha=0.05$ and $\alpha/2 =0.025$ , we need a value on the normal standard distribution thataccumulates 0.025 of the area on each tail and we got:

$z_{\alpha/2} =1.96$

If the calculated statistic $|z_{calc}| >1.96$ we can reject the null hypothesis at 5% of significance

b) Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{170+110}{200+150}=0.8$

c) $z=\frac{0.85-0.733}{\sqrt{0.8(1-0.8)(\frac{1}{200}+\frac{1}{150})}}=2.708$

d) Since the calculated value satisfy this condition 2.708>1.96 we have enough evidence at 5% of significance that we have a significant difference between the two proportions analyzed.

Step-by-step explanation:

Data given and notation

$X_{1}=170$ represent the number of people with the characteristic 1

$X_{2}=110$ represent the number of people with the characteristic 2

$n_{1}=200$ sample 1 selected

$n_{2}=150$ sample 2 selected

$p_{1}=\frac{170}{200}=0.85$ represent the proportion estimated for the sample 1

$p_{2}=\frac{110}{150}=0.733$ represent the proportion estimated for the sample 2

$\hat p$ represent the pooled estimate of p

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

$\alpha=0.05$ significance level given

Concepts and formulas to use

We need to conduct a hypothesis in order to check if is there is a difference between the two proportions, the system of hypothesis would be:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

a.State the decision rule.

For this case the value of the significanceis $\alpha=0.05$ and $\alpha/2 =0.025$ , we need a value on the normal standard distribution thataccumulates 0.025 of the area on each tail and we got:

$z_{\alpha/2} =1.96$

If the calculated statistic $|z_{calc}| >1.96$ we can reject the null hypothesis at 5% of significance

b. Compute the pooled proportion.

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{170+110}{200+150}=0.8$

c. Compute the value of the test statistic.

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.85-0.733}{\sqrt{0.8(1-0.8)(\frac{1}{200}+\frac{1}{150})}}=2.708$

d. What is your decision regarding the null hypothesis?

Since the calculated value satisfy this condition 2.708>1.96 we have enough evidence at 5% of significance that we have a significant difference between the two proportions analyzed.

5 0

3 years ago

Morgan Bowie is trying to determine the amount to set aside so that he will have enough money on hand in 3 years to overhaul the

Nostrana [21]

Answer:

$468.09

Step-by-step explanation:

first we must calculate the expected future value of the engine overhaul:

($390 x 10%) + ($570 x 30%) + ($750 x 50%) + ($790 x 10%) = $39 + $171 + $375 + $79 = $664

now we must determine the present value of $664 using a 6% interest rate:

PV = FV / (1 + r)⁶ = $664 / 1.06⁶ = $468.09

6 0

3 years ago

What is the sign? Thank you

Kay [80]

For simplicity, disregard the fractions. Then you have 48 + (- 39), since opposite signs change into a negative sign, you have 48 - 39. What is the answer?

POSITIVE

5 0

3 years ago

Write the first 4 terms for <br>f (1) = 3, f (n) = [f(n-1)]

Alexxx [7]

$f(1)=3\\\\f(n)=[f(n-1)]\\\\f(2)=[f(2-1)]=[f(1)]=[3]=3\\\\f(3)=[f(3-1)]=[f(2)]=[3]=3\\\\f(4)=[f(4-1)]=[f(3)]=[3]=3\\\\f(5)=[f(5-1)]=[f(4)]=[3]=3$

4 0

3 years ago

Coach Rivera purchases sports equipment. Baseball bats cost $45.00 each, and

Rama09 [41]

D because of since and the world

5 0

3 years ago