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3 years ago

Write the equation of a line with a slope of 5 that passes through the point (3,1)

Mathematics

1 answer:

Brut [27]3 years ago

5 0

Answer:

y-1=5(x-3)

Step-by-step explanation:

y=mx+b where m=slope and b=y-intercept,

y-y1=m(x-x1)

y-1=5(x-3)

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Jim earns a regular hourly rate of $5 and a premium hourly rate of $6. He worked 45 hours last week. What is his gross pay?

Troyanec [42]

Is 495 just multiply 5 by 45 and then sum 6 by 45

8 0

3 years ago

The quality-control manager at a compact fluorescent light bulb (CFL) factory needs to determine whether the mean life of a la

stira [4]

<h2>Answer with explanation:-</h2>

Let $\mu$ be the population mean .

By observing the given information, we have :-

$H_0:\mu=7450\\\\H_a:\mu\neq7450$

Since the alternative hypotheses is two tailed so the test is a two-tailed test.

We assume that the life of a large shipment of CFLs is normally distributed.

(a) Given : Sample size : n=81 , since n>30 so we use z-test.

Sample mean : $\overline{x}=7240$

Standard deviation : $\sigma=1350$

Test statistic for population mean :-

$z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

$\Rightarrow\ z=\dfrac{7240-7450}{\dfrac{1350}{\sqrt{81}}}\\\\\Rightarrow\ z=-1.4$

The critical value (two-tailed) corresponds to the given significance level :-

$z_{\alpha/2}=z_{0.025}=1.96$

Since the observed value of z (-1.4) is less than the critical value (1.96) , so we do not reject the null hypothesis.

Hence, we conclude that we have enough evidence to accept that the mean life is different from 7450 hours .

(b) The p-value : $2P(z>-1.4)=0.1615$ , it means that the probability that the life of CFLs less than 7240 and greater than 7240 is 0.1615.

(c) The confidence interval for population mean is given by :-

$\overline{x} \pm\ z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}\\\\=7240\pm(1.96)\dfrac{1350}{\sqrt{81}}\\\\=7240\pm294\\\\=(6946,7534)$

8 0

3 years ago

Find the value of x, rounded to the nearest tenth

tatyana61 [14]

Answer:

x ≈ 8.9

Step-by-step explanation:

Given a tangent and a secant from an external point to the circle, the the square of the tangent is equal to the product of the external part of the secant and the entire secant, that is

x² = 8(8 + 2) = 8 × 10 = 80 ( take the square root of both sides )

x = $\sqrt{80}$ ≈ 8.9 ( to the nearest tenth )

6 0

3 years ago

You have $78 in your savings account. You are buying a computer and the minimum down payment you can make is $120. Write and sol

scoundrel [369]

$120-$78= m (how much money you need to save)

3 0

3 years ago

If 2(a^2+b^2)=(a+b)^2 then, <br> >a+b=0,<br> >ab=0,<br> >a=b,<br> >2a=b

Tasya [4]

Answer:

2·(a^2 + b^2) = (a + b)^2

2·a^2 + 2·b^2 = a^2 + 2·a·b + b^2

a^2 + b^2 = 2·a·b

a^2 - 2·a·b + b^2 = 0

(a - b)^2 = 0

a = b

7 0

3 years ago