What numbers are 0.6 unit from 1.3 on a number line?

What is the y-intercept -x+5y=45

Karo-lina-s [1.5K]

To find the y-intercept, we can convert this to slope-intercept form, or replace the value of x with 0 and solve for y.

We'll do both first.

-x + 5y = 45

5y = 45

Divide both sides by 5.

y = 9

Now let's convert it to slope-intercept.

-x + 5y = 45

Add x to both sides.

5y = 45 + x

Divide both sides by 5.

y = 1/5x + 9

y = 9

<h3><u>The y-intercept of our line is 9.</u></h3>

3 0

2 years ago

Can you please answer this question

tamaranim1 [39]

$3tan^{2} \theta +7sec\theta=3$
First I converted the equation terms into sine and cosine.
$tan^{2}\theta = \frac{sin^{2}\theta}{cos^{2}\theta}$ and $sec\theta= \frac{1}{cos\theta}$
Substitution:
$\frac{3sin^2\theta}{cos^2\theta} + \frac{7}{cos\theta} =3$
Common Denominator Created:
$\frac{3sin^2\theta}{cos^2\theta} + \frac{7cos\theta}{cos^2\theta} =3$
Multiply each term by the LCD:
$3sin^2\theta+7cos\theta=3cos^2\theta$
Substitution: Recall ⇒ $sin^2\theta =1-cos^2\theta$
$3(1-cos^2\theta)+7cos\theta=3cos^2\theta$
Distribute and collect all terms on one side:
$6cos^2\theta-7cos\theta-3=0$
Factor and set each factor equal to 0:
$(2cos\theta-3)(3cos\theta+1)=0$
$2cos\theta-3=0$ ⇒ $theta=cos^{-1} \frac{3}{2}$
$3cos\theta+1=0$ ⇒ $theta=cos^{-1} \frac{-1}{3}$
The 2nd factor provides only possible answer 109.5 degrees

4 0

3 years ago

What is 12 over 35 simplified

borishaifa [10]

12/35 is simplified, as you cannot divide it into smaller numbers by a common factor.
I hope this helps!

5 0

2 years ago

Read 2 more answers

Suppose a 90% confidence interval for the mean salary of college graduates in a town in Mississippi is given by [$38,737, $50,46

JulsSmile [24]

Answer:

a. The point estimate was of $44,600.

b. The sample size was of 16.

Step-by-step explanation:

Confidence interval concepts:

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

The margin of error is the difference between the two bounds, divided by 2.

a. What is the point estimate of the mean salary for all college graduates in this town?

Mean of the bounds, so:

(38737+50463)/2 = 44600.

The point estimate was of $44,600.

b. Determine the sample size used for the analysis.

First we need to find the margin of error, so:

$M = \frac{50463-38737}{2} = 5863$

Relating the margin of error with the sample size:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.9}{2} = 0.05$

Now, we have to find z in the Z-table as such z has a p-value of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.05 = 0.95$ , so Z = 1.64.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

For this problem, we have that $\sigma = 14300, M = 5863$ . So

$M = z\frac{\sigma}{\sqrt{n}}$

$5863 = 1.645\frac{14300}{\sqrt{n}}$

$5863\sqrt{n} = 1.645*14300$

$\sqrt{n} = \frac{1.645*14300}{5863}$

$(\sqrt{n})^2 = (\frac{1.645*14300}{5863})^2$

$n = 16$

The sample size was of 16.

7 0

3 years ago

What is the gif of nine and fifty two

Novosadov [1.4K]

I assume you mean 9+52,
If so you can add the 9 and the 2 together:
9+2 = 11

Then you can add the 11 on to the 50 to get the final answer:
50+11 = 61

Hope this helps! :)

4 0

3 years ago