I have $1.00 in coins on my desk made up of nickels and dimes. I have 4 more dimes than nickels. How many nickels do I have?

Which is the graph of the line LaTeX: y-2=3\left(x-1\right)y − 2 = 3 ( x − 1 )?

andreyandreev [35.5K]

Answer:

D.

Step-by-step explanation:

The equation given takes the point-slope form which is, $y - b = m(x - a)$ . Where,

(a, b) = (x, y) coordinates of a point on the line.

m = slope of the line .

To find which graph has a line equation of $y - 2 = 3(x - 1)$ , look for the points which will give you something almost exactly as the equation if you substitute their values into $y - b = m(x - a)$ .

Let's consider option D.

We have a given point (1, 2). a = 1, b = 2.

Substitute these into $y - b = m(x - a)$

We have:

$y - (2) = m(x - (1))$

$y - 2 = m(x - 1)$

As you can see, this looks almost exactly as

$y - 2 = 3(x - 1)$ .

If you want to be certain that option D is the answer, find m by using the coordinates of any other point on the line and plug into $y - 2 = m(x - 1)$ to find m:

In graph D, let's take the points (0, -1)

$-1 - 2 = m(0 - 1)$

$-3 = m(-1)$

$-3 = -m$

Divide both sides by -1

3 = m

m = 3.

Therefore, option D is the graph of the line $y - 2 = 3(x - 1)$ .

3 0

3 years ago

(−2/3) x (5/4) =<br> test pls help

serious [3.7K]

Answer:

The answer is -5/6

Step-by-step explanation:

in pic

(hope this helps can I pls have brain list (crown) ☺️

8 0

3 years ago

Read 2 more answers

Each table below lists the squared residuals for a line of fit for a certain set of data points. Find the sum of the squared res

viva [34]

Answer:

c

Step-by-step explanation:

7 0

3 years ago

The weight of an adult swan is normally distributed with a mean of 26 pounds and a standard deviation of 7.2 pounds. A farmer ra

Snezhnost [94]

Let $X$ denote the random variable for the weight of a swan. Then each swan in the sample of 36 selected by the farmer can be assigned a weight denoted by $X_1,\ldots,X_{36}$ , each independently and identically distributed with distribution $X_i\sim\mathcal N(26,7.2)$ .

You want to find

$\mathbb P(X_1+\cdots+X_{36}>1000)=\mathbb P\left(\displaystyle\sum_{i=1}^{36}X_i>1000\right)$

Note that the left side is 36 times the average of the weights of the swans in the sample, i.e. the probability above is equivalent to

$\mathbb P\left(36\displaystyle\sum_{i=1}^{36}\frac{X_i}{36}>1000\right)=\mathbb P\left(\overline X>\dfrac{1000}{36}\right)$

Recall that if $X\sim\mathcal N(\mu,\sigma)$ , then the sampling distribution $\overline X=\displaystyle\sum_{i=1}^n\frac{X_i}n\sim\mathcal N\left(\mu,\dfrac\sigma{\sqrt n}\right)$ with $n$ being the size of the sample.

Transforming to the standard normal distribution, you have

$Z=\dfrac{\overline X-\mu_{\overline X}}{\sigma_{\overline X}}=\sqrt n\dfrac{\overline X-\mu}{\sigma}$

so that in this case,

$Z=6\dfrac{\overline X-26}{7.2}$

and the probability is equivalent to

$\mathbb P\left(\overline X>\dfrac{1000}{36}\right)=\mathbb P\left(6\dfrac{\overline X-26}{7.2}>6\dfrac{\frac{1000}{36}-26}{7.2}\right)$
$=\mathbb P(Z>1.481)\approx0.0693$

5 0

3 years ago

If the sum of two consecutive odd numbers is 28 . find the numbers.

Sauron [17]

Answer:

13 and 15

Step-by-step explanation:

13 and 15 are consecutive odd numbers and

13 + 15 = 28

7 0

3 years ago