Efgh is a parallelogram. find each measure

{(3,4)(5,8)(3,7)} is a function. True or false

True, it is a function because mainly the x and y values are the same;]

6 0

3 years ago

The mean per capita income is 15,451 dollars per annum with a variance of 298,116. What is the probability that the sample mean

docker41 [41]

Answer: 0.5467

Step-by-step explanation:

Let X be the random variable that represents the income (in dollars) of a randomly selected person.

Given : $\mu=15451$

$\sigma^2=298116\\\\\Rightarrow\ \sigma=\sqrt{298116}=546$

Sample size : n=350

z-score : $\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

To find the probability that the sample mean would differ from the true mean by less than 22 dollars, the interval will be

$\mu-22,\ \mu+22\\\\=15,451 -22,\ 15,451 +22\\\\=15429,\ 15473$

For x=15429

$z=\dfrac{15429-15451}{\dfrac{546}{\sqrt{350}}}\approx-0.75$

For x=15473

$z=\dfrac{15473-15451}{\dfrac{546}{\sqrt{350}}}\approx0.75$

The required probability :-

$P(15429$

Hence, the required probability is 0.5467.

3 0

3 years ago

The expression y2 – 10y + 24 has a factor of y – 4. What is another factor of y2 – 10y + 24?

GREYUIT [131]

Answer:

Step-by-step explanation:

If we divide 24 by 6, we get 4, which is the other factor of 24 when given the one factor of 6. Same goes here. In order to find out what the other factor of $y^2-10y+24=0$ is when given one factor of y - 4, we simply divide the second degree polynomial by y - 4 to get the quotient. The quotient, then, is the other factor. Synthetic division is the easiest way to do this.

If y - 4 is the factor, then by the Zero Product Property, y - 4 = 0 and y = 4. Setting up synthetic division:

4| 1 -10 24

____________

The rule is to start by bringing down the first term, multiplying it by the number outside, then putting that product up under the next term in line:

4| 1 -10 24

4

1

Then add the column, multiply the sum by the number outside, and put that product up under the next term in line:

4| 1 -10 24

4 -24

1 -6

And add the last column and that is the remainder. We get a 0 remainder. That means that y - 4 goes evenly into the polynomial and the other factor we are looking for is found in the numbers under the addition line. These numbers are the leading coefficients of the depressed polynomial, the polynomial that serves as the other factor: 1y - 6.

Therefore, the 2 factors that multiply together to give us $y^2-10y+24=0$ are (y - 4)(y - 6) and we can check ourselves by multiplying this out by FOILing to see if the result is the polynomial we started with. It is, so we're all done!

8 0

2 years ago

A 20-foot ladder is leaned against a wall. If the base of the ladder is 8 feet from the wall, how high up on the wall will the l

fgiga [73]

You use Pythagorean theorem to solve it and you get 18.3. Just look at the picture to see how i solved it