Factorize (x-y)^2+(x-y)

Please help! If GDEF is a square, GE=4x+1 and DF=8x-51, find the value of x.

zepelin [54]

Answer:

x = 13

Step-by-step explanation:

1. 4x + 1 = 8x - 51

2. 4x = 8x - 52

3. -4x = -52

4. x = 13

5 0

3 years ago

Read 2 more answers

Henry can write 5 1/4 pages of his novel in 3 hours how many page can he write in 8 hours

ICE Princess25 [194]

If you would like to know how many pages can Henry write in 8 hours, you can calculate this using the following steps:

5 1/4 = 21/4 pages ... 3 hours
x pages = ? ... 8 hours

21/4 * 8 = 3 * x
21 * 2 = 3 * x
3 * x = 42
x = 42 / 3
x = 14 pages

Henry can write 14 pages of his novel in 8 hours.

8 0

3 years ago

Penny's function has an output that is four more than three times the input. Johns function expressed in slope-intercept form is

jonny [76]

John's function : y = 3.5x - 4
Penny's function : y = 3x + 4

C. John's function has a greater rate of change, because 3.5 > 3

5 0

3 years ago

Due to a manufacturing error, two cans of regular soda were accidentally filled with diet soda and placed into a 18-pack. Suppos

crimeas [40]

Answer:

a) There is a 1.21% probability that both contain diet soda.

b) There is a 79.21% probability that both contain diet soda.

c) $P(X = 2)$ is unusual, $P(X = 0)$ is not unusual

d) There is a 19.58% probability that exactly one is diet and exactly one is regular.

Step-by-step explanation:

There are only two possible outcomes. Either the can has diet soda, or it hasn't. So we use the binomial probability distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And $\pi$ is the probability of X happening.

A number of sucesses $x$ is considered unusually low if $P(X \leq x) \leq 0.05$ and unusually high if $P(X \geq x) \geq 0.05$

In this problem, we have that:

Two cans are randomly chosen, so $n = 2$

Two out of 18 cans are filled with diet coke, so $\pi = \frac{2}{18} = 0.11$

a) Determine the probability that both contain diet soda. P(both diet soda)

That is P(X = 2).

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 2) = C_{2,2}(0.11)^{2}(0.89)^{0} = 0.0121$

There is a 1.21% probability that both contain diet soda.

b)Determine the probability that both contain regular soda. P(both regular)

That is P(X = 0).

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 0) = C_{2,0}(0.11)^{0}(0.89)^{2} = 0.7921$

There is a 79.21% probability that both contain diet soda.

c) Would this be unusual?

We have that $P(X = 2)$ is unusual, since $P(X \geq 2) = P(X = 2) = 0.0121 \leq 0.05$

For P(X = 0), it is not unusually high nor unusually low.

d) Determine the probability that exactly one is diet and exactly one is regular. P(one diet and one regular)

That is P(X = 1).

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 1) = C_{2,1}(0.11)^{1}(0.89)^{1} = 0.1958$

There is a 19.58% probability that exactly one is diet and exactly one is regular.

8 0

3 years ago

State whether each situation has independent or paired (dependent) samples. a. A researcher wants to compare the hand–eye coord

Alex73 [517]

Answer:

a. A researcher wants to compare the hand–eye coordination of men and women. She finds a random sample of 100 men and 100 women, and measures their hand–eye coordination = paired samples

b. A researcher wants to know whether professors with tenure have fewer office hours than professors without tenure. She observes the number of office hours for professors with and without tenure. = independent samples

Explanation:

Paired-samples t tests compare scores on two different variables but for the same group of cases; independent-samples t tests compare scores on the same variable but for two different groups of cases.

6 0

3 years ago

Factorize (x-y)^2+(x-y)​

Factorize (x-y)^2+(x-y)