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3 years ago

Multiply and simplify. (2x - 1)(6x - 7)

Mathematics

1 answer:

Kryger [21]3 years ago

8 0

Answer:

D) 12x² - 20x + 7

Step-by-step explanation:

Use FOIL when multiplying 2 binomials...

FOIL is Firsts, Outsides, Insides, Lasts. It's the order in which you multiply the numbers in the binomials...

(2x - 1)(6x - 7)

Firsts: (2x)(6x) = 12x²

Outsides: (2x)(-7) = -14x

Insides: (-1)(6x) = -6x

Lasts: (-1)(-7) = 7

Now add them up...

12x² - 14x - 6x + 7

12x² - 20x + 7

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Volume of a cube is 1728 cm3.Find its surface area

Leno4ka [110]

Answer:

Step-by-step explanation:

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8 0

3 years ago

The probability that your call to a service line is answered in less than 30 seconds is 0.85. Assume that your calls are indepen

aev [14]

Answer:

a) 0.1720

b) 0.8298

c) 19

Step-by-step explanation:

For each call, there are only two possible outcomes. Either they are answered in less than 30 seconds. Or they are not. The probabilities for each call are independent. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

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

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

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

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

And p is the probability of X happening.

In this problem we have that:

$p = 0.85$

(a) If you call 12 times, what is the probability that exactly 9 of your calls are answered within 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X = 9)$ when $n = 12$ .

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

$P(X = 9) = C_{12,9}.(0.85)^{9}.(0.15)^{3} = 0.1720$

(b) If you call 20 times, what is the probability that at least 16 calls are answered in less than 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X \geq 16)$ when $n = 20$

$P(X \geq 16) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)$

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

$P(X = 16) = C_{20,16}.(0.85)^{16}.(0.15)^{4} = 0.1821$

$P(X = 17) = C_{20,17}.(0.85)^{17}.(0.15)^{3} = 0.2428$

$P(X = 18) = C_{20,18}.(0.85)^{18}.(0.15)^{2} = 0.2293$

$P(X = 19) = C_{20,19}.(0.85)^{19}.(0.15)^{1} = 0.1368$

$P(X = 20) = C_{20,20}.(0.85)^{20}.(0.15)^{0} = 0.0388$

$P(X \geq 16) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.1821 + 0.2428 + 0.2293 + 0.1368 + 0.0388 = 0.8298$

(c) If you call 22 times, what is the mean number of calls that are answered in less than 30 seconds? Round your answer to the nearest integer.

The expected value of the binomial distribution is:

$E(X) = np$

In this question, we have $n = 22$

$E(X) = 22*0.85 = 18.7$

The nearest integer to 18.7 is 19.

7 0

3 years ago

PLS HELP ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS ASAP

RoseWind [281]

Answer:

The answer is 4 minutes

Step-by-step explanation:

I divided 825 by 3 and got 165. If you multiply 165 by all the factors, you get approximately 4 minutes. It's the closest. Try that one.

8 0

3 years ago

A college job placement office collected data about students’ GPAs and the salaries they earned in their first jobs after gradua

frez [133]

Answer:

X is the GPA

Y is the Salary

Standard deviation of X is 0.4

Standard deviation of Y is 8500

E(X)=2.9

E(Y)=47200

We are given that The correlation between the two variables was r = 0.72

a) $y = a+bx$

$b = \frac{\sum(x_i-\bar{x})(y_i-\bar{y})}{\sum(x_i-\bar{x})^2} = \frac{r \times \sqrt{var(X) \times Var(Y)}}{Var(X)} = \frac{0.72 \times \sqrt{0.4^2 \times 8500^2}}{0.4^2} = 15300$

$a=y-bx = 47200-(15300 \times 29) = 2830$

So, slope = 15300

Intercept = 2830

So, equation : $y = 2830+15300x$

b) Your brother just graduated from that college with a GPA of 3.30. He tells you that based on this model the residual for his pay is -$1880. What salary is he earning?

$y = 2830+15300 \times 3.3 = 53320$

Observed salary = Residual + predicted = -1860+53320 = 51440

c)) What proportion of the variation in salaries is explained by variation in GPA?

The proportion of the variation in salaries is explained by variation in GPA = $r^2 = (0.72)^2 =0.5184$

8 0

3 years ago

If i leave my house at 6:52 am and run 1 mile at an easy pace (8:15 per mile), then 3 miles at tempo (7:12 per mile) and 1 mile

FinnZ [79.3K]

Running 2 miles at 8:15 per mile takes 16:30 minutes.

Running 3 miles at 7:12 per mile takes 21:36 minutes.

The total running time is 16:30 + 21:36 = 38:06 minutes. That length of time after 6:52 am is 7:30:06 am.

You get home for breakfast at 6 seconds past 7:30 am.

8 0

3 years ago