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cestrela7 [59]
3 years ago
7

9. The expression x(x-7)+4(x-7) is equivalent to each of the following except which choice?

Mathematics
1 answer:
Rus_ich [418]3 years ago
6 0

Answer:

I the answer is number 3

x(x-7)+4(x-7)

x²-7x + 4x-28

=x²-3x-28

(x+4)(x-7)

x²-7x+4x-28

=x²-3x-28

(x-7)(x+4)

x²+4x-7x-28

=x²-3x-28

x2 – 3x – 28

the factored form is

=(x+4)(x-7)

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20 pts if you answer 23 AND 24.
Wittaler [7]
23 is 800,000 people
24 is 2 to the 4th power or 16 inches tall
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3 years ago
The two square pyramids are similar. The side length of the smaller pyramid is 3/4 the side length of the larger pyramid.
Triss [41]

Answer:9/16

Step-by-step explanation:

Since we know it's 3/4 use

r=(3/4)²  .... (\frac{3}{4} x\frac{3}{4} ) =\frac{9}{16}

3 0
3 years ago
It costs $12 to get into the San Diego County Fair and $1.50 per ride.
yan [13]

Answer:

8

Step-by-step explanation:

(24-12)/1.50=8

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.

So

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

So

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

So

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

So

E(X) = 22*0.85 = 18.7

The nearest integer to 18.7 is 19.

7 0
3 years ago
6. You begin work at 8:30 am. You take an unpaid lunch break from 11:45 am to 12:30 pm
STALIN [3.7K]

Answer:

7 hours 15 minutes

7.25 hours

Step-by-step explanation:

Break from 11:45 am to 12:30 pm = 45 minutes

Two 15-minute unpaid coffee breaks during the day = 30 minutes

Total break hours = 45 minutes + 30 minutes

= 1 hour 15 minutes

Total work day hours from 8:30 am to 5:00 pm = 8 hours 30 minutes

How many hours are you paid?

Total hours paid = Total work day hours - Total unpaid break hours

= 8 hours 30 minutes - 1 hour 15 minutes

= 7 hours 15 minutes

b) Express your answer as a decimal in hours only

7 hours 15 minutes as a decimal

15 minutes to hour = 60 minutes/15 minutes

= 1/4

= 0.25 hours

7 hours 15 minutes as a decimal = 7 hours + 0.25 hours

= 7.25 hours

7 0
3 years ago
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