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Alexandra [31]
3 years ago
14

Gabriel saves 40% of his monthly paycheck for college.He earned $270 last month.How much money did Gabriel save for college?

Mathematics
1 answer:
egoroff_w [7]3 years ago
4 0
$108
270 × .40= 108
to find percentage, turn into a decimal and multiply
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I have asked so many times and no one will answer. :(
andrew-mc [135]

Answer:

1) \frac{1}{2^7} ; 2) 11^7

Step-by-step explanation:

1) Using the Power of a Fraction Rule (\frac{a}{b} )^x = (\frac{a^x}{b^x} ),

(\frac{1}{2} )^7 = (\frac{1^7}{2^7} ), which can just be simplified to \frac{1}{2^7}.

2) Using the Negative Exponent Rule, a^{-x}  = \frac{1}{a^{x}},

(\frac{1}{11} )^{-7} = \frac{1}{\frac{1}{11^7}}, which can be simplified to 11^7.

4 0
2 years ago
Suppose small aircraft arrive at a certain airport according to a Poisson process with rate a 5 8 per hour, so that the number o
timurjin [86]

Answer:

(a) P (X = 6) = 0.12214, P (X ≥ 6) = 0.8088, P (X ≥ 10) = 0.2834.

(b) The expected value of the number of small aircraft that arrive during a 90-min period is 12 and standard deviation is 3.464.

(c) P (X ≥ 20) = 0.5298 and P (X ≤ 10) = 0.0108.

Step-by-step explanation:

Let the random variable <em>X</em> = number of aircraft arrive at a certain airport during 1-hour period.

The arrival rate is, <em>λ</em>t = 8 per hour.

(a)

For <em>t</em> = 1 the average number of aircraft arrival is:

\lambda t=8\times 1=8

The probability distribution of a Poisson distribution is:

P(X=x)=\frac{e^{-8}(8)^{x}}{x!}

Compute the value of P (X = 6) as follows:

P(X=6)=\frac{e^{-8}(8)^{6}}{6!}\\=\frac{0.00034\times262144}{720}\\ =0.12214

Thus, the probability that exactly 6 small aircraft arrive during a 1-hour period is 0.12214.

Compute the value of P (X ≥ 6) as follows:

P(X\geq 6)=1-P(X

Thus, the probability that at least 6 small aircraft arrive during a 1-hour period is 0.8088.

Compute the value of P (X ≥ 10) as follows:

P(X\geq 10)=1-P(X

Thus, the probability that at least 10 small aircraft arrive during a 1-hour period is 0.2834.

(b)

For <em>t</em> = 90 minutes = 1.5 hour, the value of <em>λ</em>, the average number of aircraft arrival is:

\lambda t=8\times 1.5=12

The expected value of the number of small aircraft that arrive during a 90-min period is 12.

The standard deviation is:

SD=\sqrt{\lambda t}=\sqrt{12}=3.464

The standard deviation of the number of small aircraft that arrive during a 90-min period is 3.464.

(c)

For <em>t</em> = 2.5 the value of <em>λ</em>, the average number of aircraft arrival is:

\lambda t=8\times 2.5=20

Compute the value of P (X ≥ 20) as follows:

P(X\geq 20)=1-P(X

Thus, the probability that at least 20 small aircraft arrive during a 2.5-hour period is 0.5298.

Compute the value of P (X ≤ 10) as follows:

P(X\leq 10)=\sum\limits^{10}_{x=0}(\frac{e^{-20}(20)^{x}}{x!})\\=0.01081\\\approx0.0108

Thus, the probability that at most 10 small aircraft arrive during a 2.5-hour period is 0.0108.

8 0
3 years ago
Two sporting goods stores are having discount sales on basketballs at one store a basketball is on sale for 25% off the regular
Reil [10]

Answer:

0.66

Step-by-step explanation:

24.95 x 25%=6.23

24.94 - 6.23 = 18.72

25.80 x 30% = 7.74

25.80 - 7.74 = 18.06

18.72 -18 .06 = 0.66

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Which of the following was a result of prison reform during the 1800s
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<span>Which of the following was a result of prison reform during the 1800s
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