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spin [16.1K]
3 years ago
6

Explain how the Quotient of Powers was used to simplify this expression. (2 points) 2 to the fifth power, over 8 = 22

Mathematics
2 answers:
katovenus [111]3 years ago
7 0

Answer:

The Quotient of Powers Rule helps to simplify exponents.

That is, If our expression is \frac{a^m}{a^n}

Then after applying Quotient of Powers Rule,

We can write, \frac{a^m}{a^n}=a^{m-n}

Here our expression, 2 to the fifth power over 8 = \frac{ 2 ^5}{8}

= \frac{ 2 ^5}{2^3}

= 2^{5-3} ( By applying quotient of power rule)

= 2^{2}

= 4

masya89 [10]3 years ago
3 0
2^5/8
2^5/2^3
2^(5-3)
2^2
=4
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Applicants who wish to be admitted to a certain professional school in a large university are required to take a screening test
Elden [556K]

Answer:

Probability of eligible applicants who pass the exam is 0.665

probability of applicants who are ineligible but pass the exam 0.063

Step-by-step explanation:

Total percentage eligible applicants who pass the exam

\textrm {89\%  of 70\%}= \dfrac{89\times70}{100}=62.3\%

Total  ineligible applicants  who pass the exam

\textrm {14\%  of 30\%}= \dfrac{14\times30}{100}=4.2\%

All applicants who pass this exam 62.3% + 4.2% = 66.5%

Probability of applicants who pass the exam

\textrm{probability }= \dfrac{66.5}{100}=0.665

Out of 66.5% applicants who pass the exam , 4.2% applicants are ineligible

\textrm{so the probability is}\dfrac{4.2}{66.5}=0.063

Probability of applicants who pass the exam is 0.665

probability of applicants who are ineligible but pass the exam 0.063

6 0
3 years ago
The mean time it takes to walk to the bus stop is 8 minutes (with a standard deviation of 2 minutes) and the mean time it takes
11111nata11111 [884]
(a) Average time to get to school
Average time (minutes) = Summation of the two means = mean time to walk to bus stop + mean time for the bust to get to school = 8+20 = 28 minutes

(b) Standard deviation of the whole trip to school
Standard deviation for the whole trip = Sqrt (Summation of variances)

Variance = Standard deviation ^2
Therefore,
Standard deviation for the whole trip = Sqrt (2^2+4^2) = Sqrt (20) = 4.47 minutes

(c) Probability that it will take more than 30 minutes to get to school
P(x>30) = 1-P(x=30)
Z(x=30) = (mean-30)/SD = (28-30)/4.47 ≈ -0.45
Now, P(x=30) = P(Z=-0.45) = 0.3264
Therefore,
P(X>30) = 1-P(X=30) = 1-0.3264 = 0.6736 = 67.36%

With actual average time to walk to the bus stop being 10 minutes;

(d) Average time to get to school
Actual average time to get to school = 10+20 = 30 minutes

(e) Standard deviation to get to school
Actual standard deviation = Previous standard deviation = 4.47 minutes. This is due to the fact that there are no changes with individual standard deviations.

(f) Probability that it will take more than 30 minutes to get to school
Z(x=30) = (mean - 30)/Sd = (30-30)/4.47 = 0/4.47 = 0

From Z table, P(x=30) = 0.5
And therefore, P(x>30) = 1- P(X=30) = 1- P(Z=0.0) = 1-0.5 = 0.5 = 50%
8 0
3 years ago
What is a peregrine falcon's maximum speed while diving to catch prey,
Sergeu [11.5K]

This is an incomplete question, here is a complete question.

What is a peregrine falcon's maximum speed while diving to catch prey 200 miles per hour in feet per second? (Round your answer to the nearest whole number. (1  mile = 5280 feet)

Answer : The speed in feet per second is, 293 feet/s

Step-by-step explanation :

As we are given that the speed of peregrine falcon's is 200 miles per hour. Now we  have to determine the speed in feet per second.

As we know that:

1  mile = 5280 feet

1 hour = 3600 second

So,

1 mile/hr = 1.4667 feet/s

As, 1 mile/hr = 1.4667 feet/s

So, 200 mile/hr = \frac{200\text{ mile/hr}}{1\text{ mile/hr}}\times 1.4667\text{ feet/s}

                          = 293.34 feet/s ≈ 293 feet/s

Therefore, the speed in feet per second is, 293 feet/s

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