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miskamm [114]
3 years ago
10

Write the rules for factoring. x method, difference of squares

Mathematics
1 answer:
ch4aika [34]3 years ago
6 0
Difference-of-Squares Formula:

For a difference of squares a2 – b2, the factorization is:

(a – b)(a + b)

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Evaluate the given expression. Subscript 5 Baseline P Subscript 2 a. 40 c. 25 b. 32 d. 20
Leto [7]

Answer:

d. 20

Step-by-step explanation:

The given question implies 5 permutation 2, i.e _{5}P_{2}.

But,

_{n}P_{r} = \frac{n!}{(n - r)!}

So that for _{5}P_{2}, n = 5 and r = 2.

_{5}P_{2} = \frac{5!}{(5 - 2)!}

     = \frac{5!}{3!}

    = \frac{5*4*3*2!}{3*2!}

Cancel out 3 and 2 with respect to the numerator and denominator.

_{5}P_{2} = 5 * 4

     = 20

Therefore,

_{5}P_{2} = 20

So that the correct option is D.

6 0
3 years ago
Read 2 more answers
The University of Washington claims that it graduates 85% of its basketball players. An NCAA investigation about the graduation
Nonamiya [84]

Probabilities are used to determine the chances of events

The given parameters are:

  • Sample size: n = 20
  • Proportion: p = 85%

<h3>(a) What is the probability that 11 out of the 20 would graduate? </h3>

Using the binomial probability formula, we have:

P(X = x) = ^nC_x p^x(1 - p)^{n -x}

So, the equation becomes

P(x = 11) = ^{20}C_{11} \times (85\%)^{11} \times (1 - 85\%)^{20 -11}    

This gives

P(x = 11) = 167960 \times (0.85)^{11} \times 0.15^{9}

P(x = 11) = 0.0011

Express as percentage

P(x = 11) = 0.11\%

Hence, the probability that 11 out of the 20 would graduate is 0.11%

<h3>(b) To what extent do you think the university’s claim is true?</h3>

The probability 0.11% is less than 50%.

Hence, the extent that the university’s claim is true is very low

<h3>(c) What is the probability that all  20 would graduate? </h3>

Using the binomial probability formula, we have:

P(X = x) = ^nC_x p^x(1 - p)^{n -x}

So, the equation becomes

P(x = 20) = ^{20}C_{20} \times (85\%)^{20} \times (1 - 85\%)^{20 -20}    

This gives

P(x = 20) = 1 \times (0.85)^{20} \times (0.15\%)^0

P(x = 20) = 0.0388

Express as percentage

P(x = 20) = 3.88\%

Hence, the probability that all 20 would graduate is 3.88%

<h3>(d) The mean and the standard deviation</h3>

The mean is calculated as:

\mu = np

So, we have:

\mu = 20 \times 85\%

\mu = 17

The standard deviation is calculated as:

\sigma = np(1 - p)

So, we have:

\sigma = 20 \times 85\% \times (1 - 85\%)

\sigma = 20 \times 0.85 \times 0.15

\sigma = 2.55

Hence, the mean and the standard deviation are 17 and 2.55, respectively.

Read more about probabilities at:

brainly.com/question/15246027

8 0
2 years ago
Which of these equations are in slope-intercept form?
maxonik [38]

Answer:

y = mx + b

Step-by-step explanation:

6 0
2 years ago
Someone help me!!!please
gregori [183]

9514 1404 393

Answer:

  115 square units

Step-by-step explanation:

The area of a parallelogram is the product of base length and height. The height is the perpendicular distance between the bases.

  A = bh

  A = (23)(5) = 115 . . . . square units

8 0
2 years ago
What is 37% of 600<br> gkftcchkfhkfufjfvghvhchcfhcgc
Scilla [17]

Answer:

222

Step-by-step explanation:

Let me know if it is correct!

3 0
2 years ago
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