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Travka [436]
3 years ago
7

F’(x)= 1+3 square root x f(9)=68

Mathematics
1 answer:
notka56 [123]3 years ago
8 0

Answer:

f(x) = x + 2x^\frac{3}{2} + 5

Step-by-step explanation:

I'm assuming the question here is asking for f(x)

The first step would be to find the antiderivative of f'(x)

\int{1+3\sqrt{x}} \, dx = \int{1 + 3x^\frac{1}{2}} dx

Apply the reverse power rule

x + 2x^\frac{3}{2} + C

Now solve for C when x = 9

x + 2x^\frac{3}{2} + C = 68\\9 + 2(9)^\frac{3}{2} + C = 68\\9 + 2(27) + C = 68\\9 + 54 + C = 68\\63 + C = 68\\C = 5

Now substitute into the antiderivative

f(x) = x + 2x^\frac{3}{2} + 5

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Answer:

\displaystyle \frac{2(x + 3)}{5x - 2}

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

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Step-by-step explanation:

<u>Step 1: Define</u>

\displaystyle \frac{2x^2 + 16x + 30}{5x^2 + 13x - 6}

<u>Step 2: Simplify</u>

  1. [Fraction] Factor numerator:                                                                         \displaystyle \frac{2(x + 3)(x + 5)}{5x^2 + 13x - 6}
  2. [Fraction] Factor denominator:                                                                     \displaystyle \frac{2(x + 3)(x + 5)}{(x + 3)(5x - 2)}
  3. [Fraction] Divide:                                                                                           \displaystyle \frac{2(x + 3)}{5x - 2}
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2 years ago
For each of the following binomial random variables, specify n and p. (a) A fair die is rolled 50 times. X = number of times a 5
Keith_Richards [23]

Answer:

a) n = 50, p = \frac{1}{6}

b) n = 16, p = \frac{1}{100}

c) n = 26, p = 0.25, \mu = 6.5

Step-by-step explanation:

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 combinatios 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.

(a) A fair die is rolled 50 times. X = number of times a 5 is rolled

The die is rolled 50 times, so n = 50.

Each roll can have 6 outcomes. So the probability that 5 is rolled is p = \frac{1}{6}

(b) A company puts a game card in each box of cereal and 1/100 of them are winners. You buy sixteen boxes of cereal, and X = number of times you win.

You buy 16 boxes of cereal, so n = 16.

1 of 100 are winners. So p = \frac{1}{100}.

(c) Jack likes to play computer solitaire and wins about 25% of the time. X = number of games he wins out of his next 26 games.

He plays 26 games, so n = 26.

He wins 25% of the time, so p = 0.25

We have that \mu = np. So \mu = 26*0.25 = 6.5

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3 years ago
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Given:

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Solution:

We have,

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To find the value of x, we need to isolate x on one side.

Subtract 2b from both sides.

-3x>8-2b

Divide both sides by -3. On multiplying or dividing an inequality by a negative number, we need to change the sign of inequality.

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Therefore, the correct option is A.

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