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lesantik [10]
3 years ago
14

1 Write each expression simplify when possible. 23. 24.

Mathematics
1 answer:
Oduvanchick [21]3 years ago
6 0
Before answering the exact question you sent, you have to understand one simple principle: there are two forms of a variable with a fraction as an exponent, exponential form and radical form.

Example:
exponential\ form = x^{1/3}\\radical form =  \sqrt[3]{x}

If the exponent is a fraction, the denominator of the fraction is the number on the outside of the radical sign.

So, for #23, you would change \sqrt[3]{a} to a^{1/3}. Then, because the a is the same after the 2 and the 3, you can add them up to get 5 a^{1/3}.

For #24, you'd do almost the same thing (change the radical-b's to b^{1/4} and b^{1/3}. However, you can't add them up because the exponents are different (1/4 and 1/3), so you'd leave it as 3b^{1/4} - b^{1/3}
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A stadium has two sections, A and B.
Alekssandra [29.7K]
ANSWER: a=12 b=15
Explanation: (look at work below)

4a + 1b = 63 (eq1)
5a + 3b = 105 (eq2)
-12a + -3b = -189 (subt. eq1 from eq2)
————————-
-7a = -84
a = 12
4(12) + 1b = 63 (plug in the a value)
48 + 1b = 63
b = 15
5 0
3 years ago
Ruby read 0.85. Of a book what fraction of the book does ruby have left to read? Write in simplest fom
lbvjy [14]
3/20 left to read. If you start 85/100 you take 100-85 and get 15, then you end up 15/100 which reduces to 3/20.
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3 years ago
Exercise 5.2. Suppose that X has moment generating function
soldi70 [24.7K]

Answer:

a) Mean, E(X) = - 0.5

Variance = = 9.25

b) M_{X}(t)=E(e^{tX})

or

⇒ =\sum e^{tx}p(x)

⇒ =\frac{1}{2}+\frac{1}{3}e^{-4t}+\frac{1}{6}e^{5t}

Step-by-step explanation:

Given:

moment generating function  of X as:

MX(t) = \frac{1}{2} + \frac{1}{3}e^{-4t} + \frac{1}{6} e^{5t}

a)  Now

Mean, E(X) = M_{X}'(t=0)

Thus,

M_{X}'(t)=\frac{1}{3}(-4)e^{-4t}+\frac{1}{6}(5)e^{5t}

or

M_{X}'(t)=\frac{-4}{3}e^{-4t}+\frac{5}{6}e^{5t}

also,

E(X^{2})=M_{X}''(t=0)

Thus,

M_{X}''(t)=\frac{-4}{3}(-4)e^{-4t}+\frac{5}{6}(5)e^{5t}

or

M_{X}''(t)=\frac{16}{3}e^{-4t}+\frac{25}{6}e^{5t}

Therefore,

Mean, E(X) = M_{X}'(t=0)=\frac{-4}{3}e^{-4(0)}+\frac{5}{6}e^{5(0)}

or

Mean, E(X) = - 0.5

and

E(X^{2})=M_{X}''(t=0)=\frac{16}{3}e^{-4(0)}+\frac{25}{6}e^{5(0)}

or

E(X^{2}) = 9.5

also,

Variance(X) = E(X²) - E(X)²

⇒ 9.5 - (-0.5)²

= 9.25

b) Now,

Let f(x) be the PMF of X

Thus,

M_{X}(t)=E(e^{tX})

or

⇒ =\sum e^{tx}p(x)

⇒ =\frac{1}{2}+\frac{1}{3}e^{-4t}+\frac{1}{6}e^{5t}

Therefore,

at x = 0, P(x) = \frac{1}{2}

at x= - 4 ,P(x) = \frac{1}{3}

at x = 5, P(x) = \frac{1}{6}

Thus,

E(X) =\sum xP(x)=0(\frac{1}{2})+(-4)(\frac{1}{3})+5(\frac{1}{6})

or

E(X) = - 0.5

also,E(X^{2})=\sum x^{2}P(x)=0^{2}(\frac{1}{2})+(-4)^{2}(\frac{1}{3})+5^{2}(\frac{1}{6})

E(X^{2})  = 9.5

Hence,

Var(X) = E(X²) - E(X)²

⇒ 9.5 - (-0.5)²

= 9.25

4 0
4 years ago
Which best describes the graph of the cubic function f(x) = x3 + x2 + x + 1?
EleoNora [17]

Answer:

Option A

Step-by-step explanation:

  • f(x) = x³ + x² + x + 1

This is increasing function

The first option is correct

<em>See attached graph for reference</em>

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Claire buys a computer that is on sale for 25% off the original price. The original price is $185 more than the sale price. What
frez [133]

Answer:

$740

Step-by-step explanation:

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3 years ago
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