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3 years ago

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Solve by substitution. Please help ASAP

1 answer:

Dima020 [189]3 years ago

7 0

Abcdefghijklmnopqrstuvwxyz

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Suppose a random variable x is best described by a uniform probability distribution with range 22 to 55. Find the value of a tha

const2013 [10]

Answer:

(a) The value of <em>a</em> is 53.35.

(b) The value of <em>a</em> is 38.17.

(c) The value of <em>a</em> is 26.95.

(d) The value of <em>a</em> is 25.63.

(e) The value of <em>a</em> is 12.06.

Step-by-step explanation:

The probability density function of <em>X</em> is:

$f_{X}(x)=\frac{1}{55-22}=\frac{1}{33}$

Here, 22 < X < 55.

(a)

Compute the value of <em>a</em> as follows:

$P(X\leq a)=\int\limits^{a}_{22} {\frac{1}{33}} \, dx \\\\0.95=\frac{1}{33}\cdot \int\limits^{a}_{22} {1} \, dx \\\\0.95\times 33=[x]^{a}_{22}\\\\31.35=a-22\\\\a=31.35+22\\\\a=53.35$

Thus, the value of <em>a</em> is 53.35.

(b)

Compute the value of <em>a</em> as follows:

$P(X< a)=\int\limits^{a}_{22} {\frac{1}{33}} \, dx \\\\0.95=\frac{1}{33}\cdot \int\limits^{a}_{22} {1} \, dx \\\\0.49\times 33=[x]^{a}_{22}\\\\16.17=a-22\\\\a=16.17+22\\\\a=38.17$

Thus, the value of <em>a</em> is 38.17.

(c)

Compute the value of <em>a</em> as follows:

$P(X\geq a)=\int\limits^{55}_{a} {\frac{1}{33}} \, dx \\\\0.85=\frac{1}{33}\cdot \int\limits^{55}_{a} {1} \, dx \\\\0.85\times 33=[x]^{55}_{a}\\\\28.05=55-a\\\\a=55-28.05\\\\a=26.95$

Thus, the value of <em>a</em> is 26.95.

(d)

Compute the value of <em>a</em> as follows:

$P(X\geq a)=\int\limits^{55}_{a} {\frac{1}{33}} \, dx \\\\0.89=\frac{1}{33}\cdot \int\limits^{55}_{a} {1} \, dx \\\\0.89\times 33=[x]^{55}_{a}\\\\29.37=55-a\\\\a=55-29.37\\\\a=25.63$

Thus, the value of <em>a</em> is 25.63.

(e)

Compute the value of <em>a</em> as follows:

$P(1.83\leq X\leq a)=\int\limits^{a}_{1.83} {\frac{1}{33}} \, dx \\\\0.31=\frac{1}{33}\cdot \int\limits^{a}_{1.83} {1} \, dx \\\\0.31\times 33=[x]^{a}_{1.83}\\\\10.23=a-1.83\\\\a=10.23+1.83\\\\a=12.06$

Thus, the value of <em>a</em> is 12.06.

7 0

3 years ago

Solve the inequality<br> <img src="https://tex.z-dn.net/?f=2%285c-7%29%5Cgeq%2010%28c-3%29" id="TexFormula1" title="2(5c-7)\geq

alina1380 [7]

1 Remove parentheses.

2(5c−7)≥c−3

2 Expand.
10c−14 ≥ c −3

3 Add 14 to both sides.
10c-14+14≥ c − 3+14

4 Simplify c−3+14 to c+11
10c≥c+11

5 Subtract c from both sides.

10c−c≥11

6 Simplify 10c−c to 9c
9c≥11

7 Divide both sides by 9.
c ≥11/9

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3 years ago

The coefficient of the second term in the expansion of the binomial (4x + 3y)3

Karo-lina-s [1.5K]

The coefficient of the second term is the 3 in (4x+3y)

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4 years ago

Could you please help me with this

Fantom [35]

Answer:

x=56.89

Step-by-step explanation:

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Use the expression shown below.<br> 1 = (4 x 4 x 4 x 4 x 4)<br> What is the value of the expression.

jeka57 [31]

Answer:

1024

Step-by-step explanation:

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3 years ago