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4 years ago

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Mathematics

1 answer:

In-s [12.5K]4 years ago

6 0

Answer:

1. x = 39.67

2. x = 15

3. x = 49.29

4. x = -12.8

5. x = 96

6. x = 42

7. x = 36

8. x = 0

9. x = 78

Step-by-step explanation:

Just remember to always isolate the unknown. Here are the solutions to your problem. I will explain each step for the first for you to give you an idea how the others were worked out.

1. $\dfrac{3x}{7}-2 = 15$

Add 2 to both sides to get rid of -2 on the left side.

$\dfrac{3x}{7}-2+(2)=15+(2)///dfrac{3x}{7}=17$

Multiply both sides by 7 to get rid of 7 on the left side.

$\dfrac{3x}{7}\times 7 = 17\times 7\\\\3x = 119$

Divide both sides by 3 to get rid of 3 on the left side.

$\dfrac{3x}{3} = \dfrac{119}{3}\\\\x = 39.67$

You could also transpose everything by the x to the other side of the equation. Just remember that whatever OPERATION used on the original side, must be opposite on the other side. I'll use the second problem to show this.

$\dfrac{2x}{5}+1=7$

Transpose 1 on the left to the right. It is addition on the left, then it would be subtraction on the other side.

$\dfrac{2x}{5}+1=7\\\\\dfrac{2x}{5}=7-1\\\\\dfrac{2x}{5}=6$

Transpose 5 from the left side to the right. It is division on the left, then it would be multiplication on the right.

$\dfrac{2x}{5}=6\\\\2x=6\times 5\\\\2x=30$

Transpose 2 from the left side to the right. It is multiplication on the left, then it would be division on the right.

$2x=30\\\\x=\dfrac{30}{2}\\\\x=15$

Let's move on with the rest now.

$\dfrac{7x}{15}-1=22\\\\\dfrac{7x}{15}=22+1\\\\\dfrac{7x}{15}=23\\\\7x=23\times15\\\\7x=345\\\\x=\dfrac{345}{7}\\\\x=49.29$

$\dfrac{5x}{8}+10=2\\\\\dfrac{5x}{8}=2-10\\\\\dfrac{5x}{8}=-8\\\\5x=-8\times8\\\\5x=-64\\\\x=\dfrac{-64}{5}\\\\x=-12.8$

$\dfrac{x}{6}+4=20\\\\\dfrac{x}{6}=20-4\\\\\dfrac{x}{6}=16\\\\x=16\times6\\\\x=96$

$\dfrac{x}{3}-4=10\\\\\dfrac{x}{3}=10+4\\\\\dfrac{x}{3}=14\\\\x=3\times14\\\\x=42$

$\dfrac{x}{6}+2=8\\\\\dfrac{x}{6}=8-2\\\\\dfrac{x}{6}=6\\\\x=6\times6\\\\x=36$

$\dfrac{x}{9}+8=8\\\\\dfrac{x}{9}=8-8\\\\\dfrac{x}{9}=0\\\\x=0\times9\\\\x=0$

$\dfrac{x}{6}+7=20\\\\\dfrac{x}{6}=20-7\\\\\dfrac{x}{6}=13\\\\x=13\times6\\\\x=78$

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Step-by-step explanation:

See comment for complete question

The question is an illustration of binomial probability where

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

$(a):\ P(x \ge 5)$

$n = 15$ --- marketing personnel

$p = 75\%$ --- proportion that are extroverts

Using the complement rule, we have:

$P(x \ge 5) = 1 - P(x < 5)$

So, we have:

$P(x < 5) =P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4)$

$P(x = 0) = ^{15}C_{0} * (75\%)^0 * (1 - 75\%)^{15 - 0} = 1 * 1 * (0.25)^{15} = 9.31 * 10^{-10}$

$P(x = 1) = ^{15}C_{1} * (75\%)^1 * (1 - 75\%)^{15 - 1} = 15* (0.75)^1 * (0.25)^{14} = 4.19 * 10^{-8}$

$P(x = 2) = ^{15}C_{2} * (75\%)^2 * (1 - 75\%)^{15 - 2} = 105* (0.75)^2 * (0.25)^{13} = 8.80 * 10^{-7}$

$P(x = 3) = ^{15}C_{3} * (75\%)^3 * (1 - 75\%)^{15 - 3} = 455* (0.75)^2 * (0.25)^{12} = 0.0000153$

$P(x = 4) = ^{15}C_{4} * (75\%)^4 * (1 - 75\%)^{15 - 4} = 1365 * (0.75)^4 * (0.25)^{11} = 0.000103$

So, we have:

$P(x < 5) = (9.31 * 10^{-10}) + (4.19 * 10^{-8}) + (8.80 * 10^{-7}) + 0.0000153 + 0.000103$

$P(x < 5) = 0.00011922283$

Recall that:

$P(x \ge 5) = 1 - P(x < 5)$

$P(x \ge 5) = 1 - 0.00011922283$

$P(x \ge 5) = 0.9998$

$P(x \ge 5) = 1.000$ --- approximated

$(b)\ P(x = 15)$

$n = 15$ --- marketing personnel

$p = 75\%$ --- proportion that are extroverts

So, we have:

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

$P(x=15) = ^{15}C_{15} * 0.75^{15} * (1 - 0.75)^{15-15}$

$P(x=15) = 1 * 0.75^{15} * (0.25)^{0$

$P(x=15) = 0.013$

$(c)\ P(x = 0)$

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$p = 70\%$ --- proportion that are introverts

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

$P(x = 0) = ^{5}C_0 * (70\%)^0 * (1 - 70\%)^{5-0}$

$P(x = 0) = 1 * 1 * (0.30)^5$

$P(x = 0) = 0.002$

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