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lukranit [14]
4 years ago
8

Complete the table by providing justification for each step of the proof. Conjecture: If 4(x2 – 2) = 28, then x is 3 or –3

Mathematics
1 answer:
Anika [276]4 years ago
5 0
<span>4(x2 – 2) = 28
4x^2-8=28 Distributive law of multiplication

4x^2+8=28+8 Additive identity
4x^2=36 ; adding 8 to both sides
x^2 =9, dividing both sides by 4
x= +/- 3</span>
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Suppose approximately 75% of all marketing personnel are extroverts, whereas about 70% of all computer programmers are introvert
Setler [38]

Answer:

P(x \ge 5) = 1.000 ---- At least 5 from marketing departments are extroverts

P(x=15) = 0.013 ---- All from marketing departments are extroverts

P(x = 0) = 0.002 ---------- None from computer programmers are introverts

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)

n=5 ---------- computer programmers

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

So, we have:

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

3 0
3 years ago
What is the missing number in the sentence below?
Karolina [17]
The correct answer is A: 3. This is because...
3 * 4 = 12
12 * 5 = 60
Therefore, the answer is 60.
3 0
3 years ago
If A = {w.a, t,c, h, d, 0,8} and U = {a,b,c,d, e, f, g, h, L.), k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z), find A'
Ugo [173]
Adcdefghijklmnopqrstuvwxyz
6 0
4 years ago
What is the common difference for the sequence shown below? coordinate plane showing the points 1, 5; 2, 2; and 3, negative 1?
vodka [1.7K]
The correct answer to this problem would be -3. Based on the points you've provided on the graph, -3 would be the correct common difference. :)
5 0
3 years ago
Read 2 more answers
Can someone help me please
vodomira [7]

Answer:

  DNE

Step-by-step explanation:

The left limit is +1; the right limit is -1. These are different, so the limit does not exist.

3 0
3 years ago
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