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2 years ago

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Complete the following proof

1 answer:

Nadya [2.5K]2 years ago

3 0

Answer:

Step-by-step explanation:

statment/reason

1) HK≅JK / given (S)

2) IK bisects ∠HKJ / given

3) ∠3≅∠4 / angle bisectors form congruent angles (A)

4) HK≅JK / given

5) IK ≅IK / reflexive propriety (S)

6) ΔIHK≅ΔIJK / SAS theorem of congruency

7) ∠1≅∠2 / corsponding parts of congruent Δs are ≅

8) IK bisects ∠HIJ / angle bisectors form congruent angles

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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

2 years ago

A stack of 9 different cards are shuffled and spread out face down. If 4 cards are tired face up, how many different 4-card comb

Juliette [100K]

Answer:

126.

Step-by-step explanation:

This is the number of combinations of 4 cards from 9 cards:

= 9C4

= 9! / 4! 5!.

A quick way of calculating this is

9*8*7*6

----------- = 9*2*7 = 126 combinations.

4*3*2*1

7 0

2 years ago

What is the fraction of 28 and 8

vazorg [7]

Can you add more information?

4 0

2 years ago

A line has a zero slope and passes through the point (4,-9). What is the equation of the line?

Ugo [173]

keeping in mind that a line with a slope of "0" is a horizontal line, Check the picture below.

5 0

1 year ago

What is the equation of the line that passes through the point (4,7) and has a slope of o?

Svetlanka [38]

Answer:

The equation of the line that passes through the point (4,7) and has a slope of 0 will be:

$y=7$

Step-by-step explanation:

As we know the equation of a line in a slope-intercept form of an equation is

$y = mx + b$

Here,

m is the slop

b is the y-intercept

so

substituting the point (4,7) and slope m=0

$y = mx + b$

$7=0(4)+b$

$7=0+b$

$b=7$

Therefore, the equation of the line that passes through the point (4,7) and has a slope of 0 will be:

$y = mx + b$

$y=0x+7$

$y=7$

5 0

2 years ago