A survey of 1,000 men and women asked, "Do you earn over $50,000 per year?" The table below shows the responses for males and females:Male Female Total
Income over $50,000 485 385 870
Income below $50,000 65 65 130
Total 550 450 1,000

Based on these data, are "being male" and "earning over $50,000" independent events?

A) Yes, P(being male | the person earns over $50,000) ≠ P(being male)
B) Yes, P(being male | the person earns over $50,000) = P(being male)
C) No, P(being male | the person earns over $50,000) ≠ P(being male)
D) No, P(being male | the person earns over $50,000) = P(being male)

Will give a "Brainliest answer" to the first person to respond

Answers

Answer 1

Answer: Male Female    Total
Income over $50,000   485 385   870
Income below $50,000 65   65 130
Total   550 450   1,000

Probability of being male: 550/1000 = 0.55
Probability of earning over $50,000: 870/1000 = 0.87

0.55 x 0.87 = 0.4785

Probability of being male and earning over $50,000: 485/550 = 0.8818

C) No, P(being male | the person earns over $50,000) ≠ P(being male)

Answer 2

Answer:

Based on the date given "being male" and "earning over $50,000" are NOT mutually exclusive events. That is "No, P(being male | the person earns over $50,000) ≠ P(being male)" (Option C)

What are mutually exclusive (or independent) events?

Two events are independent or mutually exclusive if they are distinct from one another and cannot alter the reaction of one another.

Calculation

Probability of being male: 550/1000 = 0.55
Probability of earning over $50,000: 870/1000 = 0.87

=0.55 x 0.87

= 0.4785

Thus, probability of being male and earning over $50,000

= 485/550

= 0.8818

Hence, we can state that P(being male | the person earns over $50,000) ≠ P(being male)

Learn more about mutually exclusive events at;
brainly.com/question/27588497
#SPJ5

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Step-by-step explanation:

$\log_(5)((2)/(3)x-2)+2=0\n\n\log_(5)((2)/(3)x-2)=-2\n\n$

This means that 5 to the power of -2 is $((2)/(3)x-2)$ , meaning that:

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Answers

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County X has a population density of 250 people per square mile. The totalpopulation of the county is 150,000. Which geometric model could be the shape of
county X?
A a parallelogram with a base of 25 miles and a height of 25 miles
B a rectangle that is 15 miles long and 45 miles wide
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D a trapezoid with base lengths of 10 miles and 30 miles and a height of
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Answers

Answer:

Option C. is the correct option.

Step-by-step explanation:

County X has a population density of 250 people per square mile.

Total population of the county is 150000.

Total area which represents the population = $\frac{\text{Total population}}{\text{Population density}}$ = $(150000)/(250)=600$ square mile.

So geometric model which has the same area as 600 square miles will be the answer.

A). Area of a parallelogram = Base × height

= 25×25

= 625 square miles

which is not equal to 600 square miles so it's not the correct option.

B). Area of a rectangle = Length×width

= 15×45 = 675 square miles ≠ 600 square miles

Therefore, not the correct option.

C). Area of a right triangle = $(1)/(2)(Base)(height)$

Since length of hypotenuse is given so we will find the length of height.

Height = √[(Hypotenuse)²- (Base)²] = $\sqrt{50^(2)-30^(2)}$

= $√(2500-900)$

= $√(1600)$

= 40 miles

So area of the right triangle = $(1)/(2)(40)(30)$

= $(1200)/(2)$

= 600 square miles

Which matches the area of County X, so it's a correct option.

D). area of trapezoid = $(1)/(2)[(base1 + base2)](height)$

= $(1)/(2)(10+30)(25)$

= $(1)/(2)(40)(25)$

= 20×25

= 500 square miles ≠ 600 miles

Therefore, this option is not correct.

C. with a 150,000 person population at 250 persons per square mile the country would be 600 square miles. The last leg would equal 40 miles and therefore making the area equal 600 square miles.

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