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When clearing the fractions in the equation below, what is the Least Common Denominator?

Answer:

a) 0.3921 = 39.21% probability that fewer than 14 of them have had a physical examination in the past two years.

b) 0.107 = 10.7% probability that at least 17 of them have had a physical examination in the past two years.

Step-by-step explanation:

For each women, there are only two possible outcomes. Either they visit their doctors for a physical examination at least once in two years, or they do not. The probability of a woman visiting their doctor at least once in this period is independent of any other women. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

70% of adult women visit their doctors for a physical examination at least once in two years.

This means that [tex]p = 0.7[/tex]

20 adult women

This means that [tex]n = 20[/tex]

(a) Fewer than 14 of them have had a physical examination in the past two years.

This is:

[tex]P(X < 14) = 1 - P(X \geq 14)[/tex]

In which

[tex]P(X \geq 14) = P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)[/tex]

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 14) = C_{20,14}.(0.7)^{14}.(0.3)^{6} = 0.1916[/tex]

[tex]P(X = 15) = C_{20,15}.(0.7)^{15}.(0.3)^{5} = 0.1789[/tex]

[tex]P(X = 16) = C_{20,16}.(0.7)^{16}.(0.3)^{4} = 0.1304[/tex]

[tex]P(X = 17) = C_{20,14}.(0.7)^{17}.(0.3)^{3} = 0.0716[/tex]

[tex]P(X = 18) = C_{20,18}.(0.7)^{18}.(0.3)^{2} = 0.0278[/tex]

[tex]P(X = 19) = C_{20,19}.(0.7)^{19}.(0.3)^{1} = 0.0068[/tex]

[tex]P(X = 20) = C_{20,20}.(0.7)^{20}.(0.3)^{0} = 0.0008[/tex]

So

[tex]P(X \geq 14) = P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.1916 + 0.1789 + 0.1304 + 0.0716 + 0.0278 + 0.0068 + 0.0008 = 0.6079[/tex]

[tex]P(X < 14) = 1 - P(X \geq 14) = 1 - 0.6079 = 0.3921[/tex]

0.3921 = 39.21% probability that fewer than 14 of them have had a physical examination in the past two years.

(b) At least 17 of them have had a physical examination in the past two years

[tex]P(X \geq 17) = P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)[/tex]

From the values found in item (a).

[tex]P(X \geq 17) = P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.0716 + 0.0278 + 0.0068 + 0.0008 = 0.107[/tex]

0.107 = 10.7% probability that at least 17 of them have had a physical examination in the past two years.

Answer:

-12 and -1

Step-by-step explanation:

(-12)+ (-1)= -13

and -12x-1=12. as - x -=+ (minus x minus=plus)

Answer:-1 and -12

Step-by-step explanation:

-12*-1= 12

-12+(-1)=-13

Answer:

okay maybe try alliteration...

Answer:

Option 2, v plus 5 greater or equal than 9

Step-by-step explanation:

For inequality represented by option 2 i.e v plus 5 greater or equal than 9

v+5 >= 9

If we put v =4 in above inequality, we get

4+5>= 9

9>= 9

Hence, option 2 is correct

Answer:

Option 2

Step-by-step explanation:

Given:

45 people will accomplish the given task in 15 days.

To find:

Days taken by 15 people to complete the same task.

Solution:

Since, 45 people of a company can finish a work in 15 days

Therefore, 1 person can accomplish the task in days = [tex]15\times45[/tex]

                                                                                        = [tex]675[/tex] days

15 people will accomplish the same task in number of days = [tex]\frac{675}{15}[/tex]

                                                                                                    = [tex]45[/tex]

Therefore, number of days taken by 15 people to accomplish the same task will be 45 days.

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Answer:

28,980

Step-by-step explanation:

Easy claps my boiiiiiiiii

Hail Hydra

Answer:

No

Step-by-step explanation:

To form a proporion, both would need to be a multiple of the same thing, whcih they aren't

A=4n

B=4n+-9

C=9n-4n

D=(n-36)4

E=4(n-9

Answer:

b•h/2

12.8•9/2=57.6

area of the triangle is 57.6

12.8•18.5=236.8

area or rectangle is 236.8

the total area is 57.6+236.8=294.4

I hope this right

Answer:

A fraction is in simplest form when the top and bottom cannot be any smaller, while still being whole numbers.

Step-by-step explanation:

Answer:

The answer is n < 6.

Step-by-step explanation:

[tex] \frac{n}{3} < 6 - 4[/tex]

[tex] \frac{n}{3} < 2[/tex]

[tex]n < 2 \times 3[/tex]

[tex]n < 6[/tex]

Therefor, the answer is n < 6.

Answer:

663

Step-by-step explanation:

the total number of students can be determined using this equation :

(total ratio of Chinese and Indian students / total ratio of students) x n = 468

total ratio of Chinese and Indian students = 4 + 8 = 12

total ratio of students 4 + 8 + 5 = 17

N = TOTAL NUMBER OF STUDENTS

12/17) x n = 468

multiply both sides of the equation by 17/12

n = 663

Answer:

N/A

Step-by-step explanation:

Get the Desmos graphing calculator app. it is very helpful when graphing and needing to be able to compare functions

Answer:

B is the correct answer

Step-by-step explanation: When you add 18+54+24=96 divide 96 by 3 and its 32!

Answer:

the answer is 3.

Step-by-step explanation:

A = L* W

when you are given the area and the width you need to divide the area by the width to find the length.

So 60/20=3

Answer:

119400

Step-by-step explanation:

The approximate population of the city was 119400

Answer:c

Use the distance formula to see if all three sides are congruent.

Step-by-step explanation:

An equilateral triangle is a triangle which has three sides with the same lengths. If we check for congruence we are checking to see if all the sides are the same :)

To prove a triangle is an equilateral triangle by using  the distance formula to see if all three sides are congruent, the correct option is C

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

Given;

To prove a triangle is an equilateral triangle

Now, we have to use the distance formula: d = sqrt( (x2 - x1)² + ( y2 - y1 )²)

When 2 sides are congruent it could be a scalene triangle, so it is not enough. All 3 sides must be congruent.

Therefore, the answer will be by use the distance formula of triangle to see if all three sides are congruent.

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#SPJ6

Answer: 7.5

Step-by-step explanation:

A1=1/2pir^2 A2=1/2pir^2

1/2(121pi) 1/2(16pi)

5.5 2

The area of a composite shape is the sum of the areas of its individual shapes

The area of the composite shape is 215.20 square feet.

From the figures, we have the following shapes

The area (A) of a semicircle is:

[tex]\mathbf{A = \frac{\pi d^2}{8}}[/tex]

So, the area of the composite shape is:

[tex]\mathbf{A = \frac{\pi (d_1^2 + d_2^2)}{8}}[/tex]

This gives

[tex]\mathbf{A = \frac{\pi (22^2 + 8^2)}{8}}[/tex]

[tex]\mathbf{A = \frac{\pi (548)}{8}}[/tex]

[tex]\mathbf{A = 68.5\pi}[/tex]

[tex]\mathbf{A = 215.20}[/tex]

Hence, the area of the composite shape is 215.20 square feet.

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Answer:

6

Step-by-step explanation:

I found that the greatest common factor for those numbers is 6

Missing information :

The model was omitted from the question ; the possible model relating to the question was browsed online and could possibly be :

N(t) = 1.07t^2.3 for 0 ≤ t ≤ 10 months

Answer:

30.9 cases per month

Step-by-step explanation:

Given the model to determine the number of rats that have developed cancer after initial exposure ; N(t) = 1.07t^2.3

N(t) = 1.07t^2.3

Take the first derivative of N with respect to t to obtain the rate of change ;

N'(t) = (1.07)(2.3)t^2.3-1

N'(t) = (1.07)(2.3)t^1.3

The rate of growth of cancer cases at the 7th month can be calculated thus :

t = 7

N'(7) = (1.07)(2.3)t^1.3

N'(7) = 1.07 * 2.3 * 7^1.3

N'(7) = 1.07 * 2.3 * 12.549529

N'(7) = 30.884

The rate of growth of cancer at the 7th month is 30.9 cases per month.

Answer:

It took 3 hours for the two to meet, and they were 12 miles from Joseph's home when they met.

Step-by-step explanation:

Since Joseph is planning to meet up with his friend Naomi, and Joseph jogs from his house traveling at a rate of 4 miles per hour, while Naomi is initially 27 miles from Joseph's house and travels towards Joseph at 5 miles per hour, for To determine how many hours went by before they met and how many miles were they from Joseph's house when they met, the following calculations should be performed:

27 - (4 + 5) = 27 - 9 = 18

27 - (4 + 5) x 3 = 0

Therefore, it took 3 hours for the two to meet.

4 x 3 = 12

Thus, they were 12 miles from Joseph's home when they met.

Answer:

c

Step-by-step explanation:

9514 1404 393

Answer:

  96 m²

Step-by-step explanation:

The total area of the two triangular bases is ...

  A = 2(1/2)bh = bh

  A = (3 m)(4 m) = 12 m²

The total area of the rectangular faces is ...

  A = Ph = (3 m +4 m +5 m)(7 m) = 84 m²

Then the total surface area of the prism is ...

  12 m² +84 m² = 96 m² . . . prism surface area

Answer:

Step-by-step explanation:

z = 119                            Vertically opposite angles are equal.

5x + 41 + 119 = 180        5x + 41  and 119 are supplementary.

4x + 160 = 180               Subtract 160 from both sides

4x = 180 - 160

4x = 20                           Divide by 4

x = 20/4

x = 5

Answer:

7

Step-by-step explanation:

2x-5 + 2x-7 = 12

this is because the length of the line is given to be 12

so the sum of the two equations should be 12

2x+2x -5-7 = 12

4x - 12 = 12

4x = 12+12

4x = 24

x = 6

there TU = 2x-5 =2(6) -5 =12-5=7

TU = 7

Answer:

If she made LESS than $48, then she worked 5 hours. But If she made exactly $48, then she worked 6 hours.

Step-by-step explanation:

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