A class contains 10 sophomores, 15 juniors, and 20 seniors. A committee of 5 students is to be chosen. Each student is equally likely to be selected to serve on the committee. Let A be the event exactly 3 juniors are selected to serve on the committee. Let B be the event exactly 2 seniors are selected to serve on the committee.

Required:
a. Find P(A)
b. Find P(A| B)

Answer:

[tex]y = \frac{1}{4} x[/tex]  

Step-by-step explanation:

1) First, find the slope of the equation. Use the slope formula [tex]m= \frac{y_2-y_1}{x_2-x_1}[/tex]. Substitute the x and y values of the given points into the formula and solve:

[tex]m = \frac{(2)-(1)}{(8)-(4)} \\m = \frac{2-1}{8-4}\\m = \frac{1}{4}[/tex]

Thus, the slope is [tex]\frac{1}{4}[/tex].

2) Now, use the point-slope formula [tex]y-y_1 = m (x-x_1)[/tex] to write the equation in point-slope form (from there we can convert it to slope-intercept). Substitute values for [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex].

Since [tex]m[/tex] represents the slope, substitute [tex]\frac{1}{4}[/tex] for it. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of one point the line intersects, choose any of the given points (it doesn't matter which one, the end result will be the same) and substitute its x and y values into the formula as well. (I chose (4,1), as seen below.) Then, isolate y to put the equation in slope-intercept form and find the answer.

[tex]y-(1) = \frac{1}{4} (x-4)\\y-1 = \frac{1}{4} x-1\\y = \frac{1}{4} x+0\\y=\frac{1}{4}x[/tex]

Answer:

14

Step-by-step explanation:

Given the following equation;

4³ - (2 + 2³) * 5

4*4*4 - (2 + 2*2*2) * 5

64 - (2 + 8) * 5

64 - (10) * 5

64 - 50 = 14

Note: the rule of BODMAS was applied.

Answer:

y=-5x/4-2

Step-by-step explanation:

4x – 5y = 20

y = (4/5)x - 4

slope is 4/5

let new slope m:

(m)(4/5)=-1

m=-5/4

point slope form:

(y-3)/(x+4)=-5/4

y-3=-5x/4-5

y=-5x/4-2

Answer:

9

Step-by-step explanation:

because 14-5=9

Answer:

y=2x+3

Step-by-step explanation:

Answer:

600 km

Step-by-step explanation:

72 (km on 6 L of gasoline) / 6 (liters of gasoline) = 12 (km per liter)

50 (liters of gasoline) * 12 (km per liter) = 600 (km that Jacqueline can drive using 50L of gasoline)

I hope this helps :)

Answer:

600

Step-by-step explanation:

took the test

Answer:

In algebra, we often study relationships where a change to one variable causes change in another variable. Describe a situation you’re familiar with where one quantity changes constantly in relation to another quantity. How are the two quantities in the situation related? If you represent the two quantities on a graph, what will it look like?

Step-by-step explanation:

Answer:

I’m not sure if this is free points or a question but the question is not clear

Step-by-step explanation:

Answer:  Uhmm where is the problem?

Answer:

x=14/3

Step-by-step explanation:

According to the corresponding angles theorem, when parallel lines are cut by a transversal, the corresponding angles are congruent. These 3 lines are all parallel, so 70 = 12x +14.

Subtract 14 from both sides

56 = 12x

Divide both sides by 12

14/3 = x

x=14/3

Answer:

h=3in  

Step-by-step explanation:

A=a+b

2h

Solving forh

h=2A

a+b=2·13.5

3+6=3in

Answer:

60 times

Step-by-step explanation:

There are a total of 5+6+7+3+4=25 marbles

Out of those 25 marbles, 5 are red.

Since there would be a 5/25=1/5 chance of selecting a red marble one time, then we can set up a proportion to find out how many red marbles Taylor will select out of 300 marbles.

1/5=x/300

(1)(300)=(5)(x)

300=5x

60=x

x=60

Therefore, using a probability model for this experiment, Taylor would pick up a red marble 60 times if she chooses a marble 300 times.

Answer:

124, I believe

Step-by-step explanation:

each day you're adding on the amount of the day,

5,7,10,14,19,25,32,40,49,59,70,82,95,109,124

days below

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15)

5 on day 1

5+2=7 day 2

7+3=10 day 3

and so on

Answer:

Step-by-step explanation:

I think you mean a² + b² = c², not ca.

a = 10, c = 26

b² = c²  - a² = 26² - 10² = 576

b = √576 = 24 ft

Answer:

Step-by-step explanation:

5/3 *2=10/6

10/6-6/6=4/6

Answer:

Step-by-step explanation:

a=11/12

Answer:

15 yards

Step-by-step explanation:

3ft=1yard

45/3=15

Answer:

The total number of dollars you pay:  Dependent

The time in months you keep your service:  Independent

Answer:

C) 0%

Step-by-step explanation:

Let’s give the square sides equaling 4. The area would equal 16.

Decreasing the top by 75% would make it 1.  Increasing the bottom by 75% makes it 7.

(1+7)/2=4

The height is still four so 4x4=16

No change in area.

Answer:

formula is 6a²= surface area

but since one side is not being painted it is

5a²= surface area

5(3.2)²

=51.2cm

Answer:

We reject the H0

Step-by-step explanation:

Given that:

Sample size, n = 200

x, = 332 ; s = 108

H0 : μ = 0

H1: μ > 0

The test statistic :

(x - μ) / s/sqrt(n)

332 / 108/sqrt(200)

332 / 7.6367532

Zstatistic = 43.47

Pvalue from Zstatistic at α = 0.05

P value is bet small < 0.00001

Pvalue < α

We reject the null

Conclusion: Amount charged on credit card under the no - fee plan increases

Answer:

111

Step-by-step explanation:

Use PEMDAS to solve this equation, so first we have to do parenthesis first. Simplify 4+16 to get 20. Simplify 2+3 to get 5. Therefore, the equation will now look like 180/(20)-8x3+7x(5). Because we can do either division or multiplication first, we have to solve the equation started from the left. Therefore, we do 180/20 which is 90. Then the equation will be 90-8x3+7x5. Multiply -8 and 3 together to get -24. Therefore, the equation will be 90-24+7x5. Because we always do multiplication/division before addition/subtraction. We have to do 7x5 which is equal to 35. Therefore, the equation will look like 90-24+35. Because there is only subtraction and addition now, we should start from the left hand side which is 90-24. Simplify this to get 76. Then the equation will be 76+35. Simplify this to get 111.

If this answer helps, please mark it as brainliest

Answer:

wouldnt it be 8 im not sure tho

Step-by-step explanation:

Answer:

1 and -0.6

Step-by-step explanation: