A father is questioning the probability his daughter will receive a scholarship. She is a finalist for two different scholarships. The awarding of these scholarships is independent. For the first scholarship (Scholarship A) there are 5 finalists and two scholarships will be awarded. For the second scholarship (Scholarship B) there are also five finalists and one scholarship will be awarded.
1. What is the probability that she will receive Scholarship A and Scholarship B?
2. What is the probability that she will receive at least one scholarship, Scholarship A or Scholarship B?
3. Should she apply for both scholarships or one of the scholarships? If just one, which one? Why?

Answers

Answer 1

Solution :

According to the question, let

A : winning first scholarship

B : winning second scholarship

So for the first scholarship, there are five finalist and only two scholarship will be awarded. And for the second scholarship there are five finalist and only one scholarship will be awarded.

Therefore,

[tex]$P(A)=\frac{2}{5}$[/tex]   and    [tex]$P(B)=\frac{1}{5}$[/tex]

1. So, [tex]$P(A \cap B ) = P(A) P(B)$[/tex]

                      [tex]$=\frac{2}{5} \times \frac{1}{5}$[/tex]

                      [tex]$=\frac{2}{25}$[/tex]                

2. [tex]$P(A \cup B) = P(A)+P(B)-P(A)P(B)$[/tex]

                   [tex]$=\frac{2}{5}+\frac{1}{5}-\frac{2}{25}$[/tex]

                   [tex]$=\frac{13}{25}$[/tex]

3. She should apply to both the scholarships, so as to have a maximum chances of winning at least one scholarship.


Related Questions

There are 396 students who are enrolled in an introductory biology course. If there are five boys to every four girls, how many boys are in the course?

Answers

Answer:

There are 220 boys in the course.

Step-by-step explanation:

If we group the five boys and four girls together, there would be 44 (396/9) groups of nine people. Since there are five boys in every group, you would do 44*5 which is 220.

Answer:

220 boys

Step-by-step explanation:

boys:girls

5:4

396 total

(5x44)+(4x44)=396

220+176=396

220 boys

If right I’ll mark brainiest need ASAP

Answers

Answer:

The answer is 8

Answer:

16 inches

Step-by-step explanation:

First, do 56/7. You do this to see how much more feet it is than the scale. The answer is 8.

Because the answer is 8, you would multiply 2 inches by 8 to be proportional to 56 feet.

GIVING OUT BRAINLIEST ANSWER !! PLS HELP ME OUT !! (last minute)

Answers

Answer:

1:[tex]\sqrt{3}[/tex];2

Step-by-step explanation:

those are the side length ratios

Answer:

1:√3:2

Step-by-step explanation:

Brainliest please

Here are the lowest temperatures recorded in the last 2 centuries for two US cities. How many more degrees colder is the record temperature for GA than FL?

Answers

Answer:

What are the temperatures

can you help me find the value of each shape plz

Answers

Answer:

Star = 10Square = 4Circle = 1

Step-by-step explanation:

Hope it helps you!

30) The sum of three consecutive numbers is 27. What are the three numbers? A. 8, 9, 10 B. 6, 7 8 C. 11, 12, 13 D. 9, 10, 11

Answers

Answer:

The answer is A. 8, 9, 10

Answer:

A. 8, 9, 10.

Step-by-step explanation:

Consecutive numbers counting numbers which are 1 greater than the other, therefore:

x + (x + 1) + (x + 2) = 27

(x + x + x) + (1 + 2) = 27

3x + 3 = 27

–3 –3

3x = 24

÷3 ÷3

x = 8.

x = 8 → [ x + (x + 1) + (x + 2) ] =

(8) + (8 + 1) + (8 + 2) = 8 + 9 + 10

PLEASE HELP WILL MARK BRAINIEST! Asap

Answers

Answer:

n=8

Step-by-step explanation:

It’s a special 30-60-90 triangle, so n=8.

Answer:

54 Ok?

Step-by-step explanation: Thats what i got

Find the value of x in the triangle shown below.
a. x=4
b.x=5
c.x=2
d.x=32

Answers

Answer:

Answer:[tex] \huge\mathfrak\pink{S} \huge\mathfrak\purple{o} \huge\mathfrak\blue{l} \huge\mathfrak\red{u} \huge\mathfrak\green{t} \huge\mathfrak\pink{i}\huge\mathfrak\purple{o}\huge\mathfrak\red{n}\huge\mathfrak\orange{➔}\ [/tex]by using Pythagoras law:h²=p²+b²

9²=x²+7²

x²=81-49

x=√32units

Nicole is solving the equation and realizes there's a mistake.
A) Determine the mistake
B) Determine the correct answer.
- 2x -4>8
-2x - 4+4>8+4
-2x >12
- 2x/2 > 12 /2
x>-6

Answers

Answer:

She forgot to multiply both sides by -1 and reverse the inequality. She also didn't flip the signs.

Step-by-step explanation:

- 2x -4>8

-2x - 4+4>8+4

-2x >12

(-2x)(-1)<12(-1)

2x<-12

2x/2<-12/2

x<-6

Hope this helped!!!

Ahmed invests $4000 in two different accounts. The first account paid 10 %, the second account paid 9% in
interest. At the end of the first year he had earned $370 in interest. How much was in each account?

Answers

Answer: 3000$ in 9% account

Step-by-step explanation: sums in accounts are x and (4000-x)

Interests are 0.09x and 0.10(4000-x) = 400-0.1x

Now you get 0.09x -0.1x + 400 = 370

Then -0.01x = -30 and x= 3000

Nolan has a points card for a movie theater.
He receives 20 rewards points just for signing up.
He earns 2.5 points for each visit to the movie theater.
He needs at least 40 points for a free movie ticket.

Write and solve an inequality which can be used to determine
v
v, the number of visits Nolan can make to earn his first free movie ticket?

Answers

Answer:

V>_8

Step-by-step explanation:

20+2.5v >_ 40

The number of visits Nolan can make to earn his first free movie ticket is 8.

How many visits before Nolan wins a free movie ticket?

The inequality that represents the information in the question is: 20 + 2.5x ≥ 40.

Where x represents the number of visits to the movie theater.

In order to determine the value of x, take the following steps combine similar terms

2.5x  ≥40 - 20

Add similar terms

2.5x  ≥ 20

Divide both sides by 2.5

x  ≥ 8

To learn more about inequality, please check: https://brainly.com/question/5031619

Can someone please solve this

Answers

This one takes time to type all the math work.

Let me see.

There are two triangles here.

They both have the same area.

A = (1/2)(base)(height) times 2

A = (1/2)(42)(56) times 2

A = 1,176 times 2

A = 2,352 inches^2.

We also have three rectangles. We need to find the area of each rectangle individually.

Area of bottom rectangle = 42 times 72 or 3,024 inches^2.

Area of back rectangle = 56 times 72 or 4,032 inches^2.

Area of slanted rectangle = 70 times 72 0r 5,040 inches^2.

We now add all the areas together to find the total area of the entire figure.

Total Area = 2,352 inches^2 + 3,040 inches^2 + 4,032 inches^2 + 5,040 inches^2

Total area = 14,448 inches^2

Done!

Did you understand what was done here?

A spinner is shown below. What is the probability of spinning a dotted or solid section?

a. 2/3
b. 1/2
c. 1/4
d. 1/5

Answers

Answer:

b

Step-by-step explanation:

There are four solid and dotted sections and eight sections in total so the probability is 4/8 or 1/2

It would probably be B

A type of hot tub holds 600 gallons of water one hose can fill the hot tub in 9 hours while another hose takes only 6 hours how long will it take for the hot tub to be filled if both hoses are used

Answers

Answer:

the answer is 40.

Step-by-step explanation:

[tex]t \: = \: \frac{600}{9 + 6} = 40[/tex]

help pleaseeeeeeeeeeeee

Answers

Answer:

B

Step-by-step explanation:

The mean is the average of all ages meaning that the ages are close to 11.6 but don't necessarily have to be 11.6.

find the sum.Use fraction strips to help 1/6 + 1/3 + 1/6 ​

Answers

Answer:

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

Step-by-step explanation:

Since [tex]\frac{1}{6} and \frac{1}{6}[/tex] have the same denominators, we add them first. We then add [tex]\frac{1}{3}[/tex] to the result.

The cosine of a 30 degree angle is equal to the sine of a

Answers

Hey I did get the wrong number for you to get the wrong number and I got a message for 35 dehumidifier

Please actually do it im gonna k m s if someone answers this with a link again ​

Answers

Answer:

Top one, least to greatest:

[tex]-\sqrt{54}[/tex], [tex]-\frac{3}{9}[/tex], [tex]\frac{9}{5}[/tex], [tex]\pi[/tex], 6.6, [tex]\sqrt{75}[/tex]

Bottom one, greatest to least

9.6, [tex]\sqrt{34}[/tex], [tex]\frac{9}{9}[/tex], -4.2, [tex]-7\frac{2}{5}[/tex], [tex]-\sqrt{85}[/tex]

Answer:

Hope I helped and the answers are bellow

Step-by-step explanation:

Part A

-_/- 54 = - 7.38

-3/9 = - 0.3333

9/5 = 1.80

Pi= 3.14

Then 6.6

And finally _/- 75 = 8.66

Part B

9.6

_/- 34 = 5.83

9/9 = 1

-4.2

-7 2/5 = -7.40

-_/- 85 = - 9.21

An angle measures 88° less than the measure of its complementary angle. What is the measure of each angle? (please see the screen shot i need 2 answers)

Answers

Answer:

1° and 89°

Step-by-step explanation:

(x + 88°) + x = 90°

2x + 88 = 90

2x = 2

x = 1°

helppppp meeeeee the sum of the squares of three consecutive integer numbers is 1454. Find the numbers. but i found 21 22 and 23. you need to find the other set plzzz​

Answers

Step-by-step explanation:

A=x

B=x+1

C=x+2

[tex] {x}^{2} + {(x + 1)}^{2} + {(x + 2)}^{2} = 1454 \\ {x}^{2} + {x}^{2} + 2x + 1 + {x}^{2} + 4x + 4 = 1454 \\ 3{x}^{2} + 6x + 5 - 1454 = 0 \\ 3 {x}^{2} + 6x - 1449 = 0 \\ {x}^{2} + 2x - 483 = 0 [/tex]

I'm sorry but I can't use the calculator, I hope this helps you anyway.

Answer:

The two sets would be 21,22,23 and -21, -22, and -23

Step-by-step explanation:

This is because a negative number squared would be positive.

So -21^2+-22^2+-23^2 would equal the same as 21^2+22^2+23^2 which would be 1454.

(5 points) The population of a state changes due to births, deaths, and immigration. The annual birth rate is 14.3 births per 1000 residents, the death rate is 11.8 deaths per 1000 residents, the immigration rate into the state is 21.6 immigrations per 1000 residents, and the emigration rate out of the state is 5.5 emigrations per 1000 residents. Find the population growth rate as a percentage.

Answers

Answer:

The population growth rate is of 1.86%.

Step-by-step explanation:

Population growth rate:

Immigration plus births subtracted by emigration and deaths.

In this question, we have that:

Birth: 14.3 per 1000

Death: 11.8 per 1000

Immigrations: 21.6 per 1000

Emigrations: 5.5 per 1000

Rate:

[tex]\frac{14.3 + 21.6 - 11.8 - 5.5}{1000} = \frac{18.6}{1000} = 0.0186[/tex]

As a percentage:

Multiply by 100%. So

0.0186*100% = 1.86%

The population growth rate is of 1.86%.

What is 4.6m2 in cm2 ?​

Answers

Answer:

4.6

Step-by-step explanation:

Hannah was setting up a room with tables for an event. The room had 12 popular tables and 3 maple tables. What is the probability that the first person to enter the room will be randomly seated at a maple table? Give your answer as a reduced fraction.

Answers

Answer:

4 , 12 divided by 3 equals 4

Step-by-step explanation:

please help me on this. the corerect answer gets brainliest

Answers

Answer:

a) 2

b) 1

c) 4

d) 8

e) 3

f)  9

g) 6

h) 5

i)  7

Step-by-step explanation:

2, 1, 4, 8, 3, 9, 6, 5, 7

The sum of a number and 4 times its reciprocal is 13/3
Find both possible numbers.

Answers

Answer:

3 ; 4/3

Step-by-step explanation:

x + 4(1/x) = 13/3

x + 4/x = 13/3

x^2 -13/3x + 4 = 0

3x^2 - 13x + 12 = 0

Δ = 169 - 144 = 25

x1 = (13 + 5)/6 = 3

x2 = (13-5)/6 = 4/3

Answer:

4/3 or 3

Step-by-step explanation:

Let, the number be x.

According to the question,

x+4×1/x=13/3

or, x+4/x=13/3

or, x^2+4/x=13/3

or, 3(x^2+4)=13x

or, 3x^2+12=13x

or, 3x^2-13x+12=0

or, 3x^2-(4+9)x+12=0

or, 3x^2-4x-9x+12=0

or, x(3x-4)-3(3x-4)=0

or, (3x-4)(x-3)=0

Either, Or,

3x-4=0 x-3=0

or, 3x=4 .•. x=3

.•. x=4/3

So, the possible numbers are 4/3 or 3.

2. State whether the number 21 is a perfect square, a perfect cube, or neither.
a. perfect square
b. neither
c. perfect cube

Answers

Answer:

B, neither

Step-by-step explanation:

21 is not a perfect square or perfect cube.

Rewrite the following sentence in the passive voice:
The people of Zanzibar extended a warm welcome to the tourists.​

Answers

Answer:

When the tourists came, the people of Zanzibar extended a warm welcome.​

What is the volume of a pentagonal prism that has a base area of 5.16 cm2 and a height of 9 cm? 46.44 cm 3 19.32 cm 3 55.32 cm 3 14.16 cm 3

Answers

Answer:

16.44 would be your right answer

Step-by-step explanation:

Answer:

46.44 cm 3

Step-by-step explanation:

What is a correct definition of P-value?

Answers

p-value is a measure of the probability that an observed difference could have occurred just by random chance.

14. A researcher wants to know if the average price of a home in Salt Lake City is higher than the average home in the entire United States. If you know that the average home price in Salt Lake City is $450,000 and the average home price in the entire country is $425,000, please conduct the appropriate test to see if Salt Lake City is more expensive under the following two conditions: (make sure to state which test you are using - they should be different, your null and alternative hypotheses, your a level, the critical score for that test, your statistical conclusion based on the observed statistic, and the meaning of your statistical conclusion in words) a. when you are given the actual standard error of the entire population of the country to be $30,000. (25 points) b. when you are given the estimated population standard deviation of homes in Los Angeles to be $30,000 for 360,000 homes (25 points)​

Answers

Answer:

25000

Step-by-step explanation:

bc the proof is solid

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