What multiplies to -120 and adds up to 19

In a competition, a school awarded medals in different categiories.40 medals in sport 25 medals in danceand 212 medals in music,

aleksley [76]

Answer:

210

Step-by-step explanation:

Given:

Medals in sports = 40

Medals in dance = 25

Medals in music = 212

Total students that received medals = 55

Total students that received medals in all three categories = 6

Required:

How many students get medals in exactly two of these categories?

Take the following:

A = set of persons who got medals in sports.

B = set of persons who got medals in dance

C = set of persons who got medals in music.

Therefore,

n(A) = 40

n(B) = 25

n(C) = 212

n(A∪B∪C)= 55

n(A∩B∩C)= 6

To find how many students get medals in exactly two of these categories, we have:

n(A∩B) + n(B∩C) + n(A∩C) −3*n(A∩B∩C)

=n(A∩B) + n(B∩C) + n(A∩C) −3*6 ……............... (1)

n(A∪B∪C)=n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)−n(A∩C)+n(A∩B∩C)

Thus, n(A∩B)+n(B∩C)+n(A∩C)=n(A)+n(B)+n(C)+n(A∩B∩C)−n(A∪B∪C)

Using equation 1:

=n(A)+n(B)+n(C)+n(A∩B∩C)−n(A∪B∪C)−18

Substitute values in the equation:

= 40 + 25 + 212 + 6 − 55 − 18

= 283 - 73

= 210

Number of students that get medals in exactly two of these categories are 210

6 0

4 years ago

The right triangle on the right is a scaled copy of the right triangle on the left. Identify the scale factor. Express your answ

Sonja [21]

Answer:

1/3

Step-by-step explanation:

the one on the left is 3 times larger than the one on the right. in other words, the right triangle's dimensions times 1/3 is equal to the left triangle's dimensions.

5 0

3 years ago

Simplify! Thank you so much if you help! This is urgent!!

Crank

The simplified form is 12x-40

4 0

3 years ago

Read 2 more answers

The probability that you roll a 3 on a six-sided die is . The probability that you flip a coin that lands on tails is . The prob

aivan3 [116]

Answer:

1/6; 1/2; 1/12; P(T|3) = 1/2; therefore, events are independent because P(T|3) = P(T).

Step-by-step explanation:

The probability of rolling a 3 on a six-sided die is 1/6. This is because there is one 3 out of 6 possibilities.

The probability of flipping a coin on tails is 1/2. This is because there is one side "tails" out of 2 possibilities.

The probability of rolling a 3 and flipping tails is 1/6(1/2) = 1/12.

P(T|3) = P(3 and Tails)/P(3) = 1/12 / (1/6) = 1/12(6/1) = 6/12 = 1/2

Since P(T|3) = P(3), these are independent events.

3 0

3 years ago

During the first 13 weeks of the television season, the Saturday evening 8:00 p.m. to 9:00 p.m. audience proportions were record

SpyIntel [72]

Part 1: Do not reject H0. There has not been a significant change in the viewing audience proportions.(The above conclusion holds as the p-value is greater than the significance level of 0.05)

Part 2:

H0:

Ha:

Part 3: The test statistic is given as 3.0081.

Part 4: The p-value is given as 0.39037

Step-by-step explanation:

As per the data

Part 2

H0:

Ha:

Part 3

As per the sample is of 300 homes, the expected values are given as

ABC=p(ABC)*300=0.30*300=90

CBS=p(CBS)*300=0.27*300=81

NBC=p(NBC)*300=0.26*300=78

IND=p(IND)*300=0.17*300=51

Now the values actually are given as

ABC=94

CBS=71

NBC=88

IND=47

So the test static is given as

So the test statistic is given as 3.0081.

Part 4

Now the degree of freedoms are given as 4-1=3

and chi square is given as 3.0081 so for α = 0.05 , the p-value is given as 0.39037

Part 1.

As the value of p in part 4 is greater than the value of α = 0.05, thus Do not reject H0. There has not been a significant change in the viewing audience proportions.(The above conclusion holds as the p-value is greater than the significance level of 0.05)

4 0

3 years ago