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
So for 1, the way to find one 'part' of the ratio, is to add up the ratio and divide the number from 180 (180 degrees in a triangle). So you would do 7 + 13 + 16 = 36. 180 divided by 36 = 5. Each part represents '5'. So to find the angles, you would do the coefficient multiplied by 5. Therefore, angle DEA is 13 * 5, which is 65 degrees, angle DFA is 16 * 5 = 80 degrees, and angle FDE is 7 * 5, which is 35. You know this is correct because 80 + 35 + 65 = 180 degrees.
For 2, you just have to set up a ratio. So we know that there are 320 cookies for 16 students, so the ratio would be set up as 320:16. So the cookie:student ratio, a.k.a, the number of cookies for each student is going to be the entire ratio divided by 16. We do this because there are 16 students, so to find the amount of cookies for 1 student, we do 16 / 16, which is 1. But of course, this affects the first part of the ratio too, so you do 320 divided by 16, which is 20. So the cookie:student ratio is 20:1. Every 1 student gets 20 cookies.
For 3, you just have to set up another ratio. If he finds 2 clovers in the first 12 minutes, the clover:minute ratio will be 2:12, or 1:6. This means that for every 6 minutes spent searching, 1 clover will be found. If he spends a total of 180 minutes searching, we can predict the number of clovers he will find by doing a proportion calculation. 180 / 6 = 30. That means we have to multiply 1:6 by 30 to find the number of clovers he will find. We multiply by 30 because 6 * 30 is 180 minutes, and obviously, this will affect the first part of the ratio too. 1 * 30 = 30. So that means the ratio is now 30:180. He will find 30 clovers in 180 minutes.
I hope you get it by now, but if you don't let me know. I'll help you answer the rest of the questions :)
Answer:
B
Step-by-step explanation:
A division between two roots that have the same index can be rewritten as a division between the two terms with a unic root
Yes! The lengths of each side must be less than the sum of the other two lengths. It looks like this:
4+4>7
7+4>4
4+7>4
Answer:
20 units
Step-by-step explanation:
The polygon has 4 vertices as indicated by the 4 coordinate points given.
(3, 1) and (8, 1) is a horizontal side of length 8 - 3 = 5
Similarly
(3, 6) and (8, 6) is the opposite horizontal side of length 8 - 3 = 5
Points (3, 1) and (3, 6) is a vertical side of length 6 - 1 = 5
(8, 1) and (8, 6) is the opposite side of length 6 - 1 = 5
The polygon is therefore a square of side 5 units.
Perimeter = 4 × 5 = 20 units
