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frosja888 [35]
2 years ago
14

A) In a group of 60 students, 15 liked maths only, 20 liked science only and 5 did not like

Mathematics
1 answer:
Paladinen [302]2 years ago
3 0

Part (i)

We have 60 students total, and 5 didn't like any of the two subjects, so that must mean 60-5 = 55 students liked at least one subject.

<h3>Answer: 55</h3>

=========================================================

Part (ii)

We have 15 who like math only, 20 who like science only, and 55 who like either (or both). Let x be the number of people who like both classes.

We can then say

15+20+x = 55

x+35 = 55

x = 55-35

x = 20

This means 20 people liked both subjects

<h3>Answer: 20</h3>

=========================================================

Part (iii)

There are 15 people who like math only, and 20 who like both. Therefore, there are 15+20 = 35 people who like math (and some of these people also like science)

<h3>Answer: 35</h3>

=========================================================

Part (iv)

We'll follow the same idea as the previous part. There are 20 people who like science only and 20 who like both subjects. That yields 40 people total who like science (and some of these people also like math).

<h3>Answer: 40</h3>

=========================================================

Part (v)

We'll draw a rectangle to represent the entire group of 60 students. This is considered the universal set. Inside the rectangle will be two overlapping circles to represent math (M) and science (S).

We'll have 15 go in circle M, but outside circle S to represent the 15 people who like math only. Then we have 20 go in circle S but outside circle M to show the 20 people who like science only. We have another copy of 20 go in the overlapped region between the circles. This is the 20 people who like both classes. And finally, we have 5 go outside both circles, but inside the rectangle. These are the 5 people who don't like either subject.

Note how all of the values in the diagram add up to 60

15+20+20+5 = 60

This helps confirm we have the correct values.

<h3>Answer: See the venn diagram below</h3>

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75+12.55 = 100 +105. <br><br> I need the Asnwer
kolezko [41]

Step-by-step explanation:

Add 75 to 12.55. the answer would be 87.55.

100+105=205

205-87.55=117.45

5 0
2 years ago
What is the value of a in the equation 5a -10b = 45 when b = 3
leva [86]
Salutations!

5a-10b = 45

value of b = 3

Multiply 10 and 3

10*3=30

Now, you can solve the equation --

5a-30=45

separate the variables aside, and the numbers aside.

5a=45 +30

5a=75

a=75/5

a=15

Hope I helped (:

Have a great day!
6 0
2 years ago
A pentagonal prism is cut be a plane perpendicular to the base . What is the shape of the cross section that is formed?
Allisa [31]

Answer:

Step-by-step explanation:

The cross section will have the same shape as the base of the pentagonal prism; the dimensions will be proportionally smaller.

3 0
3 years ago
I need the whole solution
ddd [48]

Confused what the question is. Are you looking for the product or the zeroes?

If you are looking for the product, then:

Use foil to get: sec²(1) - sec²(-csc²) -1(1) -1(-csc²)

= sec² + sec²csc² - 1 + csc²

= sec²csc² + sec² + csc² - 1

= sec²csc² + 1 - 1 (NOTE: sec² + csc² = 1 is an identity)

= sec²csc²

Answer: sec²csc²

***************************************************

If you are looking for the zeroes, then:

Using the zero product property, set each factor equal to zero and solve.

<u>First factor:</u>

sec²Θ - 1 = 0

sec²Θ = 1

secΘ = 1, -1

remember that secΘ is \frac{1}{cos}

\frac{1}{cos} = 1 \frac{1}{cos} = -1

cross multiply to get:

cosΘ = 1 cosΘ = -1

use the unit circle (or a calculator) to find that Θ = 0 and π

<u>Second factor:</u>

1 - csc²Θ = 0

1 = csc²Θ

1, -1 = cscΘ

remember that cscΘ is \frac{1}{sin}

\frac{1}{sin} = 1 \frac{1}{sin} = -1

cross multiply to get:

sinΘ = 1 sinΘ = -1

use the unit circle (or a calculator) to find that Θ = \frac{\pi}{2} and \frac{3\pi}{2}

Answer: 0, π, \frac{\pi}{2} , \frac{3\pi}{2}

7 0
3 years ago
HI can someone do these 5 problems? it will really help me out I'll give out brainliest to the person who answers them. (No link
Softa [21]

Answer:

$73.60

$345

simple interest = amount deposited x time x interest rate

600 + (600 x 0.055 x 5) = $765

600 + (600 x 0.055 x 5) > $2000

$765  $2000

He would not have $2000 in 5 years

Step-by-step explanation:

Total cost of items purchased = $75 + (2 x $8.50) = 92

If there is a 20% discount, he would pay (100 - 20%) 80% of the total cost =

0.8 x $92 = $73.60

commission earned = percentage commission x amount of sales

10% x $3450

= 0.1 x 3450 = 345

Amount he would have in his account = amount deposited + simple interest

simple interest = amount deposited x time x interest rate

600 x 0.055 x 5 = $165

Amount in his account in 5 years = $165 + 600 = $765

He would have less than $2000 in his account. he would have $765

4 0
2 years ago
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