The mean length of the sides of a triangular plot of land is 18 yards.

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

Paladinen [302]

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>

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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>

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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>

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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>

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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>

3 0

3 years ago

HELP ASAP TIMED !!!! What is the exact value of cos(c + d), given Sine c = StartFraction 24 Over 25 EndFraction for c in Quadran

Keith_Richards [23]

9514 1404 393

Answer:

D

Step-by-step explanation:

In the second quadrant, ...

c = 180° -arcsin(24/25) ≈ 106.26°

In the third quadrant, ...

d = 360° -arccos(-3/4) ≈ 221.41°

Then cos(c+d) = cos(327.67°) ≈ 0.84498

This is a positive irrational number, greater than 21/100, so the only reasonable choice is the last one:

$\dfrac{21+24\sqrt{7}}{100}\approx 0.84498$

_____

Perhaps you want to work this out using the trig identities.

cos(c) = -√(1 -sin(c)²) = -7/25

sin(d) = -√(1 -cos(d)²) = -(√7)/4

Then the desired cosine is ...

cos(c+d) = cos(c)cos(d) -sin(c)sin(d)

cos(c+d) = (-7/25)(-3/4) -(24/25)(-√7/4)

cos(c+d) = (21 +24√7)/100 . . . . matches choice D

8 0

2 years ago

Joshua is planning a 1020-mile driving trip. His car gets an average of 30 mpg, and the cost of gas is about $4.06/gallon. What

dolphi86 [110]

30 miles for a single gallon.
first we find out how many gallons would be used.
number of gallons = 1020/30
gallons = 34.
and since 1 gallon costs $4.06
34 gallons would cost = 34 x 4.06 = $138.04

4 0

3 years ago

Read 2 more answers

The hypotenuse of a right triangle has endpoints A(4, 1) and B(–1, –2). On a coordinate plane, line A B has points (4, 1) and (n

GarryVolchara [31]

Answer:

$(-1,1),(4,-2)$

Step-by-step explanation:

Given: The hypotenuse of a right triangle has endpoints A(4, 1) and B(–1, –2).

To find: coordinates of vertex of the right angle

Solution:

Let C be point $(x,y)$

Distance between points $(x_1,y_1),(x_2,y_2)$ is given by $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$AC=\sqrt{(x-4)^2+(y-1)^2}\\BC=\sqrt{(x+1)^2+(y+2)^2}\\AB=\sqrt{(4+1)^2+(1+2)^2}=\sqrt{25+9}=\sqrt{34}$

ΔABC is a right angled triangle, suing Pythagoras theorem (square of hypotenuse is equal to sum of squares of base and perpendicular)

$34=\left [ (x-4)^2+(y-1)^2 \right ]+\left [ (x+1)^2+(y+2)^2 \right ]$

Put $(x,y)=(-1,1)$

$34=\left [ (-1-4)^2+(1-1)^2 \right ]+\left [ (-1+1)^2+(1+2)^2 \right ]\\34=25+9\\34=34$

which is true. So, $(-1,1)$ can be a vertex

Put $(x,y)=(4,-2)$

$34=\left [ (4-4)^2+(-2-1)^2 \right ]+\left [ (4+1)^2+(-2+2)^2 \right ]\\34=9+25\\34=34$

which is true. So, $(4,-2)$ can be a vertex

Put $(x,y)=(1,1)$

$34=\left [ (1-4)^2+(1-1)^2 \right ]+\left [ (1+1)^2+(1+2)^2 \right ]\\34=9+4+9\\34=22$

which is not true. So, $(1,1)$ cannot be a vertex

Put $(x,y)=(2,-2)$

$34=\left [ (2-4)^2+(-2-1)^2 \right ]+\left [ (2+1)^2+(-2+2)^2 \right ]\\34=4+9+9\\34=22$

which is not true. So, $(2,-2)$ cannot be a vertex

Put $(x,y)=(4,-1)$

$34=\left [ (4-4)^2+(-1-1)^2 \right ]+\left [ (4+1)^2+(-1+2)^2 \right ]\\34=4+25+1\\34=30$

which is not true. So, $(4,-1)$ cannot be a vertex

Put $(x,y)=(-1,4)$

$34=\left [ (-1-4)^2+(4-1)^2 \right ]+\left [ (-1+1)^2+(4+2)^2 \right ]\\34=25+9+36\\34=70$

which is not true. So, $(-1,4)$ cannot be a vertex

So, possible points for the vertex are $(-1,1),(4,-2)$

7 0

3 years ago

Read 2 more answers

The rectangle has an area of x to the second power plus 13x + 36 sq.Meters and a length of x + 9 meters. What expression represe

elena-s [515]

Answer: the expression for the width is x + 4

Step-by-step explanation:

The area of the rectangle is expressed as

Area = x² + 13x + 36 square meters.

The length is expressed as

L = x + 9 meters

To determine the expression for the width of the rectangle, we would factorize the expression for the area. Hence

x² + 13x + 36 = 0

We would find two numbers such that their sum or difference is 13x and their product is 36x². The two numbers are 9x and 4x. Therefore,

x² + 9x + 4x + 36 = 0

x(x + 9) + 4(x + 9) = 0

(x + 4)(x + 9)

Therefore, the expression that represents the width of the rectangle is x + 4

7 0

3 years ago