Natural numbers are numbers known as counting numbers that contain the positive integers from 1 to infinity.

Union:

Let A and B be two sets. The union of A and B is the set of all those elements which belong to either A or B or both A and B i.e A ∪ B = {x : x ∈ A or x ∈ B}

Power Set:

Let A be a set, then the set of all the possible subsets of A is called the power set of A and is denoted by P(A).

Note: If A is a finite set with m elements. Then the number of elements (cardinality) of the power set of A is given by: n (P(A)) = 2^m.

CALCULATION

Given: A = {1, 2, 5, 7} and B = {2, 4, 6}

As we know that, A ∪ B = {x : x ∈ A or x ∈ B}.

⇒ A ∪ B = {1, 2, 4, 5, 6, 7}

As we can see that, the number of elements present in A U B = 6 i.e n(A U B) = 6

As we know that, the possible subsets of A is given by 2m.

So, the number of subsets of A U B = 2⁶ = 64

Concept

Intersection:

Let A and B be two sets. The intersection of A and B is the set of all those elements which are present in both sets A and B.

The intersection of A and B is denoted by A ∩ B i.e A ∩ B = {x : x ∈ A and x ∈ B}

If A is a non-empty set such that n(A) = m then numbers of proper subsets of A is given by 2^m - 1.

Calculation

Given: A = {1, 2, 3, 4, 5, 7, 8, 9} and B = {2, 4, 6, 7, 9}

As we know that, A ∩ B = {x : x ∈ A and x ∈ B}

⇒ A ∩ B = {2, 4, 7, 9}

As we can see that,

The number of elements present in A ∩ B = 4

i.e n(A ∩ B) = 4

As we know that;

If A is a non-empty set such that n(A) = m then

The numbers of proper subsets of A are given by 2^m - 1.

So, The number of proper subsets of A ∩ B = 2⁴ - 1 = 15

The complement of set A (A') is defined as a set that contains the elements present in the universal set (U) but not in set A.

Total consumers = 1000

Consumers who like product A = 720

Consumers who like product B = 450

Let n = number of people who like both products.

The addition of all the parts on the venn diagram should give the number of the universal set (u)

To get those who like only one product, subtract the number of people who like both products from the total number of people who like a particular product.

People who like only product A = 720 - n

People who like only product B = 450 - n

(720 - n) + n + (450 - n) = 1000

Solve for the value of n

720 - n + n + 450 - n = 1000

1170 - n = 1000

1170 - 1000 = n

170 = n

∴ 170 consumers like both the products A and B

Concept:

Equivalent set: Two sets A and B are said to be equivalent if they have the same number of elements (cardinality), regardless of what the elements are. , i.e n(A) = n(B).

Equal set: Two sets A and B are said to be equal if they have exactly the same elements. The repetition of elements does not matter in sets because a set is defined as a collection of distinct objects, so repeated elements are generally ignored.

If A = B, then n(A) = n(B) and for any x ∈ A, x ∈ B too.

Calculation

From the definition of equivalent and equal set we can see that;

Statement I is true because the number of elements in A = Number of elements in B = 3

Statement II is true because {1, 5, 9} ∈ A and {1, 5, 9} ∈ B

Total Cost = cost per card x Total number of cards

Total cost = ₵2.0645 x 400 = ₵825.80

Calculation

2.⌒0⌒6⌒4⌒5 = 20645 x 10^-4

400 = 400.0 = 4⌒0⌒0.0 = 4.0 x 10²

2.0645 x 400 = 20645 x 10^-4 x 4 x 10² = 20645 x 4 x 10^-4 x 10²

Applying law of multiplication of indices

a^m x aⁿ = a^m+n

20645 x 4 x 10^-4 x 10² = 20645 x 4 x 10^-4+2 = 20645 x 4 x 10^-2

20645 x 4

20645 x 4 x 10^-2 = 82580 x 10^-2 = 82580.0 x 10^-2 = 825.⌒8⌒0.0 = 825.80

Express (23 x 82) x 79 as (2.3 x 82) x 7.9

23 = 23.0 = 2.⌒3.0 = 2.3 x 10¹

79 = 79.0 = 7.⌒9.0 = 7.9 x 10¹

(23 x 82) x 79 = 148994

2.3 x 10¹ x 82 x 7.9 x 10¹ = 148994

2.3 x 82 x 7.9 x 10¹ x 10¹ = 148994

Apply the law of multiplication of indices

a^m x aⁿ = a^m+n

2.3 x 82 x 7.9 x 10¹⁺¹ = 148994

2.3 x 82 x 7.9 x 10² = 148994

Now we are to find the value of 2.3 x 82 x 7.9, hence we make it the subject

Divide both sides by 10²

$\frac{\mathrm{2.3\; x\; 82\; x\; 7.9\; x}{10}^2}{{10}^2}$ = $\frac{148994}{{10}^2}$

2.3 x 82 x 7.9 = $\frac{148994}{{10}^2}$

2.3 x 82 x 7.9 = 148994 x $\frac{1}{{10}^2}$

Apply the law of negative power in indices

Base^-Power = $\frac{1}{{\mathrm{Base}}^{\mathrm{Power}}}$

$\frac{1}{{10}^2}$ = 10^-2

2.3 x 82 x 7.9 = 148994 x 10^-2

148994 = 148994.0

148994 x 10^-2 = 148994.0 x 10^-2 = 1489.⌒9⌒4.0 = 1489.94

2.3 x 82 x 7.9 = 1489.94

The equation is the same as 3.14 x 18 x 17.5 = 3.14 x 3a x 17.5

Since 3.14 and 17.5 are at both sides of the equation, then 18 = 3a

You can as well divide both sides of the equation by (3.14 x 17.5) and you will still arrive at 18 = 3a

Now solve for a by dividing both sides by 3

$\frac{18}{3}$ = $\frac{\mathrm{3a}}{3}$

6 = a

Since the oranges are shared equally, you have to divide 26039 by 13 to get how many oranges each boy receive

Each will receive 2003

Given that, Diameter, AD = 34 cm.

Chord, AB = 30 cm.

Hence, the radius of the circle, OA = 17 cm

Now, consider the figure.

From the centre "O". OM is perpendicular to the chord AB.

(i.e) OM ⊥ AM

AM = $\frac{1}{2}$AB

AM = $\frac{1}{2}$(30) = 15 cm

Now by using the Pythagoras theorem in the right triangle AOM,

AO² = OM² + AM²

OM² = AO²– AM²

OM²= 17² – 15²

OM² = 289 - 225

OM² = 64

OM = √64

OM = 8 cm

Step 1

Weight of meat = $\frac{4}{5}$ x 1 kilo = $\frac{4}{5}$

Number of containers = 3

Step 2

Weight of meat in one container = $\frac{4}{5}$ ÷ 3 = $\frac{4}{5}$ ÷ $\frac{3}{1}$ =$\frac{4}{5}$ × $\frac{1}{3}$ = $\frac{\mathrm{4\; x\; 1}}{\mathrm{5\; x\; 3}}$ = $\frac{4}{15}$ kilos

Step 1

Number of bags for each batch = $\frac{1}{8}$

Number of bags used = $\frac{3}{4}$

Step 2

Apply the concept of division of fraction.

$\frac{a}{b}$ ÷ $\frac{c}{d}$ = $\frac{a}{b}$ x $\frac{d}{c}$

Number of batches of cookies prepared = $\frac{3}{4}$ ÷ $\frac{1}{8}$ =$\frac{3}{4}$ × $\frac{8}{1}$ = $\frac{3}{1}$ × $\frac{2}{1}$ = $\frac{\mathrm{3\; x\; 2}}{\mathrm{1\; x\; 1}}$ = $\frac{6}{1}$ = 6 batches

Step 1

Change the decimal to fraction

Count how many times you have to move the decimal point to get a whole number.

Multiply the whole number by 10^{-No. of counts}

Change the 10^{-No. of counts} to division by applying the law of indices

Base^-Power = $\frac{1}{{Base}^{Power}}$

0.32 = 0.⌒3⌒2 = 32 x 10^-2 = $\frac{32}{{10}^2}$ = $\frac{32}{100}$

Change percentage to fraction

27% = $\frac{27}{100}$

Step 2

The L.C.M of the denominators 100, 5 and 3 is 300

Find their equivalent fraction having the denominator of the L.C.M

100 will divide 300, 3 times. Hence we have to multiply both the numerator and the denominator by 3 for the fractions with the 100 denominator.

5 will divide 300, 60 times. Hence we have to multiply both the numerator and the denominator by 60 for the fraction with the 5 denominator.

3 will divide 300, 100 times. Hence we have to multiply both the numerator and the denominator by 100 for the fraction with the 3 denominator.

$\frac{32}{100}$ = $\frac{\mathrm{32\; x\; 3}}{\mathrm{100\; x\; 3}}$ = $\frac{96}{300}$

$\frac{2}{5}$ = $\frac{\mathrm{2\; x\; 60}}{\mathrm{5\; x\; 60}}$ = $\frac{120}{300}$

$\frac{27}{100}$ = $\frac{\mathrm{27\; x\; 3}}{\mathrm{100\; x\; 3}}$ = $\frac{81}{300}$

$\frac{1}{3}$ = $\frac{\mathrm{1\; x\; 100}}{\mathrm{3\; x\; 100}}$ = $\frac{100}{300}$

Step 3

Arrange the equivalent fractions in descending order.

Decending means from the highest to the lowest.

Since the denominator of the equivalent fractions are the same, we compare the fractions by the numerators.

$\frac{120}{300}$,$\frac{100}{300}$,$\frac{96}{300}$,$\frac{81}{300}$

Step 4

Replace the equivalent fractions by their original fractions or decimal or percentage.

$\frac{120}{300}$,$\frac{100}{300}$,$\frac{96}{300}$,$\frac{81}{300}$ = $\frac{2}{5}$,$\frac{1}{3}$,0.32,27%

Step 1

Change the ratio to fraction

8:12 = $\frac{8}{12}$

y:9 = $\frac{y}{9}$

Step 2

Since ratios are equivalent, the values are the same. Hence you can equate both fractions and solve for the value of y.

$\frac{8}{12}$ = $\frac{y}{9}$

Get rid of the denominators by multiplying both sides of the equation by the L.C.M of the denominators or the multiplication of the denominators or by cross multiplying.

(12 x 9) x $\frac{8}{12}$ = (12 x 9) x $\frac{y}{9}$ = 9 x 8 = 12 x y

Step 3

Divide both sides by the one multiplying the value you are solving for (y).

$\frac{\mathrm{9\; x\; 8}}{12}$ = $\frac{\mathrm{12\; x\; y}}{12}$

3 x 2 = y

y = 6

NOTE: 3 divides 9, 3 times and 12, 4 times. 4 also divides 8, 2 times and itself 1 time.

Step 1

Change the decimal to fraction.

Count how many times you have to move the decimal point to get a whole number.

Multiply the whole number by 10^{-No. of counts}

Change the 10^{-No. of counts} to division by applying the law of indices

Base^-Power = $\frac{1}{{Base}^{Power}}$

0.125 = 0.⌒1⌒2⌒5 = 125 x 10^-3 = $\frac{125}{{10}^3}$ = $\frac{125}{1000}$ = $\frac{1}{8}$

NOTE: 125 divides 1000, 8 times.

Alternatively

You can cancel with smaller numbers

Step 1

Cancel with 25

25 divides 125, 5 times and 1000, 40 times

Step 2

Cancel with 5

5 divides itself, 1 and 40, 8 times

$\frac{5}{40}$ = $\frac{1}{8}$

20% were eaten

Number/Amount = $\frac{Percentage}{100}$ x Total Number/Amount

Total oranges = 100

Number of oranges eaten = $\frac{20}{100}$ x 100 oranges = 20 oranges

Number of oranges left = 100 oranges - 20 eaten oranges = 80

20% of the remaining were spoiled

Number of spoiled oranges = $\frac{20}{100}$ x 80 oranges = 16 oranges spoiled

Oranges left = 80 oranges - Spoiled oranges = 80 - 16 = 64 oranges

Of means multiplication

Percentage means over 100

25% of 75 kg = $\frac{25}{100}$ x 75 kg = 18.75 kg

25 divides itself, 1 time and 100, 4 times

$\frac{75}{4}$ = 18.75

Percentage = $\frac{\mathrm{Number/Amount}}{\mathrm{Total}}$ x 100%

Number of increment = 2800000 - 2000000 = 800000

Percentage of increment = $\frac{Number\; of\; increment}{Total\; Population}$ x 100%

Percentage of increment = $\frac{800000}{2000000}$ x 100% = 40%

Step 1

Apply BODMAS

BODMAS is an acronym to help students to remember the order of mathematical operations.

Bodmas stands for B-Brackets, O-Orders (powers/indices or roots), D-Division, M-Multiplication, A-Addition, S-Subtraction.

Simplify the bracket first.

Apply the concept of division of fraction.

$\frac{a}{b}$ ÷ $\frac{c}{d}$ = $\frac{a}{b}$ x $\frac{d}{c}$

$\frac{1}{4}$ ÷ $\frac{1}{2}$ = $\frac{1}{4}$ x $\frac{2}{1}$ = $\frac{\mathrm{1\; x\; 2}}{\mathrm{4\; x\; 1}}$ = $\frac{1}{2}$

Step 2

Change the mixed fraction to improper fraction.

C$\frac{a}{b}$ = $\frac{b\; x\; C\; +\; a}{b}$

7$\frac{1}{2}$ = $\frac{\mathrm{2\; x\; 7\; +\; 1}}{2}$ = $\frac{\mathrm{14\; +\; 1}}{2}$ = $\frac{15}{2}$

7$\frac{1}{2}$ x ($\frac{1}{4}$ ÷ $\frac{1}{2}$) - $\frac{1}{4}$ = $\frac{15}{2}$ x $\frac{1}{2}$ - $\frac{1}{4}$

From BODMAS, multiplication comes first.

$\frac{15}{2}$ x $\frac{1}{2}$ - $\frac{1}{4}$ = $\frac{\mathrm{15\; x\; 1}}{\mathrm{2\; x\; 2}}$ - $\frac{1}{4}$ = $\frac{15}{4}$ - $\frac{1}{4}$ = $\frac{\mathrm{15\; -\; 1}}{4}$ = $\frac{14}{4}$ = $\frac{7}{2}$

Step 1

Change the decimals to whole number x 10^{-No. of movement counts}

64.⌒5 = 645 x 10^-1

0.⌒0⌒1⌒5 = 15 x 10^-3

Step 2

Divide and simplify.

$\frac{645\; x{10}^{-1}}{15\; x{10}^{-3}}$

Apply law of indices for the indices

$\frac{645\; x{10}^{-1}}{15\; x{10}^{-3}}$ = 43 x 10^-1-(-3) = 43 x 10^-1+3 = 43 x 10²

Step 3

Change to standard form.

For standard form, the decimal point must be after the first non-zero digit.

43 = 4⌒3.0 = 4.3 x 10 = 4.3 x 10¹

43 x 10² = 4.3 x 10¹ x 10² = 4.3 x 10¹⁺² = 4.3 x 10³

The distance from the centre of a circle to any point on it is called a radius

Prime factors of 30

$$\begin{array}{cc}2& 30\\ 3& 15\\ 5& 5\\ & 1\end{array}$$

Prime factors of 30 = 2 x 3 x 5

Q = {2, 3, 5}

7 is the second digit after the decimal point.

The second digit after the decimal point is hundredth.

Summation of all fraction parts should give the whole (1)

When you sum known fractions and you subtract the result from 1, you will get the rest of the fraction.

Total known fraction spent = $\frac{1}{5}$ + $\frac{4}{7}$ = $\frac{\mathrm{7\; x\; 1\; +\; 5\; x\; 4}}{35}$ = $\frac{\mathrm{7\; +\; 20}}{35}$ = $\frac{27}{35}$

Fraction spent on Gari = 1 - $\frac{27}{35}$

Every number is divisible by 1.

1 = $\frac{1}{1}$

Fraction spent on Gari = 1 - $\frac{27}{35}$ = $\frac{1}{1}$ - $\frac{27}{35}$ = $\frac{\mathrm{35\; x\; 1\; -\; 1\; x\; 27}}{35}$ = $\frac{\mathrm{35\; -\; 27}}{35}$ = $\frac{8}{35}$

Total Amount = Principal Amount + Simple Interest

Simple Interest = $\frac{Principal\; x\; Time\; x\; Rate}{100}$

Change the mixed fraction to improper fraction.

1$\frac{1}{2}$ = $\frac{\mathrm{2\; x\; 1\; +\; 1}}{2}$ = $\frac{\mathrm{2\; +\; 1}}{2}$ = $\frac{3}{2}$

Principal = GH₵800.00
Time = $\frac{3}{2}$
Rate = 5

Simple Interest = $\frac{\mathrm{800\; x}\frac{3}{2}x5}{100}$ = $\frac{\mathrm{400\; x\; 3\; x\; 5}}{100}$ = 4 x 3 x 5 = 60

Total Amount = 800 + 60 = GH₵860.00

Area of a circle = π x radius x radius = πr²

Step 1

Find the radius

Circumference = 2 x π x radius = 2πr

Substitute the circumference into the equation and solve for the radius.

440 = 2 x $\frac{22}{7}$ x r

440 = $\frac{\mathrm{44r}}{7}$

Multiply both sides of the equation by 7

7 x 440 = 44r

Divide both sides of the equation by 44

$\frac{\mathrm{7\; x\; 440}}{44}$ = $\frac{\mathrm{44r}}{44}$

7 x 10 = r

r = 70

Step 2

Calculate for the area

Area of a circle = π x radius x radius = πr²

Area of the circle = $\frac{22}{7}$ x 70 x 70 = 22 x 10 x 70 = 22 x 7 x 100 = 15400 m²

Express the 1000 as base 10 and compare the powers.

1000 = 10 x 10 x 10 = 10³

10^x = 10³

Since the bases are the same, the powers are also the same.

x = 3

-- = +
-(-) = - x - = +
+- = -

53-(-7)+(-15) = 53 + 7 - 15 = 60 - 15 = 45

2114_five = 2 x 5³ + 1 x 5² + 1 x 5¹ + 4 x 5⁰

2114_five = 2 x 125 + 1 x 25 + 1 x 5 + 4 x 1

2114_five = 250 + 25 + 5 + 4

2114_five = 284

Perimeter of a shape is the sum (addition) of all the sides of the shape.

Perimeter of a rectangle = Length + Length + Width + Width

Let w = width of the rectangle

Perimeter = 48
Length = 14

48 = 14 + 14 + w + w

48 = 28 + 2w

48 - 28 = 2w

20 = 2w

Divide both sides by 2

$\frac{20}{2}$ = $\frac{\mathrm{2w}}{2}$

10 = w

Width = 10 cm

Concepts

a$\left(\begin{array}{c}\mathrm{b}\\ \mathrm{c}\end{array}\right)$ = $\left(\begin{array}{c}\mathrm{a\; x\; b}\\ \mathrm{a\; x\; c}\end{array}\right)$

$\left(\begin{array}{c}\mathrm{a}\\ \mathrm{b}\end{array}\right)$ + $\left(\begin{array}{c}\mathrm{c}\\ \mathrm{d}\end{array}\right)$ = $\left(\begin{array}{c}\mathrm{a\; +\; c}\\ \mathrm{b\; +\; d}\end{array}\right)$

$\left(\begin{array}{c}\mathrm{a}\\ \mathrm{b}\end{array}\right)$ - $\left(\begin{array}{c}\mathrm{c}\\ \mathrm{d}\end{array}\right)$ = $\left(\begin{array}{c}\mathrm{a\; -\; c}\\ \mathrm{b\; -\; d}\end{array}\right)$

s = $\left(\begin{array}{c}-2\\ 5\end{array}\right)$

2r = 2$\left(\begin{array}{c}2\\ -5\end{array}\right)$ = $\left(\begin{array}{c}\mathrm{2\; x\; 2}\\ \mathrm{2\; x\; -5}\end{array}\right)$ = $\left(\begin{array}{c}4\\ -10\end{array}\right)$

3s = 3$\left(\begin{array}{c}-2\\ 5\end{array}\right)$ = $\left(\begin{array}{c}\mathrm{3\; x\; -2}\\ \mathrm{3\; x\; 5}\end{array}\right)$ = $\left(\begin{array}{c}-6\\ 15\end{array}\right)$

2r - 3s = $\left(\begin{array}{c}4\\ -10\end{array}\right)$ - $\left(\begin{array}{c}-6\\ 15\end{array}\right)$ = $\left(\begin{array}{c}\mathrm{4\; -\; (-6)}\\ \mathrm{-10\; -\; 15}\end{array}\right)$ = $\left(\begin{array}{c}\mathrm{4+6}\\ -25\end{array}\right)$ = $\left(\begin{array}{c}10\\ -25\end{array}\right)$

Probability = $\frac{\mathrm{Number\; of\; selection}}{\mathrm{Total\; Sample}}$

Total balls = 10 red balls + 15 green balls = 25 balls

Probability = $\frac{10}{25}$ = $\frac{2}{5}$

θ = 180 - $\frac{360}{\mathrm{n}}$

Step 1

Move - $\frac{360}{\mathrm{n}}$ to the left so that expression becomes positive for easy simplification of n

θ + $\frac{360}{\mathrm{n}}$ = 180

Step 2

Move θ to the other side of the equation. It is positive and when it moves to the other side, becomes negative.

$\frac{360}{\mathrm{n}}$ = 180 - θ

Step 3

Get rid of the fraction by multiplying both sides of the equation by n

n x $\frac{360}{\mathrm{n}}$ = n x (180 - θ)

360 = n x (180 - θ)

Step 4

Divide both sides of the equation by (180 - θ)

$\frac{360}{\mathrm{180\; -\; \theta }}$ = $\frac{\mathrm{n\; x\; (180\; -\; \theta )}}{\mathrm{(180\; -\; \theta )}}$

$\frac{360}{\mathrm{180\; -\; \theta }}$ = n

n = $\frac{360}{\mathrm{180\; -\; \theta }}$

Substitute the values into the equation and simplify. Square is the multiplication of the number by itself. d² = d x d

8h = 8 x h

R = $\frac{\mathrm{h}}{2}$ + $\frac{d^2}{\mathrm{8h}}$ = $\frac{\mathrm{h}}{2}$ + $\frac{\mathrm{d\; x\; d}}{\mathrm{8\; x\; h}}$

R = $\frac{6}{2}$ + $\frac{8^2}{\mathrm{8\; x\; 6}}$

R = 3 + $\frac{\mathrm{8\; x\; 8}}{\mathrm{8\; x\; 6}}$ = 3 + $\frac{8}{6}$ = 3 + $\frac{4}{3}$

$\frac{4}{3}$ = 1$\frac{1}{3}$

3 + $\frac{4}{3}$ = 3 + 1$\frac{1}{3}$ = 4$\frac{1}{3}$

NOTE: You can add the whole number part of a fraction to other whole numbers and put the fraction together

Area of a trapezium = $\frac{1}{2}$ (a+b)h

h = 6 cm
a = 12 cm
b = 18 cm

Area of a trapezium = $\frac{1}{2}$ (12+18)6 = 30 x 3 = 90 cm²

Step 1

Find the prime factors.

Prime factors of 18

$$\begin{array}{cc}2& 18\\ 3& 9\\ 3& 3\\ & 1\end{array}$$

Prime factors = 2 x 3 x 3 = 2 x 3²

Prime factors of 36

$$\begin{array}{cc}2& 36\\ 2& 18\\ 3& 9\\ 3& 3\\ & 1\end{array}$$

Prime factors = 2 x 2 x 3 x 3 = 2² x 3²

Find the prime factors of 60

$$\begin{array}{cc}2& 60\\ 2& 30\\ 3& 15\\ 5& 5\\ & 1\end{array}$$

Prime factors of 60 = 2 x 2 x 3 x 5 = 2² x 3 x 5

Step 2

Locate the common prime factors and multiply them in their lowest powers.

Common prime factors are 2 and 3

H.C.F = 2 x 3

Step 1

Find the prime factors

Prime factors of 10

$$\begin{array}{cc}2& 10\\ 5& 5\\ & 1\end{array}$$

Prime factors = 2 x 5

Prime factors of 12

$$\begin{array}{cc}2& 12\\ 2& 6\\ 3& 3\\ & 1\end{array}$$

Prime factors = 2 x 2 x 3 = 2² x 3

Prime factors of 25

$$\begin{array}{cc}5& 25\\ 5& 5\\ & 1\end{array}$$

Prime factors = 5 x 5 = 5²

Step 2

The least common multiple is the product (multiplication) of each of the prime factors in their highest powers.

L.C.M of 10,12 and 25 = 2² x 3 x 5² = 4 x 3 x 25 = 12 x 25 = 300

The significant figures are 3,8,5 and 8

The third significant figure is 5

The next digit after the third significant figure is 8, which is more than 5, hence we add 1 to 5 making 1+5 = 6

0.003858 to three significant figures is 0.00386

Concept

Sum of angles on a straight line sums up to 180^o

Sum of angles in a triangle sums up to 180^o

120 + RSQ = 180

RSQ = 180 - 120 = 60

QRS + RSQ + RQS = 180

50 + 60 + RQS = 180

110 + RQS = 180

RQS = 180 - 110 = 70^o