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**Question 1**
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Use the cumulative frequency curve to answer the question.

Estimate the median of the date represented on the graph.

**Question 2**
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Tossing a coin and rolling a die are two separate events. What is the probability of obtaining a tail on the coin and an even number on the die?

**Answer Details**

The probability of obtaining a tail on a coin is 1/2 since there are two possible outcomes (either a head or a tail) and they are equally likely. The probability of obtaining an even number on a die is 3/6 or 1/2 since there are three even numbers (2, 4, 6) and six possible outcomes (1, 2, 3, 4, 5, 6) and they are equally likely. Since the events of obtaining a tail on the coin and an even number on the die are independent (i.e., the outcome of one event does not affect the outcome of the other), we can multiply their probabilities to find the probability of obtaining both: P(tail and even) = P(tail) x P(even) = (1/2) x (1/2) = 1/4 Therefore, the probability of obtaining a tail on the coin and an even number on the die is 1/4 or 0.25.

**Question 3**
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if y = 23five $five$ + 101three $three$ find y leaving your answer in base two

**Answer Details**

First we convert the numbers to base ten

23five
$five$= 2 x 51 + 3 x 50

= 10 + 3 = 13

101five
$five$ = (1 x 32) + (0 x 31) + (1 x 30)

= 9 + 0 + 1 = 10

So, y = 13 + 10 = 23

To convert 23 to base 2 (as in the diagram above)

y = 23

= 10111five

**Question 4**
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Evaluate ∫21 $12$ 5x $\frac{5}{x}$ dx

**Answer Details**

∫5x
$\frac{5}{x}$ dx = 5 ∫1x
$\frac{1}{x}$ = 5Inx

Since the integral of 1x
$\frac{1}{x}$ is Inx

∫2
$2$ 1
$1$∫ 5x
$\frac{5}{x}$ dx = 5

dx = 5 (In<2 – InIn1)

= 3.4657

= 3.47

**Question 5**
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The figure below is a Venn diagram showing the elements arranged within sets A, B, C, ϵ $\u03f5$.

Use the figure to answer this question

What is n(A U B)c ?

**Answer Details**

A = (p, q, r, t, u, v)

B = (r, s, t, u)

A U B = Elements in both A and B = (p, q, r, s, t, u, v)

(A U B)1 = elements in the universal set E but not in (A U B)= (w, x, y, z)

n(A U B) 1 = number of the elements in (A U B)1 = 4

**Question 6**
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0.00256×0.00640.025×0.08

**Answer Details**

0.00256×0.00640.025×0.08
$\frac{{\textstyle 0.00256\times 0.0064}}{{\textstyle 0.025\times 0.08}}$

=0.0000163840.002 $=\frac{{\textstyle 0.000016384}}{{\textstyle 0.002}}$

=0.008192

=0.0000163840.002 $=\frac{{\textstyle 0.000016384}}{{\textstyle 0.002}}$

=0.008192

**Question 7**
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The pie chart shows the monthly expenditure of a public servant. The monthly expenditure on housing is twice that of school fees. How much does the worker spend on housing if his monthly income is ₦7200?

**Answer Details**

Let the monthly expenditure angle for school fees is x, then that of housing will be 2x. Since the total angle in the circle is 360.

Using 90 as the angle for transport

So, x + 2x + 120 + 90 = 360

3x + 210 = 3605

3x = 360 - 210

= 150

x = 1503
$\frac{150}{3}$ = 50

So the angle for housing is 2x = 2 × 50

= 100

Amount spent on housing = 100360
$\frac{100}{360}$ × 7200

= ₦2000

**Question 8**
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Use the quadratic equation curve to answer this question.

What is the 80th percentile?

**Answer Details**

The minimum value is the lowest value of the curve on y axis which gives a value of -5.3.

**Question 9**
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Given that sin (5x $x$ − 28)o $o$ = cos(3x $x$ − 50)o $o$, Ox $x$ < 90o $o$

Find the value of x

**Answer Details**

Sin(5x - 28) = Cos(3x - 50)………..i

But Sinα = Cos(90 - α)

So Sin(5x - 28) = Cos(90 - [5x - 28])

Sin(5x - 28) = Cos(90 - 5x + 28)

Sin(5x - 28) = Cos(118 - 5x)………ii

Combining i and ii

Cos(3x - 50) = Cos(118 - 5x)

3x - 50 = 118 - 5x

Collecting the like terms

3x + 5x = 118 + 50

8x = 168

x = 1688
$\frac{168}{8}$

x = 21o

**Question 10**
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The table below shows the frequency of children of age x years in a hospital:

x | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |

f | 3 | 4 | 5 | 6 | 7 | 6 | 5 | 4 |

Use the table to answer the question below:

How many children are in the hospital

**Answer Details**

To answer this question, we need to add up the frequency of children in each age category. Looking at the table, we can see that there are 3 children aged 1, 4 children aged 2, 5 children aged 3, 6 children aged 4, 7 children aged 5, 6 children aged 6, 5 children aged 7, and 4 children aged 8. We can add up these numbers to find the total number of children in the hospital: 3 + 4 + 5 + 6 + 7 + 6 + 5 + 4 = 40 Therefore, there are 40 children in the hospital. The correct answer is.

**Question 11**
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Express 495g as a percentage of 16.5kg

**Answer Details**

To express 495g as a percentage of 16.5kg, we need to convert both values to the same units of measurement, such as grams or kilograms. We can convert 16.5kg to grams by multiplying by 1000: 16.5kg x 1000 = 16500g Now we can express 495g as a percentage of 16500g: 495g / 16500g x 100% = 0.03 x 100% = 3% Therefore, 495g is 3% of 16.5kg. So the answer is: 3%

**Question 12**
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Which one of the following gives the members of the set Ac ∩
$\cap $ B ∩
$\cap $ C?

**Answer Details**

A1 = Elements in the universal set but not in A = {s, w, x, y, z}

B = {r, s. t, u}

C = {t, u, v, w, x}

A1 n B n C = elements common to the three sets = none = empty set = Φ

**Question 13**
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Evaluate log2 $2$ 8 – log3 $3$ 19

**Answer Details**

log2
$2$ 8 – log3
$3$ 19
$\frac{1}{9}$

= log 2
$2$ 23
$3$ – log3
$3$ 9−1
$-1$

= log2
$2$ 23
$3$ – log3
$3$ 3−2
$-2$

Based on law of logarithm

= 3 log2
$2$ 2 – (-2 log