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**Question 2**
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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 3**
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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 4**
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In how many ways can the letters LEADER be arranged?

**Answer Details**

The word LEADER has 1L 2E 1A 1D and 1R making total of 6! 61!2!1!1!1!
$\frac{6}{1!2!1!1!1!}$ = 6!2!
$\frac{6!}{2!}$

= 6×5×4×3×2×12×1
$\frac{6\times 5\times 4\times 3\times 2\times 1}{2\times 1}$

= 360

**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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If P = [Q(R−T)15 $\frac{Q(R-T)}{15}$] 13 $\frac{1}{3}$ make T the subject of the relation

**Answer Details**

Taking the cube of both sides of the equation give

P3
$3$ = Q(R−T)15
$\frac{Q(R-T)}{15}$

Cross multiplying

15P3
$3$ = Q(R - T)

Divide both sides by Q

15P3Q
$\frac{15{P}^{3}}{Q}$ = R - T

Rearranging gives

T = R - 15P3Q
$\frac{15{P}^{3}}{Q}$

= RQ−15P3Q

**Question 7**
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Integrate the expression 6x2 $2$ - 2x + 1

**Answer Details**

∫6x2−2x+1=6x2+12+1−2x1+11+1+x+c
$\int 6{x}^{2}-2x+1=\frac{{\textstyle 6{x}^{2+1}}}{{\textstyle 2+1}}-\frac{{\textstyle 2{x}^{1+1}}}{{\textstyle 1+1}}+x+c$

6x33−2x22+x+c
$\frac{{\textstyle 6{x}^{3}}}{{\textstyle 3}}-\frac{{\textstyle 2{x}^{2}}}{{\textstyle 2}}+x+c$

2x3−x2+x+c

**Question 8**
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Find the equation of the line through (5,7) parallel to the line 7x + 5y = 12.

**Answer Details**

To find the equation of a line parallel to another line, we need to use the fact that parallel lines have the same slope. The given line 7x + 5y = 12 can be rearranged into slope-intercept form, which is y = (-7/5)x + (12/5), where the slope is -7/5. Since the line we want to find is parallel to this line, it must also have a slope of -7/5. We also know that the line passes through the point (5,7). To find the equation of this line, we can use the point-slope form, which is y - y1 = m(x - x1), where (x1,y1) is the given point and m is the slope. Substituting in the values we know, we get: y - 7 = (-7/5)(x - 5) Simplifying this equation, we get: y = (-7/5)x + (49/5) So the equation of the line through (5,7) parallel to the line 7x + 5y = 12 is y = (-7/5)x + (49/5), which is option (A) 5x + 7y = 20.

**Question 9**
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A room is 12m long, 9m wide and 8m high. Find the cosine of the angle which a diagonal of the room makes with the floor of the room.

**Answer Details**

a2=122+92
${a}^{2}={12}^{2}+{9}^{2}$

a=√122+92
$a=\sqrt{{12}^{2}+{9}^{2}}$

a=15 m
$a=15\text{m}$

b2=152+82
${b}^{2}={15}^{2}+{8}^{2}$

b=√152+82
$b=\sqrt{{15}^{2}+{8}^{2}}$

b=17 m
$b=17\text{m}$

cosθ=ab=1517

**Question 10**
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Two sisters, Taiwo and Kehinde, own a store. The ratio of Taiwo's share to Kehinde's is 11:9. Later Kehinde sells 23 $\frac{2}{3}$ of her share to Taiwo for ₦720.00. Find the value of the store

**Answer Details**

The problem can be solved using algebra. Let's start by assuming that Taiwo's share is 11x and Kehinde's share is 9x. Then the total value of the store is 20x. Kehinde sells 2/3 of her share to Taiwo for ₦720.00. This means that Taiwo paid ₦720.00 for 2/3 of 9x, which is (2/3) * 9x = 6x. So we have: 6x = 720 Solving for x, we get: x = 120 Now we can find the total value of the store: 20x = 20 * 120 = ₦2,400.00 Therefore, the answer is option (B), ₦2,400.00. In summary, we used algebra to solve the problem by assuming values for Taiwo's and Kehinde's shares and finding the total value of the store. Then we used the information about Kehinde's sale to find the value of x and ultimately the total value of the store.

**Question 11**
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Divide the L.C.M of 48, 64 and 80 by their H.C.F.

**Answer Details**

LCM of 80, 64, 48 = 960

HCF of 80, 64, 48 = 16

960 ÷
$\xf7$ 16 = 60

**Question 12**
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From a point P, R is 5km due West and 12km due South. Find the distance between P and R'.

**Answer Details**

To find the distance between P and R', we first need to determine the location of R'. R' is the reflection of R across the point P. Since R is 5km due West and 12km due South of P, we can draw a diagram to represent their positions.

R | | 12km | P------5km-------> | |

To find R', we draw a line that connects R and P, then draw a perpendicular bisector to that line at point P. The intersection of the perpendicular bisector and the line RP is the point R'.

R' | | | P------5km-------> | |

The distance between P and R' is the length of the line segment PR'. To find this distance, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, we have a right triangle with sides of length 5km and 12km. The hypotenuse, which is the distance between P and R', is given by:

`sqrt(5^2 + 12^2) = sqrt(169) = 13km`

Therefore, the distance between P and R' is **13km**.

**Question 13**
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Approximate 0.9875 to 1 decimal place.

**Answer Details**

9 is on one decimal place, the next number to it is 8 which will be rounded up to 1 because it is greater than 5 and then added to 9 to give 10, 10 cannot be written, it will then be rounded up to 1 and added to 0.

So the answer is 1.0

**Question 14**
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