J maths 18

In the figure below,
\[
MX = 8 \, \text{cm}, \quad XN = 12 \, \text{cm}, \quad NZ = 4 \, \text{cm}, \quad \angle XMN = \angle XZN
\]
Calculate \(YM\).

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

The table below shows the frequency of children of age \(x\) years in a hospital:

\[
\begin{array}{|c|c|c|c|c|c|c|c|c|}
\hline
x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\
\hline
f & 3 & 4 & 5 & 6 & 7 & 6 & 5 & 4 \\
\hline
\end{array}
\]

Find the equation of the tangent at the point (2,0) to the curve y = x² - 2x

Calculate the area of an equilateral triangle of side 8cm

Evaluate:

\[
\int_{1}^{2} \frac{5}{x} \, dx
\]

Evaluate:

\[
\log_{2} 8 \;-\; \log_{3} \frac{1}{9}
\]

If y = 23_five + 101_three,find y leaving your answer in base two.

What is the loci of a distance 4cm from a given point P?

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

(0.00256×0.0064)/(0.025×0.08)

Use the quadratic equation curve to answer this questions
What is the minimum value of the graph?

Two sisters, Taiwo and Kehinde, own a store. The ratio of Taiwo's share to Kehinde's is 11:9. Later Kehinde sells ⅔ of her share to Taiwo for ₦720.00. Find the value of the store

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?

Using the cumulative frequency curve, estimate the median of the data represented on the graph.

Convert 0.04945 to two significant figures

Approximate 0.9875 to 1 decimal place.

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.

A box contains two red balls and four blue balls. A ball is drawn at random from the box and then replaced before a second ball is drawn. Find the probability of drawing two red balls.

Which one of the following gives the members of the set A1∩ B ∩ C?

Evaluate (2√3 - 4) (2√3 + 4)

Tanθ is positive and Sinθ is negative. In which quadrant does θ lies

A man's initial salary is ₦540.00 a month and increases after each period of six months by ₦36.00 a month. Find his salary in the eight month of the third year.

If
\[
p = \left( \frac{Q(R - T)}{15} \right)^{\tfrac{1}{3}},
\]
make \(T\) the subject of the relation.

Express 495g as a percentage of 16.5kg

Find the average of the first four prime numbers greater than 10

Integrate the expression 6x² - 2x+1

Given that
\[
\sin(5x - 28)^\circ = \cos(3x - 50)^\circ,\quad 0 < x < 90^\circ,
\]
find the value of \(x\).

A man stands on a tree 150cm high and sees a boat at an angle of depression of 74 degrees. Find the distance of the boat from the base of the tree.

Use the cumulative frequency curve to answer the question.

What is the 80th percentile?

Calculate 243_six - 243_five expressing your answer in base 10.

Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

How many times, correct to the nearest whole number, will a man run round a circular track of diameter 100m to cover a distance of 1000m?

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

In how many ways can the letters LEADER be arranged?

Simplify
\[
25^{\tfrac{1}{2}} \times 8^{-\tfrac{2}{3}}
\]

Add 54_eight and 67_eight giving your answers in base eight.

The figure below is a Venn diagram showing the elements arranged within sets A, B, C, ϵ. Use the figure to answer this question
What is n(A U B)^c ?

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?

Use the table to answer the question below:What is the modal age?