Combine the following questions into one: 1. Work out: 5/7 − 3/7 2. Given that set Q = prime numbers less…

Question

Combine the following questions into one: 1. Work out: 5/7 − 3/7 2. Given that set Q = prime numbers less than 10 and set R = 1, 2, 3, 4, 5. List the elements of set R-Q. 3. Solve the inequality: 2x <

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Here are the solutions to the questions:

1. Work out: $\frac{5}{7} - \frac{3}{7}$

Since the denominators are the same, subtract the numerators.
$\frac{5-3}{7}$
Simplify the numerator.
$\frac{2}{7}$
The result is $\boxed{\frac{2}{7}}$ .

2. Given that set Q = {prime numbers less than 10} and set R = {1, 2, 3, 4, 5}. List the elements of set R-Q.
List the elements of set Q.
Prime numbers less than 10 are numbers greater than 1 that are only divisible by 1 and themselves.
$Q = \{2, 3, 5, 7\}$
Identify the elements that are in set R but not in set Q.
$R = \{1, 2, 3, 4, 5\}$
Comparing R and Q, the elements in R that are not in Q are 1 and 4.
$R-Q = \{1, 4\}$
The elements of set R-Q are $\boxed{\{1, 4\}}$ .

3. Solve the inequality: $2x < -6$ .
Divide both sides of the inequality by 2.
$\frac{2x}{2} < \frac{-6}{2}$
Simplify both sides.
$x < -3$
The solution to the inequality is $\boxed{x < -3}$ .

4. Anatoli took $1\frac{1}{2}$ hours teaching a science lesson that ended at 9:45 a.m. At what time did it start?
Convert the lesson duration to minutes.
$1\frac{1}{2}$ hours = 1 hour and 30 minutes = 60 minutes + 30 minutes = 90 minutes.
Subtract the duration from the end time.
End time: 9:45 a.m.
Subtract 1 hour from 9:45 a.m. to get 8:45 a.m.
Subtract the remaining 30 minutes from 8:45 a.m. to get 8:15 a.m.
The lesson started at $\boxed{8:15 \text{ a.m.}}$ .

5. Work out the mean of 11, 15, 16 and 18.
Sum the given numbers.
$\text{Sum} = 11 + 15 + 16 + 18 = 60$
Count the number of values.
There are 4 numbers.
Calculate the mean by dividing the sum by the count.
$\text{Mean} = \frac{\text{Sum}}{\text{Count}} = \frac{60}{4} = 15$
The mean of the numbers is $\boxed{15}$ .

6. The figure below represents a roundabout in Kumi District. Find its circumference.
From the figure, the radius of the roundabout is $r = 7$ m.
Use the formula for the circumference of a circle, $C = 2\pi r$ .
We will use $\pi = \frac{22}{7}$ .
Substitute the value of the radius into the formula.
$C = 2 \times \frac{22}{7} \times 7$ $C = 2 \times 22$ $C = 44 \text{ m}$
The circumference of the roundabout is $\boxed{44 \text{ m}}$ .

Combine the following questions into one: 1. Work out: 5/7 - 3/7 2. Given that set Q = prime numbers less than 10 and set R = 1, 2, 3, 4, 5. List the elements of set R-Q. 3. Solve the inequality: 2x <

Step-by-step solution

Since the denominators are the same, subtract the numerators.

Simplify the numerator.

List the elements of set Q.

Identify the elements that are in set R but not in set Q.

Divide both sides of the inequality by 2.

Simplify both sides.

Convert the lesson duration to minutes.

Subtract the duration from the end time.

Sum the given numbers.

Count the number of values.

Calculate the mean by dividing the sum by the count.

From the figure, the radius of the roundabout is $r = 7$ m.

Use the formula for the circumference of a circle, $C = 2\pi r$ .

Substitute the value of the radius into the formula.

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