Explanation

 We are given that 78 students represent 30% of the total number of students in the class.

Let's find the total number of students (X).

Using the percentage formula:

So, the total number of students in the class is 260

Explanation

Explanation

1 km = 0.62137119 miles

0.62137119 miles ∼ 0.62 miles

∴ 1 km = 0.62 miles

Additional Information

Miles to Kilometres = Miles × 8/5 (Approximately)

Kilometers to Miles = Km × 5/8 (Approximately)

Explanation

3x-54 = 36

3x = 90

x = 30

Explanation

Let's solve for x:

6 + 5x = 30 - x

Add x to both sides:

6 + 6x = 30

Subtract 6 from both sides:

6x = 24

Divide both sides by 6:

x = 24/6

x = 4

So, the correct answer is 4.

Explanation

A non-terminating, non-recurring decimal cannot be expressed as a fraction.

It is the key characteristic of an irrational number.

Explanation

A is 4 times as fast as B, so A's rate of work is 4 times B's rate of work.

Since A finishes the work in 45 days less than B, let's assume B takes x days to finish the work. Then A takes x - 45 days to finish the work.

Since A is 4 times as fast as B, A's rate of work is 4 times B's rate of work. So, A's time to finish the work is 1/4 of B's time.

We can set up an equation based on the above: x - 45 = (1/4)x

Solve for x: x - 45 = (1/4)x --> 4x - 180 = x --> 3x = 180 --> x = 60

So B takes 60 days to finish the work, and A takes 60 - 45 = 15 days to finish the work.

Since A and B work together, their combined rate of work is the sum of their individual rates. Let's find their individual rates.

B's rate = 1/60 (work done per day)

 A's rate = 1/15 (work done per day)

Combined rate = (1/60 + 1/15) = (1/60 + 4/60) = 5/60 = 1/12

So A and B together can complete the work in 12 days.

Explanation

Since x is 20% more than z, we have:

x = z + (20% of z)

= 100 + (20/100) × 100

= 100 + 20

= 120

Since y is 80% more than z, we have:

y = z + (80% of z)

= 100 + (80/100) × 100

= 100 + 80

= 180

Now, we need to find the ratio x:y. We can simplify this by dividing both numbers by their greatest common divisor (GCD), which is 20.

x = 120 ÷ 20 = 6

y = 180 ÷ 20 = 9

So, the ratio x:y is 6:9. We can further simplify this by dividing both numbers by their GCD, which is 3.

x = 6 ÷ 3 = 2

y = 9 ÷ 3 = 3

Therefore, the ratio x:y is 2:3.

Explanation

The series is obtained by multiplying the previous term by a increasing sequence of numbers:

• 2 × 2 = 4
• 4 × 3 = 12
• 12 × 4 = 48
• 48 × 5 = 240
• 240 × 6 = 1440

Explanation

Let the number be x.

Given:

3​/11×x=22

To find x, multiply both sides by3​/11​:

x=22×11/3​=242/3​

But this gives a fractional number — let's double-check:

Actually, it's simpler to find 6/11​ of the number without finding the whole number.

We know:

3​/11​ of number =22

So, 1 part (i.e., $frac{1}{11}$) = 22/3​

Then:

6/11​=6×(22/3​)=132​/3=44