20/10/2020

title

A species of plant can have one to five flowers. The probability of each number of flowers is given by:

Number |
1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

Probability | 0.12 | 0.24 | 0.23 | 0.20 |

Peter plants 96. How many of Peter's plants will have three flowers?

Solution to follow ...

13/10/2020

What is the smallest number of beans?

A bag contains some red, some yellow and some blue beans. The probability of picking a red bean at random is 0.2. It is known that the ratio of yellow to blue beans is 5:7

Solution to follow ...

06/10/2020

Time to Fill up the Pool

The pool can be filled by a big pump in 5 hours and by a small pump on 20 hours.

How long will both pumps take to fill the pool?

Solution to follow ...

08/09/2020

Find the next three terms in this sequence

14, 24, 36, 50, 66, ..., ..., ...,

Solution to follow ...

01/09/2020

Find ∠*ABC*

*A* *C* and *D* are point on a circle centred *O*;
*AB* and *CB* are tangents to the circle;
*AD* and *CD* are chords in the circle;

∠*ADC* = 48°.

Solution to follow ...

25/07/2020

Solve Simultaneously

$\sqrt{x}+y=11$

$x+\sqrt{y}=7$

Solution:

The equations imply that x, y > 0

Both equations have integers of the RHS

implying x, y, sqrt x, sqrt y are elements of the integers

moreover x, t are perfect squares

so 0 < x < 7 and 0 < y < 11

So
$x\in \{1,4\}$
and
$y\in \{1,4,9\}$

Therefore x = 4 and y = 9

Are there any other solutions?