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## What are the factors of 23? Is 23 prime or composite?

EZ as pi
Featured 2 months ago

$23$ has only 2 factors - it is prime.

#### Explanation:

A prime number can be defined as:

"A natural number which has only 2 factors - itself and 1".

23 has only 2 factors:$\text{ } 23 = 1 \times 23$

There are no other natural numbers which are factors.
$23$ is therefore a prime number.

If it had 3 or more factors it would be composite.

1 is the only number which has 1 factor - it is neither prime nor composite.

## 1.749 to the nearest tenth is what?

EZ as pi
Featured 3 months ago

$1.749 \rightarrow 1.7$

#### Explanation:

The nearest 'tenth' means the same as to one decimal place.

To decide whether to round up to the next tenth or down to the same tenth, look at the digit in the second decimal place (hundredths).

If it is $5$ or more, round up.
If it is $4$ or less, round down.

$1.7 \textcolor{red}{4} 9$ will round to $1.7$

The $\textcolor{red}{4}$ is not big enough to affect the $7$.

Note that the thousands place is not considered at all.

## There are 450 glasses. The glasses hold 350ml. The ratio of water to fruit juice is 4:1 . How much juice is needed in litres?

EZ as pi
Featured 2 months ago

$31.5$ litres

#### Explanation:

Find the total volume first:

$450$ glasses each contain $350$ ml

$450 \times 350 = 157 , 500$ ml.

Convert to litres immediately ($\div 1000$)

$157 , 500 \div 1000 = 157.5$ litres

The ratio: $\text{ water : juice }$ is $\text{ "4" : } 1$

This means that $\frac{4}{5}$ is water and only$\frac{1}{5}$ is juice.

The volume of juice is therefore:

$\frac{1}{5} \times 157.5 = 31.5$ litres

## Express 550 meters as a fraction of 3 km. Please help?

EZ as pi
Featured 1 month ago

$\frac{550}{3000} = \frac{11}{60}$

#### Explanation:

When you write a fraction you are showing :

$\left(\text{part")/("whole}\right)$

In order to do this the units have to be the same, so you can write $3 k m$ as $3000 m$

$550 m$ is the 'part' and $3000 m$ is the 'whole'.

The fraction is : $\frac{550 m}{3000 m}$

Note:

• the units are the same, so they will cancel.
The fraction does not have a unit, it merely indicates how the two quantities compare with each other.

• 'fraction' generally refers to a common fraction.

• fractions should be given in the simplest form, Divide the numerator and denominator by the highest common factor

$\frac{550 \div 50}{3000 \div 50} = \frac{11}{60}$

## How do you evaluate #20+ 6\div 2\times 10- 5#?

Suren Abreu
Featured 2 weeks ago

The answer is $45$.

#### Explanation:

We use BODMAS to help solve this. There are no Brackets and no Orders, so we go straight to Division and then Multiplication, before going on to Addition and then Subtraction. The direction is left to right.

$20 + 6 \div 2 \times 10 - 5$

There are no Brackets and nor Orders, so we go directly to Division.

There is one Division: $6 \div 2 = 3$

Hence:

$20 + 3 \times 10 - 5$

Next comes Multiplication: $3 \times 10 = 30$

Hence:

$20 + 30 - 5$

Next comes Addition: $20 + 30 = 50$

$50 - 5$

Last is Subtraction: $50 - 5 = 45$

$45$

## Bill wants to run a total of 4,000 meters in 5 days. The table shows how far he runs each day for 4 days. Each lap is 400 meters. How many laps should he run on Friday?

Suren Abreu
Featured 3 weeks ago

Bill has to run $2 \frac{7}{8}$ laps on Friday to reach his target.

#### Explanation:

First we calculate the distance Bill has run on each day of the week from Monday to Thursday. We do that by converting the mixed fractions into improper fractions (by multiplying the whole number by the denominator and adding the product to the numerator) and multiplying them by $400$, the distance of each lap in metres.

Monday:

Number of laps: $1 \frac{1}{4} = \frac{5}{4}$

Distance: $\frac{5}{4} \times 400 = \frac{5}{1 \cancel{4}} \times 100 \cancel{400} = 5 \times 100 = 500 m$

Tuesday:

Number of laps: $1 \frac{3}{4} = \frac{7}{4}$

Distance: $\frac{7}{4} \times 400 = \frac{7}{1 \cancel{4}} \times 100 \cancel{400} = 7 \times 100 = 700 m$

Wednesday:

Number of laps: $1 \frac{5}{8} = \frac{13}{8}$

Distance: $\frac{13}{8} \times 400 = \frac{13}{1 \cancel{8}} \times 50 \cancel{400} = 13 \times 50 = 650 m$

Thursday:

Number of laps: $2 \frac{1}{2} = \frac{5}{2}$

Distance: $\frac{5}{2} \times 400 = \frac{5}{1 \cancel{4}} \times 200 \cancel{400} = 5 \times 200 = 1000 m$

Now we add the four distances to determine the total distance run by Bill in four days.

The total distance is $\left(500 + 700 + 650 + 1000\right) = 2850 m$

Bill wants to run a total of $4000 m$ in five days, so he would have to run $\left(4000 - 2850\right) = 1150 m$ on Friday to achieve that total.

Since $1$ lap is $400 m$, we divide that distance by $400$ to calculate how many laps Bill has to run.

$\frac{1150}{400} = \frac{115 \cancel{0}}{40 \cancel{0}} = \frac{23 \cancel{115}}{8 \cancel{40}} = 2 \frac{7}{8}$

Bill has to run $2 \frac{7}{8}$ laps on Friday to reach his target.

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