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3 years ago

If there are 48 students in a school play the ratio of boys to girls is 5:7 how many more girls than boys are in the play?

Mathematics

1 answer:

Andreas93 [3]3 years ago

8 0

Answer:

Step-by-step explanation:

5 + 7 = 12

48 / 12 = 4

5 x 4 = 20

7 x 4 = 28

There are 8 girls more than boys

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The total surface area of a cuboid is 600cm ^2 find LSA

Alona [7]

Answer:

Hope this help uh

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8 0

2 years ago

. The volume of a cube is 1728 . Find its edge and total surface area

emmasim [6.3K]

Answer:

Edge = 12

Total Surface Area = 72

Step-by-step explanation:

Volume of the cube = 1728

Length of the edge = $\sqrt[3]{1728} = 12$

We know that

TSA (Total Surface Area) = $6 {a}^{2}$

where a = length of edge of cube

So,

TSA of cube = $6 \times 12 = 72$

7 0

2 years ago

Find the smallest 4 digit number such that when divided by 35, 42 or 63 remainder is always 5

alex41 [277]

The smallest such number is 1055.

We want to find $x$ such that

$\begin{cases}x\equiv5\pmod{35}\\x\equiv5\pmod{42}\\x\equiv5\pmod{63}\end{cases}$

The moduli are not coprime, so we expand the system as follows in preparation for using the Chinese remainder theorem.

$x\equiv5\pmod{35}\implies\begin{cases}x\equiv5\equiv0\pmod5\\x\equiv5\pmod7\end{cases}$

$x\equiv5\pmod{42}\implies\begin{cases}x\equiv5\equiv1\pmod2\\x\equiv5\equiv2\pmod3\\x\equiv5\pmod7\end{cases}$

$x\equiv5\pmod{63}\implies\begin{cases}x\equiv5\equiv2\pmod 3\\x\equiv5\pmod7\end{cases}$

Taking everything together, we end up with the system

$\begin{cases}x\equiv1\pmod2\\x\equiv2\pmod3\\x\equiv0\pmod5\\x\equiv5\pmod7\end{cases}$

Now the moduli are coprime and we can apply the CRT.

We start with

$x=3\cdot5\cdot7+2\cdot5\cdot7+2\cdot3\cdot7+2\cdot3\cdot5$

Then taken modulo 2, 3, 5, and 7, all but the first, second, third, or last (respectively) terms will vanish.

Taken modulo 2, we end up with

$x\equiv3\cdot5\cdot7\equiv105\equiv1\pmod2$

which means the first term is fine and doesn't require adjustment.

Taken modulo 3, we have

$x\equiv2\cdot5\cdot7\equiv70\equiv1\pmod3$

We want a remainder of 2, so we just need to multiply the second term by 2.

Taken modulo 5, we have

$x\equiv2\cdot3\cdot7\equiv42\equiv2\pmod5$

We want a remainder of 0, so we can just multiply this term by 0.

Taken modulo 7, we have

$x\equiv2\cdot3\cdot5\equiv30\equiv2\pmod7$

We want a remainder of 5, so we multiply by the inverse of 2 modulo 7, then by 5. Since $2\cdot4\equiv8\equiv1\pmod7$ , the inverse of 2 is 4.

So, we have to adjust $x$ to

$x=3\cdot5\cdot7+2^2\cdot5\cdot7+0+2^3\cdot3\cdot5^2=845$

and from the CRT we find

$x\equiv845\pmod2\cdot3\cdot5\cdot7\implies x\equiv5\pmod{210}$

so that the general solution $x=210n+5$ for all integers $n$ .

We want a 4 digit solution, so we want

$210n+5\ge1000\implies210n\ge995\implies n\ge\dfrac{995}{210}\approx4.7\implies n=5$

which gives $x=210\cdot5+5=1055$ .

5 0

3 years ago

Please help again with the following 2 questions

yuradex [85]

Perimeter top one:
5+1+2+3+3+4= 18in

Perimeter bottom one:
6+1+4+3+2+4= 20in

3 0

3 years ago

~please only answer if you know for sure~

NARA [144]

JKL is similar to PQR

so they want PR

JKL is similar to PQR

So PR is similar to JL

And they also give us the sides KL and QR

JKL is similar to PQR

Both of those sides are similar, so we can form a proportion.

$\sf { \frac{PR}{JL} = \frac{QR}{KL} }$

Plug in the numbers:

$\sf { \frac{PR}{6} = \frac{15}{9} }$

Cross multiply:

$\sf{ PR \times 9 = 6 \times 15}$

Isolate PR

$\sf{ PR = \frac{6 \times 15}{9}}$

Simplify it

$\sf{ PR = 10}$

So your final answer is

$\boxed{\bf{10 centimeters}}$

6 0

3 years ago

Read 2 more answers