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2 years ago

A bag contains red, green and yellow counters.

Mathematics

1 answer:

salantis [7]2 years ago

6 0

Answer:

5/24

Step-by-step explanation:

10/12 + 3/8 + what = 1 Find a common denominator. The smallest number that 12 and 8 will both go into is 24. Rewire the fractions with 24 as the denominator.

10/12 = 10/24 Multiple the top and bottom by 2

3/8 = 9/24 Multiple the top and bottom by 3

Now we have

10/24 + 9/24 + X/24 = 24/24 (24/24 is the equivalent to 1)

24 - 10 - 9 = 5

so 10/24 + 3/24 + 5/24 = 24/24

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aliina [53]

Answer:

it would be 910

Step-by-step explanation:

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4 years ago

2a. A bicycle is $85. The tax is 6%. How much is the tax?<br> 7

iVinArrow [24]

Answer = $5.10
85 x 0.06 = $5.10

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3 years ago

10 Two factory workers win the in-house raffle with a prize of £240. Monika and Robert share the prize money in a ratio of

Leni [432]

Answer:

(d) £90

Step-by-step explanation:

Total raffle prize = £240

Ratio of sharing

Monika : Robert

3 : 5

The amount Monika get is calculated as

3/(3 + 5) × £240

= 3/8 × £240

= 3 × 30

= £90

Therefore, the amount Monika gets is £90

4 0

4 years ago

Use the substitution method to solve the system of equations. Enter your

Mazyrski [523]

Answer:

Here ya go

Step-by-step explanation:

Examples: 1+2, 1/3+1/4, 2^3 * 2^2

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y=x^2+1 (Graph Example), 4x+2=2(x+6) (Solve Example)

3 0

3 years ago

From a thin piece of cardboard 50 in. by 50 in., square corners are cut out so that the sides can be folded up to make a box. Wh

mixer [17]

Answer:

When dimension of box is 33.33 inches × 33.33 inches ×8.33 then its volume is maximum and is 9259.26 cubic inches.

Step-by-step explanation:

Let h be the length (in inches) of the square corners that has been cut out from the cardboard and that would be the height of the cardboard box.

Since the squares have been cut from cardboard, both sides of the cardboard would reduce by 2h.

Thus, The dimension of box is (50 – 2h) × (50 – 2h) × h in dimensions.

The volume V of rectangular box = (Length × Breadth × Height) cubic inches.

$V=(50-2h) \times (50-2h) \times h$

$V=(50-2h)^2 \times h$ ..............(1)

Using $(a-b)^2=a^2+b^2-2ab$

$V=h(2500+4h^2-200h)$

$V=2500h+4h^3-200h^2$

For obtaining a box of maximum volume, maximize V as a function of h.

Differentiate both sides with respect to h,

$\frac{dV}{dh}=2500+12h^2-400h$

$\frac{dV}{dh}=4(625+3h^2-100h)$

Solving quadratic equation, $625+3h^2-100h$

$\frac{dV}{dh}=4(3h^2-25h-75h+625)$

$\frac{dV}{dh}=4(h(3h-25)-25(3h-25))$

$\frac{dV}{dh}=4((h-25)(3h-25))$

For maximum, $\frac{dV}{dh}=0$

thus, $4((h-25)(3h-25))=0$

⇒ $h= 25$ or $h=\frac{25}{3}$

Now check (1) for $h= 25$ and $h=\frac{25}{3}$ .

$h= 25$ is not possible as when h is 25 inches then length and breadth becomes 0.

When $h=\frac{25}{3}$ .

(1) ⇒ $V=(50-2(\frac{25}{3}))^2 \times\frac{25}{3}=9259.2592593$

This is the maximum volume the box can assume.

Thus, when dimension of box is 33.3 inches × 33.3 inches ×8.3 then its volume is maximum and is 9259.26 cubic inches.

6 0

3 years ago