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3 years ago

15

A different breakfast cereal is made using only fruit and bran. The ratio of the weight of fruit to the weight of bran is 1 : 3

(b) What fraction of the weight of this cereal is bran?

1 answer:

kkurt [141]3 years ago

5 0

Answer:

the answer would be 2/3. I hope this helps.

Step-by-step explanation:

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Choose the correct simplification of the expression a2 ⋅ a3. a a6 a5 a−1

alina1380 [7]

Answer: The correct option is (C) $a^5.$

Step-by-step explanation: We are given to choose the correct simplification for the following expression :

$P=a^2.a^3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We will be using the following property of exponents :

$x^a.x^b=x^{a+b}.$

So, the simplification of expression (i) is as follows :

$P\\\\=a^2.a^3\\\\=a^{2+3}\\\\=a^5.$

Thus, the correct simplification of the given expression is $a^5.$

Option (C) is CORRECT.

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26. The two triangles below are similar. What<br> is the perimeter of triangle XYZ?

AveGali [126]

Answer:

24

Step-by-step explanation:

6 ÷ 15 = 0.4

X to Y = 20 × 0.4 = 8

Y to Z = 25 × 0.4 = 10

Perimeter: a + b + c

6 + 8 + 10 = 24

Even I am surprised by what I wrote. Hopefully, it is right and helps you ^-^ Please comment if you have any questions.

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2 years ago

What is the solution to this equation? 5(x - 6) + 4 = 7x - 4

dimaraw [331]

5(x - 6) + 4 = 7x - 4

5x - 30 + 4 = 7x - 4

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5x - 26 + 4 = 7x

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-22 / 2 = x

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x = -11 is the solution to the given equation

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3 years ago

Mr. Fry is building a fence around his pool. •Length of the fence is 60 feet. •Width of the fence is 30 feet. How many yards of

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Packaging By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting fl

Vikki [24]

Answer:

Height: 3/2 inches

Length: 12 inches

Width: 4 inches

Step-by-step explanation:

Let x is the side length of the square

The height of the box by cutting squares off :x

The new length of the cardboard = 15 -2x (because we cut from 4 corners)
The new width of the cardboard = 7 -2x (because we cut from 4 corners)

The new volume of it is:

V = (15 -2x) (7 -2x) x

<=> V = $4x^3 -44x^2 +105x$

To maximum volume, we use the first derivative of the volume

$\dfrac{dV}{dx} = 0$

<=> $12x^2-88x+105=0$

<=> $\left(2x-3\right)\left(6x-35\right) = 0$

<=> 2x -3 = 0 or 6x -35 = 0

<=> x = 3/2 or x = 35/6

To determine which value of x gives a maximum, we evaluate

$\dfrac{d^2V}{dx^2}$ = 24x -88

If x = 3/2, we have:

$\dfrac{d^2V}{dx^2}$ = 24(3/2) -88 = -52

If x = 35/6, we have:

$\dfrac{d^2V}{dx^2}$ = 24(35/6) -88 = 52

We choose x = 3/2 to have the maximum volume because the value of x that gives a negative value is maximum.

So the dimensions (in inches) of the box is:

Height: 3/2 inches

Length: 15-2(3/2) = 12 inches

Width: 7 - 2(3/2) = 4 inches

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3 years ago