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3 years ago

Draw a model to represent the ratio 1 to 3.Describe how to use the model to find an equivalent ratio.

2 answers:

5 0

Ratios are basically a number v a number. Like if your in a group of 30 people and 10 of them are boys, your ratio of girls to boys would be 20:10. That's like really really basic ratio and idk how advanced in rations you are but yeah.

gulaghasi [49]3 years ago

3 0

Answer:

Suppose you are in a cinema and there are 12 men and 36 women, then the ratio men to women is 12:36, dividing each term by 12 we get 1:3, which is an equivalent ratio. Other way to get an equivalent ratio is multiplying each term by some constant, for example if we multiply each term in the ratio 1:3 by 4 we get the equivalent ratio: 4:12.

Ratios are used to show the relative sizes of two values, in the example, the relative amount of men and women in some place.

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Answer:

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3 years ago

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Solve y=4x+8x for x

Semmy [17]

Answer:

x = y/12

Step-by-step explanation:

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4 years ago

If 30,000 cm2 of material is available to make a box with a square base and an open top, what is the largest possible volume (in

Cloud [144]

Answer:

The largest possible volume of the box is 2000000 cubic meters.

Step-by-step explanation:

The volume ( $V$ ), in cubic centimeters, and surface area ( $A_{s}$ ), in square centimeters, of the box with a square base are described below:

$A_{s} = l^{2}+h\cdot l$ (1)

$V = l^{2}\cdot h$ (2)

Where:

$l$ - Side length of the base, in centimeters.

$h$ - Height of the box, in centimeters.

By (2), we clear $h$ within the formula:

$h = \frac{V}{l^{2}}$

And we apply in (1) and simplify the resulting expression:

$A_{s} = l^{2}+ \frac{V}{l}$

$A_{s}\cdot l = l^{3}+V$

$V = A_{s}\cdot l -l^{3}$ (3)

Then, we find the first and second derivatives of this expression:

$V' = A_{s}-3\cdot l^{2}$ (4)

$V'' = -6\cdot l$ (5)

If $V' = 0$ and $A_{s} = 30000\,cm^{2}$ , then we find the critical value of the side length of the base is:

$30000-3\cdot l^{2} = 0$

$3\cdot l^{2} = 30000$

$l = 100\,cm$

Then, we evaluate this result in the expression of the second derivative:

$V'' = -600$

By Second Derivative Test, we conclude that critical value leads to an absolute maximum. The maximum possible volume of the box is:

$V = 30000\cdot l - l^{3}$

$V = 2000000\,cm^{3}$

The largest possible volume of the box is 2000000 cubic meters.

4 0

3 years ago

2. Margie Spencer wants to have $100,000 in her savings account in 20 years. If her account pays 6.6% annual

WITCHER [35]

$~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$100000\\ P=\textit{original amount deposited}\\ r=rate\to 6.6\%\to \frac{6.6}{100}\dotfill &0.066\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus two} \end{array}\dotfill &2\\ t=years\dotfill &20 \end{cases}$

$100000=P\left(1+\frac{0.066}{2}\right)^{2\cdot 20}\implies 100000=P(1.033)^{40} \\\\\\ \cfrac{100000}{1.033^{40}}=P\implies 27288.97\approx P$

7 0

2 years ago

Can anyone help me with the 7th and 8th question which I have taken a bad photo of?

Vsevolod [243]

Question 7:

Define x :

Let the digit in the ones place be x.
The digit in the tens place is x+2.

The sum of the digit and its reverse is 66

Find x:

10(x + 2) + x + 10x + (x + 2) = 66
10x + 20 + x + 10x + x + 2 = 66
22x + 22 = 66
22x = 44
x = 2

Find the number:

The number in the ones place = x= 2
The number in the tens place = x = 2 + 2 = 4

Answer : The number is 42.

Question 8:

Define x:

Let the digit in the tens place be x.
The digit in the ones place is x+7.

The number = 10x + x + 7 = 11x + 7

If the digit interchange,
the number = 10(x + 7) + x = 10x + 70 + x = 11x + 70

Find x:

9(11x + 7) = 2(11x + 70)
99x + 63 = 22x + 140
99x - 22x = 140 - 63
77x = 77
x = 1

Find the number:

x = 1
x + 7 = 1 + 7 = 8
So the number is 18

Answer: The number is 18.

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3 years ago