Which expression is equivalent to 18x + 9y

Jing spent 1/3 of her money on a pack of pens, 1/2 of her money on a pack of markers, and 1/8 of her money on a pack of pencils.

Reika [66]

As per the problem

Jing spent $\frac{1}{3}$ of her money on a pack of pens.

$\frac{1}{2}$ of her money on a pack of markers.

and $\frac{1}{8}$ of her money on a pack of pencils.

Total fraction of money spent cab be given as below

Fraction of Money Spent = $\frac{1}{3} +\frac{1}{2}+\frac{1}{8}$

Take the LCD of denominator, we get LCD of (3,2,8)=24

Fraction of Money Spent = $\frac{8+12+3}{24} =\frac{23}{24} \\\\$

$\\ \text{Hence fraction of Money Spent }=\frac{23}{24} \\ \\ \text{Fraction of Money left}=1-\frac{23}{24} \\ \\ \text{Simplify, we get}\\ \\ \text{Fraction of Money left}=\frac{24-23}{24} \\ \\ \text{Fraction of Money left}=\frac{1}{24}$

3 0

3 years ago

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A species of bacteria is 10 micrometers long. A virus is 10,000 times smaller than bacteria. a. Using the table above, find the

stich3 [128]

Answer:

$10^{-4}$ times 10 micrometers (or $10^{-5}$ ) is $10^{-9}$

8 0

3 years ago

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(20 points) NEED ANSWER ASAP

geniusboy [140]

The first step would be D

3 0

3 years ago

A rectangular box is to have a square base and a volume of 12 ft3. If the material for the base costs $0.17/ft2, the material fo

katen-ka-za [31]

Answer:

(a)Length =2 feet

(b)Width =2 feet

(c)Height=3 feet

Step-by-step explanation:

Let the dimensions of the box be x, y and z

The rectangular box has a square base.

Therefore, Volume of the box $V=x^2z$

Volume of the box $=12 ft^3\\$

$Therefore, x^2z=12\\z=\frac{12}{x^2}$

The material for the base costs $\$0.17/ft^2$ , the material for the sides costs $\$0.10/ft^2$ , and the material for the top costs $\$0.13/ft^2$ .

Area of the base $=x^2$

Cost of the Base $=\$0.17x^2$

Area of the sides $=4xz$

Cost of the sides= $=\$0.10(4xz)$

Area of the Top $=x^2$

Cost of the Base $=\$0.13x^2$

Total Cost, $C(x,z) =0.17x^2+0.13x^2+0.10(4xz)$

Substituting $z=\frac{12}{x^2}$

$C(x) =0.17x^2+0.13x^2+0.10(4x)(\frac{12}{x^2})\\C(x)=0.3x^2+\frac{4.8}{x} \\C(x)=\dfrac{0.3x^3+4.8}{x}$

To minimize C(x), we solve for the derivative and obtain its critical point

$C'(x)=\dfrac{0.6x^3-4.8}{x^2}\\Setting \:C'(x)=0\\0.6x^3-4.8=0\\0.6x^3=4.8\\x^3=4.8\div 0.6\\x^3=8\\x=\sqrt[3]{8}=2$

Recall: $z=\frac{12}{x^2}=\frac{12}{2^2}=3\\$

Therefore, the dimensions that minimizes the cost of the box are:

(a)Length =2 feet

(b)Width =2 feet

(c)Height=3 feet

7 0

3 years ago

Which proportion can you use to find the value of a?

Ugo [173]

Given:

The given triangle is a similar triangle.

The length of the hypotenuse is 18 units.

The length of the leg is a.

The length of the part of the hypotenuse is 16 units.

We need to determine the proportion used to find the value of a.

Proportion to find the value of a:

We shall find the proportion to determine the value of a using the geometric mean leg rule.

Applying the leg rule, we have;

$\frac{\text { hypotenuse }}{\text { leg }}=\frac{\text { leg }}{\text { part }}$

Substituting the values of hypotenuse, leg and part, we get;

$\frac{18}{a}=\frac{a}{16}$

Thus, the proportion used to find the value of a is $\frac{18}{a}=\frac{a}{16}$

Hence, Option D is the correct answer.

6 0

3 years ago

Which expression is equivalent to 18x + 9y - 6?