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3 years ago

15

The band boosters collected $2400 from the sale of hamburgers and hotdogs.The amount earned from hamburgers and hotdogs were equ

al.A hamburger sold for three dollars and a hotdog sold for two dollars how many of each were sold?

2 answers:

adell [148]3 years ago

5 0

6,000 for the hotdogs and 4,000 for the hamburgers

damaskus [11]3 years ago

4 0

400 Hamburgers
600 Hot dogs

Divide 2,400 by two because that's how many items they sold. You'll get 1,200.

Divide 1,200 by 3 because that's how much a hamburger costs and you'll end up with 400

Divide 1,200 by 2 because that's how much a hot dog costs and you'l end up with 600

To check, multiply 400x3 and 600x2

Then add the sums together- 1,200+1,200= 2,400

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The plot below shows the graphs of three functions, f, g, and h, all of which determine the population of three different cities

monitta

So, here we have an exponential function.

Remember that an exponential function has the form:

$y=a(b)^x=a(1\pm\frac{r}{100})^x$

Where a represents an initial amount, and r is the rate of this amount to change. (Increase, or decrease).

So, given that the population of City A in 2000 was 40 thousand people and the population increased by 13% each year, we can say that

$\begin{gathered} a=40 \\ b=1+\frac{13}{100}=1.13 \end{gathered}$

So,

$f(x)=40(1.13)^x$

For city B:

$\begin{gathered} a=40 \\ b=1+\frac{16}{100}=1.16 \\ g(x)=40(1.16)^x \end{gathered}$

But something different happens with city C. This is not an exponential function, this is a linear function.

So,

$h(x)=40+10x$

7 0

1 year ago

Ratio of boys to girls in a class of 27 is 1:2

kvasek [131]

9 boys and 18 girls

7 0

2 years ago

If f(x)=4/5x^2+12x what is the value of (5)

quester [9]

Answer:

f(5)=80

Step-by-step explanation:

5^2=5*5=25

(4/5)(25)=4(5)=20

12(5)=60

20+60=80

6 0

3 years ago

Match the numerical expressions to their simplest forms.

Aloiza [94]

Answer:

$(a^6b^1^2)^\frac{1}{3}$ = $a^2b^4$

$\frac{(a^5b^3)^\frac{1}{2}}{(ab)^-^\frac{1}{2}}$ = $a^3b^2$

$(\frac{a^5}{a^-^3b^-^4})^\frac{1}{4}$ = $a^2b$

$(\frac{a^3}{ab^-^6})^\frac{1}{2}$ = $ab^3$

Step-by-step explanation:

Simplify each of the expressions:

1

$(a^6b^1^2)^\frac{1}{3}$

Distribute the exponent. Multiply the exponent of the term outside of the parenthesis by the exponents of the variable.

$(a^6b^1^2)^\frac{1}{3}$

$a^6^*^\frac{1}{3}b^1^2^*^\frac{1}{3}$

Simplify,

$a^2b^4$

2

Use a similar technique to solve this problem. Remember, a fractional exponent is the same as a radical, if the denominator is (2), then the operation is taking the square root of the number.

$\frac{(a^5b^3)^\frac{1}{2}}{(ab)^-^\frac{1}{2}}$

Rewrite as square roots:

$\frac{\sqrt{a^5b^3}}{\sqrt{(ab)}^-^1}$

A negative exponent indicates one needs to take the reciprocal of the number. Apply this here:

$\frac{\sqrt{a^5b^3}}{\frac{1}{\sqrt{ab}}}$

Simplify,

$\sqrt{a^5b^3}*\sqrt{ab}$

Since both numbers are under a radical, one can rewrite them such that they are under the same radical,

$\sqrt{a^5b^3*ab}$

Simplify,

$\sqrt{a^6b^4}$

Since this operation is taking the square root, divide the exponents in half to do this operation:

$a^3b^2$

3

$(\frac{a^5}{a^-^3b^-^4})^\frac{1}{4}$

Simplify, to simplify the expression in the numerator and the denominator, the base must be the same. Remember, the base is the number that is being raised to the exponent. One subtracts the exponent of the number in the denominator from the exponent of the like base in the numerator. This only works if all terms in both the numerator and the denominator have the operation of multiplication between them:

$(\frac{a^8}{b^-^4})^\frac{1}{4}$

Bring the negative exponent to the numerator. Change the sign of the exponent and rewrite it in the numerator,

$(a^8b^4)^\frac{1}{4}$

This expression to the power of the one forth. This is the same as taking the quartic root of the expression. Rewrite the expression with such,

$\sqrt[4]{a^8b^4}$

SImplify, divide the exponents by (4) to simulate taking the quartic root,

$a^2b$

4

$(\frac{a^3}{ab^-^6})^\frac{1}{2}$

Using all of the rules mentioned above, simplify the fraction. The only operation happening between the numbers in both the numerator and the denominator is multiplication. Therefore, one can subtract the exponents of the terms with the like base. The term in the denomaintor can be rewritten in the numerator with its exponent times negative (1).

$(a^3^-^1b^(^-^6^*^(^-^1^)^))^\frac{1}{2}$

$(a^2b^6)^\frac{1}{2}$

Rewrite to the half-power as a square root,

$\sqrt{a^2b^6}$

Simplify, divide all of the exponents by (2),

$ab^3$

7 0

3 years ago

PLEASE HELP MEEEEE

Elena-2011 [213]

Answer:

a = 36 and a = 27

Step-by-step explanation:

The geometric mean of two numbers is the square root of the product of the two numbers.

Say for example we have the numbers x and y, the geometric mean z is mathematically;

z = √xy

For the first question, our z is 12, x and y are 4 and a respectively.

12 = √4a

square both sides

144 = 4a

a = 144/4

a = 36

For the second question

z is 9, x and y are 3 and a respectively

9 = √3a

square both sides

81 = 3a

a = 81/3

a = 27

5 0

3 years ago