Edmond buys 4/5 of a kilogram of butterscotch chips and 5 kilograms of milk chocolate chips.

A devastating freeze in California's Central Valley in January 2007 wiped out approximately 75% of the state's citrus crop. It t

solniwko [45]

The relationship between the percentage of frozen citrus crop, and the cost of box of oranges is an illustration of a linear function.

The linear equation of the function is: $g(P) = 22.9P+7$ .
The inverse function is: $g^{-1}(c) = \frac{1}{22.9}(c - 7)$ .
A practical domain is from 0% to 100%
A practical range is from 7 to 29.9

A. Input quantity

The input quantity is the percentage of frozen citrus crop

B. Output quantity

The output quantity is the cost of box of oranges

C. The linear function

We have:

$(P_1,c_1) = (20\%,11.58)\\(P_2,c_2) = (80\%,25.32)$

Calculate the slope of the function

$m = \frac{c_2 - c_1}{P_2 - P_1}$

$m = \frac{25.32 - 11.58}{80\%-20\%}$

$m = \frac{13.74}{60\%}$

$m = 22.9$

The linear equation is calculated as follows:

$c -c_1 = m(P-P_1)$

$c -11.58= 22.9(P-20\%)$

$c-11.58 = 22.9P-4.58$

D. Rewrite as y = mx + b

We have:

$c-11.58 = 22.9P-4.58$

Collect like terms

$c = 22.9P - 4.58 + 11.58$

$c = 22.9P+7$

The function is:

$g(P) = 22.9P+7$

E. A practical domain

The domain is the possible values of P. Because P is a percentage, its possible values are 0% to 100%.

The domain of the function is: $[0\%,100\%]$

F. A practical range

When P = 0%

$c = 22.9 \times 0\% + 7 = 7$

When P = 100%

$c = 22.9 \times 100\% + 7 = 29.9$

Hence, the range of the function is: $[7,29.9]$

G. The meaning of $g^{-1}(12)$

The inverse function of g(P) is $g^{-1}(P)$

So:

$g^{-1}(12)$ is the percentage of frozen citrus crop, when the cost is $12.

H. The inverse formula

We have:

$c = 22.9P+7$

Subtract 7 from both sides

$c - 7 = 22.9P$

Make P the subject

$P = \frac{1}{22.9}(c - 7)$

So, the inverse formula is:

$g^{-1}(c) = \frac{1}{22.9}(c - 7)$

Substitute 12 for c

$g^{-1}(12) = \frac{1}{22.9}(12 - 7)$

$g^{-1}(12) = \frac{1}{22.9} \times 5$

$g^{-1}(12) = 22\%$

Read more about linear equations at:

brainly.com/question/19770987

6 0

2 years ago

I need to know The value of f(1/2)

Lostsunrise [7]

$\huge\boxed{\textsf{a.)}\ 10}$

Substitute $\frac{1}{2}$ for $x$ .

$f\left(\frac{1}{2}\right)=5\cdot4^\frac{1}{2}$

Use $a^\frac{m}{n}=\sqrt[n]{a^m}$ .

$\begin{aligned}f\left(\frac{1}{2}\right)&=5\cdot\sqrt[2]{4^1}\\&=5\cdot\sqrt[2]{4}\\&=5\cdot2\\&=\boxed{10}\end{aligned}$

7 0

1 year ago

Please help me! Im so confused. If you could explain, too that would be great!!! <3

Zielflug [23.3K]

Answer:

the base length is 8 units

Step-by-step explanation:

You can use pythagorean theorem to solve this

8 0

1 year ago

The ratio of quarters to dimes in a coin collection is 5 : 3. You add the same number of new quarters as dimes to the collection

kondaur [170]

Answer:

Step 1. The answer is no.

Step 2. The answer is b.

Step-by-step explanation:

I think Step 2 already sort of explains the reasoning behind the answer for step 1.

Hope this helps!

3 0

3 years ago

Read 2 more answers

Multiplying by which number is equivalent to an increase of 23% ?

brilliants [131]

Answer:

1.23

Step-by-step explanation:

Increase by 23%

x + 23% of x =
x + (23/100)x =
x + 0.23x =
(1 + 0.23)x =
1.23x

1.23 is the answer

5 0

2 years ago