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lina2011 [118]
2 years ago
5

Lake Okeechobee's water level was at sea level in April. In May, the lake's level rose 4 inches and in June it rose 2 more inche

s. As a result of no rain, the lake's level fell 5 inches in July and 3 more inches in August. Select all the expressions that describe this situation. 4 – 5 4 + 2 – 5 – 3 4 + 2 – (5 – 3) 4 + 2 – (5 + 3) 4 + 2 – (– 5) – (– 3) 4 + 2 + (– 5) + (– 3)
Mathematics
1 answer:
lana [24]2 years ago
8 0

Step-by-step explanation:

If the lake's level rose 4 inches and in June it rose 2 more inches, the total amount of distance that he rose is (4+2).

Also if the lake's level fell 5 inches in July and 3 more inches in August as a result of no rain, then the total amount of fall will be (5+3).

Change in height of the lake = total rise in distance - Total fall in distance

Change in height of the lake = (4+2) - (5+3) = (5+3) - (4+2) {commutative law}

open the parenthesis

(4+2) - (5+3)= 4+2-5-3 (note that minus times plus will give minus)

<em>Hence the expressions that best describe this situation are;</em>

1.  (4+2) - (5+3)

2. (5+3)-(4+2)

3. (4+2) - 5 -3

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You wanted to join a booth fair, and you are aiming to get a profit that is twice as
sashaice [31]

You wanted to join a booth fair, and you are aiming to get a profit that is twice as  your capital. Using the given information, your sample plan may be as follows:

Product                   Organic skincare products for women

Description             An organic skincare cream and soap that brightens

                                 and moisturizes your skin.

Goal                          To provide anti-aging skin for women and

                                  maintaining  their skin body.

Capital                      15000

Fixed Cost                  7000

Variable Cost             8000

Profit function            300(a) = 450a - 150a

To prove that the profit function will yield twice the capital.

This profit function: 300(y) = 450y - 150y will help achieve twice profit as your capital.

Profit function = revenue function r(y) - cost function c(y)

300(y) = 450y - 150y

where;

  • y = no of units produced and sold.
  • p = profit sold per unit

Cost function C(y) = fixed cost + (variable cost) × (amount of unit sold)

Assumption:

Cost function C(y) = 7000 + (80 × 100)

Cost function C(y) = 7000 + 8000

Cost function C(y) = 15000

Revenue function R(y) = price per revenue sold × no of sold units

R(y) = 450 × 100

R(y) = 45000

∴

Profit function = 45000 - 15000

Profit function = 30000

Therefore, can conclude that the profit function is revenue function r(y) - cost function c(y).

Hence the formula:

Profit function = revenue function r(y) - cost function c(y)   (Proved)

Learn more about Profit function here:

brainly.com/question/16866047?referrer=searchResults

8 0
1 year ago
the costume designer decides to make the sashes a little smaller, so that each of the 8 dresses can have a sash. What fraction o
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The costume designer should use 1/8 of the fabric dedicated to sashes for each dress.
8 0
2 years ago
Arrange these functions from the greatest to the least value based on the average rate of change in the specified interval.Tiles
Ugo [173]

By definition, the average rate of change is given by:

AVR = \frac{f(x2)-f(x1)}{x2-x1}

We evaluate each of the functions in the given interval.

We have then:

For f (x) = x ^ 2 + 3x:

Evaluating for x = -2:

f (-2) = (-2) ^ 2 + 3 (-2)\\f (-2) = 4 - 6\\f (-2) = - 2

Evaluating for x = 3:

f (3) = (3) ^ 2 + 3 (3)\\f (3) = 9 + 9\\f (3) = 18

Then, the AVR is:

AVR = \frac{18-(-2)}{3-(-2)}

AVR = \frac{18+2}{3+2}

AVR = \frac{20}{5}

AVR = 4


For f (x) = 3x - 8:

Evaluating for x =4:

f (4) = 3 (4) - 8\\f (4) = 12 - 8\\f (4) = 4

Evaluating for x = 5:

f (5) = 3 (5) - 8\\f (5) = 15 - 8\\f (5) = 7

Then, the AVR is:

AVR = \frac{7-4}{5-4}

AVR = \frac{3}{1}

AVR = 3


For f (x) = x ^ 2 - 2x:

Evaluating for x = -3:

f (-3) = (-3) ^ 2 - 2 (-3)\\f (-3) = 9 + 6\\f (-3) = 15

Evaluating for x = 4:

f (4) = (4) ^ 2 - 2 (4)\\f (4) = 16 - 8\\f (4) = 8

Then, the AVR is:

AVR = \frac{8-15}{4-(-3)}

AVR = \frac{-7}{4+3}

AVR = \frac{-7}{7}

AVR = -1


For f (x) = x ^ 2 - 5:

Evaluating for x = -1:

f (-1) = (-1) ^ 2 - 5\\f (-1) = 1 - 5\\f (-1) = - 4

Evaluating for x = 1:

f (1) = (1) ^ 2 - 5\\f (1) = 1 - 5\\f (1) = - 4

Then, the AVR is:

AVR = \frac{-4-(-4)}{1-(-1)}

AVR = \frac{-4+4}{1+1}

AVR = \frac{0}{2}

AVR = 0


Answer:

from the greatest to the least value based on the average rate of change in the specified interval:


f(x) = x^2 + 3x interval: [-2, 3]

f(x) = 3x - 8 interval: [4, 5]

f(x) = x^2 - 5 interval: [-1, 1]

f(x) = x^2 - 2x interval: [-3, 4]


4 0
1 year ago
A mattress store sold 1,330 mattresses in one year. If 30% of the mattresses sold were king size mattresses, how many king size
kodGreya [7K]

The total number of mattresses that are sold in a year = 1,330

Percentage of King size mattresses sold = 30% = 30/100 = 0.3

Next, we have to calculate the actual number sold by using the formula given below:

Number of king size mattresses sold = Total mattresses sold in a year * percentage of king size mattresses sold

Number of King Size mattresses sold = 1,330*0.3 = 399

Number of king size mattresses sold = 399


3 0
2 years ago
Read 2 more answers
a lunch stand makes a $.75 profit on each chef's salad and $1.20 profit on each caesar salad. On a typical weekday, it sells bet
tangare [24]

Answer:

<em>50 Chef's salads and 50 Caesar salads should be prepared in order to maximize profit.</em>

Step-by-step explanation:

Suppose, the number of Chef's salad is x and the number of Caesar salad is y

On a typical weekday, it sells between 40 and 60 Chefs salads and between 35 and 50 Caesar salads.

So, the two constraints are:  40\leq x\leq 60 and  35\leq y\leq 50

The total number sold has never exceed 100 salads. So, another constraint will be:   x+y\leq 100

According to the graph of the constraints, the vertices of the common shaded region are:  (40,35), (60,35), (60,40), (50,50) and (40,50)   <em>(Refer to the attached image for the graph)</em>

The lunch stand makes a $.75 profit on each Chef's salad and $1.20 profit on each Caesar salad. So, the profit function will be:  P=0.75x+1.20y

For  (40, 35) ,   P=0.75(40)+1.20(35)=72

For  (60, 35) ,   P=0.75(60)+1.20(35)=87

For  (60, 40) ,   P=0.75(60)+1.20(40)=93

For  (50, 50) ,   P=0.75(50)+1.20(50)=97.5 <u><em>(Maximum)</em></u>

For  (40, 50) ,   P=0.75(40)+1.20(50)=90

Profit will be maximum when x=50 and y=50

Thus, 50 Chef's salads and 50 Caesar salads should be prepared in order to maximize profit.

6 0
2 years ago
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