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3 years ago

Use the table below to answer this question:

Mathematics

1 answer:

ch4aika [34]3 years ago

7 0

Answer:

Step-by-step explanation:

Th average rate of change is the slope of the secant line that goes through those 2 values of x. Of course, each value of x also has a value of y. The coordinates for these combinations of x's and y's are:

(-1, 5) and (4, 0). We can use the slope formula to find the average rate of change of this function without having to know what the function's equation is:

$m=\frac{0-5}{4-(-1)}=\frac{-5}{5}=-1$

So the average rate of change, aka slope, between those 2 points is -1

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Danny charges $30 for 3 hours of swimming lessons, Martin charges $44 for 4 hours of swimming lessons. Who offers a better deal?

emmasim [6.3K]

Answer:

Danny

Step-by-step explanation:

danny has a better offer

8 0

3 years ago

A manufacturer is planning to sell a new product at the price of 210 dollars per unit and estimates that if x thousand dollars i

sattari [20]

Answer:

Development costs: $2757

Promotion costs: $3155

Step-by-step explanation:

This might seem like a two-variable problem, but in actuality it's not - because the demand function is a sum of two components, each being independent and using only one variable, we can solve for the two separately.

Moreover, the price per unit and cost per unit is constant, so each product yields exactly $80 ($210 - $130).

Let's solve separately.

We need to maximize:

$80 * 160y/(y+4) - 1000y = $12800 * y/(y+4) - $1000*y

$80 * 170x/(x+7) - 1000x = $13600 * x/(x+7) - $1000*x

Let's go:

$12800 * y/(y+4) - $1000*y = $12800 * (1 - 4/(y+4)) - $1000y = $12800 - $51200/(y+4) - $1000*y

we analyze the derivative. $12800 is a constant, so we can skip it. Derivative of 1/(y+4) is -(y+4)^-2, derivative of $1000y is $1000.

deriv = $51200/(y+4)/(y+4) - $1000

We find the changepoints by analyzing $51200/(y+4)/(y+4) - $1000 = $0. We don't need to worry about y+4 = 0 because we cannot spend negative money on development/advertisement.

(y+4)^2 = $51.2

y+4 ~= 7.155417528 (or -y-4 = 7.1554... but it doesn't make sense because negative budget so we don't analyze).

y ~= 3.155417528

lastly, we should check that it's actually a maximum there - but it is, the original function goes to negative infinity.

rounding $1000y to the nearest dollar gives us $3155

Let's do the same for x:

$13600 * x/(x+7) - $1000*x = $13600 * (1 - 7/(x+7)) - $1000x = $13600 - $95200/(x+7) - $1000*x

deriv = $95200/(x+7)/(x+7) - $1000

$95200/(x+7)/(x+7) - $1000 = $0

(x+7)^2 = 95.2

(x+7) ~= 9.75704873412

x ~= 2.75704...

rounding $1000x to the nearest dollar yields $2757

3 0

3 years ago

43⋅(10025)−50 please help me someone

Mashutka [201]

$43 * (10025) - 50 = 431075 - 50 = 431025$

5 0

3 years ago

Read 2 more answers

Mai bought a television for $330. The tax rate is 8%. How much did Mai pay for the television?

Bezzdna [24]

Mai paid $412.50 for the T.V.

8 0

3 years ago

Read 2 more answers

How do you right 0.0001 in expanded form

kirza4 [7]

The expanded form of the number 0.0001 is $\bold{\frac{1}{10000}}$ .

<u>SOLUTION: </u>

Given that, we have to write 0.0001 in expanded form.

Expanded form or expanded notation is a way of writing numbers to see the math value of individual digits. When numbers are separated into individual place values and decimal places they can also form a mathematical expression.

Now, take the given number 0.0001

As there are no other digits except 0 in front of 1 our work is simplified.

Expanded form will be $\frac{1}{10000}$

Hence, the expanded form of the number 0.0001 is $\frac{1}{10000}$ .

4 0

3 years ago