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3 years ago

5

A hardware store manager reviews data that shows how well a new product is selling over an 8-week period. The data can be modele

d by the equation y = - 13.9x + 103 , where x represents time in weeks and y represents the number of units of the product left in stock. what does-13.9 represent

1 answer:

lesya692 [45]3 years ago

4 0

Answer:

-13.9 represents the slope

It is the number of units of the product left in stock per week

The negative value shows it decreases per week

Step-by-step explanation:

Here, we want to state what the value -13.9 represents

Generally, the equation of a straight line can be represented by the equation

y = mx + c

where m is the slope

In this case, -13.9 represents the slope of the model

The slope is calculated by dividing a change in y by a change in x

With respect to the question, the slope here represents number of units of the product left in stock per week

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Step-by-step explanation:

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3 years ago

1) Members at a yoga school pay $10 per class plus a one-time $100 membership fee. Non-members pay$15 per class. How many classe

Juli2301 [7.4K]

Answer:

Part 1) The number of classes must be greater than 20

Part 2) see the explanation

Part 3) $\$68.76$

Part 4) $\$12\ per\ hour$

Part 5) The equation that can be used is $27x=242.73$ and the cost of one print is $\$8.99$

Part 6) The number of classes must be greater than 30

Step-by-step explanation:

Part 1) we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the slope or unit rate

b is the y-intercept or initial value

Let

y ----> the total cost

x ----> the number of classes

we have

<em>Members</em>

The slope is $m=\$10\ per\ class$

The y-intercept is $b=\$100$

so

$y=10x+100$ ----> equation A

<em>Non-Members</em>

The slope is $m=\$15\ per\ class$

so

$y=15x$ ----> equation B

To find out how many classes would a member have to take to save money compared to taking classes as a non-member, solve the following inequality

$10x+100 < 15x$

Solve for x

subtract 10 x both sides

$100 < 15x-10x$

$100 < 5x$

Divide by 5 both sides

$20 < x$

Rewrite

$x > 20$

therefore

The number of classes must be greater than 20

Part 2) we have

The sum of 8 and 3 times a number is 23.

Let

x ----> the number

Remember that

3 times a number is the same that multiply 3 by the number ----> 3x

so

The sum of 8 and 3 times a number is 23 is the same that

$8+3x=23$

solve for x

subtract 8 both sides

$3x=23-8$

$3x=15$

Divide by 3 both sides

$x=5$

Part 3) we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the slope or unit rate

b is the y-intercept or initial value

Let

y ----> the total cost of renting a car for one day

x ----> the number of miles

we have

The slope is $m=\$0.42\ per\ mile$

The y-intercept is $b=\$36$

so

$y=0.42x+36$

For x=78 miles

substitute in the linear equation and solve for y

$y=0.42(78)+36$

$y=\$68.76$

Part 4) Let

x ----> Alice's normal hourly rate

we know that

40 hours multiplied by her normal hourly rate plus 10 hours (50 h-40 h) multiplied by 1.5 times her normal hourly rate must be equal to $660

so

The linear equation that represent this situation is

$40x+10(1.5x)=660$

solve for x

$40x+15x=660$

$55x=660$

Divide by 55 both sides

$x=\$12\ per\ hour$

Part 5) Let

x ----> the cost of one print

we know that

The cost of one print multiplied by 27 prints must be equal to $242.73

so

The linear equation is equal to

$27x=242.73$

solve for x

Divide by 27 both sides

$x=\$8.99$

Part 6) we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the slope or unit rate

b is the y-intercept or initial value

Let

y ----> the total cost

x ----> the number of classes

we have

<em>Members</em>

The slope is $m=\$7\ per\ class$

The y-intercept is $b=\$120$

so

$y=7x+120$ ----> equation A

<em>Non-Members</em>

The slope is $m=\$11\ per\ class$

so

$y=11x$ ----> equation B

To find out how many classes would a member have to take to save money compared to taking classes as a non-member, solve the following inequality

$7x+120 < 11x$

Solve for x

subtract 7x both sides

$120 < 11x-7x$

$120 < 4x$

Divide by 4 both sides

$30 < x$

Rewrite

$x > 30$

therefore

The number of classes must be greater than 30

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4 years ago

What type of function can be used to model the scenario?

solmaris [256]

Answer:

1. Exponential

2. Linear

Step-by-step explanation:

1. Exponential

Principal = 15000

Rate, r = 6.5% compounded annually

A = P(1 + r)^t

A = 15000(1 + 0.065)^t

A = 15000(1.065)^t

2. Linear

Let initial amount in bank = x

Amount added per week = 2

Number of weeks or period = t

A = x + 2t

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3 years ago

Ryan throws a baseball upward with an initial velocity of 12 m/s from a height of 2m above the ground. How long will it take for

Sonja [21]

Answer:

It will take 2.6 s for the ball to hit the ground.

Step-by-step explanation:

This is a standard physics problem

The equation that defines the movement of Ryans baseball is given by the initial velocity, and the acceleration

Distance = Do + Vo*t + 0.5*a*t^2

Where

Do is the initial distance.

(Do = 2m over the ground)

Vo is the initial velocity = 12m/s

a is the acceleration that is exerted on the body (in this case a = g = -9.8 m/s^2 )

t is the time

We substitute in the equation, and solve for t (time)

(0)= 2+ (12)*t + 0.5*(-9.8)*t^2

We get that

t = 2.606 s = 2.6 s

7 0

3 years ago