All categories

1 year ago

Find a linear equation to model this real-world application:

Mathematics

1 answer:

SSSSS [86.1K]1 year ago

3 0

The linear equation to model the company's monthly expenses is y = 2.5x + 3650

Solution:

Let "x" be the units produced in a month

It costs ABC electronics company $2.50 per unit to produce a part used in a popular brand of desktop computers.

Cost per unit = $ 2.50

The company has monthly operating expenses of $350 for utilities and $3300 for salaries

We have to write the linear equation

The linear equation to model the company's monthly expenses in the form of:

y = mx + b

Cost per unit = $ 2.50

Monthly Expenses = $ 350 for utilities and $ 3300 for salaries

Let "y" be the total monthly expenses per month

Then,

Total expenses = Cost per unit(number of units) + Monthly Expenses

$y = 2.50(x) + 350 + 3300\\\\y = 2.5x + 3650$

Thus the linear equation to model the company's monthly expenses is y = 2.5x + 3650

You might be interested in

A ball on a string moves around a complete circle, once a second, on a frictionless, horizontal table. The tension in the string

ki77a [65]

The tension in the string balances out, and thus equals the centripetal force of the ball

T = mv^2/r

if it only takes half the time to finish one orbit it has to be moving at twice the original speed. 

And since v is squared T will increase by 4 

T' = m(2v)^2/r 

T' = 4mv^/r = 4T 

T' = 24.0 N

I hope my answer has come to your help. Have a nice day ahead and may God bless you always!

5 0

2 years ago

The U.S. Bureau of Labor Statistics reports that 11.3% of U.S. workers belong to unions (BLS website, January 2014). Suppose a s

andrezito [222]

Answer:

a) Null hypothesis: $p \leq 0.113$

Alternative hypothesis: $p > 0.113$

b) $z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

Replacing we got:

$z=\frac{0.13 -0.113}{\sqrt{\frac{0.113(1-0.113)}{400}}}=1.074$

The p value for this case would be given by:

$p_v =P(z>1.074)=0.141$

c) For this case we see that the p value is higher than the significance level of 0.05 so then we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true proportion workers belonged to unions is significantly higher than 11.3%

Step-by-step explanation:

Information given

n=400 represent the random sample taken

X=52 represent the workers belonged to unions

$\hat p=\frac{52}{400}=0.13$ estimated proportion of workers belonged to unions

$p_o=0.113$ is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic

$p_v$ represent the p value

Part a

We want to test if the true proportion of interest is higher than 0.113 so then the system of hypothesis are.:

Null hypothesis: $p \leq 0.113$

Alternative hypothesis: $p > 0.113$

Part b

The statistic is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

Replacing we got:

$z=\frac{0.13 -0.113}{\sqrt{\frac{0.113(1-0.113)}{400}}}=1.074$

The p value for this case would be given by:

$p_v =P(z>1.074)=0.141$

Part c

For this case we see that the p value is higher than the significance level of 0.05 so then we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true proportion workers belonged to unions is significantly higher than 11.3%

8 0

2 years ago

Matt makes $80 a month mowing lawns. His friend James also mows lawns, but he makes x dollars less per month than Matt does. Jam

Ad libitum [116K]

Answer:

he makes $12 less.

Step-by-step explanation:

$80X12=960 - Matts income for the year

960-816=144 -How much less James makes than Matt per year

144/12=12 - How much less James makes than Mat per month

leave 5 stars and a thanks if it was helpful.

3 0

1 year ago

Read 2 more answers

Suppose the firm in this example considers a second product that has a unit profit of $5 and requires 2 hours of production time

user100 [1]

The question is incomplete, here is the complete question

Recall the production model from Section 1.3:

Max 10x

s.t. 5x ≤ 40

x ≥ 0

Suppose the firm in this example considers a second product that has a unit profit of $5 and requires 2 hours for each unit produced. Assume total production capacity remains 40 units. Use y as the number of units of product 2 produced. . Show the mathematical model when both products are considered simultaneously.

Answer:

Max Profit: 10x + 5y

5x + 2y ≤ 40

x ≥ 0, y ≥ 0

Explanation:

x= number of units of product 1 produced

y = number of units of product 2 produced

Since the first product, x, has a unit profit of $10 and Max1 is 10x

Second product, y, has a unit profit of $5, Max2 = 5y

The maximum profit when both products are considered simultaneously is 10x + 5y

Max Profit = 10x + 5y

Time required for each unit of x is 5hours

Therefore, time required for x units is 5x hours

Time required for each unit of y is 2hours

Therefore, time required for y units is 2y hours

Time required for the simultaneous production of both products is 5x + 2y

Since production capacity remains 40 units, 5x+2y ≤40

NB: The values of x and y cannot be negative

5 0

1 year ago

The baker pays $0.80 per pound for sugar and $1.25 per pound for butter. Write an expression that shows how much the baker will

alekssr [168]

X is sugar
y is butter
z is total money

$0.80x + $1.25y = z

the total money spent if the Baker bought 6 pounds of butter and 20 pounds of sugar would be $23.50.

5 0

2 years ago

Read 2 more answers