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MAVERICK [17]
2 years ago
13

Five days a week, you carpool with 3 co-workers and take turns driving each week. It is 14 miles from your home to your office.

When you drive the carpool you must go an extra 4 miles to pick up your co-workers. If your car averages 18 miles per gallon, about how many gallons of gas should you save every 4 weeks by carpooling?
Mathematics
2 answers:
Vladimir [108]2 years ago
7 0

you will save 10 gallons

Sphinxa [80]2 years ago
4 0

Answer:

You will save 21.11 gallons of gas every 4 weeks by carpooling.

Step-by-step explanation:

It is 14 miles from your home to your office. Means 28 miles total while returning.

And if there is no carpool, you will drive =28\times5\times4=560 miles

And amount of gas used will be = \frac{560}{18}=31.11 gallons

-------------------------------------------------------------------------------------------------

Now, when you are car pooling, you will save the cost for three weeks means you will take out your car for 1 week only.

But you have to go additional 8 miles (including dropping off the co worker)

So, the total journey for 1 day will be of 14+14+4+4=36 miles

Hence, for 1 week, you will drive : 36\times5\times1=180 miles.

Gallons of gas used = \frac{180}{18}=10 gallons

-------------------------------------------------------------------------------------------------

So, gallons of gas saved = 31.11-10=21.11 gallons

Hence, you will save 21.11 gallons of gas every 4 weeks by carpooling.

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Company F sells fabrics known as fat quarters, which are rectangles of fabric created by cutting a yard of fabric into four piec
jeka94

Answer:

a) Y 0 1 2

P(Y) 0.58 0.23 0.11

b) mean= 0.45, S.D= 0.6718

c) mean= 1.285, S.D= 8.74

Step-by-step explanation:

a) The following table shows the probability distribution of X:

X 0 1 2 3 4 or more

P(X) 0.58 0.23 0.11 0.05 0.03

Defect >2 = cannot be sold

Y = the number of defects on a fat quarter that can be sold by Company F.

Y = defect that can be sold

Y = Defect less or equal to 2 = 0,1,2

Probability distribution of the random variable Y:

Y 0 1 2

P(Y) 0.58 0.23 0.11

b) mean of Y (μ)

μ = Σ x*P(Y)

= (0*0.58) +(1*0.23)+(2*0.11)

= 0+0.23+0.22 = 0.45

Standard deviation of Y = σ

σ = Σ√(x-mean)^2*P(Y)

= Σ√[(x- μ )^2*P(Y)]

= √[(0-0.45)^2*0.58+ (1-0.45)^2*0.23 + (2-0.45)^2*0.11]

= √[0.11745 + 0.069575 +0.264275

= √(0.4513

σ = 0.6718

Company G:

σ for defect that be sold = 0.66

μ for defect that be sold = 0.40

Difference between μ of F and μ of G

= 0.45-0.40 = 0.05

Difference between σ of F and σ of G

= 0.67-0.66 = 0.01

Selling price of fat quarter without defect = $5

Discount per defect = $1.5

Selling price per defect = 5-1.5 = $3.5

Discount per 2 defect = $1.5*2 = $3

Selling price per defect = 5-3 = $2

Since defect to be sold cannot be greater than 2, let Y = 5,3,2

Probability distribution of the selling price Y:

Y 5 3 2

P(Y) 0.58 0.23 0.11

μ = (5*0.58) +(3.5*0.23)+(2*0.11)

μ = 2.9+0.805+0.22 =1.285

σ = Σ√[(x- μ )^2*P(Y)]

σ = √[(5-1.285)^2*0.58+ (3-1.285)^2*0.23 + (2-1.285)^2*0.11]

σ = 8.00+0.68+0.06 = 8.74

7 0
2 years ago
Amy is 1 year older than Ben. The sum of their ages is greater than 33 and less than 45 Find all possible ages of Ben
Ainat [17]

Answer:

17, 18, 19, 20, 21

Step-by-step explanation:

4 0
1 year ago
Find a linear equation to model this real-world application:
SSSSS [86.1K]

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

<em><u>Solution:</u></em>

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

3 0
1 year ago
A set of notations (SSS, SAS, ASA and RHS) is used to describe/prove that two triangles are conjurent. For each pair of triangle
lana66690 [7]

Answer:

The answer is given below

Step-by-step explanation:

The statements are not given but from this definition, you should be able to select the correct statement.

Triangles are said to be congruent if they have the same size and shape. A triangle is made up of six (three sides and three angles) but only three is usually needed to prove triangle congruence. These are:

a) Side - Side - Side (SSS): Two triangles are congruent if the length of their three sides are equal to each other.

b) Side- angle- side (SAS): If two sides and one angle of a triangle is equal to two sides and a angle of another triangle then the two triangles are congruent to each other.

c) Angle - side - angle (ASA): If two angles and a side of a triangle are equal to a corresponding two angles and a side of another triangle then the two triangles are congruenr.

d) Right angle - hypotenuse - side (RHS): If for two right angled triangles, their hypotenuse and a side (leg) are equal, then the two triangles are congruent.

4 0
1 year ago
A worker drives a 0.500 kg spike into a rail tie with a 2.50 kg sledgeham-
Marianna [84]

Total internal energy increases by 1760 J

Step-by-step explanation:

The kinetic energy of an object is the energy possessed by the object due to its motion.

It is calculated as

KE=\frac{1}{2}mv^2

where

m is the mass of the object

v is its speed

For the hammer in this problem:

m = 2.50 kg

v = 65.0 m/s

So its kinetic energy is

KE=\frac{1}{2}(2.50)(65)^2=5281 J

Then the problem says that 1/3 of the hammer's kinetic energy is converted into internal energy: therefore, the total internal energy increases by

\frac{1}{3}KE=\frac{1}{3}(5281)=1760 J

Learn more about kinetic energy:

brainly.com/question/6536722

#LearnwithBrainly

8 0
2 years ago
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