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1 year ago

Ms. Smith drove a total of 700 miles on a business to

Mathematics

1 answer:

kiruha [24]1 year ago

6 0

Answer:

The total amount of gas Ms. Smith used on the trip is $25.

Step-by-step explanation:

To solve this problem, we first must figure out how many gallons of gas Ms. Smith used on her trip. If she drove 700 miles and averaged 35 miles per gallon, if we divide 700 by 35 we can figure out how many gallons she used.

700/35 = 20

Thus, Ms. Smith used 20 gallons on her trip. Next, to figure out what the cost of the gasoline was, we must multiply the number of gallons (20) by the cost of gasoline per gallon ($1.25).

20 gallons * $1.25/gal = $25

Therefore, the cost of gasoline for the trip was $25.

Hope this helps!

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Which equation represents the line that passes through (–6, 7) and (–3, 6)? y = –y equals negative StartFraction one-third EndFr

DiKsa [7]

Answer:

$y=-\frac{1}{3} x+5$

Step-by-step explanation:

Notice that the answers they give you to choose from are all lines in slope y-intercept form, it would be very simple to just find the answer finding yourself the slope and y-intercept of the line in question.

Since they give you two points $(x_1,y_1)$ and $(x_2,y_2)$ for the line, use them to find the slope of the line that goes through them, with the formula: $slope=\frac{y_2-y_1}{x_2-x_1} =\frac{7-6}{-6-(-3)} =\frac{1}{-3} =-\frac{1}{3}$

Therefore, the slope of the line must be $-\frac{1}{3}$

Now, find the y-intercept (b) using the general form of a line with the given slope:

$y=-\frac{1}{3}x +b$

Use one of the given coordinate points to request that the line passes through it. For example, through the point (-3,6) (when x = -3, y must be 6):

$y=-\frac{1}{3} x+b\\6=-\frac{1}{3}(-3)+b\\6=1+b\\b=6-1=5$

then the y-intercept must be 5. Therefore our line is : $y=-\frac{1}{3}x +5$ which appears listed as your second choice.

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2 years ago

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An Olympic athlete of mass 80kg competes in a 100m race. What is the best estimate of his mean kinetic energy during the race?

kipiarov [429]

For this question, you need to know that the average velocity of a 100m Olympic athlete is 10 m/s before you start solving the equation. The equation is K (energy in Jules) = 1/2 mv^2 (where m is the mass in kg and v the speed in meters per second).
The correct answer is 4000J. To see how I got it, take a look at the attachment.

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2 years ago

The unit cost, in dollars, to produce bins of cat food is $3 and the fixed cost is $6972. The price-demand function, in dollars

stellarik [79]

Answer:

Revenue , Cost and Profit Function

Step-by-step explanation:

Here we are given the Price/Demand Function as

P(x) = 253-2x

which means when the demand of Cat food is x units , the price will be fixed as 253-2x per unit.

Now let us revenue generated from this demand i.e. x units

Revenue = Demand * Price per unit

R(x) = x * (253-2x)

= $253x-2x^2$

Now let us Evaluate the Cost Function

Cost = Variable cost + Fixed Cost

Variable cost = cost per unit * number of units

= 3*x

= 3x

Fixed Cost = 6972 as given in the problem.

Hence

Cost Function C(x) = 3x+6972

Let us now find the Profit Function

Profit = Revenue - Cost

P(x) = R(x) - C(x)

= $253x-2x^2 - (3x + 6972)$

= $253x-3x-2x^2-6972\\= 250x-2x^2-6972\\=-2x^2+250x-6972\\$

Now we have to find the quantity at which we attain break even point.

We know that at break even point

Profit = 0

Hence P(x) = 0

$-2x^2+250x-6972=0\\$

now we have to solve the above equation for x

Dividing both sides by -2 we get

$x^2-125x+3486=0$

Now we have to find the factors of 3486 whose sum is 125. Which comes out to be 42 and 83

Hence we now solve the above quadratic equation using splitting the middle term method .

Hence

$x^2-42x-83x+3486=0\\x(x-42)-83(x-42)=0\\(x-42)(x-83)=0\\$

Either (x-42) = 0 or (x-83) = 0 therefore

if x-42= 0 ; x=42

if x-83=0 ; x=83

Smallest of which is 42. Hence the number of units at which it attains the break even point is 42.

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2 years ago

Charlotte is redecorating the master bedroom in her house. She has already purchased a new bedroom set and also plans to paint t

jasenka [17]

Answer:

a. 30%

b. $893.59

$\frac{(351.10-x)}{893.59}\times 100\%$

Step-by-step explanation:

a. Given that the carpet costs $427.35, the labor costs $212.52 and other flooring supplies costs $75.

#To get the percent of the flooring bill that will go towards the cost of labor:

$\% labor\ cost=\frac{labor \ cost}{Total \ flooring \ cost}\times 100\%\\\\=\frac{212.52}{427.35+212.52+75}\times 100\%\\\\=\frac{212.52}{714.87}\times 100\%\\\\=29.73\%\approx30\%$

Hence, labor costs 30% of the total flooring costs.

b.The total flooring costs is :

$F_c=212.52+427.35+75\\\\=714.87$

Given that she spends 25% more on furniture than on flooring, we multiply the flooring cost by 125% to get the furniture costs:

$Furniture \ Cost= Flooring \ C\ost \times 125%\\\\=714.87\times 1.25\\\\=893.59$

Hence, she spends $893.59 on furniture.

c.To get what percentage of furniture cost was the night stand.

-Given the total furniture cost is $893.59:

Let x be the cost of the dresser and y the cost of the nightstand;

$x+y=Furniture\ cost -Bed \ cost\\\\x+y=893.59-558.49=351.1\\\\y=351.1-x$

The percentage is then calculated as:

$\% cost \ of \ nightstand=\frac{cost \ of \ nighstand}{Furniture \ Cost}\times 100\%\\\\=\frac{351.10-x}{893.59}\times 100\%\\\\=\frac{(351.10-x)}{893.59}\times 100\%$

Hnece the percentage cost of the night stand is $\frac{(351.10-x)}{893.59}\times 100\%$

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2 years ago

Elsa tries to solve the following equation, and determines there is no solution. Is she correct? Explain.

Vlad [161]

Elsa's answer is incorrect since there is a solution of the given equation. In the given logarithmic problem, we need to simplify the problem by transposing log2(3x+5) in the opposite side. The equation will now be log2x-log2(3x+5)=4. Using properties of logarithm, we further simplify the problem into a new form log (2x/6x+10)=4. Then transform the equation into base form 10^4=(2x/6x+10) and proceed in solving for x value which is equal to 1.667.

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2 years ago

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