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2 years ago

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HELP PLEASE!! The cost to fill a car's tank with gas and get a car wash is a linear function of the capacity of the tank. The co

sts of a fill-up and a car wash for three different customers are shown in the table. Write an equation for the function in slope-intercept form. Then, find the cost of a fill-up and a car wash for a customer with a truck whose tank size is 25 gallons.

2 answers:

qwelly [4]2 years ago

6 0

The equation would be y=2.10x+3.25!

Also know as A lol

If you plug in 9 as x and add 3.25 it is an easy way to check the answers for further questions!

Have a good day! :-)

If it is not correct or doesn't look quite right or needs to show proof please comment!

almond37 [142]2 years ago

6 0

Answer:

$f(x)=2.1x+3.25$

<h2>Cost for truck = $55.75.</h2>

Step-by-step explanation:

To right the linear equation in slope-intercept form, we first need to find the slop, which is defined

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Now, we choose to points from the table $(9, 22.15)$ and $(16, 36.85)$ . Using this points, we calculate the slope.

$m=\frac{36.85-22.15}{16-9}=\frac{14.7}{7}=2.1$

Now, using one point and the slope, we find the point-slope form, which is gonna give us the slope-intercept form:

$y-y_{1}=m(x-x_{1}))\\y-22.15=2.1(x-9)\\y=2.1x-18.9+22.15\\y=2.1x+3.25$

Therefore, the right choice is the first one, because it's the only one that has this linear equation.

In addition, to find the cost for a car with 25 gallons of gas size, we just have to replace this number in the x-variable:

$y=2.1(25)+3.25=55.75$

Therefore, the cost for a truck with a tank size of 25 gallons, is $55.75.

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A rectangular plot of land that contains 1500 square meters will be fenced and divided into two equal portions by an additional

WINSTONCH [101]

Let x = the length of the rectangle
Let w= the width

Two sections are required, hence 2w of fence required
2x+3w=500

this can be written as:
3w=1500-2x
w=(1500-2x)/3

Area=x*w
replacing w with our expression:
A=x(1500-2x)/3
A=(500x-2x^2)/3

This is a quadratic equation, if we find the axis of symmetry we will know what value of x gives maximum area:
Axis of symmetry: x=-b/2a
From our equation we get:
a=-2/3; b=1500/3
thus
x=(1500/3)/(-(-2/3))
x=750
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2 years ago

CRITICAL THINKING A local zoo employs 36 people to take care of the animals each day. At most, 24 of the employees work full tim

k0ka [10]

We assume all employees are either full-time or part-time.

36 = 24 + 12

If the number of full-time employees is 24 or less, the number of part-time employees must be 12 or more. (Thinking, based on knowledge of sums.)

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You can write the inequality in two stages.

First, write and solve an equation for the number of full-time employees in terms of the number of part-time employees.
Then apply the given constraint on full-time employees. This gives an inequality you can solve for the number of part-time employees.

Let f and p represent the numbers of full-time and part-time employees, respectively.

... f + p = 36 . . . . . . given

... f = 36 - p . . . . . . . subtract p. This is our expression for f in terms of p.

... f ≤ 24 . . . . . . . . . given

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2 years ago

Two machines are used for filling glass bottles with a soft-drink beverage. The filling process have known standard deviations s

stellarik [79]

Answer:

a. We reject the null hypothesis at the significance level of 0.05

b. The p-value is zero for practical applications

c. (-0.0225, -0.0375)

Step-by-step explanation:

Let the bottles from machine 1 be the first population and the bottles from machine 2 be the second population.

Then we have $n_{1} = 25$ , $\bar{x}_{1} = 2.04$ , $\sigma_{1} = 0.010$ and $n_{2} = 20$ , $\bar{x}_{2} = 2.07$ , $\sigma_{2} = 0.015$ . The pooled estimate is given by

$\sigma_{p}^{2} = \frac{(n_{1}-1)\sigma_{1}^{2}+(n_{2}-1)\sigma_{2}^{2}}{n_{1}+n_{2}-2} = \frac{(25-1)(0.010)^{2}+(20-1)(0.015)^{2}}{25+20-2} = 0.0001552$

a. We want to test $H_{0}: \mu_{1}-\mu_{2} = 0$ vs $H_{1}: \mu_{1}-\mu_{2} \neq 0$ (two-tailed alternative).

The test statistic is $T = \frac{\bar{x}_{1} - \bar{x}_{2}-0}{S_{p}\sqrt{1/n_{1}+1/n_{2}}}$ and the observed value is $t_{0} = \frac{2.04 - 2.07}{(0.01246)(0.3)} = -8.0257$ . T has a Student's t distribution with 20 + 25 - 2 = 43 df.

The rejection region is given by RR = {t | t < -2.0167 or t > 2.0167} where -2.0167 and 2.0167 are the 2.5th and 97.5th quantiles of the Student's t distribution with 43 df respectively. Because the observed value $t_{0}$ falls inside RR, we reject the null hypothesis at the significance level of 0.05

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$(\bar{x}_{1}-\bar{x}_{2})\pm t_{0.05/2}s_{p}\sqrt{\frac{1}{25}+\frac{1}{20}}$ , i.e.,

$-0.03\pm t_{0.025}0.012459\sqrt{\frac{1}{25}+\frac{1}{20}}$

where $t_{0.025}$ is the 2.5th quantile of the t distribution with (25+20-2) = 43 degrees of freedom. So

$-0.03\pm(2.0167)(0.012459)(0.3)$ , i.e.,

(-0.0225, -0.0375)

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2 years ago

Willa is building birdhouses. Each side of the birdhouse will need 9 nails. How many nails does Willa need for each birdhouse? T

erma4kov [3.2K]

The total number of nails will decrease by 14 when Willa will use 7 nails on each side.

Step-by-step explanation:

Sides of one birdhouse = 7

Nails used on each side = 9

Nails used on one birdhouse = No. of sides * Nails used for each side

Nails used on one birdhouse = 7*9 = 63 nails

If she uses 7 nails on each side, then the number of nails used on each birdhouse will be;

No. of nails = 7*7 = 49 nails

Difference = Old value - New value

Difference = 63-49 = 14

The total number of nails will decrease by 14 when Willa will use 7 nails on each side.

Keywords: multiplication, subtraction

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2 years ago

Suppose has a solution. Explain why the solution is unique precisely when has only the trivial solution. Choose the correct answ

Margarita [4]

Complete question is;

Suppose Ax = b has a solution. Explain why the solution is unique precisely when Ax = 0 has only the trivial solution. Choose the correct answer.

A. Since Ax = b is inconsistent, its solution set is obtained by translating the solution set of Ax = 0. For Ax = b to be inconsistent, Ax = 0 has only the trivial solution.

B. Since Ax = b is consistent, its solution set is obtained by translating the solution set of Ax = 0. So the solution set of Ax = b is a single vector if and only if the solution set of Ax = 0 is a single vector, and that happens if and only if Ax = 0 has only the trivial solution.

C. Since Ax = b is inconsistent, then the solution set of Ax = 0 is also inconsistent. The solution set of Ax = 0 is inconsistent if and only if Ax = 0 has only the trivial solution.

D. Since Ax = b is consistent, then the solution is unique if and only if there is at least one free variable in the corresponding system of equations. This happens if and only if the equation Ax = 0 has only the trivial solution.

Answer:

Option B: Since Ax = b is consistent, its solution set is obtained by translating the solution set of Ax = 0. So the solution set of Ax = b is a single vector if and only if the solution set of Ax = 0 is a single vector, and that happens if and only if Ax = 0 has only the trivial solution

Step-by-step explanation:

There are different ways of explaining this but we will explain it algebraic ally.

If Ax = b has a solution, then it can be said to be unique if and only if every column of A will be a pivot column. Now, If every column of A will be a pivot column, then it means that there are no free variables, and thus the homogeneous equation will have only the trivial solution.

Also homogeneous equations are always constant.

Thus the correct option is Option B: Since Ax = b is consistent, its solution set is obtained by translating the solution set of Ax = 0. So the solution set of Ax = b is a single vector if and only if the solution set of Ax = 0 is a single vector, and that happens if and only if Ax = 0 has only the trivial solution

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2 years ago