All categories

3 years ago

A truck driver travels from a distributor to a retailer every week. The driver records the

Mathematics

1 answer:

Talja [164]3 years ago

4 0

Complete question is;

A truck driver travels from a distributor to a retailer every week. The driver records the distance that he is from the retailer at different times during his trip. After several weeks of collecting data, the driver creates a scatter plot of the data. The best–fit line is y = 73.6 – 67.8x, where x is the number of hours spent driving and y is the distance, in miles, from the retailer.

Which of the following statements are true? Select all that apply.

The distance from the retailer increases with time.

The distance from the retailer decreases with time.

The distributor is 67.8 miles away from the retailer.

The distributor is 73.6 miles away from the retailer.

The truck is traveling at a rate of 67.8 miles per hour.

Answer:

B: The distance from the retailer decreases with time.

Step-by-step explanation:

Formula for best fit line is;

y = mx + b

Where;

m is slope

b is y-intercept

We are told that the best–fit line is y = 73.6 – 67.8x

This can be written as;

y = -67.8x + 73.6

This means the slope is negative and when x = 0, y = 73.6 which is the y-intercept.

We are told that x is the number of hours spent driving and y is the distance, in miles, from the retailer.

Since we have a negative slope, it means that y is decreasing with increasing values of x.

Thus, we can say that the distance from the retailer decreases with time.

You might be interested in

A scale on a map shows that 2 inches equals 25 miles. How many miles is represented by 1/4 inch on the map?

FinnZ [79.3K]

3.125

to get this answer you divide 25 by 2, then divide that by 4, which equals 3.125

good luck hope I helped:)

8 0

3 years ago

A farmer has 520 feet of fencing to construct a rectangular pen up against the straight side of a barn, using the barn for one s

Setler [38]

Answer:

$310\text{ feet and }210\text{ feet}$

Step-by-step explanation:

GIVEN: A farmer has $520 \text{ feet}$ of fencing to construct a rectangular pen up against the straight side of a barn, using the barn for one side of the pen. The length of the barn is $310 \text{ feet}$ .

TO FIND: Determine the dimensions of the rectangle of maximum area that can be enclosed under these conditions.

SOLUTION:

Let the length of rectangle be $x$ and $y$

perimeter of rectangular pen $=2(x+y)=520\text{ feet}$

$x+y=260$

$y=260-x$

area of rectangular pen $=\text{length}\times\text{width}$

$=xy$

putting value of $y$

$=x(260-x)$

$=260x-x^2$

to maximize $\frac{d \text{(area)}}{dx}=0$

$260-2x=0$

$x=130\text{ feet}$

$y=390\text{ feet}$

but the dimensions must be lesser or equal to than that of barn.

therefore maximum length rectangular pen $=310\text{ feet}$

width of rectangular pen $=210\text{ feet}$

Maximum area of rectangular pen $=310\times210=65100\text{ feet}^2$

Hence maximum area of rectangular pen is $65100\text{ feet}^2$ and dimensions are $310\text{ feet and }210\text{ feet}$

5 0

3 years ago

How much should a family deposit at the end of every 6 months in order to have $4000 at the end of 3 years? The account pays 5.9

ra1l [238]

We are asked to determine the present value of an annuity that is paid at the end of each period. Therefore, we need to use the formula for present value ordinary, which is:

$PV_{ord}=C(\frac{1-(1+i)^{-kn}}{\frac{i}{k}})$

Where:

$\begin{gathered} C=\text{ payments each period} \\ i=\text{ interest rate} \\ n=\text{ number of periods} \\ k=\text{ number of times the interest is compounded} \end{gathered}$

Since the interest is compounded semi-annually this means that it is compounded 2 times a year, therefore, k = 2. Now we need to convert the interest rate into decimal form. To do that we will divide the interest rate by 100: