(PLEASE HELP ME FAST! )

Mark made a business trip of 259.5 miles. He averaged 59mph for the first part of the trip and 57mph for the second part. If the

max2010maxim [7]

Answer:

Step-by-step explanation:

d = r * t

Let the time at 59 miles / hour be t

59*t + 57* (4.5 - t) = 259.5 Remove the brackets

59*t + 256.5 - 57*t = 259.5 Combine the left

2t + 256.5 = 259.5 Subtract 228 from both sides

2t = 259.5 - 256.5 Combine

2t = 3 Divide by 2

t = 1.5

So he spent 1.5 hours going at 59 miles per hour

He spent 4.5 - 1.5 = 3 hours going 57 miles per hour.

8 0

2 years ago

In a random sample of 16 residents of the state of Washington, the mean waste recycled per person per day was 2.8 pounds with a

kakasveta [241]

Answer: The required confidence interval would be (2.72,2.89)

Step-by-step explanation:

Since we have given that

Mean = 2.8 pounds

Standard deviation = 0.24 pounds

n = sample size = 16

We need to find the 80% confidence interval for the mean waste.

z=1.341

So, the confidence interval will be

$\bar{x}\pm z\dfrac{\sigma}{\sqrt{n}}\\\\=(2.8\pm 1.341\times \dfrac{0.24}{\sqrt{16}})\\\\=(2.8\pm 1.314\times 0.06)\\\\=(2.8-0.07884,2.8+0.07884)\\\\=(2.72116,2.87884)$

Hence, the required confidence interval would be (2.72,2.89)

4 0

3 years ago

I WILL MARK BRAINLIEST!!! 25 POINTS!!! Select ALL of the correct systems of equations.

choli [55]

The 3rd and 5th systems of equations are the answer.

Point A is at (3,-1), so all you do is input 3 for x and -1 for y into all the equations. For the systems to work, both equations must work with (3,-1).

Only the third and fifth boxes work.

8 0

3 years ago

Which statement is true?

defon

Answer:

B is correct.

7 0

2 years ago

A metal cylinder can with an open top and closed bottom is to have volume 4 cubic feet. Approximate the dimensions that require

Aleksandr-060686 [28]

Answer:

$r\approx 1.084\ feet$

$h\approx 1.084\ feet$

$\displaystyle A=11.07\ ft^2$

Step-by-step explanation:

<u>Optimizing With Derivatives </u>

The procedure to optimize a function (find its maximum or minimum) consists in :

Produce a function which depends on only one variable
Compute the first derivative and set it equal to 0
Find the values for the variable, called critical points
Compute the second derivative
Evaluate the second derivative in the critical points. If it results positive, the critical point is a minimum, if it's negative, the critical point is a maximum

We know a cylinder has a volume of 4 $ft^3$ . The volume of a cylinder is given by

$\displaystyle V=\pi r^2h$

Equating it to 4

$\displaystyle \pi r^2h=4$

Let's solve for h

$\displaystyle h=\frac{4}{\pi r^2}$

A cylinder with an open-top has only one circle as the shape of the lid and has a lateral area computed as a rectangle of height h and base equal to the length of a circle. Thus, the total area of the material to make the cylinder is

$\displaystyle A=\pi r^2+2\pi rh$

Replacing the formula of h

$\displaystyle A=\pi r^2+2\pi r \left (\frac{4}{\pi r^2}\right )$

Simplifying

$\displaystyle A=\pi r^2+\frac{8}{r}$

We have the function of the area in terms of one variable. Now we compute the first derivative and equal it to zero

$\displaystyle A'=2\pi r-\frac{8}{r^2}=0$

Rearranging

$\displaystyle 2\pi r=\frac{8}{r^2}$

Solving for r

$\displaystyle r^3=\frac{4}{\pi }$

$\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet$

Computing h

$\displaystyle h=\frac{4}{\pi \ r^2}\approx 1.084\ feet$

We can see the height and the radius are of the same size. We check if the critical point is a maximum or a minimum by computing the second derivative

$\displaystyle A''=2\pi+\frac{16}{r^3}$

We can see it will be always positive regardless of the value of r (assumed positive too), so the critical point is a minimum.

The minimum area is

$\displaystyle A=\pi(1.084)^2+\frac{8}{1.084}$

$\boxed{ A=11.07\ ft^2}$

8 0

2 years ago