Help me with this please. :(

In a sample of 700 gas stations, the mean price for regular gasoline at the pump was $2.894 per gallon and the standard deviati

frez [133]

Answer:

$P(x < 2.892) = 4.36\%$

Step-by-step explanation:

Given

$N = 700$ --- Population

$\mu = 2.894$ -- Mean

$\sigma = 0.009$ --- Standard deviation

$n = 55$ -- Sample

Required: $P(x < 2.892)$

This question will be solved using the finite correction factor

First, calculated the z score

$z = \frac{x - \mu}{\sqrt{\frac{N -n}{N -1}} * \frac{\sigma}{\sqrt n}}$

$z = \frac{2.892 - 2.894}{\sqrt{\frac{700 -55}{700 -1}} * \frac{0.009}{\sqrt {55}}}$

$z = \frac{-0.002}{\sqrt{\frac{645}{699}} * \frac{0.009}{7.42}}$

$z = \frac{-0.002}{\sqrt{0.92} * \frac{0.009}{7.42}}$

$z = \frac{-0.002}{0.95917 * 0.0012129}$

$z = -1.71$

So:

$P(x < 2.892) = P(z < -1.71)$

Using z table

$P(x < 2.892) = 0.043633$

$P(x < 2.892) = 4.36\%$

3 0

3 years ago

Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by

11111nata11111 [884]

Answer:

The dimension of the open rectangular box is $8.216\times 4.216\times 1.392$ .

The volume of the box is 8.217 cubic inches.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the open rectangular box ?

Solution :

Let the height be 'x'.

The length of the box is '11-2x'.

The breadth of the box is '7-2x'.

The volume of the box is $V=l\times b\times h$

$V=(11-2x)\times (7-2x)\times x$

$V=4x^3-36x^2+77x$

Derivate w.r.t x,

$V'(x)=4(3x^2)-2(36x)+77$

$V'(x)=12x^2-72x+77$

The critical point when V'(x)=0

$12x^2-72x+77=0$

Solve by quadratic formula,

$x=\frac{18+\sqrt{93}}{6},\frac{18-\sqrt{93}}{6}$

$x=4.607,1.392$

Derivate again w.r.t x,

$V''(x)=24x-72$

Now, $V''(4.607)=24(4.607)-72=38.568>0$ (+ve)

$V''(1.392)=24(1.392)-72=-38.592$ (-ve)

So, there is maximum at x=1.392.

The length of the box is $l=11-2x$

$l=11-2(1.392)=8.216$

The breadth of the box is $b=7-2x$

$b=7-2(1.392)=4.216$

The height of the box is h=1.392.

The dimension of the open rectangular box is $8.216\times 4.216\times 1.392$ .

The volume of the box is $V=l\times b\times h$

$V=8.216\times 4.216\times 1.392$

$V=48.217\ in.^3$

The volume of the box is 8.217 cubic inches.

5 0

3 years ago

(FIRST PERSON TO ANSWER GETS BRAINLIEST!!!) A student earned $2500.75 at his summer job making $12.50 per hour. Let h represent

laiz [17]

Answer:

$12.50 \space\ h = 2500.75$

Step-by-step explanation:

We know from the question that the student earned $12.50 per hour.

Using this information, we can say that if the student worked for h hours, they would make a total of 12.50 × h dollars.

We also know that the total money they earned is $2500.75.

∴ Therefore, we can set up the following equation:

$\boxed {12.50 \times h = 2500.75}$

From here, if we want to, we can find the number of hours worked by simply making h the subject of the equation and evaluating:

h = $\frac{2500.75}{12.50}$

= 200.6 hours

5 0

2 years ago

Read 2 more answers

A family has two cars. During one particular week, the first car consumed 15 gallons of gas. The two cars Drove a combined total

julia-pushkina [17]

Answer:

Car 1 : 40 miles per gallon

Car 2: 25 miles per gallon

Step-by-step explanation:

family has two cars. During one particular week, the first car consumed 15 gallons of gas. The second car consumed 25 gallons of gas. The two cars Drove a combined total of 1475 miles and the sum of their fuel efficiency was 65 miles per gallon. What were the fuel efficiency of each of the cars that week

Given that :

Fuel efficiency , car 1 = x

Fuel efficiency , car 2 = y

x + y = 65 - - (1)

15x + 35y = 1475 - - - (2)

x = 65 - y

15(65-y) + 35y

975 - 15y + 35y = 1475

20y = 14875 - 975

20y = 500

y = 25

Put y = 25 in (1)

x + y = 65

x + 25 = 65

x = 65 - 25

x = 40

6 0

3 years ago

What is |9|? -18 -9 9 18

Veseljchak [2.6K]

Answer:

the true answer is 9

Step-by-step explanation:

Because the product of the absolute value is the same number and positive

6 0

3 years ago

Read 2 more answers