What is the value of y?

f there are 26 students in each third-grade class and 3 third-grade classes in the school, how many students will attend an asse

kirza4 [7]

Answer:

74 students

Step-by-step explanation:

26x3=78

78-4=74

8 0

3 years ago

Find the volume of a right circular cone that has a height of 12 cm and a base with a diameter of 18 cm.

algol [13]

Answer:1017.36 cm^3

Step-by-step explanation:

Diameter=18cm

Radius=r=18/2=9cm

Height=h=12cm

Volume of cone=1/3 x π x r^2 x h

Volume of cone=1/3 x 3.14 x 9^2 x 12

Volume of cone=1/3 3.14 x 9 x 9 x 12

Volume =(1x3.14x9x9x12) ➗ 3

Volume =3052.08 ➗ 3

Volume =1017.36

Volume of cone=1017.36 cm^3

6 0

4 years ago

Graph the system of equations on graph paper. {8x+6y=48 {2x−3y=−6 Which statements are true about the solution to the system of

CaHeK987 [17]

Answer:

The x-coordinate of the solution is 3.

The ordered pair that is the solution to the system lies in Quadrant I

The y-coordinate of the solution is 4

The graph in the attached figure

Step-by-step explanation:

we have

$8x+6y=48$ ----> equation A

$2x-3y=-6$ ----> equation B

To graph the system of equations , find the intercepts of each line

Line A

Find the y-intercept (value of y when the value of x is equal to zero)

For x=0

$8(0)+6y=48\\y=8$

The y-intercept is the point is (0,8)

Find the x-intercept (value of x when the value of y is equal to zero)

For y=0

$8x+6(0)=48\\x=6$

The x-intercept is the point is (6,0)

Plot the points (0,8) and (6,0), and connect them to graph the line A

Line B

Find the y-intercept (value of y when the value of x is equal to zero)

For x=0

$2(0)-3y=-6\\y=2$

The y-intercept is the point is (0,2)

Find the x-intercept (value of x when the value of y is equal to zero)

For y=0

$2x-3(0)=-6\\x=-3$

The x-intercept is the point is (-3,0)

Plot the points (0,2) and (-3,0), and connect them to graph the line B

Remember that the solution of the system of equations is the intersection point both graphs

The solution of the system is the point (3,4)

The graph in the attached figure

Verify each statement

case 1) The x-coordinate of the solution is −3

The statement is false

Because the x-coordinate of the solution is 3

case 2) The x-coordinate of the solution is 3.

The statement is true (see the explanation)

case 3) The ordered pair that is the solution to the system lies in Quadrant I

The statement is true

Because, the x-coordinate and the y-coordinate of the solution are positive values

case 4) The y-coordinate of the solution is 4

The statement is true (see the explanation)

case 5) The ordered pair that is the solution to the system lies in Quadrant II

The statement is false

Because, the ordered pair that is the solution to the system lies in Quadrant I

case 6) The y-coordinate of the solution is 3

The statement is false

Because, the y-coordinate of the solution is 4

8 0

4 years ago

Small Sample:

agasfer [191]

Answer:

The 80% confidence interval for the proportion of companies that are planning to increase their workforce is (0.033, 0.331).

A sample size of 8852 is needed.

Step-by-step explanation:

First question:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

Only 2 of the 11 companies were planning to increase their workforce.

This means that $n = 11, \pi = \frac{2}{11} = 0.1818$

80% confidence level

So $\alpha = 0.2$ , z is the value of Z that has a pvalue of $1 - \frac{0.2}{2} = 0.9$ , so $Z = 1.28$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1818 - 1.28\sqrt{\frac{0.1818*0.8182}{11}} = 0.033$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1818 + 1.28\sqrt{\frac{0.1818*0.8182}{11}} = 0.331$

The 80% confidence interval for the proportion of companies that are planning to increase their workforce is (0.033, 0.331).

Second question:

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

A poll taken in July 2010 estimates this proportion to be 0.36.

This means that $\pi = 0.36$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.01?

This is n for which M = 0.01. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.01 = 1.96\sqrt{\frac{0.36*0.64}{n}}$

$0.01\sqrt{n} = 1.96\sqrt{0.36*0.64}$

$\sqrt{n} = \frac{1.96\sqrt{0.36*0.64}}{0.01}$

$(\sqrt{n})^2 = (\frac{1.96\sqrt{0.36*0.64}}{0.01})^2$

$n = 8851.04$

Rounding up(as a sample of 8851 will have a margin of error slightly over 0.01):

A sample size of 8852 is needed.

4 0

3 years ago

PLEASE HELP! TRIG! 7 points! I really need help

Nana76 [90]

By the law of sines,

$\dfrac{\sin\theta}{2\pi}=\dfrac{\sin110^\circ}{5\pi}\implies\sin\theta=\dfrac{2\sin110^\circ}5$

$\implies\theta=\sin^{-1}\dfrac{2\sin110^\circ}5\approx22.08^\circ$

6 0

3 years ago