Give an example of an event in which all of the outcomes are not equally likely. Explain.

A circle has an arc of length 24pi that is intercepted by a central angle of 80 degrees. what is the radius of the circle?

SashulF [63]

Circumference = 2pi r

80/360 x 2pi x r = 24pi
r = 54

8 0

3 years ago

A random sample is selected from a normally distributed population. The following sample statistics are obtained: n = 20, = 30,

Flura [38]

Answer:

b) The margin of error is approximately 3.24

e) The critical value is 1.7921.

Step-by-step explanation:

Step(i):-

Given sample size 'n' =20

Given sample standard deviation 's' = 10

 Margin of error 

The margin of error is determined by

 $M.E = \frac{t_{\alpha } S.D }{\sqrt{n} }$ 

The level of significance ∝ =0.95

The degrees of freedom = n-1 = 20-1=19

t₀.₉₅ = 1.729

$M.E = \frac{1.729 X10 }{\sqrt{20} }$

Margin of error = 3.866

Step(ii):-

 Margin of error 

The margin of error is determined by

 $M.E = \frac{t_{\alpha } S.D }{\sqrt{n} }$ 

Given another sample size n =30

The level of significance ∝ =0.95

The degrees of freedom = n-1 = 30-1=29

t₀.₉₅ = 1.70

$M.E = \frac{1.7021 X10 }{\sqrt{30} } =3.24$

Margin of error = 3.24

5 0

3 years ago

The perpendicular distance of p (3,4) from the y - a x is _____

solmaris [256]

Answer:

a

Step-by-step explanation:

The perpendicular distance from the y- axis is the value of the x- coordinate, so

perpendicular distance is 3 units

8 0

2 years ago

Use the compound interest formulas A= P (1 + r/n) ^nt and A= Pe ^ rt to solve the problem given. Round to the nearest cent. Find

Dennis_Churaev [7]

Answer:

$\$30,460$
$\$30,497$
$\$30,522$
$\$30,535$

Step-by-step explanation:

We know that,

$A=P\left (1+\dfrac{r}{n}\right )^{n\cdot t}$

where,

A = Amount after time t,

P = Principle amount,

r = Rate of interest,

n = Number of times interest is compounded per year,

t = time period in year.

Investment of $25,000 for 4 years at an interest rate of 5% if the money is compounded semiannually

Here,

P = $25,000

r = 5% = 0.05

n = 2 (as compounded semiannually)

t = 4 years

Putting the values,

$A=25000\left (1+\dfrac{0.05}{2}\right )^{2\times 4}$

$=25000\left (1+0.025\right )^{8}$

$=25000\left (1.025\right )^{8}$

$=\$30,460$

Investment of $25,000 for 4 years at an interest rate of 5% if the money is compounded quarterly.

Here,

P = $25,000

r = 5% = 0.05

n = 4 (as compounded quarterly)

t = 4 years

Putting the values,

$A=25000\left (1+\dfrac{0.05}{4}\right )^{4\times 4}$

$=25000\left (1+0.0125\right )^{16}$

$=25000\left (1.0125\right )^{8}$

$=\$30,497$

Investment of $25,000 for 4 years at an interest rate of 5% if the money is compounded monthly.

Here,

P = $25,000

r = 5% = 0.05

n = 12 (as compounded monthly)

t = 4 years

Putting the values,

$A=25000\left (1+\dfrac{0.05}{12}\right )^{12\times 4}$

$A=25000\left (1+\dfrac{0.05}{12}\right )^{48}$

$=\$30,522$

Investment of $25,000 for 4 years at an interest rate of 5% if the money is compounded continuously.

$A= Pe^{rt}$

where,

A = Amount after time t,

P = Principle amount,

r = Rate of interest,

t = time period in year.

Putting all the values,

$A= 25000e^{0.05\times 4}=\$30,535$

It can be observed that, the frequent we compound the amount, the more we get.

7 0

3 years ago

On the coordinate plan, what is the distance between the points (−1, −4) and (−1, −8)?

yaroslaw [1]

Answer:

4

Step-by-step explanation:

To find the distance between two points, we subtract the x - x coordinates and y - y coordinates.

-1 - (-1) = 0

-8 - (-4) = -4

There was only a change in the y coordinates, so we will only account for this.

The distance between the points is four units.

8 0

2 years ago