In Exercises 9 and 10, point B is between A and Con AC. Use the information to

a 1ft long piece of wire needs to be divided into two pieces which will form the shape of a circle and a square. Determine the l

yan [13]

Answer:

Length of wire for circle is 0.44 ft

Length of wire for square is 0.56 ft

Step-by-step explanation:

Let x is circumference of the circle

then

(1-x) = perimeter of the square

Find the radius of the circle

r = (x/2.π)

Find the area of the circle

a = π(x/2π)^2

a = π(x^2/4π^2)

Cancel π

a = x^2/4π

Find the area of the square:

a = (1-x/4)^2

a = (1-2x+x^2)/16

Total area

A = (x^2/4π)+(1-2x+x^2/16)

A = 4x^2+3.142-6.284x+3.142x^2

A = 7.142x^2-6.284x+3.142

Find the axis of symmetry [x = -b/(2a)]

x = -(-6.284)/{2.(7.142)}

x = 6.284/14.284

x = 0.44 ft, the piece of wire creating a circle

and

1 - 0.44 = 0.56 ft, the piece of wire creating the square

These lengths should give minimum area of the circle and square together

7 0

3 years ago

How do you know when an expression is its simplest form

marishachu [46]

Answer:

you know it is when you can't solve it any further. If the numbers cannot be divided by a common number. there is no possible way to make it any more compacted.

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

The skateboard ramp has a width of 20 and a height of 16. What is its slope ( not to scale) ?

slega [8]

Answer:

25.61 ?

Step-by-step explanation:

use Pythagoreans theorem

a^2+b^2=c^2

20^2+16^2=656

sqrt 656=25.61

4 0

2 years ago

A student wanted to construct a 95% confidence interval for the mean age of students in her statistics class. She randomly selec

VMariaS [17]

Answer:

$19.1-3.355\frac{1.5}{\sqrt{9}}=17.42$

$19.1+3.355\frac{1.5}{\sqrt{9}}=20.78$

And the best option would be:

C. [17.42,20.78]

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=19.1$ represent the sample mean

$\mu$ population mean (variable of interest)

s=1.5 represent the sample standard deviation

n=9 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=9-1=8$

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,8)".And we see that $t_{\alpha/2}=$

Now we have everything in order to replace into formula (1):

$19.1-3.355\frac{1.5}{\sqrt{9}}=17.42$

$19.1+3.355\frac{1.5}{\sqrt{9}}=20.78$

And the best option would be:

C. [17.42,20.78]

5 0

3 years ago

there were 64 basketball games during the NCAA tournament 16 of those games were decided by 3 points or less what percentage of

kirill115 [55]

Answer:

25%

Step-by-step explanation:

We can use a proportion to answer this question:

64 represent the 100% of the games

so:

x : 100 = 16 : 64

x = (16*100)/64 = 1600/64 = 25%

7 0

2 years ago