What is the negative square root of 1

A circular mirror is surrounded by a square metal frame. The radius of the mirror is 5x. The side length of the metal frame is 1

Aleks04 [339]

Answer:

$-25x^{2} (\pi -9)$

Step-by-step explanation:

The area of the metal frame is equal to the area of the square minus the area of the circle.

The area of the square is the side length squared:

$(15x)^{2}$

$=225x^{2}$

The area of the circle is $\pi r^{2}$ , with $r$ being the radius:

$\pi (5x)^{2}$

$=\pi *25x^{2}$

$=25\pi x^{2}$

Now find the area of the metal frame:

$225x^{2} -25\pi x^{2}$

$25x^{2} (9-\pi )$ Factor out the GCF, $25x^{2}$

$-25x^{2} (\pi -9)$ Factor out a $-1$

5 0

3 years ago

Kevin's bank offered him a 4.5% interest rate for his mortgage. If he purchases 3 points, what will be his new rate?

erma4kov [3.2K]

Answer:

The new rate would be 3.75%

Step-by-step explanation:

Purchasing a point simply implies negotiating for a lower rate of interest, which involves paying 1% of the loan in lieu of 1% interest reduction.

A point implies a reduction in interest rate by 0.25% while 3 points would reduce the interest rate by 0.75%(0.25%*3)

New interest rate=4.5%-0.75%=3.75%

7 0

3 years ago

at a party, everyone shook hands with everybody else. there were 66 handshakes. How many people shook hands?

Whitepunk [10]

Answer:

12

Step-by-step explanation:

0 + 1 + 2 + 3+ 4 + 5 + 6 + 7 +8 + 9 + 10 + 11 seems to equal 66. That means there are 11 + 1 = 12 people (don’t forget to count the person who shakes 0 hands)

7 0

3 years ago

Suppose that you play the game with three different friends separately with the following results: Friend A chose scissors 100 t

Yanka [14]

Answer:

Friend A

$\hat p_A= \frac{100}{400}=0.25$

$z=\frac{0.25 -0.333}{\sqrt{\frac{0.333(1-0.333)}{400}}}\approx -3.47$

Friend B

$\hat p_B= \frac{20}{120}=0.167$

$z=\frac{0.167 -0.333}{\sqrt{\frac{0.333(1-0.333)}{120}}}\approx -3.80$

Friend C

$\hat p_C= \frac{65}{300}=0.217$

$z=\frac{0.217-0.333}{\sqrt{\frac{0.333(1-0.333)}{300}}}\approx -4.17$

So then the best solution for this case would be:

-3.47 (100 out of 400; 25%), -3.80 (20 out of 120; 16.7%), -4.17 (65 out of 300; 21.7%)

Step-by-step explanation:

Data given and notation

n represent the random sample taken

X represent the number of scissors selected for each friend

$\hat p=\frac{X}{n}$ estimated proportion of scissors selected for each friend

$p_o=\frac{1}{3}=0.333$ is the value that we want to test

$\alpha$ represent the significance level

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the proportion that the friend will pick scissors is less than 1/3 or 0.333, the system of hypothesis would be:

Null hypothesis: $p\geq 0.333$

Alternative hypothesis: $p < 0.333$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

Friend A

$\hat p_A= \frac{100}{400}=0.25$

$z=\frac{0.25 -0.333}{\sqrt{\frac{0.333(1-0.333)}{400}}}\approx -3.47$

Friend B

$\hat p_B= \frac{20}{120}=0.167$

$z=\frac{0.167 -0.333}{\sqrt{\frac{0.333(1-0.333)}{120}}}\approx -3.80$

Friend C

$\hat p_C= \frac{65}{300}=0.217$

$z=\frac{0.217-0.333}{\sqrt{\frac{0.333(1-0.333)}{300}}}\approx -4.17$

So then the best solution for this case would be:

-3.47 (100 out of 400; 25%), -3.80 (20 out of 120; 16.7%), -4.17 (65 out of 300; 21.7%)

6 0

4 years ago

What is y equal to when x= -2<br><br> Y=-x+4

Alex17521 [72]

Y= -2+4

If X equals -2, you want to plug -2 in for X.

I hope I helped!

:)

5 0

4 years ago