What is the factor of this polynomial: x^2-7x+6

Find the area of the shaded regions.

Veronika [31]

Answer:

$A = A_c-A_t=4\pi -8=4.5664cm^2$

Step-by-step explanation:

The area of the shaded region can be calculated as the area of the semicircle less the area of the right triangle.

The area of the right triangle can be calculated as:

$A_t=\frac{b*h}{2} =\frac{LM*MN}{2}$

Where LM and MN have the same length because the internal angles are L=45°, M=90°, and N=45°. So the area is:

$A_t=\frac{4*4}{2}=8$

The diameter of the circle can be calculated using the Pythagorean theorem as:

$D=\sqrt{(LM)^2+(MN)^2} =\sqrt{4^2+4^4}=4\sqrt{2}$

So, the radius is $r=2\sqrt{2}$

Finally, the area of the semicircle is:

$A_c=\frac{\pi*r^2 }{2}=\frac{\pi*(2\sqrt{2})^2 }{2}=4\pi$

So, the area of the shaded region is:

$A = A_c-A_t=4\pi -8=4.5664cm^2$

6 0

3 years ago

After comparing response times between the audio and picture portions of the MIT test, the t-test resulted in a t-value of 2.97.

Veronika [31]

Answer:

e. reject the null hypothesis the p value is less than 0.05. therefore the difference is significant.

Step-by-step explanation:

given that after comparing response times between the audio and picture portions of the MIT test, the t-test resulted in a t-value of 2.97.

test statistic t = 2.97

Sample size n =250

Critical value of t at 95% is 1.96

We find that test statistic absolute value is greater than 1.96

So p value would be less than 0.05

This implies that null hypothesis stands in the rejected region.

So reject null hypothesis would be correct conclusion. Sample size cannot be said to be small as more than 30 itself is a good sample size.

e. reject the null hypothesis the p value is less than 0.05. therefore the difference is significant.

5 0

3 years ago

A concrete mix is designed to withstand 3000 pounds per square inch (psi) of pressure. The following data represent the strengt

ss7ja [257]

Answer:

Mean = 3640

Mode = 4100

Median = 3830.

Step-by-step explanation:

We are given the following data in the question:

Strength of casts (in psi):

3970,4100,3100,3200,2950,3830,4100,4050,3460

Formula:

$Mean = \displaystyle\frac{\text{Sum of all observation}}{\text{Total number of observations}}$

$\displaystyle\frac{3970+4100+3100+ 3200+ 2950+ 3830+4100+ 4050+ 3460}{9} = \displaystyle\frac{32760} {9} = 3640$

Mode is the entry with most frequency. Thus, for the given sample mode = 4100.

Median

Since n = 9 is odd,

Formula:

$Median = \displaystyle\frac{n+1}{2}th~term$

Data in ascending order:

2950,3100,3200,3460,3830,3970,4050,4100,4100

Median = 5th term = 3830.

7 0

3 years ago

Please help me I can’t fail it

Hoochie [10]

Answer:

Step-by-step explanation:

1.rational

2.irrational

3.rational

4.rational

5.rational

6.irrational

8 0

3 years ago

The daily number of miles driven by a bus driver during a week are 50, 65, 78, 54, 53, 61, 79, and 78.

marta [7]

Answer:

C Both the mean and median are appropriate measures of center.

Step-by-step explanation:

5 0

2 years ago

What is the factor of this polynomial: x^2-7x+6​

What is the factor of this polynomial: x^2-7x+6