Answer:
and ![(4.5,6.5)](https://tex.z-dn.net/?f=%284.5%2C6.5%29)
Step-by-step explanation:
we have the coordinates
A(2,7),B(2,2),C(7,6)
we know that
The mid segment of triangle ABC that is parallel to line AB is located between the mid point AC and the mid point BC
The formula to calculate the midpoint between two points is equal to
![(\frac{x1+x2}{2},\frac{y1+y2}{2})](https://tex.z-dn.net/?f=%28%5Cfrac%7Bx1%2Bx2%7D%7B2%7D%2C%5Cfrac%7By1%2By2%7D%7B2%7D%29)
step 1
Find the mid point AC
we have
A(2,7),C(7,6)
substitute in the formula
![(\frac{2+7}{2},\frac{7+6}{2})](https://tex.z-dn.net/?f=%28%5Cfrac%7B2%2B7%7D%7B2%7D%2C%5Cfrac%7B7%2B6%7D%7B2%7D%29)
![(4.5,6.5)](https://tex.z-dn.net/?f=%284.5%2C6.5%29)
step 2
Find the mid point BC
we have
B(2,2),C(7,6)
substitute in the formula
![(\frac{2+7}{2},\frac{2+6}{2})](https://tex.z-dn.net/?f=%28%5Cfrac%7B2%2B7%7D%7B2%7D%2C%5Cfrac%7B2%2B6%7D%7B2%7D%29)
![(4.5,4)](https://tex.z-dn.net/?f=%284.5%2C4%29)
therefore
The endpoints of the mid segment of triangle ABC that is parallel to line AB are
and ![(4.5,6.5)](https://tex.z-dn.net/?f=%284.5%2C6.5%29)
Question 7:
Diameter = 6.2 cm so Radius = 3.1 cm
A=πr² = 3.14 × 3.1² = 30.1754 cm² = 30.18 cm²
Question 8:
Circumference = 2πr
16π = 2πr
therefore 16 = 2r so r = 8cm
It’s definitely A
Ex: f(x)=8x+2
f(x)=8(-4)+2
f(x)=-32+2
f(x)=-30
We have that
x²<span> + 7x + c
</span><span>Group
terms that contain the same variable
</span>(x² + 7x )+ c
<span>Complete
the square. Remember to balance the equation
</span>(x² + 7x+3.5² )+ c-3.5²
Rewrite as perfect squares
(x+3.5)²+ c-3.5²
so
c-3.5² must be zero
c-3.5²=0------- c=3.5²------> c=12.25
the answer isthe value of c must be 12.25
Answer:
The 99% confidence interval for the population mean is 22.96 to 26.64
Step-by-step explanation:
Consider the provided information,
A sample of 49 customers. Assume a population standard deviation of $5. If the sample mean is $24.80,
The confidence interval if 99%.
Thus, 1-α=0.99
α=0.01
Now we need to determine ![z_{\frac{\alpha}{2}}=z_{0.005}](https://tex.z-dn.net/?f=z_%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%3Dz_%7B0.005%7D)
Now by using z score table we find that ![z_{\frac{\alpha}{2}}=2.58](https://tex.z-dn.net/?f=z_%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%3D2.58)
The boundaries of the confidence interval are:
![\mu-z_{\frac{\alpha}{2}}\times \frac{\sigma}{\sqrt{n} }\\24.80-2.58\times \frac{5}{\sqrt{49}}=22.96\\\mu+z_{\frac{\alpha}{2}}\times \frac{\sigma}{\sqrt{n} }\\24.80+2.58\times \frac{5}{\sqrt{49}}=26.64](https://tex.z-dn.net/?f=%5Cmu-z_%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%5Ctimes%20%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%20%7D%5C%5C24.80-2.58%5Ctimes%20%5Cfrac%7B5%7D%7B%5Csqrt%7B49%7D%7D%3D22.96%5C%5C%5Cmu%2Bz_%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%5Ctimes%20%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%20%7D%5C%5C24.80%2B2.58%5Ctimes%20%5Cfrac%7B5%7D%7B%5Csqrt%7B49%7D%7D%3D26.64)
Hence, the 99% confidence interval for the population mean is 22.96 to 26.64