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1 year ago

Find an equation for the perpendicular bisector of the line segment whose endpoints are (1,−8) and (9,2)

Mathematics

1 answer:

Len [333]1 year ago

7 0

Answer: $y+3=-\frac{4}{5}(x-5)$

Step-by-step explanation:

For it to bisect the segment, we need to find the midpoint.

The midpoint is $\left(\frac{1+9}{2}, \frac{-8+2}{2} \right)=(5, -3)$

Now, for it to be perpendicular, we need to use the fact that perpendicular lines have slopes that are negative reciprocals of each other.

The slope of the given segment is $\frac{-8-2}{1-9}=\frac{5}{4}$ , so the slope of the perpendicular bisector is $-\frac{4}{5}$

Thus, the equation of the line in point-slope form is $\boxed{y+3=-\frac{4}{5}(x-5)}$

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The distribution of the number of viewers for the American Idol television show follows a normal distribution with a mean of 26

hjlf

Answer:

Probability that next week's show will have between 30 and 37 million viewers is 0.2248.

Step-by-step explanation:

We are given that the distribution of the number of viewers for the American Idol television show follows a normal distribution with a mean of 26 million with a standard deviation of 8 million.

Let X = number of viewers for the American Idol television show

So, X ~ N( $\mu=26,\sigma^{2}=8^{2}$ )

Now, the z score probability distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = population mean = 26 million

$\sigma$ = standard deviation = 8 million

So, probability that next week's show will have between 30 and 37 million viewers is given by = P(30 < X < 37) = P(X < 37) - P(X $\leq$ 30)

P(X < 37) = P( $\frac{X-\mu}{\sigma}$ < $\frac{37-26}{8}$ ) = P(Z < 1.38) = 0.91621

P(X $\leq$ 30) = P( $\frac{X-\mu}{\sigma}$ $\leq$ $\frac{30-26}{8}$ ) = P(Z $\leq$ 0.50) = 0.69146

Therefore, P(30 < X < 37) = 0.91621 - 0.69146 = 0.2248

Hence, probability that next week's show will have between 30 and 37 million viewers is 0.2248.

4 0

3 years ago

If 60 is 75% of s value, what is that value

ohaa [14]

Let's write it down:
"60 is 75% of s" means:

60=75%*s

75% is $\frac{75}{100}= \frac{3}{4}$ , (percent just means "out of 100" so we just divide it by 100) so we can also write:

60= $\frac{3}{4}$ s

now, let's multiply both sides by 4:

240=3s

and divide by 3:
80=s

So we have the result that the original value, s, is 80!

3 0

3 years ago

Given f(x)=2a^2b+3a^3b^2+2a^2b^4 what is the degree?

lilavasa [31]

We have the following function:
f (x) = 2a ^ 2b + 3a ^ 3b ^ 2 + 2a ^ 2b ^ 4
We note that the function depends on x because it is f (x).
However, there is no variable x in the function.
Therefore we can assume that the function is constant, since:
a = constant
b = constant
Therefore, the degree of the function is zero
Answer:
The function is zero degree.

7 0

3 years ago

Express 8 sin^2x - 10sinxcosx in the form a+b sin(2x+c).

ladessa [460]

8 sin2x - 10sinxcosx = 8*2sinXcosX-10sinXcosX = 16sinXcosX - 10sinXcosX = 6sinXcosX=3sin2x

7 0

3 years ago

Can someone help me pleaseee :) u have to make the questions become y = mx + b

Leona [35]

Answer:

3. 8y= -7x -12

4. -3y= 4x -12

5. 7y= -2x +4

Do you want me to do the rest?

did you got it??

The rest are:

6. -3y =6x +12

7. -10y= 5x+20

8. 4y=2x +12

5 0

3 years ago