Answer:
if m and n are parallel then the value of x is 11
Answer:
∠y = 62.5°
∠x = 27.5°
Step-by-step explanation:
z is right angle. ∠z = 90°
∠x = ∠y - 35
∠x + ∠y + ∠z = 180 {Angle sum property of triangle}
y - 35 + y + 90 = 180
y + y - 35 + 90 = 180 {Combine like terms}
2y + 55 = 180
2y = 180 -55 {Subtract 55 from both sides}
2y = 125 {Divide both sides by 2}
y = 125 /2
∠y = 62.5°
∠x = 62.5 - 35 = 27.5°
Answer:
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".
The population proportion have the following distribution
Solution to the problem
We assume for this case a confidence level of 95%. In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by 
and 
. And the critical value would be given by:
The confidence interval for the mean is given by the following formula:
The margin of error for the proportion interval is given by this formula:
(a)
And if we replace the values obtained we got this:
Answer:
Second hand will turn through 74π radians.
Step-by-step explanation:
There are 37 minutes left in the class. We need to find by how much angle will the second hand turn before the end of the class.
When a second hand completes one full rotation along the clock it covers 360 degrees and completes 60 seconds.
This means:
In 60 seconds, the second hand turns by 360 degrees
Since, 60 seconds = 1 minute, we can write:
In 1 minute, the second hand turns = 360 degrees
360 degrees is equal to 2π radians. So,
In 1 minute, the second hand turns = 2π radians
Multiplying both sides by 37 gives us:
In 37 minutes, the second turns = 2π radians x 37 = 74π radians
Answer:
A) Slope = -2 and y-int = 1
Step-by-step explanation:
The easiest way to get the slope and y-intercept from an equation is to put it in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
So, let's subtract 8x from both sides, leaving 4y on the left side:
8x + 4y = 4 -> 4y = -8x + 4
Now, let's divide both sides by 4, so that we can have just y on the left side:
y = -2x + 1
-2 is the slope, and 1 is the y-intercept.
