Answer:
For problem 17a) your answer is: x=11.5 degrees
Step-by-step explanation:
1. Measure of angle BCA will be 180°-124°=46°
2. In triangle BCA, you now have two angles. 46 degrees, and 2x.
3. Measure of angle ABE is an exterior angle of triangle BCA
4. Using the exterior angle theorem, angle ABE=angle BCA+angle BAC
5. substitute!! 2x+46=6x
6. move 2x over and then divide by 4, you get x=11.5°
7. You can plug the answer back in to check if it correct!! have a nice day :>
Answer:
0.3
Step-by-step explanation:
the total of all probabilities is 1.00, or 100%.
In the Venn diagram, we have the probabilities 0.2, 0.4 and 0.1; these sum to
0.2+0.4+0.1 = 0.6+0.1 = 0.7.
This leaves us 1.00-0.7 = 0.3 for the remaining probability of no toppings.
Answer:
The 95% confidence interval for the population mean height of males of this country is between 67.136 inches and 74.864 inches.
Step-by-step explanation:
For the country, we only have the standard deviation of the sample, so we use the t distribution to build the confidence interval.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 45 - 1 = 44
Now, we have to find a value of T, which is found looking at the t table, with 44 degrees of freedom(y-axis) and a confidence level of 0.95(). So we have T = 1.68
The margin of error is:
M = T*s = 1.68*2.3 = 3.864
In which s is the standard deviation of the sample. So
The lower end of the interval is the sample mean subtracted by M. So it is 71 - 3.864 = 67.136 inches
The upper end of the interval is the sample mean added to M. So it is 71 + 3.864 = 74.864 inches
The 95% confidence interval for the population mean height of males of this country is between 67.136 inches and 74.864 inches.
9514 1404 393
Answer:
(8.49; 225°)
Step-by-step explanation:
The angle is a 3rd-quadrant angle. The reference angle will be ...
arctan(-6/-6) = 45°
In the 3rd quadrant, the angle is 45° +180° = 225°.
The magnitude of the vector to the point is its distance from the origin:
√((-6)² +(-6)²) = √(6²·2) = 6√2 ≈ 8.4859 ≈ 8.49
The polar coordinates can be written as (8.49; 225°).
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<em>Additional comment</em>
My preferred form for the polar coordinates is 8.49∠225°. Most authors use some sort of notation with parentheses. If parentheses are used, I prefer a semicolon between the coordinate values so they don't get confused with an (x, y) ordered pair that uses a comma. You need to use the coordinate format that is consistent with your curriculum materials.