To find out if a triangle is a right triangle, you can use the Pythagorean theorem(which can only be used for right triangles):
a² + b² = c² (c is the hypotenuse or the longest side) And you can plug in the side lengths into this equation. If they are the same number on both sides, it is a right triangle, if they are different numbers it is not a right triangle.
6.) a² + b² = c²
(4√3)² + (11)² = (13)²
(16(3)) + 121 = 169
48 + 121 = 169
169 = 169 It IS a right triangle
7.) a² + b² = c²
(5)² + (2√14)² = (9)²
25 + (4(14)) = 81
25 + 56 = 81
81 = 81 It IS a right triangle
8.) a² + b² = c²
(6)² + (√49)² = (√82)²
36 + 49 = 82
85 = 82 It is NOT a right triangle
9.) a² + b² = c²
(13)² + (2√39)² = (16)²
169 + (4(39)) = 256
169 + 156 = 256
325 = 256 It is NOT a right triangle
Answer:
The reasonable range for the population mean is (61%, 75%).
Step-by-step explanation:
The interval estimate of a population parameter is an interval of values that consist of the values within which the true value of the parameter lies with a certain probability.
The mean of the sampling distribution of sample proportion is,
.
One of the best interval estimate of population proportion is the 95% confidence interval for proportion,

Given:
n = 150
= 0.68
The critical value of <em>z</em> for 95% confidence level is:

Compute the 95% confidence interval for proportion as follows:


Thus, the reasonable range for the population mean is (61%, 75%).
Answer:
Correct option is (C).
The possible value of the <em>p</em>-value for a one-tailed test are 0.22 and 0.78.
Step-by-step explanation:
The <em>p</em>-value is the probability of acquiring a result as extreme as the observed result, assuming the null hypothesis statement is true.
The <em>p</em> value of a test is:
Left-tailed test:
Right-tailed test:
.
Here,
TS = Test statistic
ts = computed value of the test statistic.
The two-tailed <em>p</em>-value is:
or
.
The <em>p</em>-value of the two tailed test is, 0.44.
Compute the <em>p</em>-value for one-tailed test a follows:


Thus, the possible value of the <em>p</em>-value for a one-tailed test are 0.22 and 0.78.
The correct option is (C).
To find the slope of the line, use the rise over run formula:

Take any two points from the line and plug them into the formula.
(0,0) and (10, 5)

The slope of the line is 0.5.
Using the form y = mx, the following equation will be your answer:
To find a number that is 10 times greater than 7962, we can multiply.
7,962 * 10 = 79,620
79,620 is 10 times greater than 7,962.
Best of Luck!