Answer:
110 degrees
Step-by-step explanation:
to find the angle x, we need to use the formula to find the 50 degree angle:
(y - x) / 2 = 50
y is 210
(210 - x) /2 = 50
210-x = 100
x = 110 degrees
Answer:
Step-by-step explanation:
We want to determine a 95% confidence interval for the mean mean test score of students.
Number of sample, n = 25
Mean, u = 81.5
Standard deviation, s = 10.2
For a confidence level of 95%, the corresponding z value is 1.96. This is determined from the normal distribution table.
We will apply the formula
Confidence interval
= mean ± z score ×standard deviation/√n
It becomes
81.5 ± 1.96 × 10.2/√25
= 81.5 ± 1.96/× 2.04
= 81.5 ± 3.9984
The lower end of the confidence interval is 81.5 - 3.9984 =77.5
The upper end of the confidence interval is 81.5 + 3.9984 = 85.5
Therefore, with 95% confidence interval, the mean test score of students is between 77.5 and 85.5
Answer:
Step-by-step explanation:
If you plot this angle in the coordinate plane, you will find yourself in the fourth quadrant with a referencew angle of 30. Constructing the triangle from that reference angle and using the Pythagorean triple for a 30-60-90 triangle, you get that the side adjacent to the reference angle is √3, the side opposite the reference angle is a -1, and the hypotenuse (which is NEVER negative!) is 2. The x and y coordinates of the terminal point result from the cos (related to the x coordinate) and the sin (related to the y coordinate). The cos of 30:
and the sin of 30:
so the coordinates of the terminal point on that angle are
You could also just go to your unit circle, find the angle 330 and look at the coordiantes they give you there for (cos, sin). But I'm a high school math teacher so I wanted you to know how to find this outside of the unti circle. Cuz what if you lost it!?
You multiply 5 times 8 so that will give you 40, so the answer is 40
Answer:
Option C. The range is y≥2
Step-by-step explanation:
To solve this, we're gonna demonstrate that all options except option C. are wrong.
Option A. The vertical line confirms that the graph is a function. FALSE.
The vertical line is called the y-axis and it's used as a reference to graph functions. It does not confirm that a graph is a function.
Option B. The domain is x≥2. FALSE.
The domain of a function is the set of possible values of the independent variable "x". In this case, we can deduce from the graph that the variable "x" can take values less than 2.
Option C. The Range is x≥2. TRUE.
The range of a function is the set of all output values of a function. We can deduce from the graph that the variable "y" takes values greater than 2. For that reason, the statement is true.
Option D. This piecewise function is made out of 4 intervals. FALSE.
The function is made out of two intervals. A concave function for x≤2 and a line for x≥2.
Option E. Each interval of the piecewise function contains a graph of a linear function. FALSE.
When x≤2, the graph corresponds to a concave function. So, this interval is not linear.