A function assigns the values. The correct option is D.
<h3>What is a Function?</h3>
A function assigns the value of each element of one set to the other specific element of another set.
The given function when plotted on the graph will look as shown below. Therefore, the function is increasing on the interval (–1, ∞).
Hence, the correct option is D.
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We have been given that in a right triangle, the measure of and the side opposite to the measure of theta is 6.5 cm long. We are asked to find the length of adjacent side to the angle theta.
We know that tangent relates opposite side of right triangle adjacent side.
Therefore, the length of adjacent side to angle theta is approximately 6.97 units.
Answer:
A normal model is a good fit for the sampling distribution.
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
The standard deviation of this sampling distribution of sample proportion is:
The information provided is:
<em>N</em> = 675
<em>X</em>₁ = bodies with low vitamin-D levels had weak bones
<em>n</em>₁ = 82
<em>p</em>₁ = 0.085
<em>X</em>₂ = bodies with regular vitamin-D levels had weak bones
<em>n</em>₂ = 593
<em>p</em>₂ = 0.01
Both the sample sizes are large enough, i.e. <em>n</em>₁ = 82 > 30 and <em>n</em>₂ = 593 > 30.
So, the central limit theorem can be applied to approximate the sampling distribution of sample proportions by the Normal distribution.
Thus, a normal model is a good fit for the sampling distribution.
Answer:
<h3>Question 1</h3>
<u>Function given:</u>
<u>In the vertex form:</u>
- y = x² + 4x + 4 - 8 = (x + 2)² - 8
Axis of symmetry is the vertical line passing through the vertex.
<u>The vertex is</u>
<u>Axis of symmetry is </u>
<u>y- intercept is </u>
- x = 0 ⇒ y = -4, so the point (0, -4)
<u>Two other points are</u>
- x = 1 ⇒ y = (1 + 2)² - 8 = 9 - 8 = 1, the point is (1, 1)
- x = -1 ⇒ y = (-1 + 2)² - 8 = 1 - 8 = -7, the point is (-1, -7)
<em>See the graph with all the points plotted</em>
<h3>Question 2</h3>
<u>Function given:</u>
<u>In standard form:</u>
<u>In vertex form:</u>
- y = - 2x² + 4x - 2 + 8 = -2(x - 1)² + 8
<u>The vertex:</u>
<u>Axis of symmetry is </u>
<u>y - intercept </u>
- x = 0 ⇒ y = -2(-1)² + 8 = -2 + 8 = 6, the point is (0, 6)
<u>Two other pints:</u>
- x = -1 ⇒ y = -2(-1 - 1)² + 8 = -8 + 8 = 0, the point is (-1, 0)
- x = 2 ⇒ y = -2(2 - 1)² + 8 = -2 + 8 = 6, the point is (2, 6)
<em>The graph is attached with the points plotted.</em>
B. 8 the radius is half the diameter