Answer: 0.0108
Step-by-step explanation:
Given : ![H_0:\mu=50\\\\H_a:\mu>50](https://tex.z-dn.net/?f=H_0%3A%5Cmu%3D50%5C%5C%5C%5CH_a%3A%5Cmu%3E50)
Since the alternative hypotheses is right-tailed, so the test is a right-tailed test.
Sample size : n=30
The degree of freedom for t-distribution= ![=n-130-1=29](https://tex.z-dn.net/?f=%3Dn-130-1%3D29)
The by using the normal t-distribution table , we have
The P-value corresponds to t-statistic vale 2.43 and degree of freedom 29 , is 0.01075997 i.e. approximately 0.0108
= -8/3 + 4/6
= -16/6 + 4/6
= -12/6
= -2 answer
Answer:
Option B. ![212.1\ cm^{2}](https://tex.z-dn.net/?f=212.1%5C%20cm%5E%7B2%7D)
Step-by-step explanation:
step 1
Find the central angle of the shaded sector
Remember that the diameter divide the circle into two equal parts ( 180 degrees each part)
so
Let
x -----> the measure of the central angle of the shaded sector
∠x+72°=180°
∠x=180°-72°=108°
step 2
Find the area of the circle
The area of the circle is
![A=\pi r^{2}](https://tex.z-dn.net/?f=A%3D%5Cpi%20r%5E%7B2%7D)
we have
![r=15\ cm](https://tex.z-dn.net/?f=r%3D15%5C%20cm)
assume
![\pi=3.1416](https://tex.z-dn.net/?f=%5Cpi%3D3.1416)
substitute
![A=(3.1416)(15)^{2}](https://tex.z-dn.net/?f=A%3D%283.1416%29%2815%29%5E%7B2%7D)
![A=706.86\ cm^{2}](https://tex.z-dn.net/?f=A%3D706.86%5C%20cm%5E%7B2%7D)
step 3
Find the area of the shaded sector
Remember that the area of the complete circle subtends a central angle of 360 degrees
so
by proportion find the area of a sector by a central angle of 108 degrees
![\frac{706.86}{360}=\frac{x}{108}\\ \\x=706.86*108/360\\ \\x=212.1\ cm^{2}](https://tex.z-dn.net/?f=%5Cfrac%7B706.86%7D%7B360%7D%3D%5Cfrac%7Bx%7D%7B108%7D%5C%5C%20%5C%5Cx%3D706.86%2A108%2F360%5C%5C%20%5C%5Cx%3D212.1%5C%20cm%5E%7B2%7D)
Answer:
f(x) = -2x² + 2
Step-by-step explanation:
If you remember the y = x² parent graph, you will be able to derive your equation from visualization.
The vertex of this graph would be at (0, 2), so your degree coefficient would be negative. Your y-intercept would also be at (0, 2). Since both 1 and -1 are included, you can tell it is a parabola, and hence the 3rd option is your answer.
Answer:
<h3>5x</h3>
Step-by-step explanation:
The additive inverse of a function is that value added that will sum it up to zero
If y is the additive inverse of 4x, then y = -4x
Given the expression 17x+3y
Substitute y = -4x into the expression to have;
17x + 3(-4x)
17x -12x
5x
Hence the value of the expression in terms of x is 5x