Answer:
The percent of students who scored below 62 is 2.3%.
Step-by-step explanation:
In statistics, the 68–95–99.7 rule, also recognized as the empirical rule, is used to represent that 68.27%, 95.45% and 99.73% of the values of a Normally distributed data lie within one, two and three standard deviations of the mean, respectively.
Then,
- P (-1 < Z < 1) ≈ 0.6827
- P (-2 < Z < 2) ≈ 0.9545
- P (3 < Z < 3) ≈ 0.9973
Given:
μ = 78
σ = 8
<em>X</em> = 62
Compute the distance between the value of <em>X</em> and <em>μ</em> as follows:
![z=\frac{x-\mu}{\sigma}=\frac{62-78}{8}=-2](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%3D%5Cfrac%7B62-78%7D%7B8%7D%3D-2)
Use the relation P (-2 < Z < 2) ≈ 0.9545 to compute the value of P (Z < -2) as follows:
![P(-2](https://tex.z-dn.net/?f=P%28-2%3CZ%3C2%29%3D0.9545%5C%5CP%28Z%3C2%29-P%28Z%3C-2%29%3D0.9545%5C%5C1-P%28Z%3C-2%29-P%28Z%3C-2%29%3D0.9545%5C%5C2P%28Z%3C-2%29%3D1-0.9545%5C%5CP%28Z%3C-2%29%3D%5Cfrac%7B0.0455%7D%7B2%7D%5C%5C%3D0.02275)
The percentage is, 0.02275 × 100 = 2.275% ≈ 2.3%
Thus, the percent of students who scored below 62 is 2.3%.
Answer:
b) 12.6 inches
Step-by-step explanation:
tangent is the ratio of the side opposite over adjacent, so if we let x= length of the opposite side, 1.40=x/9, x=12.6 inches
The equation of a circle with the center (4,-3) and a radius of 3 is:
(x-4)^2+(y+3)^2=9
Step-by-step explanation:
Given
Radius = r = 3
Centre = (h,k) = (4,-3)
The general form of equation of circle is:
![(x-h)^2+(y-k)^2=r^2](https://tex.z-dn.net/?f=%28x-h%29%5E2%2B%28y-k%29%5E2%3Dr%5E2)
Putting the values of center and radius
![(x-4)^2+[y-(-3)]^2=(3)^2\\(x-4)^2+(y+3)^2=9](https://tex.z-dn.net/?f=%28x-4%29%5E2%2B%5By-%28-3%29%5D%5E2%3D%283%29%5E2%5C%5C%28x-4%29%5E2%2B%28y%2B3%29%5E2%3D9)
Hence,
The equation of a circle with the center (4,-3) and a radius of 3 is:
(x-4)^2+(y+3)^2=9
Keywords: circle, Equation of circle
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Answer:
Option D. 13122 is the answer.
Step-by-step explanation:
As we can see from the table having interval and average rate of change, figures under average rate of change are forming a geometric sequence.
Sequence is 2, 6, 18 , 54, 162, 486.
and we have to find the average rate of change from x = 8 to x = 9, means we have to find 9th term of the given sequence.
Now we know that explicit formula of the sequence can be written as ![T_{n}=ar^{n-1}](https://tex.z-dn.net/?f=T_%7Bn%7D%3Dar%5E%7Bn-1%7D)
where Tn is the nth term of the sequence.
a = first term
r = common ratio
n = number of the term
Now from this explicit formula we can find the 9th term of the sequence.
From the given table
a = 2, r = 3, n = 9
![T_{9}=2.3^{9-1}=2.3^{8}](https://tex.z-dn.net/?f=T_%7B9%7D%3D2.3%5E%7B9-1%7D%3D2.3%5E%7B8%7D)
T9 = 13122
Therefore Option D. 13122 will be the answer.
Based on the amount the annuity pays per month and the APR, the value of the annuity today is $133,349.85.
<h3>What is the present value of the annuity?</h3>
First, find the present value of the annuity at 5 years:
= 1,850 x present value interest factor of annuity, 60 months, 8/12%
= 1,850 x 49.32
= $91,242
Then find the present value of the annuity from 5 years till date:
= (1,850 x present value interest factor of annuity, 60 months, 12/12%) + ( 91,242) / (1 + 1%)⁶⁰)
= (1,850 x 44.955) + ( 91,242) / (1 + 1%)⁶⁰)
= $133,349.85
Find out more on the present value of annuities at brainly.com/question/24097261.
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