Answer:
Probability cured of cervical cancer = 18C0 (0.30)⁰(0.70)¹⁸ + 18C1(0.30)(0.70)¹⁷
Step-by-step explanation:
Given:
Patients cured = 30% = 0.30
Number of patients (n) = 18
Probability cured of cervical cancer = P(X≤1)
Probability cured of cervical cancer = P(X=0) + P(X=1)
Probability cured of cervical cancer = 18C0 (0.30)⁰(0.70)¹⁸ + 18C1(0.30)(0.70)¹⁷
Answer:
r = 0.9825; good correlation.
Step-by-step explanation:
One formula for the correlation coefficient is
![r = \dfrac{n\sum{xy} - \sum{x} \sum{y}}{\sqrt{n\left [\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [\sum{y}^{2}-\left (\sum{y}\right )^{2}\right]}}](https://tex.z-dn.net/?f=r%20%3D%20%5Cdfrac%7Bn%5Csum%7Bxy%7D%20-%20%5Csum%7Bx%7D%20%5Csum%7By%7D%7D%7B%5Csqrt%7Bn%5Cleft%20%5B%5Csum%7Bx%7D%5E%7B2%7D-%5Cleft%20%28%5Csum%7Bx%7D%5Cright%20%29%5E%7B2%7D%5Cright%5D%5Cleft%20%5B%5Csum%7By%7D%5E%7B2%7D-%5Cleft%20%28%5Csum%7By%7D%5Cright%20%29%5E%7B2%7D%5Cright%5D%7D%7D)
The calculation is not difficult, but it is tedious.
1. Calculate the intermediate numbers
We can display them in a table.
<u> </u><u>x</u> <u> y </u> <u> xy </u> <u> x² </u> <u> y² </u>
-3 -40 120 9 1600
1 12 12 1 144
5 72 360 25 5184
<u> 7</u> <u>137</u> <u> 959</u> <u>49</u> <u>18769
</u>
Σ = 10 181 1451 84 25697
2. Calculate the correlation coefficient
![r = \dfrac{n\sum{xy} - \sum{x} \sum{y}}{\sqrt{\left [n\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [n\sum{y}^{2}-\left (\sum{y}\right )^{2}\right]}}\\\\= \dfrac{4\times 1451 - 10\times 181}{\sqrt{[4\times 84 - 10^{2}][4\times25697 - 181^{2}]}}\\\\= \dfrac{5804 - 1810}{\sqrt{[336 - 100][102788 - 32761]}}\\\\= \dfrac{3994}{\sqrt{236\times70027}}\\\\= \dfrac{3994}{\sqrt{16526372}}\\\\= \dfrac{3994}{4065}\\\\= \mathbf{0.9825}](https://tex.z-dn.net/?f=r%20%3D%20%5Cdfrac%7Bn%5Csum%7Bxy%7D%20-%20%5Csum%7Bx%7D%20%5Csum%7By%7D%7D%7B%5Csqrt%7B%5Cleft%20%5Bn%5Csum%7Bx%7D%5E%7B2%7D-%5Cleft%20%28%5Csum%7Bx%7D%5Cright%20%29%5E%7B2%7D%5Cright%5D%5Cleft%20%5Bn%5Csum%7By%7D%5E%7B2%7D-%5Cleft%20%28%5Csum%7By%7D%5Cright%20%29%5E%7B2%7D%5Cright%5D%7D%7D%5C%5C%5C%5C%3D%20%5Cdfrac%7B4%5Ctimes%201451%20-%2010%5Ctimes%20181%7D%7B%5Csqrt%7B%5B4%5Ctimes%2084%20-%2010%5E%7B2%7D%5D%5B4%5Ctimes25697%20-%20181%5E%7B2%7D%5D%7D%7D%5C%5C%5C%5C%3D%20%5Cdfrac%7B5804%20-%201810%7D%7B%5Csqrt%7B%5B336%20-%20100%5D%5B102788%20-%2032761%5D%7D%7D%5C%5C%5C%5C%3D%20%5Cdfrac%7B3994%7D%7B%5Csqrt%7B236%5Ctimes70027%7D%7D%5C%5C%5C%5C%3D%20%5Cdfrac%7B3994%7D%7B%5Csqrt%7B16526372%7D%7D%5C%5C%5C%5C%3D%20%5Cdfrac%7B3994%7D%7B4065%7D%5C%5C%5C%5C%3D%20%5Cmathbf%7B0.9825%7D)
The closer the value of r is to +1 or -1, the better the correlation is. The values of x and y are highly correlated.
In geometry, similar figures are those whose ratios of the corresponding sides are equal and the corresponding angles are congruent. In relation to the volume, we determine first the cube roots of the given and find the ratio as shown below.
s1 / s2 = cube root of (512/343)
= 8/7
The square of this ratio is the ratio of the areas of the figure. If we let x be the area of the smaller figure then,
(8/7)^2 = 192 mm²/ x
The value of x from the equation is 147 mm².
The area therefore of the smaller figure is 147 mm².
A: a horizontal shrink would be caused by cos 3x.
B: a vertical stretch would be caused by 3 cos x
C: a horizontal stretch would be caused by cos (1/3)x
D: a vertical shrink would be caused by 1/3 cos x.
Answer:
80+(15x)
Step-by-step explanation:
10 times 8=80
1.5 times 10=15
so she gets 80 dollars for the first 8 hours then for every extra hour she gets 15 dollars
