Answer:
0.0713 = 7.13% probability that the result is positive.
Step-by-step explanation:
Probability of a positive test:
91% of 1/650(has the disease).
7% of 1 - 1/650 = 649/650(does not have the disease). So
![p = 0.91\frac{1}{650} + 0.07\frac{649}{650} = \frac{0.91 + 0.07*649}{650} = 0.0713](https://tex.z-dn.net/?f=p%20%3D%200.91%5Cfrac%7B1%7D%7B650%7D%20%2B%200.07%5Cfrac%7B649%7D%7B650%7D%20%3D%20%5Cfrac%7B0.91%20%2B%200.07%2A649%7D%7B650%7D%20%3D%200.0713)
0.0713 = 7.13% probability that the result is positive.
Answer: x = {-3, -1, 1, 7}
<u>Step-by-step explanation:</u>
f(x) = x⁴ - 4x³ - 22x² + 4x + 21
possible roots are: +/- 1, 3, 7, 21
Let's try x = 1
1 | 1 -4 -22 4 21
<u>| ↓ 1 -3 -25 -21 </u>
1 -3 -25 -21 0 <em>remainder is 0 so (x - 1) is a factor</em>
(x - 1)(x³ - 3x² - 25x - 21)
Next, let's try x = -1
-1 | 1 -3 -25 -21
<u>| ↓ -1 4 21 </u>
1 -4 -21 0 <em>remainder is 0 so (x + 1) is a factor</em>
(x - 1)(x + 1)(x² - 4x - 21)
Then, factor the third polynomial
(x - 1)(x + 1)(x + 3)(x - 7)
Now, set each factor equal to zero and solve each one.
(x - 1) = 0 ⇒ x = 1
(x + 1) = 0 ⇒ x = -1
(x + 3) = 0 ⇒ x = -3
(x - 7) = 0 ⇒ x = 7
C is the only one that makes sense