C bc the x is where the right angle is and the 2 sides of a right angle is going to be equal
Answer:
0.2177 = 21.77% conditional probability that she does, in fact, have the disease
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
![P(B|A) = \frac{P(A \cap B)}{P(A)}](https://tex.z-dn.net/?f=P%28B%7CA%29%20%3D%20%5Cfrac%7BP%28A%20%5Ccap%20B%29%7D%7BP%28A%29%7D)
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Test positive
Event B: Has the disease
Probability of a positive test:
90% of 3%(has the disease).
1 - 0.9 = 0.1 = 10% of 97%(does not have the disease). So
![P(A) = 0.90*0.03 + 0.1*0.97 = 0.124](https://tex.z-dn.net/?f=P%28A%29%20%3D%200.90%2A0.03%20%2B%200.1%2A0.97%20%3D%200.124)
Intersection of A and B:
Positive test and has the disease, so 90% of 3%
![P(A \cap B) = 0.9*0.03 = 0.027](https://tex.z-dn.net/?f=P%28A%20%5Ccap%20B%29%20%3D%200.9%2A0.03%20%3D%200.027)
What is the conditional probability that she does, in fact, have the disease
![P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.027}{0.124} = 0.2177](https://tex.z-dn.net/?f=P%28B%7CA%29%20%3D%20%5Cfrac%7BP%28A%20%5Ccap%20B%29%7D%7BP%28A%29%7D%20%3D%20%5Cfrac%7B0.027%7D%7B0.124%7D%20%3D%200.2177)
0.2177 = 21.77% conditional probability that she does, in fact, have the disease
Answer:
You have to follow PEMDAS or parenthesis, exponents, multiplication, division, addition, and subtraction. It's an order to solve equations. I listed the steps and the answers for you below :) I have throughly checked them so they should be correct! yw :D
Step-by-step explanation:
1. 5x + 4x - 6x = 24
9x - 6x = 24
3x = 24
24/3 = 8
<u><em>x = 8</em></u>
2. 8y + 5 - 4y + 1 = 46
8y - 4y = 4y
5 + 1 = 6
4y + 6 = 46
4y = 46 - 6
4y = 40
40/4 = 10
<u><em>y = 10</em></u>
<u><em></em></u>
3. 33 = 5 ( x + 8 ) + 3
33 = 5x + 40 + 3 <em>(because we distributed)</em>
33 = 5x + 43
5x + 43 = 33<em> (just rewriting it to make it easier)</em>
5x = 33 - 43
5x = -10
-10/5 = -2
<em><u>so x = - 2</u></em>
4. 2m + 3 ( m - 8 ) = 1
2m + 3m - 24 = 1
<em>we got 3m - 24 because we distributed the 3</em>
5m - 24 = 1
5m = 25
25/5 = 5
<em><u>m = 5</u></em>
<em><u /></em>
5. p + p - 2p + 4p = - 48
2p - 2p + 4p = - 48
4p = - 48
- 48 / 4 = - 12
<u><em>p = - 12</em></u>
<u><em></em></u>
6. 2 ( y + 5 ) + 3y = 25
2y + 10 + 3y = 25
5y + 10 = 25
5y = 25 - 10
5y = 15
15/5 = 3
<u><em>y = 3</em></u>
7. 1/4 h + 3/4 h + 1/2 h + 2 = 5
1/4 h + 3/4 h + 1/2 = 3/2 h
3/2 h + 2 = 5
3/2 h = 5 - 2
3/2 h = 3
<u><em>h = 2</em></u>
<u><em></em></u>
8. 60 = 4 ( k + 3 ) + 2 ( k - 3 )
60 = 4k + 12 + 2k - 6
4k + 12 + 2k - 6 = 60
6k + 6 = 60
6k = 60 - 6
6k = 54
<u><em>k = 9 </em></u>
<u><em></em></u>
9. - 2 ( d + 1.4 ) - 1.8 = 20.6
-2d + - 2.8 - 1.8 = 20.6
-2d - 2.8 = 22.4
-2d = 25.2
<u><em>d = - 12.6 </em></u>
<u><em></em></u>
10. 8 - 2 ( w + 4 ) = 10
8 + - 2 w + - 8 = 10
-2w + 9 + - 8 = 10
-2w = 10
10 / -2 = -5
<u><em>w = -5</em></u>
Answer:
![h_t=9ft](https://tex.z-dn.net/?f=h_t%3D9ft)
Step-by-step explanation:
From the question we are told that:
Height of child ![h_c=3ft](https://tex.z-dn.net/?f=h_c%3D3ft)
Height of child's shadow ![h_c_s=2ft](https://tex.z-dn.net/?f=h_c_s%3D2ft)
Height of tree's shadow
Since position of Sun remains constant
Generally the equation for Height of tree h_t mathematically given by
![h_t=f_{ts}\frac{h_c}{h_c_s}](https://tex.z-dn.net/?f=h_t%3Df_%7Bts%7D%5Cfrac%7Bh_c%7D%7Bh_c_s%7D)
![h_t=6*\frac{3}{2}](https://tex.z-dn.net/?f=h_t%3D6%2A%5Cfrac%7B3%7D%7B2%7D)
![h_t=9ft](https://tex.z-dn.net/?f=h_t%3D9ft)
Answer:
k ≤ 10 or k ≤ -6
Step-by-step explanation:
| -2 + k | ≤ 8
-2 + k ≤ 8
k ≤ 10
-2 + k ≤ -8
k ≤ -6