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patriot [66]
2 years ago
7

Hikers came across a part of a redwood stump. If the length of the chord is 8 feet, what was the diameter of the tree?

Mathematics
1 answer:
erastova [34]2 years ago
7 0
So in the problem, the length of the chord there is the circumference of the tree. So in order to get the diameter of the tree, we must use the formula in getting the circumference of a circle that is stated as follows. 

C = 2pi *Radius

so first we need the get the radius of the tree which represent by this formula:

Radius = C /2pi = 8/6.2832 = 1.2732 ft 
Diameter = 2*radius = 2 * 1.27 32 = 2.5465 feet 

In summary, the diameter of the tree is 2.565 feet. 


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A diagnostic test for a disease is such that it (correctly) detects the disease in 90% of the individuals who actually have the
Ne4ueva [31]

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)}

In which

P(B|A) is the probability of event B happening, given that A happened.

P(A \cap B) 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

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

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

0.2177 = 21.77% conditional probability that she does, in fact, have the disease

3 0
3 years ago
NEED HELP ASAP!!! PICTURE PROVIDED
faltersainse [42]

Answer:

(x + 9) (x - 8)

Replace a with 9

and b with -8

Step-by-step explanation:

8 0
3 years ago
A rectangle has an area of 100 ft^2 if the rectangle is 5 ft wide how long is it ?
Tema [17]
The answer is b because 5*20=100
5 0
3 years ago
Which equation represents the graph​
elena55 [62]
aaanswer : D) y=2x
8 0
2 years ago
Suppose that – in any given time period – a certain stock is equally likely to go up 1 unit or down 1 unit, and that the outcome
Scorpion4ik [409]

Answer:

Step-by-step explanation:

From the given information:

Let X represent the amount of the stock that goes up in the first period; &

Let Y denote the cumulative amount that goes up in the first three periods.

Then,

X= X_1 + X_2 \\ \\ \\EX=  EX_1 +EX_2\\ \\\\Now ; EX = 0 \\ \\ EX = \dfrac{1}{2}\times 1 + \dfrac{1}{2}\times -1 \\ \\ EX = \dfrac{1}{2}-\dfrac{1}{2} \\ \\ EX = 0

Cov(x,y) = Var(X_1) +Var(X_2) \\ \\ =\dfrac{1}{2}(1+1) + \dfrac{1}{2}(1+1) \\ \\ = \dfrac{1}{2}(2)+ \dfrac{1}{2}(2)  \\ \\ = 1+1  \\ \\ =2

Var (X) = Var (X_1+X_2)\\ \\ = 2 \ Var(X_1)  \\ \\ = 2 \times (1) \\ \\  = 2

Var (Y) = Var (X_1 +X_2+X_3) \\ \\ = 3 \times Var(X_1) = \\ \\ = 3 \times 1\\   \\ = 3

∴

Corr(x,y) = \dfrac{2}{\sqrt{6}} \\ \\ = \dfrac{2}{\sqrt{2\times 3}} \\ \\= \sqrt{\dfrac{2}{3}}

3 0
2 years ago
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