Answer:
Step-by-step explanation:
This is a question that uses the Pythagorean Theorem.
a = 35 feet
b = x which is the height of the tree.
c = 3*x + 1 so we are trying to find x. Substitute into a b and c
a^2 + b^2 = c^2
35^2 + x^2 = (3x + 1)^2
35^2 + x^2 = 9x^2 + 6x + 1 Subtract x^2 from both sides.
35^2 = 8x^2 + 6x + 1 Subtract 35^2 from both sides.
0 = 8x^2 + 6x + 1 - 35^2
0 = 8x^2 + 6x - 1224
Does this factor?
(x + 12.75)(x - 12)
x - 12 = 0 is the only value that works.
x = 12
The tree is 12 feet high.
Note: I used the quadratic formula to solve this.
Answer:
11
Step-by-step explanation:
First, write an equation to represent the situation.
34 = 2a + 12
This equation works because your combined age is half of 68, so 34. If your age is a, then yours sister's age is a + 12. if you add your age to your sister's, you get 2a + 12.
Now just solve for a.
34 = 2a + 12
First, subtract 12 from both sides.
22 = 2a
Then divide both sides by 2.
11 = a
So you are 11 years old. If you need to check your work, your age (11) plus your sister's age (11 + 12, which is 23) is 34, which is half of your grandfather's age.
The probability that the next on-the-job injury will occur within 10, 5, and 1 day are 0.632, 0.393, and 0.095
<h3>What is probability?</h3>
It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We know the exponential distribution is given by;

The probability that the next on-the-job injury will occur within 10 days:

P(X< 10) = 0.632
The probability that the next on-the-job injury will occur within 20 days:

P(X< 5) = 0.393
The probability that the next on-the-job injury will occur within 1 days:

P(X< 1) = 0.095
Thus, the probability that the next on-the-job injury will occur within 10, 5, and 1 day are 0.632, 0.393, and 0.095
Learn more about the probability here:
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Answer: b. 14 pounds
Step-by-step explanation:
Formula to calculate average :

Let x denotes the number of pounds the last person have to gain so that the group can attain its goal.
Required average = 10 pounds
Observations = 9, 13, 11, 6, 7 and x (pounds)
Number of observations= 6
Sum of all observations = 9+13+ 11+ 6+7+x=46+x
According to the question , we have

i..e the last person has to gain 14 pounds so that the group can attain its goal.
Hence, the correct answer is b. 14 pounds .