Answer:
The height of tree house is 70.71 feet
Step-by-step explanation:
We are given that A 100-foot rope from the top of a tree house to the ground forms a 45∘ angle of elevation from the ground
Refer the attached figure
Length of rope AC = Hypotenuse =100 feet
The top of a tree house to the ground forms a 45∘ angle of elevation from the ground =
We are supposed to find the height of tree house i.e.AB = Perpendicular
So, Using trigonometric ratio

Hence The height of tree house is 70.71 feet
Answer:
Expected value for 4 tickets = $ -7.6
Step-by-step explanation:
Given - A lottery offers one $900 prize, one $600 Prize, three $400 prizes, and four $100 prizes. One thousand tickets are sold at $5 each.
To find - Find the expectation if a person buys four tickets. Assume that the player's ticket is replaced after each draw and that the same ticket can win more than one prize. Round to two decimal places for currency problems.
Proof -
Given that,
A lottery offers
one $ 900 prize
one $ 600 prize
three $ 400 prizes
Four $ 100 prizes
And
One thousand tickets are sold at $ 5 each
Now,
If the person bought 1000 tickets then the prize he gets is
= 900 + 600 + 3×400 + 4×100
= 900 + 600 + 1200 + 400
= $3100
And
The cost of 1000 tickets = 5×1000 = $ 5000
Now,
Price 1 ticket =
= $ 3.1
⇒Expectation of 1 ticket = $ 3.1 - 5 = $ -1.9 (Here $5 is price of 1 ticket)
⇒Expected value for 4 tickets = $ 4× -1.9 = $ -7.6
⇒Expected value for 4 tickets = $ -7.6
I think it is 75. 60+15 = 75, 90-15=75. I think best way is to go with logic. they don't mention time in seconds or distance so logic is the best way
Answer:
X=-14
Step-by-step explanation:
16+22+x=24
38+x=24
x=24-38
x=-14
Firstly we need to count how much did the employees earn after the raises:
4% from $41,000 =
= 4/100 * 41,000 =
= 4 * 410 =
= 1644
4,5% from 43,700 =
= 45/1000 * 43,700 =
= 45 * 43,7 =
= 1966,5
3% from 39,700 =
= 3/100 * 39,700 =
= 3 * 397 =
= 1191
Now we need to sum up all the raises:
1644 + 1966,5 + 1191 = 4801,5
So now we can clearly see that answer A ($4,802) is the closest one to the total of all three raises.