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Deffense [45]
3 years ago
14

What is the distance between the zoo and the library?

Mathematics
1 answer:
KATRIN_1 [288]3 years ago
3 0
The answer is as follow

sin60° = 400√3 / H1, implies H1=  400√3 / sin60° <span>
sin30° = </span>400√3 / H2, implies H2=  400√3 / sin30° <span>
and the if the distance is D,
so we can find D such that D= H2 - H1=</span>400√3 / sin30° - 400√3 / <span>sin60°
D= </span>400√3(1/sin30°  - 1/ sin60°)=400√3(2-1.15)=338.11<span>√3</span>
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The perimeter of a rectangle is 37. The length is 1 less than 12 times the width. What is the length and width of the rectangle
iren [92.7K]
Width = W
Length = 12W - 1
Perimeter = 2L + 2W = 37

In the perimeter equation substitute the length equation in for L to get the equation in terms of W
2L + 2W = 37
2(12W - 1) + 2w = 37

Distribute
2(12W - 1) + 2w = 37
24W - 2 + 2w = 37
26W = 39
W = 3/2 = 1.5
Width = 1.5

Lastly, solve for length
L = 12W - 1
L = (12 • 1.5) - 1
L = 18 - 1
L = 17
Length = 17


3 0
3 years ago
Consider the following game, played with three standard six-sided dice. If the player ends with all three dice showing the same
ddd [48]

Answer:

a

 P(A) =  \frac{1}{36}

b

P(B) = \frac{15}{36}

c

P(U) = \frac{11}{36}

Step-by-step explanation:

From the question we are told that

   The  number of dice is  n  =  3

Generally  for all three dice to show the same number the second and the third dice must have the same outcome  as the outcome of the first dice.

This means that the number of outcome the first die can  have is  6  (6 sides), the number of outcome which the second and the third dice can have is  1 (they must match the first )

So the probability that all three dice show the same number on the first roll is mathematically represented as

      P(A) =  \frac{6}{6} * \frac{1}{6} *  \frac{1}{6}

=>   P(A) =  \frac{1}{36}

Generally for two of the three dice show the same number after the first roll then the number of outcome for  one of the  dice would be is  6 , the number of outcome for another one must be   1(i.e it must match the first ) , the number of outcome for the remaining one must be   5 (i.e it can show any of the remaining  5  sides which the first and second dice are not showing )

Now the number of ways of selecting this 2 dice that show the same number from the 3 dice is mathematically represented as

     N  =  ^3C_2

Here C stands for combination

So

      N  =  ^3C_2  = 6

So the probability that exactly two of the three dice show the same number after the first roll is mathematically represented as  

      P(B) = N   \frac{1}{6} *  \frac{5}{6}

=>  P(B) = \frac{15}{36}

Generally from the question we are told that if two dice match, the player re-rolls the die that does not match.

Now the probability that  the die that did not match the first  time will match the second time is

     P(E ) =  \frac{1}{6}

Generally if that one die does not show the same number in the second round , the probability that it will match  in the third round is

    P(R) =  \frac{5}{6} *  \frac{1}{6}

Generally the probability that he wins (i.e when all three are showing the same number ) and  exactly two is showing the same number is mathematically represented as

       P(K) =  P(E)* P(B) + P(R)* P(B)

=>    P(K) =  \frac{1}{6} * \frac{15}{36}  +  \frac{5}{6} *  \frac{1}{6} * \frac{15}{36}

=>  P(K)= \frac{165}{1296}

So the probability that the player wins, conditioned on exactly two of the three dice showing the same number after the first roll is mathematically represented as  

    P(U) =  \frac{\frac{165}{1296}}{\frac{15}{36} }

=>  P(U) = \frac{11}{36}

     

 

6 0
3 years ago
Garrett has deposited 519 in a savings account that earns interest at a rate of 4.2% compounded daily. What will the account bal
kipiarov [429]
$1059.83 Use this formula:
A=P(1+r/n) ^{nt}

P=principal of 519
r= your rate of 4.2% as a decimal
n=number of compounding periods; yours is daily or 365 day in a year.
t=time involved of the investment in years; yours is 17

7 0
3 years ago
Alex applies 350 n of force to move his stalled car 40 m how much work did alex do
Katyanochek1 [597]

Step-by-step explanation:

Work done = Force × displacement

= 350 × 40

=14000J

7 0
3 years ago
I NEED HELP PLEASE ASAP!!!
Vilka [71]

Answer:

Step-by-step explanation:

To find the surface area of a regular pyramid use the formula:

S = 1/2 × l × p + b

Surface = 1/2 × lateral height × perimeter of the base + area of the base

5 0
3 years ago
Read 2 more answers
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