Answer:
62 cm
Step-by-step explanation:
Given the expressions for width (3x + 1) and length (5x - 2) as well as the formula for the perimeter of a rectangle: 2(5x - 2) + 2(3x +10), we can first solve for the simplified expression of 'x' and then substitute the given value of x = 4cm to find the total distance:
Distribute: 2(5x - 2) + 2(3x +1) = 10x - 4 + 6x + 2
Combine like terms: 16x - 2
Plug in '4' for 'x': 16(4) - 2 = 64 -2 = 62 cm
Answer:
Length = 13 cm.
Step-by-step explanation:
If the length is L and the width is W we have the system:
2L + 2W = 32
LW = 39
From the first equation:
L + W = 16 and
L = 16 - W
Substitute this in the second equation:
W(16 - W) = 39
16W - W^2 = 39
W^2 - 16W + 39 = 0
(w - 13)(W - 3) = 0
W = 13, 3
As W < L, W must be 3 because L = 16-13 = 3 does not make sense.
So Length = 16 - 3 = 13.
Answer:
The probability that our guess is correct = 0.857.
Step-by-step explanation:
The given question is based on A Conditional Probability with Biased Coins.
Given data:
P(Head | A) = 0.1
P(Head | B) = 0.6
<u>By using Bayes' theorem:</u>
We know that P(B) = 0.5 = P(A), because coins A and B are equally likely to be picked.
Now,
P(Head) = P(A) × P(head | A) + P(B) × P(Head | B)
By putting the value, we get
P(Head) = 0.5 × 0.1 + 0.5 × 0.6
P(Head) = 0.35
Now put this value in , we get
Similarly.
Hence, the probability that our guess is correct = 0.857.
