1. you toss three coins. what is the probability P that all are heads?
2. write and simplify an expression for the perimeter of a triangle with these lengths: 1/2x, x, 5/4x
for number one, i think it might be 1/8
i'm not sure..
please help!!
yes on the first.
On the second, add the lengths. What is 5/4 + 2/4 + 4/4 ?
2 3/4
so is this (5/4 + 2/4 + 4/4) the expression?
The expression is...
Perimeter=5/4 x + 1/2 x + x
simplifying, you get
Perimeter= 2 3/4 x
To determine the probability that all three coins are heads, we can use basic probability principles.
1. Number of favorable outcomes: When tossing each coin, there are two possible outcomes: heads (H) or tails (T). Since we want all three coins to be heads (HHH), there is only one favorable outcome.
2. Number of possible outcomes: For each coin toss, there are two possible outcomes (H or T). Since there are three coins being tossed, the total number of possible outcomes is 2 × 2 × 2 = 8.
3. Probability: The probability is calculated by dividing the number of favorable outcomes by the number of possible outcomes:
P(all heads) = Number of favorable outcomes / Number of possible outcomes
= 1 / 8
= 1/8
So, your initial guess was correct; the probability that all three coins are heads is indeed 1/8.
Moving on to the second question, we need to find the perimeter of a triangle using the given side lengths: 1/2x, x, and 5/4x.
The perimeter of a triangle is found by summing the lengths of its sides. So, for this case, the perimeter (P) will be:
P = 1/2x + x + 5/4x
To simplify the expression, let's find a common denominator for the fractions. The least common multiple of 2 and 4 is 4; therefore, the expression becomes:
P = 2/4x + 4/4x + 5/4x
Simplifying the fractions, we get:
P = (2 + 4 + 5)/4x
= 11/4x
The simplified expression for the perimeter of the triangle is 11/4x.
I hope this explanation helps! Let me know if you have any further questions.