A triangle has sides that measure 4 units, 6 units, and 7.21 units. What is the area of a circle with a circumference that equal
1 answer:
Step-by-step explanation:
Given are
Sides of the triangle measure 4 units, 6 units, and 7.21 units.
We need to compute the area of a circle whose circumference matches the triangle's perimeter.
The triangle's perimeter corresponds to the circle's circumference.
4 + 6 + 7.21 = 2πr, where r is the radius of the circle.
r = 2.73 units
Circle's area is:
or
A = 24 square units
Thus, the circle’s area is 24 square units.
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Response: The following comparison is made.
Detailed explanation:
At the playground, a climbing structure is 6 feet high and stretches 4 feet horizontally.
The slope can be calculated as vertical height divided by horizontal length.
= 6/4 = 3/2 = 1.5
In contrast, a climbing structure in the gym stands 10 feet tall, extending 6 feet horizontally.
Therefore, slope, = 10/6 = 5/3 = 1.67 (approximately)
As such, <
Thus, the slope of the first climbing structure is less than that of the second.
The likelihood that at least one trip occurs before Isabella's birth is 0.7627.
Step-by-step explanation:
In this scenario, Isabella has invented a time machine, but she lacks control over where she travels. Each use of the device holds a 0.25 probability of leading her to a time preceding her birth. Over the initial year of trials, she operates her machine 5 times. If we assume every journey has an equal chance of going back in time, we can calculate the odds that at least one of these trips occurs before she was born. Here's the calculation:
The probability of traveling to a time prior to her birth is 0.25.
The chance of not traveling back in time, given that the machine is used 5 times:
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The probability that at least one trip goes before Isabella's birth is equal to 1 minus the probability of not traveling back to that period:
⇒
⇒
Consequently, the chance that at least one trip travels before Isabella's birth is 0.7627.