If a sector in a circle of radius 10 has an area of 5pi, what is the measure of the central angle that forms the sector?
2 answers:
Answer:
Step-by-step explanation:
The area (A) of the sector is calculated using the formula
A = area of circle × fraction of circle
let x be the measure of the central angle, then
A = πr² × ← substitute values
5π = π × 10² ×
5π = 100π × (cancel 50π and 2π )
5π = 50x ( divide both sides by 50 )
x = =
← central angle
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Answer:
12 years younger.
Step-by-step explanation:
Let Jan's age be J and Karyn's age be K.
Jan's age 8 years ago is 2/5 of Karyn's age 4 yeaRs from now.
=>
=> 4K = 48 X 3
=> K= 36.
=> J= 24.
So Jan is 12 years younger.
Answer:
We conclude that the population mean is 24.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 24
Sample mean, = 22.8
Sample size, n = 100
Alpha, α = 0.05
Sample standard deviation, s = 8.3
First, we design the null and the alternate hypothesis
We use Two-tailed z test to perform this hypothesis.
Formula:
Putting all the values, we have
We calculate the p-value with the help of standard z table.
P-value = 0.1498
Since the p-value is greater than the significance level, we accept the null hypothesis. The population mean is 24.
Now,
Since, the z-statistic lies in the acceptance region which is from -1.96 to +1.96, we accept the null hypothesis and conclude that the population mean is 24.