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<u><em>Answer:</em></u>
θ = 76°
<u><em>Explanation:</em></u>
<u>The given equation is:</u>
8 cotθ + 3 = 5
8 cotθ = 5-3
8 cotθ = 2
cot θ =
<u>Now, we find θ</u>
We know that the cot function is the inverse of the tan function.
The tan of an angle is positive in the first and third quadrants, therefore, the cot will be <u>positive</u> in the <u>first and third quadrants</u> as well
<u>Now, we are given the condition:</u>
0° ≤ x ≤ 90°
<u>Therefore, we know for sure that our angle is in the first quadrant</u>
θ = cot⁻¹() = 75.96° = 76° to the nearest degree
Hope this helps :)
Answer:
ρ = 35% or 0.35
ρ with ^ = or equivalently 46%
Step-by-step explanation:
ρ represents the population proportion of the bus riders, with a monthly pass, who are students.
The population proportion is simply the percentage of the entire population with a particular characteristic. We have been informed that in a city, 35% of the bus riders with a monthly pass are students. This means that 35% of the whole population of bus riders with a monthly pass are students. Therefore, our ρ is simply 35% or 0.35.
ρ with ^ represents the sample proportion of the bus riders, with a monthly pass, who are students. This is a statistic or an estimator as it is normally used to estimate the value of ρ, the population proportion. It is calculated using the formula;
ρ with ^ =
where n represents the size of the sample and x the number of individuals in the sample with a certain desired characteristic. We have been informed that;
in a random sample of 50 bus riders with monthly passes, 23 are students.
Using the above formula and the values given we have;
ρ with ^ = or equivalently 46%