QUICK ALSO BRAINLY Which graph shows a proportional relationship between the number of hours of renting a bicycle and the total
1 answer:
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Answer:
7.87 years
Step-by-step explanation:
#First we determine the effective annual rate based on the 9% compounded semi annual;
#We then use this effective rate in the compound interest formula to solve for n. Given that the principal doubles after 2 yrs:
Hence, it takes 7.87 years for the principal amount to double.
Answer:
a)
So then we conclude that is an unbiased estimator of
So then we conclude that is an unbiased estimator of
b)
Step-by-step explanation:
For this case we know that we have two random variables:
both with mean
and variance
And we define the following estimators:
Part a
In order to see if both estimators are unbiased we need to proof if the expected value of the estimators are equal to the real value of the parameter:
So let's find the expected values for each estimator:
Using properties of expected value we have this:
So then we conclude that is an unbiased estimator of
For the second estimator we have:
Using properties of expected value we have this:
So then we conclude that is an unbiased estimator of
Part b
For the variance we need to remember this property: If a is a constant and X a random variable then:
For the first estimator we have:
Since both random variables are independent we know that so then we have:
For the second estimator we have:
Since both random variables are independent we know that so then we have:
Answer:
The blimp can carry 70 passengers
Step-by-step explanation:
Lets use the ratio method to solve this problem
∵ 1 cubic meter of helium can lift about 1.1 kg
∵ A blimp can carry as much as 2 x m³ of helium
By using the ratio method
→ m³ : kg
→ 1 : 1.1
→ 2 x : x
By using cross multiplication
∴ x × 1 = 1.1 × 2 x
∴ x = 2.2 x
∵ x represents the mass that can carried by the helium
∴ 2 x m³ of helium can lift 2.2 x
kg
∵ The mass of the blimp is 2.13 x kg
- Subtract the mass of the blimp from the mass that the given
amount of helium can lift to find the mass of the passengers
∴ The mass of the passengers = 2.2 x - 2.13 x
- Subtract 2.13 from 2.2 ⇒ 2.2 - 2.13 = 0.07
∴ The mass of the passengers = 0.07 x
∵ The average mass of a person with luggage is 10² kg
- Divide the mass of the passengers by the mass of the person
to find the number of the passengers
∴ The number of passengers = 0.07 x ÷ 10²
- Subtract the exponents of 10 to find the answer
∵ ÷ 10² =
= 10³
∴ The number of passengers = 0.07 x 10³
∴ The number of passengers = 0.07 × 1000
∴ The number of passengers = 70
The blimp can carry 70 passengers