A circle has a radius of 6 cm. What is the area of the circle in terms of π?

Susie plans to run 2 miles per day the first week and then increase the daily distance by a half a mile each of the following we

AlekseyPX

Due to length restrictions, we kindly invite to see the explanation below to know the answer with respect to each component of the question concerning linear equations.

<h3>How to determine a linear equation describing the daily distance of a runner</h3>

In this question we need to derive an expression of the daily distance as a function of time. Now we proceed to complete the components:

Linear equations have an independent variable (t - time) and a dependent variable (x - daily distance).
We notice that the daily distance increases linearly in time, then then we have the following pattern:

t 1 2 3 4 5 6
x 2 2.5 3 3.5 4 4.5
The equation that represents the n-th term of the sequence is x(n) = 2 + 0.5 · (n - 1).
The week when Susie will run 10 miles per day is:

10 = 2 + 0.5 · (n - 1)
8 = 0.5 · (n - 1)
n - 1 = 16
n = 17

Susie will run 10 miles per day in the 17th week.
It is not reasonable to think that pattern will continue indefinitely as it is witnessed in the difficulties experimented by fastest runners in the world to increase their peak speeds.
A marathon has a distance of 26 miles, then we must solve the following equation:

26 = 2 + 0.5 · (n - 1)
24 = 0.5 · (n - 1)
48 = n - 1
n = 49

Susie should start her training 49 weeks before the marathon.

To learn more on linear equation: brainly.com/question/11897796

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2 years ago

A researcher plants 22 seedlings. After one month, independent of the other seedlings, each seedling has a probability of 0.08 o

Andrews [41]

Answer:

E(X₁)= 1.76

E(X₂)= 4.18

E(X₃)= 9.24

E(X₄)= 6.82

a. P(X₁=3, X₂=4, X₃=6;0.08,0.19,0.42)= 0.00022

b. P(X₁=5, X₂=5, X₄=7;0.08,0.19,0.31)= 0.000001

c. P(X₁≤2) = 0.7442

Step-by-step explanation:

Hello!

So that you can easily resolve this problem first determine your experiment and it's variables. In this case, you have 22 seedlings (n) planted and observe what happens with the after one month, each seedling independent of the others and has each leads to success for exactly one of four categories with a fixed success probability per category. This is a multinomial experiment so I'll separate them in 4 different variables with the corresponding probability of success for each one of them:

X₁: "The seedling is dead" p₁: 0.08

X₂: "The seedling exhibits slow growth" p₂: 0.19

X₃: "The seedling exhibits medium growth" p₃: 0.42

X₄: "The seedling exhibits strong growth" p₄:0.31

To calculate the expected number for each category (k) you need to use the formula:

E(X $E(X_{k}) = n_{k} * p_{k}$