Answer:
B) 376 units squared
Step-by-step explanation:
Imma put a picture that has a fully explanation. Hope this helps, good luck! ;)
Btw saw your other one got deleted •_• *sigh*
Which function describes the arithmetic sequence shown -1, 1, 3, 5, 7, 9, 11, 13, ...
1 answer:
Answer:
f(n) = 2n - 3 describes the arithmetic sequence,
-1, 1, 3, 5, 7, 9, 11, 13,.......
Step-by-step explanation:
Function:
A function is like a machine that gives an output for a given input.
A function has an independent variable which is called the input of the function.
The output for a given input is called the dependent variable.
Here. 'n' is the independent variable
f(n) is the function dependent variable i.e function of n as an output.
For Arithmetic sequence
Where
= nth number of the sequence.
a₁ = First term
d = common difference = a₂ - a₁ = a₃ - a₂ = so on
For a function which describes Arithmetic sequence,
a₁ = -1
d = 1 - -1 =2
∴ f(n) = a₁ + (n -1 )d
substituting the values we get
∴ f(n) = -1 +(n-1)2
using distributive property
∴ f(n) = - 1 + 2n - 2
∴ f(n) = 2n - 3 ..........is the required function
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Answer:
(a) Probability that a single randomly selected element X of the population is between 57,000 and 58,000 = 0.46411
(b) Probability that the mean of a sample of size 100 drawn from this population is between 57,000 and 58,000 = 0.99621
Step-by-step explanation:
We are given that a normally distributed population has mean 57,800 and standard deviation 75, i.e.; = 57,800 and
= 750.
Let X = randomly selected element of the population
The z probability is given by;
Z = ~ N(0,1)
(a) So, P(57,000 <= X <= 58,000) = P(X <= 58,000) - P(X < 57,000)
P(X <= 58,000) = P( <=
) = P(Z <= 0.27) = 0.60642
P(X < 57000) = P( <
) = P(Z < -1.07) = 1 - P(Z <= 1.07)
= 1 - 0.85769 = 0.14231
Therefore, P(31 < X < 40) = 0.60642 - 0.14231 = 0.46411 .
(b) Now, we are given sample of size, n = 100
So, Mean of X, X bar = 57,800 same as before
But standard deviation of X, s = =
= 75
The z probability is given by;
Z = ~ N(0,1)
Now, probability that the mean of a sample of size 100 drawn from this population is between 57,000 and 58,000 = P(57,000 < X bar < 58,000)
P(57,000 <= X bar <= 58,000) = P(X bar <= 58,000) - P(X bar < 57,000)
P(X bar <= 58,000) = P( <=
) = P(Z <= 2.67) = 0.99621
P(X < 57000) = P( <
) = P(Z < -10.67) = P(Z > 10.67)
This probability is that much small that it is very close to 0
Therefore, P(57,000 < X bar < 58,000) = 0.99621 - 0 = 0.99621 .