Greg bought 2 boxes of balloons he used half of them to decorate his yard he used 40 to decorate his porch he used the rest insi
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Answer:
Null hypothesis be H₀ : μ = 100
Alternative hypothesis Hₐ : μ < 100
There is sufficient statistical evidence to suggest that the average location of Wade Tract is 100
Step-by-step explanation:
Here we have;
Let our null hypothesis be H₀ : μ = 100 Average location of trees in the Wade Tract is 100
Our alternative hypothesis becomes Hₐ : μ < 100 at 95% confidence level
Proposed average location in Wade Tract, μ = 100
Sample mean, = 99.74
Standard deviation, s = 58
Sample size, n = 584
The t test formula is therefore;
Therefore, with df = 584 -1 = 583, and α = (1 - 0.95)/2 = 0.025
We have = -1.65
Plugging in the values into the t test formula, we have t = -0.108338, from which the p-value is given as p = 0.4569 which is much more than the value of α, therefore, we accept the null hypothesis as follows;
There is sufficient statistical evidence to suggest that the average location of Wade Tract = 100.
Answer:
Length A of the magazine garden is 28 feet is true.
Length B of the Magazine garden is 17.5 feet is true.
Length C of the Magazine garden is 35 feet is true.
Step-by-step explanation:
Please refer the attached figure.
Given:-
Magazine Scale is 1 inch = 3.5 feet.
Imogen's scale is 2 inches = 6 feet,
Therefore Imogen's scale is 1 inch = 3 feet.
In Triangle ABC,
side a = 8 inches, side b= 5 inches, side c= 10 inches.
To find:- The correct 3 options(actual size of sides of triangle ABC).
Solution:-
In triangle ABC,
Let,
AB=side a =8 inches
BC=side b =5 inches
AC=side c= 10 inches
Now, as per the given scale's of Magazine and Imogen's we can find the actual sizes.
Length A as per Magazine scale (1 inch = 3.5 feet) is,
-------------(as per scale)
and Length A as per Imogen's scale(1 inch =3 feet) is,
AB = side a
-------------(as per scale)
Therefore Length A of the magazine garden is 28 feet is true.
Now, Length B as per Magazine scale (1 inch = 3.5 feet) is,
BC = side b
Length B as per Imogen's scale (1 inch = 3 feet) is,
BC = side b
Therefore Length B of the Magazine garden is 17.5 feet is true.
Now, Length C as per Magazine scale (1 inch = 3.5 feet) is,
AC = side c
Length B as per Imogen's scale (1 inch = 3 feet) is,
AC = side c
Therefore Length C of the Magazine garden is 35 feet is true.
Answer:
probability that all of the sprinklers will operate correctly in a fire: 0.0282
Step-by-step explanation:
In order to solve this question we will use Binomial probability distribution because:
- In the question it is given that the sprinklers activate correctly or not independently.
- The number of outcomes are two i.e. sprinklers activate correctly or not.
A binomial distribution is a probability of a success or failures outcomes in an repeated multiple or n times.
Number of outcomes of this distributions are two.
The formula is:
b(x; n, P) =
b = binomial probability also represented as P(X=x)
x =no of successes
P = probability of a success on a single trial
n = no of trials
is calculated as:
= n! / x!(n – x)!
= 10! / 10!(10-10)!
= 1
According to given question:
probability of success i.e. p = 0.7 i.e. probability of a sprinkler to activate correctly.
number of trials i.e. n = 10 as number of sprinklers are 10
To find: probability that all of the sprinklers will operate correctly in a fire
X = 10 because we have to find the probability that "all" of the sprinklers will operate correctly and there are 10 sprinklers so all 10 of them
So putting these into the formula:
P(X=x) =
= C₁₀,₁₀ * 0.7¹⁰ * (1-0.7)¹⁰⁻¹⁰
= 1 * 0.0282 * (0.3) ⁰
= 1 * 0.0282 * 1
P(X=x) = 0.0282