Answer:
Step-by-step explanation:
The present value of the house is $120,000 and the interest rate is 5.5%, or 0.055.
We will utilize the following equation:
where 
represents the present value, 
symbolizes the interest rate, and 
refers to the number of years.
By inputting the values into the above equation, we can obtain:
In this scenario, we aim to assess if pennies are genuinely fair when tossed, indicating that they have an equal chance of landing heads or tails. Therefore, the appropriate hypotheses are as follows: Null hypothesis: Alternative hypothesis: A hypothesis can be defined as "a conjecture or theory that is based on inadequate evidence and can be subjected to further examination and experimentation. With continued investigation, a hypothesis can typically be validated as true or false." The null hypothesis is defined as "a hypothesis that posits no statistical significance between the two variables in question. It represents what the researcher seeks to refute." Conversely, the alternative hypothesis is simply "the opposite or inverse of the null hypothesis; it is what the researcher aims to substantiate." For this study, we wish to confirm if pennies are indeed fair when flipped, meaning an equal chance to land heads versus tails, hence the proper hypotheses are: Null hypothesis: Alternative hypothesis:
Answer:
Step-by-step explanation:
The probability distribution for the random variable X is provided.
X 4 5 6 7 Total
P 0.2 0.4 0.3 0.1 1
x*p 0.8 2 1.8 0.7 5.3
x^2*p 3.2 10 10.8 4.9 28.9
a) The expected value E(X), representing the mean of X, equates to 5.3.
Standard deviation is the square root of the variance, which amounts to 0.9.
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b) For the mean of the sample, we find:
Mean = 5.3
Variance = var(x)/n = 
c) 
Response:
Dimensions of the rectangular fence:
x = 14 ft
w = 7 ft
A = 98 ft²
Detailed explanation:
Dimensions of the rectangular fence:
x = length, and w = width
Then x = 2*w ⇒ w = x/2
Perimeter is
p = 2*x + 2*w
p = 2*x + 2* x/2
p = 2*x + x
3*x = 42
x = 14 ft and w = 14/2 ⇒ w = 7 ft
