Answer:
$6,020,826.711
Step-by-step explanation:
The computation of the present value of that year salary is shown below:
As we know that
Present value in case of continuous compounding, the formula is
where,
The Guaranteed amount is $9,000,000
The Time period is 6 years
And, the interest rate is 6.7%
Now placing these values
So, the present value is
= $6,020,826.711
Correlation coefficient (r) = [nΣxy - (Σx)(Σy)] / [sqrt(nΣx^2 - (Σx)^2)sqrt(nΣy^2 - (Σy)^2)]
Σx = 21 => (Σx)^2 = 21^2 = 441
Σy = 671 => (Σy)^2 = 671^2 = 450,241
Σx^2 = 1 + 4 + 9 + 16 + 25 + 36 = 91
Σy^2 = 98^2 + 101^2 + 109^2 + 117^2 + 119^2 + 127^2 = 75,665
Σxy = 1(98) + 2(101) + 3(109) + 4(117) + 5(119) + 6(127) = 2,452
r = [6(2,452) - 21(671)] / [sqrt(6(91) - 441)sqrt(6(75,665) - 450,241)] = 621/sqrt(105)sqrt(3749) = 0.99
option b is the correct answer.
So here is the answer to the given question above. Analyzing the given figure, we can see that at 0 miles, the cost is 25. Between 0 and 40 miles, the cost rises by 10. Therefore, the function that would represent this situation would be this: <span>f(x) = (10/40)x+25
</span><span> f(x) = 1/4 *x+ 25
f(x) = 0.25x + 25
Hope this is the answer that you area looking for. </span>
Answer:
The 90% confidence interval using Student's t-distribution is (9.22, 11.61).
Step-by-step explanation:
Since we know the sample is not big enough to use a z-distribution, we use student's t-distribution instead.
The formula to calculate the confidence interval is given by:
Where:
is the sample's mean,
is t-score with n-1 degrees of freedom,
is the standard error,
is the sample's size.
This part of the equation is called margin of error:
We know that:
degrees of freedom 
Replacing in the formula with the corresponding values we obtain the confidence interval:
Answer:
The greatest number of arrangements that he can make if every balloon is used is 8.
Step-by-step explanation:
The greatest number of arrangements will be the greatest common factor between 24 and 32.
GCF of 24 and 32:
We keep factoring both numbers by prime factors, while they can both be divided by the same number. So
24 - 32|2
12 - 16|2
6 - 8|2
3 - 4
There is no factor for which we can divide both 3 and 4. So the GCF is 2*2*2 = 8.
This means that the greatest number of arrangements that he can make if every balloon is used is 8.
