These are two questions and two answers.
1) Problem 17.
(i) Determine whether T is continuous at 6061.
For that you have to compute the value of T at 6061 and the lateral limits of T when x approaches 6061.
a) T(x) = 0.10x if 0 < x ≤ 6061
T (6061) = 0.10(6061) = 606.1
b) limit of Tx when x → 6061.
By the left the limit is the same value of T(x) calculated above.
By the right the limit is calculated using the definition of the function for the next stage: T(x) = 606.10 + 0.18 (x - 6061)
⇒ Limit of T(x) when x → 6061 from the right = 606.10 + 0.18 (6061 - 6061) = 606.10
Since both limits and the value of the function are the same, T is continuous at 6061.
(ii) Determine whether T is continuous at 32,473.
Same procedure.
a) Value at 32,473
T(32,473) = 606.10 + 0.18 (32,473 - 6061) = 5,360.26
b) Limit of T(x) when x → 32,473 from the right
Limit = 5360.26 + 0.26(x - 32,473) = 5360.26
Again, since the two limits and the value of the function have the same value the function is continuos at the x = 32,473.
(iii) If T had discontinuities, a tax payer that earns an amount very close to the discontinuity can easily approach its incomes to take andvantage of the part that results in lower tax.
2) Problem 18.
a) Statement Sk
You just need to replace n for k:
Sk = 1 + 4 + 7 + ... (3k - 2) = k(3k - 1) / 2
b) Statement S (k+1)
Replace
S(k+1) = 1 + 4 + 7 + ... (3k - 2) + [ 3 (k + 1) - 2 ] = (k+1) [ 3(k+1) - 1] / 2
Simplification:
1 + 4 + 7 + ... + 3k - 2+ 3k + 3 - 2] = (k + 1) (3k + 3 - 1)/2
k(3k - 1)/ 2 + (3k + 1) = (k + 1)(3k+2) / 2
Do the operations on the left side and you will find it can be simplified to k ( 3k +1) (3 k + 2) / 2.
With that you find that the left side equals the right side which is a proof of the validity of the statement by induction.
Cost of goods available for is equal
80000+160000=240000
Retail value is equal
100000+200000=300000
This means that the cost of goods sold is 80% (240000÷300000) and gross profit is 20%
Sales= 250000 and it's cost is equal 200000 (250000×0.8)
Ending inventory
=240000-200000=40000...answer
Hope it helps!
Answer:
n=2
Step-by-step explanation:
Step 1 :
1
Simplify —
2
Equation at the end of step 1 :
1
((— • (n - 4)) - 3) - -2n = 0
2
Step 2 :
Equation at the end of step 2 :
(n - 4)
(——————— - 3) - -2n = 0
2
Step 3 :
Rewriting the whole as an Equivalent Fraction :
3.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 2 as the denominator :
3 3 • 2
3 = — = —————
1 2
Answer:
The average weekly grocery bill per four-person family in the town is significantly different from the national average.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = $100
Sample mean, 
= $103.23
Sample size, n = 25
Alpha, α = 0.05
Sample standard deviation, s = $8.82
First, we design the null and the alternate hypothesis
We use Two-tailed t test to perform this hypothesis.
Formula:
Putting all the values, we have
Now,
Since,
We accept the null hypothesis.
We accept the null hypothesis and determine that the average weekly grocery bill per four-person family in the town is significantly same to the national average.
