I need help on this math problem:
2 answers:
Answer: Choice E
All values of x are solutions
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Explanation:
Let's solve the first inequality for x
11x + 4 < 15
11x < 15-4
11x < 11
x < 11/11
x < 1
In the second step I subtracted 4 from both sides to undo the "plus 4". Then a bit later on, I divided both sides by 11 to fully isolate x. The inequality sign doesn't flip since we didn't divide both sides by a negative number.
The graph of x < 1 involves an open hole at 1 on the number line. The shading is to the left.
See the diagram below. Specifically, refer to the red portion of the diagram.
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Next, we solve the other inequality
12x - 7 > -25
12x > -25+7
12x > -18
x > -18/12
x > -3/2
The graph will have an open hole at -3/2 = -1.5 and shading to the right. This is the blue portion of the graph shown below.
Notice how the two intervals, when combined together, span the entire number line. We can pick any number we want and it will satisfy one or both of these inequalities.
Therefore, All values of x are solutions (choice E)
Side note: if we changed that "OR" to "AND", then choice E would not be the answer. Instead, it would be choice A. This is because the two intervals overlap to form this restricted compound inequality.
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Answer:
a)
b)
The total amount accrued, principal plus interest, from compound interest on an original principal of $ 4,200.00 at a rate of 3.6% per year compounded 12 times per year over 10 years is $5667.28.
Step-by-step explanation:
a. Write the function that represents the value of the account at any time, t.
The function that represents the value of the account at any time, t
where
P represents the principal amount
r represents Annual Rate
n represents the number of compounding periods per unit t, at the end of each period
t represents the time Involve
b) What will the value be after 10 years?
Given
The principal amount P = $4200
Annual Rate r = 3.6% = 3.6/100 = 0.036
Compounded monthly = n = 12
Time Period = t
To Determine:
The total amount A = ?
Using the formula
substituting the values
$
Therefore, the total amount accrued, principal plus interest, from compound interest on an original principal of $ 4,200.00 at a rate of 3.6% per year compounded 12 times per year over 10 years is $5667.28.