The front of a tent is an equilateral triangle with the ratio of its base, b, to its height, h, given by b over h equal fraction
1 answer:
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Response:
Step-by-step explanation:
To calculate 5% of our number, we start by multiplying by 0.05
Next, by adding and subtracting this 5% from our original number, we can find the minimum and maximum possible values of our final answer in the specified range.
We can ascertain that fits within the acceptable range, as:
Therefore, our final answer will be:
Response:
To accumulate $7,500 in three years, the required one-time deposit is $4388.17
Step-by-step explanation:
Basic Financial Formulas
A commonly used formula for calculating present and future values is
Where FV represents the future value, PV denotes the present value, r signifies the interest rate, and n indicates the number of compounding periods. It’s essential to remember that r and n must correspond to the same compounding duration, e.g. r is compounded monthly while n is expressed in months.
The inquiry seeks to determine the PV necessary as a one-time deposit to achieve a future value of $7,500 in 3 years at an interest rate of 1.5% compounded monthly.
FV=7,500
r=1.5%=0.015
n=3*12=36 months
We have changed n to months since r is monthly compounded. The equation
must be arranged to isolate PV.
Response
: The amount necessary as a one-time deposit to accrue $7,500 in three years is $4388.17[[TAG_54]]
Utilize the details to create inequalities that reflect each limitation or requirement.
2) Label the variables.
c: count of color copies
b: count of black-and-white copies
3) Define each constraint:
i) <span>Printing a color copy requires 3 minutes while a black-and-white copy takes 1 minute.
</span><span>
</span><span>3c + b
</span><span>
</span><span>
</span><span>ii) He must print a minimum of 6 copies ⇒ c + b ≥ 6
</span><span>
</span><span>
</span><span>iv) Moreover, he must finish the prints within 12 minutes at most ⇒</span>
3c + b ≤ 12
<span />
4) Additional limits include c ≥ 0, and b ≥ 0 (meaning only non-negative counts are valid for each type of copy)
5) Here’s how to illustrate that:
i) For 3c + b ≤ 12: draw the line representing 3c + b = 12 and shade the area above and to the right of this line.
ii) For c + b ≥ 6: draw the line c + b = 6 and shade the area below and to the left of this line.
iii) Given that c ≥ 0 and b ≥ 0, the relevant region is located in the first quadrant.
iv) The concluding area is the overlap of the previously mentioned shaded regions.
v) The graph can be viewed in the attached figure.
2) Label the variables.
c: count of color copies
b: count of black-and-white copies
3) Define each constraint:
i) <span>Printing a color copy requires 3 minutes while a black-and-white copy takes 1 minute.
</span><span>
</span><span>3c + b
</span><span>
</span><span>
</span><span>ii) He must print a minimum of 6 copies ⇒ c + b ≥ 6
</span><span>
</span><span>
</span><span>iv) Moreover, he must finish the prints within 12 minutes at most ⇒</span>
3c + b ≤ 12
<span />
4) Additional limits include c ≥ 0, and b ≥ 0 (meaning only non-negative counts are valid for each type of copy)
5) Here’s how to illustrate that:
i) For 3c + b ≤ 12: draw the line representing 3c + b = 12 and shade the area above and to the right of this line.
ii) For c + b ≥ 6: draw the line c + b = 6 and shade the area below and to the left of this line.
iii) Given that c ≥ 0 and b ≥ 0, the relevant region is located in the first quadrant.
iv) The concluding area is the overlap of the previously mentioned shaded regions.
v) The graph can be viewed in the attached figure.