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Vikentia [17]
3 years ago
11

If Ben invests $4500 at 4% interest per year, how much additional money must he invest at 5 1/2% annual interest to ensure that

the interest he receives each year is 4 1/2% of the total amount invested ?
Mathematics
1 answer:
pogonyaev3 years ago
5 0

Step \; 1: \; Assing \; variable \; for \; the \; unknown \; that \; we \; need \; to \; find.\\Let \; x \; be \; additional \; money \; invested

Step \; 2: \; Use \; the \; appropriate \; formula \; of \; simple \; interest \; set \; up \; an \; equation\\Interest \; earned \; each \; year = \; Amount \; invested \times annual \; rate \; of \; interest\\\\Amount \; invested \; in \; 4 \% \; rate \; of \; interest=\$4500\\Amount \; invested \; in \; 5\frac{1}{2}\% \; rate \; of \; interest= \$x\\Amount \; invested \; totally \; in \; 4\frac{1}{2}\% \; rate \; of \; interest = \$(4500+x)

Interest \; earned \; in \; 4\% \; interest \; rate\\ = \; 4500(4\%)=180\\Interest \; earned \; in \; 5\frac{1}{2}\% \; interest \; rate\\ = x(5\frac{1}{2}\%)=0.055x\\Interest \; earned \; totally \; in \; 4\frac{1}{2}\% \; interest \; rate = (4500+x)(4\frac{1}{2}\%)\\=0.045(4500+x)

\\\\So, \; the \; equation \; would \; be:\\180+0.055x=0.045(4500+x)

Step \; 1: \; Distribute \; 0.045 \; in \; the \; right \; side\\180+0.055x=202.5+0.045x\\\\Step \; 2: \; Subtract \; 0.045x \; and \; 180 \; on \; both \; sides \; to \; get \; x \; alone\\0.055x-0.045x=202.5-180\\\\Step \; 3: \; Combine \; Like \; Terms\\0.01x=22.5\\\\Step \; 4: Divide \; 0.01 \; on \; both \; sides\\\frac{0.01x}{0.01}=\frac{22.5}{0.01}\\\\Step \; 5: \; Simplifying \; fraction \; on \; both \; sides\\x=2250

\underline{Conclusion:}\\Ben \; should \; invest \; additional \; money \; of \; \$2250

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Which of the following is an advantage of using systematic random sampling?
bekas [8.4K]

This is a question that asks about the advantages of a systematic random sampling. Thus, we first take a look at the types of sampling, and then we see the advantage of systematic random sampling.

Samples may be classified as:

Convenient: Sample drawn from a conveniently available pool.

Random: Basically, put all the options into a hat and drawn some of them.

Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.

Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.

Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.

Systematic:

One of the bigger advantages is that the systematic sampling eliminate clusters, which means that the last option is wrong.

Inadvertently missing patterns is a problem in systematic sampling, and not an advantage, thus the third option is also wrong.

It also does not reduce sampling variability, thus the first option is wrong.

From this, it can be concluded that the correct option is:

Systematic random sampling does not require a finite population size.

For another example of systematic random sampling, you can check brainly.com/question/21100042

8 0
2 years ago
Someone please help me
earnstyle [38]

(22 + 15.50 + 2.75) 15

(22 * 15) + (15.50 * 15) + (2.75 * 15)

4 0
2 years ago
Someone pls help me I turn this in today the answer is there I just need to show work pls help me​
dolphi86 [110]

Hello and Good Morning/Afternoon

<u>Let's tale this problem step-by-step</u>:

<u>What does the problem want:</u>

 \hookrightarrow \text{the unemployment compensation}

<u>Employment compensation</u> =55% of the average of the last 26-week salary

  \hookrightarrow \text{Average of Natalia's salary} = (\text{all the salaries added up}) / (\text{number of weeks})\\\hookrightarrow \text{Average of Natalia's salary} = 18940 / 26 = 728.46 \text{ (Rounded down)}

         ⇒ 55% of that average

                \hookrightarrow \frac{55}{100} *728.46 = 400.65

<u>Answer: $400.65</u>

Hope that helps!

#LearnwithBrainly

5 0
1 year ago
Please help I have no clue how to do this​
Alinara [238K]

Step-by-step explanation:

It's a question of trigonometry.

You need to remember that tangent (tan) stands for Perpendicular / Base.

So, tan P = QR / PR

By Pythagoras Theorem,

34² = 30² + x²

x² = 34² - 30²

x² = 1156 - 900

x² = 256

x = 16

Now, placing the values,

tan P = 30 / 16

tan P = 1.875

HOPE IT HELPS ^_^

5 0
2 years ago
A convenience store owner reports that seven cases of beer was stolen. Each case contains For six packs and each six pack sells
Ilia_Sergeevich [38]

Answer:

The value of the stolen merchandise is 31.43

Step-by-step explanation:

Given as :

The number of cases of beer stolen = 7

Number of packs in each cases        = 6

And The price of each six pack is 4.49  

So, As the price of each six pack is 4.49 and number of pack in each case is 6

And the number o stolen cases is 7

So, The value of total stolen item = 7 ×  4.49 = 31.43

Hence The value of the stolen merchandise is 31.43   Answer

3 0
3 years ago
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