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3 years ago

Could someone explain to me how to answer this question.

Mathematics

2 answers:

lyudmila [28]3 years ago

6 0

1/6(9/9)+8/8
1/6+1
7/6

Paul [167]3 years ago

5 0

1/6 ( $\sqrt{81}$ / 3^2) + 2^3 / |-8|

Let's simplify some things first:
The square root of 81 is 9.
3^2 = 9
2^3 = 8
|-8| = 8

1/6 (9/9) + 8/8

1/6(1) + 1

1/6 + 1 = 7/6

The answer is 7/6, or 1 and 1/6

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If your starting salary is $40,000 and you receive a 4.2% raise every year, how much TOTAL money will you make in 15 years?

Oliga [24]

The first year, the amount is 40,000

the second year is 40000 + 4.2% of 40000, or 0.042 * 4000, so 40000+(0.042*4000)
common factoring that we get 40000(1 + 0.042), or just 40000(1.042)

in short, the starting amount is 40000, and to get the next term's value you'd use the "common ratio" of 1.042, namely the multiplier of 1.042.

for the third year it'll be 40000(1.042) + (0.042 *40000(1.042) ), again, common factoring that

40000(1.042)(1 + 0.042) or 40000(1.042)(1.042) or 40000(1.042)²

therefore,

$\bf \qquad \qquad \textit{sum of a finite geometric sequence}\\\\
S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
a_1=40000\\
r=1.042\\
n=15
\end{cases}
\\\\\\
S_{15}=40000\left( \cfrac{1-1.042^{15}}{1-1.042} \right)\implies S_{15}\approx 40000\left( \cfrac{-0.8536}{-0.042} \right)
\\\\\\
S_{15}\approx 812951.42$

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3 years ago

S_A_V [24]

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2 years ago

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OLEGan [10]

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2 years ago

What is 7÷23 including the remainder

Harlamova29_29 [7]

I hope this is helpful!

Answer: 3 R2

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3 years ago

Read 2 more answers

Write 2 equations<br>and show your work<br>PLZ HELP ME ASAP I NEED HELP

Grace [21]

<h2>Explanation:</h2><h3>Part A.</h3>

You are asked to define variables that "model the situation" without being told what you care about in the situation. For that purpose, the variables you have chosen, ...

d = number of coins
q = their total value

are completely appropriate. Your choice will give rise to two equations, already solved:

d = 90 . . . . . . . . the equation for the amount of coins
q = 17.55 . . . . . . the equation for the value of the coins

___

However, that is not going to be helpful for Part B.

In Part B, you're asked for the <em>number of quarters</em>. You might expect that choosing a variable to represent this quantity would be helpful, and you'd be right. For a variety of reasons, choosing another variable to represent the <em>number of dimes</em> is also helpful. Now, we have the definitions

let q = the number of quarters in Dylan's bank
let d = the number of dimes in Dylan's bank

The corresponding system of equations is ...

q + d = 90 . . . . . the number of coins Dylan has
0.25q +0.10d = 17.55 . . . . the value of the coins Dylan has

_____

Since you're only interested in the number of quarters, it can be convenient to choose a solution method that focuses only on the q variable. Here, we'll multiply the first equation by -0.10 and add the result to the second equation. That eliminates d and gives an equation only in q.

-0.10(q +d) +(0.25q +0.10d) = -0.10(90) +(17.55)

0.15q = 8.55 . . . . . simplify

8.55/0.15 = q = 57 . . . . . . divide by the coefficient of q to find the solution

Dylan has 57 quarters in his bank.

=====

<em>Comment on "this situation" problems</em>

As you have discovered, modeling a particular "situation" needs to be informed by the aspect(s) of the situation that you care about. Many modern math texts ask for a model of "this situation" without bothering to tell you that crucial piece of information.

I find it unfortunate, and not particularly instructive in good critical thinking practice or problem solving technique.

Here, we found it helpful to read ahead for clues as to what the problem is really about. That will often be a helpful approach.

7 0

3 years ago