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BartSMP [9]
3 years ago
7

The retailer sold each package for $12.59.

Mathematics
2 answers:
juin [17]3 years ago
5 0

Answer:

✔ $4.36

✔ $8.23

Step-by-step explanation:

Lena [83]3 years ago
3 0

Answer: 8.23

Hope this helps all you young learners

You might be interested in
The angle of elevation from me to the top of a hill is 51 degrees. The angle of elevation from me to the top of a tree is 57 deg
julia-pushkina [17]

Answer:

Approximately 101\; \rm ft (assuming that the height of the base of the hill is the same as that of the observer.)

Step-by-step explanation:

Refer to the diagram attached.

  • Let \rm O denote the observer.
  • Let \rm A denote the top of the tree.
  • Let \rm R denote the base of the tree.
  • Let \rm B denote the point where line \rm AR (a vertical line) and the horizontal line going through \rm O meets. \angle \rm B\hat{A}R = 90^\circ.

Angles:

  • Angle of elevation of the base of the tree as it appears to the observer: \angle \rm B\hat{O}R = 51^\circ.
  • Angle of elevation of the top of the tree as it appears to the observer: \angle \rm B\hat{O}A = 57^\circ.

Let the length of segment \rm BR (vertical distance between the base of the tree and the base of the hill) be x\; \rm ft.

The question is asking for the length of segment \rm AB. Notice that the length of this segment is \mathrm{AB} = (x + 20)\; \rm ft.

The length of segment \rm OB could be represented in two ways:

  • In right triangle \rm \triangle OBR as the side adjacent to \angle \rm B\hat{O}R = 51^\circ.
  • In right triangle \rm \triangle OBA as the side adjacent to \angle \rm B\hat{O}A = 57^\circ.

For example, in right triangle \rm \triangle OBR, the length of the side opposite to \angle \rm B\hat{O}R = 51^\circ is segment \rm BR. The length of that segment is x\; \rm ft.

\begin{aligned}\tan{\left(\angle\mathrm{B\hat{O}R}\right)} = \frac{\,\rm {BR}\,}{\,\rm {OB}\,} \; \genfrac{}{}{0em}{}{\leftarrow \text{opposite}}{\leftarrow \text{adjacent}}\end{aligned}.

Rearrange to find an expression for the length of \rm OB (in \rm ft) in terms of x:

\begin{aligned}\mathrm{OB} &= \frac{\mathrm{BR}}{\tan{\left(\angle\mathrm{B\hat{O}R}\right)}} \\ &= \frac{x}{\tan\left(51^\circ\right)}\approx 0.810\, x\end{aligned}.

Similarly, in right triangle \rm \triangle OBA:

\begin{aligned}\mathrm{OB} &= \frac{\mathrm{AB}}{\tan{\left(\angle\mathrm{B\hat{O}A}\right)}} \\ &= \frac{x + 20}{\tan\left(57^\circ\right)}\approx 0.649\, (x + 20)\end{aligned}.

Equate the right-hand side of these two equations:

0.810\, x \approx 0.649\, (x + 20).

Solve for x:

x \approx 81\; \rm ft.

Hence, the height of the top of this tree relative to the base of the hill would be (x + 20)\; {\rm ft}\approx 101\; \rm ft.

6 0
3 years ago
Goal
morpeh [17]

The development of the personal budget that convinces parents that one can maintain an independent living is detailed as follows using the 50: 30: 20 rule:

50% for necessities (housing, food, transportation, utilities) $740

30% for luxuries, savings, vacations, entertainment, etc. $461

20% for Emergency Funds and Retirement $335

<h3>What is a personal budget?</h3>

A personal budget is the household budget for a single person for a period.

The personal budget shows an estimate of the person's revenue and expenses over the period.

<h3>Data and Calculations:</h3>

Hourly rate of earnings = $12

Working hours per week = 40 hours

Working hours per month = 160 hours (40 x 4 weeks)

Total monthly earnings = $1,920 ($12 x 160)

Assumed tax rate = 20%

After-tax take-home pay = $1,536 ($1,920 x 1 - 20%)

<h3>Monthly Necessities:</h3>

Rent of apartment = $300

Heating = $40

Water cost = $20

Sewage bill = $10

Food = $300

Transportation = $50

Other costs = $20

Total cost for necessities = $740

Thus, the development of the personal budget shows that one can maintain an independent living from the parents as a single person.

Learn more about personal budgets at brainly.com/question/1943261

#SPJ1

6 0
1 year ago
Arrange the summation expressions in increasing order of their values
Svetradugi [14.3K]
Sum of n terms  = a1  (r^n-1/ (r-1)

Sum of first one = 3 * (4^5 - 1) / 3  =  1023
  ..           2nd =  5 * (6^2 - 1) / 5 =  35
   ..            3rd = 5 ^4 - 1 / 4 =  156
   ..            4th =  4 * (5^4 - 1) / 4 = 624

So in increasing order its   2nd, 3rd, 4th and first.
3 0
3 years ago
Which of the following expressions represents the verbal description below?
Georgia [21]
  • Cube of the sum of 4 and 9 times x means (4+9x)^3
  • Product of 5times x and the difference of x and 1 means 5x(x-1)

Lets divide

Expression is

\\ \sf\longmapsto \dfrac{(4+9x)^3}{5x(x-1)}

5 0
2 years ago
Read 2 more answers
Which is a correct first step in solving 5 - 2x &lt; 8x- 3?
aliina [53]

Answer:

5 < 10x - 3

Step-by-step explanation:

Given:

The given inequality is:

5 - 2x < 8x- 3

The given inequality has variable 'x' on both sides of the inequality.

In order to solve such inequalities, we bring the variables on the same side as the first step in solving for 'x'.

Therefore, we could either add 2x on both sides or add -8x both sides to bring the variable terms on same side.

If we add 2x both sides, we get:

5 - 2x +2x< 8x+2x - 3\\5

So, among all the given options, third option matches the above inequality.

Therefore, the first step in solving the given inequality is 5 < 10x - 3

6 0
3 years ago
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