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GREYUIT [131]
3 years ago
15

The degree measure of two consecutive angles of a rhombus are represented by 5x+10 and 3x+50 find x

Mathematics
1 answer:
Readme [11.4K]3 years ago
4 0

Answer:

23

Step-by-step explanation:

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A moose population is growing exponentially following the pattern in the table shown below. Assuming that the pattern continues,
EleoNora [17]

Answer:

  •   <u> 7,692 moose.</u>

Explanation:

The table that shows the pattern for this question is:

Time (year) Population

  0                   40

  1                     62

  2                    96

  3                   149

  4                   231

A growing exponentially pattern may be modeled by a function of the form P(x) = P₀(r)ˣ.

Where P₀ represents the initial population (year = 0), r represents the multiplicative growing rate, and P(x0 represents the population at the year x.

Thus you must find both P₀ and r.

<u>1) P₀ </u>

  Using the first term of the sequence (0, 40) you get:

   P(0) = 40 = P₀ (r)⁰ = P₀ (1) = P₀

Then, P₀ = 40

<u>  2) r</u>

Take two consecutive terms of the sequence:

  • P(0) = 40 r⁰ = 40
  • P(1) = 40 r¹ = 40r = 62
  • P(1) / P(0) = 40r / 40 = 62/40
  • r = 62/40 = 1.55

 

You can verify that, for any other two consecutive terms you get the same result: 96/62 ≈ 149/96 ≈ 231/149 ≈ 1.55

<u>3) Model</u>

 

Thus, your model is P(x) = 40(1.55)ˣ

<u> 4) Population of moose after 12 years</u>

  • P(12) = 40 (1.55)¹² ≈ 7,692.019 ≈ 7,692, which is round to the nearest whole number.
7 0
2 years ago
A company makes a $5 profit on each non-faulty product it sells. Approximately 2% of the products manufactured are faulty.
galben [10]

Step-by-step answer:

The steps are much easier to follow when we know how many product it sells.  The number does not really matter, because we need the profit per item.

Say, the company made and sold 100 items of the product.

The revenue = 100*5 = $500.

On the average, 2 out of 100 are defective and need to be replaced at a cost of $100 each, so

replacement cost = 2* 100 = 200

So net profit for 100 items = $500 -$200 = $300

Net profit for each item = $300/100 = $3.00

Remark: since the product is replaced, no refund is necessary, so revenue stays at $300.

7 0
3 years ago
What is the minimum value for the function shown in the graph?<br><br> Enter your answer in the box.
Fudgin [204]

The minimum value is the lowest point of a graphed line. The would be the bottom of the "U" shape.

Looking at the graph you can see that the bottom of the U is touching the horizontal line at x = -5.5, so this would be the minimum value.

The lowest part of the line is at -5.5

5 0
3 years ago
Read 2 more answers
Help with this question plz I need the answer plz help me plz
olga nikolaevna [1]

Answer:

c

Step-by-step explanation:

45:15=3:1 not 1:3

4 0
2 years ago
Read 2 more answers
The volume of a right triangular prism is 72 cubic feet. The height of the prism is 9 feet. The triangular base is an isosceles
Maslowich

Answer:

<h2>The area of the triangular base = 8 ft²</h2>

Step-by-step explanation:

The formula of a volume of a prism:

V=A_BH

A_B-area\ of\ a\ base\\H-height

We have

V=72\ ft^3,\ H=9\ ft

Substitute:

72=9A_B             <em>divide both sides by 9</em>

8=A_B\to A_B=8\ ft^2

3 0
3 years ago
Read 2 more answers
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