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stiks02 [169]
3 years ago
15

A manufacturer producing a new product, estimates the annual sales to be 9,600 units. Each year, 8% of the units that have been

sold will become inoperative. So, 9,600 units will be in use after 1 year, [9,600 0.92(9,600)] units will be in use after 2 years, and so on. How many units will be in use after n years
Mathematics
1 answer:
Crazy boy [7]3 years ago
4 0

Answer:

After n years, 120,000(1 - 0.92ⁿ) units, will be in use.

Step-by-step explanation:

Given;

estimated annual sales, a = 9600 units

determine common ratio, r;

r = 1 - \frac{8}{100}\\\\r = 0.92

sum of the units in use after n years is calculated by applying sum of nth term;

S_n = \frac{a}{1-r} (1-r^n)

S_n = \frac{9600}{1-0.92} (1-0.92^n)\\\\S_n = \frac{9600}{0.08} (1-0.92^n)\\\\S_n = 120,000(1-0.92^n) \ units

Therefore, after n years, 120,000(1 - 0.92ⁿ) units, will be in use.

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Answer:

it would be like 90 feet

Step-by-step explanation:

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8 0
2 years ago
13. f(x) = x + 5<br> a. f(4)<br> b. f(7)<br> c. f(-3)<br> d. f(0)<br> e. f(2.4)<br> f. f(2/3)
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4 0
3 years ago
What value for the constant, h, in the equation shown below will result in an infinite number of solutions?
natta225 [31]

Using a system of equations, it is found that a value of h = 4 will result in an infinite number of solutions.

<h3>What is a system of equations?</h3>

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

If two equations are equal, the system has infinite solutions.

In this problem, the equations are:

4x - 16 = h(x - 4).

Then:

4(x - 4) = h(x - 4).

h = 4.

More can be learned about a system of equations at brainly.com/question/24342899

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5 0
2 years ago
Can someone tell me how to do this? with steps?
MrRa [10]

Answer:

Step-by-step explanation:

In Δ AFB,

∠AFB + ∠ABF + ∠A = 180   {Angle sum property of triangle}

90 + 48 + ∠1 = 180

       138 + ∠1 = 180

                 ∠1 = 180 - 138

∠1 = 42°

FC // ED and FD is transversal

So, ∠CFD ≅∠EDF   {Alternate interior angles are congruent}

     ∠2 = 39°

In ΔFCD,

∠2 + ∠3 + ∠FCD = 180

39 + ∠3 + 90 = 180

         129 +∠3 = 180

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3 0
2 years ago
Suppose that you had the following data set. 500 200 250 275 300 Suppose that the value 500 was a typo, and it was suppose to be
hodyreva [135]

Answer:

\bar X_B = \frac{\sum_{i=1}^5 X_i}{5} =\frac{500+200+250+275+300}{5}=\frac{1525}{5}=305

s_B = \sqrt{\frac{\sum_{i=1}^5 (X_i-\bar X)^2}{n-1}}=\sqrt{\frac{(500-305)^2 +(200-305)^2 +(250-305)^2 +(275-305)^2 +(300-305)^2)}{5-1}} = 115.108

\bar X_A = \frac{\sum_{i=1}^5 X_i}{5} =\frac{-500+200+250+275+300}{5}=\frac{525}{5}=105

s_A = \sqrt{\frac{\sum_{i=1}^5 (X_i-\bar X)^2}{n-1}}=\sqrt{\frac{(-500-105)^2 +(200-105)^2 +(250-105)^2 +(275-105)^2 +(300-105)^2)}{5-1}} = 340.221

The absolute difference is:

Abs = |340.221-115.108|= 225.113

If we find the % of change respect the before case we have this:

\% Change = \frac{|340.221-115.108|}{115.108} *100 = 195.57\%

So then is a big change.

Step-by-step explanation:

The subindex B is for the before case and the subindex A is for the after case

Before case (with 500)

For this case we have the following dataset:

500 200 250 275 300

We can calculate the mean with the following formula:

\bar X_B = \frac{\sum_{i=1}^5 X_i}{5} =\frac{500+200+250+275+300}{5}=\frac{1525}{5}=305

And the sample deviation with the following formula:

s_B = \sqrt{\frac{\sum_{i=1}^5 (X_i-\bar X)^2}{n-1}}=\sqrt{\frac{(500-305)^2 +(200-305)^2 +(250-305)^2 +(275-305)^2 +(300-305)^2)}{5-1}} = 115.108

After case (With -500 instead of 500)

For this case we have the following dataset:

-500 200 250 275 300

We can calculate the mean with the following formula:

\bar X_A = \frac{\sum_{i=1}^5 X_i}{5} =\frac{-500+200+250+275+300}{5}=\frac{525}{5}=105

And the sample deviation with the following formula:

s_A = \sqrt{\frac{\sum_{i=1}^5 (X_i-\bar X)^2}{n-1}}=\sqrt{\frac{(-500-105)^2 +(200-105)^2 +(250-105)^2 +(275-105)^2 +(300-105)^2)}{5-1}} = 340.221

And as we can see we have a significant change between the two values for the two cases.

The absolute difference is:

Abs = |340.221-115.108|= 225.113

If we find the % of change respect the before case we have this:

\% Change = \frac{|340.221-115.108|}{115.108} *100 = 195.57\%

So then is a big change.

8 0
3 years ago
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