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nikklg [1K]
2 years ago
5

The value of an autographed baseball from 2017 is $300. The value of the baseball exponentially increases by 5% each year after

2017. Write a one-variable inequality that could be used to solve for the number of years, x, it would take for the baseball to be worth at least $650.
Do not use any dollar signs in the inequality. Write the inequality in standard form.
Mathematics
1 answer:
WARRIOR [948]2 years ago
7 0
General exponential equation
y = A(1+r)^x
where
A = initial value
r = rate increase (+) or decrease (-)
x = time period of the change
y = projected value

y = 300(1.05)^x
in this problem, x = years after 2017
we want to find an x that makes the value more than or equal to 650

650 <= 300(1.05)^x
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Dividends Per Share Seventy-Two Inc., a developer of radiology equipment, has stock outstanding as follows: 60,000 shares of cum
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Answer and Step-by-step explanation:

The computation of dividends per share on each class of stock for each of the four years is shown below:-

Particulars                1st year     2nd-year     3rd-year     4th year

Preferred dividend

paid a                         $34,000   $38,000    $36,000    $36,000

Number of preferred

stock b                       60,000     60,000       60,000       60,000

Dividend per share

(a ÷ b)                         $0.57       $0.63          $0.60             $0.60

Dividend paid to common

stockholders c               $0             $38,000    $44,000     $64,000

Number of common stock

shares d                       410,000     410,000     410,000     410,000

Dividend per share

on common stock        $0             $0.093        $0.11          $0.16

(c ÷ d)

Working note:

Preferred dividend = Number of preferred stock shares × Par value per share × Percentage of dividend

= 60,000 × $20 × 3%

= $36,000

Preferred stock

For 1st year

= $34,000

For 2nd-year

Dividend in year 2+ Dividend balance in year 1

= $36,000 + ($36,000 - $34,000)

= $38,000

For 3rd-year

= $36,000

For 4th year

= $36,000

Common stock dividend

Particulars                      1 year        2 year       3 year       4 year

Total dividend paid       $34,000  $76,000   $80,000     $100,000

Less:

Preferred stock

dividend                      $34,000      $38,000  $36,000     $36,000

Dividend paid to common

stockholders                 $0             $38,000    $44,000     $64,000

8 0
2 years ago
Nick billups is paid a salary of $ 900 a month, a 2 % commission on all sales, and 1.8 % more on monthly sales over $ 17,500. In
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June :
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2 years ago
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Which of these is an example of acceleration? a bicyclist turning around a corner a car traveling south with its cruise control
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Answer:

A bus traveling north at 25m/s

Step-by-step explanation:

Common sense

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we know that

The measurement of <u>the external angle</u> is the semi-difference of the arcs it includes.

In this problem

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Solve for the measure of arc SU

42\°=[arc\ RU-arc\ SU]

arc\ SU=arc\ RU-42\°

arc\ SU=119\°-42\°=77\°

therefore

the answer is

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2 years ago
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lilavasa [31]

Answer:

a) For this case we have 4 programs so then if we define the event R that a CD is tested we have the following probability for each test:

P(R) =\frac{1}{4} =0.25

The failure probability for each program are given by:

P(F_1) = 0.01 , P(F_2) = 0.03 , P(F_3) = 0.02 , P(F_4) = 0.01

For this case we assume that each test is independet form the others.

We can calculate the probability that all 4 programs works properly like this:

P(4 work) = (1-0.01)*(1-0.03)*(1-0.02)*(1-0.01)= 0.932

So then the probability that any program fails would be given by:

P(F) = 1- 0.932= 0.068

And if we use the fact that we have 4 possible test the true probability of interest would be:

P(R \cap F) = P(R)*P(F) = 0.25*0.068=0.017

b) p= P(F'_1) P(F'_4) *(1- P(F'_2)*P(F'_3))

And replacing we got:

p =(1-0.01)*(1-0.01) *[1- (1-0.03)(1-0.02)]= 0.99*0.99*[1- 0.97*0.98]= 0.0484

c) From part a we now that the probability that any program fails would be given by:

P(F) = 1- 0.932= 0.068

So then if we have 100 CDs the expected number of rejected Cd's are:

100*0.068= 6.8 \approx 7

Step-by-step explanation:

Part a

For this case we have 4 programs so then if we define the event R that a CD is tested we have the following probability for each test:

P(R) =\frac{1}{4} =0.25

The failure probability for each program are given by:

P(F_1) = 0.01 , P(F_2) = 0.03 , P(F_3) = 0.02 , P(F_4) = 0.01

For this case we assume that each test is independet form the others.

We can calculate the probability that all 4 programs works properly like this:

P(4 work) = (1-0.01)*(1-0.03)*(1-0.02)*(1-0.01)= 0.932

So then the probability that any program fails would be given by:

P(F) = 1- 0.932= 0.068

And if we use the fact that we have 4 possible test the true probability of interest would be:

P(R \cap F) = P(R)*P(F) = 0.25*0.068=0.017

Part b

For this case we want the probability that it failed program 2 or 3

So then we can find this probability like this:

p= P(F'_1) P(F'_4) *(1- P(F'_2)*P(F'_3))

And replacing we got:

p =(1-0.01)*(1-0.01) *[1- (1-0.03)(1-0.02)]= 0.99*0.99*[1- 0.97*0.98]= 0.0484

Part c

From part a we now that the probability that any program fails would be given by:

P(F) = 1- 0.932= 0.068

So then if we have 100 CDs the expected number of rejected Cd's are:

100*0.068= 6.8 \approx 7

3 0
2 years ago
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