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grigory [225]
1 year ago
13

How many extraneous solutions does the equation below have?

Mathematics
2 answers:
soldi70 [24.7K]1 year ago
6 0

Answer:

A. 0

Step-by-step explanation:

How many extraneous solutions does the equation below have?

StartFraction 9 Over n squared + 1 EndFraction = StartFraction n + 3 Over 4 EndFraction

0

1

2

3

Anna71 [15]1 year ago
4 0

Answer:

We can say that the given equation has no extraneous solutions.

The correct option is A.) 0

Step-by-step explanation:

the given equation is \frac{9}{n^{2} +1} = \frac{n+3}{4}

this equals to 36 = (n^{2} +1)(n+3) = n^{3} + 3n^{2} + n + 3

therefore n^{3} +3n^{2} +n+3 = 36 \hspace{0.3cm}\Rightarrow \hspace{0.3cm}n^{3} +3n^{2} +n-33=0

Solving the equation through Newton-Raphson method we get n  \approx  2.3845.

We can say that the given equation has no extraneous solutions.

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For the answer to the question above, <span>f x is the number of days she works, she'll earn $90x </span>
<span>After buying the laptop, she'll have $90x - $700 left over, which will pay for ($90x - $700) / $150 days of travel. So we have y = ($90x - $700) / $150 = (9x - 70) / 15 = 0.6x - (14/3) </span>
<span>Note that y can't be negative. Also, if y = 0, then Emma doesn't get to travel at all, so we should avoid that. So we have: </span>
<span>0.6x - (14/3) > 0 </span>
<span>0.6x > 14/3 </span>
<span>x > (14/3) / 0.6 </span>
<span>x > 70/9 </span>
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3 0
1 year ago
Read 2 more answers
Find the difference. Express your answer in
Leokris [45]

Answer:

-4g-3

------------

g+2

Step-by-step explanation:

g+1                     5g+4

-------------  -   ------------------

g+2                     g+2

Since the denominators are the same, subtract the numerators

g+1 - (5g+4)

Distribute the negative sign

g+1 -5g-4

-4g-3

Put this back over the denominator

-4g-3

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g+2

6 0
2 years ago
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The average credit card debt for a recent year was $8,776. Five years earlier the average credit card debt was $8,189. Assume sa
Anestetic [448]

Answer:

We reject H₀.  We support that the new average credit card debt is bigger than the previous average

Step-by-step explanation:

Five years earlier

μ   = 8189

σ  =  690

Sample size   n  = 32

Recent year debt

x  =  8776

Sample size   n  = 32

a) Hypothesis Test:

Null Hypothesis                        H₀            x  =  μ   = 8189

Alternative Hypothesis           Hₐ             x >  μ

b) z(c)  Alternative Hypothesis establishes that the test is a one tail-test to the right.

z(c)   for significance level  α = 0.05    is  from z-table      z(c) = 1,64

c) z(s)  =  (  x  -   μ ) / σ /√n

z(s)  =  ( 8776  - 8189 ) / 690 /√32

z(s)  =  587 *5,66/ 690

z(s) = 4,81

d) Comparing   z(c)    and z(s)

z(s)  >  z(c)   Then z(c) is in the rejection region and we reject H₀

e) We have evidence that at 95 % of confidence the new value for the debt in credit card is now bigger than the average

7 0
1 year ago
In a relay race, each runner completes the circuit 9 seconds faster than the previous one. If the first athlete runs his lap in
Alona [7]

Answer:

31 minutes

Step-by-step explanation:

Here, we have 8 competitors with the previous runner outrunning the present by 9 seconds

1st runner time = 4 minutes 37 seconds

2nd runner time = 4 minutes 37 seconds - 9 seconds = 4 minutes 28 seconds

3rd runner time = 4 minutes 28 seconds - 9 seconds = 4 minutes 19 seconds

4th runner time = 4 minutes 19 seconds - 9 seconds = 4 minutes 10 seconds

5th runner time = 4 minutes 10 seconds - 9 seconds = 4 minutes 1 second

6th runner time s= 4 minutes 1 second - 9 seconds = 3 minutes 52 seconds

7th runner time = 3 minutes 52 seconds - 9 seconds = 3 minutes 43 seconds

8th runner time = 3 minutes 43 seconds - 9 seconds = 3 minutes 34 seconds

The total time is the addition of all the times

For clarity sake, we shall be adding all the minutes together and all the seconds together;

That will be ;

(4 * 6) + 3 minutes + ( 34 + 43 + 52 + 1 + 10 + 19 + 28 + 37)

= 27 minutes + 224 seconds

We need to convert 224 seconds to minutes

Since 60 seconds make one minute; we have

224 - 60(3) = 3 minutes and 44 seconds

Let’s add this to the minutes we had before

That would be;

27 minutes + 3 minutes + 44 seconds

= 30 minutes 44 seconds

since 44 seconds is greater than 1/2 minute (30 seconds), we can approximate it to 1 minute

So the total time is 30 minutes + 1 minute = 31 minutes

8 0
2 years ago
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11111nata11111 [884]

Answer:

One-way ANOVA

Step-by-step explanation:

One-way ANOVA(analysis of variance) a testing method in statistics that is used to compare the means of two or more independent samples, to check if the differences are statistically significant.

In this case, we have three groups which their various reaction time to caffeine is to be tested using the same testing method (amount of caffeine). Hence the appropriate test to use here is the one-way ANOVA

7 0
1 year ago
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