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2 years ago

If f(x)=x2+10sinx, show that there is a number c such that f(c)=1000.

1 answer:

7 0

F(x) is continuous for all x.

Pick a point and show that f(x) is either negative or positive. Pick another point and show that f(x) is negative, if positive, or positive, if negative.

At x = 30, f(30) - 1000 = 900 + 10sin(30) - 1000 ≤ 0
Now, show at another point f(x) - 1000 is positive, and hence, there would be root between 30 and such point.

Let's pick 40.
At x = 40, f(40) - 1000 = 1600 + 10sin(40) - 1000 ≥ 0

Since f(x) - 1000 is continuous, there lies a root between 30 and 40, and hence, 30 ≤ c ≤ 40

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madreJ [45]

Answer:

For this case we have the following info related to the time to prepare a return

$\mu =90 , \sigma =14$

And we select a sample size =49>30 and we are interested in determine the standard deviation for the sample mean. From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And the standard deviation would be:

$\sigma_{\bar X} =\frac{14}{\sqrt{49}}= 2$

And the best answer would be

b. 2 minutes

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Solution to the problem

For this case we have the following info related to the time to prepare a return

$\mu =90 , \sigma =14$

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And the standard deviation would be:

$\sigma_{\bar X} =\frac{14}{\sqrt{49}}= 2$

And the best answer would be

b. 2 minutes

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2 years ago

Caroline, Colin & Sarah share some money.

julia-pushkina [17]

Answer:

2/9

Step-by-step explanation:

After Caroline's share,

1 - 1/9 = 8/9 is left

Sarah gets:

1/(1+3) of 8/9

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2 years ago

Scott wanted to bjy a sofa which originally cost $500.Store A was selling it for 20% off plus 6.5% sales tax.Store B was selling

USPshnik [31]

Answer:

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Step-by-step explanation:

Cost of sofa =$500

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The amount of tax is

=6.5/100*500

=0.065*500

=$32.5

Total cost of the sofa

=500-100+32.5

=400+32.5

=$432.5

For store B

Discount =30% off

The amount of the discount is

=30/100*500

=0.3*500

=$150

Shipping fee $85

Total cost of sofa

=500-150+85

=350+85

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2 years ago

Katie buy a necklace for $14.50 plus a 6% tax, Sharon buys a bracelet for $12 plus a 6%tax.

UNO [17]

Answer:

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2 years ago

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PolarNik [594]

Answer:

t(d) = d/65

Step-by-step explanation:

To solve for t, divide by its coefficient:

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d/65 = t . . . . . . . simplify

Then you can write it in function form if you like:

t(d) = d/65

_____

* Of course, the rules of equality say you must divide <em>both sides</em> of the equation by the same number.

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