Ask question

Ask question

All categories

1 year ago

5

The median home price in the United States over the period 2003-2011 can be approximated by P(t) = −5t2 + 75t − 30 thousand doll

ars (3 ≤ t ≤ 11), where t is time in years since the start of 2000.† Find P'(t) and P'(5).

1 answer:

rjkz [21]1 year ago

5 0

Answer:

$P'(t) = -10t + 75$ and P'(5) = 25.

Step-by-step explanation:

We are given that,

The median home price is represented by the function, $P(t) = -5t^2 + 75t -30$ .

So, differentiating the function with respect to 't', we get,

$P'(t) = -5\times2t + 75$

i.e. $P'(t) = -10t + 75$

So, after subsituting 't=5', we get,

$P'(5) = -10\times 5+75$

i.e. P'(5) = -50+75

i.e. P'(5) = 25

Hence, we get,

$P'(t) = -10t + 75$ and P'(5) = 25.

You might be interested in

Erica earns $11.00 per hour and works a 40 - hour workweek. She is paid time and a half for every hour worked over 40 hours duri

GREYUIT [131]

Base pay = $11 x 40 or $440

$605 - 440 = $165 in overtime
Overtime is 1.5 (1 and a half times) her usual salary

11 x 1.5 = $16.50

$165 ÷ $16.50 = 10 hours of overtime.

5 0

1 year ago

A boat tour guide expects his tour to travel at a rate of x mph on the first leg of the trip. On the return route, the boat trav

Georgia [21]

<em><u>The intervals included in solution are:</u></em>

$\frac{1}{x} + \frac{1}{x}-10\ge \frac{2}{24}\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:0$

<em><u>Solution:</u></em>

Given that,

A boat tour guide expects his tour to travel at a rate of x mph on the first leg of the trip

On the return route, the boat travels against the current, decreasing the boat's rate by 10 mph

The group needs to travel an average of at least 24 mph

<em><u>Given inequality is:</u></em>

$\frac{1}{x} + \frac{1}{x} - 10\geq \frac{2}{24}$

<em><u>We have to solve the inequality</u></em>

$\frac{1}{x} + \frac{1}{x} - 10\geq \frac{2}{24}\\\\\frac{2}{x} - 10\geq \frac{2}{24}$

$\mathrm{Subtract\:}\frac{2}{24}\mathrm{\:from\:both\:sides}\\\\\frac{2}{x}-10-\frac{2}{24}\ge \frac{2}{24}-\frac{2}{24}\\\\Simplify\\\\\frac{2}{x}-10-\frac{2}{24}\ge \:0$

$\frac{2}{x}-\frac{10}{1}-\frac{2}{24} \geq 0\\\\\frac{ 2 \times 24}{x \times 24} -\frac{10 \times 24}{1 \times 24} - \frac{2 \times x }{24 \times x}\geq 0\\\\\frac{48}{24x}-\frac{240x}{24x}-\frac{2x}{24x}\geq 0\\\\Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions\\\\\frac{48-240x-2x}{24x}\geq 0\\\\Add\:similar\:elements\\\\\frac{48-242x}{24x}\ge \:0$

$\mathrm{Multiply\:both\:sides\:by\:}24\\\\\frac{24\left(48-242x\right)}{24x}\ge \:0\cdot \:24\\\\Simplify\\\\\frac{48-242x}{x}\ge \:0\\\\Factor\ common\ terms\\\\\frac{-2\left(121x-24\right)}{x}\ge \:0\\\\\mathrm{Multiply\:both\:sides\:by\:}-1\mathrm{\:\left(reverse\:the\:inequality\right)}$

When we multiply or divide both sides by negative number, then we must flip the inequality sign

$\frac{\left(-2\left(121x-24\right)\right)\left(-1\right)}{x}\le \:0\cdot \left(-1\right)\\\\\frac{2\left(121x-24\right)}{x}\le \:0\\\\\mathrm{Divide\:both\:sides\:by\:}2\\\\\frac{\frac{2\left(121x-24\right)}{x}}{2}\le \frac{0}{2}\\\\Simplify\\\\\frac{121x-24}{x}\le \:0$

$\mathrm{Find\:the\:signs\:of\:the\:factors\:of\:}\frac{121x-24}{x}\\$

This is attached as figure below

From the attached table,

$\mathrm{Identify\:the\:intervals\:that\:satisfy\:the\:required\:condition:}\:\le \:\:0\\\\0$

<em><u>Therefore, solution set is given as</u></em>:

$\frac{1}{x} + \frac{1}{x}-10\ge \frac{2}{24}\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:0$

8 0

1 year ago

Read 2 more answers

The percentage of body fat of a random sample of 36 men aged 20 to 29 found a sample mean of 14.42. Find a 95% confidence interv

Rina8888 [55]

Answer:

$14.42-1.96\frac{6.95}{\sqrt{36}}=12.150$

$14.42+ 1.96\frac{6.95}{\sqrt{36}}=16.690$

So on this case the 95% confidence interval would be given by (12.150;16.690)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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".

$\bar X=14.42$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=6.95$ represent the population standard deviation

n=36 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

Now we have everything in order to replace into formula (1):

$14.42-1.96\frac{6.95}{\sqrt{36}}=12.150$

$14.42+ 1.96\frac{6.95}{\sqrt{36}}=16.690$

So on this case the 95% confidence interval would be given by (12.150;16.690)

5 0

2 years ago

Evaluate 8a-1+0.5b8a−1+0.5b8, a, minus, 1, plus, 0, point, 5, b when a=\dfrac14a=

professor190 [17]

Answer: $6$

Step-by-step explanation:

Given the following expression:

$8a-1+0.5b$

You need to substitute the given values of "a" and "b" into the expression. Notice that these values are:

$a=\frac{1}{4}\\\\b=10$

Then;

$8a-1+0.5b=8(\frac{1}{4})-1+0.5(10)$

Now you must solve the multiplications:

$=\frac{8}{4}-1+5=2-1+5$

The final step is to add the numbers. Therefore, you get the following answer:

$=6$

7 0

2 years ago

Read 2 more answers

David can proofread15 reports in an hour while Armando can proofread 37reports in an hour. If they have 400 reports to proofread

ycow [4]

Together, it would take them 6 hours

8 0

1 year ago

Read 2 more answers