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2 years ago

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On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite direction. The numb

er b varies directly with the number a. For example b = 2a equals negative 2 and StartFraction 3 Over 4 EndFraction. when a = –2a equals negative 2 and StartFraction 3 Over 4 EndFraction.. Which equation represents this direct variation between a and b?

1 answer:

vfiekz [6]2 years ago

5 0

Answer:

b

Step-by-step explanation:

Guest

1 year ago

actually its A

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Given that a 90% confidence interval for the mean height of all adult males in Idaho measured in inches was [62.532, 76.478]. Us

grigory [225]

Answer:

The confidence interval on this case is given by:

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

For this case the confidence interval is given by (62.532, 76.478)[/tex]

And we can calculate the mean with this:

$\bar X = \frac{62.532+76.478}{2}= 69.505$

So then the mean for this case is 69.505

Step-by-step explanation:

Previous concepts

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".

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".

$\bar X$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma$ represent the population standard deviation

n represent the sample size

Assuming the X follows a normal distribution

$X \sim N(\mu, \sigma)$

The confidence interval on this case is given by:

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

For this case the confidence interval is given by (62.532, 76.478)[/tex]

And we can calculate the mean with this:

$\bar X = \frac{62.532+76.478}{2}= 69.505$

So then the mean for this case is 69.505

5 0

2 years ago

Find the ratio of black cell phone covers sold to the total number of cell phones covers sold last week. Then explain its meanin

finlep [7]

The ratio here would be 4 to 18, in which 4 represents the number of black covers sold and 18 represents the total of covers sold.

5 0

2 years ago

Read 2 more answers

A home builder wants 5 5 acres of land split into 13 13 equal sections. Three of these expressions give the number of acres of l

stepladder [879]

Answer:

Check Explanation

Step-by-step explanation:

The options to be examined for the wrong one isn't presented, and it wasn't obtainable online, So, I'll exhaustively cover all the common possible answers!

5 acres of land. Acres is a unit of measurement that is most pecuilar to land. It is basically expressing the area of the land.

So, if 5 acres of land is to be divided into 13 sections with equal areas.

Each of the 13 land areas will have an area of (5/13) = 0.385 acre

1 acre = 4046.856 m²

5 acres = 20,234.28 m²

Each of the 13 land areas will have an area of (20234.28/13) = 1556.5 m²

1 acre = 43560 ft²

5 acres = 5 × 43560 = 217,800 ft²

Each of the 13 land areas will have an area of (217800/13) = 16,753.85 ft²

1 acre = 0.00156 square miles

5 acres = 5 × 0.00156 = 0.0078 square miles

Each of the 13 land areas will have an area of (0.0078/13) = 0.0006 square miles.

So, basically, whatever units one converts the area to, just divide the value by 13 and one obtains the area of each of the 13 portions of land that makes up the 5 acres.

Hope this Helps!!!

4 0

2 years ago

Read 2 more answers

Amy makes an initial investment of $5000. The investment loses 13.5% each year. Find the amount Amy has at the end of 8 years.

Pani-rosa [81]

Answer:

$\$1,567.11$

Step-by-step explanation:

we know that

The equation of a exponential decay function is given by

$y=a(1-r)^x$

where

y is the value of the investment

x is the number of years

a is the initial value

r is the rate of change

we have

$a=\$5,000\\r=13.5\%=13.5/100=0.135$

substitute

$y=5,000(1-0.135)^x$

$y=5,000(0.865)^x$

Find the amount Amy has at the end of 8 years

For x=8 years

substitute the value of x

$y=5,000(0.865)^8=\$1,567.11$

3 0

2 years ago

In the study of population dynamics one of the most famous models for a growing but bounded population is the logistic equation

MA_775_DIABLO [31]

Answer:

If $K$ is a constant of integration, then

$P = {\displaystyle \frac{1}{b/a + Ke^{-at}}}$

Step-by-step explanation:

According to the information of the problem we know that

$\frac{dP}{dt} = P(a-bP)$

Remember that in general a Bernoulli equation is an equation of the type

$y' + p(x)y = q(x)y^n$

And the idea to solve the equation is to substitute

$v = y^{1-n}$

Now for this case

$\frac{dP}{dt} - Pa = -bP^2$

Then we substitute

$v = P^{1-2} = P^{-1}$

Therefore

$P = v^{-1}$

and if you compute the derivative of that you get that

$\frac{dP}{dt} = -v^{-2} \frac{dv}{dt}$

Now you substitute that onto the original equation and get

$\frac{dP}{dt} - Pa = -bP^2$

$-v^{-2} \frac{dv}{dt} - v^{-1} = -bv^{-2$

If you multiply everything by $-v^2$ you get that

$\frac{dv}{dt} + v = b$

That's a linear differential equation and the solution would be

$v = {\displaystyle \frac{b}{a} + Ke^{-at}} = P^{-1}$

Where $K$ is a constant of integration, then

$P = {\displaystyle \frac{1}{b/a + Ke^{-at}}}$

3 0

2 years ago