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Pie
3 years ago
14

Find the missing terms in the equation so that it is true. (3x + ?)^2=9x^2 + ?? +49y^2

Mathematics
1 answer:
valkas [14]3 years ago
8 0

Answer:

see explanation

Step-by-step explanation:

Note that 9x² and 49y² are perfect squares.

9x² = (3x)² → 3x is the first term

49y² = (7y)² → 7y is the second term

Hence

(3x + 7y)² = 9x² + 42xy + 49y²

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A term for a geometric figure that is enclosed by a circle.
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Assume that population mean is to be estimated from the sample described. Use the sample results to approximate the margin of er
Vikentia [17]

Answer:

ME=1.998 \frac{4}{\sqrt{64}}=0.999 \approx 1

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 =69 represent the sample mean for the sample  

\mu population mean

s=4.0 represent the sample standard deviation

n=64 represent the sample size  

Assuming the X follows a normal distribution

X \sim N(\mu, \sigma)

The sample mean \bar X have the following distribution:

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

The margin of error for the sample mean is given by this formula:

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}

Since we have the sample standard deviation we can estimate the margin of error like this:

ME=t_{\alpha/2}\frac{s}{\sqrt{n}}

The next step would be find the value of \z_{\alpha/2}, \alpha=1-0.95=0.05 and \alpha/2=0.025

We can find the degrees of freedom like this:

df=n-1=64-1=63

And we can find the critical value with the following code in excel for example: "=T.INV(0.025,63)" and we got:

t_{\alpha/2}=\pm 1.998

And the margin of error would be :

ME=1.998 \frac{4}{\sqrt{64}}=0.999 \approx 1

3 0
3 years ago
Let X be a normal random variable with mean 40 and standard deviation 2. Find P(X &lt; 28).
Vikki [24]

Answer:

0

Step-by-step explanation:

Given :

Mean = 40 ; Standard deviation = 2

P(x < 28)

Obtain the Zscore :

Z = (x - mean) / standard deviation

P(Z < (28 - 40) / 2))

Z = (28 - 40) / 2

Z = - 12 / 2

Z = - 6

P(Z < - 6) = 0.000000

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3 years ago
Simplify -10(10w-6-w)-w
kompoz [17]

Answer:

-91w + 60

Step-by-step explanation:

to simplify this -10(10w-6-w)-w

we have,

-10(10w-6-w)-w

-100w + 60 + 10w - w

-91w + 60

6 0
3 years ago
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