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3 years ago

A rectangle has sides of length 8 cm and 3 cm. Find the length of it's diagonals.

Mathematics

2 answers:

True [87]3 years ago

6 0

Diagonal formula: a^2 + b^2 = c^2

Now, solve for the length of the diagonal.

8^2 + 3^2 = c^2

64 + 9 = c^2

73 = c^2

√73 = √c^2

8.5 ≈ c (This is the diagonal and its rounded).

Best of Luck!

slava [35]3 years ago

4 0

Using pythagoras a^2 + b^2 = c^2
8^2 + 3^2 = c^2
64 + 9 = 73
The square root of 73 is 8.54
So the length of the diagonals are 8.54cm

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Answer the following questions regarding the graphed inequality.

arsen [322]

Answer:

m = 0.5, b = 2, greater than symbol >

Step-by-step explanation:

Slope:

We can find the slope value by choosing two points on our line (the two green dots are already chosen for us) and dividing the vertical distance between the points (this is called the rise) by the horizontal distance between the points (this is called the run)

Rise ÷ Run

1 ÷ 2 = 0.5

Y-Intercept:

The y-intercept is where the line cuts through the vertical y-axis. We can see that this is at y = 2

Inequality:

The area above the line is shaded in. This is to show that all values greater than the line are applicable, so we will use the greater than symbol, >

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3 years ago

A company ships a cube with side lengths of 2 feet in a crate that is a larger cube with side lengths of 4 feet. Packing materia

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Step-by-step explanation:

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2 years ago

Researchers are interested if a school breakfast program leads to taller children. Assume that the population of all 5 year-old

DedPeter [7]

Answer:

$39-1.96\frac{1}{\sqrt{25}}=38.608$

$39+1.96\frac{1}{\sqrt{25}}=39.392$

So on this case the 95% confidence interval would be given by (38.608;39.392)

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".

$\bar X=39$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=1$ represent the population standard deviation

n=25 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)

The margin of error is given by:

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

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 tabel to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$