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2 years ago

What is the slope of the line passing through the points (0, 4) and (6, 13)

Mathematics

1 answer:

skelet666 [1.2K]2 years ago

3 0

Answer:

The slope is $\frac{3}{2}$

Step-by-step explanation:

Hi there!

We are given the points (0, 4) and (6, 13)

We want to find the slope of the line containing these two points

Slope (m) is the steepness of the line. When calculating from two points, you use the equation $\frac{y_2-y_1}{x_2-x_1}$ , where $(x_1, y_1)$ and $(x_2, y_2)$ are points

Although we have what we need to find the slope, let's label the values of the points to avoid confusion and mistakes.

$x_1=0\\y_1=4\\x_2=6\\y_2=13$

Substitute these values into the equation

m= $\frac{y_2-y_1}{x_2-x_1}$

m= $\frac{13-4}{6-0}$

Subtract

m= $\frac{9}{6}$

Simplify

m= $\frac{3}{2}$

The slope of the line is 3/2

Hope this helps!

See more on calculating slopes from 2 points here: brainly.com/question/26738734

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2 years ago

The volume of a cylinder is 12,566.4 cm3. The height of the cylinder is 8 cm.

scoundrel [369]

Using the formulas here: http://www.1728.org/diamform.htm

A) Volume = π • r² • height
radius^2 = Volume / (PI*height)
radius^2 = 12,566.4 / (PI * 8)
radius^2 = 500.0011692175 
radius = 22.3607059195 
radius (rounded) = 22.4 cm

B) Area of base = PI * radius^2
Area of base = 3.14159265 * 500
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3 years ago

A survey of 76 commercial airline flights of under 2 hours resulted in a sample average late time for a flight of 2.55 minutes.

nika2105 [10]

Answer:

The best point of estimate for the true mean is:

$\hat \mu = \bar X = 2.55$

$2.55-1.96\frac{12}{\sqrt{76}}=-0.148$

$2.55+1.96\frac{12}{\sqrt{76}}=5.248$

Since the time can't be negative a good approximation for the confidence interval would be (0,5.248) minutes. The interval are tellling to us that at 95% of confidence the average late time is lower than 5.248 minutes.

Step-by-step explanation:

Information given

$\bar X=2.55$ represent the sample mean for the late time for a flight

$\mu$ population mean

$\sigma=12$ represent the population deviation

n=76 represent the sample size

Confidence interval

The best point of estimate for the true mean is:

$\hat \mu = \bar X = 2.55$

The confidence interval for the true mean is given by:

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

The Confidence level given is 0.95 or 95%, th significance would be $\alpha=0.05$ and $\alpha/2 =0.025$ . If we look in the normal distribution a quantile that accumulates 0.025 of the area on each tail we got $z_{\alpha/2}=1.96$