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1 year ago

Write the equation in slope-intercept form: answers y=1/2x, y=3x+1/2, y=1/2x+3, y=2x+3

Mathematics

1 answer:

AleksandrR [38]1 year ago

6 0

The equation in the slope-intercept form is:

y = (1/2)*x + 3

<h3>How to write the equation?</h3>

A general linear equation is:

y = a*x + b

Where a is the slope and b is the y-intercept.

To get the slope, we need two points on the line, by using the graph we can identify the points: (0, 3) and (2,4)

Then the slope is:

$a = \frac{4 - 3}{2 - 0} = 1/2$

And we also can see that the y-intercept is y = 3, because of the point (0,3)

Then the line is:

y = (1/2)*x + 3

If you want to learn more about lines you can read:

brainly.com/question/1884491

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A plane takes off from an airport on a bearing of 270° and travels at a speed of 320 mph. after sometime and flight, space the p

ratelena [41]

The speed of the plane after it encounters the wind is C.285mph

<h3>How to calculate the speed of the plane when it encounters the wind?</h3>

Since the plane takes off from an airport on a bearing of 270° and travels at a speed of 320 mph it's velocity is v = (320cos270°)i + (320sin270°)j

= (320 × 0)i + (320 × -1)j

= 0i - 320j

= - 320j mph

Also, the plane encounters a 35 mph wind blowing directly north. The velocity of the wind is v' = 35j mph

So, the velocity of the plane after it encounters the wind is the resultant velocity, V = v + v'

= -320j mph + 35j mph

= -285j mph

So, the speed of the plane after it encounters the wind is the magnitude of V = |-285j| mph

= 285 mph

So, the speed of the plane after it encounters the wind is C.285mph

Learn more about speed of plane here:

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8 0

2 years ago

HELP PLEASE!!! THIS IS URGENT!! When Isabel began her book-selling business, she stored her inventory in her garage. Now that he

Zanzabum

Answer:

Your question was very confusing but I tried...

Step-by-step explanation:

Area = 8,100 square feet

area of a square = a²

8,100 square feet = a²

√8,100 square feet = √a²

90 feet = a

total length each row of bookshelf is 4/5 of the length of the storage space.

90 feet * 4/5 = (90*4)/5 = 360/5 = 72 feet.

Area = (72 ft)²

Area = 5,184 square feet.

Hope this helped :)

7 0

3 years ago

A bus travels 18 km in 30 minutes. What is the average speed of the bus?

REY [17]

Answer:

36km hr

Step-by-step explanation:

3 0

2 years ago

A government report gives a 99% confidence interval for the proportion of welfare recipients who have been receiving welfare ben

juin [17]

Answer:

The estimation for the proportion for this case is $\hat p = 0.21$

And we know that the 99% confidence interval is given by:

$0.21 \pm 0.045$

So then the margin of error at 99% of confidence is 0.045, and the margin of error is given by this formula:

$ME= z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

If we decrease the confidence level this margin of error can't be higher than 0.045 so then the correct answer for this case would be:

d. 21% ± 4.8%

Because if the z value decrease from 2.58 to 1.96 not makes sense that the margin of error increase from 0.045(4.5%) to 0.048(4.8%)

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".

Solution to the problem

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

For the 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the normal standard distribution.