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3 years ago

Write the equation of the line that passes through the given lines (0,-2) and (4,1)

Mathematics

1 answer:

Gala2k [10]3 years ago

7 0

Answer:

y = 3/4x - 2

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

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

Step 1: Define

(0, -2) y-intercept

(4, 1) random point

Step 2: Find slope m

$m=\frac{1-(-2)}{4-0}$

$m=\frac{1+2}{4}$

$m=\frac{3}{4}$

y = 3/4x + b

Step 3: Write linear equation

y = 3/4x - 2

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The city of new orleans leaves union station in chicago at 6:00 am and travels south to new orleans. the train travels the 930.0

Naddik [55]

Answer: 460.6 miles South of Chicago

Explanation:

1) The City of New Orleans leaves Union Station in Chicago at 6:00 am and travels south to New Orleans. The train travels the 930.0 miles to New Orleans at an average speed of 79.0 miles per hour.

Scheme:

→to south ←to north
|----------------------|---------------------|
 A x X 930.0 - x B
 6:00 am 6:00 am
 → ←
 v = 79.0 mi/h v = 81.1 mi/h

=> x = 79.0 mi/h * t

2) at the same time the City of Chicago leaves New Orleans and travels north to Nhicago. The train travels the 930.0 miles to Chicago at an average speed of 81.1 miles per hour.

930.0 - x = 81.1 mi/h * t

3) How many miles south of chicago do the two trains pass each other?

Divide the two equations:

930.0 - x 81.1*t
------------- = ----------
 x 79*t

t cancels out =>

930.0 - x 81.1
------------- = --------
 x 79.0

Solve:

81.1x = 79.0(930.0 - x)

81.1x = 79.0 * 930.0 - 79.0x

81.1x + 79.0x = 73,470

=> 160.1x = 73,470

=> x = 73,470 / 160.1

=> x = 460.6 mi

4) Answer 460.6 miles South of Chicago.

7 0

3 years ago

I have to find an equation for a table

Anna35 [415]

Let's say imput is i and that output is o.

The formula is 2 ^ i = o

2^0 = 1

2^1 = 2

2^2 = 4

2^3 = 8

2^4 = 16

2^5 = 32

Notice how the numbers match?

Hope this helped :)

8 0

3 years ago

Before they graduate from Great Lakes High School, all 12th grade students fill out a survey about their future college plans. A

mamaluj [8]

Answer:

178/662

Step-by-step explanation:

The information given is presented and summarised in the table below. $\left|\begin{array}{c|c|c|c}&$Attending an &$Not Attending an&$Total\\&$In-State College&$In-State College\\--&--&--&--\\$Begin&178&21&199\\$Won't Begin&301&162&463\\--&--&--&--\\$Total&479&183&662\end{array}\right|$

(a)The probability that a student will begin college during the summer semester and attend an in-state college.

P(a student will begin college during the summer semester and attend an in-state college) $= 178/662$

8 0

3 years ago

(b) how many measurements must be averaged to get a margin of error of ±0.0001 with 98% confidence? (round your answer up to the

goblinko [34]

Given that the scale readings of the laboratory scale is normally distributed with an unknown mean and a standard deviation of 0.0002 grams.

Part A:

If the weight is weighted 5 times and the mean weight is 10.0023 grams, the 98% confidence interval for μ, the true mean of the scale readings is given by:

$98\% \ C. \ I.=\bar{x}\pm z_{\alpha/2}\left(\frac{\sigma}{\sqrt{n}}\right) \\ \\ =10.0023\pm2.33\left(\frac{0.0002}{\sqrt{5}}\right) \\ \\ =10.0023\pm2.33(0.000089) \\ \\ =10.0023\pm0.00021 \\ \\ =(10.0023-0.00021, \ 10.0023+0.00021) \\ \\ =(10.0021, \ 10.0025)$

Thus, we are 98% confidence that the true mean of the scale readings is between 10.0021 and 10.0025.

Part B:

To get a margin of error of +/- 0.0001 with a 98% confidence, then

$\pm z_{\alpha/2}\left(\frac{\sigma}{\sqrt{n}}\right)=\pm0.0001 \\ \\ \Rightarrow2.33\left(\frac{0.0002}{\sqrt{n}}\right)=0.0001 \\ \\ \Rightarrow\left(\frac{0.0002}{\sqrt{n}}\right)= \frac{0.0001}{2.33} =0.0000429 \\ \\ \Rightarrow\sqrt{n}= \frac{0.0002}{0.0000429} =4.66 \\ \\ \Rightarrow n=4.66^2=21.7156\approx22$

Therefore, the number of measurements that must be averaged to get a margin of error of ±0.0001 with 98% confidence is 22.

8 0

3 years ago

Sandy has 6 sheets of colored paper. She uses 4 sheets to make posters. She cuts the remaining paper into equal rectangles to ma

Vikki [24]

Answer: 8

Step-by-step explanation:

From the question, we are informed that Sandy has 6 sheets of colored paper and that she uses 4 sheets to make posters. Therefore she'll have 2 sheets of coloured paper left. This is gotten by : (6 - 4) = 2 sheets.

Since each rectangle is 1/4 of a sheet of colored paper, the number of greetings card that Sandy will make will be gotten by dividing 2 by 1/4. This will be:

= 2 ÷ (1/4)

= 2 × 4

= 8

Sandy will make 8 greeting cards

8 0

3 years ago