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3 years ago

Find the slope of the line

Mathematics

1 answer:

Maslowich3 years ago

7 0

Answer:

1/2

Step-by-step explanation:

(2,1)(4,2)

x1-y1/x2-y2

slope:m=1/2

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16 tablespoons equals 1 cup create a double number line that shows how many tablespoons you would need to use to make 5 cups of

gladu [14]

16tbsp/1cup.
Multiply by 5 for 5 cups (I recommend cross multiplying with fractions)
80tbsp/5cups
Multiply by 1.25
20tbsp/1.25cups
Multiply by 2.7
43.2tbsp/2.7cups
Since you can’t have .2 of a table spoon, we need to round up.
44tbsp/2.7cups

Total tbsp:80+20+44tbsp=144tbsp

We would need 144 tablespoons for 8.95 cups (9 for the same reason that we rounded up with the table spoons)

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4 years ago

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Consider this scenario: The population of a city increased steadily over a ten-year span. The following ordered pairs show the p

vova2212 [387]

Answer:

Regression function: $y=1986.406+0.0059x$

The function predicts that population will reach 14,000 in year 2068.

Step-by-step explanation:

We have to determine a function $y=b_0+b_1x_1$ by applying linear regression. The data we have is 5 pair of points which relates population to year.

According to the simple regression model (one independent variable), if we minimize the error between the model (the linear function) and the points given, the parameters are:

$b_0=\bar{y}+b_1\bar{x}\\\\b_1=\frac{\sum\limits^5_{i=1} {(x_i-\bar x)(y_i-\bar y)}}{\sum\limits^5_{i=1} {(x_i-\bar x)^2}}$

We start calculating the average of x and y

$\bar x=\frac{2500+2650+3000+3500+4200}{5}=\frac{15850}{5}=3170\\\\ \bar y=\frac{2001+2002+2004+2007+2011}{5}=\frac{10025}{5}=2005$

The sample covariance can be calculated as

$\sum\limits^5_{i=1} {(x_i-\bar x)(y_i-\bar y)}=(2500-3170)(2001-2005)+(2650-3170)(2002-2005)+(3000-3170)(2004-2005)+(3500-3170)(2007-2005)+(4200-3170)(2011-2005)\\\\\sum\limits^5_{i=1} {(x_i-\bar x)(y_i-\bar y)}=2680+1560+170+660+6180\\\\ \sum\limits^5_{i=1} {(x_i-\bar x)(y_i-\bar y)}=11250$

The variance of x can be calculated as

$\sum\limits^5_{i=1} {(x_i-\bar x)^2}=(2500-3170)^2+(2650-3170)^2+(3000-3170)^2+(3500-3170)^2+(4200-3170)^2\\\\\sum\limits^5_{i=1} {(x_i-\bar x)^2}=448900+270400+28900+108900+1060900\\\\\sum\limits^5_{i=1} {(x_i-\bar x)^2}=1918000$

Now we can calculate the parameters of the regression model

$b_1=\frac{\sum\limits^5_{i=1} {(x_i-\bar x)(y_i-\bar y)}}{\sum\limits^5_{i=1} {(x_i-\bar x)^2}}=\frac{11250}{1918000}=0.005865485 \\\\ b_0=\bar{y}+b_1\bar{x}=2005-0.005865485*3170=1986.406413$

The function then become:

$y=1986.406+0.0059x$

With this linear equation we can predict when the population will reach 14,000:

$y=1986.406+0.0059(14,000)=1986.406+82.117=2068.523$

6 0

3 years ago

Find the slope of the line​

Find the slope of the line