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Sliva [168]
3 years ago
10

3. Penguins can swim at speeds of up to 29 feet per second. Use dimensional analysis to

Mathematics
1 answer:
mestny [16]3 years ago
5 0

Answer:

Penguins can swim at a speed of 19.77 miles per hour.

Step-by-step explanation:

Since penguins can swim at speeds of up to 29 feet per second, to convert this speed to miles per hour, knowing that 1 mile is equal to 5280 feet, the following calculation must be performed:

1 hour = 60 minutes

1 minute = 60 seconds

1 hour = 60x60 seconds = 3,600 seconds

29 x 3,600 = feet per hour = 104,400

104,400 / 5,280 = miles per hour = 19.77

Thus, penguins can swim at a speed of 19.77 miles per hour.

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Use linear regression to find the equation for the linear function that best fits this data. Round both numbers to two decimal p
natta225 [31]

Answer:

The equation of the linear function that best fits the data is,

<em>y</em> = 18.66<em>x</em> + 66.87.

Step-by-step explanation:

The line of best is of the form: <em>y</em> = <em>mx</em> + <em>b</em>.

Here, <em>m</em> = slope of the line and <em>b</em> = intercept.

The formula to compute the intercept and slope are:

b=\frac{\sum Y.\sum X^{2}-\sum X.\sum XY}{n.\sum X^{2}-(\sum X)^{2}}

m=\frac{n.\sum XY-\sum X.\sum Y}{n.\sum X^{2}-(\sum X)^{2}}

Consider the table below for the values of <em>∑ X, ∑ Y, ∑ X² </em>and <em>∑ XY</em>.

Compute the value of  intercept and slope as follows:

b=\frac{\sum Y.\sum X^{2}-\sum X.\sum XY}{n.\sum X^{2}-(\sum X)^{2}}=\frac{(793\times91)-(21\times3102)}{(6\times91)-(21)^{2}} =66.867

m=\frac{n.\sum XY-\sum X.\sum Y}{n.\sum X^{2}-(\sum X)^{2}}=\frac{(6\times3102)-(21\times793)}{(6\times91)- (21)^{2}} =18.657

The line of best fit is:

y=mx+b\\y=18.657x+66.867\\y=18.66x+66.87

Thus, the equation of the linear function that best fits the data is <em>y</em> = 18.66<em>x</em> + 66.87.

3 0
3 years ago
Express 1500ml as a percentage of 7.5 litres?
aniked [119]
First of all change <span>milliliters</span> to litres.

1500 ml = 1,5 l

Now, 
you know that 7,5 l = 100% (the whole amound)
and you are asking how much is: 1,5 l of the whole, so you got:

7,5 = 100%
1,5 = x%

7,5 x = 150
x = 150 / 7,5
x = 20%

Answer: 1500 ml is a 20% of the 7,5 litres.


8 0
3 years ago
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