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4 years ago

14

Application of the least squares method results in values of the y-intercept and the slope that minimizes the sum of the squared

deviations between the _____.

1 answer:

alisha [4.7K]4 years ago

7 0

Answer:

The least squares method results in values of the y-intercept and the slope, that minimizes the sum of the squared deviations between the observed (actual) value and the fitted value.

Step-by-step explanation:

The method of least squares works under these assumptions

The best fit for a data collection is a function (sometimes called curve).
This function, is such that allows the minimal sum of difference between each observation and the expected value.
The expected values are calculated using the fitting function.
The difference between the observation, and the expecte value is know as least square error.

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one tamk of gasoline has an octane rating of 140 and another tank of gasoline has an octane rating of 80. To obtain a mixture of

Zarrin [17]

Answer:

20 gallons were used from the tank with the octane rating of 80.

Step-by-step explanation:

Given : One tank of gasoline has an octane rating of 140 and another tank of gasoline has an octane rating of 80. To obtain a mixture of 60 gallons with an octane rating of 120.

To find : How many gallons should be used from the tank with the octane rating of 80?

Solution : Let x be the volume of gas whose octane rating is 140 and

y be the volume of gas whose octane rating is 80.

Then, we form the equation as:

(1) $x\times140 + y\times80 = 60\times120$

$140x+80y = 7200$

or $7x+4y = 360$ .........[3]

(2) $x + y = 60$

Now multiply equation (2) by 4

$4x + 4y = 240$ ...........[4]

Subtract (4) from (3)

$7x+4y-4x-4y=360-240$

$3x=120$

$x=\frac{120}{3}$

$x=40$

Put x in equation [4] we get,

$4(40) + 4y = 240$

$160 + 4y = 240$

$4y = 80$

$y=\frac{80}{4}$

$y=20$

Therefore, x=40 and y=20

So, 20 gallons were used from the tank with the octane rating of 80.

7 0

3 years ago

Dante runs 7 miles in 60 minutes. At the same rate, how many miles would he run in 24 minutes?

denis23 [38]

<h2>Answer: 2.8 miles</h2>

Step-by-step:

We can write it in the proportion $\frac{7}{60} = \frac{x}{24}$

where x is our number of miles trying to find

We now cross multiply or use the butterfly method which I will demonstrate both

<h3>Cross Multiply</h3>

We multiply the numerator with the dominator

so $7 multiplied by 24$

and $60 multiplied by x$

$7*24=60x$

$168=60x$

$\frac{168}{60} =\frac{60x}{60}$

$2.8=x$ or $x=2.8$

Now for the

<h3>Butterfly Method </h3>

You would do 7 times 24 divided by 60 or $\frac{7*24}{60}$

Then $\frac{168}{60}$ simplify

$2.8$ so 2.8 miles in either method

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3 years ago

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scZoUnD [109]

Answer:

In mathematics, a function is a binary relation over two sets that associates to every element of the first set exactly one element of the second set. Typical examples are functions from integers to integers or from the real numbers to real numbers.

Step-by-step explanation:

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