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3 years ago

If a given data point is (1,4) and the line of best fit is y = 1.5x + 3.25, what's the residual value?

Mathematics

1 answer:

Svetlanka [38]3 years ago

4 0

Answer:

The residual value is -0.75

Step-by-step explanation:

we know that

The residual value is the observed value minus the predicted value.

RESIDUAL VALUE=[OBSERVED VALUE-PREDICTED VALUE]

where

Predicted value.--> the predicted value given the current regression equation

Observed value. --> The observed value for the dependent variable.

in this problem

we have the point (1,4)

The observed value is 4

<em>Find the predicted value for x=1 </em>

$y =1.5(1)+3.25=4.75$

predicted value is 4.75

RESIDUAL VALUE=(4-4.75)=-0.75

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Using the Law of Cosines, in triangle DEF, if e=18yd, d=10yd, f=22yd, find measurement of angle D

Ivahew [28]

Check the picture below.

$\bf \textit{Law of Cosines}\\ \quad \\
c^2 = {{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)\implies 
c = \sqrt{{{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)}
\\\\\\
\cfrac{{{ a}}^2+{{ b}}^2-c^2}{2{{ a}}{{ b}}}=cos(C)\implies cos^{-1}\left(\cfrac{{{ a}}^2+{{ b}}^2-c^2}{2{{ a}}{{ b}}}\right)=\measuredangle C\\\\
-------------------------------\\\\
\begin{cases}
d=10\\
e=18\\
f=22
\end{cases}\implies cos^{-1}\left(\cfrac{{{ 18}}^2+{{ 22}}^2-10^2}{2(18)(22)}\right)=\measuredangle D$

$\bf \implies cos^{-1}\left(0.893\overline{93}\right)=\measuredangle D\implies 26.63^o\approx \measuredangle D$

7 0

3 years ago

In the morning, the temperature was 15∘F. During the day, the temperature fell 37 degrees. Which expression shows how to find th

tino4ka555 [31]

Answer:

- 22°F

Step-by-step explanation:

Given that :

Morning temperature = 15°F

Change in temperature = fall by 37 degree

The temperature of the end of the day:

Morning temperature + (change in temperature)

Fall by 37° = decrease in temperature by 37° = - 37°

15°F + (-37°F)

15°F - 37°F

= - 22°F

6 0

2 years ago

Ax+by+c=0 solve for y

kvv77 [185]

$Answer: \large\boxed{y=\frac{-ax}{b} -\frac{c}{b}}$

Step-by-step explanation:

$ax+by+c=0\\ax+by=-c\\by=-ax-c\\y=\frac{-ax-c}{b}\\y=\frac{-ax}{b} -\frac{c}{b}$

8 0

2 years ago

Triangle FGH has the following side lengths: FG = 5 ft, GH = 10 ft, HF = 12 ft Triangle PQR is similar to triangle FGH. The long

7nadin3 [17]

The first thing we must do for this case is find the scale factor.
We have then that for the larger side of both triangle, the scale factor is:
$k = \frac{RP}{HF}$
$k = \frac{7.2}{12}$
$k = 0.6$
To find the other two sides, we must apply the scale factor on each side of the triangle FGH.
We have then:

For PQ
$PQ = k * FG

PQ = 0.6 * 5

PQ = 3$

For QR
$QR = k * GH

QR = 0.6 * 10

QR = 6$

Answer:
You have that the lengths for the other two sides of triangle PQR are:
$PQ = 3

QR = 6$

3 0

3 years ago

A mirror is in the shape of an isosceles right triangle and has a hypotenuse length of seven times the square root of two. What

frez [133]

The length of one of the legs of an isosceles right triangle and has a hypotenuse length of seven times the square root of two is 7 units.

<h3>What is an Isosceles triangle?</h3>

Isosceles triangles are triangles that has two of it sides equal to each other. The base angles of an isosceles triangle are equal.

The isosceles triangle is also a right angle triangle. The hypotenuse is the longest side of a right angle triangle.

Therefore,

hypotenuse = 7(√2)

let the length of the other legs = x

Therefore, using Pythagoras theorem

c² = a² + b²

(7(√2))² = x² + x²

49 × 2 = 2x²

98 = 2x²

x² = 98 / 2

x = √49

x = 7 units

learn more on isosceles triangle here: brainly.com/question/10412877

4 0

2 years ago