Find the angle between each of the following pair of straight line x-2y+3=0 and y=3x

Jacob Lee is a frequent traveler between Los Angeles and San Diego. For the past month, he wrote down the flight times in minute

valkas [14]

Solution :

We know that

$H_0: \mu_1 = \mu_2=\mu_3$

$H_1 :$ At least one mean is different form the others (claim)

We need to find the critical values.

We know k = 3 , N = 35, α = 0.05

d.f.N = k - 1

= 3 - 1 = 2

d.f.D = N - k

= 35 - 3 = 32

SO the critical value is 3.295

The mean and the variance of each sample :

Goust Jet red Cloudtran

$\overline X_1 =50.5$ $\overline X_2 =50.07143$ $\overline X_3 =55.71429$

$s_1^2=19.96154$ $s_2^2=14.68681$ $s_3^2=36.57143$

The grand mean or the overall mean is(GM) :

$\overline X_{GM}=\frac{\sum \overline X}{N}$

$=\frac{51+51+...+49+49}{35}$

= 52.1714

The variance between the groups

$s_B^2=\frac{\sum n_i\left( \overline X_i - \overline X_{GM}\right)^2}{k-1}$

$=\frac{\left[14(50.5-52.1714)^2+14(52.07143-52.1714)^2+7(55.71426-52.1714)^2\right]}{3-1}$

$=\frac{127.1143}{2}$

= 63.55714

The Variance within the groups

$s_W^2=\frac{\sum(n_i-1)s_i^2}{\sum(n_i-1)}$

$=\frac{(14-1)19.96154+(14-1)14.68681+(7-1)36.57143}{(14-1)+(14-1)+(7-1)}$

$=\frac{669.8571}{32}$

= 20.93304

The F-test statistics value is :

$F=\frac{s_B^2}{s_W^2}$

$=\frac{63.55714}{20.93304}$

= 3.036212

Now since the 3.036 < 3.295, we do not reject the null hypothesis.

So there is no sufficient evidence to support the claim that there is a difference among the means.

The ANOVA table is :

Source Sum of squares d.f Mean square F

Between 127.1143 2 63.55714 3.036212

Within 669.8571 32 20.93304

Total 796.9714 34

3 0

2 years ago

what is area of the triangle in a coordinate plane. a 9.0. b 14.0 c16.5. d 24.5

Tresset [83]

Answer:

Step-by-step explanation:

It's the right triangle.

The formula of an area of a right triangle:

$A=\dfrac{(leg)(leg)}{2}$

Look at the picture.

We have

$leg=3,\ leg=11$

Substitute:

$A=\dfrac{(3)(11)}{2}=\dfrac{33}{2}=16.5$

4 0

3 years ago

Trigonometry

Natasha_Volkova [10]

Answer:

Step-by-step explanation:

For a triangle the area is

$A=\frac{1}{2}bh$

If our triangle is isosceles and the 2 congruent sides each measure 4 and they include an angle of 40 degrees, let's say that the vertex angle is 40 and the sides that are not the base each measure 4. If we drop an altitude from the vertex to the base, we cut the triangle into 2 right triangles, with the vertex angle being 20 degrees and the hypotenuse being 4. To find the base, then, which is opposite the angle, we use the sin ratio:

$sin(20)=\frac{b}{4}$ and

4sin(20) = b so

b = 1.368

But we need the whole base, and that is only half of it. So

2b = 2.736

To find the height, which is adjacent to the angle, we use the cos ratio:

$cos(20)=\frac{h}{4}$ and

4cos(20) = h so

h = 3.759

Now we have enough info to find the area of the triangle using the triangle area formula from above:

$A=\frac{1}{2}(2.736)(3.759)$ and

A = 5 meters squared.

7 0

3 years ago

Match the shape with the correct formula for finding the volume.

svetlana [45]

<h2 />

━━━━━━━━━━━━━━━━━━━━━━

Formula for finding the volume of cone - ⅓πr2h

Formula for finding the volume of cylinder - πr2h

Formula for finding the volume of Triangular Prism - Bh

Formula for finding the volume of Rectangular Prism - lwh

Formula for finding the volume of Pyramid - ⅓Bh

━━━━━━━━━━━━━━━━━━━━━━

5 0

3 years ago

PLZ help<br> What system of linear inequalities is shown in the graph?

GarryVolchara [31]

In order find the Inequalities, First we need to Find the Equations of Both the Lines.

<u>Equation of First line :</u>

It is passing through the Points (0 , 2) and (4 , 0)

⇒ Slope = $\frac{2 - 0}{0 - 4} = \frac{-2}{4} = \frac{-1}{2}$

⇒ Equation of the First Line : $y - 2 = \frac{-1}{2}(x)$

⇒ Equation of the First Line : x + 2y = 4

<u>Equation of Second Line :</u>

It is passing through the Points (1.5 , 0) and (0 , -3)

⇒ Slope = $\frac{0 + 3}{1.5 - 0} = \frac{3}{1.5} = 2$

⇒ Equation of the Second Line : y + 3 = 2x

⇒ Equation of the Second Line : 2x - y = 3

As the Shaded Area of the First Line is away from the Origin :

⇒ x + 2y ≥ 4

As the Shaded Area of the Second Line is towards the Origin and it is a Dotted line :

⇒ 2x - y < 3

So, the System of Linear Inequalities are :

⇒ x + 2y ≥ 4

⇒ 2x - y < 3

4 0

3 years ago

Find the angle between each of the following pair of straight line x-2y+3=0 and y=3x​

Find the angle between each of the following pair of straight line x-2y+3=0 and y=3x