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2 years ago

Given angle 1 and angle 2 are linear pair; mangle 1 =120 degrees prove angle 2 is acute

Mathematics

1 answer:

evablogger [386]2 years ago

6 0

Answer:

angle a + angle b has to equal 180

Step-by-step explanation:

180-120=60

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Faced with rising fax costs, a firm issued a guideline that transmissions of 10 pages or more should be sent by 2-day mail inste

Volgvan

Answer:

a) The calculated value t = 5.903 > 2.572 at 0.01 level of significance

Null hypothesis is rejected at 0.01 level of significance

There is a true mean value is less than 10

b) p - value 0.00001

The p - value 0.00001 < 0.01

The result is significant at p<0.01

Step-by-step explanation:

Step(i):-

Given mean of the population = 10

Sample size 'n'= 35

Mean of the sample x⁻ = 14.44

Standard deviation of the sample 's' = 4.45

Level of significance ∝ = 0.01

Step(ii):-

Null Hypothesis H₀ : μ >10

Alternative Hypothesis : H₁ : μ < 10

Test statistic

$t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }$

$t = \frac{14.44-10}{\frac{4.45}{\sqrt{35} } }$

t = 5.903

Degrees of freedom = n-1 = 35-1 = 34

tabulated value t₀.₀₁,₃₄ = 2.572

The calculated value t = 5.903 > 2.572 at 0.01 level of significance

Null hypothesis is rejected at 0.01 level of significance

There is a true mean value is less than 10

p- value :

p - value 0.00001

The p - value 0.00001 < 0.01

The result is significant at p<0.01

8 0

3 years ago

Find an equation of the tangent plane to the given surface at the specified point. z = ln(x − 8y), (9, 1, 0)

Archy [21]

Answer:

x - 8y - z = 1

Step-by-step explanation:

Data provided according to the question is as follows

f(x,y) = z = ln(x - 8y)

Now the equation for the tangent plane to the surface

For z = f (x,y) at the point P $(x_0,y_0,z_0)$ is

$z - z_0 = f_x(x_0,y_0)(x-x_0) + f_y(x_0,y_0)(y-y_0)\\$

Now the partial derivatives of f are

$f_x(x,y) = \frac{1}{x-8y} \\\\f_y(x,y) = \frac{8}{x-8y} \\\\P(x_0,y_0,z_0) = (9,1,0)\\\\f_z(9,1,0) = (\frac{1}{x-8y})_^{(9,1,0)}$

$\\\\=\frac{1}{9-8}$

= 1

Now

$f_y(9,1,0)=(\frac{8}{x-8y})_{(9,1,0)}\\\\ = -\frac{8}{9 - 8}$

= -8

So, the tangent equation is

$z - 0 = 1\times (x - 9) -8\times (y - 1)$

Now after solving this, the following equation arise

z = x - 9 - 8y + 8

z = x - 8y - 1

Therefore

x - 8y - z = 1

4 0

3 years ago

PLS HELP IF YOU CAN!THIS IS DUE IN 30 MINUTES :(

ExtremeBDS [4]

Answer:

Length: 20 or 40 feet

Width: 40 or 20 feet

Step-by-step explanation:

Area = 800 = length*width = x*(60-x)= 60x - x^2

- x^2 + 60x - 800 = 0

x = 20

Or x = 40

So length can be either 20 feet or 40 feet and width can be 40 (60-20) or 20 (60-40)

6 0

3 years ago

3k - 2c + 8 use k = 7 and c = 4

Inga [223]

Answer:

Step-by-step explanation:

3 (7) - 2(4) + 8

21 - 8 + 8

13 + 8

6 0

3 years ago

Read 2 more answers

Factor. 2f2 + 9f + 10

Natali [406]

Answer:

11f+12

Step-by-step explanation:

Because the fs go together and so do the normal answers.

4 0

3 years ago