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3 years ago

Work out the equation of a line when the gradient is 1/2 and it passes through the point (4,-2)

Mathematics

1 answer:

BaLLatris [955]3 years ago

8 0

Answer:

The equation of the line is

$y = \frac{1}{2} x - 4$

Step-by-step explanation:

Equation of a line is y = mx + c

where m is the gradient

c is the y intercept

Gradient = 1/2

Equation of the line using point ( 4 , -2) is

$y + 2 = \frac{1}{2} (x - 4) \\ y + 2 = \frac{1}{2} x - 2 \\ y = \frac{1}{2} x - 2 - 2 \\ y = \frac{1}{2} x - 4$

Hope this helps you

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How to find a polynomial function with given zeros.

Finger [1]

First of all,

let the two zeroes be 2 and 3.

Now,

Sum of the zeros = 2 + 3 = 5

Product of the zeros = 2 × 3 = 6

Hence, the polynomial formed is,

= x² – (sum of zeros)x + Product of zeros

= x² – 5x + 6

7 0

2 years ago

What is the median of 45,50,47,52,53,45,51

Gnom [1K]

First you have to put them in numerical order.The median is the middle number so the answer would be 52.

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4 years ago

Read 2 more answers

Find the value of the variables (x + 10) (4x - 35)

ahrayia [7]

$(x+10)(4x-35)=\\\\4x^2-35x+40x-350=\\\\4x^2+5x-350$

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4 years ago

Which expressions are equivalent to the equation

Ivahew [28]

Answer:

The correct answer is option 3

2⁻¹⁰ and 1/1024

Step-by-step explanation:

Points to remember

1). ( xᵃ)ᵇ = xᵇ

2). x⁻ᵃ = 1/xᵃ

It is given that, (2⁵)⁻²

To find the equivalent of (2⁵)⁻²

(2⁵)⁻² = 2⁻¹⁰

To find the value of 2⁻¹⁰

2⁻¹⁰ = 1/2¹⁰

2¹⁰ = 1024

1/2¹⁰ = 1/1024

Therefore the correct answer is 3rd option

2⁻¹⁰ and 1/1024

5 0

3 years ago

Read 2 more answers

In 2010, the Census Bureau estimated the proportion of all Americans who own their homes to be 0.669. An urban economist wants t

Alexxandr [17]

Answer:

Sample size making use of the Census Bureau: 1,499 American adults.

Sample size without making use of the Census Bureau: 1,692 American adults

ii)

Step-by-step explanation:

The sample size n in Simple Random Sampling is given by

$\bf n=\frac{z^2p(1-p)}{e^2}$

where

z = 1.645 is the critical value for a 90% confidence level (*) 

p= 0.669 is the population proportion given by the Census

e = 0.02 is the margin of error

$\bf n=\frac{(1.645)^2*0.669*0.331}{0.02^2}=1,498.05\approx 1,499$

rounded up to the nearest integer.

(*)This is a point z such that the area under the Normal curve N(0,1) 1nside the interval [-z, z] equals 90% = 0.9

It can be obtained with tables or in Excel or OpenOffice Calc with

NORMSINV(0.95)

If she ignores the Census estimate, the she has to take the largest sample possible that meets the requirements.

Let's show it is obtained when p = 0.5

As we said, the sample size n is

$\bf n=\frac{z^2p(1-p)}{e^2}$

where

e = 0.02 is the error proportion

z = 1.645

hence

$\bf n=\frac{(1.645)^2p(1-p)}{(0.02)^2}=6765.0625p(1-p)=6765.0625p-6765.0625p^2$

taking the derivative with respect to p, we get

n'(p)=6765.0625-2*6765.0625p

and

n'(p) = 0 when p=0.5

By taking the second derivative we see n''(p)<0, so p=0.5 is a maximum of n

This means that if we set p=0.5, we get the maximum sample size for the confidence level required for the proportion error 0.02

Replacing p with 0.5 in the formula for the sample size we get

$\bf n=6765.0625*0.5-6765.0625(0.5)^2=1691.27\approx 1,692$

rounded to the nearest integer.

ii)

When we do not have a proportion but a variable whose approximate standard deviation s is known, then the sample size n in Simple Random Sampling is given by

$\bf n=\frac{z^2s^2}{e^2}$

where

z = 2.241 is the critical value for a 95% confidence level (*) 

s = 7.5 is the estimated population standard deviation

e = 2 hours is the margin of error

$\bf n=\frac{z^2s^2}{e^2}=\frac{(2.241)^2(7.5)^2}{(2)^2}=70.62\approx 71$

(*)This is a point z such that the area under the Normal curve N(0,1) inside the interval [-z, z] equals 95% = 0.95

It can be obtained in Excel or OpenOffice Calc with

NORMSINV(0.9875)

5 0

4 years ago