All categories

1 year ago

Find the equation of the line that

Mathematics

1 answer:

Sophie [7]1 year ago

6 0

Answer:

y = -1/3x + 19/3

Step-by-step explanation:

let the equation of the line be y = mx + b

since it is perpendicular to y = 3x - 1, these two lines's gradient when producted gives -1.

hence, 3 x m = -1

m = -1/3

sub m = -1/3 and (7, 4):

4 = -1/3(7) + b

b = 19/3

therefore, equation of the line is y = -1/3x + 19/3

Topic: coordinate geometry

If you would like to venture further, you can check out my Instagram page (learntionary) where I post notes and mathematics tips. Thanks!

You might be interested in

The digits of a certain three-digit number are consecutive odd numbers. If the sum of the digits is 15, find the number.

scoray [572]

The answer is 5 because it is consecutive 3 times and it is an odd number

3 0

2 years ago

Read 2 more answers

Simplify <br> -4x ^3 y ^2(7xy ^4)

avanturin [10]

<span>( -26•7y6x) thats the answer i hope its right im positive it is</span>

4 0

2 years ago

Joan pays 456.25 monthly on her mortgage. If her annual insurance premium is 1,560 and her annual real estate tax is 1,890, what

defon

The combined payment is 743.75.

The annual amount of insurance is 1560. Dividing this by 12 gives us the monthly amount paid:
1560/12 = 130.

The annual real estate taxes are 1890. Dividing this by 12 gives us the monthly amount paid:
1890/12 = 157.50

We add these to the monthly mortgage payment to find the total amount:
456.25+130+157.50 = 743.75

5 0

2 years ago

In a survey, the planning value for the population proportion is p* = 0.35. How large a sample should be taken to provide a 95%

lions [1.4K]

Answer:

$n=\frac{0.35(1-0.35)}{(\frac{0.05}{1.96})^2}=349.59$

And rounded up we have that n=350

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$p$ represent the real population proportion of interest

$\aht p$ represent the estimated proportion for the sample

n is the sample size required (variable of interest)

$z$ represent the critical value for the margin of error

Solution to the problem

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by: