All categories

3 years ago

What is the equation of the coordinate A and B if they are (4,7), (6,3) respectively. What is the equation of the straight line.

Mathematics

1 answer:

Nesterboy [21]3 years ago

3 0

Answer: y+2x=15

Step-by-step explanation:

Given

Two points A and B are (4,7) and (6,3) respectively

Using two-point form

$\Rightarrow \dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}$

Putting values

$\Rightarrow \dfrac{y-7}{x-4}=\dfrac{3-7}{6-4}\\\\\Rightarrow \dfrac{y-7}{x-4}=\dfrac{-4}{2}=-2\\\\\Rightarrow y-7=-2x+8\\\\\Rightarrow y+2x=15$

You might be interested in

David's chance of making a free throw is 80%. In a game, he takes 10 free throws. What is the probability he makes 8 or fewer fr

maks197457 [2]

Answer:

$P(X\leq 8)= 1- P(X>8) = 1-P(X\geq 9)= 1-[P(X=9)+P(X=10)]$

And we can find the individual probabilities like this:

$P(X=9)=(10C9)(0.8)^{9} (1-0.8)^{10-9}$

$P(X=10)=(10C10)(0.8)^{10} (1-0.8)^{10-10}$

And replacing we got:

$P(X\leq 8)=1-[10(0.8)^1 (1-0.8)^{1} + (0.8)^{10}]$

Step-by-step explanation:

Previous concepts

A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

The complement rule is a theorem that provides a connection between the probability of an event and the probability of the complement of the event. Lat A the event of interest and A' the complement. The rule is defined by: $P(A)+P(A') =1$

Solution to the problem

For this case we want this probability:

$P(X\leq 8)$

And for this case we can use the comlement rule and we got:

$P(X\leq 8)= 1- P(X>8) = 1-P(X\geq 9)= 1-[P(X=9)+P(X=10)]$

And we can find the individual probabilities like this:

$P(X=9)=(10C9)(0.8)^9 (1-0.8)^{10-9}$

$P(X=10)=(10C10)(0.8)^{10} (1-0.8)^{10-10}$

And replacing we got:

$P(X\leq 8)=1-[10(0.8)^9 (1-0.8)^{1} + (0.8)^{10}]$

4 0

2 years ago

Gerald is conducting an experiment with 3 possible outcomes. Kasey is conducting an experiment with 20 possible

Pepsi [2]

Answer:

Gerald will need to conduct fewer trials because experimental and theoretical results in experiments with small

numbers of possible outcomes are the same.

3 0

3 years ago

What is 7sqrt 28z+sqrt63z

Xelga [282]

Answer:

$17\sqrt{7z}$

Step-by-step explanation:

$7\sqrt{28z}+\sqrt{63z}\\ = 14\sqrt{7z}+3\sqrt{7z} \\= 17\sqrt{7z}$

5 0

1 year ago

The LCM of three numbers is 7920 and their GCD is 12. Two of the numbers are 48 and 264. Using factor notation find the third nu

12345 [234]

Answer:

The third number is 180.

Step-by-step explanation:

Let the third number be 9x where x is an integer.

48 = 2*2*2*2*3

264 = 2*2*2*3*11

9x = 3*3*x

2*2*2*2*3*3*11*x = 7920y where y is an integer

1584x = 7920y

so x = 7920y / 1584= 5y.

Now the GCD is 12 so x must have 4 as one of its factors.

Also x is a multiple of 5 so it could be 20 then y would be 4.

If x = 20 then the third number is 9*20 = 180.

This checks out OK.

5 0

3 years ago

A certain change in a process for manufacture of component parts is being considered. Samples are taken using both the existing

Katyanochek1 [597]

Answer:

a) The confidence interval is $0.00\leq\pi_1-\pi_2\leq0.02$ .

Step-by-step explanation:

We have to calculate a confidence interval (CI) of a difference of proportions.

For the existing procedure, the proportion is:

$p_1=75/1500=0.05$

For the new procedure, the proportion is:

$p_2=80/2000=0.04$

To calculate the CI, we need to estimate the standard deviation

$s=\sqrt{\frac{p_1(1-p_1)}{n_1} +\frac{p_2(1-p_2)}{n_2} }\\\\s=\sqrt{\frac{0.05(1-0.05)}{1500} +\frac{0.04(1-0.04)}{2000} }=\sqrt{ 0.000032 + 0.000019 }=\sqrt{ 0.000051 }\\\\s=0.007$

For a 90% CI, the z-value is 1.64.

Then, the CI is:

$(p_1-p_2)-z*\sigma \leq\pi_1-\pi_2\leq(p_1-p_2)+z*\sigma \\\\(0.05-0.04)-1.64*0.007\leq\pi_1-\pi_2\leq(0.05-0.04)+1.64*0.007\\\\0.01-0.01\leq\pi_1-\pi_2\leq0.01+0.01\\\\0.00\leq\pi_1-\pi_2\leq0.02$

6 0

3 years ago