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What is the distance from point (– 1, 3) to the line 3x – 4y = 10?

natta225 [31]

Answer:

5 units

Step-by-step explanation:

The distance from a point (m, n ) to the line Ax + By + C = 0 is given by

d = $\frac{|Am+Bn+C|}{\sqrt{A^2+B^2} }$

For the point (- 1, 3 ) , with m = - 1 and n = 3

3x - 4y = 10 ( subtract 10 from both sides )

3x - 4y - 10 = 0

with A = 3 , B = - 4 , C = - 10

d = $\frac{|3(-1)+(-4)3-10|}{\sqrt{3^2+(-4)^2} }$

= $\frac{|-3-12-10|}{9+16}$

= $\frac{|-25|}{\sqrt{25} }$

= $\frac{25}{5}$

= 5

5 0

3 years ago

What's the equation with a rate of change of 3 1. 3y=2x+5 2.y=6x-3 3.y=3x+12

dolphi86 [110]

Answer:

3. Y=3x+12

Explanation:

3 is used as the rate for whatever is for x

7 0

3 years ago

Help I need this answer A.S.A.P.

kiruha [24]

Answer:

i think its 31

Step-by-step explanation:

4 0

3 years ago

Suppose that 60 percent of customers at a McDonalds purchase a hamburger, and assume that the purchases of different customers a

Alborosie

Answer:

a) 83.87% probability that at most 7 of the next 10 customers will order a hamburger.

b) 25.08% probability that exactly 6 of the next 10 customers will order a hamburger

Step-by-step explanation:

For each customer at McDonalds, there are only two possible outcomes. Either they purchase a hamburguer, or they do not. The purchases of different customers are independent. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

60 percent of customers at a McDonalds purchase a hamburger

This means that $p = 0.6$

a) What is the probability that at most 7 of the next 10 customers will order a hamburger? (3 POINTS).

This is $P(X \leq 7)$ when n = 10.

We know that either at most 7 of the next customers will order a hamburguer, or more than 7 will. The sum of these probabilities is decimal 1. So

$P(X \leq 7) + P(X > 7) = 1$

$P(X \leq 7) = 1 - P(X > 7)$

In which

$P(X > 7) = P(X = 8) + P(X = 9) + P(X = 10)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 8) = C_{10,8}.(0.6)^{8}.(0.4)^{2} = 0.1209$

$P(X = 9) = C_{10,9}.(0.6)^{9}.(0.4)^{1} = 0.0403$

$P(X = 10) = C_{10,10}.(0.6)^{10}.(0.4)^{0} = 0.0001$

$P(X > 7) = P(X = 8) + P(X = 9) + P(X = 10) = 0.1209 + 0.0403 + 0.0001 = 0.1613$

$P(X \leq 7) = 1 - P(X > 7) = 1 - 0.1613 = 0.8387$

83.87% probability that at most 7 of the next 10 customers will order a hamburger.

b) What is the probability that exactly 6 of the next 10 customers will order a hamburger? (3 POINTS)

This is P(X = 6).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 6) = C_{10,6}.(0.6)^{6}.(0.4)^{4} = 0.2508$

25.08% probability that exactly 6 of the next 10 customers will order a hamburger

7 0

3 years ago

What number makes the equation true? Enter the answer in the box 16= X4

Assoli18 [71]

Answer: 4=X

Step-by-step explanation:

You divide 4x by itself, and divide 16 by 4x leaving you with X and 4 (I'm pretty sure)

3 0

3 years ago

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