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2 years ago

Given: (↔AB) ║ (↔CD)

1 answer:

8 0

1) m = y2 - y1/x2 - x1
y = mx + b
m = 7 - 0/3 - 8
y = -7/5x + 11.2
2) y= -7/5x + 12
(the slope or m stays the same because the two equations are parallel)

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X^2-x+12 solve using the quadratic formula

devlian [24]

The quadratic formula is $x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}$ .

From the problem, a is 1, b is -1, and c is 12. Plugging in these values gives:

$x=\frac{-(-1(-1)\pm\sqrt{(-1)^2-4(1)(12)} }{2(1)}$

Because there is a square root of a negative number, there is no solution.

4 0

3 years ago

Write the slope intercept form of the r question of the line parallel to the graph of 2x+y=5 that passes through (0,1)

Fofino [41]

Step-by-step explanation:

first let's get the original line in slope intercept form.

the vegetal slope intercept form is

y = ax + b

a is the slope, b is the y-intercept.

2x + y = 5

y = -2x + 5

there !

a line parallel to this line must have the same slope (-2).

but it will intersect with the y-axis at a different point.

the y-intersect is the y value when x = 0.

the given point (0, 1) is already that y-intersect (because x=0).

so, the desired parallel line function is

y = -2x + 1

if we had a different point of the line, e.g. (4, -7), we would go back to the general equation

y = ax + b

put in the slope we know (-2)

y = -2x + b

and then put in the x and y cakes if the point and calculate b

-7 = -2×4 + b

-7 = -8 + b

b = 1

and then we get again

y = -2x + 1

4 0

1 year ago

What is the difference? −43−(−18) Enter your answer in the box.

gulaghasi [49]

Hello!

Answer:

-25

Step-by-step explanation:

−43+18

−25

Hope this helps!

5 0

2 years ago

Read 2 more answers

A store manager paid $95 for an item and set the selling price at $116.85. What was the percent markup?

Neporo4naja [7]

We have been given that a store manager paid $95 for an item and set the selling price at $116.85. We are asked to find the percent mark-up.

We will use percent increase formula to solve our given problem.

$\text{Percent increase}=\frac{\text{Final}-\text{Initial}}{\text{Initial}}\times 100\%$

$\text{Percent increase}=\frac{\$116.85-\$95}{\$95}\times 100\%$

$\text{Percent increase}=\frac{\$21.85}{\$95}\times 100\%$

$\text{Percent increase}=0.23\times 100\%$

$\text{Percent increase}=23\%$

Therefore, the mark-up will be 23% and option 'b' is the correct choice.

6 0

2 years ago

According to a study done by a university student, the probability a randomly selected individual will not cover his or her mou

VikaD [51]

Complete Question

The complete question is shown on the first uploaded image

Answer:

$P(X = 8) = 0.0037$

$P(X < 5) = 0.805$

$P(X > 6) = 0.0206$

I would be surprised because the value is very small , less the 0.05

Step-by-step explanation:

From the question we are told that

The probability a randomly selected individual will not cover his or her mouth when sneezing is $p = 0.267$

Generally data collected from this study follows binomial distribution because the number of trials is finite , there are only two outcomes, (covering , and not covering mouth when sneezing ) , the trial are independent

Hence for a randomly selected variable X we have that

$X \ \ \~ \ \ { B ( p , n )}$

The probability distribution function for binomial distribution is

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

Considering question a

Generally the the probability that among 12 randomly observed individuals exactly 8 do not cover their mouth when sneezing is mathematically represented as

$P(X = 8) = ^{12} C_8 * (0.267)^8 * (1- 0.267)^{12-8}$

Here C denotes combination

$P(X = 8) = 495 * 0.000025828 * 0.28867947$

$P(X = 8) = 0.0037$

Considering question b

Generally the probability that among 12 randomly observed individuals fewer than 5 do not cover their mouth when sneezing is mathematically represented as

$P(X < 5 ) =[P(X = 0 ) + \cdots + P(X = 4)]$

=> $P(X < 5 ) =[ ^{12} C_0 * (0.267)^0 * (1- 0.267)^{12-0} + \cdots + ^{12} C_4 * (0.267)^4 * (1- 0.267)^{12-4} ]$

=> $P(X < 5 ) = 0.02406 + 0.10516 + 0.21067 + 0.25580 + 0.20964$

=> $P(X < 5) = 0.805$

Considering question c

Generally the probability that fewer than half(6) covered their mouth when sneezing(i.e the probability the greater than half do not cover their mouth when sneezing) is mathematically represented as

$P(X > 6) = 1 - p(X \le 6)$

=> $P(X > 6) = 1 - [P(X = 0) + \cdots + P(X =6)]$

=> $P(X > 6)=1 - [^{12} C_0 * (0.267)^0 * (1- 0.267)^{12-0}+ \cdots + ^{12} C_4 * (0.267)^6 * (1- 0.267)^{12-6} ]$

=> $P(X > 6)= 1 - [0.02406 + \cdots + 0.0519 ]$

=> $P(X > 6) = 0.0206$

I would be surprised because the value is very small , less the 0.05

8 0

3 years ago