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Bogdan [553]
3 years ago
9

Twelve people are standing in line to buy movie tickets. The theater is running a promotion by giving away 2 concession stand gi

ft cards to the people standing in line. What is the probability that the second and third people in line will get chosen for the gift cards?
Mathematics
1 answer:
frutty [35]3 years ago
4 0
The answer to this question is 2 out of 12
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Write the equation of the parabola that has its x-intercepts at (1+<img src="https://tex.z-dn.net/?f=%5Csqrt%7B5%7D" id="TexForm
VladimirAG [237]

Answer:

y=2x^2-4x-8

Step-by-step explanation:

<u>Factored form of a parabola</u>

y=a(x-p)(x-q)

where:

  • p and q are the x-intercepts.
  • a is some constant.

Given x-intercepts:

  • (1+√5, 0)
  • (1-√5, 0)

Therefore:

\implies y=a(x-(1+\sqrt{5}))(x-(1-\sqrt{5}))

\implies y=a(x-1-\sqrt{5})(x-1+\sqrt{5})

To find a, substitute the given point (4, 8) into the equation and solve for a:

\implies a(4-1-\sqrt{5})(4-1+\sqrt{5})=8

\implies a(3-\sqrt{5})(3+\sqrt{5})=8

\implies4a=8

\implies a=2

Therefore, the equation of the parabola in factored form is:

\implies y=2(x-1-\sqrt{5})(x-1+\sqrt{5})

Expand so that the equation is in standard form:

\implies y=2(x^2-x+\sqrt{5}x-x+1-\sqrt{5}-\sqrt{5}x+\sqrt{5}-5)

\implies y=2(x^2-x-x+\sqrt{5}x-\sqrt{5}x+\sqrt{5}-\sqrt{5}+1-5)

\implies y=2(x^2-2x-4)

\implies y=2x^2-4x-8

6 0
1 year ago
What is the equation of the line that is parallel to the line y = -1/3x+4
RUDIKE [14]

Answer:

B

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - \frac{1}{3} x + 4 ← is i slope- intercept form

with slope m = - \frac{1}{3}

Parallel lines have equal slopes, thus

y = - \frac{1}{3} x + c ← is the partial equation

To find c substitute (6, 5) into the partial equation

5 = - 2 + c ⇒ c = 5 + 2 = 7

y = - \frac{1}{3} x + 7 ← equation of parallel line

8 0
3 years ago
The lines of symmetry in a regular polygon are equal to the number of sides minus 2. True or False
galina1969 [7]

Answer:

False

Step-by-step explanation:

A regular polygon may be defined as the polygon that have sides of equal length known as equilateral and angles made up of equal angles, known as equiangular.

The $\text{number of lines}$ of symmetry in a regular polygon is always equal to the number of sides of the polygon. For example, a regular pentagon have 5 sides, so the lines of symmetry of the regular pentagon is also 5, a square having 4 sides also has 4 lines of symmetry.

6 0
3 years ago
In order to avoid staying after work, a quality control analyst inspects the first 100 items produced that day. Which sampling m
mr_godi [17]
Based on the given scenario above wherein the quality control analyst just inspects the first 100 items produced that day in order to avoid staying after work, the sampling method that she used is the CONVENIENCE SAMPLING METHOD. Hope this helps.
3 0
3 years ago
Read 2 more answers
PLEASE HELP ASAP WILL DO BRAINLIEST!!!!!!! Part A: Three equations that all represent the same function f are shown. Select the
Serga [27]

Answer:

  A: f(x)=2x^2 +12x +10

  B: f(0) = 10

Step-by-step explanation:

<u>Part A</u>:

f(0) is a constant in the equation if the form is such that for x=0, all terms are zero except one of them. Standard form is one such form. This is the equation in standard form:

  f(x) = 2x^2 +12x +10

__

<u>Part B</u>:

  f(0) = 0 + 0 + 10

  f(0) = 10

7 0
4 years ago
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