Consider the quadratic polynomial ax 2 bx c. suppose the coefficients are given by rolling a fair die three times. what is the probability that the roots of the polynomial are equal?

Answers

Answer 1

Complete the square to write

ax² + bx + c = a (x + b/(2a))² - (b² - 4ac)/(4a)

The quadratic has a double root at x = -b/(2a) if the constant term (b² - 4ac)/(4a) vanishes, which happens if b² - 4ac = 0.

Let A, B, and C be random variables representing the value of the first, second, and third roll of the die. They are independent and identically distributed with PMF

Pr [X = x] = 1/6

if x ∈ {1, 2, 3, 4, 5, 6}, and 0 otherwise.

We want to find

Pr [B² - 4AC = 0]

Note that

B² - 4AC = 0   ⇒   B² = 4AC   ⇒ (B/2)² = AC

which tells us that B must be even, and also that AC is a perfect square. Then there are 5 possible outcomes that satisfy the conditions:

• If B = 2, then AC = 1   ⇒   A = C = 1

• If B = 4, then AC = 4   ⇒   A = 1, C = 4 or A = C = 2 or A = 4, C = 1

• If B = 6, then AC = 9   ⇒   A = C = 3

and there are 6³ = 216 total possible outcomes in the sample space. So,

Pr [B² - 4AC = 0] = 5/216


Related Questions

Really need help on this problem

Answers

Solving the equation s = zr - 6zc^4 for z would give you: [tex]z = \frac{s}{r - 6c^4}[/tex].

How to Solve an Equation?

Given the equation, s = zr - 6zc^4, to solve the equation for z, follow the steps below:

We have to isolate the variable "z" to one side of the equation if we are to solve the equation for z.

s = zr - 6zc^4

Factor out variable z

s = z(r - 6c^4)

Divide both sides of the equation by (r - 6c^4)

s/(r - 6c^4) = z(r - 6c^4) / (r - 6c^4)

s/(r - 6c^4) = z

[tex]z = \frac{s}{r - 6c^4}[/tex]

Therefore, solving the equation s = zr - 6zc^4 for z would give you: [tex]z = \frac{s}{r - 6c^4}[/tex].

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What is the prime factorization 18 and 24

Answers

Answer:

(2 × 3 × 3) and (2 × 2 × 2 × 3).

Complete the sentence.
4ft= ____ in.

Answers

4ft = 48in or 4 feet is equivalent to 48 inches.

In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume or even currency to another.

A conversion factor is a number used to change one set of units to another, either by multiplying or dividing.

The sentence states an equality between units of length: feet and inches.

From there, we can say that we are asked how many inches are there in 4 feet

Converting feet to inches, we must use the conversion

1 foot = 12 inches

4ft = 4 (12 inches)

4ft = 48in

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how do you find the domain and range of a continuous graph???

Answers

Answer:

So, when talking about continuous functions, we're dealing with a function/graph that goes on and on to infinity. It never ends. In a case like this, we must define domain and range. Domain is all input values, while range goes the same but it's the output values. With this information, the domain and range on a continues graph would most likely be all real numbers due to the fact of the graph never ending, and that means the graph would have every input value thus making its domain/range infinite as well.

➲ Hope this helps.



as estimate √200 to the nearest who le numbers

Answers

Answer:

10√2

or in decimal form:

14.1

Hope this helps! <3

14

(Blank space filler)

If 9 (x-9) = -11, then x =?
O-92/9
O-20/9
O-11/9
O-2/9
O70/9

Answers

Answer:

◉ 70/9

Step-by-step explanation:

9(x - 9) = -11

9x - 81 = -11

9x = 70

x = 70/9

Consider the function f(x) = x² + 3x - 7. Find the value of f(x) when x = 3 and select the correct answer below. (5 points)
05
8
11
18

Answers

Answer: 11

(3)^2 + 3(3) - 7
9 + 9 - 7
18 - 7

The temperature at 5 p.m. is 20 degrees. the temperature at 10 p.m. is -5 degrees

Answers

In 5 hours the temperature decreased by 25 degrees

The number of people in a movie theater. Identify the set of numbers that best describes the situation. Explain your choice.

Answers

the movie theater that everyone else was in there and i is that we had to get a little bit to do that we had the one time that you were talking to me i is the

What is the approximate value of the 16th percentile of corn yield for counties in iowa?

Answers

16th percentile of corn yield for counties in iowa is 153.4.

What is percentile?

In statistics, a score below which a certain percentage of scores (k) in a frequency distribution falls is known as a k-th percentile, whereas a score at or below which a given percentage falls is known as a k-th centile (inclusive definition). The score below which (exclusive) or at which (inclusive) 50% of the scores in the distribution may be found is known as the 50th percentile (the median), for instance. For instance, if the input scores are related to human weight, the corresponding percentiles will be represented in kilograms or pounds. Percentiles are expressed in the same unit of measurement as the input scores.

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Solve the equation. 2(5 – 7) = 1

Answers

Answer:

False

Step-by-step explanation:

Distribute, do the math, and evaluate the resulting equality/statement to see if it is true

10 - 14 = 1

-4 = 1

That is not true so the answer is false

Please help math 100 points! Decimal Rounding

Answers

Answer:

a: 0.5 + 0.3 = 0.8

b: 2.7 + 28.2 = 30.9

c: 3.1 + 2.4 + 9.9 = 15.4

d: 15.2 + 1.4 + 0.8 = 17.4

e: 39.2 + 2.5 + 0.8 = 42.5

Step-by-step explanation:

I did the assignment and I got it right

Of the three types of general survivorship curves, which can be most likely expected to live closest to its maximum life expectancy?

Answers

In the given statement is :

Of the three types of general survivorship curves, which can be most likely expected to live closest to its maximum life expectancy?

In this case, In Type I Curve, organisms tend to live up to maximum life expectancy. They survive their adulthood and die when they become elderly. Humans come under this category.

Survivorship Curve:

The Survivorship Curve is used to represent the number of population that are expected to live to a certain age. There are three types of survival curves they are Type I, Type II, Type III. Each curve will show the life expectancy of a particular group of organisms.

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What number must be added to both the numerator and the denominator of the fraction 2/3 to get the fraction 7/8?

Answers

Answer:

Step-by-step explanation:

Answer is 5

2 + 5  = 7

3 + 5     8

a school authority claims that the average percentage marks of students is 68. a researcher has taken a well–designed survey and his sample mean is 64.5 and sample standard deviation is 2. the sample size is 300. which statement is correct?

Answers

The statement B is correct, i.e., The result of the survey is statistically significant.

What is statistical significance?

The probability that the difference in conversion rates between a given variation and the baseline is not the result of random chance is known as statistical significance.

Given:

Average percentage of students = 68Sample mean of researcher = 64.5Sample standard deviation = 2Sample size = 300

To find: WHich of the given statements is correct?

Finding:

According to the given data,

We can infer that there is a statistically significant result because our findings from a large sample size and relatively small standard deviation show that 64.5 is much lower than the average 68. Additionally, it differs practically.

Hence, the statement B is correct, i.e., The result of the survey is statistically significant.

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(COMPLETE QUESTION:

A school authority claims that the average percentage marks of students is 68. A researcher has taken a well-designed survey and his sample mean is 64.5 and sample standard deviation is 2. The sample size is 300.Which statement is correct?

a.)

The difference exists due to chance since the test statistic is small.

b.)

The result of the survey is statistically significant.

c.)

The sample size should be much more.

d.)

The result of the survey is not statistically significant.)

find the distance of a speed of 15m/s for 5 minutes

Answers

15m/s * 1km/1000m*60s/1 min*60 min/1hr=

You do the calculation.

Here are the conversions used in the conversion.

1km = 1000 m, 60 seconds = 1 minute, 60 minutes = 1 hour.

When you set up the problem the 15 meters is in the numerator and 1 second is in the denominator. To convert the 15 meters to km the next conversion factor needs to have 1km in the numerator and 1000 meters in the denominator. Now the 15 m will be divided by 1000 m which cancels the meters and leaves km.

The seconds in 15 m/s is in the denominator so to convert seconds to hours multiply by 60 seconds placing it in the numerator over 1 minutes. Use the same idea to set up the conversion from minutes to hours.

Practice this conversion. It is a fundamental conversion that any middle school student should know how to do.

30 pointys!!!!!
Please tell me the answer, 30 points avaliable,

Answers

Answer:

10.97 mm

Step-by-step explanation:

Hello!

First, let's construct an altitude, as shown in the picture below. An altitude is a height from one point to another side, forming a 90° angle at that intersection.

The length of the altitude is the same as the missing length, they are both parallel.

The length from the altitude to the slant line would be 6, as found by subtracting 8 from 14.

If you look closely, we can see a right triangle, and 12.5 mm is the hypotenuse. We know the measure for another side, and we can solve for the altitude using the Pythagorean Theorem: [tex]a^2 + b^2 = c^2[/tex], a and b are legs, and c is the hypotenuse.

In this case, 6 and the altitude are legs.

Solve for the Altitude[tex]a^2 + b^2 = c^2[/tex][tex]A^2 + 6^2 = 12.5^2[/tex][tex]A^2 + 36 = 156.25[/tex][tex]A^2 = 120.25[/tex][tex]A = \sqrt{120.25}[/tex][tex]A \approx 10.97[/tex]

The altitude is around 10.97, so the missing length will also be 10.97 mm.

suppose that there are seven committees with each pair of committees having a common member and each person being on two committees. how many people are there?

Answers

Minimum number of meeting required is 5 meetings required

As mentioned, if there is an edge between two committees, both the committee has atleast one member in common.

So if we consider two committees with atleast one member in common, i.e. we select two different vertices with an edge in between, the common member(s) in the committee can discuss and exchange ideas between the committees and thus they don't require a meeting to be scheduled.

So looking at the graph we can say that we only need to schedule meetings between committee with no edge connecting them.

6C2 - |E| or 15 - 10

= 5 meetings

What is the role of the committees?

Committees keep an eye on ongoing government activities, spot problems that warrant legislative scrutiny, collect and assess data, and suggest courses of action to the Senate.

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Please Help! <3 ASAP
i don't understand T.T

Answers

Answer:

3.2 miles

Step-by-step explanation:

Yesterday: 2.35 miles

Today: 2.45 miles

Total of today and yesterday: 2.35 miles + 2.45 miles = 4.8 miles

Goal: 8 miles

Number of miles left to do:

8 miles - 4.8 miles = 3.2 miles

Answer: 3.2 miles

1/3 of x is 14 plsss helppp

Answers

Answer:

42

Step-by-step explanation:

1/3 * x = 14

x/3=14

3*x/3=14*3

x=42

What is the value of 5x2 + x if x = 4?

404
84
44
24

Answers

Answer:

44

Step-by-step explanation:

(5)(4)(2) + 4 Calculate the product

40 + 4 Add

= 44

Answer: its 44 :D

have a great day young boy

a function is a relation in which each possible input value leads to exactly one output value. the input values make up the range and the output values make up the domain

Answers

A relation between sets is referred to as a function when there is exactly one output for each input.

Which statement is true?A function is a relation where each output value is assigned to exactly one input value.The domain of a function is the set of all output values, or y-values, for which the function is defined.The range of a function is the set of all input values, or x-values, for which the function is defined.To write the equation y = ax + b in function notation, substitute f(x) for y.?

To write the equation y = ax + b in function notation, substitute f(x) for y

The only true statement is the last one. A function assigns exactly one output value to each input value. The domain is the set of all input, or x-values. The range is the set of all output, or y-values.

y=ax+b can be written in function notation by replacing y with f(x).

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a candy bar box is in the shape of a triangular prism. the volume of the box is 1,200 cubic centimeters. a triangular prism is shown with base of triangle labeled 10 cm, sides of the triangles labeled 13 cm, and length of the box equal to 20 cm. part a: what is the height of the base? show your work.

Answers

The height of the box is 12cm, having volume = 1200cm ³ .

What is the volume of triangular prism?

A triangular prism's volume is the area that it takes up in all three dimensions. A prism is a solid object that has the same cross-section throughout its entire length, equal bases, and flat, rectangular side faces. Prisms can be divided into many categories and given different names depending on the form of their bases. A triangular prism has three rectangular lateral sides and two identical triangular bases.

The formula yields the volume of a triangular prism.

Volume of triangular prism  = 1/2lwh

Where,

w = width

h = height

l = length.

We may determine the height by filling in the specified measurements.

1200cm ³ = 1/2 × (20 cm) × (10 cm) × h

h = (1200 cm³) / (100 cm²))

h = 12 cm

The box has a 12 centimeter height.

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Line c passes through points (5, 1) and (9, 8). Line d is parallel to line c. What is the slope of line d?

Answers

The slope of line d is m =7/4.

Given c points (5,1) and (9,8).

and the d line is parallel to line c.

We have to find the slope of d.

The slope formula is to determine a line's slope or steepness, use the slope formula. By calculating the ratio of the change in the y-axis to the change in the x-axis, it may be used to calculate the slope of any line. A line's slope is determined by how its "y" coordinate changes in relation to how its "x" coordinate changes.

Slope m = rise/run =[tex]=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

Here, [tex](x_{1} ,y_{1} )=(5,1) and (x_{2} ,y_{2} )=(9,8)[/tex]

We get slope by substitute this points in m value.

m=(8-1)/(9-5)

m=7/4

Therefore, the slope m=7/4.

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Describe how to graph the solution of

Answers

The solution of the given inequality y ≤ -x² + 2x is (x,y) ≥ {(0,0) and (-2,-4)} obtained by plotting graph between axis.

What is inequality?

A mathematical phrase in which the sides are not equal is referred to as being unequal. In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.

Given the inequality,

y ≤ −x² + 2x

The inequality consists of two functions,

y ≤ -x² and y ≤ 2x

Now if we plot both inequalities

x = 0 ⇒ y = 0

And,

2x ≤ -x²

-x²/x ≥ 2

x ≤ -2

So,

y ≤ 2(-2)

y ≤ -4

If we plot both as shown below then the bounded region is obtained towards the right therefore the solution will be greater than this.

Therefore (x,y) ≥ {(0,0) and (-2,-4)} will be solution.

Hence "The solution of the given inequality y ≤ -x² + 2x is (x,y) ≥ {(0,0) and (-2,-4)} obtained by plotting graph between axis".

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Solve for x can you help please

Answers

Answer:

x = 13

Step-by-step explanation:

23 - 9 = 14

14 / 2 = 7

So both sides should equal to 7.

Set the two expression equal to each other and solve.
x - 6 = 2x - 19

move the 6 to the other side by adding

x = 2x - 19 + 6

x = 2x - 13

then move 2x to the other side by subtracting

x - 2x = -13

-x = -13

divide both sides by -1 to get x

x = -13/-1

x = 13

Check.
plug 13 in for x

x - 6

13 - 6 = 7

2x - 19

2(13) - 19

26 - 19 = 7

so both expressions are equal to each other now and

7 x 2 = 14

14 + 9 = 23

thus x = 13

David fills an aquarium to a depth of 3/8 meters in 3 3/5 minutes.

Answers

The  unit rate in minutes per meter is 28.8 minutes per meter when  David fills an aquarium to a depth of 3/8 meters in 3 3/5 minutes

The given Depth of the aquarium  = 3/8 meters

Time taken to fill the aquarium  = 3 3/5 minutes

To find the  the unit rate in minutes per meter, we need to divide the time taken to fill the aquarium by the depth of the aquarium

So, Unit rate in minutes per meter = 3 3/5minutes ÷ 3/8 meters

                                                            = 18/5 ÷ 3/8

                                                              = 18/5 ×8/3

                                                             = 144/15

                                                             = 28.8 minutes per meter

Hence, the unit rate in minutes per meter is 28.8 minutes per meter when  David fills an aquarium to a depth of 3/8 meters in 3 3/5 minutes

The correct question is David fills an aquarium to a depth of 3/8 meters in 3 3/5 minutes. What is the unit rate in minutes per meter?

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help please!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

1/8

Step-by-step explanation:

5/4   divided by   10/1   is the same as  

    5/4   times  1/10

       5/4 *  1/10 =  5/40    = 1/8

Answer: 1/8

Step-by-step explanation:

[tex]\displaystyle\\\frac{\frac{5}{4} }{10} =\\\\\frac{5}{4}:10=\\\\\frac{5}{4} *\frac{1}{10}=\\\\ \frac{5*1}{4*10}=\\\\\frac{5}{4*5*2} =\\\\\frac{1}{4*2}=\\\\\frac{1}{8}[/tex]

in an election for class president,jason received 170 of the 250 votes . what percent of the vote did he receive

Answers

Answer: 68%

Step-by-step explanation:

170/250=

17/25=

0.68=

0.68 * 1=

0.68 * 100%=68%

asgt 2.2 7 of 77 of 7 items on a number line, a is at 5 and b is at 50. point x is the midpoint. point t is 2/3 of the way from x to b. determine the coordinate of point t. distance of xb =

Answers

On a number line where A is at 5 and B is at 50, and X is the midpoint and T is somewhere between A and B, the coordinates of point T is 15 and the distance of XB is 22.5.

A number line is straight line divided by equal measures that serves as a visual representation of the real numbers.

If on a number line, a is at 5 and b is at 50, then AB = 50 - 5 = 45.

If point X is the midpoint of A and B, then X divides the distance of A to B into two equal parts.

let n = AX = XB

AB = AX + XB

45 = n + n

45 = 2n

n = 22.5

AX = XB = 22.5

If point T is 2/3 of the way from X to B, then

T = 2/3XB

T = 2/3(22.5)

T = 15

Hence, the coordinates of T is at 15 and the distance of XB is 22.5.

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