Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. Write the function in standard form. -2, 3, 6​

The conditional probability is 3/8

From the question, we have

total number in bit string =16

let s be the set of all bit strings

number of strings =8

probability of selecting A

P(A)=8/16=1/2

P(A∩B)=3/16

the conditional probability is,

P(A∩B)/P(A)=3/16/1/2

=3/8

Probability:

Possibility is referred to as probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.

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Answer:

5x + 6y = 12

Step-by-step explanation:

The standard form of a linear equation is  Ax + By = C.

Multiply both sides by  6

6y = 6(-5x/6 + 2)

Simplify the right side

Simplify  

6(−5x/6+2)

Apply the distributive property =  a  ( b + c )  = ab + ac

6y = 6( −5x/6) + 6 ⋅ 2

Cancel the common factor of  6

Move the leading negative in  −5x/6 into the numerator

6y = 6 −5x/6 + 6 ⋅ 2

Cancel the common factor 6

Rewrite the expression

6y  = −5x + 6 ⋅ 2

Multiply  6  by 2

6y = -5x + 12

Move all terms containing variables to the left side of the equation

Add  5x to both sides of the equation.

6y + 5x = 12

Reorder 6y and 5x

5x + 6y = 12

Statistics is the science of conducting studies to collect, organize, summarize, analyze and draw conclusions from data.

Therefore, the correct option is: c

The statistics it involves using various methods to gather and analyze data to form hypotheses, experiments and draw conclusions. In order to do so, statistics uses a variety of tools and techniques to summarize and analyze data, including descriptive statistics, inferential statistics, and hypothesis testing.

Its main goal is to draw conclusions or make decisions based on data. In order to do so, statistics uses a variety of tools and techniques to summarize and analyze data, including descriptive statistics, inferential statistics, and hypothesis testing.

Additionally, statistics can also be used to monitor, study and report on a subject by looking at different options.

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Three glasses of milk or dairy products per day are recommended for adults. One serving of milk is one cup. According to the USDA, a serving of milk-based goods is the amount that corresponds to one cup of milk.

Food items manufactured from (or containing) milk are referred to as dairy products or milk products (also known as lacticinia).

The cow, water buffalo, nanny goat, and ewe are the most popular dairy animals.

Dairy products include staples from Western grocery stores including yogurt, cheese, and butter.

A dairy is a place where dairy products are made .Various amounts of dairy products are consumed worldwide (see consumption patterns worldwide) .

After standardizing the fat content and optional homogenization or pasteurization, milk is produced in a variety of grades with the potential addition of the microorganisms Streptococcus lactis and Leuconostoc citrovorum.

Based on the type of product generated, milk can be divided into a number of distinct categories, including cream, butter, cheese, newborn formula, and yogurt.

Hence, Three glasses of milk or dairy products per day are recommended for adults. One serving of milk is one cup. According to the USDA, a serving of milk-based goods is the amount that corresponds to one cup of milk.

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Answer:

Step-by-step explanation:

Consider a utlity bill which shows a minimum initial cost plus variable costs dependent upon how many units are sold.

Then:  total cost ≥ (fixed cost) + (unit cost)(number of units sold)  

This involves the "equal to or greater than" concept.

Answer:

1. 0.0469 (4.d.p)

2. 0.05

Step-by-step explanation:

1. First we'll find the probability of drawing a blue marble.

P = (No. favourable events)/(Total events)

In this case it's:

P = (No. blue marbles)/(Total Marbles)

Therefore P(Blue) = 4/16 = 0.25

Now we find the probability of drawing a yellow marble:

The total number will be the same because the blue marble will have been put back.

P(Yellow) = 3/16 = 0.1875

Now, since we are calculating the probability of both happening we multiply together the two individual probabilities to get the combined probability of both:

0.25 x 0.1875 = 0.0469 (4.d.p)

2. The probability of drawing a blue marble is still the same so we can keep that: P(Blue) = 0.25

But this time, the marble is not replaced. This means that the total number of marbles has changed when drawing the yellow marble:

P(Yellow) = 3/15 = 0.2

Now we multiply them together again to find the combined probability of both happening:

0.25 x 0.2 = 0.05

Hope this helped!

Answer:

w = (0, 15)

Step-by-step explanation:

w²-15w =0

w(w-15)=0

w=0 , w=15

if w=0

0(0-15)=0

0(-15)=0

0=0

if w=15

15(15-15)=0

15(0)=0

0=0

The vertex is at (8, -2).The point (10, -22) is also on the parabola.

Step-by-step explanation:

Here is the graph of the function:

The vertex is at (8, -2).

To plot another point on the parabola, we can choose any x-value and plug it into the equation to solve for y.

For example, if we choose x = 10, then we have:

f(x)   = -5(x - 8)² - 2

f(10) = -5(10 - 8)² - 2

f(10) = -5(2)² - 2

f(10) = -5(4) - 2

f(10) = -20 - 2

f(10) = -22

So, the point (10, -22) is also on the parabola.

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Answer:

Second choice, 2/5

Step-by-step explanation:

12 + 9 + 10 + 11 + 8 = 50

12 red and 8 blue, the probability of getting either is 12 + 8 = 20/50 which simplified is 2/5

The difference in perimeters between the two squares is 2 inches.

Here, we have,

To find the difference in perimeters between two squares, we subtract the perimeter of the smaller square from the perimeter of the larger square.

Let's denote the side length of the larger square as S = 3/4 inch and the side length of the smaller square as s = 1/4 inch.

The perimeter of a square is given by the formula: P=4s, where s is the side length.

For the larger square with side length S = 3/4 inch, the perimeter P is:

P = 4 × 3/4

 =3 inches

For the smaller square with side length s = 1/4 inch, the perimeter p is:

p = 4 × 1/4  =1 inch

The difference in perimeters is then:

Difference = P - p

so, we get,

Difference

=P - p

=3−1

=2 inches

Therefore, the difference in perimeters between the two squares is 2 inches.

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Answer:

60

Step-by-step explanation:

Complementary angles means that the angles add up to 90 degrees

So the complementary of 30 is 60

30+60=90

Let the other Complementary Angle be x,

We know that, Sum of Complementary Angles = 90°

therefore,

Two column proof is as follows

Statement                              Reason

AB ≅ CB                                Given                  

AD ≅ CD                               Given

< BAD ≅ < BCD                     Given

< ABD = < CBD                      Definition of angle bisection

AB = CB                                 Definition of equality

BD = BD                                 Reflexive property of congruence

AD = DC                                 Definition of bisection

Δ ABD = Δ CBD                     SSS postulate of congruence

This is a method of proof that consists of five parts which include

The postulate says that when the three sides of the triangles under comparison are equal then the triangles under comparison are said to be congruent.

In the figure,

AB =CB, from the given sides

BD = BD sharing common sides

AD = CD line AC was bisected by line BD

This completes the SSS proof of congruence

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In a dataset or graph, outliers are extreme values that greatly deviate from the dominant pattern of values.

In order to identify the outlier, search for a value that is significantly greater or smaller than all the other values. Due to its extreme size compared to all other numbers, the number 267 is an outlier.

a value that "lies outside" (i.e., is significantly smaller or substantially bigger) most of the other values in a set of data For instance, both 3 and 85 in the scores 25, 29, 3, 32, 85, 33, 27 and 28 are "outliers".

A data point that is an outlier in a data graph or dataset you are dealing with is one that is extraordinarily high or extraordinarily low in comparison to the nearest data point and the rest of the nearby coexisting values. Outliers in a dataset or graph are extreme values that stand out significantly from the main pattern of values.

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Answer: I think you answer is -61 if not sorry

Step-by-step explanation:

Answer:

0.41666666, to round up, the answer is 0.42

Step-by-step explanation:

\( \frac{3}{8} + \frac{1}{8} - \frac{1}{3} + \frac{1}{4} = \frac{4}{8} - \frac{1}{3} = \frac{4}{24} + \frac{1}{4} = \frac{10}{24} = \frac{5}{12} \)

Answer:

B :)

Step-by-step explanation:

The correct answer is option (C) 55 minutes.

Let's break down the information given in the problem:

To find out how long it takes for Lauren to reach Andrea, we need to determine the time it takes for Andrea to cover half the distance between them. Once Andrea reaches the halfway point, Lauren will also have traveled the same distance.

Let's denote the time it takes for Andrea to reach the halfway point as "t" minutes. Since the distance decreases at a rate of 1 kilometer per minute, after "t" minutes, the distance between Andrea and Lauren will be reduced by "t" kilometers.

Now, let's calculate the distance traveled by Andrea in "t" minutes:

Distance = Rate × Time

Since Andrea is traveling three times as fast as Lauren, her rate is 3 times the rate of Lauren.

Distance traveled by Andrea in "t" minutes = (3 × 1) × t = 3t kilometers

The total distance between Andrea and Lauren at that time will be:

Distance between Andrea and Lauren = 20 - t kilometers

Since they meet at the halfway point, the distance traveled by Andrea (3t) will be equal to half the total distance (20 - t)/2:

3t = (20 - t)/2

To solve this equation, we can multiply both sides by 2:

6t = 20 - t

Now, solve for "t":

6t + t = 20

7t = 20

t = 20/7

Therefore, it will take Andrea 20/7 minutes to reach the halfway point.

Since Lauren continues biking for 5 more minutes after Andrea stops, the total time it takes for Lauren to reach Andrea is:

Total time = t + 5 = 20/7 + 5

To calculate this, we can convert 5 minutes to a fraction with a denominator of 7:

5 minutes = 35/7 minutes

Total time = 20/7 + 35/7 = (20 + 35)/7 = 55/7

So, Lauren will reach Andrea after 55/7 minutes.

To find the answer option that matches this time, we can calculate 55/7 and compare it to the answer choices:

55/7 ≈ 7.86

Among the given answer choices, the closest option to 7.86 is (C) 55. Therefore, the answer is (C) 55 minutes.

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Answer:

13

Step-by-step explanation:

-2(-2) - (-8) + 1

4 + 8 + 1 = 13

Answer:

13

Step-by-step explanation:

cause i did it and it was right

2,598,960 many different hands consisting of four queens and one king.

What is combination?

A combination is a choice made in mathematics from a group of different elements when the order of the choices is irrelevant (unlike permutations). For instance, if three fruits, such as an apple, an orange, and a pear, are supplied, there are three possible pairings of the two: an apple and a pear. Formally speaking, a k-combination of a set S is a subset of S's k unique components. In other words, two combinations are the same if and only if they have the same members. (It is not important how the individuals in each set are arranged.) The quantity of k-combinations for a set with n components

To choose 4 kings, there is only one way, and to choose a queen, there are four.

Thus, there are 4 different methods to draw the 5 cards as instructed.

The probability of drawing cards is taken into account while calculating the number of ways to draw 5 cards from a typical 52-card deck.

= 52!/(47!)(5!) = 2,598,960.

Hence,  2,598,960 many different hands consisting of four queens and one king.

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Answer:

D

Step-by-step explanation:

Answer:

i think h=17

Step-by-step explanation:

-18h = 17 = xh/6

Subtract xh/6 from both sides of the equation.

-18 - xh/6 = 17

Answer:

Step-by-step explanation:8

Step-by-step explanation:

5 = 5(-4)+c

5 = -20 + c

5+20= 25

25= c

so

y = 5x + 25

Answer:

m= 5

Points=(-4,5)

y-y'= m(x-x')

y-5 = 5(x-(-4)

y-5=5(x+4)

y-5=5x + 20

y - 5x -25 = 0

Or

y= 5x + 25.

Step-by-step explanation:

what is a square ? or is a number or term/expression for which the square root creates a clean result without any endless positions after the decimal point or non-integer exponents.

for the first problem a is already the right answer.

14b⁴ is not a square term, although b⁴ itself is one (= b²×b²), because 14 is not a square (its square root is an endless number).

1 is actually a square (= 1×1).

b² and y⁴ are squares (b×b and y²×y²).

16b² and 49 are squares (4b×4b and 7×7).

(b+1)⁴ and 4b⁶ are squares ((b+1)²×(b+1)² and 2b³×2b³).

factors of x² + 5x - 6

you know how generic factor multiplication works ?

(x + a)(x + b) = x² + ax + bx + ab

so by comparing, we see that

ax + bx is 5x

therefore

a + b = 5

and

ab = -6

now we could solve this ultimately quadratic problem or (much simpler) use the answer options and see which one fits.

and the right answer is c :

-1 + 6 = 5 (that fits)

-1×6 = -6 (that fits too, so this answer is correct).

To make the code in the math module available, the correct statement is "import math." In Python, to access the functions and variables defined in a module, we use the "import" statement followed by the name of the module.

The "import" statement allows us to bring the specified module into our code and make its contents available for use. Therefore, the correct statement to make the code in the math module available is "import math." This statement tells Python to import the math module, which provides various mathematical functions and constants, and make them accessible in our code. Once imported, we can use the functions and variables from the math module by referencing them as math.<function_name> or math.<variable_name>.

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The expression where the greatest common factor (GCF) is factored completely is \(2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)\)

The expression completely factored in is

\(2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)\)

Please refer below for the remaining answers.

We have,

Part A:

To rewrite the expression 2x³y + 18xy - 10x²y - 90y so that the greatest common factor (GCF) is factored completely, we can factor out the common terms.

GCF: 2y

\(2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)\)

Part B:

To completely factor the expression, we can further factor the quadratic term.

\(2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)\)

Now,

Part A:

To determine the length of each side of the square given the area expression (9x² + 24x + 16), we need to factor it completely.

The area expression (9x² + 24x + 16) can be factored as (3x + 4)(3x + 4) or (3x + 4)².

Therefore, the length of each side of the square is 3x + 4.

Part B:

To determine the dimensions of the rectangle given the area expression (16x² - 25y²), we need to factor it completely.

The area expression (16x² - 25y²) is a difference of squares and can be factored as (4x - 5y)(4x + 5y).

Therefore, the dimensions of the rectangle are (4x - 5y) and (4x + 5y).

Now,

f(x) = 2x² - 5x + 3

Part A:

To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x.

2x² - 5x + 3 = 0

The quadratic equation can be factored as (2x - 1)(x - 3) = 0.

Setting each factor equal to zero:

2x - 1 = 0 --> x = 1/2

x - 3 = 0 --> x = 3

Therefore, the x-intercepts of the graph of f(x) are x = 1/2 and x = 3.

Part B:

To determine if the vertex of the graph of f(x) is maximum or minimum, we can examine the coefficient of the x^2 term.

The coefficient of the x² term in f(x) is positive (2x²), indicating that the parabola opens upward and the vertex is a minimum.

To find the coordinates of the vertex, we can use the formula x = -b / (2a), where a and b are the coefficients of the quadratic equation.

For f(x),

a = 2 and b = -5.

x = -(-5) / (2 x 2) = 5/4

To find the corresponding y-coordinate, we substitute this x-value back into the equation f(x):

f(5/4) = 25/8 - 25/4 + 3 = 25/8 - 50/8 + 24/8 = -1/8

Therefore, the vertex of the graph of f(x) is at the coordinates (5/4, -1/8), and it is a minimum point.

Part C:

To graph f(x), we can start by plotting the x-intercepts, which we found to be x = 1/2 and x = 3.

These points represent where the graph intersects the x-axis.

Next,

We can plot the vertex at (5/4, -1/8), which represents the minimum point of the graph.

Since the coefficient of the x² term is positive, the parabola opens upward.

We can use the vertex and the symmetry of the parabola to draw the rest of the graph.

The parabola will be symmetric with respect to the line x = 5/4.

We can also plot additional points by substituting other x-values into the equation f(x) = 2x² - 5x + 3.

By connecting the plotted points, we can draw the graph of f(x).

The steps to graph f(x) involve plotting the x-intercepts, the vertex, and additional points, and then connecting them to form the parabolic curve.

The answer in part A (x-intercepts) and part B (vertex) are crucial in determining these key points on the graph.

Thus,

The expression where the greatest common factor (GCF) is factored completely is \(2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)\)

The expression completely factored in is

\(2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)\)

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Answer:

B. (x, y) → (–x, –y).

Step-by-step explanation: This is the correct answer on Edge 2021, just did the assignment. Hope this helps ^-^.

Answer: B.) (x, y) → (–x, –y)

Step-by-step explanation: i hope this helps :)

The second smallest positive x-value where the graph of f(x) has a horizontal tangent line is (1/3) * (π - arccos(1/9)).

To find the second smallest positive x-value where the graph of the function f(x) = x + 3sin(3x) has a horizontal tangent line, we need to find the points where the derivative of the function is zero.

First, let's find the derivative of f(x) with respect to x. Applying the derivative rules, we have:

f'(x) = 1 + 3cos(3x) * (3) = 1 + 9cos(3x).

To find the points where the derivative is zero, we set f'(x) = 0 and solve for x:

1 + 9cos(3x) = 0.

Subtracting 1 from both sides and then dividing by 9, we get:

cos(3x) = -1/9.

Now, we can use the inverse cosine function to solve for x:

3x = arccos(-1/9).

Dividing both sides by 3, we have:

x = (1/3) * arccos(-1/9).

Since we are looking for the second smallest positive x-value, we can use the periodicity of the cosine function to find the exact value.

The cosine function has a period of 2π, which means it repeats every 2π. The smallest positive value for arccos(-1/9) occurs at the principal value of arccos(-1/9), which is between 0 and π. Let's denote this value as θ.

Therefore, the second smallest positive x-value occurs when:

x = (1/3) * θ.

To express this value exactly, we need to determine the exact value of θ. Since cos(θ) = -1/9, we can use the Pythagorean identity for cosine:

sin(θ) = √(1 - \(cos^2\)(θ)) = √(1 - \((-1/9)^2\)) = √(1 - 1/81) = √(80/81) = √80 / 9.

Thus, the exact value of θ is:

θ = arccos(-1/9) = π - arccos(1/9).

Therefore, the second smallest positive x-value where the graph of f(x) has a horizontal tangent line is:

x = (1/3) * θ = (1/3) * (π - arccos(1/9)).

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