Consider an urn containing four balls, numbered 110, 101, 011 and 000, from which one ball is drawn at random. For k = 1, 2, 3 let Ak be the event of drawing a ball with 1 in the kth position. Show your work in answering the following:a) Are A1, A2, and A3 pairwise independent?b) Are A1, A2, and A3 mutually independent?

The work done by the force 4i−3j+2k is the scalar product of the force vector and the displacement vector between the two points. In this case, the displacement vector is (3−2, 2−(−1), −1−4) or (1,3,−5). The scalar product of these two vectors is (1)(4)+(3)(−3)+(−5)(2) = 15 units.

Work is the scalar product of the force and displacement vectors. The force vector in this problem is given as 4i−3j+2k, while the displacement vector (the vector from the starting point to the end point) is (3−2, 2−(−1), −1−4) or (1,3,−5). The scalar product of these two vectors is (1)(4)+(3)(−3)+(−5)(2) = 15 units. This means that the work done by the force is 15 units.

The work done by a force is the energy transferred to an object by the force. It is calculated by taking the scalar product of the force and displacement vectors. This scalar product gives the magnitude of the work done by the force, which in this case is 15 units. This means that the force transferred 15 units of energy to the object by moving it from the starting point to the end point.

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By solving the equation 3x = x² - 4, we know that the positive solution of the given problem is x = 4.

Using the equal symbol, they are linked.

For instance, a formula might be 3x - 5 = 16. After solving this equation, we learn that the value of the variable x is 7.

So, using the given  information, form the following equation:

3x = x² - 4

Now, solve this equation as follows:

3x = x² - 4

0 = x² - 3x - 4

0 = (x-4)(x+1)

Then, x = 4 and x = -1

Therefore, by solving the equation 3x = x² - 4, we know that the positive solution to the given problem is x = 4.

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Answer:

(3, -11)

Step-by-step explanation:

Rearranging the equation becomes a slope-intercept form:

[tex]y = 2 - 3x[/tex]

where   m = slope of equation = [tex]-3[/tex]

      and c = intercept = [tex]2[/tex]

Substitute any value of x into the above slope-intercept equation to determine it's corresponding y value. Together these x and y values will form an ordered pair.

For example:

Take x = 3 and substitute in the above mentioned equation:

[tex]y = 2 - 3(3)[/tex]

  [tex]= 2 - 9[/tex]

y = [tex]-11[/tex]

∴ An ordered pair that is a solution to the equation: (3, -11)

Answer:

Each person will get 12 ounces of soda

Step-by-step explanation:

84 ounces divided by 7 people is 12 ounces per person

Answer:

each person will get 12oz

Step-by-step explanation:

84oz divided by the 7 people will get 12oz per person

Answer:

A.  (0, 0)

Step-by-step explanation:

To find the center of the circle that can be circumscribed about the given triangle, find the triangle's circumcenter.

A circumcenter of a triangle is:

A perpendicular bisector is a line that divides another line segment into two equal parts at a right angle.

Add perpendicular bisectors to the sides of the triangle (shown in green on the attached diagram).

The point of intersection of the perpendicular bisectors is (0, 0).

Therefore, the center of the circle that can be circumscribed about the triangle is (0, 0).

The model product, P(16), predicts the number of moose to be 3545 in 1997 and 2970 in 2009.

The odds that a happening will happen or a claim will be true is measured by probability theory, a branch od arithmetic. The probability of an item is a number between 0 but also 1, where about 0 represents how frequently the event is to occurring and 1 represents certainty. A risk is a numerical illustration of the possibility that a specific occurrence will take place. Probabilities may be expressed as percentages ranging from 0percent to 100% as well as from 0 to 1. the ratio of the number of outcomes to the proportion of occurrences in a whole set of equally plausible options that lead to a specific occurrence.

given

We'll choose x on the graph to represent the number of years since 1990 and y to represent the number of moose.

On the graph, there are two points: (4, 4290) and (8, 3850)

We can determine the slope of this line using the slope formula (m = [y2 - y1]/[x2 - x1]):

Replacement: m = (3850 - 4290)/(8 - 4)

m = -440/4 Solve the parenthesis's subtraction puzzles.

m = -110 Reduce the percentage

Since we know the line's slope, we can apply the point-slope formula (y - y1 = m[x - x1]) to determine the line's equation.

P(16) = 2970

The model product, P(16), predicts the number of moose to be 3545 in 1997 and 2970 in 2009.

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Answer:

b

Step-by-step explanation:

bbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 3690.37\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{each year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]3690.37 = 3000\left(1+\frac{\frac{r}{100}}{1}\right)^{1\cdot 4} \implies \cfrac{3690.37 }{3000}=\left(1+\cfrac{r}{100} \right)^4 \\\\\\ \sqrt[4]{\cfrac{3690.37 }{3000}}=1+\cfrac{r}{100}\implies \sqrt[4]{\cfrac{3690.37 }{3000}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[4]{\cfrac{3690.37 }{3000}}=100+r\implies 100\sqrt[4]{\cfrac{3690.37 }{3000}}-100=r\implies \boxed{5.3\approx r}[/tex]

Answer:

5.3 is about r

Step-by-step explanation:

The distribution is b) skewed.

The sum of the probabilities is: 1

In a binomial distribution, p represents the probability of success. Success in the sense that the event of interest happens. In the model presented, the probability of success p is 0.4 since we are informed that 40% of adults watch a particular television show.

The next quantity of significance in a binomial model is the number of independent trials, n.

In our case there are 6 independent trials since we are told that 6 adults were selected at random. If we let the random variable K denote the number of adults out of the 6 who watch the television show, then K is a binomial random variable with parameters;

n = 6 and p = 0.4

A binomial distribution is only symmetric when either p is 0.5 or n is large. In the presented scenario none of these conditions is met since p is 0.4 while n is just 6 which is relatively small.

Thus we conclude that the distribution is not symmetric but rather skewed.

The sum of the probabilities is any discrete probability distribution such as the Bernoulli, binomial, negative binomial, Poisson, or the geometric distribution is always equal to 1. That's a rule of thumb.

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The solution to the given inequality 2x/2 - 5x -3 ≥ 0 is x ≤ - 3/8.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

We have to solve 2x/2 - 5x -3 is greater than or equal to zero algebraically.

As per the question, we have inequality as follows:

2x/2 - 5x -3 ≥ 0

2x/2 - 5x ≥ 3

Multiply by 2 on both sides of the inequality,

4x - 20x ≥ 6

-16x ≥ 6

Divided by -16 and flip the sign of the above inequality,

x ≤ - 6/16

x ≤ - 3/8

This is the solution to the given inequality.

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Therefore , the solution of the given problem of equation comes out to be another point on the line would be (3, 110).

In arithmetic equations, the identical sign (=) is used to denote the equivalence of two assertions. It is demonstrated that using mathematical methods, which have acted as manifestations of reality, it is feasible to compare different numerical factors. For fact, the equal sign splits the number 12 into two separate parts, even if the answer is y + 6 = 12. It is possible to determine how many letters are also present on either end of this character.

Here,

The equation for the total cost of a party at this venue for p people is:

C = 20p + 70

To graph this equation, you can plot two points and draw a line passing through them.

One point can be the y-intercept (0, 70), which represents the fixed event fee charged by the venue.

The second point can be any other point on the line. For example, when there are 3 people at the party, the total cost would be:

C = 20(3) + 70 = 110

So another point on the line would be (3, 110). Plotting these two points and drawing a line passing through them will give you the graph of the total cost as a function of the number of people at the party.

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The value of the varaible 'x' will be 4. And the value of the varaible 'y' will be 7.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.

a) The equation is given as,

4 / 8 = 3 / (y - 1)

1/2 = 3 / (y - 1)

y - 1 = 6

y = 7

b) The equation is given as,

5 / (7 + 2x) = 2 / (x + 2)

5(x + 2) = 2(7 + 2x)

5x + 10 = 14 + 4x

5x - 4x = 14 - 10

x = 4

The value of the varaible 'x' will be 4. And the value of the varaible 'y' will be 7.

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Answer:

2x² - 3x + 1

Step-by-step explanation:

x - 2 | 2x³ - 7x² + 7x - 2

    --   2x³ - 4x²                  <== 2x²

                - 3x² + 7x - 2

          --    - 3x² + 6x          <== -3x

                              x - 2

                     --       x - 2      <==  1    

                                   0 |  2x² - 3x + 1

Thus, the quotient is 2x² - 3x + 1

Answer:

Hello! :)

Answer:

Solved using long polynomial division: [tex]2x^{2} -3x + 1[/tex]

Solved using polynomial division: (2x-1)(x-1)

Sorry I was in a hurry and didn't type out the whole step-by-step.

The solution is Option C.

The value of the quadratic equation is 5x² + 2x = 7

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

5x² + 2x = 7  

On simplifying the equation , we get

Subtracting 7 on both sides of the equation , we get

5x² + 2x - 7 = 0   be equation (1)

Now , the roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

Substituting the values in the equation , we get

x = [ -2 ± √ ( 4 - 4 ( 5 ) ( -7 ) ] / 10

x = [ -2 ± √ ( 144 ) ] / 10

x = ( -2 ± 12 ) / 10

So , the two roots of the equation are

x = ( -2 + 12 ) / 10

x = 10/10 = 1

And , x = ( -2 - 12 ) / 10

x = -14/10

x = -7/5

Hence , the roots of the quadratic equation are 1 and -7/5

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By using the relationship between quantities, the missing values in the table are:

A = 750

B = 1,250.

In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be represented by this mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the data points contained in this 2-column table as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 250/1

Therefore, a linear equation for this proportional relationship can be correctly written as follows:

y = kx

y = 250x

When x = 3, the value of A is given by:

y = 250(3) = 750.

When x = 5, the value of A is given by:

y = 250(5) = 1,250.

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The value of x rounded to one decimal place is 176. 0 units

Using the trigonometric identity, sine, let's find the value of the hypotenuse for the smaller triangle, we have;

sin 60 = 88/x

find the value of sin 60

0. 8660x = 88

Divide both sides by 0. 8660

x = 101. 62

Then to determine the value of x, we have;;

tan 30 = 101.62/x

Find the value of the trigonometric identity, we have;

0. 5774x = 101. 62

divide both sides by the coefficient of x

x = 101. 62/0. 5774

divide the values

x = 175. 99 units

Hence, the value is 176. 0 units

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The data are discrete because the data can only take on specific values, So correct option is B.

Discrete data refers to data that can only take on specific, separate values. It is a type of data that can be counted or enumerated, but not measured. In other words, the values can't be expressed as fractions or decimals between two whole numbers. Some examples of discrete data include the number of siblings in a family, the number of pets owned by an individual, and the number of correct answers on a test. Discrete data is distinct from continuous data, which can take on any value within a certain range.

The data are discrete because the data can only take on specific values (e.g. a time of 20 minutes, 21 minutes, 22 minutes, etc.). They cannot take on any value in an interval, such as 20.5 minutes. Discrete data represent a countable number of values, while continuous data can take on any value within a given range.

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The length of the rectangular patio is 57 ft.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Given is that the perimeter of a rectangular patio is 204 feet and the width of the patio is 45 feet.

We can write -

2(L + B) = 204

L + B = 102

L = 102 - 45

L = 57

Therefore, the length of the rectangular patio is 57 ft.

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{Question in english -

The perimeter of a rectangular patio is 204 feet if the width of the patio is 45 feet what is the length of the patio}

Answer:

The area of the region inside both the square and the rectangle is 37 square units.

Step-by-step explanation:

The area of the region inside both the square and the rectangle can be found by subtracting the areas of the four triangles outside the square from the area of the rectangle.

The area of the rectangle is 4 * 8 = 32 square units. The area of each triangle can be found using the formula for the area of a triangle, which is (base * height) / 2. The base of each triangle is half the length of the side of the square, which is 5 / 2 = 2.5 units. The height of each triangle is the difference in height between the rectangle and the square, which is 4 - 5 = -1 unit. The area of each triangle is (2.5 * -1) / 2 = -1.25 square units. The area of the four triangles outside the square is 4 * -1.25 = -5 square units.

The area of the region inside both the square and the rectangle is 32 + 5 = 37 square units.

The amount of money you get paid if  the coin comes up heads 3 times is $12.

You flip a coin 3 times,

If you get o heads then $0

If you get 1 heads then $2

If you get 2 heads then $ 4

So if you toss the coin 3 times and 3 heads come up then

1 heads = $2

2 heads = $ 4

3 heads = $ 6

So , amount of money you get paid if  the coin comes up heads 3 times is $12.

The probability function that X will have a value less than or equal to x is known as the Cumulative Distribution Function (CDF) of a real-valued random variable X, assessed at x. It is employed to describe a table's random variables' probability distribution. And with this data, we can quickly make a CDF graphic on an Excel spreadsheet.

So, CDF determines the cumulative probability for the specified value.

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The required cost of carpet is $1,148.

Hence option (c) is correct.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

Cost of carpet of dimension 10 ft x 6 ft = $1230

Then cost of carpet of area 60 ft² = $1230

The cost of carpet per unit area = 1230/60

                                                      = $20.5

Area of carpet 7 ft x 8 ft =  56 ft²

Then the cost of this carpet

= 56x20.5

= 1,148

Therefore, the cost of carpet of dimension 7 ft x 8 ft = $1,148

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The quotient of 47.61 and 15.87 has the result given as follows:

47,61 : 15,87 = 3.

The operation for this problem is defined as follows:

47,61 : 15,87 =

The : symbol means that the operation is a division, that is, we must obtain the quotient of dividing 47.61 by 15.87.

Using a calculator, we have that 47.61 is three times 15.87, hence the result of the quotient is given as follows:

47,61 : 15,87 = 3.

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Answer: Yes at x = 2.

Step-by-step explanation: There are two ways to do it. Graph the function or solve it. Since im on a computer solving would be easiest for me to explain. To find a point where the two lines meet, you should set the two equations equal to each other. When you solve by subtracting 1/2x on both sides, the result is 3/2x = 3. This means that x=2. When you graph you should see that when x =2 the answer is right.

Answer: 678.58

Step-by-step explanation:

Answer:

84.8 squared centimeters

Step-by-step explanation:

You know the height is 8 cm

You know one of the bases has a length of 15.5 cm

You know one of the bases has a length of 5.7 cm

Formula to find a trapezoid:

[tex]\frac{b_{1}+b_{2}}{2}[/tex]×h

so...

substitute!!!!!

the matrix equation for the given vector equation is:

[tex][ [5 0] [5 2] [-3 3] [4 -2] ] [z_1, z_2, z_3, z_4]^T = [-3 19]^T[/tex]

An equation of the form Av = b, in which A is a m by n matrix known as the coefficient matrix, v is a n by 1 column vector, and b is a m by 1 column vector, is known as a matrix equation (also known as a matrix-vector equation).

Given the vector equation:

[tex]z_1 [5 0] + z_2 [5 2] + z_3 [-3 3] + z_4 [4 -2] = [-3 19][/tex]

We can write this as a matrix equation by defining a matrix A and a vector x, such that:

A = [ [5 0]

[5 2]

[-3 3]

[4 -2] ]

[tex]x = [z_1, z_2, z_3, z_4]^T[/tex]

The vector equation then becomes:

[tex]Ax = [-3 19]^T[/tex]

So the matrix equation for the given vector equation is:

[tex][ [5 0] [5 2] [-3 3] [4 -2] ] [z_1, z_2, z_3, z_4]^T = [-3 19]^T[/tex]

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The value of cot(θ - π/2) is 1.52.

What are trigonometry ratios?

The trigonometric functions in mathematics are real functions that relate the right-angled triangle's angle to the ratios of its two side lengths. They are extensively used in all fields of geometry-related science, including geodesy, solid mechanics, celestial mechanics, and many others.

There are six trigonometric ratios used in trigonometry: sine, cosine, tangent, secant, and cotangent. The abbreviations for these ratios are sin, cos, tan, sec, cosec(or csc), and cot. Look at the below-displayed right-angled triangle. Any two of the three sides of a right-angled triangle can be compared in terms of their respective angles using trigonometric ratios.

Given that tan θ = -1.52.

The given expression is

cot(θ - π/2)

= - cot(π/2 - θ)

Now applying the trigonometry identity cot(π/2 - θ) = tan θ:

= - tan θ

Now putting the value of tan θ = -1.52:

= - (-1.52)

= 1.52

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Dan spent 1.25 at each table.

The formula used to solve this problem is m = 16 - 6/8. The calculation is as follows: 16 is the total amount of money Dan spent, 6 is the admission fee, and 8 is the number of tables. The equation is set up to find the amount of money Dan spent at each table. Taking the total amount of money spent, 16, and subtracting the admission fee, 6, leaves us with 10. We then divide this amount, 10, by the number of tables, 8, to find the amount of money spent at each table, which is 1.25. Therefore, Dan spent 1.25 at each table.

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