Find the value of c such that the expression is a​ perfect-square trinomial.
k^2 -3k+c
k^2 -3k+c=k^2 -3k+__ ​(Type an integer or a simplified​ fraction.)

The centerline for the control chart will be 0.135.

The centerline of a control chart is the horizontal line that represents the process mean, which is calculated as the average of the sample means.

In this case, we can calculate the sample means by multiplying the sample size n by the sample proportion p for each sample and then summing these values across all samples. We can then divide this sum by the total sample size (4*180) to get the overall sample mean.

The calculations are shown below:

Sample 1 mean = n1 * p1 = 180 * 0.133 = 23.94

Sample 2 mean = n2 * p2 = 180 * 0.156 = 28.08

Sample 3 mean = n3 * p3 = 180 * 0.117 = 21.06

Sample 4 mean = n4 * p4 = 180 * 0.144 = 25.92

Overall sample mean = (23.94 + 28.08 + 21.06 + 25.92) / (4*180) = 0.135

Therefore, the centerline for the control chart would be 0.135.

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Applying the rule of  angle of intersecting chord, the value of arc AC is

The measure of arc AC is done using the concept of 2 chords intersecting inside a circle this results to the formula

angle x = 1/2 (measure of arc AC + measure of arc BD)

Solving for measure of arc AC

2 * angle x = measure of arc AC + measure of arc BD

measure of arc AC = 2 * angle x - measure of arc BD

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The granite countertop would cost $783.00.

Finding the cost of granite:

To find the cost of granite find the amount of granite that can be used for the entire kitchen.  

Since the kitchen floor is in a rectangle shape find the area of the kitchen floor using the area of a rectangle. Which will equal the amount of granite used for the kitchen.  

Use the formula for the cost of the countertop, which is the product of the area, and the cost per square meter, to determine the total cost.

Here we have

A counter in Adriana's kitchen is 1 m wide and 3 m long.

Hence, the area of the countertop can be found by multiplying the length and the width:

Area of kitchen = length x width = 3 m x 1 m = 3 m²

The cost of the granite is given by $ 261.00 per square meter

The cost of the granite countertop will equal the product of the area and the cost per square meter:

Total Cost = 3 m² x $261.00/m² = $783.00

Therefore,

The granite countertop would cost $783.00.

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Rounding to the nearest degree, the angle of depression from the airplane to the airport is 22 degrees.

What is the angles of depression from the airplane to the airport ?

We can see that the angle of depression is the angle between the horizontal ground and the line of sight from the airplane to the airport.

Using the tangent function, we have:

tan(θ) = opposite / adjacent

where opposite = height of airplane = 3 miles, and adjacent = distance from airplane to airport = 7.5 miles.

So, tan(θ) = 3 / 7.5

Taking the inverse tangent of both sides, we get:

θ = tan⁻¹(3 / 7.5) ≈ 22 degrees

Therefore, the angle of depression from the airplane to the airport is approximately 22 degrees (rounded to the nearest degree).

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Answer: x = 40 degrees and y = 80 degrees

Step-by-step explanation: Using the fact that the sum of the interior angles of a triangle is 180 degrees, we can find that x = 40 degrees in the triangle on the left. For the polygon on the right, we can use the fact that the sum of the interior angles of a quadrilateral is 360 degrees to find that y = 80 degrees.

Therefore, x = 40 degrees and y = 80 degrees.

The polynomial identity created from the columns is (x - y)(x^2 + 2xy + y^2) + (x + y)(x^2 - 2xy + y^2) = 2x^3 - 2xy^2

Introducing the new polynomial identity:

(x - y)(x^2 + 2xy + y^2) + (x + y)(x^2 - 2xy + y^2) = 2x^3 - 2xy^2

Algebraic proof:

Expanding the left side of the equation:

(x^3 - xy^2 + 2x^2y + xy^2 + y^3) + (x^3 + xy^2 - 2x^2y + xy^2 + y^3)

= 2x^3 + 2y^3

Simplifying the left side of the equation:

2x^3 - 2xy^2 = 2x^3 - 2xy^2

Therefore, the polynomial identity is true.

Numerical proof:

Let x = 2 and y = 3.

(x - y)(x^2 + 2xy + y^2) + (x + y)(x^2 - 2xy + y^2) = 2x^3 - 2xy^2

(2 -3y)(2^2 + 2(2)(3) + (3)^2) + (2 + 3)(2^2 - 2(2)(3) + 3^2) = 2(2)^3 - 2(2)(3)^2

-20 = -20

Therefore, the numerical proof also shows that the polynomial identity is true.

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Invest in our new polynomial identity today! With this identity, you can simplify complex polynomial expressions and solve equations in a much easier and quicker way.

Say goodbye to tedious algebraic manipulations and hello to the future of polynomial algebra!

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The value of x is 10, and the measure of the two angles with x is 50°

We can see that the two angles in the image are vertical angles, so their measure is the same, then we can write:

5x = 7x - 20

Solving the linear equation we get.

20 = 7x - 5x

20 = 2x

20/2 = x

10 = x

That is the value of x.

The measures of the two angles are:

5x = 5*10  =50 degrees.

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Answer: Let x be the number of race entries. In order to raise at least $55,000, we must have 45x + 17,900 ≥ 55,000 −45x ≥ −37,100 x ≤ -37,100/45 x ≤ 824.44 Therefore, the charity needs 824 or more race entries to raise at least $55,000.

In the given angles X is 73 degrees, Y is 107 degrees, and Z will be 73 degrees respectively according to the given figure.

In plane geometry, an angle is a shape made up of two rays or lines with the same terminal.

The vertex, or identical termination of the two rays, is referred to as an angle's sides.

Since we lack a measurement for angular rotation, the angle is a valuable tool for measuring angular distance.

For instance, a meter or an inch is a unit of measurement for linear motion.

So, one is 107° given the four angles.

in the opposite vertical angle:

y = 107°

Since x and z are vertically opposing angles, both will have the same value.

So,

x = z = n

The total angle will now equal 360°.

107 + x + z + y = 360

107 + 2n + 107 = 360

2n = 146 ⇒ n = 73°

Therefore, In the given angles X is 73 degrees, Y is 107 degrees, and Z will be 73 degrees respectively according to the given figure.

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The mean for grouped data can be calculated when data has been grouped into class intervals in a frequency distribution. (Option A)

When data has been grouped into class intervals, it is not possible to calculate the exact mean of the data. Instead, we use the midpoint of each class interval as a representative value for that interval. Then, we calculate the weighted average of these midpoints to find the mean for grouped data.

Options C and D, the variance and standard deviation, respectively, cannot be directly computed from grouped data. However, we can estimate them using the assumed normal distribution of the data within each class interval and the mean for grouped data.

Therefore, the correct answer is option A: the mean for grouped data can be calculated when data has been grouped into class intervals in a frequency distribution.

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Answer:

The corresponding sides:

[tex]NO[/tex]≅[tex]ZW[/tex]

[tex]PM[/tex]≅[tex]XY[/tex]

[tex]MN[/tex]≅[tex]YZ[/tex]

[tex]OP[/tex]≅[tex]WX[/tex]

The corresponding angles:

[tex]< M[/tex]≅[tex]< Y[/tex]

[tex]< P[/tex]≅[tex]< X[/tex]

[tex]< O[/tex]≅[tex]< W[/tex]

[tex]< N[/tex]≅[tex]< Z[/tex]

the correct answer is A.

5,220,000 songs were downloaded in the year 2020.

The interpretation of s(2020) = 5,220,000 is "5,220,000 songs were downloaded in the year 2020".

Therefore, the correct answer is A. 5,220,000 songs were downloaded in the year 2020.

Interpretation refers to the process of explaining or giving meaning to information, data, or phenomena. It involves analyzing and making sense of information to draw conclusions or make decisions based on the findings.

Interpretation can involve subjective judgment and may depend on the perspective, assumptions, or biases of the interpreter.

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The 3 trigonometric ratios of the right triangle with respect to angle A are as follows:

sin A = 12 / 13

cos A = 5 / 13

tan A = 12 / 5

The side of a right angle triangle can be found using trigonometric ratios as follows:

Therefore, let's find the 3 trigonometric ratios with respect to angle A.

sin A = opposite / hypotenuse

sin A =  36 / 39

sin A = 12 / 13

cos A = adjacent  / hypotenuse

cos A = 15 / 39

cos A = 5 / 13

tan A = opposite / adjacent

tan A = 36 / 15

tan A = 12 / 5

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the function f(x) in vertex form that shifts left 10 units is f(x) = (x - 0)² - 5, where the vertex is at (0, -5) and the parabola opens upwards

How to solve the question?

To write the function f(x)=x² + 5 in vertex form that shifts left 10 units, we can use the completing the square method.

First, we can factor out the coefficient of x², which is 1, and rewrite the function as f(x) = 1(x²) + 0x + 5. Then, we can add and subtract a constant term inside the parentheses that will allow us to complete the square.

f(x) = 1(x² - 0x + 0) + 5

f(x) = 1(x² - 2(0)(x) + 0² - 0²) + 5 (adding and subtracting 0)

f(x) = 1(x² - 2(0)(x) + 0² - 0² + 10 - 10) + 5 (adding and subtracting 10)

f(x) = 1[(x - 0)² - 10] + 5

Simplifying this expression, we get:

f(x) = (x - 0)² - 10 + 5

f(x) = (x - 0)² - 5

Therefore, the function f(x) in vertex form that shifts left 10 units is f(x) = (x - 0)² - 5, where the vertex is at (0, -5) and the parabola opens upwards. The shift to the left is achieved by subtracting 10 inside the parentheses, and the constant term outside the parentheses is adjusted accordingly to maintain the same value of the function at x=0.

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The length of each segment is:

YW = 5 units

WZ = 8 units

The length of each segment can be found by using "bisector of an angle in a triangle theorem".

The theorem states that "the bisector of an angle in a triangle theorem divides the opposite sides in the ratio of the sides containing the angle".

Applying the theorem on the given triangle, we can say:

XY/XZ = YW/WZ

8/12.8 = (t/2)/(t-2)

8(t-2) = 12.8(t/2)

8t - 16 = 6.4t

8t - 6.4t = 16

1.6t = 16

t = 10

YW = t/2

YW = 10/2

YW = 5 units

WZ = t - 2

WZ = 10 - 2

WZ = 8 units

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To solve this problem, we can use the binomial probability distribution. Let's define a "success" as scoring a goal and a "failure" as missing a goal.

Then, each attempt by Sky can be considered a Bernoulli trial with probability of success p = 1/2.

Let X be the number of goals that Sky scores in five attempts. Then, X follows a binomial distribution with parameters n = 5 and p = 1/2.

To find the probability that Sky scores at least two goals, we need to calculate the probability of the following events:

P(X ≥ 2) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

We can use the binomial probability formula to calculate these probabilities:

P(X = k) = (n choose k) * [tex]p^k[/tex] *[tex](1-p)^(n-k)[/tex]

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n distinct items.

Using this formula, we get:

P(X = 2) = (5 choose 2) * [tex](1/2)^2[/tex] * [tex](1/2)^3[/tex] = 10/32

P(X = 3) = (5 choose 3) * [tex](1/2)^3[/tex] * [tex](1/2)^2[/tex] = 10/32

P(X = 4) = (5 choose 4) * [tex](1/2)^4[/tex] *[tex](1/2)^1[/tex] = 5/32

P(X = 5) = (5 choose 5) * [tex](1/2)^5[/tex] * [tex](1/2)^0[/tex] = 1/32

Therefore, the probability that Sky scores at least two goals is:

P(X ≥ 2) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = (10 + 10 + 5 + 1)/32 = 26/32 = 13/16

So the probability that Sky scored at least two goals is 13/16.

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The total probability of scoring 1 goal is 5 * (1/32) = 5/32.Now we find the complementary probability:1 - (Probability of 0 goals + Probability of 1 goal) = 1 - (1/32 + 5/32) = 1 - 6/32 = 26/32.

Sky attempted to score a goal five times. For each attempt, she was equally likely to make a goal or miss. So the probability that Sky scored at least two goals is 13/16.

To find the probability that Sky scored at least two goals, we can use complementary probability, which means finding the probability that she scored fewer than two goals (either 0 or 1 goal) and subtracting that from 1.1.

Probability of scoring 0 goals: Since there are 5 attempts and she is equally likely to make a goal or miss (1/2 chance for each), the probability of missing all 5 is (1/2)^5 = 1/32.2.

Probability of scoring 1 goal: Sky could score in any of the 5 attempts, so we need to consider all possible ways of scoring one goal.

There are 5 ways (score in the 1st, 2nd, 3rd, 4th, or 5th attempt). The probability for each of these scenarios is (1/2)^5 = 1/32.

Therefore, the total probability of scoring 1 goal is 5 * (1/32) = 5/32.Now we find the complementary probability:1 - (Probability of 0 goals + Probability of 1 goal) = 1 - (1/32 + 5/32) = 1 - 6/32 = 26/32.

To express this as a common fraction, we can simplify it by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2:26/32 = (26/2) / (32/2) = 13/16So the probability that Sky scored at least two goals is 13/16.

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Point A = (5,4). If you rotated A 90 degrees about the point (2,-1), the coordinates of A' is (-1,2).

Rotation is the process of rotating an object or a point around a fixed point or axis. In mathematics, rotation refers to a transformation that preserves the size and shape of an object while changing its orientation. It is a basic geometric transformation that is used in various fields, including mathematics, physics, engineering, and computer graphics.

In a two-dimensional space, a rotation is typically described by an angle of rotation and a fixed point, which is known as the center of rotation. The angle of rotation represents the amount by which the object is rotated, while the center of rotation is the point around which the object is rotated. In a three-dimensional space, a rotation is described by an axis of rotation and an angle of rotation.

To rotate point A 90 degrees counterclockwise about the point (2,-1), we can use the following formula:

A' = (x', y') = (a + (x - a) cosθ - (y - b) sinθ, b + (x - a) sinθ + (y - b) cosθ)

where (a,b) is the center of rotation and θ is the angle of rotation (90 degrees in this case).

Substituting the given values, we get:

a = 2, b = -1, x = 5, y = 4, θ = 90 degrees

x' = 2 + (5 - 2) cos(90) - (4 + 1) sin(90) = 2 - 3 = -1

y' = -1 + (5 - 2) sin(90) + (4 + 1) cos(90) = -1 + 3 = 2

Therefore, the coordinates of A' are (-1, 2).

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Answer:

The circumference of a circle is given by the formula:

C = πd

where C is the circumference, d is the diameter, and π is a mathematical constant approximately equal to 3.14.

In this case, the diameter of the circle is given as 12.5 cm.

Substituting this value into the formula, we get:

C = π(12.5)

C = 39.25 cm

Therefore, the circumference of the circle is 39.25 cm.

Hence, the answer is 39.25 cm.

Answer: Exact Form (simplify form):

8/125

Decimal Form:

0.064

Step-by-step explanation:

The parameter of interest in this scenario is the proportion of students in the school who think of their parents or guardians as "strict".

Focussing on the strict guardians  is a population parameter, but since it is impractical to survey all 1000 students in the school, the students plan to obtain data from a sample of students.

To estimate this population proportion, the students could use the sample proportion as a statistic. They can randomly select a sample of students from the school and ask them if they consider their parents or guardians as "strict". The proportion of students in the sample who say "yes" can be used as an estimate of the proportion of all students in the school who consider their parents or guardians as "strict". The sample proportion is a statistic that provides an estimate of the population parameter of interest.

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The amount Joanna spent on renting the bike is $17.50 (option A).

The term "amount" can refer to a quantity or a numerical value of something. In essence, the term "amount" refers to a specific quantity or number of something.

The regular cost of renting a bike on Friday is $7, but Joanna only paid half that amount, which is $7/2 = $3.50.

Let's call the regular cost of renting a bike on Saturday "x". Then, according to the problem, Joanna paid $4 less than twice the regular cost of renting a bike on weekdays, which can be written as:

Cost on Saturday = 2($7) - $4 = $10

We know that Joanna paid $10 for renting the bike on Saturday, so we can solve for x in the equation:

Cost on Saturday = x - $4

$10 = x - $4

x = $14

So the regular cost of renting a bike on Saturday is $14.

Therefore, the total amount Joanna spent on renting the bike is:

$3.50 (for Friday) + $14 (for Saturday) = $17.50

Answer: The amount Joanna spent on renting the bike is $17.50 (option A).

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Answer:The solution is x= +6, -6.

Step-by-step explanation:

What is Quadratic equation?

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

The first condition for an equation to be a quadratic equation is the coefficient of x2 is a non-zero term(a ≠ 0). For writing a quadratic equation in standard form, the x2 term is written first, followed by the x term, and finally, the constant term is written.

Roots of a Quadratic Equation

The roots of a quadratic equation are the two values of x, which are obtained by solving the quadratic equation. These roots of the quadratic equation are also called the zeros of the equation.

Given:

x² - 36 =0

x² = 36

x= √36

x= ±6

hence, the solution is x= +6, -6.

The measures of variation show how data is spread out or dispersed and include range, variance, standard deviation, IQR, percentiles, and coefficient of variation.

The measures of variation show how data is spread out or dispersed from its average or central tendency. Measures of variation give information on the diversity, range, and distribution of the data. They include the following things-

By assaying the measures of variation, we can gain perceptivity into the nature and characteristics of the data and draw conclusions grounded on the degree of variation present.

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Answer: 213.75

Step-by-step explanation:

Add a zero to the hundredths place of 345.5 making it 345.50, then subtract as you would normally.

Organizational skills

Organizational skills and the ability to communicate effectively are crucial for a systems analyst who needs to work with individuals at all levels of an organization, manage conflicting user needs, and ensure that information is communicated clearly and efficiently. Interpersonal skills are important to a systems analyst who must work with people at all organizational levels, balance conflicting needs of users, and communicate effectively. The knowledge and skills in leadership and strategic management are essential for the creation and achievement of an organizational vision and strategy. These skills include effective communication, decision-making, and the ability to evaluate and measure success, as well as a deep understanding of the organization and its environment. Leadership and strategic management play a crucial role in the success of any organization. A strong and effective leader with a well-developed understanding of strategic management is essential for the creation and achievement of an organizational vision and strategy.

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Answer:

3.14×10.1×10.1

3.14×102.01

320.311

=320.300