Identify the roots of the quadratic function. What is the product when the roots are multiplied?

a. The probability that a student makes more than $30,000 is 0.0668.

b. The probability that a student makes between $27,000 and $32,000 is 0.9545.

c. The probability that a student makes less than $23,150 is 0.0062.

Probability is the likelihood that something will occur. When we don't know how an occurrence will turn out, we can discuss the likelihood or likelihood of various events. Statistics is the study of occurrences that follow a chance distribution.

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Answer:

Below

Step-by-step explanation:

See Venn diagram below :

Answer:

Representation B does not show the amount of time Kaleigh spent watching TV at this rate. Representation B only shows the total time she would have spent based on the number of episodes watched, assuming each episode is 30 minutes long. It does not take into account the actual time it took for Kaleigh to watch the episodes, which may have varied depending on how quickly she watched them.

Step-by-step explanation:

In response to the supplied query, we may state that Therefore, the Pythagorean theorem length of the hypotenuse is approximately 25.5 inches.

The Pythagorean Theorem, often known as the Pythagorean Theorem, is the fundamental Euclidean geometry relationship between the three sides of a right triangle. The area of a square with the hypotenuse side equals the sum of the areas of squares with the other two sides, according to this rule. The Pythagorean Theorem says that the square that spans a right triangle's hypotenuse opposite the right angle equals the sum of the squares that span its sides. It is sometimes written as the general algebraic notation a2 + b2 = c2.  

The Pythagorean theorem may be used to calculate the hypotenuse's length. According to the Pythagorean theorem, the square of the length of the hypotenuse (c) in a right triangle equals the sum of the squares of the lengths of the legs (a and b):

[tex]c^2 = a^2 + b^2[/tex]

[tex]c^2 = 19^2 + 17^2\\c^2 = 361 + 289\\c^2 = 650\\c =\sqrt(650)\\c = 25.5\\c = 25.5 inches[/tex]

Therefore, the length of the hypotenuse is approximately 25.5 inches.

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By algebra properties, the factor form of polynomials are listed below:

In this problem we need to factor 13 cases of polynomials, whose results must be derived by algebra properties. The factor form of the polynomial is:

Case 1:

a² - b²

(a + b) · (a - b)

Case 2:

a³ + b³

(a + b) · (a² - a · b + b²)

Case 3:

a³ - b³

(a - b) · (a² + a · b + b²)

Case 4:

x⁴ - 36

(x² + 6) · (x² - 6)

(x² + 6) · (x + √6) · (x - √6)

Case 5:

64 · c³ + 1

(4 · c + 1) · (16 · c² - 4 · c + 1)

Case 6:

k³ - 27

(k - 3) · (k² + 3 · k + 9)

Case 7:

54 · x³ + 250 · y³

(∛54 · x + ∛250 · y) · [(∛54 · x)² - (∛54 · x) · (∛250 · y) + (∛250 · y)²]

Case 8:

3 · m⁴ - 48 · n²

(√3 · m² - 4√3 · n) · (√3 · m² + 4√3 · n)

3 · (m² - 4 · n) · (m² + 4 · n)

3 · (m - 2 · √n) · (m + 2 · √n) · (m² + 4 · n)

Case 9:

a⁷ · b² - a · b²

a · b² · (a⁶ - 1)

a · b² · (a³ + 1) · (a³ - 1)

a · b² · (a + 1) · (a² - a + 1) · (a - 1) · (a² + a + 1)

Case 10:

x³ · y² - 343 · y⁵

y² · (x³ - 343 · y³)

y² · (x - 7 · y) · (x² + 7 · x · y + 49 · y²)

Case 11:

9 · y⁷ - 144 · y

y · (9 · y⁶ - 144)

y · (3 · y³ - 12) · (3 · y³ + 12)

9 · y · (y³ - 4) · (y³ + 4)

9 · y · (y - ∛4) · [y² + ∛4 · y + (∛4)²] · (y + ∛4) · [y² - ∛4 · y + (∛4)²]

Case 12:

w² - 13 · w + 36

(w - 4) · (w - 9)

Case 13:

p³ + 5 · p² - 84 · p

p · (p² + 5 · p - 84)

p · (p + 12) · (p - 7)

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Answer:

Step-by-step explanation:

The slope is 2 so rise / run = 2 / 1, or up two right one.

The volume of the figure is 144 cubic inches.

The volume of an object is the three dimensional space that it fills up. Since there are different shapes, thus their volume can be expressed with different equations.

In the given shape, divide it into two cuboid so that;

volume of a cuboid = length*width*height

volume of cuboid 1 = 12 * 2* 4

                               = 96

volume of cuboid 1 is 96 cubic inches.

volume of cuboid 2 = 12*4*1

                                = 48

Volume of the figure = 96 + 48

                              = 144 cubic inches

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Yes, Tanner has enough spray paint for his arrow.

What is an Area?

The amount of space occupied by a flat (2-D) surface or an object's shape is known as its area. A planar figure's area is the area that its perimeter encloses. The quantity of unit squares that completely encircle the surface of a closed figure is its area. Square measurements for area include cm2 and m2.

Given : paint available in can = 12 ft²

We know that the arrow is comprised of a triangle and a rectangle.

So, the area of given arrow = area of rectangle + area of triangle

Now, area of triangle = 1/2 ×base × height

                                   = 1/2 × 3 × (6 - 5 1/3)

                                   = 3/2 × ( 6 - 16/3)

                                   = 3/2 × ( 18-16)/3

                                   = 3/2 × 2/3

                                    = 1 ft²

Similarly, area of rectangle =  length × breadth

                                            = 5 1/3 × 2

                                            = 16/3 × 2

                                            = 32/3 ft²

Hence, area of arrow = area of triangle +area of rectangle

                                   = 1 + 32/3

                                   = 35/3 ft²

                                   = 11.67 ft²

So, he has sufficient paint to cover the arrow.

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Answer:

area = (1/2) · (p + q) · h

Step-by-step explanation:

The given conditions imposed on the variables \( a, b, c, d \) and \( x \) are:

To determine if the statements in Exercises 1-12 are true or false, use the given conditions to evaluate the expressions in the statement. If the statement matches the conditions, it is true; if it does not, it is false. For example, if the statement is: " \( a + b = d \) ", then this is false, as \( a + b \neq d \).

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Mika's estimate was 216 and the actual sum of the numbers is 216.27. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

All real numbers are supposed to be explicable by the four fundamental operations, often known as "arithmetic operations". Quotient, product, sum, and difference are the four operations in mathematics that follow division, multiplication, addition, and subtraction.

We are given numbers as 189.27, 15.8 and 11.2.

Mika's estimate is as follows:

189 + 16 + 11 = 216

Actual sum of numbers is as follows:

189.27 + 15.8 + 11.2 = 216.27

Hence, Mika's estimate was 216 and the actual sum of the numbers is 216.27.

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The mechanic must mix 12 gallons of a 40% antifreeze solution with 4 gallons of an 80% antifreeze solution to create 16 gallons of a 50% antifreeze solution.

To find out how much of a 40% antifreeze solution must be mixed with an 80% antifreeze solution to create 16 gallons of a 50% antifreeze solution, we can use the following equation:

40% x + 80% y = 50% (16)

Where x is the amount of 40% antifreeze solution and y is the amount of 80% antifreeze solution.

We can also use the fact that the total amount of solution must equal 16 gallons:

x + y = 16

Now we can solve for one variable in terms of the other. Let's solve for x in the second equation:

x = 16 - y

And substitute this value of x into the first equation:

40% (16 - y) + 80% y = 50% (16)

Simplifying:

[tex]6.4 - 0.4y + 0.8y = 8[/tex]

0.4y = 1.6

y = 4

Now we can substitute this value of y back into the equation for x:

x = 16 - 4

x = 12

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Yes, Tanner has enough spray paint for his arrow.

What is an Area?

The amount of space occupied by a flat (2-D) surface or an object's shape is known as its area. A planar figure's area is the area that its perimeter encloses. The quantity of unit squares that completely encircle the surface of a closed figure is its area. Square measurements for area include cm2 and m2.

Given : paint available in can = 12 ft²

We know that the arrow is comprised of a triangle and a rectangle.

So, the area of given arrow = area of rectangle + area of triangle

Now, area of triangle = 1/2 ×base × height

                                    = 1/2 × 3 × (6 - 5 1/3)

                                    = 3/2 × ( 6 - 16/3)

                                    = 3/2 × ( 18-16)/3

                                    = 3/2 × 2/3

                                    = 1 ft²

Similarly, area of rectangle =  length × breadth

                                             = 5 1/3 × 2

                                             = 16/3 × 2

                                             = 32/3 ft²

Hence, area of arrow = area of triangle +area of rectangle

                                    = 1 + 32/3

                                    = 35/3 ft²

                                    = 11.67 ft²

So, he has sufficient paint to cover the arrow.

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The answers are:
a. \( \mathbf{v}=\overrightarrow{P Q} = (4, 4) \)
b. \( \|\mathbf{v}\| = 4\sqrt{2} \)
c. \( \overrightarrow{P Q}+\overrightarrow{Q P} = (0, 0) \)

The given points are point \( P \) be \( (-1,3) \) and point \( Q \) be \( (3,7) \).

a. To find \( \mathbf{v}=\overrightarrow{P Q} \), we subtract the coordinates of point \( P \) from the coordinates of point \( Q \):

\( \mathbf{v}=\overrightarrow{P Q} = (3-(-1), 7-3) = (4, 4) \)

b. To find \( \|\mathbf{v}\| \), we use the distance formula:

\( \|\mathbf{v}\| = \sqrt{(4-0)^2 + (4-0)^2} = \sqrt{16 + 16} = \sqrt{32} = 4\sqrt{2} \)

c. To find \( \overrightarrow{P Q}+\overrightarrow{Q P} \), we add the coordinates of \( \overrightarrow{P Q} \) and \( \overrightarrow{Q P} \):

\( \overrightarrow{P Q}+\overrightarrow{Q P} = (4, 4) + (-4, -4) = (0, 0) \)

Therefore, the answers are:

a. \( \mathbf{v}=\overrightarrow{P Q} = (4, 4) \)

b. \( \|\mathbf{v}\| = 4\sqrt{2} \)

c. \( \overrightarrow{P Q}+\overrightarrow{Q P} = (0, 0) \)

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The average salary of 36 employee was 4650. Using historical data, we will assume that the population standard deviation is 165. The 98% confidence interval for the population mean salary is 4650±70.84. The correct answer is option c. 4650±70.84.

To find the 98% confidence interval for the population mean salary, we will use the formula:

CI = X ± Z* (σ/√n)

Where:
CI = Confidence Interval
X = Sample mean
Z = Z-score for the given confidence level
σ = Population standard deviation
n = Sample size

Plugging in the given values, we get:

CI = 4650 ± 2.33* (165/√36)

CI = 4650 ± 70.84

Therefore, the 98% confidence interval for the population mean salary is 4650±70.84. The correct answer is C.

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Answer:

The equation that represents a linear function is:

y equals one half times x minus 5

This is a linear equation because it has a constant rate of change, or slope, of one half. This means that for every increase of 1 in x, y will increase by 1/2. The equation is also in the standard form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.

The other equations are not linear functions:

x = 3 is a vertical line, which is not a function because it fails the vertical line test.

y equals three fourths times x squared is a quadratic function because it includes an x-squared term.

3x − 6 = 4 is a linear equation, but it is not in the standard form of y = mx + b. It can be rearranged to y = (3/1)x - 2, which is a linear equation in slope-intercept form.

The functions are continuous at all points except where the denominator of a fraction is equal to zero. This is because division by zero is undefined and causes a discontinuity in the function.

(a) f(x)=(9x^(2)-4)/(3x-2): This function is continuous everywhere except where 3x-2=0, which is when x=2/3. Therefore, the function is continuous at all points except x=2/3.

(b) f(x)=x2^(sinx): This function is continuous everywhere because there are no denominators that could equal zero.

(c) f(x)=sin(1)/(2x): This function is continuous everywhere except where 2x=0, which is when x=0. Therefore, the function is continuous at all points except x=0.

(d) f(x)={(x^(2)-1,x>3),(8,n=3),(2^(x),x<3):} This function is continuous for x>3 and x<3, but there is a discontinuity at x=3 because the function is not defined for x=3. Therefore, the function is continuous at all points except x=3.

In conclusion, the functions are continuous at all points except where the denominator of a fraction is equal to zero, causing a discontinuity. The functions are continuous at all other points.

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The continuity of a function can be determined by examining the values of the function at different points in its domain. If the function is continuous at a point, it means that the limit of the function as it approaches that point from both the left and the right is equal to the value of the function at that point. A function is continuous over an interval if it is continuous at every point in that interval.

(a) The function f(x)=(9x^(2)-4)/(3x-2) is continuous everywhere except at x = 2/3, where the denominator is equal to zero and the function is undefined.

(b) The function f(x)=x2^(sinx) is continuous everywhere. The exponential function 2^(sinx) is continuous for all values of x, and the product of two continuous functions is also continuous.

(c) The function f(x)=sin(1)/(2x) is continuous everywhere except at x = 0, where the denominator is equal to zero and the function is undefined.

(d) The function f(x)={(x^(2)-1,x>3),(8,n=3),(2^(x),x<3):} is continuous for x > 3 and x < 3, but it is not continuous at x = 3, where there is a jump discontinuity from 8 to 2^(3).

In conclusion, the functions are continuous at the following points:
(a) f(x)=(9x^(2)-4)/(3x-2): continuous everywhere except at x = 2/3
(b) f(x)=x2^(sinx): continuous everywhere
(c) f(x)=sin(1)/(2x): continuous everywhere except at x = 0
(d) f(x)={(x^(2)-1,x>3),(8,n=3),(2^(x),x<3):}: continuous for x > 3 and x < 3, but not continuous at x = 3

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Answer:

The discount on the skateboard is 12% of its original price, so the discounted price is:

Discounted price = $79.28 - 0.12($79.28) = $69.78

Now we need to calculate the sales tax on the discounted price. The sales tax rate is 8.25%, so the amount of sales tax is:

Sales tax = 0.0825($69.78) = $5.76

Adding the discounted price and the sales tax, we get the total cost of the skateboard:

Total cost = $69.78 + $5.76 = $75.54

Therefore, the total cost of the skateboard, including the discount and sales tax, is $75.54.

The simplified expressions are: (a) z = 1/4, (b) 3z^2, (c) -4z, and (d) 3z^2.

To simplify each expression by performing the indici, we need to follow the order of operations and combine like terms. Here are the steps for each expression:

(a) z + 3z = 1
First, we need to combine the like terms on the left side of the equation. Since both terms have the variable z, we can add them together:
4z = 1
Next, we need to solve for z by isolating the variable on one side of the equation. We can do this by dividing both sides of the equation by 4:
z = 1/4

(b) z * 3z
To simplify this expression, we just need to multiply the two terms together:
3z^2

(c) -z - 3z
To simplify this expression, we need to combine the like terms. Since both terms have the variable z, we can add them together:
-4z

(d) (-z)(-3z)
To simplify this expression, we just need to multiply the two terms together. Remember that a negative times a negative is a positive:
3z^2

So the simplified expressions are: (a) z = 1/4, (b) 3z^2, (c) -4z, and (d) 3z^2.

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equation is 4x + 3.25y

To maximize their profit, the coffee company needs to define the variables x and y, which represent the number of pounds of Columbian Supreme and Columbian Treat respectively. Then, the complete list of constraint inequalities can be written as:

Finally, the target (objective) equation is 4x + 3.25y, which represents the total profit from selling x pounds of Columbian Supreme and y pounds of Columbian Treat.

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Answer:

B

Step-by-step explanation:

The correct answer is Option C - Type 1 and Type 2. The power of a test is the probability of rejecting the null hypothesis when it is false; in other words, it is the probability of avoiding a type II error.

The power may also be thought of as the likelihood that a particular study will detect a deviation from the null hypothesis given that one exists. A Type 1 error occurs when a hypothesis test results in rejecting a true null hypothesis, and a Type 2 error occurs when a hypothesis test fails to reject a false null hypothesis.

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To prove that T is a linear transformation, we need to show that T(c~u + ~v) = cT(~u) + T(~v) for any scalar c and any vectors ~u and ~v in R2.

Let ~u = (u1, u2) and ~v = (v1, v2) be two vectors in R2 and let c be any scalar. Then,

T(c~u + ~v) = T(cu1 + v1, cu2 + v2) = (3(cu1 + v1) - 2(cu2 + v2), 2(cu2 + v2))

= (3cu1 + 3v1 - 2cu2 - 2v2, 2cu2 + 2v2)

= (3cu1 - 2cu2, 2cu2) + (3v1 - 2v2, 2v2)

= c(3u1 - 2u2, 2u2) + (3v1 - 2v2, 2v2)

= cT(~u) + T(~v)

Therefore, T is a linear transformation.

To find the standard matrix A of T, we can use the fact that T(~e1) and T(~e2) are the first and second columns of A, respectively, where ~e1 = (1, 0) and ~e2 = (0, 1) are the standard basis vectors of R2.

T(~e1) = T(1, 0) = (3(1) - 2(0), 2(0)) = (3, 0)

T(~e2) = T(0, 1) = (3(0) - 2(1), 2(1)) = (-2, 2)

Therefore, the standard matrix A of T is:

A = [ 3  -2 ]
     [ 0   2 ]

To determine if T is one-to-one, we can use the fact that a linear transformation is one-to-one if and only if its standard matrix A has linearly independent columns. In this case, the columns of A are linearly independent because they are not scalar multiples of each other. Therefore, T is one-to-one. Alternatively, we can use the fact that a linear transformation is one-to-one if and only if its standard matrix A has a nonzero determinant. In this case, the determinant of A is (3)(2) - (0)(-2) = 6, which is nonzero. Therefore, T is one-to-one.

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The associationA \mapsto g_{A} is an isomorphism between the space of m x n matrices with coefficients in K and the space of bilinear forms in Km x K​​​​​​​n.

The associationA \mapsto g_{A} is an isomorphism between the space of m x n matrices with coefficients in K and the space of bilinear forms in Km x K​​​​​​​n if it satisfies the following conditions:

1. It is a one-to-one correspondence, meaning that for every matrix A there is a unique bilinear form g_{A} and vice versa.
2. It preserves the structure of the spaces, meaning that the operations of addition and scalar multiplication are preserved.

To show that the associationA \mapsto g_{A} is a one-to-one correspondence, we can start by assuming that g_{A} = g_{B} for two matrices A and B. Then, for any vectors u \in Km and v \in K​​​​​​​n, we have:

g_{A}(u,v) = g_{B}(u,v)

A \cdot (u \otimes v) = B \cdot (u \otimes v)

(A - B) \cdot (u \otimes v) = 0

Since this is true for all u and v, we can conclude that A - B = 0, or A = B. This means that the associationA \mapsto g_{A} is a one-to-one correspondence.

To show that the associationA \mapsto g_{A} preserves the structure of the spaces, we can start by considering the addition of two matrices A and B and the scalar multiplication of a matrix A by a scalar c. Then, for any vectors u \in Km and v \in K​​​​​​​n, we have:

g_{A + B}(u,v) = (A + B) \cdot (u \otimes v) = A \cdot (u \otimes v) + B \cdot (u \otimes v) = g_{A}(u,v) + g_{B}(u,v)

g_{cA}(u,v) = (cA) \cdot (u \otimes v) = c(A \cdot (u \otimes v)) = c g_{A}(u,v)

This means that the associationA \mapsto g_{A} preserves the operations of addition and scalar multiplication.

Therefore, the associationA \mapsto g_{A} is an isomorphism between the space of m x n matrices with coefficients in K and the space of bilinear forms in Km x K​​​​​​​n.

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Answer:

Step-by-step explanation:

For any cube the total edge length is equal to 12n, with n being the length of an edge side. Knowing this:

Cube A - Total edge length = 12(3) or 36

Cube B - 12(5) or 60

Cube C - 12(9.5) or 114

If any cube has edge length s, the total edge length is 12s

Hope this helps!

Hello there! To find f ∘ g, g ∘ f, and g ∘ g, let's first recall the definition of function composition: given two functions f and g, their composition f ∘ g is defined as the function that results from applying g to the result of applying f to its argument. Specifically, for a given input x, we can express the composition f ∘ g as follows: (f ∘ g)(x) = f(g(x)).

Given f(x) = x4 and g(x) = 1/x, we can find each composition as follows:

(a) f ∘ g = f(g(x)) = f(1/x) = (1/x)4

(b) g ∘ f = g(f(x)) = g(x4) = 1/(x4)

(c) g ∘ g = g(g(x)) = g(1/x) = 1/(1/x) = x

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Answer:

In the novel "The Witch of Blackbird Pond" by Elizabeth George Speare, in chapters 13-15, several townsmen gather at the Wood household until late at night because they suspect that Kit's grandfather, Matthew Wood, is hiding royalist sympathies. The men search through Matthew's belongings and find books and pamphlets that are considered to be treasonous, including a pamphlet by William Penn. They also find a prayer book that Matthew had brought with him from England. The men take the items and leave, warning the Woods to be careful about their political leanings. This event foreshadows the tension and conflict that will arise later in the novel between the royalists and the patriots.

Step-by-step explanation:

cuz graaa thag boys a lier da boys a lier

Step-by-step explanation:

-10, -8, 0, 7 is the answer

The answer should be:

-10, -8, 0, 7

Answer:

Step-by-step explanation:

25 becuase 3 times 52 is that plus 32 is 73 and isabella with be rivher then ever than muh hahaha

The years 1960–1965 saw the greatest change in temperature variation per unit of time.

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

The graph for average temperature variation v/s time is given.

To find during which year maximum temperature variation with time:

We have to find the year with maximum magnitude of slope |m|.

Slope m = [tex]\frac{y_2-y_1}{x_2-x_1}\\[/tex]

Consider m for year 1950-1955:

m = 0 [line parallel to x-axis]

Consider m for year 1955-1960:

[tex]\frac{-0.05-0}{1955-1960}\\\\= 0.01[/tex]

Consider m for year 1960-1965:

[tex]\frac{-0.15-0}{1965-1960}\\\\= -0.03[/tex]

Consider m for year 1965-1970:

m = 0.01 {same as of 1955-1960}

Consider m for year 1970-1975:

m = 0 [line parallel to x-axis]

Consider m for year 1975-2000:

[tex]\frac{0.4-(-0.1)}{2000-1975}\\\\= 0.02\\[/tex]

|m| is maximum for year 1960-1965

Hence, the temperature variation changed the most per unit time in the year 1960-65.

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