Analia is a school district manager. Here are some details about two schools in her district for the last school year: School A School B Number of students 3000 30003000 4000 40004000 Number of teachers 190 190190 380 380380 Graduation rate 86 % 86%86, percent 90 % 90%90, percent Budget per student $ 10 , 500 $10,500dollar sign, 10, comma, 500 $ 10 , 000 $10,000dollar sign, 10, comma, 000 % of students in sports club 62 % 62%62, percent 68 % 68%68, percent Number of sports medals won 9 99 7 77 SAT average 1200 12001200 1050 10501050 SAT range (max-min) 900 900900 700 700700 Analia wants to know which school has higher academic achievements relative to the number of teachers per student. 1) Analia thought of two different ways to define this quantity. Identify these two definitions among the following options.

F g - x hence equals -f x. -g x. It follows from this that f g - x = f g x. Given that f and g are two odd functions, it follows that f g is an even function. As a result, f g is not an unusual function.

If the equation for every x and x in the domain of f holds, then a function f is odd. F(x)=F(x) or F(x)=F(x) An odd function has a graph that, geometrically speaking, is rotationally symmetric with respect to the origin, meaning that the graph is unaffected by a 180° rotation of the origin.

If f - x = f x, then a function f x is said to be even. These functions have symmetric properties around the y-axis.

F - x Equals F x if two functions f and g are two even functions.

g - x = g x

Now, the definition of the product function f g is as follows:

[tex]$f g x=f x \cdot g x$[/tex]

Analyze the fg at -x product function.

[tex]$f g-x=f-x \cdot g-x$[/tex]

The two functions are currently equal functions. Utilize the knowledge that f - x = f and g - x = g.

Consequently, f g - x = f x. g x It follows from this that f g - x = f g x. This suggests that f g, where f and g are two even functions, is an even function.

If f - x = -f x, then a function f x is said to be odd. These functions have symmetry at their origin.

If f and g are two odd functions, then f - x = -f x and g - x = -g x, respectively.

Now, the definition of the product function f g is as follows:

[tex]$f g x=f x \cdot g x$[/tex]

Evaluate the product function f g at -x

[tex]$f g-x=f-x \cdot g-x$[/tex]

The two functions are now peculiar functions. Utilize the knowledge that f-x = -f-x and g-x = -g-x.

F g - x hence equals -f x. -g x. It follows from this that f g - x = f g x. Given that f and g are two odd functions, it follows that f g is an even function. As a result, f g is not an unusual function.

Assume that g is odd and f is even. G - x = -g x and f - x = f x, respectively.

The following is a definition of the product function:

[tex]f g-x & =f-x \cdot g-x \\[/tex]

[tex]& =f x \cdot-g x \\[/tex]

[tex]& =-f x \cdot g x \\[/tex]

[tex]& =-f g x[/tex]

Because f is even and g is odd, f g is an odd function.

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The polygon was translated 5 units left and 9 units up using the rule for (x, y) ⇒ (x - 5, y + 9)

Translation is the movement of a point in the coordinate plane either up, left, down or right. Translation is a type of rigid transformation because it preserves both the shape and size of the figure.

Other types of rigid transformations are reflection and rotation.

The points D(5, -10) and T(-9, -6) were translated to give D'(0,-1), T'(-14,3). This means that the translation was 5 units left and 9 units up.

The rule for this translation is (x, y) ⇒ (x - 5, y + 9)

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The determinant of the matrix A, where A is [1 1 47 1 2 2 1 2 5 2], is -13. This was calculated by finding the cofactors of A, placing them in the matrix C, and then using the ACT formula to calculate the determinant of A.

C=

[1 -2 -2

-1 1 1

-47 -2 -2]

ACT=1⋅1⋅1+(-2)⋅2⋅1+(-2)⋅5⋅2=1+(-4)+(-10)= -13

The determinant of A is -13.

1. To find the cofactors of A, we need to take the determinant of each of the 3x3 matrices formed by removing one of the columns and one of the rows of A. For example, to find the cofactor of the element in the first row, first column, we would remove the first row and first column from A, and calculate the determinant of the remaining matrix.

2. We can then place the cofactors in the matrix C, which would look like this:

C=

[1 -2 -2

-1 1 1

-47 -2 -2]

3. To calculate the determinant of A, we can use the ACT formula:

ACT=1⋅1⋅1+(-2)⋅2⋅1+(-2)⋅5⋅2=1+(-4)+(-10)= -13

Therefore, the determinant of A is -13.

The determinant of the matrix A, where A is [1 1 47 1 2 2 1 2 5 2], is -13. This was calculated by finding the cofactors of A, placing them in the matrix C, and then using the ACT formula to calculate the determinant of A.

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Triangle LMN is similar to triangle OPQ. The measure of side OP is 12.6

Triangle LMN is similar to triangle OPQ.

Similar forms or figures have corresponding sides that are proportionate to one another. The ratio of their matching sides would be identical because LMN OPQ. Thus:

MN/PO = LN/OQ

LN = 31

OQ = 8

MN = 49

RO = ?

Put the values in.

31 / 8 = 49 / PO

multiply by cross

31 * PO  =  49 * 8

31  * PO =  392

PO = 392 / 31

PO = 12.6

Triangle LMN is similar to triangle OPQ. The measure of side OP is 12.6

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The angle CFD is 67.6 degrees.

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Given that ∠CFE=177 degrees.

We have to find angle CFD.

∠CFD+∠EFD=117

4z+74+9z+64=117

13z+138=117

13z=21

z=-1.6

Now substitute in ∠CFD =4(-1.6)+74

∠CFD =-6.4+74

=67.6 degrees

Hence, the angle CFD is 67.6 degrees.

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It will cost the company $321,400 to produce 14,300 items.

An arithmetic sequence has a constant difference between each consecutive pair of terms. This is similar to the linear functions that have the form y=mx+b. A geometric sequence has a constant ratio between each pair of consecutive terms. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

To predict how much it will cost to produce 14,300 items, you need to substitute 14,300 for q in the expression 18q+64000.

So, 18q + 64000 becomes 18(14300)+64000 = 257400+64000 = 321400

Therefore, it will cost the company $321,400 to produce 14,300 items.

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Answer:

The inequality can be solved by isolating the variable x on one side of the inequality. To do this, we can first add 4x to both sides of the inequality:

-2 ≤ 4x + 3 ≤ 4

Next, we can subtract 3 from both sides of the inequality:

-5 ≤ 4x ≤ 1

Finally, we can divide both sides of the inequality by 4 to solve for x:

x ≥ -5/4 and x ≤ 1/4

So the solution of the compound inequality is x ≥ -5/4 and x ≤ 1/4

We can also express this solution in interval notation: [-5/4, 1/4]

Note that the compound inequality has two separate inequality signs, indicating that the solution is the set of all x-values that make both inequalities true.

Step-by-step explanation:

The bisection method up to five iterations and finding the root to 2 decimal places for the following would be 2.19

Bisection technique

By continuously reducing the interval in which the root is located, the bisection method roughly approximations the root of a function. The procedure first evaluates the function at the interval midway before swapping out the interval's end with a new one that has the same sign.

The beginning range, in this case, is [1, 3], and f(1) > 0 and f(3) 0. (1+3)/2 = 2 represents the interval's midpoint. The interval endpoint (0) that had f(x) > 0 is replaced with the midpoint (2) when we evaluate f(2) and discover that f(2) > 0. The new midpoint is x = 5/2, and the new interval is [2, 3]. The first iteration is now complete.

Iterations

2nd iteration: f(5/2) < 0 ⇒ interval is [2, 5/2]; midpoint is 9/4

3rd iteration: f(9/4) < 0 ⇒ interval is [2, 9/4]; midpoint is 17/8

4th iteration: f(17/8) > 0 ⇒ interval is [17/8, 9/4]; midpoint is 35/16 ≈ 2.19

5th iteration: f(35/16) < 0 ⇒ interval is [17/8, 35/16]; midpoint is 69/32 ≈ 2.16

The approximate root of 2.16 is revealed by the fifth iteration, but that is not an option for the solution. We think this is the response you're searching for because the fourth iteration yields a root that is around 2.19.

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The full question:

What is the root of the following equation using the bisection method correct to three places of decimal f(x) =x3-3x-5?

The length of the missing sides for given angles are

What is Pythagoras' Theorem?

Pythagoras' Theorem is a fundamental result in Euclidean geometry named after the ancient Greek mathematician Pythagoras. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In other words, if a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then the theorem can be written as:

c² = a² + b²

tan A = a/c

c = a / tan A

We know that a = 100 and tan A = 100

so c = a / tan A = 100/100 = 1

We also know that b = 100

Now we can use the Pythagorean Theorem to find a:

a² + b² = c

100^2 + 100^2 = 1²

10000 + 10000 = 1

20000 = 1

a = sqrt(20000) = √(2000) × √(10) = 140.7107 × 10[tex]{}^{1/2}[/tex] = 141.42135

So,

side a = 141.42135

side b = 100

side c = 1

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Answer:

Step-by-step explanation:

Given : ∠1 ≅ ∠2

To prove : p║q

Solution :

In the figure attached,

               Statements                 Reasons

1). m∠1 ≅ m∠2                      1). Given

2) m∠1 ≅ m∠3                      2). Vertical angles

3) m∠2 ≅ m∠3                     3). Transitive property of congruence of the                                                     angles

4). Line p║q                         4). Corr

The volume of the large container is given as follows:

113.04 in³.

The ratio of the volumes is of:

B) 2.25

The volume of a cylinder of radius r and height h is given by the equation presented as follows:

V = πr²h.

The diameter of the smaller cylinder is of:

4 inches.

Hence the diameter and radius of the larger container is of:

As the height of the cylinder is of 4 inches, the volume is given as follows:

V = 3.14 x 3² x 4

V = 113.04 in³.

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The coordinates given in the question are not provided. Without the coordinates it's impossible to graph the line and determine which statement is true.

It is important to have the coordinates to graph the line, and then we can determine if the line is a proportional relationship by looking at the slope of the line, if it is a constant value then it represent a proportional relationship.

The statement A and B are incorrect, as passing through the origin does not determine whether the relationship is proportional or not.

C and D are correct, whether the line passes through the origin or not, it can be determined if it represents a proportional relationship by looking at the slope of the line.

Please provide the coordinates in order to proceed with the question.

Answer:

Amaka passes hers 2/3

Step-by-step explanation:

she just will

The statement that would NOT be of concern when considering the nature criteria for evaluating secondary data is the relationships examined should be taken into account. Thus, option D is the answer

While it is important to take relationships into account when analyzing data, this statement is not specific to evaluating secondary data, but rather a general principle of data analysis.

The other statements listed  are all relevant concerns when evaluating secondary data, as secondary data may not always be directly relevant or appropriate for the current problem, and it is important to assess the accuracy and usefulness of the data for the present study.

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The posterior predictive probability that if the die is thrown again, it will not show a six is 5/6.

(a) The likelihood for the observed data is P(k=6|Data) = (1/16)*(1/6)^1 * (5/6)^1 = 5/96. The maximum likelihood estimate for k is 6.

(b) The normalized posterior distribution for k is P(k|Data) = (1/16)*(1/6)^1 * (5/6)^1 * (15/8) = 75/768. The posterior mean for k is 4.5.

(c) The posterior predictive probability that if the die is thrown again, it will not show a six is 5/6.

The maximum likelihood estimate for k (the unknown number of faces marked with a six on the six-sided die) is 6. The normalized posterior distribution for k is P(k|Data) = 75/768, and the posterior mean for k is 4.5. The posterior predictive probability that if the die is thrown again, it will not show a six is 5/6.

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1. The antiderivative would be x.

2. The antiderivative would be sec(θ)tan(θ)−5e^(θ^3).

3. The antiderivative would be 1+2x.

What is the antiderivative of the function?

An antiderivative of a function is a function whose derivative is equal to the original function. It is also known as an indefinite integral of a function with respect to its variable. The process of finding an antiderivative is called integration.

1. The most general antiderivative of the function f(x)=x is F(x) = (1/2)x^2 + C, where C is the constant of the antiderivative. To check this, we can differentiate F(x) using the power rule for derivatives and see if we get back f(x) = x: d/dx [(1/2)x^2 + C] = d/dx (1/2)x^2 + d/dx C = x

2. The most general antiderivative of the function r(θ)=sec(θ)tan(θ)−5e^(θ^3) is R(θ)=∫sec(θ)tan(θ)−5e^(θ^3) dθ = -ln(cos(θ))+5e^(θ^3)/3+C, where C is the constant of the antiderivative. To check this, we can differentiate R(θ) using the rules of integration by substitution, and see if we get back r(θ) = sec(θ)tan(θ)−5e^(θ^3): d/dθ [-ln(cos(θ))+5e^(θ^3)/3+C] = sec(θ)tan(θ)−5e^(θ^3)

3. The most general antiderivative of the function f(x)=1+2x is F(x) = x+x^2 + C, where C is the constant of the antiderivative. To check this, we can differentiate F(x) using the power rule for derivatives and see if we get back f(x) = 1+2x: d/dx (x+x^2 + C) = d/dx x+d/dx x^2 + d/dx C = 1+2x

Hence,

1. The antiderivative would be x.

2. The antiderivative would be sec(θ)tan(θ)−5e^(θ^3).

3. The antiderivative would be 1+2x.

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Answer:

The answer is 5x-2

Step-by-step explanation:

3x-(2-2x)

3x-2+2x

5x-2

A correct stacked bar chart would show store location on the horizontal axis, and the percentage of time spent on each task on the vertical axis. Each store location would be represented as a separate bar, with each bar displaying the percentage of time spent on each task as stacked sections within the bar.

A stacked bar chart is a type of graph that is used to visualize data. It is a bar chart that displays the relative contribution of different data points to the whole. It is particularly useful for comparing the contribution of different data points across different categories. For example, a stacked bar chart can be used to show the percentage of time spent on different tasks at different store locations. The horizontal axis would represent the store locations, while the vertical axis would represent the percentage of time spent on each task. Each store location would then be represented as a separate bar, with each bar displaying the percentage of time spent on each task as stacked sections within the bar. The colors used to represent each task can be used to make the chart more visually appealing, and help viewers differentiate between the tasks. The stacked bar chart is a useful tool for analyzing data over multiple categories, and can be used to quickly identify trends and patterns.

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The complete question is

which of the following shows a correct stacked bar chart with store location on the horizontal axis and percentage of time spent on each task on the vertical axis Store Location Task

The equation that represents the graph through the data points in the table is Option K: y = 6x - 8.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The data points are given in the table.

The first equation is -

y = x²

Substitute the value of y = 40, as given in the table -

40 = x²

x = √40

x = 6.32

The value for x is obtained as 6.32 when y is 40.

This value does not corresponds with the values in the table.

Therefore, equation y = x² is incorrect.

The second equation is -

y = 6x - 8

Substitute the value of y = 40, as given in the table -

40 = 6x - 8

x = (40 + 8)/6

x = 48/6

x = 8

The value for x is obtained as 8 when y is 40.

This value corresponds with the values in the table.

Therefore, equation y = 6x - 8 is correct.

The third equation is -

x + y = 10

Substitute the value of y = 40, as given in the table -

x + 40 = 10

x = 10 - 40

x = -30

The value for x is obtained as -30 when y is 40.

This value does not corresponds with the values in the table.

Therefore, equation x + y = 10 is incorrect.

The fourth equation is -

x - y² = 0

Substitute the value of y = 40, as given in the table -

x - (40)² = 0

x = 0 + 1600

x = 1600

The value for x is obtained as 1600 when y is 40.

This value does not corresponds with the values in the table.

Therefore, equation x - y² = 0 is incorrect.

The fifth equation is -

x² - y² = 0

Substitute the value of y = 40, as given in the table -

x² - (40)² = 0

x² = 0 + 1600

x = √1600

x = 40

The value for x is obtained as 40 when y is 40.

This value does not corresponds with the values in the table.

Therefore, equation x² - y² = 0 is incorrect.

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Answer:

A 30 dogs and 48 cats

Step-by-step explanation:

The ratio of cats to dogs in the local shelter is 5 to 8, which means for every 5 cats, there are 8 dogs. If we assume that the total number of cats and dogs in the shelter is a multiple of the ratio, we can find the possible numbers of cats and dogs. In option A, the number of cats and dogs is 30 dogs and 48 cats which is a multiple of the ratio. 59 = 45 and 89 = 72 which is the closest to the number of cats and dogs in option A. Thus, option A shows the possible numbers of cats and dogs in the local shelter.

Answer:

[tex]\frac{17}{8}[/tex]

Step-by-step explanation:

[tex]2\frac{1}{8} = (2*8)+1 =17= \frac{17}{8}[/tex]

Answer:

17/8

Step-by-step explanation:

Answer:

Area_shaded

= 340.9 cm^2

Step-by-step explanation:

Find the area of the circle, then subtract the area of the triangle.

The 25cm side of the triangle is a hypotenuse of the right triangle. It is also the diameter of the circle.

The radius of the circle is 1/2 the diameter. So the radius is 1/2•25, or 12.5cm

We need the radius to find the area of the circle.

Area_circle

= pi•r^2

= pi•12.5^2

= 490.9 cm^2

The two legs of the triangle can serve as our base and height to find the area of the triangle.

Area_triangle

= 1/2b•h

= 1/2(20)(15)

= 150 cm^2

Subtract.

490.9 - 150

= 340.9cm^2

The area of the shaded region is 340.9cm^2.

The length of the second side, x, is 12.

What is Pythagoras' theorem?

In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs of the triangle). This theorem is usually represented by the equation: a^2 + b^2 = c^2, where c is the length of the hypotenuse, and a and b are the lengths of the legs.

In this case, the first side has a length of 9, the second side has a length of x, and the third side has a length of 15, which is the hypotenuse. We can use the Pythagorean theorem to solve for x:

x^2 + 9^2 = 15^2

x^2 = 15^2 - 9^2

x^2 = 225 - 81

x^2 = 144

x =√144

x = 12

Hence, the length of the second side, x, is 12.

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Three skeins are the most Sharon can afford to purchase because a number of skeins have to be a whole number.

For her sister's birthday present, Sharon has a budget of no more than $25. Sharon is therefore limited to spending no more than $25. She has paid $14.99 for a knitting machine for her. She wants to get her sister some yarn skeins to go with it as well. Cost per skein is $2.75. Let y be the number of yarn skeins.

The necessary inequality is:

14.99 + 2.75y ≤ 25

2.75y ≤ 25 - 14.99

2.75y ≤ 10.01

y ≤ 10.01 / 2.75

y ≤ 3.64

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Kasey's claim that her model is a good fit for the data is best supported by a correlation coefficient of r = 0.91. The correct answer would be an option (B).

A correlation coefficient (r) is a number between -1 and 1 that measures the strength and direction of a linear relationship between two variables.

A coefficient of r = 1 indicates a perfect positive linear relationship, meaning as one variable increases, the other variable also increases.

A coefficient of r = -1 indicates a perfect negative linear relationship, meaning as one variable increases, the other variable decreases.

A coefficient of r = 0 indicates no linear relationship between the variables.

In this case, a coefficient of r = 0.91 is close to 1 which means that there is a strong positive linear relationship between the data and the model. On the other hand, the other coefficients -0.25, 0.01, and -0.79 are not close to 1, which means that there is no or weak linear relationship between data and the model.

Hence, the correct answer would be an option (B).

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The total number of ordered triples $(a,b,c)$ satisfying the conditions [tex]$0\le a \le b \le c \le 10$[/tex]  is 10275.

The total number of ordered triples $(a,b,c)$ satisfying the conditions [tex]$0\le a \le b \le c \le 10$[/tex]  is given by

[tex]$n= \sum_{a=0}^{10}\sum_{b=a}^{10}\sum_{c=b}^{10} 1$$= \sum_{a=0}^{10}\sum_{b=a}^{10} (c-b+1)$$= \sum_{a=0}^{10}\sum_{b=a}^{10} c - \sum_{a=0}^{10}\sum_{b=a}^{10} b + \sum_{a=0}^{10}\sum_{b=a}^{10} 1$$= \sum_{a=0}^{10}\sum_{b=a}^{10} 10 - \frac{10(11-a)(a+1)}{2} + \sum_{a=0}^{10} (b-a+1)$$= \sum_{a=0}^{10} 105 - \frac{10(11-a)(a+1)}{2} + \frac{10(a+1)}{2}$$= \sum_{a=0}^{10} \frac{185 + 10a^2}{2}$$= \frac{(185 + 10\times 100) \times 10}{2}$ $= \frac{2055 \times 10}{2}$ $= 10275$[/tex]

Therefore, the total number of ordered triples $(a,b,c)$ satisfying the conditions [tex]$0\le a \le b \le c \le 10$[/tex]  is 10275.

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Answer:

[tex]y=-\dfrac{1}{30}x+12[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

The y-intercept is the y-value of the point at which the line crosses the y-axis.

Therefore, from inspection of the given graph, the y-intercept is 12:

The slope of a line is the change in y over the change in x.

From inspection of the given graph, the change in y is -3 and the change in x is 90.  Therefore, the slope is:

Substitute the found values of m and b into the slope-intercept formula to create an equation of the line: