There are 100 teachers in a school. 60 teach science, 25 teach humanities, 15 teach both science and humanities. 6Find the number of teachers who teach: (a) science but not humanities. (b) Humanities but not science. (c) Humanities or science.​

The new image of the rectangle after a translation of two units to the left is of option D

Suppose the graph is drawn on the coordinate plane.

Let the shifting be (x,y) → (x+a, y+b)

Then, add 'a' to all x coordinates of the graph's points. Add 'b' to all y coordinates of the graph's points.

The resultant set of new points will be plotted.

Given;

A rectangle area on graph with coordinates (1,0), (6,0),(6,2), (1,2)

Now after the shift of 2 unit left, the x coordinates will be affected;

=(1-2,0), (6-2,0),(6-2,2), (1-2,2)

=(-1,0), (4,0),(4,2), (-1,2)

Therefore, the coordinates of shifted graph will be (-1,0), (4,0),(4,2), (-1,2)

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Yes b can be written as linear combination of 3 vectors

A linear combination of vectors is a sum of scaled vectors, where the scaling factors are scalars. In other words, it's a linear combination of the form a_1v_1 + a_2v_2 + ... + a_n*v_n, where v_1, v_2, ..., v_n are vectors and a_1, a_2, ..., a_n are scalars. This is a fundamental concept in linear algebra and vector spaces and is used in many areas of mathematics and physics.

if b is linear combination of [tex]a_1,a_2,a_3[/tex]

then [tex]xa_1+ya_2+za_3=b[/tex]

from here we got :

x+5z = 2

-2x+y-6z = -1

2y + 8z = 6

after solving the above equation we get the solution as

{x,y,x} = {2,3,0} is a solution to the above equation so b is a linear combination of [tex]a_1,a_2,a_3[/tex]

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Complete question:

determine if b is a linear combination of [tex]a_1,a_2,a_3[/tex]

[tex]a_1[/tex] = [tex]\left[\begin{array}{ccc}1\\-2\\0\end{array}\right][/tex]      , [tex]a_2 = \left[\begin{array}{ccc}0\\1\\2\end{array}\right][/tex]   , [tex]a_3 = \left[\begin{array}{ccc}5\\-6\\8\end{array}\right][/tex] ,  b= [tex]\left[\begin{array}{ccc}2\\-1\\6\end{array}\right][/tex]

Answer:

$0.50

50 cents per ounce.

Step-by-step explanation:

To get the unit price, you take the cost of the package divided by the parts it has. Since Marissa has a package of yogurt that costs $3.50 and there are seven ounces in the package we have this equation:

($3.50)/(7 ounces)= $0.50 = 50 cents = the second answer available.

Answer:

$30

Step-by-step explanation:

1kg= $8

3kg *$8= $24

3/4= 0.75

$8 *0.75= $6

$24+$6= $30

3.75 kg * $8= 30

* = multiply

17. The equation can be rewritten as 2x²-8x+1=0.

18. The axis of symmetry is x = 5. The parabola opens up and has a maximum at the vertex (5, 6). The quadratic equation has two solutions, x = 4 and x = 6.

17.

The equation can be rewritten as 2x²-8x+1=0.

Vertex:

The vertex is (4, -1). A minimum.

Axis of symmetry:

The axis of symmetry is x = 4.

The parabola opens up.

The graph has 1 solution.

18. How many solutions does the quadratic

have?

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17. The equation can be rewritten as 2x²-8x+1=0. 18. The axis of symmetry is x = 5. The parabola opens up and has a maximum at the vertex (5, 6). The quadratic equation has two solutions, x = 4 and x = 6.

17. The equation can be rewritten as 2x²-8x+1=0.

Vertex:

The vertex is (4, -1). A minimum.

Axis of symmetry:

The axis of symmetry is x = 4.

The parabola opens up.

The graph has 1 solution.

18. The coefficient of x, which is -10, is multiplied by two to determine the axis of symmetry, which is x = 5.

This is due to the fact that the axis of symmetry is always located halfway between the two x-intercepts.

The parabola widens, indicating that the vertex is where its maximum is located. The vertex is (5, 6), which is determined by solving for y while changing x = 5 in the equation.

There are two answers to the quadratic equation: x = 4 and x = 6. The equation must be made equal to 0 in order to get the solutions.

Either factoring or applying the quadratic formula can be used to accomplish this.

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The area of the shaded region and the length of the boundary is 86.59 cm^2 and 44cm respectively.

A semicircle is a shape that is half of a circle. It is defined by a center point and a radius, and it is made up of an arc that is 180 degrees of the full circle.

The circumference of a semicircle is given by the formula: C = π * d, where C is the circumference and d is the diameter of the semicircle.

Diameter of the biggest semi-circle = 14cm.

Diameter to two small semi-circles = 3.5cm.

Diameter of other semi-circle = 14 - 2(Diameter to two small semi-circles)

                                                 =14 - 7 cm

                                                = 7cm

Length of boundary = Circumference of bigger semi-circle + Circumference of small semi-circle + 2 ×circumference of the smaller semi-circles

∴Length of boundary= [tex]\pi R+\pi r_{1}+2\pi r_{2}[/tex]

=> Length of boundary=[tex]\pi (R+r_{1})+2\pi r_{2}[/tex]

=> [tex]\frac{22}{7}(7+3.5)+2X\frac{22}{7}X1.75[/tex]

=> 44cm

Area of the biggest semi-circle = [tex]\frac{1}{2}\pi (7)^{2} cm^{2}[/tex]

Area of two small semi-circles = [tex]\pi (1.75)^{2}cm^{2}[/tex]

Area of other semi-circle= [tex]\frac{1}{2}\pi (3.5)^{2}cm^{2}[/tex]

Area of shaded region= π×(24.5−3.0625+12.25)

                                      =π×27.5625 cm^2 =86.59 cm^2

Therefore, the area of the shaded region and the length of the boundary is 86.59 cm^2 and 44cm respectively.

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Answer:

Is this what youre asking?

Step-by-step explanation:

Price before tax: $ 590.00

+ Sales tax (32.45%): $ 191.46

Total price including tax: $ 781.46

Answer: To graph y = f(x) = -(x+4)²+1 and y = 1/f(x) on the same axes, you can follow these steps:

Plot the y-intercept of y = f(x) which is (0,-1)

For y = f(x), the parabola opens downward since the coefficient of x² is -1, thus the vertex is at (-4,1)

Plot the x-intercepts of y = f(x) which are x = 4 and x = -8

The parabola of y = f(x) is symmetric about the y-axis, so the graph will be reflected about the y-axis.

For y = 1/f(x), the x-intercepts will be the same as y = f(x) and the y-intercept is (0,1)

To graph y = 1/f(x), we can start by plotting the x-intercepts and the y-intercept, and then connecting the points.

Label the x-intercepts, y-intercepts, and vertex for both graphs

Shade the regions above the parabola of y = f(x) and below the graph of y = 1/f(x)

Note: It is important to remember that the graph of y = 1/f(x) is a reflection of the graph of y = f(x) across the x-axis, so the y-intercept of y = 1/f(x) is (0,1)

Step-by-step explanation:

The value of 6 1/2 divided by 1 2/3 is 3 9/10

From the question, we have the following parameters that can be used in our computation:

6 1/2 divided by 1 2/3

When represented as an expression, we have

6 1/2 / 1 2/3

Convert to improper fractions

13/2 / 5/3

Express as products

13/2 * 3/5

So, we have

39/10

Express as mixed number

3 9/10

Hence, the solution is 3 9/10

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(a) The number of four-digit numbers with distinct digits in {1, 2, 3, 4, 5, 6} is 6543 = 360.

(b) The number of four-digit numbers in {1, 2, 3, 4, 5, 6} that are even is (3543)/2 = 270.

(c) The number of four-digit numbers in {1, 2, 3, 4, 5, 6} that are even and have distinct digits is (321*1)/2 = 3.

For (a) the total number of four-digit numbers with digits in {1, 2, 3, 4, 5, 6} is 6 options for the first digit, 5 for the second, 4 for the third and 3 for the last one. So, 654*3 = 360.

For (b) since digits in {1, 2, 3, 4, 5, 6} the even digits are 2,4,6. for each of the even digits we have 5 options for the second digit, 4 for the third and 3 for the last one. In total, we have 354*3= 270 even numbers.

For (c) The total number of four-digit numbers with distinct digits that are even is 211 = 2, since there are 2 even digits in {1,2,3,4,5,6} and only one of each can be used. However, this count is double-counting the numbers, so we divide by 2 to get 3.

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An example of a question that can be solved using the associative method is : (2/5) * (3/4) * (5/6)

One example of a problem involving multiplication of fractions that can be made easier using the associative property is:

(2/5) * (3/4) * (5/6)

Using the associative property of multiplication, we can change the grouping of the fractions to make the problem easier. The associative property states that the way we group the numbers being multiplied does not change the product. For example,

(2/5) * (3/4) * (5/6) = (2/5 * 3/4) * (5/6) = (6/20) * (5/6) = 30/120

This simplification makes it easier to see that the final answer is 1/4.

By using the associative property, we can first multiply (2/5) * (3/4) = (6/20) which is easier to cancel out the common factor and then multiply it with (5/6) = (5/6) * (6/20) = (30/120) = 1/4 which is the final answer

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The number of feet that should be on each side of the painting is 4 feet.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

Let x be the number of feet on each side of the painting.

The equation to determine the number of feet on each side of the painting would be:

x + 5 + x = 13

So x = (13-5)/2

x = 4

So there should be 4 feet on each side of the painting.

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On the coordinate plane, the segment from D(-6, 3) to E(2, 3) forms one side of ADEF. The possible point F are (5,-4), (1, 10), (7,4), (-6, 10).

Since we are aware that the triangle's area is 28 square units and that the base is the segment DE, which has a length of 8 units, we can construct the equation:

Area equals (1/2) × base × height =  (1/2) × 8 × height=28

We can calculate the height and discover that it is 7 units.

Point F must be situated 7 units above or below the line DE since the triangle's height is perpendicular to the base DE. Therefore, any position that is 7 units above or below the line DE, which is determined by the equation y = 3, is considered to be at point F.

So the possible point F are (5,-4), (1, 10), (7,4), (-6, 10)

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Complete question -

On the coordinate plane, the segment from D(-6, 3) to E(2, 3) forms one side of ADEF. The

triangle has an area of 28 square units. Select all of the points where F could be. (5,-4), (1, 10), (7,4),(-6, 10)

BFS has an exponential space complexity with respect to d because it stores all the nodes at the same depth level before moving on to the next level

DFS doesn't have an exponential space complexity with respect to d because it only stores the nodes that need to be visited next.

The space complexity of breadth-first search (BFS) is O([tex]b^d[/tex]) and the space complexity of depth-first search (DFS) is O(bd), where b is the maximum branching factor of the search tree and d is the maximum depth of the tree.

The reason for the difference in the space complexities is that BFS uses a queue to store the nodes to be visited, while DFS uses a stack.

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The equation has a solution of x= 3/4 will be B. 8x = 6

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

In this case, the value of x in 3x = 6 will be:

x = 6 / 3

x = 2

The value of x in 8x = 6 will be:

x = 6 / 8

x = 3 / 4

The value of x in 4x = 2 will be:

x = 2/4

x = 1/2

The value of x in 3x = 15 will be:

x = 15 / 3

x = 5

The correct option is B.

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Complete question

Which equation has a solution of x= 3/4?

A. 3x = 6

B. 8x = 6

C. 4x = 2

D. 3x = 15

The solution set to inequality - 5 ≤ (1 / 2) · (2 · m + 2) ≤ 14 is equal to - 6 ≤ m ≤ 13. (Correct choice: A)

Herein we find a simultaneous inequality, that is, the combination of two inequalities. We find the following case below by algebra properties:

- 5 ≤ (1 / 2) · (2 · m + 2) ≤ 14

(1 / 2) · (2 · m + 2) ≥ - 5 and (1 / 2) · (2 · m + 2) ≤ 14

Now we proceed to determine the solution set to this inequality by algebra properties:

2 · m + 2 ≥ - 10 and 2 · m + 2 ≤ 28

2 · m ≥ - 12 and 2 · m ≤ 26

m ≥ - 6 and m ≤ 13

- 6 ≤ m ≤ 13

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The greatest common factor (GCF) of two or more expressions is the largest monomial that divides each expression exactly.

To find the GCF of 36x^2 and 18xy^2, we can factor out the greatest common factor from each expression.

The prime factorization of 36 is 2^2 * 3^2 and of 18 is 2*3^2

The GCF of 36x^2 and 18xy^2 is 18x^2y^2 = 2*3^2 * x^2 * y^2

So, the GCF of 36x^2 and 18xy^2 is 18x^2y^2

Answer:

18xy

Step-by-step explanation:

The domain is [0,100].[0,100]. The range is [0,1500] [0,1500]

(a) To find the cost of making 25 items substitute

x=25 in the equation

=10+500(25)

=10(25)+500(25)=750

c(x)=10x+500

c(25)=10(25)+500

c(25)=750

the cost of making 25 items is

$750

(b)

Since the maximum cost allowed is

$1500  

10+500≤1500

10x+500≤1500

To solve this inequality

First, subtract 500 from both sides

10≤1000

10x≤1000

Divide both sides by 10

≤100x≤100

This means you can make at most 100 items.

The domain is

[0,100].[0,100].

The range is

[0,1500] [0,1500].

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The product of the two complex number c₁c₂ is thus 10 + 9i.

Let c₁ = a + ib and c₂ = c + id. Also z₁ represent 2 + 2i and z₂ represent 5 + i. The length of side of the equilateral triangle formed can be obtained by

|z₁ - z₂| = r = √((5 - 2)² + (1 - 2)² = √10

a² + b² - 4a - 4b + 8 = 10

a² + b² - 10a - 2b + 26 = 10

So 6a - 2b = 18 that is 3a - b = 9

Thus b = 3a - 9

Similarly c² + d² - 4c - 4d + 8 = 10

c² + d² - 10c - 2d + 26 = 10

So 3c - d = 9, that is d = 3c - 9

Midpoint of line joining c₁ and c₂ is same as that of z₁ and z₂, so

(c + a)/2 = ( 5 + 2)/ 2 and (d + b)/2 = (1 + 2)/2

So midpoint is 3.5 + 1.5i

Altitude of equilateral triangle of side a is √3a/2

That is √(a - 3.5)² + (b - 1.5)² = √3×√10/2

√(a - 3.5)² + (3a - 9 - 1.5)² = √30 /2

a² - 7a + 12.25 + 9a² - 63a + 110.25 = 30/4

On solving a = (7 ± √3)/ 2

So a = (7 - √3)/ 2, c = (7 + √3)/ 2

b = 3a - 9 = (3 - 3√3)/ 2, d = (3 + 3√3)/2

So c

c₁ = (7 - √3)/2 + i (3 - 3√3)/ 2

c₂ = (7 + √3)/2 + i (3 + 3√3)/ 2

So the product c₁c₂ is

= ((7 - √3)/ 2) * ((7 + √3)/ 2) - ((3 - √3)/ 2) * ((3 + √3)/ 2) + i (((7 - √3)/ 2) * ((3 + √3)/ 2) + ((7 + √3)/ 2) * ((3 - √3)/ 2))

= 10 + 9i

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There are many similarities between Vanguard and Fidelity, but there are also some significant distinctions. Vanguard focuses primarily on long-term, buy-and-hold investing.

Fidelity, on the other hand, caters to investors who prefer a more hands-on approach.

There are more than 8,300 domestic investment-grade bonds held by the Vanguard Total Bond Market ETF.

Therefore, You'll need to study two (or more) sets of statements, keep track of several phone numbers, access a number of websites, and comprehend and keep track of hundreds of different funds.

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There are many similarities between Vanguard and Fidelity, but there are also some significant distinctions. Vanguard focuses primarily on long-term, buy-and-hold investing. Fidelity, on the other hand, caters to investors who prefer a more hands-on approach.

Bonds are issued by borrowers to attract capital from investors ready to extend a loan to them for a specific period of time. When you purchase a bond, you are making a loan to the issuer, which could be a corporate, government, or municipality.

By purchasing a bond, you are effectively lending the issuer money. In exchange, they commit to repay you the face amount of the loan on a particular date and to make periodic interest payments—typically twice a year—along the way. Unlike stocks, which grant you ownership rights, bonds issued by corporations do not.

Therefore, Vanguard's primary investment strategy is long-term buy-and-hold investing. On the other hand, Fidelity caters to investors who favor a more active strategy.

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The value of three subsets is [tex]n(x_{1})=36, n(x_{2})=9, & n\left(x_3\right)=54[/tex].

A set is a collection of objects or elements, grouped in the curly braces, such as {a, b, c, d}. If a set A is a collection of even number and set B consists of {2,4,6}, then B is said to be a subset of A, denoted by B⊆A and A is the superset of B.

The elements of sets could be anything such as a group of real numbers, variables, constants, whole numbers, etc. It consists of a null set as well.

If set A has {X, Y} and set B has {X, Y, Z}, then A is the subset of B because elements of A are also present in set B.

Let the number of elements in [tex]$x_2$[/tex] be [tex]$x$[/tex], then

[tex]$$\begin{aligned}& n\left(x_1\right)=4 x \\& n\left(x_2\right)=x \\& n\left(x_3\right)=6 x\end{aligned}$$[/tex]

Given that number of elements in [tex]$x=99$[/tex]

[tex]$$\begin{aligned}\Rightarrow & n\left(x_1\right)+n\left(x_2\right)+n\left(x_3\right)=99 \\\Rightarrow & 4 x+x+6 x=99 \\\Rightarrow & 11 x=99 \\\Rightarrow & x=9 \\\therefore & n\left(x_1\right)=4 x=4 \times 9=36 \\& n\left(x_2\right)=x=9 \\& n\left(x_3\right)=6 x=6 \times 9=54\end{aligned}$$[/tex]

Therefore, the value of  [tex]& n\left(x_3\right)[/tex][tex]=54[/tex].

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The percent by mass of a solution is  29.21.

To calculate the percent by mass of a solution, divide the mass of the solute (13.687 grams) by the total mass of the solution (46.833 grams). Then, multiply this value by 100 to get the percent.

% by mass = (mass of solute/total mass of solution) x 100

% by mass = (13.687/46.833) x 100 = 29.21.This calculation can be used to determine the amount of a solute in a given solution. It is important to know the percent by mass of a solution in order to make sure the solution is composed of the desired amount of solute. Knowing the percent by mass can also be used to compare the solutions of different concentrations.

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The cost of each shirt is $6 and the cost of each pant for the given condition is $9.

The elimination approach involves taking one variable out of the system of linear equations by utilising addition or subtraction together with multiplication or division of the variable coefficients.

Let us suppose the cost of shirt = x.

Let us suppose the cost of pant = y.

Given that 3 shirts and 3 pants cost $45, this is represented as:

3x + 3y = 45 (equation 1)

1 shirt and 2 pants cost $24, this is represented as:

x + 2y = 24 (equation 2)

Using the elimination method to solve:

Multiply the second equation with 3 and change the signs of all the variables.

(x + 2y = 24) (3)

-3x - 6y = -72 (equation 3)

3x + 3y = 45

Comparing equation 1 and equation 3, the x term is cancelled, and the remaining equation after subtracting both equations is:

- 3y = -27

y = 9

Substitute the value of y in equation 2.

x + 2y = 24

x + 2(9) = 24

x + 18 = 24

x = 24 -18

x = 6

Hence, the cost of each shirt is $6 and the cost of each pant is $9.

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Use 1.75 cups of blue and 1 cup of yellow

What is a mixture?

Mixture can be defined as a substance made by combining two or more different materials in such a way that no chemical reaction occurs. A mixture can usually be separated back into its original components.

The given problem can be placed in the category of ratios and proportions.

There is a ratio of color mixing which contains the proportion of two colors i.e blue and yellow. When we use 2 cups of yellow with 3.5 cups of yellow then we get green color so if we mix half of their amounts then we can get less or simply half amount of color too.

Therefore adding 1 cup of yellow and 1.75 cup of blue will give us small amount in result.

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This formula states that each term in the sequence is equal to the previous term plus 3.

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Step-by-step explanation:

To show that the function f(x,y) = 2x^2 − xy is differentiable at any point (a,b), we need to show that the partial derivatives of f with respect to x and y exist and are continuous at that point.

The partial derivative of f with respect to x is:

∂f/∂x = 4x - y

The partial derivative of f with respect to y is:

∂f/∂y = -x

We can see that both of these partial derivatives are continuous functions of x and y and are defined for all (x,y) in the domain of f. Therefore, f is differentiable at any point (a,b).

The derivative of f at (a,b) is the gradient vector of f evaluated at (a,b), which is given by:

Gradient vector of f(a,b) = ∇f(a,b) = ( ∂f/∂x, ∂f/∂y ) = (4a-b, -a)

So the derivative of f at (a, b) is (4a-b, -a).

For the solution that satisfies, sketch the solution curve and estimate the following y(0)=0: y(1)≈0.75, y(-1)≈0.5; Y(0)=4: Y(0.5)≈-0.5, Y(-1)≈0.75; Y(0)=-1: Y(1)≈-1.5, Y(-1)≈-1.5.

(a) To sketch the solution curve for the given slope field, beginning at the point (0, 0) and following the arrows, draw a curved line that gradually moves from left to right, gradually increasing in value and then slowly decreasing. The estimated value of y(1) is 0.75 and y(-1) is 0.5.

(b) To sketch the For the solution that satisfies, sketch the solution curve and estimate the following y(0)=0: y(1)≈0.75, y(-1)≈0.5; Y(0)=4: Y(0.5)≈-0.5, Y(-1)≈0.75; Y(0)=-1: Y(1)≈-1.5, Y(-1)≈-1.5. curve for the given slope field, beginning at the point (0, 4) and following the arrows, draw a curved line that gradually moves from right to left, gradually decreasing in value and then slowly increasing. The estimated value of Y(0.5) is -0.5 and Y(-1) is 0.75.

(c) To sketch the solution curve for the given slope field, beginning at the point (0, -1) and following the arrows, draw a curved line that gradually moves from left to right, gradually increasing in value and then slowly decreasing. The estimated value of Y(1) is and y(-1) is -1.5.

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