our indiscrete mathematics course has 18 students from the the college of liberal arts and social sciences, 11 of whom are seniors; 19 students from the the college of education, 6 of whom are seniors; 27 students from the the college of science and health, 14 of whom are seniors. how many ways can we choose a single class rep?

The sum of the interior angles of a triangle is always 180°, using that we will see that x = 80°

The first thing you can notice is that we have a triangle with two equal sides, that means that the two bottom angles have the same measure.

Also, remember that the sum of the interior angles of any triangle is always equal to 180°, then we can write the equation:

50° + 50° + x = 180°

Solving that for x we will get:

x = 180° - 50° - 50° = 80°

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The expression 12x - 24 is factorized to give -12(x + 2)

Algebraic expressions are defined as expressions that are composed of terms, factors, constants, variables and coefficients.

They are also seen as expressions with arithmetic operations, such as;

To factor an algebraic expression is to find the greatest common multiples of the terms in the expression

From the information given, we have that;

-12x - 24

Factor the common terms

-12(x + 2)

Hence, the expression is -12(x + 2)

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The price of each shirt is $7.5.

The price of each pant is $18.5.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 7 is an equation.

We have,

Cost of shirts = x

Cost of pants = y

Lisa buys her children four shirts and three pairs of pants for $85.50.

She returns the next day and buys three shirts and five pairs of pants for $115.00.

This means,

We can make two equations.

4x + 3y = 85.50

3x + 5y = 115

Now,

4x + 3y = 85.50

4x = 85.50 - 3y

x = (85.50 - 3y)/4

Substituting in 3x + 5y = 115.

3 (85.50 - 3y)/4 + 5y = 115

256.5 - 9y + 20y = 460

11y = 460 - 256.6

11y = 203.4

y = 18.5

And,

x = (85.50 - 3y)/4

x = (85.50 - 55.5)/4

x = 30/4

x = 7.5

Thus,

The cost of the shirt is $7.5.

The cost of the pant is $18.5.

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Answer:

$1,972.41

Step-by-step explanation:

Half of $4587 is:

2,293.50$

What is 7% of 4587$?

The answer to that is, what I quote:

321.09$

Now lets do some fairly simple math:

2,293.50$

   321.09$   -

------------------

1,972.41$

Thus, your answer is:

1,972.41$

Answer:

$1,972.41

Step-by-step explanation:

The required surface area of a rectangular container is 588cm² using a volume of 1,372 cm³.

The quantity of space enclosing a three-dimensional shape's exterior is its surface area.

In comparison to the definition of arc length for one-dimensional curves or the definition of surface area for polyhedra (i.e., objects with flat polygonal faces), where the surface area is equal to the sum of the areas of its faces, the mathematical definition of surface area in the presence of curved surfaces is significantly more complex.

The surface area of smooth surfaces, such as spheres, is determined using their representation as parametric surfaces.

Partial derivatives and double integration are used in this definition of surface area, which is based on infinitesimal calculus techniques.

So, we have the volume:

1,372 cm³

Then, h = 1372/s².

Now, calculate as follows:

4 s 1372/s^2 + s^2 = area

5488/s + s^2 = area

s^2 + 5488 (s^-1) = area    

2s - 5488 s^-2 = 0

5488 s^-2 = 2s

5488 = 2 s^3

2744 = s^3    

s =  14        

s * h * s = 1372    

Then, we will have: h = 7

Surface area = 14*14+4*7*14 = 196+4*7*14 = 588 cm²

Therefore, the required surface area of a rectangular container is 588cm² using a volume of 1,372 cm³.

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Answer:

2, 3, 5

Step-by-step explanation:

To test whether a graph is a function, we use the line test. If one x has two y then that graph is not a function. In all the graphs 2,3,5 represent a function.

Answer:

Start by evening out the sides

6x + 6 = -12

      -6 = -6

6x = 18

Divide by six (bc variable in front of x)

x = 3

dy/dx = 0 when x = - 2, and x = 2/3 is not possible.

dy/dx = 0 when x = - 1, and x = 5.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 7 is an equation.

We have,

y = x³ - 6x² - 15x - 7

Differentiating w.r.t x.

[ d[tex]x^n[/tex]/dx = n[tex]x^{n - 1}[/tex] ]

[ dc/dx = 0 ]

dy/dx = dx³/dx - 6dx²/dx - 15dx/dx - d7/dx

dy/dx = 3[tex]x^{3 - 1}[/tex]dx/dx - 6 x 2[tex]x^{2-1}[/tex]dx/dx - 15 - 0

dy/dx = 3x² - 12x - 15

Now,

dy/dx = 0

3x² - 12x - 15 = 0

3(x² - 4x - 5) = 0

x² - 4x - 5 = 0

x² - (5 - 1)x - 5 = 0

x² - 5x + x - 5 = 0

x(x - 5) + 1(x - 5) = 0

(x - 5) (x + 1) = 0

x - 5 = 0

x = 5 _____(1)

x + 1 = 0

x = -1 _____(2)

Now,

For x = 2,

dy/dx = 3x² - 12x - 15

dy/dx = 3 x 4 + 24 - 15

dy/dx = 12 - 24 - 15

dy/dx = 12 - 39

dy/dx = -27 _____(3)

For x = 2/3,

dy/dx = 3x² - 12x - 15

dy/dx = 3 x 4/9 + 24 x 2/3 - 15

dy/dx = 4/3 + 16 - 15

dy/dx = 4/3 + 1

dy/dx = 7/3 _____(4)

From (1), (2), (3), and (4)

dy/dx = 0 when x = - 2 and x = 2/3 is not possible.

Thus,

dy/dx = 0 when x = - 1, and x = 5.

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The series 16+24+36+54+... diverges.

Divergent series are those that contain an infinite series that never converges and an infinite sequence of partial sums with no finite limit. In contrast, a series is considered to be convergent when its limits converge to its finite range of values. A limit that is finite in nature and exists for the partial sum of the series is crucial since only at that point will the series converge.

The given series in question 16 + 24 + 36 + 54 + deviates from the series. 16n, where n is the number of terms, can be used to denote the series' overall term. The total of the terms in the series also increases as n increases since 16n grows along with n, too. This indicates that the series diverges since it does not reach a particular finite value.

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Answer:12

Step-by-step explanation:

x+21 is the length of GH from the given figure.

A triangle is a three-sided polygon that consists of three edges and three vertices.

A triangle GHJ, M is the intersection of the three medians.

Given that GJ is twenty one.

GJ=21

We need to find the length of GH.

Let the length of HJ is x.

Now GH=HJ+GJ

GH=x+21

Hence, x+21 is the length of GH from the given figure.

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The area in square ft that is covered by the department would be = 9,600 ft²

The length of the retail store = 160 ft long

The width of the retail store = 120 ft wide

The formula used to calculate the area of a square= length × width

A = 160×120

= 19,200

The area of the retail = 19,200/2 = 9,600 ft²

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The number of revolutions per foot is 1/4 and the slope is 1/4

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

The graph

The graph passes through the origin

So, we can make use of a point to determine the required

So, we have

Revolution = y/x

This gives

Revolution = 1/4

This is also the same as the slope

i.e. slope = 1/4

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The probability of the spinner not stopping at a white section 0.82.

The probability of the spinner not stopping at a white section is 1 minus the probability of the spinner stopping at a white section.

= 1 - probability of the spinner stopping at a white section

Since there are 2 white sections out of 11 total sections, the probability of stopping at a white section

= required outcome / possible outcome

= 2/11.

Therefore, the probability of not stopping at a white section

= 1 - 2/11

= 9/11.

Rounded to the nearest hundredth, this value is 0.82.

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There are 150 different types of this shirt made.

There are 25 different colors, two different versions (male and female), and three different sizes for each. To calculate the total number of different types of shirt, we can use the formula: (25 colors) x (2 versions) x (3 sizes) = 150. Therefore, there are 150 different types of this shirt made.

To further illustrate, each color is available in both male and female versions, and each version has three sizes (small, medium, and large). As a result, 25 colors x 2 versions x 3 sizes = 150 different types of shirts. So, if you wanted a yellow shirt in size medium, there would be a total of 150 different types of this shirt to choose from. There are 150 different types of this shirt made.

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A formula one race car will travel for 193.45 miles before changing its tires.

From the case, we know that:

tires diameter = 26 in.

1 set of tires = 150,000 rotations

12 in = 1 ft

1 miles = 5280 ft

We need to find the circumference of the tires before finding the total travel length.

Circumference = πd

Circumference = π(26in)

Circumference = 81.714 in.

We need to find the tires circumference in mile scale:

Circumference = 81.714 in : (12 inc/ft) : (5280 ft/miles)

Circumference = 0.0013 miles

Total travel distance = tires circumference x rotations

Total travel distance = 0.0013 x 150,000

Total travel distance = 193.45 miles

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The total surface area of the square pyramid is 240 ft².

A three-dimensional figure is a pyramid. Its base is a flat polygon. The remaining faces are all triangles and are referred to as lateral faces.

The number of sides on its base is equal to the number of lateral faces. The line segments that two faces intersect to form its edges. The intersection of three or more edges forms a vertex.

The total surface area of the square-shaped pyramid is the sum of areas four similar triangles having a height of 8 feet,

And a base of 12 feet and the area of a square having sides lengths of 12 feet which is,

= 4[(1/2)×8×12] + 12×12 ft².

= 4×4×12 + 144 ft².

= 96 + 144 ft².

= 240 ft².

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Answer:

Below

Step-by-step explanation:

X is tha same as the samll angle next to 77°

77+ x = 90    shows x = 13 degrees

Answer:

x=13 degrees

Step-by-step explanation:

by vertical angles, angle FGD = angle CGE = x

by supplementary angles, angle AGD = 90 degrees because angle AGC = 90 degrees

Because you know that AGF = 77 degrees, you can determine that

FGD = AGD-AGF

FGD = 90-77

FGD = 13

because of vertical angles, x = 13 degrees

The only option in which B can be the limiting reagent is A/B = 1.

The molecular equation for this hypothetical reaction is 3A + 3B → 3C + 3D. To determine which reactant is the limiting reagent, we must calculate the mole ratios of the reactants. In this case, we need to compare the ratio of A to B.

If we assume that the equation is balanced, then this means that there are an equal number of moles of A and B in the reaction. Therefore, the mole ratio of A to B is 1:1 (A/B = 1).

The other given options are 2A/7B, A/4B and A/5B. All of these ratios are greater than 1, meaning that B is in excess and will not be the limiting reagent. Therefore, the only option in which B can be the limiting reagent is A/B = 1.

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Answer:

20/6 = 3.33

20 - 6 = 14

Answer:

Step-by-step explanation:

1=3x3)=9+2=11

The amount in weight the baby elephant grew each month is given by the equation m = 38 kilograms

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the amount in weight the baby elephant grew each month be m

Now , the equation will be

The initial weight of the baby elephant a = 134 kilograms

The final weight of the baby elephant b = 362 kilograms

Now , the number of months = n

The value of n = 6 months

So , amount in weight the baby elephant grew each month m = ( b - a ) / n

Substituting the values in the equation , we get

Amount in weight the baby elephant grew each month is

m = ( 362 - 134 ) / 6

On simplifying the equation , we get

m = 228/6

m = 38 kilograms

Hence , the baby elephant grew 38 kg every month

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The  greatest possible area of the shaded region is 462 square centimeter.

The area of Rectangle is length times of width.

In the given figure there are two rectangles.

In one rectangle the length is 28 cm and width is 15cm.

The area of small rectangle=28×15

Area of small rectangle 420

Another rectangle with length 42cm and width 21 cm

The area of large rectangle=42×21

Area of large rectangle 882 square centimeter.

The area of shaded region is 882-420

462

Hence, the  greatest possible area of the shaded region is 462 square centimeter.

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Step-by-step explanation:

14.2% of adults practice meditation in the us

a) Y can be found using the midpoint formula, which states that the midpoint of a line segment has coordinates equal to the average of the coordinates of its endpoints. In this case, the coordinates of Y are equal to the average of the coordinates of X and M.

The formula for finding the midpoint of two points is:

Midpoint = ( (x1 + x2) / 2, (y1 + y2) / 2 )

So, the midpoint of X and Y is ( ( -4 + 4 ) / 2, ( 2 + 3 ) / 2 ) = (0, 2.5)

b) In the same way, the midpoint of X and Y is ( ( -1 + 1 ) / 2, ( -3 + -3 ) / 2 ) = (0, -3)

c) The midpoint of X and Y is ( ( 6 + 2 ) / 2, ( -3 + 1 ) / 2 ) = (4, -1)

d) The midpoint of X and Y is ( ( 4 + 0 ) / 2, ( -3 + -3 ) / 2 ) = (2, -3)

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The translation from figure 1 to figure 2 is 4 units to the left and one unit up.

Here we have two figures, the blue one is figure 1 and the orange one is figure 2.

Clearly we have a translation here, to identify the translation just analyze one of the vertices.

The top vertex at the blue figure is (2, 1)

The top vertex at the orange figure is (-2, 2)

The translation is given by:

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

So we have a translation of 4 units to the left and one unit up.

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Answer:

Step-by-step explanation:

answer is a

Answer:

6

Step-by-step explanation:

3/4 * x/7 = 9/14

x= 6

Answer:

5x18=90

19x17=36

Step-by-step explanation: