Set B is the set of positive two-digit even numbers less than 36 that do not contain the digit 2 .

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 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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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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The inequality of the statement is x ≤ 30

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

The bus has a maximum capacity of 30 passengers

Represent the bus capacity with x

This means that the value of x cannot exceed 30

The term cannot exceed implies less than or equal to

So, we have

x ≤ 30

Hence, the inequality is x ≤ 30

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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:

Step-by-step explanation:

for every 24 apples there is 12 bananas

so if you dived it by 2 it will be 12 apples 6 bananas

so it will always be half amount of bananas

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:

Answer:

1,547

Step-by-step explanation:

15' x 20' = 300 square feet

2,275 / 300 = $7.583 per square foot

12 x 17 = 204 square feet

204 x 7.583 = 1,547

The best prediction possible for the number of times you will pick a marble that is not orange, is 7 times.

The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.

Given:

There are 4 pink marbles and 3 orange marbles.

The probability of not picking orange marbles,

= 4/(3 + 4)

= 4/7

If you do this 7 times,

the best prediction possible for the number of times you will pick a marble that is not orange,

= 4/7 x 7

= 4 times

Therefore, number of times is 4.

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The complete question:

There are 4 pink marbles and 3 orange marbles.

You select a marble without looking and then put it back. If you do this 7 times, what is the best prediction possible for the number of times you will pick a marble that is not orange?

The water stream's parabola has the equation y = 48 - (x2)/(20*sqrt(3)), with the vertex at (0, 48) and the point of impact at (10sqrt(3), 0).

The equation of the parabola created by the water stream has a vertex at (0, 48), which is where the pipe ends. It is a quadratic equation. The pipe serves as the middle of the parabola's base, which is symmetrical and has a vertex at that location. The vertex form of a parabola can be used to determine the equation of the parabola, which is y = 48 - (x2)/(20*sqrt(3)). The parabola opens downward, with the highest point at (0, 48) and the lowest point at (10sqrt(3), 0), where the water stream hits the ground, according to the equation. The parabola's vertex and point of impact with the ground are described by the equation for the water's journey.

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Answer:

460

Step-by-step explanation:

Let b = base speed and w = wind power.

Here's what we know:

b + w = 490

b - w = 430

From here, we can use the elimination method. If we treat each variable and constant as columns, we do the following:

b + b = 2b

w - w = 0

490 + 430 = 920

Leaving us with:

2b = 920

Divide by 2:

2b / 2 = b

920 / 2 = 460

So b = 460 mph

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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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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Answer:

16

Step-by-step explanation:

It's the number where the line crosses the y-axis

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

In the land area of Statesville, NC there would be 133.54 persons per square foot.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, One mile is 5280 feet so a square mile is

(5280 × 5280) = 27878400 square feet.

Therefore, The number of persons in each square foot should be,

= 322900000/27878400  persons per square foot.

= 3229000/278784 persons per square foot.

= 133.54 persons per square foot.

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Answer:

14

Step-by-step explanation:

First we can find Wednesdays inventory by doing 16-5, giving us 11

We can do the same thing for Saturday. Doing -2+20 because the change was positive 20, not negative. That brings Saturdays inventory to 18

They said Saturdays change was -4

So taking the 18 and subtracting 4 gets you Sundays inventory of 14

As per the interpolation method, the proportion of orders that are processed in less than 240 seconds is 0.17

The interpolation method is defined as a method of deriving a simple function from the given discrete data set such that the function passes through the provided data points.

Here we have given that at a small coffee shop, the distribution of the number of seconds it takes for a cashier to process an order is approximately normal with mean 276 seconds and standard deviation 38 seconds.

And the proportion of orders that are processed in less than 240 seconds is calculated as,

Here we know that 1 standard deviation below mean = 16% = M - d

Then we apply the value on it, then we get,

=> 276 s - 38 s = 238 s

Here we know that the mean of distribution is,

=> 50% which is equal to 276 s

And the proportion less than 240 s is consider that x%, then by using the interpolation method it can be calculated as,

=> (240 - 238) / (276 - 238) = (x - 16) / (50 - 16)

When we simplify this one then we get,

=> 1/19 = x - 16 / 34

Which can be rewritten as,

=> 19(x - 16)  = 34

=> 19x - 304 = 34

=> 19x = 338

=> x = 17.78%.

Therefore the closest to the proportion of orders that are processed in less than 240 seconds is 17% that is equal to the value of 0.17.

Hence the correct option is (A).

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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

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

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Player 2 is more likely to hit the ball than Player 1 because P(Player 2) > P(Player 1). Therefore, option B is the correct answer.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

Given that, three softball players discussed their batting averages after a game.

Probability:

Player 1: 4/7 =0.57

Player 2: 5/8 =0.625

Player 3: 3/6 =0.5

Therefore, option B is the correct answer.

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Answer:

308/9

Step-by-step explanation:

Answer: 34 + 4/9 x 1/2 = 34 + 2/9 = 36/9.

Decimal Form: 34 + 4/9 x 1/2 in decimal form is 34.22222222.

Step-by-step explanation:

The expression models the total cost for a visitor to go on n rides (c) is 4.00+1.50n

What is Expressions?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.

total cost for a visitor to go on n rides (c) = 4.00+1.50n

Admission fee = 4.00

Cost of each ride = 1.50

Now the cost of each ride is doubled.

New cost of each ride = 2×1.50 = 3.00

New cost model (C') for n rides = 4.00+ 3n

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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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1. Optimal strategy for solving this problem would be to feel for the socks, and grab two socks of the same color at random, as they have a 50% chance of being a match.

2. The total number of different ways they could be combined in pairs, assuming all 20 socks are different colors, is calculated by using the formula (nCr) = n! / (r! * (n-r)!)

So, the total number of different ways they could be combined in pairs would be (20*19)/2 = 190.

3. The total number of different ways they could be combined in pairs would be 10, as there are 10 black and 10 white socks, and they can only be paired with one another.

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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)

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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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]