Mason plans to study for 1 and 1-half hours. Once he has studied for 1-third of the planned time, he will take a break. Mason has been studying for 12 minutes.
Question
How many ,begin emphasis,more,end emphasis, minutes does Mason need to study before he takes a break? Enter the answer in the box.
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Answer:

Relative frequency of selecting a 2 = 8/50 = 0.16 = 16%

Step-by-step explanation:

You are selecting a random number between 1 and 5, and you perform this task 50 times.

Out of these 50 times, the outcome "2" appears 8 times.

Therefore the relative frequency of selecting the number 2 is:

f(2) = 8/50 = 0.16 which is 16%

The evaluation of the constraints with regards to the production of the polo and t-shirts, and to maximize the profit, using linear programming indicates that we get;

a. x = The number of polo shirts produced, y = The number of t-shirts produced

b. The inequalities representing the constraints are;

2·x + y ≤ 84

x + 2·y ≤ 106

x ≤ 36

x ≥ 0, y ≥ 0

c. P = 30·x + 22·y

d. Please find attached the graph of the feasible region

To maximize profit, the company should produce;

21 polo shirts and 43 t-shirts

Linear programming is a method used for optimizing (maximizing or minimizing a value) operations with some specified constraints.

a. The details indicates that the question is related to linear programming. Let x represent the number of polo shirt produced, and let y represent the number of t-shirts produced.

x = The number of polo shirt produced

y = The number of t-shirts produced

b) The constraints are;

Pattern and cutting section; 2·x + y ≤ 84

Sewing section; x + 2·y ≤ 106

Sales constraints; x ≤ 36

The values of x and y are non negative, numbers, therefore;

x ≥ 0, y ≥ 0

c) The objective of the company is to maximize profit, P, therefore, the objective function is; P = 30·x + 22·y

d) The graph can be plotted from the constraint inequalities, by making y the subject in the inequalities that includes both x and y as follows;

2·x + y ≤ 84, therefore; y ≤ 84 - 2·x

x + 2·y ≤ 106, therefore; y ≤ 53 - x/2

x ≤ 36

Please find attached the graph of the inequalities, showing the feasible region which is the polygon with boundaries which are the lines representing the constraints.

The objective function evaluated at the vertices of the feasible region indicates that we get;

[tex]\begin{tabular}{ | l | l | c | }\cline{1-3}(x, y)& 30\cdot x + 22\cdot y & P(\$) \\ \cline{1-3}(0, 53 & 30\times 0 + 22\times 53 & 1166 \\\cline{1-3}(21, 42.5 & 30\times 21 + 22\times 42.5 & 1565 \\\cline{1-3}(32, 12) & 30\times 36 + 22\times 12 & 1344 \\\cline{1-3}(36, 0) & 30\times 36 + 22\times 0 & 1080 \\\cline{1-3}(0, 0) & 30\times 0 + 22\times 0& 0 \\\cline{1-3}\end{tabular}[/tex]

The feasible region and the objective function indicates that the values of x and y that maximizes the profit is; (x, y)  = (21, 42.5)

Therefore, to maximize profit, the number of polo and t-shirts the company should produce are 21, and 42.5 ≈ 43 respectively.

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Answer: E

Step-by-step explanation:

Step-by-step explanation:

The coordinates and vertices

which reflected over the y- axis are

r(-2,0) , s(2,-3) , and t(2,3).

Answer:

Step-by-step explanation:

To format and solve the equation "f(x) - 4" with the given function "f(x) = 2x + 1," we substitute the function into the equation and solve for x. Here's how it can be done:

f(x) - 4 = 2x + 1 - 4

Simplifying further:

f(x) - 4 = 2x - 3

To answer the question "f(4)" using the function f(x) = 2x + 1, we substitute x = 4 into the function:

f(4) = 2(4) + 1

Simplifying further:

f(4) = 8 + 1

f(4) = 9

Therefore, the value of f(4) is 9 when using the function f(x) = 2x + 1.

The parametric equation of the line passing through P1(2, 4, -3) and P(3, -1, 1) is:

x = 2 + t

y = 4 - 5t

z = -3 + 4t

To find the parametric equation of the line passing through points P1(2, 4, -3) and P(3, -1, 1), we can use the vector equation of a line.

Let's denote the direction vector of the line as d = (a, b, c). Since the line passes through P1 and P, the vector between these two points can be used as the direction vector.

d = P - P1 = (3, -1, 1) - (2, 4, -3) = (1, -5, 4)

Now, we can express the parametric equation of the line as follows:

x = x0 + at

y = y0 + bt

z = z0 + ct

where (x0, y0, z0) is a point on the line and (a, b, c) is the direction vector.

Let's choose P1(2, 4, -3) as the point on the line. Substituting the values, we get:

x = 2 + t

y = 4 - 5t

z = -3 + 4t

Therefore, the parametric equation of the line passing through P1(2, 4, -3) and P(3, -1, 1) is:

x = 2 + t

y = 4 - 5t

z = -3 + 4t

where t is a parameter that varies along the line.

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In general form, the equation 2x^2 - 4x + 6 = 1 can be represented as A = 2, B = -4, and C = 5.

To determine the values of A, B, and C in the general form of the quadratic equation 2x^2 - 4x + 6 = 1, we can compare the given equation with the standard form of a quadratic equation, which is ax^2 + bx + c = 0.

In the given equation, we have:

2x^2 - 4x + 6 = 1

To put it in the general form, we need to move all the terms to the left side of the equation, so the right side is equal to 0:

2x^2 - 4x + 6 - 1 = 0

2x^2 - 4x + 5 = 0

Now we can identify the coefficients A, B, and C in the general form:

A = 2 (coefficient of x^2)

B = -4 (coefficient of x)

C = 5 (constant term)

The values of A, B, and C in the general form of the equation 2x^2 - 4x + 6 = 1 are A = 2, B = -4, and C = 5.

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The cost per trainee for the 5-week training course is $7,000.

To find the cost per trainee, we divide the total cost of the training course by the number of trainees.

Total cost of the training course = $140,000

Number of trainees = 20

Cost per trainee = Total cost of the training course / Number of trainees

Cost per trainee = $140,000 / 20

Cost per trainee = $7,000

Therefore, the cost per trainee for the 5-week training course is $7,000.

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The customer would need to use more than 12.5 megabytes for Plan B to be a better deal. (Option 1) more than 12.5 megabytes).

To determine when Plan B would be a better deal than Plan A, we need to compare the charges for both plans based on the number of megabytes used.

Plan A is represented by the linear function y = 10x, where x represents the total number of megabytes used, and y represents the charge for the plan.

Plan B is represented by the linear function y = 4x + 75, where x represents the total number of megabytes used, and y represents the charge for the plan.

To find the point at which Plan B becomes a better deal, we need to find the x-value where the charge for Plan B is less than the charge for Plan A.

In other words, we need to find the x-value that satisfies the inequality:

4x + 75 < 10x

To solve this inequality, we subtract 4x from both sides:

75 < 6x

Then, we divide both sides by 6:

12.5 < x

Therefore, the customer would need to use more than 12.5 megabytes for Plan B to be a better deal.

This means that option 1) "more than 12.5 megabytes" is the correct answer.

For any value of x greater than 12.5, the charge for Plan B will be less than the charge for Plan A, making it a better deal for the customer.

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The systematic sample would be A. The city manager takes a list of the residents and selects every 6th resident until 54 residents are selected.

The random sample would be C. The botanist assigns each plant a different number. Using a random number table, he draws 80 of those numbers at random. Then, he selects the plants assigned to the drawn numbers. Every set of 80 plants is equally likely to be drawn using the random number table.

The cluster sample is C. The host forms groups of 13 passengers based on the passengers' ages. Then, he randomly chooses 6 groups and selects all of the passengers in these groups.

A systematic sample involves selecting items from a larger population at uniform intervals. A random sample involves selecting items such that every individual item has an equal chance of being chosen.

A cluster sample involves dividing the population into distinct groups (clusters), then selecting entire clusters for inclusion in the sample.

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Answer:

8

Step-by-step explanation:

The value of x is 5625 when √x + √y=138 and x-y=1656.

To solve for x using the given equations, we will use the method of substitution. Let's go through the steps:

Start with the equation √x + √y = 138.

We want to express y in terms of x, so solve for y in terms of x by isolating √y:

√y = 138 - √x

Square both sides of the equation to eliminate the square root:

(√y)² = (138 - √x)²

y = (138 - √x)²

Now, substitute the expression for y in the second equation x - y = 1656:

x - (138 - √x)² = 1656

Expand the squared term:

x - (138² - 2 * 138 * √x + (√x)²) = 1656

Simplify the equation further:

x - (19044 - 276 * √x + x) = 1656

Combine like terms and rearrange the equation:

-19044 + 276 * √x = 1656

Move the constant term to the other side:

276 * √x = 20700

Divide both sides of the equation by 276 to solve for √x:

√x = 20700 / 276

√x = 75

Square both sides to solve for x:

x = (√x)²

x = 75²

x = 5625

Therefore, the value of x is 5625.

By substituting this value of x back into the original equations, we can verify that √x + √y = 138 and x - y = 1656 hold true.

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The expression that represents the statement "Divide the difference of 27 and 3 by the difference of 16 and 4" is (27 - 3) / (16 - 4), which simplifies to 2.

The statement "Divide the difference of 27 and 3 by the difference of 16 and 4" can be represented using algebraic expressions.

To find the difference between two numbers, we subtract one from the other. So, the difference of 27 and 3 is 27 - 3, which can be expressed as (27 - 3). Similarly, the difference of 16 and 4 is 16 - 4, which can be expressed as (16 - 4).

Now, we need to divide the difference of 27 and 3 by the difference of 16 and 4. We can use the division operator (/) to represent the division operation.

Therefore, the expression that represents the given statement is:

(27 - 3) / (16 - 4)

Simplifying this expression further, we have:

24 / 12

The difference of 27 and 3 is 24, and the difference of 16 and 4 is 12. So, the expression simplifies to:

2

Hence, the expression (27 - 3) / (16 - 4) is equivalent to 2.

In summary, the expression that represents the statement "Divide the difference of 27 and 3 by the difference of 16 and 4" is (27 - 3) / (16 - 4), which simplifies to 2.

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Two sets that contain exactly the same elements are called "equal sets" or "identical sets."

In set theory, the concept of equality between sets is defined by the axiom of extensionality, which states that two sets are equal if and only if they have the same elements.

To illustrate this concept, let's consider two sets: Set A and Set B. If every element of Set A is also an element of Set B, and vice versa, then we say that Set A and Set B are equal sets. In other words, the sets have the exact same elements, regardless of their order or repetition.

For example, if Set A = {1, 2, 3} and Set B = {3, 2, 1}, we can observe that both sets contain the same elements, even though the order of the elements is different. Therefore, Set A is equal to Set B.

In summary, equal sets refer to two sets that possess exactly the same elements, without considering the order or repetition of the elements. The concept of equality is fundamental in set theory and forms the basis for various operations and theorems in mathematics.

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Answer:

Step-by-step explanation:

Akira has 3 cheeses to arrange on a cheese board. She would like to arrange them in a row

The number of permutations of n distinct objects is given by n! (n factorial). In this case, Akira has 3 cheeses to arrange in a row. Therefore, the number of different orders she can arrange them is 3! = 6¹⁴.

So Akira can arrange the 3 cheeses in 6 different ways.

Answer:

(x^3+2x-1) * (x^4-x^3+3)

Step-by-step explanation:

To simplify this expression, we can multiply each term in the first expression by each term in the second expression and combine like terms:

(x^3)(x^4) + (x^3)(-x^3) + (x^3)(3) + (2x)(x^4) + (2x)(-x^3) + (2x)(3) + (-1)(x^4) + (-1)(-x^3) + (-1)*(3)

Simplifying further:

x^7 - x^6 + 3x^3 + 2x^5 - 2x^4 + 6x - x^4 + x^3 - 3

Combining like terms:

x^7 - x^6 + 2x^5 - 3x^4 + 4x^3 + 6x - 3

Therefore, the expression representing the product of (x^3+2x-1) and (x^4-x^3+3) is x^7 - x^6 + 2x^5 - 3x^4 + 4x^3 + 6x - 3.

The area of the segment is 9( π-2) units²

The area of a figure is the number of unit squares that cover the surface of a closed figure.

A segment is the area occupied by a chord and an arc. A segment can be a major segment or minor segment.

Area of segment = area of sector - area of triangle

area of sector = 90/360 × πr²

= 1/4 × π × 36

= 9π

area of triangle = 1/2bh

= 1/2 × 6²

= 18

area of segment = 9π -18

= 9( π -2) units²

therefore the area of the segment is 9(π-2) units²

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The solution to the system of equations using the inverse matrix method is x = -1, y = 2, z = 3.

To solve the system of equations using the inverse matrix method, we need to represent the system in matrix form.

The given system of equations can be written as:

| 5 -4 1 | | x | = | 12 |

| 1 7 -1 | [tex]\times[/tex]| y | = | -9 |

| 2 3 3 | | z | | 8 |

Let's denote the coefficient matrix on the left side as A, the variable matrix as X, and the constant matrix as B.

Then the equation can be written as AX = B.

Now, to solve for X, we need to find the inverse of matrix A.

If A is invertible, we can calculate X as [tex]X = A^{(-1)} \times B.[/tex]

To find the inverse of matrix A, we can use the formula:

[tex]A^{(-1)} = (1 / det(A)) \times adj(A)[/tex]

Where det(A) is the determinant of A and adj(A) is the adjugate of A.

Calculating the determinant of A:

[tex]det(A) = 5 \times (7 \times 3 - (-1) \times 3) - (-4) \times (1 \times 3 - (-1) \times 2) + 1 \times (1 \times (-1) - 7\times 2)[/tex]

= 15 + 10 + (-13)

= 12.

Next, we need to find the adjugate of A, which is obtained by taking the transpose of the cofactor matrix of A.

Cofactor matrix of A:

| (73-(-1)3) -(13-(-1)2) (1(-1)-72) |

| (-(53-(-1)2) (53-12) (5[tex]\times[/tex] (-1)-(-1)2) |

| ((5(-1)-72) (-(5(-1)-12) (57-(-1)[tex]\times[/tex](-1)) |

Transpose of the cofactor matrix:

| 20 -7 -19 |

| 13 13 -3 |

| -19 13 36 |

Finally, we can calculate the inverse of A:

A^(-1) = (1 / det(A)) [tex]\times[/tex] adj(A)

= (1 / 12) [tex]\times[/tex] | 20 -7 -19 |

| 13 13 -3 |

| -19 13 36 |

Multiplying[tex]A^{(-1)[/tex] with B, we can solve for X:

[tex]X = A^{(-1)}\times B[/tex]

= | 20 -7 -19 | | 12 |

| 13 13 -3 | [tex]\times[/tex] | -9 |

| -19 13 36 | | 8 |

Performing the matrix multiplication, we can find the values of x, y, and z.

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The value of tan(80°) × tan(10°) + sin(70°) + sin(20°) ​= 2.28171276

Trigonometry is the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). These six trigonometric functions in relation to a right triangle are displayed in the figure.

Given:

tan(80°) × tan(10°) + sin(70°) + sin(20°)

Using Trigonometric identity

sin (A · B) = sin A cos B - cos A sin B

So, tan(80°) × tan(10°) + sin(70°) + sin(20°)

[tex]\rightarrow \tan (80 \times 10)=1[/tex]

[tex]\rightarrow\sin(70^\circ+20^\circ)=1.28171276[/tex]

[tex]\rightarrow 1.28171276+1=\bold{2.28171276}[/tex]

Hence,  tan(80°) × tan(10°) + sin(70°) + sin(20°) = 2.28171276

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Answer:

Mean = 59.1, Median = 61

(there might have been a mistake in calculation (a lot of numbers!))

Step-by-step explanation:

The sample size is 40,

Now, the formula for the mean is,

Mean = (sum of the sample values)/(sample size)

so we get,

[tex]Mean = (49+63+78+22+41+39+75+61+63+65+58+37+45+52+81+75+78+72+68+59+72+85+63+61+75+39+41+48+59+55+61+25+61+52+58+71+75+82+49+51)/40\\Mean = 2364/40\\Mean = 59.1[/tex]

To find the median, we have to sort the list in ascending (or descending)order,

we get the list,

22,25,37,39,39,41,41,45,48,49,

49,51,52, 52,55,58, 58, 59, 59, 61,

61, 61, 61, 63, 63, 63, 65, 68, 71, 72,

72, 75, 75, 75, 75, 78, 78, 81, 82, 85

Now, we have to find the median,

since there are 40 values, we divide by 2 to get, 40/2 = 20

now, to find the median, we takethe average of the values above and below this value,

[tex]Median = ((n/2+1)th \ value + (n/2)th \ value )/2\\where, \ the\ (n/2)th \ value \ is,\\n/2 = (total \ number \ of \ samples) /2\\n/2=40/2\\(n/2)th = 20\\Hence\ the (n/2)th \ value \ is \ the \ 20th \ value[/tex]

And the (n+1)th value is the 21st value

Now,

The ((n/2)+1)th value is 61 and the nth value is 61, so the median is,

Median = (61+61)/2

Median = 61

(a) Based on the total attendance data provided, a bar chart can be constructed to visualize the attendance trends over time. The horizontal axis represents the years (2011, 2012, 2013, 2014), and the vertical axis represents the total attendance. The bars will correspond to the attendance numbers for each year.

(b) A side-by-side bar chart can be created to compare the attendance by visitor category with the year as the variable on the horizontal axis. The visitor categories (school, general, member) will be represented by different colors or patterns, and the bars will show the attendance for each category in each year.

(c) By analyzing the charts from parts (a) and (b), we can observe the trends in zoo attendance.

(a) The bar chart of total attendance over time shows the following trend: In 2011, the attendance was 350,621. It decreased slightly in 2012 to 341,875, remained relatively stable in 2013 at 342,340, and then decreased again in 2014 to 330,113.

(b) The side-by-side bar chart showing attendance by visitor category with year as the variable on the horizontal axis provides a visual comparison of attendance for each category over the years.

The chart reveals that the general category consistently had the highest attendance throughout the years, followed by the school category. The member category consistently had the lowest attendance.

(c) Based on the charts from parts (a) and (b), it can be observed that there has been a general decline in zoo attendance over the years, with a notable decrease from 2011 to 2014.

The drop in attendance could indicate a potential issue that the zoo needs to address in order to attract more visitors.

Additionally, the consistently lower attendance in the member category suggests that the zoo may need to reconsider its membership benefits and strategies to retain and attract more members.

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The distance from point A to point B is approximately 16.64 units. None of the given options (A, B, C, D) match this value exactly, so there seems to be an error in the options provided.

To find the distance from point A to point B, we can use the distance formula in Euclidean geometry. The distance formula between two points (x1, y1) and (x2, y2) is given by:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

In this case, point A is (-8, -3) and point B is (6, 6). Plugging these values into the distance formula, we have:

distance = sqrt((6 - (-8))^2 + (6 - (-3))^2)

= sqrt((6 + 8)^2 + (6 + 3)^2)

= sqrt(14^2 + 9^2)

= sqrt(196 + 81)

= sqrt(277)

≈ 16.64

Thus, the distance between points A and B is roughly 16.64 units. Since none of the available options (A, B, C, or D) exactly match this value, there appears to be a problem with the options.

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Answer:

B

Step-by-step explanation:

SAS Similarity theorem: If two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.

Side 28 is congruent to side 11.2, whereas side 20 is congruent to side 8 and both angles are congruent. Therefore both triangles are similar.

Answer:

$7000

Step-by-step explanation:

700,000 dollars is equal to 70,000,000 pennies.

To convert 700,000 to pennies.

We need to multiply the number by 100, since there are 100 pennies in a dollar.

1 dollar = 100 pennies.

So,  700,000 × 100

= 70,000,000

Therefore, 700,000 is equal to 70,000,000 pennies.

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The total volume of the dill spears is 425 cm³.

To find the total volume of the dill spears, we can subtract the volume of the pickle juice from the volume of the jar.

The jar is in the shape of a cylinder with a base area of 45 cm² and a height of 13 cm. Therefore, the volume of the jar can be calculated using the formula:

Volume of the jar = base area * height

Volume of the jar = 45 cm² * 13 cm

Volume of the jar = 585 cm³

Now, we know that the measuring cup collected 160 cm³ of pickle juice. So, we subtract this volume from the total volume of the jar to find the volume of the dill spears.

Volume of the dill spears = Volume of the jar - Volume of the pickle juice

Volume of the dill spears = 585 cm³ - 160 cm³

Volume of the dill spears = 425 cm³

Therefore, the total volume of the dill spears is 425 cm³.

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Answer:   there are 20 people who claimed to be neither CDO partisans nor ANC partisans.

Step-by-step explanation:

To determine the number of people who are none of these two parties, we need to subtract the total number of people who claimed to be CDO partisans, ANC partisans, and those who claimed to be both from the total number of people surveyed.

Total surveyed people = 130

Number claiming to be CDO partisans = 80

Number claiming to be ANC partisans = 60

Number claiming to be both ANC and CDO = 30

To find the number of people who are none of these two parties, we can calculate it as follows:

None of these two parties = Total surveyed people - (CDO partisans + ANC partisans - Both ANC and CDO)

None of these two parties = 130 - (80 + 60 - 30)

None of these two parties = 130 - 110

None of these two parties = 20

Answer:

I wish you good luck in finding your answer

Domain: The domain is the range of valid heights for the mountain, which is from 3300 feet to 8920 feet.

Range: The range is the set of all possible heights of the linear model, which in this case is also from 3300 feet to 8920 feet.

Domain: The domain of the linear model in this context would represent the possible values for the x variable, which is associated with the height of the mountain.

In this case, the meaningful domain would be the range of valid heights that the mountain can have.

Since the top of the mountain is at 8920 feet and the base is at 3300 feet, the meaningful domain would be the range of heights between 3300 feet and 8920 feet.

Therefore, the domain in this scenario would be [3300, 8920].

Range: The range of the linear model in this context would represent the possible values for the y variable, which is associated with the height of the mountain.

The range would be the set of all possible heights that the linear model can produce.

In this case, since the top of the mountain is at 8920 feet and the base is at 3300 feet, the range would encompass all the valid heights within this range.

Therefore, the range in this scenario would be [3300, 8920].

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Answer:

x intercept : -1

y intercept : 3

Step-by-step explanation:

We have 3x - y = -3 ---eq(1)

The x intercept is the value of x when y = 0 in eq(1),

⇒ 3x - 0 = -3

⇒ x = -3/3

⇒ x = -1

The y intercept is the value of y when x = 0 in eq(1),

⇒ 3(0) - y = -3

⇒ -y = -3

⇒ y = 3