35 out of 56 students want pancakes and the rest want waffles. What is the ratio of the number of students who want waffles to the total number of students?

The values of x in the triangles are 9.23 and 7.5

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

The triangle

Using the above as a guide, we have the following:

cos(52) = x/15

Make x the subject of the formula

So, we have the following representation

x = 15 * cos(52)

Evaluate

x = 9.23

For the second triangle, we have

x = 17 * sin(26)

x = 7.5

Hence, the solution is 9.23 and 7.5

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The Click-O Pen Company produced a total of 7.2×106 pencils during those 4 years.

What is the arithmetic operations?

The basic arithmetic operations are the fundamental mathematical operations used in arithmetic, which include:

To find the total number of pencils produced by the Click-O Pen Company during the 4 years, we need to multiply the number of pencils produced each year by the number of years.

We are given that the company produced 1.8×106 pencils each year for 4 years. Therefore, the total number of pencils produced is:

1.8×106 pencils/year × 4 years = 7.2×106 pencils

Hence, the Click-O Pen Company produced a total of 7.2×106 pencils during those 4 years.

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Answer:

The Click-O Pen Company produced 1.8 x 10^6 pencils each year for 4 years.

To find the total number of pencils produced during those 4 years, we need to multiply the number of pencils produced per year by the number of years:

Total number of pencils produced = (1.8 x 10^6) x 4

= 7.2 x 10^6

Therefore, the Click-O Pen Company produced a total of 7.2 million pencils during those 4 years.

Step-by-step explanation:

Start by identifying the number of pencils produced each year by the Click-O Pen Company. According to the problem statement, the company produced 1.8 x 106 pencils per year.

Next, determine how many years the company produced pencils for. In this case, we know that the company produced pencils for 4 years.

To calculate the total number of pencils produced during those 4 years, we need to multiply the number of pencils produced per year by the number of years. This gives us:

Total number of pencils = 1.8 x 106 pencils/year x 4 years

We can simplify this expression by multiplying 1.8 x 4 to get:

Total number of pencils = 7.2 x 106 pencils

Therefore, the Click-O Pen Company produced a total of 7.2 x 106 pencils during the 4-year period.

The zoo received 1100 visitors that day

You will earn R450 in interest ($1500 x 0.10 x 3 = $450). Simple interest is calculated by multiplying the principal by the interest rate and the number of years.

The interest earned on a fixed deposit of R1500 at 10% p.a simple interest for 3 years will be R450.

To calculate the interest earned, we need to use the simple interest formula:

where I is the interest earned, P is the principal amount, r is the interest rate and t is the time period.

P = R1500

r = 10%

t = 3 years

I = 1500 * 0.10 * 3

I = R450

The interest rate of 10% per annum is the same for each year, and the interest is calculated on the initial principal, not the accumulated interest from previous years. This is why the formula for simple interest is so simple - the same calculation is applied each year, so the amount of interest earned increases each year, but at a slower rate than with compound interest.

The total amount of interest earned over the 3 years is R450, which is calculated by multiplying the principal by the interest rate and the number of years.

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These lines never intersect, there are no solutions to the equation.

In mathematics, a graph is a visual representation of a set of objects and the relationships between them. Graphs are widely used in many areas, including mathematics, computer science, engineering, social sciences, and more.

A graph consists of two main components: vertices (also known as nodes) and edges. The vertices represent the objects, and the edges represent the connections or relationships between them. The edges can be directed or undirected, meaning they can be one-way or two-way relationships.

There are many types of graphs, including:

Undirected graphs: Graphs in which edges have no direction.

Directed graphs: Graphs in which edges have a direction, often represented by arrows.

Weighted graphs: Graphs in which edges have weights or values, representing some kind of numerical data.

Bipartite graphs: Graphs in which the vertices can be divided into two distinct sets, with edges only connecting vertices in different sets.

Complete graphs: Graphs in which every vertex is connected to every other vertex by an edge.

Graphs are used to model and analyze various kinds of data, such as social networks, transportation systems, financial transactions, and more. They are also used in algorithms and data structures, such as shortest path algorithms and tree data structures. In addition, graphs are often visualized using software tools to help people better understand complex relationships and patterns in data.

The given equation is 3x + 1 = 3x + 2.

Subtracting 3x from both sides, we get:

1 = 2

This is a contradiction and there are no values of x that can satisfy this equation.

On a graph, this can be seen as follows:

Plotting the graphs of y = 3x + 1 and y = 3x + 2, we get two parallel lines.

Since these lines never intersect, there are no solutions to the equation.

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The number of students in the van are 6 and in the bus are 35.

A system of equations is a combination of equations with a common solution pair.

Given is that the senior class at high school A rented and filled 3 vans and 7 buses with 263 students. High school B rented 12 vans and 3 buses with 177 students. every van had the same number of students in it as did the buses.

Assume that there are {x} students in each van and {y} students in each bus. We can write the system of equations as -

3x + 7y = 263

12x + 3y = 177

Now, we can write -

3x + 7y = 263

3x = 263 - 7y

4 x 3x = 4(263 - 7y)

12x = 1052 - 28y

So -

1052 - 28y + 3y = 177

25y = 1052 - 177

25y = 875

y = 35                                           ... { 1 }

and

3x + 7 x 35 = 263

3x = 18

x = 6                                            ... { 2 }

Therefore, the number of students in the van are 6 and in the bus are 35.

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Correct statement is that m∠BAD = m∠CAD

A angle bisector is a line that bisects an angle into two equal angles. A bisector means dividing a shape or  object into two equal parts. When we draw a ray that bisects an angle into two equal parts of equal magnitude, it is called angle bisector.

Given,

In triangle ABC,

AD is angle bisector, D lies on BC,

which means, angle BAC is bisected

So,

magnitude of angle BAC will be divided into two equal parts.

m∠BAD = m∠CAD

Hence, m∠BAD = m∠CAD is correct statement given.

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With the help of using Pythagoras Theorem, we find out the value of C in this abc right angled triangle. A = 12units, B = 5 units and C = 13 units.

assuming that A and B are the lengths of the legs of a right angled  triangle and we need to find the length of the hypotenuse (c), we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. Using this theorem, we can write:

c² = a² + b²

Substituting the given values, we get:

c² = 12² + 5²

c² = 144 + 25

c² = 169

c = √169

c = 13

Therefore, the length of the hypotenuse (c) is 13 units. the Pythagorean theorem is a mathematical formula that relates to the sides of a right angled triangle. It states that in a right angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides (legs). The Pythagorean theorem is named after the ancient Greek mathematician Pythagoras and is widely used in geometry and other fields of mathematics. It is a fundamental concept in trigonometry, which deals with the relationships between the angles and sides of triangles.

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Answer: He needs 32 cups of water and 12 cups of drink mix.

Step-by-step explanation: 8 cups + 3 cups = 11 cups

So we know that 8 cups of water + 3 cups of drink mix = 11 cups of 'special energy drink'. Now, Jerome assumes that each person wants 2 cups so we perform the following equation: 22 people x 2 cups = 44 cups. We know that 8 cups of water and 3 cups of drink mix is equal to 11 cups so we just divide: 44 cups/11 cups = 4. Now we need to multiply 8 and 3 by 4 because he needs 4 x 11 cups, that is why we need to multiply  

each of the numbers that make up 11 by 4. 8 cups x 4 = 32 cups,

3 cups x 4 = 12 cups

Answer: He needs 32 cups of water and 12 cups of drink mix.

Step-by-step explanation:

The equation of the axis of symmetry is x = 5/2

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

y = x^2 - 5x + 1

The above equation si a quadratic equation

Differentiate the equation

SO, we have

y' = 2x - 5

Set the differentuated equation to 0

This gives

2x = 5

Evaluate

x =5/2

Hence, the equation is x =5/2

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There are a total of 2π Radians in a circle that is equal to 360°.

A circle is the locus of all those points which are at the same distance from a particular point called center in any plane. A radian is basically another unit of measuring the angle, it is equivalent to the standard degrees measures that we use commonly to find an angle.

When we make a circle, the angle it makes is equal to 360°. This is a characteristics property of a circle.

Now, we know,

π Radians = 180°

2 x 180° = 2xπ Radians

360° = 2π Radians

So, the circle will have a total of 2π Radian in it.

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There have been three main categories of operation on groups in the field of number theory:

In algebra, addition, subtraction, multiplication, and division are the four fundamental arithmetic procedures that represent algebraic operations on trigonometric functions.

1 millisecond is equal to 0 point 001 or 1/1000 of a second. Using the formula seconds = (milliseconds/1000), you can convert milliseconds to seconds.

As per the Time Relationships:

One minute equals 60 seconds.

One hour has 60 minutes.

One Day = 24 hours.

One week is comprised of 7 days.

Twelve months equal one year.

One year is made up of fifty-two weeks.

A year has 365 days (or 366 in leap years) in total.

Ten years equal one decade.

One century is equal to 100 years.

One millennium equals 1000 years.

In Conversion principle:

Multiply from big to little.

Separate, from small to large.

This implies that you must multiply if you change a larger unit to a smaller one. However, you must divide if you take a smaller unit and make it into a larger one.

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We can fill in the given blanks as follows:

x1 =6, x2 = 7 , y1 = -1,  y2 =3. The slope is 4.

What is meant by the slope of a line?

We have seen lines drawn on the coordinate plane in geometry. The best approach to determine without using any geometrical tools if the lines are parallel, perpendicular, or at any angle is to measure the slope. A line's steepness can be determined by looking at its slope. A line's slope in mathematics is defined as the ratio of the change in the y coordinates to the change in the x coordinates. By calculating the difference between the coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of a straight line between them. The letter "m" is frequently used to denote slope.

Given,

(x1, y1)  = (6, −1)

(x2, y2) = (7, 3)

The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] = 3 -(-1) / 7-6 = 4/1 = 4

Therefore we can fill in the given blanks as follows:

x1 =6, x2 = 7, y1 = -1,  y2 =3. The slope is 4.

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Percent difference is a measure of the difference between two values expressed as a percentage of their average.

The formula for percent difference is:

Percent difference = (|value 1 - value 2| / ((value 1 + value 2) / 2)) x 100%

where |value 1 - value 2| is the absolute value of the difference between the two values

((value 1 + value 2) / 2) is their average.

So the Percent difference is a measure of the difference between two values expressed as a percentage of their average.

To calculate percent difference, follow these steps:

Determine the two values you want to compare.

Calculate the absolute difference between the two values by subtracting one from the other and taking the absolute value of the result.

Calculate the average of the two values by adding them together and dividing by 2.

Divide the absolute difference by the average, and multiply by 100% to get the percent difference.

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Answer:

93.6

Step-by-step explanation:

First, convert the time you have to work with to hours:

1 hour 15 minutes = 1.25 hours

required speed to cover 117 miles in 1.25 hours =

distance ÷ time = 117 miles ÷ 1.25 hours = 93.6 miles per hour (apprx.)

Answer:

Option B. y=x+5

Step-by-step explanation:

If x=2 and y=7

Inserting the values into y=x+5

7=5+2

7=7

If x=3 and y=8

y=x+5

8=3+5

8=8

If x=4 and y=9

y=x+5

9=4+5

9=9

If x=5 and y=10

y=x+5

10=5+5

10=10

The new functions are:

(f + g)(x) = 3x - 4

(g - h)(x) = 6x - 4

(f o g)(x) = 2x - 4

(g o h)(x) = -8x - 1

And the value of (f-g)(3) = -2.

To find new functions, we can combine the given functions using arithmetic operations.

(f + g)(x) = f(x) + g(x) = (x - 1) + (2x - 3) = 3x - 4

(g - h)(x) = g(x) - h(x) = (2x - 3) - (1 - 4x) = 6x - 4

(f o g)(x) = f(g(x)) = f(2x - 3) = (2x - 3) - 1 = 2x - 4

(g o h)(x) = g(h(x)) = g(1 - 4x) = 2(1 - 4x) - 3 = -8x - 1

To find (f-g)(3), we need to evaluate the function (f - g) at x = 3:

(f - g)(3) = f(3) - g(3) = (3 - 1) - (2(3) - 3) = 1 - 3 = -2

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The given question is incomplete, the complete question is

If  f(x) = x -1, g(x) = 2x - 3, and h(x) = 1 - 4x, find the following new functions, as well as any values (f-g)(3)

(f + g)(x)

(g - h)(x)

(f o g)(x)

(g o h)(x)

Answer: The answer is {x,y}={17/5,-68/5}

The domain is 0 ≤ x ≤ 52. The maximum number of laws that she can mow with 13 gallons is of 52, and the minimum number is of 0.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The graph touches the y-axis at y = 13, hence the intercept b is given as follows:

b = 13.

When x increases by 20, y decays by 5, hence the slope m is given as follows:

m = -5/20

m = -0.25.

Hence the function is:

y = -0.25x + 13.

From the intercept, the minimum amount can be mowed is given as follows:

0.

The maximum amount is given as follows:

-0.25x + 13 = 0

0.25x = 13

x = 13/0.25

x = 52.

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The conversion factor for converting centimetres to inches (in.) is 0.3937. Thus, the conversion of 167 centimetres to inches is equals to the 68.89 inches.

To convert from one unit to another, multiply by a conversion factor. The centimeter (cm) is the fractional part of the meter, the international standard unit of length, and is approximately equal to 39.37 inches. An inch is a unit of length or distance in measurement system of common American units and British Imperial units. One inch is defined as 1/12 of a feet. To convert a centimeter value to its equivalent inch value, simply multiply the centimeter value by 0.39370078740 (the conversion factor). The formula to convert centimeters to inches is: Inches

= Centimeters × 0.39370078740.

The factor 0.39370078740 is the result of dividing 1/2. So the best formula is inches = centimeters / 2.54. Now we need to convert 175 cm to inches. So, according to the formula, inches = 175 cm / 2.54

= 68.8976377953 ~ 68.89

Hence, required value is 68.89 inches.

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"6x - 5" is the expressions that can be subtracted from 9x to give the result in expression 3x+5.

To find the expression that can be subtracted from 9x to result in the expression 3x+5.

Let the expression be (a - b = c),

Here a = 9x

and the result, c = 3x + 5

We have to find out b = ?

Substitute the values of a and b in the above equation then we get;

9x - b = 3x + 5

9x - (3x + 5) = b

b = 6x - 5

Hence the expressions that can be subtracted from 9x to result in the expression 3x+5 is 6x - 5

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Ashley thinks the lines are parallel is correct. Meanwhile, Alexandro is wrong, he thinks the lines are neither.

The two lines, y = -2x + 7 and 6x + 3y = 21, are parallel because they have the same slope.

To determine if two lines are parallel, we need to check if their slopes are equal.

The slope of the first line, y = -2x + 7, is -2.

The slope of the second line, 6x + 3y = 21, can be found by rearranging the equation to solve for y:

3y = -6x + 21, divided by 3

y = -2x + 7

The slope of the second line is also -2. Since the slopes are equal, the lines are parallel.

However, to determine if two lines are perpendicular, we need to check if the product of their slopes is -1. The slope of the first line is -2, and the slope of the second line is -2.

The product of their slopes is (-2)(-2) = 4, which is not equal to -1. Therefore, the lines are not perpendicular.

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the equation that represents the value of the car after 5 years is Value of car after 5 years = 21,100 x 0.98^5 = 19,105.08

Given:

The cost price of the car, P = $21100,

The depreciation rate = 2%

Calculate the value of the car after 6 years by the following formula,

A = P (1- r / 100)ⁿ

Here A is the value of the car after 6 years.

Substitute the values,

A = 21100 × (1- 2 / 100)^5,

A = $19,105.08

Therefore, the equation that represents the value of the car after 5 years is Value of car after 5 years = 21,100 x 0.98^5 = 19,105.08

The amount after 5 years with a simple interest of 5 % is A = $ 875

Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Given data ,

Let the amount in the bank after 5 years be A

Let the simple interest be represented as I

Now , the principal amount invested = $ 700

The rate of interest r = 5 %

The number of years n = 5 years

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

On simplifying , we get

Simple Interest I = ( 700 x 5 x 5 ) / 100

Simple Interest I = 25 x 7

Simple Interest I = $ 175

Now , the amount after 5 years = P + I = 700 + 175

The amount after 5 years = $ 875

Hence , the amount after 5 years in the bank is $ 875

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The expressions that have 3 as the greatest common factor are b + 3 + 6c, 27n + 66p, and 36 - 9j + 6k.

Thus,

b + 3 + 6c         - Yes

-30 - 24z           - No

27n + 66p         - Yes

36 - 9j + 6k       - Yes

From the question, we are to determine if 3 is the greatest common factor of the given expressions

b + 3 + 6c

3(b + 1 + 2c)

The greatest common factor is 3

-30 - 24z

6(-5 -4z)

The greatest common factor is not 3. The greatest common factor is 6

27n + 66p

3(9n + 22p)

The greatest common factor is 3

36 - 9j + 6k

3(12 - 3j + 2k)

Thus, The greatest common factor is 3

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Answer: The other angle would be 60 degrees.

Step-by-step explanation:

Any of the given ordered pairs could be the outlier depending on the overall distribution of the data.

A pair of items that have a specific significance for the order of their placements is called an ordered pair, as the name suggests.

A point that deviates significantly from the general trend of the other data points is referred to as an outlier. The outlier point would be one that does not fit the pattern, if we assume that the other plotted points constitute a general pattern or trend.

We cannot identify with certainty which point would be the outlier without knowing the other plotted points or the context of the scatter plot. Depending on the overall distribution of the data, any of the ordered pairings that are presented could be an outlier.

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