Solve each trigonometric function IN THE INTERVAL [0, 360)

sin 2x − √3 / 2 = 0

Each comic costs $4.71 and each novel costs $7.29.

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.

Let x be the cost of one comic and y be the cost of one novel.

From Amanda's purchase, we know that:

4x + y = $19

From Janelle's purchase, we know that:

x + 2y = $17

We can use the first equation to solve for y in terms of x:

y = $19 - 4x

We can substitute this expression for y into the second equation:

x + 2($19 - 4x) = $17

x + 2$19 - 8x = $17

-7x = $17 - 2$19

-7x = -$33

x = $33/-7 = $4.71

We can use this value of x to find the value of y:

y = $19 - 4($4.71) = $7.29

Hence, each comic costs $4.71 and each novel costs $7.29.

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The output of a function is returned by the inverse function, which also returns the initial value. Consider the inverse relationship between the functions f and g: f(g(x)) is g(f(x)) is x.

Write the function y as a function of x, i.e., y = f(x), and then solve for x as a function of y, to determine the inverse of a function.

steps for determining a function's inverse.

In the equation expressing the function, swap out f(x) with y.

Swap out x and y. To put it another way, swap out every x for a y and vice versa.

Solve for y.

Change y to f-1 (x).

The output of a function is returned by the inverse function, which also returns the initial value. Consider the inverse relationship between the functions f and g: f(g(x)) = g(f(x)) = x.

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The slope intercept form of the expressions are 0 ≤ x, y > 4 and 5 ≥ x

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

The slope intercept form of an inequality is represented as

y > mx + c

Note that the symbol > can be replaced by the appropriate inequality symbol

When the given expressions are rewritten, we have

0 ≤ x

y > 4

5 ≥ x

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The general solution of an exact differential equation can also be found by solving the associated homogenous equation and adding the particular solution obtained from the original equation.

1. Identify the exact differential equation.

2. Find the integrating factor by multiplying the equation by an expression of the form e^(f(x)).

3. Multiply the integrating factor with the equation to make it exact.

4. Integrate both sides of the equation to obtain the general solution.

5. Check the solution by differentiating it to confirm that it satisfies the original equation.

6. Add the particular solution obtained from the original equation to the homogenous solution to get the general solution.

The general solution of an exact differential equation can be found by using an integrating factor. An integrating factor is a function of the independent variable which can be multiplied with the equation in order to make it exact. Once the equation has been made exact, it can be solved using the standard integration techniques. In addition, the general solution can be found by solving the associated homogenous equation and then adding the particular solution obtained from the original equation.

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Answer: C

Step-by-step explanation:

The length of the PR would be 82.

Option (A) is correct.

What is an expression?

An expression is a combination of numbers, variables, and mathematical operations that represents a value or a computation. Expressions can be simple or complex and can include constants, variables, and various mathematical operations such as addition, subtraction, multiplication, and division. Expressions are often used to represent mathematical operations in algebraic, trigonometric, and calculus problems. They can be evaluated to find a numerical value or simplified to reveal underlying mathematical relationships.

In the given figure, the length of both line segments is equal, hence

PR = 10x + 842

PQ + QR = 10x + 842

8x + 678 + 12 = 10x + 842

First we can subtract 12 from both sides of the equation:

8x + 678 = 10x + 830

Then we can subtract 8x from both sides of the equation:

678 = 2x + 830

Then we can subtract 830 from both sides of the equation:

-152 = 2x

Then we can divide both sides of the equation by 2:

x = -76

So PR = 8x + 678 + 12

PR = 8(-76) + 678 + 12

PR = -608 + 678 + 12

PR = -608 + 690

PR = 82

Hence, the length of the PR would be 82.

Option (A) is correct.

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If 12 out of every 15 people prefer eating at a restaurant, then 12/15 of the people who took the survey chose that option. We know that 12/15 of the total number of people who took the survey is equal to 400 people, so we can set up the equation:

(12/15)x = 400

To find the total number of people who took the survey, we can solve for x by multiplying both sides of the equation by 15/12:

x = (400)(15/12)

x = 500

So, 500 people took the survey.

The height of the fabric is 8 ft.

Now, According to the question:

Rachel is making a tent.

The triangular piece of fabric for the front of her tent has an area of 24 [tex]ft^2[/tex]

and, it is 6 feet long at it's base.

We have to find the height of the fabric .

Now, Based on the given condition:

Formulate the problem:

24 × 2 ÷ 6

Cross out the common factor:

4 × 2

Calculate the product or quotient :

= 8

Hence, the height of the fabric is 8 ft.

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y = 32 home runs will Mario hit during his ninth season.

Now, According to the question:

Linear models describe a continuous response variable as a function of one or more predictor variables. They can help you understand and predict the behavior of complex systems or analyze experimental, financial, and biological data. Linear regression is a statistical method used to create a linear model.

According to the graph, we have

The equation is:

y = 3x + 5

Put the value of x = 9

We get:

y = 3 × 9 + 5

y = 32

(Figure out the function of the image, and then bring the value of 'x' into it.)

Hence, y = 32 home runs will Mario hit during his ninth season.

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Here is one possible system of equations to represent the information provided:

Let x be the number of apple pies, y be the number of pumpkin pies, and z be the number of key lime pies.

The number of apple pies is the same as the number of pumpkin and key lime pies combined, since both tables have the same number of pies: x = y + z

There are twice as many pumpkin pies as key lime pies: y = 2z

There are 5 more apple pies than pumpkin pies: x = y + 5

Solving for y in the second equation, we have: y = 2z

Substituting that into the first equation we have: x = 2z + z = 3z + 5

Substituting that into the third equation we have: x = y + 5 = 2z + 5

So we have a system of equations:

Now we can solve for any of the variables. Let's find the number of PUMPKIN pies

y = 2z

We can substitute in any value of z to get y.

For example, if we let z=5, we can find that

y=2(5)=10 pumpkin pies

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The required equation is x × 3 = 528.75 - 60.

The cost of the labor per hour is $156.25

How do equations work?

The definition of an equation is a mathematical statement with at least two terms that contain variables or equal numbers.

Let x be the cost of the labor per hour.

We know that

x × 3 = labor cost

60 + x × 3 = total cost

We also know that the total cost is $528.75

So we can write the equation:

60 + x × 3 = 528.75

Solving for x:

x × 3 = 528.75 - 60

x × 3 = 468.75

x = 468.75/3

x = 156.25

Therefore, the cost of the labor per hour is $156.25

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The total number of quarters James and his brother will be 5x

Addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.

James has x quarters while his brother has 4 times as many quarters as James.

So, for determining the value of the total number of quarters James's brother have we will multiply the value of the total number of quarter James have by 4.

So, the value of the total quarter James's brother has = 4*x = 4x

Now for determining the total number of quarters of James and his brother we will add both values.

The total number of quarters James and his brother will be= x+4x = 5x

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Answer: The equation provided is already solved, on the left side of the equation it shows the step by step solution of the equation:

3(x-2)+x-1 = 3(x-2) + x - 1 = 5

3x - 6 + x - 1 = 5

Combining like terms

4x - 7 = 5

Adding 7 to both sides

4x = 12

Dividing both sides by 4

x = 3

So the value of x that makes the equation true is x = 3

Step-by-step explanation:

Range, because it measures the distinction between the highest and lowest values in a dataset, providing a clear estimate of variability for both sets of data. It is unaffected by skewness or symmetry, making it a useful measure of variability for comparing the temperature consistency of Desert Landing and Flower Town.

A histogram is a rough illustration of how numerical values are distributed. Karl Pearson coined the phrase at the beginning.

A histogram is a visual representation of statistical data that makes use of rectangles to illustrate the frequency of data points over a range of successive numerical intervals of equal width. The independent variable and dependent variable are plotted along the horizontal axis and the vertical axis, respectively, in the most typical type of histogram.

A common tool for graphing is the histogram. It is employed to summarise continuous or discrete data that is measured on an interval scale. It is frequently used to provide a convenient manner of illustration for the main characteristics of the data distribution.

Therefore, the correct answer is both option c) and d) Range, because Flower Town is skewed and symmetric.

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Answer:

The correct answer is:

Range, because Flower Town is symmetric

Using inequality, the minimum number of towels in the pack is t = 6.

We can start by using the inequality 2.85t > 22, where t is the number of towels in the pack.

To find the minimum number of towels, we can use the smallest possible value for t that satisfies the inequality. Since the hand towels were available in packs of 4, 5, 6, and 8, we can use t = 4 in the inequality:

2.85(4) > 22

Simplifying the left side of the inequality gives:

11.4 > 22

This is not true, so t = 4 does not satisfy the inequality.

Next, we can use t = 5:

2.85(5) > 22

Simplifying the left side of the inequality gives:

14.25 > 22

This is also not true, so t = 5 does not satisfy the inequality.

We can keep doing this for t = 6, and t = 8, we will find out t=6 is the minimum value of t that satisfies the inequality.

2.85(6) > 22

Simplifying the left side of the inequality gives:

17.1 > 22

This is true, so t = 6 is the minimum number of towels in the pack.

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When White Oak is 15 miles from River City and the scale is 1 in.=3 mi, the distance in the map is 5 inches.

The ratio that describes the relationship between the actual figure and its model is called the scale. It serves as a representation of the actual figures in smaller units on maps. A scale of 1:5, for instance, means that 1 on the map is equivalent to the size of 5 in the real world.

A scale of 1:5, for instance, means that the size of 1 unit in the drawing corresponds to the size of 5 units in the real world. A scale of 1:5 is evident, for instance, if a giraffe that stands 150 inches tall in real life is depicted on the drawing as 30 inches tall.

In this case, when White Oak is 15 miles from River City and the scale is 1 in.=3 mi, the distance in the map is:

= 15 / 3

= 5 inches.

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Answer:

12ft  x 9ft

Step-by-step explanation:

1/6" equals 1' actual ==> 1"=6'actual.

1.5" = 9'

2" = 12'

By utilizing the given scale of 1/6 inch equals 1 foot, the actual length of the bathroom is calculated to be 9 feet and width is 12 feet, from the given measurements of the drawing.

The mentioned math problem is based on scale conversion, specifically in the realm of measurement. Given that every 1/6 inch on the scale drawing equals 1 foot in reality, the first step to solving this problem is to convert the measurements of the drawing into scale inches. To convert the length of 1 1/2 inches to the actual length, multiply 1.5 by 6 (as 1 inch is 6 times of 1/6 inch). This equals to 9 feet. Similarly, for the width of 2 inches, multiply 2 by 6 to get 12 feet.

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The amount of money in Davinder's account after five years is equal to £236.

Mathematically, simple interest can be calculated by using this formula:

S.I = PRT or S.I = A - P

Where:

Substituting the given parameters into the simple interest formula, we have;

S.I = 200 × 4.5/100 × 5

S.I = 200 × 0.045 × 4

S.I = £36.

Next, we would calculate the future value as follows;

Future value, A = S.I + P

Future value, A = £36 + £200

Future value, A = £236.

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There is sufficient evidence at 0.10 level of significance that the machine is overfilling the bags. So the option 1 is correct.

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 418 gram setting.

For the given question,

The Hypothesis for the test would be:

H(0): μ = 418

H(1): μ > 418

The fact that the null hypothesis is rejected means that there is enough data to conclude that the machine is significantly overfilling the bags at the 0.10 level of significance.

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The complete question is:

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 418 gram setting. Is there sufficient evidence at the 0.10 level that the bags are overfilled? Based on a 24 bag sample, the manufacturer decides to reject the null hypothesis. What is the conclusion?

1. There is sufficient evidence at the 0.10 level of significance that the machine is overfilling the bags.

2. There is not sufficient evidence at the 0.10 level of significance that the machine is overfilling the bags.

These two lines intercept on a graph on the coordinate X(0, 1) Y(9, 7).

The term "intercept" refers to the location where a line or curve intersects an axis on a graph. An object's x-intercept is defined as where a point crosses the x-axis. The term "y-intercept" refers to a point that crosses the y-axis. The intersection of the x-axis and the y-axis is what is meant by a line's intercept.

step1

y=-2x+9

graph the line using the slope and y intercept or two points

y=-2x+9

X(0,1) Y(9,7)

step2

y=3x-6

slope 3 y intercept (0,-6)

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Answer:

Since Marshall gives away 13 buttons out of b buttons, it means that b is an expression of a number which is greater than 13. Therefore,the answer is b - 13.

Total number of  a customer uses his phone each day in hour 0.25t + 1.75

Total number of  a customer uses his phone each day in hour (e) =  the customer spend time in hour on calls +  the customer spend time in hour on texts.

total number of  a customer uses his phone each day in hour (e) =  the customer spend time in hour on calls +  the customer spend time in hour on texts.

the customer spend time in hour on calls = the number of calls the customer made per day (t) times the average time spent by customers per day per hour (0.25 hours)

The number of hours the customer spend on texts is given as 1.75 hours each day.

Therefore required equation is:

e = 0.25t + 1.75

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The surface area of the pyramid is 1702.8 ft².

The area of a three dimensional object on it's outer surface is called the surface area of the object.

Rectangular pyramid has a rectangular base and four triangular faces.

Net of the pyramid is shown below.

Area of the rectangular base = 25 × 22 = 550 ft²

Now we have to find the area of four triangular faces.

Area of a triangle = [tex]\frac{1}{2}[/tex] × base × height

Heights of the triangle BCX and ADZ can be found as below :

Combined height of both triangles = 74.8 - 25 = 49.8

Height of each triangle = 49.8 / 2 = 24.9 ft

Area of triangles BCX and ADZ = 2 × ( [tex]\frac{1}{2}[/tex] × base × height)

                                                    = Base × height

                                                    = 22 × 24.9

                                                    = 547.8 ft²

Similarly,

Combined height of triangles ABW and CDY = 70.4 - 22 = 48.4

Height of each triangle = 48.4 / 2 = 24.2 ft

Area of triangles ABW and CDY = Base × height

                                                      = 25 × 24.2

                                                      = 605 ft²

Total surface area of the pyramid = 550 ft² + 547.8 ft² + 605 ft²

                                                        = 1702.8 ft²

Hence 1702.8 ft² is the total surface area of the pyramid.

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deci nu știi să faci matematică?

The age of Bryson today is 11 1/3 years

From the question, we have the following mathematical statements:

Bryson's dad age = 38

Bryson's dad age = 4 + 3 * Bryson's age

Represent Bryson's age with x

So, we have the following equation

Bryson's dad age = 38

Bryson's dad age = 4 + 3x

substitute the known values in the above equation, so, we have the following representation

4 + 3x = 38

Evaluatet the like terms

3x = 34

Divide by 3

x = 11 1/3 years

Hence, Bryson's age as per the mathematical statement is 11 1/3 years

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The amount of money Rashon would need to invest is equal to $8,300.46.

Mathematically, the compound interest on an investment can be calculated by using this mathematical expression:

A(t) = P(1 + r/n)^{nt}

Where:

In this scenario, Rashon's investment is compounded quarterly at an interest rate of 6.9% as follows:

Quarterly interest rate = 0.069/4

Quarterly interest rate = 0.01725%

20,200 = P(1 + 0.01725)^{4 × 13}

20,200 = P(1.01725)^52

20,200 = 2.4336P

Principal, P = 20,200/2.4336

Principal, P = $8,300.46.

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Answer:

In this scenario, Rashon's investment is compounded quarterly at an interest rate of 6.9% as follows:

Quarterly interest rate = 0.069/4

Quarterly interest rate = 0.01725%

20,200 = P(1 + 0.01725)^{4 × 13}

20,200 = P(1.01725)^52

20,200 = 2.4336P

Principal, P = 20,200/2.4336

Principal, P = $8,300.46.

Answer:

0.82

Step-by-step explanation:

A： area =2( 0.8*0.6*+0.6*1+0.8*1) =2(0.48+0.6+0.8)=2*1.88 =3.76

B：area = 2(1.4*0.5+0.5*1.2+1.4+1.2) =2(0.7+0.6+1.68)=2*2.98=5.96

total 9.72

cost = $6.79* 9.72/80 =$0.82

Answer:

So there are 11 mg of calcium in apples.

38 mg of calcium in oranges.

And 6 mg of calcium in bananas.

So if he ate 7 apples, that adds up to:

7 * 11 = 77 mg of calcium.

4 oranges adds up to:

4 * 38 = 152 mg of calcium

2 bananas adds up to:

2 * 6 = 12 mg of calcium.

In total:

77 + 152 + 12 = 241

Alen ate 241 mg of potassium

Step-by-step explanation:

Hope it helps! =D

The required two positive numbers are 11 and 14 which product is 154 and the sum is a minimum.

A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9.

The product is 154 and the sum is a minimum.

As per the question, the required solution would be as:

product           sum  

1 x 154         1 + 154 = 155

2 x 77          2 + 77 = 79

11 x 14          11 + 14 = 25

7 x 22         7 + 22 = 29

Here, we can arrange these numbers as:

25 < 29 < 79 < 155

This means the sum (11 + 14 = 25) is a minimum.

So the minimum value = 11

And the maximum value = 14

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The function g(x) with a graph that is the reflection of the graph of f(x) = - square root 14x across the x-axis is given as follows:

[tex]g(x) = \sqrt{14x}[/tex]

The parent function f(x) is defined as follows:

[tex]f(x) = -\sqrt{14x}[/tex]

The rule for a reflection over the x-axis is given as follows:

g(x) = -f(x).

Meaning that only the signal of the function is changed.

Removing the negative signal, the function g(x) is then defined as follows:

[tex]g(x) = \sqrt{14x}[/tex]

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Answer:

4.34

Step-by-step explanation:

proportional: 2.8/2.5 =1.12

body + tail = body + 1.12 body = 2.12 body = 9.2.

so body = 9.2/2.12 = 4.34