If tan(theta)= 3/4 and 180 degree < theta < 270 degrees, what is sin(theta)?

The number of students going on the trip is 105 students. The cost per student is $ 243 per student. The number of hotel rooms needed is 27 hotel rooms.

The number of buses needed is 3 buses. The cost to rent snow boots for turbing is $ 6.

Let's define the variables:

s = number of students going on the trip

c = cost per student

h = number of hotel rooms needed for the students

b = number of buses needed

r = cost to rent snow boots for tubing

The equations would then be:

s = 7 chaperones × 15 students/chaperone

$25,515 = s × c

h = ceil (s / 4)

b = ceil ((s + 7) / 48)

$29 = $23 + r

Solving the equations then gives:

Number of students on trip:

s = 7 × 15 = 105 students

Cost per student :

$25,515 = 105 × c

c = $25,515 / 105

= $243 per student

Number of hotel rooms :

ceil(105 / 4) = 27 hotel rooms

Number of buses :

= ceil((105 + 7) / 48)

= ceil(112 / 48)

= 3 buses

Cost per student for snow boots ;

r = $29 - $23

= $6

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Answer: The equation x^2+3x+4 is a quadratic equation.

A quadratic equation is a second-degree polynomial equation in one variable (usually x), where the highest power of the variable is squared (x^2).

In this case, x^2+3x+4 is a second-degree polynomial with the variable x raised to the power of 2. Therefore, it is a quadratic equation.

Linear equations, on the other hand, are first-degree polynomial equations in one variable, where the variable is not raised to any power higher than 1.

Step-by-step explanation:

Ted's work to evaluate the expression 21 ÷ 3 + 5* 3 is incorrect, as he evaluated the division before the multiplication. He follow the wrong order of operations. The correct answer is 22, not 36.

Ted's work is incorrect. In step 1, he evaluated the division before the multiplication, which is incorrect according to the order of operations (PEMDAS). According to the order of operations, multiplication and division should be done before addition and subtraction. Therefore, the correct way to evaluate the expression is as follows:

21 ÷ 3 + 5 * 3

= 7 + 15 (evaluating multiplication before addition)

= 22

Thus, the correct answer is 22, not 36 as Ted calculated. It is important to follow the order of operations in order to arrive at the correct answer.

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_____The given question is incomplete, the complete question is given below:

Ted tried to evaluate the expression 21 ÷ 3 + 5* 3. Here, is his work:

21 ÷ 3 + 5* 3

= 7 + 5 * 3          step 1

= 12 * 3              step 2

= 36

Is his work correct?

Answer:

$84

Step-by-step explanation:

Let's assume, Mary had x $

Now we can make an equation:

[tex]x - 49 - \frac{2}{5} \times (x - 49) = \frac{1}{4} x[/tex]

(After she spent $49, she had (x - 49) dollars left)

Let's multiply this whole equation my 20 (since it's a common denominator):

20x - 980 - 8(x - 49) = 5x

20x - 980 - 8x + 392 = 5x

20x - 8x - 5x = -392 + 980

7x = 588 / : 7

x = 84

The approximate value of the home in 1987 is approximately $161,872.

The formula to calculate the approximate value of a home in 1987 is:

V1987 = 81600 x (1 + 0.12)^7

V1987 = 81600 x 1.987

V1987 = 161872

Therefore, the approximate value of the home in 1987 is approximately 161,872.

To arrive at this answer, we first started with the value of the home in 1980, which was 81,600. We then multiplied this value by 1.12, which is the 12% increase every year, to the seventh power. This resulted in a value of 1.987. We then multiplied this value by the original value of the home in 1980, which gave us the approximate value of the home in 1987. We then rounded the answer to the nearest hundred dollars, which resulted in the answer of 161,872.

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As a result, the function's average rate of change from x = 0 to x = 3 is 4/3 as  the average rate of change of the function from x = 0 to x = 3.

A function is a rule in mathematics that links every element of one set, known as the domain, to a certain element of some other set, known as the range. A function is just a relationship between the values of the input and the output, where the outcome specifically depends on the input. A function can be depicted in a number of different ways, including as an equation, a chart, or a list of values. For instance, the function f(x) = 2x multiplies the input value x by two to get the output value f. (x). The range of this function is indeed the set of all real numbers, and its domain is any set of real numbers.

given

To determine (3, f(3)) on the function graph the average rate of change of the function from x = 0 to x = 3.

According to the graph, the point (0, f(0)) is on the y-axis and has a y-coordinate of 2, while the point (3, f(3)) is on the line that connects the points (2, 0) and (4, 6) and has a slope of m = 3. As a result, we have:

f(0) = 2 and f(3) = 6

We can determine the slope of the line connecting these two points using the slope formula:

m = (f(3) - f(0)) / (3 - 0) = (6 - 2) / 3 = 4/3

As a result, the function's average rate of change from x = 0 to x = 3 is 4/3 as  the average rate of change of the function from x = 0 to x = 3.

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The length and the width of the rectangle are 1cm and 8/3cm

The formula that is used to calculate the area of a rectangle is expressed with the equation;

A = lw

Given that the parameters are;

From the information given, we have that;

Length = 3w - 7

Substitute the values, we have;

40 = (3w - 7)w

expand the bracket

40 = 3w² - 7w

3w² - 7w - 40 = 0

3w² + 15w - 8w - 40 = 0

3w(w + 5) - 8(w + 5) = 0

w = 8/3 or - 5

Length = 3(8/3) - 7 = 1

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The function representing the value of car is 10000 (1 - 0.045)[tex]^{(4t)}[/tex]. The percentage rate of change per quarter is 0.68%. The solution has been obtained by using the substitution method.

What is the substitution method?

The substitution approach is a widely used method in algebra for solving simultaneous linear equations. The name of the method implies that the value of one variable from one equation is changed in the second equation.

We are given that the value of car depreciates 18% every year.

Let f(t) represent the car's worth after t years.

So, we get the function as:

⇒ f(t) = 10000 (1 - 0.18/4)[tex]^{(4t)}[/tex]

⇒ f(t) = 10000 (1 - 0.045)[tex]^{(4t)}[/tex]

Now, the percentage rate of change per quarter is:

⇒ r = [tex](1-q)^{4}[/tex] - 1

Here, q = 0.045

On substituting the value, we get

⇒ r = [tex](1-0.045)^{4}[/tex] - 1

⇒ r = -0.68%

Hence, the required solutions have been obtained.

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Therefore, the answer is option 4: a reflection over the line y=-x-6.

In mathematics, a transformation is a process that changes the position, size, or shape of a geometric object in some way. Transformations are often used in geometry and other branches of mathematics to study the properties of shapes and their relationships to each other.

Here,

To determine which transformation carries the rhombus onto itself, we need to identify the symmetries of the rhombus. A rhombus has two types of symmetry: rotational symmetry and reflectional symmetry.

Option 1: a rotation of 180 degrees clockwise about (-2,-2)

This transformation takes each point of the rhombus and rotates it 180 degrees clockwise about the point (-2,-2). Since the rhombus has rotational symmetry of order 2 (i.e., a rotation of 180 degrees carries the rhombus onto itself), this transformation carries the rhombus onto itself.

Option 2: a rotation of 90 degrees counterclockwise about (-2,-2)

This transformation takes each point of the rhombus and rotates it 90 degrees counterclockwise about the point (-2,-2). Since the rhombus does not have rotational symmetry of order 4 (i.e., a rotation of 90 degrees does not carry the rhombus onto itself), this transformation does not carry the rhombus onto itself.

Option 3: a reflection over the line y=x+10

This transformation reflects each point of the rhombus over the line y=x+10. Since the rhombus does not have reflectional symmetry over this line, this transformation does not carry the rhombus onto itself.

Option 4: a reflection over the line y=-x-6

This transformation reflects each point of the rhombus over the line y=-x-6. Since the rhombus has reflectional symmetry over this line, this transformation carries the rhombus onto itself.

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The angle of depression formed by the cable is approximately 41.4 degrees.

The angle of depression is the angle formed by the horizontal line and the line of sight from the observer to an object that is lower than the observer's position. In this case, the observer is at the top of the tower and the object is at the end of the cable that is stretched to a point 350 feet away from the base of the tower.

To find the angle of depression, we can draw a diagram as follows:

where h is the height of the tower, d is the horizontal distance from the base of the tower to the point where the cable is attached, and θ is the angle of depression that we want to find.

From the diagram, we can see that

tan(θ) = h / d

We know that the length of the cable is 500 feet and the horizontal distance from the base of the tower to the point where the cable is attached is 350 feet. We can use the Pythagorean theorem to find the height of the tower:

h^2 = 500^2 - 350^2

h = sqrt(500^2 - 350^2)

h = 300

Now we can substitute the values we have found into the equation for tan(θ) to get:

tan(θ) = 300 / 350

θ = tan^-1(300/350)

θ ≈ 41.4 degrees

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Applying the linear pair theorem, the measures of the angles in degrees are:

m<ABD = 112°; m<DBC = 68°

The Linear Pair Theorem, also known as the Linear Pair Postulate, is a basic postulate in geometry that describes the relationship between two adjacent angles that form a straight line.

According to the Linear Pair Theorem, if two angles are adjacent and form a straight line, then they are supplementary. In other words, their measures add up to 180 degrees.

Therefore, according to the linear pair theorem, we have:

m<ABD + m<DBC = 180°

Substitute:

7x + 196 + 9x + 176 = 180

16x + 372 = 180

16x = 180 - 372

16x = -192

x = -192/16

x = -12

m<ABD = 7x + 196 = 7(-12) + 196 = 112°

m<DBC = 9x + 176 = 9(-12) + 176 = 68°

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As per the combination method, there are 1260 ways in which a team of 10 students with 6 boys and 4 girls can be formed from a middle school classroom containing 15 students with 9 boys.

To solve this problem, we need to use the concept of combinations. A combination is a way of selecting items from a larger group where the order of selection does not matter. In this problem, we are selecting a team of 10 students, and the order in which we select the students does not matter.

Using this formula, we can find the number of ways to select 6 boys from a group of 9 as:

⁹C₆ = 9! / (6! x (9-6)!) = 84

Similarly, the number of ways to select 4 girls from a group of 6 is:

⁶C₄ = 6! / (4! x (6-4)!) = 15

To find the total number of ways to form a team of 10 students with 6 boys and 4 girls, we need to multiply the number of ways to select 6 boys and 4 girls. This is because the selection of boys and girls is independent of each other, and we can choose them in any order.

Therefore, the total number of ways to form a team of 10 students with 6 boys and 4 girls is:

84 x 15 = 1260

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After answering the provided question, we can conclude that As a result,  normal distribution  the new height requirement for women to join this branch of the military is 57.1 inches to 68.6 inches.

The normal distribution is an example of a constant distribution of probabilities, in which the majority of the points cluster near the range's center and the ones that are left decrease symmetrically towards one of the extremes. The mean of the spread is another term for the range's centre. According to the bell curve, also known as the Distribution function, which is symmetrical well about mean, data that are near the median are more frequent than data that are far from the mean. I'm using heuristics in normality to obtain a child's SAT scores from an innovative exam prep course. The data have a normal distribution with a mean (M) of 1150 and a standard deviation (SD) of 150.

a. To calculate the percentage of women who meet the height requirement, find the area under the normal distribution curve between 58 and 80 inches.

For x = 58 inches: z = (58 - 63.4) / 2.5 = -2.16

For x = 80 inches: z = (80 - 63.4) / 2.5 = 6.64

This means that all women with heights ranging from 58 to 80 inches meet the requirement.

b. For the shortest 1%, we need to find the height that corresponds to z = -2.33:

-2.33 = (x - 63.4) / 2.5

x = 57.1 inches

So the new minimum height requirement is 57.1 inches.

For the tallest 2%, we need to find the height that corresponds to z = 2.05:

2.05 = (x - 63.4) / 2.5

x = 68.6 inches

So the new maximum height requirement is 68.6 inches.

As a result, the new height requirement for women to join this branch of the military is 57.1 inches to 68.6 inches.

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Answer:

(i) 4x

2

−5x−3=0

Let us consider, a=4,b=−5,c=−3

So, by using the formula,

x=

2a

−b±

b

2

−4ac

​

​

So let, b

2

−4ac=D

x=

2a

−b±

D

​

​

D

​

=b

2

−4ac

=(−5)

2

−4(4)(−3)

=25+48

=73

​

So

x=[−(−5)±

73

​

]/2(4)

=[5±8.54]/8

=[5+8.54]/8 or [5−8.54]/8

=13.54/8 or −3.54/8

=1.6925 or -0.4425

∴ Value of x=1.69 or -0.44

Hope it helps

A statement about the model that is true include the following: A. the number of customers visiting the bodega decrease by 25 for every inch of rainfall.

In Mathematics, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;

y = mx + c

Where:

Based on the information provided above, an equation that models the situation is given by;

y = 90 + (-25)x

y = 90 - 25x

By comparison of the two equations, we have:

mx = -25x

Slope, m = -25.

In conclusion, the rate of change is -25 customers per inch of rain.

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so we can look at this as two triangles, one on the upper part, it has a base of 5+5 and a height of 5, and another triangle on the lower part, it has a base of 5+5 and a height of 12, let's get their area and sum them up.

[tex]\stackrel{ \textit{upper part} }{\cfrac{1}{2}(\underset{b}{5+5})(\underset{h}{5})}~~ + ~~\stackrel{ \textit{lower part} }{\cfrac{1}{2}(\underset{b}{5+5})(\underset{h}{12})}\implies25+60\implies \text{\LARGE 85}[/tex]

Answer:

Step-by-step explanation:

17y-12

11y+3(2y-4)

11y+6y-12

17y-12

I hope this helps!

Answer:

y = mx + b

the is the slope intercept formula

The vertices after the dilation arE:

C A'(4, 4), B'(8, 4), C'(8, 6)

The original vertices are  A(2, 2), B(4, 2), and C(4, 3). And we apply a dilation of scale factor 2, then to get the new coordinates ust multiply all the coordinates by 2, we will get.

A' = (2*2, 2*2) = (4, 4)

B' = (4*2, 2*2) = (8, 4)

C' = (4*2, 3*2) = (8,6)

Then the correct option in this case is:

C A'(4, 4), B'(8, 4), C'(8, 6)

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The amount Sylvia should deposit today: P = A / (1 + r/n)^(nt)Where:P = P = $ ___The principal amount is $9,463. So, Sylvia has to deposit $9,463 today.

Sylvia wants to go on a cruise in 4 years. She could earn 7.3% compounded monthly in a bank account if she were to deposit the money today. She needs to have $14,000 in 4 years. To determine the amount Sylvia should deposit today to earn $14,000 in 4 years with a 7.3% interest rate compounded monthly,

we can use the formula for compound interest:A = P(1 + r/n)^(nt)Where:A = the amount of money at the end of the time periodP = the principal, or initial amount of moneyr = the annual interest raten = the number of times interest is compounded per yeart = the time period, in yearsWe need to solve for P.

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The percentage of males who prefer football to baseball and basketball is 20%.

The percentage refers to the quotient or ratios between two values or quantities.

In this situation, the percentage of males who prefer football to baseball or basketball is expressed as the number of football fans over the total number of the three sports fans.

To compute the percentage, the quotient is multiplied by 100.

            Baseball    Basketball     Football     Total

Male         13                  15                 20          48

Female    23                  16                  13          52

Total        36                  31                 33        100

Percentage of males who prefer football = 20% (20/100 x 100)

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Thus, the price of regular brand blueberries is less than the Price of 2 container of Kroger brand blueberries. Hence, Regular Brand is better deal.

A linear equation with two variables is shown by the equation axe + by = r if a, b, and r are all real values and they are not equal to 0. The equation's two variables are represented by the letters x and y. The coefficients are denoted by the numerals a and b.

Given data:

Price of 1 container of Kroger brand blueberries with discount: 3.75 with 15% off.

= 3.75 - 0.15*3.75

= 3.1875

Price of 1 container of Kroger brand blueberries:  $3.1875

Price of 2 container of Kroger brand blueberries:

= 3.1875 * 2

= $6.375

Now,

Price of 2 container of  regular brand blueberries:  $6.25

Thus, the price of regular brand blueberries is less than the Price of 2 container of Kroger brand blueberries. Hence, Regular Brand is better deal.

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Answer: 4 hours

Step-by-step explanation:

3/1=12/x

3x=12

x=4

Yes, Gloria's concern about the computation of the margin of error for a confidence interval for the population proportion being affected by the fact that the population size for all Michigan residents is much smaller than that for all US adults is true.

Sample

A subset of the population is known as a sample. A sample is a smaller group of individuals or things chosen from the population.

Error

The distinction between the estimated value of a population parameter and the true, but unknown, value of that parameter is referred to as an error. Sampling error is the difference between the sample statistic and the population parameter. Inference is less accurate if the sample is too small or if the sample is biased, and the resulting sample statistics may differ from the actual population parameters. 

Hence, from the above, we can conclude that yes the Gloria's concern about the computation of the margin of error for a confidence interval for the population proportion being affected by the fact that the population size for all Michigan residents is much smaller than that for all US adults is true.

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the simplified difference is -1 - 4x + 524. To simplify the difference (1 + 2x) - (6x+2-524), we need to first distribute the negative sign to the second expression inside the parentheses:

(1 + 2x) - (6x+2-524) = 1 + 2x - 6x - 2 + 524  

Now we can simplify by combining like terms:

1 + 2x - 6x - 2 + 524 = (1 - 2) + (2x - 6x) + 524

Simplifying further:

-1 - 4x + 524

Therefore, the simplified difference is -1 - 4x + 524.

It's worth noting that this expression could be simplified further by combining like terms, but it depends on the context and purpose of the expression. For example, if we were trying to solve an equation involving this difference, we might want to simplify it further to make it easier to solve. However, if we were simply asked to simplify the expression, then the answer we have above is sufficient.

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When Frederick purchases a cup of coffee, he gets handed €1.65 in change rather than the expected €1.50. The error percentage is 9.09%

The variation between the real value and the predicted value, in relation to the theoretical value, is known as percentage error.

When compared to the real number and expressed in percent format, percentage error seems to be the gap between the anticipated amount and the actual number. The equation is as follows:

To put it another way, you divide the deviation between the true answer and the answer you guessed by the true answer to get the percent.

Amount paid by Fredrick for cup of coffee:  €1.65

Actual amount: €1.50.

percentage error = (amount paid - actual amount)/amount paid * 100 %

percentage error = (1.65 - 1.50)/1.65 * 100

percentage error = 9.09%

Thus, When Frederick purchases a cup of coffee, he gets handed €1.65 in change rather than the expected €1.50. The error percentage is 9.09%

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30 ÷ (15÷2.5) + 7

Given: 16 · (4.5 + 3) ÷ 10= ____

First let us do PEMDAS (Parenthesis, Equation, Multiply, Divide. Add, Subtract) upon the given value.

16 · (7.5) ÷ 10 = ____

       120 ÷ 10 = ____

                     = 12

We now understand that the given is equal to the value of 12, now we will calculate each equation with PEMDAS until we find the equivalent value.

20.8 + (3 · 4) ÷ 4 =

   20.8 + 12 ÷ 4   =

          20.8  +  3  =

                            = 23.8

24 ÷ (8 − 4) + 8.2 =

       24 ÷ 4 + 8.2 =

               6 + 8.2 =

                            = 14.2

30 ÷ (15 ÷ 2.5) + 7 =

            30 ÷ 6 + 7 =

                     5 + 7 =

                              = 12

36 ÷ (9 − 4.2) + 3 =

       36 ÷ 4.8 + 3 =

                7.5 + 3 =

                            = 10. 5

It is safe to say the following:

16 · (4.5 + 3) ÷ 10 ≠ 20.8 + (3 x 4) ÷ 4

16 · (4.5 + 3) ÷ 10 ≠ 24 ÷ (8 − 4) + 8.2

16 · (4.5 + 3) ÷ 10 = 30 ÷ (15 ÷ 2.5) + 7

16 · (4.5 + 3) ÷ 10 ≠ 36 ÷ (9 − 4.2) + 3

Therefore, the answer is:

16 · (4.5 + 3) ÷ 10 = 30 ÷ (15 ÷ 2.5) + 7

Hope this helps =D, happy learning !

The slope of the line is -1, and the y-intercept is 4.

What is linear function ?

A linear function is a type of mathematical function where the graph of the function is a straight line. It is a function that has a constant rate of change (or slope) between any two points on the line.

In the form of the equation y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis). This equation represents a linear function since the graph of the function is a straight line.

Linear functions are used in many areas of mathematics and science, as well as in real-world applications such as engineering, economics, and physics. They are useful in modeling and predicting relationships between variables that have a constant rate of change over time.

To find the equation of the linear function in the form y = mx + b, we need to determine the slope (m) and y-intercept (b) of the line.

From the graph, we can see that the y-intercept is 4, since the line intersects the y-axis at the point (0, 4).

To find the slope, we can choose two points on the line and use the slope formula:

slope (m) = (y2 - y1) / (x2 - x1)

Let's choose the points (2, 6) and (6, 2):

slope (m) = (2 - 6) / (6 - 2) = -4 / 4 = -1

Therefore, the equation of the linear function is:

y = -x + 4

So, the slope of the line is -1, and the y-intercept is 4.

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