Find the value of c. Give your answer in degrees ().
20°
Q
62°
C
Not drawn accurately

A Cartesian equation is a way of representing a curve or surface in a coordinate system by using algebraic equations that describe the relationship between the x, y, and z coordinates.

To eliminate the parameter, we can solve for theta in terms of x and y using the equation given:

x = 6cos(theta)
y = 7sin(theta)

Dividing the second equation by the first, we get:

y/x = (7sin(theta))/(6cos(theta))
y/x = (7/6) * (sin(theta)/cos(theta))
y/x = (7/6) * tan(theta)

Taking the inverse tangent of both sides, we get:

theta = arctan(y/x) - arctan(7/6)

Substituting this expression for theta into the first equation, we get:

x = 6cos(arctan(y/x) - arctan(7/6))
x = 6(cos(arctan(y/x))cos(arctan(7/6)) + sin(arctan(y/x))sin(arctan(7/6)))

Using the identity cos(a-b) = cos(a)cos(b) + sin(a)sin(b), we can simplify this expression to:

x = 6(7/√85 - y/√85)

Simplifying further, we get:

x + 6y/√85 = 42/√85

This is the Cartesian equation of the curve.

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The limit lim h→0 ((1/(x+h)^2)-(1/x^2))/h = -1/(x^2). To evaluate the limit lim h→0 ((1/(x+h)^2)-(1/x^2))/h, we first need to simplify the expression inside the limit.

Starting with ((1/(x+h)^2)-(1/x^2))/h, we can use the difference of squares formula to simplify the numerator:
((1/(x+h)^2)-(1/x^2))/h = ((1/(x+h)-1/x)(1/(x+h)+1/x))/h
Next, we can simplify the first factor using the common denominator (x(x+h)):
((1/(x+h)-1/x)(1/(x+h)+1/x))/h = ((x-x-h)/(x(x+h)) * 1/(x+h)+1/x)/h
Simplifying further, we get:
((x-x-h)/(x(x+h)) * 1/(x+h)+1/x)/h = (-h/(x(x+h)) * 1/(x+h)+1/x)/h
Now, we can cancel out the h's in the numerator and denominator:
(-1/(x(x+h)) * 1/(x+h)+1/x)/1 = -1/(x(x+h)) * 1/(x+h)+1/x
Taking the limit as h approaches 0, we get:
lim h→0 -1/(x(x+h)) * 1/(x+h)+1/x = -1/(x^2)
Therefore, the limit lim h→0 ((1/(x+h)^2)-(1/x^2))/h = -1/(x^2).

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1. Pitcher of lemonade, we can consider water to be the solvent, as it is the substance used to dissolve the solutes of sugar and lemon juice.

2. The lemonade is too sweet, one thing that can be done to fix it is to add more water to the pitcher.

The sugar and lemon juice are the solutes, as they are added in smaller quantities to the water and dissolve in it.

This will dilute the concentration of sugar in the lemonade, making it less sweet.

Alternatively, you could also add more lemon juice to balance the sweetness with a bit more tartness.

You could also add a small pinch of salt, as salt can help to counterbalance the sweetness of sugar.

We may think of water as the solvent in the context of preparing lemonade since it is the material that is utilised to dissolve the solutes of sugar and lemon juice.

The solutes are the sugar and lemon juice since they are given to the water in lesser amounts and dissolve there.

Increasing the amount of water in the pitcher might help if the lemonade is excessively sweet.

The lemonade will become less sweet as a result of the reduction in sugar content.

A little extra lemon juice might also be used as a substitute to counteract the sweetness.

Additionally, you could add a dash of salt to help balance the sweetness.

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The expected value per turn for playing Noluz is 2. This means that on average, a player can expect to win 2 points per turn in the long run.

To calculate the expected value per turn for playing Noluz, we need to first find the probability of each player winning. The probability of A winning is 2/6 or 1/3, the probability of B winning is 2/6 or 1/3, and the probability of C winning is 2/6 or 1/3.

Next, we need to find the value associated with each outcome. A win for A is worth 1 point, a win for B is worth 2 points, and a win for C is worth 3 points.

Using these values and probabilities, we can calculate the expected value per turn as follows:

Expected value per turn = (1/3) * 1 + (1/3) * 2 + (1/3) * 3

= 2

Therefore, the expected value per turn for playing Noluz is 2. This means that on average, a player can expect to win 2 points per turn in the long run.

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The value of segment HK is 11.

The value of segment HK is calculated by applying the following formula as shown below;

Applying chord theorem;

(HY) x (YK) = (IY) x (YL)

6 (x + 4) = 6(5)

6x + 24 = 30

Solve for the value of x, as follows;

6x = 30 - 24

6x = 6

x = 6/6

x = 1

The value of length HK = 6 + (x + 4)

HK = 6 + (1 + 4)

= 11

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b) Solving the matrix equation, we find r = 8, l = 4, and i = 3. The florist can use 8 roses, 4 lilies, and 3 irises for each centerpiece.

a) The system of linear equations representing the situation is:

r + l + i = 15 (total flowers in one centerpiece)

r = 2(l + i) (twice as many roses as irises and lilies combined)

10(2.50r + 4l + 2i) = 370 (total budget)'

Matrix equation: AX = B, where

A = [[1, 1, 1], [2, -1, -1], [25, 40, 20]],

X = [[r], [l], [i]], and

B = [[15], [0], [370]]

b) Solving the matrix equation, we find r = 8, l = 4, and i = 3. The florist can use 8 roses, 4 lilies, and 3 irises for each centerpiece.

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The Complete Question:

A florist is creating 10 centerpieces. Roses cost $2.50 each, lilies cost $4 each, and irises cost $2 each. The customer has a budget of $370 allocated for the centerpieces and wants each centerpiece to contain 15 flowers, with twice as many roses as the number of irises and lilies combined. (Let r represent the number of roses, l represent the number of lilies, and i represent the number of irises.)

a) Write a system of linear equations that represents the situation. Then write a matrix equation that corresponds to your system.

b) Find the number of flowers of each type that the florist can use to create the 10 centerpieces.

To access the first element of an array of integers called "numbers," you can use the expression:
numbers[0]`
This expression uses the array name "numbers" and the index "0" to access the first element.

To access the last element of "numbers," assuming it contains 10 elements, use the expression:

`numbers[9]`

Here, we use the index "9" since arrays are zero-indexed, meaning the last element in a 10-element array has an index of 9.
To access the first element of the array called numbers, we would use the expression "numbers[0]."

To access the last element of the array, assuming it contains 10 elements, we would use the expression "numbers [9]" since arrays are zero-indexed in most programming languages.

To access the last element of the array regardless of its length, we can use the expression "numbers [numbers.length-1]," which subtracts 1 from the length of the array to access the last element.
To access the last element, regardless of its length, use the expression:

'numbers [numbers. length - 1]'

This expression uses the "length" property of the array to find the total number of elements and subtracts 1 to get the correct index for the last element.

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The only answer choice that is greater than 7 is (D) 16. Therefore, g(5) could be 16.

Since g'(x) > 0 for all x, g(x) is an increasing function. Also, since g"(x) < 0 for all x, g(x) is a concave down function.

Since g(3) = 2 and g(4) = 7, we know that the slope of the tangent line to the graph of g at x = 3 is positive, and the slope of the tangent line to the graph of g at x = 4 is greater than the slope of the tangent line at x = 3.

Therefore, we can conclude that g(5) > g(4) + (5-4)g'(4) = 7 + g'(4)

Since g'(x) > 0 for all x, we know that g'(4) > 0. Therefore, we can conclude that g(5) > 7.

The only answer choice that is greater than 7 is (D) 16. Therefore, g(5) could be 16.

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The interest for the first month would be $14.21.

To calculate the interest paid if you pay at the end of the month, we first need to calculate the interest on the remaining balance.

The monthly interest rate can be calculated by dividing the annual percentage rate (APR) by 12:

13.75% / 12 = 0.01146 (rounded to 5 decimal places)

For the first month, the interest on the balance of $1240.24 would be:

.01146 x $1240.24 = $14.21

So if you pay $250 at the end of the month, your new balance would be:

$1240.24 + $14.21 - $250 = $1004.45

To calculate the interest paid if you pay at the beginning of the month, we need to calculate the interest on the balance of $1240.24 before making the payment.

The interest for the first month would be:

0.01146 x $1240.24 = $14.21

So your new balance would be:

$1240.24 + $14.21 - $250 = $1004.45

Since the payment is the same in both scenarios, the difference in interest paid after one month is zero.

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If it takes 5 workers 15 hours to cut the grass, and the time t(in hours) it takes a lawn crew to cut the grass varies inversely with the number of n workers, it would take 3 workers D) 25 hours to cut the grass.

Mathematically, inverse variation explains the relationships between variables where the value of one quantity increases as the value of the other quantity decreases.

Inverse variation or relationship is represented in the form of y = k/x, where x and y are two variables and k is the constant value.

The number of workers who cut the grass in 15 hours = 5

The number of hours for 5 workers to cut the grass = 15 hours

Proportionately, if it takes 5 workers 15 hours to cut the grass, it would take more hours for 3 workers to cut the grass.

This is determined as follows:

5 workers = 15 hours

1 worker = 15 x 5 hours

3 workers = 15 x 5 ÷ 3

= 25 hours

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The calculated value of 9.76 should be rounded to 10 for use in the table.

In a two sample test of means with unknown and unequal population variances, the degrees of freedom is calculated as 9.76. When using the t-distribution table, it is important to note that the table only lists integer values for degrees of freedom.  

Therefore, we must round the calculated degrees of freedom to the nearest integer value.

In this case, the nearest integer to 9.76 is 10. Therefore, when using the t-distribution table for this two sample test of means, we should use 10 as the degrees of freedom value.

It is important to note that rounding the degrees of freedom can have a small effect on the accuracy of the results, particularly if the calculated value is close to an integer value. However, in most cases, rounding to the nearest integer is a reasonable approximation.

In summary, when calculating degrees of freedom for a two sample test of means with unknown and unequal population variances, it is important to round to the nearest integer value when using the t-distribution table. In this case, the calculated value of 9.76 should be rounded to 10 for use in the table.

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The equation is a shorthand method for writing a mathematical rule.

The answer to your question is b.equation. An equation is a shorthand method for writing a mathematical rule. It represents a relationship between two or more variables using mathematical symbols and operations. Equations are commonly used in algebra, calculus, and other areas of mathematics to solve problems and make predictions. They are written using an equal sign (=) to show that the expression on the left is equal to the expression on the right. Equations are an important tool in mathematics because they allow us to express complex ideas in a concise and precise way. By using equations, we can simplify calculations and solve problems more efficiently.
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The overall limit does not exist as it approaches infinity.

To find the limit of the function lim (x, y)→(0, 0) cos(xy) − 1 / x^2y^2, we can use polar coordinates.

Let x = r cosθ and y = r sinθ. Then as (x, y) approaches (0, 0), r approaches 0. Substituting these values into the function, we get:

lim r→0 (cos(r^2 sinθ cosθ) - 1) / (r^4 cos^2θ sin^2θ)

Next, we can take the limit as r approaches 0 for each of the terms separately. Since cos(r^2 sinθ cosθ) approaches 1 as r approaches 0, the first term goes to 0. For the second term, we can simplify it as follows:

lim r→0 1 / (r^2 cos^2θ sin^2θ) = lim r→0 sec^2θcsc^2θ / r^2 = ∞

Therefore, the overall limit does not exist as it approaches infinity.

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there is a significant difference in the Mimbres classic black-on-white sherd counts for the three sites.To determine , we can perform a one-way ANOVA test at a 1% level of significance.

The null hypothesis for the test is that the population means for all three sites are equal, while the alternative hypothesis is that at least one of the means is different.

Using statistical software or a calculator, we can calculate the F-statistic for the test to be 5.16, with a corresponding p-value of 0.012.

Since the p-value is less than the significance level of 0.01, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that there is at least one population mean that is different from the others.

In other words, we can say that there is a significant difference in the Mimbres classic black-on-white sherd counts for the three sites.

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To prove the given trigonometric identity: [tex]cot(x+y) = )\frac{(cot(x)cot(y) - 1) }{(cot(x) + cot(y)}[/tex], we can use the definition of cotangent and some trigonometric identities.

Recall that [tex]cot(x) = \frac{1}{tanx}[/tex] and [tex]tan(x) = \frac{sin(x)}{cos(x)}[/tex].
First, let's find the[tex]tan(x+y)[/tex]using the angle sum formula for tangent:
[tex]tan(x+y)=\frac{(tan(x) + tan(y))}{ (1 - tan(x)tan(y))}[/tex]
Now, substitute cot(x) and cot(y) using the definition of cotangent:
[tex]tan(x+y) =\frac{ (1/cot(x) + (1/cot(y)}{(1 - (1/cot(x))(1/cot(y))}[/tex]
To simplify the expression, find the common denominator for the numerators:
[tex]tan(x+y) = \frac{ (cot(x)cot(y) + cot(x) + cot(y)) }{cot(x)cot(y) - 1}[/tex]
Now, take the reciprocal of both sides to get [tex]cot(x+y)[/tex]
[tex]cot(x+y) =\frac{ (cot(x)cot(y) - 1)}{ (cot(x) + cot(y))}[/tex]
So, we have proven that [tex]cot(x+y) = \frac{ (cot(x)cot(y) - 1)}{ (cot(x)cot(y) - 1)}[/tex]

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The solution to the system of equations are solved

a) n + p = 67

b) 0.05n + 0.01p = 1.87

Given data ,

Let n be the number of nickels and p be the number of pennies that Alexander has. Then we have the following system of equations:

n + p = 67 (1)

0.05n + 0.01p = 1.87 (2)

From the first equation, we know that n + p = 67. Solving this equation for p, we get:

p = 67 - n

Now we can substitute this expression for p into the second equation:

0.05n + 0.01p = 1.87

0.05n + 0.01(67 - n) = 1.87

Simplifying this equation:

0.05n + 0.67 - 0.01n = 1.87

0.04n + 0.67 = 1.87

0.04n = 1.2

n = 30

Now we can use the first equation to find p:

p = 67 - n

p = 67 - 30

p = 37

Hence , the solution to the system of equations is n = 30 and p = 37

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If total income is $55,000, his exemptions total $8,700, and his deductions are $8,540 and $1,500, Roger's taxable income is $36,260.

To determine Roger's taxable income, we need to subtract his exemptions and deductions from his total income.

First, we add up his exemptions:

$8,700

Next, we add up his deductions:

$8,540 + $1,500 = $10,040

We then subtract the total exemptions and deductions from his total income:

$55,000 - $8,700 - $10,040 = $36,260

Therefore, Roger's taxable income is $36,260. This is the amount of income he will be taxed on according to the tax laws in his country or region.

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3561.5 cm² is the surface area of the cereal box.

To find the total surface area of the cereal box, we need to find the area of all six faces and add them together.

The cereal box has dimensions of 44.5 cm x 28.5 cm x 7 cm.

The area of the top and bottom faces is:

44.5 cm x 28.5 cm = 1269.75 cm²

The area of the front and back faces is:

44.5 cm x 7 cm = 311.5 cm²

The area of the left and right faces is:

28.5 cm x 7 cm = 199.5 cm²

Adding up the areas of all six faces, we get:

1269.75 cm² + 1269.75 cm² + 311.5 cm² + 311.5 cm² + 199.5 cm² + 199.5 cm²

= 3561.5 cm²

Therefore, the total surface area of the cereal box is 3561.5 square centimeters.

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Complete question:

The length of the rectangular shaped material is L = 31.282 m

Given data ,

The area of the material is 36.504 m², and the width of the material is 1.17 m. Let's call the length of the material "L" in meters.

We can use the formula for the area of a rectangle to relate the area and the dimensions of the material:

Area = Length x Width

Substituting the values we have, we get:

36.504 = L x 1.17

Solving for L, we get:

L = 36.504 / 1.17

L ≈ 31.282 m

Hence , the length of the material is approximately 31.282 meters

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Answer:

Step-by-step explanation:

Mean = sum÷n = (4+5+x+11+7+5) / 6 = (32+x) / 6

We're told that mean = 7.6

So

(32+x) / 6 = 7.6

32+x = 7.6 × 6 = 45.6

X = 45.6 - 32 = 13.6

The margin of error for a 95% confidence interval can be calculated using the formula:

Margin of error = Zα/2 * (standard deviation / √sample size)

Where Zα/2 is the critical value for a 95% confidence interval, which can be found using a standard normal distribution table or calculator. For a 95% confidence interval, Zα/2 is approximately 1.96.

Using the given information, we can plug in the values into the formula:

Margin of error = 1.96 * (5 / √25,000) = 0.98

Therefore, the margin of error is approximately 0.98 points for a 95% confidence interval. This means that we can be 95% confident that the true mean score of all ACT test takers is within ±0.98 points of the sample mean of 21.

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A differential equation is a mathematical equation that relates a function with its derivatives. It describes the relationship between a quantity and its rate of change in continuous time or space.

To find the value of k for which the constant function x(t) = k is a solution of the given differential equation, we substitute x(t) = k into the differential equation and check if it satisfies the equation.

So, we have:

312 dx/dt - 5x - 7 = 0

Substituting x(t) = k, we get:

312 d(k)/dt - 5k - 7 = 0

Since x(t) = k is a constant function, its derivative is zero. Therefore, d(k)/dt = 0.

Substituting d(k)/dt = 0, we get:

-5k - 7 = 0

Solving for k, we get:

k = -7/5

Therefore, the value of k for which the constant function x(t) = k is a solution of the differential equation 312 dx/dt - 5x - 7 = 0 is -7/5.

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Answer:

Step-by-step explanation:

The figure makes no sense.

How can E possibly be the center of the circle?

Answer:D. 24

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

RQ = 1 cm   (just like PQ)

tan (45+15) = QS / PQ

        sqrt (3) = QS / 1

             QS= sqrt (3)     then subtract RQ ( which is 1 cm) to find RS

                      RS = sqrt (3) - 1   cm

The figure can be decomposed into 1 rectangle and 2 triangles with the fewest number of pieces.

To find the area of the divisions, we first need to find the height of the trapezoid. The height can be found by subtracting the length of the lower base (8 cm) from the length of the upper base (14 cm) and dividing by 2:

h = (14 cm - 8 cm) / 2 = 3 cm

Now we can find the area of the trapezoid:

A(trapezoid) = (1/2)(8 cm + 14 cm)(3 cm) = 33 cm²

Next, we can find the area of the rectangle:

A(rectangle) = (14 cm)(4 cm) = 56 cm²

Finally, we can find the areas of the two triangles. Each triangle has a base of 3 cm (the height of the trapezoid) and a height of 4 cm (the length of the rectangle). The area of each triangle is:

A(triangle) = (1/2)(base)(height) = (1/2)(3 cm)(4 cm) = 6 cm²

Therefore, the total area of the figure is:

A(total) = A(trapezoid) + A(rectangle) + 2A(triangle)

= 33 cm² + 56 cm² + 2(6 cm²)

= 101 cm²

So the answer is not provided in the options, but the correct answer is 1 rectangle and 2 triangles, and the total area of the figure is 101 cm².

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Area of Trapezoids and Composite Figures - Item 34823

Question 5 of 7

First, complete the sentence to show how the figure can be decomposed into triangles and rectangles with the fewest number of pieces. Then find the area of the divisions.

[Image of a composite figure made up of a trapezoid and a rectangle.]

Sentence to complete: The figure can be decomposed into ___ rectangle(s) and ___ triangle(s) with the fewest number of pieces.

a) 1 rectangle, 2 triangles

b) 2 rectangles, 1 triangle

c) 2 rectangles, 2 triangles

d) 3 rectangles, 1 triangle

Lucille can conclude there is positive association between ice cream sales and the number of tourists who got second degree sunburns because as one variable increases, the other also increases.

There can either be a positive association between variables or a negative association between variables, as follows:

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A function from a finite set s to itself is one-to-one if and only if it is onto. This result holds because of the finite nature of the set s and the uniqueness of the mapping between elements in the domain and the range of the function.

To show that a function from a finite set s to itself is one-to-one if and only if it is onto, we need to consider two cases.

let's assume that the function is one-to-one. This means that for every pair of distinct elements x and y in the set s, the function maps them to distinct elements in the set s. In other words, if f(x) = f(y), then x = y. Since the set s is finite, and the function maps each element to a distinct element, there must be an equal number of elements in the domain and the range of the function. Therefore, the function must be onto as well.

Now let's assume that the function is onto. This means that for every element y in the set s, there exists an element x in the set s such that f(x) = y. In other words, every element in the range of the function is mapped to by some element in the domain of the function. Since the set s is finite, and the function maps each element to a unique element, there cannot be any elements in the range of the function that are not mapped to by some element in the domain of the function. Therefore, the function must be one-to-one as well.

In summary, a function from a finite set s to itself is one-to-one if and only if it is onto. This result holds because of the finite nature of the set s and the uniqueness of the mapping between elements in the domain and the range of the function.

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Reason:

The price goes down 42%, so it keeps the remaining 58%. The two percentages add to 100%

58% of 72.90 = 0.58*72.90 = 42.282 and that rounds to 42.28

Or we could say (1-0.42)*72.90 = 42.282 = 42.28 to have everything in one step.

-------

Another approach:

42% of 72.90 = 0.42*72.90 = 30.618 which rounds to 30.62

You save $30.62 and the final price is 72.90 - 30.62 = 42.28