50 Points!!! Use triangle PQR for questions 2-4. What are the values of the trigonometric ratios for R in this triangle?


2. What is the value for sin R? Enter your answer as a fraction.


3. What is the value for cos R? Enter your answer as a fraction.


4. What is the value for tan R? Enter your answer as a fraction

Let the cost of 1 pound of zucchini be 'z' and the cost of 1 pound of tomatoes be 't'. We can set up two equations using the given information:

9z + 6t = 21.15 (equation 1)

4z + 3t = 9.83 (equation 2)

We can solve for 'z' and 't' using the method of substitution:

From equation 2, we can express 4z as 9.83 - 3t:

4z = 9.83 - 3t

Substituting this expression for 4z in equation 1, we get:

9(9.83 - 3t)/4 + 6t = 21.15

Multiplying both sides by 4 to eliminate the fraction, we get:

9(9.83 - 3t) + 24t = 84.6

Expanding the left side, we get:

88.47 - 27t + 24t = 84.6

Combining like terms, we get:

-3t = -3.87

Dividing both sides by -3, we get:

t = 1.29

Substituting this value of 't' in equation 2, we get:

4z + 3(1.29) = 9.83

Simplifying, we get:

4z = 5.56

Dividing both sides by 4, we get:

z = 1.39

Therefore, 1 pound of zucchini costs $1.39 and 1 pound of tomatoes costs $1.29 at the farm stand.

Answer:

z = 1.39

Step-by-step explanation:

The area of this trapezoid is 66 cm².

To find the area of a trapezoid, we use the formula:

Area = (a + b) x h / 2

Where:

a and b are the lengths of the parallel sides of the trapezoid

h is the height

If we assume that the 22 cm and 11 cm sides are parallel sides, that is

a = 22

b = 11

and h = 4 cm

Now we can use the formula to find the area:

Area = (22 cm + 11 cm) x 4 / 2

Area = 66 cm²

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Answer: -3

Step-by-step explanation:

The slope is the number being multiplied by x.

Answer:

m = -3

Step-by-step explanation:

I would respond that Bonnie is correct. A pyramid with 6 vertices, or corners, would have a hexagonal base, which means it would be a pyramid with a base that is a hexagon. Therefore, the correct name for this type of pyramid is a hexagonal pyramid.

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The value of m² - 1 + 1/m² is 5, given that m + 1/m = 3.

In mathematics, a quadratic equation is one with degree 2, which means that its maximum exponent is 2. A quadratic has the standard form y = ax2 + bx + c, where a, b, and c are all numbers and a cannot be zero. All of these are examples of quadratic equations: y = x2 + 3x + 1.

The equation m + 1/m = 3 must first be changed in order to solve for m2 - 1 + 1/m2.

When we multiply both sides by m, we obtain:

m² + 1 = 3m

Rearranging gives us:

m² - 3m + 1 = 0

We can find m using the quadratic formula:

m = (3 ± sqrt(5))/2

When we enter these values into m2 - 1 + 1/m2, we obtain:

((3 + sqrt(5))/2) = m2 - 1 + 1/m2² - 1 + (2/(3 + sqrt(5)))²

If we condense this phrase, we get:

m² - 1 + 1/m² = 5

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Yes, we can determine the sampling distribution of the sample mean.

The name of the distribution is the Student's t-distribution. The mean of the sampling distribution is the same as the mean of the population, which is $51000. The standard error of the sampling distribution is calculated by dividing the standard deviation of the population by the square root of the sample size. So, the standard error is $5500 / sqrt(18) = $1296.56.

Here is the answer formatted in HTML:
Yes, we can determine the sampling distribution of the sample mean. The name of the distribution is the Student's t-distribution.

The mean of the sampling distribution is the same as the mean of the population, which is $51000. The standard error of the sampling distribution is calculated by dividing the standard deviation of the population by the square root of the sample size. So, the standard error is $5500 / sqrt(18) = $1296.56.

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Answer:

B is correct

Step-by-step explanation:

The points all go downhill as you move from left to right. We can draw a straight line that is fairly close to all of them. This is known as the regression line. The regression line having a negative slope tells us the linear association is negative. This means the correlation coefficient r is negative, so,  (r = -1 is not possible as not all points fall on the same straight line)

The surface area of the cylinder with a height of 8 yards and a radius of 82.13 yards is  46,486.93 sq. yards.

What is a cylinder?

One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. One of the fundamental three-dimensional shapes in geometry is the cylinder, which has two distant, parallel circular bases. At a predetermined distance from the centre, a curved surface connects the two circular bases. The axis of the cylinder is the line segment connecting the centres of two circular bases. The height of the cylinder is defined as the distance between the two circular bases.

Given,

The height of the cylinder = 8 yards

 The circumference of the cylinder = 515.79 yards

We are asked to find the surface area of the cylinder.

Now the formula to find the surface area of a cylinder is:

SA = 2πr( r+h)

where r = radius

      h = height

Radius can be found from the circumference formula

2πr = 515.79

r = 515.79/ 2π = 515.79 / (2*3.14) = 82.13 yards

Then,

SA = 2πr( r+h) = 2*3.14*82.13 ( 82.13+8) = 46,486.93 sq. yards

Therefore the surface area of the cylinder with a height of 8 yards and a radius of 82.13 yards is  46,486.93 sq. yards.

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Emily can buy 9 paperback books and 1 hardcover book without spending more than $45.

Let's start by defining our variables

Let x be the number of paperback books

Let y be the number of hardcover books

We know that a paperback book costs $4.50 and a hardcover book costs $10. If Emily buys x paperback books and y hardcover books, then the total cost of her purchase can be calculated using the following equation:

Total cost = 4.50x + 10y

We also know that Emily cannot spend more than $45. So we can set up the following inequality

4.50x + 10y ≤ 45

Now we can use this inequality to find the maximum number of paperback and hardcover books that Emily can buy.

First, let's rearrange the inequality to solve for y:

10y ≤ 45 - 4.50x

y ≤ (45 - 4.50x) / 10

y ≤ 4.5 - 0.45x

So, Emily can buy up to 4.5 - 0.45x hardcover books for every x paperback books. Let's make a table to see the possibilities

From the table, we can see that the maximum number of paperback books that Emily can buy is 12, and the maximum number of hardcover books she can buy is 0. However, this is not a feasible option since she would be spending $54, which is over her budget of $45.

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Anstoo blurry

Step-by-step explanation:

The translated function from y=|x| that has a shrink of ( 1)/(4), a reflection over the x-axis and a vertical shift of 8 units down is y=-|(1)/(4)x|-8.

If f(x) is a function, then a translated function can be defined by adding or subtracting a constant value a to the variable x inside the function, resulting in a new function g(x) = f(x-a) or g(x) = f(x+a), respectively.

To create the translated function from y=|x|  we can follow these steps:
1. Shrink the function by multiplying the input by (1)/(4): y=|(1)/(4)x|
2. Reflect the function over the x-axis by multiplying the output by -1: y=-|(1)/(4)x|
3. Shift the function 8 units down by subtracting 8 from the output: y=-|(1)/(4)x|-8,

Therefore, the translated function is y=-|(1)/(4)x|-8.

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The probability of getting two heads and three tails in a single throw of five unbiased coins is 0.3125.

The probability of getting two heads and three tails in a single throw of five unbiased coins can be calculated using the formula:

P = (5! / (2! * 3!)) * (0.5)^2 * (0.5)^3

Where 5! is the factorial of 5, 2! is the factorial of 2, and 3! is the factorial of 3.

First, calculate the factorial of 5, 2, and 3:

5! = 5 * 4 * 3 * 2 * 1 = 120
2! = 2 * 1 = 2
3! = 3 * 2 * 1 = 6

Next, plug these values into the formula:

P = (120 / (2 * 6)) * (0.5)^2 * (0.5)^3

Simplify:

P = (120 / 12) * (0.25) * (0.125)

P = 10 * 0.25 * 0.125

P = 0.3125

Therefore, the probability of getting two heads and three tails in a single throw of five unbiased coins is 0.3125.

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'x' is an unknown variable, so a value that is not known

The height of the trapezoid is 23 cm.

What is a trapezoid?

A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the other two sides are called the legs. The height of a trapezoid is the perpendicular distance between the two bases.

To find the height of a trapezoid given its parallel sides and area, you can use the formula:

height = 2 * area / (sum of bases)

In this case, the sum of the bases is 12 cm + 18 cm = 30 cm, and the area is 345 cm². Substituting these values into the formula, we get:

height = 2 * 345 cm² / 30 cm

height = 23 cm

Therefore, the height of the trapezoid is 23 cm.

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Answer:

To find the value of b x6 when b = 7, we simply need to substitute 7 for b in the expression and perform the multiplication.

b x 6 = 7 x 6

Multiplying 7 by 6 gives us:

b x 6 = 42

Therefore, when b = 7, the value of b x 6 is 42.

creativeitechnology

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By answering the above question, we may infer that As a result, the inequality answer is 2 x 1.

A connection between two expressions or values that is not equal is known as an inequality in mathematics. Inequality follows imbalance, therefore. In mathematics, an inequality makes a connection between two values that are not equal. Egality and inequality are different. The not equal symbol is often used to indicate that two values are not equal (). Various inequalities are employed to contrast values of all sizes. By changing the two sides until just the variables are left, one may solve many straightforward inequalities. However a variety of factors support inequality: Negative values are split or added on either side. Switch between the left and right.

We may take 3 off of all sides to find the solution to the inequality 1 x + 3 4:

[tex]1 < x + 3 < 4 \s-3 -3 -3 \s-2 < x < 1[/tex]

As a result, the answer is 2 x 1.

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Answer: 7.5

Step-by-step explanation:

     A percent divided by 100 becomes a decimal.

           10% / 100 = 0.1

     Next, since we are finding 10% of 75, we will multiply.

     This will give us 10% of 75.

           0.1 * 75 = 7.5

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Answer:

x = 9

Step-by-step explanation:

given a line parallel to a side of the triangle and intersecting the other 2 sides, then it divides those sides proportionally.

[tex]\frac{x-1}{3x+1}[/tex] = [tex]\frac{6}{21}[/tex] = [tex]\frac{2}{7}[/tex] ( cross- multiply )

7(x - 1) = 2(3x + 1) ← distribute parenthesis on both sides

7x - 7 = 6x + 2 ( subtract 6x from both sides )

x - 7 = 2 ( add 7 to both sides )

x = 9

Answer:

90 degrees clockwise rotation

Step-by-step explanation:

The way to do this is by looking at your transformation rules, where you will find that in a 90 degree clockwise rotation you take your original X and Y, swap them, and make Y negative (y, -x).

To find this, pick any two points from each rectangle (Each point must have the same letter) and compare them:

Example:

Q is at (4, 2) and Q' is at (2,-4). When comparing the two points you will find that X and Y have been swapped, and Y is now negative. This matches the 90 degree clockwise rotation rule

The mean of the given probability distribution is 2.8.

To find the mean, we multiply each possible value of X (the number of adults with a college degree) by its corresponding probability, and then add up the products.

So, the mean is:

(0)(0.0081) + (1)(0.0756) + (2)(0.2646) + (3)(0.4164) + (4)(0.2401) = 2.8

This means that on average, out of 4 randomly selected adults in the town, 2.8 of them will have a college degree. This is a useful measure of the central tendency of the probability distribution, as it gives us an idea of what to expect if we were to repeat this process of randomly selecting 4 adults many times.

It's important to note that the mean is not necessarily a value that is actually observed in the data, but rather a summary statistic that tells us about the distribution as a whole. In this case, it tells us that the distribution is slightly skewed towards higher values, since the mean is greater than the median (which would be the value of X with cumulative probability of 0.5, or 2 in this case).

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Therefore, the lengths of the sides of quadrilateral HIJK are √(65),  13, √(65), and √(52).

A quadrilateral is a polygon with four sides and four vertices. The sum of the interior angles of a quadrilateral is always equal to 360 degrees. There are many different types of quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombuses, and kites. Each type of quadrilateral has its own unique properties, such as having four equal sides (square), having opposite sides parallel (parallelogram), or having two pairs of equal adjacent sides (kite). Quadrilaterals can be classified based on their sides, angles, or both.

Here,

The point H has coordinates (-5, 6), which means it is located 5 units to the left of the y-axis and 6 units above the x-axis. The point I has coordinates (3, 4), which means it is located 3 units to the right of the y-axis and 4 units above the x-axis. The point J has coordinates (0, -8), which means it is located at the intersection of the x-axis and the y-axis, but 8 units below the x-axis. Finally, the point K has coordinates (-7, -2), which means it is located 7 units to the left of the y-axis and 2 units below the x-axis.

We can see that HIJK is a general quadrilateral, meaning that it does not have any special properties like being a rectangle or a parallelogram. We can find the lengths of its sides and the measures of its angles by using the distance formula and the slope formula, respectively. The distance formula gives us the distance between any two points (x1, y1) and (x2, y2):

distance = √((x2 - x1)² + (y2 - y1)²)

The slope formula gives us the slope of a line passing through two points (x1, y1) and (x2, y2):

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

Using these formulas, we can find that the lengths of the sides of HIJK are:

HI = √((3 - (-5))² + (4 - 6)²) = √(65)

IJ = √((0 - 3)² + (-8 - 4)²) = √(169) = 13

JK = √((-7 - 0)² + (-2 - (-8))²) = √(65)

KH = √((-7 - (-5))² + (-2 - 6)²) = √(52)

We can also find the slopes of the lines passing through each pair of adjacent vertices:

The slope of line segment HI passing through points H and I is:

(4 - 6) / (3 - (-5)) = -1/2.

The slope of line segment IJ passing through points I and J is:

(-8 - 4) / (0 - 3) = 4/3.

The slope of line segment JK passing through points J and K is:

(-2 - (-8)) / (-7 - 0) = 6/7.

The slope of line segment KH passing through points K and H is:

(6 - (-2)) / (-5 - (-7)) = 4/3.

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Complete question:

Quadrilateral HIJK has vertices at H(-5,6), I(3,4), J(0,-8), and K(-7,-2). find the length of sides as well as the slopes.

If Alan and Robert worked together, it would take them 6.857 hours to move the inventory from the truck to the shelves

If Robert can move the inventory from his store from the truck to the shelves in 12 hours and Alan can do the same job in 16 hours, then we can find the time it would take for them to do the job together by using the formula for combined work rate:

1/t = 1/12 + 1/16

Multiplying both sides of the equation by 48t gives us:

48 = 4t + 3t

Simplifying and solving for t gives us:

48 = 7t

t = 48/7

t = 6.857 hours

It would take Alan and Robert approximately 6.857 hours to move the inventory working together.

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Answer: By the Vertical Angles Theorem, we know that vertical angles are congruent. Therefore:

x + 8 = 5x - 148

Solving for x:

8 + 148 = 5x - x

156 = 4x

x = 39

So, we have:

x + 8 = 39 + 8 = 47 degrees

5x - 148 = 5(39) - 148 = 47 degrees (by the Vertical Angles Theorem)

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

that means we put -6 into every place, where n is showing in the expression, and then we simply calculate.

cubic root(4n - 3) + n

n = -6

cubic root(4×-6 - 3) - 6 = cubic root(-27) - 6 =

= -3 - 6 = -9

To determine the sample size needed to estimate the proportion of supporters with a margin of error of 2.3% and a 90% confidence level,

we can use the formula:
n = (Z^2 * p * (1-p)) / E^2
Where:
- n is the sample size
- Z is the Z-score for the desired confidence level (for 90% confidence, Z = 1.645)
- p is the estimated proportion of supporters (if we have no prior knowledge, we can use 0.5 as a conservative estimate)
- E is the desired margin of error (2.3% or 0.023)

Plugging in the values, we get:
n = (1.645^2 * 0.5 * (1-0.5)) / 0.023^2
n = 752.3
Since we cannot have a fraction of a person, we round up to the nearest whole number to get a sample size of 753.

Therefore, a sample size of 753 is needed to estimate the proportion of supporters with a margin of error of 2.3% and a 90% confidence level.

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Answer: C | SAS

Step-by-step explanation:

C. SAS - This acronym stands for Side-Angle-Side congruence. This criteria implies that △ABC≅△DEF if two sides and the included angle of one triangle are congruent to two sides and the included angle of the other triangle.

The area of the rhombus is 16√39 sq. cm.

A four-sided polygon with equal-length sides is known as a rhombus. A rhombus is an unique kind of parallelogram, like a square, in which the opposing sides are parallel and congruent. Yet, a rhombus lacks right angles, unlike a square.

Given that, sides = 10cm and the diagonal = 16 cm.

Using the Pythagorean theorem, we can find the length of the other diagonal as follows:

a^2 + b^2 = c^2

(10/2)^2 + b^2 = 16^2/4

25 + b^2 = 64

b^2 = 39

b = √39

The length of the other diagonal is 2*√39 cm.

Now, we can use the formula for the area of a rhombus:

A = (d1d2)/2 = (162√39)/2 = 16√39

Hence, the area of the rhombus is 16√39 sq. cm.

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The area of the rhombus is approximately 62.4 cm².

A rhombus is a quadrilateral with four sides of equal length. It is also known as a diamond or a lozenge. A rhombus has two pairs of parallel sides, and opposite angles are equal to each other. The diagonals of a rhombus bisect each other at right angles, meaning they cut each other in half and form a right angle at their intersection point.

The properties of a rhombus are similar to those of a square, but unlike a square, a rhombus does not have right angles. However, a square can be considered a special case of a rhombus, where all four angles are right angles.

The area of a rhombus can be calculated using the formula:

Area = (diagonal 1 x diagonal 2) / 2

where diagonal 1 and diagonal 2 are the lengths of the two diagonals of the rhombus.

Let's use the Pythagorean theorem to find the length of the shorter diagonal. We know that a rhombus has two pairs of congruent right triangles. Let's call the length of the shorter diagonal d.

Using Pythagorean theorem:

(10/2)² + (d/2)² = (16/2)²

5² + (d/2)² = 8²

25 + (d/2)² = 64

(d/2)² = 39

d/2 = √(39)

d = 2 * √(39)

Now we can use the formula for the area of a rhombus:

Area = (diagonal1 * diagonal2) / 2

Area = (10 * 2 * √(39)) / 2

Area = 10 * √(39)

Therefore, the area of the rhombus is approximately 62.4 cm².

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We can estimate that 900 people in attendance would prefer mustard on a hot dog.

What is proportion?

Proportion is a mathematical concept that refers to the relationship between two quantities, expressed as a ratio or a fraction. It represents the size of one quantity relative to another quantity, typically within a larger population or sample.

To determine the number of people who would prefer mustard on a hot dog, we need to use the proportion of people in the sample who prefer mustard and apply it to the total number of people in attendance.

The proportion of people in the sample who prefer mustard is:

27/150 = 0.18

To estimate the number of people who prefer mustard in the entire population of 5,000 attendees, we can multiply this proportion by the total number of attendees:

0.18 x 5,000 = 900

Therefore, we can estimate that 900 people in attendance would prefer mustard on a hot dog.

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The angle measures, considering the linear pair formed by angles 1 and 2, are given as follows:

When a parallel line is cut by a transversal, a linear pair is formed when two adjacent angles add up to 180 degrees. A linear pair of angles is always formed by two adjacent angles that are supplementary, which means that they add up to 180 degrees.

In this case, a linear pair is formed by two adjacent angles that are formed by the intersection of the transversal with each of the parallel lines.

Hence, angles 1 and 2 are supplementary, meaning that the sum of their measures is of 180º, hence the value of x is obtained as follows:

3x + 5 + 2x + 10 = 180

5x + 15 = 180

5x = 165

x = 33.

Then the measures are given as follows:

The diagram that represents the situation is given by the image presented at the end of the answer.

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