A study was conducted at a local college to analyze the average cumulative GPA’s of students who graduated last year. In each of the following situations, identify the population, Statistic, Parameter, Variable, Data and the Sample.

a) all students who attended the college last year

b) the cumulative GPA of one student who graduated from the college last year

c) 3.65, 2.80, 1.50, 3.90

d) a group of students who graduated from the college last year, randomly selected e) the average cumulative GPA of students who graduated from the college last year

f) all students who graduated from the college last year

g) the average cumulative GPA of students in the study who graduated from the college last year
​

To find a particular solution of the non-homogeneous equation and the general solution of the equation, we can use the method of variation of parameters.

First, let's find the Wronskian of the homogeneous solutions y1(x) and y2(x):

W(y1, y2) = | y1 y2 |

| y1' y2' |

We have y1(x) = sin(x) / √x and y2(x) = cos(x) / √x. Differentiating these functions, we get:

y1'(x) = (cos(x) / √x - sin(x) / (2√x^3))

y2'(x) = (-sin(x) / √x - cos(x) / (2√x^3))

Substituting these values into the Wronskian:

W(y1, y2) = | sin(x) / √x cos(x) / √x |

| (cos(x) / √x - sin(x) / (2√x^3)) (-sin(x) / √x - cos(x) / (2√x^3)) |

Expanding the determinant:

W(y1, y2) = (sin(x) / √x) * (-sin(x) / √x - cos(x) / (2√x^3)) - (cos(x) / √x) * (cos(x) / √x - sin(x) / (2√x^3))

Simplifying:

W(y1, y2) = -1 / (2√x)

Now, we can find the particular solution using the variation of parameters formula:

y_p(x) = -y1(x) * ∫(y2(x) * g(x)) / W(y1, y2) dx + y2(x) * ∫(y1(x) * g(x)) / W(y1, y2) dx

Here, g(x) = 3x√xsin(x). Substituting the values:

y_p(x) = -((sin(x) / √x) * ∫((3x√xsin(x)) * (-1 / (2√x))) dx + (cos(x) / √x) * ∫((3x√xsin(x)) / (2√x)) dx

Simplifying the integrals:

y_p(x) = -(∫(-3sin^2(x)) dx) + (∫(3xcos(x)sin(x)) dx)

Integrating:

y_p(x) = 3/2 (xsin^2(x) - cos^2(x)) - 3/2 (xcos^2(x) + sin^2(x)) + C

Simplifying:

y_p(x) = 3x(sin^2(x) - cos^2(x)) + C

The general solution of the equation is given by the sum of the homogeneous solutions and the particular solution:

y(x) = C1 * (sin(x) / √x) + C2 * (cos(x) / √x) + 3x(sin^2(x) - cos^2(x)) + C

where C1, C2, and C are arbitrary constants.

Answer: I WOULD SAY 45%

Step-by-step explanation:

The percentage increase in miles per gallon from Toyota city driving to highway driving is 33.33%.

The percentage increase in miles per gallon from Toyota city driving to highway driving can be calculated using the formula:

Percentage increase = ((new value - old value) / old value) x 100

Let's say the old miles per gallon for city driving is 30 and the new miles per gallon for highway driving is 40:

Therefore, there is a 33.33% increase in miles per gallon from Toyota city driving to highway driving.

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The blanket's width is determined by adding up the widths of each individual stripe, resulting in a total width of 104 inches.

To find the width of Alyssa's blanket, we need to calculate the total width of all the pink and white stripes combined.

Given that there are 7 pink stripes and 6 white stripes, and each stripe is 8 inches wide, we can calculate the total width as follows:

Total width = (Number of pink stripes [tex]\times[/tex] Width of each pink stripe) + (Number of white stripes [tex]\times[/tex] Width of each white stripe)

Substituting the values into the equation:

Total width [tex]= (7 \times 8) + (6 \times 8)[/tex]

= 56 + 48

= 104 inches.

Therefore, Alyssa's blanket is 104 inches wide.

In this case, we multiply the number of pink stripes by the width of each pink stripe (7 [tex]\times[/tex] 8) and add it to the product of the number of white stripes and the width of each white stripe (6 [tex]\times[/tex] 8) to obtain the total width of the blanket.

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The coefficient of variation or CV of the given numbers is 45.64%.

Given numbers are,

5, 8, 9, 2, 6

We have to find Coefficient of variation.

CV = (Standard deviation / sample mean ) × 100

Sample mean = Sum of the values / total number of values

                       = (5 + 8 + 9 + 2 + 6) / 5

                       = 6

Standard deviation = √[(Σ(x - mean)² / (n - 1)]

Σ(x - mean)² = (5 - 6)² + (8 - 6)² + (9 - 6)² + (2 - 6)² + (6 - 6)²

                    = 30

Standard deviation = √(30 / (5 - 1) = 2.7386

CV = (2.7386 / 6) × 100

     = 45.64%

Hence CV is 45.64%.

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Answer:

  B)  15/17

Step-by-step explanation:

You want the sine of acute angle A in the right triangle shown.

The sine of the angle is the ratio ...

  Sin = Opposite/Hypotenuse

We can go to the trouble to figure the hypotenuse, or we can choose the only suitable answer from the list provided. (It is the one marked already.)

The leg lengths of the triangle shown are 8 and 15, with leg 15 being opposite angle A. This is the first clue that the ratio will have 15 in the numerator. Only answer choice B matches.

The value of the sine function is never greater than 1, eliminating answer choices A, C, and E, leaving choices B and D.

Since the side opposite angle A is the longest of the two legs, we know that angle A is more than 45°, and its sine is more than √2/2. That means choice D can be eliminated, since it is less than 1/2.

The sine of angle A is 15/17.

<95141404393>

The given data set: 4, 5, 6, 6, 7, 7, 7, 7, 8, 8, 9, 10 is skewed right or positively skewed due to a cluster of values towards the center and a gradual increase on the right side. The correct answer is A) Skewed Right.

The given data set is: 4, 5, 6, 6, 7, 7, 7, 7, 8, 8, 9, 10.

To determine the shape of the data set, we can analyze its distribution.

Looking at the data set, we can observe that the values are gradually increasing from 4 to 10. However, there are multiple occurrences of the numbers 6, 7, and 8. This indicates that the data set has a cluster or mode around these values.

Since the data set has a cluster of values towards the center and a gradual increase on the right side, it suggests that the data set is skewed right or positively skewed.

Therefore, the correct answer is A) Skewed Right.

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Answer:

The correct equation is D)

Step-by-step explanation:

The answer is equation D)

To find how many [tex]\frac{1}{3}[/tex] inches are in [tex]\frac{5}{6}[/tex] of an inch, you must divide [tex]\frac{5}{6}[/tex] by [tex]\frac{1}{3}[/tex].  

When diving fractions, you find the reciprocal of the second fraction (flip the fraction) & then you multiply the fractions.

[tex]\frac{5}{6}[/tex] ÷ [tex]\frac{1}{3}[/tex]

In this case, [tex]\frac{1}{3}[/tex] is the second fraction you must find the reciporcal of.

Flipping the fraction will give you the reciprocal as 3.

Multiply [tex]\frac{5}{6}[/tex] by 3.

Cross-cancellation:

[tex]\frac{5}{6}[/tex] x [tex]\frac{3}{1}[/tex]

As 3 can go into 6, you can divide both 3 by 3 & 6 by 3. The second fraction will be cancelled out ([tex]\frac{1}{1}[/tex]) and you will have [tex]\frac{5}{2}[/tex] left over (since anything multiplied by 1 will remain the same).

Simplification:

[tex]\frac{5}{6}[/tex] x [tex]\frac{3}{1}[/tex]

[tex]\frac{15}{6}[/tex]

Divide both numerator & denominator by 3 (the Greatest Common Factor) to simplify.

= [tex]\frac{5}{2}[/tex]

So, as a result, the correct equation is equation D).

Given statement solution is :- Carla's Catering provides the lowest total cost for 12 lunches, and the difference is $11.00.

To determine which company will provide the lowest total cost for 12 lunches, let's calculate the costs for both Carla's Catering and Dan's Diner.

Carla's Catering:

Using the equation provided, y = 6.75x + 25, where x represents the number of lunches:

For x = 12:

y = 6.75(12) + 25

y = 81 + 25

y = 106

The total cost for 12 lunches from Carla's Catering is $106.

Dan's Diner:

We are given the following data points for Dan's Diner:

Number of Lunches (x) Total Cost (y)

5 $57.50

10 $100.00

15 $142.50

From this data, we can calculate the rate at which the cost increases per lunch:

Rate = (Change in Total Cost) / (Change in Number of Lunches)

Rate = (100 - 57.50) / (10 - 5)

Rate = 42.50 / 5

Rate = 8.50

Now, let's calculate the cost for 12 lunches using the rate:

For x = 12:

y = 100 + (8.50 * (12 - 10))

y = 100 + (8.50 * 2)

y = 100 + 17

y = 117

The total cost for 12 lunches from Dan's Diner is $117.

Comparing the costs:

Carla's Catering: $106

Dan's Diner: $117

Carla's Catering provides the lowest total cost for 12 lunches, and the difference is $11.00.

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Answer:

Lucy has ridden 25% of the course so far. This means she has completed a quarter of the total distance.

Step-by-step explanation:

To determine the percentage of the course Lucy has ridden so far, we can use the following formula:

Percentage = (Distance ridden / Total distance) * 100

Given that the total distance of the bike course is 88 miles and Lucy has

ridden 22 miles, we can substitute these values into the formula:

Percentage = (22 miles / 88 miles) * 100

Simplifying the equation:

Percentage = (1/4) * 100

Percentage = 25

Therefore, Lucy has ridden 25% of the course so far. This means she has completed a quarter of the total distance.

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The approximate x-values for the local maximum and the local minimum are given as follows:

D) max ≈ -0.3 , min ≈ 2.3.

Hence the critical points of the graphed function are given as follows:

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Answer:

43.98

Step-by-step explanation:

43.98 to nearest hundredth

Answer:

  a. x = licensed riders; y = junior racers

  b. x + y = 321; 25x +15y = 6935

  c. see attached. (x, y) = (212, 109); 212 licensed riders; 109 junior racers

Step-by-step explanation:

You want to determine the number of racers of each type, given 321 racers total paid $6935 in fees. Licensed racers paid $25 each, and junior racers paid $15 each. You want a system of equations and a graphical solution.

In general, the variables represent the values the question is asking for. In part (b), we see that we want to find the number of racers of each type. Since our graphing program prefers the variables x and y, we will assign those in the same order the descriptions of the types of racers appear in the problem statement. (Keeping the order can avoid confusion later.)

  x = the number of licensed riders

  y = the number of junior racers

The relations given in the problem statement give rise to two equations:

The attached graph shows the solution to these equations is (x, y) = (212, 109). There were 212 licensed riders and 109 junior racers.

<95141404393>

Answer:

To solve for x, we need to isolate x on one side of the equation.

First, we can start by subtracting 2 1/4 from both sides of the equation:

5 1/6x = 10 - 2 1/4

5 1/6x = 7 3/4

Next, we can simplify the left side of the equation by multiplying the whole equation by the reciprocal of 5 1/6, which is 6/31:

(6/31) * 5 1/6x = (6/31) * 7 3/4

x = 3/2

Therefore, the value of x in the equation is 3/2.

To find the average velocity of the ball between t = 1 and t = 2, we need to calculate the displacement of the ball during that time interval and divide it by the duration.

The displacement of an object can be determined by finding the difference in its position at the beginning and end of the interval. In this case, we can find the height of the ball at t = 1 and t = 2 using the given equation:

h(1) = -5(1)² + 30(1) + 5

= -5 + 30 + 5

= 30 meters

h(2) = -5(2)² + 30(2) + 5

= -20 + 60 + 5

= 45 meters

The displacement of the ball between t = 1 and t = 2 is:

Displacement = h(2) - h(1)

= 45 - 30

= 15 meters

The duration of the interval is 2 - 1 = 1 second.

Finally, we can calculate the average velocity using the formula:

Average velocity = Displacement / Duration

= 15 meters / 1 second

= 15 m/s

Therefore, the average velocity of the ball between t = 1 and t = 2 is 15 m/s.

The length of one side of the square is 36 meters.In general, the perimeter of a rectangle can be found by adding up the lengths of all four sides.

If we know the length and width of the rectangle, we can use the formula:

Perimeter = 2(length + width)

To find the length of the rectangle using the Pythagorean Theorem, we would need to be given some additional information, such as the width and the length of one of the sides or one of the diagonals. Once we have the length and width of the rectangle, we can use the formula above to find its perimeter.

If the diagonals of a square measure 36 meters, what is the length of a side of the square?(Use Pythagorean Theorem to find the side of the square)

Let s be the length of one side of the square. Since the diagonals of a square are equal in length, we have:

s² + s² = 36²

Simplifying the left-hand side:

2s² = 1296

Dividing both sides by 2:

s² = 648

Taking the square root of both sides:

s = √648 = 18√4 = 36.

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We cannot determine the exact number of complex zeros for the given polynomial.

We have,

To determine the number of complex zeros of the polynomial

f(x) = 6x^6 - 5x^4 + 2x^3 - x^2 + 12

We need to analyze the degree and sign changes of the polynomial.

The degree of the polynomial is 6, which means it is a polynomial of degree 6.

According to the Fundamental Theorem of Algebra, a polynomial of degree n can have at most n complex zeros (counting multiplicity).

To analyze the sign changes, we can write down the coefficients of the polynomial in a row:

6, -5, 2, -1, 0, 0, 12

By observing the sign changes in the row of coefficients, we see that there are no sign changes.

This indicates that the polynomial has either zero or an even number of positive real zeros.

Since we are interested in complex zeros, this information alone does not provide conclusive evidence.

To determine the number of complex zeros, we would need more information or further analysis.

It is possible that some of the zeros are complex or imaginary, but without more details or a complete factorization of the polynomial, we cannot determine the exact number of complex zeros.

Thus,

We cannot determine the exact number of complex zeros.

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The coordinates of one of the points in Carlos' pattern would be (2, 3).

To determine the coordinates of the points in Carlos' pattern, we can assign the term number as the x-coordinate and the corresponding term value as the y-coordinate. Let's go through each term:

Term 1: 1

The first term is 1. So, the coordinate for this term is (1, 1).

Term 2: 3

The second term is obtained by adding 2 to the previous term. The previous term had the coordinate (1, 1). Therefore, the coordinate for this term is (2, 3).

Term 3: 5

The third term is obtained by adding 2 to the previous term. The previous term had the coordinate (2, 3). Therefore, the coordinate for this term is (3, 5).

Term 4: 7

The fourth term is obtained by adding 2 to the previous term. The previous term had the coordinate (3, 5). Therefore, the coordinate for this term is (4, 7).

From the given options, we can see that the coordinates (2, 3) match one of the points in Carlos' pattern. Therefore, the correct answer is B) (2, 3).

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Answer:

area= 39 square meters

Step-by-step explanation:

10×6=60m²

60m²÷2=30m² is the area of the bigger triangle

6×3=18m²

18m²÷2=9m²

9m²+30m²=39m²

[tex]u=(\sqrt{3}~~,~-1)\hspace{5em}v=(3~~,~-4) \\\\\\ u\cdot v\implies (\sqrt{3}\cdot 3)~~ + ~~(-1\cdot -4)\implies \stackrel{ \textit{dot product} }{3\sqrt{3}+4}[/tex]

1. The of jigsaw puzzles is 216 and crossword puzzle is 261.

2. 22 table lamps were left in the warehouse.

1. Crossword Puzzle Books and Jigsaw Puzzles:

Let's the number of jigsaw puzzles as "x".

then, the number of crossword puzzle books will be "x + 45"

Now, Number of sold crossword puzzle books = (5/9) (x + 45)

= (25/100) x

= x/4

It is also given that there were 91 more crossword puzzle books sold than jigsaw puzzles. Therefore, we can set up the equation:

(5/9) (x + 45) - (x/4) = 91

(5/9)x + 25 - (x/4) = 91

(20/36)x + 25 - (9/36)x = 91

(11/36)x = 91 - 25

(11/36)x = 66

x = (36/11)  66

x ≈ 216

So, the number of jigsaw puzzles is 216 and the number of crossword puzzle books is 216 + 45 = 261.

2. Table Lamps and Standing Lamps:

Let's the number of table lamps as "x".

then, the number of standing lamps will be "155 - x"

So, Number of table lamps = (60/100) x = 0.6x

and, Number of standing lamps

= (80/100) (155 - x)

= 0.8(155 - x)

= 124 - 0.8x

Therefore, the number of table lamps left will be:

Remaining table lamps = (70/100) * 0.6x = 0.42x

To find the value of x, we can set up the equation:

0.42x = x - 30

Simplifying the equation:

x - 0.42x = 30

0.58x = 30

x = 30 / 0.58

x ≈ 51.72

So, the number of table lamps left is 0.42 x 51.72 ≈ 21.68.

Thus, 22 table lamps were left in the warehouse.

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Hola !

1500/10 = 150

una rata tiene 150 nervios por bigote

Answer:

150

Step-by-step explanation:

We need to divide 1500 by 10 since the seal has 10 more than the rat

1500 ÷ 10 = 150

Therefore the answer is 150

The sequence of transformations that transform the the pre-image and the congruence of the pre-image and image are indicated by the option D.

D. Reflection, then rotation results in an image that is congruent to the original

A transformation is the performance of a rotation, reflection, translation, or dilation, that produces an image with a different size, location, orientation or shape.

The coordinates of the points on the triangle ABC are laterally equidistant from the vertical line in the middle between the triangles ABC and triangle DEF, such that the line in the middle is the line of reflection.

The vertical height of the coordinates of the triangle ABC and DEF, which are the same indicates that the transformation from triangle ABC to EFD is a reflection across the line in the middle between the two triangles. The side GH in triangle IGH corresponds to the side EF in the triangle EFD,

The length of GH = EF = 4 units

Similarly, IH = DE, and IG = DF, therefore;

Triangle EFD and triangle HGI are congruent by SSS congruence rule

The orientation of the side EF of the triangle EFD which is vertical and the side HG which is horizontal indicates a rotation of the triangle EFD by 90 degrees to obtain the triangle HGI

The correct option is therefore, the option D.

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Answer:2nd one

Step-by-step explanation:

All six trigonometric ratios of the triangle are :

sin (θ) = 3/5, cos (θ) = 4/5, tan (θ) = 3/4

cosec (θ) = 5/3, sec (θ) = 5/4, cot (θ) = 4/3

Given a triangle, which is right angled.

Length of hypotenuse = √(20² + 15²) = 25

Given an angle θ.

We have to find the six trigonometric ratios which are sin, cos, tan, cosec, sec and cot.

sin (θ) = opposite side / hypotenuse = 15/25 = 3/5

cos (θ) = adjacent side / hypotenuse = 20/25 = 4/5

tan (θ) = opposite side / adjacent side = 15/20 = 3/4

cosec (θ) = 1 / sin (θ) = 5/3

sec (θ) = 1 / cos (θ) = 5/4

cot (θ) = 1 / tan (θ) = 4/3

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For calculating a 95% confidence mean range for the typical number of visits for patients receiving physical therapy.

a. We employ a t-distribution to calculate the confidence interval.

b. The population mean number of visits per physical therapy patient is between 9.454 and 19.000 visits, with a 95% confidence interval.

c. If multiple groups of 11 randomly chosen physical therapy patients are examined, roughly 95% of these confidence intervals will contain the genuine population mean number of visits per patient, and around 5% will not.

a. T-distribution is used to calculate the confidence interval for the mean number of visits. This is so because the population standard deviation is unknown and the sample size is tiny (only 11). The t-distribution is used in place of the conventional normal distribution when certain conditions are satisfied.

b. We have two options for calculating the confidence interval: we can do it manually or with statistical software. We determine the sample mean to be 13.182 and the sample standard deviation to be 6.446 using the provided data (13, 6, 25, 11, 11, 10, 21, 20, 9, 20, 9). Given the limited sample size and a 95% level of confidence, we use the t-distribution to establish the critical value. Using a calculator or the t-distribution table, determine the critical value for a 95% confidence level with 10 degrees of freedom is approximately 2.228.

The formula for the confidence interval is:

Sample Mean (Critical Value) * (Standard Error) = Confidence Interval

Sample Standard Deviation / sqrt(sample size) gives the standard error.

By entering the values, we can determine the confidence interval using the formula below:

The confidence interval is equal to 13.182 (2.228) * (6.446 / sqrt(11)).

9.454 visits make up the lower bound and 19.000 visits make up the upper bound of the confidence interval. The population mean number of visits per physical therapy patient is therefore expected to range between 9.454 and 19.000 visits, with a 95% confidence interval.

c. Confidence intervals for each group of 11 randomly chosen physical therapy patients can be constructed, and roughly 95% of these intervals will contain the actual population mean number of visits per patient. This is due to the fact that we are employing a 95% confidence level, which indicates that over time, 95% of the confidence intervals created will accurately reflect the underlying population mean.

On the other hand, around 5% of these confidence intervals won't include the actual population mean for visits per patient. These intervals are referred to as Type I errors or "misses". The likelihood of rejecting the actual null hypothesis is represented by the significance level, or alpha, which is represented by the 5%.

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The required, general solution for x that satisfies the equation cos(x + 30) = -1 is x = (2n + 1)π - 30.

To find the general solution for the equation cos(x + 30) = -1, we can start by considering the general form of the cosine function. The cosine function has a period of 2π, meaning it repeats every 2π radians.

In this equation, we have cos(x + 30) = -1. Since the cosine function has a maximum value of 1 and a minimum value of -1, the only way for cos(x + 30) to equal -1 is if x + 30 is an odd multiple of π. We can write this as:

x + 30 = (2n + 1)π

Here, n is an integer representing the number of periods of the cosine function. To find the general solution, we can solve for x by subtracting 30 from both sides:

x = (2n + 1)π - 30

This equation gives us the general solution for x that satisfies the equation cos(x + 30) = -1. We can see that for each integer value of n, we have a different solution.

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The solution is: 0.003 area of of the room's area is, covered by one sheet of newspaper.

Here, we have,

given that,

60 cm * 50 cm what is the area covered by one sheet of newspaper if the area of the room is 79.2 m square​.

we know, that,

area of one sheet of newspaper = 60 cm * 50 cm

                                                      = 3000 cm^2

we know that,

100 cm = 1 m

so, 3000 cm^2 = 0.3 m^2

now, we have,

the area of the room is 79.2 m square​.

so, we get,

the area covered by one sheet of newspaper = 0.3/ 79.2

                                                                            = 0.003

Hence, The solution is: 0.003 area of of the room's area is, covered by one sheet of newspaper.

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In the given diagram, we have a triangle with one angle labeled as 2x + 10° and another angle labeled as 3x - 5°. To solve for x, we can set up an equation using the sum of angles in a triangle, which is 180°.

The sum of the angles in a triangle is given by the equation:

Angle1 + Angle2 + Angle3 = 180°

Substituting the given angle measurements, we have:

(2x + 10°) + (3x - 5°) + 95° = 180°

Combining like terms, we get:

5x + 100° = 180°

Next, we can isolate the variable x by subtracting 100° from both sides:

5x = 180° - 100°

5x = 80°

Finally, we can solve for x by dividing both sides by 5:

x = 80° / 5

x = 16°

Therefore, the value of x is 16°.