what value represents the number of ways in which the expected classes are free to vary in the chi‑square goodness‑of‑fit test?

The equation connecting y and x when y is directly proportional to x and y = 30 when x = 6 is y = 5x.

If y is directly proportional to x, we can write the equation in the form:

y = kx

where k is the constant of proportionality.

To find k, we can use the values of y and x given:

y = 30, x = 6

When we enter these values into the formula above, we obtain:

30 = k * 6

Solving for k, we get:

k = 30/6 = 5

Therefore, the equation connecting y and x when y is directly proportional to x is:

y = 5x

When two variables are directly proportional, it means that when one variable increases or decreases, the other variable changes in the same proportion. In this scenario, we are given that y is directly proportional to x and we are also given a specific point on the line, (6, 30). Using this information, we can solve for the constant of proportionality k and write the equation connecting y and x as y = kx, where k is 5.

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Answer:22.61 degrees

Step-by-step explanation:

Use reverse tangent

The value of x for the trapezoid quadrilateral is equal to 5.

The quadrilateral is an isosceles trapezoid, with a line parallel to both opposing lines splitting the other two unparallelly going lines into equal halves. Hence, according to normal relations, the mid length is 5x-1.

The lengths of the opposing sides are 21 and 27 respectively. As a result, we may write 2(5x - 1) = 21 + 27.

Growing further, 10x - 2 = 48

10x = 48 + 2

10x = 50

Divide all sides by ten.

x = 50/10

x = 5

As a result, the value of x is 5.

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Answer:

Equation: 4(x + 1.5) = 38

Ticket Cost: $8, or x = 8

Step-by-step explanation:

The processing fee for each ticket is $1.50, or 1.5. This applies to each ticket, meaning that the price of one ticket (or x) should be added to 1.5. x + 1.5 represents the sum of a ticket and the processing fee. Since there were 4 tickets purchased, x + 1.5 is multiplied 4 times. That results in 4(x + 1.5). Finally, the total amount of money spent was $38, so 4(x + 1.5) = 38.

4(x + 1.5) = 38

4x + 6 = 38

4x = 32

x = 8

Check:

4 * 8 = 32 (cost of 4 tickets)

4 * 1.5 = 6 (cost of 4 processing fees)

32 + 6 = 38 (4 tickets + 4 processing fees = total)

Answer:

(9y + 4)(5x + 7)

Step-by-step explanation:

Answer:

Your answer is 60%.

Step-by-step explanation:

[tex]10 + 15=25[/tex] and [tex]\frac{15}{25}[/tex] [tex]=0.6[/tex] [tex]= 60[/tex]%

The measure of each angle in complementary angles with measures 3x and 6x - 18 degrees is 36° and 54°.

We are given two angles 3x and 6x - 18 and these angles are complementary angles.

Complementary angles are those whose combined angle is 90 degrees or less. In other terms, two angles are said to be complimentary if they combine to make a right angle.

So, sum of 3x and 6x - 18 is 90°

     3x + 6x - 18 = 90°

                    9x = 108°

                      x = 12°

So, 3x = 3 × 12 = 36°

     6x - 18 = 6 × 12- 18 = 54°

Hence, the measure of each angle is 36° and 54°.

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The probability of having at most 8 clear days in Juneau, 14 or more in Hilo, 20 or more in Phoenix, 18 or less in Las Vegas, and between 5 and 10 in Seattle is 0.7608, 0.7367, 0.4672, 0.9590, and 0.5385, respectively.

1. P(r≤8) = P(r=0) + P(r=1) + P(r=2)+ P(r=3)+ P(r=4)+ P(r=5)+ P(r=6)+ P(r=7)+ P(r=8)= 0.7608

2. P(r≥14) = 1 - P(r≤13) = 1 - (P(r=0) + P(r=1) + P(r=2)+ P(r=3)+ P(r=4)+ P(r=5)+ P(r=6)+ P(r=7)+ P(r=8)+ P(r=9)+ P(r=10)+ P(r=11)+ P(r=12)+ P(r=13))= 0.7367

3. P(r≥20) = 1 - P(r≤19) = 1 - (P(r=0) + P(r=1) + P(r=2)+ P(r=3)+ P(r=4)+ P(r=5)+ P(r=6)+ P(r=7)+ P(r=8)+ P(r=9)+ P(r=10)+ P(r=11)+ P(r=12)+ P(r=13)+ P(r=14)+ P(r=15)+ P(r=16)+ P(r=17)+ P(r=18)+ P(r=19))= 0.4672

4. P(r≤18) = P(r=0) + P(r=1) + P(r=2)+ P(r=3)+ P(r=4)+ P(r=5)+ P(r=6)+ P(r=7)+ P(r=8)+ P(r=9)+ P(r=10)+ P(r=11)+ P(r=12)+ P(r=13)+ P(r=14)+ P(r=15)+ P(r=16)+ P(r=17)+ P(r=18)= 0.9590

5. P(5≤r≤10) = P(r=5) + P(r=6) + P(r=7)+ P(r=8)+ P(r=9)+ P(r=10)= 0.5385

The probability of having at most 8 clear days in Juneau, 14 or more in Hilo, 20 or more in Phoenix, 18 or less in Las Vegas, and between 5 and 10 in Seattle is 0.7608, 0.7367, 0.4672, 0.9590, and 0.5385, respectively.

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A test score that is 1.4 standard deviations above the mean is 107. This means that a student who scored 107 on this standardized test would be above average, as the mean is 100 and the standard deviation is 5.

To find the test score that is 1.4 standard deviations above the mean, we need to use the formula:

z = (x - μ) / σ

where z is the number of standard deviations from the mean, x is the test score, μ is the mean, and σ is the standard deviation.

In this case, we know that z = 1.4, μ = 100, and σ = 5. So we can rearrange the formula to solve for x:

x = z * σ + μ

Substituting the values we know, we get:

x = 1.4 * 5 + 100 = 107

Therefore, a test score that is 1.4 standard deviations above the mean is 107. This means that a student who scored 107 on this standardized test would be above average, as the mean is 100 and the standard deviation is 5.

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The measures of the angles formed by the cords and secant in the circle are found using circle theorems and presented as follows;

A secant is a line that has two points of intersection on a circle.

The specified parameters are;

1. The measure of arc  [tex]m\widehat{AB}[/tex] = 80°, and the measure of [tex]m\widehat{CD}[/tex] = 15°

Angle at the center of the circle = 2 × Angle at the circumference

Angle at the center of the circle = The arc angle of the circle

Therefore;

m∠DAC = 15°/2 = 7.5°

m∠ACO = 80°/2 = 40°

The external angle of a triangle theorem, indicates that we get;

m∠1 = 40° + 7.5° = 47.5°

m∠1 = 47.5°

2. m∠BOD = 100°, [tex]m\widehat{AC}[/tex] = 90°

The intersecting chords theorem indicates that we get;

m∠BOD = (1/2)×([tex]m\widehat{AC}[/tex] + [tex]m\widehat{BD}[/tex])

Therefore; 100° = (1/2)×(90° + [tex]m\widehat{BD}[/tex])

[tex]m\widehat{BD}[/tex] = 2 × 100° - 90° = 110°

[tex]m\widehat{BD}[/tex] = 110°

3. [tex]m\widehat{AB}[/tex] = 90°, [tex]m\widehat{CD}[/tex] = 20°

Therefore; m∠ACO = 90°/2 = 45°

m∠DAC = 20°/2 = 10°

The external angle theorem indicates that we get;

m∠COD = 45° + 10° = 55°

m∠COD = 55°

4. m∠1 = 35°, [tex]m\widehat{AB}[/tex] = 50°, therefore;

m∠ACO = 50°/2 = 25°

m∠CAO = 35° - 25° = 10°

[tex]m\widehat{CD}[/tex] = 2 × m∠CAO

Therefore; [tex]m\widehat{CD}[/tex] = 2 × 10° = 20°

[tex]m\widehat{CD}[/tex] = 20°

5. m∠AOC = (1/2)×([tex]m\widehat{AC}[/tex] + [tex]m\widehat{BD}[/tex])

Therefore; m∠AOC = (1/2)×(90° + 110°) = 100°

m∠AOC = 100°

6. [tex]m\widehat{CD}[/tex] = 20° and [tex]m\widehat{AB}[/tex] = 70°

The external secant, tangent theorem, indicates that we get;

m∠APB = (1/2) × ([tex]m\widehat{AB}[/tex] - [tex]m\widehat{CD}[/tex])

m∠APB = (1/2) × (70° - 20°) = 25°

m∠APB = 25°

7. [tex]m\widehat{AB}[/tex] = 50°,

The angle at the center of a circle is twice the angle subtended at the circumference, therefore;

m∠ADB = 50°/2 = 25°

m∠ADB = 25°

8. m∠CAD = 45°

The angle formed by an arc at the center of a circle theorem, indicates that we get;

[tex]m\widehat{CD}[/tex] = 2 × m∠CAD

[tex]m\widehat{CD}[/tex] = 2 × 45° = 90°

[tex]m\widehat{CD}[/tex] = 90°

9. m∠ACB = 70°

m∠ACB is the angle subtended by the arc [tex]m\widehat{AB}[/tex] on the circumference

Therefore;

[tex]m\widehat{AB}[/tex] = 2 × m∠ACB

[tex]m\widehat{AB}[/tex] = 2 × 70° = 140°

[tex]m\widehat{AB}[/tex] = 70°

10. m∠AOB = 80°, [tex]m\widehat{AB}[/tex] = 60°

m∠(AOB) = (1/2) × ([tex]m\widehat{AB}[/tex] + [tex]m\widehat{CD}[/tex])

Therefore; m∠(AOB) = 80° =  (1/2) × (60 + [tex]m\widehat{CD}[/tex])

80° =  (1/2) × (60 + [tex]m\widehat{CD}[/tex])

[tex]m\widehat{CD}[/tex] = 2 × 80° - 60° = 100°

[tex]m\widehat{CD}[/tex] = 100°

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The width of the bedroom is approximately 7.32 feet.

A rectangle is a four-sided figure with opposite sides being equal and parallel. The area of a rectangle is given by multiplying the length and width of the rectangle.

Let's assume that the width of the bedroom is 'x' feet. We know that the length of the room is 5 feet longer than its width. Therefore, the length of the room will be (x+5) feet.

Now, we can use the given area of the bedroom to set up an equation:

Area of rectangle = Length x Width

84 = (x+5) x x

Simplifying this equation, we get:

84 = x² + 5x

Rearranging, we get:

x² + 5x - 84 = 0

This is a quadratic equation that can be solved using the quadratic formula:

x = (-b ± √(b² - 4ac))/2a

In this case, a = 1, b = 5 and c = -84. Substituting these values in the formula, we get:

x = (-5 ± √(5² - 4(1)(-84)))/2(1)

Simplifying this, we get:

x = (-5 ± √721)/2

We can ignore the negative root since the width of the bedroom cannot be negative. Therefore, the width of the bedroom is:

x = (-5 + √721)/2

x ≈ 7.32 feet

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Answer: $35.

Step-by-step explanation: Let A = 2 movers and one truck for hour = $65

B = 3 movers and one truck for hour = $80

So, 1 mover = B - A

                  = $80 - $65

                  = $15

Hence, 2 movers cost = 2 × $15

                                  = $30

SO, rent of the truck hourly = A - cost of 2 movers

                                          = $65 - $30

                                          = $35

Therefore cost of renting the truck for an hour = $35

Step-by-step explanation:

the equation we use here is [items to choose from] to the power of [required items]; in this case, we get [tex]10^{3}[/tex].

The equation which correctly shows the relationship between x, number of hours and y, the amount of money she makes is; y = 12x + 7.

It follows from the task content that the relationship between y and x is to be.

By comparison with the slope-intercept equation; y = mx + c.

Since, slope, m is the rate of change; m = 12$ per hour.

Also, the nonrefundable one-time fee for showing up represents the y-intercept, c.

Therefore, the required equation is;

y = 12x + 5.

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In a case whereby Jonah has $7,586 in an account that earns 10% interest compounded annually, the amount he will have in 3 years is $10,096.97

The concept that will be used here is counpound interest.

The  amount that will be present in the  account in 3 years can be estimated using the expression beleow which is:

FV = P(1 + r)^n

P represent the  amount in the account which is  $7,586

r  represen the interest rate which is 10/100 =0.01

n represent the number of years

FV  represent the future value

We can input all these values as :

FV =[ 7,586(1 + 0.1)^3]

= (7,586 x 1.1^3 )

= $10,096.97

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complete question:

Jonah has $7,586 in an account that earns 10% interest compounded annually.

To the nearest cent, how much will he have in 3 years?

The number that, when raised to the power of three, equals 500000 is approximately 100.

To find this number, we can use the cube root function:

x^3 = 500000

x = cube root of (500000)

x = approximately 100

So, the number that, when raised to the power of three, equals 500000 is approximately 100.

Answer:it guarantees that people can all read and solve a problem in the same way.

Step-by-step explanation:

There are 840 ways for the person to get 6 fives, 3 ones, and 1 two in 10 rolls of a six-sided die.

To calculate the number of ways to roll 6 fives, 3 ones, and 1 two in 10 rolls of a six-sided die, we can use the formula for combinations with repetition.

The number of ways to choose 6 rolls to be fives out of 10 is given by the combination formula:

C(10, 6) = 10! / (6! * (10 - 6)!) = 210

Similarly, the number of ways to choose 3 rolls to be ones out of the remaining 4 rolls is:

C(4, 3) = 4! / (3! * (4 - 3)!) = 4

Finally, there is only one way to choose the remaining roll to be a two.

Therefore, the total number of ways to roll 6 fives, 3 ones, and 1 two in 10 rolls of a six-sided die is:

210 * 4 * 1 = 840.

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Answer:

With the information given, I would say a dialation.

Step-by-step explanation:

Rotation of 180 degree around point (1, 0). Therefore, option (3) is the correct answer.

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure. The original shape of the object is called the Pre-Image and the final shape and position of the object is the Image under the transformation.

Given that, the square with vertices (-1, 2), (-1, -2), (3, -2) and (3, 2).

(1) Reflection over the y-axis

Then the vertices become (1, 2), (1, -2), (-3, -2) and (-3, 2)

So, the transformation carries the square onto itself.

(2) Reflection over the x-axis

Then the vertices become (-1, -2), (-1, -2), (3, 2) and (3, -2)

So, the transformation carries the square onto itself.

(3) Rotation of 180 degree around point (1, 0)

(x, y) becomes (-y, x) 180° clockwise

So, the coordinate points are (-2, -1), (2, -1), (2, 3) and (-2, 3)

So, the transformation does not carries the square onto itself.

Therefore, option (3) is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

A square is graphed on the set of axes below, with vertices at (-1,2), (-1,-2), (3,-2), and (3.2). Which transformation would not carry the square onto itself.

(1) Reflection over the y-axis

(2) Reflection over the x-axis

(3) Rotation of 180 degree around point (1, 0)

(4) Reflection over the line y=x-1

Answer:

369 cans

Step-by-step explanation:

Add the two numbers of cans collected by each:

Alan:   154 cans

Betty:  215 cans

Total:  369 cans

The presented statement states that a square pyramid has a surface area of 340 cm².

For instance, we may calculate the area of a rectangle by multiplying its length by its width. The area of the rectangle seen above is 24 or 8. There are eight little squares in all if you count them.

The following formula may be used to determine a square pyramid's surface area:

(Base Area) + Surface Area (Area of 4 triangular faces)

The base area of the pyramid would have been 10 cm x 10 cm, or 100 cm2, as the pyramid's base is a squares with a diameter of ten centimeters.

Each triangle face's area may be calculated using the formula for

Area = (1/2)bh

where b denotes the bottom and h the top.

The area of each triangle face will be (1/2) x 10 cm x 12 cm = 60 cm², given that the pyramid's height is 12 cm.

As a result, the pyramid's total surface area would be as follows: 100 cm² + (4 x 60 cm²) = 100 cm² + 240 cm² = 340 cm².

So, the correct response is B) 340 cm².

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Answer:

Improper fraction: -31/30

Mixed number: -1   1/30

Step-by-step explanation:

If x = -5/6 and y = -2/5, we can start by replacing x and y in the equation x + 1/2y.

x+1/2y -> -5/6+1/2(-2/5)

Now we can start solving the equation:

According to the Order of Operations, we have to start with multiplication before addition. So, let's multiply 1/2 and -2/5. We get -2/10, which simplifies to -1/5.

Now we have to do the addition: -5/6+(-1/5)

To add fractions together, we have to find a common denominator. We can do this by finding the LCM of the two denominators(Least common multiple).

6: 6, 12, 18, 24, 30, 36...

5: 5, 10, 15, 20, 25, 30, 35...

The LCM is 30.

-5/6 x 5/5 = -25/30 <-- the equivalent fraction of -5/6

-1/5 x 6/6 = -6/30 <-- the equivalent fraction of -1/5

-25/30 + (-6/30) = -31/30

The answer is -31/30 in improper fraction form, and -1 1/30 in mixed number form.

Answer:

< 1 is acute (less than 90⁰)

<2 is acute

<BOA is obtuse (greater than 90⁰)

The expressions, in terms of t, for each vehicle so that the vehicles start separated and meet at 10 seconds is:

Tractor's position = Vt * t

Scooter's position = Vs * t

Let's assume that the starting point for both the tractor and the scooter is at "0". We can then write the expressions for their positions in terms of time "t" as follows:

For the tractor:

Tractor's speed = Vt

Tractor's position = Vt * t

For the scooter:

Scooter's speed = Vs

Scooter's position = Vs * t

Now, as both the vehicles meet at 10 seconds, we can write the equation:

Vt * 10 = Vs * 10

The above equation represents the position of both the vehicles at 10 seconds. If we assume the speed of the tractor and the scooter to be constant, then the equation gives us the relationship between their speeds.

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The required probability of loosing both the contracts with 61% chances of winning first contract and 74% chances of second contract is equal to 0.1014.

Probability of winning the first contract 'P(A)' = 61%

                                                                  = 0.61

Probability of winning the second contract 'P(B)' = 74%

                                                                       = 0.74

Probability of loosing both the contracts is

=  [ 1 - P(A) ] × [ 1 - P(B) ]

= [ 1 - 0.61 ]  × [ 1 - 0.74 ]

= 0.39 × 0.26

= 0.1014

Therefore, the probability of loosing both the contracts as per given contracts winning possibility is equal to 0.1014.

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The area of the lawn in the scale drawing is approximately 996 square feet.

1. Measure the length and width of the lawn in inches on the scale drawing.

Length = 16.5 inches

Width = 15.5 inches

2. Convert the measurements to feet by dividing the inches by 12.

Length = 16.5/12 = 1.375 feet

Width = 15.5/12 = 1.291 feet

3. Calculate the area of the lawn by multiplying the length and width.

Area = 1.375 x 1.291 = 1.75 square feet

4. Multiply the area by the scale factor (in this case, 560) to get the actual area.

Area = 1.75 x 560 = 996 square feet

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Each of the following measurements contain a) 1, b) 4,c) 3,d) 1,e) 2,f) 4,g) 2  significant figures.

Significant digit -Precision refers to the number of digits to which a value can be assigned. Therefore, numbers that can have a value of digits are called significant digits.

Below are the key figures for each value reported.

(a) 2- 1significant digits

(b) 81.640 - 4 significant digits;

(c) 7.03 - 3 Significant Figures

(d) 0.003 - 1significant digits

(e) 0.0086 to 2 significant digits

(f) 3236 - 4 significant digits

(g) 8700 - 2 significant digits

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The most appropriate chart to see the correlation between car mileage and year the car was built for various car models would be a scatterplot chart.

In a scatterplot chart, each point represents a pair of values: one value on the x-axis (in this case, year the car was built) and another value on the y-axis (in this case, mileage). By plotting these pairs of values for each car model in the sample, we can visually examine the relationship between mileage and year built for each car model and determine if there is a correlation between the two variables.

A line chart is used to display data that changes over time, typically for a single variable. A heatmap chart is used to show the magnitude of values for different categories using different colors. Therefore, neither of these chart types would be appropriate to show the correlation between mileage and year built for various car models.

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Probability of a successful call 0.3157 = 31.57%  

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will learn the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

A probability is the number of desired outcomes divided by the number of total outcomes.

The odds of making a sale on a single call are 6 to 13.

This means that in 6+13 = 19 calls, 6 are successful.

What is the probability of a successful call?

p = 6/19 =

0.3157 = 31.57% probability of a successful call.

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Answer D

Step-by-step explanation: