From the large appliance sales example in class, here is the summary table for the Goodness of Fit analysis.
Category Obs. Freq Expected Freq Contribution to Chi Square
Refrigerator 70 60 1.6667
Dish Washer 50 40 2.5
Range 20 30 3.3333
Clothes Washer 30 40 2.5
Clothes Dryer 30 30 0.0
What is the total Chi-Square Test Statistic?

b) 'The probability of success remains the same from trial to trial' is true for a binomial distribution.

A binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent trials, where the probability of success remains constant from trial to trial.

The Poisson distribution, on the other hand, is a discrete probability distribution that describes the number of events occurring in a fixed interval of time or space, where the events are rare and random, and the mean number of events per interval is constant.

The number of possible outcomes in a binomial distribution depends on the number of trials and the number of possible outcomes in each trial, and there is no specific requirement for a minimum number of outcomes.

The value of T is not relevant or defined in the context of a binomial distribution.

Correct Question :

Which is true for a binomial distribution?

a) It approximates the Poisson distribution

b) The probability of success remains the same from trial to trial

c) There are ten or more possible outcomes

d) The value of T Is equal to 1.50,

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Answer:

A.

Step-by-step explanation:

Because If you are simplifying then -3 would become -1 and -5 would become -3 and -4 would become -2 so your basically just simplifying

Examples of capital letters with different symmetry types are "T" with Z1 symmetry,  "H" with D1 symmetry, "S" with Z2 symmetry, and "X" with D2 symmetry. All the four options a), b), c) and d) are correct.

An example of a capital letter of the alphabet that has Z1 symmetry type is the letter "T". The letter "T" has a single axis of symmetry that runs vertically through its center.

An example of a capital letter of the alphabet that has D1 symmetry type is the letter "H". The letter "H" has two perpendicular axes of symmetry that bisect each other at its center.

An example of a capital letter of the alphabet that has Z2 symmetry type is the letter "S". The letter "S" has a center of symmetry, which is a point that is equidistant from all points on the letter.

An example of a capital letter of the alphabet that has D2 symmetry type is the letter "X". The letter "X" has two perpendicular axes of symmetry and a center of symmetry, which together form the dihedral group of order 8. The correct answer options are a), b), c) and d) as they shows symmetry.

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P = $18,500 (Principal amount)

r = 6% (Interest rate per year)

t = 4 years (Loan duration)

The interest amount, I, can be calculated using the formula I = Prt.

The total loan amount, A, is equal to the principal amount plus the interest amount, A = P + I.

The monthly installment, d, can be calculated by dividing the total loan amount by the number of months in the loan duration.

In the given scenario, the principal amount, P, is $18,500. The interest rate, r, is 6%, and the loan duration, t, is 4 years.

To find the interest amount, I, we can use the formula I = Prt. Substituting the given values, I = $18,500 * 6% * 4 = $4,440.

The total loan amount, A, is the sum of the principal amount and the interest amount. Therefore, A = $18,500 + $4,440 = $22,940.

To calculate the monthly installment, d, we need to divide the total loan amount by the number of months in the loan duration. Since there are 12 months in a year, the loan duration of 4 years corresponds to 4 * 12 = 48 months. Therefore, d = $22,940 / 48 = $477.92 (rounded to two decimal places).

Therefore, Justin's monthly installment for the car loan would be approximately $477.92.


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For the given case the Null hypothesis is The mean mpg of the 91 cars tested is equal to the manufacturer's mpg rating of 55.7 and the  Alternative hypothesis is The mean mpg of the 91 cars tested is less than the manufacturer's mpg rating of 55.7.

In order to determine whether the cars underperform the manufacturer's mpg rating, the independent testing firm would need to perform a hypothesis test. To do this, they would need to compare their sample mean of 55.2 mpg with the manufacturer's mpg rating of 55.7. They would also need to know the standard deviation of the sample, which is 3.24.

The independent testing firm would then calculate the z-score by subtracting the manufacturer's rating from the sample mean, and dividing it by the standard deviation. If the z-score is greater than the critical value for a 0.05 level of significance, then there is sufficient evidence to reject the null hypothesis.

In this case, the z-score is -1.51. Since the critical value for a 0.05 level of significance is 1.96, the z-score is less than the critical value. Therefore, there is not sufficient evidence to reject the null hypothesis, and we cannot conclude that the cars underperform the manufacturer's mpg rating.

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A letter to a student who will be taking this math class next year to give them some advice about this class has been written below.

(Sender's address)

20/01/2023

Dearest,

I was happy to see your letter, and I hope this letter finds you in the best of health. I have wanted to go on a trip with you for a long time but I guess that would happen later since you have to start attending classes soon.

I have a list of things to keep in mind when you start your classes. I was always too scared of mathematics, and I know you are too, but I have always wanted to tell you how fruitful it is to learn a subject that will help you in every field you want to go in. Let me know what you think about it after you finish reading this letter. I know it is no secret that maths is a difficult subject but you can master it if you keep what I am going to tell you in mind. Practice your concepts daily. Keep brushing up on whatever your teacher teaches you. Remember the formulas and you will know how to answer any question.  I know for sure that it is going to be worth it too.

I will make sure that I meet you next weekend so that we can meet before you begin the classes. If you try hard, you can make this work. See you soon.

Love,

(Sender's name)

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Answer:

- 6

Step-by-step explanation:

The rate of change of the values is the slope m

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 2, 32) and (x₂, y₂ ) = (0, 20) ← 2 ordered pairs from the table

m = \(\frac{20-32}{0+2}\) = \(\frac{-12}{2}\) = - 6 ← rate of change

Simplifying the expression, we can find the time it will take for the newer pump to drain the pool on its own.

If two pumps can drain a pool together in a certain number of hours and it takes the older pump a certain number of hours to drain the pool alone, we can determine how long it will take the newer pump to drain the pool on its own.

Let's assume that the older pump can drain the pool alone in x hours. The rate of the older pump is 1/x of the pool drained per hour. If two pumps can drain the pool together in y hours, their combined rate is 1/y of the pool drained per hour.

Now, to find the rate of the newer pump, we subtract the rate of the older pump from the combined rate of both pumps:

1/y - 1/x = 1/t

Here, t represents the time it would take for the newer pump to drain the pool on its own. By rearranging the equation, we can solve for t:

1/t = 1/y - 1/x

To find t, we can take the reciprocal of both sides of the equation:

t = 1 / (1/y - 1/x)

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Answer: F(x)= x-5

Step-by-step explanation:

Answer:

Y is 5 and X Is 5 Very easy . . . so it's just 5

The exercise involves finding the product C = AB, where matrix A is given by [2 9] and matrix B is given by [3 6 1]. We need to perform the matrix multiplication to obtain the resulting matrix C.

Let's calculate the matrix product C = AB step by step:

Matrix A has dimensions 2x1, and matrix B has dimensions 1x3. To perform the multiplication, the number of columns in A must match the number of rows in B.

In this case, both matrices satisfy this condition, so the product C = AB is defined.

Calculating AB:

AB = [23 + 912 26 + 94 21 + 95]

[103 + 612 106 + 64 101 + 65]

Simplifying the calculations:

AB = [6 + 108 12 + 36 2 + 45]

[30 + 72 60 + 24 10 + 30]

AB = [114 48 47]

[102 84 40]

Therefore, the product C = AB is:

C = [114 48 47]

[102 84 40]

In summary, the matrix product C = AB, where A = [2 9] and B = [3 6 1], is given by:

C = [114 48 47]

[102 84 40]

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Answer:

1-0.07/100*7=0.9951

Answer:

A

Step-by-step explanation:

Answer:  A.  85

Step-by-step explanation:

To set up an equation to solve for x you need to know:

The to 2 interior (inside) angles,  opposite of the exterior,  added together is equal to the exterior (outside) angle.

2x + 3 + 5x - 2 = 8x - 11

7x + 1 = 8x - 11

x = 12

Plug x back into the exterior angle outside angle

8(12)-11

96-11

85

The effect of temperature on seafood can impact its quality, safety, and taste. Higher temperatures can cause the growth of harmful bacteria, spoilage, and changes in texture, color, and flavor, while lower temperatures can help preserve freshness and quality.

a. The experimental unit for temperature is the cold storage unit. There are three cold storage units randomly assigned to be operated at each of the three temperatures (0, 5, and 10 degrees).

b. The experimental unit for seafood type is the shelf within each storage unit. Oysters and mussels are randomly assigned to be stored on one of the two shelves in each storage unit.

c. To write the model for the data, we will consider the main factors: temperature (T), seafood type (S), and their interaction (TS). The model can be written as:

Y_ijk = μ + T_i + S_j + (TS)_ij + ε_ijk

where:
- Y_ijk represents the bacterial count for the kth observation of seafood type j at temperature i,
- μ is the overall mean bacterial count,
- T_i represents the effect of temperature i on the bacterial count,
- S_j represents the effect of seafood type j on the bacterial count,
- (TS)_ij represents the interaction effect between temperature i and seafood type j on the bacterial count, and
- ε_ijk represents the random error associated with the kth observation of seafood type j at temperature i.

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Answer:

1

3

130

Step-by-step explanation:

as shown on the lines, it takes the bird one second to fly 13 meters. the answer to the first blank is 1

using this ratio, 13 meters per second, we can find how long it takes for the bird to fly 39 meters.

13/1=39/x

this is 13x=39

x=3 seconds

use the same ratio to find distance

13/1=x/10

13=x/10

130=x

Answer:

1/45

Step-by-step explanation:

P(Y,Y) = 2/10 x 1/9 which is 1/45 simplified

Answer:

the anwers is the 5,5

u hope this hepl

Answer:

(3,2)

(2,4)

(-4,-3)

I have the same test and I got it right

Answer:

Amplitude = 2

Step-by-step explanation:

The amplitude of this sine wave is 2 denoted by the coefficient -2 in front of the sin(x).  The negative of the coefficient denotes that the sine wave is the opposite of the standard sine wave.

Cheers.

The rate of change for the equation y - x = 10 is 1.

To find the rate of change for the equation y - x = 10, we need to determine how y changes with respect to x.

We can rewrite the equation as y = x + 10 by adding x to both sides.

Now, we can observe that the coefficient of x is 1. This means that for every unit increase in x, y will increase by 1. Therefore, the rate of change for this equation is 1.

In other words, as x increases by 1 unit, y will increase by 1 unit as well.

As a result, 1 represents the rate of change for the equation y - x = 10.

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Answer: The final price is less than the original

Step-by-step explanation:

    Let us break this down a bit.

The original price is $500

-> At the beginning, the price was marked up by 20%

-> At the end, the price at the beginning of the season is marked down by 20%

    We are solving for: "How does the final price compare with the original price of $500​"

        First, we will find the price at the beginning.

-> Please note a percent divided by 100 becomes a decimal

20% / 100 = 0.2

$500 * 0.2 = $100

$500 + $100 = $600

     Now, we will find the price at the end.

$600 * 0.2 = $120

$600 - $120 = $480

     The final price is less than the original price of $500.

Answer:

Step-by-step explanation:

price marked up by 20%= 500+ \(\frac{20}{100}\)×500

                                        =$600

price marked down by 20%= 600- \(\frac{20}{100}\)×600

                                             =$480

the final price is less than the original price

The correct logarithm form is: a. log5 125 = 3

Question is about finding the logarithm form of 5³ = 125 using the given options.

The correct logarithm form is:

a. log5 125 = 3

Here's the step-by-step explanation:

1. The exponential form is given as 5³= 125.
2. To convert it to logarithm form, you have to express it as log(base) (argument) = exponent.
3. In this case, the base is 5, the argument is 125, and the exponent is 3.
4. Therefore, the logarithm form is log5 125 = 3.

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Answer:

1. 75 degrees

2.  63 degrees

Step-by-step explanation:

1. 180 - (58 + 47) = 75 degrees

2. 180 - 96 - 21 = 63 degrees

The given asymptote, intercepts and holes of the given function depends

on the numerator and denominator of the function from which we have;

The given function is presented as follows;

\(f(x) = \mathbf{ \dfrac{3 \cdot (x - 3) \cdot (x + 2) \cdot (x - 4)}{8 \cdot (x + 9) \cdot (x - 3)}}\)

Given that there is a common factor of (x - 3) in the numerator and the denominator,  we have;

\(f(x) = \mathbf{\dfrac{3 \cdot (x + 2) \cdot (x - 4)}{8 \cdot (x + 9)}}\)

The asymptote is obtained by equating the denominator to zero as follows;

8·(x + 9) = 0

x = -9

The intercepts is given by the points the x or y-value are zero, which gives;

\(At \ an \ intercept, \ f(x) = \dfrac{3 \cdot (x - 3) \cdot (x + 2) \cdot (x - 4)}{8 \cdot (x + 9) \cdot (x - 3)}= 0\)

3·(x - 3)·(x + 2)·(x - 4) = 0

Therefore;

\(At \ the \ \mathbf{y-intercept}, \ f(0) = \dfrac{3 \cdot (0- 3) \cdot (0 + 2) \cdot (0 - 4)}{8 \cdot (0 + 9) \cdot (0 - 3)}= -\dfrac{1}{3}\)

The hole is given by the point where the function is zero.

Placing (x - 3) = 0 in the denominator

Therefore;

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Answer:

2x^2 +x-6

3x^2-6 answer

this is not equal to zero

Euler's formula can be used to derive the trigonometric identities.

Euler's formula states that for any real number x, the complex exponential function can be represented as follows:

\(\[e^{ix} = \cos(x) + i\sin(x)\]\)

where \(e\) is the base of the natural logarithm, \(i\) is the imaginary unit, \(\cos(x)\) represents the cosine function, and \(\sin(x)\) represents the sine function. This formula provides a powerful connection between exponential functions and trigonometric functions.

To derive trigonometric identities using Euler's formula, we can start with the exponential form of Euler's formula and manipulate it algebraically. Let's consider the complex exponential function for two angles, \(x\) and \(y\):

\(\[e^{ix} \cdot e^{iy}\]\)

Using the properties of exponents, we can simplify this expression:

\(\[e^{ix} \cdot e^{iy} = e^{i(x + y)}\]\)

Now, applying Euler's formula to both sides, we get:

\(\[\cos(x) + i\sin(x) \cdot \cos(y) + i\sin(y) = \cos(x + y) + i\sin(x + y)\]\)

By comparing the real and imaginary parts of this equation, we obtain the sum and product formulas for cosine and sine:

\(\[\cos(x) \cdot \cos(y) - \sin(x) \cdot \sin(y) = \cos(x + y)\]\[\sin(x) \cdot \cos(y) + \cos(x) \cdot \sin(y) = \sin(x + y)\]\)

These are known as the angle addition formulas, and they form the basis for deriving other trigonometric identities. By manipulating and applying these formulas, we can establish relationships such as double-angle formulas, half-angle formulas, and more.

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