Mrs. Bailey bought 20 gallons of gasoline for $58.65. What was the cost per gallon?

a) There are 36 possible sample points. b) The sample points are: (1,1), (1,2), (1,3), ..., (6,5), (6,6). c) The probability of obtaining a sum of 7 is 6/36 = 1/6. d) The probability of obtaining a sum of 9 or greater is 10/36 = 5/18.  e) The given statement " each roll has six possible even values (2, 4, 6, 8, 10, and 12) and only five possible odd values (3, 5, 7, 9, and 11), the dice should show even values more often than odd values." is true. Because there are more ways to obtain even sums than odd sums. f) The method used to assign probabilities is the classical method.

There are 36 possible sample points in this experiment. (6 possible outcomes for the first die multiplied by 6 possible outcomes for the second die)

Sample points:

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)

The probability of obtaining a value of 7 is 6/36 or 1/6. This can be determined by counting the number of sample points that result in a sum of 7 (there are 6 of them) and dividing by the total number of sample points.

The probability of obtaining a value of 9 or greater is 10/36 or 5/18. This can be determined by counting the number of sample points that result in a sum of 9 or greater (there are 10 of them) and dividing by the total number of sample points.

Yes, we agree with this statement. There are more possible outcomes that result in an even sum than an odd sum. Specifically, there are 18 even sums and only 18 odd sums.

This is because an even sum can be obtained by either adding two even numbers, or adding an odd number and an even number (which gives an even result). An odd sum can only be obtained by adding an odd number and an even number.

We used the classical method to assign probabilities, which assumes that all outcomes are equally likely. This method works well for simple random experiments like rolling dice, but may not be appropriate for more complex experiments.

Other methods for assigning probabilities include the empirical method (based on observed frequencies in past data) and the subjective method (based on personal judgment or expert opinion).

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The factors of the polynomial are (x - 4)(x - 4)(x + 7), and the polynomial is completely factored.

For the polynomial x³ - 7x² - 16x + 112, the following statements are true:

1. The factors of the polynomial are (x - 4)(x - 4)(x + 7).

2. The polynomial is completely factored.

To factor the polynomial completely, we can use different factoring techniques such as grouping, factoring by grouping, or synthetic division.

In this case, we observe that the number 4 is a root of the polynomial since when we substitute x = 4 into the polynomial, we get zero.

Using synthetic division or long division, we can divide the polynomial by (x - 4) twice to obtain the factored form (x - 4)(x - 4)(x + 7).

Hence, the factors of the polynomial are (x - 4)(x - 4)(x + 7), and the polynomial is completely factored.

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If in a survey, 200 college students were asked whether they live on campus and if they own a car, 55% of college students in the survey don't own a car.

To find the percent of college students who don't own a car, we need to add up the number of students who don't own a car and divide it by the total number of students in the survey. In this case, the total number of students in the survey is 200.

From the table, we can see that there are 88 students who live on campus and don't own a car, and 22 students who don't live on campus and don't own a car. So the total number of students who don't own a car is 88 + 22 = 110.

To find the percentage, we divide the number of students who don't own a car by the total number of students in the survey and then multiply by 100 to get the percentage:

Percentage of students who don't own a car = (110/200) x 100% = 55%

When working with percentages, we need to divide the number we are interested in by the total and then multiply by 100 to get the percentage.

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Answer:

Step-by-step explanation:

(-2, 2)   (2, -3)

(-3 - 2)/(2 + 2)

-5/4 the slope

y - 2 = -5/4(x + 2)

y - 2 = -5/4x - 5/2

y- 4/2 = -5/4x - 5/2

y = -5/4x - 1/2

Answer:greengrocer should Dell 17 kg before profit. 500$ profit

Step-by-step explanation:

Answer:

C..... I think it is a answer

The correct prime numbers x that make this inequality true is,

⇒ x = 7, 11, 13, 17, 19

We have to given that;

The expression is,

''5 is less than x and x is less than or equal to 19.''

Now, We can formulate;

⇒ 5 < x ≤ 19

Hence, Possible prime numbers that make this inequality true are,

⇒ x = 7, 11, 13, 17, 19

Thus, The correct prime numbers x that make this inequality true is,

⇒ x = 7, 11, 13, 17, 19

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There were 682 children's and 332 adults were admitted when the entrance charge to an park is $4 for adults and $1.50 for children.

Given that,

The entrance charge to an amusement park is $4 for adults and $1.50 for children. 351 persons visited the park on one particular day, and 1014 dollars in entrance fees were collected.

We have to find how many people and kids were allowed inside.

We know that,

We get equations as,

1.5x+4y=351 ----->equation(1)

The other equation is

x+y=1014 ----->equation(2)

Take the equation(2)

x+y=1014

y=1014-x

Substitute y=1014-x in equation(1)

1.5x+4y=351

1.5x+4(1014-x)=351

1.5x+2056-4x=351

1.5x-4x=351-2056

-2.5x=-1705

2.5x=1705

x=1705/2.5

x=682

Substitute x=682 in equation(2)

y=1014-x

y=1014-682

y=332

Therefore, There were 682 children's and 332 adults were admitted when the entrance charge to an amusement park is $4 for adults and $1.50 for children.

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Answer:

c Calculate the product of the length and width, height and width and height and length then

multiply by 2.

Step-by-step explanation:

it will look like this 2lw+2hw+2hl

The answer for your problem is 192

The pH of a 0.498 M aqueous hypochlorous acid solution at the start of the titration, before any sodium hydroxide has been added is 0.303.

pH is the hydrogen ion concentration of an solution. It is given  by pH = -log[H⁺] where H⁺ = hydrogen ion concentration.

Since a 23.8 mL sample of a 0.498 M aqueous hypochlorous acid solution is titrated with a 0.318 M aqueous sodium hydroxide solution. To find the pH at the start of the titration, before any sodium hydroxide has been added, we proceed as follows.

First we write the dissociation equation of the hypochlorous acid solution. So,

HClO(aq) → H⁺(aq) + ClO⁻(aq)

So, we see that the mole ratios are 1 : 1 : 1.

Since the HClO concentration is 0.498 M before the addition of sodium hydroxide, and there is a a 1 : 1 dissociation of hydrogen ion, then the hydrogen ion concentration H⁺ = 0.498 M

So, the pH = -logH⁺

= -log(0.498)

= -(-0.3028)

= 0.3028

≅ 0.303

So, the pH is 0.303

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Therefore, there are 480 different ways to arrange individuals in a row so that no two engineers sit together.

An alternative name for a combo is a choice. A combination is a choice made from a predetermined group of options. I won't organize anything here. They will be my choice. The number of distinct r selections or combinations from a set of n objects is indicated by the symbol \(^nC_{r}\).

There are eight participants in the focus group, including three software engineers, two nurses, one doctor, and two technicians.

So the 3 software engineers =3! ways, 2 nurses =2! ways,

doctor =1! way , 2 technicians =2! ways.

We must determine how many different configurations are possible so that no two pieces of software may coexist.

In order to prevent two software engineers from being seated next to each other, we first arrange five persons in a row with a space between them.

\(We get that in 6 places they can sit in ^6C_{3} ways\\ xi.e ^6C_3 = 20 (by formula of combination)\\ Therefore total ways are,6 X 2 X 1 X2 X 20 = 480.\)

Therefore, there are 480 different ways to arrange individuals in a row so that no two engineers sit together.

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Answer:

5x43

it can only be divided by 1, 5, and 43.

When 215 is written as a product of its prime factor, the result is 5 × 43.

To find the prime factorization of 215, we'll divide it by its smallest prime factor and continue the process until we get all the prime factors. Here's the step-by-step breakdown:

Divide 215 by the smallest prime number, which is 5. We get:

215 ÷ 5 = 43

43 is a prime number, so we stop here.

Now, the prime factorization of 215 is:

215 = 5 × 43

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The function in the context of this problem is modeled as follows:

t(r) = 12/(6 + r)

In which the input and output of the function are given, respectively, by:

Then the numeric value at t = 3 represents the time in hours it takes for the boat to cross the river when the velocity of the river is of 3 kilometers per hour.

The vertical asymptote of a function are the values of the input for which the function is not defined.

A fraction is not defined at the zeros of the denominator, hence:

t + 6 = 0

t = -6 is the vertical asymptote of the function.

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In the east town hatchery, around (d) 95% of the fish will have z-scores between 2 and -2.

A z-score is a measure of how far a specific point is away from the mean in terms of standard deviations. A z-score of 2 means that the point is 2 standard deviations above the mean, while a z-score of -2 means that the point is 2 standard deviations below the mean.

In this case, the mean length of a baby sunfish is 2.2 inches and the standard deviation is 0.6 inches. Therefore, a z-score of 2 means that the fish is 2 * 0.6 = 1.2 inches above the mean, while a z-score of -2 means that the fish is 2 * 0.6 = 1.2 inches below the mean.

The 68-95-99.7 rule tells us that approximately:

68% of the fish will have z-scores between -1 and 1.

95% of the fish will have z-scores between -2 and 2.

99.7% of the fish will have z-scores between -3 and 3.

Therefore, approximately (d) 95% of the fish in the east town hatchery will have z-scores between 2 and -2.

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Answer:

Step-by-step explanation:

a. The range of G is the set of possible values that G can take. G represents the distribution over the number of girls chosen, so G can take any value between 0 and 2, inclusive. That is, the range of G is {0, 1, 2}.

b. To give the distribution over the random variable G, we need to determine the probability of each possible value of G.

Let's consider each possible value of G in turn:

If no girls are chosen (G=0), then both representatives must be boys. The probability of choosing a boy on the first draw is 3/10, and the probability of choosing another boy on the second draw is 2/9 (since there are only 2 boys left). Therefore, the probability of G=0 is (3/10) * (2/9) = 1/15.

If one girl is chosen (G=1), then one representative must be a girl and the other must be a boy. There are two ways this can happen: either the girl is chosen first and then the boy, or the boy is chosen first and then the girl. The probability of choosing a girl on the first draw is 7/10, and the probability of choosing a boy on the second draw is 3/9 (since there are 3 boys left). The probability of choosing a boy on the first draw is 3/10, and the probability of choosing a girl on the second draw is 7/9 (since there are 7 girls left). Therefore, the probability of G=1 is (7/10) * (3/9) + (3/10) * (7/9) = 14/45.

If two girls are chosen (G=2), then both representatives must be girls. The probability of choosing a girl on the first draw is 7/10, and the probability of choosing another girl on the second draw is 6/9 (since there are 6 girls left). Therefore, the probability of G=2 is (7/10) * (6/9) = 7/15.

Therefore, the distribution over the random variable G is:

G=0 with probability 1/15

G=1 with probability 14/45

G=2 with probability 7/15

False. All values in a dataset with a normal distribution can be converted to a z-score.

False. All values in a dataset with a normal distribution can be converted to a z-score. The z-score standardizes the data, allowing for comparisons across different distributions by representing the number of standard deviations a data point is away from the mean.

A continuous random variable that tends to cluster around a centre or average value with a particular degree of spread or variation is described by the normal distribution, commonly referred to as the Gaussian distribution. The maximum frequency is near the mean and decreases in frequency as one moves farther away from the mean in both directions. It is a symmetrical bell-shaped curve.

The standard normal distribution, in which the mean and standard deviation are both 0, is a particular instance of the normal distribution. The standard score, also referred to as the z-score, is a measurement of how many standard deviations a data point deviates from the distribution's mean. The difference between the observation's value and the mean is used to calculate it.

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False. All values in a dataset with a normal distribution can be converted to a z-score.

The z-score transformation is used precisely to transform values from a normal distribution to a standard normal distribution, which has a mean of 0 and a standard deviation of 1.

All values in a dataset with a normal distribution can be converted to a z-score.

The statement "not all values in a dataset with a normal distribution can be converted to a z-score" is false.

A z-score represents the number of standard deviations a data point is away from the mean of a distribution and can be calculated for any value within a normal distribution.

In fact, the conversion of values to z-scores is a common method of standardizing data for statistical analysis.
To calculate a z-score, you subtract the mean of the distribution from the individual value and then divide the result by the standard deviation of the distribution.

This transformation allows for easier comparison between data points and across different datasets.

Z-scores can also be used to calculate probabilities and determine the likelihood of certain events occurring within a distribution.
While it is true that some datasets may not follow a normal distribution, this does not mean that z-scores cannot be calculated for all values within the dataset.

The distribution is not normal, other statistical techniques such as transformation or non-parametric tests may be necessary.

A normally distributed dataset, every value can be converted to a z-score, allowing for standardized comparisons and analysis.

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The probability that a second call will not arrive in the next 20 seconds is approximately 0.2636 or 26.36%.

Poisson probability is a mathematical concept that describes the probability of a certain number of events occurring in a fixed interval of time or space, given a known average rate of occurrence. The Poisson probability distribution is named after French mathematician Siméon Denis Poisson, who introduced it in the early 19th century to model the occurrence of rare events, such as errors in counting or measurement, accidents, or phone calls.

The Poisson probability distribution is a discrete probability distribution that gives the probability of a certain number of events (x) occurring in a fixed interval (t), when the average rate of occurrence (λ) is known. The Poisson probability distribution assumes that the events occur independently and at a constant average rate over time or space. The formula for Poisson probability is:

P(x; λ) = (\(e^{-\lambda}\)) * λˣ) / x!

where:

P(x; λ) = the probability of x occurrences in a given interval, when the average rate is λ

e = a mathematical constant e (approximately 2.71828)

λ = it is the average rate of occurrence in the given interval

x = it is number of occurrences in the given interval

Given that calls for dial-in connections arrive at an average rate of four per minute and follow a Poisson distribution, we can use the Poisson probability formula to solve this problem. The Poisson probability formula is:

P(x; λ) =  (\(e^{-\lambda}\)) * λˣ) / x!

where:

P(x; λ) = the probability of x occurrences in a given interval, when the average rate is λ

e = a mathematical constant e (approximately 2.71828)

λ = the average rate of occurrence in the given interval

x = it is the number of occurrences in the given interval

In this problem, we are interested in finding the probability that a second call will not arrive in the next 20 seconds, given that a call has already arrived at the beginning of a one-minute interval. Since we are given the average rate of calls per minute, we need to adjust the interval to 20 seconds, which is 1/3 of a minute. Therefore, the average rate of calls per 20 seconds is:

λ = (4 calls/minute) * (1/3 minute) = 4/3 calls/20 seconds

Using the Poisson probability formula, we can calculate the probability of no calls arriving in the next 20 seconds:

P(0; 4/3) = ( \(e^{-4/3}\)* (4/3)⁰) / 0! = \(e^{-4/3}\) ≈ 0.2636

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E(U) = 4, which is an integer.

What is Linearity of expectation?

Linearity of expectation is a fundamental property of expected value that states that the expected value of a sum or difference of random variables is equal to the sum or difference of their individual expected values.

To find E(U), where U = 2X - Y - 4, we can use the properties of expected value.

First, let's find the expected values of 2X, Y, and 4 separately using the linearity of expectation:

E(2X) = 2E(X) = 2 * 6 = 12

E(Y) = 4 (given)

E(4) = 4

Now, let's calculate the expected value of U:

E(U) = E(2X - Y - 4)

Since expected value is a linear operator, we can rearrange and simplify the expression:

E(U) = E(2X) - E(Y) - E(4)

= 12 - 4 - 4

= 4

Therefore, E(U) = 4, which is an integer.

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Answer:

The answer is A. Only rotate one line

Step-by-step explanation:

If you have a set of parallel lines, and you rotate one line upwards, the lines would change to a perpendicular angle.

a)  P(X=330) is approximately 0.0002. b)P(X>340) is approximately 0.0294. c) P(335≤X≤345) is approximately 0.6415. d) P(X=300) is approximately 0.0004 of given probabilities

To find the probabilities using Excel's function options, we can use the binomial distribution function, which is provided as BINOM.DIST in Excel.

a) P(X=330):

=BINOM.DIST(330, 400, 0.8, FALSE)

The first argument is the specific value (330), the second argument is the total number of trials (400), the third argument is the probability of success (0.8), and the fourth argument FALSE indicates that we want the probability for a specific value.

The result is approximately 0.0002.

Therefore, P(X=330) is approximately 0.0002.

b) P(X>340):

=1 - BINOM.DIST(340, 400, 0.8, TRUE)

Since we want the probability of X being greater than 340, we can subtract the cumulative probability of X up to 340 from 1. We use the TRUE argument to indicate that we want the cumulative probability.

The result is approximately 0.0294.

Therefore, P(X>340) is approximately 0.0294.

c) P(335≤X≤345):

=BINOM.DIST(345, 400, 0.8, TRUE) - BINOM.DIST(334, 400, 0.8, TRUE)

To find the probability of X being between 335 and 345 (inclusive), we subtract the cumulative probability of X up to 334 from the cumulative probability of X up to 345.

The result is approximately 0.6415.

Therefore, P(335≤X≤345) is approximately 0.6415.

d) P(X=300):

=BINOM.DIST(300, 400, 0.8, FALSE)

The first argument is the specific value (300), the second argument is the total number of trials (400), the third argument is the probability of success (0.8), and the fourth argument FALSE indicates that we want the probability for a specific value.

The result is approximately 0.0004.

Therefore, P(X=300) is approximately 0.0004.

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The student's error could be in the wrong formula he used. The  area of the sector is 245.043 sq.

The formula for area of a sector is

A = (θ/360) * π * r^2

where:

θ is the central angle of the sector in degrees

r is the radius of the circle

In this case, the central angle θ is 45 degrees and the radius r is 25 cm. So the area of the sector should be:

A = (45/360) * π * (25)^2

A = (1/8) * π * 625

A = 78.125π ≈ 245.043 sq. cm

The student could have made an error during any step of the calculation.

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The height of the helium tank is; Option D: 36 inches

The formula for the volume of a cylinder is;

V = πr²h

Where;

V is volume

r is radius

h is height

We are given;

Radius(r) = diameter/2 = 12/2

r = 6 inches

Volume; V = 1296π in³

1296π = π * 6² * h

h = 1296/36

h = 36 inches

We conclude that is the height if the helium tank

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Answer:

its height is 36 inches

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

y = x - 1

2x + y = 8

2x + x - 1 = 8

3x - 1 = 8

+ 1 + 1

3x = 9

3x / 3 = 9 / 3

x = 3

Answer:

- m - 6n + 10

Step-by-step explanation:

-(m + 6n - 10)

|

|

v

- m - 6n + 10

The solution involves calculating the likelihood function, maximizing it, and using the estimated value to find the probability of no dropped connections in the next two calls.

(a) To find the maximum likelihood estimate of λ, the mean number of dropped connections per call, we need to use the Poisson distribution to calculate the likelihood function L(λ) for the given data. The Poisson distribution is given by:

P(X = x | λ) = (λ^x * e^(-λ)) / x!

where X is the random variable representing the number of dropped connections per call, λ is the parameter representing the mean number of dropped connections per call, and x is the observed number of dropped connections in a call.

The likelihood function for four calls with observed numbers of dropped connections 2, 0, 3, and 1 can be expressed as:

L(λ) = P(X = 2 | λ) * P(X = 0 | λ) * P(X = 3 | λ) * P(X = 1 | λ)

= (λ^2 * e^(-λ)) / 2! * (e^(-λ)) / 0! * (λ^3 * e^(-λ)) / 3! * (λ^1 * e^(-λ)) / 1!

= (λ^6 * e^(-4λ)) / 6

Taking the derivative of L(λ) with respect to λ, setting it equal to zero, and solving for λ.

d/dλ [L(λ)] = d/dλ [(λ^6 * e^(-4λ)) / 6]

= [(6λ^5 * e^(-4λ) - 4λ^6 * e^(-4λ)) / 6]

Setting this derivative equal to zero, we get:

2λ - 3λ^2 = 0

λ = 0 or λ = 2/3

Since λ = 0 is not a valid solution for a Poisson distribution, the maximum likelihood estimate of λ is λ = 2/3.

Therefore, the maximum likelihood estimate of the mean number of dropped connections per call is 2/3.

(b) To obtain the maximum likelihood estimate that the next two calls will be completed without any accidental drops, we can use the estimated value of λ = 2/3 to calculate the probability of no dropped connections in each of the next two calls, using the Poisson distribution:

P(X = 0 | λ = 2/3) = (2/3)^0 * e^(-2/3) / 0! = e^(-2/3) ≈ 0.5134

P(both calls have no drops | λ = 2/3) = P(X = 0 | λ = 2/3)^2 ≈ 0.2637

Therefore, the maximum likelihood estimate that the next two calls will be completed without any accidental drops is approximately 0.2637.

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The required answer is the double declining-balance method is $9,840.

To calculate the depreciation expense for 2020 using the double declining-balance method, we first need to determine the asset's straight-line depreciation rate. This is calculated by subtracting the residual value from the cost of the asset and dividing by the asset's useful life:

Depreciation base = $30,000 - $3,000 = $27,000
Annual depreciation expense (straight-line) = Depreciation base / Useful life = $27,000 / 5 = $5,400

Next, we need to determine the double declining-balance rate, which is twice the straight-line rate. Therefore:
Double declining-balance rate = 2 x (1 / Useful life) = 2 x (1 / 5) = 0.40 or 40%
Now we can calculate the depreciation expense for 2020:
Depreciation expense (2020) = Book value (beginning of year) x Double declining-balance rate

The book value at the beginning of 2020 would be the cost of the asset minus accumulated depreciation for the first year:
Book value (beginning of 2020) = $30,000 - ($5,400 x 1) = $24,600
As a result, depreciation increases during the initial year of possession and decreases thereafter.

Therefore:

Depreciation expense (2020) = $24,600 x 0.40 = $9,840

So the amount of depreciation expense for 2020, the second year of the asset's life,

using the double declining-balance method is $9,840.

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