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The approximate probability that "x" will be within 0.5 of population mean is (c) 0.3026.

We use "Central-limit-theorem" to find probability that "x" will be within 0.5 of population mean. According to the central limit theorem, the distribution of sample means approaches a "Normal-Distribution" with mean μ and standard deviation σ/√(n), where μ = population mean, σ = population standard deviation, and n = sample size,

In this case, we have, sample-size of (n) = 49, population mean (μ) = 43, and population "standard-deviation" of (σ) = 9.

So, standard-deviation of sample mean distribution is:

standard deviation = σ/√(n) = 9/√(49) = 1.2857,

To find the probability that x will be within 0.5 of the population mean, we need to standardize the interval using the standard deviation of the sample mean distribution,

z = (x - μ)/(σ/√n) = (43 + 0.5 - 43)/(1.2857) = 0.3892,

The probability that "x" will be within 0.5 of the population mean is the area under the standard normal distribution curve between z = -0.3892 and z = 0.3892.

P(-0.3892 < Z < 0.3892) = P(Z < 0.3892) - P(Z < -0.3892)

= 0.6513 - 0.3487

= 0.3026

Therefore, the correct option is (c).

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The given question is incomplete, the complete question is

Suppose that a random sample of size 49 is to be selected from a population with mean 43 and standard-deviation 9. What is the approximate probability that "x" will be within 0.5 of the population mean?

(a) 0.5026

(b) 0.6974

(c) 0.3026

(d) 0.6053

The length of the tangent x is 11.2 units.

Given is circle with radius 8.4 units and a tangent with x units, we need to find the length of the tangent,

Since we know that the tangents are perpendicular to the circle, so to find the length,

Using Pythagoras theorem,

Hypotenuse is 5.6+8.4 = 14 units,

So,

14² = 8.4² + x²

x = √196 - 70.56

x = 11.2

Hence the length of the tangent x is 11.2 units.

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Answer:

the answer is B 6t and t are like terms

the statement "if you always test whether the number is positive or negative, big endian is more easy to use than little endian" is incorrect.

Endianness refers to the way in which a computer stores data in memory. In big endian, the most significant byte is stored at the smallest address and the least significant byte is stored at the largest address. In little endian, the least significant byte is stored at the smallest address and the most significant byte is stored at the largest address.

The choice between big endian and little endian has no impact on testing whether a number is positive or negative. Both endianness formats can store positive and negative numbers in the same way.

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Based on the results of the 40 trials, the estimated probability of randomly choosing a red cube from the bag is 2/5 in its simplified form.

     To arrive at this answer, we can use the formula for probability: Probability of an event = Number of favorable outcomes / Total number of outcomes. In this case, the favorable outcome is selecting a red cube, and the total number of outcomes is 40 (since a cube is selected and put back in the bag before each trial). We know that a red cube was selected 16 times out of 40 trials, so the number of favorable outcomes is 16. Thus, the probability of selecting a red cube is 16/40, which simplifies to 2/5. Therefore, based on the results of the 40 trials, the estimated probability of randomly choosing a red cube from the bag is 2/5.

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The proportion of students that choose nachos is given as follows:

0.3333.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The proportion of students choosing nachos is the probability that a single student choose nachos.

Out of 33 students, 11 choose nachos, hence the proportion is given as follows:

11/33 = 1/3 = 0.3333.

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Answer:

  4

Step-by-step explanation:

You want to know the leaf unit corresponding to data value 0.014 when values are rounded to thousandths.

The leaf unit for data values in a stem-and-leaf plot is the least-significant digit of the data value, when all data values are expressed to the same precision.

The least significant digit of 0.014 is 4. The leaf unit is 4.

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After 20 years, the investment compounded periodically will be worth $ 3, 238. 47 more than the investment compounded annually.

First, find the value of the investment when it is compounded periodically, 12 times a year.

The formula is:

= Amount invested x ( 1 + rate ) ^ number of periods

= 9, 000 x ( 1 + 9 % / 12 ) ^ ¹² ˣ ²⁰

= $ 53, 678. 16

If compounded annually, the value would be :

= 9, 000 x ( 1 + 9 % ) ²⁰

= $ 50, 439. 69

The difference is :

= 53, 678. 16 - 50, 439. 69

= $ 3, 238. 47

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Possible committees contain at least one member of each class is 5235.

Number of freshman = 3

Number of sophomores = 4

Number of juniors = 4

Number of seniors = 5

Total = 3 + 4+ 4 + 5 = 16

Number of committees of five members of the council would contain at least one member of each class is given by = total - Number of possibility without freshmen - Number of possibility without sophomores - Number of possibility without juniors - Number of possibility without seniors

= [tex](\left \116 \atop 5\right. ) - (\left \413 \atop 5\right. ) -(\left \112 \atop 5\right. )-(\left \112 \atop 5\right. )-(\left \111 \atop 5\right. )[/tex]

= 8568 - 1287 - 792 - 792 - 462

= 5235

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The probability that a pack of 16 baseballs would have an average weight of more than 147 grams, given our assumptions, is approximately 1 - 0.0082 = 0.9918, or 99.18%.

What is probability?

Probability is a way to gauge how likely or unlikely something is to happen. It measures the degree of ambiguity surrounding the result of a single event or a series of related occurrences. Typically, probability is stated as a number between 0 and 1, with 0 denoting an impossibility and 1 denoting a certain or guaranteed event.

To determine the probability that a pack of 16 baseballs would have an average weight of more than 147 grams, we need information about the distribution of baseball weights. Without specific information about the distribution, it is challenging to provide an exact probability.

However, assuming the weights of baseballs follow a normal distribution with a known mean and standard deviation, we can provide a general guideline for calculating the probability using the Central Limit Theorem.

Let's assume the mean weight of a baseball is μ grams, and the standard deviation is σ grams. Since we don't have the exact values, we'll need to make some assumptions. Let's say the mean weight of a baseball is 150 grams, and the standard deviation is 5 grams.

The average weight of the 16 baseballs follows a normal distribution with a mean equal to the population mean (μ) and a standard deviation equal to the population standard deviation divided by the square root of the sample size (σ/[tex]\sqrt[1]{n}[/tex]).

In this case, the mean is 150 grams, and the standard deviation is 5 grams divided by the square root of 16 (since we have 16 baseballs). The square root of 16 is 4.

The standard deviation of the average weight is 5 grams / 4 = 1.25 grams.

Now, we want to calculate the probability that the average weight is more than 147 grams. To do this, we can convert it into a standard normal distribution by subtracting the mean (150 grams) and dividing by the standard deviation (1.25 grams).

The z-score for 147 grams is (147 - 150) / 1.25 = -2.4.

Using a standard normal distribution table or calculator, we can find the probability associated with a z-score of -2.4. Let's assume it is P(Z < -2.4) = 0.0082.

However, since we are interested in the probability that the average weight is more than 147 grams, we need to consider the area to the right of the z-score (-2.4). This is equal to 1 - P(Z < -2.4).

Therefore, the probability that a pack of 16 baseballs would have an average weight of more than 147 grams, given our assumptions, is approximately 1 - 0.0082 = 0.9918, or 99.18%.

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Check the picture below.

Answer:

x = 5

Step-by-step explanation:

12x + 5 = 65

subtract 5 from both sides

12x + 5 - 5 = 65 - 5

12x = 60

divide by 12

x = 5

Coressponding angles in parallel lines are equal and for u and v to be parallel,

So we have,

[tex]12x + 5 = 65[/tex]

[tex]12x = 65 - 5[/tex]

[tex]12x = 60[/tex]

[tex]x = \frac{60}{12} [/tex]

[tex]x = 5[/tex]

Hence the value of x must be 5° to make the lines u and v parallel

The equation which is equivalent to 3x - 12 = -9 is 3(x - 4) { -9

3x - 12 = -9

The equation is divided into two parts; right part and left part

From the left part; find the common factor of 3x and 12 which is 3

So,

3(x - 4) = -9

3x - 12 = -9

Add 12 to both sides

3x = -9 + 12

3x = 3

divide both sides by 3

x = 3/3

x = 1

Hence, the value of x based on the given equation is 2

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Therefore, the angle between the biker's line of sight and the trail is changing at a rate of approximately 0.039 radians per second when she is 25 feet away from the tree.

To solve this problem, we need to use trigonometry and calculus. Let's call the angle between the biker's line of sight and the trail θ, and let's call the distance from the traffic cone to the aspen tree x. Then we can use the tangent function to relate θ and x:

tan(θ) = x/15

We can also use the Pythagorean theorem to relate x and the distance d between the biker and the tree:

d^2 = x^2 + 25^2

Taking the derivative of both sides with respect to time t, we get:

2d (dd/dt) = 2x (dx/dt)

Now we can substitute the equation for x in terms of θ and solve for (dθ/dt):

tan(θ) = x/15

sec^2(θ) (dθ/dt) = (1/15) (dx/dt)

(dθ/dt) = (1/15) (dx/dt) sec^2(θ)

We can use the equation for d to solve for x:

x^2 = d^2 - 25^2

2x (dx/dt) = 2d (dd/dt)

(dx/dt) = (d/dd) (sqrt(d^2 - 25^2)) (dd/dt)

(dx/dt) = (d/ sqrt(d^2 - 25^2)) (dd/dt)

Now we can substitute this expression for (dx/dt) into the previous equation and evaluate it when d = 25 and θ = arctan(15/25):

(dθ/dt) = (1/15) [(d/ sqrt(d^2 - 25^2)) (dd/dt)] sec^2(arctan(15/25))

(dθ/dt) = (1/15) [(25/ sqrt(25^2 - 25^2)) (13)] sec^2(arctan(15/25))

(dθ/dt) = (13/375) sec^2(arctan(15/25))

(dθ/dt) ≈ 0.039 radians per second

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Answer: Therefore, the coordinates of point B that partitions the segment AC such that AB:BC is 1:2 are (1.17, -2.17).

Step-by-step explanation:

Let's first find the coordinates of the midpoint of AC, which will be the coordinates of point B if AB:BC is 1:2.

The x-coordinate of the midpoint = (x-coordinate of A + x-coordinate of C) / 2 = (-5 + 4) / 2 = -0.5

The y-coordinate of the midpoint = (y-coordinate of A + y-coordinate of C) / 2 = (4 - 5) / 2 = -0.5

So the midpoint of AC is B(-0.5, -0.5).

Now we can find the coordinates of A by using the midpoint formula:

The x-coordinate of A = (2 * x-coordinate of B + x-coordinate of C) / 3 = (2 * (-0.5) + 4) / 3 = 1.17

The y-coordinate of A = (2 * y-coordinate of B + y-coordinate of C) / 3 = (2 * (-0.5) - 5) / 3 = -2.17

So the coordinates of point A are (1.17, -2.17).

Therefore, the coordinates of point B that partitions the segment AC such that AB:BC is 1:2 are (1.17, -2.17).

The asked probabilities are 1/3, 6/7 and 50/71.

Given that are events we need to find the required probability,

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability (Event) = Favorable Outcomes/Total Outcomes = x/n

There is a likelihood to rain or not rain. Here we can apply probability. Probability is used to predict the outcomes for the tossing of coins, rolling of dice, or drawing a card from a pack of playing cards.

The probability is classified into theoretical probability and experimental probability.

so,

Probability = favorable outcomes / total outcomes

1) P(Morgan is a vocalist) = 9/27 = 1/3

2) P(Angela is not a guitarist) = 18/21 = 6/7

3) P(Gina is a vocalist) = 50/71

Hence the probabilities are 1/3, 6/7 and 50/71.

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To find the probability of getting at least 4 fives, we sum up the probabilities of these two cases:

P(at least 4 fives) = P(4 fives and 1 non-five) + P(5 fives)

To calculate the probability of getting at least 4 fives when rolling a fair die 5 times, we need to consider the different possible outcomes.

The probability of rolling a five on a fair die is 1/6, and the probability of not rolling a five is 5/6.

To determine the probability of getting exactly 4 fives and 1 non-five, we use the binomial probability formula:

P(4 fives and 1 non-five) = (5 choose 4) * (1/6)^4 * (5/6)^1

Similarly, for getting exactly 5 fives, we have:

P(5 fives) = (5 choose 5) * (1/6)^5 * (5/6)^0

Rounding the result to the nearest thousandth, we get the probability of getting at least 4 fives when rolling a fair die 5 times.

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Answer:

------------------

The angle formed by two secants is half the difference of the intercepted arc measures:

Substitute values and solve for x:

The tax allowance for a person with two kids and no dependent relative earning 180,000 naira per month before tax is 34,375 naira.

The tax allowance is calculated by first determining the individual's annual income before tax, which in this case is 2,160,000 naira (180,000 x 12 months). Next, the individual's personal allowance of 1,500,000 naira is subtracted from their annual income.

The resulting figure is 660,000 naira, which is then multiplied by 5% to give a tax allowance of 33,000 naira. An additional 375 naira is added to this figure for each child, resulting in a total tax allowance of 34,375 naira for an individual with two kids and no dependent relative earning 180,000 naira per month before tax. This tax allowance reduces the individual's taxable income, thereby reducing the amount of tax they would be required to pay.

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Answer:

Step-by-step explanation:

The distribution of the mean of random samples of size 4 can be approximated by a normal distribution with a mean of 154 Ibs (same as the population means) and a standard deviation of 11.5 Ibs (which is the population standard deviation divided by the square root of the sample size, i.e. 23 Ibs/ sqrt (4)= 11.5 Ibs). This is known as the Central Limit Theorem.

Answer: 50 1/3

Step-by-step explanation: (30 X 5 +4) divided by 3 = 50 1/3

The value of x and y are 10 and 10√3

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

Here the hypotenuse is 20 and the opposite to angle 30 is x and the adjacent is y

Therefore;

sin30 = x/20

1/2 = x/20

2x = 20

x = 20/2 = 10

cos 30 = y/20

√3/2 = y/20

2y = 20√3

y = 20√3/2

y = 10√3

therefore the value of x and y are 10 and 10√3

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The mean distance thrown is approximately 37.31 feet. the Average distance thrown by the heavy ball.

To find the mean of the distances thrown from the stem-and-leaf plot, we need to add up all the distances and divide by the total number of throws.

From the stem-and-leaf plot, we can see that there are 13 throws in total.

To add up the distances, we can use the key to interpret the plot: for example, the number "31" means that one throw went 3.1 feet. Using this method, we can find the following distances:

20, 22, 25, 31, 33, 34, 41, 41, 45, 50, 56, 67, 71

Adding up these distances, we get a total of 485.

To find the mean, we divide by the total number of throws:

mean = 485/13 ≈ 37.31

Therefore, the mean distance thrown is approximately 37.31 feet.  the average distance thrown by the heavy ball.

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Learning statistics is essential for students as it helps them make sense of data and draw meaningful conclusions. It enables students to understand and analyze complex data, make informed decisions, and solve real-world problems.

Explanation:

Statistics is used in many fields of study, including business, economics, psychology, and social sciences. As a student, learning statistics can help you make sense of the vast amounts of data you encounter, whether it's in research papers, surveys, or experiments. Statistics enables you to analyze and interpret data, identify trends and patterns, and draw meaningful conclusions.

This can be useful in making informed decisions, solving problems, and developing new theories. Moreover, knowledge of statistics can also be valuable in your future career, as many professions require an understanding of data analysis and statistical methods. In short, learning statistics is an essential skill that can help you succeed academically and professionally.

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The Fahrenheit temperature of the cup of water, after 4.5 minutes, is given as follows:

155ºF.

The temperature function is defined as follows:

[tex]T(t) = T_a + (T_0 - T_a)e^{-kt}[/tex]

Considering the surrounding and initial temperature, we have that the function is given as follows:

[tex]T(t) = 69 + 135e^{-kt}[/tex]

The temperature after 1.5 minutes is of 185ºF, hence the coefficient k is obtained as follows:

[tex]185 = 69 + 135e^{-1.5k}[/tex]

[tex]e^{-1.5k} = \frac{116}{135}[/tex]

[tex]k = -\frac{\ln{\left(\frac{116}{135}\right)}}{1.5}[/tex]

k = 0.1011.

Hence:

[tex]T(t) = 69 + 135e^{-0.1011t}[/tex]

Hence the temperature after 4.5 minutes is given as follows:

[tex]T(4.5) = 69 + 135e^{-0.1011 \times 4.5}[/tex]

T(4.5) = 155ºF.

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Answer:

87

Step-by-step explanation:

beause

The hotel should overbook enough rooms to maximize revenue without incurring expensive costs due to last-minute cancellations. To determine the optimal number of rooms to overbook, consider the following:

1. The average number of cancellations is 5 with a standard deviation of 3.
2. The average room rate is $80.
3. The cost of accommodating overbooked customers in a nearby hotel is $200.

Using these figures, the hotel can calculate the expected revenue for each room overbooked, while considering the risk of cancellations. The best approach is to use a probabilistic model, such as the normal distribution, to estimate the optimal number of rooms to overbook based on these statistics.

A detailed analysis would require further calculations and simulations, which are beyond the scope of this answer. However, a basic guideline for the hotel would be to overbook only a few rooms (e.g., 1-3) to minimize the risk of incurring the high cost of accommodating customers in nearby hotels while still maximizing the revenue from potential cancellations.

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