(x^3+6x^2+5x-6)÷(x+2)

The best estimate for the perimeter of the triangle is 23.7 inches when rounded to the nearest tenth.

In a triangle with angles measuring 30°, 60°, and 90°, we can determine the lengths of the sides using trigonometric ratios. Since it's a right triangle, we can use the sine, cosine, or tangent functions to find the side lengths.

Given that the hypotenuse of the triangle measures 10 inches, let's denote the lengths of the other two sides as a and b.

In a right triangle, the side opposite the 30° angle (a) is given by a = (1/2) * hypotenuse.

a = (1/2) * 10 inches

a = 5 inches

The side opposite the 60° angle (b) can be found using the sine function:

sin(60°) = b / hypotenuse

b = sin(60°) * 10 inches

b = (sqrt(3)/2) * 10 inches

b ≈ 8.66 inches (rounded to two decimal places)

Now, we can calculate the perimeter of the triangle by summing the lengths of all three sides:

Perimeter = a + b + hypotenuse

Perimeter ≈ 5 inches + 8.66 inches + 10 inches

Perimeter ≈ 23.66 inches (rounded to two decimal places)

Therefore, the best estimate for the perimeter of the triangle is 23.7 inches when rounded to the nearest tenth.

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The position vector of point C which divides the line segment AB internally is  determined as 1.75i + 3j.

The position vector of point C is calculated using the following formula as shown below.

C = (mb + na) / (m + n)

where;

The ratios and position vector A and B is given as;

m = 3,  n = 1.

a = i - 3j

b = 2i + 5j

The position vector of point C is calculated as follows;

r = (3 (2i + 5j) + 1(i - 3j)) / (3 + 1)

= (6i + 15j + i - 3j) / 4

= (7i + 12j) / 4

= 1.75i + 3j

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Two units of length used in ancient Egypt were cubits and palms, where 1 cubit is equivalent to 7 palms. The Great Sphinx statue in Giza is approximately 140 cubits long.

We can convert the length of the Great Sphinx statue from cubits to palms by using the conversion factor given: 1 cubit is equivalent to 7/11 palms.

We know that 1 cubit is equivalent to 7/11 palms. Hence, we can multiply the length of the statue in cubits by the conversion factor to get the length in palms. Therefore:

140 cubits * 7/11 palms = 980/11 palms.

Thus, the length in palms of the Great Sphinx statue is approximately 980/11 palms, which is about 89.09 palms.

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The Great Sphinx of Giza, which is approximately 140 cubits long, would measure approximately 980 palms long, using the conversion of 1 cubit equaling 7 palms.

The Great Sphinx in Giza, which measures approximately 140 cubits in length, can be converted to palms using the historical equivalency of 1 cubit totalling approximately 7 palms. Therefore, if you knew that 1 cubit equals 7 palms, to find out how long the Great Sphinx is in palms, you'd multiply the length in cubits (140) by how many palms are in each cubit (7).

140 cubits * 7 palms/cubit equals 980 palms.

Therefore, the Great Sphinx approximates to being 980 palms long.

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The correct option is : c. Valid

Does the logical relationship between the premises and conclusion in the given argument hold true?

Yes, the logical relationship between the premises and conclusion in the given argument holds true.

To evaluate the given argument, we can break it down into its premises and conclusion:

Premises:

1.e ⊃ j (If e, then j)

2.b ⊃ q (If b, then q)

3.d ⊃ (j • ∼q) (If d, then (j and not q))

Conclusion:

(e • b) ≡ d ((e and b) if and only if d)

To determine the validity and cogency of the argument, we need to assess whether it is logically valid and whether its premises are true.

Validity: An argument is valid if the truth of its premises guarantees the truth of its conclusion. Let's analyze each premise:

1.e ⊃ j (If e, then j)

This premise asserts a conditional statement. If e is true, then j must also be true. This premise seems reasonable.

2.b ⊃ q (If b, then q)

Similar to the first premise, this premise asserts a conditional statement. If b is true, then q must also be true. This premise seems reasonable as well.

3.d ⊃ (j • ∼q) (If d, then (j and not q))

Once again, this premise states a conditional relationship. If d is true, then both j and not q must be true. This premise also seems reasonable.

Now let's consider the conclusion:

(e • b) ≡ d ((e and b) if and only if d) This conclusion states an equivalence, asserting that (e and b) is true if and only if d is true.

Given that all the premises are reasonable and logically valid, we can conclude that the argument is valid.

Therefore, the correct answer is:

c. Valid.  

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Je vais décrire les étapes pour tracer les figures demandées à main levée et indiquer les informations pertinentes sur chaque figure. Cependant, je ne suis pas en mesure de les tracer en "vraie grandeur" ici, car je ne peux fournir que des représentations textuelles. Voici les étapes pour les deux figures :

1) Figure IFGH :

2) Figure RSTU de centre O :

Assurez-vous de tracer les segments et les angles avec soin et de les proportionner selon les dimensions indiquées.[tex][/tex]

To find the variance of the number of hours worked by a student, we first need to simplify the given numbers. The simplified numbers are 11, 9, 14, 12, 13, 8, 10, and 15.

Variance is a measure of how spread out the data is from the mean. To calculate the variance, we follow these steps:

1. Find the mean:

Add up all the simplified numbers and divide the sum by the total number of data points. In this case, the mean is (11 + 9 + 14 + 12 + 13 + 8 + 10 + 15) / 8 = 12.

2. Subtract the mean from each data point:

Take each simplified number and subtract the mean from it. The differences are as follows: -1, -3, 2, 0, 1, -4, -2, and 3.

3. Square the differences:

Square each of the differences obtained in the previous step. The squared differences are: 1, 9, 4, 0, 1, 16, 4, and 9.

4. Find the mean of the squared differences:

Add up all the squared differences and divide the sum by the total number of data points. In this case, the mean of the squared differences is (1 + 9 + 4 + 0 + 1 + 16 + 4 + 9) / 8 = 44 / 8 = 5.5.

Therefore, the variance of the number of hours worked by the student is 5.5. The variance indicates the average squared deviation from the mean, providing a measure of the spread or variability in the data set.

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The value of the chi-square test statistic and the degrees of freedom for this test is A. χ‑2 = 7.47, df = 4

The chi-square test statistic is calculated as follows:

χ² = Σ(O - E)² / E

The expected counts are calculated as follows:

E = N * p

In this case, the total sample size is 150, so the expected counts are:

City: 50 * 0.25 = 12.5

Rural: 50 * 0.50 = 25

Suburbs: 50 * 0.25 = 12.5

The chi-square test statistic is then:

χ² = (10 - 12.5)² / 12.5 + (60 - 25)² / 25 + (40 - 12.5)² / 12.5

= 7.47

The degrees of freedom for this test are the number of categories minus one, which is 5 - 1 = 4.

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Answer:

z = 142°

Step-by-step explanation:

the bearing of B from A is the measure of the clockwise angle from the north line (N) at A to B

given the bearing of B from A is 218°

the angle around A is 360° , that is

z + 218° = 360° ( subtract 218° from both sides )

z = 142°

The situation which is modeled by linear-function is (c): "An amusement-park allows 50 people to enter every 30 minutes."

A "Linear-Function" represents a relationship that has constant-rate of change. In this case, the number of people entering the amusement-park increases by a constant amount of 50 every 30 minutes. The rate of change is consistent, and it can be expressed as a linear function.

The Option (a) cannot be modeled by a linear function because the population of bacteria triples every day, which represents exponential-growth rather than a linear relationship.

The Option (b) cannot be modeled by a linear function either because the value of a cell phone depreciates at a constant rate of 3.5% each year, which also represents exponential decay.

The Option (d) does not follow a linear pattern either. In a baseball tournament, the number of teams gets halved after each round, resulting in an exponential decrease rather than a linear relationship.

Therefore, the correct option is (c).

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The given question is incomplete, the complete question is

Which situation can be modeled by a linear function?

(a) The population of bacteria triples every day,

(b) The value of a cell phone depreciates at a rate of 3.5% each year,

(c) An amusement park allows 50 people to enter every 30 minutes,

(d) A baseball tournament eliminates half of the teams after each.

The point on the graph where the tangent plane is parallel is (52, 52, -5382).

What is the tangent plane?

The surface that contains all tangent lines of the curve at a point, $P$, that lies on the surface and passes through the point is represented by the tangent plane. We discovered earlier in our talks of derivatives and tangent lines that we can use tangent lines to mimic the behavior of a graph. We may employ tangent planes for a similar reason now that we're working with multivariable functions and three-dimensional coordinate systems.

Here, we have

Given: Let P be the tangent plane to the graph of g(x, y) = 26 – 13x² – 26y² at the point (4, 2, –286). Let f(x, y) = 26 – x² - y².

We have to find the point on the graph where the tangent plane is parallel.

Let P be the tangent plane to the graph z = g(x, y) = 26 – 13x² – 26y² at the point (4, 2, –286).

φ(x,y,z) = 13x² + 26y² + z - 26

Δφ = 26xi + 52yj + k

Δφ(4, 2, –286) = 104i + 104j + k

Then,

P: 104(x-4) + 104(y-2)+1(z+286) = 0

104x + 104y + z = 338...(1)

Now, Let

ψ(x,y,z) =  x² + y² + z - 26

Δψ = 2xi + 2yj + k

Let (x₀,y₀,z₀) be the point of the graph z = f(x,y) = 26 – x² - y² where the tangent plane in the plane is parallel to equation (1).

Δψ (x₀,y₀,z₀)  =  (2x₀,2y₀,1)

= 2x₀/104 = 2y₀/104 = 1/1

x₀ = 52 = y₀

Now, z₀ = 26 – x₀² - y₀² = 26 – 52² - 52²= -5382

Hence,  the point on the graph where the tangent plane is parallel is (52, 52, -5382).

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Governments may restrict trade for several reasons, despite the general consensus among economists that it is detrimental to trade and reduces government efficiency. One primary reason is to protect domestic industries and jobs from foreign competition.

Trade restrictions such as tariffs and quotas can shield domestic producers from international competition, allowing them to maintain market share and employment levels. Governments may also impose trade restrictions for strategic reasons, such as protecting national security interests or preventing the outflow of critical resources.

Trade restrictions refer to government-imposed barriers and regulations that limit the flow of goods and services across international borders.

These restrictions can take various forms, such as tariffs, quotas, embargoes, and regulatory barriers. The reasons for implementing trade restrictions can vary depending on the specific circumstances and goals of the government.

Additionally, political considerations and pressure from special interest groups can influence trade policy decisions. While economists emphasize the benefits of free trade, governments often face complex trade-offs between economic efficiency, domestic interests, and political considerations when formulating trade policies.

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Answer:

2.5

Step-by-step explanation:

slope is rise/run, (y2-y1)/(x2-x1)

We have two points clearly given to us on this graph so let's just use those.

(-1,-3) and (1,2)

= (-3-2)/(-1-1)

=(-5)/(-2)

=2.5

17. The point on the line 2x - 4y = 3 that is closest to the origin is (-3/10, 3/20).

To solve this problem using Lagrange multipliers, we can define the distance squared function as D² = x² + y², which represents the square of the distance from any point (x, y) to the origin. The constraint equation is given by 2x - 4y = 3.

We set up the Lagrange function L = D² - λ(2x - 4y - 3), where λ is the Lagrange multiplier. To find the minimum of L, we take partial derivatives with respect to x, y, and λ and set them equal to zero:

∂L/∂x = 2x - 2λ = 0

∂L/∂y = 2y + 4λ = 0

∂L/∂λ = 2x - 4y - 3 = 0

Solving this system of equations gives x = -3/10, y = 3/20, and λ = -1/20.

Thus, the point on the line closest to the origin is (-3/10, 3/20).

To find the point on the line closest to the origin, we need to minimize the distance between any point on the line and the origin. This can be done by minimizing the distance squared function D² = x² + y².

However, we have a constraint given by the equation of the line 2x - 4y = 3.

By introducing the Lagrange multiplier λ, we create a Lagrange function L = D² - λ(2x - 4y - 3). Taking the partial derivatives and setting them equal to zero, we find the critical point that minimizes the Lagrangian function.

Solving the resulting system of equations gives us the coordinates of the point on the line closest to the origin.

In this case, the point is (-3/10, 3/20).

18. The point on the line y = 2x + 3 that is closest to (4,2) is (2, 7).

To solve this problem using Lagrange multipliers, we can define the distance squared function as D² = (x - 4)² + (y - 2)², which represents the square of the distance from any point (x, y) to (4, 2). The equation of the line is y = 2x + 3.

We set up the Lagrange function L = D² - λ(y - 2 - 2x - 3), where λ is the Lagrange multiplier. To find the minimum of L, we take partial derivatives with respect to x, y, and λ and set them equal to zero:

∂L/∂x = 2(x - 4) - 2λ = 0

∂L/∂y = 2(y - 2) - λ = 0

∂L/∂λ = y - 2x - 3 = 0

Solving this system of equations gives x = 2, y = 7, and λ = -2. Thus, the point on the line closest to (4, 2) is (2, 7).

To find the point on the line closest to the given point (4, 2), we need to minimize the distance between any point on the line and (4, 2).

This can be done by minimizing the distance squared function D² = (x - 4)² + (y - 2)².

The equation of the line y = 2x + 3 serves as the constraint. By introducing the Lagrange multiplier λ, we create a Lagrange function L = D² - λ(y - 2 - 2x - 3).

Taking the partial derivatives and setting them equal to zero, we find the critical point that minimizes the Lagrange function.

Solving the resulting system of equations gives us the coordinates of the point on the line closest to (4, 2). In this case, the point is (2, 7).

20. The point on the plane 4x + 3y + z = 2 that is closest to (1,-1,1) is (2/7, -4/7, 2/7).

To solve this problem using Lagrange multipliers, we can define the distance squared function as D² = (x - 1)² + (y + 1)² + (z - 1)², which represents the square of the distance from any point (x, y, z) to (1,-1,1). The equation of the plane is 4x + 3y + z = 2.

We set up the Lagrange function L = D² - λ(4x + 3y + z - 2), where λ is the Lagrange multiplier. To find the minimum of L, we take partial derivatives with respect to x, y, z, and λ and set them equal to zero:

∂L/∂x = 2(x - 1) - 4λ = 0

∂L/∂y = 2(y + 1) - 3λ = 0

∂L/∂z = 2(z - 1) - λ = 0

∂L/∂λ = 4x + 3y + z - 2 = 0

Solving this system of equations gives x = 2/7, y = -4/7, z = 2/7, and λ = 1/7. Thus, the point on the plane closest to (1,-1,1) is (2/7, -4/7, 2/7).

To find the point on the plane closest to the given point (1,-1,1), we need to minimize the distance between any point on the plane and (1,-1,1).

This can be done by minimizing the distance squared function D² = (x - 1)² + (y + 1)² + (z - 1)².

The equation of the plane 4x + 3y + z = 2 serves as the constraint. By introducing the Lagrange multiplier λ, we create a Lagrange function L = D² - λ(4x + 3y + z - 2).

Taking the partial derivatives and setting them equal to zero, we find the critical point that minimizes the Lagrange function.

Solving the resulting system of equations gives us the coordinates of the point on the plane closest to (1,-1,1). In this case, the point is (2/7, -4/7, 2/7).

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To find the probability that the sample mean will lie between 78 and 81, we need to calculate the z-scores corresponding to these values and then use the standard normal distribution to determine the probability.

The Central Limit Theorem states that when the sample size is large enough, the distribution of sample means will be approximately normally distributed, regardless of the shape of the population distribution. In this case, since the sample size is 64 (which is considered large), we can assume that the sample mean follows a normal distribution.

To calculate the probability, we first convert the sample mean values of 78 and 81 into z-scores using the formula:

z = (x - μ) / (σ / √n)

where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

For 78:

z = (78 - 80) / (10 / √64) = -2 / 1.25 = -1.6

For 81:

z = (81 - 80) / (10 / √64) = 1 / 1.25 = 0.8

We can then use a standard normal distribution table or a calculator to find the probability associated with these z-scores. The probability that the sample mean will lie between 78 and 81 is the difference between the cumulative probabilities corresponding to these z-scores.

P(78 ≤ x ≤ 81) = P(-1.6 ≤ z ≤ 0.8)

Using a standard normal distribution table or calculator, we can find the cumulative probabilities associated with these z-scores and calculate the probability.

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( ) In the same OSM, all pages must have the same size. - False

( ) In the same OSM, all segments must have the same size. - False

( ) Internal fragmentation is a problem of paging. - True

( ) External fragmentation is a problem of segmentation. - True

( ) Paging and segmentation cannot co-exist in the same OSM - False

In an Operating System Memory (OSM), all pages do not have to have the same size. Pages can have different sizes depending on the system's memory management scheme, such as demand paging or memory segmentation.

Similarly, segments in the same OSM do not have to have the same size. Segmentation allows for variable-sized memory segments based on program requirements.

Internal fragmentation refers to wasted memory within a single memory block due to allocation granularity. It is typically associated with paging, where fixed-size pages can lead to inefficient memory utilization.

External fragmentation refers to unallocated or unusable memory scattered throughout the system. It is more commonly associated with memory segmentation, where varying sizes of memory segments can result in fragmented memory space.

Paging and segmentation can coexist in the same OSM. Many operating systems use a combination of both techniques, known as segmented paging or hybrid memory management, to leverage the advantages of each method and optimize memory allocation.

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Answer:

20 tins

Step-by-step explanation:

divide the shape (like in diagram) into 3 trapezia.

Area of trapezium = ½ X (sum of parallel sides) X distance between them.

area of bottom trapezium = 1/2 X (6 + 16) X (14 - 10)

= 1/2 X 22 X 4

= 44.

area of top left trapezium = 1/2 X (10/2 + 16/2) X 10

= 1/2 X (5 + 8) X 10

= 1/2 X 13 X 10

= 65

area of top right trapezium = area of top left trapezium = 65.

total area = 44 + 65 + 65 = 174ft².

we need 174/9

= 19.33333 tins.

that is, we need 20 tins

The industrialization-policy which is used by developing countries to resource allocation is : (a) export promotion.

The "Export-Promotion" is an industrialization policy which is used by "developing-countries" which emphasis on "comparative-advantage" principle as guide to resource-allocation.

The Comparative-advantage suggests that countries should focus on producing and exporting goods or services in which they have a relative advantage or lower opportunity cost compared to other nations.

Under export promotion, developing countries allocate resources to industries and sectors where they have a comparative advantage.

Therefore, the correct option is (a).

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The given question is incomplete, the complete question is

Which industrialization policy used by developing countries places emphasis on the comparative advantage principle as a guide to resource allocation?

(a) export promotion

(b) import substitution

(c) international commodity agreements

(d) Infant Industry promotion

(e) intra-industry trade practice

August, with a Z-score of 2. The correct answer is B.

To determine which month had a higher Z-score for sales on the 15th, we need to calculate the Z-scores for both July and August using the given information.

For July:

Mean (μ) = $270

Standard Deviation (σ) = $30

Value (X) = $315

Z-score (Z) = (X - μ) / σ

Z = (315 - 270) / 30

Z ≈ 1.5

For August:

Mean (μ) = $250

Standard Deviation (σ) = $25

Value (X) = $300

Z-score (Z) = (X - μ) / σ

Z = (300 - 250) / 25

Z = 2

Comparing the Z-scores, we can see that August had a higher Z-score for sales on the 15th with a value of 2. This indicates that the sales on the 15th of August were relatively higher compared to the average daily sales for August. July had a Z-score of approximately 1.5, suggesting that the sales on the 15th of July were slightly above average but not as high as in August.

Therefore, the correct answer is: b.) August, with a Z-score of 2.

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Sabrina's basis in her partnership interest immediately after contributing a building with an adjusted basis of $80,000 and a fair market value of $100,000 would be $100,000.

When Sabrina contributes the building to the partnership, her basis in her partnership interest is equal to the fair market value of the contributed property. In this case, the fair market value of the building is $100,000. Therefore, immediately after the contribution, Sabrina's basis in her partnership interest would also be $100,000.

The basis of a partner's interest in a partnership is important for determining the partner's share of partnership profits, losses, and distributions. It represents the partner's initial investment in the partnership and is adjusted over time based on various factors such as additional contributions, share of partnership income or losses, and distributions received.

In this scenario, since the fair market value of the building exceeds its adjusted basis, Sabrina's basis in her partnership interest is equal to the fair market value of the contributed property. This means that if the partnership were to sell the building for its fair market value, Sabrina would not recognize any gain on the sale for tax purposes.

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Answer:

4th quadrant

Step-by-step explanation:

If you were to imagine a quadrant plane you would see a plus. Quadrant one is two positives. Quadrant two is one negative and then one positive. Quadrant 3 is two negatives. So, its quadrant 4 because it is one positive and one negative.

The question that is best answered using a parametric design is: "Does one level of the independent variable result in an increase/decrease in levels of behavior when compared to another level of that independent variable, for given participants?"

A parametric design is characterized by manipulating and comparing different levels or conditions of an independent variable. It aims to determine whether there are significant differences between these levels in terms of the dependent variable. The design typically involves controlling extraneous variables and randomizing the assignment of participants to different conditions.

The question mentioned above aligns with the purpose of a parametric design as it seeks to compare the effects of different levels of the independent variable on behavior. By manipulating and systematically varying the independent variable while holding other factors constant, researchers can assess the impact of different conditions and determine if there are statistically significant differences in behavior between them.

The other answer choices provided do not explicitly involve comparing different levels or conditions of the independent variable, which is a key characteristic of a parametric design.

Therefore, the question that is best answered using a parametric design is: "Does one level of the independent variable result in an increase/decrease in levels of behavior when compared to another level of that independent variable, for given participants?"

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The daily interest rate for May 23 on this account, rounded to the nearest millionths place, is approximately 0.000990

To calculate the daily interest rate for an account that pays 9.5% interest, compounded daily, we can use the following formula:

Daily interest rate = (1 + Annual interest rate)^(1/Number of compounding periods) - 1

In this case, the annual interest rate is 9.5% and there are 91 days in the quarter, which will be considered as the number of compounding periods.

Let's calculate the daily interest rate:

Daily interest rate = (1 + 0.095)^(1/91) - 1

Using a calculator, the daily interest rate, rounded to the nearest millionths place, is approximately 0.000990674.

Therefore, the daily interest rate for May 23 on this account, rounded to the nearest millionths place, is approximately 0.000990.

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Monique's father suggests that she practice her balance before attempting to surf in a town where surfing is popular. This will help her prepare for the physical demands of surfing and improve her chances of success.

Surfing requires good balance and stability to navigate the waves effectively. By practicing her balance, Monique can develop the core strength and stability necessary to maintain her equilibrium while riding the surfboard.

One activity that can help improve balance is yoga. Yoga poses and sequences require concentration, body awareness, and the engagement of various muscles to maintain balance. Practicing yoga can enhance Monique's proprioception, body control, and stability, which are essential for surfing.

Additionally, activities such as skateboarding, paddleboarding, or even simply standing on one leg can also be beneficial for improving balance and preparing Monique for the challenges of surfing.

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The number that, when increased by 20 times itself, equals 48, is 2.

Let's assume the number is x. According to the given information, when x is increased by 20 times itself (20x), it results in 48. Mathematically, we can represent this as:

x + 20x = 48

Combining like terms:

21x = 48

To solve for x, we divide both sides of the equation by 21:

x = 48 / 21 = 2.2857...

However, since we are looking for a whole number, the closest whole number to 2.2857... is 2.

Therefore, the number we are looking for is 2.

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To be at least 70% sure of knowing the identity of at least one missing card from a deck missing seven out of 52 cards, you would need to remove and look at 22 cards.

When cards are removed from the deck without replacement, the probability of identifying a missing card increases with each card drawn. In this case, since the deck is missing seven cards, there are 45 cards remaining in the deck. To calculate the number of cards needed to reach at least 70% certainty, we can use the concept of complementary probability.

The complementary probability is the probability of not knowing the identity of any missing card. To be at least 70% sure, the complementary probability should be less than or equal to 30%. We need to find the smallest value of n (number of cards drawn) for which the probability of not knowing any missing card is less than or equal to 30%.

By using the formula for the complementary probability, we can calculate the number of cards needed to reach the desired certainty. In this case, n = 22 is the minimum number of cards you need to remove and look at before you can be at least 70% sure of knowing the identity of at least one of the missing cards.

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The gain or loss on the sale of the batting cage is $0. The selling price is equal to the net book value, indicating that Strike Company sold the equipment for its carrying amount without incurring a gain or loss on the transaction.

To calculate the gain or loss on the sale of the batting cage by Strike Company, we can subtract the net book value (original cost - accumulated depreciation) from the selling price. Here are the calculations:

Original cost: $211,850

Accumulated depreciation: $31,778

Net book value: Original cost - Accumulated depreciation = $211,850 - $31,778 = $180,072

Selling price: $180,072

To determine the gain or loss, we subtract the net book value from the selling price:

Gain or Loss = Selling Price - Net Book Value

Gain or Loss = $180,072 - $180,072 = $0

Based on the calculations, the gain or loss on the sale of the batting cage is $0.

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The answer to the question is option B: "The slot machine didn't give me a winning amount for over an hour, so chances now are going to be that I hit the jackpot soon."

The first paragraph explains how slot machines and cell phones can create a sense of excitement and false hope, leading to addictive behaviors. It highlights the manipulation by app designers and the negative impact on interpersonal relationships. The second paragraph asks for an example of the Gambler's Fallacy.

The answer to the question is option B: "The slot machine didn't give me a winning amount for over an hour, so chances now are going to be that I hit the jackpot soon." This statement reflects the Gambler's Fallacy, which is the belief that previous outcomes will influence future outcomes in a game of chance. In this case, the person assumes that because they haven't won for a while, their chances of hitting the jackpot have increased. However, each spin of the slot machine is independent and has no connection to previous outcomes. The Gambler's Fallacy is a common misconception that can lead to risky and irrational behavior in gambling situations.

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The approximate probability that the sample mean is less than 5 is approximately 0.966 (rounded to three decimal places).

What is probability?

Probability is a branch of mathematics that deals with quantifying the likelihood or chance of an event occurring. It provides a way to measure and express uncertainty in various situations.

To find the approximate probability that the sample mean is less than 5, we can use the Central Limit Theorem. The Central Limit Theorem states that the distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the shape of the original distribution.

In this case, since we have an exponential distribution with a mean of 4, the population mean (μ) is also 4. The standard deviation (σ) of the exponential distribution can be calculated using the formula σ = mean / √n, where n is the sample size.

To approximate the probability, we need to standardize the sample mean using the Z-score formula:

Z = (X - μ) / (σ / √n)

Where X is the value of interest (in this case, 5), μ is the population mean (4), σ is the standard deviation, and n is the sample size.

Since we don't have the sample size (n) provided in the question, we cannot calculate the exact standard deviation (σ). However, we can still approximate the probability using the fact that the Central Limit Theorem applies when the sample size is reasonably large (typically n > 30).

Let's assume a sample size of n = 30. Using this value, we can calculate the approximate standard deviation (σ) as:

σ = mean / √n = 4 / √30 ≈ 0.7303

Now we can calculate the Z-score:

Z = (5 - 4) / (0.7303 / √30) ≈ 1.837

Using the Z-score, we can find the approximate probability using a standard normal distribution table or a calculator. From the standard normal distribution table, the probability corresponding to a Z-score of 1.837 is approximately 0.9663.

Therefore, the approximate probability that the sample mean is less than 5 is approximately 0.966 (rounded to three decimal places).

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