4. Part A
James has a board that is foot long. He wants to cut the board into pieces
that are each foot long.
How many pieces can James cut from the board? Explain how James can use
the number line diagram to determine the number of pieces he can cut from
the board.
Enter your answer and your explanation in the space provided.
Part B
Write an equation using division that represents how James can find the
number of pieces he can cut from the board.

The Total surface area of the given prism is: 312 ft²

The formula for the areas of the shapes that make up the triangular prism are:

Area of triangle = ¹/₂bh

where:

b is base

h is height

Area of rectangle = L * W

where:

L is length

W is width

Thus:

Total surface area = 2(¹/₂ * 6 * 4) + 2(5 * 18) + (18 * 6)

Total surface area = 24 + 180 + 108

Total surface area = 312 ft²

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Answer:a to b is 21 and b to c is 6 so I think you would need 21+6 divided by 2 i don't know for sure.

Step-by-step explanation:

The probability that a randomly selected adult has an IQ greater than 133.2 is 0.0436 or 4.36%.

To find the probability that a randomly selected adult has an IQ greater than 133.2, assuming adults have IQ scores that are normally distributed with a mean of 97.6 and a standard deviation of 20.9, follow these steps:

1. Calculate the z-score: z = (X - μ) / σ, where X is the IQ score, μ is the mean, and σ is the standard deviation.
  z = (133.2 - 97.6) / 20.9
  z ≈ 1.71

2. Use a z-table or a calculator to find the area to the left of the z-score, which represents the probability of having an IQ score lower than 133.2.
  P(Z < 1.71) ≈ 0.9564

3. Since we want the probability of having an IQ greater than 133.2, subtract the area to the left of the z-score from 1.
  P(Z > 1.71) = 1 - P(Z < 1.71) = 1 - 0.9564 = 0.0436

So, the probability that a randomly selected adult has an IQ greater than 133.2 is approximately 0.0436 or 4.36%.

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You can take the reciprocal of the opportunity cost of producing Product A in terms of Product B to determine the cost of producing Product B in terms of Product A,

To determine the cost of producing Product B in terms of Product A, you can take the reciprocal of the opportunity cost of producing Product A in terms of Product B.

If the opportunity cost of producing 1 unit of Product A is 2 units of Product B, then the cost of producing 1 unit of Product B would be 1/2 unit of Product A.

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The standard error of the survey's estimate for the mean is approximately 0.09 and the probability that the survey misses the true mean of 3.5 by more than 0.1 points is approximately 0.13 or 13%.

(a)The standard error of the survey's estimate for the mean is given by:

[tex]SE=\frac{I}{\sqrt{n} }[/tex]

In this case, σ = 1.4, n = 240, so:

[tex]SE= \frac{1.4}{\sqrt{240} } = 0.09[/tex]

Therefore, the standard error of the survey's estimate for the mean is approximately 0.09.

(b) To find the probability that the survey misses the true mean of 3.5 by more than 0.1 points, we need to find the probability that the absolute difference between the sample mean and the true mean is greater than 0.1:

Using a standard normal table or calculator, we can find that the probability of a standard normal random variable being greater than 0.1 / SE ≈ 1.11 is approximately 0.13.

Therefore, the probability that the survey misses the true mean of 3.5 by more than 0.1 points is approximately 0.13 or 13%.

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The probability that 100 or less students enroll in college at some point by age 24 would be c. 97.8%

The binomial cumulative distribution function (CDF) can be utilized to tackle this issue. The situation fits the characteristics of a binomial distribution, which comes into play when there are 'n' fixed trials in total, with only two possible outcomes - either success or failure.

Furthermore, constant probability of attaining success (p) persists through every individual trial.

The formula is:

P ( X ≤ 100 ) = ∑ [ C ( n , k ) x p^ k x q ^ ( n - k ) ] for k = 0 to 100

Using a binomial calculator, we find out that:

P ( X ≤ 100 ) = 0. 978 or 97. 8 %

In conclusion, option C is correct.

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We can estimate that each square formed by dividing the rectangle has a side length of approximately 5.57 units.

Let's denote the width of the rectangle as x. Then, according to the problem, the length of the rectangle is twice the width, so its length is 2x. The area of the rectangle is given as 62 square units, so we can write:

Area of rectangle = length x width

62 = 2x * x

62 = 2x^2

Solving for x, we get:

x^2 = 31

x ≈ 5.57

Therefore, the width of the rectangle is approximately 5.57 units, and its length is approximately 2 * 5.57 = 11.14 units.

Now, we are asked to estimate the side length of each square that can be formed by dividing the rectangle into two equal parts. Since the area of each square is half of the area of the rectangle, we can write:

Area of each square = (1/2) × (length × width)

Area of each square = (1/2) × (2x × x)

Area of each square = x^2

Substituting the value of x from above, we get:

Area of each square ≈ 31

The side length of each square ≈ √31 ≈ 5.57

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The relative frequency of the coin turning up heads in this experiment is 0.47

First, let's determine the number of times the coin came up heads. Maria flipped the coin 60 times, and it came up tails 32 times. Therefore, it came up heads 60 - 32 = 28 times. Now, let's calculate the relative frequency of the coin turning up heads. The relative frequency is the ratio of the number of times an event occurs to the total number of trials.

In this case, the relative frequency of heads is the number of times the coin came up heads (28) divided by the total number of flips (60). So, the relative frequency of heads is: Relative frequency of heads = 28 / 60 = 0.4666...

Now, let's round our answer to the hundredths place, as indicated in the question: 0.4666... ≈ 0.47

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The rule for the nth term of the geometric sequence is given as follows:

[tex]a_n = 2^n[/tex]

Hence the 10th term of the sequence is given as follows:

1024.

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.

The explicit formula of the sequence is given as follows:

[tex]a_n = a_0q^{n}[/tex]

In which [tex]a_0[/tex] is the first term.

The parameters in this problem are given as follows:

Hence the rule is given as follows:

[tex]a_n = 2^n[/tex]

Hence the 10th term of the sequence is given as follows:

2^10 = 1024.

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When multiplying or dividing mixed numbers, you must first convert them to improper fractions. The Option B is correct.

In order to convert a mixed number to an improper fraction, you need to multiply the whole number by the denominator of the fractional part, then, we will add the numerator of the fractional part.

The result becomes new numerator of the improper fraction and the denominator remains the same. Once we converted both mixed numbers to improper fractions, you can then proceed with the multiplication or division operation. So, after this is complete, you may simplify the resulting fraction back to a mixed number if necessary.

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since we don't have the value for b, we can't calculate the estimate for σ2.

a) Here is the complete ANOVA table:

b) To test the equality of the yield resulting from each of the 4 fertilizers, we can use the F-test. The null hypothesis is that the mean yield for all fertilizers is equal, and the alternative hypothesis is that at least one mean yield is different. The test statistic is the ratio of the mean square for the Fertilizer source of variation to the mean square for the Residuals source of variation:

F = (a/c-d) / (b/36)

We need to compare this F value to the critical F value at a significance level of alpha = 0.05 with degrees of freedom (3,36) from the ANOVA table or using a calculator. If the calculated F value is greater than the critical F value, we reject the null hypothesis and conclude that at least one mean yield is different.

Unfortunately, we don't have enough information to calculate the F value since we only have the sum of squares for the Fertilizer and Residuals sources of variation, not the actual values for a, b, c, and d.

c) To estimate the common variance σ2, we can use the mean square for the Residuals source of variation, which is b/36. Therefore, the estimate for the common variance is:

σ2 = b/36

However, since we don't have the value for b, we can't calculate the estimate for σ2.

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Answer:

The answer to your problem is, the range of the temperature data in degrees Fahrenheit is 15°F.

Step-by-step explanation:

In this scatter plot it represents the average daytime temperatures recorded in New York for a week.

highest temperature in a week from the scatter plot is 45°F.

lowest temperature in a week from the scatter plot is 30°F.

Range = 45°F - 30°F

= 15°F

Thus the answer to your problems is, the range of the temperature data in degrees Fahrenheit is 15°F.

Max(A) exists and is equal to 2.

To prove that 2 is the least upper bound for A, we will assume the opposite, i.e., there exists a smaller upper bound for A, say c < 2. Then, by definition of an upper bound, we have x ≤ c for all x ∈ A. In particular, we can choose x = 1 + (c - 1)/2, which satisfies (x - 1) < 1 and x > c, contradicting the assumption that c is an upper bound for A. Therefore, 2 is the least upper bound for A.

To prove that 2 is an upper bound for A, we need to show that x ≤ 2 for all x ∈ A. By definition of A, we have (x - 1) < 1, which implies x < 2. Therefore, 2 is an upper bound for A.

Since 2 is the least upper bound for A and 2 is in A, we have max(A) = 2. This follows from the fact that max(A) is the smallest number that is an upper bound for A, and we have already shown that 2 is the least upper bound for A. Therefore, max(A) exists and is equal to 2.

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The expected number of problems to be resolved today is 10, the standard deviation is 1.3693, the probability that 10 problems can be resolved today is 0.2146, the probability that 10 or 11 problems can be resolved today is 0.3246, and the probability that more than 8 problems can be resolved today is 0.816.

To answer these questions, we will use the binomial distribution since we are dealing with a fixed number of independent trials (the 13 cases reported) with only two possible outcomes (resolved or not resolved).

Let's start with the first question:

Expected number of problems resolved today:

E(X) = n * p = 13 * 0.75 = 9.75

So we would expect about 9.75 problems to be resolved today, but since we cannot have a fraction of a problem, we should round this to 10.

Now let's move on to the second question:

Standard deviation:

σ = sqrt(np(1-p)) = sqrt(13 * 0.75 * 0.25) = 1.3693 (rounded to 4 decimal places).

For the third question:

Probability that 10 of the problems can be resolved today:

P(X=10) = (13 choose 10) * (0.75)^10 * (1-0.75)^(13-10) = 0.2146 (rounded to 4 decimal places).

For the fourth question:

Probability that 10 or 11 of the problems can be resolved today:

[tex]P(X=10 or X=11) = P(X=10) + P(X=11) = (13 choose 10) * (0.75)^10 * (1-0.75)^(13-10) + (13 choose 11) * (0.75)^11 * (1-0.75)^(13-11) = 0.3246 (rounded to 4 decimal places).[/tex]

For the fifth question:

Probability that more than 8 of the problems can be resolved today:

P(X>8) = 1 - P(X<=8) = 1 - (P(X=0) + P(X=1) + ... + P(X=8))

[tex]= 1 - ∑(13 choose i) * (0.75)^i * (1-0.75)^(13-i), for i=0 to 8.[/tex]

= 1 - 0.0003 - 0.0033 - 0.0191 - 0.0672 - 0.1562 - 0.2529 - 0.2897 - 0.2072 - 0.0881

= 0.816 (rounded to 4 decimal places).

Therefore, the probability more than 8 of the problems can be resolved today is 0.816 (rounded to 4 decimal places).

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Step-by-step explanation:

6(3h - 4) = 18h + (-24) = 18h -24

The compute limit value of

[tex]lim_{n→\infty} \frac{6a_n b_n}{ 4 a_n - 3 b_n}[/tex] where, [tex]lim_{n → \infty} a_n [/tex], [tex]lim_{n → \infty} b_n = - 2[/tex] is equal to the [tex] \frac{ - 12}{5} [/tex]. So, option(3) is correct choice for answer.

The limit of a sequence is a numeric value that occur when a sequence approaches as the number of terms goes to infinity. This value depends on the sequence.

We have nᵗʰ terms of two sequence aₙ and bₙ. The limit of sequence aₙ is

[tex]lim_{n → \infty} a_n = 6 [/tex] and for bₙ, [tex]lim_{n→\infty} b_n= -2 [/tex]. We have to determine the limit value for the following: [tex]lim_{n→\infty} \frac{6a_n b_n}{ 4 a_n - 3 b_n}[/tex]

Solving the above expression step by step, [tex] = \frac{ 6 \: lim_{n → \infty} a_n .lim_{n → \infty}b_n }{4 \: lim_{n → \infty} a_n - 3 \: lim_{n → \infty} b_n } \\ [/tex]

Using the above values in formula,

[tex]= \frac{ 6 ×6 × -2}{4 ×6 \: - \: 3 ×- 2}[/tex]

[tex]= \frac{ -72 }{30} [/tex]

[tex]= \frac{ -12 }{5} [/tex]

Hence, required value is [tex]= \frac{ -12 }{5} [/tex].

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Complete question:

Compute the value, [tex]lim_{n→\infty} \frac{6a_n b_n}{ 4 a_n - 3 b_n}[/tex]

where [tex]lim_{n -> \infty} a_n = 6 [/tex]

[tex]lim_{n → \infty} b_n = - 2 [/tex]

1) Limit = -37/15

2) limit = 12/5

3) limit = - 12/5

4) limit does not exist

5) limit = 37/15

The local extreme value is -n * e^(-1).

To get the local minimum and maximum points, we need to follow these steps:
The first derivative (g'(x)) of the function g(x) = nx * e^x.
Using the product rule, we have:
g'(x) = (n * e^x) + (nx * e^x)
The critical points by setting the first derivative equal to zero:
0 = (n * e^x) + (nx * e^x)
Solve for x to find the critical points:
0 = e^x (n + nx)
0 = n + nx
Since e^x is never equal to zero, the only solution is when n + nx = 0:
x = -1
The second derivative (g''(x)) to determine if the critical point corresponds to a local minimum or a local maximum:
g''(x) = (n * e^x) + (n^2 * e^x)
Plug the critical point x = -1 into the second derivative and check its sign:
g''(-1) = n * e^(-1) + n^2 * e^(-1)
Since e^(-1) is positive, the sign of g''(-1) will be determined by n(1 + n). If n > 0, g''(-1) > 0 and we have a local minimum. If n < 0, g''(-1) < 0 and we have a local maximum.
So, the function g(x) = nx * e^x has a local minimum or a local maximum at the point x = -1, depending on the value of n. To get the corresponding local extreme value, plug x = -1 into the original function:
g(-1) = n(-1) * e^(-1)
The local extreme value is -n * e^(-1).

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The area of the shaded region will be 8 square unit as per the given figure.

The rectangle has dimensions 2 x 4, so its area is:

Area of rectangle = length x width = 2 x 4 = 8 square units

The triangle has dimensions 4 x 8, so its area is:

Area of triangle = (1/2) x base x height = (1/2) x 4 x 8 = 16 square units

To find the area of the shaded region, we need to subtract the area of the triangle from the area of the rectangle.

Area of shaded region = Area of the triangle - Area of rectangle

Area of shaded region = 16-8

Area of shaded region = 8

The area of the shaded region will be 8 square units.

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Complete question:

a. At the 0.05 level of​ significance, there is evidence of a linear relationship between the plate gap of the​ bag-sealing machine and the tear rating of a bag of​ coffee.

b. A​ 95% confidence interval estimate of the population​ slope, betaβ1 is (0.5590, 0.8606).

a. To test for the linear relationship between plate gap and tear rating, we can use the null and alternative hypotheses:

H0: β1 = 0 (there is no linear relationship)
Ha: β1 ≠ 0 (there is a linear relationship)

We can use the t-test to test this hypothesis. The test statistic is calculated as:

t = b1 / (S1 / [tex]\sqrt(n)[/tex])

where b1 is the sample slope, S1 is the standard error of the slope, and n is the sample size. Substituting the values given in the question, we get:

t = 0.7098 / (0.2146 / sqrt(30)) = 5.05

Using a t-distribution with n-2 = 28 degrees of freedom and a significance level of 0.05, we can find the critical values as ±2.048. Since the calculated t-value of 5.05 is greater than the critical value of 2.048, we reject the null hypothesis and conclude that there is evidence of a linear relationship between plate gap and tear rating at the 0.05 level of significance.

b. To construct a 95% confidence interval estimate of the population slope β1, we can use the formula:

b1 ± tα/2(S1 / [tex]\sqrt(n)[/tex])

where tα/2 is the critical value from the t-distribution with n-2 degrees of freedom and a confidence level of 95%. Substituting the values given in the question, we get:

b1 ± 2.048(0.2146 / [tex]\sqrt(30)[/tex]) = 0.7098 ± 0.1508

Therefore, the 95% confidence interval for the population slope β1 is (0.5590, 0.8606).

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The stereo system installer needs 170 ft of speaker wire.

In this case, the two diagonals of the rectangular room are the longest sides of two right triangles. The length of one diagonal can be found by:

d1 = √(40² + 75²)

d1 = √(1600 + 5625)

d1 = √7225

d1 = 85 ft

Similarly, the length of the other diagonal is also 85 ft.

Total speaker wire = 2 × 85 ft = 170 ft

So, the stereo system installer needs 170 ft of speaker wire.

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There are 16 different validated tickets are needed if every punching machine in town creates 4 holes on a ticket

When a ticket is punched by a punching machine, it creates a hole in the ticket. In this case, each hole can either be punched or not punched, so there are 2 possibilities for each hole.

Since there are 4 holes on a ticket, the total number of possible combinations is calculated by multiplying the number of possibilities for each hole:

2 x 2 x 2 x 2 = 16

So, there are 16 possible combinations of holes on a ticket, which means that a fee evader would need 16 different validated tickets to cover all possible combinations. This assumes that each punching machine creates the same pattern of holes, which may not be the case in practice.

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The total price Donte paid for the computer was $155.52.

The regular price of the computer was $180.

Donte got a 20% discount, which means he paid 100% - 20% = 80% of the regular price.

So, Donte paid 80% of $180, which is

(80/100) x $180 = $144.

Next, an 8% sales tax was added to the cost of the computer.

The amount of tax is

(8/100) x $144 = $11.52

Therefore, the total price Donte paid for the computer was

$144 + $11.52 = $155.52.

sales tax is a consumption tax imposed by the government on the sale of goods and services. A conventional sales tax is levied at the point of sale, collected by the retailer, and passed on to the government.

Sales tax is always a percentage of a product's value which is charged at the point of exchange or buy and is indirect.

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The guy wire is attached to the tower at a height of approximately 15.95 meters.

Length of the guy wire (hypotenuse) = 18.5 m

Angle between the ground and the guy wire = 59º

Using the sine function to find the height of the tower.
sin(angle) = height/hypotenuse

Putting in the known values and solving for the height.
sin(59º) = height/18.5 m
height = sin(59º) × 18.5 m

Calculating the height
height ≈ 15.95 m

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To determine if the sequence {an} is a solution of the recurrence relation an = 8an-1 – 16an-2, we need to substitute the given values of an and check if the equation holds true.

a) If an = 1, then we have:

an = 1
an-1 = a0 (since we don't have any values before a0)
an-2 = a-1 (which is not defined since a-1 is outside the domain of the sequence)

Substituting these values in the recurrence relation, we get:

1 = 8a0 - 16a-1 (using a0 = a-1 = 0, since they are undefined)

Simplifying this equation, we get:

1 = 0, which is not true. Therefore, the sequence {an} is not a solution of the recurrence relation if an = 1.

b) If an = 4, then we have:

an = 4
an-1 = a3
an-2 = a2

Substituting these values in the recurrence relation, we get:

4 = 8a3 - 16a2

Simplifying this equation, we get:

2 = 4a3 - 8a2
1/2 = 2a3 - 4a2
1/8 = a3 - 2a2

Therefore, the sequence {an} is a solution of the recurrence relation if an = 4.

In summary, the sequence {an} is not a solution of the recurrence relation if an = 1, but it is a solution if an = 4. This is because the recurrence relation is not satisfied for an = 1, but it is satisfied for an = 4.

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The function that has the greatest x-intercept is the function h(x)

The x-intercept of a function is the x-value of the function when the y-value is 0, which is the set of points at which the graph of the function intersects the x-axis.

The x-intercept of each function are found as follows;

f(x) = 3·x - 9 = 0

x = 9/3 = 3

g(x) = |x + 3| = 0

(x + 3) > 0 and |x + 3| = x + 3 = 0

x = 0 - 3 = -3

|x + 3| < 0 and |x + 3| = -(x + 3) = 0

x = -3

h(x) = 2·x - 16 = 0

x = 16/2 = 8

x = 8

j(x) = -5·(x - 2)² = 0

The x-intercept is x = 2

The function that has the greatest x-intercept is therefore the function h(x) = 2·x - 16

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The first theorem of welfare economics states that a competitive equilibrium is Pareto efficient, meaning that no one can be made better off without making someone else worse off. However, this theorem may not hold for economies with production because the production process may create externalities or market power, leading to inefficiencies.

For example, a monopolistic firm may restrict production and charge higher prices, leading to a lower quantity produced and a less efficient allocation of resources. Similarly, production processes may generate pollution or other negative externalities that are not reflected in market prices, leading to inefficient levels of production. Therefore, while the first theorem of welfare economics is a powerful tool for analyzing markets, it is important to consider the specific features of each market and the potential for inefficiencies in production.


The first theorem of welfare economics states that a competitive equilibrium is Pareto efficient, meaning no one can be made better off without making someone else worse off. However, this theorem may not hold for economies with production if:

1. There are externalities: Externalities occur when the production or consumption of a good affects other people who are not directly involved in the transaction. Positive externalities, such as the benefits of education, can lead to underproduction, while negative externalities, like pollution, can lead to overproduction. In both cases, the competitive equilibrium may not be Pareto efficient.

2. There are public goods: Public goods are non-excludable and non-rivalrous, meaning that once they are produced, everyone can benefit from them and one person's consumption does not reduce the availability for others. Due to their nature, public goods are often underprovided by the market, leading to a suboptimal competitive equilibrium.

3. There are imperfect competition or market failures: Imperfect competition can arise from factors such as monopolies, oligopolies, or asymmetric information. These market structures can lead to an inefficient allocation of resources and prevent the competitive equilibrium from being Pareto efficient.

4. There are increasing returns to scale: If a firm experiences increasing returns to scale in production, it means that as it produces more, its average cost of production decreases. This can lead to natural monopolies, where a single firm can produce the entire market demand at a lower cost than multiple firms. In this case, the competitive equilibrium may not be Pareto efficient.

In summary, the first theorem of welfare economics may not hold for economies with production if there are externalities, public goods, imperfect competition, or increasing returns to scale. These factors can lead to an inefficient allocation of resources and prevent the competitive equilibrium from being Pareto efficient.

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Answer:48 yd2

Step-by-step explanation:

The area of the yard that William would have to mow would be C. 112 yards ²

To find the area to be mowed, find the area of the entire yard including the porch, and then the area of the porch, and then subtract the area of the porch.

Area of yard :

= 12 x 12

= 144 yard ²

The area of the porch is:

= ( 12 - 8 ) x ( 12 - 4 )

= 4 x 8

= 32 yards ²

The area to be mowed is:

= 144 - 32

= 112 yards ²

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The value of the sides are;

CB = 13.8

CD = 6. 9

To determine the value of the sides of the triangle, we need to know the different trigonometric identities are;

From the information given, we have that;

Using the sine identity, we have that;

tan 60 = CD/4

cross multiply the values, we have;

CD = 4(1.73)

multiply the values

CD = 6.9

To determine the value;

sin 30 = 6.9/CB

CB = 13.8

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The expected value of the number of rejected items per day is 2.7.

The variance and standard deviation of rejected items per day are 0.107 and 0.327, respectively.

a) The completed probability mass function (PMF) and cumulative distribution function (CDF) tables are as follows:

X f(x) F(x)

0 0 0

1 1/20 1/20

2 0.05 3/40

3 7/20 1/2

4 0.1 9/20

5 4/20 1

b) P(X=5) = 4/20 = 0.2

c) P(X ≤ 2) = F(2) = 1/20 + 0.05 = 0.1 + 0.05 = 0.15

d) The expected value (or mean) of X is:

E(X) = ∑[x * f(x)] = (0 * 0) + (1 * 1/20) + (2 * 0.05) + (3 * 7/20) + (4 * 0.1) + (5 * 4/20) = 2.7

Therefore, the expected value of the number of rejected items per day is 2.7.

e) The variance of X is:

Var(X) = ∑[(x - E(X))^2 * f(x)] = (0 - 2.7)^2 * 0 + (1 - 2.7)^2 * 1/20 + (2 - 2.7)^2 * 0.05 + (3 - 2.7)^2 * 7/20 + (4 - 2.7)^2 * 0.1 + (5 - 2.7)^2 * 4/20

= 0.81 * 0 + 0.49 * 0.05 + 0.0225 * 0.05 + 0.09 * 0.35 + 0.0225 * 0.1 + 0.49 * 0.2

= 0.107

The standard deviation of X is:

SD(X) = sqrt(Var(X)) = sqrt(0.107) = 0.327

Therefore, the variance and standard deviation of rejected items per day are 0.107 and 0.327, respectively.

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Answer:

see explanation

Step-by-step explanation:

A

3x² + 36x ← factor out common factor of 3x from each term

= 3x(x + 12)

B

- 36x - 4x² ← factor out common factor of - 4x from each term

= - 4x(9 + x)