Health programs routinely study the number of days that patients stay in hospitals. In one study, a random sample of 12 men had a mean of 7. 95 days and a standard deviation of 6. 2 days, and a random sample of 19 women had a mean of 7. 1 days and a standard deviation of 5. 0 days. The sample data will be used to construct a 95 percent confidence interval to estimate the difference between men and women in the mean number of days for the length of stay at a hospital. Have the conditions been met for inference with a confidence interval?
By answering the above question, we may state that we have assumed equation that the prerequisites for inference using a confidence interval have been satisfied.
What is equation?A math equation is a mechanism for connecting two claims by using the equals sign (=) to indicate equivalence. A mathematical statement that establishes the equivalence of two mathematical expressions is known as an equation in algebra. The equal symbol, for example, splits the numbers 3x + 5 and 14. A mathematical formula can be used to describe the relationship between two phrases written on opposite sides of a letter. The logo and programme are frequently the same. 2x - 4 Equals 2, for example.
Sample Size: The sample size should be large enough to guarantee that the mean sampling distribution is roughly normal. There is no hard and fast rule regarding what makes a "big enough" sample size, although a sample size of at least 30 is regarded sufficient. The sample size for both men and women is fewer than 30 in this situation.
We may proceed with generating a 95% confidence interval to estimate the difference between men and women in the mean number of days for the duration of stay at a hospital since we have assumed that the prerequisites for inference using a confidence interval have been satisfied.
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help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The function f(x) = \(-3x^2\) + 18x + 3 has the maximum value of 30 at x = 3
The quadratic function is
f(x) = \(-3x^2\) + 18x + 3
The general form of the quadratic function is
y = \(ax^2\) + bx + c
If a < 0, the quadratic function has maximum value
Here the value of a = -3
Therefore the function has maximum value.
Maximum value will be at x = -b / 2a
= -18 / 2(-3)
= -18 / -6
= 3
The maximum value of quadratic function will be (4ac - \(b^2\)) /4a
Substitute the value in the equation
(4ac - \(b^2\)) /4a = (4×-3×3 - 18×18) / 4×-3
= (-36 - 324 / -12
= -360 / -12
= 30
Hence, the function f(x) = \(-3x^2\) + 18x + 3 has the maximum value of 30 at x = 3
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What is the value of x? enter your answer in the box. x = cm
The value of x in the given equation will be 2/5
From the data,
We have to determine the value of x.
The given equation is: 18x-16=-12x-4
For determining the value of x, we will first shift the like terms on one side of the equation.
So, for solving the value of x we will shift the terms containing x and the constant on both sides of the equation.
So, shifting -12x from the right-hand side of the equation to the left-hand side of the equation,
We will get it as:
18x+12x = -4+16
30x=12
Now for solving the value of x we will shift x from the left side of the equation to the right side of the equation.
So, the value of x will be = 12/30 = 2/5
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The correct question may be:
What is the value of x
18x-16=-12x-4
Enter your answer in the box.
Original TV cost: $700
Current TV cost: $500
Find the percent of decrease
round to the nearest whole percent
Answer: 29%
Step-by-step explanation:
To find the percent of decrease, you need to first calculate the difference between the original cost and the current cost of the TV. You can do this by subtracting the current cost from the original cost: $700 - $500 = $200.
Next, divide the difference by the original cost and multiply by 100% to express the result as a percentage: ($200 / $700) * 100% = 28.57%.
Rounding this result to the nearest whole percent, we get that the percent of decrease is 29%.
Rounded to the nearest whole percent, the answer is 29%.
Marta walked 4.9 miles per hour for 0.57 hours. How far did she walk?
Answer:
\(\huge\boxed{\sf Distance = 2.793\ miles}\)
Step-by-step explanation:
Given Data:
Speed = 4.9 mph
Time = 0.57 hours
Required:
Distance = ?
Formula:
Distance = Speed * Time
Solution:
Distance = 4.9 * 0.57
Distance = 2.793 miles
\(\rule[225]{225}{2}\)
Hope this helped!
~AH1807if the heights of 99.7 of american men are between 5 and 7 what is the estimate of the standard deveiation of the height of american men
The value of 99.7% is the closest to the percentage of these heights that is within 3 standard deviations of the mean.
What is the empirical rule?
If your distribution follows a normal distribution, the standard deviation and mean can tell you where the majority of the data are.
It is given that the heights of a large population of ostriches are normally distributed. The percentage of these heights is within 3 standard deviations of the mean.
As we know from the empirical rule:
It is the rule of 68-95-99.7.
From the data given in the question: The height of a large population of ostriches is normally distributed.
X ~ (u, б²)
Normal distribution.
P{u - 3б < X < u + 3б}
From the distribution table:
P{u - 3б < X < u + 3б} = 99.7%
Thus, the value of 99.7% is the closest to the percentage of these heights that is within 3 standard deviations of the mean.
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John is 48 years old. He is planning on retireing when he is 65. He has opened an IRA with an APR of 3.5% compounded daily. If he makes daily deposits of $750.00 to the account. How much will he have in the account when he is ready to retire? Use the formula on page 439 example #1 a $2,250,650 b $6,422,659 c $13,422 d $6,358,659 e $52,801 f $6,422 g $7,422,659 h $68,537 i $1,222,659
The amount of money that John would have in his account when he is ready to retire is $6,351,400.21.
How much would be in the retirement account?The formula that can be used to determine the future value of the annuity is
Future value = Daily deposit x annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = 3.5 / 365 = 0.0096%n = (65 - 48) x 365 = 6205Annuity factor = [(1.000096^6205) - 1] / 0.000096 = $8468.53
Future value = 750 x $8468.53 = $6,351,400.21
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Find the equation using the diagram attached.
The equation representing the graph as shown in the figure is y =
- 5.01x³ + 36.02x
What is the degree of a cubic equation?The degree of a cubic polynomial is three.
Given is the general cubic equation as -
ax³ + bx² + cx + d
Now, the graph shows that the equation of this cubic equation passing through 3 points as -
(- 6, 0) , (2, 32) , (6, 0)
This means that these coordinates will satisfy the equation ax³ + bx² + cx + d = y.
Therefore -
For x = - 6 :
a(-6)³ + b(-6)² - 6c + 0 = 0
- 216a + 36b - 6c = 0 .. [1]
For x = 2 :
8a + 4b + 2c + 0 = 32 .. [2]
For x = 6 :
a(6)³ + b(6)² - 6c + 0 = 0
216a + 36b + 6c + 0 = 0 .. [3]
Adding Eq[1] and Eq[3], we get -
- 216a + 36b - 6c + 216a + 36b + 6c = 0
72b = 0
b = 0
Then equation [2] will become -
8a + 2c = 32
4a + c = 16 .. [4]
Subtracting Eq[1] and Eq[3], we get -
216a + 36b + 6c - (- 216a + 36b - 6c) = 0
216a + 36b + 6c + 216a - 36b + 6c = 0
432a + 12c = 0 .. [5]
Multiply [4] by 12, we get -
48a + 12c = 1922 .. [6]
Subtracting Eq[6] and Eq[5], we get -
432a + 12c - 48a - 12c = - 1922
384a = - 1922
a = - 5.01
Then -
4 x - 5.01 + c = 16
c = 16 + 20.02
c = 36.02
So -
[a] = - 5.01
[b] = 0
[c] = 36.02
[d] = 0
Therefore, the equation representing the graph as shown in the figure is y = - 5.01x³ + 36.02x
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the completion times for a certain marathon race was 2.4 hours with a standard deviation of 0.5 hours. what can you determine about these data by using chebyshev's inequality with latex: k=2?
The answer is \(P(1.4 \leq X \leq 3.4) \geq 1-\frac{1}{k^2}=1-\frac{1}{4}=0.75\), by using the Chebyshev's inequality with k=2.
Chebyshev's inequality applied to data sets of any type; that is, there is no need that the distribution of data is to be symmetric. And as per this inequality, the proportion of \((1-\frac{1}{k^{2} } )\) data values will fall within the k number of standard deviation from the value of mean.
Using Chebyshev's inequality with k=2, we can determine that at least 75% of the marathon runners completed the race within 3.4 hours (2.4 + 2*0.5). It means at least 75% of the marathon runners completed the race in less than 3.4 hours. Mathematically, this can be represented as:
\(P(1.4 \leq X \leq 3.4) \geq 1-\frac{1}{k^2}=1-\frac{1}{4}=0.75\)
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There are 5 positions available in the new school. Of the applicant, 12 are men and 8 are women. In how many ways can 3 men and 2 women be chosen if they are equally considered?
There are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting
What is the multiplication principle of countingThe multiplication principle states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.
To find the number of ways to choose 3 men from the 12 men, we can use the formula for combination, which is: ⁿCᵣ = n! / (r! (n-r)!).
where n is the total number of men and r is the number of men chosen
so, the number of ways to choose 3 men from the 12 men = ¹²C₃ = 1.
Similarly, we evaluate the number of ways to choose 2 women from the 8 women
as = ⁸C₂ = 14
Now, using the multiplication principle, we can find the total number of ways 3 men and 2 women be chosen if they are equally considered.
220 x 14 = 3080
Therefore, there are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting
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Lisa must choose a number between 61 and 107 that is a multiple of 2, 8, and 16. Write all the numbers that she could choose. If there is more than one
number, separate them with commas.
Mrs. Bergstedt teaches four classes. Each class has 15 students. Her first class has 9 juniors, her second class has 12 juniors, her third class has 6 juniors, and her fourth class has 3 juniors. If Mrs. Bergstedt chooses four students at random, what is the probability that exactly two of the students are juniors (rounded to the nearest thousandth)?
The probability that exactly two of the students are juniors is given as follows:
0.270 = 27%.
What is the hypergeometric distribution formula?The mass probability formula is presented as follows:
\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.The values of these parameters for this problem are given as follows:
\(N = 60, n = 4, k = 18\)
Hence the probability that exactly two of the students are juniors is calculated as follows:
\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)
\(P(X = 2) = h(2,60,4,18) = \frac{C_{18,2}C_{42,2}}{C_{60,4}} = 0.270\)
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Learn with an example
A line that includes the point (1, 2) has a slope of 9. What is its equation in slope-intercept
form?
Answer:
y = 9x + (-7) should be the answer
Ray GI bisects ∠DGH so that m∠DGI is 3x-9 and m∠IGH is 2x + 21. Find the m< DGI.
Answer:
\(3x - 9 = 2x + 21 \\ 3x - 2x - 9 = 2x - 2x + 21 \\ x - 9 = 21 \\ x - 9 + 9 = 21 + 9 \\ x = 30\)
m<DGI = 80°
\(3x - 9 = \\ 3(30) - 9 = \\ 90 - 9 = 81\)
The measure of angle ∠DGI can be obtained by finding the solution of the equation as 81°.
What is a linear equation?A linear equation in two variable has the general form as y = ax + by + c, where a, b and c are integers and a, b ≠ 0.
It can be represented as a straight line on a graph.
The ray GI bisects ∠DGH.
It implies that the new angles are equal in measurement.
⇒ m∠DGI = m∠IGH
⇒ 3x - 9 = 2x + 21
⇒ x = 30
Then, in order to calculate m∠DGI, plug x = 30 in 3x - 9 as,
3 × 30 - 9 = 81
Hence, the measure of angle ∠DGI is given as 81°.
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select all that apply. the study did not randomly assign treatments the difference of 0.4 miles per week could be too small to attribute to the tummeric and might just be due to random chance. the study was not large enough this is an experiment, thus it does show causation the study is observational and lacks control of too many lurking variables the study should be replciated with other populations
The statement that is true is "the study is observational and lacks control of too many lurking variables" and "the study should be replicated with other populations."Here are the reasons why:
The study is observational and lacks control of too many lurking variables:
This statement is true since the study was done with people who used turmeric in the meals they consume. There are a lot of things that could affect the difference in mileage walked by the turmeric users compared to those who do not consume it. For instance, the intensity of exercise, lifestyle, and overall diet could have been contributing factors. Thus, there is no guarantee that turmeric is solely responsible for the difference in miles walked.
The study should be replicated with other populations:
This statement is true since the study was carried out with a small sample size and in one geographic location. This means that there is a possibility that the results were just unique to that region. Replicating the study in a different location would help to establish the generalizability of the results and whether or not they are consistent across populations.
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Perform the second correlation on an independent variable (such as Relationship with Direct Supervisor) and the dependent variable (such as Workplace Happiness Rating). Calculate the Pearson product-moment correlations between at least two sets of variables in your data set.
The resulting value will be the Pearson product-moment correlation coefficient, which ranges from -1 to 1. A positive value indicates a positive correlation, a negative value indicates a negative correlation, and values closer to -1 or 1 indicate stronger correlations.
To perform a Pearson product-moment correlation between the independent variable "Relationship with Direct Supervisor" and the dependent variable "Workplace Happiness Rating," you would need a dataset that includes measurements of both variables for multiple individuals or cases. Let's assume you have such a dataset.
To calculate the Pearson correlation coefficient, you can follow these steps:
1. Gather the data: Collect the values for the independent variable (e.g., Relationship with Direct Supervisor) and the dependent variable (e.g., Workplace Happiness Rating) for each individual or case in your dataset.
2. Calculate the means: Calculate the mean (average) of the independent variable and the mean of the dependent variable.
3. Calculate the deviations: For each individual or case, subtract the mean of the independent variable from its value, and subtract the mean of the dependent variable from its value. These are called deviations.
4. Calculate the product of deviations: Multiply the deviations of the independent variable by the deviations of the dependent variable for each individual or case.
5. Calculate the squared deviations: Square each deviation of the independent variable and the dependent variable for each individual or case.
6. Sum the squared deviations: Add up all the squared deviations of the independent variable and the dependent variable, respectively.
7. Calculate the product-moment correlation: Divide the sum of the product of deviations by the square root of the product of the sum of squared deviations for both variables.
The resulting value will be the Pearson product-moment correlation coefficient, which ranges from -1 to 1. A positive value indicates a positive correlation, a negative value indicates a negative correlation, and values closer to -1 or 1 indicate stronger correlations.
Performing the second correlation between different sets of variables in your dataset would follow a similar process. You would gather the data for the second pair of variables, calculate the means, deviations, product of deviations, squared deviations, and then calculate the Pearson correlation coefficient using the same formula as described above.
Remember to have a sufficient sample size and ensure that the assumptions of the Pearson correlation (linearity, independence, and normality) are met for accurate and meaningful results.
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(PLEASE ANSWER QUICKLY!!!!)(Two-Column Tables LC)
The data below lists the number of pages Tamara read and the time it took her to read them.
Tamara read 35 pages in 42.5 minutes.
Tamara read 41 pages in 59 minutes.
Tamara read 56 pages in 72 minutes.
Determine which table below represents a two-column table for the given data.
Pages Time
35 42.5
59 41
72 56
Pages Time
42.5 35
59 41
72 56
Pages Time
35 42.5
41 59
56 72
Pages Time
42.5 35
41 59
56 72
The two-column table that represents the number of pages Tamara read and the time it took her to read them is Table C.
Table C:
Pages Time
35 42.5
41 59
56 72.
What is a two-column table?A two-column table is a tabular way of displaying or visualizing data with two variables.
One column shows the data for an independent variable while the other column shows the data for the dependent variable.
For instance, a two-way table can be used to display in visual format, the data of the number of pages Tamara read and the time it took her to read the various pages.
Thus, the correct two-column table is Table C.
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Suppose Earth’s axis was not tilted. What would be the effect of this on temperature variation?
Step-by-step explanation:
If earth did not tilt and orbited in an upright position around the sun, there would be minor variations in temperatures and precipitation throughout each year as Earth moves slightly closer and farther away from the sun. Basically, we would not have any seasons.
Answer:
Assuming you're saying the earth is flat in hence scenerio it would be hotter or. Colder depending how far the sun's placement is from the earth
Step-by-step explanation:
Closer to sun warmer you are
Shift in moon causes water drought or water rise
designing control charts involves two key issues: sample size and sampling frequency. a. true b. false
Designing control charts involves two key issues: sample size and sampling frequency is a true statement.
Control Charts depict how the process [ data ] changes over time. It comprises a central line for average, lower line for the lower control limit and an upper line for upper control limit.
There are many types of control chart -X bar control chart.
Range “R” control chart. Standard Deviation “S” control chart. Attribute Control Charts.“u” and “c” control charts. “p” and “np” control charts.Sample size can be defined as the number of measurement values taken for a test feature .
Sampling frequency can be defined as the average number of samples obtained in one second.
Hence, designing control charts involves two key issues: sample size and sampling frequency is a true statement.
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The first 300 natural numbers are written in an ascending order of sequence. Now all the numbers at the odd places of this sequence are removed and, thus a new sequence is formed. From this new sequence, all the numbers at odd places are removed once again. This process continues till only one number remains at the end. What is this number?
The final number remaining in this sequence is the number 2.
We start with the first 300 natural numbers written in ascending order. We remove the numbers at odd places, which means we remove all the numbers at positions 1, 3, 5, and so on.
After the first removal, we are left with the numbers at even positions: 2, 4, 6, and so on.
Now, we repeat the process and remove the numbers at odd positions again. We remove numbers at positions 1, 3, 5, and so on from the remaining sequence.
After the second removal, we are left with the numbers at even positions again: 4, 8, 12, and so on.
We can observe that in each removal, the sequence reduces to half its size, and we are left with the numbers at even positions.
Continuing this process, we will eventually reach a point where we have only one number left.
Since we start with 300 numbers, after the first removal, we have 150 numbers. After the second removal, we have 75 numbers. After the third removal, we have 38 numbers. After the fourth removal, we have 19 numbers. After the fifth removal, we have 10 numbers. After the sixth removal, we have 5 numbers. After the seventh removal, we have 3 numbers. After the eighth removal, we have 2 numbers. Finally, after the ninth and last removal, we are left with a single number.
Therefore, the final number remaining in this sequence is the number 2.
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If Fx) = x-5 and G(x) = x2 , what is G(F(x))?
Explanation:
Given the functions
f(x) = x-5
G(x) = x^2
We are to find the composite function G(f(x))
write an equation of the line passing through the point A(-6,5) that is parallel to the line y=1/2x-7
The required equation of a line parallel to y = (1/2)x - 7 is, y = (1/2)x + 8.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at
x = 0.
We know, Lines parallel to each other have the same slope.
Therefore, A line passing through the point A(- 6, 5) that is parallel to the line y = (1/2)x - 7, Also has a slope of (1/2).
Now, 5 = - (1/2)(6) + b.
5 = - 3 + b.
b = 8.
y = (1/2)x + 8.
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anybody know this ? please help :(
Answer:
C.
Step-by-step explanation:
Your formula will always be for simple interest: A = P(1 + r)^t
Plugging in all the variables will give you C as the answer.
WILL GIVE BRAINLIEST
Answer:
its 3 you du... a...
Step-by-step explanation:
it says that abc os the same and A to C is the same mesure to B and E
models run on computers provide approximate representations of real systems using mathematical relationships.
Models run on computers indeed provide **approximate representations** of real systems using mathematical relationships. These models are designed to simulate and mimic real-world phenomena, allowing researchers, scientists, and engineers to study and understand complex systems without the need for physical experiments or direct observations.
Computer models utilize mathematical equations, algorithms, and data inputs to simulate the behavior and interactions of various components within a system. By incorporating known principles, physical laws, and empirical data, these models aim to capture the essential features and dynamics of the real system being studied.
It's important to note that computer models are inherently approximations of reality. They simplify complex systems into mathematical formulas and assumptions to make them computationally tractable. Due to limitations in our understanding, available data, and computational power, models may not perfectly capture all the intricacies and nuances of the real system. However, they provide valuable insights, predictions, and understanding that can guide decision-making, further research, and experimentation.
Computer models are widely used across various disciplines, such as physics, biology, economics, climate science, engineering, and more. They allow researchers to explore different scenarios, test hypotheses, and make predictions about the behavior of the system under different conditions. Models can help answer "what if" questions, analyze potential outcomes, and optimize strategies or designs.
Despite being approximations, computer models have proven to be highly valuable tools for understanding and predicting complex systems. They provide a means to simulate scenarios that would otherwise be impractical, expensive, or even impossible to study directly. By refining and validating models through comparison with empirical data and observations, researchers continuously improve the accuracy and reliability of their representations, enhancing our understanding of the real systems they seek to simulate.
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What are the values of x for which the denominator is equal to zero for y = x+3/x²+4x
x² + 4x
X = -4
x=0, x=-4
no points of discontinuity
x = 0,X = 4
Answer:
hello
x² + 4 x = 0
x ( x + 2 ) = 0
x = 0 or - 2
Simplify √9 x 3√27 please answer
Answer:
I got \(27\sqrt{3}\) which is 46.76537.... in decimal form.
Step-by-step explanation:
Factor
16x^3 + 8x^2 + x
5) Graph the inequalities, be sure to shade the appropriate area.
a) 6x-6y≥18
The graph of the inequality 6x - 6y ≥ 18 is shown in figure.
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
We have to given that;
The inequality is,
⇒ 6x - 6y ≥ 18
Now,
Since, The inequality is,
⇒ 6x - 6y ≥ 18
⇒ 6 (x - y) ≥ 18
Divide by 6, we get;
⇒ x - y ≥ 3
Thus, The graph of the inequality x - y ≥ 3 is shown in figure.
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: Write the equation of the line in Point-Slope Form given the information below. Slope=-2 Point=(1,-1)
Answer: y+1=-2(x-1)
Step-by-step explanation:
The point-slope formula is \(y-y_{1}=m(x-x_{1})\). Since we know the coordinate and slope, we can directly plug them in.
\(y-(-1)=-2(x-1)\)
\(y+1=-2(x-1)\)