Find exact values for x and y

Answers

Answer 1

The value of x and y for the given set of values in triangle are 8√3 units and 12 units.

What is triangle?

A triangle is a polygon with three sides and three angles. It is the simplest polygon that can exist in Euclidean geometry. The sum of the three interior angles of a triangle is always 180 degrees. Triangles can be classified according to the length of their sides and the measure of their angles. The most common classifications are:

Scalene triangle: A triangle with all three sides of different lengths.

Isosceles triangle: A triangle with two sides of equal length.

Equilateral triangle: A triangle with all three sides of equal length.

Acute triangle: A triangle in which all angles are less than 90 degrees.

Obtuse triangle: A triangle in which one angle is greater than 90 degrees.

Right triangle: A triangle in which one angle is exactly 90 degrees.

Here,

Using the given information:

side1 = 8√3

angle1 = 60°

We can use trigonometric ratios to find the values of x and y:

sin(60°) = y / side1

Simplifying:

y = side1 * sin(60°)

y = 8√3 * sin(60°)

y = 8√3 * (√3 / 2)

y = 12

Therefore, x = 8√3 and y = 12.

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Related Questions

use laplace transforms to solve the initial value problem where primes indicate derivatives with respect to t.

Answers

To use Laplace transforms to solve the initial value problem where primes indicate derivatives with respect to t, follow these steps.

Write down the given differential equation and initial conditions. Apply the Laplace transform to both sides of the differential equation, using the properties of Laplace transforms for derivatives. Substitute the initial conditions into the transformed equation to get a new equation with no derivatives.Solve this new equation for the Laplace transform of the desired solution function. Apply the inverse Laplace transform to find the solution function in the time domain.Remember to be accurate and concise while solving the problem.

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Which equation represents a line which is perpendicular to the x-axis

Answers

A line perpendicular to the x-axis is a vertical line, which means it has an undefined slope. Therefore, the equation of a line perpendicular to the x-axis is of the form x = a, where "a" is a constant.

olympic gold medal has a gram of 586 grams. what is the mass of a 2018 olympic gold medal in hectograms

Answers

The mass of a 2018 Olympic gold medal in hectograms is 58.6 hg.

First, we need to know the mass of the Olympic gold medal in grams. According to the question, the mass of an Olympic gold medal is 586 grams.

To convert grams to hectograms, we need to divide the mass in grams by 100. This is because there are 100 grams in 1 hectogram.

To do the division, we can use a calculator. Dividing 586 by 100 gives us 5.86.

The answer we get is in hectograms, so we can write it as 5.86 hg. This means that the mass of a 2018 Olympic gold medal is 5.86 hectograms.

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Costumers at Al's Toy Barn took a survey. The results showed that 90 customers rated the store's decorations as being "very festive." This number represented 45% of the total number of customer who took the survey. How many customers took the survey?

Answers

Answer: 200

Step-by-step explanation: x = 90 ÷ 0.45

x = 200

a wooden artifact from an ancient tomb contains 70% of the carbon-14 that is present in living trees. how long ago was the artifact made?

Answers

The artifact was made about 3102.5 years ago.

An artifact from an ancient tomb contains 70% of the carbon-14 that is present in living trees, how long ago was the artifact made?

Carbon dating is used to estimate the age of organic materials, and it is used to determine the age of an artifact in this situation. The method used to estimate the age of an artifact based on its carbon-14 content is known as carbon dating. Carbon-14 has a half-life of 5,730 years. As a result, the amount of carbon-14 present in an object can be used to determine how long it has been since the object was last in contact with the atmosphere, and therefore how long it has been since it was alive.

Let C0 be the amount of carbon-14 present in living trees and C1 be the amount of carbon-14 present in the wooden artifact. After 5,730 years, C1 will have decayed to 1/2 of C0. After 2(5,730) = 11,460 years, C1 will have decayed to 1/4 of C0. After 3(5,730) = 17,190 years, C1 will have decayed to 1/8 of C0. After 4(5,730) = 22,920 years, C1 will have decayed to 1/16 of C0. After 5(5,730) = 28,650 years, C1 will have decayed to 1/32 of C0.

We'll have to solve the following equation to find the age of the artifact.

C1 = (70/100) * C0

Substitute the value of C0 into the equation and solve for t,

t = ln(0.7) / ln(1/2) = 3102.5 years

The artifact was made about 3102.5 years ago.

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Jason has a block of clay that is made up of two rectangular pieces of
different colors. Find the volume of the block of clay.
The measurements of the two clay blocks are:
6 cm
4 cm
3 cm
5 cm

Answers

Answer: 132 cubic centimeters

Step-by-step explanation:

To find the volume of the block of clay, we need to add the volumes of the two rectangular pieces.

The volume of a rectangular solid can be found by multiplying its length, width, and height. Let's call the first rectangular piece A and the second rectangular piece B. Then the dimensions of A are 6 cm (length), 4 cm (width), and 3 cm (height), and the dimensions of B are 5 cm (length), 4 cm (width), and 3 cm (height).

The volume of A is:

Volume of A = length x width x height = 6 cm x 4 cm x 3 cm = 72 cubic centimeters

The volume of B is:

Volume of B = length x width x height = 5 cm x 4 cm x 3 cm = 60 cubic centimeters

So the total volume of the block of clay is:

Volume of block = Volume of A + Volume of B = 72 cubic centimeters + 60 cubic centimeters = 132 cubic centimeters

Therefore, the volume of the block of clay is 132 cubic centimeters.

Function "p" is in the form y = ax2 + c. If the values of "a" and "c" are both less than 0, which graph could represent "p"?

Question 6 options:

Graph D

Graph A

Graph C

Graph B

Answers

The correct option is - Graph B, represent quadratic function "p", when values of "a" and "c" are both less than 0.

Explain about the quadratic function?

f(x) = ax² + bx + c, in which a, b, and c are numbers and an is not equal to zero, is a quadratic function.

A parabola is the shape of a quadratic function's graph. Although the "width" or "steepness" of a parabola can vary as well as its direction of opening, they all share the same fundamental "U" form.Regarding a line known as the axis of symmetry, all parabolas are symmetric. The vertex of a parabola is the location where the axis of symmetry of the curve crosses.You are aware that a line is defined by two points. This implies that there is only one line that incorporates both points if you are provided any two points in the plane.Standard form refers to the quadratic function f(x) = a(x - h)² + k, where an is not equal to zero. The graph opens either upward or downward depending on the value of a. The vertex is the point, while the line of symmetry is really the vertical line x = h. (h,k).

The given function :

y = ax² + c.

a < 0 and c <0.

Thus, Graph B, represent function "p", when values of "a" and "c" are both less than 0, and the graph will open downward with c less than 0.

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given the following frequency table of values, is the mean, median, or mode likely to be the best measure of the center for the data set? valuefrequency 351 364 376 386 395 631

Answers

For the given following frequency table of values 351, 362, 373, 381, 391, The mode is likely to be the best measure of the center for the data set.

The given frequency table is as follows:

Value frequency 351, 362, 373, 381, 391.

To find the most appropriate measure of central tendency for a dataset, we need to analyze the spread of data.

The mean, median, and mode are measures of central tendency in statistics.

We can find the following measures from the given data set:

Mean: It is calculated by summing up all the values and then dividing the result by the total number of values. This measure of central tendency is appropriate when the data are symmetrical.

Median: It is the middle value of the data set when arranged in order. It is suitable for skewed data.

Mode: It is the most common value in the data set. It is appropriate when data is discrete. The data in the frequency table appear to be discrete.

Because the data are discrete, the most appropriate measure of central tendency is the mode. So, the mode is likely to be the best measure of the center for the given value frequency data set.

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Prove that 3:8 is equivalent to 12:32

Answers

Answer:

3:8 = 12:32

For easier understanding, we make 3:8 into 3/8 and 12:32 into 12/32

3/8 = 12/32

Cross multiply

3*32 = 8*12

96 = 96

Since the products are equal, the ratios are equivalent.

You can also simplify 12:32

12 / 4 = 3

32 / 4 = 8

7. Diane started to rearrange the following inequalities into slope-
intercept form so she can graph them. The first step is completed for
you. Complete the rest of the steps to get each inequality in slope
intercept form:
Inequality 1:
y-42-2(x + 3)
Step 1: y-4≥-2x-6
Ə
Inequality 2:
4x - 3y -12
<
Step 1: -3y <-4x - 12
J
ә

Answers

The slope-intercept form of the inequality is given as follows:

y-4≥-2x-6y ≥ -2x -6 + 4y ≥ -2x-2.

What is the slope-intercept format of a function?

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.

Hence the inequality for this problem is simplified as follows:

y-4≥-2x-6y ≥ -2x -6 + 4y ≥ -2x-2.

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Identify the asymptotes, domain, and range of each function.

Answers

The function f(x) = 5/(x+3), vertical asymptote at x = -3, domain of the function is all real numbers except x = -3, range is all real numbers except 0.

Describe Function?

A function is a mathematical object that takes one or more inputs (usually represented as variables) and produces a single output. In other words, a function is a relation between sets of inputs and outputs that associates each input value with exactly one output value.

A function can be represented by an equation or a graph. The most common way to write a function is in the form f(x) = y, where x is the input variable and y is the output variable. The function f maps each value of x to a corresponding value of y.

Functions can be classified based on their properties, such as their domain (set of allowable input values), range (set of output values), and behavior (e.g., increasing, decreasing, constant, etc.). Some common types of functions include linear, quadratic, exponential, trigonometric, and logarithmic functions.

The function f(x) = 5/(x+3) has a vertical asymptote at x = -3, since the denominator becomes zero at that point.

The domain of the function is all real numbers except x = -3, since division by zero is undefined.

To find the range, we can consider what happens to the function as x approaches -3 from both sides. As x approaches -3 from the left (i.e., as x gets closer and closer to -3 from values less than -3), the function becomes increasingly negative. As x approaches -3 from the right (i.e., as x gets closer and closer to -3 from values greater than -3), the function becomes increasingly positive. This means that the range of the function is all real numbers except 0.

Therefore, the asymptote is x = -3, the domain is all real numbers except x = -3, and the range is all real numbers except 0.

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how many five-card hands from a normal deck of cards contain exactly two aces and have exactly two red cards.

Answers

There are 816 possible five-card hands from a normal deck of cards containing exactly two aces and having exactly two red cards.

There are 80 possible five-card hands from a standard deck of 52 cards that contain exactly two aces and have exactly two red cards.

To calculate this, first count the total number of combinations of two aces from the four aces in the deck. This can be done using the combination formula C(n, r) where n is the number of items (4 aces) and r is the number of items to choose (2 aces). Therefore, the number of combinations of two aces is C(4,2) = 6.

Next, count the number of combinations of two red cards. There are 26 red cards in a deck, which can be divided into the two suits of spades and hearts. For each of these suits, calculate the number of combinations of two cards using the same formula as before, C(n, r). Therefore, the number of combinations of two red cards is C(13,2) * 2 = 156.

Finally, multiply the two values together to get the total number of possible five-card hands with exactly two aces and two red cards. This equals 6 * 156 = 960. This value must be reduced by the number of hands that contain more than two aces and/or more than two red cards. This value can be calculated using the same formula. For instance, the number of hands with three aces is C(4,3) * C(13,2) * 2 = 144. This value must be subtracted from 960, leaving a total of 960 - 144 = 816.

Therefore, there are 816 possible five-card hands from a normal deck of cards containing exactly two aces and having exactly two red cards.

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Tom makes $273.60 in 6 days. How much does he make in 4 days?

Answers

Answer:

Step-by-step explanation:

$105.20

the thicknesses of 13 randomly selected linoleum tiles were found to have a standard deviation of 4.76 . construct the 90% confidence interval for the population standard deviation of the thicknesses of all linoleum tiles in this factory. round your answers to two decimal places.

Answers

The 90% confidence interval for the population standard deviation of the thicknesses of all linoleum tiles in this factory (3.27, 7.78)

To construct the 90% confidence interval for the population standard deviation of the thicknesses of all linoleum tiles in the factory, we need to use the chi-square distribution since the population standard deviation is unknown.

1. Identify the sample size (n) and sample standard deviation (s):
n = 13 (13 randomly selected linoleum tiles)
s = 4.76 (standard deviation of the thicknesses)

2. Determine the degrees of freedom (df):
df = n - 1 = 13 - 1 = 12

3. Find the chi-square values for the 90% confidence interval using a chi-square table or calculator:
The lower tail value (with 5% in the lower tail) is χ² = 4.404
The upper tail value (with 5% in the upper tail) is χ² = 21.026

4. Calculate the confidence interval for the population standard deviation:
Lower limit = √[(n - 1) * s² / χ²_upper] = √[(12 * (4.76)²) / 21.026] ≈ 3.27
Upper limit = √[(n - 1) * s² / χ²_lower] = √[(12 * (4.76)²) / 4.404] ≈ 7.78

The 90% confidence interval for the population standard deviation is approximately (3.27, 7.78).

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you flip a coin 4 times and get 4 heads in a row what is the probability that the 5th coin flipped is a head

Answers

The probability of flipping a coin 4 times and getting 4 heads in a row is 0.0625, and the probability of getting a head on the 5th coin flip is 0.5.

The probability of getting a head on the 5th flip is still 50%. This is because each coin flip is an independent event, and each coin flip is not affected by the outcome of the previous coin flips. Thus, the probability of getting a head on the 5th coin flip is 0.5, regardless of the previous 4 coin flips.

To summarize, the probability of flipping a coin 4 times and getting 4 heads in a row is 0.0625, and the probability of getting a head on the 5th coin flip is 0.5.

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Let Y have a distribution function given by 0, Fly) = y <0 y 20. - e Find a transformation G(U) such that, if U has a uniform distribution on the interval (0, 1), G(U) has the same distribution as Y. G(U) = |(-In(1–u))(7

Answers

Let Y have a distribution function given by 0, Fly) = y <0 y 20.

To find a transformation G(U) such that if U has a uniform distribution on the interval (0, 1), G(U) has the same distribution as Y, follow these steps:

1. Identify the distribution function of Y:

F(y) = 0 for y < 0, and F(y) = 1 - e^(-y) for y ≥ 0.
2. Set F(y) equal to the cumulative distribution function (CDF) of a uniform distribution on the interval (0, 1):

F(y) = U.
3. Solve for y in terms of U to obtain the transformation G(U).

So, for y ≥ 0,
1 - e^(-y) = U

Now, solve for y:
e^(-y) = 1 - U
-y = ln(1 - U)
y = -ln(1 - U)

Therefore, the transformation G(U) is given by G(U) =. ln(1 - U)

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Please answer my question by the way the number 4 and 5 is FOIL.

Answers

Using FOIL method for the multiplication, we have:

1: 3x (5x - 4) = 15x² - 12x

2: x²(5x² + 3y + 1) = 5x⁴ + 3x²y + x²

3: (4x + 3)(4x -5) = 16x² - 8x - 15

4: (7x - 3)(4x - 5) = 28x² - 47x + 15

How to carry out multiplication using FOIL?

FOIL is an acronym that stands for "First, Outer, Inner, Last". It is a mnemonic device that is commonly used to remember the process of multiplying two binomials.

No. 1

3x (5x - 4) = 3x*5x + 3x*(-4)

= 15x² - 12x

No. 2

x²(5x² + 3y + 1) = x²*5x² + x²*3y + x²*1

= 5x⁴ + 3x²y + x²

No. 3

(4x + 3)(4x -5) = 4x(4x-5) + 3(4x-5)

= 4x*4x + 4x*(-5) + 3*4x + 3*(-5)

= 16x² - 20x + 12x - 15

= 16x² - 8x - 15

No. 4

(7x - 3)(4x - 5) = 7x(4x - 5) - 3(4x - 5)

= 7x*4x + 7x*(-5) - 3*4x - 3*(-5)

= 28x² - 35x -12x + 15

= 28x² - 47x + 15

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Los números que hace verdadera a una ecuación se les denomina

Answers

soluciones o raices de la ecuación

Maths, completing the square, please help! I don't know why my answer is wrong. Please explain how to do this question.

Answers

Answer:

[tex](x+2)^2-16[/tex]

Step-by-step explanation:

Given quadratic expression:

[tex]x^2+4x-12[/tex]

To complete the square, add and subtract the square of half the coefficient of the term in x after the term in x:

[tex]\implies x^2+4x+\left(\dfrac{4}{2}\right)^2-\left(\dfrac{4}{2}\right)^2-12[/tex]

Simplify:

[tex]\implies x^2+4x+\left(2\right)^2-\left(2\right)^2-12[/tex]

[tex]\implies x^2+4x+4-4-12[/tex]

The first three terms form a perfect square trinomial which can be factored:

[tex]\implies \boxed{x^2+4x+4}-4-12[/tex]

[tex]\implies \boxed{(x+2)^2}-4-12[/tex]

Finally, subtract the numbers:

[tex]\implies (x+2)^2-16[/tex]

in a sample of men, said that they had less leisure time today than they had years ago. in a sample of women, women said that they had less leisure time today than they had years ago. at , is there a difference in the proportions? use for the proportion of men with less leisure time

Answers

The test static for sample of 50 men, 44 said that they had less leisure time today than they had 10 years ago is 0.2377.

A number derived from a statistical test of a hypothesis is the test statistic. It displays how closely your actual data fit the distribution predicted by the statistical test's null hypothesis.

In order to determine whether to accept or reject your null hypothesis, the test statistic is utilised to calculate the p value of your findings.

In a sample of 50 men, 44 said that they had less leisure time today than they had 10 years ago.

In a sample of 50 women, 48 women said that they had less leisure time than they

had 10 years ago.

p-hat men:: 44/50 = 0.22

p-hat women:: 48/50 = 0.24

Test Stat:

z(0.24-0.22) =[tex]\frac{0.02}{\sqrt{[(0.22*0.78/50)+(0.24*0.76/50)]} }[/tex] = 0.2377

At [tex]\alpha[/tex] = .05, is there a difference in the proportions between the men and women

[tex]p-value = 2*P(z > 0.2377) = 0.8121[/tex]

Since the p-value is greater than 5%, fail to reject H.

H: p(men)-p(women) = 0

Ha: p(men)-p(women) # 0 = .05, is there a difference in the proportions between the men and women

p-value = 2*P(z > 0.2377) = 0.8121

Since the p-value is greater than 5%, fail to reject H.

H: p(men)-p(women) = 0

Ha: p(men)-p(women) # 0

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Complete question:

In a sample of 50 men, 44 said that they had less leisure time today than they had 10 years ago. In a sample of 50 women, 48 women said that they had less leisure time than they had 10 years ago. What is the test statistic? At [tex]\alpha[/tex] = .05, is there a difference in the proportions between the men and women?

how many different arrangements are there of eight peo- ple seated at a round table, where two arrangements are considered the same if one can be obtained from the other by a rotation?

Answers

The number of different arrangements of eight people seated at a round table, where two arrangements are considered the same if one can be obtained from the other by a rotation, is (8-1)!/2 = 7!/2 = 2,520.

To solve this problem, we use the formula for arranging objects in a circle, which is (n-1)!, where n is the number of objects. In this case, there are 8 people, so the formula gives us (8-1)! = 7! arrangements if we do not consider rotations.

However, we need to eliminate the arrangements that are the same due to rotations. Since there are 8 people, we can rotate the table 8 times and still get the same arrangement. Thus, we divide 7! by 8 to eliminate these duplicate arrangements, which gives us (7!)/8.

But we are not done yet, because there is an additional duplicate arrangement that is not eliminated by the division. Specifically, we can flip the table over and get another arrangement that is the same as the original. Since we do not want to count this duplicate, we divide (7!)/8 by 2, giving us the final answer of 2,520.

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planets x, y and z take $360$, $450$ and $540$ days, respectively, to rotate around the same sun. if the three planets are lined up in a ray having the sun as its endpoint, what is the minimum positive number of days before they are all in the exact same locations again?

Answers

By using LCM, we find that the three planets x, y and z will be in the exact same locations again after $5400$ days.

To find the minimum positive number of days before the planets are all in the exact same locations again, we need to find the least common multiple (LCM) of the three given periods of rotation.

The prime factorization of each of the given periods of rotation is as follows

$360 =[tex]2^3 \cdot 3^2 \cdot 5$[/tex]

$450 =[tex]2 \cdot 3^2 \cdot 5^2$[/tex]

$540 =[tex]2^2 \cdot 3^3 \cdot 5$[/tex]

To find the LCM, we need to take the highest power of each prime factor that appears in any of the three factorizations. So the LCM is:

[tex]$LCM = 2^3 \cdot 3^3 \cdot 5^2 = 2^3 \cdot 27 \cdot 25 = 5400$[/tex]

Therefore, the three planets will be in the exact same locations again after $5400$ days.

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calculate the width of an 80% ci for the mean of a normal distribution with unknown variance, sample mean 9, sample variance 6 and sample size 15. use two decimal places.

Answers

With the given parameters, the width of the 80% CI for the normal distribution's mean is roughly 1.5.

The following formula can be used to determine the width of an 80% confidence interval (CI) for the mean of a normal distribution with unknown variance, the sample mean 9, sample variance 6, and sample size 15:

width = t * (s / √(n))

where s is the sample standard deviation (the square root of the sample variance), n is the sample size, and t is the value from the t-distribution with n-1 degrees of freedom for an 80% CI (from a t-table or calculator).

We must first determine the sample standard deviation:

s = √(6) ≈ 2.45

Then, we can find the worth of t from a t-table or mini-computer for a 80% CI with 14 levels of opportunity (15-1):

t = 1.339

Lastly, these numbers can be used to calculate the 80% CI width:

width = 1.339 * (2.45 / √(15)) = 1.5

With the given parameters, the width of the 80% CI for the normal distribution's mean is roughly 1.5.

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i need help ASAP
Calculate the amount of interest on $2,000.00 for 4 years, compounding daily at 2.25 % APR.

From the Monthly Interest Table use $1.094171 in interest for each $1.00 invested

A $2,088.34

B $2188.34

C $2,288.34

D $2,388.34

Answers

Answer:

Step-by-step explanation:

First, we need to calculate the annual interest rate from the given APR.

APR = 2.25%

Daily interest rate = 2.25% / 365 = 0.00616438

Now, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the final amount

P = the principal (initial amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = time in years

In this case, P = $2,000, r = 0.00616438, n = 365 (daily compounding), and t = 4.

A = 2000(1 + 0.00616438/365)^(365*4)

A = 2000(1.00616438)^1460

A = $2,388.34 (rounded to the nearest cent)

Therefore, the answer is option D) $2,388.34.

The graphs of line a and b are shown in this coordinate grid
Match each line with it's equation. Drag each equation to the corresponding box for each line

Answers

The correct option for the given graph is option 1 and option 3. The equation matches the intersection point (1,1).

For option 1: intersection point (1,1)