Thus, the smallest value of k that satisfies the condition is: k = ceil(mn / (r + n + 1)).
To find the smallest value of k such that the rank-k approximation uses the same or more amount of data as the original picture, we need to compare the sizes of the original picture and the rank-k approximation. The rank-k approximation of a matrix A can be obtained by performing singular value decomposition (SVD) on A and keeping only the k largest singular values.
Let m and n be the dimensions of the original picture (assuming it is a grayscale image) and let r be the rank of the image. The number of data points (i.e., pixels) in the original picture is mn, and the number of data points in the rank-k approximation is kr + k + kn. The first term kr corresponds to the k singular values, the second term k corresponds to the k left singular vectors, and the third term kn corresponds to the k right singular vectors.
We want to find the smallest value of k such that kr + k + kn is greater than or equal to mn. Using the values above, we can write this as:
kr + k + kn >= mn
Simplifying, we get:
k(r + n + 1) >= mn
Dividing both sides by (r + n + 1), we get:
k >= mn / (r + n + 1)
Therefore, the smallest value of k that satisfies the condition is:
k = ceil(mn / (r + n + 1))
where ceil is the ceiling function (i.e., rounding up to the nearest integer).
To obtain this result, we first calculated the number of data points in the original picture and the rank-k approximation, and then set them equal to each other. We simplified the resulting inequality to get an expression for k in terms of the other variables, and then used the ceiling function to round up to the nearest integer.
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I really need help please
Area of the triangle is 6cm²
Area of the square = 4cm²
Area of the rectangle = 35cm²
Probability of landing in triangle = 13. 3%
Probability of landing in square = 8. 8%
Probability of landing in triangle or square = 22. 2%
Probability of not landing in triangle = 86. 6%
How to determine the valuesThe formula for calculating the area of a rectangle is expressed with the equation;
Area = lw
Such that;
l is the lengthw is the width of the rectangle.Area of a triangle = 1/2 × base × height
Substitute the values
Area = 1/2 × 3 × 4
Multiply the values
Area = 6cm²
The area of the square = a²
Area = 2²
Find the square
Area = 4cm²
The area of the rectangle = 7(5)
Multiply the values
Area = 35cm²
Probability of landing in triangle = 6/45 = 0. 13× 100 = 13. 3%
Probability of landing in square = 4/45 = 8. 8%
Probability of landing in triangle or square = 13.3 + 8. 8 = 22. 2%
Probability of not landing in triangle = 39/45 = 86. 6%
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records show that the time a person spends in the shower are normally distributed. if a random sample of 13 people has a mean shower time of 6.2 minutes and a standard deviation of 1.7 minutes, find a 95% confidence interval for the mean time spent by someone in the shower.
Requried, we can be 95% confident that the true mean time spent by someone in the shower is between 5.172 and 7.227 minutes.
Sample mean (X) = 6.2 minutes
Sample standard deviation (s) = 1.7 minutes
Sample size (n) = 13
Confidence level = 95%
Since the sample size is less than 30, we will use the t-distribution for calculating the confidence interval.
First, we need to find the t-value for a 95% confidence level with 12 degrees of freedom (n-1).
From the t-distribution table, we find the t-value to be 2.179.
Calculate the margin of error (E) using the formula:
E = t×value × (s/√n)
E = 2.179 × (1.7/√13)
E = 1.027
The confidence interval by adding and subtracting the margin of error from the sample mean:
CI = (X - E, X + E)
CI = (6.2 - 1.182, 6.2 + 1.182)
CI = (5.172, 7.227)
Thus, we can be 95% confident that the true mean time spent by someone in the shower is between 5.172 and 7.227 minutes.
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Which box-and-whisker plot matches the data?
The box and whisker plot that matches the data-set is given as follows:
Second plot.
What does a box-and-whisker plot shows?A box and whisker plots shows these five features from a data-set, listed as follows:
The minimum non-outlier value.The 25th percentile, which is the median of the bottom 50%.The median, which splits the entire data-set into two halfs, the bottom 50% and the upper 50%.The 75th percentile, which is the median of the upper 50%.The maximum non-outlier value.The ordered data-set for this problem is given as follows:
13, 18, 18, 20, 27, 27, 27, 31, 31, 33, 37, 37
Hence the halves are given as follows:
First half of 13, 18, 18, 20, 27 with minimum value of 13 and median = first quartile of 18.Second half of 31, 31, 33, 37, 37, with maximum value of 37 and median = third quartile of 33.The median of the data-set is given as follows:
(27 + 27)/2 = 27.
Hence the second plot is the correct plot.
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the depth of water in tank a in inches is modeled by a differentiable and increasing function h for
The depth of water in tank A is modeled by a differentiable and increasing function h.
This means that the function h describes how the depth of water changes as time passes.
The fact that it is differentiable means that the function has a well-defined slope at every point, which indicates how quickly the depth is changing. This means that the function is continuous and smooth, with no sharp turns or corners.
Furthermore, the fact that the function is increasing means that the depth is always getting higher over time.
This makes sense since water is constantly being added to the tank.
Hence, the depth of water in tank A is described by a differentiable and increasing function h, which means that the function has a well-defined slope at every point and that the depth is always getting higher over time.
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Ellie is getting her pool ready for the summer the water in the pool is 10 inches deep,and she is adding water at a rate of 3 inches every 30 minutes you can use a function to describe the depth of the water in the pool after she fills it after x minutes write an equation for the function
The equation for the function is d = (1/10)t + 10.
We have,
Let's call the depth of the water in inches "d" and the time in minutes "t".
We know that the pool starts with a depth of 10 inches, and Ellie is adding water at a rate of 3 inches every 30 minutes.
This means that for every 30 minutes, the depth of the water increases by 3 inches.
To write an equation for this function, we can use the slope-intercept form of a linear equation, where "m" is the slope and "b" is the y-intercept:
d = mt + b
In this case, the slope is the rate of increase in depth per minute, which is 3/30 = 1/10 inches per minute.
The y-intercept is the initial depth of the pool, which is 10 inches.
So the equation for the function is:
d = (1/10)t + 10
This equation tells us that after "x" minutes, the depth of the water in the pool will be:
d = (1/10)x + 10 inches.
Thus,
The equation for the function is d = (1/10)t + 10.
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A number is subtracted from 8 and the result divided by 5. If the final result is 1, what is the number?
Answer: To solve the problem, we can use algebra. Let x be the number that is subtracted from 8. Then, we can write the equation:
(8 - x) / 5 = 1
To solve for x, we can first multiply both sides by 5:
8 - x = 5
Next, we can isolate x by subtracting 8 from both sides:
x = 3
Therefore, the number that is subtracted from 8 is 3.
What two numbers multiply to get -40 and add up to get -3
Answer:
-8 (or) 5 and 5 (or) -8
Step-by-step explanation:
Let one of the numbers = x
Let other number = y
As the sum of two numbers = -3
x + y = -3
x = -3-y
As the the result of multiplication = -40
xy = -40
(-3-y)*y = -40
-3y-y² = -40
-y²-3y+40 = 0
-(y²+3y-40) = 0
-(y+8)(y-5) = 0
(-y-8)(y-5) = 0
-y-8 = 0 (or) y-5 = 0
-y = 8 (or) y = 5
y = -8 (or) y = 5
when y = -8
x = -3-y
x = -3-(-8)
x = -3+8
x = 5
when y = 5
x = -3-y
x = -3-5
x = -8
5x+3=17
So 5x+1=?
PLEASE HELP WHAT IS X
2.8
Step-by-step explanation:
17-3=14
So 5x=14
14÷5=2.8
So x=2.8
Answer:
your answer is..15
Step-by-step explanation:
A rectangular container 8 cm long and 9cm wide was filled with water to a depth of 6cm. When 12 marbles of equal size were added to the container, the depth of the water became 7. 5 cm. Find the volume of one marble
The volume of one marble is 27 cubic centimeters.
First, let's calculate the initial volume of water in the container. We know that the container is 8 cm long, 9 cm wide, and filled with water to a depth of 6 cm. Therefore, the initial volume of water in the container can be calculated as follows:
Volume of water = length x width x height
= 8 cm x 9 cm x 6 cm
= 432 cm³
Next, we need to find the final volume of water in the container after the 12 marbles were added. We are given that the depth of the water increased from 6 cm to 7.5 cm. Therefore, the final height of the water can be calculated as follows:
Final height of water = 7.5 cm - 6 cm
= 1.5 cm
Now, we can find the final volume of water in the container as follows:
Volume of water = length x width x height
= 8 cm x 9 cm x 1.5 cm
= 108 cm³
The difference between the initial volume of water and the final volume of water is equal to the volume of 12 marbles that were added to the container. Therefore, we can calculate the volume of one marble as follows:
Volume of one marble = (Final volume of water - Initial volume of water) / Number of marbles
= (108 cm³ - 432 cm³) / 12
= 324 cm³ / 12
= 27 cm³
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need help with this!
Answer: i think its 242
In a newspaper's survey of 454 people, 52. 6% said that we should replace passwords with biometric security, such as fingerprints. The accompanying Statdisk display results from a test of the claim that half of us say that we should replace passwords with biometric security. Use the normal distribution as an approximation to the binomial distribution. Use the display and a 0. 10 significance level to complete parts (a) through (e)
According to the binomial distribution concept,
a) The null hypothesis is 0.5
b) The alternative hypothesis is 0.5
c) The value of z - score is 2.131
d) The value of the variable p-value is 0.0326
e) There is evidence to suggest that the proportion of respondents who believe we should replace passwords with biometric security is significantly different from 0.5.
The null hypothesis is that exactly half of the respondents believe we should replace passwords with biometric security. In other words, the proportion of respondents who believe this is 0.5.
The alternative hypothesis is that the proportion of respondents who believe we should replace passwords with biometric security is significantly different from 0.5.
The test statistic is the z-score, which measures how many standard deviations the sample proportion is from the null hypothesis proportion. In this case, we can calculate the z-score as follows:
z = (p - P) / √(P(1 - P)/n)
where:
p is the sample proportion (0.526)
P is the null hypothesis proportion (0.5)
n is the sample size (454)
Plugging in these values, we get:
z = (0.526 - 0.5) / sqrt(0.5(1 - 0.5)/454)
z = 2.131
To calculate the p-value, we can use a normal distribution table or a calculator. Using a calculator, we find that the area to the right of z = 2.131 is 0.0163. Since this is a two-tailed test, we need to double this value to get the p-value:
p-value = 2(0.0163) = 0.0326
Since the p-value (0.0326) is less than the significance level (0.10), we reject the null hypothesis. Specifically, since the sample proportion is greater than 0.5, we can conclude that more than half of the respondents believe we should replace passwords with biometric security.
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A Manufacturer Offers A Warranty On Its Coffee Makers. The Coffee Makers Have A Mean Lifespan Of 4. 5 Years, With A Standard Deviation Of 0. 7 Years. For How Long Should The Coffee Makers Be Covered By The Warranty, If The Manufacturer Wants To Repair No More Than 2. 5% Of The Coffee Makers Sold?
The number of years that coffee makers are covered by warranty is 3.128 years, under the condition that the Manufacturer wants to repair no more than 2. 5% of the coffee makers sold.
In order to solve this problem, we have to find the z-score that corresponds to a probability of 0.025 (2.5%). We need to utilize the standard normal distribution table
The formula derived for z-score is
z = (x - μ) / σ
here
x= value we want to find the probability
μ= mean
σ= standard deviation.
For the given case, we have to find the value of x such that P(X > x) = 0.025,
Here X is the lifespan of a coffee maker.
Applying a standard normal distribution table we evaluate that the z-score corresponding to a probability of 0.025 is -1.96.
Now we conduct the formula for z-score to find x:
-1.96 = (x - 4.5) / 0.7
x - 4.5 = -1.372
x = 3.128
The number of years that coffee makers are covered by warranty is 3.128 years.
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what is the ratio of 48 and 6 in simplest form
Answer: the answer is 8:1
Step-by-step explanation:
48:6/6
8:1
ten different people walk into a delicatessen to buy a sandwich. four always order tuna fish, two always order chicken, two always order roast beef, and two order any of the three types of sandwich. (a) (5 points) how many different sequences of sandwiches are possible? (b) (5 points) how many different (unordered) collections of sandwiches are possible?
(a) There are 81 different sequences of sandwiches are possible
(b) The total number of different (unordered) collections of sandwiches is 3.
First, we need to determine the number of ways the four tuna fish sandwiches can be ordered. Since all four sandwiches are the same, there is only one way to order them. Similarly, there is only one way to order the two chicken sandwiches and the two roast beef sandwiches. For the two people who can choose any sandwich, there are three options for each person, giving a total of 3 x 3 = 9 possible sandwich combinations.
Therefore, the total number of different sequences of sandwiches is:
1 (tuna fish) x 1 (chicken) x 1 (roast beef) x 9 (any sandwich) x 9 (any sandwich) = 81
For part (b), we need to determine the number of different (unordered) collections of sandwiches. We can use combinations to solve this problem. We need to select 10 sandwiches from the total of 10 sandwiches available. Since there are four tuna fish sandwiches, we need to select four of them.
Similarly, we need to select two chicken sandwiches and two roast beef sandwiches. Finally, we need to select two more sandwiches from the remaining three (since two people can choose any sandwich). The number of ways to select these sandwiches is:
combination(4,4) x combination(2,2) x combination(2,2) x combination(3,2) = 3
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What are the features of the function
f(x) = 2 graphed below?
12
11
10
9
8
7
6
-12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
-1
9
î
5
4
3
2
2
2 3 4 5 6 78 0 12
-2
-3
-4
-5
-6
-7
-8
y
-9
-10
-11
The function f(x) is
1
2 3 4 5 6 7 8 9 10 11 12
asymptote of
The range of the function is
◆ function with a
and it is
on its domain of
behavior on the LEFT side is as
î
◆. The end
and the end behavior on
the RIGHT side is as
X
The graph of function f(x) is a curve that starts at the point (0,1) and grows exponentially as x increases.
We have,
The function f(x) = 2^x has several features:
- Exponential growth:
As x increases, the output of the function f(x) grows exponentially.
This means that the function grows very quickly, and the rate of growth increases as x gets larger.
- Increasing function:
The function f(x) is always increasing, which means that as x increases, so does the value of f(x).
- Continuous function:
The function f(x) is continuous, meaning that there are no breaks or jumps in the graph of the function.
- Domain and range:
The domain of f(x) is all real numbers, and the range of f(x) is all positive real numbers.
- Asymptote:
The function f(x) does not have a horizontal asymptote, meaning that the function grows without bound as x increases.
- Intercept:
The function f(x) has a y-intercept of 1, meaning that f(0) = 1.
Thus,
The graph of function f(x) is a curve that starts at the point (0,1) and grows exponentially as x increases.
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in an attempt to increase business on monday nights, a restaurant offers a free dessert with every dinner order. before the offer, the mean number of dinner customers on monday was . following are the numbers of diners on a random sample of days while the offer was in effect. can you conclude that the mean number of dinners changed while the free dessert offer was in effect? use the level of significance and the -value method with the ti-84 plus calculator.
By using the level of significance and p-value method with the TI-84 Plus calculator, we can determine if the mean number of dinners changed while the free dessert offer was in effect.
To perform the one-sample t-test on the TI-84 Plus calculator, we need to input the sample data and the null hypothesis. We will use the following steps:
Press STAT and then ENTER to access the list editor.
Enter the sample data into a list.
Press STAT again and then scroll right to TESTS.
Select t-Test and then highlight "Stats."
Enter the sample list name, the null hypothesis, and the level of significance.
Press ENTER and the calculator will output the t-statistic, degrees of freedom, and the p-value.
If the p-value is less than 0.05, we can reject the null hypothesis and conclude that the mean number of dinners changed while the free dessert offer was in effect.
If the p-value is greater than or equal to 0.05, we cannot reject the null hypothesis and conclude that there is insufficient evidence to suggest that the mean number of dinners changed.
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when representing a frequency distribution with a bar graph which bars will be the tallest? A) a bar representing a frequency of 15 B) a bar representing a frequency of 5 C) a bar representing a frequency of 20 D) a bar representing a frequency of 10
The bar graph representing a frequency of 20 will be the tallest
Given data ,
The tallest bar in a bar graph will represent the highest frequency. So, in the given options:
A) a bar representing a frequency of 15
B) a bar representing a frequency of 5
C) a bar representing a frequency of 20
D) a bar representing a frequency of 10
The tallest bar will be C) a bar representing a frequency of 20, as it has the highest frequency among the options given.
In a bar graph, the frequency or count of a certain category or data point is represented by the height of the bars, with larger bars denoting greater frequencies or counts.
Hence , the bar graph is solved
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A shop sells apples and pears
4 apples and 3 pears cost £4.10
5 apples and 8 pears cost £6.40
Find the price of the apples and pears at the shop.
Leave your answer in pence
The price of the apples and pears at the shop are £0.8 and £0.3, respectively
Finding the price of the apples and pears at the shop.Given that
4 apples and 3 pears cost £4.105 apples and 8 pears cost £6.40So, we have
4x + 3y = 4.10
5x + 8y = 6.40
Where
x = apple and y = pears
When solved graphically, we have
x = 0.8 and y = 0.3
Hence, the price of the apples and pears at the shop are £0.8 and £0.3, respectively
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Which of the following can be used to find the slope between two points?
What is the rate of change between (3, 2) and (6, 10)?
Answer:
1: Use the slope formula to find the slope of a line given the coordinates of two points on the line. The slope formula is m=(y2-y1)/(x2-x1), or the change in the y values over the change in the x values.
2: im not suree
Step-by-step explanation:
What must be a factor of the polynomial function f(x) graphed on the coordinate plane below?
-6 -4 2
O X-2
x-1
OX+2
Ox+3
S
-
19
8
X
K
A factor of the polynomial graphed is
O X + 2How to determine the factor of the polynomialThe zeros, which is the solution of the graph is used find the factor of the polynomial on the graph.
The graph shows that zeros includes
x = -2, x = 0 and x = 3
x = -2 is same as x + 2 = 0 hence this is a factor as in the third option.
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Review the graph of function g(x). On a coordinate plane, y = g (x) has a straight line connecting point (negative 5, 4) and (negative 2, 1), a curved line connected (negative 2, 1) and (0, negative 1), and a straight line connecting (0, negative 1) and (4, negative 2). Determine the value of g–1(4). –5 Negative one-half 2 3
The value of the inverse function at x = 4 is:
[tex]y = g^-^1^(^4^) =-5[/tex]
From the attachment of graph :
Points available on the graph 'g' are (-5, 4), (-2, 1), (0, -1), (4, -2).
Since, rule to get the points lying on the graph of the inverse of the given function is,
(x, y) → (y, x)
And, (x, y) is the function of g and (y , x) is the inverse function of the g.
By the given rule, points on [tex]g^-^1^(^x^)[/tex] will be,
(4, -5), (1, -2), (-1, 0), (-2, 4)
Therefore, value of the inverse function at x = 4 will be:
[tex]y = g^-^1^(^4^) =-5[/tex]
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a billboard is 30 ft tall. as a horizontal distance x feet form the billboard, the angle of elevation to the bottom of the billboard is 15 degrees and the angle of elevation to the top of the sign is 40 degrees. how far is away is the billboard?
The main answer to the question is that the distance away from the billboard is approximately 69.5 feet.
To arrive at this answer, we need to use trigonometry. We can set up two right triangles, one for the bottom of the billboard and one for the top. In both triangles, the height of the billboard is the same (30 ft), and the angles of elevation are given (15 and 40 degrees). We can use the tangent function to find the length of the adjacent side (the distance from the billboard), and then use the Pythagorean theorem to find the hypotenuse (the total distance away).
For the bottom of the billboard, we have:
tan(15) = 30/x
x = 30/tan(15)
x ≈ 114.1 ft
For the top of the billboard, we have:
tan(40) = 30/x
x = 30/tan(40)
x ≈ 36.1 ft
To find the total distance away, we can subtract the two distances:
distance away = x - 30 cot(15) - 30 cot(40)
distance away ≈ 69.5 ft
Therefore, we can conclude that the distance away from the billboard is approximately 69.5 feet.
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The measure of ∠DBE is (0.1x−32)° and the measure of ∠CBE is (0.3x−42)°. Find the value of x.
50
Step-by-step solution:
0.3x-42=0.1x-32
-0.1x
0.2x-42=-32
+42
0.2x=10
0.2
x=50
Find an equation in slope-intercept form for the line: slope , y-intercept = -5
An equation in slope-intercept form for the line is y = 2x - 2.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.Based on the information provided about this equation, we have the following slope and y-intercept;
Slope, m = 2.
y-intercept, c = -5.
By substituting the given parameters, we have the following:
y = mx + c
y = 2x + (-2)
y = 2x - 2
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Complete Question:
Find an equation in slope-intercept form for the line: slope 2, y-intercept = -5
Here r two right angle triangles.............. :)
The value of x for the right triangles is derived to be x = 1 or x = -2/3 using the trigonometric ratio of tangent for the angles a and b
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
tan a = (x + 2)/x and tan b = 4/(3x - 1) {opposite/adjacent}
(x + 2)/x = 4/(3x - 1)
(3x - 1)(x + 2) = 4x {cross multiplication}
by expansion we have a quadratic equation;
3x² - x - 2 = 0
we can rewrite the equation and factorise as follows;
3x² + 2x - 3x - 2 =0
x(3x + 2) - 1(3x + 2) = 0
(x - 1)(3x + 2) = 0
x = 1 or x = -2/3
Therefore, the value of x for the right triangles is derived to be x = 1 or x = -2/3 using the trigonometric ratio of tangent for the angles a and b.
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a builder has a 100-acre plot of ground. he sets aside 20% for a school and playground; 15% for roads, drainage ditches, and sidewalks; and 15% for a strip shopping area with parking and buffer. he plans to build three houses per acre. how many homes can be built on this property?
Answer:
(3 houses/acre)(100 acres)(.5) =
150 houses
The remaining land is 50 acres (100-50), and the builder plans to build three houses per acre. So, the number of houses that can be built on this property is (50 x 3) = 150 acres.
First, let's determine how much of the 100-acre plot is left for building houses after setting aside land for the school, playground, roads, drainage ditches, sidewalks, and the strip shopping area with parking and buffer.
1. School and playground: 20% of 100 acres = 0.20 * 100 = 20 acres
2. Roads, drainage ditches, and sidewalks: 15% of 100 acres = 0.15 * 100 = 15 acres
3. Strip shopping area with parking and buffer: 15% of 100 acres = 0.15 * 100 = 15 acres
Now, add up these reserved areas: 20 acres + 15 acres + 15 acres = 50 acres
The builder has set aside 20 acres for the school and playground, 15 acres for roads, drainage ditches, and sidewalks, and another 15 acres for the strip shopping area with parking and buffer. Therefore, the total area that has been allocated is 50 acres (20+15+15).
Subtract the total reserved area from the total plot area to find the area available for building houses: 100 acres - 50 acres = 50 acres
Since the builder plans to build three houses per acre, we can multiply the available area by the number of houses per acre: 50 acres * 3 houses/acre = 150 houses
The builder can build 150 homes on this property.
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A bag contains 6 marbles. There are 2 red marbles, 2 green marbles, and 2 yellow marbles. A marble is randomly selected from the bag and then set aside. A second marble is then selected from the bag. What is the probability that both marbles are red?
The probability that both marbles are red is 0.33
Probability :The probability formula defines the likelihood of the happening of an event. It is the ratio of favorable outcomes to the total favorable outcomes.
P(A) = Number of favorable outcomes/ total no. of possible outcomes
We have the information from the question:
Total marbles are there in bag is = 6
Red Marbles = 2
Green Marbles = 2
Yellow Marbles = 2
To find the probability that both marbles are red.
Now, According to the question:
The probabilities that are desirable for our cases are:
P(RR) = 2/6 = 1/3 = 0.33
Hence, The probability that both marbles are red is 0.33
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What is the volume of the cube
Answer:V=a3
Step-by-step explanation:
Answer: V=a3
Step-by-step explanation:
Which graph represents the equation y equals one half times x minus 2?
Answer: y=[tex]\frac{1}{2}[/tex]x - 2
Step-by-step explanation:
No graphs were shown to choose from but it would look like a line that has a positive slope, goes throuh y-axis at -2 and slope of 1/2
Rayn's backyard deck cost $87. 85 per square to build. The deck is 8 yards wide and 12 yards long. How much did it cost to build the deck?
Answer:
$8421.60
Step-by-step explanation:
First, we need to convert the dimensions of the deck from yards to square yards, since the cost is given per square yard.
The area of the deck is the product of its length and width:
8 yards * 12 yards = 96 square yards
So, the cost to build the deck is:
$87.85/square yard * 96 square yards = $8421.60
Therefore, it cost $8421.60 to build the deck.
