He needs an additional $0.23 to buy the football with the coupon after the discount coupon.
What is Discount?A discount is a reduction in the price of a product or service. It is often used as a marketing tool to attract customers and increase sales. Discounts can be expressed as a percentage or a dollar amount.
What is discounted price?The discounted price is the price of a product or service after a discount has been applied. The discount is usually expressed as a percentage or a dollar amount and is subtracted from the original price.
In the given question,
The discount Justin can get is 12% of the original price, which is:
0.12 x 22.99 = 2.76
So the discounted price of the football is:
22.99 - 2.76 = 20.23
Since Justin has exactly $20, he doesn't have enough money to buy the football with the coupon. He needs:
20.23 - 20 = 0.23
So he needs an additional $0.23 to buy the football with the coupon.
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analysis of a pert problem shows the estimated time for the critical path to be 108 days with a variance of 64. there is a .90 probability that the project will be completed before approximately day: group of answer choices 108. 98. 115. 118. 109.
There is a .90 probability that the project will be completed before approximately day 118.
The given information can be solved by using the formula of z-score as follows:
Z = (X - μ)/σ
Where: Z = z-score
X = the time for project completion
μ = the mean time for the critical path
σ = standard deviation for the critical path
σ² = variance of the critical pathσ = √64
σ = 8
Given that the mean time for the critical path is μ = 108 days and σ = 8 days,
Therefore, the z-score of the completion of the project before 108 days is given by:
Z = (X - μ)/σ0.90
= P(Z < z)
= P(Z < (X - 108)/8)P(Z < (X - 108)/8)
= 0.90
Using a z-table or calculator, we find the z-value to be 1.28.
Then,1.28 = (X - 108)/8
Multiplying both sides by 8, we get:10.24 = X - 108
Adding 108 to both sides, we get: X = 118.24
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A rectangular garden has a walkway around it. The area of the garden is 6(5. 5x+2. 5). The combined area of the garden and the walkway is 6. 5(8x+4). Find the area if the walkway around the garden as the sum of two terms
The area of the walkway can be expressed as the sum of two terms is 9x + 7 and 10x + 4.
We are given that the area of the garden is 6(5.5x + 2.5). This means that the garden has a length of 5.5x + 2.5 units and a width of 6 units (since the problem doesn't specify which side is the length or width, we can assume either). We can use the formula for the area of a rectangle to find the area of the garden:
Area of the garden = length x width = (5.5x + 2.5) x 6 = 33x + 15
Next, we are given that the combined area of the garden and the walkway is 6.5(8x + 4). This means that the garden and the walkway together have a length of 8x + 4 units and a width of 6.5 units. We can again use the formula for the area of a rectangle to find the combined area:
Combined area = length x width = (8x + 4) x 6.5 = 52x + 26
To find the area of the walkway, we need to subtract the area of the garden from the combined area. This will give us the area of the walkway alone.
Area of the walkway = Combined area - Area of the garden
= (52x + 26) - (33x + 15)
= 19x + 11
Finally, we are asked to express the area of the walkway as the sum of two terms. This means we need to find two numbers that add up to 19 and two numbers that add up to 11. We can use trial and error to find these numbers. One possible solution is:
19x + 11 = (9x + 7) + (10x + 4)
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WHATS THE ANSWER????
Answer:
They are congruent by AA- because the only thing they have in common is the 65 degree angles but the sides are all different
Step-by-step explanation:
how can the union and intersection of n sets that all are subsets of the universal set u be found using bit strings?
The union and intersection of n sets that are all subsets of the universal set u can be found using bit strings.
Bit strings are a way of representing sets as strings of binary digits. To represent a set, each element is assigned a digit of 0 or 1. A 1 indicates that the element is in the set, while a 0 indicates that the element is not in the set.
The union of the sets is found by combining the bit strings and setting any digit that is 1 in any of the sets to a 1. The intersection is found by comparing the bit strings and setting any digit that is 1 in all of the sets to a 1.
By using bit strings, we can quickly and accurately find the union and intersection of n sets that are all subsets of the universal set u.
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I NEED HELP ON THIS ASAP!
Answer:
16 represents the hours available to sew gloves.
2 represents the cost of producing gloves for a small pair.
Step-by-step explanation:
the probability that a randomly selected case will have a score beyond either +1.00 or -1.00 standard deviation of the mean is select one a 6826
b 5000 c 3174 d 1/2 of the area of 1 standard deviation
Correct option is (c) 3174
The probability that a randomly selected case will have a score beyond either +1.00 or -1.00 standard deviation of the mean depends on the type of distribution and the area under the curve beyond these values.
Assuming a normal distribution, approximately 68% of the cases fall within one standard deviation from the mean, and approximately 32% of the cases fall beyond either +1.00 or -1.00 standard deviation of the mean.
To calculate the probability of a randomly selected case falling beyond either +1.00 or -1.00 standard deviation of the mean, we need to calculate the area under the curve beyond these values. Since the distribution is symmetric, we can calculate the area on one side of the mean and multiply it by 2.
Using a standard normal distribution table or calculator, we can find the area under the curve beyond +1.00 standard deviation from the mean as 0.1587 and the area under the curve beyond -1.00 standard deviation from the mean as 0.1587.
Therefore, the total probability of a randomly selected case falling beyond either +1.00 or -1.00 standard deviation of the mean is 0.1587 + 0.1587 = 0.3174, which is approximately 32%.
Hence, the correct option is (c) 3174.
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t-test is used when you have two samples or data coming from 2 groups, and you want to compare whether or not they're distinct (in other words, is the data coming from 2 separate populations, or not?)
The result is the t-statistic, which is used to compare the two samples.
The t-test is used to compare the means of two independent samples. The formula for the t-test is:
[tex]t = (x1 - x2) / √[s2/n1 + s2/n2][/tex],
where x1 is the mean of the first sample, x2 is the mean of the second sample, s2 is the variance of the two samples, and n1 and n2 are the sizes of each sample.
To calculate the t-test, first you need to calculate the mean for each sample. If the sample size is small (less than 30), then you should use the sample standard deviation.
Next, calculate the variance for each sample by taking the sum of the squared differences from the mean, and dividing by n-1 (where n is the sample size).
Finally, calculate the t-test statistic by substituting the means and variances into the formula above. The result is the t-statistic, which is used to compare the two samples.
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pls help math scientific notation (view photo)
Just ignore this answer, its incorrect
*edited*
the coefficient of correlation is a useful measure of the linear relationship between two variables. true false
The statement is true.
The coefficient of correlation, also known as the Pearson correlation coefficient, is a measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, with a value of -1 indicating a perfect negative correlation, a value of 0 indicating no correlation, and a value of 1 indicating a perfect positive correlation.
The coefficient of correlation is useful in many applications, including research, business, and finance. It allows us to quantify how closely related two variables are, which is important when analyzing data and making predictions.
For example, in finance, the correlation coefficient can be used to measure the degree of correlation between the returns of two assets, which is important when building diversified portfolios. It is important to note, however, that the coefficient of correlation only measures the strength and direction of the linear relationship between two variables.
It does not indicate causation, nor does it capture any non-linear relationships that may exist between the variables. Therefore, it should be used in conjunction with other analytical tools to fully understand the nature of the relationship between the variables.
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Which statement describes the graph of this polynomial function?
f (x) = x Superscript 5 Baseline minus 6 x Superscript 4 Baseline + 9 x cubed
Answer:
The statement that describes the graph of the polynomial function f (x) = x^5 - 6x^4 + 9x^3 is that it has a local maximum at x = 0 and a local minimum at x = 2. The degree of the polynomial is 5, which means it has five zeros or x-intercepts. The leading coefficient is positive, which indicates that the graph will rise to the left and right. The function has a point of inflection at x = 1.5, where the concavity changes from up to down. Overall, the graph of this polynomial function has a typical "upside-down U" shape with local extrema and a point of inflection.
The yard pictured below has algebraic expressions for its side lengths, in metres.
Find a simplified algebraic expression for the perimeter of the yard.
Use your expression to find the perimeter in meters, if the value of x=3 m . Show your steps.
The simplified algebraic expression for the perimeter of the yard is 28m+10x, and if x=3m, then the perimeter is 58m.
The simplified algebraic expression for the perimeter of the yard is 28m+10x, and if x=3m, then the perimeter is 58m.
In the given figure, the yard is in the shape of a rectangle with dimensions (4x - 6) m and (2x + 3) m. The perimeter of a rectangle is the sum of the lengths of all four sides, which can be expressed as:
Perimeter = 2(Length + Width)
Perimeter = 2(4x - 6 + 2x + 3) m
Perimeter = 2(6x - 3) m
Perimeter = 12x - 6 m
So, a simplified algebraic expression for the perimeter of the yard is 12x - 6 m.
To find the perimeter in meters when x = 3 m, substitute x = 3 into the algebraic expression for perimeter:
Perimeter = 12(3) - 6 m
Perimeter = 30 m
Therefore, the perimeter of the yard when x = 3 m is 30 meters.
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Rita started the day with R apps. then she deleted 5 apps and still had twice the amount of Cora (36). write an equation that represents the number of apps both girls have
Answer:
Step-by-step explanation:lllllLet's start by using "R" to represent the number of apps that Rita started with, and "C" to represent the number of apps that Cora started with.
We know that Rita deleted 5 apps, so she would have (R-5) apps remaining. And we know that she still had twice the amount of Cora, which is 36.
So we can write the equation:
R-5 = 2C
And we also know that Cora had 36 apps, so we can substitute that value in for C:
R-5 = 2(36)
Simplifying the right side:
R-5 = 72
Finally, we can solve for R by adding 5 to both sides:
R = 77
So Rita started with 77 apps, and Cora started with 36 apps. We can check that Rita deleted 5 and had twice as many as Cora by plugging our values into the original equation:
77 - 5 = 72
2(36) = 72
Both sides are equal, so our solution is correct.
the number 5/3 can be best described as a(n) ___.
Answer: Proper fraction
Step-by-step explanation:
A proper fraction is a fraction that has its numerator value less than the denominator.
For example, ⅔, 6/7, 8/9, etc. are proper fractions.
The graph below shows the relationship between life expectancy and infant mortality in a random sample of countries.
Answer choices.
Positive linear association
Negative linear association
Non linear association
No association
Answer:
negative linear association
Step-by-step explanation:
The best description of the association between life expectancy and infant mortality rate in the given graph is option B. Countries with higher infant mortality rates tended to have shorter life expectancies.
The negative linear association between life expectancy and infant mortality rate in the attached graph,
Life Expectancy,
Life expectancy refers to the average number of years a person is expected to live from birth.
In the graph, life expectancy is represented on the vertical axis (y-axis).
Infant Mortality Rate,
Infant mortality rate refers to the number of deaths of infants under one year of age per 1,000 live births.
In the graph, the infant mortality rate is represented on the horizontal axis (x-axis).
Negative Linear Association,
A negative linear association means that as one variable increases, the other variable tends to decrease at a consistent rate.
here, as the infant mortality rate increases (moving right on the x-axis), the life expectancy tends to decrease (moving down on the y-axis).
Interpretation,
Looking at the graph, we can see that countries with higher infant mortality rates are positioned towards the right side of the graph,
and they tend to have shorter life expectancies, which are positioned towards the bottom of the graph.
Conversely, countries with lower infant mortality rates are positioned towards the left side of the graph, and they tend to have longer life expectancies,
which are positioned towards the top of the graph.
Implication,
The negative linear association in the graph indicates that countries with higher rates of infant mortality are likely to have lower life expectancies.
This is because higher infant mortality rates often indicate poorer healthcare systems, lower living standards,
and other factors that can impact life expectancy negatively.
Therefore, based on the graph's trend, we can conclude that the statement B is the best description of the association between life expectancy and infant mortality rate.
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The above question is incomplete , the complete question is :
The Graph Below Shows The Relationship Between Life Expectancy And Infant Mortality Rate In A Random Sample Of Countries.
Which statement is the best description of the association between these variables? Choose all that apply.
A. Countries with higher infant mortality rates tended to have longer life expectancies.
B. Countries with higher infant mortality rates tended to have shorter life expectancies.
C. There is no clear relationship between infant mortality rates and life expectancy.
Attached graph.
help i don’t know how to solve number 11, please
Answer: 21, 32. 6, 12.
Step-by-step explanation:
10 + 3d = 43. 3d = 33. d = 11.
3 x [tex]r^{3}[/tex] = 24. [tex]r^{3}[/tex] = 8. r = 2.
a collection of five positive integers has mean $4.4$, unique mode $3$ and median $4$. if an $8$ is added to the collection, what is the new median? express your answer as a decimal to the nearest tenth.
To begin, we know that the median of the original collection of five positive integers is 4, which means that the middle number is 4. We also know that the unique mode is 3, which means that there is only one number in the collection that occurs more frequently than any other number.
Let's call the five positive integers in the original collection a, b, c, d, and e.
Since the mean of the original collection is 4.4, we can set up the equation:
(a+b+c+d+e)/5 = 4.4
Multiplying both sides by 5 gives:
a+b+c+d+e = 22
We also know that the mode is 3, which means that one of the numbers in the collection must be 3. Let's assume that a = 3, then we have:
3+b+c+d+e = 22
b+c+d+e = 19
Since the median is 4 and 3 is the unique mode, we can conclude that b, c, d, and e must be either 4 or 5. However, since there is only one unique mode, we know that there is only one number in the collection that is equal to 3. Therefore, we can conclude that the collection of five positive integers must be: 3, 4, 4, 4, 5.
If we add 8 to this collection, the new collection becomes: 3, 4, 4, 4, 5, 8. The new collection has six numbers, so the median is now the average of the two middle numbers. Since the middle two numbers are 4 and 5, the median is (4+5)/2 = 4.5.
Therefore, the new median is 4.5, expressed as a decimal to the nearest tenth.
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Use the image below to answer the question
Answer:
∠ FZG = 38°
Step-by-step explanation:
∠ HZJ and ∠ FZG are vertically opposite angles and are congruent , then
∠ ZFG = ∠ HZJ = 38°
the contingency table shows the results of a survey of students in two math classes. find p(more than 1 hour of tv | 6th period class). round to the nearest thousandth. did you watch more than one hour of tv last night?
The probability of P(more than 1 hour of TV | 6th period class) is option (D) 0.765
To find P(more than 1 hour of TV | 6th period class), we need to use conditional probability formula
P(more than 1 hour of TV | 6th period class) = P(more than 1 hour of TV and 6th period class) / P(6th period class)
The number of students who watched more than 1 hour of TV and were in the 6th period class is 13. Therefore, P(more than 1 hour of TV and 6th period class) = 13 / (13 + 10) = 13/23.
The total number of students in the 6th period class is 13 + 10 = 23. Therefore, P(6th period class) = 23 / (6 + 23) = 23/29.
Putting it all together
P(more than 1 hour of TV | 6th period class) = P(more than 1 hour of TV and 6th period class) / P(6th period class) = (13/23) / (23/29) = 0.765 (rounded to the nearest thousandth)
Therefore, the correct option is (D) 0.765
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The given question is incomplete, the complete question is:
The table shows the results of a survey of students in two math classes. Find P(more than 1 hour of TV | 6th period class). Round to the nearest thousandth. Did You Watch More Than One Hour of TV Last Night? Yes No 3rd period class 6 6th period class 13 10 A) 0.647 B) 0.565 C) 0.435 D) 0.765
Please Help Quickly ASAP Hurry ASAP
What is the value of θ for the acute angle in a right triangle?
sin(θ)=cos(44°)
Therefore, the value of θ for the acute angle in a right triangle is 46°.We can use the fact that the sine and cosine of complementary angles are equal to find θ.
To find the value of θ for the acute angle in a right triangle, we need to use one of the trigonometric ratios. In this case, we are given the sine of θ and the cosine of 44°. Recall that the sine of an angle θ is defined as the ratio of the opposite side to the hypotenuse in a right triangle:
sin(θ) = opposite / hypotenuse
And the cosine of an angle φ is defined as the ratio of the adjacent side to the hypotenuse:
cos(φ) = adjacent / hypotenuse
In a right triangle, the two acute angles are complementary, which means that their sum is 90°. That is,θ + 90° = 90°
θ = 90° - 44°.Now we can use the given equation sin(θ) = cos(44°) and substitute θ: sin(90° - 44°) = cos(44°) => sin(46°) = cos(44°)
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Pls help me with 10 asap I will mark brainiest if it’s correct
The value of p from the given equation is 4.5.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign [tex]=\\[/tex].
The given equation is [tex]0.5p-3.45=-1.2[/tex]
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
The equation can be solved as follows
[tex]0.5p-3.45=-1.2[/tex]
[tex]0.5p= -1.2+3.45[/tex]
[tex]0.5p= 2.25[/tex]
[tex]p= 2.25\div0.5[/tex]
[tex]p= 4.5[/tex]
Therefore, the value of p is 4.5.
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there are 75 people at the city swim park today. everyone in the park was wearing swim suits or sunglasses, some people had both. how many people had swim suits on but not sunglasses, if you know 63 people have swim suits on and 43 have sunglasses?
If you know 63 people have swim suits on and 43 have sunglasses, 32 people have swim suits on but not sunglasses.
To find out how many people have swim suits on but not sunglasses, we can use the principle of inclusion-exclusion.
We know that there are 75 people in the park, and 63 of them have swim suits on. We also know that 43 people have sunglasses. However, some people have both swim suits and sunglasses. Let's denote the number of people who have both by x. Then we can use the formula:
total = swim suits + sunglasses - both
Substituting in the given values, we get:
75 = 63 + 43 - x
Simplifying, we get:
x = 31
Therefore, 31 people have both swim suits and sunglasses, and the number of people who have swim suits on but not sunglasses is:
63 - 31 = 32
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1. Kendra owns a restaurant. She charges $1. 50 for 2 eggs and one piece of toast, and $. 90 for one egg
and one piece of toast. Determine how much she charges for each egg and each piece of toast
Kendra cost $0.60 for each egg and $0.30 for each piece of toast.
Let's assume that the cost of one egg is x and the cost of one piece of toast is y.
From the given information, we can set up two equations:
2x + y = 1.5
x + y = 0.9
We can solve this system of equations by either substitution or elimination method.
Using the elimination method, we can multiply the second equation by -2 to eliminate y:
-2x - 2y = -1.8
2x + y = 1.5
Adding these two equations, we get:
-1y = -0.3
y = 0.3
Substituting y = 0.3 in either of the two equations, we get:
x = 0.6
Therefore, Kendra charges $0.60 for each egg and $0.30 for each piece of toast.
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a certain positive integer has exactly 8 factors. two of these factors are 15 and 21. what is the sum of all eight factors?
The sum of all eight factors is 96
Let's express the integer as a product of its prime factors, in the form
n = p1^a1 × p2^a2 × ... × pn^an
where p1, p2, ..., pn are prime numbers and a1, a2, ..., an are positive integers.
We know that the integer has 8 factors, which means that its prime factorization must have the form:
n = p1^2 × p2^2 × p3^4
since (2+1) × (2+1) × (4+1) = 3 × 3 × 5 = 45, which is the total number of factors for this product.
We also know that 15 and 21 are factors of the integer, so they must be expressible in terms of the prime factors of n. We can write
15 = 3 × 5 = p1 × p2
21 = 3 × 7 = p1 × p3
From these expressions, we can see that p1 = 3, p2 = 5, and p3 = 7.
Therefore, the prime factorization of n is
n = 3^2 × 5^2 × 7^4
The eight factors of n are
1, 3, 5, 7, 9, 15, 21, and 35
Their sum is
1 + 3 + 5 + 7 + 9 + 15 + 21 + 35 = 96
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the probability that a dessert sold at a certain cafe contains chocolate is 86%. the probability that a dessert containing chocolate also contains nuts is 30%. find the probability that a dessert chosen at random contains nuts given that it contains chocolate. round to the nearest tenth of a percent.
The probability that a dessert chosen at random contains nuts given that it contains chocolate is 34.9%.
The likelihood of any event A happening when another event B related to A has already happened is known as conditional probability. This implies that the likelihood of event A relies on event B.
The conditional probability symbol is P(A|B). Conditional probability P(A|B) is crucial for any exam that is part of a competition. The concept of conditional probability P(A|B), formula, and examples with solutions are all covered in this article. The Bayes theorem predicts the likelihood that an event connected to any condition would occur. For the situation of conditional probability, this theorem is taken into account.
Let A : a certain cafe contains chocolates
B: a dessert contains Nuts
P(A) = 86% = 0.86
P(AB) = 30% = 0.3
[tex]P(B|A) =\frac{P(AB)}{P(A)}[/tex]
= 0.3/0.86
= 34.9 %
So the answer is 34.9%
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PLEASE HELP!
Write a function that models the situation: a $4000 deposit earns a 2% annual interest compounded semiannually after t years.
A = P(1 + r/n)^(nt)
Where:
A = the amount of money after t years
P = the principal amount (in this case, $4000)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year (in this case, twice a year, so n = 2)
t = the number of years
Plugging in the given values, we get:
A = 4000(1 + 0.02/2)^(2t)
Simplifying, we get:
A = 4000(1.01)^2t
Therefore, the function that models the situation is:
A = 4000(1.01)^(2t)
As shown below, Ghana makes a triangular decoration out of clay.
When she fires it in the kiln, it shrinks proportionally. If the base of the
finished decoration is only 9 inches after firing, what is the height, in inches,
of the finished decoration?
A
B
с
D
4
5
6
10 in.
8
15 in.
TIPS AND F
Check your answe
makes sense. Since
half of 15, the answ
more than half of 10
Answer:
Since the decoration is in the shape of a triangle, we can use the formula for the area of a triangle to solve for its height. The area of a triangle is given by:
Area = (1/2) x base x height
Let's call the height of the decoration h. We know that the base after firing is 9 inches, so we can plug in the given values and solve for h:
Area = (1/2) x 9 x h
Area = 4.5h
We don't know the exact area of the decoration, but we do know that the decoration maintains its shape after firing. This means that the ratio of the areas before and after firing is the same, and so is the ratio of the heights and bases. Since the height and base are proportional, we can write:
h / 15 = 9 / 10
Simplifying the equation, we get:
h = (9/10) x 15
h = 13.5
Therefore, the height of the finished decoration is 13.5 inches.
answers on a multiple choice test have choices a, b, c, d. the instructor has chosen answers randomly according to a discrete uniform distribution. what is the probability the first 3 questions have the same answer choice?
The probability that the first three questions have the same answer choice is 1/4, since there are four answer choices and the instructor is randomly selecting the answers according to a discrete uniform distribution. This means that each answer choice has an equal probability of being chosen. Therefore, the probability of all three questions having the same answer is 1/4.
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A four-sided figure is resized to create a scaled copy. The lengths of its four sides
change as in the table below.
Original Figure Scaled Copy
64
88
104
8
11
13
Find the constant of proportionality from the original figure
to the scaled copy. Express your answer as a fraction in
reduced terms.
1
The scale of proportionality is given as 8 from the table that you have presented
How to solve for the scale of proportionalityThe table here was not properly arranged in the question. I have done so below
64 88 104
8 11 13
lets say that 8p = 64
then p = 64 / 8
p = 8
we would have to determine if the value 8 when multiplied with scaled factor would be able to give us the original factor
8 * 11 = 88
8 * 13 = 104
Hence the scale of proportionality is given as 8
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The diagram below shows the dimensions
of a rectangular tabletop.
6 3/4 feet
3 feet
The wood to make the tabletop costs
$12.40 per square foot. What is the cost
of the tabletop?
A $232.50
B $243.00
© $251.10
D$260.40
The cost of the tabletop is $251.10. Option C
How to determine the costThe formula for calculating the area of a rectangle is expressed as;
Area = lw
Such that the parameters are;
l is the length of the rectangle.w is the width of the rectangle.From the diagram shown, we have;
The width = 6 3/4 feet = 27/4 feet
The length = 3 feet
Substitute the values
Area = 27/4 × 3
Multiply
Area = 20. 25 square feet
But;
1 square foot = $12.40
Then 20. 25 square feet = x
x = $251. 10
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evaluate the double integral. 8y2 da, d is the triangular region with vertices (0, 1), (1, 2), (4, 1) d
The value of the double integral is 128/27 - 32/9 + 8ln2/3. From triangular region with vertices (0, 1), (1, 2), (4, 1) d.
To evaluate the double integral, we first need to set up the limits of integration. Since the region D is a triangle, we can use the following limits:
0 ≤ x ≤ 1
1 + x ≤ y ≤ 4 - x
The integral then becomes:
∫0^1 ∫1+x^4-x 8y^2 dy dx
Evaluating the integral with respect to y first, we get:
∫0^1 ∫1+x^4-x 8y^2 dy dx = ∫0^1 [(8/3)(y^3)]1+x^4-x dx
= ∫0^1 [(8/3)(1+x^3)^3 - (8/3)(1+x^2)^3] dx
= 128/27 - 32/9 + 8ln2/3
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