If the room is 12'x20' with 8' ceilings and the tile costs $4.75 per square foot, the total cost is $1140.
To calculate the cost of replacing the tile in the kitchen, we need to first calculate the total area of the floor.
Area of the floor = Length x Width = 12 ft x 20 ft = 240 sq ft
Since we know the cost per square foot of tile, we can now multiply the total area of the floor by the cost per square foot to find the total cost:
Total cost = Area of the floor x Cost per square foot
Total cost = 240 sq ft x $4.75/sq ft
Total cost = $1140
Therefore, it will cost $1140 to replace the tile in the kitchen, assuming there are no additional costs such as labor or materials for removing the old tile.
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PLEASE HELP I'LL RATE 5 STARS
What is the value of this logarithmic expression?
Answer: 2
Step-by-step explanation:
We can simplify the given logarithmic expression using the logarithmic property that states:
log a base b - log c base b = log (a/c) base b
Using this property, we can rewrite the expression as follows:
log 16 base 2 - log 4 base 2 = log (16/4) base 2
Simplifying the numerator of the logarithm, we get:
log (16/4) base 2 = log 4 base 2
Now, we can evaluate the logarithm using the definition of logarithm, which states that:
log b base a = x if and only if a = b^x
In this case, we have:
log 4 base 2 = x if and only if 2^x = 4
We know that 2 raised to what power gives 4? It is 2, because 2^2 = 4.
Therefore, we have:
log 4 base 2 = 2
Hence, the value of the given logarithmic expression is 2.
Compare and contrast the direct write-off method and the allowance method for bad debts.
At a minimum, please consider the following in your answer:
When is the expense for uncollected accounts receivable recognized under each method?
Why is the direct write-off method not considered to follow generally accepted accounting
The direct write-off method and the allowance method are two different ways of accounting for uncollectible accounts receivable.
How do the direct write-off method and the allowance method compare ?The direct write-off method is a simple method of accounting for bad debts, where the uncollectible accounts receivable are written off as an expense at the time they are deemed uncollectible.
In contrast, the allowance method is a more complex method of accounting for bad debts, where the company estimates the amount of bad debt expense that it expects to incur over time and creates an allowance account to record this estimate.
The main difference between the two methods is the timing of the recognition of bad debt expense. Under the direct write-off method, bad debt expense is recognized only when an account is written off, whereas under the allowance method, bad debt expense is recognized in advance based on an estimate of the amount of bad debts.
The direct write-off method is not considered to follow generally accepted accounting principles (GAAP) because it violates the matching principle, which requires that expenses be matched with the revenues they generate in the same accounting period.
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The unknown triangle ABC has angle A=56∘ and sides a=32 and c=34. How many solutions are there for triangle ABC?
The value of angle B and C are 63° and 61° respectively.
What is sine rule?The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.
Therefore;
32/sin56 = 34/sinC
32sinC = 34sin56
32sinC = 28.187
divide both sides by 32
sinC = 28.187/32
sinC = 0.88
C = sin^-1(0.88)
C = 61°( nearest degree)
The sum of angle in a triangle is 180°
therefore, B = 180-(61+56)
B = 180-(117)
B = 63°
therefore the value of angle B and C are 63° and 61°.
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find the values of variables, then find the lengths of the sides of each quadrilateral
The variables are as follows:
x = 4
y = 4.8
The lengths of the sides of the kites are 4.5 and 6.8 units.
How to find the side of a kite?A kite is a quadrilateral with 2 pairs of consecutive congruent sides. The diagonals are perpendicular in a kite.
The non vertex angles are congruent.
Therefore,
x + 0.5 = 2x - 3.5
2x - x = 0.5 + 3.5
x = 4
y + 2 = 2y - 2.8
2y - y = 2 + 2.8
y = 4.8
Hence,
length of one pair = 4 + 0.5 = 4.5 units
length of the other pair = 4.8 + 2 = 6.8 units
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Max had 1 litre of syrup. He used 1/5 litre of the syrup on Saturday and 5/6 of the remaining syrup on Sunday. How many litres of syrup did Max have left?
Answer:
2/15 litre
Step-by-step explanation:
There is 1 litre in total. Max used 1/5 litre.
1 - 1/5 = 4/5 litre
Then he used 5/6 of the remaining 4/5 litre. He would have 1/6 of 4/5 litre left.
1/6 * 4/5 = 2/15 litre
or
You could do 5/6 * 4/5 to find out how much syrup he used on Sunday and then subtract that from 4/5 litre. It will give you the same answer
You pick a card at random. 2 3 4 What is P(prime)?
The probability of picking a prime number is 2/3 or approximately 0.667.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Out of the given options of 2, 3, and 4, only 2 and 3 are prime numbers. Therefore, the probability of picking a prime number is:
P(prime) = number of prime options / total number of options
P(prime) = 2/3
So the probability of picking a prime number is 2/3 or approximately 0.667.
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What are the asymptotes of the function? Check all that apply.
x = 0
x = 19,800
y = 0
y = 19,800
The horizontal asymptote of the given function is 0
Given the function y = 19800/x
Vertical asymptote occurs at when f(x) = 0 where;
f(x) is the denominator of the given function.
From the expression given: f(x) = x
Since f(x) => 0, hence x = 0
To get the horizontal asymptote, we will look at the degree of the numerator and denominator.
If the degree of numerator is less than the denominator,
the horizontal asymptote will be zero. From the function, we can see that the degree of the numerator is zero (being a constant) and that of the denominator is 1.
Since 0<1, hence the horizontal asymptote is 0
x = 0, y = 0
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Form a polynomial whose zeros and degree are given.
Zeros: 6, multiplicity 1; 3, multiplicity 2; degree 3
Type a polynomial with integer coefficients and a leading coefficient of 1 in the box below.
f(x) = (Simplify your answer.)
The polynomial with integer coefficients and a leading coefficient of 1 is (x-6) (x-3)² which in turn will be: f(x) = x³ - 12x² + 45x - 54
What is the polynomial?Based on the question, If the zeros of a polynomial are said to be 6, 3, and 3, one can say that the polynomial can be written in factored form such as
f(x) = (x - 6)(x - 3)(x - 3)
The to solve this, we have to multiply it:
f(x) = (x - 6) (x² - 6x + 9)
f(x) = x³ - 6x² + 9x - 6x² + 36x - 54
f(x) = x³ - 12x² + 45x - 54
Therefore, the polynomial with integer coefficients and a leading coefficient of 1 will be f(x) = x³ - 12x² + 45x - 54
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find the value of 5 1/10 minus 1 9/10
The value after solving mixed fraction is 32/10=3.2
What is fraction?A fraction is a metric unit for describing a piece or component of a whole. It represents the appropriate parts of the totality. A fraction is made up of two parts: the numerator and the denominator. The number at the top is the numerator, and the number at the bottom is the denominator. The numerator indicates the number of equal parts that were actually taken, whereas the denominator shows the total number of equal parts in the whole.
What is mixed fraction?The quotient and remainder of a fraction are used to represent it, making it a mixed fraction. For instance, 2 1/3, where 2 is the quotient and 1 is the remainder, is a mixed fraction. A mixed fraction is a combination of a whole number and a recognised fraction.
according to question,
=51/10 - 19/10
=32/10
=3.2
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The value of 5 1/10 minus 1 9/10 is 16/5 or 3 1/5.
What is mixed fraction?It is a mixed fraction when the remainder and quotient of a fraction are utilised to represent it. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. A whole number and a recognised fraction are combined to form a mixed fraction.
To subtract mixed numbers like 5 1/10 and 1 9/10, you need to convert them to improper fractions first.
5 1/10 can be converted to an improper fraction as follows:
5 1/10 = (5 x 10 + 1)/10 = 51/10
1 9/10 can be converted to an improper fraction as follows:
1 9/10 = (1 x 10 + 9)/10 = 19/10
Now we can subtract the two fractions:
51/10 - 19/10 = (51 - 19)/10 = 32/10
32/10 can be simplified to 16/5 by dividing both the numerator and denominator by the greatest common factor, which is 2.
So, the value of 5 1/10 minus 1 9/10 is 16/5 or 3 1/5.
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A psychologist is studying the self image of smokers, which she measures by the self-image (SI) score from
a personality inventory. She would like to estimate the mean SI score, μ, for the population of all smokers.
She plans to take a random sample of SI scores for smokers and estimate u via this sample. Assuming that
the standard deviation of SI scores for the population of all smokers is 82, what is the minimum sample size
needed for the psychologist to be 90% confident that her estimate is within 12 of µ?
Carry your intermediate computations to at least three decimal places. Write your answer as a whole number
(and make sure that it is the minimum whole number that satisfies the requirements).
Psychologist requires a sample size of at least 126 SI scores.
We may use the following calculation to get the minimal sample size required to estimate the mean SI score of smokers with a margin of error of 12 and a 90% confidence level:
[tex]n = [Z * (\sigma / E)]^2[/tex]
Where:
Z = the z-score associated with the confidence level (90%), which can be found using a z-score table or calculator.
For a 90% confidence level, Z is approximately 1.645.
σ = the population standard deviation (82)
E = the desired margin of error (12)
Plugging in the values, we get:
n = [1.645 * (82 / 12)]^2
n = 126.2
We round up to the closest integer as the sample size must be a whole number in order to guarantee that the sample size is sufficient to fulfill the required confidence level and margin of error.
Thus, n = 126 is the required minimum sample size.
In order to estimate the mean SI score of smokers with 90% confidence that the estimate is within 12 of the actual population mean, the psychologist requires a sample size of at least 126 SI scores.
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Consumer Price Index, 1970-2002
Year
1970
1975
1980
1985
1990
1995
2002
Source: World Almanac 2003
CPI
116.3
161.2
248.8
322.2
391.4
456.5
535.8
Describe how the CPI is related to the year.
As the year increases, the CPI decreases and then increases.
As the year increases, the CPI increases and then decreases.
As the year increases, the CPI decreases.
d. As the year increases, the CPI increases.
C.
a.
b.
The computation of the increased in salary is $500.
Here, we have,
Explanation:
Data provided in the question
Salary for the first year = $50,000
CPI increase during the year = 4%
Overstated inflation = 1% i.e. 5%
The computation of the increased in salary is shown below:
= Salary of the first year × inflation rate - salary of the first year × CPI increase during the year
= $50,000 × 5% - $50,000 × 4%
= $2,500 - $2,000
= $500
Hence, The computation of the increased in salary is $500.
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complete question:
Mark's wage contract specifies a $50,000 salary for the first year, and specifies a salary increase equal to the percentage increase in the CPI during the second year. The increase in the CPI during the year was 4.0%. If the CPI overstates inflation by 1.0% (that is, the actual price increase was 3% and not 4%), at the end of the first year Mark's salary increased by $________ more than it would have without the upward bias.
Find the values of a and b such that
x²-x+ 5 = (x-a)² + b
Please, the person that explains it explain it with the part of
(x+b/2)^2 - (b/2)^2 + c
-because if not I won’t understand :)
x2−1x5=(x−a)2+b2−15=(−)2+
Find the area of the regular polygon
Round to nearest tenth
On solving the provided question we can say that area of the polygon is 24 cm sq.
What is quadrilateral?A four-sided polygon having four edges and four corners is referred to as a quadrilateral. The word is derived from the Latin words quadri and latus, both of which imply "side". An object with a rectangle's four sides, four vertices, and four corners is a two-dimensional shape. There are essentially two sorts of concave and convex surfaces. Convex quadrilaterals also include the subclasses of trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up the two-dimensional shape of a rectangle. There are many different shapes for quadrilaterals, such as parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.
Area of this polygon is -
A = 1/2 * 6* 8
A = 24 cm sq.
Hence, area of the polygon is 24 cm sq.
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The medians of Jill are jn, Jn, and lm. They meet at a single point q. Suppose qp = 11, qm= 10, and jn = 39. Find the following lengths: lm, jq, kq
The lengths we found are:
LM = 20
JQ = 26
KQ = 800 / 117
Let's call the length of the median from vertex J to the opposite side LM, and the length of the median from vertex L to the opposite side JN. We can use the fact that the centroid divides each median into two parts, with the ratio of the longer part to the shorter part being 2:1.
First, we can find LM:
LM = 2 x QM = 2 x 10 = 20
Next, we can find JQ:
JQ = 2/3 x JN = 2/3 x 39 = 26
Finally, we can find KQ:
To find KQ, we need to use the fact that the three medians of a triangle divide each other into six smaller triangles with equal areas. Let's call the length of the third median KX. We know that the area of triangle JLK is:
1/2 x LM x JN = 1/2 x 20 x 39 = 390
Similarly, the areas of triangles JNQ, LMQ, JKP, LKP, and JLP are all equal to 390. Let's call this common area A. Then we have:
1/2 x KX x LM = A
1/2 x KX x JN = A
Dividing these two equations, we get:
LM / JN = KX / LM
Substituting the values we know, we get:
20 / 39 = KX / 20
Solving for KX, we get:
KX = 20 x (20 / 39) = 400 / 39
Now we can find KQ:
KQ = 2/3 x KX = 2/3 x (400 / 39) = 800 / 117
Therefore, the lengths we found are:
LM = 20
JQ = 26
KQ = 800 / 117
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the product of a number and 6 less than the number is 27. find the number
Answer:
Let's call the unknown number "x". According to the problem, we know that:
x * (x - 6) = 27
Expanding the left side of the equation, we get:
x^2 - 6x = 27
Subtracting 27 from both sides, we get:
x^2 - 6x - 27 = 0
Now we can use the quadratic formula to solve for x:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
In this case, a = 1, b = -6, and c = -27, so:
x = (-(-6) ± sqrt((-6)^2 - 4(1)(-27))) / 2(1)
x = (6 ± sqrt(180)) / 2
x = (6 ± 6sqrt(5)) / 2
x = 3 ± 3sqrt(5)
So the two possible solutions are:
x = 3 + 3sqrt(5) ≈ 8.746
x = 3 - 3sqrt(5) ≈ -2.746
Since the problem statement doesn't specify whether the number should be positive or not, both solutions are valid.
Answer: The answer could be 9 or -3.
Step-by-step explanation: The product(multiply) of a number(x) and 6 less than a number(x-6) is 27.
x(x-6)=27
x^2-6x-27=0
(x-9) (x+3)=0
x=9 or x=-3
The number is 9 or -3.
I need help pleaseeee
The result of the carrying out the operation, Add -4(row 1) to row 3, on the given matrix is:
[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]
Reducing matricesFrom the question, we are to perform the given row operation on the given matrix
The given matrix is:
[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\4&-1&6&-8\end{array}\right][/tex]
The operation we are to carry out is:
Add -4(row 1) to row 3
This essentially means we should multiply the first row (row 1) by -4. Then, we will add each of the elements from the results to the corresponding elements on the third row
Multiplying by -4
-4 × [ 1 2 1 | -5
-4 -8 -4 | 20
Now, we will add the result from the multiplication to the corresponding elements in row 3
4 -1 6 | -8
+ -4 -8 -4 | 20
------------------------
0 -9 2 | 12
Hence,
The resulting matrix becomes
[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]
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Claim: A majority of adults would erase all of their personal information online if they could. A software firm survey of 498 randomly selected adults showed that 62% of them would erase all of their
personal information online if they could. Complete parts (a) and (b) below.
a. Express the original claim in symbolic form. Let the parameter represent the adults that would erase their personal information.
(Type an integer or a decimal. Do not round.)
Find the volume?? Of the triangular prism
Answer:
216 mi^3
Step-by-step explanation:
First of all you need to find the area of the base (or top, they are the same)
It is a right-angled triangle, you can simply calculate the area of the base by
A = 6*8/2 = 24 mi^2
The volume of prism is (base area)*height
volume = 24*9 = 216 mi^3
10 is redundant anyway
Answer: the volume of the prism is 62.35 mi cube
Step-by-step explanation:
so first we will find the area of triangular base of the prism, using heron formula.
and s(semi-perimeter)= a+b+c/2= 6+8+10/2= 24/2=12
Area of triangle= A = sqrt [s(s-a)(s-b)(s-c)] = sqrt {12*(12-6)(12-8)(12-10)} = sqrt {6*4*2} = sqrt (48)= 6.92 mi square
Volume = Area x Height
V= 6.92 x 9 = 62.35 mi cube.
Identify the line that appears tangent to circle O and includes point B.
Answer:
D. Line O
Step-by-step explanation:
We can simply tell which one it is by looking at the picture. A tangent line is a line that intersects at one point only. Line L doesn't even touch the circle. Line M and N touch the circle in more than one place. If we look at O, we can see that it is "scraping" the edge of the circle, which is what pretty much every tangent line looks like.
Therefore, the answer is D.
rewrite this non-statistical question as a statistical question. How much does the teacher make? PLEASE HELP ME
A statistical question would be: What is the average salary of teachers in this school district?
What is a statistical question?When a question can be answered statistically, it can be done so by gathering and analysing data, for example. This particular question aims to comprehend a population or a phenomenon by using numerical data. In contrast to non-statistical questions, which are more concerned with acquiring information or opinions, statistical questions are more concerned with getting and analysing data. Statistical procedures including sampling, data analysis, and inference are frequently used to answer statistical issues.
A statistical question would be: What is the average salary of teachers in this school district?
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What is the area of a circle with diameter of 16 meters? Leave the answer in terms of pi
Answer:
64π
Step-by-step explanation:
Use the formula for an area of a circle
[tex]A = \pi r^2[/tex]
Half of 16 is 8.
8*8 = 64.
The area of a circle with a diameter of 16 meters is equal to 64π or 200.96 square meters.
How to calculate the area of a circle?Mathematically, the area of a circle can be calculated by using this formula:
[tex]\text{Area} = \pi \text{r}^2[/tex]
Where:
[tex]\text{r}[/tex] represents the radius of a circle.
[tex]\text{Note:} \ \text{Radius} = \dfrac{\text{diameter}}{2} = \dfrac{16}{2} = 8 \ \text{meters}.[/tex]
By substituting the radius into the formula for the area of a circle, we have the following;
[tex]\text{Area of circle} = \pi \times 8^2[/tex]
[tex]\bold{Area} \ \text{of circle} = 64\pi \ \text{or} \ 200.96[/tex] square meters.
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Please help. I'm so confused
i need help on problems 5-11
A scatter plot would be an appropriate data display to show the relationship between the speed of the vehicle and the number of accidents.
Why is a scatter plot appropriate for showing the relationship between speed and accidents?A scatter plot is a graphical representation of two continuous variables, where data points are plotted on a Cartesian coordinate system. The horizontal axis can represent the speed of the vehicle, while the vertical axis can represent the number of accidents. Each data point on the scatter plot would represent a specific observation of speed and the corresponding number of accidents.
By using a scatter plot, the EMT can visually display how changes in vehicle speed are related to the number of accidents. Scatter plots are effective for identifying trends, patterns, and outliers in data, making them suitable for illustrating the relationship between two continuous variables.
Answered question "An EMT wants to use a data display to show students the relationship between the speed of the vehicle and the number of accidents. Choose an appropriate data display for the situation. Explain your reasoning"
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Question 7 (3 points)
The graph and table below represent the constant rate for the amount of time it takes for a given
number of gallons of water to flow from a hose.
a. Find the rate of both the graph and table. Be sure to show all work.
b. Which one has the greater rate? Explain how you know.
The rate of water flow is 6 gallons per unit of time.
What is slope?
Slope is a measure of the steepness of a line. It is defined as the change in y-coordinate divided by the change in x-coordinate between any two points on the line.
a. To find the rate, we need to calculate the amount of water that flows per unit of time.
Method 1: Using the Graph
First, we can plot the points (5,30), (7,42), and (10,60) on a graph and connect them with a line.
From the graph, we can see that the line passes through the points (5,30) and (10,60), which means that the change in y-values is 60 - 30 = 30, and the change in x-values is 10 - 5 = 5.
So, the slope of the line is:
slope = change in y-values / change in x-values
= (60 - 30) / (10 - 5)
= 6
Therefore, the rate of water flow is 6 gallons per unit of time.
Method 2: Using the Table
We can also find the rate by calculating the differences in y-values and x-values in the table.
x y Difference in y Difference in x Rate (y/x)
-------------------------------------------------------
5 30 - - -
7 42 12 2 6
10 60 18 3 6
From the table, we can see that the rate of water flow is 6 gallons per unit of time.
b. Both the graph and table have the same rate of 6 gallons per unit of time. We know this because we calculated the rate using both methods, and they gave us the same result.
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Find the volume of a composite solid with a radius of 6 and a height of 12
The volume of the composite solid is 452. 160 ft³
How to determine the volumeFirst, it is important to note that the formula for calculating the volume of a cone is expressed as;
V = πr²h/3
Such that the parameters of the formula are;
V is the volumer is the radius of the cone.h is the height of the cone.From the information given,
substitute the values
Volume = 3.14 × 6² × 12/3
Divide the values
Volume = 31.4 × 36 × 4
Multiply the values
Volume = 452. 160 ft³
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please help. I don't quite understand this. Approximate the area under the function between a and b using a right-hand sum with the given number of intervals
Using a right-hand sum with three intervals, the approximate area under the curve of the function f(x) = x³ between the limits of integration a=0 and b=3 is 36 square units.
What is function?Numbers and their variants, equations and related structures, forms and their arrangements, and the places where they might be found are all topics covered in mathematics. The term "function" describes the relationship between a collection of inputs, each of which has a corresponding output.
To estimate the area under the curve of the function f(x) = x3 between the limits of integration a=0 and b=3, we must divide the interval [0, 3] into three subintervals of equal width.
Each subinterval's width, x, may be calculated as follows:
Δx = (b - a) / n = (3 - 0) / 3 = 1
So, the three subintervals are:
[0, 1], [1, 2], [2, 3]
To compute the right-hand total, we evaluate the function at each subinterval's right endpoint and multiply it by the breadth of the subinterval. Then we add these products together to calculate the area under the curve. The right-hand sum may be stated mathematically as follows:
RH = Δx * [f(1) + f(2) + f(3)]
where x represents the width of each subinterval, f(x) = x3 represents the function we are integrating, and f(i) represents the function's value at the right endpoint of the i-th subinterval.
RH = 1 * [f(1) + f(2) + f(3)]
= 1 * [(1³) + (2³) + (3³)]
= 1 * [1 + 8 + 27]
= 36
Using a right-hand sum with three intervals, the approximate area under the curve of the function f(x) = x³ between the limits of integration a=0 and b=3 is 36 square units.
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what's the answer(s) I have no idea how to do this pleaseeeeee
i need answer asap my computer about to die
The answer of the given question based on the graph coordinate is , the rule for the values in the table is: Y = 7X - 0.
What is Coordinate?In mathematics, a coordinate is a set of values that specifies the position of a point in space. Coordinates are used to locate points, lines, and other geometric objects in a plane, a three-dimensional space, or even higher dimensions.
X Y
5 35
1 7
4 28
2 14
One possible way to do this is to calculate the differences between successive pairs of X and Y values, and then see if there is a constant difference or ratio between them.
Taking the first two rows as an example, we have:
X Y
5 35
1 7
The difference between the X values is 5 - 1 = 4, and the difference between the Y values is 35 - 7 = 28. Dividing the difference in Y by the difference in X gives us:
(35 - 7) / (5 - 1) = 28 / 4 = 7
This means that for every increase of 1 in X, the corresponding increase in Y is 7. We can check this for the other pairs of values in the table and see that it holds true:
X Y
5 35
4 28 (decrease of 1 in X, decrease of 7 in Y)
2 14 (decrease of 2 in X, decrease of 14 in Y)
So the rule for the values in the table is:
Y = 7X - 0.
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In ΔFGH, f= 67 inches, m∠G=66° and m∠H=30°. Find the length of g to the nearest inch
Answer:
38 inches
Step-by-step explanation:
We can use the Law of Sines to solve for the length of side g:
sin(66°)/67 = sin(30°)/g
Cross-multiplying, we get:
g*sin(66°) = 67*sin(30°)
Dividing both sides by sin(66°), we get:
g = 67*sin(30°)/sin(66°) ≈ 38 inches (rounded to the nearest inch)
Therefore, the length of side g is approximately 38 inches.
Q11: Triangle D has been dilated to create triangle D′. Use the image to answer the question.
image of a triangle labeled D with side lengths of 18, 24, and 30 and a second triangle labeled D prime with side lengths of 6, 8, and 10
Determine the scale factor used.
Scale factor of one third
Scale factor of 3
Scale factor of 4
Scale factor of one fourth
the scale factor used in the dilation of triangle D to create triangle D' is one-third. This means that every length in triangle D' is one-third the length of the corresponding length in triangle D.
How to solve the question?
To determine the scale factor used in the dilation of triangle D to create triangle D', we need to compare the corresponding sides of both triangles. The corresponding sides of two similar triangles are proportional, meaning that they have the same ratio.
In this case, we can see that the length of every side of triangle D' is one-third the length of the corresponding side of triangle D. For example, the length of the shortest side of triangle D is 18, while the length of the shortest side of triangle D' is 6. Similarly, the length of the longest side of triangle D is 30, while the length of the longest side of triangle D' is 10.
We can use this information to find the scale factor by dividing the length of any side of triangle D' by the length of the corresponding side of triangle D. Let's choose the shortest side for this calculation:
scale factor = length of corresponding side in D' / length of corresponding side in D
scale factor = 6 / 18
scale factor = 1/3
Therefore, the scale factor used in the dilation of triangle D to create triangle D' is one-third. This means that every length in triangle D' is one-third the length of the corresponding length in triangle D.
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Random sample of 250 students taken with a population of 7500 surveyed about their majors. In the sample, 75 students were Art majors. How many students in total population are are Art majors?
Therefore, we estimate that there are 2250 Art majors in the total population.
What is proportion?In mathematics, a proportion is an equation that states that two ratios are equal. A ratio is a comparison of two quantities expressed as a fraction or a decimal. Since both sides of the equation are equal, the proportion is true. Proportions are used in many mathematical and real-world contexts, such as in geometry, finance, and statistics. They are useful for comparing and scaling quantities, and for solving problems involving unknown quantities or variables.
Here,
We can use proportions to estimate the total number of Art majors in the population based on the proportion of Art majors in the sample.
The proportion of Art majors in the sample is:
75/250 = 0.3
We can assume that this proportion is representative of the proportion of Art majors in the population.
So, if x is the total number of Art majors in the population, then we can set up the following proportion:
0.3 = x/7500
To solve for x, we can cross-multiply and simplify:
0.3 * 7500 = x
x = 2250
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