Yes, the production manager should be concerned about production rate variations. Based on the data provided, the standard deviation of the daily production rate of fiberglass boats from Dhaka Glass is 4.6 boats, which is higher than the threshold of 3 boats a day set by the production manager. This indicates that there are significant variations in the production rate of fiberglass boats, which should be a cause for concern.
To further explain, the standard deviation measures the spread of a set of data. In this case, the data provided shows that the daily production rate of fiberglass boats can vary from 17 to 32 boats a day. The large standard deviation of 4.6 boats suggests that the daily production rate can vary significantly from the average, and this can lead to instability in production.
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4/5x + 3 =7
What is x?
Answer: 5
Step-by-step explanation:
To solve 4/5x + 3 = 7 for x, we must isolate x on one side of the problem.
To begin, remove 3 from both sides to get:
4/5x = 4
Hence, we can multiply both sides by 5/4 to isolate x:
x = 5
As a result, the answer to the equation 4/5x + 3 = 7 is x = 5.
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In 2010, bachelor's degrees conferred by colleges and universities in the United States were 1.2 million. In 2020, the number of bachelor's degrees awarded was 1.7 million.
Assume that the relationship between time and degree conferred is linear.
(a) Find an equation describing the number N bachelor's degrees awarded t years after 2010
(b) If the trend continues, estimate the number of bachelor's degrees to be awarded in 2023.
(c) Write a practical sentence expressing how the number of bachelor's degrees awarded changes yearly.
(d) Graph the number of bachelor's degree line over the time period stated in (a)
The equation that describe the number N bachelor's degrees awarded is N = 0.05t + 1.2 (a). The estimated number of bachelor's degrees to be awarded in 2023 is 1.85 million (b).
The practical sentence is "The number of bachelor's degrees awarded increases by 0.05 million, or 50,000, each year." (c). The graph, see the attachment.
The Explanation to Each Answer(a) To find the equation describing the number N of bachelor's degrees awarded t years after 2010, we can use the formula for a linear equation: N = mt + b, where m is the slope and b is the y-intercept.
We can find the slope by using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line. In this case, the two points are (2010, 1.2 million) and (2020, 1.7 million).
The y-intercept is the value of N when t = 0, which is the number of bachelor's degrees awarded in 2010, or 1.2 million. So the equation is:
N = 0.05t + 1.2(b) To estimate the number of bachelor's degrees to be awarded in 2023, we can plug in the value of t = 2023 - 2010 = 13 into the equation:
N = 0.05(13) + 1.2N = 0.65 + 1.2N = 1.85 millionSo the estimated number of bachelor's degrees to be awarded in 2023 is 1.85 million.
(c) A practical sentence expressing how the number of bachelor's degrees awarded changes yearly is: "The number of bachelor's degrees awarded increases by 0.05 million, or 50,000, each year."
(d) To graph the number of bachelor's degree line over the time period stated in (a), we can plot the two points (2010, 1.2) and (2020, 1.7) and draw a line through them.
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Which expression uses the commutative property to make it easier to evaluate (-3/4)x1/5x(-16)?
A. (-3/4)x(-16)x1/5
B. (-16)x1/5x(-3/4)
C. (-3/4)x5/1x(-16)
D. (4/3)x(-16)x1/5
The expression which uses the commutative property to make it easier to evaluate (-3/4)x1/5x(-16) is (-3/4)x(-16)x1/5) which is therefore denoted as option A.
What is Commutative property?
This states that the change in the order of two numbers in an addition or multiplication operation does not change the sum or the product.
In the expression (-3/4)x1/5x(-16) , there is the need to arrange them so as to make it easier for them to be reduced to their lowest factor which is why -16 was put close to the (-3/4).
(-3/4)x(-16)x1/5 = 12 × 1/5 = 12/5
This is therefore the reason why option A was chosen as the correct choice.
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What would be the answer to this?
Please help I'll mark brainliest !
Answer:
x = -3 to x = 2
Step-by-step explanation:
The function is decreasing where the slope is negative, seen when the y-values decrease as the x-values increase. Your answer is correct.
Answer:
X is - 3 to x is 2
Step-by-step explanation:
Look at the x axis, the point where the curve slopes down is the decreasing point
Where x is - 3 is a peak point, it begins to slope from there and rises when x is 3
5. Martin is a telemarketer and receives $75 every day he works. He make a baseline of 35 calls (c) every hour. For every call he makes over 35 in one hour, Martin receives a bonus of $5.50 per call. Martin works for 4 hours every day and makes the same number of calls every hour. Write a function to express the total amount of money Martin will make as a function of the number of calls he makes. If Martin makes a total of 45 calls every hour, how much money will Martin make for the day?
Answer: The function to express the total amount of money Martin will make as a function of the number of calls he makes is:
Total Money = (Number of hours worked x Base pay per hour) + (Bonus pay per hour x Number of bonus calls)
Where:
Number of hours worked = 4
Base pay per hour = $75 / 4 = $18.75 (since he works for 4 hours every day and receives $75)
Bonus pay per hour = ($5.50 x (Number of bonus calls)) / 4 (since he works for 4 hours every day and receives a bonus of $5.50 per call over 35 in one hour, which is equivalent to $5.50 / 4 per call)
Number of bonus calls = (Total calls - (Number of hours worked x Baseline calls per hour))
Using this formula, we can calculate how much money Martin will make for the day if he makes a total of 45 calls every hour:
Number of bonus calls = (45 - (4 x 35)) = 5
Bonus pay per hour = ($5.50 x 5) / 4 = $6.875
Total Money = (4 x $18.75) + (4 x $6.875) = $75 + $27.50 = $102.50
Therefore, if Martin makes a total of 45 calls every hour, he will make $102.50 for the day.
Step-by-step explanation:
Properties of Rhombi/Rhombus
Please show your work !
The properties of Rhombus are:
Opposite angles are equalConsecutive anglesDiagonals bisect each otherDiagonals are perpendicularSymmetryAreaPerimeterExplain about parallelogram ?
A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length and parallel to each other. The opposite angles are also equal in measure.
Properties of a parallelogram:
Opposite sides are parallel.
Opposite sides are equal in length.
Opposite angles are equal in measure.
Consecutive angles are supplementary, i.e. their sum is 180 degrees.
Diagonals bisect each other.
Given by the question:
A rhombus, also called a diamond, is a type of parallelogram in which all four sides are equal in length. A rhombus also has the following properties:
Opposite angles are equal: The opposite angles of a rhombus are equal in measure. This means that if angle A is equal to angle C, and angle B is equal to angle D.Consecutive angles are supplementary: The consecutive angles of a rhombus are supplementary, meaning they add up to 180 degrees. For example, if angle A is equal to 80 degrees, then angle B is equal to 100 degrees.Diagonals bisect each other: The diagonals of a rhombus bisect each other at right angles, dividing the rhombus into four congruent right triangles. In other words, the line segment connecting the midpoint of one side to the midpoint of an adjacent side is perpendicular to the line segment connecting the midpoints of the other two sides.Diagonals are perpendicular: The diagonals of a rhombus are perpendicular bisectors of each other, meaning they cut each other at right angles.Symmetry: A rhombus has two lines of symmetry that run through the opposite vertices and bisect the opposite sides.Area: The area of a rhombus can be found by multiplying the length of one diagonal by the length of the other diagonal and dividing by 2. That is, Area = (d1 x d2)/2, where d1 and d2 are the lengths of the diagonals.Perimeter: The perimeter of a rhombus is equal to four times the length of one of its sides. That is, Perimeter = 4s, where s is the length of one side.To know more about parallelogram visit:
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Collins Middle School has 228 sixth grade students. If the sixth grade is 30% of the total school, how many students are in the middle school?
Answer:
760 students
Step-by-step explanation:
divide 228 ÷ 30%
30% = 0.30
228 ÷ 0.30 = 760
A deli owner has room for 65 containers of shredded Parmesan cheese. He has 5-oz and 10-oz containers, and a total of 400 oz of cheese. If 5-oz containers sell for $7 and 10-oz containers sell for $13, how many of each should he sell to maximize his revenue? What is his maximum revenue?
He should sell 50 5-oz containers and 15 10-oz containers to maximize his revenue.
What is cοntainer?A cοntainer is a standard unit οf sοftware that packages up cοde and all its dependencies sο the applicatiοn runs quickly and reliably frοm οne cοmputing envirοnment tο anοther. Cοntainers are a sοlutiοn tο the prοblem οf hοw tο get sοftware tο run reliably when mοved frοm οne cοmputing envirοnment tο anοther. This cοuld be frοm a develοper’s laptοp tο a test envirοnment, frοm a staging envirοnment intο prοductiοn, and perhaps frοm a physical machine in a data center tο a virtual machine in a private οr public clοud.
Corner point (x, y) Value of 8x+14y
0(0,0) 0
A(65,0) 520
B(50, 15) 610
C(0,40) 560
So, the maximum value is 610
Therefore, the maximum point is B(50, 15)
∴ x = 50, y = 15
So, the maximum value is
Therefore, the maximum point is
Hence, he should sell 50 5-oz containers and 15 10-oz containers to maximize his revenue.
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1. the variance for the following distribution of ungrouped
data to its right is:
a. 0.79 b. 2.01 c. 0.89 d.2.45
Dato (x) Frecuensia
3.2 3
1.3 4
2.4 2 2. the variance for the following distribution of ungrouped
data to its right is:
A.8.00
b. 65.60
c. 7.81
d. 62.57
edad (x) frecuencia (f) xf x^2 f
6 7 42 252
7 12 84 588
8 10 80 640
9 8 72 648
10 5 50 500
Total 42 328 2628
The correct answer is c. 7.81.
To find the variance for the distribution of ungrouped data, we need to use the formula:
Variance = (Σ(x^2)f - (Σxf)^2 / n) / n
Where x is the data value, f is the frequency of the data value, and n is the total number of data values.
For the first question:
1. The variance for the following distribution of ungrouped data to its right is:
Dato (x) Frecuencia (f) xf x^2f
3.2 3 9.6 30.72
1.3 4 5.2 6.76
2.4 2 4.8 11.52
Total 9 19.6 49
Variance = (49 - (19.6)^2 / 9) / 9
Variance = (49 - 42.46) / 9
Variance = 0.73
Therefore, the correct answer is a. 0.79.
For the second question:
2. The variance for the following distribution of ungrouped data to its right is:
Edad (x) Frecuencia (f) xf x^2f
6 7 42 252
7 12 84 588
8 10 80 640
9 8 72 648
10 5 50 500
Total 42 328 2628
Variance = (2628 - (328)^2 / 42) / 42
Variance = (2628 - 2570.29) / 42
Variance = 1.38
Therefore, the correct answer is c. 7.81.
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Question 16(Multiple Choice Worth 3 points)
(01.04 MC)
A forensics expert analyzes the ink of handwriting on a piece of paper. The ink has yellow, red, and blue pigments in it. The size of ink particles is measured in
nanometers (nm). Here is a chart of the size of each molecule: image below
If the forensics expert performs chromatography on the ink sample, in what order from the bottom to the top would the ink pigments appear on the chromatography
paper?
O Red, blue, yellow
O Blue, red, yellow
O Yellow, blue, red
O They will all be on the same line.
The order of the colors is Red, blue, yellow
What is chromatography?
Chromatography is a laboratory technique used to separate and analyze mixtures of different compounds based on their physical and chemical properties. It involves passing a mixture through a stationary phase, which may be a solid or a liquid, and a mobile phase, which may be a liquid or a gas.
As the mixture passes through the stationary phase, the different compounds in the mixture interact with the stationary phase to varying degrees, causing them to separate. The mobile phase carries the separated components through the stationary phase, and the separated components are detected and analyzed using a detector, such as a spectrophotometer.
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A city will soon be voting on a bond issue which will provide the necessary funds for a new middle school. The school board wants to know how likely it is that the bond issue will pass. They randomly sample three groups of 200 people and ask each person whether they are for or against the bond issue. The results are recorded in the table below.
For Against
Sample #1 221 79
Sample #2 114 186
Sample #3 210 90
Based on the collected data, do you think the bond issue will pass or fail? How confident are you? Explain your reasoning using complete sentences.
Using the mean of the samples, approximately how many of the 16,000 voters would you expect to vote against the bond issue?
Approximately 11,800 of the 16,000 voters would be expected to vote against the bond issue.
What is data in math?Data in math is information that can be quantified and organized. It can include numeric values, words, dates, and other types of data. Data is used to analyze relationships and make predictions. Data can be used to create charts, graphs, and tables that display trends, patterns, and relationships. Data can also be used to inform decisions and help solve problems.
Based on the collected data, it is likely that the bond issue will pass. Out of the three samples, only one showed a majority of people against the bond issue, and the other two samples showed a majority of people in favor. This indicates that there is a strong likelihood of the bond issue passing. I am confident in this assessment because the samples are representative of the same population, and there is a clear majority of people in favor of the bond issue.
Using the mean of the samples, approximately 11,800 of the 16,000 voters would be expected to vote against the bond issue.
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Solve :-7x-6y=4
When x=-3y+8
Kareem has 216 role playing game cards.His goal is to collect all 15 sets of cards.There are 72 cards in a set.How many more cards does Kareem need to reach his goal?
Answer:
864 cards
Step-by-step explanation:
Goal: 15 set of cards
*72 cards in a set*
15 x 72 = 1080
15 sets of cards = 1080 cards in total
However Kareem so far has 216 cards.
To find out how much more cards Kareem need to reach his goal, you do the following:
1080 - 216 = 864
Kareem needs 864 more cards to reach his goal.
hope this helped....
Mr. Lucy has 10 1/4 feet of rope. If he needs 1/8 OF the rope
for a project, how many feet of rope will he use?
The amount of rope used by Mr.Lucy is given by equation A = 1.28125 feet of rope
What do you mean by an Equation?Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.
It displays the similarity of the connections between the phrases on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are examples of the parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.
Given data ,
Let the amount of rope used be represented as A
Now , the equation will be
The total amount of feet of rope Mr.Lucy has = 10 1/4 feet
So , total amount of feet of rope Mr.Lucy has = 10.25 feet
Now , the amount of rope used = ( 1/8 ) of the total amount
On simplifying , we get
The amount of rope used A = ( 1/8 ) x 10.25 feet
The amount of rope used A = ( 41 / 32 ) feet
The amount of rope used A = 1 9/32 feet
The amount of rope used A = 1.28125 feet of rope
Hence , the amount of rope used is A = 1.28125 feet of rope
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HELPPPPPP DUE TONIGHTTT
The scatter plot shows the number of hours worked, x, and the amount of money spent on entertainment, y, by each of 23 students.
(a) Write an approximate equation of the line of best fit for the data. It doesn't have to be the exact line of best fit.
(b) Using your equation from part (a), predict the money spent on entertainment for a student who works 10 hours.
Note that you can use the graphing tools to help you approximate the line.
Answer:
Step-by-step explanation:
A is y=x+4
b is y=14
6a +5a + 1 =12
What is a?
Answer:
a = 1
Step-by-step explanation:
6a + 5a + 1 = 12
Subtract one to both side leaving a by itself.
6a + 5a = 12 - 1
Now simply by add or subtracting, multiply or dividing.
11a = 11
Divide 11 to both side leaving a = ?
a = 1
Answer:
a= 1
Step-by-step explanation:
6a + 5a + 1 = 12
(-1) + 6a + 5a +1 = 12 -1
6a + 5a = 11
11a = 11
11a/11 = 11/11
a= 1
Find the total surface area of a large round bowl (hollow hemisphere) with outer radius of 12 cm and thickness of 1 cm. 1cm 12cm
The total surface area of the hollow hemisphere is 1736.4 cm²
The total surface area of a large round bowl (hollow hemisphere) can be calculated by finding the surface area of the outer hemisphere and the surface area of the inner hemisphere and area of the ring and adding them together.
The formula for the surface area of a hemisphere is 2πr^2, where r is the radius of the hemisphere.
The outer radius of the bowl is 12 cm, so the surface area of the outer hemisphere is:
Surface area of outer hemisphere = 2π(12)^2 = 2π(144) = 288π
The inner radius of the bowl is the outer radius minus the thickness, which is 12 - 1 = 11 cm. So the surface area of the inner hemisphere is:
Surface area of inner hemisphere = 2π(11)^2 = 2π(121) = 242π
area of the concentric circle joining the outer surface and inner surface is π(12²-11²)= 23π
The total surface area of the bowl is the sum of the surface area of the outer hemisphere and the surface area of the inner hemisphere:
Total surface area = 288π + 242π + 23π = 553π
So the total surface area of the bowl is 530π cm^2.
then we can use the approximation π ≈ 3.14 to find the total surface area:
Total surface area ≈ 553*(3.14) ≈ 1736.4 cm^2
So the total surface area of the bowl is approximately 1736.4 cm^2.
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The length of an arc RV of circle M with a radius of 6 units is 3pi/2 units. What is the approximate measure of angle RMV?
the options are
A- 15
B- 45
C-66
D-231
Answer:
The formula for the length of an arc of a circle is given by:
length of arc = (central angle/360) x 2πr
where r is the radius of the circle and the central angle is measured in degrees.
In this problem, we know the length of arc RV is 3π/2 units and the radius of circle M is 6 units. Therefore, we can solve for the central angle using the formula above:
3π/2 = (central angle/360) x 2π(6)
3π/2 = (central angle/180) x π x 6
3/2 = (central angle/180) x 6
central angle = (3/2) x (180/6) = 45 degrees
So the approximate measure of angle RMV is 45 degrees, which corresponds to option B.
Problem \# 6: Let R^4 have the Euclidean inner product. Find a unit vector with a positive first component that is orthogonal to all three of the following vectors. u = (1,-1, 7, 0) ; v=(8,1,0,1) ; w=(1,0,6,1)
Problem \#6: Enter your answer symbolically, as in these Enter the four components of your vector, separated with commas.
To find a unit vector with a positive first component that is orthogonal to all three of the given vectors, we need to find a vector x = (x1, x2, x3, x4) that satisfies the following equations:
= 0
= 0
= 0
This means that:
x1 - x2 + 7x3 = 0
8x1 + x2 + x4 = 0
x1 + 6x3 + x4 = 0
We can solve this system of equations to find x. One possible solution is x = (1, -1, 0, 1). However, this is not a unit vector, so we need to divide each component by the length of the vector to get a unit vector:
x = (1, -1, 0, 1) / ||(1, -1, 0, 1)|| = (1/sqrt(3), -1/sqrt(3), 0, 1/sqrt(3))
So, the unit vector with a positive first component that is orthogonal to all three of the given vectors is (1/sqrt(3), -1/sqrt(3), 0, 1/sqrt(3)).
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The length of a radius is three-fourths the height of a cone. The surface area is 3750
square units.
What are the height and the radius of the cone?
The height of the cone is approximately 28.867 units and the radius is approximately 21.65 units.
How to Find the Height and Radius of a Cone?Let's denote the height of the cone as "h" and the radius as "r".
From the problem statement, we know that:
r = (3/4)h ...(1) (given)
The surface area of the cone is given as 3750 square units. The formula for the surface area of a cone is:
Surface Area of Cone = πr(r + l),
where "l" is the slant height of the cone. Since the slant height is not given in the problem, we need to express "l" in terms of "r" and "h" using the Pythagorean theorem:
l² = r² + h²
l² = (3/4)² h² + h²
l² = (9/16)h² + h²
l² = (25/16)h²
l = (5/4)h
Substituting this expression for "l" and the expression for "r" from equation (1) into the surface area formula, we get:
3750 = πr(r + l)
3750 = π[(3/4)h] [(3/4)h + (5/4)h]
3750 = π (9/16 + 15/16) h²
3750 = π (24/16) h²
3750 = (3/2) π h²
h² = (2500/3π)
h ≈ 28.867
Substituting this value of "h" into equation (1), we get:
r = (3/4)h
r ≈ 21.65
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Answer: Radius 37.5 & height 50
Step-by-step explanation: correct in edmuntum/plato
Natasha wants to average at least 90% in math class. Her test scores so far are 94%, 89%,88%,92%, and 85% What score does she need to earn on her next test to reach her goal
Answer:
Let x be the score Natasha needs to earn on her next test to reach an average of 90%.
To find x, we can use the formula for the average:
average = (sum of scores) / (number of scores)
We know that Natasha has taken 5 tests so far, with scores of 94%, 89%, 88%, 92%, and 85%. We can plug these values into the formula and solve for x:
90% = (94% + 89% + 88% + 92% + 85% + x) / 6
Multiplying both sides by 6, we get:
540% = 448% + x
Subtracting 448% from both sides, we get:
92% = x
Therefore, Natasha needs to earn a score of at least 92% on her next test to reach an average of 90%.
Problem C:
A farmer has potatoes planted in a large garden.
The field is 14 yards long and 10-yards wide.
What is the area of the farmer's potato garden?
-
Answer:
140 square yards
Step-by-step explanation:
To calculate the area of the farmer's potato garden, we need to multiply the length by the width of the garden.
Area of the potato garden = Length x Width
Given that the length of the potato garden is 14 yards and the width is 10 yards, we can substitute the values into the formula and get:
Area of the potato garden = 14 yards x 10 yards
Area of the potato garden = 140 square yards
Therefore, the area of the farmer's potato garden is 140 square yards.
Answer:140[tex]yards^{2}[/tex]
Step-by-step explanation: to find the area you multiply two different lengths of the rectangle together to get 140
Please help, Progress reports for the semester coming out soon!!
(Look at screenshot) <33
Answer:
The graph will be parallel with x-axis and intersects y at -8
Step-by-step explanation:
For the function y = -8, whatever the x is, y is always -8.
x y
-10 8
-9 8
-3 8
-2 8
2 8
The graph will be parallel with x-axis and intersects y at -8
if anyone can help me with this and its the right answer i will give brainy please i really need this
Question 11
Which values in the data set are outliers? Show all work.
72, 81, 82, 83, 83, 85, 100, 54, 75, 81, 83
List the following (and show work if needed): Q1, Median, Q3, Lower Fence, Upper Fence, and Outliers
The dataset's median, which has a value of 82 and a total of 11 values, is the sixth figure.
what is median ?When a dataset is ordered from smallest to largest, the median, a measure of central tendency, shows the middle value of the dataset. It is frequently used as a more reliable substitute for the mean, which can be vulnerable to anomalies in the data with extremely high or low values. We must first sort the numbers in a dataset from smallest to largest before we can determine the median. The median is just the middle value when the dataset has an odd number of numbers. For instance, the median, or middle number, in the dataset "2, 5, 7, 10, 12" is 7.
given
Values that are noticeably higher or lower than the remainder of the dataset are found using the fences.
Step 1: Sort the information by size, starting from the smallest:
[tex]54, 72, 75, 81, 81, 82, 83, 83, 83, 85, 100[/tex]
Step 2: Calculate the middle
The dataset's median represents its middle number. The median is the sixth number in the dataset, which contains 11 values total:
Average: 82
Step 3: Determine the first and third quartiles (Q1 and Q3, respectively):
The medians for the dataset's lower and upper halves are Q1 for the lower part and Q3 for the upper. We don't use the median value to determine Q1 and Q3 because the dataset has an odd amount of values.
54, 72, 75, 81, 81 in the bottom half.
Top half: 83, 83, 83, 83, 85, and 100
Q1 = 75 for the bottom half's median.
Q3 = 83 for the top half's median.
The dataset's median, which has a value of 82 and a total of 11 values, is the sixth figure.
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Benjamin's math teacher finds that there's roughly a linear relationship between the amount of time students spend on their homework and their weekly quiz scores. This relationship can be represented by the equation y=8x+57 where y represents the expected quiz score and x represents hours spent on homework that week. What is the meaning of the x-value when y = 98?
When the quiz score is expected to be 98, the corresponding x-value, which represents the number of hours spent on homework, is approximately 5.125 hours.
What is the linear equation in two variables?
A linear equation in two variables is an equation of the form:
ax + by = c
where x and y are variables, a, b, and c are constants, and a and b are not both zero. The graph of a linear equation in two variables is a straight line, and any point on the line satisfies the equation.
The given equation is:
y = 8x + 57
where y is the quiz score and x is the hours spent on homework.
To find the meaning of the x-value when y = 98, we can substitute y = 98 into the equation and solve for x:
98 = 8x + 57
Subtracting 57 from both sides, we get:
41 = 8x
Dividing both sides by 8, we get:
x = 5.125
when the quiz score is expected to be 98, the corresponding x-value, which represents the number of hours spent on homework, is approximately 5.125 hours. This suggests that students who spend around 5 hours and 7.5 minutes on homework per week can expect to score around 98 on their weekly quiz.
Therefore, when the quiz score is expected to be 98, the corresponding x-value, which represents the number of hours spent on homework, is approximately 5.125 hours.
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Part C What does the mapping found in part B tell you about the relationship between the two circles? Explain your reasoning.
In conclusion, the mapping in part B informs us that the two circles are equation congruent, i.e., that their size and shape are the same and that the mapping preserves all of their geometrical characteristics.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
The mapping in part B informs us that the points on the two circles correspond exactly to one another. In other words, there is exactly one point on the bigger circle for every point on the smaller circle, and vice versa.
In conclusion, the mapping in part B informs us that the two circles are congruent, i.e., that their size and shape are the same, and that the mapping preserves all of their geometrical characteristics.
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please help. Shape Y is an enlargement of shape X by a scale factor of 3. Work out lengths a and b. no
Answer:
a = 3, b = 9
Step-by-step explanation:
What is a scale factor?A scale factor is the number that you multiply each side of a shape to enlarge it. A scale factor of 3 means that each side of the new shape is three times the size of the original.
If the new shape is 3 times the size of the original, then we can take the side lengths (3 and 1) and multiply them by 3.
3 × 1 = 3 (side a)3 × 3 = 9 (side b)Therefore, the length of a is 3, whereas the length of b is 9.
Let X be a random variable having the gamma
distribution with shape parameter α and scale parameter γ, where α is
know and γ is unknown. let Y = σ log X. Show that
(i) if σ > 0 is unknown, then the distribution of Y is in a location-scale
family;
(ii) if σ > 0 is known, then the distribution of Y is in an exponential family.
Compulsory both subparts required .
i) If σ > 0 is unknown, then the distribution of Y is in a location-scale family with the parameters: Location parameter: α and Scale parameter: γ
ii) If σ > 0 is known, then the distribution of Y is in an exponential family with the parameters: Shape parameter: α and Scale parameter: σγ
(i) If σ > 0 is unknown, then the distribution of Y is in a location-scale family. This is because the distribution of Y can be expressed as a linear transformation of the distribution of X. Specifically, Y = σ log X = σ(log X - E[log X]) + E[log X], where E[log X] is the expected value of log X. This is the form of a location-scale family, with location parameter E[log X] and scale parameter σ.
(ii) If σ > 0 is known, then the distribution of Y is in an exponential family. This is because the distribution of Y can be expressed as an exponential family distribution with natural parameter -1/σ and sufficient statistic log X. Specifically, the probability density function of Y can be written as f_Y(y) = f_X(e^(y/σ)) * (1/σ) * e^(y/σ) = (1/σ) * e^(-(y-E[log X])/σ) * f_X(e^(E[log X]/σ)), where f_X is the probability density function of X. This is the form of an exponential family distribution, with natural parameter -1/σ and sufficient statistic log X.
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Find the lateral area and total surface area of the rectangular prism. 12in, 7in, 5in
Answer:
The lateral area of the prism is 190 square inches and the total surface area is 358 square inches.
Step-by-step explanation:
To find the lateral area and total surface area of a rectangular prism, we need to use the following formulas:
Lateral Area = perimeter of the base x height
Total Surface Area = 2 x base area + lateral area
Where the base area is simply the product of the length and width of the rectangular prism.
Let's apply these formulas to the rectangular prism with dimensions 12in x 7in x 5in:
Lateral Area:
To find the perimeter of the base, we add up the lengths of all four sides of the rectangle:
Perimeter of the base = 2(length + width) = 2(12in + 7in) = 2(19in) = 38in
Now, we multiply the perimeter of the base by the height of the prism:
Lateral Area = 38in x 5in = 190in^2
Therefore, the lateral area of the rectangular prism is 190 square inches.
Total Surface Area:
To find the base area, we simply multiply the length and width of the rectangular prism:
Base Area = length x width = 12in x 7in = 84in^2
Now, we can use the formula for total surface area:
Total Surface Area = 2 x base area + lateral area
Total Surface Area = 2(84in^2) + 190in^2
Total Surface Area = 168in^2 + 190in^2
Total Surface Area = 358in^2
Therefore, the total surface area of the rectangular prism is 358 square inches.
So the lateral area of the prism is 190 square inches and the total surface area is 358 square inches.