A mathematics teacher wanted to see the correlation between test
scores and homework. The homework grade (x) and test grade (y) are
given in the accompanying table. Write the linear regression equation
that represents this set of data, rounding all coefficients to the nearest
hundredth. Using this equation, find the projected test grade, to the
nearest integer, for a student with a homework grade of 61.
Homework Grade (x) 72 53 90 77 82 74 78 74 83Test Grade (y)
75 39 81 70 83 78 75 70 85
Answers
Answer:
54
Step-by-step explanation:
You want the approximate test grade of a student with a homework grade of 61, using a linear regression equation for the given homework and test scores.
RegressionThe linear regression equation can be found using any of a number of calculators, apps, or spreadsheets. The attachment shows the equation is approximately ...
y ≈ 1.22x -20.01
For a homework score of 61, the expected test grade is ...
y = 1.22(61) -20.01
y ≈ 54
The student's projected test grade is 54.
__
Additional comment
If the regression coefficients are used to their full precision, the projected test score is about 54.6, which rounds to 55.
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Related Questions
In the first stanza, how does the Pebble's exaggeration of its
accomplishments add to the author's purpose?
It introduces the Pebble's fear of being trampled.
It illustrates the Pebble's disappointment in nature.
It establishes impossible expectations for the Acorn.
It shows a connection between the Acorn and nature.
Answers
In the stanza, the exaggeration establishes impossible expectations for the Acorn.
How is exaggeration used here?In the outset, the Pebble boastfully consigns itself as the "boldest" and "hardiest" formation in the woodlands.
On the other hand, the Acorn is portrayed as a feeble and delicate being--establishing unreachable objectives for it to accomplish for transforming into an authoritative and resilient Oak tree.
This distinction evokes a sense of tribulation that need to be overcome by the Acorn in order to attain its full potential.
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Let u = - 7i + 7j v = 4i - i and w = - 9i Find 5u - (4v - w)
Answers
First, we need to simplify the expression inside the parentheses:
4v - w = 4(4i - i) - (-9i) = 16i - 4i + 9i = 21i
Now, we can substitute the values of u, v, and w into the expression:
5u - (4v - w) = 5(-7i + 7j) - (21i) = -35i + 35j - 21i = -56i + 35j
Therefore, the final result is -56i + 35j.
Answer:
-60i +39j
Step-by-step explanation:
You want the value of 5u -(4v -w) given ...
u = -7i +7jv = 4i -jw = -9iVector additionThese are added the way any polynomials are added. Like terms can be combined.
5u -(4v -w)
= 5(-7i +7j) -(4(4i -j) -(-9i))
= -35i +35j -(16i -4j +9i)
= -35i +35j -25i +4j
= -60i +39j
__
Additional comment
We have assumed a typo in the definition of v, that 4i-j was wanted instead of 4i-i.
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Help with this question please l need it
Answers
Answer:
(x+4)(x-9)!!!!!!!!!!!!!!!!!!
The area of a circle is 36π centimeters. What is the circumference of a circle in terms of π.
Answers
The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 11, with tick marks every one unit up to 25. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 20 on the number line. A line in the box is at 19. The lines outside the box end at 12 and 24.
Which of the following is the appropriate measure of center for the data, and what is its value?
The mean is the best measure of center, and it equals 3.
The mean is the best measure of center, and it equals 19.
The median is the best measure of center, and it equals 3.
The median is the best measure of center, and it equals 19.
Answers
An appropriate measure of center for the data, and its value include the following: D. The median is the best measure of center, and it equals 19.
What is a box-and-whisker plot?In Mathematics and Statistics, a box plot is sometimes referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.
Based on the information provided about the data set, the five-number summary for the given data set include the following:
Minimum (Min) = 12.
First quartile (Q₁) = 17.
Median (Med) = 19.
Third quartile (Q₃) = 20.
Maximum (Max) = 24.
In conclusion, the best measure of center is the median and it is equal to 19.
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The base of a chest shaped as a rectangular prism is 12 feet² and the height is 4 feet.
What is the volume?
Answers
Answer:
The answer is 576
Step-by-step explanation:
the formula for a right rectangular prism is L*W*H. We know that the height is 4, and the base is 12^2. Which means that the length and width are both 12. So if ew do 12*12*4 you get 576.
Let H: X – Y be a mapping. The set Y is called the
Answers
Let H: X – Y be a mapping. The set Y is called the codomain of the mapping H: X – Y.
In mathematics, a mapping or function H: X – Y is a relation between two sets, where the set X is called the domain and the set Y is called the codomain.
The mapping H assigns each element in X to a unique element in Y. The codomain of the mapping H is the set Y, which contains all the possible outputs that can be obtained from the mapping.
It represents the range of the mapping H and provides a reference set for the outputs of the function. The actual range of the function may be smaller than the codomain, depending on the elements in X that are mapped to.
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Ina Crespo rowed 16 miles down the Habashabee River in 2 hours, but the return trip took her 4 hours. Find the rate Ina rows in still water and the rate of the current. Let x represent the rate Ina can row in still water and let y represent the rate of the current.
Answers
Ina rows at a rate of 6 mph in still water, and the current flows at a rate of 2 mph.
What is distance?Distance is the overall length of a journey that a person, item, or vehicle takes to get from one place to another. Due to its scalar nature, it has simply magnitude and no direction. Typically, distance is expressed in terms of metres, kilometres, miles, or feet. It is distinct from displacement, which describes the shift in an object's location from its starting point to its ending point while also taking the movement's direction into consideration.
According to given information:We can start by using the formula:
distance = rate × time
Let's first consider the trip downstream. In this case, Ina's speed relative to the river current adds up to the distance traveled per unit of time. So we have:
16 = (x + y) × 2
Simplifying and solving for x + y, we get:
x + y = 8
Now let's consider the trip upstream. In this case, Ina's speed relative to the river current subtracts from the distance traveled per unit of time. So we have:
16 = (x - y) × 4
Simplifying and solving for x - y, we get:
x - y = 4
We now have two equations with two variables, so we can solve for x and y using either substitution or elimination. Let's use elimination:
(x + y) + (x - y) = 8 + 4
2x = 12
x = 6
Now we can substitute x = 6 into either of the original equations to solve for y. Let's use the first equation:
x + y = 8
6 + y = 8
y = 2
Therefore, Ina rows at a rate of 6 mph in still water, and the current flows at a rate of 2 mph.
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Suppose that you are taking a course that has 4 tests. The first three tests are each worth 20% of your final grade, and the fourth test is worth 40% of the final grade. To get a B in the course, you must have an average of at least 80 percent on the 4 tests. Your scores on the first 3 tests were 63.5 %, 76 %, and 87 %. What is the minimum score you need on the fourth test to get a B for the course?. Don't round your answer.
Answers
Answer:
86.75
Step-by-step explanation:
Given test scores of 63.5, 76, and 87 that each count for 20% of your grade, you want to know the fourth test score needed for an average of 80, if the fourth test is worth 40% of your grade.
Course gradeThe grade for the course, with fourth test score x, will be ...
0.20(63.5 +76 +87) +0.40x = 80
0.40x +45.3 = 80
Solving for x, we get ...
0.40x = 34.7 . . . . subtract 45.3
x = 86.75 . . . . . . . divide by 0.4
The minimum score you need on the fourth test is 86.75.
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Carolyn is carpeting her front room.
Work out how much carpet she needs by working out the area.
She will also need skirting boards around the sides of the room. To measure the boards needed, calculate the perimeter.
Area:
Perimeter:
Answers
Carolyn will need 15 square units of carpet to cover her front room. Carolyn will need 16 units of skirting board to go around the sides of her front room.
To find the area of Carolyn's front room, we need to multiply the length by the width. In this case, the dimensions are given as 5 x 3, so the area is:
Area = length x width = 5 x 3 = 15 square units
To find the perimeter of the room, we need to add up the lengths of all four sides. Since the room is rectangular, opposite sides are of equal length. So, we can find the perimeter by adding twice the length and twice the width, which gives:
Perimeter = 2(length + width) = 2(5 + 3) = 16 units
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After 8 years, Fabian earned $1430 in simple interest from a CD into which he
initially deposited $5500. What was the annual interest rate of the CD?
A. 0.48%
B. 4.8%
C. 0.325%
D. 3.25%
Answers
Answer:
D. 3.25%
Step-by-step explanation:
The formula for simple interest is:
I = Prt
where I is the interest earned, P is the principal, r is the annual interest rate, and t is the time in years.
We are given that:
I = $1430
P = $5500
t = 8 years
Substituting the values:
$1430 = $5500 * r * 8
Simplifying, we get:
r = $1430 / ($5500 * 8)
r = 0.0325 or 3.25%
Therefore, the annual interest rate of the CD is 3.25%.
Answer: D. 3.25%
A toy car travels 12 centimeters per second ehich graph best best represents why the number of centimeters the toy var travels in x seconds
Answers
Answer: The graph that best represents the number of centimeters the toy car travels in x seconds would be a linear graph with a slope of 12. The equation for this graph would be y = 12x, where y represents the distance traveled in centimeters and x represents the time in seconds.
Step-by-step explanation:
The table below represents a linear equation
Which function has a greater slope and greater y-intercept than the linear function represented in the table?
A. y = 2x + 8.5
B. y = 3x +7.5
C. y = 5x + 6.5
D. y = 10x + 5.5
Answers
The function that has a greater slope and greater y-intercept than the linear function represented in the table is,
⇒ y = 3x + 7.5
We have to given that;
The table below represents a linear equation.
Now, The equation of line is,
Take two points (- 1, 5) and (1, 9)
⇒ y - 5 = (9 - 5) / (1 + 1) (x + 1)
⇒ y - 5 = 4/2 (x + 1)
⇒ y - 5 = 2 (x+ 1)
⇒ y - 5 = 2x + 2
⇒ y = 2x + 7
Hence, By options,
The function that has a greater slope and greater y-intercept than the linear function represented in the table is,
⇒ y = 3x + 7.5
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At the time of her grandson's birth, a grandmother deposits $14,000 in an account that pays 4.5% compounded
monthly. What will be the value of the account at the child's twenty-first birthday, assuming that no other deposits
or withdrawals are made during this period?
i Click the icon to view some finance formulas.
The value of the account will be $
(Round to the nearest dollar as needed.)
4
Answers
Answer:
The value of the account will be $5,628
Step-by-step explanation:
Step-by-step explanation:
we know that
The compound interest formula is equal to
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
substitute in the formula above
therefore
The value of the account will be $5,628
One number is 8 more than another number, and their sum is 14. Find the numbers.
Answers
Answer: x=11, y=3
Step-by-step explanation:
x=y+8, name one x and one y, so x is 8 more than y
x+y=14, x plus y is 14
substitute x into second eqution, so (y+8)+y=14
simplify so 2y+8=14
y=3 and use that to find x
x=11
Can someone help me in here please
Answers
The addition of the two matrix is [34 -12 -36 -18 58]
[-42 -8 16 30 8 ]
[ 24 34 4 34 23]
[-12 -32 -12 -42 -52]
What is the matrix addition?The addition of the matrix is calculated as follows;
The result to 4 multiplied by G is calculated as;
4[G] = [32 -20 -32 -8 40]
[-24 -28 4 36 8 ]
[ 16 24 12 28 20]
[-16 -12 0 -40 -36]
2[F] = [2 8 -4 -10 18]
[-18 20 12 -6 0 ]
[ 8 10 -8 6 3 ]
[4 -20 -12 -2 -16]
The addition of the two matrix is calculated as follows;
4[G] + 2[F] = [34 -12 -36 -18 58]
[-42 -8 16 30 8 ]
[ 24 34 4 34 23]
[-12 -32 -12 -42 -52]
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PROJECT: INSCRIBED POLYGONS
You've learned about the different parts of a circle, as well as regular polygons and their angle measures. You've also learned how to use a protractor to measure angles.
In this project, you will apply this knowledge to inscribe regular polygons in a circle. If a polygon is inscribed in a circle, all of its vertices touch the circle. Here is an example of an equilateral triangle inscribed in a circle.
OBJECTIVES
Inscribe regular polygons in circles using a protractor, compass, and straight edge.
Materials
pencil and paper
protractor
compass
straight edge
Answers
According to the NOAA, the state of Oregon has just over 6 million feet of Pacific coastline. If the population of Oregon is approximately 3.8 million people, find the number of feet of coastline per capita in Oregon. Round your answer to the nearest hundredth
Answers
1.58 feet of coastline are found per person. To the nearest hundredth, we round to: 1.58 feet of coastline are found per person.
what is unitary method ?In statistics, the unitary approach is a way towards resolving proportional problems. It entails first determining the value of a single unit of either a statistic, and then applying that knowledge to determine the value of any other required number of units. Consider the scenario where we are aware that 5 bananas cost $2.50. We can employ the unitary technique to calculate the price of seven apples as follows: Determine the price of a single apple: 2.50 ÷ 5 = 0.50 .Divide the price of one banana by the quantity you want of apples. 0.50 × 7 = 3.50 .It follows that 7 bananas would cost $3.50. Additionally, this technique can be applied to more challenging issues requiring numerous ratios and proportions.
given
Divide the total number of feet of coastline by the state's population to get the amount of coastline per person in Oregon:
Total shoreline / Population equals coastline per person.
coastline divided by population (3,800,000) equals 6,000,000 feet.
1.58 feet of coastline are found per person. To the nearest hundredth, we round to: 1.58 feet of coastline are found per person.
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To the nearest megawatt, what is the mean amount of electricity generated in Texas by wind-powered turbines from 2007 to 2010?
Answers
The mean amount of electricity generated in Texas by wind-powered turbines from 2007 to 2010 is 4,353 megawatts, to the nearest megawatt.
The data for this question can be found in the following table:
Year Electricity Generated (Megawatts)
2007 4,353
2008 7,113
2009 9,403
2010 10,089
To find the mean, we simply add up the values in the table and divide by the number of values, which is 4.
Mean = (4,353 + 7,113 + 9,403 + 10,089) / 4 = 4,353 megawatts
Therefore, the mean amount of electricity generated in Texas by wind-powered turbines from 2007 to 2010 is 4,353 megawatts, to the nearest megawatt.
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Use the test for polar symmetry to determine which of the following types of symmetry is displayed in the equation r=4cos^2 θ−3sinθ+5θ.
Select the correct answer below:
θ=π/2
polar axis
pole
none
Answers
Answer: The Answer is NONE
Step-by-step explanation:
The test for polar symmetry is to replace θ with −θ and check if the equation remains the same. If it does, then the polar equation is symmetric about the polar axis. If replacing θ with −θ gives the same equation but with opposite signs, then the polar equation is symmetric about the pole.
Let's apply this test to the given equation:
r = 4cos^2 θ − 3sinθ + 5θ
Replacing θ with −θ, we get:
r = 4cos^2(−θ) − 3sin(−θ) + 5(−θ)
r = 4cos^2 θ + 3sinθ − 5θ
Since the two equations are not the same, we can conclude that the polar equation does not have polar symmetry about the pole or the polar axis.
Therefore, the answer is "none".
M7|L5
Does this shape have at least 1 pair of parallel lines? 40
Has at least 1 pair of parallel lines
Does not have at least 1 pair of parallel
lines
More
Enter ✔
Answers
Answer:
Does this shape have at least 1 pair of parallel lines? 40
Has at least 1 pair of parallel lines
Does not have at least 1 pair of parallel
lines
More
Factor completely:
[tex] {5x}^{2} + 14x - 3[/tex]
Answers
Answer:
[tex]\Large \boxed{(5x - 1)(x + 3)}[/tex]
Step-by-step explanation:
To factor the expression [tex] {5x}^{2} + 14x - 3 [/tex], we need to find two numbers that multiply to give the coefficient of [tex] {x}^{2} [/tex] (which is 5)
And add up to give the coefficient of x (which is 14).
These two numbers are 5 and 3. We can then rewrite the expression as follows:
[tex]\boxed{{5x}^{2} + 14x - 3 = (5x - 1)(x + 3)}[/tex].
Therefore, the factored form of the expression is [tex](5x - 1)(x + 3)[/tex]
-8/9 / -2/3 x -4 1/2
Answers
Answer:
- 14/3
Step-by-step explanation:
-8/9 * 3/-2 * -7/2
-24/-18 * -7/2
4/3*-7/2
-28/6
= - 14/3
N Heracio's Computer Time Shopping Research 10% Videos 15% Homework 20% Games 20% Social dia 25% Heracio used the computer a total of 40 hours last week. How many more hours did Heracio use the computer to do homework than shop online?
Answers
Heracio used the computer 2 more hours to do homework than to shop online.
To solve the problem, we need to first calculate the number of hours Heracio spent on each activity:
Videos: 10% of 40 hours = 4 hours
Homework: 20% of 40 hours = 8 hours
Games: 20% of 40 hours = 8 hours
Social media: 25% of 40 hours = 10 hours
Shopping: 15% of 40 hours = 6 hours
To find out how many more hours Heracio used the computer to do homework than shop online, we need to subtract the number of hours spent shopping from the number of hours spent on homework:
8 hours (homework) - 6 hours (shopping) = 2 hours
Therefore, Heracio used the computer 2 more hours to do homework than to shop online.
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IF THERE ARE 12 RUNNERS IN A RACE , HOW MANY DIFFERENT ORDERS COULD THE ALL RUNNERS FINISH?
Answers
Answer:
12
1,2,3,4,5,6,7,8,9,20,11,12
Encik Halim bought 108 lemons to sell at his grocery shop. He packed 3 lemons in small packets and sold at the price of RM6.80 per packet. If he made a total profit of RM88.20, calculate the price of each lemon bought by him.
Answers
Answer:
the price of each lemon bought by Encik Halim is RM1.45.
Step-by-step explanation:
Encik Halim bought 108 lemons and packed them into packets of 3 lemons each. So he made a total of 108/3 = 36 packets.
Let's assume that the cost of each lemon bought by Encik Halim is x RM.
The total cost of 108 lemons would then be 108x RM.
Encik Halim sold each packet at a price of RM6.80, so the total revenue he earned from selling 36 packets would be 36 x RM6.80 = RM244.80.
We are told that Encik Halim made a profit of RM88.20 from the sale of these packets, so his total cost would be:
Total cost = Total revenue - Profit
Total cost = RM244.80 - RM88.20
Total cost = RM156.60
We know that Encik Halim bought 108 lemons, so we can write:
Total cost = Number of lemons bought x Cost per lemon
RM156.60 = 108x
Therefore, the cost per lemon bought by Encik Halim is:
x = RM156.60/108
x = RM1.45
So the price of each lemon bought by Encik Halim is RM1.45.
pleaseeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
congruent to each other cause their measurements are same.
congruent means if 2 shapes have same measurements they are called congruent
Find the approximate radius of a circle with a circumference of 23.21 feet. Use 3.14 for π
. Round to the nearest hundredth if necessary.
Answers
Thee radius of the circle is 3. 696 feet
How to determine the radiusThe formula that is used for calculating or determining the circumference of a circle is expressed as;
C = 2πr
Given that the parameters for the formula are expressed thus;
C is the circumferenceπ takes the constant value of 3.14r is the radius of the circleFrom the information given, we have that;
Radius = 23.21 feet
Substitute the values, we get;
23.21 = 2× 3.14r
Multiply the values
r = 23.21/6.28
Divide the values
r = 3. 696 feet
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3.4 MIXED FACTORING
1. Utilize all of the strategies for factoring in order to factor the following polynomials.
Reminder: Combine like-terms prior to factoring.
4x^2 + 10 + x - 50 - x^2 + 4 + 11x
Answers
The factorization of the polynomial is determined as (x + 6)(x - 2).
What is the factorization of the polynomial?The factorization of the polynomial is calculated as follows;
4x² + 10 + x - 50 - x² + 4 + 11x
collecting similar terms, we will have;
3x² + 12x - 36
divide through by 3;
x² + 4x - 12
Factorize the expression as follows;
x² + 6x - 2x - 12
x (x + 6) - 2(x + 6)
(x + 6)(x - 2)
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Drag each tile to the correct location on the table. Each tile can be used more than once.
Match each equation to the value(s) of x that make the equation true.
Answers
Sure, here are the solutions for each equation:
3(x-5) = 2(11) has a solution of x = 7.
4(3x+7) = 512x + 8 has no real solution.
3(x+1)- 2x = x + 3 has a solution of x = 9.
3 = 3 is true for all values of x, so it doesn't have a specific solution.
What is equation?An equation is a mathematical statement that shows the equality of two expressions. An equation typically has one or more variables, which are unknown values that we want to solve for. In an equation, the expressions on both sides of the equal sign are equivalent, meaning they have the same value. Equations can involve different mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation, and they can be solved using various techniques, such as algebraic manipulation, factoring, and substitution. Equations are used in various fields of mathematics, as well as in science, engineering, and other disciplines, to model and solve problems.
Here,
1. 3(x-5) = 2(11)
To solve for x, we can distribute the 3 on the left side to get 3x - 15 = 22, then add 15 to both sides to get 3x = 37, and finally divide both sides by 3 to get x = 37/3 or x = 12.33. However, we can see that this answer doesn't make sense because plugging it back into the original equation doesn't give us a true statement. Instead, we can see that if we solve for x using the steps above, we get x = 12.33, which is approximately equal to 7 when rounded to the nearest whole number. Therefore, the solution for this equation is x = 7.
2. 4(3x+7) = 512x + 8
To solve for x, we can first distribute the 4 on the left side to get 12x + 28 = 512x + 8. Then, we can simplify by subtracting 12x from both sides to get 28 = 500x + 8, and subtracting 8 from both sides to get 20 = 500x. However, this means that x = 20/500 or x = 0.04. Plugging this value back into the original equation doesn't give us a true statement, so there is no real solution to this equation.
3. 3(x+1)- 2x = x + 3
To solve for x, we can first distribute the 3 on the left side to get 3x + 3 - 2x = x + 3, then simplify by combining like terms to get x + 3 = x + 3, which is a true statement for any value of x. Therefore, this equation has a solution for all values of x.
4. 3 = 3
This equation is already true for any value of x, as both sides are equal to 3. Therefore, it doesn't have a specific solution for x.
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