The table gives performance data for a boat powered by a certain outboard motor. Find a
quadratic regression model (y = ax²+bx+c) for boat speed y (in miles per hour) as a function of
engine speed (in revolutions per minute). Estimate the boat speed at an engine speed of 3,200
revolutions per minute.
Complete the quadratic regression calculator screen below.
QuadReg
Answers
A quadratic function is one that has the formula f(x) = ax² + bx + c, where a, b, and c are all integers with a not equal to zero.
What is meant by quadratic regression?To choose the parabola equation that best fits a collection of data, a statistical method known as quadratic regression is performed. To get the equation of the straight line that best fits a collection of data, this sort of regression is an extension of simple linear regression.
Using a collection of data with a parabola-like form, quadratic regression seeks the best-fitting equation. Making a scatter plot is the initial stage in regression.
A quadratic function is one that has the formula f(x) = ax² + bx + c, where a, b, and c are all integers with a not equal to zero. A parabola is the shape that makes up the graph of a quadratic function. If a parabola opens up.
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Related Questions
11*90+5-20=?
I really don't know the answer to it and I'm not going to use a calculator on this
Show your work
Answers
Answer:
To solve this problem, we need to follow the order of operations (PEMDAS) which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
First, we need to perform the multiplication.
11*90 = 990
Next, we add 5 to 990:
990+5 = 995
Finally, we subtract 20 from 995:
995-20 = 975
Therefore, the solution is 975
In summary, we first multiplied 11 and 90, then added 5 to the result, and finally subtracted 20. This is why the order of operations is important because it determines the order in which we perform the calculations in the equation.
Without solving the quadratic equation 2x^2-10x+12=0, find the sum of the cubes of its roots
Answers
Answer: The sum of the cubes of the roots of a quadratic equation with coefficients a, b, and c can be found using the formula:
x³ + y³ = (x + y)(x² - xy + y²) = -b
Where x and y are the roots of the equation ax² + bx + c = 0.
In this case, the equation is 2x² - 10x + 12 = 0, so a = 2, b = -10, and c = 12.
So, the sum of the cubes of the roots is:
x³ + y³ = -b = -(-10) = 10
Therefore, the sum of the cubes of the roots of the equation 2x² - 10x + 12 = 0 is 10.
Step-by-step explanation:
Please show me how to work out these math problems. Only the ones with stairs next them please. Thank you.
Answers
First you would separate the shapes into two rectangle like in the picture. You then find the area(length x width) of those two shapes and add the answers together. So the answer to the first question would be 36. I hope this makes sense, let me know if you have questions!
What percentage of the students in both grades prefer hot dogs for lunch?
Answers
A shop keeper bought 26 apples from a fruit vendor for $37.70. How much did each apple cost?
PLEASE ADD A PICTURE TO HELP ME PLS!!!!!!!!!!!
Answers
Answer:each apple cost $1.45
Step-by-step explanation:l----------l
Please help
Each angle of a regular ___-gon measures 165.6 degrees.
Answers
Answer:
A 25 sided polygon or the mathematical name for it is an icosikaipentagon or a pentacosagon
Step-by-step explanation:
So you firstly do 180-165.6=14.4° we need to do this as each interior angle adds up to 180° and 14.4° would be the value of one exterior angle. For all shapes, the total of all the interior angles will add up to 360° so then you do 360° divided by 14.4°= 25. This means that it is a 25 sided shape.
What color printer prints 11 pages in 6 minutes how many minutes does it take per page
Answers
Answer:
11/7 = 1.6
Step-by-step explanation:
11 pages divide 7 1.57 pages
____ = __________
7 minutes divide 7 1 minute
Solve linear system by graphing
State if their is a solution or no solution
X+3y=6
3x+9y=18
Answers
The given linear system of equation has no solution.
What is no solution?In Mathematics, no solution is also referred to as zero solution, and an equation is said to have no solution when the left hand side and right hand side of the equation are not the same or equal.
In this scenario, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;
x + 3y = 6 ........equation 1.
3x + 9y = 18 ........equation 2.
Based on the graph (see attachment), we can logically deduce that the given system of equations has no solution because both lines are the same and lie on the same co-ordinate.
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A Ferris wheel at a carnival has a diameter of 54 feet. Suppose a passenger is traveling at 7 miles per hour. (A useful fact: 1mi = 5280ft.)
(a) Find the angular speed of the wheel in radians per minute.
(b) Find the number of revolutions the wheel makes per hour. (Assume the wheel does not stop.)
Do not round any intermediate computations, and round your answer to the nearest whole number.
Answers
The angular speed of the wheel in radians per minute is 23 radians per minute and the number of revolutions is 218 revolutions per hour.
What is Angular Speed?Angular speed is defined as the rate of change of the angular displacement.
Angular speed is commonly denoted as ω.
We have a relation,
v = r ω
where v is the tangential speed and ω is the angular speed. r is the radius.
Given
v = 7 miles per hour
Diameter, d = 54 feet = 0.0102 miles
r = d / 2 = 0.0051
ω = v / r
ω = 1368.89 radian per hour
= 1368.89 / 60 radians per minute
= 22.815 radians per minute
= 23 radians per minute
(b) n = v / 2π r
= 7 / (π × 0.0102)
= 217.865 revolutions per hour
= 218 revolutions per hour
Hence the angular speed of the Ferris wheel is 23 radians per minute and there are 218 revolutions per hour.
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Currently, the temperature of a bowl of ramen is 57°C above room temperature. The temperature of the ramen decreases based on the function f(t) = 57(0.89)t where t represents time elapsed in minutes. Where does the graph of f(t) cross the y-axis, and what does this represent in the context of the problem?
a
f(57) = 0; the time it takes for the above-room temperature to reach 0°C
b
f(0) = 57; the time it takes for the above-room temperature to reach 0°C
c
f(57) = 0; the above-room temperature of the ramen at time t = 0
d
f(0) = 57; the above-room temperature of the ramen at time t = 0
Answers
The solution is Option D.
The value of the equation f ( 0 ) = 57 ; the above-room temperature of the ramen at time t = 0
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
f ( t ) = 57 ( 0.89 ) ^ t be equation (1)
Now , t represents time elapsed in minutes
Substituting the value of t = 0 , we get
The time elapsed be 0 minutes , the above room temperature will be
f ( t ) = 57 ( 0.89 ) ^ t
when t = 0
f ( 0 ) = 57 ( 0.89 )⁰
Any number raised to the power of 0 is 1
So , the value of the equation is
f ( 0 ) = 57
And , f ( 0 ) is the above room temperature at the time t = 0
Hence , the equation is solved
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The solution to an inequality is graphed on the number line. A number line going from negative 5 to positive 5. A solid circle appears between positive 4 and positive 5. The number line is shaded from the circle to negative 5. What is another way to represent this solution set? {x | x < 4. 5} {x | x ≤ 4. 5} {x | x > 4. 5} {x | x ≥ 4. 5}.
Answers
Another way to represent this solution set is to express it as a set notation, which is {x | x ≤ 4.5}. This notation represents all values of x that are less than or equal to 4.5.
What is inequality?Inequality in mathematics is when two values are not equal. It can be expressed using symbols such as >, <, ≥ and ≤. This can be used to compare two values, express a range of values, or indicate that one value is greater or less than another. Inequality is a powerful tool for solving mathematical problems, as it can be used to deduce relationships between different variables.
To graph this set, a closed circle would be placed at the 4.5 mark on the number line, and the numbers to the left of the circle would be shaded. This would indicate that all of the numbers to the left of the 4.5 mark, including the 4.5 mark itself, are part of the solution set.
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An eastbound train and a westbound train meet each other on parallel tracks heading in opposite directions. The eastbound train travels 12 miles per hour faster than the westbound train. After 2 hours, they are 216 miles apart. At what speeds are the two trains traveling?
Answers
The speed of the westbound train is 48 miles per hour and the speed of the eastbound train is 60 miles per hour.
What is the relative speed between two moving objects?The relative speed is the net speed of two different objects with respect to each other.
If two objects move in the same direction we take the difference between their speeds.
If two objects move in the opposite direction we take the sum of their speeds.
Given, An eastbound train and a westbound train meet each other on parallel tracks heading in opposite directions.
Let, The speed of the westbound train be 'x', So the speed of the eastbound train is (x + 12).
We know, Distance = Time×Speed.
Therefore,
2[(x + 12) + x] = 216.
x + 12 x = 108.
2x = 96.
x = 48 miles per hour, Hence the speed of the eastbound train is 60 miles per hour.
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In how many years will N750.00 gain
an interest of N60.00 at 4% per
annum?
(a)2yrs (b) 4yrs (c) 1yr (d) 3yrs (e) 5yrs
Answers
The basic interest rate that will be earned, according to the information provided, is 13.6%.
How do we define interest?Interest is the cost of borrowing money or the fee you charge to lend it. Most frequently, interest is shown as an annual percentage of the loan amount. The interest rate for the loan is denoted by this proportion.
The basic interest rate that will be earned, according to the information provided, is 13.6%.
Principal is $5250.
Simple Interest is $6500-$5250, or $1250.
21 months is 1.75 years.
PRT / 100 is a formula for simple interest.
1250 = (5250 × 1.75 × R) / 100
the cross-multiply
125000 = 9187.5R
R = 125000 / 9187.5
R = 13.6%.
The complete question is,
What annual simple interest rate will you receive if you pay $5,250 for a simple interest note with a 21-month maturity of $6,500?
12.4% \s13.6%
15.8% \s14.3%.
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You are choosing between two health clubs. Club A offers membership for a fee of $19 plus a monthly fee of $12. Club B offers membership for a fee of $14 plus a monthly fee of
$13.
After how many months will the total cost of each health club be the same?
What will be the total cost for each club?
Answers
The month at which the total cost of each health club would be the same = 5 months and the total cost for each club = $79 each.
How to calculate the total cost of each club?Let the equal month of membership be represented by x and y represent the total cost for each.
Club A offers the following; y = 19 + 12x
Club B offers the following; y = 14 + 13x
Because we know that the prices,y, would be equal, we can set the two equations equal to each other.
That is,
19+12x = 14+13x
Bring the like terms together;
19-14 = 14x-13x
5 = x
The total cost for club A;
y = 19+12(5)
y = 19+60
y= $79
The total cost for club B;
y = 14 + 13(5)
y= 14+65
y = $79
Therefore the total cost for each club would be the same which is = $79.
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erik is drawing a picture of his school's basketball court. The actual basketball court is 84 ft long an 50ft wide. If erik draws the court with a length of 21 in., what will be the width?
Answers
The outer dimensions are 84 feet long by 50 feet wide. The half court line is, as the name would suggest, halfway between each end line.
What court dimensions measures 84 feet long by 50 feet wide?A basketball court for a junior high or high school is 50 feet wide and 84 feet long. For all courts, the foul line or free throw line is 15' from the front of the backboard.
For NBA or FIBA, the free throw lane is 16 feet wide; for college, high school, and junior high basketball, it is 12 feet wide. three Point lines vary in the ways that: On NBA basketball courts, a straight line that extends out 16 feet 9 inches from the baseline forms a 3-point arc that measures 22 feet to the centre of the rim on both sides.
The line continues 23 feet 9 inches past those spots from the rim's centre.
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12/1 divided by 1 1/5
Answers
NEED HELP ASAP PLS AND THX Picture is attached
Answers
M<2 + M<3 = 180 degrees, as this is the sum of all angles in a triangle.
Right angle triangleA right angle triangle is a triangle with one angle will be 90 degrees. It is the most basic type of triangle and is often used in mathematics and geometry. The other two angles of a right angle triangle must be acute angles, meaning that their measure must be less than 90 degrees. The three sides of a right angle triangle are referred to as the hypotenuse, the adjacent side, and the opposite side. The hypotenuse is the longest side of the triangle, the adjacent side is the side that is next to the right angle, and the opposite side is the side that is across from the right angle. The Pythagorean Theorem states that the sum of the squares of the two shorter sides of a right angle triangle is equal to the square of the hypotenuse. This theorem can be used to calculate the length of the sides of a right angle triangle if the lengths of two sides are known.To learn more about Right angle triangle refer to:
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Solve the following word problem by setting up systems of equations: Rob hosted a party last week. He purchased 24 pizzas and 24 sodas for $282.00. This week he purchased 15 pizzas and 8 sodas for $157.00. Determine the cost for each pizza and soda.
Answers
Answer:$2.75 for soda 9$ for pizza
Step-by-step explanation: Let p = pizza and s = soda. For the first week, we have the following:
24p+24s = 282
Now, for the next week, we have:
15p + 8s = 157.
We can multiply the equation 15p+8s=157 by -3 which ends up equaling
-45p -24s = -471
Now, we add them.
24p+24s = 282
-45p-24s = -471.
The s cancels out and we have -21p = -189. each pizza costs $9, so each soda costs (157-135)/8 which equals $2.75
5. The cylinder shown below
has a diameter of 5.2 cm on
the base and a height of 7.1
cm. Label the
measurements and find the
lateral surface area of the
cylinder.
6.
Answers
The lateral surface area of the cylinder is 51.22 cm2.
What is surface area?Surface area is a two-dimensional measure that refers to the total area of a surface, such as the area of a two-dimensional shape, a three-dimensional solid, or a combination of both. It is the sum of the areas of all the faces of a solid object. It is also referred to as the area of the boundary of a three-dimensional object. It can be used to calculate the volume of an object, and is also used in other calculations like area of the base of a triangle, area of a circle, and more.
The cylinder shown below has a diameter of 5.2 cm on the base and a height of 7.1 cm. The diameter of the base is referred to as 'd' and the height of the cylinder is referred to as 'h'. The lateral surface area of the cylinder can be found by using the formula LSA = 2πrh, where 'r' is the radius of the base.
The radius of the base of this cylinder is half of the diameter, or 2.6 cm. Therefore, the lateral surface area of the cylinder is: 2π x 2.6 x 7.1 = 51.22 cm2.
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What is the vertex form of f(x) = (x-2)(x+6)
Answers
Answer:
[tex]y=(x+2)^2-16[/tex]
Step-by-step explanation:
Divide using synthetic division
Answers
To divide a polynomial by a binomial of the form x - c using synthetic division.
What is synthetic division? In algebra, synthetic division is a method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than long division. It is mostly taught for division by linear monic polynomials, but the method can be generalized to division by any polynomial.“Synthetic division can be defined as a simplified way of dividing a polynomial with another polynomial equation of degree 1 and is generally used to find the zeroes of polynomials” This division method is performed manually with less effort of calculation than the long division method.Synthetic division is a shorthand method for dividing a polynomial by a linear factor such as x + 3, and it's much simpler and faster.
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Jacob needs 48 ounces of tomatoes for the spaghetti sauce. He is choosing between two brands of tomatoes. Find the unit rate for each brand. Round to the nearest cent (hundredth).
Brand A costs
per ounce.
Brand B costs
per ounce.
Answers
Answer:
Brand A Costs 37.38 per ounce and Brand B cost 31.19 per ounce hope this helped ^-^
Find three consicutive integers such that twice the sum of te two is 11 more than three times the largest
Answers
Answer: Let's call the smallest of the three consecutive integers "x". Then the next two integers will be "x+1" and "x+2".
We know that the sum of the three integers is twice the largest integer plus 11. We can use this information to set up the following equation:
x + (x+1) + (x+2) = 2(x+2) + 11
Simplifying, we get:
3x + 3 = 2x + 5 + 11
So we can get:
x = 3
Therefore, the three consecutive integers are 3, 4 and 5.
Step-by-step explanation:
Answer:
11 & 1
Step-by-step explanation:
11*1=11
11+1=12
12>11
11>1
263.76 to the nearest whole number
Answers
263.76 to the nearest whole number.
When rounding, you’re always going to look back a place. If the number is greater than 5, round up. If it’s less than 5, round down. And if it’s 5, round up or down, depending on the problem and your teacher’s instructions. I usually round up.
So in this case, we’re going to look at 7, the fourth number from the left. 7 is the first number after the decimal point. We’re looking at 7 because we’re rounding the number to the nearest WHOLE NUMBER. So no decimals. Now is 7 greater or less than 5? Greater! You round up.
3 becomes 4.
Your answer is 264.
Hope this helped!
A rectangular field with a width of 48 feet
has an area of 3,456 square feet. Inside
the field is a rectangular fenced-in area
with length and width that are each
one-fourth as long as the corresponding
side of the field. What is the area of the
fenced-in area?
Answers
Answer:
216 square feet
Step-by-step explanation:
Area of rectangular field = 3456 sq ft
Width = 48
So length = 3456/48 = 72
The length and width of the fenced-in area are 1/4th of that of the field
So for fenced-in area
length = 72/4 = 18
width = 48/4 = 12
Area of fenced-in portion = length x width = 18 x 12 = 216 square feet
Additional Note
Since we know the area of the field and the fact that the fenced-in area has a width and length 1/4th of the field, it can be computed by knowing the area alone
If both length and width are 1/4th, then area is reduced to 1/16th of original area
3456/16 = 216
No need to know the field width or length to answer this question
can someone please answer this question?
Answers
The value of x is, x = 7°.
What is isomorphic triangles?
Simple polygon triangulation is a common problem in computational geometry with applications in many fields of study. There are many algorithms, and it has been thoroughly studied. This page focuses on a slightly different issue: how to triangulate two straightforward polygons in a way that results in an isomorphic mapping between the two triangulations. As a result, any triangulation algorithm won't work for us.
Given:
ΔADB ≅ ΔCBD
∠ADB = 49° and ∠CDB = 7x
We have to find the value of x.
As the triangles are isomorphic, so their angles are also isomorphic.
⇒ ∠A ≅ ∠C, ∠D ≅ ∠D, ∠B ≅ ∠B
⇒ 49° = 7x
⇒ x = 7°
Hence, the value of x is, x = 7°.
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5. What is the area of a rectangle with a length of x-a and a width of x + b? (A) x²-a² (B) x² + b² (C) x² - abx + ab (D) x²-ax-bx - ab (E) x² + bx - ax - ab
Answers
'x^2+bx-ax-ab' is the area of a rectangle with a length of x-a and a width of x + b.
What is area of rectangle?
A rectangle basically is a four-sided shape with four right angles. It is one of the most basic shapes in geometry and can be defined by its length and width. The area of a rectangle is the product of its length and width. This measure is typically expressed in square units, such as square feet or square meters. The area of a rectangle can also be found by multiplying the length and width of a given rectangle.
L=x-a
B=x+b
Area of rectangle=?
Area of rectangle=l*b
=(x-a)(x+b)
=x² + bx - ax - ab
Hence, the correct option is Option (E) x² + bx - ax - ab.
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in a certain state about 3/5 of registred voters particated in 2016 election what fraction of registred voters did not
Answers
The requried fraction of the registered voters who didn't vote is given as 2/5.
What is the fraction?Fraction is defined as the number of compositions that constitutes the Whole. Fraction is generally denoted as a / b, where a = numerator and b = denominator.
In a certain state about 3/5 of registered voters participated in the 2016 election.
Let the fraction of registered voters to did not vote to be x,
So,
According to the question,
1 = 3/5 + x
x = 1 - 3/5
x = 2 / 5
Thus, the requried fraction of the registered voters who didn't vote is given as 2/5.
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Two contestants on Get Fit TV Show are Valerie and Oscar. Their weight loss progress is shown below.
Valerie's weight loss is shown by this function, where W is her weight in pounds and t is the time in weeks.
W=235−2.5t
Oscar's weight loss is tracked in the table below.
Weeks 0 2 5 6
Weight 247 243 237 235
True or False: Oscar is losing weight faster than Valerie
Answers
How cool is that! I love real-life problems, do you?
V = 236 - 2.5t
O = 0, 2, 5, 6
247, 243, 237, 235
So let's try substituting some numbers in for Valerie. Let's do 0, 2, 5 and 6 to compare them to Oscar.
V = 236 - 2.5(0)
V = 236
She started at a lesser weight than Oscar.
Week 2:
V = 236 - 2.5(2)
V = 236 - 5
V = 231
So already, at week 2, Valerie lost 5 pounds compared to her first weight. Oscar lost 4 pounds. Valerie is losing weight faster than Oscar.
Week 5:
V = 236 - 2.5(5)
V = 236 - 12.5
V = 223.5
From week 2, she lost 12.5 pounds. Oscar lost 6 pounds. Looks like Valerie is losing weight faster!
So now, week 6.
V = 236 - 2.5(6)
V = 236 - 15
V = 221
Valerie lost 2.5 pounds compared to week 5.
Oscar lost 2 pounds compared to week 5.
True or False: you decide! :)
Karen, Chau, and Goran sent a total of 112 text messages over their cell phones during the weekend. Chau sent 3 times as many messages as Goran. Goran sent 8 more messages than Karen. How many messages did they each send?
Answers
Karen sent 16, Chau sent 72 and Goran sent 24 messages over their phones during the weekend.
Finding Unknown quantity:Here we use the concept of Linear equation to find the Number of messages sent by each person. A linear Equation is a mathematical statement that is formed by constant and variable terms.
Given that
Karen, Chau, and Goran sent a total of 112 text messages over their cell phones during the weekend.
[Since we don't know the number of messages sent by each person take them as different variables. ]
Let x, y, and z be the number of messages that Karen, Chau, and Goran sent respectively
=> x + y + z = 112 ---- (1)
Given that
Chau sent 3 times as many messages as Goran.
=> y = 3z --- (2)
Goran sent 8 more messages than Karen.
=> z = x + 8
=> x = z - 8 --- (3)
From (1) (2) and (3)
=> z - 8 + 3z + z = 112
=> 5z = 120
=> z = 24
From (3)
=> x = 24 - 8 = 16
From (2)
=> y = 3(24) = 72
Therefore,
Karen sent 16, Chau sent 72 and Goran sent 24 messages over their phones during the weekend.
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