Please help! Create a scatterplot for the data in the table. Let English scores be X and History Scores be Y.
Part 2: draw line of fit
Part 3: choose two points, find slope, and record slope decimal
Answers
A way to pinpoint a point's location on the planet is through the use of a coordinate system. In most coordinate systems, a point's location is determined by two numbers called a coordinate. Each of these values represents the separation between the point and the origin, a fixed point of reference.
Explain about the coordinate system?A two-dimensional number line, such as two perpendicular axes, can be thought of as a coordinate system.
The x-axis stands for the horizontal axis, and the y-axis for the vertical axis.
A coordinate system's origin is its centre (in which the lines intersect). The axes cross if x and y are both 0.
The coordinates of the origin are (0, 0).
for the posed query.
"English score" is one of the independent variables on the x-axis.
The dependent variables "History score" are displayed on the y-axis.
The scattered points are used to plot the graph for the provided table.
Take note of these two points on the graph:
(x₁, y₁) = (60, 65) (60, 65)
(x₂, y₂) = (61, 61) (61, 61)
The slope will then be;
m = (y2 - y1)/(x2 - x1) is the slope.
the values in.
m = (61 - 65)/(61 - 60) (61 - 60)
m = -4
The slope is -4.
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Related Questions
The regulation height of a basketball hoop is 10 feet. Let the location of thebasket be represented in the coordinate plane by the point (0, 10). Let the ballbe thrown at a 45° angle with the ground.1. Suppose Nancy is standing a horizontal distance of 10 feet from thebasket at the point (-10, 0), and she shoots a basket from 6 feet in theair with an initial velocity of 22 ft/s.a. Write parametric equations that represent the ball's motion throughthe air.b. Graph the parametric equations on your calculator in an appropriatewindow and sketch the results below.
Answers
SOLUTION:
a. The parametric equations that represent the balls motion is;
[tex]\begin{gathered} x(t)=x_0+(v_0cos\theta)t \\ y(t)=y_0+(v_0sin\theta)t+0.5gt^2 \end{gathered}[/tex]Inserting the values;
[tex]\begin{gathered} x(t)=-10+(22cos45)t \\ y(t)=6+(22sin45)t+0.5(-32)t^2 \end{gathered}[/tex]Simplifying, we have;
[tex]\begin{gathered} x(t)=15.56t-10 \\ y(t)=-16t^2+15.56t+6 \end{gathered}[/tex]b. The graph of the parametric equation is given below;
what percent of 8,7 is 17.4
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The number 17.4 is 200 percent of 8.7
How to determine the percentage?The statement is given as
"what percent of 8.7 is 17.4"
From the above statement, we have the following parameters
Dividend = 17.4
Divisor = 8.7
The percentage is then calculated as
Percentage = Dividend/Divisor x 100%
Substitute the known values in the above equation
So, we have
Percentage = 17.4/8.7 x 100%
Evaluate the quotient
Percentage = 2 x 100%
Evaluate the product
Percentage = 200%
Hence, the percentage is 200%
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Can you please help me translate the argument into symbolic form?
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Let p be: John goes to the beach
Let q be: He will go surfing.
Then in symbolic form, the argument becomes:
[tex]\begin{gathered} p\Rightarrow q \\ p \\ ----------- \\ \therefore q \end{gathered}[/tex]p ⇒ q
p
---------------------
∴ q
An argument is valid if the conjuction of the premises implies the conclusion.
p | q | p ⇒ q | (p ⇒ q) ∧ p | [(p ⇒ q) ∧ p] ⇒ q
---------------------------------------------------------------------\
F | F | T | F | T
F | T | T | F | T
T | F | F | F | T
T | T | T | T | T
The table above shows that the argument is a tautology.
Hence, the argument is valid
What is anequation of the line that passes through the points (-6,5) and (6,-7)?
Answers
The line that passes through the given point may be stated as
y - y1 = m(x - x1)
where (x1, y1) and (x2, y2) = (-6,5) and (6,-7)
m = (y2 - y1)/(x2 - x1)
= (-7 - 5)/(6 - -6)
= -12/12
= -1
Hence the equation of the line that passes through the given points is
(y - 5) = -1(x - -6)
y - 5 = - x - 6
y = -x - 6 + 5
y = -x - 1
Find the area of the following circles. Leave your answer in terms of pi or round to the nearest 10th.
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To find the area of a circle, we use the formula for area
A = pi r^2 where r is the radius
We are given the diameter
d = 2r
8 = 2r
Solving for r
8/2 =r
4= r
A = pi (4)^2
A = 16 pi
Expand and simplify: 3(2a+5) + 5(a-2)
Answers
Answer:
11
a
+
5
Step-by-step explanation: you're welcome. Brainlyest?
A roofer earns $22 per hour for regular hours worked and $30per hour for overtime hours worked. If he puts in 40 hours of regular time during a certain week and he wishes to earn $1050, how many hours of overtime should he work?The roofer should work ___ hours of overtime.(Type an integer, proper fraction, or mixed number.)
Answers
The roofer should work 5 2/3 hours of overtime.
Explanation:Given:
Earnings for regular hours = $22 per hour
Earnings for overtime = $30 per hour
Time spent on regular hours = 40 hours
Total amount to be earned = $1050
To find:
The number of hours worked overtime
let the number of hours worked overtime = h
Earnings for regular hours (number of hours) + Earnings for overtime (number of hours) = 1050
[tex]\begin{gathered} 22(40)\text{ +}30(h)\text{ = 1050} \\ 880\text{ + 30h = 1050} \end{gathered}[/tex][tex]\begin{gathered} collect\text{ like terms:} \\ 30h\text{ = 1050 - 880} \\ 30h\text{ = 170} \\ \\ divide\text{ both sides by 30:} \\ h\text{ = 170/30} \\ h\text{ = 17/3 = 5}\frac{2}{3}\text{ hours} \end{gathered}[/tex]Solve -3(x+2) > 10+5x
Answers
-3(x+2)>10+5x
-3x-6>10+5x
-3x-6-5x>10
-3x-5x>10+6
-8x>16
X<-2
help meeee please !!
thank you
Answers
The answers are :
a) The average price of a new home (y) is given by a linear equation which is y = -800x + 294000.
b) The average price of a new home in year 2014 will be $286000.
What is the point slope form of a line ?
Point slope form is used to represent a straight line using its slope and a point on the line.
a)
We know that the two point -slope form of a line is given by :
y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex])
where : m is slope and represented by
m = [tex]\frac{y_{2}- y_{1}}{x_{2}-x_{1}}[/tex]
As per the questions hint is that two points that is (-2 , 11) and (1 , -4).
These points can be represented by :
([tex]x_{1}[/tex] , [tex]y_{1}[/tex]) = (0 , 294000)
([tex]x_{2}[/tex] , [tex]y_{2}[/tex]) = (7 , 288400)
So : the slope will be :
m = [tex]\frac{y_{2}- y_{1}}{x_{2}-x_{1}}[/tex]
m = [tex]\frac{288400-294000}{7 - 0}[/tex]
m = -5600 / 7
m = -800
So , the point -slope form of line will be :
y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex])
y - 294000 = -800 ( x - 0)
y - 294000 = - 800 x
or
y = -800x + 294000
So , the average price of a new home (y) is given by a linear equation which is :
y = -800x + 294000
b)
As per the question y is the average price of a new home in year x and is given by :
y = -800x + 294000
It is given that x = 0 meant year 2004. So , for year 2014 value of x will be x =10.
Substituting this value to get the value of y or average price of a new home in year 2014 , we get :
y = -800x + 294000
y = - 800 × 10 + 294000
y = -8000 + 294000
or
y = $ 286000
Therefore , the answers are :
a) The average price of a new home (y) is given by a linear equation which is y = -800x + 294000.
b) The average price of a new home in year 2014 will be $286000.
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3x^2-4x+5-x^2+x
Combine like terms
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find the basic feasible solution at this point by setting the non-basic variables equal to 0
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To determine wether a variable is a basic variable or not in a simplex tableu we have to look for the variables which have a one in a column and all the other values are zero, the variables that fullfil this condition are the basic ones.
Looking at the tableu we notice that the basis variables are: x2, s5 and Z. Now that we know that, we look at each row where the number one appear and put all the other variables equal to zero, with this in mind we conclude that:
[tex]\begin{gathered} x_1=0 \\ x_2=17 \\ s_3=0 \\ s_4=0 \\ s_5=29 \\ Z=12 \end{gathered}[/tex]Makayla bought 1/4 pound of ham and 5/8 pound of turkey. How much more turkey did she buy
Answers
How many different permutations can be formed using all the letters in the word COLORADO?
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Ok, the number of different permutations are:
8!/3! (Considering the three O's)
An aircraft factory manufactures airplane engines. The unit cost C (the cost in dollars to make each airplane engine) depends on the number of engines made. Ifx engines are made, then the unit cost is given by the function C(x) = 0.5x ^ 2 - 150x + 26, 777 . How many engines must be made to minimize the unit cost?Do not round your answer.number of airplane engines________
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EXPLANATION:
We are given the unit cost to produce x number of airplanes as follows;
[tex]C(x)=0.5x^2-150x+26777[/tex]However, to minimize the unit cost, we need to first take the derivative of the cost function and then find its value at zero.
Thuis is shown below;
[tex]C(x)=0.5x^2-150x+26777[/tex][tex]\frac{d}{dx}=2(0.5)x^{2-1}-1(150)x^{1-1}+0[/tex]Note that for a derivative, the constant term is always equal to zero. We can now simplify what we have above;
[tex]\frac{d}{dx}=1x^1-150[/tex][tex]\frac{d}{dx}=x-150[/tex]We now set this equal to zero and simplify;
[tex]x-150=0[/tex]Add 150 to both sides;
[tex]x=150[/tex]ANSWER:
Therefore, to minimize the unit cost, 150 engines must be made.
There are 3 consecutive even integers that have a sum of 30. What are the integers?
Answers
Answer:
8, 10, 12
Step-by-step explanation:
x+x+2+x+4=30
3x+6=30
3x=30-6
3x=24
x=8
Find the area of this figure. Round your answer to the nearest hundredth. Use 3.14 to approximate A = [ ? ] ft.
Answers
The area of the figure = Area of the Triangle + Area of the semi-circle
Area of the Triangle = 1/2 x b x h
Base = 6 feet
Height = 8 feet
Area of the Triangle = 1/2 x 6 x 8 = 48/2 = 24 feet^2
Area of the circle = pi x r ^2 radius = 8/2 = 4 ft
= 3.14 x 4 x 4
= 50.24 feet^2
Total area = 24 + 50.24 = 74. 24 feet ^2
Question 2 of 1010 PointsWhich inequality below satisfies the solution set graphed on the following number line?
Answers
ANSWER
C. x² - x ≥ 6
EXPLANATION
Let's analyze the solution set graphed first. We can see that the values -2 and 3 are included in the set, and all values below -2 and above 3. So, the solution set is (-∞, 2] U [3, ∞).
To find which inequality satisfies this solution set we have to solve them. To do so, we will be using the quadratic formula:
[tex]\begin{gathered} ax^2+bx+c=0 \\ \\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \end{gathered}[/tex]A. To solve this one, first, add x to both sides,
[tex]-x^2+x+6\geqslant0[/tex]Now, apply the quadratic formula to find the zeros. For this inequality, a = -1, b = 1, and c = 6
[tex]\begin{gathered} x=\frac{-1\pm\sqrt{1^2-4(-1)6}}{2(-1)}=\frac{-1\pm\sqrt{1+24}}{-2}=\frac{-1\pm\sqrt{25}}{-2} \\ \\ x_1=\frac{-1-5}{-2}=\frac{-6}{-2}=3 \\ \\ x_2=\frac{-1+5}{-2}=\frac{4}{-2}=-2 \end{gathered}[/tex]But in this case, the solution set is [-2, 3] - note that for any value outside this interval the inequality is false.
B. Similarly, apply the quadratic formula for a = -3, b = 3, c = 18,
[tex]\begin{gathered} x=\frac{-3\pm\sqrt{3^2-4(-3)18}}{2(-3)}=\frac{-3\pm\sqrt{9+216}}{2(-3)}=\frac{-3\pm\sqrt{225}}{-6}=\frac{-3\pm15}{-6} \\ \\ x_1=\frac{-3+15}{-6}=\frac{12}{-6}=-2 \\ \\ x_2=\frac{-3-15}{-6}=\frac{-18}{-6}=3 \end{gathered}[/tex]Again, the solution set is [-2, 3] since for any value outside the interval the inequality is not true.
C. Subtract 6 from both sides,
[tex]x^2-x-6\geqslant0[/tex]Apply the quadratic formula, with a = 1, b = -1, and c = -6,
[tex]\begin{gathered} x=\frac{-(-1)\pm\sqrt{(-1)^2-4\cdot1(-6)}}{2\cdot1}=\frac{1\pm\sqrt{1+24}}{2}=\frac{1\pm\sqrt{25}}{2}=\frac{1\pm5}{2} \\ \\ x_1=\frac{1+5}{2}=\frac{6}{2}=3 \\ \\ x_2=\frac{1-5}{2}=\frac{-4}{2}=-2 \end{gathered}[/tex]In this case, if we take any value between -2 and 3, for example 1,
[tex]\begin{gathered} 1^2-1\ge6 \\ \\ 0\ge6 \end{gathered}[/tex]We can see that the inequality is false, while if we take a value greater than 3 or less than -2, for example, -5,
[tex]\begin{gathered} (-5)^2-(-5)\ge6 \\ \\ 25+5\ge6 \\ \\ 30\ge6 \end{gathered}[/tex]We can see that the inequality is true.
Hence, we can conclude that inequality C satisfies the solution set graphed.
The slope of this line and the unit rate are the same.Price of Cookies at Bakery141210Find the unit ratefor the number ofcookies per dollar008Number of Cookies464[?] cookies$[ ]22 4 6 8 10 12 146 8Price ($)
Answers
SOLUTION
We want to find the unit rate for number of cookies per dollar. This can be done using the diagram below
So the unit rate is calculated thus
[tex]\begin{gathered} \text{Unit rate = }\frac{rise\text{ }}{\text{run}} \\ =\frac{14\text{ cookies }}{7\text{ dollars }} \\ =\frac{14}{7} \\ 2\text{ cookies per dollar} \end{gathered}[/tex]Hence the answer is 2
A bird flies downward 2 feet per second for 6 seconds. Then the bird flies up 7 feet. Which equation represents the total distance the bird travels
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The equation that represents the total distance the bird travels would be; d = 1/3.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be one degree.
Given that bird flies downward 2 feet per second for 6 seconds. Therefore, the bird flies up 7 feet.
Since, a bird flies 2 feet = 1 second
Thus, for 6 seconds = 6 x 2 = 12 feet.
for 6 seconds = 12 feet.
Similarly, the bird flies up 7 feet = 6/12 x 7
= 42/12 = 3.5
Hence, the equation that represents the total distance the bird travels would be; d = 2/6 = 1/3.
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please answer by correcting the math equation asap
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The error in the subtraction of the given fraction is that the LCM was not used before subtraction of numerators and as such if correctly answered the final fraction is; -15/4
How to subtract fractions?
We are given the subtraction of fraction expression as;
3/4 - 9/2
Now, the first step in this subtraction is to find the L.C.M of both denominators.
Factors of 2 ; 1, 2
Factors of 4; 1, 2, 4
Thus, the L.C.M of both denominators is; 2 * 2 = 4
Now, the next step is to divide the LCM by the denominator and multiply by the numerator while retaining the LCM as common denominator to get;
[(3 * 4/4) - (9 * 4/2)]/4
= (3 - 18)/4
= -15/4
The method used in the question to subtract the fraction did not take into account finding the LCM.
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M(5,-10) is rotated 270 degrees what is M’?
Answers
Problem
M(5,-10) is rotated 270 degrees what is M’?
Solution
For this case we need to remember that is we have any point A =(x,y) when we apply a transformation fo 270° then the new coordinates would be:
M' = (x,-y)
And for this case if we apply this transformation we got:
M'= (5, -(-10))= (5,10)
A health inspector from the Food and Drug Administration was tasked with oversight of a pharmaceutical company in their development of a new medication. He used a 99% confidence interval to estimate the true mean amount of propionic acid in each 800 mg pill. Propionic acid is an important ingredient in several medications, including ibuprofen. His confidence interval was (3.2 mg, 6.5 mg). Which one of the following is the best interpretation of this confidence interval?
Answers
The best interpretation of the confidence interval is given by:
We are 99% sure that the true mean amount of propionic acid in all 800 mg pills of the new medication is between 3.2 mg and 6.5 mg.
What is the interpretation of a x% confidence interval?The x% confidence interval means that it is x% likely that the population parameter(mean/proportion/standard deviation) is between the bounds a and b of the confidence interval
The bounds of the confidence interval are given by the estimate plus/minus the margin of error.
In this problem, the bounds of the problem are already given, as follows:
3.2 mg.6.5 mg.The variable of interest is given by:
Mean amount of propionic acid in all 800 mg pills of the new medication
The level of confidence is of 99%, hence, considering the variable and the bounds, the interpretation of the interval is:
We are 99% sure that the true mean amount of propionic acid in all 800 mg pills of the new medication is between 3.2 mg and 6.5 mg.
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One brand of cereal sells for $3.15 for 10 ounces. What is the unitprice per pound?a. $.31b. $5.04c. $ 3.49d. $50.40
Answers
Answer:
[tex]\begin{gathered} \\ B\colon\text{ \$5.04} \end{gathered}[/tex]Explanation:
Here, we want to get the unit price per pound
From the question, the brand sells for $3.15 per 10 ounces
Mathematically, 1 ounce is 0.0625 pound
Thus $3.15 is the price for 0.625 pounds (10 * 0.0625 pounds)
if $3.15 is for 0.625 pounds
$x will be for 1 pound
Mathematically:
[tex]\begin{gathered} 3.15\times1\text{ = 0.625}\times x \\ x\text{ = }\frac{3.15}{0.625} \\ x\text{ = \$5.04} \end{gathered}[/tex]Given: 14-2(x + 8) = 5x - (3x - 34); Prove: x = -9
help pls lol
Answers
The value of x is -9.
Here the equation is :
14 - 2(x + 8) = 5x -( 3x - 34)
We have to prove that x = -9.
From the above-given equation, we have to find the value of x.
So by evaluating the equation we have:
14 -2(x +8) = 5x - (3x - 34)
= 14 - 2x - 16 = 5x - 3x + 34
= -2 -2x = 2x + 34
= 4x = -34 - 2
= 4x = -36
=x = -9
Therefore the value of the above-given equation x = -9.
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The perimeter of the figure is given. Find the length of the indicated side.?4x - 4Perimeter = 16x + 6The length of the indicated side is
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Width = 4x + 7
Explanation:The perimeter of the rectangle shown = 16x + 6
The width of the rectangle = 4x - 4
Perimeter of a rectangle = 2(Length + Width )
16x + 6 = 2[ (4x - 4) x Width]
(16x + 6)/2 = (4x - 4) x width
8x + 3 = (4x - 4) x width
Width = 8x + 3 - (4x - 4)
Width = 8x - 4x + 3 + 4
Width = 4x + 7
3 years ago I was 2/3 as old as I will be 8 years from now. How old am I?
Answers
Considering the definition of an equation and the way to solve it, if 3 years ago I was 2/3 as old as I will be 8 years from now, I am 25 years old.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign. One or more unknown values appear in it, in addition to certain known data.
Solving an equation is determining the value or values of the unknowns that transform the equation into an identity. To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.My ageBeing "x" the my age today, and knowing that 3 years ago I was 2/3 as old as I will be 8 years from now, the equation in this case is:
x -3= 2/3×(x +8)
Solving:
x -3= 2/3x +2/3×8
x -3= 2/3x +16/3
x - 2/3x= 16/3 + 3
1/3x= 25/3
x= 25/3 ÷ 1/3
x= 25
Finally, I am 25 years old.
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The hypotenuse of right triangle is 226 miles long. The difference between the other two sides is 194 miles. Find the missing sides. Use exact values.
Find the value of the short and ling leg.
Answers
Answer: short line: 30 miles, ling leg: 224 miles
Step-by-step explanation:
Intro:
We will be using Pythagoras theorm, which states, if we have a 90 degree triangle which has 3 side as H, B and P defined as Hypotenuse, Base and Perpendicular, then H² = B² + P²
In your case, we know that hypotenuse is 226.
We also know that (A + B)² = A² + B² + 2AB
Given:
H = 226
B - P = 194
Solution:
B = 194 + P
So
(226)² = (194 + P)² + P²
51076 = (194)² + P² + (2 x 194 x P) + P²
51076 = 37636 + 2P² + 388P
51076 - 37636 = 2P² + 388P
13440 = 2P² + 388P
6720 = P² + 194P
P² + 194P - 6720 = 0
P² - 30P + 224P - 6720 = 0
P(P - 30) + 224(P - 30) = 0
(P - 30) x (P + 224) = 0
P = 30 or -224
As miles cannot be negative, we will choose answer as 30 miles.
Now we have H = 226 and P = 30
Using Pythagoras theorm:
(226)² = (30)² + B²
51076 = 900 + B²
50176 = B²
B = 224 miles.
So the missing miles are 224 miles and 30 miles
It takes you 52 seconds to walk from the first (ground) floor of a building to the third floor. How long will it take you to walk from the first floor to the sixth floor (at the same pace, assuming all floors have the same height)?
Answers
From the given information. Write the recursive and explicit functions for each arithmetic sequence. Use these terms please; recursive f(1) = first term, f(n) = pattern+f(n-1). Explicit: y = pattern*x + 0 term. work backwards to find 0 term
Answers
An arithmetic sequence has the form:
[tex]f(n)=f(1)+d(n-1)[/tex]where d is the common difference.
For this sequence the common difference is 3 and the first term is:
[tex]f(1)=3[/tex]Plugging this values in the general expression we have:
[tex]\begin{gathered} f(n)=3+3(n-1) \\ f(n)=3n-3+3 \\ f(n)=3n \end{gathered}[/tex]Therefore the sequence is:
[tex]f(n)=3n[/tex]Now, from this expression we can determine the value of the zeroth term:
[tex]\begin{gathered} f(0)=3(0) \\ f(0)=0 \end{gathered}[/tex]Hence the zeroth term is:
[tex]f(0)=0[/tex]The Matrix Fishing Company does fishing in Toluca Lake the first year of the company's operation it managed to catch a 190,000 fish due to population decreases the number of fish the company was able to catch decreased by 8% each year how many total fish did the company catch over the first 12 years round to the nearest whole number
Answers
Solution
For this case we can model the number of fishes with the following equation:
[tex]A=19000(1-0.08t)[/tex]And for this case we want to find the value for t =12 and replacing we got:
[tex]A=190000\cdot(1-0.08\cdot12)=7600[/tex]And then the number of fishes after 12 years would be 7600
so then they catched 182400
