The scatter plot shows the time spent studying, x, and the quiz score, y, for each of 25 students
(a) Write an approximate equation of the line of best fit for the data. It doesn't have to be the exact ett
(b) using your equation from part (a), predict the quiz score for a student who spent 50 minutes studying
Note that you can use the graphing tools to help you apprimate the line.
Answers
a). y = 0.833x + 20 is a rough equation for the line that best fits the data.
b). A student who spent fifty minutes studying received a quiz score of 62.
Describe equation ?A mathematical statement that demonstrates the equality of two expressions is known as an equation. In most cases, it has two sides and an equal sign "=" in the centre. The left-hand side (LHS) and right-hand side (RHS) of the equation refer to the expressions on each side of the equal sign.
In mathematics, equations are used to depict connections between quantities or to resolve issues. They may include constants, which are fixed values that never change, as well as variables, which are symbols that denote uncertain values.
Depending on the maximum power of the variable in the equation, equations can be linear, quadratic, cubic, or of a higher degree. Depending on the quantity of terms and the complexity of the expressions used, they may also be simple or complex.
The line that fits the data the best is:
y = mx + c --------------> (1)
(a) Now, we use the points \((x_1,y_1)=(0,20)\) and \((x_2,y_2)=(60,70)\) to find the line of best fit.
So, slope
\(m=\frac{y_2-y_1}{x_2-x_1} \\\\m=\frac{70-20}{60-0}\\ \\m=\frac{50}{60} \\\\m=\frac{5}{6}\)
Thus, (1) becomes
y= x + c --------------> (2)
Now, using (0,20) in (2)
20 = .0 + c = c=20
Consequently, the correct formula for the line of best fit is
y= x + 20 -----------> (3)
or y = 0.833x + 20
(b) For quiz score after 50 min, put x= 50 in (3)
y = . 50 +20= 41.66 + 20 = 61.67
Therefore, the quiz's final score after 50 minutes will be roughly y = 62.
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Related Questions
12. Mrs. Sands' class had an ice-cream party. Of all the students, 2/5 chose 5 points vanilla ice cream, 3/10 chose chocolate ice cream, and the rest chose strawberry ice cream. What fraction of the class chose strawberry ice cream? * 5/10 O 3/10 3/5 7/10
Answers
3/10 (option B)
Explanation:fraction that chose vanilla ice cream = 2/5
fraction that chose chocolate ice cream = 3/10
let the fraction that chose strawberry ice cream = y
Total fraction = 1
fraction that chose vanilla ice cream + fraction that chose chocolate ice cream + fraction that chose strawberry ice cream = 1
2/5 + 3/10 + y = 1
\(\begin{gathered} \frac{2}{5}+\frac{3}{10}+y=1 \\ \frac{2(2)+3(1)}{10}+y\text{ = 1} \\ \frac{4+3}{10}+y\text{ = 1} \end{gathered}\)\(\begin{gathered} \frac{7}{10}+y\text{ = 1} \\ y\text{ = 1-}\frac{7}{10} \\ y\text{ = }\frac{10(1)-7}{10} \\ y\text{ =}\frac{10-7}{10} \\ y\text{ = 3/10} \end{gathered}\)Fraction of the class chose strawberry ice cream is 3/10 (option B)
4.7 x 10^-2 in standard form.
Answers
To write in standard form, Since the exponent is negative 2, move the decimal point two units to the left.
\(0.047\)Which is not a combination?
(why am i so stuck on this omg)
A. choosing 3 toppings for your pizza
B. lining 3 students up in a row
C. choosing 2 desserts from a tray of 10
D. choosing 5 students to represent a class of 30
Answers
Answer: B
Step-by-step explanation: because
PLEASE ANSWER FAST PLEASE ILL GIVE 100 POINTS
AND BRAINLIEST
What is the distance between the two points plotted?
A graph with the x-axis starting at negative 10, with tick marks every one unit up to 10. The y-axis starts at negative 10, with tick marks every one unit up to 10. A point is plotted at 3, 5 and at 3, negative 6.
1 unit
11 units
−11 units
−1 unit
Answers
Answer:
11 units
Step-by-step explanation:
To find the distance between the two points, you can use the distance formula, which is derived from the Pythagorean theorem. The formula is:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the distance between the two points (3, 5) and (3, -6):
Distance = √((3 - 3)^2 + (-6 - 5)^2)
= √(0^2 + (-11)^2)
= √(0 + 121)
= √121
= 11
Therefore, the distance between the two points is 11 units.
Y=tan ( cos ( pi t)+. 5)+2
Estimate the total area under this curve on the interval [0, 12] with a Riemann sum using 36 equal subdivisions and circumscribed rectangles. Hint: use symmetry to make this problem easier
Answers
The estimated total area under the curve is approximately 58.628, calculated using a Riemann sum with 36 equal subdivisions and circumscribed rectangles.
By leveraging symmetry, we can simplify the problem and calculate the area of half the interval [0, 6] instead.
To estimate the total area, we divide the interval [0, 12] into 36 equal subdivisions, resulting in a subinterval width of 1/3. Since the function exhibits symmetry around the y-axis, we can focus on calculating the area for the first half of the interval, [0, 6].
We evaluate the function at the right endpoints of each subdivision and construct circumscribed rectangles. For each subdivision, we find the maximum value of the function within that interval and multiply it by the width of the subdivision to get the area of the rectangle.
Using this approach, we calculate the area for each rectangle in the first half of the interval and sum them up. Finally, we double the result to account for the symmetry of the function.
The estimated total area under the curve is approximately 58.628.
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Answer: The answer is 86.634
At noon, Trevor and Kim start running from the same point. Trevor runs east at a speed of 8 km/h and Kim runs west at a speed of 6 km/h. At what time will they be 21 km apart?
Answers
Trevor and Kim will be situated 21 kilometers apart from each other at 1:30 PM. They will be separated by a distance of 21 km when the clock strikes 1:30 in the afternoon.
To determine at what time Trevor and Kim will be 21 km apart, we can set up a distance-time equation based on their relative speeds and distances.
Let's assume that t represents the time elapsed in hours since noon. At time t, Trevor would have traveled a distance of 8t km, while Kim would have traveled a distance of 6t km in the opposite direction.
Since they are running in opposite directions, the total distance between them is the sum of the distances they have traveled:
Total distance = 8t + 6t
We want to find the time when this total distance equals 21 km:
8t + 6t = 21
Combining like terms, we have:
14t = 21
To solve for t, we divide both sides of the equation by 14:
t = 21 / 14
Simplifying, we find:
t = 3 / 2
So, they will be 21 km apart after 3/2 hours, which is equivalent to 1 hour and 30 minutes.
Therefore, Trevor and Kim will be 21 km apart at 1:30 PM.
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solve and show your complete solution.
-thank you
Answers
Answer:
4x
Step-by-step explanation:
Given
\(\frac{\frac{2x^3}{3y} }{\frac{x^2}{6y} }\)
= \(\frac{2x^3}{3y}\) ÷ \(\frac{x^2}{6y}\)
Leave the first fraction, change division to multiplication, turn the second fraction upside down, that is
\(\frac{2x^3}{3y}\) × \(\frac{6y}{x^2}\)
Cancel 3y and 6y by 3y and 2x³ and x² by x²
= \(\frac{2x}{1}\) × \(\frac{2}{1}\)
= 2x × 2
= 4x
Help please!!! Tyyyyyy
Answers
Answer:
D
Step-by-step explanation:
So we have the equation:
\(ax+by+c=0\)
First, let's convert this to slope-intercept form.
Subtract ax from both sides:
\(by+c=-ax\)
Subtract c from both sides:
\(by=-ax-c\)
Divide everything by b:
\(y=-\frac{a}{b}x-\frac{c}{b}\)
We are told that a>0, b<0, and c>0.
In other words, a is positive, b is negative, and c is positive.
The slope of the equation is -a/b.
Since a is positive and b is negative, we will have:
-(+)/(-).
The negatives will cancel out. Therefore, our slope will be positive.
Since our slope is positive, our line must be upwards sloping. Eliminate answers A and C.
Also, our y-intercept is:
-c/b.
c is positive and b is negative. Thus, similarly:
-(+)/(-).
Again, the negatives cancel. This means that the y-intercept must be positive.
Out of B and D, the graph that has a positive y-intercept is D.
D is our answer :)
The diameter of a circle is 16 in. Find its area in terms of π
Answers
Answer:
64\(\pi\)
Step-by-step explanation:
A=\(\pi r^{2}\)
Divide 16 by two to get the diameter: 8
Square 8: 64
Since the answer is in terms of pi, the answer is 64\(\pi\)
Answer:
64 π
Step-by-step explanation:
Diameter = 16 inches
Radius = 16/2 = 8 inches
Area of circle = πr²
= π(8)²
= 64 π sq inches
one card is selected from a deck of 52 cards and placed in a second deck (also 52 cards). a card then is selected from the second deck. (a) what is the probability that the second card is an ace? (b) given that an ace was drawn from the second deck, what is the conditional probability that an ace was transferred?
Answers
The probability of drawing an ace from the second deck is 1/13. Given that an ace was drawn from the second deck, the conditional probability that an ace was transferred is 1/17.
Probability that the second card is an ace:
There are initially 4 aces in the second deck.
The total number of cards in the second deck is 52.
Therefore, the probability of drawing an ace is 4/52.
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 4/52
Probability = 1/13
Conditional probability that an ace was transferred, given that an ace was drawn from the second deck:
Since an ace was drawn from the second deck, we know that the second card is one of the four aces.
There was initially one card transferred from the first deck to the second deck, so there are now 51 cards left in the second deck.
Out of these 51 cards, only 3 are aces (since one ace has already been drawn).
Conditional Probability = Number of favorable outcomes / Total number of remaining outcomes
Conditional Probability = 3/51
Conditional Probability = 1/17
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(x+a)^2 -7 = x^2 +10x +b
Work out the value of a and b.
Answers
Answer:
(x+a)²-7=x²+10x+b
simplifying,we get
x²+2ax+a²-7=x²+10x+b
the coefficient of x on both sides should be equal
therefore
2a=10
a=10/2=5
also for b
a²-7=b
5²-7=25-7=b
b=18
a=5
A line that includes the points (-10, W) and (10, 6) has a slope of I. What is the value of w?
Can someone please help me?
Thank you!
Answers
Step-by-step explanation:
(6 - W)/(10+10)= (6 - W)/20= 2
6 - W= 40
-W= 34
W= -34
Answer:
line can be described by the equation y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis.
Since we are given that the line has a slope of 1 and includes the point (10, 10), we can plug these values into the equation to solve for the y-intercept. We get:
10 = 1 * 10 + b
b = 10 - 10
b = 0
So the equation of the line is y = x + 0, or simply y = x.
Since we are also given that the line includes the point (u, 9), we can substitute this value for y in the equation of the line to solve for u. We get:
9 = x
x = 9
Therefore, the value of u is 9.
Uday Tahlan
line that includes the points (-10, W) and (10, 6) has a slope of I. What is the value of w?
Can someone please help me?
Thank you!
To find the value of W, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
Since we are given that the line includes the points (-10, W) and (10, 6) and has a slope of I, we can use these two points to find the value of W.
First, we can plug in the coordinates of one of the points and the value of the slope into the equation to solve for the y-intercept. Let's use the point (10, 6):
6 = I * 10 + b
b = 6 - 10I
Then, we can plug the values of the slope and y-intercept into the equation and solve for W using the coordinates of the other point (-10, W):
W = I * (-10) + (6 - 10I)
= -10I + 6 - 10I
= 6 - 20I
Therefore, the value of W is 6 - 20I.
Consider the following function. g(x) = x3 + 3x2 - 5 on [-3, 1] Find the derivative of the function. g'(x) = 3x2 + 6x ✓ Find any critical numbers of the function. (Enter your answers as a comma-separated list enter DNE.) x = 1 X Find the absolute maximum value and the absolute minimum value, if any, of the function enter DNE.) maximum 9 X minimum 9 X Need Help? Read It Consider the following function. g(x) = x3 + 3x2 - 5 on [-3, 1] Find the derivative of the function. g'(x) = 3x2 + 6x ✓ Find any critical numbers of the function. (Enter your answers as a comma-separated list enter DNE.) x = 1 X Find the absolute maximum value and the absolute minimum value, if any, of the function enter DNE.) maximum 9 X minimum 9 X Need Help? R
Answers
The following can be answered by the concept of Differentiation.
The derivative of the function is g'(x) = 3x² + 6x.
The critical numbers are x = 0 and x = -2.
The absolute maximum value is -1 and the absolute minimum value is -11.
To find the derivative of g(x), we can take the derivative term by term. The derivative of x² is 3x², the derivative of 3x² is 6x, and the derivative of -5 is 0.
Therefore, g'(x) = 3x² + 6x.
To find the critical numbers of the function, we need to find the values of x where the derivative is equal to zero or undefined. Setting g'(x) = 0, we get 3x² + 6x = 0, which can be factored as 3x(x + 2) = 0.
Therefore, the critical numbers are x = 0 and x = -2.
To find the absolute maximum and minimum values of the function on the interval [-3, 1], we need to check the values of the function at the endpoints and the critical numbers. We have g(-3) = -11, g(0) = -5, g(-2) = -7, and g(1) = -1.
Therefore, the absolute maximum value is -1 and the absolute minimum value is -11.
The derivative of the function is g'(x) = 3x² + 6x.
The critical numbers are x = 0 and x = -2.
The absolute maximum value is -1 and the absolute minimum value is -11.
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help me piz piz piz
.......................
Answers
Answer:
see explanation
Step-by-step explanation:
Dividing 10.5 by 5 gives the number of trees required for 1 cabin.
10.5 ÷ 5 = 2.1 ← trees , thus
3 cabins = 3 × 2.1 = 6.3
7 cabins = 7 × 2.1 = 14.7
Thus
number of trees number of cabins
--------------------------------------------------------
10.5 5
6.3 3
14.7 7
Answer:
7 cabins = 14.7 trees & 3 cabins = 6.3 trees
Step-by-step explanation:
Divide 10.5 by 5 to get how many trees it takes to make ONE cabin.
10.5/5=2.1
ONE cabin needs 2.1 trees to be existent. This can help you figure out how many trees it takes to make any number of cabins.
The ratio for one cabin = 2.1:1
Multiply this by 3 to get how many trees you need for 3 cabins.
2.1*2=6.3 trees needed to make 3 cabins
Do the same for 7 cabins.
2.1*7=14.7 trees needed to build 7 cabins.
4. An acre is 43,560 square feet. How much would it cost to fence in a 4 acre rectangle of land at
$0.55 cents per foot?
Answers
Answer:
174,242.2
hope tis help
Step-by-step explanation:
cale tables on page drawing. A pencil which has been sharpened at each end just fits along the diagonal of the base of 2 box. See Figure 17.15. If the box measures 14 cm by 8 cm, find the length of the pencil.
Answers
The length of this pencil is 16.12 cm.
How to determine the length of the pencil?In order to determine the length of this pencil (diagonal of rectangular figure), we would have to apply Pythagorean's theorem.
In Mathematics and Geometry, Pythagorean's theorem is represented by the following mathematical equation (formula):
x² + y² = z²
Where:
x, y, and z represents the length of sides or side lengths of any right-angled triangle.
By substituting the side lengths of this rectangular figure, we have the following:
z² = x² + y²
z² = 14² + 8²
z² = 196 + 64
z² = 260
z = √260
y = 16.12 cm.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Find the value of x. Round your answer to the nearest tenth. (One number after the decimal.)
19
21
Answers
Answer:
x = ~8.9
Step-by-step explanation:
a^2 + b^2 = c^2
c is the long side
a and b are the other two shorter sides
this means
x^2 + 19^2 = 21^2
x^2 + 361 = 441
x^2 = 441- 361
x^2 = 441- 361
x^2 = 80
square root of 80 = ~8.9
x = ~8.9
Answer:
8.9
Step-by-step explanation:
\(4\sqrt{5}\)=8.9444
rounded = 8.9
Can someone please give me the answer
Answers
Answer:
6/10
Step-by-step explanation:
30/50=3/5
3/5=3/5
15/25=3/5
3/5*2/2=6/10
In the diagram, MZACB = 65. mzECD = А E B C С D
Answers
Answer:
m<ECB = 65°
Step-by-step explanation:
<ACB and <ACD are vertical angles. That means they are congruent and have equal measures.
m<ECB = 65°
help with this questions please!
Answers
Answer:
Area = 1/4 * pi * diameter^2
The area is 78.5^2
Identify the volume of a cone with diameter 18 cm and height 15 cm.
a. V = 3817 cm^(3)
b. V = 1272.3 cm^(3)
c. V = 1908.5 cm^(3)
d. V = 1424.1 cm^(3)
Answers
The volume of a cone with diameter 18 cm and height 15 cm is b. V = 1272.3 cm^(3).
To calculate the volume of a cone, we use the formula:
V = (1/3) * π * r^2 * h
where V is the volume, π is the mathematical constant approximately equal to 3.14159, r is the radius of the cone's base, and h is the height of the cone.
Given that the diameter of the cone is 18 cm, we can calculate the radius by dividing the diameter by 2:
r = 18 cm / 2 = 9 cm
Substituting the values into the volume formula:
V = (1/3) * π * 9^2 * 15
Calculating:
V ≈ 1272.3 cm^3
Therefore, the volume of the cone is approximately 1272.3 cm^3.
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What is the solution to -2|x − 1| = -4? A. x = 3 B. x = -1 or x = 3 C. x = 1 or x = 3 D. No solutions exist.
Answers
Answer:
B
Step-by-step explanation:
-2|x - 1| = -4
|x - 1| = 2
since we are dealing with a function that brings 2 values to the same result, the reverse function (needed to find the values of x that create the result y) has 2 branches :
(x - 1) = 2
and
(x - 1) = -2
x - 1 = 2
x = 3
x - 1 = -2
x = -1
therefore, B is the right answer.
in a probability model, the sum of the probabilities of all outcomes must equal 1. (true or false)
Answers
True, in a probability model, the sum of the probabilities of all outcomes must equal 1.
The statement is true. In a probability model, the probabilities assigned to all possible outcomes must add up to 1. This principle is known as the Law of Total Probability and is a fundamental property of probability theory.
When working with probabilities, we assign a probability value to each possible outcome or event. These probabilities must satisfy certain conditions, one of which is that their sum must be equal to 1. This ensures that the total probability accounts for all possible outcomes and covers the entire sample space.
The sum of probabilities equal to 1 reflects the notion that the entire sample space represents the complete set of possible outcomes, and therefore, the sum of their probabilities must encompass the entire probability space.
If the sum of the probabilities of all outcomes does not equal 1, it would violate the principles of probability theory, leading to inconsistencies and invalid calculations. Therefore, ensuring that the sum of probabilities equals 1 is crucial for a valid and coherent probability model.
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The equation below were created by a student who was asked to write equivalent expressions on either side of
the equals sign. Imagine you are a teacher. Your job is to decide whether their work is right or wrong. If it is
wrong show the the correct way
2(n+3)= 2n +3
Answers
Answer: There are no values of n that make the equation true.
Step-by-step explanation:
you can not add terms that are not alike
Write the equation in slope-intercept form.
7x = 3y − 12
A. y=73x+4
B. 3y−7x=12
C. y−11=73(x−3)
D. y=37x+4
Answers
3y = 7x + 12
y = 3/7x + 4
So what do you think?
Step-by-step explanation:
this is my answer you should mind your own business
There are 25 students in the class. 36% of the students ate hotdogs for lunch. How many students ate hotdogs?
Answers
Answer:
9
Step-by-step explanation:
25 times .36 is 9!
I hope this helps!
Answer:
36% x 25= 9
9 students ate hotdogs
Step-by-step explanation:
just find out how many students are 36% of the class, all i did was take the precent of the class and multiplied it by the number of students in the class in this case 25
find the slope of the tangent line to the polar curve =5 2θ at the point specified by the value θ=π/3.
Answers
Simplifying this expression will give you the slope of the tangent line to the polar curve at θ = π/3.
What is derivative?
The derivative provides information about the slope or steepness of a curve at various points and can be used to find critical points, determine the concavity of a function, and solve optimization problems. The derivative is denoted using various notations, such as f'(x), dy/dx, or df/dx, depending on the context and notation conventions.
To find the slope of the tangent line to the polar curve r = 5 + 2θ at the point specified by θ = π/3, we need to determine the derivative of the polar curve with respect to θ and evaluate it at θ = π/3.
The polar curve r = 5 + 2θ can be expressed in Cartesian coordinates as x = (5 + 2θ) * cos(θ) and y = (5 + 2θ) * sin(θ).
Now, let's find the derivative of y with respect to x using the chain rule:
dy/dx = (dy/dθ) / (dx/dθ)
To find dy/dθ and dx/dθ, we differentiate the expressions for y and x with respect to θ:
dy/dθ = d/dθ [(5 + 2θ) * sin(θ)] = (2 + 2θ) * sin(θ) + (5 + 2θ) * cos(θ)
dx/dθ = d/dθ [(5 + 2θ) * cos(θ)] = (2 + 2θ) * cos(θ) - (5 + 2θ) * sin(θ)
Now, we can calculate the derivative of y with respect to x:
dy/dx = [(2 + 2θ) * sin(θ) + (5 + 2θ) * cos(θ)] / [(2 + 2θ) * cos(θ) - (5 + 2θ) * sin(θ)]
To find the slope of the tangent line at θ = π/3, substitute θ = π/3 into the expression for dy/dx:
dy/dx = [(2 + 2(π/3)) * sin(π/3) + (5 + 2(π/3)) * cos(π/3)] / [(2 + 2(π/3)) * cos(π/3) - (5 + 2(π/3)) * sin(π/3)]
Simplifying this expression will give you the slope of the tangent line to the polar curve at θ = π/3.
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Solve for 90 degrees
Answers
Answer:
5
Step-by-step explanation:
5x + 65 = 90
5x = 90 - 65
x= 25 / 5 = 5
I hope im right !!
What is the radius of convergence of a power series function?
Answers
The radius of convergence of a power series function is a positive real number R that determines the interval of values for which the power series converges.
It represents the distance from the center of the power series expansion, within which the series converges. The radius of convergence is determined by the properties of the coefficients in the power series. Specifically, it is defined as the reciprocal of the limit superior of the absolute values of the coefficients. Mathematically, if we have a power series function of the form:
f(x) = ∑(n=0 to ∞) aₙ(x - c)ⁿ
where aₙ represents the coefficients and c is the center of the series, then the radius of convergence R is given by:
R = 1 / lim sup |aₙ|^(1/n)
The power series converges for all values of x within the interval (c - R, c + R). If |x - c| > R, the series diverges.
It's important to note that the radius of convergence can be zero, indicating that the power series only converges at the center point (x = c), or it can be infinite, indicating that the series converges for all values of x.
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On Monday, 5 painters took 7 hours and 36 minutes to paint an office.
On Tuesday, 8 painters are painting another office the same size.
a) Assuming the painters work at the same rate, how long will it take 8 painters to paint the office?
Give your answer in hours and minutes.
Answers
The 8 painters will take 12 hours and 9.6 minutes to paint the office. The result is obtained by comparing the two variables, worker and time duration.
How to calculate working time for a certain number of workers?On Monday, 5 painters took 7 hours and 36 minutes to paint an office.On Tuesday, 8 painters are painting another office with the same size.If the they work at the same rate, find the time needed for the 8 painters to finish their job!
Let's say
w = number of workerst = time durationWe convert the unit of time in hours.
t₁ = 7 h 36 min
t₁ = (7 + 36/60) h
t₁ = (7 + 0.6) h
t₁ = 7.6 hours
If they work at the same rate, the number of workers and time durations of each day are directly proportional. So,
w₁/w₂ = t₁/t₂
5/8 = 7.6/t₂
t₂ = 8/5 × 7.6
t₂ = 12.16 hours
In hours and minutes,
t₂ = 12 h + (0.16 × 60) min
t₂ = 12 h 9.6 min
Hence, to paint the office, the 8 painters will take 12 hours and 9.6 minutes.
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