a) The regression prediction for a classroom with 22 students is 651.24.
b) The predicted change in the classroom's average test score for a change from 19 to 23 students is 23.28.
c) The sample average of the test scores across the 100 classrooms is approximately 639.88.
d) The R-squared (R²) measure is 0.08, which indicates a relatively small amount of variation in test scores is explained by variation in class size.
e) The magnitude of the coefficient of correlation (r) is 0.283, indicating a weak positive linear association between class size and test scores.
f) The sample standard deviation of test scores across the 100 classrooms is approximately 11.28.
a) If a classroom has 22 students, then the regression prediction for that classroom's average test score would be:
S = 520.4 + 5.82(22) = 651.24
b) If last year a classroom had 19 students and this year it has 23 students, then the predicted change in the classroom's average test score would be:
ΔS = 5.82(23-19) = 23.28
Note that this calculation assumes that the other factors affecting test scores remain the same, which may not be realistic.
c) The sample average class size across 100 classrooms is 21.4. To find the sample average of the test scores across the 100 classrooms, we simply plug in the average class size into the regression equation:
S = 520.4 + 5.82(21.4) = 639.88
Therefore, the sample average of the test scores across the 100 classrooms is approximately 639.88.
d) The R-squared (R²) measure in this model is 0.08. This is a relatively small value, which means that only 8% of the variation in test scores can be explained by variation in class size. The remaining 92% of the variation is due to other factors that are not captured by the regression model.
e) The magnitude of the coefficient of correlation (r) in this model can be found by taking the square root of R²:
r = √0.08 = 0.283
The interpretation of r is that there is a weak positive linear association between class size and test scores. This means that as class size increases, test scores tend to increase slightly, but the relationship is not very strong.
The difference between R² and r is that R² measures the proportion of variance in the dependent variable (test scores) that is explained by the independent variable (class size) and any other variables in the model, while r measures the strength and direction of the linear association between the two variables.
f) The standard error of the regression (SER) is given as 11.5. This represents the average amount of variation in test scores that is not explained by the regression model. The sample standard deviation of test scores can be estimated by multiplying SER by the square root of (1 - R²) and dividing by the square root of the number of observations:
s = SER × √(1 - R²) / √n
= 11.5 × √(1 - 0.08) / √100
= 11.28
Learn more about standard deviation here
brainly.com/question/14853042
#SPJ4
Melanie owns a food truck that sells tacos and burritos. She on
ingredients to make 102 tacos or burritos.Write an inequality t
possible values for the number of tacos sold, t, and the number
that would satisfy the constraint.
The inequality is represented as t + b ≤ 102 , where t is the number of tacos and b is the number of burritos
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Let the number of tacos be = t
Let the number of burritos be = b
The total number of burritos or tacos be = 102
On simplifying , we get
t + b = 102
So , the maximum number of tacos and burritos to be sold is
t + b ≤ 102
Hence , the inequality is t + b ≤ 102
To learn more about inequality equations click :
https://brainly.com/question/11897796
#SPJ1
1. The table below gives the amount of time students in a class studied for a test and their test scores. Graph the data on a scatter plot, find the line of best fit, and write the equation for the line you draw.
The equation for the line of best fit is y = 5.43x + 76.41.
The correlation coefficient is 0.79
How to find an equation of the line of best fit for the data?In order to determine a linear equation for the line of best fit (trend line) that models the data points contained in the table, we would have to use a graphing calculator (scatter plot).
In this scenario, the number of hours would be plotted on the x-axis of the scatter plot while the test scores would be plotted on the y-axis of the scatter plot.
On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the number of hours and test scores, a linear equation for the line of best fit is given by:
y = 5.43x + 76.41
In conclusion, the type of correlation between the variables is a strong positive correlation.
Read more on scatter plot here: brainly.com/question/28605735
#SPJ1
3x - 3 = root^2 of 3x^2 + 177 What is the sum of all the solutions to the above equation? A - 11 B) -3
C) 3
D) 7
We start by isolating the square root on one side of the equation:
3x - 3 = sqrt(3x^2 + 177)
Squaring both sides of the equation gives:
(3x - 3)^2 = 3x^2 + 177
Expanding the left-hand side gives:
9x^2 - 18x + 9 = 3x^2 + 177
Simplifying gives:
6x^2 - 18x - 168 = 0
Dividing both sides by 6 gives:
x^2 - 3x - 28 = 0
We can now solve for x using the quadratic formula:
x = (3 ± sqrt(3^2 + 4128)) / 2
x = (3 ± 7) / 2
Therefore, the solutions are x = -2 and x = 5, and their sum is -2 + 5 = 3.
Thus, the answer is (C) 3.
For more questions like equation visit the link below:
https://brainly.com/question/20885007
#SPJ11
A tennis player ran a simulation twice to estimate the proportion of wins to expect using a new game strategy. Each time, the simulation ran a trial of 1,000 games. The first simulation returned 172 wins, and the second simulation returned 205 wins. Construct and interpret 95% confidence intervals for the outcomes of each simulation.
The confidence interval from the first simulation is (0. 149, 0. 195), and the confidence interval from the second simulation is (0. 180, 0. 230). For the first trial, we are 90% confident the true proportion of wins with the new game strategy is between 0. 149 and 0. 195. For the second trial, we are 90% confident the true proportion of wins with the new game strategy is between 0. 180 and 0. 230.
The confidence interval from the first simulation is (0. 149, 0. 195), and the confidence interval from the second simulation is (0. 180, 0. 230). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0. 149 and 0. 195. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0. 180 and 0. 230.
The confidence interval from the first simulation is (0. 152, 0. 192), and the confidence interval from the second simulation is (0. 184, 0. 226). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0. 152 and 0. 192. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0. 184 and 0. 226.
The confidence interval from the first simulation is (0. 152, 0. 192), and the confidence interval from the second simulation is (0. 184, 0. 226). For the first trial, we are 90% confident the true proportion of wins with the new game strategy is between 0. 152 and 0. 192. For the second trial, we are 90% confident the true proportion of wins with the new game strategy is between 0. 184 and 0. 226
The correct answer is: The confidence interval from the first simulation is (0. 149, 0. 195), and the confidence interval from the second simulation is (0. 180, 0. 230). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0. 149 and 0. 195. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0. 180 and 0. 230.
What is the confidence interval?The confidence interval is a range of values that is likely to contain the true proportion of wins with the new game strategy based on the sample data.
A 95% confidence interval means that if the simulation is repeated many times, the proportion of wins with the new game strategy will fall within this range 95% of the time.
The correct interpretation of the confidence intervals is that for the first simulation, we are 95% confident that the true proportion of wins with the new game strategy is between 0.149 and 0.195.
This means that if we were to repeat the simulation many times, we would expect the true proportion of wins to fall between these values in 95% of the trials.
Similarly, for the second simulation, we are 95% confident that the true proportion of wins with the new game strategy is between 0.180 and 0.230.
Therefore, the correct answer is an option (b).
To learn more about the confidence interval visit:
https://brainly.com/question/17212516
#SPJ1
At the fair, the Double Shot
ride costs $6. 00 per ride. The
operator of the ride muchi pay
$200 per day for the ride
rental and $65 per day for a
safety inspection. If he wants
to inake a profit of at least
$1,000 each day, what is the
minimum number of people
that must ride the Double
Shot?
The minimum number of people is not possible for the given situation operator has to revise the cost.
Let us consider the minimum number of people ride the Double Shot be x.
Cost per ride = $6.00
Revenue earned from the ride = $6.00x
Rental fee of the ride = ($200).
Safety inspection fee = ($65)
Cost of the rides = 6x
⇒ Total Cost = $200 + $65 + ($6.00)x
Profit of at least $1,000 each day.
This implies,
Revenue ≥ Total Cost + Desired Profit
Substituting the expressions for revenue and total cost,
$6.00x ≥ $200 + $65 + ($6.00)x + $1,000
Simplifying the above expression we get,
$6.00x ≥ $1,265 + ($6.00)x
Subtracting ($6.00)x from both sides we get,
$0.00x ≥ $1,265
⇒No solution for x, because the number of riders cannot be negative.
⇒Operator must either increase the price per ride, decrease the costs, or revise their profit goal.
Therefore, for the given cost it is impossible to get the minimum number of people.
Learn more about minimum number here
brainly.com/question/30584387
#SPJ4
Find the length of each leg,hyp,opp,adj
The length of the legs are 2 units and 3.464 units
How to determine the length of the legsFrom the question, we have the following parameters that can be used in our computation:
The triangle
The legs can be calculated using sine and cosine ratios
Using the above as a guide, we have the following:
sin(30) = PQ/Hyp
cos(30) = RQ/Hyp
Substitute the known values in the above equation, so, we have the following representation
PQ/4 = 0.5
RQ/4 = 0.8660
So, we have
PQ = 4 * 0.5
RQ = 4 * 0.8660
Evaluate
PQ = 2
RQ = 3.464
Hence, one of the leg is 3.464 units
Read more about right triangle at
https://brainly.com/question/2437195
#SPJ1
Looking at the merry-go-round above, if Max begins where it says "start", what is the
the shortest distance that Max is from the wall when the merry-go-round starts?
____feet (Write only the numbers)
Looking at the merry-go-round above, if Max begins where it says "start", what is the
shortest distance that Max will be from the wall during the ride?
___feet
the first answer is 40
the second answer is 15
if Max is at "start," he is 40ft away from the wall.
40 - 25 = 15ft
~ -8 - (-6)
~ -3 - (-7)
~ 6 - (-7)
~ -2 - (-15)
~ -12 - 3
~ -4 - 12
~ 9 - (-5)
Answer:
Using the rules of arithmetic, we can simplify the given expressions as follows:
-8 - (-6) = -8 + 6 = -2
-3 - (-7) = -3 + 7 = 4
6 - (-7) = 6 + 7 = 13
-2 - (-15) = -2 + 15 = 13
-12 - 3 = -15
-4 - 12 = -16
9 - (-5) = 9 + 5 = 14
Therefore, the simplified expressions are:
-2, 4, 13, 13, -15, -16, and 14.
HELP ME ASAP!!!!
2) Practice: Organizing Information
Fill in the blanks to complete the flowchart.
How to Use Elimination to Solve a System of Two Linear Equations
1. Elimination
2. Variable
3. Equation
4. Solve
5. Equation
6. Variable
7. Substitution
My best estimate
Elimination , variable ,equation , Solve , equation, variable, substitution .
Describe Equation?An equation is a mathematical statement that asserts that two expressions are equal. It consists of two sides, the left-hand side and the right-hand side, separated by an equal sign (=). The expressions on both sides of the equation can be numbers, variables, or a combination of both, and the equal sign indicates that the two expressions have the same value.
Equations are used in mathematics to represent relationships between quantities, to solve problems, and to describe various phenomena. They are used in many areas of science, engineering, and economics, as well as in everyday life.
For example, the equation "2x + 3 = 7" represents the relationship between an unknown quantity x and the value 7. By solving this equation, we can find the value of x that makes the equation true. In this case, the solution is x = 2.
Identify elimination as the best method for the problem.
Find a variable with equal or opposite coefficients in the system.
Add or subtract one equation from the other.
Solve the one-variable equation.
Substitute the value of that variable into the other equation.
Solve for the second variable.
Check your answer. Use substitution and/or graphing.
To know more about coefficients visit:
https://brainly.com/question/28975079
#SPJ1
Been stuck on this assignment for a while and it's overdue. I want to turn it in today. Can someone help me get a head start so I can get it done today? This would be a nice birthday present, I'm 18 on March 1 :)
Answer:
Its mostly a step by step process
Step-by-step explanation:
Just Put your full name and the date your depositing the money where the date is and how many bills your depositing how many coins if you don't have coins don't answer it the total amount would be 800 and the net deposit. I added a link just in case. Happy birthday btw.
What is the area of the unshaded part of the following composite figure? Round your answer to the nearest tenth. NEED THE ANSWER ASAP.
Answer:
60m^2
Step-by-step explanation:
15.1×10.3=155.53
155.53÷2=77.765
2.8×6.5=18.2
77.765-18.2= 59.565
rounded to nearest 10th = 60m^2
A vector u and a set S are given. If possible, write u as a linear combination of the vectors in S. U = [3], S= {[1], [2], [-2}}
[8] {[2] [3] [-5]}
Therefore, one possible way to write vector u as a linear combination of the vectors in set S is:
u = [2] + [3]
To write vector u as a linear combination of the vectors in set S, we need to find scalars a, b, and c such that:
u = a[1] + b[2] + c[-2]
Substituting the given values of u and the vectors in S, we get:
[3] = a[1] + b[2] + c[-2]
To solve for the scalars a, b, and c, we can set up a system of equations:
3 = a + 2b - 2c
Since we only have one equation and three unknowns, there are infinitely many solutions to this system. One possible solution is:
a = 1, b = 1, c = 0
Substituting these values back into the equation, we get:
[3] = 1[1] + 1[2] + 0[-2]
Therefore, one possible way to write vector u as a linear combination of the vectors in set S is:
u = [1] + [2]
Similarly, for the second set of vectors, we need to find scalars d, e, and f such that:
u = d[2] + e[3] + f[-5]
Substituting the given values of u and the vectors in S, we get:
[8] = d[2] + e[3] + f[-5]
To solve for the scalars d, e, and f, we can set up a system of equations:
8 = 2d + 3e - 5f
Since we only have one equation and three unknowns, there are infinitely many solutions to this system. One possible solution is:
d = 2, e = 2, f = 0
Substituting these values back into the equation, we get:
[8] = 2[2] + 2[3] + 0[-5]
Therefore, one possible way to write vector u as a linear combination of the vectors in set S is:
u = [2] + [3]
Learn more about linear combination
brainly.com/question/30888143
#SPJ11
Jan is researching the average annual income that people earn in her state based on the level of education they have received.
Based on the table, how much more would someone with a bachelor’s degree earn compared to someone with a high school diploma over a period of 30 years?
Step-by-step explanation:
well, we don't need to look for any fancy calculation tricks.
all we need to do is calculate the amounts in both cases and then calculate the difference.
bachelor's degree income in 30 years :
59,100×30 = $1,773,000
high school diploma income in 30 years :
35,250×30 = $1,057,500
the difference is
$1,773,000 - $1,057,500 = $715,500
a person with a bachelor's degree would earn
$715,500
more over a period of 30 years than a person with only a high school diploma.
this is not considering the changes of the income levels over the period of 30 years (that adds insult to injury ...).
12. Use the diagram below to solve for x.
(MGSE9-12.G.C.2)
в
362
A
a. 115°
b. 50.5°
65
X
D
c. 94°
d. 324
Answer:
c.
Step-by-step explanation:
the inner angle is half of the sum of both outer angles.
65 = 1/2 × (36 + x)
130 = 36 + x
x = 130 - 36 = 94°
True or false? a. A 95% confidence interval for the odds ratio between MI (yes, no) and treatment (placebo, aspirin) is (1.44, 2.33). If we form the table with aspirin in the first row (instead of placebo), the confidence interval is (1/2.33, 1/1.44) = (0.43, 0.69). b. A survey of college students analyzes the association between opinion about whether it should be legal to (1) use marijuana, (2) drink alcohol if you are 18 years old. We may get a different odds ratio value if we treat marijuana use as the response variable than if we treat alcohol use as the response variable. c. Interchanging two rows or interchanging two columns in a contingency table has no effect on the value of the X? or G-chi-squared statistics. Thus, these tests treat both the rows and the columns of the contingency table as nominal scale, and if either or both variables are ordinal, the test ignores that information. d. Suppose that income (high, low) and gender are conditionally independent, given the type of job (secretarial, construction, service, professional, ...). Then, income and gender are also independent in the 2 x 2 marginal table. e. According to the Pew Research Center (www.people-press.org), when adults in the US were asked in 2010 whether there is solid evidence that the average temperature on Earth has been getting warmer over the past few decades, the esti- mated odds of a yes response for a Democrat was 2.96 times higher than for an Independent, and it was 2.08 times higher for an Independent than for a Repub- lican. The estimated odds ratio between opinion on global warming and whether one is a Democrat or a Republican equals 2.96 x 2.08 = 6.2.
a. False. If we form the table with aspirin in the first row (instead of placebo), the confidence interval is (1/2.33, 1/1.44) = (0.43, 0.69).
b. True. We may get a different odds ratio value if we treat marijuana use as the response variable than if we treat alcohol use as the response variable.
c. False. Interchanging two rows or interchanging two columns in a contingency table does have an effect on the value of the X2 or G-chi-squared statistics. Thus, these tests treat both the rows and the columns of the contingency table as nominal scale, and if either or both variables are ordinal, the test takes that information into account.
d. False. Income and gender are not necessarily independent in the 2 x 2 marginal table, even if they are conditionally independent given the type of job.
e. False. The estimated odds ratio between opinion on global warming and whether one is a Democrat or a Republican does not equal 2.96 x 2.08 = 6.2, it equals (2.96/2.08) = 1.42.
Learn more about marijuana
brainly.com/question/13402559
#SPJ11
The graph shows the amount of water in a sink after several minutes.
Which function represents this situation?
A. y = -2x + 5
B. y = -3/2x + 5
C. y = -2/3x + 5
D. y = 2/3x + 5
The correct answer is B. The graph shows the amount of water in a sink after several minutes, so it is a decreasing function.
What is graph?Graph is a mathematical structure used to represent connections or relationships between objects. It consists of nodes, which are connected by edges. Graphs are used in computer science and other fields to represent networks of communication, data organization, computational devices, the flow of computation, and other objects. Graphs are also used to represent the abstract connections between objects in a more visual way. Graph theory is the study of graphs and their properties.
Option B, y = -3/2x + 5, is a linear function with a negative slope, which is the correct representation for this situation. This equation can be used to find the amount of water in the sink after any given number of minutes.
To know more about graph click-
https://brainly.com/question/19040584
#SPJ1
Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle A?
The measure of angle A is 85^o.
What is a quadrilateral?A quadrilateral is any form of plane figure which is bounded by four straight sides. Examples include: square, rhombus, rectangle trapezium etc. Each example of quadrilateral has differentiating properties.
The given quadrilateral ABCD inscribed in the circle has the shape of a rhombus. So we have:
the measure of opposite internal angles of a rhombus are congruent, so that;
x + (2x + 1) + 148 + (2x + 1) = 360
5x + 150 = 360
5x = 360 - 150
5x = 210
x = 210/ 5
= 42
x = 42^o
Thus measure of angle A = (2x + 1)
= 2*42 + 1
= 85^o
Learn more about quadrilaterals at https://brainly.com/question/26481983
#SPJ1
how to calculate 8+3(5-7)
Answer:
How to calculate 8 + 3(5 - 7)
Use Pemdas
Pemdas
8 + 3(5 - 7)
5 - 7
= -2
8 + 3 ⋅ -2
Pemdas
8 + 3 ⋅ -2
3 x -2
= -6
8 + -6
Pemdas
8 + -6
= 28 + 3(5 - 7) = 2Step-by-step explanation:
You're welcome.
Answer:
8+3(5-7)=-2
You will use the"Bracket Of Division Multiplication Addition and Subtraction(BODMAS)" method. Hence solve the one in the bracket first. So it's going to be 5-7 which is -2.Then you continue with the multiplication of 3 by the -2 you got making -6. Finally add the 8 to the -6 making 2.
The net profit in dollars per day for a small business owner is given by the equation f(x)= -0.1x2 + 8x +5, where x is the number of employees he hires. If he hires the number of employees that will maximize his profit, what will his profit be in dollars per day? Enter an exact number.
The maximum profit is $165 per day when the business owner hires 40 employees.
To find the maximum profit, we need to find the vertex of the quadratic function f(x)= -0.1x2 + 8x +5. The x-coordinate of the vertex can be found using the formula x = -b/2a, where a = -0.1 and b = 8.
x = -8/(2*-0.1) = -8/(-0.2) = 40
Now, we can plug in the x-value of the vertex into the function to find the maximum profit:
f(40) = -0.1(40)2 + 8(40) + 5 = -0.1(1600) + 320 + 5 = -160 + 320 + 5 = 165
Therefore, the maximum profit is $165 per day when the business owner hires 40 employees.
For more about net profit:
https://brainly.com/question/22024991
#SPJ11
state the values of sec x, csc x, and cot x if x is an angle in standard position and the terminal side passes through (6,-5)
pls help
The values of sec x, csc x, and cot x are:
sec x = sqrt(61)/6
csc x = -sqrt(61)/5
cot x = -6/5
What is the Pythagoras Theorem?
Pythagoras Theorem is the way in which you can find the missing length of a right-angled triangle.
We can use the Pythagorean theorem to find the length of the hypotenuse of the right triangle formed by the terminal side and the x- and y-axes. Then, we can use the definitions of the trigonometric ratios to find the values of sec x, csc x, and cot x.
Let r be the length of the hypotenuse:
r = sqrt(6^2 + (-5)^2) = sqrt(61)
Then, we have:
cos x = adjacent/hypotenuse = 6/sqrt(61)
sin x = opposite/hypotenuse = -5/sqrt(61)
From these, we can find:
sec x = hypotenuse/adjacent = sqrt(61)/6
csc x = hypotenuse/opposite = -sqrt(61)/5 (Note that csc x is negative because sin x is negative in the third quadrant)
cot x = adjacent/opposite = -6/5
Hence, the values of sec x, csc x, and cot x are:
sec x = sqrt(61)/6
csc x = -sqrt(61)/5
cot x = -6/5
To learn more about Pythagoras Theorem, Visit
https://brainly.com/question/343682
#SPJ1
Question 2 (1 point)
What is the value of the following
The value of the expression 7₂ + 3₃ is 10₅.
What is an expression?One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is a number used before a phrase.
Given:
An expression is 7₂ + 3₃.
To find the value of the expression, first, add 7 and 3.
That means, 7 + 3 = 10.
Now add 2 and 3,
2 +3 = 5
So, the value of the expression is 10₅.
Therefore, the result is 10₅.
To learn more about the expression;
brainly.com/question/24242989
#SPJ1
I really need help, this is due tomorrow
Answer:
Your answer:
6. x = 8
8. x = 3
Step-by-step explanation:
Basic calculation involving adding/subtracting and multiplying and dividing.
Formula for Area of a Rectangle:
Area = Length * Width.
6. Given information
A = 165 cm^2
length = 4x + 1
width = 5
(4x + 1) * 5 = 165 cm^2
5 * (4x + 1)= 165
20x + 5 = 165
20x = 160
x = 8
8. Given information
A = 40 cm^2
length = 7x - 1
width = 2
(7x - 1) * 2 = 40 cm^2
2 * (7x - 1)= 40
14x - 2 = 40
14x = 42
x = 3
What is the coefficient a in the factorization: \[ x^{2}+a x y+b y^{2}=(x+5 y)(x-4 y) \] Select one: a. \( -20 \) b. 5 c. \( -1 \) d. \( -4 \) e. 1
The coefficient a in the factorization [ x²+a x y+b y²=(x+5 y)(x-4 y) ] is -1. The correct answer is C
Terms are the sum of the numbers or variables, factors are the sum of the numbers or variables multiplied, and coefficient is the number multiplied by the variable.
To find the coefficient a, we can expand the right side of the equation and compare it to the left side.
Expanding the right side gives us: [ (x+5 y)(x-4 y)=x²-4 x y+5 x y-20 y² ]
Simplifying the right side gives us: [ x²+x y-20 y² ]
Comparing this to the left side of the equation, we can see that the coefficient a is -1.
Therefore, the correct answer is c. ( -1 ).
To learn more about factorization visit:
brainly.com/question/27733205.
#SPJ11
For the following exercises, decide if the function continuous at the given point. If it is discontinuous, what type of discontinuity is it?
Both the limits are equal to -1, which means the function is continuous at x=1. Therefore, there is no discontinuity at x=1. So, The function is continuous at x=1.
To determine if the function is continuous at x=1, we need to evaluate the left and right limits of the function at x=1 and see if they are equal.
Left limit as x approaches 1:
\lim_{x\to 1^-}\frac{2x^2-5x+3}{x-1} = \frac{2(1)^2-5(1)+3}{1-1} = \frac{0}{0}
Right limit as x approaches 1:
\lim_{x\to 1^+}\frac{2x^2-5x+3}{x-1} = \frac{2(1)^2-5(1)+3}{1-1} = \frac{0}{0}
Since both limits are indeterminate forms of 0/0, we can use L'Hopital's Rule to evaluate them.
Taking the derivative of the numerator and denominator of the original function, we get:
\lim_{x\to 1^-}\frac{4x-5}{1} = -1
\lim_{x\to 1^+}\frac{4x-5}{1} = -1
Both limits are equal to -1, which means the function is continuous at x=1. Therefore, there is no discontinuity at x=1.
To learn more about L'Hopital's Rule
https://brainly.com/question/29480665
#SPJ4
Select all the trinomials that have (3x + 2) as a factor.
6x² +19x+10
6x²-x-2
6x² +7x-3
6х2 - 5x - 6
-
12x²-x-6
Answer: To check if (3x + 2) is a factor of a trinomial, we can use long division or synthetic division. However, we can also use the factor theorem, which states that if f(c) = 0 for a polynomial f(x) and a constant c, then (x - c) is a factor of f(x).
In this case, we can use the factor theorem with c = -2/3 to check if (3x + 2) is a factor:
f(-2/3) = 0 if and only if 3(-2/3) + 2 = 0, which is true. Therefore, (3x + 2) is a factor of f(x) if and only if f(-2/3) = 0.
Using this method, we can check each trinomial:
6x² +19x+10: f(-2/3) = 0. Therefore, (3x + 2) is a factor of 6x² +19x+10.
6x²-x-2: f(-2/3) = 0. Therefore, (3x + 2) is a factor of 6x²-x-2.
6x² +7x-3: f(-2/3) ≠ 0. Therefore, (3x + 2) is not a factor of 6x² +7x-3.
6х2 - 5x - 6: f(-2/3) ≠ 0. Therefore, (3x + 2) is not a factor of 6х2 - 5x - 6.
12x²-x-6: f(-2/3) ≠ 0. Therefore, (3x + 2) is not a factor of 12x²-x-6.
Therefore, the trinomials that have (3x + 2) as a factor are:
6x² +19x+10
6x²-x-2
Note: We could also use long division or synthetic division to confirm our results.
Step-by-step explanation:
Your sucessful art supply store, Warpz, just solf 30% of its inventory over the weekend. If on the second day you only sold 15% of the inventory that was left in the store, what percent of the total inventory was sold?
Please give an explanation!
18% of the total inventory was sold.
What is percentage?A percentage is a fraction of an amount expressed as a particular number of hundredths of that amount.
Given that, 30% of the inventory is sold over the weekend, on the second day only 15% of the inventory that was left in the store to be sold,
Let x be the total inventory,
Sold inventory = 30% of x,
The second day = x - 30% of x is sold
x -30% of x = 15% of x
x - 0.3x = 0.15x
x = 0.3x+0.15x
x = 0.18x
x = 18% of x,
Hence, 18% of the total inventory was sold.
Learn more about percentage, click;
https://brainly.com/question/28269290
#SPJ1
you spend 8% doing homework if you had to add 4% of your time to doing homework, how many hours a day would you spend doing homework now?
The number of hours one would spend doing homework now would be; 2.88 hours.
What is the number of hours spent doing homework now?As evident in the task content; One spends 8% doing homework, if one adds 4% more.
The total percent of time spent doing homework is; 12%.
Since there are 24 hours in a day; it follows that the number of hours spent doing one's homework is;
= 12% of 24 = 0.12 × 24.
= 2.88 hours.
Read more on percentages;
https://brainly.com/question/28398580
#SPJ1
\ all shoe 25 PERCENTAGE says the sign. what will be the sale
price of pair of dress shoes originally at $69.98 type o-*
The sale price of a pair of dress shoes originally at $69.98 with a 25% discount will be $52.49.
To find the sale price, you need to calculate the discount amount and subtract it from the original price.
Step 1: Find the discount amount by multiplying the original price by the discount percentage.
$69.98 x 0.25 = $17.49
Step 2: Subtract the discount amount from the original price to get the sale price.
$69.98 - $17.49 = $52.49
Therefore, the sale price of the dress shoes will be $52.49.
To know more about percentage click here:
https://brainly.com/question/29306119
#SPJ11
Which statement is an example of the transitive property of congruence?
A. if KLM= PQR and PQR= STU , then KLM=STU
B. If KLM= PQR, then PQR= STU.
C. If KLM= PQR, then PQR= KLM.
D. KLM=KLM
Option A → If KLM ≅ PQR and PQR ≅ STU , then KLM ≅ STU, is the correct answer for the transitive property of congruence.
What is congruency?In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
Given is to write the transitive property of congruence.
Transitive Property of Congruence →The transitive property of congruence states that “ if two shapes are congruent to the third shape, then all the shapes are congruent to each other. So, we can conclude that option A is the correct answer.
Therefore, Option A → If KLM ≅ PQR and PQR ≅ STU , then KLM ≅ STU, is the correct answer for the transitive property of congruence.
To solve more questions on congruency, visit the link-
https://brainly.com/question/7888063
#SPJ1
Find X (the missing variable)
14
33
19
27
pls, I really need this!
In the triangle the value οf x is D) 27.
What is triangle?A triangle is a fοrm οf pοlygοn with three sides; the intersectiοn οf the twο lοngest sides is knοwn as the triangle's vertex. There is an angle created between twο sides. One οf the crucial elements οf geοmetry is this.
Certain fundamental ideas, including the Pythagοrean theοrem and trigοnοmetry, rely οn the characteristics οf triangles. The angles and sides οf a triangle determine its kind.
Here in the given triangle, using ratiο then
=> [tex]\frac{x+8}{10}=\frac{2x-5}{14}[/tex]
=> [tex]14\times(x+8)=10(2x-5)[/tex]
=> 14x+112=20x-50
=> 20x-14x=112+50
=> 6x = 162
=> x =[tex]\frac{162}{6}[/tex]
=> x = 27
Hence the cοrrect οption is D)27.
To learn mοre about triangle refer the below link
https://brainly.com/question/17335144
#SPJ1