Answers
Hello there. To solve this question, we'll have to remember some properties about scatter plots and slope of a line.
Given the scatter plot of the data information, we have to determine the slope of the line.
For this, we could determine it numerically using the least squares method, if we knew the data (the coordinates of the points we're plotting the best fit).
In this case, we simply need to find, by inspection, two points contained in the line and use the slope formula.
Given two points (x0, y0) and (x1, y1) that a line L passes through, then the slope m of this line is given by:
[tex]m=\frac{y_1-y_0}{x_1-x_0}[/tex]By inspection, we can easily spot the points (16, 12) and (28, 20).
Plugging these coordinates in the formula, we get:
[tex]m=\frac{20-12}{28-16}[/tex]Add the numbers and simplify the fraction
[tex]m=\frac{8}{12}\overset{:4}{=}\frac{2}{3}[/tex]This is the slope of this line.
Related Questions
Analyze the solution. If there is an error, circle the error and show the correct solution
Answers
Notice that on the second step, we have the following:
[tex]\begin{gathered} -2(x-7)=6 \\ +2\text{ +2} \end{gathered}[/tex]in this case, the -2 is multiplying x-7, then to eliminate it, we have to divide by 2 both sides of the equation.
if we divide by -2, we have the following:
[tex]\begin{gathered} -2(x-7)=6 \\ \Rightarrow x-7=\frac{6}{-2}=-3 \\ \Rightarrow x-7=-3 \end{gathered}[/tex]finally, if we add7 on both sides, we get:
[tex]\begin{gathered} x-7+7=-3+7 \\ \Rightarrow x=4 \end{gathered}[/tex]therefore, x = 4
Write in CER format
C-claim
E-evidence
R-reasoning
Constructed Response: Answer the following _ question in CER format!
Why did the author of the Federal Pillars political cartoons use "pillars" to represent the states' ratification of the U.S. Constitution?
Answers
Claim - The vertical pillars represent a state that has ratified the new government.
Evidence - The evidence is given in the document itself and is reflected in the cartoon. See the image attached.
Reasoning - The Massachusetts Centinel, August 2, 1789, "The Federal Pillars," via Library of Congress. The Massachusetts Centinel published a series of cartoons illustrating the Constitution's ratification. Each vertical pillar indicates a state that has approved the new administration.
When was the US Consitution Fully Ratified?The Constitution became the formal structure of the government of the United States of America on June 21, 1788, when New Hampshire became the ninth of 13 states to ratify it.
The Constitution has been revised 27 times, the most recently in 1992, despite the fact that over 11,000 modifications have been suggested since 1789. Article V of the Constitution specifies two procedures for proposing revisions to the document.
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Suppose ΔPQR is rotated 270° about the origin, (0,0). Find the coordinates of P′, Q′, and R′. Then sketch ΔP′Q′R′.
Answers
In case it is a 270º Counter-clockwise rotation:
P'(3,-3), Q'(5,-5), R'(6,-3)
In case it is a 270º Clockwise rotation:
P'(-3, 3), Q'(-5,5), R'(-6,3)
1) Since in this case, there is a 270º rotation about the origin then we can write out the following:
As there is no mention of the direction then we'll do it for both cases.
2) For a 270º Counter-Clockwise rotation
Pre-image rule Image
P(3,3) (x,y)=(y,-x) P'(3,-3)
Q(5,5) Q'(5,-5)
R(3,6) R'(6,-3)
3) For a Clockwise Direction
Pre-image rule Image
P(3,3) (x,y)=(-y,x) P'(-3, 3)
Q(5,5) Q'(-5,5)
R(3,6) R'(-6,3)
Simplify √50 over √2
Answers
In order to simplify this expression, we need to use the following property:
[tex]\frac{\sqrt[]{a}}{\sqrt[]{b}}=\sqrt[]{\frac{a}{b}}[/tex]So we have that:
[tex]\frac{\sqrt[]{50}}{\sqrt[]{2}}=\sqrt[]{\frac{50}{2}}=\sqrt[]{25}=5[/tex]So the answer is 5.
A recipe Carmen is
making calls for 4 cups of milk. She has 1 liter of milk.
Her sister says she has enough milk. Is her sister
correct? Explain.
Answers
Answer:
Step-by-step explanation:
Yes, Carmen's sister is correct because 1 liter equals 4.227 (rounded) so yes carmen would have enough milk!
Please help me help help me please help help me
Answers
1. Subtract 5 in both sides of the equation:
[tex]\begin{gathered} 5-5+2\ln (x)=4-5 \\ 2\ln (x)=-1 \end{gathered}[/tex]2. Divide both sides of the euqation into 2:
[tex]\begin{gathered} \frac{2\ln (x)}{2}=-\frac{1}{2} \\ \\ \ln (x)=-\frac{1}{2} \end{gathered}[/tex]3. Wrie the lograrithm in exponential form:
[tex]\begin{gathered} \ln (x)=b \\ x=e^b \\ \\ \\ \ln (x)=-\frac{1}{2} \\ \\ x=e^{-\frac{1}{2}} \end{gathered}[/tex]4. Use properties of powers to rewrite:
[tex]\begin{gathered} x=\frac{1}{e^{\frac{1}{2}}} \\ \\ x=\frac{1}{\sqrt[]{e}} \end{gathered}[/tex]5. Evaluate:
[tex]x\approx0.607[/tex]Then, the solution for the given equation is approximately 0.6075.Mitchell's dog is 1 as old as Katie's cat. The sum of their ages is 123years. How old isMitchell's dog?A 3 years old8 years oldD. 9 years oldB. 4 years old
Answers
Given: Mitchell's dog is 1/3 as old as Katie's cat. The sum of their ages is 12 years.
Required: To find out how old is Mitchell's dog.
Explanation: Let Mitchell's dog be x years old. Then Katie's cat is 3x. Now according to the question-
[tex]\begin{gathered} x+3x=12 \\ 4x=12 \\ x=\frac{12}{4} \\ x=3 \end{gathered}[/tex]Hence Mitchell's dog is 3 years old.
Final Answer: Mitchell's dog is 3 years old.
mZPQT = ? 20 P O 5y - 36 30° T 810 55 s 4x – 12 R
Answers
Given the parallelogram in the attached image.
Recall that two adjacent angles in a parallelogram add up to 180 degrees.
So;
[tex]m\angle\text{PQR}+m\angle QRS=180^{\circ}[/tex]Given;
[tex]undefined[/tex]Under his cell phone plan, Logan pays a flat cost of $58 per month and $3 per gigabyte. He wants to keep his bill under $70 per month. Use the drop-down menu below to write an inequality representing gg, the number of gigabytes he can use while staying within his budget
Answers
WILL GIVE BRAINLIEST
please solve using order of elimination and show work pleasse
Answers
Answer:
c. no solution
d. x = 11, y = -5
Step-by-step explanation:
c.
3x - y = 7----->3x - (3x - 2) = 7
y = 3x - 2 3x - 3x + 2 = 7
2 = 7, so no solution
d.
x + 2y = 1 ----> 3x + 6y = 3
3x + 5y = 8----> 3x + 5y = 8
-----------------
y = -5
x + 2(-5) = 1
x - 10 = 1
x = 11
Hi I need help with this question please thank you!
Answers
Answer:
• The factoring pattern: Difference of two squares (Option A)
,• The factored form: (a+9)(a-9).
Explanation:
Given the expression:
[tex]a^2-81[/tex]81 is the square of 9, thus, the expression above can be written in the form below.
[tex]=a^2-9^2[/tex]The expression is a difference of two squares.
By the factoring pattern of the difference of two squares:
[tex]\begin{gathered} a^2-b^2=(a+b)(a-b) \\ \implies a^2-9^2=(a+9)(a-9) \end{gathered}[/tex]Thus, we have that:
• The factoring pattern: Difference of two squares (Option A)
,• The factored form: (a+9)(a-9).
Arturo asked all of his classmates if they prefer soccer or football. He found that 16 students prefer football while 20 prefer soccer. Which ratio represents the number of students who prefer soccer to the total number of students in Arturo's class? 5 4 4 Mark this and return Save and Exit Next Submit J ContentViewers/AssessmentViewer/Activity#
Answers
The number of students who prefer soccer to the total number of students in Arturo's class is represented by:
16:20
Dividing by 4 on each side of the proportion we have
4:5
Final answer is: 4:5
Devon lives in a city an estimated population of 240,000people which statement about this population is true
Answers
Part D: There are more than 200,000 people in this city is the correct option
The population of the city in which Devon lives <=240000
Data interpretation: The process of examining data through some predetermined processes in order to give it some meaning and reach a pertinent conclusion is known as data interpretation. It entails using the outcomes of the data analysis to draw conclusions about the relationships that were looked at.
Part a:
According to this part, more than 300,000 people live in this city, which may be possible but we cannot be sure about it.
Part b:
According to this part more than 250,000 people live in the city, which may or may not be possible as we are sure only about 240,000 people
Part c:
According to this part, more than 245,000 people live in this city, which is again a may or may not be possible situation given the fact
Part d:
According to this part, more than 200,000 people live in the city. We are sure about this because it is estimated that 240,000 people live in the city. Hence this is the correct option
Although a part of your question is missing, you might refer to this full question: Devon lives in a city with an estimated population of 240,000 people. Which statement about this population is true?
A) There are more than 300,000 people in this city.
B) There are more than 250,000 people in this city.
C) There are more than 245,000 people in this city.
D) There are more than 200,000 people in this city
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Wich of the following will be the coordinate of the vertices of triangle A'B'C'?
Answers
You have to translate the triangle ABC using the translation rule:
(x,y) → (x-1,y+2)
This rule indicates that the triangle will be translated 1 unit left and 2 units up. To determine the coordinates of each vertex after the translation, you have to subtract 1 to the x-coordinate of each point and add 2 to the y-coordinate.
Original → Translation
A(6,1) → A'(6-1,1+2) = A'(5,3)
B(1,7) → B'(1-1,7+2) = B'(0,9)
C(-3,-2) → C'(-3-1,-2+2) = C'(-4,0)
The coordinates of the vertices of triangle A'B'C' will be
A'(5,3)
B'(0,9)
C'(-4,0)
The correct option is C.
Solve for x:
X=
76⁰
9x+1
40°
Answers
7 is the value of x, and 64° is the measure of the unknown angle.
Triangle angles of 76°, (9x+1)°, and 40° are provided.
According to the triangle's "angle sum property," a triangle's angles add up to 180 degrees. Three sides and three angles, one at each vertex, make up a triangle. The sum of the interior angles in a triangle is always 180o, regardless of whether it is acute, obtuse, or right.
One of the most commonly applied properties in geometry is the triangle's angle sum property. Most often, the unknown angles are calculated using this attribute.
Now, the total of a triangle's three angles equals
76°+(9x+1)°+40°= 180°
⇒ 116+9x+1 = 180
⇒ 9x + 117 = 180
⇒ 9x = 63
⇒ x = 7
So, 9x+1=64°
As a result, x is equal to 7 and the unmeasured angle is 64°.
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Marcus just got a summer job as acashier making $8.50 an hour andhas already saved $50. If he wantsto earn at least $475 for a newcomputer, how many hours musthe work? Write an inequality andsolve.
Answers
Marcus's hourly income = $8.50
Amount that has already been saved by Marcus = $50
If Marcus wants to earn at least $475 for a new computer:
Let the amount of hours he will work to earn $475 = t
Since he earns $8.50 hourly and he already saved $475, the inequality will be of the form:
50 + 8.50t ≥ 475
8.50t ≥ 475 - 50
8.50t ≥ 425
t ≥ 425 / 8.50
t ≥ 50
Marcus must work for at least 50 hours
orm Effects?s
Countdown: Days:-2 Time:-06:43:38
Parking survey: For a class assignment, a group of statistics students set up a table near the the answer.
student parking lot. They asked students who passed by to complete a quick survey about
whether they support the building of a multi-level parking structure that would add 425 new spaces at the college.
to points
They used the information from the survey to calculate the 95% confidence interval: (0.53, 0.72). To which population
does the confidence interval apply?
A. O They apply to all students at the college.
B.O They apply only to the population of those who use the student parking lot.
C. The results do not apply to any population because this was a convenience sample.
D. O They apply only to the population of those students who drive to the college.
Answers
Answer:
Step-by-step explanation:
The results do not apply to any population because this was a convenience sample.
The confidence interval (0.53, 0.72) applies only to the population of those students who drive to the college. The correct answer is D.
The confidence interval is a statistical measure used to estimate an unknown population parameter, such as the proportion of students who support the building of a multi-level parking structure.
In this case, the students conducting the survey set up a table near the student parking lot and asked students who passed by to complete the survey. Therefore, the sample used for the survey consists only of students who use the student parking lot.
Since the survey was conducted exclusively among students who use the parking lot, the results and the subsequent confidence interval can only be generalized to that specific population.
The confidence interval (0.53, 0.72) represents the estimated range of proportions of students who support the parking structure within the population of students who drive to the college. It cannot be extended to the entire student body, students who do not use the parking lot, or any other population beyond those who drive to the college.
The correct answer is D.
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Pls help me with this ill give brainlist
Answers
As per the graph, the line passes through coordinates - (1,0) and (0,3)
Since the line passes through both these coordinates, these are the solutions of the equation.
For Option b, 6x + 2y = 6,
If (1,0) is the solution of 6x + 2y = 6, then
⇒ 6(1) + 2(0) = 6
⇒ 6 + 0 = 6
⇒ 6 = 6
If (0,3) is the solution of 6x + 2y = 6, then
⇒ 6(0) + 2(3) = 6
⇒ 0 + 6 = 6
⇒ 6 = 6
Since, these two are solutions of this equation, hence the equation of the given line is: 6x + 2y = 6
What are Coordinates?Coordinates are a pair of numbers that identify a specific point on a coordinate plane, which is a grid of integers. A point in a plane has specific coordinates, as we are aware. Any point's location on a plane can be described by an ordered pair of values (x, y), which are referred to as coordinates. In our daily lives, we employ coordinates for things like map locations and in-class seating arrangements.The cartesian coordinate system is used to find a point's location in a plane.The idea of two mutually perpendicular axes is used to represent a point's coordinate.To learn more about Coordinates, refer to:
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Write four examples of ordered pairs, each
located in a different quadrant of the
coordinate plane.
Answers
The ordinate and abscissa of the x coordinate, along with two values specified in parentheses in a specific order, make up an ordered pair.
Placing a concept on the Cartesian plane can help make it easier to visualize a point.
Numerical values of an ordered pair may be fractions or integers.
(x, y) represents an ordered pair, with x being the separation between a point and the primary axis (x).
In addition, y = ordinate calculates a location's separation from the secondary axis "y."
The point P will be represented mathematically as follows:
P = (6, 4) (6, 4)
The first number in the pair indicates the separation from the "x" axis, which is 6 pixels.
The second value in the ordered pair represents the 4 distance from the "y" axis.
Start from the origin and indicate the point on the Cartesian plane. Starting from the origin, move 6 steps in the direction of the "x" axis (to the right). Take 4 steps forward from this point to the "y" axis (upwards).
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What whole number n makes 6/78<1/n<5/55 true?
Answers
the expression is,
[tex]\frac{6}{78}<\frac{1}{n}<\frac{5}{55}[/tex][tex]\begin{gathered} \frac{6}{78}<\frac{1}{n} \\ n<\frac{78}{6} \\ n<13 \end{gathered}[/tex]Now,
[tex]\begin{gathered} \frac{1}{n}<\frac{5}{55} \\ \frac{1}{n}<\frac{1}{11} \\ n>11 \end{gathered}[/tex]so the number n is between 11 and 13
that is n = 12
thus, the answer is n = 12
HELP
PLEAE I NEED HELP EPKPELPELPEL
Answers
Answer:
[tex]\sqrt{89}[/tex] cm
Step-by-step explanation:
use the pythagorean theorem
[tex]5^{2} +8^{2} =x^{2}[/tex]
25+64=[tex]x^{2}[/tex]
89=[tex]x^{2}[/tex]
[tex]\sqrt{89} =x[/tex]
Which of the following is NOT Linear/does not increase at a constant rate?
Answers
Answer: The one that starts with (-4,10)
Step-by-step explanation:
Linear means that the numbers are going up at a constant rate. It means, that the y will go up corrosponding x.
1) Linear
X goes up 2 per 4 y
2) Linear
X goes up 1 per 3y
3) Linear
X goes up 2 per 4y
4) Not Linear
X goes up 2 per Unequal growth y.
You can tell because it goes up by +5 until the last where it goes up +7
I have completed 33 problems on a 60 problem test. What percent of the test have I completed?
Answers
Answer:
You have completed about 55%
Answer: I would say you have completed about 55% on the test.
ii) A plate holds 7 cup cakes, each with a different colour icing,
and 4 brownies, each of a different size. Find the number of different
ways these 11 cakes can be arranged in a row if no brownie is next to
another brownie.
iii) A plate of biscuits holds 4 identical chocolate biscuits, 6
identical shortbread biscuits and 2 identical gingerbread biscuits.
These biscuits are all placed in a row. Find how many different
arrangements are possible if the chocolate biscuits are all kept
together.
Answers
Using the arrangements formula, the number of ways to organize the plates in each case is given as follows:
ii) No brownie next to another brownie: 570,240
iii) Chocolate biscuits kept together: 8,709,120.
What is the arrangements formula?The number of possible arrangements of a set of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
In item a, if the brownies cannot be together, we have that:
In 8 of the 11 positions(combination), the arrangements will be of 4! and 4!, due to the 4 brownies and the 4 cupcakes.In the remaining 3 positions, they will be organized in 3! ways.Hence the number of ways to organize the cupcakes is:
[tex]C_{11,8} \times 4! \times 4! \times 3! = \frac{11!}{8!3!} \times 4! \times 4! \times 3! = 570,240[/tex]
In item b, the chocolate biscuits have to be kept together, hence:
The 4 biscuits can be ordered in 9 positions, from 1-4 to 9-12.In these positions, they are arranged in 4! ways.The remaining biscuits are arranged in 8! ways.Hence the number of ways that the biscuits can be arranged is:
9 x 4! x 8! = 8,709,120.
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The following table shows the rental charge of a room in a lodge for different number of days. Find the rate of change.
Answers
Rate of change is $35.
Define rate of change.The momentum of a variable is represented by the rate of change, which is used to mathematically express the percentage change in value over a specified period of time. Divide the change in y-values by the change in x-values to determine the average rate of change. Identifying changes in measurable parameters like average speed or average velocity calls for the knowledge of the average rate of change. The rate of change is expressed by a line's slope. It is frequently used while discussing momentum and is typically expressed as a ratio of one variable's change to another's corresponding change. This ratio is graphically represented by a line's slope.
Given,
Table shows the rental charge of a room in a lodge for different number of days.
y₂ = 245
y₁ = 105
x₂ = 7
x₁ = 3
Rate of change = [tex]\frac{y_{2}-y_{2} }{x_{2}-x_{1} }[/tex]
Rate of change = [tex]\frac{245-105}{7 -3}[/tex]
Rate of change = 35
Rate of change is $35.
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What value does the 4 represent in the number 347, 490
Answers
A.40
Explanation
Step 1 (with number 347 and 490)
347
the digit 7 is at one's place
digit 4 is at ten's place
and digit 3 is at hundred's place
then
[tex]347=(3\cdot100)+(4\cdot10)+(7\cdot1)[/tex]the value 4 represents is
[tex]\begin{gathered} \text{value}=4\cdot10=40 \\ \\ \text{value =40} \end{gathered}[/tex]
Answer: 40,000
Step-by-step explanation:
347800:three hundered and forty-seven thousand. Big chunugess
s
Liam bought 6 9/8 pounds of steak. He used 2 1/18 pound of steak for a cookoutfill in each blankRounded to the closest benchmark, Liam bought ??? pounds of steak.Rounded to the closest benchmark, Liam used about ??? pounds of steak for the cookout.Liam has about ??? pounds of steak remaining after the cookout.
Answers
Given:
[tex]\begin{gathered} \text{ Amount of steak Liam bought = 6}\frac{9}{8}\text{ pounds} \\ \\ \text{Amount of steak he used = 2}\frac{1}{18}\text{ pounds} \end{gathered}[/tex]Let's answer the following rounded to the closest benchmark.
2. Technology required.
X
2.3
2.8
3.1
3
3.5
3.8
y
6.2
5.7
4.7
3.2
3
2.8
a. What is the equation of the line of best fit? Round
numbers to 2 decimal places.
b. What does the equation estimate for y when x is 2.3?
Round to 3 decimal places.
c. How does the estimated value compare to the actual value
from the table when x is 2.3?
Answers
The line of best fit using Desmos has the equation y = approximately y=-2.45x+11.82.When x = 2.3 y = 6.18.The residual is thus 0.02.
What is the residual value ?The line of best fit using Desmos has the equation y = approximately -2.45 x + 11.82y=-2.45x+11.82.When x = 2.3, y = about 2.45 x 2.3 + 11.82 = 6.18.The calculated difference between the expected value and the actual value is nearly 6.2 - 6.18 = 0.02. Therefore, there is hardly any difference at all. The residual is thus 0.02When x = 3, y = roughly 2.45 x 3 + 11.82, or 4.47 y = 2.45 x 3 + 11.82, or 4.47 when x = 3. Since the actual value is 3.2, the discrepancy between it and the projected value is equal to 3.2 - 4.47, or -1.27. The residual is thus 1.27.so The line of best fit using Desmos has the equation y = approximately y=-2.45x+11.82.When x = 2.3 y = 6.18.The residual is thus 0.02.To learn more about residual refer to:
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The table on the right gives the annual income for eight families, in thousands of dollars.Find the mean and standard deviation for family incomo.Family A B C D E F G HIncome 47 42 44 45 43 45 48 46The mean of the data set is thousand dollars. (Round to three decimal places as needed)
Answers
We can compute the mean by;
[tex]\operatorname{mean}=\frac{47+42+44+45+43+45+48+46}{8}=45[/tex]and the standard deviation by;
[tex]\frac{\sum ^{}_{}(x-\operatorname{mean})^2}{\sum ^{}_{}f}=\frac{28}{8}=3.5[/tex]So the mean of the data set is 45.
The standard deviation is 3.5
Hello, I need some help with this precalculus question for my homework, please HW Q12
Answers
In order to find the solution to this equation graphically, let's use each side of the equation as a function, and then graph both functions in the same coordinate plane:
[tex]\begin{gathered} y_1=e^x\\ \\ y_2=-3x \end{gathered}[/tex]Graphing y1 in red and y2 in blue, we have:
The intersection point between the graphs is located at (-0.26, 0.77), therefore the solution to the equation is:
[tex]The\text{ }solution\text{ }set\text{ }is\text{ }\lbrace x=-0.26\rbrace[/tex]