Lin has a summer reading assignment. After reading the first 30 pages of the book, she plans to read 40 pages each day until she finishes. Lin makes the graph shown here to track how many total pages she'll read over the next few days.
After day 1, Lin reaches page 70, which matches the point (1,70) She made it on her graph. After day 4, Lin reaches page 190, which does not match the point (4,160) She made it on her graph. Lin is not sure what went wrong since she knows she followed her reading plan.
Sketch a line showing Lin's original plan on the axes.Click on the graph and select edit to complete the graph. Once done, hit save and close to see your completed graph.
What does the vertical intercept mean in this situation? How do the vertical intercepts of the two lines compare?
What does the slope mean in this situation? How do the slopes of the two lines compare?
Answers
1. The graph of Lin mistake is shown below.
2. The Vertical intercept of Lin graph is less than the correct graph.
3. The slope of Lin graph (m= 30) is less than Correct graph (m=40).
What is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
1. Lin started with reading 30 pages.
Then, after 1sr day she will read the 40 pages per day.
So, if number of days represented by x- coordinates and number pages pages by y- coordinate we get
On first day (0. 30)
On second day (1, 30+40)= 91. 70)
On third day (2, 70+40)= (2, 110)
On fourth day (3, 110+40) = (3, 150)
and, On fifth day (4, 150+40)= (4, 190)
Hence, Line made mistake as after 4 days he completed 190 pages.
2. The Vertical intercept of Lin graph is less than the correct graph.
3. The slope of Lin graph (m= 30) is less than Correct graph (m=40).
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Related Questions
Solve the following quadratic by
completing the square.
f(x) = x² + 2x - 12
+√[]
x = [?] +
Answers
Answer:
{x = -1 + √13 , x = -1 - √13}
Step-by-step explanation:
Completing the square:
f(x) = x² + 2x - 12
= x² + 2x + 1 - 1 - 12
= (x² + 2x + 1) - 1 - 12
= (x + 1)² - 13
Solving:
f(x) = 0
⇔ (x + 1)² - 13 = 0
⇔ (x + 1)² = 13
⇔ x + 1 = √13 or x + 1 = -√13
⇔ x = -1 + √13 or x = -1 - √13
How do you find
arcsin (-1)
Answers
By the definition of inverse functions, we will get:
[tex]arcsin(-1) = -pi/2[/tex]
How to find the arcsin of -1?The function arcsin(x) is the inverse of the sine function, such that, if:
[tex]sin(x) = y\\\\arcsin(y) = x[/tex]
Now, we know that:
[tex]sin( -pi/2) = -1[/tex]
Where pi = 3.14
Then, using the above rule:
[tex]arcsin(-1) = -pi/2[/tex]
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what’s ten times ten
Answers
This is because when you multiply the number 10 ten times, it is 100.
Multiply 1 and 1 then add 2 zeros
Given: Circle X with Radius r and circle Y with radius s
Prove: Circle X is similar to Circle Y
Answers
It can be proved that Circles X and Y are similar.
How can we prove that the circles are similar?We were told that circle Y have a radius of s
And X have the Radius r
Going with the theorem that Similar shapes are proportional, we can find the scale factor from circle X to circle Y by making a division on the radii of both circles.
Then the scale factor is [tex]\frac{s}{r}[/tex] which implies that circle Y will gotten by dilation of circle Y.
Therefore, both circles are similar
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The compound inequality 8.00 ≤ x < 9.50 represents all values, x, for which college students are paid hourly as teacher assistants. What is another way of writing this compound inequality?
x ≤ 8.00 and x < 9.50
x ≤ 8.00 or x < 9.50
x ≥ 8.00 and x < 9.50
x ≥ 8.00 or x < 9.50
Answers
Answer:
The 3rd answer down
Step-by-step explanation:
If I broke apart the initial answer, I would see that x is equal to or greater than 8 and x is less than 9.5
The programmer at a local public radio station is compiling data on listeners who stream podcasts. an executive for the national broadcaster has communicated that the overall population mean is 20,500 with a standard deviation of 2,180. the local programmer has a sample of 30 podcasts for her station. by the central limit theorem, which interval do about 99.7% of the sample means fall within?
Answers
The interval in which 99.7% of the sample means fall within 3 standard deviations of the mean is 19,306 to 21,694.
What is the central limit theorem?According to the central limit theorem,
Sample mean = Population mean = μ
Sample standard deviation = (Population standard deviation)/√n = σ/√n
where n is at least 30.
Calculation:It is given that,
The overall population mean = 20,500
Population standard deviation σ = 2180
Sample size n = 30
Since n = 30, the central limit theorem can be applied.
According to the Empirical rule(68-95-99), 99.7% of the sample means fall within the 3 standard deviations of the mean.
So, the interval is calculated by
Sample mean = Population mean = μ = 20500
Standard deviation(sample) = σ/√n
⇒ S = 2180/√30 =398.011 ≅ 398
Thus,
The lower bound = 20500 - 3 × 398 = 19,306
The upper bound = 20500 + 3 × 398 = 21,694
Therefore, the required interval is from 19,306 to 21,694.
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Meredith found the following partial containers of detergent in the basement: 12 quart, 114 gallons, and 34 gallon. how many quarts of detergent did meredith find in all?
Answers
Quarts of detergent 1208
First, we convert each unit to its pint equivalent.
1 gallon =eight US Pint
114 gallons =114 X eight =912 Pint
34 gallon =34 X 8 =272 Pint
further, 1 quart =2 Pint
12 quart = 12 X 2 Pint =24 Pint
including the three values
912+272+24=1208 Pint
therefore, Meredith will want 1,208 Pint boxes.
The unitary technique is a way of solving trouble by way of first finding the fee of a single unit, and then finding the essential value with the aid of multiplying the unmarried unit price.
The system of the unitary technique is to locate the fee of an unmarried unit after which multiply the fee of a single unit to a wide variety of devices to get the vital fee.
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A science test, which is worth 100 points, consist of 24 questions. Each question is worth either 3 points or 5 points. If X is the number of 3 point questions and why is the number of 5 point questions, the system shown represents this situation. X+y=24, 3x+5y=100. What does the solution of this system indicate about the questions on the test?
Answers
Answer:
x= 10 y=14 : 10 3 point, 14 5 point
Step-by-step explanation:
Write your equation down vertically,
3x + 5y = 100
x + y = 24
Next find multiply bottom equation by one number from the tops opposite,
3x + 5y = 100
(-3)x +(-3)y = (-3)24
3x + 5y = 100
-3x - 3y= -72
Add the two functions to isolate y
2y= 28 y=14
Plug y back into original and solve
3x +5(14) =100 --> 3x + 70 =100 --> 3x = 30 x=10
Suppose you vote in an election for a slate of candidates from a particular party.The percentage of votes the party wins in a district determines how many seats in a district the party will gain at the national legislature. These districts are best characterized as
Answers
These districts are best characterized as Proportional Representation districts.
What is Proportional Representation?
There are numerous types of proportional representation systems, but they all have two things in common. They start by using districts with multiple members.
Proportional Representation, abbreviated as PR, uses significantly bigger districts that elect multiple members at once, such as five or ten, rather than electing one member of the legislature in each local district. Second, the percentage of votes a party receives in these districts with several members determines which candidates gain the seats.
The Proportional Representation system of America overcomes the wide ranging drawbacks of single-district voting system like not representing the large number of voters, discrimination against third parties, etc.
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Question 20
Points 3
The height of a lighthouse is 98 meters and the distance between the top of the lighthouse and boat is 125 meters. Find the distance
between the bottom of the lighthouse and the boat.
O 125 m
O 77.6 m
Answers
The distance between the bottom of the lighthouse and the boat is 77.6m.
What is the distance between the bottom of the lighthouse and the boat?
The lighthouse and the boat would form a right triangle. The height would be the height of the lighthouse. The distance between the top of the lighthouse and boat would be the hypotenuse. The distance between the bottom of the lighthouse and the boat would be the base.
In order to determine the required distance, Pythagoras theorem would be used.
The Pythagoras theorem: a² + b² = c²
where:a = lengthb = basec = hypotenuse
125² = 98² + b²
b² = 125² - 98²
b = √(25² - 98² )
b = 77.6m
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Evaluate. (-3 2/3)^2
Answers
Answer:
answer is 121/9
Step-by-step explanation:
13.4444444444 (decimal form)
121/9 (improper fraction form)
13 4/9 (mixed fraction form)
Solve this system of equations: y = x2 – 3x 12 y = –2x 14 1.isolate one variable in the system of equations, if needed. y = x2 – 3x 12 y = –2x 14 2.use substitution to create a one-variable equation. –2x 14 = x2 – 3x 12 3.solve to determine the unknown variable in the equation. what are the values of x? {–2, 1} {–2, 4} {–1, 2} {–1, 4}
Answers
Answer:
our answer is X=2 or X= -1
Answer: C. {-1,2}
Correct on Edge 2023
How much wood is needed to replace the entire roof of this gazebo that is in the
shape of a right pyramid on top of a regular octagon? (Note: The roof's base does
not require wood.)
Answers
formula 1/2(b*h)n
1/2(6*8)8
1/2(48)8
24*8
192
Which of the following is equal to the fraction below ?
(answers are in the picture)
Answers
The citizens of a state may only register to vote after proving to have submitted their census survey.
Answers
The citizens of a state may only register to vote after proving to have submitted their census survey is a "false" statement.
What is census survey?In order to create statistics that define populations and their characteristics, such as age, education, housing, and income, the U.S. Census Bureau compiles data from households.
The purpose of census survey are-
We obtain this information by posing questions to members of the household regarding the occupants of the home, apartment, mobile home, or group housing.The census helps our communities decide where to build everything from homes to hospitals, from schools to supermarkets, and it provides information about who we are as a country and where we are headed. It aids in the government's decision-making about the allocation of cash and assistance to cities and states.It aids in predicting the nation's economic needs, such as those for electricity, housing, food, etc. figuring out the country's population size, standard of life, and number of unemployed people.To know more about census, here
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The complete question is-
The citizens of a state may only register to vote after proving to have submitted their census survey.(True/False)
chegg find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative f(x)
Answers
The derivative and domain of the function f(x) = x²-2x³ is :[tex](-\infty, \infty)[/tex].
What is derivative of the function (differentiation)?The slope of a function's graph or, more precisely, the slope of the tangent line at a point can be used to interpret a function's derivative.
Its computation actually stems from the slope formula for a straight line, with the exception that curves require the employment of a limiting procedure.
Calculation for the derivative:
Step 1: Use the definition of the derivative. Remember that f(x+h) means plug (x+h) into everywhere there is an "x" in f(x).
[tex]\begin{aligned}f^{\prime}(x) &=\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h} \\&=\lim _{h \rightarrow 0} \frac{(x+h)^{2}-2(x+h)^{3}-\left(x^{2}-2 x^{3}\right)}{h} \\&=\lim _{h \rightarrow 0} \frac{\left(x^{2}+2 h x+h^{2}\right)-2(x+h)(x+h)^{2}-x^{2}+2 x^{3}}{h} \quad \text { cancel } x^{2}\end{aligned}[/tex]
[tex]\begin{aligned}&=\lim _{h \rightarrow 0} \frac{\left(2 h x+h^{2}\right)-2(x+h)\left(x^{2}+2 h x+h^{2}\right)+2 x^{3}}{h} \\&=\lim _{h \rightarrow 0} \frac{\left(2 h x+h^{2}\right)-2\left(x^{3}+2 h x^{2}+h^{2} x+h x^{2}+2 h^{2} x+h^{3}\right)+2 x^{3}}{h} \\&=\lim _{h \rightarrow 0} \frac{2 h x+h^{2}-2 x^{3}-4 h x^{2}-2 h^{2} x-2 h x^{2}-4 h^{2} x-2 h^{3}+2 x^{3}}{h}\end{aligned}[/tex]
[tex]=\lim _{h \rightarrow 0} \frac{2 h x+h^{2}-6 h x^{2}-6 h^{2} x-2 h^{3}}{h}[/tex]
Step 2: Cancel out a factor of h from each term in the numerator with the h in the denominator. Then direct substitute h=0.
[tex]\begin{aligned}&=\lim _{h \rightarrow 0}\left(2 x+h-6 x^{2}-6 h x-2 h^{2}\right) \\&=2 x+0-6 x^{2}-6(0) x-2(0)^{2} \\&=2 x-6 x^{2}\end{aligned}[/tex]
f and f' are polynomials, so their domains are all real numbers.
Therefore, for f(x) = x²-2x³ domain of f and f' :[tex](-\infty, \infty)[/tex].
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The complete question is -
Find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative f(x) = x²-2x³.
4 2/7 - 2 1/3 =
4,5 - 2 5/8 =
5 2/8 - 15% =
Thanks for answer!
Answers
The simplified form of the expressions: 4 2/7 - 2 1/3, 4.5 - 2 5/8 and 5 2/8 - 15% are 41/21, 15/8 and 51/10 respectively.
What are the simplified form of the expression?1) 4 2/7 - 2 1/3
First we convert the mixed fraction 4 2/7 and 2 1/3 into an improper fraction.
4 2/7 = (7×4 + 2 )/7 = 30/7
2 1/3 = (3×2 + 1 )/3 = 7/3
Hence,
30/7 - 7/3
( 30×3 - 7×7 )/21
( 90 - 49 )/21
41/21
2) 4.5 - 2 5/8
First we convert both 4.5 and 2 5/8 into an improper fraction.
4.5 = 4 5/10 = (4×10 + 5)/10 = 45/10 = 9/2
2 5/8 = (2×8 + 5 )/8 = 21/8
Hence,
9/2 - 21/8
(9×8 - 21×2 )/16
(72 - 42 )/16
30/16
15/8
3) 5 2/8 - 15%
First we convert both 5 2/8 and 15% into an improper and proper fraction respectively.
5 2/8 = (5×8 + 2)/8 = 42/8 = 21/4
15% = 15/100 = 3/20
Hence
21/4 - 3/20
(21×20 - 3×4 )/80
(420 - 12 )/80
408/80
51/10
Therefore, the simplified form of the expressions: 4 2/7 - 2 1/3, 4.5 - 2 5/8 and 5 2/8 - 15% are 41/21, 15/8 and 51/10 respectively.
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PLEASE HELP GEOMETRY
answer both parts
Answers
1) vertical angles theorem
2) transitive property of congruence
Select the correct answer. Identify the expression equivalent to 4(x + x + 7) - 2x + 8 - 4 by substituting x= 1 and x = 2.
A. 6x + 11
B. 3(x + 7)
C. 2(3x + 16)
D. 3x + 16
Answers
Answer:
C is correct
Step-by-step explanation:
I'm not sure what the substituting part has to do anything, but here is how I got the answer
4(x+x+7)-2x+8-4
4(2x+7)-2x+4
8x+28-2x+4
6x+32
Factor and you get
2(3x+16), which is answer choice C
You can check that the answer is right by plugging in x=1 and x=2 into the original equation and the answer choice, which may be what that is asking.
If Avogadro's number of pennies is divided equally among the 246 million men, women, and children in the United States, how many dollars would each receive
Answers
USD per person = $[tex]2.31[/tex] × [tex]10^{13}[/tex].
What is the US dollar?The US dollar is the official currency of the United States and a number of other countries. The Coinage Act of 1792 established the United States dollar on equal footing with the Spanish silver dollar, divided it into 100 cents, and authorized the minting of coins denominated in dollars and cents.To find how many dollars would each receive:
Avogadro's number of pennies is divided equally among 261 million people.
Avogadro's number is [tex]6.022[/tex] × [tex]10^{23}[/tex].
To find the number of pennies each person will receive, we divide [tex]6.022[/tex] × [tex]10^{23}[/tex] by 261 million.
Pennies per person = [tex]\frac{6.022 * 10^{23} }{261 million} = \frac{6.022 * 10^{23} }{261 * 10^{6} } = 2.31 * 10^{15}[/tex]
This is equal to the number of cents each person receives.
To convert pennies into dollars, 1 USD = 100 pennies, divide [tex]2.31 * 10^{15}[/tex] by [tex]100[/tex].
USD per person = [tex]\frac{2.31 * 10^{15} }{100} = $2.31 * 10^{13}[/tex]
Therefore, USD per person = $[tex]2.31[/tex] × [tex]10^{13}[/tex].
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The question you are looking for is here:
If Avogadro's number of pennies is divided equally among the 261 million men, women, and children in the United States, how many dollars would each receive?
Help me with this question please
Answers
Answer:
x- axis , quadrant 2 , quadrant 3
Step-by-step explanation:
(9.5, 0 ) ← is located on the x- axis
(- 4, 7 ) ← is located in Quadrant II
(- 1, - 8 ) ← is located in Quadrant III
P(x) · Q(x) = R(x); if P(x) = x + 1 and R(x) = 2x³ + 2x²- 3x-3, what is Q(x)?
A. 2x² - 3
B. 2x² - 2
C. 2x² + 2
D. 2x² + 3
Answers
Answer: A
Step-by-step explanation:
[tex]P(x) Q(x)=R(x)\\\\(x+1)Q(x)=2x^3 + 2x^2 - 3x-3\\\\Q(x)=\frac{2x^3 + 2x^2 - 3x-3}{x+1}\\\\Q(x)=\frac{2x^2 (x+1)-3(x+1)}{x+1}\\\\Q(x)=2x^2 - 3[/tex]
Two cans each hold 750ml by how many ml is their total volume less than 1.8 liters
Answers
If two cans hold 750ml ,then their voLume is 0.3 liters less than 1.8 liters.
Given volume of two cans being 750 ml each.
We are required to calculate the quantity in liters of how much the volume of two cans less than 1.8 liters.
Volume is the quantity of substance a container can hold in its capacity.
So volume of cone means quantity of liquid cone can hold if fully filled.
Volume of first cone=750 ml
Volume of second cone=750 ml
Total volume=750+750
=1500 ml
1 liter= 1000 ml
so 1500 ml will be equal to 1500/1000
=1.5 liter
We are required to do comparison with 1.8 liters.
Difference =1.8-1.5
=0.3 liters.
Hence two cans have 0.3 liters less than 1.8 liters.
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write an equation for the graph of a linear function that has slope -1/3 and a y intercept -3
Answers
Answer: y=-(1)/(3)x-3
Please mark brainiest
How many non-square numbers lie between the 215to the power of 2 and 216 to the power of 2
Answers
There are 430 non square numbers that lie between [tex]215^{2}[/tex] and [tex]216^{2}[/tex].
Given two numbers [tex]215^{2}[/tex] and [tex]216^{2}[/tex] and we are require to find non square numbers that lie between them.
Numbers can be consecutive numbers or non consecutive numbers. In our question we will find the consecutive numbers.
Square numbers are those numbers whos square is in a proper number means decimal should not be there.
First number=[tex]215^{2}[/tex]
Second number=[tex]216^{2}[/tex]
First we have to find the exact value of numbers by finding the square of these numbers.
First number=215*215=46225
Second number=216*216=46656
Numbers that lie between them=(46656-46225)-1
=431-1
=430
Hence 430 numbers lie between [tex]215^{2}[/tex] and [tex]216^{2}[/tex].
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help me with this pls asap
Answers
Answer:
your picture is blank if you can fix it i will be glad to help you
Step-by-step explanation:
Answer:
First option
Step-by-step explanation:
The line corresponds to the f(x).
Hope this helps
uppose you want to test the value of the mean in a population. You collect a random sample of 60 which yields a sample mean and sample standard deviation. You only know sampled information to perform the test. What type of procedure is appropriate for your data
Answers
To test the value of the mean in a population when only sample mean and sample deviation are known to perform the test then it is appropriate to use z-test procedure.
What is a Z-test?
A statistical method of testing a hypothesis is the z-test where either:
We are aware of the population variance, which is equal to 2.Despite the fact that we are unsure of the population variance, our sample size, n 30, is sizable. In this instance, we estimate the population variance using the sample variance.A t-test unlike of z-test must be used if the sample size is less than 30 and the population variance is unknown.Additional prerequisites for using the z-test include the following:
Data must follow a normal distribution.Independent data points are required.The variances for each sample must be equal.To know more about the z-test..........
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given that
5x : 8 = 7 : 2
calculate the value of x
give your answer in its simplest form
Answers
Answer: x=5.6 or 5 3/5
Step-by-step explanation:
Cross multiplication is when you have two fractions (ratios) that are equivalent and you can multiply the numerator of the first one by the denominator of the second one, and the denominator of the first one by the numerator of the first one. The answers to these two are equivalent.
So, 5x/8 = 7/2
10x=56
x=5.6
x= 5 3/5
17. If13=xy-5 and y = 6, what is the value of x? (A) 0 (B) 3 (C) 6 (D) 8
Answers
Answer:
Option B: 3
Step-by-step explanation:
#1: Substitute in 6 for [tex]y[/tex] and 3 for [tex]x[/tex]: [tex]13=(3)(6)-5[/tex]
#2: Multiply 3 and 6: [tex]13=18-5[/tex]
#3: Evaluate the equation: [tex]13=18-5[/tex] → [tex]13=13[/tex]
#4: Check if the solution is equal: [tex]13=13[/tex] ✓
[tex]x[/tex] is equal to 3 (Option B).
A set of golf clubs and bag cost $225. The clubs cost $60 more than the bag. How much do the clubs cost?
Answers
Answer:
$142.5
Step-by-step explanation:
225-60=165
165/2=82.5
82.5+60=142.5