A system of equations that model the situation are e = a - 12 and a + e = 100.
The number of tickets Alberto won is 56 tickets.
The number of tickets Elian won is 44 tickets.
How to determine the number of each type of tickets won?In order to write a system of linear equations to describe this situation, we would assign variables to the number of tickets Alberto won and number of tickets Elian won, and then translate the word problem into an algebraic equation as follows:
Let the variable a represent the number of tickets Alberto won.Let the variable e represent the number of tickets Elian won.Since Alberto won 12 tickets less than Elian, a linear equation that models this situation is given by:
e = a - 12 .....equation 1.
Additionally, when they put their tickets together they have exactly 100 tickets;
a + e = 100 .....equation 2.
By solving the system of linear equations simultaneously, we have:
a + a - 12 = 100
2a = 112
a = 112/2
a = 56 tickets.
For the number of tickets (e) Elian won, we have:
e = a - 12
e = 56 - 12
e = 44 tickets.
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PLEASE HELP DUE TODAY!!!!!!!
Consider the functions g(x) = 2x + 1 and h(x) = 2x + 2 for the domain 0 < x < 5
a. Without evaluating or graphing the functions, how do the ranges compare?
b. graph the 2 functions and describe each range over the given interval
Answer:
see the images and explanation
Step-by-step explanation:
for the graph:
the domain 0 < x < 5
the range for each functions:
g(x) = 2x + 1
g(x) = y , 1 < y < 11
h(x) = 2x + 2 , 2 < y < 12
what is the confidence interval estimate of the population mean examination score if a sample of applications provided a sample mean (to the nearest whole number
This means that we can be 95% confident that the true population means examination score falls within this range based on the sample data.
The confidence interval estimate of the population means examination score can be calculated using the sample mean and the margin of error. The margin of error depends on the level of confidence and the sample size.
For example, if a sample of 100 applications provided a sample mean score of 80, and a 95% confidence level is used, the confidence interval estimate of the population mean examination score would be:
Margin of error = (critical value) x (standard error)
The critical value for a 95% confidence level with 99 degrees of freedom is 1.984. The standard error can be calculated using the formula:
Standard error = (standard deviation) / sqrt(sample size)
If the standard deviation of the examination scores is known, it can be used in the formula. If not, the sample standard deviation can be used as an estimate.
Assuming a sample standard deviation of 10, the standard error would be:
[tex]Standard\ error = \frac{10} { \sqrt{(100)}} = 1[/tex]
Therefore, the margin of error would be:
Margin of error = 1.984 x 1 = 1.984
The confidence interval estimate of the population means examination score would be:
80 ± 1.984, or between 78.016 and 81.984.
This means that we can be 95% confident that the true population means examination score falls within this range based on the sample data.
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The 95% confidence interval for the population mean examination score would be between 72.23 and 77.77, to the
nearest whole number.
To determine the confidence interval estimate of the population mean examination score based on a sample mean
provided to the nearest whole number, we need to know the sample size and the level of confidence.
Assuming a normal distribution and a level of confidence of 95%, we can use the following formula to calculate the
confidence interval estimate:
Confidence interval = sample mean +/- (critical value) x (standard error)
The critical value can be found using a t-distribution table or a calculator, based on the sample size and degrees of
freedom (n-1). For a sample size of 30 or more, we can use the z-score instead of the t-score.
The standard error is the standard deviation of the sample divided by the square root of the sample size.
For example, if a sample of 50 applications provided a sample mean of 75, and the standard deviation was 10, the
standard error would be 10/sqrt(50) = 1.41.
Assuming a level of confidence of 95%, the critical value for a sample size of 50 and degrees of freedom of 49 would be 1.96.
Therefore, the confidence interval estimate would be:
75 +/- 1.96 x 1.41 = 75 +/- 2.77
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Problem
The table compares the heights (in centimeters) and the weights (in kilograms) of Karim's friends.
Can the weight of Karim's friends be represented as a function of their height?
Height (centimeters) Weight (kilograms)
163
163163
65
6565
167
167167
70
7070
154
154154
60
6060
172
172172
70
7070
167
167167
68
6868
159
159159
58
5858
160
160160
64
6464
166
166166
69
6969
Choose 1 answer:
Choose 1 answer:
(Choice A) Yes
A
Yes
(Choice B) No
B
No
Weight cannot be represented as a function of height.
Can the weight be represented as a function of their height?No, the weight of Karim's friends cannot be represented as a function of their height.
To represent weight as a function of height, there should be a consistent relationship between the height and weight values.
However, from the given data, we can see that for the same height, there are different weight values, and for the same weight, there are different height values.
This indicates that there is no one-to-one relationship between height and weight, and hence weight cannot be represented as a function of height.
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Jaxon made 5% of his free throws over the season. If he shot 220 free throws, how many did he make?
Answer:
Jaxon made 11 free throws over the season.
Step-by-step explanation:
If he made 5% of his free throws, we know that he will make 5% of the total number of free throws he took, which is 220:
We multiply 220 by 0.05, or 5% to find out how many free throws he made:
220*0.05 = 11
After that, we now know that Jaxon made 11 of his free throws out of 220 over the course of the season, or 5%.
5. Select Yes or No to indicate whether each ordered pair is a point of intersection
between the line x - y = 6 and the circle y² - 26 = -x².
Ordered Pair
(1,-5)
(1,5)
(5,-1)
To determine if each ordered pair is a point of intersection between the line x - y = 6 and the circle y² - 26 = -x², we need to substitute the values of x and y in both equations and see if they are true for both.
Select Yes or No to indicate whether each ordered pair is a point of intersectionFor the ordered pair (1, -5):
x - y = 6 becomes 1 - (-5) = 6, which is true.
y² - 26 = -x² becomes (-5)² - 26 = -(1)², which is false.
Therefore, (1, -5) is not a point of intersection.
For the ordered pair (1, 5):
x - y = 6 becomes 1 - 5 = -4, which is false.
y² - 26 = -x² becomes (5)² - 26 = -(1)², which is true.
Therefore, (1, 5) is a point of intersection.
For the ordered pair (5, -1):
x - y = 6 becomes 5 - (-1) = 6, which is true.
y² - 26 = -x² becomes (-1)² - 26 = -(5)², which is false.
Therefore, (5, -1) is not a point of intersection.
So the answer is:
(1,-5) - No
(1,5) - Yes
(5,-1) - No
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Evan takes 100 milligrams of medicine. The amount of medicine in his bloodstream decreases by 0.4 milligram each minute for a number of minutes, m, after that. He writes the expression 100 - 0.4m to find the amount of medicine in his bloodstream after m minutes. Which statement about his expression is true?
The statement that is true about Evan's expression is that it represents a linear function of the amount of medicine in his bloodstream, where the initial amount is 100 milligrams and the rate of change is -0.4 milligrams per minute.
What is the equivalent expression?
Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.
The expression 100 - 0.4m represents the amount of medicine in Evan's bloodstream after m minutes, where the amount of medicine decreases by 0.4 milligrams each minute.
The coefficient of the variable m (-0.4) represents the rate of change of the amount of medicine in Evan's bloodstream per minute. It tells us that for every one minute that passes, the amount of medicine in his bloodstream decreases by 0.4 milligrams.
The constant term (100) represents the initial amount of medicine in Evan's bloodstream before the medicine starts to decrease.
Therefore, the statement that is true about Evan's expression is that it represents a linear function of the amount of medicine in his bloodstream, where the initial amount is 100 milligrams and the rate of change is -0.4 milligrams per minute.
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a prescription for ear drops specifies that the patient put 2 drops in each ear twice a day for 9 days. approx how many millilitres of medication would be needed for this prescription? ( dosage×frequency×day supply )
approximately 3.6 milliliters of medication would be needed for this prescription.
To calculate the total milliliters of medication needed for this prescription, we will use the formula dosage × frequency × day supply.
In this case, the dosage is 2 drops per ear, the frequency is twice a day, and the day supply is 9 days.
First, let's find out how many drops are needed per day:
2 drops/ear × 2 ears = 4 drops
Since the frequency is twice a day, multiply this number by 2:
4 drops × 2 = 8 drops per day
Now, multiply the number of drops per day by the day supply (9 days):
8 drops/day × 9 days = 72 drops
Typically, 1 drop is approximately 0.05 millilitres. To find out how many millilitres of medication are needed, multiply the total number of drops by the volume of one drop:
72 drops × 0.05 mL/drop = 3.6 mL
So, approximately 3.6 millilitres of medication would be needed for this prescription.
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Approximately 1.8 milliliters of medication would be needed for this prescription.
To calculate how many milliliters of medication would be needed for this prescription, we need to use the following formula:
dosage × frequency × day supply.
The dosage is 2 drops, the frequency is twice a day, and the day supply is 9 days.
First, we need to convert drops to milliliters.
One drop is equal to approximately 0.05 milliliters.
2 drops would be equal to 0.1 milliliters.
Next, we can plug in the values into the formula:
[tex]0.1 milliliters/drop \times 2 drops/twice a day \times 9 days = 1.8 milliliters. [/tex]
The patient will be using exactly 2 drops in each ear for each dose, and that there will be no waste or spillage of the medication.
To determine how many milliliters of medicine would be required for this prescription:
dose frequency day supply.
The recommended dosage is 2 drops, twice day, with a 9-day supply.
We must first convert droplets to milliliters.
A drop is around 0.05 milliliters in volume. As a result, 2 drops are equivalent to 0.1 milliliters.
The values may then be entered into the formula as follows:
0.1 milliliters each drop times twice daily for nine days equals 1.8 milliliters.
As a result, this prescription would require about 1.8 milliliters of medicine.
It's crucial to note that this estimate is predicated on the patient applying precisely 2 drops to each ear for each dose.
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Anyone have the answers
Answer:
The answer is 7 pens
Trigonometric funcions
Which equation are true
Answer:
C and D
Step-by-step explanation:
cosA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{4}{5}[/tex] ⇒ C
sinA = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{3}{5}[/tex] ⇒ D
Label the net for the cylinder. Then find the surface area of the cylinder. Give your answer in terms of π and as a decimal number rounded to the nearest tenth.
The surface area of the cylinder is approximately 94.2 ft².
What is surface area?Surface area refers to the total area of the external or outer part of an object. It is the sum of the areas of all the individual surfaces or faces of the object. Surface area is typically measured in square units, such as square inches (in²), square feet (ft²), or square meters (m²), depending on the unit of measurement used.
According to the given information:
The surface area of a cylinder is the sum of the lateral surface area (the curved surface) and the area of the two circular bases.
The formula for the lateral surface area of a cylinder is given:
Lateral Surface Area = 2πrh
where r is the radius of the cylinder and h is the height of the cylinder.
Plugging in the given values for the radius (r = 3 ft) and height (h = 2 ft), we can calculate the lateral surface area:
Lateral Surface Area = 2π * 3 * 2 = 12π ft²
The formula for the area of a circle (which represents the bases of the cylinder) is given:
Circle Area = πr²
Plugging in the given value for the radius (r = 3 ft), we can calculate the area of each circular base:
Circle Area = π * 3² = 9π ft²
Since there are two bases in a cylinder, we multiply this by 2 to account for both bases:
2 * Circle Area = 2 * 9π = 18π ft²
Now, we can add the lateral surface area and the area of the two bases to find the total surface area of the cylinder:
Total Surface Area = Lateral Surface Area + 2 * Circle Area
= 12π + 18π
= 30π ft²
As a decimal rounded to the nearest tenth, the surface area of the cylinder is approximately 94.2 ft²
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help Here is your graph of the points on the previous screen.
Connect the points in order to create polygon `ABCDEF`.
1.2 Enter the length of the segment betwee
The length of the given line AB is 6 units and the polygon ABCDEF has been created.
What is a graph?A graph is a mathematical structure made up of a collection of points called VERTICES and a set of lines connecting some pair of VERTICES that may or may not be empty.
There is a chance that the edges will be directed, or orientated.
If the lines are directed or undirected, respectively, they are referred to as ARCS or EDGES.
Make a sequence of bars on graph paper as an example of a graph.
So, in the given situation the polygon ABCDEF has been created:
(Refer to the graph attached below)
Now, the length of the side AB:
Count the units as follows which comes to 6 units.
Therefore, the length of the given line AB is 6 units and the polygon ABCDEF has been created.
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Correct question:
Help Here is your graph of the points on the previous screen.
Connect the points in order to create polygon `ABCDEF`.
1.2 Enter the length of the segment between A and B.
cuantos números
primos son a la vez la suma y la diferencia
Answer: there is only one number
Answer:
Solo hay un número primo que se puede escribir como suma de dos números primos y también como diferencia de dos números primos.
Espero haber ayudado :D
Nina uploaded a funny video on her website, which rapidly gains views over time.
The relationship between the elapsed time, ttt, in days, since Nina uploaded the video, and the total number of views, V(t)V(t)V, left parenthesis, t, right parenthesis, is modeled by the following function:
V(t)=500⋅(1. 8)t
Complete the following sentence about the daily percent change in the views of the video.
Every day,
\%%percent of views are
the total number of views of the video
Every day, the number of views of the video increases by 80% of the previous day's views.
Every day, the number of views of the video increases by a certain percentage. To find the daily percent change in the views, we can use the formula for percent change, which is given by:
percent change = ((new value - old value) / old value) * 100
In this case, the old value is the number of views at the start, which is 500, and the new value is the number of views after one day, which is given by:
V(1) = 500*(1.8)^1 = 900
Substituting these values into the formula, we get:
percent change = ((900 - 500) / 500) * 100 = 80%
In other words, for every day that passes, the number of views of the video is multiplied by a factor of 1.8.
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What are the domain and range of this exponential function?y=2x–9
The value of both domain and range of this exponential function is (−∞,∞).
y = 2x-9
The domain of the function can be defined as all real numbers except the ones where the expression is undefined. In the case of 2x-9, there is no real number for which this expression is undefined. Therefore, a domain of this exponential function is (−∞,∞).
The range of the function is defined as the set of all valid y values. In this case, all real numbers are valid values of y. Therefore, the range of this exponential function is (−∞,∞).
Therefore, domain of y = 2x-9 is (−∞,∞) and range is also (−∞,∞).
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clerks at mosier data systems key in thousands of insurance records each day for a variety of client firms. samples of the work of 20 clerks are gathered. ceo donna mosier carefully examines 100 records entered by each clerk and counts the number of errors. mosier wants to set control limits to include 99.73% of the random variation in the data entry process. which type of process control chart should she use?
Donna Mosier should use an Individuals control chart to set control limits for the data entry process.
An Individuals control chart is a type of process control chart used to monitor the process when the sample size is one. In this case, Mosier is examining 100 records entered by each of the 20 clerks, making the sample size one.
To set control limits that include 99.73% of the random variation in the data entry process, Mosier can use the following steps:
Calculate the mean and standard deviation of the number of errors for each clerk based on the 100 records examined.Calculate the Upper Control Limit (UCL) and Lower Control Limit (LCL) using the formulas: UCL = mean + 3 * standard deviation and LCL = mean - 3 * standard deviation.Plot the individual data points for each clerk on the Individuals control chart, with the UCL and LCL as the upper and lower boundaries, respectively.Monitor the data points over time to detect any trends, shifts, or out-of-control points that may indicate a process issue.By using an Individuals control chart, Mosier can set control limits to monitor the data entry process and detect any issues before they become major problems.
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a frog is placed at the origin on the number line, and moves according to the following rule: in a given move, the frog advances to either the closest point with a greater integer coordinate that is a multiple of $3$, or to the closest point with a greater integer coordinate that is a multiple of $13.$ a move sequence is a sequence of coordinates which correspond to valid moves, beginning with $0,$ and ending with $39.$ for example, $0,\ 3,\ 6,\ 13,\ 15,\ 26,\ 39$ is a move sequence. how many move sequences are possible for the frog?
There are 16 possible move sequences for the frog.
The possible moves that the frog can make.
The frog can move to either the closest point with a greater integer coordinate that is a multiple of 3, or to the closest point with a greater integer coordinate that is a multiple of 13.
Let's consider the first type of move, where the frog moves to the closest point with a greater integer coordinate that is a multiple of 3.
If the frog is at the point [tex]$n$[/tex], then the closest point with a greater integer coordinate that is a multiple of 3 is either [tex]$n+3$ or $n+6$[/tex].
Similarly, if the frog is at the point [tex]$n$[/tex] and wants to move to a multiple of 13, then the closest point with a greater integer coordinate that is a multiple of 13 is either[tex]$n+13$[/tex] or [tex]$n+26$[/tex].
Constructing move sequences.
The sequence starts with 0 and ends with 39.
The frog has two choices for its first move: either move to 3 or move to 13.
Let's assume that the frog moves to 3.
From there, the frog has two choices again:
move to 6 or move to 13. If the frog moves to 6, then it has two choices again: move to 9 or move to 13.
If it moves to 13, then it has two choices: move to 26 or move to 16.
We can continue this process until we reach 39.
We can create a tree diagram to help us keep track of the possible move sequences:
0
|
3 or 13
/ \
6 or 13 13 or 26
/ \ / \
9 13 16 26
/ \ / \ / \ / \
... ... ... ... ... ... ... ...
Each branch represents a different move sequence.
We can see that there are 16 possible move sequences in total.
We can also see that some sequences are longer than others.
The longest sequence has 7 moves, while the shortest sequence has only 2 moves.
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Your friend incorrectly factors the expression below as 7x(5-2xy). Factor the expression below correctly. What error did your friend make?
35x - 14xy
Answer:
The answer is 7x(5-2y)
Step-by-step explanation:
35x-14xy
7x(5-2y)
the error made is the x in the bracket
Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 13 people took the trip. She was able to purchase coach tickets for $380
and first class tickets for $1200. She used her total budget for airfare for the trip, which was $9040. How many first class tickets did she buy? How many coach tickets did she buy?
number of first class tickets bought=
Answer: Sarah bought 5 first class tickets and (13-5) = 8 coach tickets.
Step-by-step explanation: The taken a toll of one to begin with lesson ticket is $1200 and the fetched of one coach ticket is $380.
So, the full taken a toll of first class tickets would be 1200x and the entire cost of coach tickets would be 380(13-x) = 4940 - 380x.
The overall fetched of the tickets is given as $9040, so we will set up the taking after condition:
1200x + 4940 - 380x = 9040
Streamlining and tackling for x, we get:
820x = 4100
x = 5
y
∝
√
x
If
y
=
60
when
x
=
36
find,
x
when
y
=
80
If y is proportional to the square root of x and y = 60 when x = 36, then the value of x when y = 80 is 64
We are given that y is proportional to the square root of x, or y ∝ √x.
Using the constant of proportionality k, we can write this relationship as:
y = k√x
To solve for k, we can use the values given in the problem
y = 60, x = 36
60 = k√36
60 = k × 6
k = 60 / 6
Divide the numbers
k = 10
Now that we know k, we can use the same equation to find x when y = 80
80 = 10√x
Squaring both sides, we get
6400 = 100x
x = 64
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The given question is incomplete, the complete question is:
y ∝ √x If y = 60 when x = 36, find x when y = 80.
#4 Please help!!!!!!!!!!
Answer:150°
Step-by-step explanation:
In ABC, m A= 62° and mB=39⁰.
In XYZ, m Y=39° and m Z=79⁰.
Include in Your Answer:
What is mC?
What is mX?
• Is it possible for these two triangles to be similar? Why or
why not?
Explain why the value of 0.6 is greater than the value of 0.39.
Answer:
B
Step-by-step explanation:
The value of 0.6 is greater than the value of 0.39 because 0.6 represents a larger proportion or fraction of a whole than 0.39 does.
To compare these two values, we can think of them as parts of a whole. For example, we can consider 0.6 as 60% of a whole and 0.39 as 39% of the same whole. When we compare 60% and 39%, it is clear that 60% is greater than 39%.
Another way to compare these two values is to convert them to fractions. 0.6 can be written as 6/10 or 3/5, while 0.39 can be written as 39/100.
When we compare 6/10 and 39/100, we can see that 6/10 is greater than 39/100 because 6/10 represents 6 parts out of 10, while 39/100 represents 39 parts out of 100.
Therefore, we can conclude that the value of 0.6 is greater than the value of 0.39 because it represents a larger proportion or fraction of a whole.
In morning Emily studied 40 minutes for a math exam. Later that evening Emily studied for x more minutes. Write an equation that represents the total number of minutes y emily studied for the math exam
Equation that represents the total number of minutes y Emily studied for the math exam is y = 40 +x.
We can represent the total number of minutes Emily studied for the math exam using the equation,
y = 40 + x
Here, 'y' represents the total number of minutes Emily studied for the math exam, '40' represents the number of minutes she studied in the morning, and 'x' represents the number of minutes she studied later that evening.
By adding the number of minutes studied in the morning to the number of minutes studied later that evening, we can calculate the total number of minutes Emily studied for the math exam.
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please help! and explain and show work of how you got the answer. I will mark you brainliest.
Answer: i dont know if this is right but i put a^4+b^4=c^4
Step-by-step explanation:
I have no idea tho
lee had scored the following points in his first 8 games 12,14,14,15,8,10,3,15 enter the number of points lee needs to score in the nest game to increase his keam score to 13 points
Lee needs to score a total of 26 points in the next game to increase his mean score to 13 points.
Calculating the score in the next gameGiven that
Scores = 12,14,14,15,8,10,3,15
To increase his mean score to 13 points,
Lee needs to have a total of 13 x 9 = 117 points after the next game.
He has already scored a total of 12+14+14+15+8+10+3+15 = 91 points in the first 8 games.
Therefore, Lee needs to score a total of 117 - 91 = 26 points in the next game to increase his mean score to 13 points.
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for a normal distribution, a positive value of z indicates that group of answer choices all the observations must have had positive values. the area corresponding to the z is either positive or negative. the sample mean is smaller than the population mean. the sample mean is larger than the population mean.
For a normal distribution ,a positive value of z simply means that the observation or sample mean is above the population mean this implies
none of the options provided is completely accurate.
All the observations must have had positive values,
It is not necessarily true for a positive value of z.
The value of z indicates how many standard deviations away from the mean a particular observation or sample mean is.
A positive value of z simply means that the observation or sample mean is above the population mean.
The area corresponding to the z is either positive or negative,
It is also not accurate.
The area under the normal curve corresponds to probabilities, not positive or negative values.
The area to the right of the mean corresponds to positive z-values, and the area to the left of the mean corresponds to negative z-values.
The sample mean is smaller than the population mean,
It is a possibility when the z-value is negative, indicating that the sample mean is below the population mean.
The sample mean is larger than the population mean,
It is a possibility when the z-value is positive, indicating that the sample mean is above the population mean.
Therefore, the sample mean can be either larger or smaller than the population mean depending on the direction of the z-value.
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rosanne makes 112 liters of strawberry lemonade. she pours 14 of a liter of lemonade into a thermos to take to the park. her brother drinks 25 of the remaining lemonade. how much lemonade does rosanne's brother drink?write your answer as a whole number, fraction, or mixed number. simplify any fractions. liters
If rosanne makes 112 liters of strawberry lemonade, she pours 14 of a liter of lemonade into a thermos to take to the park, rosanne's brother drink 25 liters of lemonade
To solve this problem, we can start by subtracting the 14 liters of lemonade that Rosanne poured into the thermos from the total 112 liters to get the amount of lemonade that remained:
112 - 14 = 98 liters
Next, we need to subtract the amount of lemonade that Rosanne's brother drank, which is 25 liters, from the remaining amount:
98 - 25 = 73 liters
Therefore, Rosanne's brother drank 25 liters of lemonade.
To check our answer, we can add the amount of lemonade in the thermos, the amount that Rosanne's brother drank, and the remaining amount to see if it adds up to the original 112 liters:
14 + 25 + 73 = 112
Since the sum is indeed equal to 112, we can be confident that our answer of 25 liters for the amount of lemonade that Rosanne's brother drank is correct.
In summary, to find the amount of lemonade that Rosanne's brother drank, we subtracted the amount that Rosanne poured into the thermos and the amount that her brother drank from the total amount of lemonade that Rosanne made. The answer is 25 liters.
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A classmate of yours stated that a solid line is not a good representation of an arithmetic sequences. What logical assumption is your classmate using?
The classmate is not correct. A line is a good representation of an arithmetic sequence.
A line is a series of dots that represent each value of the sequence.
A line has the same slope as the common difference in the sequence.
An arithmetic sequence is a set of discrete values, whereas a line is a continuous set of values.
The logical assumption used is: An arithmetic sequence is a set of discrete values, whereas a line is a continuous set of values.
What is arithmetic sequence?An arithmetic sequence is a set of numbers where, with the exception of the first term, each term is obtained by adding a fixed constant to the term before it. Every pair of following terms in the sequence has the same fixed constant, which is known as the common difference. A1 stands for the first term in an arithmetic sequence, while an is used to represent the nth term.
A solid line symbolises continuous numbers, whereas the classmate's logical presumption is that an arithmetic series comprises of discrete values. This presumption is untrue, though, as a line can effectively represent an arithmetic series.
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Find H. C. F of each set of number using long division method 80,215,245and720
The H. C. F of 80,215,245 and 720 using long division method is 5.
The long division method to find the Highest Common Factor (H.C.F.) of 80, 215, 245, and 720.
Divide the largest number by the smallest number.
720 ÷ 80 = 9 with a remainder of 0
Divide the smallest number by the remainder from the previous step.
80 ÷ 40 = 2 with a remainder of 0
Divide the remainder from the previous step by the next smallest number.
40 ÷ 5 = 8 with a remainder of 0
Divide the remainder from the previous step by the next smallest number.
5 ÷ 5 = 1 with a remainder of 0
We have reached a remainder of 0, which means that 5 is the H.C.F. of the given numbers.
Therefore, the H.C.F. of 80, 215, 245, and 720 is 5.
We can also verify this by listing the factors of each number and finding the common factors:
80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
215: 1, 5, 43, 215
245: 1, 5, 7, 35, 49, 245
720: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720
The common factors are 1, 5, and 40.
The largest common factor is 5, which is the same as what we obtained using the long division method.
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Show your work please
Answer:
Perimeter:
[tex]2( \frac{2}{3} + \frac{1}{2} ) = 2( \frac{4}{6} + \frac{3}{6} ) = 2( \frac{7}{6} ) = \frac{7}{3} = 2 \frac{1}{3} [/tex]
The perimeter is 2 1/3 inches.
Area:
[tex] \frac{2}{3} \times \frac{1}{2} = \frac{1}{3} [/tex]
The area is 1/3 of a square inch.