Find the error(s) and solve the problem correctly.
Sarah was asked to solve the following problem. Identify her errors and explain how to correct her mistakes.
Answers
Answer:
\(5x^3-18x^2+2x+21\)
Step-by-step explanation:
In the second step, -9x-21 should be 9x+21. This is because -3 in x-3, and -3x-7 in 5x²-3x-7 are both negative, so each term's product should be positive.
Also, in the third line, she wrote -3x²-15x² as -18x⁴ instead of -18x²,and similarly, she wrote -7x-9x as -16x² (however this is wrong anyway because step 2 was done incorrectly).
If we continued off from the second step with these corrected errors:
\(5x^3-3x^2-7x-15x^2+9x+21\\5x^3-18x^2+2x+21\)
Therefore, the correct simplification is \(5x^3-18x^2+2x+21\).
Answer:
5x^3-18^2 +2x +21
Step-by-step explanation:
Related Questions
Describe how the data is dispersed in a box plot with the following data set: 25, 36, 21, 30, 20, 32, 38, 19, 36, 31, 26, 33, 27, 18, 24.
AND PLEASE ACTUALLY EXPLAIN/DESCRIBE!
Answers
In a box plot, also known as a box-and-whisker plot, the data is dispersed and represented visually to provide a summary of the distribution and key characteristics of the dataset. Let's describe how the data is dispersed in the box plot for the given data set: 25, 36, 21, 30, 20, 32, 38, 19, 36, 31, 26, 33, 27, 18, 24.
1. Median (Q2): The median represents the middle value of the dataset when arranged in ascending order. In this case, the median is around 27 or 28, as it lies between the values 27 and 30.2. Lower Quartile (Q1): The lower quartile marks the boundary between the lower 25% of the data and the upper 75%. It is located approximately around 22 or 23, as it falls between the values 21 and 24.3. Upper Quartile (Q3): The upper quartile marks the boundary between the lower 75% of the data and the upper 25%. It is located around 34 or 35, as it lies between the values 33 and 36.4. Interquartile Range (IQR): The IQR is the range between the upper and lower quartiles (Q3 - Q1). In this case, the IQR is approximately 12 (35 - 23).5. Whiskers: The whiskers represent the range of the data excluding any outliers. They extend from the lower quartile (Q1) to the minimum value and from the upper quartile (Q3) to the maximum value. However, in some cases, the whiskers can also be defined based on certain criteria, such as 1.5 times the IQR. Outliers, if present, are depicted as individual data points beyond the whiskers.6. Outliers: Outliers are data points that significantly deviate from the rest of the dataset. In this case, there are no clear outliers based on the data provided.7. Box: The box in the box plot spans from the lower quartile (Q1) to the upper quartile (Q3) and represents the middle 50% of the data. In this case, the box spans approximately from 23 to 35.By observing the box plot, we can see that the data is moderately dispersed, with the majority of values concentrated around the median. The range of the data is approximately 20 to 38, with some variability within the dataset.
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
Minimum value: 18
First quartile (Q1): 22
Median: 29
Third quartile (Q3): 36
Maximum value: 38
The box plot is created using these values. A box is drawn from Q1 to Q3 with a line inside the box at the median. Whiskers are drawn from the box to the minimum and maximum values. Any data points beyond the whiskers are plotted as individual points.
In this box plot, the data is dispersed fairly evenly, with no outliers beyond the whiskers. The box is centered around the median, indicating that the data is roughly symmetric. The lower half of the data is slightly more spread out than the upper half, as indicated by the longer whisker on the left side of the box. Overall, the box plot shows that the data is relatively consistent, with no extreme values.
The circumference of a circular park is approximately 18 feet. What is the approximate area inside the circular park?
Answers
Answer:
25.685 square feet.
Step-by-step explanation:
Circumference = 2 * π * radius
From this, we can derive the formula for the radius:
radius = Circumference / (2 * π)
Let's substitute the value of the circumference and calculate the approximate radius:
radius = 18 / (2 * π)
radius ≈ 18 / (2 * 3.14159)
radius ≈ 2.865 feet
Now that we have the approximate radius, we can calculate the area:
Area ≈ π * radius²
Area ≈ 3.14159 * (2.865)²
Area ≈ 3.14159 * 8.193225
Area ≈ 25.685 square feet
Therefore, the approximate area inside the circular park is approximately 25.685 square feet.
C = 2πr
where C is the circumference and r is the radius of the circle.
In this case, we are given that the circumference is approximately 18 feet, so we can set up the following equation:
18 = 2πr
Solving for r, we get:
r = 9/π ≈ 2.864 feet
Now we can use the formula for the area of a circle:
A = πr^2
Substituting the value we found for r, we get:
A = π(2.864 ft)^2 ≈ 25.85 ft^2
Therefore, the approximate area inside the circular park is approximately 25.85 square feet.
The question is below pls helppppppppp
Answers
Paloma ran 3 3/4 miles around the school track. If each lap is 1/2 mile , how many laps did she run?
Answers
the bottom of a ladder must be placed 3 feet from the wall. The ladder is 10 ft long. How far above the ground does the ladder touch the wall? please draw a picture. yes, I actually need a picture I just do.
Answers
Answer:
The distance between the top of the ladder an the ground is 9.5ft
A group of 4 children and 2 adults pay a total of $32 to take a swim class. A group of 2 children and 5 adults take the same class for $48. How much does it cost for 1 child to take the class?
Answers
Answer:
Ticket problems are algebra word problems that involve various tickets of different values ... The cost of tickets for a play is $3.00 for adults and $2.00 for children. ... Step 1: Set up a table with quantity and value. ... Step 2: Fill in the table with information from the question. ... Step 3: Add down each column to get the equations..
Step-by-step explanation:
the ratio of the number of oranges to apples to bananas is 8:5:2. if there are 120 fruits in total, how many bananas are there
Answers
Answer:
Step-by-step explanation:
To find the number of bananas, we need to determine the proportion of bananas in the total number of fruits based on the given ratio.
Let's assume that the ratio of oranges, apples, and bananas can be represented by 8x, 5x, and 2x, respectively, where x is a common multiplier.
The sum of the parts in the ratio is 8x + 5x + 2x = 15x.
We know that the total number of fruits is 120. Therefore, we can set up the following equation:
15x = 120
To solve for x, we divide both sides of the equation by 15:
x = 120 / 15
x = 8
Now that we know the value of x, we can find the number of bananas by multiplying it by the corresponding part of the ratio:
Number of bananas = 2x = 2 * 8 = 16
So, there are 16 bananas in total.
We can add all the parts to the ratio and get 15. Out of 15 parts, 2 are bananas. Now we can calculate how many fruits are in one part. One fifteenth of 120 is 8, so there are 8 fruits in one part. 2 parts are bananas, so multiplying 8 with 2 gives us our answer, 16.
According to the 2019 census data, the population of Texas was about 2.5 x 10^7 people. The land area of Texas is about 2.6 x 10^5. What was the average number of people per square mile in 2010?
a. 0.96 x 10^2
b. 9.6 x 10^1
c. 0.96 x 10^35
d. 9.6 x 10^12
Answers
Finding people/square mile
There are x number of people in y area. To find x number of people in a single unit of area, divide by area.
\(\frac{(2.5 * 10^7) }{(2.6*10^5)}\)
2.5/2.6 = 0.96
10^7
____ subtract exponents, so 10^2
10^5
answer is (a) 0.96 x 10^2
The stem-and-leaf plot displays data collected on the size of 15 classes at two different schools.
Mountain View School Seaside School
0 5, 8
9, 8, 2, 0 1 0, 1, 2, 5, 6, 8
8, 7, 6, 5, 5, 4, 4, 3, 1, 0 2 5, 5, 7, 7, 8
0 3 0, 6
Key: 2 | 1 | 0 means 12 for Mountain View and 10 for Seaside
Part A: Calculate the measures of center. Show all work. (2 points)
Part B: Calculate the measures of variability. Show all work. (1 point)
Part C: If you are interested in a smaller class size, which school is a better choice for you? Explain your reasoning. (1 point)
Answers
For Mountain View School:
Data: 0, 0, 0, 0, 1, 2, 3, 4, 4, 5, 5, 5, 5, 6, 7, 8, 8, 8, 9
Mean: (0 + 0 + 0 + 0 + 1 + 2 + 3 + 4 + 4 + 5 + 5 + 5 + 5 + 6 + 7 + 8 + 8 + 8 + 9) / 19
= 100 / 19
≈ 5.26
To find the median, we need to arrange the data in ascending order: 0, 0, 0, 0, 1, 2, 3, 4, 4, 5, 5, 5, 5, 6, 7, 8, 8, 8, 9.
The median is the middle value, which is the 10th value in this case.
Median: 5
For Seaside School:
Data: 0, 0, 0, 1, 1, 2, 2, 4, 5, 5, 5, 5, 6, 7, 7, 8, 8, 8, 9
Mean: (0 + 0 + 0 + 1 + 1 + 2 + 2 + 4 + 5 + 5 + 5 + 5 + 6 + 7 + 7 + 8 + 8 + 8 + 9) / 19
= 80 / 19
≈ 4.21
To find the median, we need to arrange the data in ascending order: 0, 0, 0, 1, 1, 2, 2, 4, 5, 5, 5, 5, 6, 7, 7, 8, 8, 8, 9.
The median is the middle value, which is the 10th value in this case.
Median: 5
Now let's calculate the measures of variability, specifically the range and interquartile range (IQR).
Range: The range is the difference between the largest and smallest values in the dataset.
For Mountain View School:
Range: 9 - 0 = 9
For Seaside School:
Range: 9 - 0 = 9
Interquartile Range (IQR): The IQR is the difference between the third quartile (Q3) and the first quartile (Q1) and measures the spread of the middle 50% of the data.
For Mountain View School:
Q1 = 3
Q3 = 7
IQR = Q3 - Q1 = 7 - 3 = 4
For Seaside School:
Q1 = 2
Q3 = 7
IQR = Q3 - Q1 = 7 - 2 = 5
To determine which school is a better choice for a smaller class size, we can consider both the mean and the median.
Both the mean and median for Mountain View School are higher than those for Seaside School. This suggests that, on average, the class sizes at Mountain View School are larger than those at Seaside School. Therefore, if you are interested in a smaller class size, Seaside School would be a better choice
For Mountain View School:
- Median: The median class size is the middle value, which is 25.
- Mean: The mean class size is the sum of all the class sizes divided by the total number of classes, which is (29 + 28 + 28 + 27 + 25 + 24 + 24 + 23 + 21 + 20 + 19 + 18 + 15 + 13 + 10) / 15 = 21.27.
For Seaside School:
- Median: The median class size is the middle value, which is 20.
- Mean: The mean class size is the sum of all the class sizes divided by the total number of classes, which is (25 + 25 + 27 + 27 + 28 + 28 + 28 + 30 + 31 + 35 + 36 + 38 + 40 + 43 + 45) / 15 = 31.13.
Part B:
For Mountain View School:
- Range: The range is the difference between the largest and smallest values, which is 29 - 10 = 19.
- Interquartile Range (IQR): The IQR is the difference between the third quartile (Q3) and the first quartile (Q1). From the stem-and-leaf plot, we can see that Q1 is 20 and Q3 is 28. Therefore, the IQR is 28 - 20 = 8.
For Seaside School:
- Range: The range is the difference between the largest and smallest values, which is 45 - 25 = 20.
- Interquartile Range (IQR): The IQR is the difference between the third quartile (Q3) and the first quartile (Q1). From the stem-and-leaf plot, we can see that Q1 is 27 and Q3 is 38. Therefore, the IQR is 38 - 27 = 11.
Part C:
If you are interested in a smaller class size, Mountain View School is a better choice for you because it has a lower mean and median class size than Seaside School.
Hi could someone please help me
Answers
Answer: y = -1/4x - 6
Step-by-step explanation: the slope is -1/4 because slope = rise/run, the rise is 1, and the run is 4 and the slope is negative. the y intercept is -6 because it passes through -6 at the y axis.
Answer:
-1/4x + -6
Step-by-step explanation:
The slope is -1/4 because slope = \(\frac{rise}{run}\),
So:
-\(\frac{1}{4}\) is the slope, also is negative.
The y intercept is -6 because it passes through -6 at the y axis.
( I also checked it on khan Academy and it was correct)
Hope this helps :)
Pls brainliest...
help
please help me.
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Answers
Kiara has 6 coins. She puts the same
number of coins in each of 3 envelopes.
How many coins does Kiara put in each
envelope?
Answers
Answer:
2 coins
Step-by-step explanation:
If she has 6 coins in total
And only 3 envelopes
Then 6 divided by 3 => 2
So she has 2 coins in each envelope
:0 x
Carrie had a homework assignment where she had to chart the amount of snowfall during a 4 month period over 2 consecutive years. In January of the first year, it snowed 3 inches, and in the second year, it snowed 5 inches. In February of the first year it snowed 1.5 inches, and in the second year, it snowed 4 inches. In March of the first year, it snowed 2.5 inches, and in the second year, it snowed 7 inches. In April of the first year it snowed 4 inches, and in the second year, it snowed 6 inches. In which month did the highest ratio of snowfall?
Answers
Answer:
Step-by-step explanation:
The ratio would be first year (fy) over second year (sy).
fy/sy
January: 3/5 = 0.6
February: 1.5/4 = 0.375
March: 2.5/7 = 0.3571428
April: 4/6 = 0.666..
April is the largest number. Therefore the month with the highest ratio of snowfall is April
Please tell the answer to
1/8 × -8/7 + 3/8 - 8/7 × 3/4
Answers
Answer:
-5/8Step-by-step explanation:
1/8 × -8/7 + 3/8 - 8/7 × 3/4 =
1/7 - 3/8 + 6/7 =
(-8 + 21 - 48)/56 =
-35/56 =
-5/8
Kenneth graphed a system of equations.
Kenneth says the system has no solution
Do you agree?
Yes or No
Answers
The scale of the architectural drawing is 2 inches = 5 feet. If a building is 10 inches wide on the drawing, how wide will it be in real life?
A
35 feet
B
20 feet
C
30 feet
D
25 feet
Answers
Answer:
The answer is D!
Step-by-step explanation:
Firs you have to do 10 divided into 2, the answer is 5. Now you have to do 5 x 5 that will get you 25. So D is the answer! (25 feet)
If you have any question ask me please! :)
2, 3, 5, 9, 17, 22, 31, 39
Regina kept track of the points she scored during her team’s first eight basketball games. What is Regina’s mean score?
Responses
A 3939
B 1616
C 3737
D 1313
E 17
Answers
Answer:
Mean = 16
Step-by-step explanation:
MEAN can be find bg the sum of all score divided by the amount of the score.
Mean = total amount / number of amount
Total amount = 2 + 3 + 5 + 9 + 17+ 22 + 31 + 39
= 128
number of amount = 2, 3, 5, 9, 17, 22, 31, 39
= 8
Then we can calculate mean as
Mean = 128/8
Mean = 16
2+3+5+9+17+22+31+39=128
128/8=16
Measure the length of this segment in inches.
1: 3 5/8 inches
2: 3 1/4 inches
3: 3 3/4 inches
4: 3 1/2 inches
Answers
Answer: The length of the segment from R to S is 3 5/8 inches. I looked at the other ones and this is the closest answer
Step-by-step explanation:
Find the volume of a prism. Show your work.
Answers
Answer:
Step-by-step explanation:
11 times 22
the area of its cross-section multiplied by the length
answer: 242cm squared
If the components of a type of matter can be separated by evaporation, is the matter classified as a mixture or compound? Explain.
PLZ HURRY WILL MARK BRAINLIEST
Answers
Answer:
Matter can be classified into several categories. Two broad categories are mixtures and pure substances. ... Pure substances may be divided into two classes: elements and compounds. Pure substances that cannot be broken down into simpler substances by chemical changes are called elements.
Step-by-step explanation:
Interpreting graphs of functions
8th grade math
15 points for correct answer
Answers
Answer:
The hourly charge for the first three hours is 4 dollars. The hourly charge for the next three hours is 2 dollars. The hourly charge for the next four hours is 1 dollar. The maximum price of the bike rental is 30 dollars.
Step-by-step explanation:
Looking at the graph, we see that the slope, which is the bike rental price per hour, is constant for the first three hours. Then, it changes and remains constant between the 3rd and 6th hour. After that, it changes and remains constant between the 6th and 10th hours. Finally, the cost becomes a constant after 10 hours, meaning the slope becomes 0. This is consistent with the information given in the answer section. Now, we can proceed with the problem.
We have to remember that the slope of the graph is the hourly charge because the y-axis is the cost and the x-axis is the time.
The first part of the question deals with the first three hours. Between hour 0 and hour 3, the price goes up from 8 to 20. We can calculate the slope (m) by calculating the rise over the run (divide the difference in the prices by the difference in the hours):
\(m=\frac{20-8}{3-0}=\frac{12}{3}=4\)
We can also see visually that the price goes up by 4 for every hour. Either way, the hourly charge for the first three hours is 4 dollars
Between hours 3 and 6, which is the second part of the question, the price goes from 20 to 26. Here is the calculation of the slope:
\(m=\frac{26-20}{6-3}=\frac{6}{3}=2\)
Therefore, the hourly charge for the next three hours is 2 dollars
Between hours 6 and 10, which is the third part of the question, the price goes from 26 to 30. Here is the calculation of the slope:
\(m=\frac{30-26}{4-0}=\frac{4}{4}=1\)
Therefore, the hourly charge for the next four hours is 1 dollar
Finally, after hour 10, the price consistently stays at 30. The slope is 0 because the line on the graph is horizontal. The horizontal line is also the maximum portion of the graph. Therefore, the maximum price of the bike rental is 30 dollars.
A botanist separates plants into equal groups of 5 for an experiment. Is the total number of plants in the experiment prime or composite?
Answers
Answer:
The total number of plants will be a composite.
Step-by-step explanation:
She is separating them into equal groups of five. So the total number will be a multiple of 5. Five is a prime number. Multiples of prime numbers are composite numbers.
The total number of plants will be a composite.
What are prime and composite numbers?A prime number only has two factors: one and itself. A composite number is made up of at least three components, and occasionally many more.
Any positive integer that may be created by multiplying two other positive integers is referred to as a composite number. It is, in other words, a positive integer that has at least one divisor besides itself and the number 1.
Given that a botanist separates plants into equal groups of 5 for an experiment.
She is separating them into equal groups of five. So the total number will be a multiple of 5. Five is a prime number. Multiples of prime numbers are composite numbers.
Therefore, the total number of plants will be a composite.
To know more about prime and composite numbers follow
https://brainly.com/question/18297531
#SPJ2
For a beverage, Lisa mixes cups of lemonade to cups of iced tea in a ratio of 3:7. Which of the following best describes the amount of lemonade to iced tea? (4 points)
Group of answer choices
For every 3 cups of lemonade, there are 7 cups of iced tea.
For every 3 cups of lemonade, there are 4 cups of iced tea.
For every 7 cups of lemonade, there are 4 cups of iced tea.
For every 7 cups of lemonade, there are 3 cups of iced tea
Answers
Answer:
For every 3 cups of lemonade, there are 7 cups of iced tea.
Step-by-step explanation:
hope it helps give person below brainliest plz
Which expression has a value that is equivalent to 5n + 13 when n=−5?
A).4n + 8
B).n² + 13
C).n + 8
D).2n + 2
Answers
Answer:Option A
Step-by-step explanation:
Because 5(-5) = -25 + 13 = -12
And 4 x n = -20 + 8 = -12
Thus making both equal. Option a is correct
Part I: Making the Race
Henri is Emile's younger brother and they are having a walking race. Emile can walk 2.5 meters per second whereas Henri walks 1 meter per second. Because Emile is faster, they give Henri a 45 meter head start. Emile knows Henri would enjoy winning the race, but they do not want to make the race so short that it is obvious Emile let Henri win.
1. How long should the race be so that Henri will win in a close race?
2. Describe or show your strategy on how you came up with your answer for #1.
Answers
Answer:
Step-by-step explanation:
To make the race close, the length of the race should be 450 meters.
Here's the reasoning behind the answer:
Let's first calculate how long it would take for Emile to catch up to Henri, assuming Henri starts 45 meters ahead.
The time it takes Emile to cover the same 45-meter distance is 45/2.5 = 18 seconds.
During this time, Henri would have walked a distance of 1 x 18 = 18 meters.
So, after 18 seconds, Emile will have caught up to Henri and will be 27 meters ahead of him (45 - 18 = 27).
To make the race close, we want Henri to finish just a split second before Emile. So, we can assume that Henri will finish the race just as Emile catches up to him.
Let's call the total distance of the race "d."
So, Henri will walk d meters, while Emile will walk d + 27 meters (the 27 meters is the distance Emile has to walk after catching up to Henri).
We can set up an equation to solve for d:
d/1 = (d + 27)/2.5
Solving for d, we get:
d = 450
So, the race should be 450 meters long for Henri to win in a close race.
i need -4.18 - 3.234 written out
Answers
Answer:
−7.414
Step-by-step explanation:
-4.18
-
-3.234
= -7.414
Helpppp Meeeee T-T Plssss
An investor has an account with stock from two different companies. Last year, his stock in Company A was worth $1800 and his stock in Company B was worth $1930. The stock in Company A has decreased 16% since last year and the stock in Company B has decreased 20%. What was the total percentage decrease in the investor's stock account? Round your answer to the nearest tenth (if necessary).
Answers
I dont know if i will be any help, but.
If you add both company's together, and add the 16% + 20% just subtract the 36% from the total balance of the account which is 3730, which gives you 2387.2
Answer option A: 2387
Answer option B: 36%
GIVING BRAINLIEST
Look at the stem-and-leaf plot. What is the mode?
A) 0
B) 1
C) 20
D) 31
Answers
help pleaseeeeeeeeeeeee fastttt
Answers
Answer:times by 2
Step-by-step explanation:
If xx and y vary directly and y is 21 when x is 7, find y when x is 5
Answers
Answer:
y = 15
Step-by-step explanation:
We need to solve for k
y = x
21 = 7k Divide both sides by 7 to solve for k
3 = k
y = xk
y = 5(3)
y = 15
Answer: y = 15
Step-by-step explanation: