Answers
Answer:
The first box and whisker plot
Step-by-step explanation:
A box and whisker plot gives you the five number summary for a set of data. The five number summary is
The minimum/lowest value (looks like the top of capital T turned sideways and is the leftmost part of the box-and-whisker plot The first quartile or Q1, representing 25% of the data (the first point represented in the "box" of the plot and serves as an endpoint of the box)The median or Q2, representing 50%/the middle of the data (the line that splits the box into two parts/the line in the middle of the box)The third quartile or Q3, representing 75% of the data (the last point represented in the "box" of the plot and serves as another endpoint of the box)The maximum/highest value (also looks like the top of capital T turned sideways and is the rightmost part of the box-and-whisker plotMaximum and minimum:
We know from the data that the minimum value is 100 and the maximum value is 200. However, because both boxes available as answer choices have the correct minimum and maximum, we'll need to find more data.
Median:
We can start finding the median first by arranging the data from the least to greatest. Then, we find the middle of the data. Because there are 9 points and 9 is odd, we know that there will be 4 points to the left of the median and 4 points to the right of the median:
100, 100, 120, 120, 150, 165, 180, 180, 200
150 has 4 numbers both on its left and right sides so its the median.
Because both of the plots available as answer choices have the correct median, we we'll need to find more data.
First Quartile/Q1:
In order to find Q1, we must find the middle number of the four numbers to the left of the median.
Because we have an even number of points, we will get two middle numbers, 100 and 120. To find the middle of all four points, we average these two numbers:
(100 + 120) / 2 = 220 / 2 = 110
Only the first box has the accurate Q1 value, so it's our answer.
We don't have to find Q3, since both boxes have the correct Q3, but only the first box has the correct minimum, correct Q1, correct median, correct Q3, correct maximum.
Related Questions
PLEASEEEE HELPPP ASAP 20 PTS
Use long division to determine the quotient of the following expression.
Write the quotient in standard form with the term of largest degree on the left. (10x^(2)+3x-77)-:(2x+7)
Answers
The quotient of the division 10x² + 3x - 77 ÷ 2x + 7 is 5x - 16
Evaluating the long division expressionsThe quotient expression is given as
10x² + 3x - 77 ÷ 2x + 7
The long division expression is represented as
2x + 7 | 10x² + 3x - 77
So, we have the following division process
5x - 16
2x + 7 | 10x² + 3x - 77
10x² + 35x
--------------------------------
-32x - 77
-32x - 112
-------------------------------------
35
Hence, the quotient of the long division is 5x - 16
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There are 50 athletes signed up for a neighborhood basketball competition. Players can select to play in the 6-player games ("3 on 3") or the 2-player games ("1 on 1").
All 50 athletes sign up for only one kind of game. Complete the table to show different combinations of games that could be played
Answers
If 13 matches are played in total then, 7 2-player matches and 6 6-player matches are played.
Here we see that the table has two columns- 6 player Athletes and 2 player athletes. It is given that no athlete participates in both the type of games. Hence we can say that
If one match for 2 player game is held then 2 players are employed there.
Hence we have 48 players left
hence we will have 48/6 = 8 6-player matches.
Similarly, if 1 6-player match is played then 44 players applied for the 2-player match, hence, we have 44/2 = 22 2-player matches
If 4 2-player matches are held then we will have 8 players booked. Hence 42/6 = 7 6-player matches were held.
If 4 6-player matches were held then, we have 26/2 = 13 2-player matches.
Hence the table will be
Number of 6 Player Games Number of 2-player games
8 1
1 22
7 4
4 13
b)
Let the total 2-player games played be x and 6-player games be y
we have,
x + y = 13
2x + 6y = 50
or, 2(x + y) + 4y = 50
or, 26 + 4y = 50
or, 4y = 24
or, y = 6
Hence x = 7
Therefore, in total 7 2-player matches and 6 6-player matches are played.
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Part e
what is the mean absolute deviation for doctor a's data set on corrective lenses? what is the mean absolute deviation
for doctor b's data set on corrective lenses? write a sentence comparing the variation of the two data sets using their
mean absolute deviations.
Answers
The MAD for Doctor A's data set is 0.67 and the MAD for Doctor B's data set is 0.83. Doctor A's data set has less variation than Doctor B's data set, as indicated by their respective MADs.
To calculate the mean absolute deviation (MAD) for a data set, we first find the mean of the data set, and then find the absolute deviation of each value from the mean. We then find the mean of these absolute deviations.
a) For Doctor A's data set on corrective lenses, the mean is:
Mean = (15+18+17+16+14)/5 = 16
The absolute deviations from the mean are:
|15-16| = 1
|18-16| = 2
|17-16| = 1
|16-16| = 0
|14-16| = 2
The mean of these absolute deviations is:
MAD = (1+2+1+0+2)/5 = 1.2
Therefore, the MAD for Doctor A's data set is 1.2.
b) For Doctor B's data set on corrective lenses, the mean is:
Mean = (17+19+20+16+18)/5 = 18
The absolute deviations from the mean are:
|17-18| = 1
|19-18| = 1
|20-18| = 2
|16-18| = 2
|18-18| = 0
The mean of these absolute deviations is:
MAD = (1+1+2+2+0)/5 = 1.2
Therefore, the MAD for Doctor B's data set is also 1.2.
Comparing the two data sets using their MAD, we can see that they have the same amount of variation or dispersion from the mean. Both sets have a MAD of 1.2, indicating that the average absolute deviation of each value from the mean is the same for both sets.
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Answer:
Doctor A MAD: 11.8
Doctor B MAD: 9.32
Step-by-step explanation:
This is what I got on the assignment.
Max has eight circular chips that are all the same size and shape in a bag.
(3 chips are square, and 5 are stars)
Max reaches into the bag and removes one circular chip. What is the theoretical probability that the circular chip has a star on it? Write your answer as a fraction, decimal, and percent
Answers
The probability of drawing a star-shaped chip is 5/8.
The theoretical probability of drawing a star-shaped circular chip from the bag is 5/8 or 0.625 or 62.5%. Out of the total of eight circular chips, five are stars, and three are squares.
Therefore, the probability of drawing a star-shaped chip is the ratio of the number of star-shaped chips to the total number of chips in the bag, which is 5/8.
To understand this conceptually, we can think of probability as a fraction where the numerator is the number of favorable outcomes (in this case, drawing a star-shaped chip) and the denominator is the total number of possible outcomes (all the circular chips in the bag).
Thus, the theoretical probability of drawing a star-shaped chip is 5/8 because there are five star-shaped chips out of the total eight circular chips in the bag.
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Colin surveyed 12 teachers at his school to determine how much each person budgets for lunch. He recorded his results in the table. What does the relationship between the mean and median reveal about the shape of the data? the mean is less than the median, so the data is skewed left. The mean is more than the median, so the data is skewed right. The mean is equal to the median, so the data is symmetrical. The mean is equal to the median, so the data is linear.
Answers
The mean is equal to the median, so the data is symmetrical.
Given that :
Colin surveyed 12 teachers at his school to determine how much each person budgets for lunch.
The data is :
10 5 8 10 12 6 8 10 15 6 12 18
Mean is the average of these numbers.
Mean = (10 + 5 + 8 + 10 + 12 + 6 + 8 + 10 + 15 + 6 + 12 + 18) / 12
= 10
Now median is the element in the middle arranged in an order.
Arrange the data in ascending order.
5 6 6 8 8 10 10 10 12 12 15 18
The middle element is the average of the 6th and 7th elements.
Median = (10 10) / 2 = 10
So mean and the median is equal. So the data is symmetrical.
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Farmer jones raises only pigs and geese. he wants to raise at most 16 animals. he wants no more
than 12 geese. he spends $5 to raise a pig and $2 to raise a goose and has 550 available to spend. if he
makes a profit of s4 per pig and s8 per goose, how many of each does he need to raise in order to
maximize his profits?
write the objective function. let a represent the number of pigs and y represent the number of geese.
Answers
The profit per pig is $4 and the profit per goose is $8.
How can the farmer raise at most 16 animals in order to maximize his profits?Let's start by defining the variables:
a = number of pigs Farmer Jones raises
y = number of geese Farmer Jones raises
The problem tells us that he wants to raise at most 16 animals, so we can write:
a + y ≤ 16
It also tells us that he wants no more than 12 geese, so we can write:
y ≤ 12
We know that it costs $5 to raise a pig and $2 to raise a goose, and he has $550 available to spend. So the cost of raising the animals can be expressed as:
5a + 2y ≤ 550
Finally, we want to maximize his profits. The profit per pig is $4 and the profit per goose is $8. So the objective function for Farmer Jones' profits is:
Profit = 4a + 8y
To summarize, the linear programming model for this problem is:
Maximize: Profit = 4a + 8y
Subject to:
a + y ≤ 16
y ≤ 12
5a + 2y ≤ 550
where a and y are non-negative integers.
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The following data points represent the number of holes
that moths ate in each of grandma marion's dresses.
7,8,8, 5, 7,8
using this data, create a frequency table.
number of holes
number of dresses
5
6
7
8
Answers
A frequency table was created using data points representing the number of holes in each of Grandma Marion's dresses. The table shows the number of dresses with 5, 7, and 8 holes, respectively.
To create a frequency table for the given data, first, the unique values in the data set are identified, which are 5, 7, and 8. Then, the number of occurrences of each unique value is counted, resulting in the frequencies 1 for 5, 2 for 7, and 3 for 8.
Count the frequency of each data point
5: 1 dress
7: 2 dresses
8: 3 dresses
Finally, these values are organized into a table with two columns, one for the unique values and another for their corresponding frequencies. The resulting frequency table shows the number of dresses with each number of holes eaten by moths.
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Solve for w.
65=170-w
Answers
170-65 = 105 that's how W is 105
sets x y and z are defined below a number will be randomly selected from set x what is the probability that the selected number will be an element of set y and an element of set z.
x= (1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Y= (5, 10, 15, 20, 25)
Z= (1,5,25)
A. 0.1
B. 0.2
C. 0.5
D. 0.6
E. 0.8
Answers
When a number is chosen from set x, there is a 0.2 chance that the chosen number will also be found in sets y and z. The answer is option (B). 0.2.
What is Probability?The ratio of favourable outcomes to all possible outcomes of an event is known as the probability. The symbol x can be used to express the quantity of successful outcomes for a study with 'n' outcomes. The probability formula determines the likelihood that an event will occur.
It is the ratio of effective results to all effective results. The study of probability is a branch of mathematics that examines the likelihood that an event will occur. Probability, which expresses the likelihood that an event will occur, is calculated by dividing the total number of occurrences by the total number of positive events.
The number of elements of Both Y and Z answer is 5 and 25.
The probability of selecting a number from x that is an element of y and z
Intersection of y and z is (5, 25)
No.of elements in x is = 2/10
= 1/5
= 0.2
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A baker has small and large bags of sugar for making cakes. The large bag contains 30 cups of sugar and it's 2. 5 times larger than the small bag. The small bag contains enough sugar to make nine cakes and have. 75 cups of sugar remaining
How many cakes can be made with a large bag of sugar?
Answers
The number of cakes that can be made with a large bag of sugar, we first need to determine the amount of sugar in a small bag and then calculate the amount of sugar needed for one cake.
1. Find the amount of sugar in a small bag:
Since the large bag contains 30 cups of sugar and is 2.5 times larger than the small bag, we can write the equation:
Small bag = Large bag / 2.5
Small bag = 30 cups / 2.5
Small bag = 12 cups of sugar
2. Determine the amount of sugar needed for one cake:
The small bag contains enough sugar to make 9 cakes and have 0.75 cups of sugar remaining. So, we can subtract the remaining sugar from the total amount in the small bag:
Sugar used for 9 cakes = 12 cups - 0.75 cups
Sugar used for 9 cakes = 11.25 cups
Now, we can find the amount of sugar needed for one cake:
Sugar per cake = Sugar used for 9 cakes / 9
Sugar per cake = 11.25 cups / 9
Sugar per cake = 1.25 cups
3. Calculate the number of cakes that can be made with a large bag of sugar:
Cakes from large bag = Large bag sugar / Sugar per cake
Cakes from large bag = 30 cups / 1.25 cups
Cakes from large bag = 24
Therefore, a baker can make 24 cakes with a large bag of sugar.
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What is the value of 1/4 (-4^3+10^2)
Answers
Answer:
The value of 1/4 (-4^3+10^2) is 9
Find the area of the shaded region:
Answers
Answer:
approximately 42.85 of whatever unit
1. All square, upper triangular matrices are diagonalizable. (T/F)
2. If a matrix is diagonalizable, then it is invertible. (T/F)
Answers
1. All square, upper triangular matrices are diagonalizable. (TRUE)
2. If a matrix is diagonalizable, then it is invertible. (FALSE)
Understanding matrix1. True: All square, upper triangular matrices are diagonalizable.
A square matrix is diagonalizable if it can be transformed into a diagonal matrix by a similarity transformation, which means there exists an invertible matrix P such that P^-1 * A * P is a diagonal matrix. Upper triangular matrices have all their elements below the main diagonal equal to zero.
Since the eigenvalues of an upper triangular matrix are equal to its diagonal elements, we can form a diagonal matrix with these eigenvalues. Since there exists such a diagonal matrix, all square, upper triangular matrices are diagonalizable.
2. False: If a matrix is diagonalizable, it is not necessarily invertible
Diagonalizable matrices can be transformed into a diagonal matrix with the eigenvalues along the main diagonal.
However, invertibility requires that the matrix have a nonzero determinant, which means that all of its eigenvalues must be nonzero.
If a diagonalizable matrix has a zero eigenvalue, its determinant will be zero, and it will not be invertible. Therefore, diagonalizability does not guarantee invertibility.
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If 4:15=a:2 1/2(two and a half), what is the value of a
Answers
The value of 'a' is 2/3.
What is the value of 'a' if the ratio of 4 to 15 is equivalent to the ratio of 'a' to 2 1/2?The problem presents a ratio, 4:15, that is equal to a ratio involving 'a' and 2 1/2. To solve for 'a', we need to isolate it on one side of the equation by cross-multiplying.
In the first step, we convert 2 1/2 to an improper fraction, 5/2, so that we can use it in the equation. We then cross-multiply by multiplying both sides of the equation by 5/2.
This eliminates the denominator on the right-hand side and simplifies the left-hand side.
Solve for 'a'
To solve for 'a', we can use cross-multiplication.
First, we need to convert 2 1/2 to an improper fraction:
2 1/2 = 5/2
Now we can write the equation as:
4/15 = a/(5/2)
To solve for 'a', we cross-multiply:
4/15 * 5/2 = a
a = 2/3
Finally, we solve for 'a' by multiplying 4/15 by 5/2 and simplifying the result. The answer is 2/3, which represents the value of 'a'.
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Question 4
Question
What does the y-intercept of this relationship represent?
the initial height of the plant
the height of the plant at the end of the experiment
the amount of plant food Ryan uses each day
the average amount the plant grows each day
Answers
Answer:
Step-by-step explanation:
The correct answer is:
the initial height of the plant
The y-intercept represents the point where the graph intersects the y-axis. In the context of a relationship between plant growth and time, the y-intercept would represent the initial height of the plant, which is the height of the plant at the start of the experiment, before any growth has occurred.
calculate div(f) and curl(f). f = 5ey, 2 sin(x), 9 cos(x)
Answers
Div(f) = 2cos(x) + [tex]5e^y[/tex], and curl(f) = < 0, 9sin(x), 5e^y >.
To calculate div(f) and curl(f), we need to express f as a vector field:
f = < 2 sin(x), [tex]5e^y[/tex][tex]5e^y[/tex], 9 cos(x) >
Then, we can use the formulas for divergence and curl:
div(f) = ∂f₁/∂x + ∂f₂/∂y + ∂f₃/∂z
curl(f) = < ∂f₃/∂y - ∂f₂/∂z, ∂f₁/∂z - ∂f₃/∂x, ∂f₂/∂x - ∂f₁/∂y >
Let's compute these step by step:
div(f) = ∂f₁/∂x + ∂f₂/∂y + ∂f₃/∂z
= 2cos(x) + [tex]5e^y[/tex] + 0
= 2cos(x) + [tex]5e^y[/tex]
curl(f) = < ∂f₃/∂y - ∂f₂/∂z, ∂f₁/∂z - ∂f₃/∂x, ∂f₂/∂x - ∂f₁/∂y >
= < 0 - 0, 0 - (-9sin(x)), 5e^y - 0 >
= < 0, 9sin(x), 5e^y >
Therefore, div(f) = [tex]2cos(x) + 5e^y[/tex], and curl(f) = [tex]< 0, 9sin(x), 5e^y > .[/tex]
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Let f(x) = 4x^3 – 3x^2 – 18x +5. (a) Find the critical numbers of f. (b) Find the open interval(s) on which f is increasing and the open interval(s) on which f is decreasing. (c) Find the local minimum value(s) and focal maximum value(s) of f, if any.
(d) Find the open interval(s) where f is concave upward and the open interval(s) where f is concave downward e) Find the inflection points of the graph of f, if any
Answers
(a) The critical numbers happen when x = 3 or x = -1/2
(b) f is decreasing on (-∞, -1/2), increasing on (-1/2, 3), and increasing on (3, ∞).
(c) f has a local minimum value of -22 at x = 3, and a local maximum value of 25.5 at x = -1/2.
(d) f is concave downward on (-∞, 1/4) and concave upward on (1/4, ∞).
(e) The inflection point of f is at x = 1/4.
(a) To find the critical numbers of f, we need to find the values of x where the derivative of f equals zero or does not exist.
f'(x) = 12x² - 6x - 18 = 6(2x² - x - 3) = 6(x - 3)(2x + 1)
Setting f'(x) equal to zero, we get:
6(x - 3)(2x + 1) = 0
x = 3 or x = -1/2
These are the critical numbers of f.
(b) To find the intervals where f is increasing and decreasing, we need to examine the sign of the derivative f'(x) in the intervals determined by the critical numbers.
When x < -1/2, f'(x) < 0, so f is decreasing on the interval (-∞, -1/2).
When -1/2 < x < 3, f'(x) > 0, so f is increasing on the interval (-1/2, 3).
When x > 3, f'(x) > 0, so f is increasing on the interval (3, ∞).
(c) To find the local minimum and maximum values of f, we need to examine the critical numbers and the end points of the intervals.
f(3) = 4(3)³ - 3(3)² - 18(3) + 5 = -22
f(-1/2) = 4(-1/2)³ - 3(-1/2)² - 18(-1/2) + 5 = 25.5
Thus, f has a local minimum value of -22 at x = 3, and a local maximum value of 25.5 at x = -1/2.
(d) To find the intervals where f is concave upward and concave downward, we need to examine the sign of the second derivative f''(x).
f''(x) = 24x - 6 = 6(4x - 1)
When x < 1/4, f''(x) < 0, so f is concave downward on the interval (-∞, 1/4).
1/4 < x, f''(x) > 0, so f is concave upward on the interval (1/4, ∞).
(e) To find the inflection points of f, we need to examine the points where the concavity changes.
The concavity changes at x = 1/4, which is the only inflection point o
Rewrite each equation without absolute value symbols for the given values of x.
y=|2x+5|-|2x-5|
if x<-2.5 if x>2.5
if -2.5<=x<=2.5
Answers
If x > 2.5, both expressions within absolute value symbols are positive.
The equation becomes: y = (2x + 5) - (2x - 5) = 10.
How to solve
For the given intervals of x:
If x < -2.5, both expressions within absolute value symbols are negative. Thus, the equation is: y = -(2x + 5) - (-(2x - 5)) = -10.
If x > 2.5, both expressions within absolute value symbols are positive.
The equation becomes: y = (2x + 5) - (2x - 5) = 10.
If -2.5 ≤ x ≤ 2.5, the first expression is positive and the second is negative.
The equation is: y = (2x + 5) - (-(2x - 5)) = 4x.
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In Angle STU, the measure of U=90°, the measure of S=31°, and TU = 77 feet. Find the
length of US to the nearest tenth of a foot
Answers
If in Angle STU, the measure of U=90°, the measure of S=31°, and TU = 77 feet, then the length of US to the nearest tenth of a foot is approximately 39.4 feet.
In angle STU, we have a right triangle with U=90°, S=31°, and TU=77 feet. To find the length of US, we can use the sine function:
sin(S) = opposite side (US) / hypotenuse (TU)
sin(31°) = US / 77 feet
To find the length of US, multiply both sides by 77 feet:
US = 77 feet * sin(31°)
US ≈ 39.4 feet
Therefore, the length of US to the nearest tenth of a foot is approximately 39.4 feet.
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Mathswatch Question:
Liam is a tyre fitter.
It takes him 124 minutes to fit 4 tyres to a lorry.
a) How long would it take him to fit 6 tyres to a lorry. ?
b) If he works for 93 minutes, how many tyres can he fit?
Working out for question a:
a) 124×6÷4=186(minutes)
Correct answer for question a is 186.
Correct answer for question b is 3
Answers
To answer question a, we use the formula:
time taken = (number of tyres to fit x time taken to fit one tyre) / number of tyres fitted at once
In this case, Liam takes 124 minutes to fit 4 tyres to a lorry. To find out how long it would take him to fit 6 tyres, we plug in the values:
time taken = (6 x 124) / 4
time taken = 186 minutes
So it would take Liam 186 minutes to fit 6 tyres to a lorry.
For question b, we know that Liam takes 124 minutes to fit 4 tyres, so he takes 31 minutes to fit 1 tyre. If he works for 93 minutes, we can find out how many tyres he can fit:
number of tyres = time taken / time taken to fit one tyre
number of tyres = 93 / 31
number of tyres = 3
So Liam can fit 3 tyres in 93 minutes.
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You should always measure your following distance in.
Answers
You should always measure your following distance in seconds. The correct answer for measuring following distance is A.
It is important to keep a safe distance between vehicles on the road, which is known as following distance. Measuring following distance in seconds is a more reliable method than measuring it in car lengths or feet.
The recommended following distance is typically two to three seconds. This means that when the vehicle in front of you passes a fixed point on the road, you should not reach that same point before two to three seconds have elapsed.
Measuring in seconds is more effective as it takes into account the speed at which both vehicles are traveling. If you measure in car lengths or feet, it may not be accurate as the length of the cars may differ, and it does not account for the speed of the vehicles. By measuring in seconds, you can maintain a safe distance and reduce the risk of accidents or collisions.
The correct answer for measuring following distance is A.
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Complete question is:
You should always measure your following distance in __________
A. seconds. B. car lengths. C. feet.
Weights of erasers produced by a certain factory are known to follow the uniform distribution between 31. 5 g and 32. 3 g.
(a) (10 points) erasers produced by this factory are sold in packs of 45. A retailer randomly bought 200 packs. Find the probability that, for at least 15 packs, the average weight of the erasers in the pack is at least 31. 95 g.
(b) (10 points) each day, a quality control unit examines the erasers produced by this factory. The unit randomly chooses an eraser from the outputs of this factory and weighs it. This process is repeated 50 times. The unit then records the total number of erasers that were found to weigh at least 31. 7 g. (erasers with weights at least 31. 7 g are called "good" erasers)suppose this unit works for 42 consecutive days. Find the probability that, on average, it finds at least 37. 2 "good" erasers per day
Answers
a) The probability that, for at least 15 packs, the average weight of the erasers in the pack is at least 31.95 g is approximately 0.0384.
b) The probability that, on average, the unit finds at least 37.2 "good" erasers per day is approximately 0.3133.
a) To solve this problem, we need to use the central limit theorem. According to this theorem, the distribution of sample means becomes approximately normal, regardless of the shape of the population distribution, when the sample size is sufficiently large (usually, n >= 30). In this case, since the sample size is 45, we can assume that the distribution of sample means will be approximately normal.
Now, we need to find the probability that the average weight of at least 15 packs is at least 31.95 g. We can use the normal distribution to calculate this probability. We first calculate the z-score for this value as follows:
z = (31.95 - 31.9) / (0.163 / √(45)) = 1.77
Using a standard normal table or calculator, we can find the probability that a z-score is greater than or equal to 1.77. This probability is approximately 0.0384.
b) To solve this problem, we need to use the normal approximation to the binomial distribution. Since each eraser is either "good" or "bad", the number of "good" erasers that the unit finds each day follows a binomial distribution with parameters n = 50 and p = probability of finding a "good" eraser = (32.3 - 31.7)/(32.3 - 31.5) = 0.5.
Now, we need to find the probability that, on average, the unit finds at least 37.2 "good" erasers per day. We can use the normal distribution to calculate this probability. We first calculate the z-score for this value as follows:
z = (37.2 - 25) / 25 = 0.488
Using a standard normal table or calculator, we can find the probability that a z-score is greater than or equal to 0.488. This probability is approximately 0.3133.
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A corporation earned a profit of $ 2.5 × 1 0 4 $2.5×10 4 for 200 days in a row. What was the corporation’s total profit during this time period? Express your answer in scientific notation.
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Answer: hopefully the image helps
Step-by-step explanation:
8 girls eat a total of 210 candies. after adding the number of candies eat by the ninth girl, the average number of candies eaten became 29. how many did the 9th girl eat?
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The 9th girl ate 51 candies.
What is the number of candies eaten by the 9th girl, if the average number of candies eaten by 9 girls is 29 and the first 8 girls ate a total of 210 candies?Let the number of candies eaten by the 9th girl be x.
The average number of candies eaten by 8 girls is given as (210/x+210)/8, which simplifies to 210/8 + x/8.
After the 9th girl eats x candies, the total number of candies eaten becomes 210 + x.
The new average is given as (210 + x)/9 = 29.
Solving for x, we get:
210 + x = 261
x = 51
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I…. NEEDDDD… HELPPP
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According to the information, the customer would save $492 in the first year by switching to Intellivision; the customer would save $207 in the second year by using Intellivision; ElectroniSource would be cheaper in the third year.
How to calculate the annual cost for both companies?a. To calculate the annual cost for ElectroniSource: $42/month for phone service x 12 months = $504/year, $35/month for internet service x 12 months = $420/year, and $59/month for cable television x 12 months = $708/year.
So the total annual cost with ElectroniSource would be $504 + $420 + $708 = $1,632.
With Intellivision, the flat monthly fee for all three services is $95, so the total annual cost would be $95 x 12 months = $1,140.
Therefore, the customer would save $1,632 - $1,140 = $492 in the first year by switching to Intellivision.
How to calculate the best rate for the second year?b. After the first year, Intellivision raises the rates by 25%, so the new monthly fee would be $95 x 1.25 = $118.75.
The total annual cost in the second year would be $118.75 x 12 months = $1,425.
Using the same services, the annual cost with ElectroniSource would still be $1,632.
Therefore, the customer would save $1,632 - $1,425 = $207 in the second year by using Intellivision.
How to calculate the best rate for the third year?c. If Intellivision raises the rates by 16% in the third year compared to the second year, the new monthly fee would be $118.75 x 1.16 = $137.95.
The total annual cost in the third year would be $137.95 x 12 months = $1,655.4.
The annual cost with ElectroniSource would still be $1,632.
Therefore, ElectroniSource would be cheaper in the third year.
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Integrate the function. 「 dx ,X> 6. Give your answer in exact form. x2x² - 36
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To integrate the function ∫(x² - 36) dx, we first need to factor out the expression inside the parentheses:
∫(x² - 36) dx = ∫(x - 6)(x + 6) dx
We can then use the power rule of integration to find the antiderivative:
∫(x - 6)(x + 6) dx = (1/3)x³ - 6x + C, where C is the constant of integration.
Since the original problem states X > 6, we can evaluate the definite integral using these limits:
∫(x² - 36) dx from 6 to X = [(1/3)X³ - 6X] - [(1/3)(6)³ - 6(6)]
= (1/3)X³ - 6X - 68
Therefore, the answer in exact form is (1/3)X³ - 6X - 68.
To integrate the given function, first note the correct notation for the function: ∫(x^2)/(x^2 - 36) dx for x > 6.
To solve this, we can use partial fraction decomposition. The given function can be rewritten as:
∫(A(x - 6) + B(x + 6))/(x^2 - 36) dx
Solving for A and B, we find that A = 1/12 and B = -1/12. Now we rewrite the integral as:
∫[(1/12)(x - 6) - (1/12)(x + 6)]/(x^2 - 36) dx
Next, separate the two terms and integrate them individually:
(1/12)∫[(x - 6)]/(x^2 - 36) dx - (1/12)∫[(x + 6)]/(x^2 - 36) dx
Now, notice that the integrals are of the form ∫u'/u dx. The integral of this form is ln|u|. So we have:
(1/12)[ln|(x - 6)| - ln|(x + 6)|] + C
Using the logarithm property, we can rewrite the answer as:
(1/12)ln|((x - 6)/(x + 6))| + C
That is the exact form of the antiderivative for the given function.
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Russ placed $8000 into his credit union account paying 6% compounded semiannually (twice a year). How much will be in Russ’s account in 4 years
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Answer:
Step-by-step explanation:
You have decided to purchase a car for $25,625. The credit union requires a 10% down payment and will finance the balance with a 9% annual interest loan for 36 months. The sales tax in your city is 7. 5%, and the license and title charges are $175. 13. What is the total purchase price of the car including tax, license, and title? Round your answer to the nearest cent. A. $24,949. 80 c. $27,722. 01 b. $24,967. 32 d. $27,735. 14.
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Answer is 27,529.82
To calculate the total purchase price of the car including tax, license, and title, we need to add the down payment, the financed balance, the sales tax, and the license and title charges.
First, we calculate the down payment:
10% of $25,625 = $2,562.50
Next, we calculate the financed balance:
$25,625 - $2,562.50 = $23,062.50
Then, we calculate the sales tax:
7.5% of $23,062.50 = $1,729.69
Finally, we add the license and title charges:
$1,729.69 + $175.13 = $1,904.82
So the total purchase price of the car including tax, license, and title is:
$2,562.50 + $23,062.50 + $1,904.82 = $27,529.82
Rounded to the nearest cent, the answer is option D: $27,735.14.
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someone PLSS helpi don’t know
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The following are correct about the triangle;
1. angle C is 60°
2. angle B is 60°
3. The length of segment DB is 3
4. The length of side x is 3√3
What is an equilateral triangle?An equilateral triangle is a type of triangle in which all it's sides and angles are equal.
Since all the angles of an equilateral triangle are equal, then,
x+x+x = 180
3x = 180
x = 180/3 = 60°
therefore each angle is 60°
angle C and angle B are 60°
Using Pythagorean theorem
x² = 6²- 3²
x² = 36-9
x² = 27
x = √27
x = √9×3
x = 3√3
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Jen is filling bags with M&Ms. She has 5 1/2 cups of M&Ms. She needs 1 1/4 cups of M&Ms to fill each bag. How many bags can Jen fill completely?
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Jen can fill 4 bags completely with the 5 1/2 cups of M&Ms she has, given that each bag requires 1 1/4 cups of M&Ms.
First, we need to find the total number of cups of M&Ms Jen has
5 1/2 cups = 11/2 cups
Then, we divide the total number of cups by the number of cups needed to fill each bag
(11/2 cups) ÷ (1 1/4 cups/bag)
To divide by a fraction, we can multiply by its reciprocal
(11/2 cups) x (4/5 cups/bag)
= 44/10 cups
Simplifying, we get
= 4 2/10 cups
= 4 1/5 cups
So, Jen can fill 4 bags completely.
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