The volume of the table tent 3 cmH8 cm12 cm is 288 cubic cm.
How to determine the volume of the table tentThe volume of the table tent can be found by multiplying the length, width, and height of the tent.
Volume = length x width x height
In this case, the length is 12 cm, the width is 8 cm, and the height is 3 cm.
Volume = 12 cm x 8 cm x 3 cm
Volume = 288 cubic cm
Therefore, the volume of the table tent is 288 cubic cm.
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Solve the following equation:
8 x five sixths
To solve the equation 8 x five sixths, we first convert the fraction to a decimal by dividing the numerator (5) by the denominator (6), which gives us 0.83.
We then multiply 8 by 0.83 to get the final answer of 6.64. Therefore, 8 x five sixths = 6.64.
In general, to multiply a whole number by a fraction, we can convert the fraction to a decimal and then multiply the whole number by the decimal.
Alternatively, we can convert the whole number to a fraction with a denominator of 1 and then multiply the two fractions by cross-multiplying and simplifying.
In this case, we could also write 8 as 8/1 and multiply it by 5/6 to get (8 x 5)/(1 x 6) = 40/6, which simplifies to 6 and 4/6 or 6.67 (rounded to two decimal places). However, converting the fraction to a decimal is often simpler and more practical.
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Cindy weighed the hydrogen peroxide in two containers. the hydrogen peroxide in one container weighed 6.4 ounces. the hydrogen peroxide in the second container weighed 4.07 ounces. find the total number of ounces of hydrogen peroxide using the rules of significant digits.
The total number of ounces of hydrogen peroxide, rounded to up to 1 significant digit after the decimal point, is 10.5 ounces.
According to the question the hydrogen peroxide in the first container weighed 6.4 ounces, and the hydrogen peroxide in the second container weighed 4.07 ounces.
According to the rules of significant digits, the numbers after the decimal point in a sum of difference is the least of that of the numbers to be added or subtracted.
This means that when 6.4 and 4.07 is added, then we will see numbers of decimal places in each number. 6.4 has 1 number after decimal point and 10.47 has 2.
Hence the result of 6.4 + 10.47 will have a minimum of 2 which is 1 decimal place.
Now, 6.4 + 4.07
= 10.47
Rounding it off from the above-mentioned criteria gives us 10.5 ounces.
Therefore, the total number of ounces of hydrogen peroxide, rounded to up to 1 significant digit after the decimal point, is 10.5 ounces.
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Amelia is saving up to buy a new phone. She already has $100 and can save an
additional $9 per week using money from her after school job. How much total
money would Amelia have after 6 weeks of saving? Also, write an expression that
represents the amount of money Amelia would have saved in w weeks.
The expression that represents the amount of money Amelia would have saved in w weeks is: $9w + $100
Amelia starts with $100 and saves an additional $9 per week for 6 weeks. To find the total amount of money she has after 6 weeks, you can use this formula:
Total money = Initial amount + (Weekly savings × Number of weeks)
Total money = $100 + ($9 × 6)
Total money = $100 + $54
Total money = $154
So, Amelia would have $154 after 6 weeks of saving.
For an expression representing the amount of money Amelia would have saved in w weeks:
Total money (w) = $100 + ($9 × w)
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Plot the points A(-2,1), B(-6, -9), C(-1, -11) on the coordinate axes below. State the
coordinates of point D such that A, B, C, and D would form a rectangle. (Plotting
point D is optional.)
The value of the coordinates of point D is, (3, - 1)
We have to given that;
All the coordinates of rectangles are,
A(-2,1), B(-6, -9), C(-1, -11)
Now, Let the fourth coordinate of rectangle is,
D (x, y)
Hence, Midpoint of AC and BD are same.
So., Midpoint of AC is,
⇒ AC = (- 2 + (- 1))/ 2, (1 + (- 11))/2
= (- 3/2 , - 5)
And, Midpoint of BD,
⇒ BD = (- 6 + x)/2, (- 9 + y)/2
By comparing;
⇒ (- 6 + x)/2 = - 3/2
⇒ - 6 + x = - 3
⇒ x = - 3 + 6
⇒ x = 3
⇒ (- 9 + y)/2 = - 5
⇒ - 9 + y = - 10
⇒ y = -10 + 9
⇒ y = - 1
Thus, The value of the coordinates of point D is, (3, - 1)
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Approximately how many inches of ground does kameron cover in
3
full rotations of the unicycle wheel? (use
3.14
as an approximation of pi.)
The total count of inches that a Kameron cover is 301.44 inches, under the condition that we have to use 3.14 as an approximation of π.
The circumference formula of a circle is
C=πd
Here
C = refers to circumference
d = refers to diameter.
Since we know that the spoke length is 16 inches, we can evaluate the diameter by multiplying it by 2. Hence, the diameter of the wheel is 32 inches.
Now that we know the diameter of the wheel, we calculate its circumference using the formula
C=πd.
Staging in this formula
d=32 inches
π=3.14
C = πd
= 3.14 x 32
= 100.48 inches
So Kameron covers 100.48 inches of ground in one full rotation of the unicycle wheel.
Now in order to evaluate how many inches of ground Kameron covers in 3 full rotations of the unicycle wheel, we simply need to multiply this value by 3
100.48 x 3
= 301.44 inches
Thus, Kameron covers approximately 301.44 inches of ground in 3 full rotations of the unicycle wheel.
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Matthew is saving money for a pet turtle. The data in the table represent the total amount of money in dollars that he saved by the end of each week.
A graph of the points that represent this data are shown on the coordinate plane attached below.
How to construct and plot the data in a scatter plot?In this scenario, the week number would be plotted on the x-axis (x-coordinate) of the scatter plot while the amount of money (in dollars) would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.
On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the week number and the amount of money (in dollars), a linear equation for the line of best fit is as follows:
y = 1.19x + 1.05
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The value of a stock in 1940 is $1. 25. Its value grows
by 7% each year after 1940.
A. ) Write an equation representing the value of the
stock, V(t), in dollars, t years after 1940.
The equation representing the value of the stock, V(t), in dollars, t years after 1940 is V(t) = $1.25 * [tex]1.07^t[/tex].
Let V(0) be the value of the stock in 1940, which is given as $1.25. Then, the value of the stock after t years (t > 0) can be found by multiplying the initial value with the growth factor of 1.07 raised to the power of the number of years of growth. Thus, the equation representing the value of the stock, V(t), in dollars, t years after 1940 is:
V(t) = V(0) * [tex](1 + 0.07)^t[/tex]
Substituting the given value of V(0) = $1.25, we get:
V(t) = $1.25 * [tex](1 + 0.07)^t[/tex]
Simplifying this expression, we get:
V(t) = $1.25 * [tex]1.07^t[/tex]
Therefore, the equation representing the value of the stock, V(t), in dollars, t years after 1940 is V(t) = $1.25 * [tex]1.07^t[/tex].
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A group of students collected old newspapers for a recycling project. The data shows the mass, in kilograms, of old newspapers collected by each student.
23, 35, 87, 64, 101, 90, 45, 76, 105, 60, 55
98, 122, 49, 15, 57, 75, 120, 56, 88, 45, 100.
What percent of students collected between 49 kilograms and 98 kilograms of newspapers? Explain how you got to your solution
Therefore, approximately 45.45% of students collected between 49 and 98 kilograms of newspapers.
Total number of students is 22.
To find the percentage of students who collected between 49 and 98 kilograms of newspapers, we first need to count the number of students who collected within this range. From the given data, we can see that the following students collected between 49 and 98 kilograms of newspapers
87, 64, 90, 76, 60, 55, 57, 75, 56, 88
Percentage of students = (number of students in range / total number of students) x 100
= (10 / 22) x 100
= 45.45%
Therefore, approximately 45.45% of students collected between 49 and 98 kilograms of newspapers.
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Americans consume on average 32. 3 lbs of cheese per year with a standard deviation of 8. 7 lbs. Assume that the amount of cheese consumed each year by an American is normally distributed. An American in the middle 70% of cheese consumption consumes per year how much cheese?
An American in the middle 70% of cheese consumption consumes between 23.1 lbs and 41.5 lbs of cheese per year.
To find the amount of cheese consumed by an American in the middle 70% of cheese consumption, we need to find the z-scores that correspond to the lower and upper bounds of the middle 70% and then convert those z-scores back to the original scale of measurement.
First, we need to find the z-score that corresponds to the 15th percentile (lower bound) and the z-score that corresponds to the 85th percentile (upper bound) of the normal distribution. We can use a standard normal table or a calculator to find these values. Using a calculator, we get:
z_15 = invNorm(0.15) = -1.036
z_85 = invNorm(0.85) = 1.036
Next, we can use the formula:
z = (x - mu) / sigma
where x is the amount of cheese consumed by an American, mu is the mean amount of cheese consumed (32.3 lbs), and sigma is the standard deviation (8.7 lbs), to convert the z-scores back to the original scale of measurement:
For the lower bound:
-1.036 = (x - 32.3) / 8.7
x = -1.036 * 8.7 + 32.3 = 23.1 lbs
For the upper bound:
1.036 = (x - 32.3) / 8.7
x = 1.036 * 8.7 + 32.3 = 41.5 lbs
Therefore, an American in the middle 70% of cheese consumption consumes between 23.1 lbs and 41.5 lbs of cheese per year.
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Over what interval is the function shown in the table increasing? Decreasing? Y=6x2
A car can be rented for $75 per week plus $0. 15 per mile. How many miles can be driven if you have at most $180 to spend for weekly transportation
You can drive at most 700 miles within the $180 budget for weekly transportation.
To determine how many miles can be driven with a budget of $180 for weekly transportation, we'll use the given information: $75 per week for car rental and $0.15 per mile driven. First, subtract the weekly rental cost from the total budget:
$180 - $75 = $105
Now, divide the remaining budget by the cost per mile to find the maximum number of miles that can be driven:
$105 ÷ $0.15 ≈ 700 miles
So, you can drive at most 700 miles within the $180 budget for weekly transportation.
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What does the mapping found in part b tell you about the relationship between the two circles? explain your reasoning.
The term "mapping" refers to the process of creating a mathematical correspondence between points or objects in two different sets. In this case, the mapping found in part b tells us that there exists a one-to-one correspondence between the points in Circle A and the points in Circle B.
There is a one-to-one correspondence between the points in Circle A and the points in Circle B, and that this correspondence preserves distance.
This means that for every point in Circle A, there is exactly one corresponding point in Circle B that is the same distance away from the center of the circle as the original point.
Since the correspondence is one-to-one, it follows that the two circles have the same number of points. That is, if Circle A has n points, then Circle B also has n points.
Therefore, we can conclude that the two circles have the same size.
Furthermore, because the correspondence preserves distance, any transformation that maps one circle onto the other must be a rigid motion, meaning it preserves angles and distances.
In particular, the transformation must be an isometry.
Therefore, we have shown that the two circles are congruent. That is, they have the same size and shape, and can be transformed onto one another by a combination of translations, rotations, and reflections.
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The population of a certain bacteria is known to double every 10 hours. Assuming exponential growth, determine the time that it would take for the bacteria to triple in number
It would take approximately 20 hours for the bacteria to triple in number.
Given that the bacteria population doubles every 10 hours, we can use exponential growth to determine the time it would take for the population to triple.
Let's represent the initial population as P0 and the time it takes for the population to triple as t.
Using the concept of exponential growth, we can express the population at time t as P(t) = P0 * 2^(t/10).
Since we want the population to triple, we set P(t) = 3 * P0:
3 * P0 = P0 * 2^(t/10).
We can cancel out P0 from both sides of the equation:
3 = 2^(t/10).
To solve for t, we can take the logarithm of both sides. Using the base-2 logarithm (log2) gives us:
log2(3) = t/10.
Using a calculator, we find that log2(3) is approximately 1.585.
Now, we can solve for t:
1.585 = t/10.
Multiplying both sides of the equation by 10 gives us:
15.85 = t.
Rounding to the nearest hour, the time it would take for the bacteria population to triple is approximately 16 hours.
Therefore, the bacteria population would take approximately 20 hours to triple in number.
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WILL GIVE BRAINLIEST!! ANSWER FAST!!!
Given a graph for the transformation of f(x) in the format g(x) = f(x) + k, determine the k value.
k = −3
k = 1
k = 4
k = 5
Answer:
k = -3.
Step-by-step explanation:
To answer this question, we need to use our own knowledge and information. Adding a constant k to a function f(x) shifts the graph of f(x) vertically by k units. If k is positive, the graph moves up. If k is negative, the graph moves down. The value of k can be found by comparing the y-coordinates of corresponding points on the graphs of f(x) and g(x). For example, if g(x) = f(x) + 2, then the graph of g(x) is 2 units above the graph of f(x), and any point (x, y) on f(x) corresponds to a point (x, y + 2) on g(x). Therefore, the answer is: k is the vertical shift of the graph of f(x) to get the graph of g(x). It can be found by subtracting the y-coordinate of a point on f(x) from the y-coordinate of the corresponding point on g(x).
Looking at the graph given, we can see that the graph of g(x) is below the graph of f(x), which means that k is negative. We can also see that one point on f(x) is (0, 3), and the corresponding point on g(x) is (0, 0). Using the formula above, we get:
k = y_g - y_f
k = 0 - 3
k = -3
Therefore, the correct option is k = -3.
PLEASEEEEEE HELP ME!!!!!
VERY IMPORTANT!!!!
Amelie spins the following spinner, which has 10
equally sized spaces numbered 1
through 10. The numbers 1 and 7 are colored blue; the numbers 2, 4, and 6 are red; and the numbers 3, 5, 8, 9, and 10 are green. What is the probability that Amelie spins either an odd number or a red number?
Enter your answer as a reduced fraction, like this: 3/14
Answer:
4/5
Step-by-step explanation:
In probability, if there are two events and "or" is used, we will add the probabilities of each event. Since the event that an odd number is spun does not affect whether a red number is spun, we can calculate the probability of each event separately:
Probability of spinning an odd number:
5/10 because there are 5 odd numbers possible & 10 outcomes
Probability of spinning a red number:
3/10 because there are 3 red numbers & 10 outcomes
Now add the probability of each event:
5/10 + 3/10 = 8/10 = 4/5
Alexandra and her mother are planting a rectangular garden. In the middle of the garden they will plant the vegetables and they will plant flowers around vegetable garden, as shown below.
If the area around the vegetable garden is of uniform width (labeled with x) and the dimensions of the vegetable garden is 45 feet by 20 feet, what expression represents the area of the flower garden?
Make sure to show all of your steps in your answer, including the area of the vegetable garden and the area of the entire garden.
The expression for the area of the flower garden is (45+2x)(20+2x) - 900.
How to solveArea of vegetable garden:
[tex]A_v = 45 ft * 20 ft[/tex] = 900 sq ft
Dimensions of entire garden:
Length = 45 ft + 2x
Width = 20 ft + 2x
Area of entire garden:
[tex]A_e = (45+2x)(20+2x)[/tex]
Area of flower garden:
[tex]A_f = A_e - A_v = (45+2x)(20+2x) - 900 sq ft[/tex]
So, the expression for the area of the flower garden is (45+2x)(20+2x) - 900.
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A sterling silver platter is made up of a mixture of silver and copper. The ratio of silver to copper is 37:3 by mass. If the platter has a mass of 600 grams, what is the mass, in grams, of the copper in the platter?
A) 18
B) 45
C) 222
D) 555
The mass of copper in the platter is 45 grams, which corresponds to option (B).
What is ratio ?
In mathematics, a ratio is a comparison of two quantities, often expressed as a fraction. Ratios can be used to describe how two quantities relate to each other, and they can be used to make predictions and solve problems in a variety of contexts.
The ratio of silver to copper in the platter is 37:3 by mass, which means that for every 37 grams of silver, there are 3 grams of copper.
Let's call the mass of silver in the platter "s" and the mass of copper "c". We know that the total mass of the platter is 600 grams, so:
s + c = 600
We also know that the ratio of silver to copper is 37:3, which means that:
s÷c = 37÷3
We can use this second equation to solve for s in terms of c:
s:c = 37:3
s = (37÷3)c
Now we can substitute this expression for s into the first equation:
s + c = 600
(37÷3)c + c = 600
(40÷3)c = 600
c = (3÷40) * 600
c = 45
Therefore, the mass of copper in the platter is 45 grams, which corresponds to option (B).
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PLS HELP FAST I ONLY HAVE A LIL TIME LEFT! WILL MARK BRAINLIEST
Answer:
DStep-by-step explanation:
In this set,
the maximum is 35
the minimum is 6
So, we can cross out options A, B
the median is 14
The only option that works for this set is option D
without a calculator find out
√28 ÷ √7
Step-by-step explanation:
= sqrt ( 28 ÷7) = sqrt (4) = 2
Answer:
2
Step-by-step explanation:
First we put the two equations together so it would be like this
[tex]\sqrt \frac{28}{7}[/tex]
the square root of that is 4 because 7 goes into 28 four times
so now we have this [tex]\sqrt{4}[/tex]
and the square root of 4 is 2
A rectangular portrait is 4 feet wide and 6 feet high. It costs $1. 64 per foot to put a gold frame around the portrait. How much will the frame cost?
The cost of the Portrait frame cost is: $32.8
What is the total cost per length?The formula for the perimeter of a rectangle is given by the expression:
A = 2(L + W)
Where:
L is Length
W is Width
We are given that:
Width: W = 4 ft
Height: H = 6 ft
Thus:
Perimeter = 2(6 + 4)
= 20 ft
Cost of the rectangular portrait per foot is $1.64
Thus:
Total cost = 20 * 1.64
= $32.8
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A dilation always produces a similar figure. Similar figures have the same ______ but different ______.
Answer:
A dilation always produces a similar figure. Similar figures have the same shape but different sizes.
In a dilation, each point of the original figure is transformed by multiplying its coordinates by a scale factor, which determines the change in size. However, the shape and proportions of the figure remain unchanged. Therefore, the figures obtained through dilation are similar, meaning they have the same shape but different sizes.
Buying three movie tickets and a popcorn, which costs $5.50, is the same price as buying two tickets snacks worth a total of 16.50. How much does one movie ticket cost
If buying three movie tickets and a popcorn, which costs $5.50, is the same price as buying two tickets snacks worth a total of 16.50, one movie ticket costs $2.20.
Let the cost of one movie ticket be represented by x.
According to the problem, buying three movie tickets and a popcorn costs $5.50, so we can set up the equation:
3x + $5.50 = 2y
where y is the cost of snacks.
Similarly, buying two tickets and snacks worth a total of $16.50 can be represented by the equation:
2x + y = $16.50
We can solve this system of equations by substituting the first equation into the second equation for y:
2x + (3x + $5.50) = $16.50
5x + $5.50 = $16.50
5x = $11
x = $2.20
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You are going to run at a constant speed of 7.5
miles per hour for 45
minutes. You calculate the distance you will run. What mistake did you make in your calculation? [Use the formula S=dt
.]
The value of the distance you will run is 5.62500 miles
Calculating the value of the distance you will runFrom the question, we have the following parameters that can be used in our computation:
You are going to run at a constant speed of 7.5 miles per hour For 45 minutesThis means that
Speed = 7.5 miles per hour
Time = 45 minutes
The distance you will run is calculated as
Distance = Speed * Time
Substitute the known values in the above equation, so, we have the following representation
Distance = 7.5 miles per hour * 45 minutes
Evaluate the product
Distance = 5.62500 miles
Hence, the distance is 5.62500 miles
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Twenty-four pairs of adult brothers and sisters were sampled at random from a population. The difference in heights, recorded in inches (brother’s height minus sister’s height), was calculated for each pair. The 95% confidence interval for the mean difference in heights for all brother-and-sister pairs in this population was (–0. 76, 4. 34). What was the sample mean difference from these 24 pairs of siblings?
–0. 76 inches
0 inches
1. 79 inches
4. 34 inches
The sample mean difference in heights for these 24 pairs of siblings is 1.79 inches. So the third option is correct.
The 95% confidence interval for the mean difference in heights for all brother-and-sister pairs in the population was (–0.76, 4.34).
This means that if we were to repeat this sampling process many times, we would expect 95% of the resulting confidence intervals to contain the true mean difference in heights for all brother-and-sister pairs in the population.
To find the sample mean difference from these 24 pairs of siblings, we take the midpoint of the confidence interval. The midpoint is the average of the lower and upper bounds, which is:
(-0.76 + 4.34) / 2 = 1.79
Therefore, the sample mean difference in heights for these 24 pairs of siblings is 1.79 inches.
So the correct answer is third option.
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Write 5.3*10^-5 in standard notation.
The scientific notation 5.3*10‐⁵ in standard notation gives 0.000053
Writing the number 5.3*10‐⁵ in standard notation.From the question, we have the following parameters that can be used in our computation:
Write 5.3*10‐⁵ in standard notation.
The above number is written in scientific notation
The standard notation of a number a * 10ⁿ is represented as
a000 where the 0's are in n places
Using the above as a guide, we have the following:
5.3 * 10‐⁵ = 0.000053
Hence, 5.3*10‐⁵ in standard notation is 0.000053
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an airplane is 58 m long. a scale model of the plane is 40.6 cm long.
determine the scale factor used to create the model as a decimal rounded
to the nearest thousandth
If a scale model of the plane is 40.6 cm long, the scale factor used to create the model is approximately 1:142.857 or 0.007 rounded to the nearest thousandth.
To determine the scale factor used to create the model, we need to divide the length of the actual airplane by the length of the model airplane:
58 m / 40.6 cm
To perform this calculation, we need to convert the units so that they match. We can convert 58 m to cm by multiplying by 100:
58 m = 58 × 100 cm = 5800 cm
Now we can divide:
5800 cm / 40.6 cm = 142.857...
Rounding to the nearest thousandth, we get:
142.857... ≈ 142.857
Therefore, the scale factor used to create the model is approximately 1:142.857 or 0.007 rounded to the nearest thousandth.
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An art teacher times his students, in minutes, to see how long it takes them to paint a 12-inch canvas. He makes a box plot for the data. Paint Times
10 15 20 25 30 35 40 45 50 55
How long could a student take to paint their canvas if they are slower than 75% of the other students? 15 minutes O 25 minutes O 40 minutes 0 46 minutes
To find the answer, we need to identify the quartiles of the data set and use them to construct the box plot.
First, we need to order the data set in increasing order:
10, 15, 20, 25, 30, 35, 40, 45, 50, 55
Next, we need to find the median (Q2) of the data set. Since we have an even number of data points, we take the average of the two middle values:
Q2 = (25 + 30) / 2 = 27.5
This value represents the median of the data set.
To find Q1 and Q3, we divide the data set into two halves:
10, 15, 20, 25, 30 | 35, 40, 45, 50, 55
Q1 is the median of the lower half:
Q1 = (15 + 20) / 2 = 17.5
Q3 is the median of the upper half:
Q3 = (45 + 50) / 2 = 47.5
We can now use this information to construct the box plot:
| -------
| /
| -------
| /
|-------
| 10 20 30 40 50
Q1 Q2 Q3
The box represents the middle 50% of the data (from Q1 to Q3), while the whiskers represent the minimum and maximum values that are not outliers.
Since we want to find the paint time for a student who is slower than 75% of the other students, we need to look at the upper quartile (Q3) of the data set. 75% of the data is contained between Q1 and Q3, so a student who is slower than 75% of the other students would have a paint time greater than Q3.
Therefore, the answer is 46 minutes, which is greater than Q3 (47.5 minutes).
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Walter is planning a trip to morocco. he is trying to decide which cities he would like to visit while he is there. the table below shows some possible cities walter could visit, along with the amount of money he expects to spend on food, lodging, travel, and similar expenses for each city. all prices are given in moroccan dirham (mad). city cost (mad) tangier 610 casablanca 466 agadir 950 rabat 927 oujda 683 fes 478 marrakech 965 kenitra 778 walter’s original itinerary included trips to marrakech, fes, kenitra, and oujda, but because he only has a budget of mad 2,500, he must alter his plans to be more affordable. which of the following itinerary changes will allow walter to stay within his budget? (consider each option individually, rather than as a group.) i. replace kenitra with tangier and oujda with casablanca. ii. drop fes. iii. replace marrakech with casablanca. a. i and ii b. ii and iii c. iii only d. none of these will put walter under budget.
Walter can stay within his budget by dropping Fes (option ii).
Walter's original itinerary includes trips to Marrakech, Fes, Kenitra, and Oujda, which will cost him a total of 478 + 478 + 778 + 683 = MAD 2,417. This exceeds his budget of MAD 2,500.
Option i suggests replacing Kenitra with Tangier and Oujda with Casablanca, which will cost a total of 610 + 466 + 610 + 466 = MAD 2,152. However, this still exceeds Walter's budget.
Option iii suggests replacing Marrakech with Casablanca, which will cost a total of 965 + 466 + 778 + 683 = MAD 2,892, which is over Walter's budget.
Therefore, the only option that allows Walter to stay within his budget is to drop Fes from his itinerary, which will cost a total of 478 + 778 + 683 = MAD 1,939. This is well within his budget of MAD 2,500. So optio 2 is correct.
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Classify each series as absolutely convergent conditionally convergent, or divergent. DO «Σ a (-1)k+1 k! k=1 b. Σ ka sin 2
For series Σ a(-1)^(k+1)k!, convergence depends on the limit of |a(k+1)/a(k)|. For series Σ ka sin(2), it diverges.
Consider the series Σ a(-1)^(k+1)k!, where a is a sequence of real numbers.
To determine the convergence of this series, we can use the ratio test
lim┬(k→∞)〖|a(k+1)(-1)^(k+2)(k+1)!|/|ak(-1)^(k+1)k!| = lim┬(k→∞)〖(k+1)|a(k+1)|/|a(k)||〗
If this limit is less than 1, then the series converges absolutely. If the limit is greater than 1, the series diverges. If the limit is equal to 1, then the test is inconclusive.
Let's evaluate the limit
lim┬(k→∞)〖(k+1)|a(k+1)|/|a(k)||〗 = lim┬(k→∞)〖(k+1)!/(k!k)|a(k+1)/a(k)||〗 = lim┬(k→∞)〖(k+1)/(k)|a(k+1)/a(k)||〗
Since lim┬(k→∞)〖|a(k+1)/a(k)||〗 exists, we can apply the ratio test again:
if the limit is less than 1, the series converges absolutely.
if the limit is greater than 1, the series diverges.
if the limit is equal to 1, the test is inconclusive.
Therefore, we can classify the series Σ a(-1)^(k+1)k! as either absolutely convergent, conditionally convergent, or divergent depending on the value of the limit.
Consider the series Σ ka sin(2), where a is a sequence of real numbers.
To determine the convergence of this series, we can use the alternating series test, which states that if a series Σ (-1)^(k+1)b(k) is alternating and |b(k+1)| <= |b(k)| for all k, and if lim┬(k→∞)〖b(k) = 0〗, then the series converges.
In this case, we have b(k) = ka sin(2), which is alternating since (-1)^(k+1) changes sign for each term. We also have
|b(k+1)|/|b(k)| = (k+1)|a|/k < k|a|/k = |b(k)|/|b(k-1)|
Therefore, |b(k+1)| <= |b(k)| for all k. Finally, we have
lim┬(k→∞)〖b(k) = lim┬(k→∞)〖ka sin(2)〗 = ∞〗
Since the limit does not exist, the series diverges.
Therefore, we can classify the series Σ ka sin(2) as divergent.
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in each hand of a card game, there is a 54% chance of winning 3 points and a 46% chance of losing 4 points. is the game a fair game? explain
Answer: yes, the game is fair.
Step-by-step explanation:
The game is fair because:
a. you are playing with multiple players, and they have equal odds
b. the odds of winning are higher, so there is balance since you earn less points.
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