Mean:
Bus: 17.5
Walking: 20.5
Median:
Bus: 15
Walking: 21
Mode:
Bus: 15 and 14
Walking: 21 and 20
Range:
Bus: 17
Walking: 3
According to the given table,
Bus: 16, 14, 15, 14, 31, 15 number of observations = 6
Walking: 22, 19, 21, 20, 21, 20 number of observations = 6
Now mean of bus = (16 + 14 + 15 + 14 + 31 + 15)/6
= 17.5
Now mean of walking = (22 + 19 + 21 + 20 + 21 + 20)/6
= 20.5
To find the median,
Arranging these into ascending order:
Bus: 14, 14, 15, 15, 16, 31
Walking: 19, 20, 20, 21, 21, 22
Since 6 is an even number thus median is
For Bus:
⇒ (6/2th term + (6/2 + 1)term)/2
⇒ (15 + 15)/2
⇒ 15
For walking:
⇒(20+21)/2
Hence median is 21
Now mode for Bus is 14 and 15 as it is repeating more times
And mode for walking is 20 and 21.
Since we know that
Range = largest observation - lowest observation
Therefore,
Range of bus = 31 - 14
= 17
Range of Walking = 22 - 19
= 3
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Is 0.03 greater than 3.7
We have that 0.03 is smaller than 3.7.
Given parallelogram ABCD Find the area
Answer:
Area = ab sinx
Area = (8)(18) sin32
Area = 144 sin32
Area = 79.41
Please solve this
∫ (log(1 + x ^ 2))/((x + 1) ^ 2) dx
The final result of the integral is:
∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,
where Li(x) is the logarithmic integral function and C is the constant of integration.
We have,
To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.
Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:
∫ (log(1 + (u-1)²) / u²) du.
Expanding the numerator, we have:
∫ (log(1 + u² - 2u + 1) / u²) du
= ∫ (log(u² - 2u + 2) / u²) du.
Now, let's split the logarithm using the properties of logarithms:
∫ (log(u² - 2u + 2) - log(u²)) / u² du
= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.
We can simplify the second integral:
∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.
Using the power rule for integration, we can integrate both terms:
∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.
Now, let's focus on the second integral:
∫ (log(u) / u³) du.
This integral does not have a simple closed-form solution in terms of elementary functions.
It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).
Therefore,
The final result of the integral is:
∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,
where Li(x) is the logarithmic integral function and C is the constant of integration.
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Suppose a population contains 20,000 people. All else being equal, a study
based on a population sample that includes which of the following numbers
of respondents would be the most reliable?
A. 200
OB. 20
C. 2000
D. 2
A study based on a population sample that includes 2000 respondents would be the most reliable out of the given options.
In statistical analysis, the reliability of a study depends on the representativeness and size of the sample.
A larger sample size generally provides more reliable results as it reduces the sampling error and increases the precision of the estimates.
Given that the population contains 20,000 people, we need to consider which number of respondents would yield the most reliable study.
Option A: 200 respondents
This represents only 1% of the population.
While it is better than having just 2 respondents, it may not be sufficient to accurately capture the characteristics of the entire population.
Option B: 20 respondents
This represents only 0.1% of the population.
With such a small sample size, the study would likely suffer from a high sampling error and may not provide reliable results.
Option C: 2000 respondents
This represents 10% of the population.
While it is a larger sample size compared to the previous options, it still only captures a fraction of the population.
The study may provide reasonably reliable results, but there is room for potential sampling error.
Option D: 2 respondents
This represents an extremely small sample size, accounting for only 0.01% of the population.
With such a small sample, the study would be highly susceptible to sampling bias and would likely yield unreliable results.
Based on the options provided, option C with 2000 respondents would be the most reliable study.
Although it does not include the entire population, a sample size of 2000 respondents provides a larger representation of the population and reduces the potential for sampling error.
However, it's important to note that the reliability of a study depends not only on sample size but also on the sampling method, data collection techniques, and other factors that ensure representativeness.
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PLEASE HELP 12 POINTS!!
Answer:
Substitution property
Step-by-step explanation:
When you substitute x=4 into the first equation, the equation becomes equal to 30. This is only the case because of the substitution property. Hope this helps!
find the greatest number that divides 36 and 60 without leaving a remainder
Answer:
12
Step-by-step explanation:
36= 2 × 2 × 3 × 3
60= 2 × 2 × 3 × 5
HCF(36, 60)= 2 × 2 × 3 = 12
12 is the greatest number that divides 36 and 60 without leaving a remainder
In a survey of 1,600 people who owned a certain type of car, 720 said they would buy
that type of car again. What percent of the people surveyed were satisfied with the car?
The percentage of the people surveyed that were satisfied with the car is 45%.
Given the following data:
Total population = 1,600 peopleNumber of car owner = 720 people.To determine the percentage of the people surveyed that were satisfied with the car:
How to solve for a percentage.In this exercise, you're required to calculate the percentage of the total population in this survey that would by a particular type of car again because they were satisfied with it. Thus, we would solve for the percentage as follows;
\(Percent = \frac{Satisfied\;persons}{Total\; population} \times 100\)
Substituting the given parameters into the formula, we have;
\(Percent = \frac{720}{1600} \times 100\\\\Percent = 0.45 \times 100\)
Percent = 45%
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Which of the following is a zero-dimentional geometric object?
Answer:
its a point
Step-by-step explanation:
Answer:
Point
Step-by-step explanation:
A point is something having position but not spatial extent, magnitude, dimension, or direction. That satisfies your condition; therefore, point is the correct answer.
Easy geometry please help!!
In the given parallelogram ABCD the values for variables are - g = 6, y = 5 and x = 4.
What is a parallelogram?
A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.
We know that in a parallelogram, opposite sides are congruent and parallel, and diagonals bisect each other.
Using this information, we can set up equations to solve for the variables.
From the given information, we have -
AE = CE = 2x - 5 = 5x - 17 (since diagonals bisect each other at point E)
BE = x + 2
DE = BE = (x + 2) = g (since diagonals bisect each other at point E)
We also know that opposite sides of a parallelogram are parallel.
Therefore, 10 is parallel to 2y, which means they have the same slope. We can write this as -
10/1 = 2y/1
10 = 2y
y = 5
Now we can use equation (1) to solve for x -
2x - 5 = 5x - 17
12 = 3x
x = 4
Finally, we can use x to solve for g -
(x + 2) = g
(4 + 2) = g
g = 6
Therefore, the values of x, y, and g are 4, 5, and 6, respectively.
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Complete the table and find the balance A if $3100 is invested at an annual percentage rate of 4% for 10 years and a compounded n times a year. Complete the table
The balance for each value of n is calculated by using the formula A = P(1 + r/n) ^nt. The rounded balance values are shown in the last column of the table above.
To complete the table and find the balance A if $3100 is invested at an annual percentage rate of 4% for 10 years and compounded n times a year.
The formula for calculating compound interest is as follows:
A = P(1 + r/n) ^nt,
where P represents the principal investment amount, r is the interest rate, n is the number of times the interest is compounded, t represents the time in years, and A represents the total amount, which includes the principal amount and the interest earned.
The table is given below:
\(\begin{array}{|c|c|c|} \hline \text{n} &
\text{A = P(1 + r/n) }^{nt} &
\text{Balance (rounded to nearest cent)} \\ \hline \text{1} &
\text{3100(1 + 0.04/1)}^{1*10} &
\text{\$4788.03} \\ \hline \text{2} &
\text{3100(1 + 0.04/2)}^{2*10} &
\text{\$4798.76} \\ \hline \text{4} &
\text{3100(1 + 0.04/4)}^{4*10} &
\text{\$4817.46} \\ \hline \text{12} &
\text{3100(1 + 0.04/12)}^{12*10} &
\text{\$4861.94} \\ \hline \end{array}\)
The balance is obtained by substituting the values of P, r, n, and t into the compound interest formula.
In this case, the investment is $3100, the annual interest rate is 4%, the investment is for 10 years, and n is the number of times the interest is compounded.
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. Why is the following arrangment of squares not an array?
When it comes to arrays in mathematics, it usually involves objects or numbers that are arranged in rows and columns.In order for a set of squares to be considered an array, it must meet certain requirements. These requirements are:All rows must have the same number of squares. All columns must have the same number of squares. Squares must be organized in an orderly manner. A set of squares that does not meet these requirements is not an array.
An array is a set of objects or values that are organized in a specific order. It is used in programming, mathematics, and other fields to make data manipulation and analysis easier.
When it comes to arrays in mathematics, it usually involves objects or numbers that are arranged in rows and columns.In order for a set of squares to be considered an array, it must meet certain requirements. These requirements are:All rows must have the same number of squares. All columns must have the same number of squares. Squares must be organized in an orderly manner. A set of squares that does not meet these requirements is not an array.
For example, if a set of squares is arranged in a random or disorganized manner, it cannot be considered an array because it does not meet the orderly requirement. Additionally, if the number of squares in each row or column is different, it cannot be considered an array because it does not meet the uniformity requirement.
Overall, it is important to remember that an array is a specific type of organization and cannot be applied to any random set of objects or values.
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How many ways can you scramble the word “Oaxaca”
Answer:
oaxaca
oacaxa
xaoaca
xacaoa
caoaxa
caxaoa
aoaxac
axaoac
aoacax
acaoax
axacao
acaxao
aoxaca
aocaxa
acoaxa
acxaoa
axoaca
axcaoa
aoaxca
axaoca
aoacxa
axacoa
acaoxa
acaxoa
Looks like 24 to me.
6 arrangements of “oa” “xa” and “ca”
those same 6 reversed
those same 6 with the first pair reversed
those same 6 with the first two pairs reversed.
reversing the last pair or the last two pairs only is illegal, so this is comprehensive.
Step-by-step explanation:
please i need HELPPP
Answer:
vertex point is (4,-6)
and it opens upwards as the coefficient of x is positive.
I assume B is the correct answer, good luck!
In ΔXYZ, y = 500 inches, � m∠Y=117° and � m∠Z=10°. Find the length of z, to the nearest inch.
The length of z in the triangle is 97 inches.
How to find the side of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
Therefore, let's find the side z of the triangle XYZ using sine law as follows:
a / sin A = b / sin B = c / sin C
Hence,
500 / sin 117 = z / sin 10
cross multiply
500 sin 10 = z sin 117
divide both sides by sin 117
z = 500 sin 10 / sin 117
z = 86.8240888335 / 0.89100652418
z = 97.4410774411
Therefore,
z = 97 inches
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Find the equation of the line that passes through the point (-6, 18) and has slope . Simplify your equation to the following form.
Answer:
rawr
Step-by-step explanation:
gotem
DEFG maps out Carrie’s dog walking route. If she does one complete loop, how far does she walk with her dogs?
Answer:
Step-by-step explanation:
Actually it’s 4 square root 17
A marching band needs to raise $13,500 for a trip to the Rose Bowl. The director told the band members that one-third of the amount that has been raised so far is equal to half of the amount that is still needed. How much more money needs to be raised for the trip?
Answer: $5400
Step-by-step explanation:
x = amount raised so far
13500 - x = amt. still needed
x/3 = (13500 - x)/2
2x = 3(13500 - x)
2x = 40500 - 3x
5x = 40500
x = 40500/5 = 8100 (amt. raised so far)
13500 - 8100 = 5400 (amt. still needed)
2. Audiologists recently developed a rehabilitation program for hearing-impaired patients
in a Canadian program for senior citizens. A simple random sample of the 30
residents of a particular senior citizens home and the seniors were diagnosed for
degree and type of sensorineural hearing loss which was coded as follows:
1 = hear within normal limits,
2 = high-frequency hearing loss,
3 = mild loss,
4 = mild-to-moderate loss,
5 = moderate loss, hon
6 = moderate-to-severe loss, and
7 = severe-to-profound loss.
The data are as follows:
6 7 1 1
2
6 4 6 4 2 5 2 5 15
4 6 6 5 5 5 2 5 3 6 4 6 642
boxplot of the data.
Son bis 910essig boole
cription of the distribution of the data
A2 IEC
We are 95% confident that the true mean hearing loss of senior citizens is between 3.5249 and 4.8751
What is 95% Confidence Interval?A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. The 95% confidence level is the most usual, but other levels, such 90% or 99%, are occasionally used to generate a confidence range.
How to calculate:
From the given data:
n= 30
x = 4.2
s = 1.808
d.f = n-1 = 30-1 = 29
At 95% confidence interval:
t\(\alpha /2\) = 2.0452
The 95% C.I for the mean is:
x ± t\(\alpha /2\)
= 4.2 ± 2.045 \(\frac{1.808}{\sqrt{30} }\)
= 4.2 ± 0.6751
( 3.5249, 4.8751)
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If I had 60 units needed and units per case was 14 how many full cases and additional items are needed to fufill the order
The image of B translated using (x + 2, y + 3) would have what coordinates?
Answer:
(5, 4)
Step-by-step explanation:
(x + 2, y + 3)
Substitute x and y for that of B's position.(3 + 2, 1 + 3)
(5, 4)
Answer:
B' (5, 4 )
Step-by-step explanation:
the translation rule (x, y ) → (x + 2, y + 3 )
means add 2 to the original x- coordinate and add 3 to the original y- coordinate , then
B (3, 1 ) → B' (3 + 2, 1 + 3 ) → B' (5, 4 )
Let f(x) = x ^ 2 g(x) = sqrt(x - 1) and h(x) = 2x + 3 Express each function k as a composite of two out of these three functions.
k(x) = sqrt(x ^ 2 - 1)
We can write k(x) as the composition of g(x) and f(x).
k(x) = g(f(x))
How to express k(x) as a composition?A composition of two functions means that we need to evaluate one function in the other one.
Here we have the functions:
f(x)= x²
g(x) = √(x - 1)
h(x) = 2x + 3
And we know that:
k(x) = √(x² - 1)
So we have a square root, then we need to evaluate g(x), and the argument is a square, then we need to evaluate in f(x), the composition is:
k(x) = g(f(x))
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Explain why having a significant linear correlation does not imply causality. Give an example to support your answer.
Correlation may not always indicate causality shown below.
What do you mean by corelation and causation?
We can determine how strongly a pair of variables are linearly associated and change together using the statistical technique of correlation. It only states that there is a relationship; it doesn't explain why or how it came to be. Correlation goes one step farther than causality. It states that any change in one variable's value will result in a change in another variable's value, or that one variable causes the occurrence of another. It also goes by the name "cause and effect."
may not always indicate causality. with a well-known instance.
In New York, ice cream sales and homicide rates are associated (Study)
The frequency of homicides fluctuates along with ice cream sales. Does ice cream consumption result in deaths of people?
No. The mere correlation of two events does not imply causation.
Since correlation does not imply causation in our example, ice cream is not to blame for any fatalities.
There are occasionally some unspoken aspects that are somehow connected. Weather is the underlying factor that drives both ice cream sales and homicide rates, as in our example. The increase in ice cream sales and killings is actually a result of the weather.
Therefore, significant linear correlation does not imply causality.
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The sum of a number and seven is one more than twice the number. What is the number
Answer: x+7=1+2x
Step-by-step explanation:
If x represents the number,The sum of a number and 7 is x + 7One more than twice the number is 1 + 2xThe IS in the middle of the sentence means =So, x + 7 = 1 + 2x Solve this equation,If you need further assistance message me.
Share N250,ooo in The ratio 7:3
Answer:
\(\huge\boxed{7 parts=175000}\)
\(\huge\boxed{3parts=75000}\)
Step-by-step explanation:
The first step in sharing 250,000 in the ratio of 7:3 is to work out the total number of parts. To do this you would add 7 to 3, which gives you 10. This is because you can imagine there being 7 and 3 equally sized rectangles with the same amount contained within each of them. In total there will be 10 rectangles.
The next step is to work out the value of each part of the ratio. This can be done by dividing 250,000 by 10, this gives you 25,000. This is because you are sharing the total of 250,000 among the 10 equal parts.
To work out the value of 7 parts you would need to multiply 7 by the value of one part, which is 25000. This gives you 175,000.
To work out the value of 3 parts you need to multiply 3 by the value of one part, which is 25000. This gives you 75,000.
1) Add 7 to 3.
\(7+3=10\)
2) Divide 250,000 by 10.
\(\frac{250000}{10}=25000\)
3) Multiply 25,000 by 7.
\(25000*7=175000\)
4) Multiply 25,000 by 3.
\(25000*3=75000\)
A spinner with 10 equal sized slices has 4 yellow slices, 3 red, and 3 blue slices. Kala spun the dial 1000 times and got the following results.
Kala spun the spinner 1000 times and got the following results:
- Yellow: 400 times
- Red: 300 times
- Blue: 300 times
1. Calculate the amount of sales tax:
- The item costs $350 before tax.
- The sales tax rate is 14%.
- To find the sales tax amount, multiply the cost of the item by the tax rate:
Sales tax = $350 * 0.14 = $49.
2. Determine the total cost of the item including tax:
- Add the sales tax amount to the original cost of the item:
Total cost = $350 + $49 = $399.
3. Analyze the spinner results:
- The spinner has 10 equal-sized slices.
- There are 4 yellow slices, 3 red slices, and 3 blue slices.
- Kala spun the dial 1000 times.
4. Calculate the frequency of each color:
- Yellow: Kala got 400 yellow results out of 1000 spins.
- Red: Kala got 300 red results out of 1000 spins.
- Blue: Kala got 300 blue results out of 1000 spins.
5. Calculate the probability of landing on each color:
- Yellow: Probability = Frequency of yellow / Total spins = 400 / 1000 = 0.4.
- Red: Probability = Frequency of red / Total spins = 300 / 1000 = 0.3.
- Blue: Probability = Frequency of blue / Total spins = 300 / 1000 = 0.3.
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Which of the following statements best describes the graph of x + y = 2? (5 points)
Group of answer choices
It is a line which intersects the x-axis at (2, 2).
It is a line which intersects the y-axis at (2, 2).
It is a line joining the points whose x- and y-coordinates add up to 2.
It is a line joining the points whose x- and y-coordinates add up to 4.
The best description of the graph is option B) It is a line which intersects the y-axis at (2, 2). This is because the line has a y-intercept of 2 and intersects the y-axis at the point (0, 2). Option B
To determine the best description of the graph of the equation x + y = 2, we can rearrange the equation into slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
Rearranging the equation, we have:
y = -x + 2
From this equation, we can see that the slope is -1, meaning that for every unit increase in x, y decreases by 1. The y-intercept is 2, indicating that the line intersects the y-axis at the point (0, 2).
Therefore, the best description of the graph is option B) It is a line which intersects the y-axis at (2, 2). This is because the line has a y-intercept of 2 and intersects the y-axis at the point (0, 2).
Option A) It is a line which intersects the x-axis at (2, 2) is incorrect because the line intersects the x-axis at the point (2, 0), not (2, 2).
Option C) It is a line joining the points whose x- and y-coordinates add up to 2 is incorrect because the equation represents a line and not a set of points.
Option D) It is a line joining the points whose x- and y-coordinates add up to 4 is incorrect because the equation represents a line where the x- and y-coordinates add up to 2, not 4.
Option B
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The decimal 105.7 becomes 1,057 when multiplied by 10. The same number becomes 10.57 when multiplied by 0.10. Explain why.
-Multiplying by 10 makes the number
(Type whole numbers or decimals.)
by a factor of Multiplying by 0.10 makes the number
by a factor of
At an amusement park, 15 riders ride the race cars every 20 minutes and 35 riders ride the ferris wheel every 60 minutes. Which ride has the greater ratio of riders?
Answer: the Ferris Wheel
Step-by-step explanation:
What is 29% of 150?
Show work
Answer:
To find 29% of 150, we can first express 29% as a decimal by dividing 29 by 100. 29% is the same as 0.29.
Then, we multiply 0.29 by 150 to find the answer:
0.29 * 150 = 43.5
So, 29% of 150 is equal to 43.5.
Here's the work:
29% * 150 = 0.29 * 150 = 43.5
\(\huge\text{Hey there!}\)
\(\mathsf{29\%\ of \ 150}\)
\(\mathsf{= \dfrac{29}{100} \ of \ 150}\)
\(\mathsf{= \dfrac{29}{100} \times 150}\)
\(\mathsf{= \dfrac{29}{100} \times \dfrac{150}{1}}\)
\(\mathsf{= \dfrac{29(150)}{100(1)}}\)
\(\mathsf{= \dfrac{4,350}{100}}\)
\(\mathsf{= \dfrac{4,350 \div 50}{100 \div 50}}\)
\(\mathsf{= \dfrac{87}{2}}\)
\(\mathsf{= 43 \dfrac{1}{2}}\)
\(\mathsf{= 43.5}\)
\(\huge\text{Therefore, your answer should be:}\)
\(\huge\boxed{\mathsf{\dfrac{87}{2}}}\huge\checkmark\)
\(\huge\boxed{\mathsf{43 \dfrac{1}{2}}}\huge\checkmark\)
\(\huge\boxed{\mathsf{43.5}}\huge\checkmark\)
\(\large\text{Either of those should work because they are all equivalent to each}\\\large\text{other}\uparrow\)
\(\huge\text{Good luck on your assignment \& enjoy your day! }\)
HELPPPPPPPP ASAP !!!!!!!!!!!!!!!
Answer
(4x-5) = -20 (2x+8) = 2
Step-by-step explanation:
2 x − 8 = 2 2x-8=2 2x−8=2. Add 8 to both sides. Simplify 2 + 8 2+8 2+8 to 10. Divide both sides by 2. If its wrong then I’m very sorry but I’m sure this is correct.