Answers
2a. To calculate the average number of violations committed, we add up all the violations and divide by the number of offenders:
Average number of violations = (15+20+10+25+5+22+8+12+18+7+23+6+24+19+11) / 15
Average number of violations = 187 / 15
Average number of violations ≈ 12.47
Therefore, the average number of violations committed by the offenders in the sample is approximately 12.47.
2b. To calculate the sample mean for the given data, we add up the five samples and divide by the number of samples:
Sample mean = (22 + 8 + 19 + 7 + 24) / 5
Sample mean = 80 / 5
Sample mean = 16
Therefore, the sample mean for the five samples is 16.
2c. To estimate the mean interval with 95% confidence level, we can use the t-distribution and the formula:
Sample mean ± t-value (α/2, n-1) x (standard deviation / square root of n)
We are not given the standard deviation of the population, so we need to estimate it using the sample standard deviation:
s = sqrt [ Σ(xi - x)^2 / (n - 1) ]
where xi is the i-th sample, x is the sample mean, and n is the number of samples.
Using the five samples given in part (b), we can calculate the sample standard deviation:
s = sqrt [ ((22-16)^2 + (8-16)^2 + (19-16)^2 + (7-16)^2 + (24-16)^2) / (5-1) ]
s = sqrt [ (36 + 64 + 9 + 81 + 64) / 4 ]
s ≈ 9.17
Using a t-distribution table with α/2 = 0.025 and degrees of freedom = n-1 = 4, we find that the t-value is 2.776.
Plugging in the values, we get:
Sample mean ± t-value (α/2, n-1) x (standard deviation / square root of n)
16 ± 2.776 x (9.17 / sqrt(5))
16 ± 9.55
Therefore, with 95% confidence, we estimate that the mean number of violations committed by the population of lawbreakers is between 6.45 and 25.55.
To estimate the number of violations when the road area is 6 meters, we need to use the regression equation Y = a + bX. However, we are not given the values of a and b.
Without knowing the values of a and b, we cannot estimate the number of violations when the road area is 6 meters or use the regression equation to make any predictions.Answer:
Step-by-step explanation:
For a population of 300 lawbreakers:
2. a. average number of violations is 12.b. sample mean is 16.c. confidence interval is 6.09, 25.913. traffic violations using regression equation is n = 4, ΣX = 18, ΣY = 15.How to solve random samples?2. a. To calculate the average number of violations committed, find the mean of the given data set.
Mean = (15 + 20 + 10 + 25 + 5 + 22 + 8 + 12 + 18 + 7 + 23 + 6 + 24 + 19 + 11) / 15
Mean = 180 / 15
Mean = 12
Therefore, the average number of violations committed is 12.
b. To calculate the sample mean, we need to find the mean of the given sample data set.
Sample mean = (22 + 8 + 19 + 7 + 24) / 5
Sample mean = 80 / 5
Sample mean = 16
Therefore, the sample mean is 16.
c. To estimate the mean interval with 95% confidence level, we can use the t-distribution with n-1 degrees of freedom, where n is the sample size. The formula for the confidence interval is:
Confidence interval = sample mean ± (t-value x standard error)
where t-value is the value obtained from the t-distribution table for a 95% confidence level and n-1 degrees of freedom, and standard error is the standard deviation of the sample data divided by the square root of the sample size.
First, find the standard deviation of the sample data set.
Standard deviation = √[(Σ(x - μ)²) / (n - 1)]
where Σ is the sum of the values, x is each value in the sample data set, μ is the sample mean, and n is the sample size.
μ = 16 (from part b)
n = 5
x values = 22, 8, 19, 7, 24
Standard deviation = √[((22-16)² + (8-16)² + (19-16)² + (7-16)² + (24-16)²) / (5 - 1)]
Standard deviation = √[(36 + 64 + 9 + 81 + 64) / 4]
Standard deviation = √(254 / 4)
Standard deviation = √63.5
Standard deviation ≈ 7.97
Next, find the t-value for a 95% confidence level and 4 degrees of freedom. From the t-distribution table, the t-value is 2.776.
Confidence interval = 16 ± (2.776 x (7.97 / √5))
Confidence interval = 16 ± (2.776 x 3.57)
Confidence interval = 16 ± 9.91
Therefore, the mean interval with 95% confidence level is (16 - 9.91, 16 + 9.91), or approximately (6.09, 25.91).
3. To estimate the number of violations for a road area of 6 meters, we need to use the regression equation Y = a + bX, where Y is the number of violations and X is the road area in meters.
First find the values of a and b from the given data.
Using the formula:
b = [(nΣXY) - (ΣX)(ΣY)] / [(nΣX²) - (ΣX)²]
a = (ΣY - bΣX) / n
where n is the number of data points, Σ is the sum of the values, and X and Y are the variables.
n = 4
ΣX = 18
ΣY = 15
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Image transcribed:
QUESTIONS
2. There are 300 lawbreaker as a population
X = the number of law violations by the 1st lawbreaker in 1 year. Researched as many as 15 offenders as a random sample. It turns out that the number of violations committed by them is :
15 20 10 25 5
22 8 12 18 7
23 6 24 19 11
Questions:
a. Calculate the average number of violations committed
b. If 5 samples are taken, namely: 22 8 19 7 24
Calculate the sample mean
c. Estimate the mean interval with 95% confidence level
3. The number of traffic violations in city A every day (several times) is:
Road area (X) in meter | 4 3.5 5 5.5
Violation (Y) | 3 3 2 7
Approximately how many violations if the road area is 6 meters? If the regression equation is:
Y = a+bX
Related Questions
Select all that apply. By making the financially irresponsible decision of maxing out your credit card limit, you might...
A) not have money for an emergency situation.
B) get a very low interest rate when you want to buy a house.
C) not be able to buy the things you need.
D) have enough saved up for retirement.
Answers
By making the financially irresponsible decision of maxing out your credit card limit, you might not have money for an emergency situation.
As, There is no foolproof technique to determine how much you can spend in excess of your credit limit, but you can go over it.
When determining the risk of accepting an over-the-limit transaction, card issuers may take into account a number of criteria, including your prior payment history.
Now, maxing out credit card leads to negative results.
So, either not have money for an emergency situation or not be able to buy the things you need.
But we can still spend after maxing out the limit.
Thus, not have money for an emergency situation is correct option.
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Do you use integration by parts to solve this problem? If so, how? I can't seem to figure out the right answer
Answers
The integral of [tex]\int\limits^e_1 {x^{1/2}lnx } \, dx[/tex] is (2/3)[tex]e^{3/2}[/tex] - (4/9).
To find the integral of [tex]\int\limits^e_1 {x^{1/2}lnx } \, dx[/tex] , we can use integration by parts. Let u = ln x and dv = [tex]x^{1/2}[/tex] dx. Then du/dx = 1/x and v = (2/3) [tex]x^{3/2}[/tex] .
Using the formula for integration by parts, we have:
∫[tex]x^{1/2}[/tex]lnx dx = uv - ∫v du/dx dx
= ln x * (2/3) [tex]x^{3/2}[/tex] - ∫(2/3) [tex]x^{3/2}[/tex] * (1/x) dx
= ln x * (2/3) [tex]x^{3/2}[/tex] - (2/3) ∫ [tex]x^{1/2}[/tex] dx
= ln x * (2/3) [tex]x^{3/2}[/tex] - (4/9) [tex]x^{3/2}[/tex] + C
where C is the constant of integration.
To evaluate the definite integral from 1 to e, we substitute e for x in the expression above and subtract the result when x = 1:
[tex]\int\limits^e_1 {x^{1/2}lnx } \, dx[/tex] = [(2/3) [tex]e^{3/2}[/tex] ln e - (4/9) [tex]e^{3/2}[/tex] ] - [(2/3)[tex]1^{3/2}[/tex]ln 1 - (4/9)[tex]1^{3/2}[/tex]]
= (2/3) [tex]e^{3/2}[/tex] - (4/9)
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3 1/2 be classified as integer
Answers
Answer:
False.
Step-by-step explanation:
A integer in math is defined as a whole number. Therefore, the presence of fractions (which, in this case, is 1/2) and decimals, would mean that the term is in fact, not a integer.
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2 grams =
milligrams
Answers
There are 2000 milligrams in 2 grams of a substance, and it constitutes 40% of a 5-gram sample.
How to solveConvert grams to milligrams:
2 grams = 2 * 1000 milligrams
2 grams = 2000 milligrams
Calculate the percentage in a 5-gram sample:
Percentage = (2000 milligrams / 5000 milligrams) * 100
Percentage = (2 / 5) * 100
Percentage = 0.4 * 100
Percentage = 40%
Thus, there are 2000 milligrams in 2 grams of a substance, and it constitutes 40% of a 5-gram sample.
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2 grams = milligrams
How many milligrams are there in 2 grams of a substance, and what is the percentage of this amount in a 5-gram sample?
what is the value of RP
Answers
The calculated value of the length RP is 107 units
Calculating the value of the length RPFrom the question, we have the following parameters that can be used in our computation:
The circles and the tangent lines
Start by calculating the segment PQ using the following Pythagoras theorem
PQ² = (50 + 11)² + 11²
Evaluate
PQ² = 3842
So, we have
PQ = 62
The value of the length RP is then calculated as
RP = PQ + TU
So, we hav
RP = 62 + 45
Evaluate
RP = 107
Hence, the value of the length RP is 107 units
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Suppose that the function h is defined as follows.
Answers
The graph of the piecewise function is given by the image presented at the end of the answer.
What is a piece-wise function?A piece-wise function is a function that has different definitions, depending on the input of the function.
All the five definitions of the function in this problem are constant, hence the graph will be composed by horizontal lines.
The definitions are given as follows:
y = -3 between x = -2.5 and x = -1.5.y = -2 between x = -1.5 and x = -0.5.y = -1 between x = -0.5 and x = 0.5.y = 0 between x = 0.5 and x = 1.5.y = 1 between x = 1.5 and x = 2.5.More can be learned about piece-wise functions at brainly.com/question/19358926
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Collect a set of data (from the internet) about any school-appropriate topic. Examples: rainfall data, and testing scores. Or make up your own set of data. The data set must contain at least 20 values. Fill out the questions below regarding your data.
1. List your data below in numerical order.
2. Explain your data. What does each data point represent?
3. What is the mean of your data?
4. What is the minimum and maximum within your data?
Answers
Here is the data collected as a result of the experiment.
1) Numerical order is: 0.20, 0.20, 0.46, 0.46, 2.10, 2.10, 5.50, 11.80, 12.20, 12.20, 13.22, 14.65, 16.07, 17.49, 18.91, 20.33, 20.50, 20.50, 21.75, 23.18
2) The data represents rainfall in millimeters over a 20-day period.
3) Mean = 11.69 mm.
4) The minimum rainfall is 0.20 mm ;
the maximum is 23.18 mm.
1) The data is listed as follows.
0.20 12.20 2.10 0.46 20.50 5.50 11.80 13.22 14.65 16.07 17.49 18.91 20.33 21.75 23.18 0.20 12.20 2.10 0.46 20.502) The data represents the amount of rainfall in millimeters over a 20 day period.
3) The mean rainfall over the 20 day period is 11.69 mm.
= (0.20 + 0.20 + 0.46 + 0.46 + 2.10 + 2.10 + 5.50 + 11.80 + 12.20 + 12.20 + 13.22 + 14.65 + 16.07 + 17.49 + 18.91 + 20.33 + 20.50 + 20.50 + 21.75 + 23.18) /20
Mean (x) = 11.69 mm.
3) The minimum rainfall is 0.20 mm and the maximum is 23.18 mm.
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consider the time taken to completion time (in months) for the construction of a particular model of homes: 4.1 3.2 2.8 2.6 3.7 3.1 9.4 2.5 3.5 3.8 Find the mean, median mode, first quartile and third quartile. Find the outlier?
Answers
Sum
Mean = (4.1 + 3.2 + 2.8 + 2.6 + 3.7 + 3.1 + 9.4 + 2.5 + 3.5 + 3.8) / 10
Mean = 36.7 / 10
Mean = 3.67
To find the median, we need to put the values in order:
2.5, 2.6, 2.8, 3.1, 3.2, 3.5, 3.7, 3.8, 4.1, 9.4
The middle number is the median, which is 3.35 in this case (3.2+3.5)/2.
To find the mode, we look for the value that appears most often. In this case, there is no mode as no value appears more than once.
To find the first quartile (Q1), we need to find the value that separates the bottom 25% of the data from the top 75%. We can do this by finding the median of the lower half of the data:
2.5, 2.6, 2.8, 3.1, 3.2
The median of this lower half is 2.8, so Q1 = 2.8.
To find the third quartile (Q3), we need to find the value that separates the bottom 75% of the data from the top 25%. We can do this by finding the median of the upper half of the data:
3.7, 3.8, 4.1, 9.4
The median of this upper half is 3.95, so Q3 = 3.95.
To find the outlier, we can use the rule that any value more than 1.5 times the interquartile range (IQR) away from the nearest quartile is considered an outlier. The IQR is the difference between Q3 and Q1:
IQR = Q3 - Q1
IQR = 3.95 - 2.8
IQR = 1.15
1.5 times the IQR is 1.5 * 1.15 = 1.725.
The only value that is more than 1.725 away from either Q1 or Q3 is 9.4. Therefore, 9.4 is the outlier in this data set.
Answer:
Step-by-step explanation:
Mean is the average of the data vales : 38.7 (sum of all values) divided by 10 (the number of values). Mean = 38.7/10 = 3.87
Median is the "middle" number" = put the date in order and find the middle value:
2.5, 2.6, 2.8, 3.1, 3.2, 3.5, 3.7, 3.8, 4.1, 9.4, since there is no middle data value, find the average of the 2 in the middle.
3.2 + 3.5/2 = 6.7 ÷ 2 = 3.35 - median
All values appear once so there is no mode.
First quartile is the middle of the lower set of data = 2.8
Third quartile is the middle of the upper set = 3.8
The outlier is 9.4.
How to calculate the outlier:
First you need the IQR which is the diffence of Q3 - Q1,
so the IQR is 3.8- 2.8 = 1
Outliers are the quartile + or - (1.5)(IQR)
Q1 -(1.5)(1) = 2.8 - 1.5 = 1.3
Q3 - (1.5)(1)= 3.8 + 1.5 =4.5
So anything below 1.3 or above 4.5 is an outlier.
There is one 9.4
17. The Amethyst Woodstar species of
hummingbird beats its wings about
80 times per second. If there are
60 seconds in a minute, about how
many times does the Amethyst
Woodstar beat its wings in
9 minutes?
A 12,600
B 37,800
C50,400
D 43,200
Answers
Answer: D
Step-by-step explanation: 60x9=540 and 540x80=43,200
USE THE FACTOR THEOREM
YES OR NO
Answers
Answer:
yes
Step-by-step explanation:
the factor theorem says if (x + a) is a factor of a polynomial f(x) then f(- a) = 0
given (x+ 5) then if f(- 5) = 0 , (x + 5) is a factor
4[tex](-5)^{4}[/tex] + 16(- 5)³ - 6(- 5)² + 73(- 5) + 15
= 4(625)+ 16(- 125) - 6(25) - 365 + 15
= 2500 - 2000 - 150 - 350
= 500 - 500
= 0
then (x + 5) is a factor of the given polynomial
Question 2 (1 point)
Thomas's football team lost 3 yards in their first drive while Derrek's
football team gained 5 yards in their first drive. The first drives for each
team can be compared on a number line, where 0 represents the line
of scrimmage for each play.
Select the correct numbers for Derrek and Thomas' football teams.
Oa Derrek's Team has-5
Ob Thomas' Team has +3
OcThomas' Team has -3
Od Derrek's Team has +5
Answers
The correct numbers for Derrek and Thomas' football teams are :
c. Thomas' Team has -3d. Derrek's Team has +5How to find the numbers ?According to the information given, Thomas's football team lost 3 yards in their first drive, which means they moved backward 3 yards from the line of scrimmage. This can be represented as -3 on the number line.
On the other hand, Derrek's football team gained 5 yards in their first drive, which means they moved forward 5 yards from the line of scrimmage. This can be represented as +5 on the number line.
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Suppose that you are taking a course where the total class grade is the weighted average of your homework, worksheets, quizzes and tests.
The homework is worth 15% of the course grade, worksheets are worth 20% of the course grade, the quizzes are worth 25% of the course grade, and tests are worth 40% of the course grade. To get a B in the course, you must have an overall average of at least 80%.
Your current grades in each category are:
Homework =
73
%, Worksheets =
79
%, and Quizzes =
84
%.
What is the minimum test average you need to get a B in the course?.
Your answer is:
% (Round to at least 1 decimal place)
Answers
The minimum grade you need to get a B in the course is given as follows:
x = 80.625.
How to calculate the mean of a data-set?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.
The grades and their percentages are given as follows:
73 worth 15%.79 worth 20%.84 worth 25%.x worth 40%.You want a grade of 80, hence the minimum test average is obtained as follows:
0.15 x 73 + 0.2 x 79 + 0.25 x 84 + 0.4x = 80
47.75 + 0.4x = 80
x = (80 - 47.75)/0.4
x = 80.625.
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help please PLEASE !!!!!
Answers
Answer:
Positive Association
Complementary Angles
Negative Association
Clusters in Data
Supplementary Angle
Non-linear Association
Step-by-step explanation:
Match the boxes on the left to the answers:
Positive Association
Complementary Angles
Negative Association
Clusters in Data
Supplementary Angle
Non-linear Association
Use the even and odd properties of the following functions to answer the questions:
a) If secθ=-3.1,then sec(-θ)=?
b)If sinθ=0.62,then sin(-θ)=?
Answers
Answer:
[tex]sec(-\theta)=-3.1[/tex]
[tex]sin(-\theta)=-0.62[/tex]
Step-by-step explanation:
Part a.
[tex]sec(\theta)[/tex] is related to [tex]cos(\theta)[/tex] through a reciprocal relationship [tex]sec(\theta)=\frac{1}{cos(\theta)}[/tex].
Since [tex]cos(\theta)[/tex] is an even function (reflecting left-right across the y-axis doesn't change the graph), then [tex]sec(\theta)[/tex] is also an even function.
For any input in the domain, even functions produce the same output if the opposite of the input is used. In other words, if "f" is an even function, for all x in the domain of f, [tex]f(x)=f(-x)[/tex].
Thus, for the secant function, if a mystery value "x" is used as an input, and -3.1 is obtained as an output, then if the opposite of x, or -x, is input into the secant function, the output will also be -3.1.
[tex]sec(-\theta)=-3.1[/tex]
Part b.
The [tex]sin(\theta)[/tex] function does not reflect left-right across the y-axis to produce the same graph, so the sine function is not even.
However, the sine function can be rotated 180 degree about the origin, sometimes thought of as reflecting through the origin, to produce the same graph. Visually, this is an "odd" function.
For any input in the domain, if the opposite of the input is used, odd functions produce the opposite of the original output. In other words, if "g" is an odd function, for all x in the domain of g, [tex]-g(x)=g(-x)[/tex].
Thus, for the sine function, if a mystery value "x" is used as an input, and 0.62 is obtained as an output, then if the opposite of x, or -x, is input into the sine function, the output will be the opposite of 0.62, meaning -0.62.
[tex]sin(-\theta)=-0.62[/tex]
find x
find x
find x
Answers
Add the total length + the length outside of the circle and set it equal to the other segment’s total length + the length outside of the circle. Like this: (10+8)(8) = x(18 + x).
Then simplify to 144 = x^2 + 18x.
Use the quadratic formula (see picture), and x=6, x=-24. Except x ≠ -24 because the length cannot be a negative value. So x = 6!!
Here is a picture of my work:
I’m on my phone so it’s harder to type out the equations. Hope this helps!
Factor the polynomial completely. If the polynomial is prime, so state.
x2 - x - 35
Answers
The given polynomial is a prime polynomial.
The given polynomial is
x² - x + 35
Since we know that discriminant of quadratic polynomial
p(x)= ax² + bx + c is b² - 4ac
Therefore, discriminant of the given polynomial be,
⇒ (-1)² - 4x1x35
⇒ - 139
Since discriminant is negative number so it has no real roots.
And an irreducible or primal polynomial is a polynomial with integer coefficients that cannot be factored into polynomials of lower degree and also with integer coefficients.
Hence it is not factored completely.
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please help me with this problem
Answers
Make log 9 x the subject and substitute 14-4y. Then, solve the equation like the picture attached
Ask me if there’s any more question ;)
College Level Trig Question!
Answers
The value of theta in the given trigonometry function is 45⁰.
What is the value of theta?The value of theta in the given trigonometry function is calculated as follows;
9 sin²θ tanθ - 9 sin²θ = 0
Solve the equation as follows;
9 sin²θ tanθ = 9 sin²θ
divide both sides by 9 sin²θ;
(9 sin²θ tanθ)/9 sin²θ = 9 sin²θ /9 sin²θ
tanθ = 1
Now, solve for θ as follows;
θ = tan⁻¹ (1)
θ = 45⁰
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The table below shows the amount of time 80 people spent watching television during a week.
Time (hours)
Frequency
0 < h ≤ 10
5
10 < h ≤ 20
15
20 < h ≤ 30
50
30 < h ≤ 40
10
Calculate an estimate for the mean time spent watching television.
Give your answer to 1 d.p.
Answers
An estimate for the mean time spent watching television is approximately 24.375 hours.
How to calculate the meanMidpoint of 0 < h ≤ 10 = (0 + 10) / 2 = 5
Midpoint of 10 < h ≤ 20 = (10 + 20) / 2 = 15
Midpoint of 20 < h ≤ 30 = (20 + 30) / 2 = 25
Midpoint of 30 < h ≤ 40 = (30 + 40) / 2 = 35
Sum of observations = (5 × 5) + (15 × 15) + (25 × 50) + (35 × 10) = 125 + 225 + 1250 + 350 = 1950
Total number of observations = 5 + 15 + 50 + 10 = 80
Mean = Sum of observations / Total number of observations = 1950 / 80 = 24.375
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I would love some help please 18-20
Answers
18. C
(m / 2) - 6 = (m / 4) + 2
---Multiply everything by the LCM of the denominators
---LCM = 4
2m - 24 = m + 8
m - 24 = 8
m = 32
19. A
k / 12 = 25 / 100
---We can simplify 25/100
---We want to simplify enough to where the denominator of 25/100 is a multiple or factor of 12
k / 12 = 1 / 4
---4 x 3 = 12, 1 x 3 = 3
k = 3
20. A
9 / 5 = 3x / 100
---Cross multiply and solve algebraically
(5 * 3x) = (9 * 100)
15x = 900
x = 60
Hope this helps!
19.A
20.A
are the answers
Please Factorise 8x - 6
Answers
Answer:
2(4x-3)
Step-by-step explanation:
Find common numbers between 8 and 6, which is 2. 2x4= 8 2x3=6
x is only on 8 so you can't put x on the outside of the bracket. so you put it with the 4 so it comes out correct
In QA, if m/DBG= 32° and mGFE = 149°, find mDG.
A. mDG = 62°
B. mDG=85°
C. mDG = 107°
D. mDG = 117°
E
Mark this and return
Answers
The tangent secant exterior angle measure theorem indicates that the measure of the arc DG, m[tex]\widehat{DG}[/tex] is 85°, the correct option is the option B.
B. m[tex]\widehat{DG}[/tex] = 85°
What is the tangent secant exterior angle measure theorem?The tangent secant exterior angles theorem states that if two secant or tangent or a secant and tangent intersect on the exterior to a circle, the measure of the angle formed is half the difference of the arcs they intercept.
The possible options in the question indicates that the possible drawing in the consists of a tangent and a secant, with the angle m∠DBG, being external to the circle.
The tangent secant exterior angle measure theorem indicates that we get;
m∠DBG = (1/2) × (m[tex]\widehat{GFE}[/tex] - m[tex]\widehat{DG}[/tex])
The question indicates; m[tex]\widehat{GFE}[/tex] = 149°
m∠DBG = 32°
Therefore;
32 = (1/2) × (149° - m[tex]\widehat{DG}[/tex])
149° - m[tex]\widehat{DG}[/tex] = 2 × 32° = 64°
m[tex]\widehat{DG}[/tex] = 149° - 64° = 85°
The measure of the arc DG, m[tex]\widehat{DG}[/tex] is 85°
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Which equation accurately represents this statement? Select three options. Negative 3 less than 4.9 times a number, x, is the same as 12.8. Negative 3 minus 4.9 x = 12.8 4.9 x minus (negative 3) = 12.8 3 + 4.9 x = 12.8 (4.9 minus 3) x = 12.8 12.8 = 4.9 x + 3
Answers
The equation accurately represents this statement is "Negative 3 less than 4.9 times a number, x, is the same as 12.8"
how to determine the equation that accurately represents the statementThe statement is "Negative 3 less than 4.9 times a number, x, is the same as 12.8." We can break it down into two parts:
"4.9 times a number, x": This means we need to multiply a number, x, by 4.9. So the first part of the equation is 4.9x.
"Negative 3 less than 4.9 times a number, x, is the same as 12.8":
This means we need to subtract 3 from the result of multiplying x by 4.9. So the second part of the equation is -3.
Putting it all together, we get:
4.9x - 3 = 12.8
This equation accurately represents the given statement.
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If the median of a data set is 13 and the mean is 13, which of the following is most likely?
Select the correct answer below:
a. The data are skewed to the left.
b. The data are skewed to the right.
c. The data are symmetrical.
Answers
Answer:
C
Step-by-step explanation:
if the mean and median are the same, the graph will be symmetrical
Kyle has three times as much money in his savings account as Hayden Hayden has twice as much money in his savings account as Jeremy combine Kyle Hayden and Jeremy have a total of 612 how much money does Kyle have in his account
Answers
Kyle has $306 in his account so, right answer is Option D.
Let Kyle's money = x
Hayden's money = y
Jeremy's money = z
Given that Kyle has three times as much money in his savings account as Hayden.
x = 3y .....Eqn 1
Hayden has twice as much money in his savings account as Jeremy.
z = 2y ..... Eqn 2
Now Combined Kyle, Hayden, and Jeremy have a total of $612.
x+y+z=612 .....Eqn 3
Putting value of x and z from Eqn 1 and 2 in Eqn 3
6y = 612
y = 106
Putting in Eqn 1;
x = 306
Thus, Kyle has $306 in his account.
The right answer is Option D.
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Find the approximate area of the shaded region below, consisting of a right triangle with a circle cut out of it. Use 3.14 as an
approximation for pi.
O 1.254 square meters
O 312 square meters
O2, 822 square meters
O 314 square meters
Answers
Answer:
(a) 1.254 square metersStep-by-step explanation:
We are given a figure, consisting of a right triangle with a circle cut out of it.
To Calculate : area of the shaded region below,
First Let's find the Area of the right triangle:
Area(triangle) = 1/2 × Base × Height
= 1/2 × 56 × 56
= 1/2 × 3136
= 3136/2
= 1568 m².
Now, We are diameter of the circle = 20 m
Radius of the circle = 20/2 = 10 m
Area of circle = πr²Acc. to question we have to use 3.14 as an
approximation for pi.
Area (circle) = 3.14 × 10 × 10
Area (circle) = 3.14 × 100
Area (circle) = 314 m²
Area of shaded region = Area of triangle - Area of circle =
= 1568 m² - 314 m²
= 1.254 square meters
Therefore, The approximate area of the shaded region is 1.254 square meters.
Option (a) is the required answer
Based on the scenario, determine if it would be better to use the mean or median to describe the data set.
1 Workers at a plant are trying to show that they work too many hours. There are five part-time workers along with ten full time workersWhat summary statistic would best defend their position?
2Mrs. Smith is trying to show that her class did really well on the last test. She has four students that should have been in honors mathbut instead stayed in regular math. What summary statistic should she use to defend her position?
3. A CEO is trying to determine the average salary of his workersHe has some workers that work part- time and some very highly paid workersIf he wants a true idea of the average salarywhat summary statistic should he use?
4. Henry is trying to determine his average test grade in a class. All of his grades have been within five points of each other. He needs the average in order to calculate his overall gradeWhat summary statistic should he use?
____median
____median
____mean
____mean
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1. It would be better to use the median to describe the data set.
2. It would be better to use the median to describe the data set.
3. It would be better to use the mean to describe the data set as the average salary of the workers is to be calculated.
4. It would be better to use the mean to describe the data set as the average test grade of the class is to be calculated.
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The length of a rectangle is five times its width.
If the perimeter of the rectangle is 108 cm, find its length and width.
Answers
Answer:
Let the width of the rectangle be w. Then the length of the rectangle is 5w.
The perimeter of a rectangle is the sum of all four sides. So, the perimeter of the rectangle is 2w+2(5w)=108 cm.
Simplifying the right side of the equation, we get 12w=108 cm.
Dividing both sides of the equation by 12, we get w=9 cm.
Since the width is 9 cm, the length of the rectangle is 5w=5(9)=45 cm.
Therefore, the length of the rectangle is 45 cm and the width is 9 cm.
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4, 6, 14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9, 18, 20, and 22. There are two dots above 6, 10, 12, 14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.
Bus 18, with a median of 13
Bus 47, with a median of 16
Bus 18, with a mean of 13
Bus 47, with a mean of 16
Answers
The correct option regarding which bus has the least spread among the travel times is given as follows:
Bus 14, with an IQR of 6.
How to solveTo obtain measures of spread, we can use the dot plot to visualize the frequency of each observation in the data-set, and then calculate the interquartile range (IQR).
For a group of 15 students, we can find the quartiles as follows:
The first quartile (Q1) is the median of the first half of the data-set, which consists of the first seven students.
Looking at the dot plot, the fourth dot represents the median of the first half. For Bus 14, Q1 = 12. For Bus 18, Q1 = 9.
The third quartile (Q3) is the median of the second half of the data-set, which consists of the last seven students. Looking at the dot plot, the eleventh dot represents the median of the second half. For Bus 14, Q3 = 18.
For Bus 18, Q3 = 16.
We can then calculate the IQR as the difference between Q3 and Q1:
For Bus 14, IQR = Q3 - Q1 = 18 - 12 = 6.
For Bus 18, IQR = Q3 - Q1 = 16 - 9 = 7.
Based on the IQR values, we can conclude that Bus 14 is more consistent than Bus 18, as it has a lower IQR.
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Can the sides of a right triangle have lengths 7,9 and the square Root of 155
Answers
Answer:
No
Step-by-step explanation:
In order for a triangle to be a right angle, the sum of the squares of the two legs (a and b) must be equal the square of the longest side, known as the hypotenuse (c):
[tex]a^2+b^2=c^2[/tex]
The square root of 155 is the longest side as it is approximately 12.45. Thus, if the triangle is a right triangle, the square root of 155 must be the hypotenuse.
We can now check to see whether the sum of the squares of 7 and 9 equal the square of the square root of 155:
[tex]7^2+9^2=(\sqrt{155})^2\\ 49+81=155\\130=155[/tex]
The equation is not true since 130 is less than and not equal to 155. Therefore, a triangle with side lengths 7, 9, and the square root of 155 cannot be a right triangle.