The shape of the distribution in histogram is skewed left and mean=43.071429 and standard deviation= 15.886445 are used together to measure the center and spread of the data.
What is histogram?
A grouped frequency distribution with continuous classes is graphically represented by a histogram. It is an area diagram, and its size is proportional to the frequencies in the associated classes. Due to the base's coverage of the spaces between class boundaries, all of the rectangles in such representations are contiguous.
We can make a sideways histogram. (makes it easier if typing text, but if you are writing on paper then you don't have to make it sideways) Each row will represent a range of 10 (1st row is 10 to 19, 2nd row is 20 to 29, etc)
=> 13 23 28 33 34 38 44 45 49 50 55 59 65 67
The data looks like it is slightly skewed left (hump towards the right [down]). The mean and the standard deviation are used together to measure the center and spread of the data.
Mean = [tex]\frac{ 13+23+28+33+34+38+44+45+49+50+55+59+65+67}{14}=\frac{603}{14}[/tex] = 43.071429
Standard deviation = 15.886445
Hence the shape of the distribution in histogram is skewed left and mean=43.071429 and standard deviation= 15.886445 are used together to measure the center and spread of the data.
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Given two events E and F with Pr(E) = 0. 4, Pr(F) = 0. 5, and Pr(EnF) = 0. 3, a) Pr(E|F) = b) Pr(F|E) = c) Are E and F independent? (Enter YES or NO)
Given two events E and F with Pr(E) = 0. 4, Pr(F) = 0. 5, and Pr(EnF) = 0. 3 then:
a) Pr(E|F) = 0.6
b) Pr(F|E) = 0.75
c) NO, E and F are not independent.
a) To find Pr(E|F), we use the formula: Pr(E|F) = Pr(EnF)/Pr(F). Substituting the given values, we get Pr(E|F) = 0.3/0.5 = 0.6.
b) Similarly, to find Pr(F|E), we use the formula: Pr(F|E) = Pr(EnF)/Pr(E). Substituting the given values, we get Pr(F|E) = 0.3/0.4 = 0.75.
c) We can check for independence by seeing if Pr(E) = Pr(E|F) or Pr(F) = Pr(F|E). However, since Pr(E) ≠ Pr(E|F) and Pr(F) ≠ Pr(F|E), we can conclude that E and F are not independent.
In other words, the occurrence of one event affects the probability of the other event occurring. Specifically, the fact that Pr(EnF) ≠ Pr(E)Pr(F) indicates that the events are dependent.
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The average price of a two-bedroom apartment in the uptown area of a prominent American city during the real estate boom from 1994 to 2004 can be approximated by p(t) = 0.17e⁰.¹⁰ᵗ million dollars (0 ≤ t ≤ 10) where t is time in years (t = 0 represents 1994). What was the average price of a two-bedroom apartment in this uptown area in 2002, and how fast was it increasing? (Round your answers to two significant digits.) p(8) = $ million p' (8) = $ million per yr
In 2002, the average price of a two-bedroom apartment in the uptown area was approximately $0.316 million, and it was increasing at a rate of about $0.0328 million per year.
To find the average price of a two-bedroom apartment in 2002 (t=8), you need to evaluate the given function p(t) = 0.17e^(0.10t) at t=8:
p(8) = 0.17e^(0.10 * 8)
p(8) = 0.17e^0.8 ≈ 0.316 million dollars
To find the rate at which the price was increasing in 2002, you need to find the derivative of the function p(t) with respect to t, and then evaluate it at t=8:
p'(t) = d/dt (0.17e^(0.10t))
p'(t) = 0.17 * 0.10 * e^(0.10t)
Now, evaluate p'(t) at t=8:
p'(8) = 0.17 * 0.10 * e^(0.10 * 8)
p'(8) ≈ 0.0328 million dollars per year
So, in 2002, the average price of a two-bedroom apartment in the uptown area was approximately $0.316 million, and it was increasing at a rate of about $0.0328 million per year.
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37% of 42 is equal to 74% of what number?
Answer: 50
Step-by-step explanation:
37 is 74 percent of what number
We already have our first value 37 and the second value 74. Let's assume the unknown value is Y which answer we will find out.
As we have all the required values we need, Now we can put them in a simple mathematical formula as below:
STEP 1 37 = 74% × Y
STEP 2 37 = 74/100× Y
Multiplying both sides by 100 and dividing both sides of the equation by 74 we will arrive at:
STEP 3 Y = 37 × 10074
STEP 4 Y = 37 × 100 ÷ 74
STEP 5 Y = 50
Finally, we have found the value of Y which is 50 and that is our answer.
Express u = (7, -10) as a linear combination u = rv + sw, where v = (2, 1) and w = (1,4).
(Use symbolic notation and fractions where needed.)
To express u = (7, -10) as a linear combination u = rv + sw, where v = (2, 1) and w = (1,4), we need to find the values of r and s such that:
u = rv + sw
Substituting the given values, we get:
(7, -10) = r(2, 1) + s(1,4)
Using the symbolic notation, we can write this as a system of equations:
7 = 2r + s
-10 = r + 4s
We can solve this system of equations by using the elimination method:
Multiply the second equation by 2:
7 = 2r + s
-20 = 2r + 8s
Subtracting the first equation from the second, we get:
-27 = 7s
Dividing both sides by 7, we get:
s = -27/7
Substituting this value of s into the first equation, we get:
7 = 2r - 27/7
Multiplying both sides by 7, we get:
49 = 14r - 27
Adding 27 to both sides, we get:
76 = 14r
Dividing both sides by 14, we get:
r = 38/7
Therefore, u = (7, -10) can be expressed as the linear combination:
u = (38/7)(2,1) + (-27/7)(1,4)
Using fractions where needed, the answer is:
u = (76/7, 38/7) + (-27/7, -108/7)
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Here is the income statement for Teal Mountain Inc.
TEAL MOUNTAIN INC.
Income Statement
For the Year Ended December 31, 2022
Sales revenue
$431,600
Cost of goods sold
234,300
Gross profit
197,300
Expenses (including $16,200 interest and $22,500 income taxes)
75,200
Net income
$ 122,100
Additional information:
1. Common stock outstanding January 1, 2022, was 26,700 shares, and 36,000 shares were outstanding at December 31, 2022.
2. The market price of Teal Mountain stock was $13 in 2022.
3. Cash dividends of $24,200 were paid, $6,600 of which were to preferred stockholders.
Compute the following measures for 2022. (Round all answers to 2 decimal places, e. G. 1. 83 or 2. 51%)
(a) Earnings per share
$enter earnings per share in dollars
(b) Price-earnings ratio
enter price-earnings ratio in times
times
(c) Payout ratio
enter payout ratio in percentages
%
(d) Times interest earned
enter times interest earned
times
Using the given information we can compute several financial ratios that help us evaluate the company's financial performance.
To calculate these ratios, we need to use information from the income statement and the additional information provided.
One important financial ratio is earnings per share (EPS), To compute EPS, we divide net income by the average number of common shares outstanding during the year. To find the average number of shares outstanding, we add the beginning and ending shares and divide by 2.
Net income = $122,100
Average number of common shares outstanding = (26,700 + 36,000) / 2 = 31,350
EPS = $122,100 / 31,350 = $3.89
Another important financial ratio is the price-earnings (P/E) ratio, To compute the P/E ratio, we divide the market price per share by the EPS.
Market price per share = $13
EPS = $3.89
P/E ratio = $13 / $3.89 = 3.34 times
The payout ratio measures the proportion of earnings that is paid out as dividends. To compute the payout ratio, we divide total dividends by net income. However, we need to adjust for the fact that some of the dividends were paid to preferred stockholders. To do this, we subtract the preferred dividends from the total dividends before dividing by net income.
Total dividends = $24,200
Preferred dividends = $6,600
Common dividends = $24,200 - $6,600 = $17,600
Net income = $122,100
Payout ratio = $17,600 / $115,500 = 15.24%
The times interest earned (TIE) ratio, To compute the TIE ratio, we divide earnings before interest and taxes (EBIT) by interest expense.
Interest expense = $16,200
EBIT = Gross profit - Expenses + Interest expense = $197,300 - $75,200 + $16,200 = $138,300
TIE ratio = $138,300 / $16,200 = 8.54 times
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There's a question I've been trying for 2 days to get solved but either I'm missing something or maybe I haven't been using the right method but I hope someone will help me here. ________________________________________
Substitution, Manipulation, Elimination
Solve Simultaneously. Use the method you find easiest. (title of the question)
________________________________________
4x-3y=11
5x-9y=-2
Answer:
(x, y) = (5, 3)
Step-by-step explanation:
You want the solution to the system of equations ...
4x -3y = 115x -9y = -2SolutionIt is convenient to subtract the second equation from 3 times the first:
3(4x -3y) -(5x -9y) = 3(11) -(-2)
12x -9y -5x +9y = 33 +2
7x = 35 . . . . . . . simplify
x = 5 . . . . . . . . . . divide by 7
4(5) -3y = 11 . . . . . substitute into the first equation
9 = 3y . . . . . . . . add 3y-11 to both sides
y = 3 . . . . . . . . divide by 3
The solution is (x, y) = (5, 3).
__
Additional comment
We find using a graphing calculator to be the easiest way to solve a pair of simultaneous equations. The attachment shows the solution is the one we found above.
The approach of "substitution" is straightforward, if error-prone. Basically, you solve one equation for either variable, then use that expression in the other equation. Here, for example, you can solve the first for x:
x = (11 +3y)/4
Then use that in the second equation:
5(11 +3y)/4 -9y = -2
5(11 +3y) -36y = -8 . . . . eliminate the denominator
55 +15y -36y = -8 . . . . . eliminate the parentheses
-21y = -63 . . . . . . . . . . . simplify, subtract 55
y = 3 . . . . . . . . . . . . divide by -21
x = (11 +3(3))/4 = 20/4 = 5 . . . . find x
In the above, we used "elimination." We took advantage of the fact that the y-coefficients were related by a factor of 3. To cancel y-terms, we need to have the equations we "add" have opposite signs for the y-terms. Here, we do that by multiplying the first by 3 (to make -9y), then subtracting the second equation (which has -9y, so will cancel). We could have subtracted 3 times the first from the second, but that would make all the resulting coefficients be negative, which we like to avoid.
Or, we could have multiplied the first equation by -3 to make the y-coefficients opposite, then added the results. (Again, that would give negative coefficients in the sum.) Planning ahead can help avoid mistakes due to minus signs.
Twenty people each choose a number from a choice of, 1,2,3,4 or 5. the mode is larger than the median. the median is larger than the mean
fill in a set of possible frequency
To satisfy the conditions that the mode is larger than the median, and the median is larger than the mean, one possible set of frequencies is 1 person chooses 1, 3 people choose 2, 4 people choose 3, 1 person chooses 4 and 11 people choose 5 This results in a mode of 5, a median of 4, and a mean of approximately 3.75.
Since we are given that the mode is larger than the median, that means that at least 11 people must choose the same number. Let's assume that 11 people choose the number 5.
Now, since the median is larger than the mean, we want to make sure that the remaining 9 people choose numbers that are smaller than 5. If they all choose 1, 2, or 3, then the median will be 3, which is larger than the mean. Therefore, we need to make sure that at least one person chooses 4.
So one possible set of frequencies could be
1 person chooses 1
3 people choose 2
4 people choose 3
1 person chooses 4
11 people choose 5
This set of frequencies gives us a mode of 5 (since 11 people choose 5), a median of 4 (since the middle value is 4), and a mean of
(11 + 32 + 43 + 14 + 11*5) / 20 = 3.7
Since the median is larger than the mean, this set of frequencies satisfies all the given conditions.
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The following dot plots show the amount of time it takes each person, in a random sample, to complete two similar problems. what is the mean time for each problem? make a comparative inference based on the mean values.
the mean time for problem 1 is ___ minutes.
If the mean time for problem 1 is 10 minutes, and the mean time for problem 2 is 15 minutes, The dot plots show the amount of time it takes each person in a random sample to complete two similar problems.
To find the mean time for each problem, we need to add up all the times and divide by the total number of people in the sample. Let's assume that the first dot plot represents problem 1 and the second dot plot represents problem 2.
After calculating the mean times for each problem, we can make a comparative inference based on the mean values. For instance, if the mean time for problem 1 is 10 minutes, and the mean time for problem 2 is 15 minutes, we can infer that problem 2 takes longer to complete on average than problem 1.
Comparative inference refers to the process of comparing two or more sets of data to draw conclusions about their similarities or differences. In this case, we are comparing the mean times for two similar problems to see which one takes longer on average.
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Karoline needs to jog 30.5
miles over the next 7
days to train for a race.
She plans to jog 4.25
miles each day.
Answer: 7x=30.5
Step-by-step explanation: If you were to answer this equation with the given information it would not be correct. 7(4.25)=29.75. You need to go through BEDMAS to answer this.
You what you need to do is divide 30.5 by 7 to get the amount she needs to jog for a week, if you do that you get 4.37 miles each day to get to 30.5 in a week.
Ms. Redmon gave her theater students an assignment to memorize a dramatic monologue to present to the rest of the class. The graph shows the times, rounded to the nearest half minute, of the first 10 monologues presented.
A number line going from 0.5 to 5. 0 dots are above 0.5 0 dots are above 1. 2 dots area above 1.5. 1 dot is above 2. 3 dots are above 2.5. 1 dot is above 3. 2 dots are above 3.5. 1 dot is above 4. 0 dots are above 2.5. 0 dots are above 5.
The next student presents a monologue that is about 0.5 minutes long. What effect will this have on the graph?
The median will decrease.
The mean will decrease.
The median will increase.
The mean will increase.
The effect of the student presenting such a monologue would be B. The mean will decrease.
How to find the effect ?Order the data points:
1. 5, 1. 5, 2, 2. 5, 2. 5, 2. 5, 3, 3. 5, 3. 5, 4
Find the mean ;
= (1. 5 + 1. 5 + 2 + 2. 5 + 2. 5 + 2. 5 + 3 + 3. 5 + 3. 5 + 4) / 10
= 27 / 10
= 2. 7
Then find the new mean after the student presents the monologue:
= ( 0. 5 + 1. 5 + 1. 5 + 2 + 2. 5 + 2. 5 + 2. 5 + 3 + 3. 5 + 3. 5 + 4) / 11
= 2. 5
The mean therefore reduced.
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Answer:
b
Step-by-step explanation:
For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 40 N acts on a certain object, the acceleration
of the object is 10 m/s². If the force is changed to 36 N, what will be the acceleration of the object?
Answer:
The answer to your problem is, F = 15N
Step-by-step explanation:
You have: F = ka
Where F is the force acting on the object, A is the object's acceleration and is the constant of proportionality.
Which will be our letters that we will NEED to use for today.
You can calculate the constant of proportionality by substituting F = 18 and a = 6 into the equation and solving for k: Then we can now figure out the “ formula of expression “
18 = k6
k = [tex]\frac{18}{6}[/tex]
K = 3
We would need to calculate the force when the acceleration of the object becomes 5 m/s², as following: F = 3 x 5 ( Basic math )
= F = 15
Thus the answer to your problem is, F = 15N
Use the slope of a line formula to find the slope of the following points: (3, 9) and (8, 15)
Answer:
m = 6/5
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Points (3, 9) and (8, 15)
We see the y increase by 6 and the x increase by 5, so he slope is
m = 6/5
Answer:
The slope of the points is 6/5.
Step-by-step explanation:
SOLUTION :
Using slope of a line formula to find the slope of the points :
[tex]\quad\dashrightarrow{\sf{m = \dfrac{y_2 - y_1}{x_2 - x_1}}}[/tex]
[tex]\pink\star[/tex] m = slope[tex]\pink\star[/tex] [tex](x_1, y_1)[/tex] coordinates of first point in the line[tex]\pink\star[/tex] [tex](x_2, y_2) [/tex] = coordinates of second point in the lineSubstituting all the given values in the formula to find the slope of the points :
[tex]\quad\dashrightarrow{\sf{m = \dfrac{y_2 - y_1}{x_2 - x_1}}}[/tex]
[tex]\blue\star[/tex] y_2 = 15[tex]\blue\star[/tex] y_1 = 9[tex]\blue\star[/tex] x_2 = 8[tex]\blue\star[/tex] x_1 = 3[tex]\quad\dashrightarrow{\sf{m = \dfrac{15 - 9}{8 -3}}}[/tex]
[tex]\quad\dashrightarrow{\sf{m = \dfrac{6}{5}}}[/tex]
[tex]\quad{\star\underline{\boxed{\sf{\red{m = \dfrac{6}{5}}}}}}[/tex]
Hence, the slope of the points is 6/5.
————————————————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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The Average Rate Of Change In The Interval (0, 2) Of The Function F F(X) = X^2 – 3x Is
To find the average rate of change of a function in a given interval, we need to calculate the difference in the function values at the endpoints of the interval and divide it by the length of the interval.
In this case, the interval is (0,2) and the function is f(x) = x^2 - 3x.
At the left endpoint, x=0, we have f(0) = 0^2 - 3(0) = 0.
At the right endpoint, x=2, we have f(2) = 2^2 - 3(2) = -2.
Therefore, the difference in the function values is f(2) - f(0) = -2 - 0 = -2.
The length of the interval is 2 - 0 = 2.
So the average rate of change of f(x) over the interval (0,2) is:
(-2)/2 = -1
Therefore, the average rate of change of f(x) over the interval (0,2) is -1.
Hi! To find the average rate of change in the interval (0, 2) for the function f(x) = x^2 - 3x, you can use the following formula:
Average Rate of Change = (f(b) - f(a)) / (b - a)
In this case, a = 0 and b = 2. First, calculate the function values at these points:
f(0) = (0)^2 - 3(0) = 0
f(2) = (2)^2 - 3(2) = 4 - 6 = -2
Now, apply the formula:
Average Rate of Change = (f(2) - f(0)) / (2 - 0) = (-2 - 0) / (2) = -2 / 2 = -1
So, the average rate of change in the interval (0, 2) for the function f(x) = x^2 - 3x is -1.
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A telephone line hangs between two poles 14 m apart in the shape of the catenary y = 17 cosh x 17 − 12, where x and y are measured in meters. A telephone line hanging between two poles is on the x y coordinate plane. The left pole is located at x = −7 and the right pole is located at x = 7. The line hangs between the poles crossing the y-axis at y = 5. The acute angle formed by the right pole and the hanging line is labeled theta. (a) Find the slope of this curve where it meets the right-hand pole. (Round your answer to four decimal places. ) (b) Find the angle theta (in degrees) between the line and the pole. (Round your answer to two decimal places. ) theta = °
(a) To find the slope of the curve where it meets the right-hand pole, we need to differentiate the given equation with respect to x. y = 17cosh(x/17) - 12.
Using the chain rule, we get dy/dx = (17/17)sinh(x/17) = sinh(x/17). Therefore, at x = 7, the slope of the curve is sinh(7/17) ≈ 0.6968.
(b) To find the angle theta between the line and the pole, we can use trigonometry. The slope of the curve at the right-hand pole is the same as the tangent of the angle theta.
Therefore, tan(theta) = 0.6968. Taking the inverse tangent of both sides, we get theta = arctan(0.6968) ≈ 34.33 degrees. Therefore, the acute angle formed by the right pole and the hanging line is approximately 34.33 degrees.
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the average time it takes a salesperson to finish a sale on the phone is exponentially distributed with a mean of 18 minutes. find the probability that more than 2 minutes pass before a sale is completed.
The probability that more than 2 minutes pass before a sale is completed is approximately 0.895 or 89.5%.
The CDF of the exponential distribution is given by:
F(x) = 1 - e^(-λx)
where λ is the rate parameter, which is the reciprocal of the mean, λ = 1/18 in this case. The variable x is the time it takes for a sale to be completed.
To find the probability that more than 2 minutes pass before a sale is completed, we need to find the complement of the probability that a sale is completed within the first 2 minutes. That is:
P(X > 2) = 1 - P(X ≤ 2)
Substituting into the CDF formula:
P(X > 2) = 1 - F(2) = 1 - [tex](1 - e^{(-\lambda_2)} = e^{(-\lambda_2)}[/tex]
Plugging in the value of λ:
P(X > 2) = [tex]e^{(-(1/18)\times2)}[/tex] ≈ 0.895
This means that there is a high chance that it will take more than 2 minutes for a sale to be completed on the phone.
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Which angle in AXYZ has the largest measure? 4 Y A. LX B. LY C.
(A) ∠X is the largest angle in the given triangle as the side opposite is also the largest.
What are angles?An angle is formed when two straight lines or rays meet at a single terminal.
The place where two points converge is known as an angle's vertex. The name "angle" comes from the Latin word "angulus," which means "corner."
Two lines that meet at the same point or two planes that meet at the same line form a geometric figure.
The angle in degrees separates these lines or planes.
So, we know that:
The side opposite to the largest angle is also the largest side of the triangle and vica-versa.
Remembering this we can easily conclude that ∠X is the largest angle as the largest is 9 units and X is opposite of the side YZ which measures 9 units.
Therefore, (A) ∠X is the largest angle in the given triangle as the side opposite is also the largest.
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Correct question:
Which angle in AXYZ has the largest measure?
A. ∠X
B. ∠Y
C. ∠Z
D. Cannot be determined
Ben's Barbershop has a rectangular logo for their measuresb 7 1/5 feet long with an area that is exactly the maximum area allowed by thr building owner.
Create an equation that could be used to determine M, the unknown side length of the logo
An equation that could be used to determine M, the unknown side length of the logo is X = (36/5) x M
Let's assume that the unknown side length of the logo is 'M'. The logo is a rectangle, and the area of a rectangle is given by multiplying its length and width. Since we know the length of the logo is 7(1)/(5) feet, we can write the equation:
A = L x W
where A is the area of the logo, L is the length of the logo, and W is the width of the logo.
Substituting the given values, we get:
A = (7(1)/(5)) x M
or
A = (36/5) x M
Now, we know that the area of the logo is exactly the maximum area allowed by the building owner. Let's assume this maximum area is 'X'. So, we can write another equation:
A = X
Combining both equations, we get:
X = (36/5) x M
This is the required equation that could be used to determine the unknown side length 'M' of the logo if we know the maximum area allowed by the building owner 'X'.
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Question 7(Multiple Choice Worth 2 points)
(Creating Graphical Representations MC)
A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.
Sport Basketball Baseball Soccer Tennis
Number of Students 17 12 27 44
Which of the following graphs correctly displays the data?
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
Question 8(Multiple Choice Worth 2 points)
(Circle Graphs MC)
A New York City hotel surveyed its visitors to determine which type of transportation they used to get around the city. The hotel created a table of the data it gathered.
Type of Transportation Number of Visitors
Walk 120
Bicycle 24
Car Service 45
Bus 30
Subway 81
Which of the following circle graphs correctly represents the data in the table?
circle graph titled New York City visitor's transportation, with five sections labeled walk 80 percent, bus 16 percent, car service 30 percent, bicycle 20 percent, and subway 54 percent
circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 40 percent, bus 8 percent, car service 15 percent, bicycle 10 percent, and walk 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 80 percent, bicycle 20 percent, car service 30 percent, bus 16 percent, and walk 54 percent
The correct graph to display the data is: C. Bar graph with the title "favorite sport" and the x-axis labeled "sport" and the y-axis labeled....
Why is a Bar Graph appropriate?A bar graph is an appropriate choice for displaying the data collected from the middle school students because it allows us to compare discrete categories (in this case, sports) and their corresponding frequencies (number of students).
In this case, the data is as follows:
Basketball: 17 studentsBaseball: 12 studentsSoccer: 27 studentsTennis: 44 studentsThe correct bar graph has the title "Favorite Sport" to indicate the subject of the data being represented.
The x-axis is labeled "Sport" and lists the four sports - basketball, baseball, soccer, and tennis - in separate, distinct categories. The y-axis is labeled "Number of Students" and displays the frequency or count of students who chose each sport as their favorite.
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The president of the student council wants to survey the student population about parking. She decides to use a
random number table to take a random sample of 100 of the 1,020 students at the school. What is the smallest number
of digits that should be used to label the population?
The smallest number of digits that should be used to label the population is 4, since there are 1,020 students in the school.
To determine the smallest number of digits needed to label the population, we will follow these steps:
1. Determine the total number of students in the population.
2. Identify the number of digits needed to represent the largest student number.
3. Apply this number of digits to all student labels.
Let's apply these steps to your question:
1. The total number of students is 1,020.
2. The largest student number is 1,020, which requires 4 digits (since it has four numbers: 1, 0, 2, and 0).
3. To label the entire student population consistently, use 4 digits for all student labels.
So, the smallest number of digits that should be used to label the population is 4.
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How do you solve for average daily balance?
Therefore , the solution of the given problem of unitary method comes out to be (Sum of Daily Balances) / Average Daily Balance (Number of Days in Period).
Definition of a unitary method.The well-known minimalist approach, current variables, and any crucial elements from the initial Diocesan tailored query can all be used to accomplish the work. In response, you can be granted another chance to utilise the item. If not, important impacts on our understanding of algorithms will vanish.
Here,
You must be aware of an account's daily balance over a specific time period in order to determine the average daily amount. how to get an average daily balance:
The time frame for which you wish to compute the average daily balance should be chosen. This could, for instance, be a month, a quarter, or a year.
Find the account balance at the end of each day during the specified period.
Sum up each day's balance for the duration.
By the number of days in the time frame, divide the sum. You are then given the daily average balance.
The formula for determining the typical daily balance is as follows:
=> (Sum of Daily Balances) / Average Daily Balance (Number of Days in Period)
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Help please! This is for a grade... (35 points)
Which points lie on the graph of the inverse of f(x)=5x−2?
Select all that apply.
Points lie on the graph of the inverse of f(x)=5x−2.
Hence, the correct option is C,E,F.
To find the points on the graph of the inverse of f(x), we need to switch the x and y coordinates of each point on the graph of f(x). Then, we can simplify the equation to isolate y and get the inverse function.
f(x) = 5x - 2
y = 5x - 2 (replace f(x) with y)
x = 5y - 2 (switch x and y)
x + 2 = 5y (add 2 to both sides)
y = (x + 2)/5 (divide both sides by 5)
So, the inverse function of f(x) is
[tex]f^{-1}[/tex](x) = (x + 2)/5
Now, we can substitute each point from the given options into the inverse function to see if it lies on the graph of the inverse of f(x).
1. (0, -2)
[tex]f^{-1}[/tex](0) = (0 + 2)/5 = 2/5
No, this point does not lie on the graph of the inverse of f(x).
2. (1, 3)
[tex]f^{-1}[/tex](1) = (1 + 2)/5 = 3/5
No, this point does not lie on the graph of the inverse of f(x).
3. (-2, 0)
[tex]f^{-1}[/tex](-2) = (-2 + 2)/5 = 0
Yes, this point lies on the graph of the inverse of f(x).
4. (2/5, 1)
[tex]f^{-1}[/tex](2/5) = (2/5 + 2)/5 = 6/25
No, this point does not lie on the graph of the inverse of f(x).
5. (0, 2/5)
[tex]f^{-1}[/tex](0) = (0 + 2)/5 = 2/5
Yes, this point lies on the graph of the inverse of f(x).
6. (3, 1)
[tex]f^{-1}[/tex](3) = (3 + 2)/5 = 1
Yes, this point lies on the graph of the inverse of f(x).
Therefore, the points that lie on the graph of the inverse of f(x) are (-2, 0), (0, 2/5) and (3, 1),
Hence, the correct option is C,E,F.
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Given the following side lengths of a triangle 2,10,11 what type of triangle is formed
The type of triangle formed from the side lengths of a triangle 2, 10, 11 is a scalene triangle.
Based on the given side lengths of a triangle (2, 10, 11), we can determine the type of triangle formed by examining their relationships. First, let's check if these side lengths can form a valid triangle using the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides must be greater than the length of the remaining side. In this case, 2 + 10 > 11, 2 + 11 > 10, and 10 + 11 > 2, so a triangle can be formed.
Now let's identify the type of triangle. There are three main categories to consider: equilateral, isosceles, and scalene. An equilateral triangle has all three sides equal in length, which doesn't apply here. An isosceles triangle has two sides with equal lengths, but in this case, all three sides have distinct lengths. Therefore, the triangle is a scalene triangle, meaning it has no sides of equal length.
In summary, the triangle formed by side lengths 2, 10, and 11 is a scalene triangle because all three sides have different lengths and satisfy the Triangle Inequality Theorem.
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March 1, 2020, Dorchester Company's beginning work in process inventory had 6,000 units. This is its only production department. Beginning WIP units were 50% complete as to conversion costs. Dorchester introduces direct materials at the beginning of the production process. During March, all beginning WIP was completed and an additional 24,500 units were started and completed. Dorchester also started but did not complete 6,500 units. These units remained in ending WIP inventory and were 50% complete as to conversion costs. Dorchester uses the weighted-average method. Use this information to determine for March 2020 the equivalent units of production for conversion costs. Round to whole number (no cents)
For March 2020, the equivalent units of production for conversion costs are 30,750, rounded to the nearest whole number.
To determine the equivalent units of production for conversion costs in March 2020 for Dorchester Company, we need to follow these steps:
Calculate the equivalent units for the beginning work in process inventory:
Beginning WIP units = 6,000
Completion percentage for conversion costs = 50%
Equivalent units for beginning WIP = 6,000 * 50% = 3,000
Calculate the equivalent units for the units started and completed during March:
Units started and completed = 24,500
Completion percentage for conversion costs = 100%
Equivalent units for started and completed units = 24,500 * 100% = 24,500
Calculate the equivalent units for the ending work in process inventory: Ending WIP units = 6,500
Completion percentage for conversion costs = 50%
Equivalent units for ending WIP = 6,500 * 50% = 3,250
Sum up the equivalent units from steps 1, 2, and 3:
Total equivalent units for conversion costs = 3,000 (beginning WIP) + 24,500 (started and completed units) + 3,250 (ending WIP) = 30,750
So, for March 2020, the equivalent units of production for conversion costs are 30,750, rounded to the nearest whole number.
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Circle W has a center at (15,–2) and has a radius of 4. Circle W' has a center of (–5,–5) with a radius of 4. What is the transformation of circle W to circle W'?
The correct answer is "Translated to the left 10 and down 3 and then reflected about the y-axis."
Understanding Transformation of CircleTransformation is a process that changes the position, orientation, size, or shape of a geometric object. Transformations are often described using matrices, vectors, or other mathematical operations.
Types of Transformations
Translation - moving object on a straight lineRotation - turning an object around a fixed point by a certain angleScaling - changing the size of an object by a fixed factor.Reflection - flipping an object over a fixed lineFrom the problem statement, to move the center from (15,-2) to (-5,-5), we need to translate the circle to the left by 10 units and down by 3 units. So the first transformation is a translation to the left 10 units and down 3 units.
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As President of Spirit Club, Rachel organized a "Day of Decades" fundraiser where students could pay a fixed amount to dress up as their favorite decade. Of the 19 students who participated, 15 of them dressed up as the '40s.
If Rachel randomly chose 16 of the participants to take pictures of for the yearbook, what is the probability that exactly 13 of the chosen students dressed up as the '40s?
Write your answer as a decimal rounded to four decimal places.
The probability of choosing exactly 13 students who dressed up as the 40s out of the 16 selected students is approx. 0.4334.
What is the probability of choosing exactly 13 students who dressed up as the 40s?We can model this situation as a hypergeometric distribution, where we have a population of 19 students, 15 of whom dressed up as the 40s.
We want to choose a sample of 16 students and find the probability that exactly 13 of them dressed up as the '40s.
The probability of choosing exactly 13 students who dressed up as the 40s can be calculated:
(number of ways to choose 13 students who dressed up as the 40s) * (number of ways to choose 3 students who dressed up as other decades) / (total number of ways to choose 16 students)
The number of ways to choose 13 students who dressed up as the '40s is the number of combinations of 15 choose 13:
(15 choose 13) = 105
The number of ways to choose 3 students who dressed up as other decades is the number of combinations of 4 choose 3, which is:
(4 choose 3) = 4
The total number of ways to choose 16 students from 19 is the number of combinations of 19 choose 16, which is:
(19 choose 16) = 969
105 * 4 / 969 = 0.4334
Therefore, the probability of choosing exactly 13 students who dressed up as the 40s = 0.4334 (rounded to four decimal places)
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Same increased the amount of protein she eats every day 45g to 58. 5g. By what percentage did Sam increase the amount of protein she eats
Sam increase the amount of protein she eats by a percentage of 30%.
To find the percentage increase, we can use the formula: (change in amount / original amount) x 100%.
Percentage is a way to express a number as a fraction of 100. It is a convenient method for comparing ratios or proportions because it standardizes them to a common denominator of 100. In this case, we want to find the percentage increase in Sam's daily protein consumption.
First, we need to determine the change in amount. This can be found by subtracting the original amount from the new amount: 58.5g - 45g = 13.5g.
Next, we'll divide the change in amount by the original amount: 13.5g / 45g = 0.3. To express this as a percentage, we'll multiply by 100: 0.3 x 100% = 30%.
Therefore, Sam increased her daily protein intake by 30%. This percentage helps us understand the relative change in her protein consumption compared to her initial intake.
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A certain product is marked down to $82. 81 after a 15. 5% decrease. Determine the original price. (4 points)
$69. 90
$92. 50
$98. 00
$128. 35
The original price of the product was approximately $98.00.
How to determine the original price of a product after a given markdown?To determine the original price before the 15.5% decrease, we can use the following equation:
Original price - (15.5% of original price) = $82.81
Let's solve for the original price:
Original price - (0.155 * Original price) = $82.81
Simplifying the equation:
0.845 * Original price = $82.81
Dividing both sides by 0.845:
Original price = $82.81 / 0.845
Calculating the original price:
Original price ≈ $98.00
Therefore, the original price of the product was approximately $98.00.
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Using the probability distribution represented by the graph
below, find the probability that the random variable, X, falls
in the shaded region.
Using probability, we can find probability of the random variable, x falling in the shaded region as to be 5/8.
Define probability?Probability is the ratio of favourable outcomes to all other potential outcomes of an event. The symbol x can be used to express the quantity of successful outcomes for an experiment with 'n' outcomes. The following formula can be used to determine an event's probability.
Positive Outcomes/Total Results = x/n = Probability(Event)
Let's look at a simple example to better understand probability. Imagine that we need to predict whether it will rain or not. The right response to this question is "Yes" or "No." Whether it rains or not is uncertain. Probability is used to predict the outcomes when tossing coins, rolling dice, or drawing cards from a deck of cards.
Here in the question,
Total region = 8.
Shaded region = 5
So, probability of falling in the shaded region = 5/8
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