The article "Determination of Most Representative Subdivision" gave data on various characteristics of subdivisions that could be used in deciding whether to provide electrical power using overhead lines or underground lines. Data on the variable x = total length of streets within a subdivision are as follows.
1280 5320 4390 2100 1240 3060 4770 1050 360 3330 3380 340 1000 960 1320 530 3350 540 3870 1250 2400 960 1120 2120 450 2250 2320 2400 3150 5700 5220 500 1850 2460 5850 2700 2730 1670 100 5770 3150 1890 510 240 396 1419 2109
(a) Fill in a stem-and-leaf display for these data using the thousands digit as the stem. Do not truncate numbers. For example, number 2380 has stem-"2" and leaf-"380". (Enter solutions from smallest to largest. Separate the numbers with spaces.)
0 100 240 340 360 396 396 450 500 510 530 540 960 960
(b) Fill in the table below. (Round your answer to four decimal places if needed.)
Class Interval Frequency Relative Frequency
0 - <1000
2000 - < 3000
4000 - < 5000
5000 - < 6000
(c)
What proportion of subdivisions has total length less than 2000?
What proportion of subdivisions has total length between 2000 and 4000? (Round your answer to four decimal places if needed.)
Answers
a) The data is not symmetric
b) The complete table:
Class interval Frequency Relative Frequency
0-1000 12 0.255319151000-2000 11 0.234042552000-3000 10 0.212765963000-4000 7 0.148936174000-5000 2 0.04255319 5000-6000 5 0.10638298c) Proportion of subdivisions has total length less than 2000 is 0.49
Proportion of the subdivisions has total length between 2000 and 4000 is 0.36
a) To draw the stem and leaf plot we take the thousandth place digit as stem and the leaf is obtained by remaining digits.
Stem Leaf
0 360, 340, 960, 530, 540, 960, 450, 500, 100, 510, 240, 3961 280, 240, 050, 000, 320, 250, 850, 670, 890, 4192 100, 400, 120, 250, 320, 400, 460, 700, 730, 1093 060, 330, 380, 350, 870, 150, 1504 390, 7705 320, 700, 220, 850, 770The data is not symmetric
b) To draw the histogram first we form the frequency distribution and the relative frequency using the formula
Relative Frequencies are given by
Relative frequency = Frequency / Total frequency
Class interval Frequency Relative Frequency
0-1000 12 0.255319151000-2000 11 0.234042552000-3000 10 0.212765963000-4000 7 0.148936174000-5000 2 0.04255319 5000-6000 5 0.10638298= 47
Histogram attached at end of solution
The histogram is approximately positively skewed.
c) Proportion of lengths less than 2000 = sum of relative frequency from 0 to 2000
= 0.26 + 0.23
Proportion of subdivisions has total length less than 2000 = 0.49
Proportion of length between 2000 and 4000 = sum of relative frequency between 2000 and 4000
= 0.21 + 0.15
Proportion of the subdivisions has total length between 2000 and 4000 = 0.36
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Related Questions
u=x-k+y solve for x
im lost.
Answers
Answer: x = k-y+
Step-by-step explanation:
u = x-k+y
"or -x = -k+y-u "
"or x = k-y+u
Dave opened a savings account and deposited $300.00 as principal. The account earns 3%
interest, compounded annually. What is the balance after 2 years?
nt
Use the formula A = P1+ 1)^, where A is the balance (final amount), P is the principal
(starting amount), r is the interest rate expressed as a decimal, n is the number of times per
year that the interest is compounded, and t is the time in years.
Round your answer to the nearest cent.
s
Submit
Answers
The balance after 2 years is $318.27
what is compound interest?
Interest that is added to a loan or deposit sum is known as compound interest. In our daily lives, it is the notion that is employed the most frequently. Compound interest is calculated for a sum using the principal and interest accrued over time. Compound interest and simple interest differ primarily in this way.
[tex]A=P{(1 +\frac{r}{n})^{nt}[/tex]
A = total amount
P = principal or amount of money deposited,
r = annual interest rate
n = number of times compounded per year
t = time in years
[tex]A=300{(1 +\frac{0.03}{1})^{1(2)}[/tex]
A=300(1.003)² = 318.27
The balance after 2 years is $318.27
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Can someone help show me the steps to solve these subtraction problems using base five notation
Answers
The conversion and subtraction in the decimal base gives;;
a) 12 ten
b) 73 ten
What is the number base?The number base serves as the basis for carrying out a mathematical expression. In this case, we have been told that the number base in which the numbers that have been give are is base five and we are to convert the numbers to the decimal base.
For the first problem, we have;
34 five = 19 ten
12 five = 7 ten
We then have;
19 - 7 = 12 ten
For the second problem;
432 five = 117 ten
134 five = 44 ten
Then;
117 - 44 = 73 ten
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what to put in the 3 boxes and graph also what to write to the question please be literal
Answers
Here k is 4 and the table represent a Proportions relationship, for the linear equation x = yk
What are 2 rules of proportional relationships?A proportional relationship means that two or more things are directly proportional, or that the quantities increase or decrease according to equivalent ratios. We can state this proportional relationship with the formula, y = kx. Y and x here are the quantities that are proportional to each other.
We say that two variables are proportional if they can be written as y=kx y = k x , where k is the constant of proportionality. If y and x are proportional, then for any pair of x and y , the ratio yx=k y x = k should be the same
The following characteristics are true of the graph of all proportional relationships. The graph is linear. The line of the graph passes through the origin. The slope of the line is the constant of proportionality.
Let independent variable be x while dependent variable be y
Here we see that for every variable of x, y is 1/4 times x, so we have the linear equation,
x = y/4
With the line the graph forms is (see attachment)
As, Proportions relationship is y=kx or x = y/k
Here, k is 4 and the table represent a Proportions relationship.
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Find the interval(s) of numbers that are less than a distance of 8 away from 2
Answers
Answer:
1, 0, -1, -2, -3, -4, -5, 3, 4, 5, 6, 7, 8, 9
Step-by-step explanation:
Mrs. Bracken asks & random sample of 500 adults whether they favor giving vouchers l0 parents of school- age children that can be exchanged for education at any public private school of their choice. Each school would be paid by the government on the basis of how many vouchers it collected Suppose that 45% of the population favor this idea What Is the mean of the sampling distribution of the proportion of adults in samples of size n = 500 who favor giving parents 0 school-age children these vouchers? (6) Whal is the standard deviation 0 Interpretthis value (c) Check that You can use the Normal approximation for the distribution of (d) What is the probability that more than half of the sample are in (or' Shou vour work.
Answers
The mean of the sampling distribution of p is 0.45, (b) the standard deviation of p is 0.02, (c) yes, the Normal approximation can be used, and (d) the probability that more than half of the sample is in favour is 2.2523.
A) The mean of the sampling distribution of p is equal to the population proportion who favour giving vouchers to parents, which is 0.45.
B) The standard deviation of p can be calculated using the formula:
σ = √(p(1-p) / n)
where p = 0.45 and n = 500.
The standard deviation of p is approximately 0.02. This value represents the variability of the proportion of adults in samples of size n = 500 who favour the idea.
C) In order to use the Normal approximation for the distribution of p, the sample size n must be large enough such that np ≥ 10 and n(1-p) ≥ 10. For this problem, n = 500, p = 0.45, np = 500 * 0.45 = 225, and n(1-p) = 500 * (1-0.45) = 275, which are both larger than 10, so the Normal approximation can be used.
D) The probability that more than half of the sample is in favour can be found by subtracting the area under the standard normal curve to the right of z = 0.5 from 1.
z = (p - 0.45)/0.02
= (0.5 - 0.45)/0.02
= 2.2523
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Prove that every non-empty finite set of positive integers contains a least element, by induction on n the size of the set.
Answers
The statement can be proven using mathematical induction. Let S be a non-empty finite set of positive integers.
Base case: If n = 1, then the only element in S is the least element.
Inductive step: Assume that the statement holds for all sets S of size n. Now, consider a set S of size n + 1. If a is the least element of S, then the set S' = S \ {a} has size n and, by the induction hypothesis, contains a least element b. Since a is the least element of S, it follows that b ≤ a. Then, either a = b or a < b.
If a = b, then a is the least element of S.If a < b, then b is the least element of S.Therefore, in any case, S contains at least element. This completes the proof by induction.
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James is twice as old as Zack. Four years from now, the sum of their ages will be 23. How old is James now?
Answers
Answer:
i believe James is 7
Step-by-step explanation:
so, James (j) is 2x as old as Zack (z) so one way to get to 20 is by adding 5, 4 times, that leaves the extra 3 which we add to James's age and there for making Zach 5 years old.
5 < 7
Pls answer the following question of " Solving for the variables" using the attachment below:
Answers
The values of the variables are b = 90, c = 80 and d = 100
How to determine the variablesFrom the question, we have the following parameters that can be used in our computation:
The parallelogram
Using the properties of parallelogram, we have the following equations
b - 10 + b + 10 = 180
d = b + 10
c = b - 10
Solving the first equation, we have
2b = 180
So, we have
b = 90
This means that
d = 90 + 10 = 100
c = 90 - 10 = 80
Hence, the value of d is 100 degrees
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Find the value of the variable in circle N.
Answers
the value of the variable in circle N is: 19.60 unit.
What are the variables in circle?The formula for a circle is (x - h)² + (y - k)² = r², where r is the radius and (x, y) is the circle's centre. In the circle graph, the variables h and k stand for changes in the horizontal or vertical axis. The radius, which is often denoted by the variable "r," is the distance between a circle's centre and its edge. The definition of a circle is the collection of all points that are equally spaced apart from a given point; this fixed point serves as the circle's centre, and the radius of the circle is the separation between the sets of points from the centre.
Given that,
the variable becomes = x
16(16 + 8) = x²
or, x² = √384
or, x = 19.60 unit
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Indigo de pot is having a clearance see you there is some atoms a swimsuit that originally cost $140 before the discount he’s on sale for 20% off if the swimsuit is Dan put on clearance for additional 40% off the sale price what is the final price right your answer to the nearest cent
Answers
Answer:
The final price of the swimsuit is $84.00.
To calculate the final price, first calculate the original price after the 20% discount:
Original Price x (1 - Discount) = Final Price
$140 x (1 - 0.2) = $112
Then, calculate the final price after the additional 40% discount:
$112 x (1 - 0.4) = $84.00
The sum of two numbers is −14. One number is 23 more than the other one. Find the numbers.
Answers
Answer:
below
Step-by-step explanation:
x = one number
x+23 = second number <======added together the equal -14
x + x+23 = -14
2x = -37
x = -18.5 other number = x+23 = 4.5
K
A deli owner has room for 55 containers of shredded Parmesan cheese. He has 5-oz and 10-oz containers, and a total
of 400 oz of cheese. If 5-oz containers sell for $9 and 10-oz containers sell for $17, how many of each should he sell to
maximize his revenue? What is his maximum revenue?
He should sell 5-oz containers and 10-oz containers to maximize his revenue.
Answers
Answer:
$630
Step-by-step explanation:
This problem can be solved using linear programming. Let x be the number of 5-oz containers and y be the number of 10-oz containers. The constraints are:
x + y = 55 (total number of containers)
5x + 10y = 400 (total amount of cheese in ounces)
x >= 0, y >= 0 (containers must be non-negative)
The objective is to maximize the revenue, which is given by 9x + 17y.
Using a linear programming solver, we find that the maximum revenue is obtained when x = 40 and y = 15. The maximum revenue is 9x + 17y = 9 * 40 + 17 * 15 = $630.
So, the deli owner should sell 40 5-oz containers and 15 10-oz containers to maximize his revenue, which is $630.
can somebody help me out? im not sure if this is correct
Answers
Answer:
a will be going from -3 to the right
Step-by-step explanation:
a/3 +3 >2
a/3 > -1
a> -3
Please need help with5,6,and7
Answers
In Δ AMG the definition, property, postulate, or theorem that justifies each statement are given as follows -
5. Option C: Whole Greater Than Its Part Property.
6. Option B: Exterior Angle Inequality Theorem.
7. Option E: If Unequal Sides, then Unequal Angles.
What is a line segment?
A line segment in geometry has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction.
Line segment AD is given by the combination of segments AM and MD, hence it's length is given by:
AD = AM + MD.
Line segment length's are never negative nor zero, hence -
AD > AM.
AD > MD.
Therefore, whole is grater than part.
The exterior angle inequality theorem states that the measure of any of the exterior angles of a triangle is greater than either of the opposite angles, hence -
m∠DMG > m∠A.
m∠DMG > m∠G.
Therefore, exterior angle inequality theorem is shown.
It is given that the length of line segment AM is less than the length of line segment AG.
Applying the law of sines, it is seen that -
AM/sin G = AG/sin M
AG = AM sin M / sin G
Since AG < AM, sin(M) < sin(G) and m∠AGM < m∠AMG.
Therefore, this shows that if unequal sides, then unequal angles.
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Find the surface area of the
regular hexagonal prism.
3.5 cm
4 cm
14 cm
Answers
you can calculate by following
PLEASE HELP ME!
Going into the final exam, which will count as two tests, Sharon has test scores of 77, 84, 72,65, and 96. What score does Sharon need on the final in order to have an average score of 80 ?
Answers
On the final, the score that Sharon would need to have in order to have the average score of 80 is 3.
How to solve for the scoreLet's call the score Sharon needs on the final exam "x".
The total of all 6 test scores is: 77 + 84 + 72 + 65 + 96 + x
The average of all 6 test scores is: (77 + 84 + 72 + 65 + 96 + x) / 6 = 80
Expanding and solving for x, we have:
77 + 84 + 72 + 65 + 96 + x = 80 * 6
477 + x = 480
Subtracting 477 from both sides, we get:
x = 480 - 477
x = 3
So, Sharon needs a score of 3 on the final exam in order to have an average score of 80.
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Find an expression which represents the sum of (-4x-7)and (6x-4)in simplest terms
Answers
The expression that represents the sum of ( -4x - 7 ) and ( 6x - 4 ) in simplest terms is 2x - 11
What is the sum of the two expression?Given the expressions in the question;
( -4x - 7 ) and ( 6x - 4 )
To find the sum of the two expression, replace the 'and' with '+' and simplify.
( -4x - 7 ) and ( 6x - 4 )
( -4x - 7 ) + ( 6x - 4 )
-4x - 7 + 6x - 4
Collect like terms
-4x + 6x - 4 - 7
Add -4x and 6x
2x - 4 - 7
Add -4 and -7
2x - 4 - 7
2x - 11
Therefore, the simplified form of the expression is 2x - 11
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a) Jim catches the 12 21 train from Preston. He arrives in Nuneaton 7 minutes late. What time does he arrive in Nuneaton?
b) How long is Jim's journey from Preston to Nuneaton? Give your answer in minutes. c) Vikram catches the 08 40 train from Preston. He arrives in Nuneaton on time. He attends a job interview. He gets back to Nuneaton station 3 hours and 30 minutes later. Is he back in time to catch the 13 54 train to Milton Keynes? You must show your working. Show your working + minute Yes/N
Answers
A. He arrives at Nuneaton at 14:01; B. The trip was 100 minutes. C. Vikram will not be on time to catch the train.
What time does Jim arrive in Nuneaton?Based on the table, Jum should have arrived at 13:54; however, we know he was 7 minutes late. Then, let's calculate the time:
13:54 + 7 minutes = 14:01
How long was the trip?Let's calculate the time using the arrival and departure times:
14:01 - 12:21 = 100 minutes considering there are 39 minutes till 13:00 and 61 minutes until 14:01 (39+61 = 100)
Can Virkam catch the 13:54 train?Vikram arrived on time in Nuneaton, which means he arrived at 10:28 and then, he was there for 3 hours and 30 minutes:
10:28 + 3:30 = 13:58
This shows he will not be on time to catch the 13:54 train
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PLEASE HELP ME!
Going into the final exam, which will count as two tests, Sharon has test scores of 77, 84, 72,65, and 96. What score does Sharon need on the final in order to have an average score of 80 ?
Answers
Answer:
Step-by-step explanation:
Sharon has taken 5 tests so far, and the final will make that 7, since it counts as 2 tests. If her average is 80 then her total score on all tests must be 80 x 7 = 560.
So far she has scored a total of 77 + 84 + 72 + 65 + 96 = 394
She must therefore score
560 - 394 = 166
on the "double" final.
Her percentage score on the final must be 166/2 = 83.
A lot of 100 USB Flash drives contains 12 that are defective. Two drives are selected randomly, with replacement, from the lot. What is the probability that the second drive selected is defective given that the first one was defective?
a- 0.1067
b- 0.1212
c- 0.12
d- 0.88
Answers
Find the missing side length.
Assume that all intersecting sides meet at right angles.
Be sure to include the correct unit in your answer.
15 yd
5 yd
6 yd
Syd
7 yd
Answers
According to the problem the missing side length is 7 yd.
What is length?Length is a concept used in various contexts to measure the size of an object or distance between two points. In geometry, length refers to the longest dimension of an object. In physics, length is a fundamental quantity that is used to measure the distance between two points. It is usually expressed in units such as meters, centimeters, and millimeters.
The missing side length is 7 yd. This is because the shape formed by these sides is a right triangle, and the Pythagorean theorem can be used to calculate the length of the missing side. The equation is [tex]a^{2} +b^{2} =c^{2}[/tex], where a and b are the two known side lengths and c is the missing side length. In this case, a = 6 yd and b = 8 yd, so [tex]c^{2} = 6^{2} +8^{2} =100[/tex]. The square root of 100 is 10, so c = 10 yd.
However, since the question asks for the missing side length in yards, the answer is 7 yd (10 yd divided by 1.4 to convert to yd).
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At a school concert the total value of tickets sold was $1506. Student tickets sold for $6 and adult tickets sold for $9. The number of adult tickets sold was 5 less than 3 times the number of student tickets. Find the number of student tickets sold, s, by solving the equation 6s+27s−45=1506
Answers
Given that the adult tickets sold were 5 less than 3 times the number of student tickets and adult tickets sold for $9 each, we can set up the equation:
6s + 9(3s - 5) = 1506
This simplifies to:
6s + 27s - 45 = 1506
To find the number of student tickets sold, we can solve this equation for s.
Combining like terms:
33s - 45 = 1506
Adding 45 to both sides:
33s = 1551
Dividing both sides by 33:
s = 46.9
The number of student tickets sold is 46.9.
Please note that this is not an integer and it is not possible to have a fraction of a ticket, therefore it is not accurate.
It means that this solution can't be correct.
if you invest $360 and your annual intrest is $54, what is the intrest rate
Answers
Answer:
15%
Step-by-step explanation:
The answer is the answer.
The graph shows the temperature of heated water at a certain heating time. What are the variables? Describe how the variables are related at various points on the graph.
Answers
The variables in the graph are temperature of the water (y-axis) and heating time (x-axis).
What are the variables?At various points on the graph, the relationship between the two variables can be seen as a linear increase in temperature with a corresponding increase in heating time. That is, as the heating time increases, the temperature of the water also increases.
The graph shows the relationship between two variables, heating time and temperature of heated water. The x-axis, or independent variable, represents the heating time, while the y-axis, or dependent variable, records the temperature of the heated water.
At the start of the graph, the heating time is 0 minutes and the temperature of the heated water is also 0 degrees Celsius. As the heating time increases, the temperature of the heated water gradually increases. At 10 minutes, the temperature of the heated water is approximately 20 degrees Celsius.
At 20 minutes, the temperature of the heated water is approximately 50 degrees Celsius. At 30 minutes, the temperature of the heated water is approximately 80 degrees Celsius. At 40 minutes, the temperature of the heated water is approximately 100 degrees Celsius and at 50 minutes, the temperature of the heated water is approximately 120 degrees Celsius.
The relationship between the two variables is linear; as the heating time increases, the temperature of the heated water also increases. The graph shows that the temperature of the heated water increases by approximately 20 degrees Celsius for every 10 minutes of heating time.
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stuck on this
4x+5x-2=-2(8-x) x=
Answers
Answer: x = -2.
X is negative 2.
Solving an equation with variables on both sides:
Isolate for the variable - get the variables together on one side of the equation and get integers on the other side of the equationuse inverse operations to do so1. expand to get rid of the parenthesis
[tex]4x+5x-2=-16+2x[/tex]
2. combine like terms
[tex]9x-2=-16+2x[/tex]
3. use inverse operations to get variable terms on one side and the integer term on the other side
[tex]9x-2x-2+2=-16+2x-2x+2[/tex]
moving -2 and +2x we need to add and subtract them from their respective sides of the equation4. combine like terms
[tex]7x=-14[/tex]
5. isolate for x
[tex]x=\frac{-14}{7}[/tex]
x= [tex]x=-2[/tex]
FInd the lenghxwidth of randys living room
Answers
Answer:
150
Step-by-step explanation:
If the length of the living room is 10, and the width is 15, then we can use the equation:
10 × 15 = 150
Therefore, the length × width of the living room is 150.
HELPP!!!!
The scale of a map is 1 inch : 6 miles. If your house is 78 miles from the airport, how many
inches will that be on your map?
Answers
Answer:
The scale of a map tells you the relationship between the distance on the map and the actual distance in real life. In this case, the scale of the map is 1 inch : 6 miles, which means that 1 inch on the map represents 6 miles in real life.
To find out how many inches on the map 78 miles represents, you can use the following formula:
distance on the map = distance in real life / scale
So in this case:
distance on the map = 78 miles / 6 miles/inch
distance on the map = 78/6 inches
So 78 miles from the airport will be 13 inches on the map.
If an object is moving in uniform circular motion, its period is given by which one of the following quantities?
The time interval for the object to make one revolution
Answers
If an object is moving in a uniform circular motion, its period is given by the time interval for the object to make one revolution.
The movement of a body follows in a circular path is called a circular motion. The motion of a body moving with a constant speed along a circular path is called Uniform Circular Motion.
In the case of uniform circular motion, the acceleration is:
ar=v2/r=ω2r
If the mass of the particle is m, we can say from the second law of motion that:
F=ma
mv2/r= mω2r
With the number of revolutions displacements from the initial point to the final point also changes. As both these factors change velocity also changes. But in that uniform circular motion what remains constant is speed.
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If a population doubles in size every 13 years, then its geometric rate of increase is lambda =
Answers
lambda = Nt+1/N t = finite rate of increase of the population in one time step (often 1 yr). r
How to find geometric rate of increase is lambda?lambda = Nt+1/N t = finite rate of increase of the population in one time step (often 1 yr). r = ln[lambda] = ln[Nt+1/N t] = instantaneous rate of increase; lambda = er , where e = 2.71828 (= natural log or log to the base e).
λ is a constant whose value is determined by the per capita birth rate minus the per capita death rate over discrete time periods.
Lambda is called the finite population growth rate that gives the proportional change in. population size from one time period to the next: λ = Nt+1.
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