To show that there are arbitrarily long strings of consecutive integers each divisible by a perfect square greater than 1,
Solution:
follow these steps:
1. Choose an arbitrary positive integer, n.
2. Define a string of consecutive integers, starting with the product of the first n+1 positive perfect squares:
S = (2^2 * 3^2 * ... * (n+1)^2).
3. The next n consecutive integers will be S+1, S+2, ..., S+n.
4. Each of these consecutive integers, S+i (where 1 <= i <= n), is divisible by a perfect square greater than 1.
Here's why:
- S is divisible by all perfect squares from 2^2 to (n+1)^2, which are greater than 1.
- S+1 is divisible by 2^2, as S = (2^2 * 3^2 * ... * (n+1)^2) is an even number and (S+1) - 1 = 2^2 * K (where K is some integer).
- S+2 is divisible by 3^2, as S = (2^2 * 3^2 * ... * (n+1)^2) is divisible by 3^2 and (S+2) - 2 = 3^2 * K (where K is some integer).
- Continuing this pattern, S+i is divisible by (i+1)^2, for all 1 <= i <= n.
Thus, we have demonstrated that there are arbitrarily long strings of consecutive integers each divisible by a perfect square greater than 1.
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iii) iv) 1 km 200 m - 500 m = 876 m + 1 km 500 m = v) 2 km 50 m - 950 m =I want answers my questions
The solution to the conversion of units are:
iii) 1 km 200 m - 500 m = 700 m
iv) 876 m + 1 km 500 m = 2km 376 m
v) 2 km 50 m - 950 m = 1 km 100 m
How to carry out conversion of units?iii) We want to solve:
1 km 200 m - 500 m
From conversion factors, we know that:
1 km = 1000 m
Thus:
1 km 200 m = 1000m + 200 m = 1200 m
Thus:
1 km 200 m - 500 m = 1200 m - 500 m
= 700 m
iv) We want to solve:
876 m + 1 km 500 m
From conversion factors, we know that:
1 km = 1000 m
Thus:
876m = 0.876 km
1 km 500 m = 1.5 km
Thus:
876 m + 1 km 500 m = 0.876 km + 1.5 km
= 2.376 km or 2km 376 m
v) We want to solve:
2 km 50 m - 950 m
From conversion factors, we know that:
1 km = 1000 m
Thus:
2 km 50 m = 2.05 km
950m = 0.95 km
Thus:
2 km 50 m - 950 m = 2.05 km - 0.95 km
= 1.1 km or 1 km 100 m
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The solution to the equation -2(x + 11) = -8 is x = _
From the given information provided, the value of x for given solution of equation is -7.
An equation is a statement that shows the equality of two expressions. A solution of an equation is a value or values of the variable(s) that make the equation true.
Let's solve the equation step by step:
-2(x + 11) = -8
First, we can distribute the -2 to the term inside the parentheses:
-2x - 22 = -8
Next, we can add 22 to both sides of the equation to isolate the variable term:
-2x = 14
We can divide both sides of equation by -2 to solve for x:
x = -7
The solution to the equation -2(x + 11) = -8 is x = -7.
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help will be much appreciated
The average speed of the total journey is 75 kilometres per hour.
How to find average speed?Anil completes the 72 kilometres journey between Bristol and Cardiff for 48 minutes. He then drive 69 kilometres from Cardiff to Swansea at an average speed of 60 kilometres per hour.
Therefore, let's find Anil average speed for the total of his journey as follows:
speed of his first journey = distance / time
speed of his first journey = 72 / 48
speed of his first journey = 1.5 km/minutes = 90 km/hrs
Therefore,
average speed of the total journey = 90 + 60 / 2
average speed of the total journey = 150 / 2
average speed of the total journey = 75 kilometres per hour
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Hi! im new to this i i coudnt go to school today becuase im sick and im trying to do mah and i cant figure this out anyone can help,
surface area of the prism.
5yd 4yd 2yd
The surface area is
[tex]2(5\times4)+2(5\times2)+2(4\times2)=[/tex]
[tex]40+20+16=[/tex]
76 square yards
Answer:
The surface area of the prism.
5 yd, 4 yd, 2 yd
76 square yardsStep-by-step explanation:
You're welcome.
a sock drawer contains 18 black socks and 12 red socks. if you randomly choose two socks at once, what is the probability you get a matching pair?
There are 12 red socks and 18 black socks in a sock drawer. If you randomly choose two socks at once, the probability you get a matching pair is 50%.
The probability of getting a matching pair of socks can be calculated as follows:
First, we can calculate the total number of ways to choose 2 socks out of 30:
C(30, 2) = 30! / (2! * (30-2)!) = 435
Now, we need to calculate the number of ways to choose 2 socks such that they are both black or both red:
Number of ways to choose 2 black socks: C(18, 2) = 153
Number of ways to choose 2 red socks: C(12, 2) = 66
Therefore, the total number of ways to choose a matching pair of socks is 153 + 66 = 219.
Finally, we can calculate the probability of getting a matching pair of socks by dividing the number of ways to choose a matching pair by the total number of ways to choose 2 socks:
P(matching pair) = 219 / 435 ≈ 0.5034
Therefore, the probability of getting a matching pair of socks is approximately 0.5034 or 50.34%.
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what is the probability of rolling a sum less than or equal to 7 ? express your answer as a fraction or a decimal number rounded to four decimal places.
The probability of rolling a sum of 7 or less on two dice is 11/36. This can be expressed as a decimal number rounded to four decimal places as 0.3056.
We need to look at the possibilities when rolling two dice. Each die has six sides, which means the total number of outcomes when rolling two dice is 36. There are 11 combinations of two dice that produce a sum of 7 or less: (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (3,1), (3,2). So, 11/36 can be simplified to 1/4, or 0.3056.
To understand this in a more visual way, you can draw a table and use colored dots to indicate the possible combinations. This will show you that out of 36 total possibilities, 11 of them produce a sum of 7 or less.
In summary, the probability of rolling a sum of 7 or less on two dice is 11/36, which can be expressed as a decimal number rounded to four decimal places as 0.3056.
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The prisms are similar. What is the surface area of Prism B? Prism A is 10 m. Prism B is 6 m. Surface area = 880m2
Answer:
79.92m
Step-by-step explanation:
here you go hope this helps
Solve for n: 8л = 56
n/8⋅л=56. You’re welcome!
are the following statements true or false? if false, correct the statement. a. the precision of your answer is determined by the largest place of significance when adding and subtracting.
The statement "the precision of your answer is determined by the largest place of significance when adding and subtracting" is False because The precision of your answer is determined by the number of decimal places when adding and subtracting.
For example, if one number is given to the nearest hundredth and the other is given to the nearest tenth, then the result should be given to the nearest tenth. This is because the tenths place is the largest place of significance in this case.
When adding and subtracting, it is important to take into account the precision of each number before adding or subtracting.
If one number is given to the nearest tenth and the other is given to the nearest hundredth, then the result should be given to the nearest hundredth, as the hundredths place is the largest place of significance.
The same applies for any other number of decimal places.
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An architect is designing a house. He wants the bedroom to have the dimensions of 10 ft by 6 ft by 7 ft. The architect doubles all three dimensions to create the den. Does that mean the den will have double the volume of the bedroom? First, find the volume of the bedroom. Solve on paper. Then check your work on Does doubling all three dimensions mean the den will have double the volume of the bedroom? Why or why not? Does doubling all three dimensions mean the den will have double the volume of the bedroom? No If he doubles all three dimensions, the den's volume will be more than double the volume of the bedroom.
Answer:
(2 x 10) x (2 x 6) x (2 x 7) = 3360ft³ <-- the den would be that
The volume:
10 x 6 x 7 = 420ft³ Volume = 8
How much more interest do vour parents have to pay at the end of the first month because their (i point) rating 15 good rather than excellent?
The more interest do your parents have to pay at the end of the first month because their rating is good rather than excellent is option (D) $19.02.
First, we need to calculate the sales tax on the mobile home purchase:
Sales tax = 4.2% of $89,000 = 0.042 x $89,000 = $3,738
The total cost of the mobile home including sales tax is
Total cost = $89,000 + $3,738 = $92,738
After making a down payment of $3,000, the amount to be financed is:
Amount financed = $92,738 - $3,000 = $89,738
To calculate the interest, we need to know the monthly interest rate. Let's assume the loan term is 30 years, which is 360 months. Then, the monthly interest rate for an excellent credit rating would be:
Monthly interest rate (excellent) = 4.75 / 1200 = 0.00396
And for a good credit score
Monthly interest rate (good) = 5.00 / 1200 = 0.00417
The interest for the first month for an excellent credit rating would be:
Interest (excellent) = $89,738 x 0.00396 = $355.33
And for a good credit rating:
Interest (good) = $89,738 x 0.00417 = $374.43
The difference in interest is:
Difference in interest = $374.43 - $355.33 = $19.02
Therefore, the correct option is (D) $19.02.
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The given question is incomplete, the complete question is:
Your parents are purchasing a mobile home for $89,000. The sales tax is 4.2%, they make a $3,000 down payment. How much more interest do your parents have to pay at the end of the first month because their rating is good rather than excellent?
Secured Unsecured
Credit APR (%) APR (%)
Excellent 4.75 5.50
Good 5.00 5.90
Average 5.85 6.75
Fair 6.40 7.25
Poor 7.50 8.40
Options:
A) $29.39
B) $21.10
C) $18.71
D) $19.02
The diameter of a softball is 3.8 inches. Estimate the volume within the softball. Round answers to the nearest
whole number and leave in the answer.
a. Volume: 73
b. Volume: 14
c. Volume: 9
d. Volume: 58
The volume of the ball is 9π (optionC)
What is volume of a sphere?A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center.
The ball takes the shape of the sphere. The volume of a sphere is therefore calculated as ;
V = 4/3 πr³
r = d/2 = 3.8/2 = 1.9
V = 4/3 × π × 1.9³
V = 27.44 π/3
V = 9π ( nearest whole number)
therefore the volume of the ball is 9π (nearest whole number)
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How do I work this out
Answer:
(5x+40)+x+2(2x+20)=360
5x+40+x+4x+40=360
10x+80=360
10x=360-80
10x=280
x=28°
substitute x=28° into (5x+40)
=140+40= 180
therefore line Ac is the diameter of a he circle because a diameter divides a circle into 2 equal part and the angle on the line is 180° showing that the circle is on a straight line
Find the exact value of X.
In the given right angled triangle, using Pythagorean theorem, the value of x is 12.73 units.
What is Pythagorean theorem?The Pythagorean theorem, also known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this rule, the length of the squares on the other two sides add up to the length of the square whose side is the hypotenuse, or the side across from the right angle. This theory can be expressed as the Pythagorean equation, which is an equation relating the lengths of the sides a, b, and the hypotenuse c:
a² + b² =c²
What is Hypotenuse?The longest side of a right-angled triangle, or the side across from the right angle, is called the hypotenuse.
In the given right angled triangle, using Pythagorean theorem,
x² = (9[tex]\sqrt{2}[/tex] )²+ (9[tex]\sqrt{2}[/tex] )²
x² = 81×2
x = [tex]\sqrt{162}[/tex]
x = 12.73 units
Therefore, the value of x will be 12.73 units.
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how do we ensure trigonometric functions compute values appropriately? what is the value of this expression?
We can ensure trigonometric functions compute values appropriately by validating the results against known values. In order to ensure that the argument is in a short interval surrounding a place where an approximation is highly accurate, one performs a range reduction prior to computing things like a cos or sin.
By comparing the results to established values, we can make sure trigonometric functions compute values correctly. As an example, if we wanted to validate the cosine of 45 degrees, we could compare the result to the known value of 0.707. If the computed value is within a small margin of error of the known value, then we can assume the trigonometric function is computing values appropriately.
In order to calculate functions like cos or sin, one must first perform a range reduction to make sure the input is inside a narrow range surrounding a point where an approximation is highly accurate. It is typically close to zero.
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during the summer of 2018, coldstream country club in cincinnati, ohio collected data on 443 rounds of golf played from its white tees. the data for each golfer's score on the twelfth hole are contained in the datafile coldstream12. (round your answers to four decimal places.) (a) construct an empirical discrete probability distribution for the player scores on the twelfth hole.
Given information:
During the summer of 2018, Coldstream Country Club in Cincinnati, Ohio collected data on 443 rounds of golf played from its white tees. The data for each golfer's score on the twelfth hole are contained in the datafile coldstream12. (Round your answers to four decimal places.)
Construct an empirical discrete probability distribution for the player scores on the twelfth hole.
A probability distribution is a tabulation of probabilities for every outcome in a sample space. It is a summary of the probabilities for all possible values of a random variable. In statistics, there are two types of probability distributions: empirical and theoretical.
An empirical distribution is a frequency distribution of observed data. A theoretical distribution is a distribution that is derived from theory.
To construct the empirical probability distribution, we will use the following steps:
Step 1: Calculate the range of the data set, which is the difference between the maximum and minimum values. Range = Maximum value – Minimum value = 8 – 3 = 5.
Step 2: Divide the range by the number of intervals (or classes) desired. In this case, we will use 6 intervals. Interval size = Range / Number of intervals = 5 / 6 = 0.833333333.
Step 3: Determine the lower limit of each interval by subtracting the interval size from the minimum value.
Lower limit of first interval = Minimum value – Interval size = 3 – 0.833333333 = 2.166666667.
Lower limit of second interval = Lower limit of first interval + Interval size = 2.166666667 + 0.833333333 = 2.999999999 ≈ 3.
Lower limit of third interval = Lower limit of second interval + Interval size = 3 + 0.833333333 = 3.833333333.
Lower limit of fourth interval = Lower limit of third interval + Interval size = 3.833333333 + 0.833333333 = 4.666666666.
Lower limit of fifth interval = Lower limit of fourth interval + Interval size = 4.666666666 + 0.833333333 = 5.499999999 ≈ 5.
Lower limit of sixth interval = Lower limit of fifth interval + Interval size = 5 + 0.833333333 = 5.833333333.
Step 4: Count the number of data points that fall in each interval. The table below shows the frequency distribution for the data set.
Interval Lower Limit Upper Limit Frequency Relative Frequency
1 2.166666667 2.999999999 33 0.0745
2 3 3.833333333 93 0.2096
3 3.833333333 4.666666666 74 0.1669
4 4.666666666 5.499999999 56 0.1264
5 5.5 6.333333333 8 0.0180
6 5.833333333 6.666666666 4 0.0090
Total - - 268 1.0000
From the above table, the empirical discrete probability distribution is constructed.
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ginas journal has a square cover with the side length shown. what is the perimeter of the journal? what is the area of the jouranl?
The given is of the square cover of Gina's journal with a side length of 24 cm. So the perimeter of the journal is 96 cm and the area of the journal would be 576 square cm.
If Gina’s journal has a square cover with a side length of 24 cm, then the perimeter of the journal would be 4 times the side length,
Which is 4 x 24 = 96 cm.
To calculate the area of a square, you need to multiply the length of one of its sides by itself.
The formula for the area of a square is,
Area = Side x Side or Area = Side².
Therefore, the area of the journal would be the side length squared,
Which is 24 x 24 = 576 square cm.
Question: Gina's journal has a square cover with the side length shown as 24 cm. what is the perimeter of the journal? what is the area of the journal?
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There are many cylinders with a radius of 6 meters. Let h represent the height in meters and v represent the volume in cubic meters. Write an equation that represents the volume, v , as a function of the height, h
The equation that represents the volume, v, as a function of the height, h is given as: V(h) = 36πh,
where h is the height in meters and V is the volume in cubic meters.
The volume of a cylinder can be calculated using the formula V=πr²h.
Here, we have a number of cylinders with a radius of 6 meters.
Let h represent the height in meters and v represent the volume in cubic meters.
To write an equation that represents the volume, v,
as a function of the height, h,
we can substitute the value of r (radius) with 6m in the formula of the cylinder’s volume,
V = πr²h.
So we get:
V = π(6m)²h
V = 36πh
This equation tells us that the volume of any cylinder with a radius of 6 meters can be expressed as 36πh,
where h is the height of the cylinder.
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Vincent flipped three coins during a probability experiment. The outcomes of the first 40 trials are shown
Based on the information in the table, in how many of the next 120 trials will the outcome be exactly two of the coins showing heads? in the table.
Answer:
I'm sorry, but I cannot see the table you are referring to. However, I can explain the general approach to solving this type of problem.
When flipping a fair coin, there are two possible outcomes: heads or tails. The probability of getting heads on any one flip is 1/2, and the probability of getting tails is also 1/2.
If Vincent has already flipped the coins 40 times and recorded the outcomes, we can use that information to estimate the probability of getting exactly two heads in the next 120 flips.
One way to do this is to find the proportion of the 40 trials that resulted in exactly two heads. Let's say that out of the 40 trials, 10 of them resulted in exactly two heads. Then the proportion of trials that resulted in two heads is:
10/40 = 1/4
This means that the probability of getting exactly two heads in one trial is 1/4.
To find the expected number of trials out of the next 120 that will result in exactly two heads, we can multiply the probability of getting two heads in one trial by the total number of trials:
(1/4) x 120 = 30
Therefore, we would expect that out of the next 120 trials, approximately 30 of them would result in exactly two heads. However, this is just an estimate based on the information given. The actual number of trials that result in exactly two heads could be more or less than 30 due to random variation.
Bo and Erica are yoga instructors. Between the two of them, they teach 37 yoga classes each week. If Erica teaches 14 fewer than
twice as many as Bo, how many classes does each instructor teach per week?
OA. 19 Bo; 18 Erica
OB. 14 Bo; 23 Erica
OC. 21 Bo; 16 Erica
OD. 17 Bo; 20 Erica
Answer:
The correct answer is OD.
Step-by-step explanation:
To find how many classes each instructor teaches per week, you need to set up and solve a system of equations based on the given information. In other words,
Let x be the number of classes Bo teaches per week and y be the number of classes Erica teaches per week.
The first equation is based on the total number of classes they teach
x + y = 37
The second equation is based on the relationship between their numbers of classes
y = 2x - 14
To solve this system, you can use substitution or elimination methods. For example, using substitution, you can plug in y = 2x - 14 into the first equation and get
x + (2x - 14) = 37
Simplify and solve for x
3x - 14 = 37
So, Bo teaches 17 classes per week and Erica teaches 20 classes per week.
Answer:
A. 19 Bo; 18 Erica
Step-by-step explanation:
im good like that hehe
a bond is worth 100$ and grows in value by 4 percent each year. f(x) =
To represent the value of the bond after x years, we can use the function:f(x) = 100 * (1 + 0.04)^xwhere x is the number of years the bond has been held.The expression (1 + 0.04) represents the growth factor of the bond per year, since the bond grows in value by 4 percent each year. By raising this factor to the power of x, we obtain the cumulative growth of the bond over x years.Multiplying the initial value of the bond, 100$, by the growth factor raised to the power of x, gives us the value of the bond after x years. This is the purpose of the function f(x).
now standardize this distance by dividing it by the population standard-deviation (or standard error). in other words, how many population-standard-deviations (or standard-error) away is your sample mean from the population mean?
Population-standard-deviations (or standard-error) away is your sample mean from the population mean is therefore (x - μ) / σ.
In order to standardize the distance, we must divide it by the standard deviation of the population (or standard error).How far the sample mean is from the population mean in terms of population-standard-deviations (or standard-error) can be determined by dividing it by the population standard deviation (or standard error). The equation for the same is as follows:
z = (x - μ) / σ
where,
z = standard score,
x = sample mean,
μ = population mean,
σ = population standard deviation.
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license plates are made using 2 letters followed by 2 digits. how many plates can be made if repetition of letters and digits is allowed?
The number of license plates that can be made if repetition of letters and digits is allowed is:
67,600
How to determine the number of plates when repeating the letters and numbers?Can be found by multiplying the number of possibilities for each position.
License plates are made using 2 letters followed by 2 digits. In this case, repetition is allowed, which means that each of the 2 letters can be any of the 26 letters of the English alphabet, and each of the 2 digits can be any of the 10 digits from 0 to 9. Thus, the total number of possible license plates can be found by multiplying the number of possibilities for each position.
There are 26 choices for each of the two letter positions, and 10 choices for each of the two digit positions, so the total number of possible license plates is:
26 x 26 x 10 x 10 = 67,600
Therefore, there are 67,600 plates that can be made if repetition of letters and digits is allowed.
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Isla will deposit $800 in an account that earns 5% simple interest every year. Her sister Aven will deposit $750 in an account that earns 7% interest compounded annually. The deposits will be made on the same day, and no additional money will be deposited or withdrawn from the accounts. Which statement is true about the balances of the girls’ accounts at the end of 48 months?
To compare the balances of the two accounts, we need to calculate the future value of each account after 48 months.
For Isla's account with simple interest, the interest earned every year is:
$800 x 0.05 = $40
After 48 months (4 years), the interest earned is:
$40 x 4 = $160
So the balance of Isla's account after 48 months is:
$800 + $160 = $960
For Aven's account with compound interest, we can use the formula:
A = P(1 + r/n)^(nt)
where A is the future value, P is the principal (initial deposit), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time in years.
For Aven's account, P = $750, r = 0.07, n = 1 (compounded annually), and t = 4. Plugging these values into the formula, we get:
A = $750(1 + 0.07/1)^(1 x 4) = $1039.14
Therefore, the statement "Aven's account will have a higher balance than Isla's account at the end of 48 months" is true.
the phone calls to a computer software help desk occur at a rate of 3 per minute in the afternoon. compute the probability that the number of calls between 2:00 pm and 2:10 pm is: (a) exactly 25. (b) more than 25.
The probability that the number of phone calls between 2:00 pm and 2:10 pm is exactly 25 is 1/110,592,893.
To calculate this probability, use the Poisson distribution formula: P(x) = (e^-λ * λ^x) / x!, where λ = 3 x 10 = 30. Therefore, P(25) = (e^-30 * 30^25) / 25! = 1/110,592,893.
The probability that the number of phone calls between 2:00 pm and 2:10 pm is more than 25 is the sum of probabilities of all calls more than 25. That is, the probability is 1 - (e^-30 * (30^0 + 30^1 + 30^2 + ... + 30^25)) / (0! + 1! + 2! + ... + 25!).
By using the same Poisson distribution formula, the probability is 1 - 0.99988822 = 0.00011178.
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3. Consider the following statement: For each positive real number r, if r2 = 18, then r is irrational (a) If you were setting up a proof by contradiction for this statement, what would you assume? Carefully write down all conditions that you would assume. (b) Complete a proof by contradiction for this statement.
(a) To set up a proof by contradiction for the statement "For each positive real number r, if r^2 = 18, then r is irrational," we will assume the opposite of the given statement. Specifically, we would assume that there exists a positive real number r such that r^2 = 18, and r is rational (not irrational).
(b) To complete the proof by contradiction, follow these steps:
1. Assume that there exists a positive real number r such that r^2 = 18, and r is rational.
2. Since r is rational, we can write it as a fraction a/b, where a and b are integers with no common factors other than 1 (i.e., a and b are coprime) and b ≠ 0.
3. We have r^2 = 18, so (a/b)^2 = 18.
4. Squaring both sides, we get a^2 / b^2 = 18.
5. Rearrange the equation: a^2 = 18b^2.
6. Since 18 is an even number, a^2 is also an even number, which implies that a is an even number (let's say a = 2k, where k is an integer).
7. Substitute a with 2k: (2k)^2 = 18b^2, which simplifies to 4k^2 = 18b^2.
8. Divide both sides by 2: 2k^2 = 9b^2.
9. Now, we see that the left side of the equation is an even number (2k^2), which implies that 9b^2 is also an even number. However, 9 is an odd number, so for 9b^2 to be even, b must be even.
10. Both a and b are even, which contradicts our original assumption that a and b are coprime (having no common factors other than 1).
Therefore, our assumption that there exists a positive real number r such that r^2 = 18 and r is rational leads to a contradiction. Thus, the original statement is true: for each positive real number r, if r^2 = 18, then r is irrational.
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A future interest usually exists in conjunction with which of the following real property interests at the time that it is the interest granted?
A future interest in real property typically exists in conjunction with a present interest in that same property at the time the future interest is granted.
What is a future interest?
Future interests are created when a property owner grants an interest in their property that will take effect at a later time, such as after their death or the expiration of a lease.
These interests are typically created in the form of a trust or a will, and they can be used to ensure that property is distributed according to the owner's wishes, to provide for the future needs of family members, or to protect property from creditors or other claims.
Examples of future interests include remainders, reversions, and executory interests.
Complete questin:
A future interest usually exists in conjunction with which of the following real property interests at the time that it is the interest granted?
1) future interest
2) protect property
3) both a and b
4) None of these
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A rectangular garden plot has a length of 4 meters and a width of 3.5 meters. Jackson wants to put a fence around the garden. He also wants to install landscape fabric over the entire plot to prevent weeds. How much fencing will he need to buy? How much landscape fabric will he need to buy?
Using the formula of area and perimeter of the rectangle, the answers to both subparts are shown:
(A) The fencing required is 15 meters.
(B) The fabric required is 14m².
What is a rectangle?An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°).
A rectangle has equal and parallel opposite sides.
Four sides make up a rectangle, which has opposing sides that are parallel and of equal length.
It belongs to a category of quadrilaterals where each of the four angles is a straight angle or measures 90 degrees.
An example of a parallelogram with equal angles is a rectangle.
It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal.
A square is a rectangle with four equally long sides.
(A) The required fencing:
Perimeter = 2(l+w)
Perimeter = 2(7.5)
Perimeter = 15
The fencing required is 15 meters.
(B) The landscape fabric required:
Area = l*w
Area = 4*3.5
Area = 14m²
The fabric required is 14m².
Therefore, using the formula of area and perimeter of the rectangle, the answers to both subparts are shown:
(A) The fencing required is 15 meters.
(B) The fabric required is 14m².
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traveling for 3 hr into a steady headwind, a plane flies 1650 mi. the pilot determines tha tflying with the same wind for 2 hr, he could make a trip of 1300. find the rate of the plane and the wind speed
The rate of the plane (in still air) is 600 miles per hour and the speed of the wind is 50 miles per hour.
Let's denote the rate of the plane (in still air) by p and the speed of the wind by w.
From the first part of the problem, we know that the plane flies 1650 miles in 3 hours against the headwind. This means that the effective speed of the plane (relative to the ground) was 1650/3 = 550 miles per hour slower than its speed in still air, i.e., p - w = 550.
From the second part of the problem, we know that the plane could make a trip of 1300 miles in 2 hours with the same wind. This means that the effective speed of the plane (relative to the ground) was 1300/2 = 650 miles per hour faster than its speed in still air, i.e., p + w = 650.
Now we have two equations with two unknowns, which we can solve using a system of equations. Adding the two equations, we get:
2p = 1200
Therefore, p = 600 miles per hour. Substituting this value into one of the equations, we get:
600 + w = 650
Therefore, w = 50 miles per hour.
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the support for a basketball hoop forms a right triangle as shown. what is the length, x, of the horizontal portion of the support?
According to Pythagorean Theorem, The length of the horizontal portion of the support, x, is 3.87 feet.
The length of the horizontal portion of the support, x, can be determined by using the Pythagorean Theorem. The Pythagorean Theorem states that a2 + b2 = c2, where a and b are the sides of a right triangle and c is the hypotenuse.
In this case, a = 7 feet, b = x, and c = 8 feet. We can use the Pythagorean Theorem to solve for x: 72 + x2 = 82, or 49 + x2 = 64. This can be solved for x to get x2 = 15 and x = √15 ≈ 3.87 feet.
Therefore, the length of the horizontal portion of the support, x, is 3.87 feet.
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