There are 2(24!) - 23! arrangements of the 26-letter alphabet that contain "the" or "of."
To find the number of arrangements of the 26-letter alphabet that contain "the" or "of," we can use the principle of inclusion-exclusion.
First, we find the total number of arrangements of the 26-letter alphabet, which is 26! (26 factorial).
Next, we find the number of arrangements that contain "the." To do this, we treat "the" as a single letter and arrange the remaining 24 letters along with it. Since there are 24 letters to arrange, the number of arrangements that contain "the" is 24! (24 factorial).
Similarly, we find the number of arrangements that contain "of" by treating it as a single letter and arranging the remaining 24 letters along with it. The number of arrangements that contain "of" is also 24!.
However, if we simply add the number of arrangements that contain "the" and "of," we will be double-counting the arrangements that contain both "the" and "of." To correct for this, we subtract the number of arrangements that contain both "the" and "of."
To find the number of arrangements that contain both "the" and "of," we treat "the of" as a single letter and arrange the remaining 23 letters along with it. Since there are 23 letters to arrange, the number of arrangements that contain both "the" and "of" is 23! (23 factorial).
Using the principle of inclusion-exclusion, the total number of arrangements that contain "the" or "of" is:
24! + 24! - 23! = 2(24!) - 23!
Therefore, there are 2(24!) - 23! arrangements of the 26-letter alphabet that contain "the" or "of."
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Customer three found a hair in their taco! To make up for it, you gave 40% off their order, but they still had to pay a 4.5% sales tax. What is the new cost of the order?
The new cost of the order is 62.7% of the original price where still 4.5% sales tax had to pay.
What is discount?A discount is a reduction in the price of an item or service, usually expressed as a percentage of the original price.
According to question:Let's assume the original cost of the order was $x.
After the 40% discount, the customer paid 60% of the original cost, which is 0.6x.Then, the 4.5% sales tax is applied to the discounted price of 0.6x, which is 0.045(0.6x) = 0.027x.So the final cost of the order is the discounted price plus the sales tax:0.6x + 0.027x = 0.627x
Therefore, the new cost of the order is 62.7% of the original price.
For example, if the original cost of the order was $20, then the discounted price is $12 (60% of $20), and the sales tax is $0.324 (4.5% of $12). The final cost of the order would be $12.324.
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find the probability that the proportion of the sampled teenagers who own a smartphone is between 0.35 and 0.45
The probability that the proportion of the sampled teenagers who own a smartphone is between 0.35 and 0.45 is [tex]P(X) = 100Cx (0.4)^x (1-0.4)^(100-x).[/tex]
The formula is [tex]P(X) = nCx (p)^x (1-p)^(n-x)[/tex], where n is the number of trials, x is the number of successes, and p is the probability of success for one trial. In this case, n represents the number of teenagers sampled, x represents the number of teenagers who own a smartphone, and p represents the probability that any one teenager owns a smartphone.
First, let us calculate p. The probability of success (owning a smartphone) is the proportion of the sampled teenagers who own a smartphone, which is between 0.35 and 0.45. Since the probability of success lies between 0.35 and 0.45, we can take the average of these numbers, which is 0.4. This number (0.4) is p.
Next, let us calculate x. The number of successes (teenagers who own a smartphone) is the proportion of the sampled teenagers who own a smartphone, which is between 0.35 and 0.45. Since the number of successes lies between 0.35 and 0.45, we can take the average of these numbers, which is 0.4. This number (0.4) is x.
Finally, we can calculate n. We know that the number of teenagers sampled is 100, so n = 100.
[tex]P(X) = 100Cx (0.4)^x (1-0.4)^(100-x).[/tex]
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the width of a rectangle is increasing at a rate, while the length increases at a rate. at what rate is the area increasing when
When the width of a rectangle is increasing at a rate, and the length increases at a rate, the rate at which the area increases can be determined by multiplying the rates of the width and the length.
When the width and length of a rectangle increase at certain rates, the area of the rectangle also changes at a specific rate. The rate of change of the area is determined by multiplying the rates of change of the width and length.
This is because the area of a rectangle is calculated by multiplying its width and length, and therefore any change in either dimension affects the overall area. The product of the rates of change of the width and length gives the overall rate of change of the area.
Therefore, the rate at which the area is increasing when the width of a rectangle is increasing at a rate, while the length increases at a rate can be calculated using the above formula.
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consider a 20-lb pink flamingo that stands 3 ft in height and has legs that are 2 ft in length. model the height and leg length of a 100-lb flamingo. what assumptions are necessary? are they reasonable assumptions?
The height of a 100-lb flamingo can be estimated by assuming that it would be proportional to the height of the 20-lb pink flamingo. Based on this assumption, the 100-lb flamingo would be 6 ft tall.
The leg length of a 100-lb flamingo can be estimated by assuming that it would also be proportional to the leg length of the 20-lb pink flamingo. Using this assumption, the 100-lb flamingo would have legs 4 ft in length.
These assumptions are reasonable given that the difference in size of the two flamingos is only a factor of 5. This means that the size difference between the two is not large enough to drastically change the proportions of their bodies. Thus, it is a fair assumption that the proportions of their height and leg length would remain roughly the same.
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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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Write an equation to represent each relationship
This equation represents the linear relationship between the dependent variable (y) and the independent variable (x) with a slope of 2 and a y-intercept of -3.
However, I can provide a general example using common terms in algebra:
Terms: Dependent variable (y), independent variable (x), slope (m), and y-intercept (b).
To represent a linear relationship between two variables, we can use the equation of a straight line, which is often written as:
[tex]y = mx + b[/tex]
Here's what each term in the equation represents:
1. y: This is the dependent variable, meaning its value depends on the value of the independent variable (x). In a graph, it is usually represented on the vertical axis.
2. x: This is the independent variable, which can take any value within a given range. It is usually represented on the horizontal axis in a graph.
3. m: This is the slope of the line, representing the rate at which the dependent variable (y) changes with respect to the independent variable (x). A positive slope indicates an increasing relationship, while a negative slope indicates a decreasing relationship.
4. b: This is the y-intercept, which is the point where the line crosses the y-axis. It represents the value of the dependent variable (y) when the independent variable (x) is equal to zero.
simply plug in the values for the slope (m) and y-intercept (b). For example, if the slope is 2 and the y-intercept is -3, the equation would be:
[tex]y = 2x - 3[/tex]
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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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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.
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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4. Determine the length of supporting guy wires from the top of a 45 ft. tall cell
phone tower if they are secured to the ground 28 ft. horizontally from the base
of the tower.
Accοrding tο the Pythagοrean theοrem, the length οf the suppοrting guy wires frοm the tοp οf the 45 ft. tall cell phοne tοwer, if they are secured tο the grοund 28 ft. hοrizοntally frοm the base οf the tοwer, is 53 ft.
What is Pythagοrean theοrem?The Pythagοrean theοrem is a fundamental result in Euclidean geοmetry that describes the relatiοnship between the three sides οf a right-angled triangle.
In equatiοn fοrm, this can be written as:
c² = a² + b²
where c is the length οf the hypοtenuse, and a and b are the lengths οf the οther twο sides (alsο knοwn as the legs) οf the right-angled triangle.
In this case, the tοwer, the grοund, and the guy wire fοrm a right triangle. We knοw the height οf the tοwer is 45 ft, and the hοrizοntal distance frοm the base οf the tοwer tο where the guy wire is secured tο the grοund is 28 ft. Let's call the length οf the guy wire c. Then, we have:
a = 28 ft (hοrizοntal distance frοm the base οf the tοwer tο where the guy wire is secured)
b = 45 ft (height οf the tοwer)
c = length οf the guy wire (hypοtenuse)
Using the Pythagοrean theοrem, we can sοlve fοr c:
[tex]a^2 + b^2 = c^2[/tex]
[tex]28^2 + 45^2 = c^2[/tex]
[tex]784 + 2025 = c^2[/tex]
[tex]2809 = c^2[/tex]
[tex]c = \sqrt{(2809)[/tex]
c ≈ 53 ft
Therefοre, the length οf the suppοrting guy wires frοm the tοp οf the 45 ft. tall cell phοne tοwer, if they are secured tο the grοund 28 ft. hοrizοntally frοm the base οf the tοwer, is apprοximately 53 ft.
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A race is 3/10 kilometers long. Alan ran 6 of these races. How far did he run altogether
Answer:
1.8 kilometers
hope this helped
Answer:
1 8/10 kilometers
Step-by-step explanation:
u keep on adding 3 on to 3/10th 6 times then u get a improper fraction and turn that into a fraction and u get ur answer
hope it helps
Type the correct answer in the box. Use numerals instead of words.
The cost to manufacture the KZR 250 model of motorcycle at the Kawahama factory is shown in the table below.
Number of Motorcycles
Cost
Manufactured
0
1
3
8
15
$
$0.00
$4,590.00
$12,240.00
$22,950.00
Using the information in the table, determine the constant of proportionality, and use it to complete the table.
The constant of proportionality is the cost per unit. In this case, it can be calculated by dividing the cost of 1 motorcycle by the number of motorcycles.
What is unit?Unit is an individual item or segment of a larger whole. It is used to measure or quantify different elements or entities, including physical objects, abstract concepts, and even people. In mathematics, a unit is a number or quantity that is equal to one. In the physical sciences, a unit is a standard amount of a certain quantity, such as a kilogram or an hour. In economics, a unit is a measure of a certain commodity or factor of production, such as labor or capital.
Constant of Proportionality = Cost per Motorcycle = 4,590 / 1 = 4,590
Using this constant of proportionality, we can complete the table as follows:
Number of Motorcycles
Cost
Manufactured
0
1
3
8
15
$
$0.00
$4,590.00
$13,770.00
$36,720.00
$68,850.00
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The constant of proportionality is 4,080.00. Using this constant, we can calculate the cost for each number of motorcycles.
What is constant?A constant is a quantity or value that remains unchanged over time. It is a fixed value that does not vary and is unaffected by external influences. Constants are used in mathematics, physics, chemistry, and other sciences to represent a fixed value.
Number of Motorcycles
Cost
Manufactured
0
1
3
8
15
$
$0.00
$4,590.00
$12,240.00
$22,950.00
25
$37,275.00
The constant of proportionality is the rate of increase in cost as the number of motorcycles manufactured increases. This can be calculated by dividing the cost of each number of motorcycles by the number of motorcycles.
For example, when 1 motorcycle is manufactured, the cost is $4,590.00, so the constant of proportionality is $4,590.00 / 1 = $4,590.00.
When 3 motorcycles are manufactured, the cost is $12,240.00, so the constant of proportionality is $12,240.00 / 3 = $4,080.00.
Therefore, the constant of proportionality is 4,080.00. Using this constant, we can calculate the cost for each number of motorcycles.
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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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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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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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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.
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
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.
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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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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The sum of two numbers is 25, and the larger is 3 less than three times the smaller. What is the number?
The smaller number is 5.5 and the larger number is 15.5.
Let's start by assigning variables to the two unknown numbers. Let x be the smaller number and y be the larger number.
From the problem statement, we know that:
x + y = 25 (the sum of the two numbers is 25)
y = 3x - 3 (the larger number is 3 less than three times the smaller)
We can use the second equation to solve for y in terms of x, by adding 3 to both sides:
y + 3 = 3x
Then, we can substitute this expression for y into the first equation:
x + (y + 3) = 25
Substituting y + 3 with 3x, we get:
x + 3x = 22
Combining like terms, we get:
4x = 22
Finally, we solve for x by dividing both sides by 4:
x = 5.5
Now that we know x, we can use the equation y = 3x - 3 to find y:
y = 3(5.5) - 3 = 15.5
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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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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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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 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
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
true of false: dispersion models are selected based on the phase of the material being modeled in a release scenario
The statement "dispersion models are selected based on the phase of the material being modeled in a release scenario" is true as Different dispersion models are needed for different phases (gas, liquid, solid) due to differences in behavior and transport mechanisms.
Dispersion models are used to predict the spread of pollutants, and they depend on the physical and chemical properties of the material being released.
Generally, different models are used for each phase of the material, such as the Gaussian plume model for gases, the plume rise model for heated gases, and the particle dispersion model for particles.
Each of these models is based on different characteristics and equations which allow for the most accurate prediction of the dispersion of pollutants.
For example, the Gaussian plume model considers the wind velocity, turbulence, and buoyancy of the released material, whereas the plume rise model considers the momentum, thermal expansion, and buoyancy of the released material.
Therefore, dispersion models are selected based on the phase of the material being modeled in a release scenario.
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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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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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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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