The original price of the refurbished phone before the 35% discount was £120. If a refurbished phone is sold at a 35% discount with a final price of £78.
To find the original price of a refurbished phone before the discount of 35%, let's use the following formula:
discount = original price - discounted price
35% of the original price can be represented as 0.35 times the original price. This will result in the equation below:
0.35x = original price - 78
Where x is the original price. So, to find the value of x, we can rearrange the equation to get:
0.35x + 78 = original price
Now we substitute the given values into the equation above:
0.35x + 78 = original price
0.35x + 78 = x - 44.1 (if x represents the original price)
Let's subtract 0.35x from both sides to isolate the x variable:
78 = 0.65x
Then, let's divide both sides by 0.65 to solve for x (the original price):
x = £120
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What values of p will the equation x^2=p have 0 real number solution why
The equation x^2 = p has 0 real number solution when p is less than or equal to 0. This is because the square of any real number is always non-negative. Therefore, if p is less than or equal to 0, then there is no real number x such that x^2 = p.
For example, if p = -1, then the equation x^2 = -1 has no real number solutions. This is because the square of any real number is always non-negative. Therefore, there is no real number x such that x^2 = -1.
However, if p is greater than 0, then there are two real number solutions to the equation x^2 = p. These solutions are x = sqrt(p) and x = -sqrt(p).
For example, if p = 4, then the equation x^2 = 4 has two real number solutions. These solutions are x = 2 and x = -2.
In conclusion, the equation x^2 = p has 0 real number solution when p is less than or equal to 0. This is because the square of any real number is always non-negative.
Using the Smith's BBQ Report, based on the data provided, what beverage (liquor, beer, or wine) consistently yielded the highest profit?
To identify the beverage that consistently yielded the highest profit according to the Smith's BBQ Report, we need to compare the profit margins of liquor, beer, and wine. By analyzing the profit margins over time, we can determine which beverage consistently had the highest margin, indicating the highest profit.
To determine which beverage consistently yielded the highest profit, we need to analyze the data provided in the Smith's BBQ Report. The report likely includes information on the sales and profits generated from liquor, beer, and wine. By comparing the profit margins of each beverage over a period of time, we can identify the one that consistently yielded the highest profit.
1. Analyzing profit margins: To determine the beverage with the highest profit, we examine the profit margins for liquor, beer, and wine. Profit margin is calculated by subtracting the cost of goods sold (COGS) from the revenue and dividing the result by the revenue. By comparing the profit margins of each beverage, we can identify which one consistently had the highest margin.
For example, if the profit margin for beer is consistently higher than that of liquor and wine across different time periods, it suggests that beer consistently yielded the highest profit. The profit margin analysis would provide insights into the beverage that generated the most profit for Smith's BBQ consistently.
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please and thank youuu
The 27th term of the arithmetic sequence with the first term [tex]\(a_1 = -13\)[/tex] and a common difference of 4 is 91.
To find the 27th term of an arithmetic sequence, we can use the formula:
[tex]\[a_n = a_1 + (n - 1)d\][/tex]
where [tex]\(a_n\)[/tex] represents the [tex]\(n\)[/tex]th term, [tex]\(a_1\)[/tex] is the first term, [tex]\(d\)[/tex] is the common difference, and [tex]\(n\)[/tex] is the term number.
Given that [tex]\(a_1 = -13\)[/tex] and the common difference [tex]\(d = 4\)[/tex], we will simply substitute these values into the given formula:
[tex]\[a_{27} = -13 + (27 - 1) \cdot 4\][/tex]
Simplifying the equation, we have:
[tex]\[a_{27} = -13 + 26 \cdot 4\][/tex]
Calculating the expression, we get:
[tex]\[a_{27} = -13 + 104\][/tex]
Finally, evaluating the sum, we find:
[tex]\[a_{27} = 91\][/tex]
Therefore, the 27th term of the arithmetic sequence with the first term [tex]\(a_1 = -13\)[/tex] and a common difference of 4 is 91.
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Alli has $382. 45 in her checking account and $450 in her savings account. She writes a check for $400. Alli’s bank automatically takes money from her savings to cover the amount of a check if the money in the checking account is not sufficient. Unfortunately for Alli, the bank also withdraws $25 from her savings account for this service. Once the check has cleared, how much money does Alli have in her savings account?
$17. 55
$17. 55
$42. 55
$42. 55
$407. 45
$407. 45
$442. 55
$442. 55
Once the check has cleared, Alli has $17.55 in her savings account. Finally, the amount of money Alli has in her savings account after the check has cleared is $25, so the answer is option A: $17.55.
Initial amount in Alli's checking account = $382.45
Initial amount in Alli's savings account = $450
Amount Alli withdrew from checking account = $400
Amount the bank withdrew from Alli's savings account = $25
Total cost of the check = 400+25
=425
Since the initial amount in her checking account was insufficient, the bank automatically withdrew $25 from her savings account to cover the cost of the check. This means that Alli has a total of $425 - $400 = $25 left in her savings account.After the withdrawal from her savings account, Alli's remaining savings balance is $450 - $25 = $425. However, she spent $400 to cover the check, so her final savings balance is $425 - $400 = $25.
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A proposed mechanism for ozone destruction in the late spring over northern latitudes in the lower stratosphere begins with the photochemical decomposition of ClONO_2 to Cl and NO_3, followed by photochemical decomposition of the later to NO and O_2. Deduce a catalytic ozone destruction cycle, requiring no atomic oxygen, that incorporates these reactions. What is the overall reaction?
A catalytic ozone destruction cycle requires no atomic oxygen and it incorporates the photochemical decomposition of ClONO₂ to Cl and NO₃, and photochemical decomposition of the later to NO and O₂. The overall reaction is NO + O₃ → NO₂ + O₂
In the lower stratosphere, a proposed mechanism for ozone destruction in the late spring over northern latitudes begins with the photochemical decomposition of ClONO₂ to Cl and NO₃. This reaction is catalyzed by sunlight in the lower stratosphere. The photodissociation of NO₃ is the next step in the cycle, and it results in the production of NO and O₂.
The NO then reacts with O₃ in the following reaction: NO + O₃ → NO₂ + O₂The NO₂ that is produced then reacts with atomic oxygen to form NO₃, and the cycle starts again with the photodissociation of ClONO₂. The NO that is produced during the reaction between NO₂ and O₃ can also react with atomic oxygen to form NO₂, which can then go on to form NO₃.However, the catalytic cycle that has been proposed requires no atomic oxygen to be present. The NO that is produced during the reaction between NO₂ and O₃ reacts with more O₃ to form NO₃ and O₂: NO + O₃ → NO₂ + O₂NO₂ + O₃ → NO₃ + O₂The NO₃ that is produced in this reaction can then go on to react with more O₃, starting the cycle over again. Thus, the overall reaction for the catalytic ozone destruction cycle is:NO + O₃ → NO₂ + O₂NO₂ + O₃ → NO₃ + O₂NO₃ + O₃ → NO + 2O₂The cycle continues as long as the necessary reactants are available.
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What is the sum of a geometric series of 12 terms that begins with 10 and has a common ratio of 2?
A) 240
B) 252
С) 20,480
D) 40,950
The sum of the geometric series with 12 terms, starting from 10 and with a common ratio of 2, is 40,950.
To find the sum of a geometric series, we can use the formula:
S = a * (1 - r^n) / (1 - r)
Where:
S is the sum of the series,
a is the first term of the series,
r is the common ratio,
n is the number of terms in the series.
In this case, the first term (a) is 10, the common ratio (r) is 2, and the number of terms (n) is 12.
Plugging in the values into the formula, we have:
S = 10 * (1 - 2^12) / (1 - 2)
Simplifying further:
S = 10 * (1 - 4096) / (1 - 2)
S = 10 * (-4095) / (-1)
S = 10 * 4095
S = 40,950
Therefore, the sum of the geometric series with 12 terms, starting from 10 and with a common ratio of 2, is 40,950.
The correct answer is D) 40,950.
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From his eye, which stands 1. 62 meters above the ground, Amadou measures the angle of elevation to the top of a prominent skyscraper to be 44^{\circ}∘. If he is standing at a horizontal distance of 164 meters from the base of the skyscraper, what is the height of the skyscraper?
Based on Amadou's measurements, the height of the skyscraper is approximately 97.2 meters.
Amadou measures the angle of elevation from his eye to the top of the skyscraper as 44 degrees. To determine the height of the skyscraper, we can use trigonometry. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side.
In this case, the opposite side represents the height of the skyscraper, and the adjacent side represents the horizontal distance from Amadou to the base of the skyscraper. We are given that the adjacent side is 164 meters and the angle of elevation is 44 degrees.
Using the tangent function, we can set up the following equation:
tan(44 degrees) = height of skyscraper / 164 meters
To solve for the height of the skyscraper, we rearrange the equation:
height of skyscraper = tan(44 degrees) * 164 meters
Using a scientific calculator or trigonometric table, we find that tan(44 degrees) is approximately 0.9659. Multiplying this value by 164 meters gives us the height of the skyscraper:
height of skyscraper ≈ 0.9659 * 164 meters ≈ 97.2 meters
Therefore, based on Amadou's measurements, the height of the skyscraper is approximately 97.2 meters.
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Noah needs to peel a lot of potatoes before a dinner party. He has already peeled some potatoes. If he keeps peeling at the same rate, will he finish all the potatoes in time?
If the remaining time is greater than or equal to N/P minutes, he will finish in time. Otherwise, he won't be able to finish before the dinner party.
To determine if Noah will finish peeling all the potatoes in time for the dinner party, we need to consider the amount of time he has left and his peeling rate.
Let's assume Noah has N potatoes left to peel and he can peel P potatoes per minute. If he keeps peeling at the same rate, the time required to peel all the remaining potatoes is given by N/P minutes.
If Noah has enough time before the dinner party, meaning the remaining time is greater than or equal to N/P minutes, he will be able to finish peeling all the potatoes.
However, if the remaining time is less than N/P minutes, it means there isn't enough time for Noah to finish peeling all the potatoes before the dinner party.
Therefore, to determine if Noah will finish peeling all the potatoes in time, compare the remaining time with N/P minutes. If the remaining time is greater than or equal to N/P minutes, he will finish in time. Otherwise, he won't be able to finish before the dinner party.
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Differentiate from the first principle I obtain the gradient of the tangent to the curve
Y=2x2-5x+3 at the point where x=2
In calculus, there are different ways to differentiate the tangent to a curve. The first principle is one of the ways to differentiate the tangent to a curve.
Differentiation is the foundation of calculus, and it's used to find rates of change, maxima and minima, and the behavior of functions in general.The first principle of differentiation.
The first principle is the fundamental approach to finding derivatives, which involves finding the limit of the difference quotient, or f(x + h) – f(x) / h as h approaches zero. This difference quotient represents the slope of the line tangent to the curve at the point (x, f(x)).
The first principle formula for differentiation is given by:lim h → 0 [f(x + h) – f(x) / h]To differentiate the tangent to the curve y = 2x² – 5x + 3 at the point where x = 2 using the first principle, we need to find the slope of the line tangent to the curve at x = 2. We start by finding the equation of the tangent line and then calculate its slope using the first principle.To find the equation of the tangent line, we differentiate the given function, y = 2x² – 5x + 3:dy/dx = 4x – 5At x = 2, dy/dx = 4(2) – 5 = 3.
Thus, the slope of the tangent line at x = 2 is 3.
Now, we can use the point-slope form of the equation of a line to find the equation of the tangent line:
y – f(2) = m(x – 2)y – (2(2)² – 5(2) + 3) = 3(x – 2)y – 4 = 3x – 6y = 3x – 2
This is the equation of the tangent line to the curve
y = 2x² – 5x + 3
at the point where x = 2. The slope of the tangent line is 3.
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If a bookseller earns a profit of 25 percentage by selling a novel worth rs 300 calculate the selling price of the novel
The selling price of the novel would be Rs 375. The bookseller should sell the novel for Rs 375 to earn a profit of 25%. Profit percentage is a measure of the profit earned as a percentage of the cost price.
In this case, the bookseller earns a profit of 25%. To calculate the selling price, we need to determine the profit earned and add it to the cost price.
To find the profit earned, we multiply the cost price by the profit percentage. In this case, the cost price of the novel is given as Rs 300, and the profit percentage is 25%. To calculate the profit, we multiply Rs 300 by (25/100) or 0.25. The result is Rs 75, indicating that the bookseller earns a profit of Rs 75.
To obtain the selling price, we add the profit to the cost price. In this case, the cost price is Rs 300, and the profit is Rs 75. Adding them together, we get Rs 375 as the selling price of the novel.
To calculate the selling price, we need to determine the profit earned by the bookseller and add it to the cost price.
Given:
Profit percentage = 25%
Cost price of the novel = Rs 300
To calculate the profit, we multiply the cost price by the profit percentage:
Profit = 25% of Rs 300 = (25/100) * 300 = Rs 75
The selling price is obtained by adding the profit to the cost price:
Selling price = Cost price + Profit = Rs 300 + Rs 75 = Rs 375.
Therefore, the selling price of the novel is Rs 375.
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Question 4
1
Justin regularly eats in the Cafeteria at work. On Monday
Justin bought 2 hamburgers and 1 carton of milk for $2. 85.
On Tuesday Justin purchased 3 hamburgers and 2 cartons of
milk for $4. 45. How much does a carton of milk cost?
a. $0. 35
b. $0. 50
c. $0. 75
d. $0. 85
The cost of a carton of milk is a) $0.35.
To find the cost of a carton of milk, we can set up a system of equations based on the given information.
Let's assume the cost of a hamburger is "h" and the cost of a carton of milk is "m".
From the information given, we can create the following equations:
Equation 1: 2h + 1m = 2.85 (from Monday's purchase)
Equation 2: 3h + 2m = 4.45 (from Tuesday's purchase)
We can solve this system of equations to find the value of "m", the cost of a carton of milk.
Multiplying Equation 1 by 2 and Equation 2 by 1, we can eliminate "h" and solve for "m":
4h + 2m = 5.70
3h + 2m = 4.45
Subtracting Equation 2 from Equation 1, we get:
(4h + 2m) - (3h + 2m) = 5.70 - 4.45
h = 1.25
Now, we can substitute the value of "h" back into Equation 1 or Equation 2 to find the value of "m":
2(1.25) + 1m = 2.85
2.50 + m = 2.85
m = 2.85 - 2.50
m = 0.35
Therefore, the cost of a carton of milk is $0.35.
The correct answer is option a) $0.35.
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Kent put $8,500 into an 18 month CD. The interest rate is 3.25% How much money will Kent earn in interest?
Kent will earn $553.12 in interest from his 18-month CD with an interest rate of 3.25%.
To calculate the interest earned, we can use the formula: Interest = Principal × Rate × Time. In this case, the principal (amount invested) is $8,500, the interest rate is 3.25% (or 0.0325 as a decimal), and the time is 18 months (or 1.5 years). Plugging in these values into the formula, we get: Interest = $8,500 × 0.0325 × 1.5 = $553.12. Therefore, Kent will earn $553.12 in interest from his CD.
It's important to note that the interest rate is typically expressed as an annual rate. In this case, the interest rate is 3.25%, which means that for a full year, Kent would earn 3.25% of the principal amount. However, since the CD term is 18 months (or 1.5 years), we need to adjust the formula accordingly. By multiplying the principal by the interest rate and the time, we can determine the total interest earned over the given period. In this case, the interest earned is $553.12.
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Which equation represents this problem? Twelve dollars is divided equally among 4 people
The equation that represents the problem of dividing twelve dollars equally among four people is as follows:12 / 4 = 3The given problem of dividing twelve dollars equally among four people can be represented by the equation 12/4 = 3.
Here, 12 represents the total amount of money that is being divided and 4 represents the number of people among whom the money is being divided .In this problem, we divide the total amount of money by the number of people to find out how much money each person will get. As there are four people to divide the money among, we divide the total amount of $12 by 4 to get $3 as the share of each person. Therefore, the equation that represents this problem is 12/4 = 3.
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Gena and her friends each estimated the quotient of –137. 56 divided by –6. 12 using compatible numbers. Which shows the best estimate using compatible numbers?.
The best estimate using compatible numbers is approximately 23.33.
To find the best estimate using compatible numbers for the quotient of -137.56 divided by -6.12, we need to identify compatible numbers that are close to the given values.
Compatible numbers are numbers that are easy to work with mentally and provide a close approximation of the actual values.
Let's consider compatible numbers for -137.56 and -6.12:
For -137.56, we can use -140, which is close to -137.56.
For -6.12, we can use -6, which is close to -6.12.
Now, let's calculate the estimate:
-137.56 ÷ -6.12 ≈ -140 ÷ -6
Dividing -140 by -6, we get:
-137.56 ÷ -6.12 ≈ 23.33
Therefore, the best estimate using compatible numbers is approximately 23.33. By selecting compatible numbers close to the given values and performing the division using those numbers, we can obtain a reasonable estimate of the quotient.
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Ed invested $500 at 3% annual interest compounded quarterly. Write an equation and find how much money he will have in 7 years.
We can use the formula for compound interest: after 7 years, Ed will have approximately $617.
To determine how much money Ed will have after 7 years of investing $500 at an annual interest rate of 3% compounded quarterly, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = the annual interest rate (expressed as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case, P = $500, r = 3% (or 0.03), n = 4 (quarterly compounding), and t = 7. Plugging these values into the formula, we can calculate the final amount:
A = 500(1 + 0.03/4)^(4*7)
Simplifying the equation, we get:
A = 500(1.0075)^(28)
Calculating the expression within the parentheses, we find:
A = 500(1.234)
Finally, we can compute the final amount:
A = $617
Therefore, after 7 years, Ed will have approximately $617.
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There are
128
128128 ounces in a gallon. There are
4
44 quarts in a gallon.
How many ounces are in a quart?
There are 32 ounces are in a quart
How to determine how many ounces are in a quart?From the question, we have the following parameters that can be used in our computation:
128 ounces in a gallon
Also, we have
4 quart in a gallon
using the above as a guide, we have the following:
128 ounces = 4 quart
Divide both sides by 4
So, we have
32 ounces = 1 quart
Hence, there are 32 ounces are in a quart
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An item originally costs $175. 0. The item is now on sale for $99. 75. What percent
is the sale price of the original price? Is this an example of percent increase or
decrease? Explain how you know. *
It is percentage decrease by 43 percent.
Given that, the original cost of item = $175.00 and the sale price of item = $99.75.
Percentage increase or decrease = (Original Price - Sale Price)/Original Price ×100
= (175.00-99.75)/175.00 ×100
= 75.25/175.00 ×100
= 0.43×100
= 43%
Therefore, it is percentage decrease by 43 percent.
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7th grade math
Paula measured the auditorium and made a scale drawing. The stage, which is 56 feet long in real life, is 84 inches long in the drawing. What scale did Paula use?
3 inches : ____ feet
Paula made a scale drawing of the auditorium, which is a replica of the actual auditorium, but smaller in size. The scale drawing shows measurements of the actual auditorium at a reduced size.
Paula needs to determine the scale used to draw the auditorium. The scale is the ratio of the lengths of the corresponding sides of the actual auditorium and the scale drawing. We can use the following formula to find out the scale of the drawing:
Scale = (Length of the corresponding side of the actual object) / (Length of the corresponding side of the scale drawing)First, we have to convert 56 feet to inches:1 foot = 12 inches56 feet = 56 x 12 = 672 inchesNow, we can find the scale of the drawing as follows:
Now, we can use the scale to determine the length of other parts of the auditorium. For example, if a door in the auditorium is 32 inches long on the drawing, its actual length would be 32 x 8 = 256 inches or 21.3 feet. Therefore, the missing value in the ratio 3 inches : ____ feet is 2.333 feet. (This is obtained by dividing 84 inches by 36 inches, which is equivalent to 3 feet. Then multiplying the result by 3 inches, which gives 7/12 or 0.5833 feet or 7 inches. This can be written as 2.333 feet.)
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Based on statistics from a worldwide health organization, in 2005 there were 31. 6 million people worldwide living with a certain disease, and 2. 4 million deaths from the disease. By , 2015 the number of people living with the disease had fallen to 27. 3 million, and 1. 2 million deaths were reported. Find the percent change for each statistic, and write any conclusions you can draw
There was a decrease of approximately 13.6% in the number of people living with the disease from 2005 to 2015.
There was a decrease of 50% in the number of deaths from the disease from 2005 to 2015.
To calculate the percent change, we'll use the following formula:
Percent Change = ((New Value - Old Value) / Old Value) * 100
Let's calculate the percent change for each statistic:
1. Number of people living with the disease:
Percent Change = ((27.3 million - 31.6 million) / 31.6 million) * 100
≈ (-4.3 million / 31.6 million) * 100
≈ -0.136 * 100
≈ -13.6%
Conclusion: There was a decrease of approximately 13.6% in the number of people living with the disease from 2005 to 2015.
2. Number of deaths from the disease:
Percent Change = ((1.2 million - 2.4 million) / 2.4 million) * 100
≈ (-1.2 million / 2.4 million) * 100
≈ -0.5 * 100
≈ -50%
Conclusion: There was a decrease of 50% in the number of deaths from the disease from 2005 to 2015.
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Rob spends 1/2 of his earnings this weeks on bills and then buys a video game for $25. 75. How many much of his earnings from this week does rob have left?
Rob has (1/2) * x - $25.75 of his earnings left from this week. This is obtained by subtracting the amount spent on bills and the cost of the video game from his total earnings.
To find out how much of his earnings Rob has left, we need to calculate the portion he spent and subtract it from his total earnings.
Given that Rob spends 1/2 of his earnings on bills, he has 1 - 1/2 = 1/2 of his earnings remaining.
If Rob buys a video game for $25.75, we can subtract this amount from his remaining earnings.
Let's say Rob's total earnings for the week were x dollars.
Amount spent on bills: (1/2) * x
Amount spent on the video game: $25.75
Remaining earnings: x - [(1/2) * x + $25.75]
Simplifying the expression, we have:
Remaining earnings: x - (1/2) * x - $25.75
Remaining earnings: (1/2) * x - $25.75
So, Rob has (1/2) * x - $25.75 of his earnings left from this week.
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Which could be used to solve this equation? 3 and one-fifth n = 9 Subtract 3 and one-fifth from both sides of the equation. 3 and one-fifth minus 3 and one-fifth n = 9 3 and one-fifth Add 3 and one-fifth to both sides of the equation. 9 3 and one-fifth = 12 and one-fifth.
To solve the equation 3 and one-fifth n = 9, we can use the method of subtracting or adding the same value to both sides of the equation to isolate the variable.
In this case, we can subtract 3 and one-fifth from both sides or add 3 and one-fifth to both sides of the equation.
To solve the equation 3 and one-fifth n = 9, we can subtract 3 and one-fifth from both sides of the equation, which gives us:
3 and one-fifth n - 3 and one-fifth = 9 - 3 and one-fifth.
Simplifying the left side of the equation, we get:
n = 9 - 3 and one-fifth.
Alternatively, we can add 3 and one-fifth to both sides of the equation, which gives us:
3 and one-fifth n + 3 and one-fifth = 9 + 3 and one-fifth.
Simplifying the left side of the equation, we get:
n = 9 + 3 and one-fifth.
In either case, we have isolated the variable n and obtained the solution by either subtracting or adding the same value to both sides of the equation.
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An acute triangle A B C has three heights AD, BE and CF respectively. Prove that the perimeter of triangle DEF is not over half of the perimeter of triangle ABC.
The perimeter of triangle DEF is not over half of the perimeter of triangle ABC.This is proven below.
How to illustrate tej proofGiven: Triangle ABC is acute with heights AD, BE, and CF.
To prove: Perimeter of triangle DEF is not over half of the perimeter of triangle ABC.
1. Let the side lengths of triangle ABC be a, b, and c.
2. Then the lengths of the heights are h1 = a/2, h2 = b/2, and h3 = c/2.
3. The perimeter of triangle ABC is a + b + c.
4. The perimeter of triangle DEF is h1 + h2 + h3 = a/2 + b/2 + c/2.
5. 1/2 < 1, so a/2 + b/2 + c/2 < a + b + c.
6. Therefore, the perimeter of triangle DEF is not over half of the perimeter of triangle ABC.
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Tommy walks 2 miles to school each morning. During his walk he sees billboards every 1/5 of a mile. How many billboards does he see each morning?
Tommy walks 2 miles to school each morning, and he sees a billboard every 1/5 of a mile.
To find out how many billboards he sees, we can divide the total distance he walks (2 miles) by the distance between each billboard (1/5 of a mile).
Number of billboards = Total distance / Distance between billboards
= 2 miles / (1/5 mile)
= 2 miles * (5/1)
= 10 billboards
Therefore, Tommy sees 10 billboards each morning.
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There are 212 grams of sugar in a 2 liter bottle of soda. how many grams of sugar are there in a 3 liter bottle
There would be 318 grams of sugar in a 3-liter bottle of soda. To determine the number of grams of sugar in a 3-liter bottle of soda, we can set up a proportion using the given information about the 2-liter bottle.
Let's assume that x represents the number of grams of sugar in a 3-liter bottle. We can set up the proportion: 2 liters is to 212 grams as 3 liters is to x grams.
Using cross-multiplication, we have 2 * x = 3 * 212. Solving for x, we get: x = (3 * 212) / 2 = 636 / 2 = 318 grams.Therefore, there would be 318 grams of sugar in a 3-liter bottle of soda.
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Jillian is trying for the cross country team. To make it she must run 3 1/2 miles in less than 40 minutes. will jillian make the team
The 11.43 minutes is less than 12 minutes, Jillian has a good chance of making the team. Therefore, Jillian might make the cross country team.
Jillian is trying for the cross country team. To make it she must run 3 1/2 miles in less than 40 minutes.
To find out if Jillian will make the cross country team, we must check if she can run 3 1/2 miles in less than 40 minutes. The time required for Jillian to run one mile is found by dividing 40 minutes by 3.5:40 / 3.5 = 11.43Jillian must complete one mile in 11.43 minutes to be eligible for the cross country team.
Since ,11.43 minutes is less than 12 minutes, Jillian has a good chance of making the team. Therefore, Jillian might make the cross country team.
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Write a Polynomial in standard form with a degree of 6 with only complex solutions.
A polynomial in standard form with a degree of 6 and only complex solutions can be represented as P(x) = (x - z₁)(x - z₂)(x - z₃)(x - z₄)(x - z₅)(x - z₆), where z₁, z₂, z₃, z₄, z₅, and z₆ are complex numbers.
A polynomial in standard form with a degree of 6 is written as P(x) = a₆x⁶ + a₅x⁵ + a₄x⁴ + a₃x³ + a₂x² + a₁x + a₀, where a₆ ≠ 0 and a₀, a₁, a₂, a₃, a₄, a₅, and a₆ are coefficients.
To ensure that the polynomial has only complex solutions, we need to make sure that all of its roots are complex numbers.
Complex numbers have the form a + bi, where a and b are real numbers and i is the imaginary unit (√(-1)).
By factoring the polynomial into linear factors, we can ensure that each factor (x - zᵢ) contributes a complex root.
Here, z₁, z₂, z₃, z₄, z₅, and z₆ represent complex numbers.
Since the polynomial has a degree of 6, we need six complex factors to form the polynomial.
The product of these factors will give us the desired polynomial with complex solutions.
Therefore, the polynomial in standard form with a degree of 6 and only complex solutions can be represented as P(x) = (x - z₁)(x - z₂)(x - z₃)(x - z₄)(x - z₅)(x - z₆), where z₁, z₂, z₃, z₄, z₅, and z₆ are complex numbers.
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Select the correct answer.
Solve the exponential equation for X.
216 6(41 +11)
OA.
I = 2
OB.
I = -2
OC.
I = 3
OD.
= -3
The given equation is I = -2OD where I is the intensity of light, O is the aperture of the lens and D is the distance between the lens and the object. This equation is known as the Inverse Square Law of Light.
The equation states that the intensity of light decreases as the square of the distance between the object and the ens increases. This means that if we double the distance between the object and the lens, the intensity of light becomes 1/4th of its original value.Similarly, if we triple the distance between the object and the lens, the intensity of light becomes 1/9th of its original value. This law is applicable to all types of light sources, including natural light sources like the sun and artificial light sources like bulbs.One practical application of this law is in photography. If a photographer wants to capture an image of a subject that is far away, they need to use a lens with a larger aperture to let in more light. This will ensure that the image is bright and clear even when the distance between the subject and the camera is large.Similarly, if a photographer wants to capture an image of a subject that is close to the camera, they need to use a lens with a smaller aperture to reduce the amount of light that enters the camera. This will prevent the image from being overexposed and washed out.Overall, the Inverse Square Law of Light is an important principle that governs the behavior of light in various applications, including photography, cinematography, and physics.For such more question on Square Law
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For the functions f(x)=3x2+3x+2andg(x)=2x2−2x+3, find:
The sum of f(x) = 3x^2 + 3x + 2 and g(x) = 2x^2 - 2x + 3 is 5x^2 + x + 5, while the difference is x^2 + 5x - 1. These results are obtained by adding and subtracting the corresponding terms of the two functions.
To find the sum and difference of the functions f(x) = 3x^2 + 3x + 2 and g(x) = 2x^2 - 2x + 3, we add and subtract the corresponding terms.
For the sum, we add the like terms: (3x^2 + 2x^2) + (3x - 2x) + (2 + 3) = 5x^2 + x + 5.
For the difference, we subtract the like terms: (3x^2 - 2x^2) + (3x + 2x) + (2 - 3) = x^2 + 5x - 1.
Therefore, the sum of the functions is given by f(x) + g(x) = 5x^2 + x + 5, and the difference of the functions is given by f(x) - g(x) = x^2 + 5x - 1.
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asap please and thank you
The correct statement is given as follows:
The can of pringles has a z-score close to zero, which means it's more likely to happen.
How to interpret z-scores?The z-score formula is given as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
In which:
X is the measure.[tex]\mu[/tex] is the population mean.[tex]\sigma[/tex] is the population standard deviation.The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, and can be positive(above the mean) or negative(below the mean).
The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure represented by X in the distribution.
The z-score for pretzels is given as follows:
Z = (25 - 23)/1.2
Z = 1.67.
The z-score for pringles is given as follows:
Z = (40 - 34)/4
Z = 1.5. -> closer to zero -> more likely to happen.
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Jema has a 45% coupon for a new curling iron. She buys the curling iron for a final price of $49. 95 after the discount is taken off. What is the original cost of the curling iron? Round to the nearest cent if necessary
The original cost of the curling iron was approximately $90.82.
Jema had a 45% coupon for a new curling iron, which means she was eligible for a discount of 45% on the original cost of the curling iron. The final price she paid after the discount was $49.95. To find out the original cost of the curling iron, we can use the formula:
Original cost = Final price / (1 - Discount rate)
In this case, since the discount rate is 45%, or 0.45 as a decimal, the formula becomes:
Original cost = $49.95 / (1 - 0.45)
Original cost = $49.95 / 0.55
Original cost ≈ $90.82
Therefore, the original cost of the curling iron was approximately $90.82.
This calculation shows that Jema took advantage of a significant discount on the original cost of the curling iron. By using the coupon, she was able to save around $41.87 on the purchase. This demonstrates the importance of looking for discounts and deals when shopping, as they can help save money and get more value for your purchases.
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