The customers of Rhythm Time, an online music service, downloaded 397,970 songs last year.
How many songs did they download?Rhythm Time, an online music service, had 278,579 songs downloaded this year by its customers. That figure is 30% less than last year. Last year
We can begin by assuming that the total number of songs downloaded last year was x. According to the problem statement, 278,579 songs were downloaded this year, which is 30% less than last year. We can write it as an equation:x - 0.30x = 278,579 Simplifying, we get:0.70x = 278,579 Dividing both sides by 0.70, we get:x = 397,970Therefore, last year, Rhythm Time's customers downloaded 397,970 songs.
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4. What is the solution to 2 + 3(2a + 1) = 3(a + 2)?
Answer:
a=1/3
Step-by-step explanation:
First, expand the brackets by doing multiplication:
2+6a+3=3a+6
Then, move the unknown to the left and the numbers to the right:
3a=6-5
3a=1
a=1/3
The solution to the given equation is -1.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
The given equation is 2+3(2a+1)=3(a+2)
2+6a+3=3a+2
6a+5=3a+2
6a-3a=2-5
3a=-3
a=-1
Therefore, the solution to the given equation is -1.
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18. The signs show the costs of different games at a math festival. How much would it cost n people to play Decimal Decisions and Ratio Rage? MAIHEEST DECITAL PROBABILITY DECISIONS POSSIBILITIES Cost (s) of 1 Game: 12.70 -n +9 Cost(s) of 1 Game: 5.5-3 RATIO RAGE! Cost (5) of 1 Game
The cost of playing Ratio Rage is provided by the equation "Cost(s) of 1 expression Game: 5.5-3 RATIO RAGE!", but we don't know the value of the game's ratio.
what is expression ?An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematic, and form. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.
The equation "Cost (s) of 1 Game: 12.70 - n +9" gives the cost of playing Decimal Decisions, but we don't know the number of n, thus we can't determine the overall cost for a group of n persons.
Similarly, the cost of playing Ratio Rage is provided by the equation "Cost(s) of 1 Game: 5.5-3 RATIO RAGE!", but we don't know the value of the game's ratio.
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Solution of inequality ((x - 1)(x - 5))/(x - 3) > 0
Answer:
(1, 3) ∪ (5, ∞)
Step-by-step explanation:
You want the solution to the inequality ((x -1)(x -5))/(x -3) > 0.
Sign changesThe sign of the function changes at values of x that make the factors zero, at x = 1, 3, 5. The function is positive for x > 5, so will also be positive for 1 < x < 3
The solution is ...
1 < x < 3 or 5 < x
__
Additional comment
If any linear factor has an even degree (even multiplicity), there will not be a sign change. The numerator factors correspond to function zeros. The denominator factors correspond to function vertical asymptotes.
The attached graph shows zeros at x=1 and x=5, and a vertical asymptote with a sign change at x=3.
Nicolas drinks to third liter of water in the morning and 1/2 liter of water at lunch during basketball practice he drinks another 2/3 liter of water. What is the total amount of water in liters that Nicolas drinks?
Nicolas drinks 3/2 liters of water in total - 1/3 liters of water in the morning, 1/2 liter of water at lunch, and 2/3 liter of water during basketball practice.
Nicolas drinks to third liter of water in the morning, which is 1/3 liters of water. At lunchtime, he drinks 1/2 litre of water. During basketball practice, he drinks another 2/3 liter of water.
To find the total amount of water that Nicolas drinks, we need to add these quantities together:
Total amount of water = 1/3 + 1/2 + 2/3
To add these fractions, we need to find a common denominator, which is 6 in this case. We can convert each fraction to have a denominator of 6 as follows:
1/3 = 2/6
1/2 = 3/6
2/3 = 4/6
Now we can add the fractions with the same denominator:
Total amount of water = 2/6 + 3/6 + 4/6
Total amount of water = 9/6
We can simplify this fraction by dividing both the numerator and denominator by 3:
Total amount of water = 3/2
Therefore, Nicolas drinks 3/2 litres of water in total.
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What is the value of X?
Answer: 8
Step-by-step explanation:
The sum of the interior angles in a triangle in 180.
So we can add up all the values and set it equal to 180 to find x.
4x + (5x + 5) + 103 = 180
9x + 108 = 180
9x = 72
x = 8
Answer:
x=8
Step-by-step explanation:
4x+5x+5+103=180
9x+108=180
9x=180-108
9x=72
x=72÷9
x=8
I need to show my work please help
Answer: m= 2 n =7
Step-by-step explanation:
i think to find the answer you can make the sides equal each other so 7m+4 = 9m 2m=4m m =2
and for the other angle
2n-1 = n+6 n - 1 = 6 n = 7
Write the HCF of x
3y
4z
2 and x
2y
3z
5, where x, y, z are
distinct prime numbers
the HCF of x, 2y, 3y, 4z, x², 3z, and 5, where x, y, z are
distinct prime numbers is 1.
To find the highest common factor (HCF) of the given numbers, we need to find the common factors of each pair of numbers and then find the highest common factor of all the resulting common factors.
First, let's find the prime factors of the given numbers:
x = a prime number (distinct from y and z)
2y = 2 × y
3y = 3 × y
4z = 2² × z
3z = 3 × z
x² = a prime number squared (distinct from y and z)
5 = a prime number
Next, we can pair up the numbers and find their common factors:
Common factors of x and 2y: 1, 2, y
Common factors of 3y and 4z: 1, 2, 3, y, z, 6
Common factors of x² and 3z: 1, 3, x, z, xz
Common factors of 5 and 2: 1
Finally, we find the highest common factor of all the resulting common factors:
The highest common factor of x, 2y, 3y, 4z, x², 3z, and 5 is 1, since it is the only factor that is common to all the pairs.
Therefore, the HCF of x, 2y, 3y, 4z, x², 3z, and 5 is 1.
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1- Label the lengths of the 3-on 3 court (perimeter only).
2- Explain how you calculated the court's length and width.
the perimeter of the 3-on-3 court is 86 meters.
Why it is?
The lengths of the 3-on-3 court (perimeter only) are:
Length: 28 meters
Width: 15 meters
To calculate the length and width of the 3-on-3 court, we can use the dimensions provided by FIBA, the international basketball federation. According to FIBA, the official size of a 3-on-3 court is 15 meters in width and 28 meters in length.
The perimeter of the 3-on-3 court is the sum of all four sides, which can be calculated as follows:
Perimeter = 2 × Length + 2 × Width
Substituting the values of length and width from FIBA's dimensions, we get:
Perimeter = 2 × 28 meters + 2 × 15 meters = 56 meters + 30 meters = 86 meters
Therefore, the perimeter of the 3-on-3 court is 86 meters. It's important to note that the dimensions of the court may vary depending on the location and the level of play, so it's always a good idea to check the official regulations before setting up a court.
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The grades on a midterm were Normally distributed with a mean of 120 and a standard deviation of 17. The passing score was 111 or higher. Use the z-table to answer the question.
What percent of students passed the midterm?a. 10%
b. 50%
c. 70%
d. 62%
The percentage of students passing the partial exam is:
Option c. 70%
What is the percentage of students passing the partial exam?To answer this question, we use the Z-table. We have:
Given, mean (μ) = 120 and standard deviation (σ) = 17
Passing Score = 111
To find out what percentage of students passed the midterm, we need to find the probability that a score picked at random from the distribution is greater than or equal to 111. We can convert this score into a standard score (Z-score) using the Z-table. We have:
Z-score = (111 - μ) / σ
= (111 - 120) / 17
= -0.53
Using the Z-table, we can find the area (probability) to the left of this Z-score as follows:
Area to the left of Z-score = 0.2981 (from Z-table)
The area to the right of this Z-score (i.e. the probability that a score picked at random from the distribution is greater than or equal to 111) is:
Area to the right of Z-score = 1 - 0.2981
= 0.7019
= 70.19%
Therefore, the percentage of students who passed the midterm is approximately 70% (Option C).
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Answer:
C. 70%
Step-by-step explanation:
The Tire Rack, America’s leading online distributor of tires and wheels, conducts extensive testing to provide customers with products that are right for their vehicle, driving style, and driving conditions. In addition, the Tire Rack maintains an independent consumer survey to help drivers help each other by sharing their long-term tire experiences. The following data show survey ratings (1 to 10 scale with 10 the highest rating) for 18 maximum performance summer tires (Tire Rack website, February 3, 2009). The variable Steering rates the tire’s steering responsiveness, Tread Wear rates quickness of wear based on the driver’s expectations, and Buy Again rates the driver’s overall tire satisfaction and desire to purchase the same tire again. (Data is in TireRack file)
1. Develop an estimated regression equation that can be used to predict the Buy Again rating given based on the Steering rating. At the .05 level of significance, test for a significant relationship. Interpret the coefficients (Say what they mean in terms of change in you corresponding to a change in x)
2. Did the estimated regression equation developed in part (a) provide a good fit to the data? Explain.
3. Develop an estimated regression equation that can be used to predict the Buy Again rating given the Steering rating and the Tread Wear rating.
4. Is the addition of the Tread Wear independent variable significant? Use 0.05 level of significance.
1 Tire Steering read WeaBuy Again 2 Goodyear 8.9 8.5 8.1 3 Michelin F89 9 8.3 4 Michelin H 8.3 8.8 8.2 5 Dunlop SI 8.2 8.5 7.9 6 Goodyear 7.9 7.7 7.1 7 Yokoham 84 8.2 8.9 8 Yokoham 7.9 7 7.1 9 Kumho P 7.9 7.9 8.3 10 Goodyear 7.6 5.8 4.5 11 Hankook 7.8 6.8 6.2 12 Michelin E 7.4 4.8 13 IMichelin N7 14 Michelin S 6.9 15 Kumho 776.6 16 Dunlop SI 6.2 4.2 17 Bridgestof 5.7 5.5 18 Goodyear 5.7 5.4 19 Dunlop SI57 5 5 34 3.6 2.9 3.3
Tire Steering Tread Wear Buy Again
Goodyear Assurance TripleTred 8.9 8.5 8.1
Michelin HydroEdge8.9 9 8.3
Michelin Harmony 8.3 8.8 8.2
Dunlop SP 60 8.2 8.5 7.9
Goodyear Assurance ComforTred 7.9 7.7 7.1
Yokohama Y372 8.4 8.2 8.9
Yokohama Aegis LS4 7.9 7 7.1
Kumho Power Star 758 7.9 7.9 8.3
Goodyear Assurance 7.6 5.8 4.5
Hankook H406 7.8 6.8 6.2
Michelin Energy LX4 7.4 5.7 4.8
Michelin MX4 7 6.5 5.3
Michelin Symmetry 6.9 5.7 4.2
Kumho 722 7.2 6.6 5
Dunlop SP 40 A/S 6.2 4.2 3.4
Bridgestone Insignia SE200 5.7 5.5 3.6
Goodyear Integrity 5.7 5.4 2.9
Dunlop SP20 FE 5.7 5 3.3
Show transcribed image text
The survey ratings provide valuable feedback for drivers who are looking for quality tires for their vehicles. These ratings can give insight on steering responsiveness, how quickly a tire wears, and overall customer satisfaction. Drivers can also see how their tire of choice stacks up against other tires, making it easier to make an informed decision when shopping for tires.
The Tire Rack is America’s leading online distributor of tires and wheels. They conduct extensive testing to ensure that customers are provided with the most suitable tires for their vehicles, driving styles, and driving conditions. They also use an independent consumer survey to help drivers gain insight on long-term tire experiences.
The following data show survey ratings on a 1-10 scale, with 10 being the highest rating, of 18 maximum performance summer tires, as of February 3, 2009 (Tire Rack website). The variables are Steering (steering responsiveness), Tread Wear (quickness of wear), and Buy Again (overall tire satisfaction and desire to purchase the same tire again). The Yokohama Aegis LS4 has a Steering rating of 7.9, Tread Wear rating of 7, and Buy Again rating of 7.1. The Dunlop SP20 FE has a Steering rating of 5.7, Tread Wear rating of 5, and Buy Again rating of 3.3.
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Given ΔABC with measure of angle B equals 78 degrees, measure of angle C equals 52 degrees, and a = 16 inches, what is the length of b?
To find the length of side b in triangle ABC, we can use the Law of Sines. The length of side b is approximately 20.058 inches.
To find the length of side b in triangle ABC, we can use the Law of Sines. The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides and angles in a triangle.
Using the Law of Sines, we have:
sin(A)/a = sin(B)/b
We are given the measure of angle B as 78 degrees and side a as 16 inches. We can substitute these values into the equation:
sin(A)/16 = sin(78)/b
To find sin(A), we can use the fact that the sum of the angles in a triangle is 180 degrees:
A + B + C = 180
A + 78 + 52 = 180
A = 180 - 78 - 52
A = 50 degrees
Now we can substitute the values into the equation again:
sin(50)/16 = sin(78)/b
To solve for b, we can cross-multiply and isolate b:
b = (16 * sin(78))/sin(50)
We can calculate the length of side b by evaluating this expression using a calculator. The measurement will be roughly 20.058 inches.
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Could you please answer b and d
I will mark brainliest for the first answer
Answer: 50 uk pounds
Step-by-step explanation:
Step-by-step explanation:
See image below
a new surgery is successful of the time. if the results of such surgeries are randomly sampled, what is the probability that at least of them are successful? carry your intermediate computations to at least four decimal places, and round your answer to two decimal places. (if necessary, consult a list of formulas.)
The probability that at least one surgery is successful, given that a new surgery is successful 80% of the time, is 99.20%.
Let X denote the number of successful surgeries out of n randomly selected surgeries. The random variable X follows a binomial distribution. The probability of X = x successful surgeries out of n randomly selected surgeries is given by:
P(X=x)=nCxp^x(1−p)^n−x
where p is the probability that a new surgery is successful, and (1-p) is the probability that a new surgery is unsuccessful. In this case, p = 0.80 and (1-p) = 0.20. Let n = 5. Then, we have:
P(X≥1)=1−P(X=0)=1−nC0p0(1−p)n−0
=1−(0.20)5
=0.9936 ≈ 99.20%
Therefore, the probability that at least one surgery is successful is 99.20%.
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A savings account is started with an initial deposit of $500. The account earns 1.5% interest compounded
annually.
swer:
(a) Write an equation to represent the amount of money in the account as a function of time in years.
(b) Find the amount of time it takes for the account balance to reach $800. Show your work.
Answer:
Step-by-step explanation:
(a) The formula to calculate the amount of money in the account after t years with an initial deposit of P and an annual interest rate r compounded annually is:
A = P(1 + r)^t
In this case, P = $500, r = 0.015 (1.5% expressed as decimal), and the interest is compounded annually, so the equation is:
A = 500(1 + 0.015)^t
Simplifying this gives:
A = 500(1.015)^t
Therefore, the equation that represents the amount of money in the savings account as a function of time in years is A = 500(1.015)^t.
(b) To find the amount of time it takes for the account balance to reach $800, we can set the equation A = 500(1.015)^t equal to 800 and solve for t:
500(1.015)^t = 800
Dividing both sides by 500:
(1.015)^t = 1.6
Taking the natural logarithm of both sides:
ln(1.015)^t = ln(1.6)
Using the power rule of logarithms:
t ln(1.015) = ln(1.6)
Dividing both sides by ln(1.015):
t = ln(1.6) / ln(1.015)
Using a calculator:
t ≈ 24.7
Therefore, it takes approximately 24.7 years for the account balance to reach $800.
Find the coordinates of the midpoint of the line segment with the endpoints J(−2, 3) and K(4, −1)
Answer:
jwjwi7svwisg, I have y2ywgeu
-11 +23-46+ (-12)
how to solve it
Answer:
-46
Step-by-step explanation:
-11 +23-46+ (-12) =
12 - 46 + (-12) =
-34 - 12 =
-46
The organizer of a late night street fair in a popular tourist city wants to analyze the relationship between daily revenue and the following variables: the number of male visitors, the number of female visitors, the number of retail stands, the number of food (and beverage) stands, and the number of performances that take place on a given night. The regression output table is provided below. Based on these results and using a 10% significance level, the organizer thinks he can improve the model. He wants to try removing at least one variable from the analysis to create and compare new models. Which variable or variables would you recommend that he consider removing from the regression model? SELECT ALL THAT APPLY.
The variables that the organizer can consider removing from the regression model are the Number of male visitors and Number of performance.
Based on the regression table provided, we can answer this question. The following is the regression table:Regression output table for night street fair variableNameCoefficientStandard Errort-StatP-ValueConstantb0.340.1402.430.023Number of male visitorsb10.6130.51320.750.462Number of female visitorsb10.9070.57918.830.000Number of retail standsb0.1160.0452.570.016Number of food (and beverage) standsb0.3160.0575.500.000Number of performanceb0.1460.1071.360.184The null hypothesis is rejected if p-value < 0.1; that is, there is a significant difference between the independent and dependent variables. The p-value of the Number of male visitors, the Number of female visitors, the Number of retail stands, the Number of food (and beverage) stands, and the Number of performances variables are 0.462, 0.000, 0.016, 0.000, and 0.184, respectively. As a result, the variables that are significant at the 10% level are the Number of female visitors, the Number of retail stands, and the Number of food (and beverage) stands. Therefore, the organizer should consider removing the Number of male visitors and Number of performance variables from the regression model. The variables that the organizer can consider removing from the regression model are the Number of male visitors and Number of performance.
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if you randomly select a card from a well-shuffled standard deck of 52 cards, what is the probability that the card you select is a diamond or 9? (your answer must be in the form of a reduced fraction.)
The probability of selecting a diamond or 9 is 1/13.
Step by step explanation: There are 4 suits (diamonds, clubs, hearts, and spades) and 13 ranks (2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace). The probability of selecting a card from a standard deck of 52 cards is 1/52.
To calculate the probability of selecting a diamond or a 9, you must first calculate the total number of diamonds and nines in the deck, which is 8 (4 diamonds and 4 nines). The probability of selecting a diamond or 9 is 8/52, which reduces to 1/13.
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how many 5-letter passords can be made using the letters a thought z if... a) repetition of letters is allowed? b) repetition of letters is not allowed?
Answer:
Order is important: If allowed 11881376
Order is important:If rep. Is not allowed 7893600
Step-by-step explanation:
If the order isnt important and repetition is not allowed 65780
If order isn’t important and repetition is allowed 142506
Use the equation to explain why the rule is a linear function
The linear function rule is y = (1/5)x - 5 .
What is a linear equation, exactly?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. There are numerous instances of linear equations, including 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3.
The graph of a linear function is a straight line.
f(0) = -5 means that (0,-5) is a point on the line. Similarly, (-5,-6) is also a point on the line.
Slope of line = m = [-6-(-5)]/[-5-0] = -1/(-5) = 1/5
Using the point-slope form, an equation of the line is:
y - (-5) = (1/5)(x - 0)
So, y = (1/5)x - 5
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The complete question is -
Write a rule for a linear function y=f (x), given that f (0) =-5 and f (-5) =-6. Write answers using fractions or integers.
The function rule is f(x) =
Fay read an article that said 26%, percent of Americans can speak more than one language. She wants to test if this figure is higher in the city she lives, so she plans on taking a sample of people to see what proportion of them speak more than one language.
Let p represent the proportion of people in Fay's city that speak more than one language.
Which of the following is an appropriate set of hypotheses for her significance test?
Answer:
The appropriate set of hypotheses for Fay's significance test is:
Null Hypothesis: p = 0.26 (the proportion of people in Fay's city who can speak more than one language is the same as the national average)
Alternative Hypothesis: p > 0.26 (the proportion of people in Fay's city who can speak more than one language is higher than the national average)
In other words, Fay is testing if the proportion of people in her city who speak more than one language is significantly different from the national average of 26%. The null hypothesis assumes that the proportion is the same as the national average, while the alternative hypothesis assumes that it is higher.
To conduct her significance test, Fay would need to collect a random sample of people from her city and determine how many of them speak more than one language. Based on this sample proportion, she can calculate a test statistic and determine if it is significantly different from what would be expected under the null hypothesis. If the test statistic is sufficiently large, she can reject the null hypothesis and conclude that the proportion of people in her city who speak more than one language is higher than the national average.
Step-by-step explanation:
Answer:4
Step-by-step explanation:
4
consider the following page reference string: 0, 1, 7, 0, 1, 2, 0, 1, 2, 3, 2, 7, 1, 0, 3, 1, 0, 3 how many page faults would occur for the following page replacement algorithms? assume no pre-paging occurs, and show what pages are in memory at each given time. three frames are allocated to the process.
a. fifo b. optimal c. lru
Will rate after, make sure answer is correct show work
In the following question, among the conditions given, For the page reference string provided, the number of page faults for the following page replacement algorithms are as follows: A. FIFO: 8-page faults, B. Optimal: 6-page faults, C. LRU: 7-page faults.
To learn about them in brief-
A. FIFO: 8-page faults
At each given time, the pages in memory are:
Step 1: 0
Step 2: 0, 1
Step 3: 0, 1, 7
Step 4: 0, 1, 2
Step 5: 0, 1, 2
Step 6: 0, 1, 2
Step 7: 0, 1, 2
Step 8: 0, 1, 3
Step 9: 2, 7, 1
Step 10: 2, 0, 3
Step 11: 2, 1, 0
Step 12: 2, 1, 3
Step 13: 2, 0, 3
Step 14: 1, 0, 3
Step 15: 1, 2, 0
B. Optimal: 6-page faults
At each given time, the pages in memory are:
Step 1: 0
Step 2: 0, 1
Step 3: 0, 1, 7
Step 4: 0, 1, 2
Step 5: 0, 2, 3
Step 6: 1, 2, 3
Step 7: 1, 0, 3
Step 8: 1, 2, 0
Step 9: 1, 0, 3
Step 10: 2, 0, 3
Step 11: 2, 1, 0
Step 12: 2, 1, 3
Step 13: 2, 0, 3
Step 14: 1, 0, 3
Step 15: 1, 2, 0
C. LRU: 7-page faults
At each given time, the pages in memory are:
Step 1: 0
Step 2: 0, 1
Step 3: 0, 1, 7
Step 4: 0, 1, 2
Step 5: 0, 1, 2
Step 6: 1, 0, 2
Step 7: 1, 0, 3
Step 8: 1, 2, 0
Step 9: 2, 0, 3
Step 10: 2, 1, 0
Step 11: 2, 1, 3
Step 12: 0, 1, 3
Step 13: 0, 2, 3
Step 14: 1, 2, 3
Step 15: 1, 0, 3
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What is the percent change of 31 to 7
The percent change of 31 to 7 is found as 77.42% which is percent decrease of the number.
Explain about percent change?You can determine the amount of change that has occurred over this time period if you have data at two points in time. The outcome is known as the rate of change, sometimes known as the percentage change, and is given in percentage form (in absolute numbers, it really is merely a difference).
Using a percentage is one method of calculating a percent of change. Keep in mind that a percentage indicates "per 100." You can rephrase your problem as a % out of 100 by first describing the change as a fraction and measuring the amount of change to the original.
Original number = 31
Final number = 7
percent change = (7 - 31)/31 *100
percent change = - 24*100 / 31
percent change = - 77.42
Here negative sign shows the percent decrease of the number.
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how can i slove this??
Answer:
[tex]5x {}^{3} - x + 5x + 2[/tex]
Step-by-step explanation:
Greetings!!!
So to find the sum of (f+g)(x) just simply add these two functions
f(x)+g(x)3x²+5x-2+(5x³-4x²+4)Add like terms together
5x³-x²+5x+2If you have any questions tag it on comments
Hope it helps!!!
A 64-foot tall monument casts a shadow 16 feet long. If Kyle is standing nearby and 6’3” tall, find the length of his shadow.
All monuments cast a shadow when the sun is shining, as they block the sunlight and create a shadow on the ground or nearby surfaces. T
What is the monument casts a shadow?The size and shape of the shadow will depend on the position of the sun in the sky, the orientation of the monument, and its size and shape.
Some famous monuments that cast impressive shadows include the Pyramids of Giza, the Eiffel Tower, the Washington Monument, and the Stonehenge.
We can use proportions to solve the problem.
Let x be the length of Kyle's shadow.
We know that the length of the monument's shadow is 16 feet, and its height is [tex]64 f[/tex] Feet. So the ratio of the length of the monument's shadow to its height is:
[tex]16/64 = 1/4[/tex]
This ratio is equal to the ratio of Kyle's shadow length to his height:
[tex]x/6.25 = 1/4[/tex]
To solve for x, we can cross-multiply:
[tex]x = 6.25/4 = 1.5625[/tex]
Therefore, the length of Kyle's shadow is approximately [tex]1.56[/tex] feet (or [tex]18.72 inches)[/tex] .
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n one region of the country, the mean length of stay in hospitals is 5.5 days with standard deviation 2.6 days. Because many patients stay in the hospital for considerably more days, the distribution of length of stay is strongly skewed to the right. Consider random samples of size 100 taken from the distribution with the mean length of stay, x, recorded for each sample. Which of the following is the best description of the sampling distribution of x ?a.Strongly skewed to the right with mean 5.5 days and standard deviation 2.6 daysb, Strongly skewed to the right with mean 5.5 days and standard deviation 0.26 dayc. Strongly skewed to the right with mean 5.5 days and standard deviation 0.026 dayd. Approximately normal with mean 5.5 days and standard deviation 2.6 dayse. Approximately normal with mean 5.5 days and standard deviation 0.26 day
(e): Approximately normal with mean 5.5 days and standard deviation 0.26 days.
What is standard deviation?
Standard deviation is a measure of the spread or dispersion of a set of data from its mean or average. It measures how far the values in a dataset are from the mean of the dataset.
The sample size needed for this approximation to hold depends on the shape of the population distribution, but a commonly used rule of thumb is that a sample size of at least 30 is sufficient for most cases.
In this case, the sample size is 100, which is larger than 30, so we can use the central limit theorem to approximate the sampling distribution of the sample mean.
The mean of the population distribution is 5.5 days, and the standard deviation is 2.6 days. The standard deviation of the sampling distribution of the sample mean can be approximated using the formula:
standard deviation of the sample mean = standard deviation of the population / square root of sample size
= 2.6 / sqrt(100)
= 0.26
Therefore, the best description of the sampling distribution of x is option (e): approximately normal with mean 5.5 days and standard deviation 0.26 days.
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can someone help pls 16=3x-7/2
Answer: To solve the equation 16=3x-7/2, you can follow these steps:
Multiply both sides of the equation by 2 to get rid of the fraction:
16 * 2 = (3x - 7/2) * 2
32 = 6x - 7
Add 7 to both sides of the equation to isolate the term with x:
32 + 7 = 6x
39 = 6x
Divide both sides of the equation by 6 to solve for x:
39 / 6 = x
6.5 = x
Therefore, the solution to the equation 16=3x-7/2 is x = 6.5.
Step-by-step explanation:
Answer:
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ㅤㅤ [tex]\large{\blue{\star} \: {\underline{\boxed{\pmb{\tt{x = \dfrac{13}{2}}}}}}}[/tex]
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Step-by-step explanation:
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[tex]\large{\pmb{\tt{16 = 3x - \dfrac{7}{2}}}}[/tex]
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[tex]\large{\pmb{\tt{\leadsto{16 + \dfrac{7}{2} = 3x}}}}[/tex]
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[tex]\large{\pmb{\tt{\leadsto{\dfrac{2 \times 16 + 7}{2} = 3x}}}}[/tex]
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[tex]\large{\pmb{\tt{\leadsto{\dfrac{32 + 7}{2} = 3x}}}}[/tex]
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[tex]\large{\pmb{\tt{\leadsto{\dfrac{39}{2} = 3x}}}}[/tex]
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[tex]\large{\pmb{\tt{\leadsto{39 = 2 \times 3x}}}}[/tex]
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[tex]\large{\pmb{\tt{\leadsto{39 = 6x}}}}[/tex]
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[tex]\large{\pmb{\tt{\leadsto{\dfrac{\cancel{39}}{\cancel{6}} = x}}}}[/tex]
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[tex]\large{\purple{\boxed{\pmb{\tt{\leadsto{\dfrac{13}{2} = x}}}}}}[/tex]
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━━━━━━━━━━━
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[tex]\large{\underline{\underline{\sf{Verification:-}}}}[/tex]
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• Substituting the value of (x) in the given equation,
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[tex]\large{\pmb{\tt{\leadsto{16 = 3 \times \dfrac{13}{2} - \dfrac{7}{2}}}}}[/tex]
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[tex]\large{\pmb{\tt{\leadsto{16 = \dfrac{39}{2} - \dfrac{7}{2}}}}}[/tex]
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[tex]\large{\pmb{\tt{\leadsto{16 = \dfrac{39 - 7}{2}}}}}[/tex]
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[tex]\large{\pmb{\tt{\leadsto{16 = \dfrac{\cancel{32}}{\cancel{2}}}}}}[/tex]
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[tex]\large{\pmb{\tt{\leadsto{16 = 16}}}}[/tex]
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As LHS = RHS,
Hence Verified
In the figure below, m 24 = 106°. Find mZ1, m/2, and m 23. 1 X 3 2 ترا = 0° m 22 = ° m2 1 = m 23 = °
Answer:
m<1=74
m<2=106
m<3=74
Step-by-step explanation:
m<1:
=180-106
=74
m<2:
=106
m<3;
if m<1 is 74, m<s will also be 74
Find the volume of the cylinder given the height and radius shown.
14
21
Answer:
volume=12930.79
Step-by-step explanation:
[tex]v=\pi r^{2} h\\v=\pi (14)^{2} (21)\\v=12930.79[/tex]
consider a completely randomized design with k treatments. assume all pairwise comparisons of treatment means are to be made using a multiple comparisons procedure. determine the total number of pairwise comparisons for k.
The total number of pairwise comparisons for k is (k*(k-1))/2.
There are (k*(k-1))/2 pairwise comparisons in a completely randomized design with k treatments. For example, if there are 4 treatments, there will be 6 pairwise comparisons (4C2 = 6). Here's the explanation:In a completely randomized design, the treatments are randomly assigned to the experimental units. The main objective of such a design is to determine whether the treatment means are different from each other or not.To compare the treatment means, we use the mean square between treatments (MST) and mean square error (MSE). The test statistic used to compare the means is F = MST/MSE.The ANOVA table for a completely randomized design has the following format:Source of variationSum of SquaresDegrees of freedomMean SquareF-testtreatmentSS(k-1)k-1MST=MSTrMSEResidualSSTn-kMSEReference: https://www.stat.yale.edu/Courses/1997-98/101/anovar.htmNow, we need to compare each pair of treatments using a multiple comparisons procedure. A pairwise comparison involves comparing the means of two treatments only.The total number of pairwise comparisons is given by the combination formula:$$ \frac{k!}{2!(k-2)!} = \frac{k(k-1)}{2} $$Therefore, the total number of pairwise comparisons for k is (k*(k-1))/2.
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