Responde las siguientes preguntas
4. Expresa en lenguaje algebraico: el dinero ahorrado que tienen Luis y Julio juntos en el
banco, si se sabe que Julio tiene el triple de ahorro que Luis.
Answers
The algebraic expression for the total money saved by Luis and Julio together is 4L.
Let's denote the amount of money saved by Luis as 'L'. According to the given information, Julio has triple the savings of Luis, so we can represent Julio's savings as '3L'.
To express the total money saved by Luis and Julio together, we can use algebraic notation. Let's denote the total savings as 'S'. It can be expressed as:
S = L + 3L
Simplifying the expression, we have:
S = 4L
Therefore, the algebraic expression for the total money saved by Luis and Julio together is 4L.
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Related Questions
what is 28.5 inches in height?
Answers
ONLY ANSWER IF YOU KNOW. What is the probability that either event will occur?
Answers
Answer:
0.67
Step-by-step explanation:
Hope this helps!
Round 87,365,241 to the nearest ten million,
Answers
Answer:
i don't know
Step-by-step explanation:
Answer:
90,000,000 or 90 million
Scenario 1A Calculate the following amounts for a participating provider who bills Medicare and has no deductible left. Submitted charge (based on provider’s regular fee) $650 Medicare participating physician fee schedule (PFS) $450 Coinsurance amount (20% paid by) $ Medicare payment (80 percent of the PFS) $ Provider write-off $ Scenario 1B Calculate the following amounts for a participating provider who bills Medicare and remaining annual deductible for the patient. Submitted charge (based on provider’s regular fee) $650 Medicare participating physician fee schedule (PFS) $450 Patient pays $100 remaining on their deductible $ Remaining amount for Insurance and patient to pay $ (PFS - $100) Coinsurance amount (20% of remaining amount) $ Total paid by patient (deductible & 20% of remaining) $ Medicare payment (80 percent of the remaining amount) $ Provider write-off $
Answers
Scenario 1A:
Coinsurance amount is $90
Medicare payment is $360
Provider write-off is $290
Scenario 1B:
Remaining amount for Insurance and patient to pay is $350
Coinsurance amount is $70
Total paid by patient is $170
Medicare payment is $280
Provider write-off is $370
Scenario 1A:
Submitted charge: $650
Medicare participating physician fee schedule (PFS): $450
Coinsurance amount (20% paid by patient): $
Medicare payment (80% of the PFS): $
Provider write-off: $
To calculate the missing amounts, we can use the provided information:
Coinsurance amount (20% paid by patient):
Coinsurance amount = 20% of the Medicare participating physician fee schedule (PFS)
Coinsurance amount = 0.2 * $450 = $90
Medicare payment (80% of the PFS):
Medicare payment = 80% of the Medicare participating physician fee schedule (PFS)
Medicare payment = 0.8 * $450 = $360
Provider write-off:
Provider write-off = Submitted charge - Medicare payment
Provider write-off = $650 - $360 = $290
Scenario 1B:
Submitted charge: $650
Medicare participating physician fee schedule (PFS): $450
Patient pays $100 remaining on their deductible
Remaining amount for Insurance and patient to pay: $
Coinsurance amount (20% of remaining amount): $
Total paid by patient (deductible & 20% of remaining): $
Medicare payment (80% of the remaining amount): $
Provider write-off: $
To calculate the missing amounts, we can use the provided information:
Remaining amount for Insurance and patient to pay:
Remaining amount for Insurance and patient to pay = PFS - remaining deductible
Remaining amount for Insurance and patient to pay = $450 - $100 = $350
Coinsurance amount (20% of remaining amount):
Coinsurance amount = 20% of the remaining amount
Coinsurance amount = 0.2 * $350 = $70
Total paid by patient (deductible & 20% of remaining):
Total paid by patient = remaining deductible + coinsurance amount
Total paid by patient = $100 + $70 = $170
Medicare payment (80% of the remaining amount):
Medicare payment = 80% of the remaining amount
Medicare payment = 0.8 * $350 = $280
Provider write-off:
Provider write-off = Submitted charge - Medicare payment
Provider write-off = $650 - $280 = $370
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Evaluate the expression for p = 3.
2p =
Answers
Answer:
6
Step-by-step explanation:
2 x 3
Which expressions are equivalent to 8(-10x+3.5y-7) Select two options
Negative 80 x + 24.5 y minus 56
Negative 80 x + 28 y minus 56
80 x + 28 y + 56
4 (negative 20 x + 7 y minus 14)
Negative 4 (negative 20 x + 7 y minus 14)
Answers
Answer:
Negative 80 x + 28 y minus 56
4 (negative 20 x + 7 y minus 14)
students in an ap statistics class were asked how many hours of television they watch per week (including online streaming). this sample yielded an average of 4.73 hours, with a standard deviation of 4.11 hours. is the distribution of number of hours students watch television weekly symmetric? if not, what shape would you expect this distribution to have? explain your reasoning.
Answers
Based on the information provided, it is likely that the distribution of the number of hours students watch television weekly is not perfectly symmetric and might have a slight right-skew.
To determine if the distribution of the number of hours students watch television weekly is symmetric, we can consider the characteristics of the average and the standard deviation.
In a symmetric distribution, the mean (average) and the median are equal, and the data values are distributed evenly on both sides of the mean. Additionally, the standard deviation provides information about the spread of the data.
Given that the average number of hours is 4.73 hours, it suggests that the distribution is not perfectly symmetric. If the distribution were symmetric, we would expect the mean and the median to be very close or equal. However, we cannot conclude definitively without further information about the median.
To determine the shape of the distribution, we can look at the standard deviation of 4.11 hours. A larger standard deviation indicates a wider spread of data points around the mean.
Based on the information provided, it is likely that the distribution of the number of hours students watch television weekly is not perfectly symmetric and might have a slight right-skew. This means that there may be a concentration of data points towards the lower end of the distribution, with a tail extending towards higher values.
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In a recent survey, the proportion of adults who indicated mystery as their favorite type of book was 0.325. Two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0.325. Simulation A will consist of 1,500 trials with a sample size of 100. Simulation B will consist of 2,000 trials with a sample size of 50. Which of the following describes the center and variability of simulation A and simulation B?
Answers
Option c) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B
According to the information given in the question,
A true proportion of 0.325 represents that the two simulations will be conducted for sampling proportions from a population
Simulation A -
Sample size - 100
Trials - 1500
Simulation B -
Sample size - 50
Trials - 2000
Now due to the relation of simulation A and simulation B, they are closely equal-
The total sample size of simulation A= 1500 x 100
= 150000
The total sample size of simulation B = 2000 x 50
= 100000
From the above calculations of simulations A and B, we can see that while comparing the,
Sample Size = Simulation A > Simulation B
Variability = Simulation B < Simulation B
Therefore, option c) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B is correct.
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In a recent survey, the proportion of adults who indicated mystery as their favorite type of book was 0.325. Two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0.325. Simulation A will consist of 1,500 trials with a sample size of 100. Simulation B will consist of 2,000 trials with a sample size of 50. Which of the following describes the center and variability of simulation A and simulation B?
A) The centers will roughly be equal, and the variabilities will roughly be equal.
B) The centers will roughly be equal, and the variability of simulation A will be greater than the variability of simulation B.
C) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B.
D) The center of simulation A will be greater than the center of simulation B, and the variability of simulation A will roughly be equal to the variability of simulation B.
E) The center of simulation A will be less than the center of simulation B, and the variability of simulation A will be greater than the variability of simulation B.
Anyone wanna help me
Answers
Answer:
w^2 -18w + 81
Step-by-step explanation:
Simply, what we have to do here is to divide the coefficient of w by 2, then square it
we have this as -18/2 = -9
Squaring is -9^2 = 81
How many permutations can be formed from all of the letters of the word houston?.
Answers
Answer: 2,520 distinct permutations can be formed from all of the letters of the word Houston.
find the area between a large loop and the enclosed small loop of the curve r = 2 + 4 cos(3θ).
Answers
Therefore, the area between the large loop and the small loop of the curve r = 2 + 4cos(3θ) is 70π/3.
To find the area between the large loop and the small loop of the curve, we need to find the points of intersection of the curve with itself.
Setting the equation of the curve equal to itself, we have:
2 + 4cos(3θ) = 2 + 4cos(3(θ + π))
Simplifying and solving for θ, we get:
cos(3θ) = -cos(3θ + 3π)
cos(3θ) + cos(3θ + 3π) = 0
Using the sum to product formula, we get:
2cos(3θ + 3π/2)cos(3π/2) = 0
cos(3θ + 3π/2) = 0
3θ + 3π/2 = π/2, 3π/2, 5π/2, 7π/2, ...
Solving for θ, we get:
θ = -π/6, -π/18, π/6, π/2, 5π/6, 7π/6, 3π/2, 11π/6
We can see that there are two small loops between θ = -π/6 and π/6, and two large loops between θ = π/6 and π/2, and between θ = 5π/6 and 7π/6.
To find the area between the large loop and the small loop, we need to integrate the area between the curve and the x-axis from θ = -π/6 to π/6, and subtract the area between the curve and the x-axis from θ = π/6 to π/2, and from θ = 5π/6 to 7π/6.
Using the formula for the area enclosed by a polar curve, we have:
A = 1/2 ∫[a,b] (r(θ))^2 dθ
where a and b are the angles of intersection.
For the small loops, we have:
A1 = 1/2 ∫[-π/6,π/6] (2 + 4cos(3θ))^2 dθ
Using trigonometric identities, we can simplify this to:
A1 = 1/2 ∫[-π/6,π/6] 20 + 16cos(6θ) + 8cos(3θ) dθ
Evaluating the integral, we get:
A1 = 10π/3
For the large loops, we have:
A2 = 1/2 (∫[π/6,π/2] (2 + 4cos(3θ))^2 dθ + ∫[5π/6,7π/6] (2 + 4cos(3θ))^2 dθ)
Using the same trigonometric identities, we can simplify this to:
A2 = 1/2 (∫[π/6,π/2] 20 + 16cos(6θ) + 8cos(3θ) dθ + ∫[5π/6,7π/6] 20 + 16cos(6θ) + 8cos(3θ) dθ)
Evaluating the integrals, we get:
A2 = 80π/3
Therefore, the area between the large loop and the small loop of the curve r = 2 + 4cos(3θ) is:
A = A2 - A1 = (80π/3) - (10π/3) = 70π/3
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Ronald drank orange juice from a 500 ml bottle. He found that 2/5 was remaining. How much did he drink?
Answers
Answer:
200ml
Step-by-step explanation:
2/5 of 500ml
=2/5*500
=1000/5
=200ml
T/F: at each iteration of the algorithm, the correct position in the sorted section is found for the next element in the unsorted section.
Answers
True.
In an algorithm like insertion sort, at each iteration, the algorithm finds the correct position in the sorted section for the next element in the unsorted section.
The algorithm iterates through the unsorted section, compares each element with the elements in the sorted section, and inserts the element in the correct position to maintain the sorted order.
This process continues until all elements in the unsorted section are inserted into their correct positions, resulting in a fully sorted array.
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Multiply.
(2x2 – 3x + 1)(x2 - 4x - 3)
O A. 3x2 - 7x-2
O B. 2A - 11x3 + 7x2 + 5x - 3
O C. 2x4 + 12x2 – 3
O D. 244 - 4x2 + 12x-3
Answers
B. 2x^4-11x^3+7x^2+5x-3
HELP
What is the measure of an exterior angle of a regular 45-gon?
Answers
Answer:Sum of exterior angle of any polygon is 360o . As each exterior angle is 45o , number of angles or sides of the polygon is 360o45o=8 . Further as each exterior angle is 45o , each interior angle is 180o−45o=135o .
Step-by-step explanation: hope this helps ;)
Answer:
8
Step-by-step explanation:
Import customs officials sometimes randomly select crates of cargo for close, but time-consuming, inspection. Suppose there are nine crates of cargo from the following companies, and customs officials will randomly select four for close inspection. Random Nuber To do this, use the numerical labels attached to the previous names and the following list of random digits. Read the list of random digits from left to right, starting at the beginning of the list. 74803 12009 45287 71753 98230 66419 84533 11793 04951 20597 11384 The simple random sample is
Answers
The simple random sample is Cherryport, Dallhoise, Foxwood, and Sapphire.
What is the meaning of probability in math?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.Three Types of Probability
Classical: (equally probable outcomes) Let S=sample space (set of all possible distinct outcomes). Relative Frequency DefinitionSubjective Probability.the list of random digits from left to right, starting at the beginning of the list.
74803 12009 45287 71753 98230 66419 84533 11793 04951 20597 11384
The simple random sample is Cherryport, Dallhoise, Foxwood, and Sapphire.
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CC has the following beginning balances in its stockholders' equity accounts on January 1, 2012: Common Stock, $100,000; Additional Paid-in Capital, $4,100,000; and Retained Earnings, $3,000,000. Net income for the year ended December 31, 2012, is $800,000. Court Casuals has the following transactions affecting stockholders' equity in 2012:
May 18 Issues 25,000 additional shares of $1 par value common stock for $40 per share.
May 31 Repurchases 5,000 shares of treasury stock for $45 per share.
July 1 Declares a cash dividend of $1 per share to all stockholders of record on July 15. Hint: Dividends are not paid on treasury stock.
July 31 Pays the cash dividend declared on July 1.
August 10 Reissues 2,500 shares of treasury stock purchased on May 31 for $48 per share.
Taking into consideration all the entries described above, prepare the statement of stockholders' equity for the year ended December 31, 2012.
Answers
Total stockholders’ equity 7,800,000
Statement of stockholders’ equity for CC for the year ended December 31, 2012:Particulars Amount ($)
Common Stock 100,000
Additional Paid-in Capital 4,100,000
Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000
Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
Total stockholders’ equity 7,800,000
Explanation:The given information is as follows:Common Stock on January 1, 2012 = $100,000Additional Paid-in Capital on January 1, 2012 = $4,100,000
Retained Earnings on January 1, 2012 = $3,000,000Net Income for the year ended December 31, 2012 = $800,000Cash Dividend Declared on July 1 and paid on July 31 = $200,000
To prepare the statement of stockholders’ equity for the year ended December 31, 2012, we will begin by preparing the opening balances of each of the equity accounts. We will then add the net income to the retained earnings account.
The closing balance for retained earnings is then computed by subtracting the cash dividend declared and paid from the total retained earnings. Finally, the total stockholders' equity is calculated by adding the balances of all the equity accounts.
Calculations:Opening balance of common stock = $100,000
Opening balance of additional paid-in capital = $4,100,000
Opening balance of retained earnings = $3,000,000
Net Income for the year ended December 31, 2012 = $800,000
Retained earnings (Opening Balance) = $3,000,000
Add: Net Income for the year ended December 31, 2012 = $800,000
Total retained earnings = $3,800,000Less: Cash Dividend Declared on July 1 and paid on July 31 = $200,000Retained earnings (Closing balance) = $3,600,000
Total stockholders’ equity = Common Stock + Additional Paid-in Capital + Retained Earnings (Closing balance) = $100,000 + $4,100,000 + $3,600,000 = $7,800,000
Therefore, the statement of stockholders’ equity for CC for the year ended December 31, 2012, is as follows:Particulars Amount ($)
Common Stock 100,000
Additional Paid-in Capital 4,100,000
Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000
Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
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The school choir is printing t-shirts for its members. The printing company charges a certain amount for each shirt plus a setup fee of $30. There are 28 students in the choir. If there are 28 students in the club and the t-shirt order costs a total of $295, how much does each t-shirt cost?
Answers
Answer:
Each t-shirt costs about $9.46
Step-by-step explanation:
We can represent as the function
\(f(x)=28x+30\)
\(295=28x+30\)
\(265=28x\)
\(x=9.46\)
Answer:
That's the 9.46
Step-by-step explanation:
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a fishing boat accidentally spills 15 barrels of diesel oil into the ocean. each barrel contains 42 gallons. if the oil film on the ocean is 2.5 x 102 nm thick, how much area in square meters will the oil slick cover? assume 1 gal
Answers
The area in square meters will the oil slick cover is 9.5×10⁶ m².
15 barrels of diesel spilt into the ocean, where each barrel contains 42 gallons. Thereby the total volume of the oil spilt by 15 barrels is calculated as follows:
The total volume of the oil spilt by 15 barrels = 15× 42 gallons.
=630 gallons
1 gallon = 3.78541 liters
Volume in L = 630 gallons × 3.78541 liters/ 1 gallon
= 2384.8083 L
1 L = 10⁻³ m³
2384.8083 L = 2384.8083 × 10⁻³ m³
= 2.3848083 m³
The area covered by the oil spill has to be determined, where the thickness of the oil spill is given to be 2.5×10² nm.
1 nm = 10⁻⁹ m
Thereby, 2.5×10² nm = 2.5×10²×10⁻⁹ m
= 2.5×10⁻⁷ m
Area (m²) = volume (m³)/thickness (m)
= 2.3848083 m³/ 2.5×10⁻⁷ m
= 0.95392×10⁷ m²
= 9.5×10⁶ m²
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Matti is making moonshine in the woods behind his house. He’s
selling the moonshine in two different sized bottles: 0.5 litres
and 0.7 litres. The price he asks for a 0.5 litre bottle is 8€, for
a
Answers
Based on the calculation, it appears that Matti had approximately 94 bottles of 0.5 litres and 11 bottles of 0.7 litres in the last patch of moonshine that he sold.
To solve the problem using the determinant method (Cramer's rule), we need to set up a system of equations based on the given information and then solve for the unknowns, which represent the number of 0.5 litre bottles and 0.7 litre bottles.
Let's denote the number of 0.5 litre bottles as x and the number of 0.7 litre bottles as y.
From the given information, we can set up the following equations:
Equation 1: 0.5x + 0.7y = 16.5 (total volume of moonshine)
Equation 2: 8x + 10y = 246 (total earnings from selling moonshine)
We now have a system of linear equations. To solve it using Cramer's rule, we'll find the determinants of various matrices.
Let's calculate the determinants:
D = determinant of the coefficient matrix
Dx = determinant of the matrix obtained by replacing the x column with the constants
Dy = determinant of the matrix obtained by replacing the y column with the constants
Using Cramer's rule, we can find the values of x and y:
x = Dx / D
y = Dy / D
Now, let's calculate the determinants:
D = (0.5)(10) - (0.7)(8) = -1.6
Dx = (16.5)(10) - (0.7)(246) = 150
Dy = (0.5)(246) - (16.5)(8) = -18
Finally, we can calculate the values of x and y:
x = Dx / D = 150 / (-1.6) = -93.75
y = Dy / D = -18 / (-1.6) = 11.25
However, it doesn't make sense to have negative quantities of bottles. So, we can round the values of x and y to the nearest whole number:
x ≈ -94 (rounded to -94)
y ≈ 11 (rounded to 11)
Therefore, based on the calculation, it appears that Matti had approximately 94 bottles of 0.5 litres and 11 bottles of 0.7 litres in the last patch of moonshine that he sold.
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Question
Matti is making moonshine in the woods behind his house. He’s selling the moonshine in two different sized bottles: 0.5 litres and 0.7 litres. The price he asks for a 0.5 litre bottle is 8€, for a 0.7 litre bottle 10€. The last patch of moonshine was 16.5 litres, all of which Matti sold. By doing that, he earned 246 euros. How many 0.5 litre bottles and how many 0.7 litre bottles were there? Solve the problem by using the determinant method (a.k.a. Cramer’s rule).
What is the sign of \dfrac bc c b start fraction, b, divided by, c, end fraction? Choose 1 answer: Choose 1 answer: (Choice A) A Positive (Choice B) B Negative (Choice C) C Zero
Answers
Answer:
A Positive
Step-by-step explanation:
If we input the fraction given to us by using the text editor, we have:
\dfrac{b}{c}
OUTPUT:
\(\dfrac{b}{c}\)
The sign before that fraction term is known as positive.
Answer:
a. postive
Step-by-step explanation:
Evaluate (224 mm)(0.00557 kg)/(37.6 N) to three significant figures and express the answer in Sl units using an appropriate prefix. Express your answer in micrometer-kilograms per newton.
Answers
0.0013294918 kg·m/s^2 = 1.3294918 μg·μm/NTo evaluate the expression (224 mm)(0.00557 kg)/(37.6 N) and express the answer in SI units using an appropriate prefix, we need to convert the given values to SI units first.
1 mm = 1 × 10^(-3) m (millimeter to meter conversion)
1 kg = 1 kg (kilogram to kilogram conversion)
1 N = 1 kg·m/s^2 (newton to kilogram-meter per second squared conversion)
Converting the values, we have:
(224 mm)(0.00557 kg)/(37.6 N) = (224 × 10^(-3) m)(0.00557 kg)/(37.6 kg·m/s^2)
Simplifying the expression, we get:
(224 × 10^(-3) × 0.00557)/(37.6) = 0.0013294918 kg·m/s^2
To express the answer in micrometer-kilograms per newton, we convert the units:
1 kg = 1 × 10^6 μg (kilogram to microgram conversion)
1 m = 1 × 10^6 μm (meter to micrometer conversion)
Therefore, the answer is:
0.0013294918 kg·m/s^2 = 1.3294918 μg·μm/N
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if the system has a radius of 40 cm, what is the tangential acceleration (in m/s2) of a point on its outermost edge at t = 0.5 s?
Answers
The angular acceleration of the system times the system's radius, which is 40 cm, or 0.4 m, gives rise to the tangential acceleration at the system's farthest edge at time t = 0.5 s. Thus, 0.4 m/s2 is the tangential acceleration.
The radius of the system multiplied by the system's angular acceleration gives the tangential acceleration of a point at its furthest edge. The system's radius in this instance is 40 cm, or 0.4 metres, and the time is 0.5 seconds. As a result, the tangential acceleration at time t = 0.5 s is equal to the system's angular acceleration times its radius, which is 0.4 m. We multiply the angular acceleration by the system's radius, which is 0.4 m, to determine the tangential acceleration. Thus, 0.4 m/s2 is the tangential acceleration at time t = 0.5 s. This indicates that a point on the system's outermost edge accelerates by 0.4.
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are the expression -7 + -2 and -7 - 2 equivalent why or why not? include the solutions for each expression for full credit
Answers
Answer:
Yes, they are both equal.
Step-by-step explanation:
This is because in both cases, you are subtracting, -7 + -2 = -9. -7 - 2 = -9.
let m be the number of php2,300.000 monthly payments made to purchase a colored tv set brainly
Answers
#carryonlearning
#learningwithbrainly
Answer:
what
Step-by-step explanation:
wot
u2+6u27=0(solve the equation) help
Answers
Answer:
u=0
Step-by-step explanation:
Find the missing factor 8^3=(-2x)(A)
Answers
-256.
how? 8 times 8 times 8 is 512.
512/2 is 256. But two negatives make a positive. So, it's -256.
what is the probability to get a sample average of 51 or more customers if the manager had not offered the discount?
Answers
The probability to get a sample average of 51 or more customers if the manager had not offered the discount is 1.36%
We can use the formula for the standard error of the mean to calculate the standard deviation of the sample means. The standard error of the mean is given by:
standard error of the mean = standard deviation / √(sample size)
In this case, the standard error of the mean is:
standard error of the mean = 10 / √(6) = 4.08
To find the probability of observing a sample mean of 51 or more customers, we need to standardize the sample mean using the standard error of the mean. This gives us the z-score, which we can use to look up the probability in a standard normal distribution table.
The z-score is given by:
z-score = (sample mean - population mean) / standard error of the mean
In this case, the population mean is 42, and the sample mean is 51. Therefore, the z-score is:
z-score = (51 - 42) / 4.08 = 2.21
Using Table 1 (or a calculator or statistical software), we can find that the probability of observing a z-score of 2.21 or higher is approximately 0.0136 or 1.36%.
This means that if the manager had not offered the discount, there would be a 1.36% chance of observing a sample mean of 51 or more customers.
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Complete Question:
A small hair salon in Denver, Colorado, averages about 42 customers on weekdays with a standard deviation of 10. It is safe to assume that the underlying distribution is normal. In an attempt to increase the number of weekday customers, the manager offers a $4 discount on 6 consecutive weekdays. She reports that her strategy has worked since the sample mean of customers during this 6-weekday period jumps to 51. Use Table 1.
What is the probability to get a sample average of 51 or more customers if the manager had not offered the discount?
Which fraction has a repeating decimal as its decimal expansion?
3/25
3/16
3/11
3/8
Answers
Answer:
3/11
Step-by-step explanation:
3/11 equals 0.272727273 which is a repeating decimal.
Answer:
3/11 is C
Step-by-step explanation:
Solve dy/dx=1/3(sin x − xy^2), y(0)=5
Answers
The general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is: y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5
To solve this differential equation, we can use separation of variables.
First, we can rearrange the equation to get dy/dx on one side and the rest on the other side:
dy/dx = 1/3(sin x − xy^2)
dy/(sin x - xy^2) = dx/3
Now we can integrate both sides:
∫dy/(sin x - xy^2) = ∫dx/3
To integrate the left side, we can use substitution. Let u = xy^2, then du/dx = y^2 + 2xy(dy/dx). Substituting these expressions into the left side gives:
∫dy/(sin x - xy^2) = ∫du/(sin x - u)
= -1/2∫d(cos x - u/sin x)
= -1/2 ln|sin x - xy^2| + C1
For the right side, we simply integrate with respect to x:
∫dx/3 = x/3 + C2
Putting these together, we get:
-1/2 ln|sin x - xy^2| = x/3 + C
To solve for y, we can exponentiate both sides:
|sin x - xy^2|^-1/2 = e^(2C/3 - x/3)
|sin x - xy^2| = 1/e^(2C/3 - x/3)
Since the absolute value of sin x - xy^2 can be either positive or negative, we need to consider both cases.
Case 1: sin x - xy^2 > 0
In this case, we have:
sin x - xy^2 = 1/e^(2C/3 - x/3)
Solving for y, we get:
y = ±√[(sin x - 1/e^(2C/3 - x/3))/x]
Note that the initial condition y(0) = 5 only applies to the positive square root. We can use this condition to solve for C:
y(0) = √(sin 0 - 1/e^(2C/3)) = √(0 - 1/e^(2C/3)) = 5
Squaring both sides and solving for C, we get:
C = 3/2 ln(1/25)
Putting this value of C back into the expression for y, we get:
y = √[(sin x - e^(x/2)/25)/x]
Case 2: sin x - xy^2 < 0
In this case, we have:
- sin x + xy^2 = 1/e^(2C/3 - x/3)
Solving for y, we get:
y = ±√[(e^(2C/3 - x/3) - sin x)/x]
Again, using the initial condition y(0) = 5 and solving for C, we get:
C = 3/2 ln(1/25) + 2/3 ln(5)
Putting this value of C back into the expression for y, we get:
y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x]
So the general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is:
y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5
y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x], if sin x - xy^2 < 0 and y(0) = 5
Note that there is no solution for y when sin x - xy^2 = 0.
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