Answer:
4.1 >
Step-by-step explanation:
Answer:
Among 4.1 and 4.085
4.1 is greater
:))
How do I find A’?
Let U={a,b,c,d,e,f,g} and A={a,b,e,f}
Let U={a,b,c,d,e,f,g,h}
A={a,c,d}
B={b,c,d}
C={b,e,f,g,h}
A toilet manufacturer has decided to come out with a new and improved toilet. The fixed cost for the production of this new toilet line is $16,600 and the variable costs are $63 per toilet. The company expects to sell the toilets for $160. Formulate a function C(x) for the total cost of producing x new toilets and a function R(x) for the total revenue generated from the sales of x toilets. How many toilets need to be sold to break even?
Answer:
C(x)=16600+63x
R(x)=160x
Break-even Point, x=172
Step-by-step explanation:
Let x be the number of Toilets Produced.
Fixed cost = $16,600
Variable costs = $63 per toilet.
Total Cost, C(x)=16600+63x
The company expects to sell the toilets for $160.
Selling Price Per Toilet=160
Total Revenue for x Toilets, R(x)=160x
Next, we determine the break-even point.
The break-even point is the point where the Cost of Production equals Revenue generated.
i.e. C(x)=R(x)
16600+63x=160x
16600=160x-63x
16600=97x
x=171.13
The company needs to sell at least 172 Toilets to break even.
To formulate the functions C(x) and R(x) for the total cost and revenue of producing and selling x toilets, we can use the given information about fixed costs, variable costs, and selling price. By setting the total cost equal to the total revenue, we can find the number of toilets needed to break even, which is approximately 171.
Explanation:To formulate the function C(x) for the total cost of producing x new toilets, we need to consider the fixed cost and the variable cost. The fixed cost is $16,600, which remains constant regardless of the number of toilets produced. The variable cost is $63 per toilet, so we multiply it by x to account for the number of toilets produced. Therefore, the function C(x) can be expressed as:
C(x) = 16,600 + 63x
The function R(x) for the total revenue generated from the sales of x toilets can be found by multiplying the selling price of each toilet by the number of toilets sold. Since each toilet is sold for $160, the function is:
R(x) = 160x
To find the number of toilets needed to break even, we need to determine the value of x when the total cost is equal to the total revenue. In other words, we set C(x) = R(x) and solve for x:
16,600 + 63x = 160x
Subtracting 63x from both sides:
16,600 = 97x
Dividing both sides by 97:
x = 170.10
Therefore, the company needs to sell approximately 171 toilets to break even.
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Write a real-world problem that can be represented by the equation 1/2x+6=20
Step-by-step explanation:
The given expression in word problem can be translated as:
Six more than half of a number is 20
A real-world problem for the equation 1/2x + 6 = 20 could be determing the number of days a person should work, earning a rate of half the square of the number of days, to achieve a total sum of $20. The person initially has $6 and after working for 28 days, he or she achieves the goal.
Explanation:Consider a real-world example represented by the equation 1/2x + 6 =20. Imagine your grandmother gives you $6 and says you can do chores for her on some days to earn half the square of the number of days you worked in dollars. If you want to accumulate $20 in total, how many days should you work? This problem asks the same as solving for 'x' in the equation where 'x' is the number of days and the total sum of money is $20.
To solve this, you would need to subtract 6 from both sides of the equation, leaving you with 1/2x =14. Then, you multiply both sides by 2 to get x = 28, so it takes 28 days of work.
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In the first semester, Jonas took seven tests in his math class. His scores were: 88 81 94 84 100 94 96.
What is the Median of his scores?
For a certain candy, 20% of the pieces are yellow, 5% are red, 5% are blue, 10% are green, and the rest are brown. a) If you pick a piece at random, what is the probability that it is brown? it is yellow or blue? it is not green? it is striped? b) Assume you have an infinite supply of these candy pieces from which to draw. If you pick three pieces in a row, what is the probability that they are all brown? the third one is the first one that is red? none are yellow? at least one is green?
Answer:
A) i) the probability it is brown = 60%. (ii)The probability it is yellow or blue = 25% (iii) The probability it is not green = 90% (iv)The probability it is striped =0%
B) i)The probability they are all brown = 21.6%. (ii) Probability the third one is the first one that is red = 4.51% (iii) Probability none are yellow = 51.2% (iv) Probability at least one is green = 27.1%
Step-by-step explanation:
A) The probability that it is brown is the percentage of brown we have. However, Brown is not listed, so we subtract what we are given from 100%. Thus;
100 - (20 + 5 + 5 + 10) = 100 - (40) = 60%.
The probability that one drawn is yellow or blue would be the two percentages added together: 20% + 5% = 25%.
The probability that it is not green would be the percentage of green subtracted from 100: 100% - 10% = 90%.
Since there are no striped candies listed, the probability is 0%.
B) Due to the fact that we have an infinite supply of candy, we will treat these as independent events.
Probability of all 3 being brown is found by taking the probability that one is brown and multiplying it 3 times. Thus;
The percentage of brown candy is 60% from earlier. Thus probability of all 3 being brown is;
0.6 x 0.6 x 0.6 = 0.216 = 21.6%
To find the probability that the first one that is red is the third one drawn, we take the probability that it is NOT red, 100% - 5% = 95% = 0.95
Now, for the first two and the probability that it is red = 5% = 0.05
Thus for the last being first one to be red = 0.95 x 0.95 x 0.05 = 0.0451 = 4.51%.
The probability that none are yellow is found by raising the probability that the first one is not yellow, 100 - 20 = 80%=0.80, to the third power:
0.80³ = 0.512 = 51.2%.
The probability that at least one is green is; 1 - (probability of no green).
We first find the probability that all three are NOT green:
0.90³ = 0.729
1 - 0.729 = 0.271 = 27.1%.
Final answer:
To find the probability of an event happening, divide the number of favorable outcomes by the total number of possible outcomes. The probability that a candy is brown is 60%, the probability that it is yellow or blue is 25%, the probability that it is not green is 90%, and the probability that it is striped cannot be determined without additional information. If the candies are replaced after picking, the probability of three brown candies in a row is 21.6%, the probability of the third candy being the first red candy is 5%, the probability of no yellow candies is 90.25%, and the probability of at least one green candy is 27.1%.
Explanation:
To find the probability of an event occurring, we divide the number of favorable outcomes by the total number of possible outcomes.
a) The probability of picking a brown candy is 100% - (20% + 5% + 5% + 10%) = 60%. The probability of picking a yellow or blue candy is 20% + 5% = 25%. The probability of not picking a green candy is 100% - 10% = 90%. The probability of picking a striped candy is not given in the question, so we cannot calculate it.
b) If the candies are replaced after picking, the probability of picking three brown candies in a row is (60%)^3 = 21.6%. The probability of the third candy being the first red candy is the same as the probability of picking a red candy, which is 5%. The probability of none of the candies being yellow is (100% - 5%)^2 = 90.25%. The probability of at least one candy being green is 1 - (100% - 10%)^3 = 27.1%.
Please Hurry 20 Points. Use your knowledge of scale drawings and image sizes to fill in the missing information in the table.
Empire State Building
Original Image
Actual Height (in feet)
1,450
1,450
1,450
Reduced Image
Model Height (in blocks)
145
Scale Factor
1/25
1 /50
Answer:
it 1595
Step-by-step explanation:
For the reduced image with a scale factor of 1/25, the model height is 58 blocks; with a 1/50 scale, it's 29 blocks.
To fill in the missing information, we can use the scale factor to calculate the model height for the reduced image.
For the reduced image with a scale factor of [tex]\( \frac{1}{25} \)[/tex], we can calculate the model height by dividing the actual height by the scale factor:
[tex]\[ \text{Model Height} = \frac{\text{Actual Height}}{\text{Scale Factor}} \][/tex]
[tex]\[ \text{Model Height} = \frac{1450}{25} = 58 \text{ blocks} \][/tex]
For the reduced image with a scale factor of [tex]\( \frac{1}{50} \)[/tex], we repeat the calculation:
[tex]\[ \text{Model Height} = \frac{1450}{50} = 29 \text{ blocks} \][/tex]
Now, the completed table looks like this:
| | Original Image | Reduced Image |
|-------------|----------------|---------------|
| Actual Height (in feet) | 1,450 | 1,450 |
| Model Height (in blocks) | - | 58 (1/25 scale) |
| | - | 29 (1/50 scale) |
Thus, the missing information in the table has been filled in using the scale factor and calculations based on the actual height of the Empire State Building.
5/4 - 4/4 ples tell me
The value of the expression 5/4 - 4/4 will be equal to 1 / 4.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The given expression is ( 5 / 4) - ( 4 / 4). The value of the expression will be solved as,
E = 5 / 4 - 4 / 4
E = (5 - 4) / 4
E = 1 / 4
Therefore, the value of the expression 5/4 - 4/4 will be equal to 1 / 4.
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A particular solution and a fundamental solution set are given for the nonhomogeneous equation below and its corresponding homogeneous equation. (a) Find a general solution to the nonhomogeneous equation. (b) Find the solution that satisfies the specified initial conditions.
y(1)--2, y'(1)-1, and y'(1)--36
Answer:
A.y=2x^5 + c1+ c2x + c3x^5
B. Y = 2x² + 9+7x+2x^5
Step-by-step explanation:
See attached file
Place all the nummbers from 1 to 6
Answer:
Step-by-step explanation:
1 2 3 4 5 6
If you are a student with no assets of any value and have liability insurance on an old car that pays a maximum of $50,000 per accident, what is most likely to happen if you cause an accident that results in $75,000 in damage to the passengers in another car?
A. They will not pursue any action against you or your insurance company
B. They will sue you, personally, for more than $100,000
C. They will accept the $50,000 maximum offered by your insurance company
D. They will sue for the entire $75,000
Answer:
They will accept the $50,000 maximum offered by your insurance company
In this scenario, with $50,000 liability insurance, if you cause a $75,000 accident, the other party is likely to accept the $50,000 from your insurance (Option C) but could also sue you for the remaining $25,000 (Option D).
In this scenario, if you cause an accident resulting in $75,000 in damage to the passengers in another car, your liability insurance has a maximum coverage limit of $50,000 per accident. Typically, insurance policies cover up to the policy limits, and the insurance company would pay out up to $50,000 to the injured parties.
The most likely outcome in this situation would be that the injured parties may initially pursue a claim with your insurance company, and the insurance company would pay up to its policy limit of $50,000. However, since the damages exceed the policy limit, the injured parties may still have the option to sue you personally for the remaining $25,000 to cover their damages.
So, the answer could be a combination of options C and D: They may accept the $50,000 maximum offered by your insurance company but could also potentially sue you for the remaining $25,000 if they believe it's necessary to cover their damages. The actual outcome may vary depending on the specific circumstances, local laws, and the decisions made by the injured parties and their legal advisors. It's crucial to notify your insurance company as soon as an accident occurs so they can handle the situation accordingly.
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Consider the following time series: t sales 1 6 2 11 3 9 4 16 5 17 Use simple linear regression analysis with t as the predictor variable to find the parameters for the line that minimizes MSE for this time series. Enter the data into Excel and use Excel for your calculations. Enter the exact answers. a) y-intercept, b0 = -0.67 b) slope, b1 = 0.31 What is the MSE if this model is used to forecast sales for time periods 1-5? c) MSE = What is the forecast for time period t = 6?\
Answer:
Check the explanation
Step-by-step explanation:
Period, X Actual , Y
1 6
2 11
3 9
4 16
5 17
Y= intercept + slope*x
Answer a and b:
INTERCEPT(known Y's,known X's) Slope(known Y's,known X's)
3.7 2.7
Simple linear regression equation is
Forecast, Y= 3.7+ 2.7*x
Period, X Actual , Y linear Absolute squared
trend deviation= deviation=
Forecast, |Forecast - (absolute
Y= 3.7+ 2.7*x Actual| deviation)^2
1 6 6.40 0.4 0.2
2 11 9.10 1.9 3.6
3 9 11.80 2.8 7.8
4 16 14.50 1.5 2.3
5 17 17.20 0.2 0.0
6 19.90
2.78
MSE
Answer c: MSE= 2.78
Answer d: Forecast for x= 6= 19.90
A cognitive psychologist wants to investigate whether memory for a shopping list is affected by the strategy used to study the list. She selects 20 random students and assigns each of them randomly to one of four different groups. Each group is given a different strategy by which to study the list. After the students study the list, they try to recall as many items as they can. The number of items remembered from the list for each students is given below.
Is there sufficient evidence to conclude that different strategies lead to different memory performance? Use significance level 0.05
Answer:
There is no sufficient evidence
Step-by-step explanation:
See attached files
is 0 an irrational
number
Answer: no
Step-by-step explanation:
0 is a rational number.A rational number is a number that can be expressed as the quotient or fraction m/n of two integers, a numerator m and a non-zero denominator n.0 can be expressed as 0/n ;therefore 0 is a rational number.SpymoreA small private college is interested in determining the percentage of its students who live off campus and drive to class. Specifically, it was desired to determine if less than 20% of their current students live off campus and drive to class. Find the large-sample rejection region for the test of interest to the college when using a level of significance of 0.01.
Answer:
The rejection region is the one defined by z<-2.326.
Step-by-step explanation:
We have to calculate the critical value for a test of hypothesis on the proportion of students of this college who live off campus and drive to class.
The sample is large enough, so we can use the z-statistic.
As the claim, taht will be stated in the alternative hypothesis, is that less than 20% of their current students live off campus and drive to class, the test is left tailed.
Alternative hypothesis:
[tex]Ha: \pi<0.20[/tex]
Then, for a significance level of 0.01, 99% of the data has to be over (or 1% below) this critical z-value.
In the standard normal distribution this z-value is z=-2.326.
[tex]P(z<-2.326)=0.01[/tex]
The critical value that divide the regions is z=-2.326. The rejection region is the one defined by z<-2.326.
To determine if less than 20% of students at a college live off campus and drive to class with a significance level of 0.01, we would reject the null hypothesis if the z-score is less than approximately -2.33. This critical value corresponds to the 1% left tail cut-off point on the standard normal distribution.
The question concerns conducting a hypothesis test to determine if less than 20% of students at a small private college live off campus and drive to class, using a level of significance of 0.01. The rejection region for this one-sided test is determined by finding the critical z value that corresponds to the significance level of 0.01. Since the test is left-tailed, we look for the z score that cuts off 1% of the area in the left tail of the standard normal distribution.
Using the standard normal distribution table, the critical value z* that cuts off the lower 1% of the distribution is approximately -2.33. Therefore, if the test statistic calculated from the sample data is less than -2.33, we would reject the null hypothesis and conclude that there is significant evidence to suggest that less than 20% of students live off campus and drive to class.
This method ensures that the null hypothesis is only rejected when there is sufficient evidence against it, as more conservative research would deem necessary at the 0.01 level of significance.
Simplify the expression 13+(x+8)=?
Answer:
x +21
Step-by-step explanation:
13+(x+8)=
Combine like terms
x +13+8
x +21
Which rational function models the time, y, in hours, that it takes the train to travel between the two cities at an average speed of x miles per hour?
y= x/6.4
y= x/160
y= 6.4/x
y= 160/x
Answer:
[tex]y=\frac{x}{6.4}[/tex]
Step-by-step explanation:
The complete question in the attached figure
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
In this problem, we have a proportional relationship between the average speed (x) and the time (y)
Find the constant of proportionality k
Fox =32, y=5
[tex]k=\frac{5}{32}[/tex]
substitute
[tex]y=\frac{5}{32}x[/tex]
we have
[tex]\frac{5}{32}=\frac{1}{6.4}[/tex]
therefore
[tex]y=\frac{x}{6.4}[/tex]
What is the solution to the system of equations graphed below?
A. (2, 4)
B. (4, 2)
C. (0, 6)
D. (6, 0)
Given:
Given that the graph of the system of equations.
We need to determine the solution to the system of equation.
Solution:
The solution to the system of equations is the point of intersection of these two lines.
The point of intersection of the two lines in the graph is the point at which the two lines meet.
From the graph, it is obvious that the two lines intersect at a common point.
Thus, the common point is the point of intersection of the two lines.
Hence, the point of intersection is (4,2)
Thus, the solution to the system of equation is (4,2)
Therefore, Option B is the correct answer.
Answer:
its B (4,2)
Step-by-step explanation:
Data on the numbers of hospital admissions resulting from motor vehicle crashes are given below for Fridays on the 6th of a month and Fridays on the following 13th of the same month. Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal. Construct a 95% confidence interval estimate of the mean of the population of differences between hospital admissions. Use the confidence interval to test the claim that when the 13th day of a month falls on a Friday, the numbers of hospital admissions from motor vehicle crashes are not affected.
Answer:
a) 95% confidence interval estimate of the mean of the population of differences between hospital admissions = (1.69, 11.91)
b) This confidence interval shows there is indeed a significant difference between the number of hospital admissions from motor vehicle crashes on Friday the 13th and the number of hospital admissions from motor vehicle crashes on Friday the 6th as the interval obtained doesn't contain a zero-value of difference.
Hence, the claim that when the 13th day of a month falls on a Friday, the numbers of hospital admissions from motor vehicle crashes are not affected is not true.
Step-by-step explanation:
The missing data from the question
The numbers of hospital admissions from motor vehicle crashes
Friday the 6th || 10 | 8 | 4 | 4 | 2
Friday the 13th | 12 | 10 | 12 | 14 | 14
The differences can then be calculated (number on the 13th - number on the 6th) and tabulated as
Friday the 6th || 10 | 8 | 4 | 4 | 2
Friday the 13th | 12 | 10 | 12 | 14 | 14
Differences ||| 2 | 2 | 8 | 10 | 12
To obtain the confidence interval, we need the sample mean and sample standard deviation.
Mean = (Σx)/N
= (2+2+8+10+12)/5 = 6.80
Standard deviation = σ = √[Σ(x - xbar)²/N]
Σ(x - xbar)² = (2-6.8)² + (2-6.8)² + (8-6.8)² + (10-6.8)² + (12-6.8)² = 84.8
σ = √[Σ(x - xbar)²/N] = √(84.8/5) = 4.12
Confidence Interval for the population's true difference between the number of hospital admissions from motor vehicle crashes on Friday the 6th and Friday the 13th is basically an interval of range of values where the population's true difference can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample true difference) ± (Margin of error)
Sample Mean = 6.8
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the sample true difference)
Critical value will be obtained using the t-distribution. This is because there is no information provided for the population mean and standard deviation.
To find the critical value from the t-tables, we first find the degree of freedom and the significance level.
Degree of freedom = df = n - 1 = 5 - 1 = 4.
Significance level for 95% confidence interval
(100% - 95%)/2 = 2.5% = 0.025
t (0.025, 4) = 2.776 (from the t-tables)
Standard error of the mean = σₓ = (σ/√n)
σ = standard deviation of the sample = 4.12
n = sample size = 5
σₓ = (4.12/√5) = 1.84
95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]
CI = 6.8 ± (2.776 × 1.84)
CI = 6.8 ± 5.10784
95% CI = (1.69216, 11.90784)
95% Confidence interval = (1.69, 11.91)
b) This confidence interval shows there is a significant difference between the number of hospital admissions from motor vehicle crashes on Friday the 13th and the number of hospital admissions from motor vehicle crashes on Friday the 6th as the interval obtained doesn't contain a difference of 0.
Hope this Helps!!!
A large moving box has a volume of 45 cubic meters. The width of the box i:
1.5 meters. The length and the height of the box are each whole number
measurements that are greater than 2 meters. What could be the dimension
the box? Give two possible answers,
Answer:
3x10, 6x5
Step-by-step explanation:
45 / 1.5 = 30
Find any two factors of 30 and you have an answer.
2x15 and 1x30 don't work because they are less than or equal to 2.
Answer:
3x10x1.5, 6x5x1.5
Step-by-step explanation:
45 / 1.5 = 30
Find any two factors of 30 and you have an answer.
2x15 and 1x30 don't work because they are less than or equal to 2.
Suppose the horses in a large stable have a mean weight of 975lbs, and a standard deviation of 52lbs. What is the probability that the mean weight of the sample of horses would differ from the population mean by less than 15lbs if 31 horses are sampled at random from the stable? Round your answer to four decimal places.
Answer:
0.8926 = 89.26% probability that the mean weight of the sample of horses would differ from the population mean by less than 15lbs if 31 horses are sampled at random from the stable
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
[tex]\mu = 975, \sigma = 52, n = 31, s = \frac{52}{\sqrt{31}} = 9.34[/tex]
What is the probability that the mean weight of the sample of horses would differ from the population mean by less than 15lbs if 31 horses are sampled at random from the stable?
pvalue of Z when X = 975 + 15 = 990 subtracted by the pvalue of Z when X = 975 - 15 = 960. So
X = 990
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{990 - 975}{9.34}[/tex]
[tex]Z = 1.61[/tex]
[tex]Z = 1.61[/tex] has a pvalue of 0.9463
X = 960
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{960 - 975}{9.34}[/tex]
[tex]Z = -1.61[/tex]
[tex]Z = -1.61[/tex] has a pvalue of 0.0537
0.9463 - 0.0537 = 0.8926
0.8926 = 89.26% probability that the mean weight of the sample of horses would differ from the population mean by less than 15lbs if 31 horses are sampled at random from the stable
Suppose shirts are one of 3 colors (red, blue, and purple) and pants are black, brown, or white. An outfit consists of a shirt and pants. What is the minimum number of people that need to be in a room together to guarantee that at least two of them are wearing same-colored outfits
Answer:
10 people
Step-by-step explanation:
Given:
Colors of shirts: 3 (red, blue, and purple)
Colors of pants: 3 (black, brown, or white)
Total number of outfits ( both shirts and pants) =
3 * 3 = 9
The minimum number of people that need to be in a room together to guarantee that at least two of them are wearing same-colored outfits will be:
Total number + 1
= 9 + 1
= 10 people
If L || m, solve for x (9x+2) 119
Alternate angles in a transversal are congruent.
The value of x is 13
See attachment for the image of the transversal,
Where [tex](9x + 2)[/tex] and [tex]119[/tex] are alternate angles
This means that:
[tex]9x + 2 = 119[/tex] ---- alternate angles are equal
Collect like terms
[tex]9x = 119 - 2[/tex]
[tex]9x = 117[/tex]
Divide both sides by 9
[tex]x = 13[/tex]
Hence, the value of x is 13
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jackie makes 15 dollars an hour by babysitting. George makes 18.50 for mowing the lawn. if jackie babysits for 4 hrs and george mows the lawn for 3 hours. who makes more money?
Answer:
Jackie
Step-by-step explanation:
Find how much each person makes by multiplying their hourly wage by hours worked
Jackie
hourly wage * hours worked
15*4=60
$60
George
hourly wage * hours worked
18.50*3=55.5
$55.50
Jackie made more money because 60>55.5
After calculating the total earnings, Jackie makes more money ($60) than George ($55.50) based on their hourly rates and the number of hours worked.
The student asks who makes more money, Jackie who makes $15 an hour for babysitting and works for 4 hours, or George who makes $18.50 an hour for mowing the lawn and works for 3 hours. To solve this, let's calculate the total money each person makes:
Jackie's earnings: 4 hours * $15/hour = $60George's earnings: 3 hours * $18.50/hour = $55.50Comparing the earnings, Jackie makes a total of $60, while George makes $55.50. Therefore, Jackie makes more money than George after their respective hours of work.
Find the area of the fairway between two streams on a golf course
What Is The Area Of The Trapezoid
Answer:
256 m2
Step-by-step explanation:
- First, know the formula A = (a+b/2)h
- Using this, we will fill the equation in with our variables. For example...
A = ((13+19)/2)16
A = (32/2)16
A = (16)(16)
A = 256 m2
- Hope this helps! If you need a further explanation or step by step practice please let me know.
if a rabbit can move 4/5 of a mile every hour then how many hours would it take for a rabbit to go 8 Miles
We want to find the maximum and minimum values of f(x,y)=12x2+13y2 on the disk D: x2+y2≤1. What is the critical point in D? (x,y)=( , ) Now focus on the boundary of D, and solve for y2. Restricting f(x,y) to this boundary, we can express f(x,y) as a function of a single variable x. What is this function and its closed interval domain? f(x,y)=f(x)= where ≤x≤ What are the absolute maximum and minimum values of the function along the BOUNDARY of D? maximum value: minimum value: What are the absolute maximum and minimum values of f(x,y) over all of D? maximum value: minimum value:
Answer:
Over the boundary: maximum:13, minimum:12
Over D: maximum:13, minimum:0
Step-by-step explanation:
We are given that [tex]f(x,y) = 12x^2+13y^2[/tex] and D is the disc of radius one. Namely, [tex]x^2+y^2\leq 1[/tex].
First, we want to find a critical point of the function f. To do so, we want to find the values(x,y) such that
[tex] \nabla f (x,y) =0[/tex].
Recall that [tex] \nabla f (x,y) = (\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y})[/tex].
So, let us calculate [tex] \nabla f (x,y)[/tex] (the detailed calculation of the derivatives is beyond the scope of the answer.
[tex]\frac{\partial f}{\partial x} = 24x[/tex]
[tex]\frac{\partial f}{\partial y} = 26y[/tex]
When equalling it to 0, we get that the critical point is (0,0), which is in our region D. Note that the function f is the sum of the square of two real numbers multiplied by some constants. Hence, the function f fulfills that [tex]f(x,y)\geq 0[/tex]. Note that f(0,0)=0, so without further analysis we know that the point (0,0) is a minimum of f over D.
If we restrict to the boundary, we have the following equation [tex] x^2+y^2=1[/tex]. Main idea is to replace the value of one of the variables n the function f, so it becomes a function of a single variable. Then, we can find the critical values by using differential calculus:
Case 1:
Let us replace y. So, we have that [tex]y^2=1-x^2[/tex]. So, [tex]f(x,y) = 12x^2+13(1-x^2) = -x^2+13[/tex].
So, we will find the derivative with respect to x and find the critical values. That is
[tex] \frac{df}{dx} = -2x=0[/tex]
Which implies that x =0. Then, [tex] y =\pm 1[/tex]. So we have the following critical points (0,1), (0,-1). Notice that for both points, the value of f is f(0,1) = f(0,-1) = 13. If we calculate the second derivative, we have that at x=0
[tex] \frac{d^2f}{dx^2} = -2<0[/tex]. By the second derivative criteria, we know that this points are local maximums of the function f.
Case 2:
Let us replace x. So, we have that [tex]x^2=1-y^2[/tex]. So, [tex]f(x,y) = 12(1-y^2)+13y^2 = y^2+12[/tex].
So, we will find the derivative with respect to y and find the critical values. That is
[tex] \frac{df}{dx} = 2y=0[/tex]
Which implies that y =0. Then, [tex] x =\pm 1[/tex]. So we have the following critical points (-1,0), (1,0). Notice that for both points, the value of f is f(1,0) = f(-1,0) = 12. If we calculate the second derivative, we have that at y=0
[tex] \frac{d^2f}{dx^2} = 2>0[/tex]. By the second derivative criteria, we know that this points are local minimums of the function f.
So, over the boundary D, the maximum value of f is 13 and the minimum value is 12. Over all D, the maximum value of f is 13 and the minimum value is 0.
Final answer:
The critical point of f(x, y) on the disk D is (0, 0). f(x) restricted to the boundary of D is f(x) = 12x^2 + 13(1 - x^2) with the domain [-1, 1]. The absolute maximum and minimum values of f(x, y) over all of D are 25 and 0, respectively.
Explanation:
To find the critical point of the function f(x, y) = 12x2 + 13y2 on the disk D: x2+y2 ≤ 1, we need to set the partial derivatives of f with respect to x and y equal to zero.
The partial derivative with respect to x is 24x, and setting it to zero gives x = 0. Similarly, the partial derivative with respect to y is 26y, which implies y = 0. Therefore, the critical point is (0, 0).
On the boundary of D, where x2+y2 = 1, we can solve for y2 as y2 = 1 - x2. Substituting into f, we get a function of a single variable x: f(x) = 12x2 + 13(1 - x2) with the closed interval domain [-1, 1].
The maximum value on the boundary occurs at x = ±1, giving a maximum of f(±1) = 25. The minimum on the boundary is at x = 0, which gives f(0) = 13.
Across the entire disk D, the absolute minimum is at the critical point (0,0), with f(0, 0) = 0, and the absolute maximum is the same as the boundary maximum, f(x) = 25.
what does 3(7y − 1) =
Answer: 21y-3
Step-by-step explanation:
3(7y-1)=
3(7y)-3(1)=
21y-3
Answer: 21y-3
Step-by-step explanation: The way to get a answer out of this problem you have to multiply 3 time 7, and 1 then subtract the two numbers you get which is 21y and 3 and the problem with this question is that you can’t subtract because of the variable but sense they aren’t the same put the answer like this 21y-3 hope this helps!
Butterflies: • Alice, Bob, and Charlotte are looking for butterflies. They look in three separate parts of a field, so that their probabilities of success do not affect each other. • Alice finds 1 butterfly with probability 17%, and otherwise does not find one. • Bob finds 1 butterfly with probability 25%, and otherwise does not find one. • Charlotte finds 1 butterfly with probability 45%, and otherwise does not find one. Let X be the number of butterflies that they catch altogether. A) Find the expected value of X. B) Write X as the sum of three indicator random variables, X1,X2,X3 that indicate whether Alice, Bob, Charlotte (respectively) found a butterfly. Then X=X1+X2+X3. Find the expected value of X by finding the expected value of the sum of the indicator random variables.
Answer:
The expected value is 0.87.
Step-by-step explanation:
a) To calculate the expected value X we will first see the posible outcomes. So could take value of 0,1,2,3. We will calculate the probability of each outcome. To do so, we will introduce the following notation. Consider the following tuple (A,B,C) where A is the number of butterflies found by Alice, B the number found for by Bob and C the number found by C. To calculate the probability of the tuple (A,B,C) we will do as follows. If the entry of the tuple is 1, then we will multiply by the probability of the person that found the butterfly. So, if A =1, we will multiply by 0.17(Alice finds a butterfly with probability 0.17). On the other side, if the entry of the tuple is 0, we will multiply by (1-p) where p is the probability of the person that found the butterly. So, if A=0, we will multiply by 0.83. So, for example, consider the tuple (1,0,1). The probability of having this result is 0.17*0.75*0.45 (Alice and Charlotte found a butterfly, but Bob didn't). We can do this since we are said that their probabilities of success don't affect others' probabilities.
We will see the total number of butterflies and the tuples associated to that number. That is
X number of butterflies - tuples
0 butterflies - (0,0,0)
1 butterfly - (1,0,0) or (0,1,0) or (0,0,1)
2 butterflies - (1,1,0) or (1,0,1) or (0,1,1)
3 butterflies - (1,1,1)
To find the probability of the value of X, we will sum up the probability of the associated tuples. The values of the probabilities are as follows
(0, 0, 0) = 0.342375
(0, 0, 1 ) = 0.280125
(0, 1, 0) = 0.114125
(0, 1, 1 ) = 0.093375
(1, 0, 0) = 0.070125
(1, 0, 1 ) = 0.057375 = 0.17*0.75*0.45
(1, 1, 0) = 0.023375
(1, 1, 1) = 0.019125
In this case,
P(X=0) = 0.342375 ,
P(X=1) = 0.464375 = 0.280125 +0.114125+ 0.070125
P(X=2) = 0.174125
P(X =3 ) = 0.019125
So, the expected value of X is given by
0* 0.342375 +1 * 0.464375 +2* 0.174125+3*0.019125 = 0.87
b)Let X1 be the number of butterflies found by Alice, X2 the number found by Bob and X3 the number found by Charlotte. Then X = X1+X2+X3. Using the expected value properties and the independence of X1, X2 and X3 we have that E(X) = E(X1)+E(X2)+E(X3).
Recall that each variable is as follows. Xi is equal to 1 with probability p and it is 0 with probability (1-p). Then, the expected value of Xi is
[tex]1\cdot p + 0\codt (1-p)=p[/tex]. Note that the value of p for X1,X2 and X3 is 17%, 25% and 45% respectively.
Then E(X) = 17%+25%+45%= 0.87.
So the expected number of butterflies is 0.87.
Final answer:
The expected value of the total number of butterflies, X, that Alice, Bob, and Charlotte catch is 0.87. This is found by summing their independent probabilities of catching a butterfly (0.17 for Alice, 0.25 for Bob, and 0.45 for Charlotte). X is also represented as the sum of three indicator random variables X1, X2, and X3, leading to the same expected value.
Explanation:
Expected Value of the Number of Butterflies Caught
In this scenario with Alice, Bob, and Charlotte searching for butterflies in separate parts of a field, the random variable X represents the total number of butterflies they catch. The expected value of X, or E(X), is calculated by adding the individual probabilities of finding a butterfly, since their probabilities are independent.
To find the expected value of X:
Multiply the probability of each person finding a butterfly by the number of butterflies they would find in that event (which is 1 since each either finds 1 butterfly or none), and
Add these products together.
The expected value is thus 0.17 + 0.25 + 0.45 = 0.87 butterflies. We can also express X as X1 + X2 + X3, where each Xi is an indicator random variable for whether Alice (X1), Bob (X2), or Charlotte (X3) found a butterfly.
The expected value for each indicator variable is the same as the person's probability of success. So, E(X1) = 0.17, E(X2) = 0.25, and E(X3) = 0.45. By the linearity of expectation, E(X) = E(X1) + E(X2) + E(X3), which also equals 0.87 butterflies.
Karla spent 9/2 hours of her time for preparing the exam and 5/2 hours on homework per day. If she sleeps 7 hours per day, how many spare hours does she have?
Answer:
2 hours if they go to school.
10 hours if they dont go to school.
Step-by-step explanation:
add up the hours.
9/2+5/2=14/2=7hours +7 hour of sleep= 14 hours.
if they go to school for 8 hours then add 8. then it =22 hours witch gives you 2 hours
if they dont go to school then you got 24-14 hours=10 hours.