Answer:
X= 4. Y = 3.
Step-by-step explanation:
If you have a graphing calculator, put the first equation into Y1. And second equation into Y2. Then, find the intersection of the two equations. That's how you find your answer.
In the lexicographic ordering of the permutations of the set {A,B,C,D,E,F,G,H} , what is the next permutation after GAEDBHFC? (Assume the usual alphabetic order of letters.)
a. HAEFBDCG b. GAEDCBFH c. DEHBFGCA d. None of the other answers is correct. e. FDAEGBCH
In the lexicographic ordering of the permutations of the set {A,B,C,D,E,F,G,H} , the next permutation after GAEDBHFC will be GAEDBHFD.
What is lexicographic ordering?
Lexicographic ordering or dictionary ordering is a way of ordering elements based on their alphabetical or numerical values.
To find the next permutation in the lexicographic ordering, we need to find the smallest possible permutation that is greater than GAEDBHFC by considering the order of the letters.
Let's analyze the given permutation:
GAEDBHFC
To find the next permutation, we start from right to left and look for the first occurrence of a letter that can be replaced by a greater letter. In this case, the first such occurrence is "C" (after "H").
Next, we need to find the smallest letter that is greater than "C" from the remaining letters. From the letters {C, D, E, F, G, H}, the smallest greater letter than "C" is "D".
Now, we swap "C" with "D":
GAEDBHFD
After swapping, we need to sort the remaining letters in ascending order to obtain the smallest permutation. The remaining letters are {B, E, F, G, H}. Sorting them gives:
GAEDBHFD
Therefore, the next permutation after GAEDBHFC is GAEDBHFD.
The correct answer is:
b. GAEDBHFD
To know more about permutations, refer here:
https://brainly.com/question/29990226
#SPJ4
Prove the following is equivalent: n* (n-1 C 2) = nC2 * (n − 2) .
The equivalence of the expressions n × ([tex]{}^{(n-1)}C_2[/tex]) and [tex]{}^nC_2[/tex] × (n − 2) has been proven mathematically.
To prove the equivalence of the expressions n × ([tex]{}^{(n-1)}C_2[/tex]) and [tex]^{n}C_2[/tex] × (n − 2), we can demonstrate that they yield the same result.
First, let's simplify each expression:
n × ([tex]{}^{(n-1)}C_2[/tex]) = n × [(n-1)! / 2!(n-1-2)!]
= n × [(n-1)! / 2!(n-3)!]
= n × [(n-1)(n-2) / 2]
= n × (n² - 3n + 2) / 2
= (n³ - 3n² + 2n) / 2
[tex]{}^nC_2[/tex] × (n − 2) = [n! / 2!(n-2)!] × (n-2)
= [n! / 2!(n-2)!] × (n-2)
= [(n)(n-1)(n-2)! / 2!(n-2)!] × (n-2)
= [(n)(n-1)] / 2
= (n² - n) / 2
By comparing the two simplified expressions, we can see that (n³ - 3n² + 2n) / 2 is equal to (n² - n) / 2.
Hence, we have proven that n × ([tex]{}^{(n-1)}C_2[/tex]) is equivalent to [tex]{}^nC_2[/tex] × (n − 2).
Learn more about equivalency at
https://brainly.com/question/14672772
#SPJ4
Which figure can be formed from the net?
Answer:
#1 is the answere
Step-by-step explanation:
Check the sides
PLEASE HELP ME ASAP I SWEAR IT WOULD BE A BIG HELP.
Jethro has sat 5 tests.
Each test was marked out of 100 and Jethro's mean mark for the 5 tests is 74
Jethro has to sit one more test that is also to be marked out of 100
Jethro wants his mean mark for all 6 tests to be at least 77
Work out the least mark that Jethro needs to get for the last test.
This paper will discuss the mathematics involved in determining the least mark that Jethro needs to get for the last test in order to end up with a mean mark of 77 over all 6 tests.
Jethro has sat 5 tests and each test was marked out of 100. Therefore, Jethro’s marks for the 5 tests can be represented by x1, x2, x3, x4, and x5. Jethro’s mean mark for the 5 tests is 74, which can be represented by the mathematical equation: (x1 + x2 + x3 + x4 + x5) / 5 = 74.
Jethro needs to sit one more test that is also marked out of 100 and he wants his mean mark for all 6 tests to be at least 77. Therefore, the least mark that Jethro needs to get for the last test can be found by rearranging the equation to: (x1 + x2 + x3 + x4 + x5 + x6) / 6 = 77. This can be written in its simplified form as: 6x6 = 77(x1 + x2 + x3 + x4 + x5).
In order to find the least mark that Jethro needs to get for the last test, x6, the other terms must be known. Since Jethro has already sat the 5 tests the marks for these tests are known, so they can be added together. This results in: x6 = 77(x1 + x2 + x3 + x4 + x5) / 6. Therefore, Jethro needs to get a mark of at least 77.6 (rounded to the nearest tenth) on the last test in order to end up with a mean mark of 77.
Find the mean of the following probability distribution? Round your answer to one decimal.
x 0,1,2,3,4
P(x) 0.0017, 0.3421, 0.065, 0.4106, 0.1806
mean = ___
The mean of the given probability distribution is 2.4.
To find the mean of a probability distribution, we multiply each value of x by its corresponding probability and then sum them up. Using the provided data:
x: 0, 1, 2, 3, 4
P(x): 0.0017, 0.3421, 0.065, 0.4106, 0.1806
mean = 0(0.0017) + 1(0.3421) + 2(0.065) + 3(0.4106) + 4(0.1806)
= 0 + 0.3421 + 0.13 + 1.2318 + 0.7224
= 2.4263
Therefore, the mean of the given probability distribution is approximately 2.4 (rounded to one decimal place).
To learn more about probability distribution: https://brainly.com/question/23286309
#SPJ11
Find the potential function f for the field F.
F = -1/x i+1/y j-1/z k
The potential function for the given field is f = ln |y| - ln |z| - ln |x| + C, where C is a constant of integration.
Given field is F = (-1/x) i+ (1/y) j- (1/z) k
The potential function f is given by
∂f/∂x = -1/x .........(1)∂f/∂y = 1/y .........(2)∂f/∂z = -1/z .........(3)
Using the equation (1)
we get
f = -ln |x| + C1
Using the equation (2)
we get
f = ln |y| + C2
Using equation (3) we get
f = -ln |z| + C3
On adding the above three equations we get
f = ln |y| - ln |z| - ln |x| + C
where C = C1 + C2 + C3 is a constant of integration.
Therefore, the potential function for the given field is f = ln |y| - ln |z| - ln |x| + C, where C is a constant of integration.
To know more about the potential function, click here;
https://brainly.com/question/30098140
#SPJ11
Martina runs 6 miles in 50 minutes. At the same rate, how many miles would she run in 35 minutes?
Answer:
4.2 miles
Step-by-step explanation:
Martina runs 6 miles in 50 minutes, we have to find the rate at which she is running. Put it in a fraction [tex]\frac{6}{50}[/tex] or she runs 6 miles every 50 minutes. When we divide we get that she is running, 0.12 miles evrey minute. The question askes us how far Matina will run in 35 minutes, so we multiply 0.12 by 35, and we get that she will run 4.2 miles.
A recent stocktake measured the price of BBQs at a large hardware store. From the stocktake, it was determined that the price was normally distributed with a mean of 500 dollars and a standard deviation of 50 dollars. Twenty per cent of the BBQs would cost more than what price? Select from the answers below.
575.5
542
526
459
The price at which twenty percent of the BBQs would cost more is $542 and it follows a normal distribution.
In this case, we are given that the price of BBQs at a large hardware store follows a normal distribution with a mean of $500 and a standard deviation of $50. We want to find the price at which twenty percent of the BBQs would cost more.
To solve this problem, we need to find the value, denoted as x, for which 20% of the BBQs are priced higher. This can be done by finding the z-score corresponding to the 20th percentile and then converting it back to the original scale.
The z-score is calculated using the formula:
z = (x - μ) / σ,
where μ is the mean and σ is the standard deviation.
To find the z-score corresponding to the 20th percentile, we can use a standard normal distribution table or a statistical calculator. The z-score corresponding to the 20th percentile is approximately -0.84.
Now we can use the z-score to find the corresponding value in the original scale:
-0.84 = (x - 500) / 50.
Solving for x, we get:
-0.84 * 50 = x - 500,
-42 = x - 500,
x = 500 - 42,
x = 458.
So, twenty percent of the BBQs would cost more than $458. However, since we need to choose from the given options, the closest price to $458 is $459.
Therefore, the answer is $459.
To know more about normal distribution, refer here:
https://brainly.com/question/31327019#
#SPJ11
The average American consumes 81 liters of alcohol per year. Does the average college student consume more alcohol per year? A researcher surveyed 10 randomly selected college students and found that they averaged 97.7 liters of alcohol consumed per year with a standard deviation of 23 liters. What can be concluded at the the α = 0.01 level of significance?
The α = 0.01 level of significance, we can conclude that the average alcohol consumption of college students is significantly higher than that of the average American population.
To determine if the average alcohol consumption of college students is significantly different from the average consumption of the average American, we can conduct a hypothesis test.
Let's set up the hypotheses:
Null hypothesis (H0): The average alcohol consumption of college students is equal to the average American consumption. (μ = 81)
Alternative hypothesis (H1): The average alcohol consumption of college students is greater than the average American consumption. (μ > 81)
We can use a one-sample t-test to analyze the data. Since we don't have information about the population standard deviation, we'll use the t-distribution and the sample standard deviation instead.
Given that the sample mean (x) of the 10 randomly selected college students is 97.7 liters and the sample standard deviation (s) is 23 liters, we can calculate the t-statistic using the following formula:
t = (x - μ) / (s / √n)
Where:
x = sample mean
μ = population mean
s = sample standard deviation
n = sample size
Plugging in the values, we get:
t = (97.7 - 81) / (23 / √10)
Calculating this expression gives us the t-value.
However, we also need to determine the critical value for the test based on the significance level (α = 0.01) and the degrees of freedom = n - 1.
Since we have 10 randomly selected college students = 10 - 1 = 9.
To find the critical value, we can consult the t-distribution table. With α = 0.01 and df = 9, the critical t-value is approximately 2.821.
Comparing the calculated t-value to the critical t-value, we can draw a conclusion. If the calculated t-value is greater than the critical t-value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.
Now let's calculate the t-value:
t = (97.7 - 81) / (23 / √10)
≈ 16.700
Since the calculated t-value (16.700) is much greater than the critical t-value (2.821), we can reject the null hypothesis.
Therefore, based on the given data and the α = 0.01 level of significance, we can conclude that the average alcohol consumption of college students is significantly higher than that of the average American population.
Learn more about hypothesis test click;
https://brainly.com/question/17099835
#SPJ4
Dubnium-262 has a half-life of 34 s. How long will it take for 500.0 grams to
decay to just 1.0 g? *
Answer:
the time taken for the radioactive element to decay to 1 g is 304.8 s.
Step-by-step explanation:
Given;
half-life of the given Dubnium = 34 s
initial mass of the given Dubnium, m₀ = 500 grams
final mass of the element, mf = 1 g
The time taken for the radioactive element to decay to its final mass is calculated as follows;
[tex]1 = 500 (0.5)^{\frac{t}{34}} \\\\\frac{1}{500} = (0.5)^{\frac{t}{34}}\\\\log(\frac{1}{500}) = log [(0.5)^{\frac{t}{34}}]\\\\log(\frac{1}{500}) = \frac{t}{34} log(0.5)\\\\-2.699 = \frac{t}{34} (-0.301)\\\\t = \frac{2.699 \times 34}{0.301} \\\\t = 304.8 \ s[/tex]
Therefore, the time taken for the radioactive element to decay to 1 g is 304.8 s.
The time required to decay 500 grams to 1 gram is 304.8 seconds and this can be determined by using the given data.
Given :
Dubnium-262 has a half-life of 34 s.
Final mass = 1 gram
Initial mass = 500 gram
Time taken by a radioactive element to decay is:
[tex]1 = 500(0.5)^{\frac{t}{34}}[/tex]
Simplify the above equation.
[tex]\rm \dfrac{1}{500} = (0.5)^{\frac{t }{34}}[/tex]
Now, take the log on both sides in the above equation.
[tex]\rm log(0.002 ) = \dfrac{t}{34}\times log(0.5)[/tex]
[tex]\rm \dfrac{log(0.002)}{log(0.5)} \times 34 = t[/tex]
t = 304.8 sec
So, the time required to decay 500 grams to 1 gram is 304.8 seconds.
For more information, refer to the link given below:
https://brainly.com/question/13911928
Based on meteorological records the probability that it will snow in a certain town on January 1st is 0.185. Find the probability that in a given year it will not snow on January 1st in that town rack Dic 0.815 0.227 ack Die 5.405 1.185 ack Die
The probability that it will not snow on January 1st in that town in a given year is 0.815.
Based on the meteorological records, A probability forecast includes a numerical expression of uncertainty about the quantity or event being forecast. Ideally, all elements (temperature, wind, precipitation, etc.)
The probability that it will not snow in a certain town on January 1st in a given year is 0.815. Here's how to arrive at the answer:Given that the probability of snowing on January 1st in that town is 0.185. Then, the probability of not snowing on January 1st is 1 - 0.185 = 0.815.
To know more about probability:
https://brainly.com/question/31828911
#SPJ11
The given information probability of it not snowing on January 1st of a given year in that town is 0.815.
Therefore, the probability of it not snowing on January 1st of a given year in that town is 0.815.
Here's how to solve the problem: Given: The probability of it snowing on January 1st of a given year in that town is 0.185. The complement of the probability of it snowing on January 1st is the probability of it not snowing on January 1st of a given year in that town, which is:
P(not snowing on January 1st) = 1 - P(snowing on January 1st)
P(not snowing on January 1st) = 1 - 0.185
P(not snowing on January 1st) = 0.815
Therefore, the probability of it not snowing on January 1st of a given year in that town is 0.815.
To know more about probability visit
https://brainly.com/question/32004014
#SPJ11
no links
The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $4 and each adult ticket sells for $8. The auditorium can hold a maximum of 110 people. The drama club must make at least $570 from ticket sales to cover the show's costs. Also, they must sell at least 20 student tickets and a maximum of 70 adult tickets. If xx represents the number of student tickets sold and yy represents the number of adult tickets sold, write and solve a system of inequalities graphically and determine one possible solution.
Answer:
hgfxjdt
Step-by-step explanation:
answer easy question quick
Answer:
Step-by-step explanation:
a) 9.80- 98/10
b) 7.3- 73/10
a) 7/100- 0.07
b) 82/10- 8.2
Hope this helps
Fraction:
a) 98/100
b) 73/10
Decimal:
a) 0.07
b) 8.2
Hello!
What's Eri's teddys name?
Answer:
Werid I don’t know
Step-by-step explanation:
The mean score in a physics test is 75% with the standard deviation 6.5%. Suppose that the scores in the test are approximately normally distributed. What is the probability that a randomly selected student scores more than 82%? Round your answer for 4 decimal places.
__________
The probability that a randomly selected student scores more than 82% on the physics test, we can use the standard normal distribution and the given mean and standard deviation.
The z-score formula is given by z = (x - μ) / σ, where z represents the z-score, x is the observed value, μ is the mean, and σ is the standard deviation. In this case, the observed value is 82%, the mean is 75%, and the standard deviation is 6.5%. Plugging these values into the formula, we calculate the z-score as z = (0.82 - 0.75) / 0.065 = 1.0769.
Next, we need to find the area to the left of the z-score in the standard normal distribution table or using a calculator. The area to the left of 1.0769 corresponds to the probability of scoring less than 82%. Let's assume this area is P(z < 1.0769).
The probability of scoring more than 82%, we subtract P(z < 1.0769) from 1: P(z > 1.0769) = 1 - P(z < 1.0769).
Using a standard normal table or a calculator, we can find P(z < 1.0769) to determine the probability.
To learn more about probability click here: brainly.com/question/31828911
#SPJ11
If p(x)= 2^x, what is the value of p(3) - p(2)?
Answer:
4
Step-by-step explanation:
p(3) = 2³ = 8
p(2) = 2² = 4
8-4 = 4
Hey I'm Chloe Can you Help Me, I will give Brainlest, Thank you :)
Stefan sells Jin a bicycle for $104 and a helmet for $17. The total cost for Jin is 110 % of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin?
Answer:
Stefan spent 108.9$ and made 12.1$
Step-by-step explanation:
Hey I'm Aiden I can help you, I will take Brainlest, Your welcome :)
take 10% of 121 and subtract it from 121 and you get the price he paid and made
What is your dream career and why ?
Answer:
Step-by-step explanation:
Professional dancers cause I’ve danced since I was 3 and I’ve always wanted to do it. And I wanna model on the side
Answer:
Detective/Forensics scientist
Step-by-step explanation:
I want to be a detective/ forensic scientist because I am interested in science and investigating.
Show all steps please!
Suppose you are told that 3.59% of Wendigos are less than 273cm tall while only 4.01% are taller than 326.25 cm tall. Find the mean and standard deviation of the heights of Wendigos.
The mean of the heights of Wendigos ≈ 302.523 cm, and the standard deviation ≈ 14.165 cm.
To obtain the mean and standard deviation of the heights of Wendigos, we can use the information given about the percentiles.
Let's denote the mean as μ and the standard deviation as σ.
Step 1: Finding the Z-scores
First, we need to find the Z-scores corresponding to the given percentiles.
For the lower percentile:
Z = (X - μ) / σ = -1.880
For the upper percentile:
Z = (X - μ) / σ = 1.880
Step 2: Finding the corresponding values using Z-scores
Next, we need to find the values corresponding to the Z-scores using a standard normal distribution table or a calculator.
For the lower percentile:
Z = -1.880 corresponds to a cumulative probability of 0.0359
For the upper percentile:
Z = 1.880 corresponds to a cumulative probability of 0.9601
Step 3: Calculating the values
Using the cumulative probabilities obtained, we can find the corresponding values.
For the lower percentile:
X = Z * σ + μ
273 = -1.880 * σ + μ
For the upper percentile:
X = Z * σ + μ
326.25 = 1.880 * σ + μ
Step 4: Solving the equations
We now have a system of equations with two unknowns (μ and σ).
273 = -1.880 * σ + μ (Equation 1)
326.25 = 1.880 * σ + μ (Equation 2)
We can solve this system of equations to find the values of μ and σ.
Subtracting Equation 1 from Equation 2, we get:
326.25 - 273 = 1.880 * σ + μ - (-1.880 * σ + μ)
53.25 = 3.760 * σ
Dividing both sides by 3.760, we get:
σ ≈ 14.165
Substituting this value of σ into Equation 1, we can solve for μ:
273 = -1.880 * 14.165 + μ
273 + 1.880 * 14.165 = μ
μ ≈ 302.523
Therefore, mean is approximately 302.523 cm, and the standard deviation is approximately 14.165 cm.
To know more about standard deviation refer here:
https://brainly.com/question/13498201#
#SPJ11
What is the value of x in the equation below?
12 – 2(x-1)=6
Should i trust the links people say "Their is an imagine in this link that contains the answer" usually these links are from sus profiles. So should i use it or no?
Answer:
no don't ever click on links okay.
Step-by-step explanation:
Rewrite the expression in the form x^n
Answer:
[tex]x^{\frac{5}{3} }[/tex]
Step-by-step explanation:
[tex]\frac{2}{3} *\frac{5}{2} \\\\\frac{5}{3}[/tex]
Factor 9z^2 - 6x +1.
pls will mark you brainiest
Answer:
It is not factorable
Step-by-step explanation:
The expression is not factorable with rational numbers.
Answer:
This is not factorable.
Step-by-step explanation:
This is not factorable.
y−3=5(x−2) what is the slope?
Answer:
y=5(x-2)+3 or y= 5x+7
Step-by-step explanation:
Stop and Shop sells 6 cases of Pepsi for $21.60. What is the constant of proportionality?
Answer: $3.60 per case
Step-by-step explanation: $21.60 divided by 6 = 3.60
A person visits the store and picks up five kg vegetables for did he buy?
£6.25. Which vegetable
Tomato - £1.50 per kg Carrot - £1.75 per kg Cabbage - £2 per kg Beetroot - £1.25 per kg
An experiment was performed to test whether caffeine in Coca-Cola would improve performance on an intelligence test. One randomly chosen group of subjects was given an 8 oz. cup of Coca-Cola containing caffeine to drink 10 minutes before taking the intelligence test. Another randomly chosen group was given an 8 oz. cup of decaffeinated Coke to drink 10 minutes before taking the test. Neither group had any food or drink for three hours before the experiment began. What are the levels or conditions of the independent variable
Answer:
8 oz of cocacola drink containing caffeine
8 oz of Decaffeinated Coke
Step-by-step explanation:
Th independent variables is that variable which causes a change in the output or the dependent or response variable. In the scenario described above, the type of drink Given to the participants is the independent variable
The Independent variable is the type of drink Given to the subjects with two levels ;
Levels :
cocacola drink containing caffeine
Decaffeinated Coke
Therefore, we can conclude that, there are two levels Of the jndependent variable, which are stated above.
MARKING BRAINLIEST TO FIRST PERSON WHO IS CORRECT!
I need help with #13
Answer:
True
False
False
Step-by-step explanation:
One hundred tickets, numbered 1, 2, 3, …, 100, are sold to 100 people for a drawing. Four different prizes are awarded, including a grand prize (a trip to Tahiti). How many ways are there to award the prizes if a) the person holding ticket 47 wins one of the prizes? b) the people holding tickets 19 and 47 both win prizes?
Solution :
It is given that four different prizes were awarded. So,
a). 4 ways for person 47 to win a prize
99 ways to give out the 2nd prize
98 ways to give the 3rd prize
97 ways to give the last prize
∴ P(99,3) = 99 x 98 x 97
b). 1 way to give person 47 their prize
1 way to give person 19 their prize
98 ways to give out the 3rd prize
97 ways to give out the last prize
So, P(98,2) = 98 x 97
Will Mark Brainliest To First Correct Answer.
Properties of Kites on IXL. I Only need to get one more correct and dont want to get reset...
Step-by-step explanation:
[tex]ei = \sqrt{ {45}^{2} - {27}^{2} } = \\ = \sqrt{2025 - 729} = \\ = \sqrt{1296} = \\ = 36[/tex]