The number of strings of decimal digits of length 6 with the following properties.
a) all even digits - 15,625
b) begin and end with the same digit - 100,000
c) contains at least one 0 - 468,559
d) contains exactly three 7’s - 14,580
e) contains exactly two 3’s or exactly three 4’s - 113,995
What are the possible digits for string of length 6?
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Remember that 0 cannot be placed as the first digit, since the number will then become a 5-digit string.
a) To count the number of strings of decimal digits of length 6 with all even digits, we need to consider that each digit can be chosen from the set {0, 2, 4, 6, 8}. Since all digits need to be even, each digit has 5 possible choices. Therefore, the total number of strings satisfying this property is [tex]5^6[/tex] = 15,625.
b) To count the number of strings that begin and end with the same digit, we can choose any digit for the first and last positions (10 choices) and then have 10 choices for each of the remaining 4 digits. Therefore, the total number of strings satisfying this property is [tex]10 * 10^4[/tex] = 100,000.
c) To count the number of strings that contain at least one 0, we can consider the complement of this condition, which is counting the number of strings that have no 0. Since each digit can be chosen from the set {1, 2, 3, 4, 5, 6, 7, 8, 9} (excluding 0), there are 9 choices for each digit. Therefore, the total number of strings with no 0 is [tex]9^6[/tex] = 531,441. To find the number of strings with at least one 0, we subtract this from the total number of strings without any restrictions, which is [tex]10^6[/tex] = 1,000,000. So, the number of strings satisfying this property is 1,000,000 - 531,441 = 468,559.
d) To count the number of strings that contain exactly three 7's, we can choose the positions for the three 7's in [tex]^6C_3[/tex] ways (6 choose 3). For each of the remaining three positions, we have 9 choices (excluding 7). Therefore, the total number of strings satisfying this property is [tex]^6C_3 * 9^3[/tex] = 20 * 729 = 14,580.
e) To count the number of strings that contain exactly two 3's or exactly three 4's, we need to consider the two cases separately and then sum up the results.
For exactly two 3's:
- We can choose the positions for the two 3's in [tex]^6C_2[/tex] ways.
- For each of the remaining four positions, we have 9 choices (excluding 3).
- Therefore, the total number of strings satisfying this case is [tex]^6C_2 * 9^4[/tex] = 15 * 6561 = 98,415.
For exactly three 4's:
- We can choose the positions for the three 4's in [tex]^6C_3[/tex] ways.
- For each of the remaining three positions, we have 9 choices (excluding 4).
- Therefore, the total number of strings satisfying this case is [tex]^6C_3 * 9^3[/tex] = 20 * 729 = 14,580.
To find the total number of strings satisfying either case, we add the results: 98,415 + 14,580 = 113,995.
In summary:
a) Number of strings with all even digits: 15,625
b) Number of strings that begin and end with the same digit: 100,000
c) Number of strings that contain at least one 0: 468,559
d) Number of strings that contain exactly three 7's: 14,580
e) Number of strings that contain exactly two 3's or exactly three 4's: 113,995
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The atmospheric pressure on an object decreases as altitude increases. If a is the height (in km) above sea level,
then the pressure P(a) (in mmHg) is approximated by P(a) = 760e-0.13a. Determine the atmospheric pressure at
8.47 km. Round to the nearest whole unit.
Answer:
253 mmHg
Step-by-step explanation:
Since the atmospheric pressure, [tex]P(a) = 760e^{-0.13a}[/tex]
when a = height (in km) = 8.47 km, then the atmospheric pressure P(a) is
[tex]P(a) = 760e^{-0.13a}\\P(8.47) = 760e^{-0.13X8.47}\\P(8.47) = 760e^{-1.1011} \\P(8.47 )= 760 X 0.33251 \\P(8.47)= 252.7 mmHg\\[/tex]
P(8.47) ≅ 253 mmHg
Using a 0.05 significance level, what decision and conclusion should you make regarding the null hypothesis? (1 point) LOOK AT ANALYSIS OF VARIENCE TABLE
a.Because p-value > 0.05, we fail to reject H0 and conclude that age can be used to predict disease activity score.
b.Because p-value > 0.05, we fail to reject H0 and conclude that age cannot be used to predict disease activity score.
c.Because p-value > 0.05, we reject H0 and conclude that age can be used to predict disease activity score.
d.Because p-value > 0.05, we reject H0 and conclude that age cannot be used to predict disease activity score.
e.Because p-value < 0.05, we reject H0 and conclude that age can be used to predict disease activity score.
The correct answer is:
[tex]\textbf{b.}[/tex] Because the p-value is > 0.05, we fail to reject H0 and conclude that age cannot be used to predict disease activity scores.
What is a null hypothesis?
The null hypothesis, denoted as H0, is a fundamental concept in statistical hypothesis testing. It is a statement or assumption that suggests there is no significant difference, effect, or relationship between variables in a population.
The decision and conclusion depend on the p-value obtained from the analysis of variance (ANOVA) table.
If the p-value is greater than 0.05, we fail to reject the null hypothesis (H0), implying that there is not enough evidence to support the alternative hypothesis.
If the p-value is less than 0.05, we reject the null hypothesis (H0), indicating that there is sufficient evidence to support the alternative hypothesis.
Therefore, the correct answer is:
Because the p-value > 0.05, we fail to reject H0 and conclude that age cannot be used to predict disease activity score.Using a 0.05 significance level, what decision and conclusion should you make regarding the null hypothesis?
\textbf{Answer:}
The decision and conclusion depend on the p-value obtained from the analysis of variance (ANOVA) table.
If the p-value is greater than 0.05, we fail to reject the null hypothesis (H0), implying that there is not enough evidence to support the alternative hypothesis.
If the p-value is less than 0.05, we reject the null hypothesis (H0), indicating that there is sufficient evidence to support the alternative hypothesis.
Therefore, the correct answer is:
\textbf{b.} Because the p-value > 0.05, we fail to reject H0 and conclude that age cannot be used to predict disease activity score.Using a 0.05 significance level, what decision and conclusion should you make regarding the null hypothesis?
\textbf{Answer:}
The decision and conclusion depend on the p-value obtained from the analysis of variance (ANOVA) table.
If the p-value is greater than 0.05, we fail to reject the null hypothesis (H0), implying that there is not enough evidence to support the alternative hypothesis.
If the p-value is less than 0.05, we reject the null hypothesis (H0), indicating that there is sufficient evidence to support the alternative hypothesis.
Therefore, the correct answer is:
\textbf{b.} Because the p-value > 0.05, we fail to reject H0 and conclude that age cannot be used to predict disease activity score.Using a 0.05 significance level, what decision and conclusion should you make regarding the null hypothesis?
\textbf{Answer:}
The decision and conclusion depend on the p-value obtained from the analysis of variance (ANOVA) table.
If the p-value is greater than 0.05, we fail to reject the null hypothesis (H0), implying that there is not enough evidence to support the alternative hypothesis.
If the p-value is less than 0.05, we reject the null hypothesis (H0), indicating that there is sufficient evidence to support the alternative hypothesis.
Therefore, the correct answer is:
\textbf{b.} Because the p-value > 0.05, we fail to reject H0 and conclude that age cannot be used to predict disease activity score.Using a 0.05 significance level, what decision and conclusion should you make regarding the null hypothesis?
\textbf{Answer:}
The decision and conclusion depend on the p-value obtained from the analysis of variance (ANOVA) table.
If the p-value is greater than 0.05, we fail to reject the null hypothesis (H0), implying that there is not enough evidence to support the alternative hypothesis.
If the p-value is less than 0.05, we reject the null hypothesis (H0), indicating that there is sufficient evidence to support the alternative hypothesis.
Therefore, the correct answer is:
\textbf{b.} Because the p-value > 0.05, we fail to reject H0 and conclude that age cannot be used to predict disease activity score.Using a 0.05 significance level, what decision and conclusion should you make regarding the null hypothesis?
\textbf{Answer:}
The decision and conclusion depend on the p-value obtained from the analysis of variance (ANOVA) table.
If the p-value is greater than 0.05, we fail to reject the null hypothesis (H0), implying that there is not enough evidence to support the alternative hypothesis.
If the p-value is less than 0.05, we reject the null hypothesis (H0), indicating that there is sufficient evidence to support the alternative hypothesis.
Therefore, the correct answer is:
[tex]\textbf{b.}[/tex] Because the p-value > 0.05, we fail to reject H0 and conclude that age cannot be used to predict disease activity scores.
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ill give brainliest
Your options are:
A. 115
B. 42
C. 159
D. 21
Answer:
the answer is D
Step-by-step explanation:
3x-21=x+7
2x-21=7
2x=28
x=14
substitute x for 14
14+7=21
2X14-21+21
What is the value of A when we rewrite 3^x as A^5x
The value of A when we rewrite 3^x as A^5x is 3^⅕
We have given that,
The value of A when we rewrite 3^x as A^5x.
What is power?The power (or exponent) of a number says how many times to use the number in a multiplication. It is written as a small number to the right and above the base number.
3^x
(3^⅕)^(5x)
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Answer:
3^1/5
Step-by-step explanation:
( Need help !!!!!!!!!! Pls )
Intuitively, a larger sample should lead to a smaller confidence interval (fixing the level of confidence). Which of the following most accurately gives a reason for this in the mathematics we use to make the confidence interval? And the t'-value associated to the t-distribution goes down because t_n have "smaller tails" as n gets large. (And other aspects remain the same.)r The standard error goes down because of the greater sample size in the denominator. (And other aspects remain the same.) The standard error goes down because the standard deviation of the sample will go down. And the t*-value associated to the t-distribution goes down because t_n have "smaller tails" as n gets large. O The standard error goes down because the standard deviation of the sample will go down. (And other aspects remain the same.) The mean will be more accurate with a larger sample size. The standard error goes down because of the greater sample size in the denominator. And the t-value associated to the t-distribution goes down because t_n have "smaller tails" as n gets large.
Intuitively, a larger sample should lead to a smaller confidence interval (fixing the level of confidence). The following most accurately gives a reason for this in the mathematics we use to make the confidence interval:
The standard error goes down because of the greater sample size in the denominator. (And other aspects remain the same.) And the t'-value associated to the t-distribution goes down because t_n have "smaller tails" as n gets large. This is true.
The standard error goes down because of the greater sample size in the denominator. This is because the formula for the standard error involves taking the square root of the sample size in the denominator. Therefore, as the sample size increases, the denominator of the standard error formula increases, causing the standard error to decrease. And the t'-value associated to the t-distribution goes down because t_n have "smaller tails" as n gets large. This is because the t-distribution is symmetrical and bell-shaped, with fatter tails than the normal distribution. As the sample size n increases, the t-distribution approaches the normal distribution, with thinner tails, which means that the t-values become smaller as n increases.
Hence, the correct option is (O) The standard error goes down because the standard deviation of the sample will go down. (And other aspects remain the same.) The mean will be more accurate with a larger sample size. The standard error goes down because of the greater sample size in the denominator. And the t-value associated with the t-distribution goes down because t_n has "smaller tails" as n gets large.
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Combine the like terms to create an equivalent expression for -k+3k
Answer:
2k
Step-by-step explanation:
-k+3k
2k
how to write 6 in a expanded form?
Answer: 6 × 1
To write a number in expanded form, add the places by it's number.
Ex: 231 → 200 + 30 + 1 = 231
In the problem, 6 is what we're expanding.
Since 6 is only just 1 digit, it is possible to expand a 1 digit number. All you'll need to do it multiply the digit by 1.
6 → 6 × 1 = 6
Therefore, 6 × 1 is the expanded form of 6.
Which of the following is the Laplace transformation L {f(t)} if f(t)=(sin(-4t) 2 ? 32 33 +645 O None of them s2 $4 + 3252 +256 $+32 S + 64s ) 16 54 + 3252 +256
The Laplace transform of f(t) = (sin(-4t))^2 is not among the given options.
The Laplace transform of f(t) = (sin(-4t))^2 is none of the given options. Let's find the correct Laplace transform for the given function.
The Laplace transform of a function f(t) is denoted as L{f(t)} and is defined as:
L{f(t)} = ∫[0 to ∞] f(t) * e^(-st) dt,
where s is the complex variable.
In this case, f(t) = (sin(-4t))^2. To find its Laplace transform, we need to apply the definition of the Laplace transform and evaluate the integral:
L{f(t)} = ∫[0 to ∞] (sin(-4t))^2 * e^(-st) dt.
However, before proceeding with the integration, we can simplify the function using trigonometric identities:
(sin(-4t))^2 = (-sin(4t))^2 = sin^2(4t).
Now, we can rewrite the Laplace transform as:
L{f(t)} = ∫[0 to ∞] sin^2(4t) * e^(-st) dt.
At this point, we can utilize a well-known trigonometric identity that relates the square of the sine function to a combination of 1 and cosine functions:
sin^2(θ) = (1 - cos(2θ))/2.
Applying this identity to our expression:
L{f(t)} = ∫[0 to ∞] (1 - cos(8t))/2 * e^(-st) dt.
Now, we can split this integral into two parts and simplify further:
L{f(t)} = (1/2) ∫[0 to ∞] e^(-st) dt - (1/2) ∫[0 to ∞] cos(8t) * e^(-st) dt.
The first integral represents the Laplace transform of 1, which is 1/s:
L{f(t)} = (1/2) * (1/s) - (1/2) ∫[0 to ∞] cos(8t) * e^(-st) dt.
The second integral can be evaluated using standard Laplace transform formulas. However, without additional information or constraints on the Laplace transform variable 's', we cannot simplify it further.
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Place each function below in the appropriate cell to show the transformation from f to g. (Desmos)
Answer:
First row: 2,1
Second row: 3,4
Hybrid and electric cars have gained in popularity in the last decade as a consequence of high gas prices. But their great gas mileages often come with higher car prices. There may be savings, but how much and how long before those savings are realized? Suppose you are considering buying a Honda Accord Hybrid, which starts around $31,665 and gets 48 mpg. A similarly equipped Honda Accord will run closer to $26,100 but will get 31 mpg. How long would it take for the Prius to recoup the price difference with its lower fuel costs, assuming you drive 800 miles per month? First, use the following formula for gas savings, where GM stands for gas mileage, to determine how far you will need to drive to recoup the cost difference in the vehicles. Use the known values and the average price of gas in your area to write a specific equation. $Gas is $4.35 Determine the type of equation that results, and then solve it algebraically. $Saved = $Gas x (distance driven) x ( GM now GM improved) Choose a Tesla (electric car) that has NO gas cost and compare it in a similar way to a gas-powered cari, the Honda Accord. How long will it take to recoup the price difference for the miles you drive per month? Assume you still drive 800 miles a month. Be sure to consider TOTAL COST of each car. Explain what you thought TOTAL COST meant in the previous question.
The Honda Accord Hybrid would recoup the price difference with its lower fuel costs in approximately 6.8 years when driving 800 miles per month.
How long does it take for the Honda Accord Hybrid to recover the price difference with its lower fuel costs, assuming a monthly mileage of 800 miles?The Honda Accord Hybrid, priced at $31,665, has a fuel efficiency of 48 mpg, while the gas-powered Honda Accord, priced at $26,100, has a fuel efficiency of 31 mpg. To determine the distance that needs to be driven to recoup the cost difference, we can use the formula: $Saved = $Gas x (distance driven) x (GM now / GM improved). Considering the average gas price of $4.35, we can substitute the values into the formula and solve for the distance driven.
Using algebraic calculations, we find that the distance needed to recoup the price difference is approximately 50,472 miles. With a monthly mileage of 800 miles, it would take approximately 63 months or 6.8 years to recover the cost difference between the two vehicles.
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3yd 4yd what is the length of the hypotenuse
Answer:
5 yd
Step-by-step explanation:
Use Pythagorean theorem,
Hypotenuse² = base² + altitude²
= 3² + 4²
= 9 + 16
= 25
Hypotenuse = √25 = √5*5 = 5 yd
1. A psychologist was interested in the effect of Vitamin A deficiency on maze learning rats. A group of nine rats learned a simple maze. Next, these same rats were deprived of Vitamin A for six weeks and were then tested again on their ability to learn a second maze equal in difficulty to the first. The scores represent the number of maze errors made under the two treatment conditions. Perform an appropriate two-tailed test of the significance of the mean difference.
Answer: hello your question has some missing information attached below is the missing information
we fail to reject H0 hence μ1 = μ2mean difference ( d ) = -2.444Step-by-step explanation:
H0 : μ1 = μ2
Ha : μ1 ≠ μ2
where : μ1 = mean number of errors made in pretest
μ2 = mean number of errors made in post test
n = 9
attached below is the detailed solution
Landon is going to invest in an account paying an interest rate of 4.3%
compounded continuously. How much would Landon need to invest, to the
nearest hundred dollars, for the value of the account to reach $11,300 in 14
years?
Answer:
$6,100
Step-by-step explanation:
So to solve this problem, let's give the amount of money the variable "x". We just need to do x - 0.043 × x. Then we replace x with our answer and repeat the process 13 more times.
Answer:
$6200
Step-by-step explanation:
Consider the hypothetical study described below. Based solely on the information given, do you have reason to question the results of the study? Explain your reasoning.
Researchers design five survey questions to determine whether Norwegian citizens are happier than American citizens.
Is there reason to question the results? Select all that apply.
A.
No, there is not reason. The goal of the study is clear.
B.
Yes, there is reason. It is not clear how the variable of interest is defined.
C.
Yes, there is reason. The people being surveyed will likely not be representative of the population.
D.
Yes, there is reason. It is not clear how the variable of interest is measured.
E.
No, there is not reason. There is no bias in the study.
F.
No, there is not reason. It is unlikely that there are any confounding variables in the study.
There are reasons to question the results of the survey comparing the happiness of Norwegian and American citizens due to potential issues with defining the variable of interest.
The given options present various perspectives on whether there are reasons to question the results of the survey comparing the happiness of Norwegian and American citizens. Among the provided options, options B, C, and D are the most appropriate selections.
B. Yes, there is reason. It is not clear how the variable of interest is defined:
C. Yes, there is reason. The people being surveyed will likely not be representative of the population:
D. Yes, there is reason. It is not clear how the variable of interest is measured:
By considering these factors, it becomes apparent that there are reasons to question the survey results, highlighting the importance of clear definitions, representative sampling, and transparent measurement methods to ensure the validity and reliability of the study.
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according to a survey taken at an amusement park about visitors favorite rides. 15 of the (15/50) visitors surveyed like the roller coasters the best. What percent of people chose the roller coasters their favorite ride
Answer:
30%
Step-by-step explanation:
You are to create a password using 8 letters from the alphabet (repetition allowed). What is the probability that no letter is repeated if the letters were randomly chosen to be in the password?
The probability that no letter is repeated in the password is approximately 0.0000194293, or about 0.0019%.
To calculate the probability that no letter is repeated in a password created using 8 letters from the alphabet (repetition allowed), we need to consider the total number of possible passwords and the number of passwords without repeated letters.
The number of possible passwords can be calculated by considering that each letter in the password can be chosen independently from the 26 letters in the alphabet. Therefore, there are 26 choices for each of the 8 positions, resulting in a total of 26^8 possible passwords.
To calculate the number of passwords without repeated letters, we can consider the choices for each position. For the first position, we have 26 options. For the second position, we have 25 options (since we cannot repeat the letter chosen for the first position). Similarly, for the third position, we have 24 options, and so on.
Using the multiplication principle, the number of passwords without repeated letters is given by 26 * 25 * 24 * 23 * 22 * 21 * 20 * 19.
Therefore, the probability that no letter is repeated in the password can be calculated as:
Probability = (Number of passwords without repeated letters) / (Total number of possible passwords)
= (26 * 25 * 24 * 23 * 22 * 21 * 20 * 19) / (26^8)
Calculating this probability:
Probability ≈ 0.0000194293
So, the probability that no letter is repeated in the password is approximately 0.0000194293, or about 0.0019%.
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Suppose you are interested in learning about how much time seventh grade students at your school spend outdoors on a typical school day. Select all the samples that are a part of the population you are interested in. a. The 20 students in a seventh grade math class. b. The first 20 students to arrive at school on a particular day. c. The seventh grade students participating in a science fair put on by the four middle schools in a school district. d. The 10 seventh graders on the school soccer team. e. The students on the school debate team.
Answer:
1. The 20 students in a seventh grade math class.
4. The 10 seventh graders on the school soccer team.
Step-by-step explanation:
I just submitted the form and these are the right answers :)
It might be not on time but still lol.
I AM SURE THOSE ARE RIGHT ANSWERS !!! :)))
The 20 students in a seventh grade math class, the seventh grade students participating in a science fair put on by the four middle schools in a school district and the 10 seventh graders on the school soccer team are the samples.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
The samples that are a part of the population of interest, which is seventh grade students at your school, are:
The 20 students in a seventh grade math class.
The seventh grade students participating in a science fair put on by the four middle schools in a school district (if the students are from your school).
The 10 seventh graders on the school soccer team (if they are from your school).
The samples that are not a part of the population of interest are:
The first 20 students to arrive at school on a particular day (as this may include students from different grades or schools).
The students on the school debate team (as this may include students from different grades or schools).
Hence, the 20 students in a seventh grade math class, the seventh grade students participating in a science fair put on by the four middle schools in a school district and the 10 seventh graders on the school soccer team are the samples
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What is the IQR of the data set below?
15, 13, 25, 18, 15, 12, 10, 35, 30, 52,
Answer:
17
Step-by-step explanation:
IQR = Q3 - Q1
1st Quartile: 13
3rd Quartile: 30
IQR = 30 - 13 = 17
A recent Gallup poll asked American adults if they had COVID-19 symptoms, would they avoid seeking treatment due to the high costs of healthcare? The poll contained a sample of 1,017 American adults and 143 of them said they would avoid seeking treatment due to the high costs of healthcare. Construct the 95% confidence interval for the proportion of the American adult population who would avoid seeking treatment for COVID-19 due to the high costs of healthcare.
What is N in this study? _____
What is P in this study? _____
The solution to the given problem is as follows:N in this study = 1017P in this study = 143/1017 = 0.1407 (rounded to 4 decimal places)
Given, the sample size n = 1017, and the sample proportion of people who would avoid seeking treatment due to high healthcare costs = 143/1017 = 0.1407
Since we need to calculate the 95% confidence interval for the proportion of the American adult population who would avoid seeking treatment for COVID-19 due to the high costs of healthcare, we need to calculate the standard error of the proportion.
The formula to calculate the standard error of the proportion is:
Standard error of the proportion = sqrt [ p * (1 - p) / n ]
Substituting the values, we get:
Standard error of the proportion = sqrt [ 0.1407 * (1 - 0.1407) / 1017 ]= 0.0141 (rounded to 4 decimal places)
To calculate the 95% confidence interval, we use the following formula:
95% confidence interval = sample proportion ± margin of error
Margin of error = Z * (standard error of the proportion)
where Z is the Z-score corresponding to the confidence level.
For 95% confidence level, Z = 1.96.
Substituting the values, we get:
Margin of error = 1.96 * 0.0141= 0.0276 (rounded to 4 decimal places)
Therefore, the 95% confidence interval for the proportion of the American adult population who would avoid seeking treatment for COVID-19 due to the high costs of healthcare is given by:
0.1407 ± 0.0276= (0.1131, 0.1683) (rounded to 4 decimal places)
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Write down the formula for calculating an unbiased estimate, Sry, of the covariance coefficient of variables x and y of a large (but finite) population, based on a random sample of n items. Define any symbols you use.
The formula for calculating an unbiased estimate
of the covariance coefficient of variables x and y of a large (but finite) population, based on a random sample of n items is:
(1/n-1) * ∑(Xi - X bar) * (Yi - Y bar)`,
where Xi and Yi are the values of the it h observation of x and y, X bar and Y bar are the means of x and y, respectively, and n is the sample size.
If we have to get an unbiased estimate of the covariance coefficient of variables x and y of a large (but finite) population, based on a random sample of n items, then we can use the formula:
(1/n-1) * ∑(Xi - X bar) * (Yi - Y bar)
where, the unbiased estimate of the covariance coefficient of x and y
Xi = the value of the it h observation of x
Yi = the value of the it h observation of y
X bar = the mean of x
Y bar = the mean of y
n = the sample size of the population
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What is the area of this triangle in the coordinate plane? 5 units 6 units 7 units 12 units?
Answer:
6 units
Step-by-step explanation:
Using readings taken from the coordinate upon which the triangle is drawn :
The area of triangle is given as :
Area of triangle = 0.5 * base * height
The base of the triangle = 4 units
The height of the triangle = 3 units
The Area of the triangle is thus :
0.5 * 4 * 3
0.5 * 12
= 6 units
Answer:
The area of the given triangle is 6 units²
If a hotel has 33 king-size beds, 24 queen-size beds, 25 double beds, and 24 twin beds, what is the probability that you will be given a queen-size or a twin-bed when you register, if the beds are chosen randomly?
The probability of being given a queen-size or a twin bed when registering is approximately 0.453 or 45.3%.
To calculate the probability of being given a queen-size or a twin bed, we need to determine the total number of queen-size and twin beds available, as well as the total number of beds overall.
Total number of queen-size beds = 24
Total number of twin beds = 24
Total number of beds = 33 (king-size) + 24 (queen-size) + 25 (double) + 24 (twin) = 106
To calculate the probability, we divide the number of favorable outcomes (queen-size or twin bed) by the number of possible outcomes (total number of beds).
Number of favorable outcomes = Number of queen-size beds + Number of twin beds = 24 + 24 = 48
Probability = Number of favorable outcomes / Total number of beds
Probability = 48 / 106 ≈ 0.453
Therefore, the probability of being given a queen-size or a twin bed when registering is approximately 0.453 or 45.3%.
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Gavyn was thinking of a number. Gavyn doubles it, then adds 14 to get an answer of 17.2. What was the original number?
Answer:
Original number we'll call "x".
2x + 14 = 17.2
x = 1.6
Step-by-step explanation:
Answer:
Original number we'll call "x".
2x + 14 = 17.2
x = 1.6
Step-by-step explanation:
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can someone please help me find the slope on khan academy? and please provide an explanation if possible
Answer: 7/4
Step-by-step explanation: To find the slope of a line, pick any two integer points, in this scenario the only two are (3,4) and (-1,-3). The slope is the rise over run, so think about it. To get from (-1,-3) to )3,4) you need to rise 7 units (difference in y coordinates) and from there you need to run 4 units, so it is 7/4. Keep in mind that rising up is positive for y and running to the right is positive for x.
Answer:
[tex]\frac{7}{4}x[/tex]
Step-by-step explanation:
How do you find slope on a graph? The slope is "rise/run" where "rise" is how much y spaces are moved to the next point and "run" is the how much spaces are moved to the next x point.
Step One: In this case, the point moves up 7 spaces to the next point, so that's the "rise" and then it moves 4 spaces to the right to the next point, so that's the "run"
Step Two: When we put it together, it is 7/4x. The x is just an indication that this is slope, and you don't have to worry about it until you learn how to plug it in.
If the conclusion of a valid argument is false, then all of the premises must be false. O True O False
False. "If the conclusion of a valid argument is false, then all of the premises must be false" is incorrect.
The statement "If the conclusion of a valid argument is false, then all of the premises must be false" is incorrect. In a valid argument, the truth of the premises guarantees the truth of the conclusion, but it does not guarantee the truth of the conclusion in reverse. This means that even if the conclusion of a valid argument is false, it does not necessarily imply that all of the premises must be false.
A valid argument is one in which the conclusion logically follows from the premises. It is possible for the premises to be true and still lead to a false conclusion due to errors in reasoning or incorrect logical connections. In such cases, the argument is considered valid but unsound.
To illustrate this, consider the following example:
Premise 1: All birds have feathers.
Premise 2: Penguins are birds.
Conclusion: Therefore, penguins can fly.
This argument is logically valid because the conclusion follows logically from the premises. However, the conclusion is false because penguins cannot fly. In this case, the premises are true, but the conclusion is false.
Therefore, the statement that all of the premises must be false if the conclusion of a valid argument is false is incorrect.
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Three of these fractions are equivalent: B. 12 C . 21 D. 74 30 A. . 70 Which one is the odd one out?
Answer:
12/30
Step-by-step explanation:
Here is the complete question
Three of these fractions are equivalent A.30/70 B.12/30 C.9/21 D.6/14 which one is the odd one out
to determine the equivalent fractions, convert the fractions to percentage
[tex]\frac{30}{70}[/tex] × 100 = 42.86%
[tex]\frac{12}{30}[/tex] × 100 = 40%
[tex]\frac{9}{21}[/tex] × 100 = 42.86%
[tex]\frac{6}{14}[/tex] x 100 = 42.86%
Another method is to convert the fraction to its simplest form
30/70
To transform to the simplest form. divide both the numerator and the denominator by 10 = 3/7
12/30
To transform to the simplest form. divide both the numerator and the denominator by 6 = 2/5
9/21
To transform to the simplest form. divide both the numerator and the denominator by 3 = 3/7
6/14
To transform to the simplest form. divide both the numerator and the denominator by 2 = 3/7
Using either methods, 12/30 is the odd one out
A cat is stuck in the tree and the fire department needs a ladder to rescue the cat. The fire truck available has a 95-foot ladder, which starts 8 feet above ground. Unfortunately, the fire truck must park 75 feet away from the tree. If the cat is 60 feet up the tree, does the cat get rescued? If not, what ladder length is need to allow the cat to be rescued?
Group of answer choices
A. No because an 117-foot ladder is needed but the truck has only a 95-foot ladder.
B. No because an 96-foot ladder is needed but the truck has only a 95-foot ladder.
C. Yes because only a 75-foot ladder is needed and the truck has a 95-foot ladder.
D. Yes because only a 91-foot ladder is needed and the truck has a 95-foot ladder.
Answer:
I guess the ans d is correct because using pythagoras theorem we get 91.26 ft .
Please explain steps
= If two events A and B are collectively exhaustive with P(A) = P(B). Given, P(AUB) = 0.60, find P(AB). =
The question asks us to find P(AB) given that A and B are collectively exhaustive events with P(A) = P(B) and P(AUB) = 0.60.
This means that A and B are mutually exclusive, and they together represent the entire sample space. Therefore, we can write the following equations: P(A) + P(B) = 1 (Collectively exhaustive events)
P(A) = P(B) (Given)P(AUB) = P(A) + P(B) - P(AB) (Addition rule of probability)
We know that P(AUB) = 0.60 and P(A) = P(B).
Substituting these values in the above equations, we get:
0.60 = 2P(A) - P(AB) ...(1)P(A) + P(B) = 1P(A) + P(A) = 1 (P(A) = P(B))2P(A) = 1P(A) = 1/2
Substituting P(A) in equation (1), we get:0.60 = 2(1/2) - P(AB)P(AB) = 1 - 0.60P(AB) = 0.40
Therefore, P(AB) = 0.40.
Hence, this is the required answer.
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fx=x-2, state the domain and range for the function and its inverse. Write each step.
The function f(x) = x - 2 has a domain of all real numbers and a range of all real numbers. Its inverse function, f^(-1)(x), also has a domain and range of all real numbers.
The domain of a function represents the set of all possible input values for the function. In the case of f(x) = x - 2, since there are no restrictions or limitations on the input variable x, the domain is all real numbers.
To find the range of the function, we consider the possible output values. The function f(x) = x - 2 is a linear function with a slope of 1. It means that for any input value of x, the output value will be that input value minus 2. Therefore, the range is also all real numbers.
To find the inverse function, we swap the roles of the input and output variables and solve for the new output variable. For the given function, we have f(x) = x - 2. Replacing f(x) with y, we get the equation y = x - 2. To find the inverse, we isolate x:
x = y + 2
Now, we replace x with the inverse function notation f^(-1)(x) and y with x:
f^(-1)(x) = x + 2
The inverse function has the same domain and range as the original function, which is all real numbers.
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