True. The determinant of an n x n matrix can be defined as a sum of multiples of determinants of (n-1) x (n-1) submatrices, which are called the minors of the matrix.
The determinant of an n x n matrix can be defined as a sum of multiples of determinants of (n-1) x (n-1) submatrices, which are called the minors of the matrix.
More specifically, let A be an n x n matrix with entries a_ij. The determinant of A, denoted by det(A), can be defined recursively as follows:
- If n = 1, then det(A) = a_11.
- If n > 1, then det(A) = sum((-1)^(i+j) * a_ij * det(A_ij)), where the sum is taken over the first row or first column of A. Here, A_ij denotes the (n-1) x (n-1) submatrix obtained by deleting the i-th row and j-th column of A.
This recursive definition shows that the determinant of an n x n matrix can be expressed as a sum of (n-1) x (n-1) determinants of submatrices, with appropriate signs and coefficients. This is known as the cofactor expansion of the determinant along the first row or first column of the matrix.
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Two different linear functions are shown in the table.
Which key feature is different for the two functions?
A.Domain B.Range C.End behavior D.Slope
The key feature that is different for the two functions is (d) the slope
Which key feature is different for the two functions?From the question, we have the following parameters that can be used in our computation:
Linear functions on a graph and a table
As a general rule
All linear functions have the same domain, the same range
The slope of the table is
Slope = (8 - 6)/(-8 + 4) = -1/2
The slope of the graph is
Slope = (2 + 1)/(0 - 1) = -3
This means that their slopes are different
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A random sample of size 15 is taken from a population, and a 95% confidence interval for the population mean is calculated from the sample data to be (64.06, 66, 96). Which choice below gives the best interpretation of this interval?
(A) 95% of the population measurements lie within the interval.
(B) If many random samples of size 15 are taken from this population, then 95% of the time the population mean will lie within the interval.
(C) If many random samples of size 15 are taken from this population, then 95% of the time the sample mean will lie within the interval.
(D) If many random samples of size 15 are taken from this population, then 95% of the confidence intervals will contain the population mean.
(E) If many random samples of size 15 are taken from this population, then 95% of the confidence intervals will contain the sample mean.
(D) If many random samples of size 15 are taken from this population, then 95% of the confidence intervals will contain the population mean.
The best interpretation of the 95% confidence interval (64.06, 66.96) for the population mean, based on a random sample of size 15, is choice (B). This interpretation correctly states that if many random samples of size 15 are taken from the same population, then 95% of the time the population mean will lie within the interval. In other words, we can be 95% confident that the true population mean falls within this range based on the sample data. It is important to note that this does not mean that 95% of the population measurements lie within the interval (choice A), nor does it mean that 95% of the sample means will lie within the interval (choice C) or that 95% of the confidence intervals will contain the population mean (choice D) or the sample mean (choice E). These options are incorrect because they either misinterpret or generalize the confidence interval beyond its intended scope. Therefore, the best interpretation is the one that accurately reflects the meaning and purpose of a confidence interval.
(D) If many random samples of size 15 are taken from this population, then 95% of the confidence intervals will contain the population mean.
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What is the area, measured in square centimeters, of the parallelogram
below? Do not include units in your answer.
3 cm
4 cm
Answer here
Answer: 12
Step-by-step explanation:
3*4=12
11) Use a linear approximation (or differentials) to estimate the given number. (2.001)^5
Therefore, using the linear approximation, we estimate that (2.001)⁵ ≈ 32.016.
We can use the linear approximation to estimate the given number by using the following formula:
f(x + Δx) ≈ f(x) + f'(x)Δx
where Δx is a small change in x, f'(x) is the derivative of the function f(x), and f(x + Δx) is the approximate value of the function for x + Δx.
In this case, we can let f(x) = x⁵, x = 2, and Δx = 0.001. Then,
f'(x) = 5x⁴
So,
f(2.001) ≈ f(2) + f'(2)Δx
f(2.001) ≈ 2⁵ + 5(2⁴)(0.001)
f(2.001) ≈ 32.016
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Interest is compounded every three months at Money Bank at an annual rate of 5. 5%. A new client opens an account with $7200. How much money will be in the account at the end of six years?
The money that will be in the account at the end of six years is $8,404.5
The initial deposit = P = $7200
Rate = r = 5.5% per year
Time = 6 years ( Compounded Quarterly)
As per the question, the compound interest calculation can be used to determine how much money will be in the account after six years. Compound interest may be thought of as the addition of the loan's interest to the deposit's principal amount. As a result, it is computed using the Principal plus any prior interest.
Using, the formula for compound interest is:
A = [tex]P(1 + r/n)^(nt)[/tex]
Substituting the values -
A = [tex]7200(1 + 0.055/4)^(4 x 6)[/tex]
A = [tex]7200(1.01375)^24[/tex]
A = 7200 x 1.1657
A ≈ 8,404.5
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Write the formula that shows the dependence of the edge length a on the volume V of a cube.
Answer:
To calculate the edge length, take the cube root of the total volume of the cube.
Step-by-step explanation:
hope this helps ! :)
The formula that shows the dependence of the edge length 'a' on volume V of a cube will be a = ∛V.
What is a volume of a cube?All the edges of the cube are congruent with each other. Suppose that: The side length of the considered cube is 'a' units. Then, we get:
Volume of that cube = a³ cubic units.
Solve the equation for 'a', then we have
V = a³
a³ = V
a = ∛V
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In 2001, the Gallup poll found that 81% of American adults believed that there was a conspiracy in the death of President Kennedy. In 2013, the Gallup poll asked 1,039 American adults if they believe there was a conspiracy in the assassination, and found that 634 believe there was a conspiracy ("Gallup news service," 2013). Do the data show that the proportion of Americans who believe in this conspiracy has decreased? Test at the 1% level.
According to the Gallup poll, the proportion of American adults who believe in conspiracy theory has decreased significantly since 2001.
To test whether the proportion of Americans who believe in the conspiracy surrounding the death of President Kennedy has decreased, we need to conduct a hypothesis test. Let us assume that the null hypothesis is that the proportion of Americans who believe in the conspiracy theory has remained the same or increased, while the alternative hypothesis is that the proportion has decreased.
Let p be the true proportion of American adults who believe in the conspiracy theory, and let p0 be the proportion in 2001 (81%). The sample proportion in 2013 is 634/1039=0.61. The sample size is sufficiently large (1039>30), so we can use the z-test.
The test statistic is:
z = [tex](p - p0) / \sqrt{[p0*(1-p0)/n]}[/tex]
= (0.61 - 0.81) / [tex]\sqrt{[0.81*(1-0.81)/1039]}[/tex]
= -11.08
At the 1% level of significance, the critical value for a two-tailed test is z* = 2.58. Since the test statistic (z = -11.08) is much smaller than the critical value (z* = 2.58), we reject the null hypothesis in favour of the alternative hypothesis. Therefore, the data provide strong evidence that the proportion of Americans who believe in the conspiracy theory surrounding the death of President Kennedy has decreased since 2001.
In conclusion, according to the Gallup poll, the proportion of American adults who believe in conspiracy theory has decreased significantly since 2001. The sample size is sufficiently large, and the z-test was used to reach this conclusion at the 1% level of significance.
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Two students each write a function, C(n), that they think can be used to find the
number of circles needed to make the nth figure in the pattern shown.
Use the drop-down menus to explain why each function does or does not represent the
number of circles needed to make the n thi figure in the pattern.
The relationship between the figure number and the number of circle is
2n - 1How each figure represents the number of circlesEach figure represents the number of circles as in the pattern shown in figures 1 , 2, and 3
The pattern used in the getting the number of circles is twice the figure number minus 1. This is expressed mathematically as
2n - 1
where
n = figure number
hence we have that: figure 1, that is n = 1, such that
2n - 1
= 2 x 1 - 1
= 2 - 1
= 1
figure 2, n = 2, such that
2n - 1
= 2 x 2 - 1
= 4 - 1
= 3
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you do not need to know the rules of probability and the laws of expected value and variance to derive the sampling distribution true false
In order to derive the sampling distribution, it is necessary to have a solid understanding of the rules of probability and the laws of expected value and variance.
The sampling distribution refers to the distribution of a statistic, such as the mean or standard deviation, calculated from multiple samples taken from the same population. In order to calculate the probability of obtaining a certain value for the statistic, one must understand the rules of probability, such as the addition and multiplication rules. Additionally, the laws of expected value and variance provide a framework for understanding how the sampling distribution behaves, including its central tendency and variability.
Without knowledge of these concepts, it would be difficult to accurately derive and interpret the sampling distribution. Therefore, a solid understanding of the rules of probability and the laws of expected value and variance is essential for working with sampling distributions.
The answer is False.
To derive the sampling distribution, understanding the rules of probability, the laws of expected value, and variance is essential. The rules of probability help in determining the likelihood of various outcomes within a sample. The laws of expected value provide the average of all possible outcomes, weighted by their probability, while variance measures the dispersion of data points in a distribution.
Sampling refers to the process of selecting a subset of individuals from a larger population. The sampling distribution is the probability distribution of a sample statistic, such as the mean or variance, based on repeated random sampling from the same population.
To create an accurate sampling distribution, it is important to comprehend and apply the rules of probability to identify the likelihood of different sample outcomes. The laws of expected value and variance play a crucial role in summarizing the central tendency and variability of the sampling distribution, respectively.
In summary, it is false to assume that one does not need to know the rules of probability, expected value, and variance when deriving the sampling distribution. These concepts are fundamental to understanding and constructing a valid sampling distribution that reflects the properties of the larger population.
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find the value of 3+4(16-9),49 58 31
Answer:
31
Step-by-step explanation:
Note: I'm assuming that the three values after your expression (49, 58, and 31) are the possible answers. Let me know if they're actually a part of the expression.
Following PEMDAS, we're going to have to start by evaluating the expression inside the parentheses. That expression is 16 - 9, which is equivalent to 7.
Now, we're left with this expression: 3 + 4(7). Still following PEMDAS, we're going to have to evaluate the multiplication next. 4(7) = 28, so we are now left with the simple addition problem 3 + 28, and this is equal to 31. The entire work with no explanation is shown below.
3 + 4(16 - 9) = 3 + 4(7) = 3 + 28 = 31
Hopefully, that's helpful. Let me know if you need further clarification. :)
3. Mel has a bag of 8 marbles: 2 red, 3 yellow, and 3 green. She draws a marble from the bag,
writes down the color, replaces it, and draws again. She repeats this process for 40 trials and
records drawing a yellow marble 12 times. How does the experimental probability of selecting
a yellow marble compare to the theoretical probability? Explain.
We can see that the experimental probability is smaller than the theoretical one.
How do the probabilities compare?The theoretical probability is equal to the quotient between the number of yellow marbles and the total number, so here we have:
T = 3/8 = 0.375
The experimental probability is equal to the quotient between the number of times that Mel got a yellow marble and the total number of trials, so here we have:
E = 12/40 = 0.3
So the experimental probability is smaller than the theoretical one.
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It has been found that times taken by people to complete a particular tax form follow a normal distribution with a mean of 100 minutes and a standard deviation of 30 minutes. A random sample of nine people who have completed this tax form was taken. a) What is the probability that the sample mean time taken is less than 85 minutes?
The probability that the sample mean time taken is less than 85 minutes is 0.067 or 6.7%.
To answer this question, we can use the central limit theorem, which states that the distribution of sample means of a population with any distribution will approach a normal distribution as the sample size increases.
Given that the times taken to complete the tax form follow a normal distribution with a mean of 100 minutes and a standard deviation of 30 minutes, we can assume that the sample mean time taken also follows a normal distribution with a mean of 100 minutes and a standard deviation of 30 / sqrt(9) = 10 minutes (since the sample size is 9).
To find the probability that the sample mean time taken is less than 85 minutes, we need to standardize the sample mean using the formula z = (x - mu) / (sigma / sqrt(n)), where x is the sample mean, mu is the population mean, sigma is the population standard deviation, and n is the sample size.
Plugging in the values, we get z = (85 - 100) / (10) = -1.5.
We can then look up the probability of getting a z-score of -1.5 or lower in a standard normal distribution table or using a calculator. The probability is approximately 0.067 or 6.7%.
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a ladder is resting against a wall. the top of the ladder touches the wall at a height of 6 ft. find the length of the ladder if the length is 2 ft more than its distance from the wall.
Answer:
10 ft
Step-by-step explanation:
Let x = the distance between the wall and ladder.
So the length of the ladder is x + 2.
Applying Pythagorean theorem:
AC² = AB² + BC² (1)
Substituting the measurements into (1)
(x+2)² = 6² + x²
x² + 4x + 4 = 6² + x²
4x + 4 = 36
x = (36 - 4)/4 = 8
So the length of the ladder is x + 2 = 8 + 2 = 10 ft
The distance from the wall is 8 feet. Using y = x + 2, we get:
y = 10
So the length of the ladder is 10 feet.
To solve this problem, we can use the Pythagorean theorem, which states that for any right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the ladder forms a right-angled triangle with the wall and the ground. The height at which the ladder touches the wall is 6 ft, and the distance from the wall is represented by x. Since the ladder's length is 2 ft more than its distance from the wall, the ladder's length will be x + 2.
Applying the Pythagorean theorem:
Length of ladder² = (Distance from the wall)² + (Height on wall) ²
(x + 2)² = x² + 6²
Expanding and simplifying the equation:
x² + 4x + 4 = x² + 36
4x = 32
x = 8
So, the distance from the wall is 8 ft, and the length of the ladder is x + 2 = 8 + 2 = 10 ft.
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The product of two rational numbers can always be written as
an irrational number.
a whole number.
an integer.
a fraction.
The product of two rational numbers can always be written as a fraction. The Option D is correct.
What can product of two rational numbers result in?The product of 2 rational numbers can not be written as either irrational or whole number. This is because it will be expressed as the ratio of two integers and the product of two ratios of integers will always result in another ratio of integers.
For example, if we multiply 3/5 & 2/7 (rational numbers), we get (3/5) x (2/7) = 6/35 which is also a rational number. Therefore, the product of two rational numbers will always be a rational number or a fraction.
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Graph the piecewise function on the coordinate plane:
() = {−2 < −1
− 1 ≥ −1
The graph of the piecewise function is attached accordingly.
What is a piecewise function?A piecewise-defined function in mathematics is one that is composed of several smaller functions, each of which has a certain interval of the domain it applies to.
Instead of being a property of the function itself, piecewise definition is a means to represent the function.
There are several configurations for piecewise specified functions. Their "pieces" might be entirely linear or comprise a variety of functional forms, including constant, linear, quadratic, cubic, square-root, cube-root, exponential, etc. There is no "parent function" for piecewise defined functions because of this variety.
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Full Question:
Although part of your question is missing, you might be referring to this full question: See the attached image.
over which interval is the graph of y=cos(x) strictly increasing?
The solution is :
D. π < x < 2π, over this interval is the graph of y=cos(x) strictly increasing.
Given the function
y=cos(x)
Referring to the intervals [0, 2π].
It decreases from the interval [0, π ] and then starts increasing in the interval [π, 2π ]
Proving by taking derivative:
Taking derivative of the function, y=cos(x)
dy/dx = - sinx
In the interval [π, 2π ], sinx is negative i.e. sinx < 0.
Therefore
-sinx > 0
When, the derivative of a function is positive, then the function is strictly increasing.
So, the answer is:
D. π < x < 2π
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suppose that in the past, 94% of all hispanic grocery shoppers were women. perhaps due to changing cultural values, we believe that more hispanic men are now grocery shopping. we randomly sample 689 hispanic grocery shoppers from around the united states and 606 are women. does this result provide enough evidence to conclude that a lower proportion of hispanic grocery shoppers now are women? test at alpha
Therefore, we can conclude that the changing cultural values have resulted in more Hispanic men grocery shopping by -3.81 percent.
To determine if a lower proportion of Hispanic grocery shoppers are women, we need to perform a hypothesis test using the given sample data.
Let p be the true proportion of Hispanic grocery shoppers who are women. The null hypothesis is that p = 0.94, while the alternative hypothesis is that p < 0.94. We will use a one-tailed test with a significance level of α = 0.05.
The test statistic is calculated as:
z = (x - np) / √(np(1-p))
where x is the number of women in the sample (606), n is the sample size (689), and p is the null hypothesis value (0.94).
z = (606 - 6890.94) / √(6890.94*0.06)
z = -3.81
The critical value for a one-tailed test with α = 0.05 and degrees of freedom of 688 is -1.645. Since the calculated z value of -3.81 is less than the critical value of -1.645, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that a lower proportion of Hispanic grocery shoppers are women.
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Write an explicit formula for � � a n , the � th n th term of the sequence 8 , 40 , 200 , . . . 8,40,200,
The explicit formula for the nth term of the sequence 8, 40, 200, ..., is:
[tex]a_n = 8 \times 5^{(n-1)}[/tex]
To find the explicit formula for the nth term of the sequence 8, 40, 200, ..., we first notice that each term is obtained by multiplying the previous term by 5. That is:
a₁ = 8
a₂ = 5a¹ = 40
a₃ = 5a² = 200
a₄ = 5a³= 1000
...
In general, we can write:
[tex]a_n = 5a_n-1[/tex]
where n is the index of the term in the sequence.
Using the initial term a₁ = 8, we can use the recursive formula to find the value of any term in the sequence. However, to find an explicit formula for the nth term, we can use the formula for a geometric sequence, which is:
[tex]a_n = a_1 \times r^{(n-1)}[/tex]
where r is the common ratio. In this case, the common ratio is 5, so we can substitute it into the formula to get:
[tex]a_n = 8 \times 5^{(n-1)}[/tex]
The explicit formula for the nth term of the sequence 8, 40, 200, ..., is:
[tex]a_n = 8 \times 5^{(n-1)}[/tex]
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Not sure how to do this
Answer:
(28.8°/360°)(75) = .08(75) = 6
6 of the 75 fraternity members are Biology majors.
the proportion of professional golfers who are left-handed is claimed to be 0.06. believing this claimed value is incorrect, a researcher surveys a large random sample of professional golfers and finds the proportion of left-handed golfers in the sample to be 0.03. when a hypothesis test is conducted at a significance (or alpha) level of 0.01, the p- value is found to be 0.04. what decision should the researcher make based on the results of the hypothesis test? a. the null hypothesis should be rejected because 0.03 is greater than 0.01. b. the null hypothesis should not be rejected because 0.04 is greater than 0.03. c. the null hypothesis should be rejected because 0.03 is less than 0.06. d. the null hypothesis should not be rejected because 0.04 is greater than 0.01. e. the null hypothesis should be rejected because 0.04 is less than 0.06.
The researcher makes decisions based on the results of the hypothesis test : d. The null hypothesis should not be rejected because 0.04 is greater than 0.01.
The correct decision for the researcher to make based on the results of the hypothesis test is d. The null hypothesis should not be rejected because 0.04 is greater than 0.01. The researcher's sample provides evidence that the proportion of left-handed professional golfers is less than the claimed value of 0.06, which supports rejecting the null hypothesis.
The p-value of 0.04 is greater than the significance level of 0.01, but this does not impact the decision as the decision is based on the comparison between the sample proportion and the claimed value.
The researcher should make the decision based on the comparison of the p-value with the significance level (alpha).
In this case, the significance level (alpha) is 0.01 and the p-value is 0.04.
Since the p-value (0.04) is greater than the significance level (0.01), the researcher should not reject the null hypothesis.
Therefore, the correct answer is:
d. The null hypothesis should not be rejected because 0.04 is greater than 0.01.
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−15y^4 =(D)(3y^2 ) help is about Factor monomials
The Factor monomials of the -15[tex]y^4[/tex] = (D)(3y²) is -15[tex]y^4[/tex] = -5y² × 3y² or -15[tex]y^4[/tex] = -15y² × y², and the value of D could be 5 or -15 depending on simplification.
To factor the monomial -15[tex]y^4[/tex] as the product of two monomials, one of which is D and the other is 3y², we need to determine what constant D is.
To do this, we can divide -15[tex]y^4[/tex] by 3y², which gives us -5y². Therefore, we can write:
-15[tex]y^4[/tex] = (D)(3y²)
-5y^2 = D
So, the factored form of -15[tex]y^4[/tex] is:
-15[tex]y^4[/tex] = -5y² × 3y²
or
-15[tex]y^4[/tex] = -15y² × y²
Note that either way of writing the factored form is correct, as the order of the factors in a multiplication does not matter.
We divide the monomial by one of the factors, then use the quotient as the constant in the other factor to factor the monomial as the product of two monomials.
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Using the t tables, software, or a calculator, estimate the values asked for in parts (a) and (b) below.
a) Find the critical value of t for a 95% confidence interval with df = 24. t= ___(Round to two decimal places as needed.) b) Find the critical value of t for a 98% confidence interval with df = 79.
t= ___ (Round to two decimal places as needed.)
a) The critical value of t for a 95% confidence interval with df = 24 is approximately 2.064.
b) The critical value of t for a 98% confidence interval with df = 79 is approximately 2.626.
We have,
a) To find the critical value of t for a 95% confidence interval with
df = 24, we can use a t-table or a statistical calculator.
For a 95% confidence level and df = 24, we need to find the t-value corresponding to an alpha value of 0.05 (1 - confidence level).
Using a t-table or a statistical calculator, we find that the critical value of t for a 95% confidence interval with df = 24 is approximately 2.064.
b)
Similarly, for a 98% confidence interval with df = 79, we need to find the t-value corresponding to an alpha value of 0.02 (1 - confidence level).
Using a t-table or a statistical calculator, we find that the critical value of t for a 98% confidence interval with df = 79 is approximately 2.626.
Therefore,
a) The critical value of t for a 95% confidence interval with df = 24 is approximately 2.064.
b) The critical value of t for a 98% confidence interval with df = 79 is approximately 2.626.
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Cruz purchased a large pizza for $14.10. It serves 6 people. What is the cost per serving?
$1.41 per serving
$2.35 per serving
$3.04 per serving
$8.46 per serving
Two homebuyers are financing $137,000 to purchase a condominium. They obtained a 15-year, fixed-rate loan with a rate of 5.05%. They have
been given the option of purchasing up to four points to lower their rate to 4.81%. How much will the four points cost them?
O $1,370
O $1,730
$4,580
O $5,480
The four points that the homebuyers are purchasing to lower their rate from 5.05% to 4.81% will cost them D. $5,480.
What are the points in loans?The points purchased for loans are charges that the borrower pays upfront to lower their interest rates.
Each point equals a percentage of the loan amount.
For example, four points on a $137,000 loan are 4 percent of the loan amount, or $5,480.
The loan amount for the purchase of the condominium = $137,000
Fixed interest rate = 5.05%
Loan period = 15 years
Loan option rate = 4.81%
Four points = $5,480 ($137,000 x 4%)
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e)
E
F
7
S
Statement
R
24
16
X+2
Reason
f)
Using the knowledge of similar triangles for the figure the value of x would be
12How to solve for xThe value of x is solved in a two column table as shown
Statement Reason
EF || RS given
EA / SA = FA / RA proportions of similar triangles are equal
24/16 = (7 + (x + 2)) / (x+2) substitution property of equality
24(x + 2) = 16(x + 9) simplifying
24x - 16x = 144 - 48 gathering like terms
8x = 96 division property of equality
x = 12
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a football coach randomly selected the varisty or junior varsity team and then asks all players from that team their opinion on a new logo. the sample is a sample.
The given scenario describes an example of a cluster sampling technique.
The responses given by the players can be considered representative of the opinions held by the entire team.
The action taken by the football coach in selecting either the varsity or junior varsity team and asking for the opinion of all players on a new logo constitutes a randomly selected sample.
This means that the coach did not specifically choose certain players or a particular group to provide feedback, but rather included all members of one of the two teams.
Therefore, the responses given by the players can be considered representative of the opinions held by the entire team.
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Points (-3,6 ) (-2,9 ) the equation in point slope form step by step
Work Shown:
Let's start things off by finding the slope.
[tex](x_1,y_1) = (-3,6) \text{ and } (x_2,y_2) = (-2,9)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{9 - 6}{-2 - (-3)}\\\\m = \frac{9 - 6}{-2 + 3}\\\\m = \frac{3}{1}\\\\m = 3\\\\[/tex]
The slope is 3.
Now use point-slope form to determine the equation.
[tex]\text{y}-\text{y}_1 = \text{m}(\text{x} - \text{x}_1)\\\\\text{y}-6 = 3(\text{x} - (-3))\\\\\boldsymbol{\textbf{y}-6 = 3(\text{x} + 3)}[/tex]
. a simple undirected graph has 10 edges. 2 of the vertices are of degree 4, and the rest of the vertices are of degree 3. how many vertices are in this graph?
There are 4 vertices with degree 3, and 2 vertices with degree 4. So, there are a total of 6 vertices in this graph.
In a simple undirected graph with 10 edges, 2 vertices have a degree of 4 and the rest have a degree of 3. To determine the number of vertices in this graph, use the formula:
Sum of degrees = 2 * number of edges
Let x be the number of vertices with degree 3. Then:
(2 * 4) + (3 * x) = 2 * 10
8 + 3x = 20
3x = 12
x = 4
We also know that two of the vertices have a degree of 4, which means that together they contribute 8 to the sum of all vertex degrees. This leaves us with 20 - 8 = 12 degrees left to distribute among the other vertices. Since the remaining vertices all have a degree of 3, we can set up the equation 3x = 12, where x is the number of remaining vertices. Solving for x, we get x = 4. Therefore, the graph has a total of 6 vertices - two with a degree of 4 and four with a degree of 3.
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Mr tuyen uses 5/8 of a tank of gas each week to drive to and from his job. How many tanks of gas does Mr.tuyen
used in five weeks write your answer two different ways.
Mr. Tuyen uses 25/8 or 3 1/8 (or 3 1/64) tanks of gas in five weeks.
As per the question,
Multiply the amount of gas used in one week (5/8 tank) by the number of weeks (5):
5/8 x 5 = 25/8 tanks of gas.
Simplify the fraction 25/8 by dividing the numerator and denominator by 8: 25/8 ÷ 8/8 = 25/64.
25/64 is an improper fraction, so we can convert it to a mixed number:
3 1/64 tanks of gas.
Alternative method:
In one week, Mr. Tuyen uses 5/8 of a tank of gas.
In five weeks, he uses 5/8 x 5 = 25/8 tanks of gas.
25/8 is an improper fraction, so we can convert it to a mixed number: 3 1/8 tanks of gas.
Therefore, Mr. Tuyen uses 25/8 or 3 1/8 (or 3 1/64) tanks of gas in five weeks.
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Use the given information to complete parts I and II. In your final answer, include all calculations. Mars has an approximate diameter of 6. 794 · 10 9 millimeters. The sun has a diameter of 1. 391 · 10 6 kilometers. Part I: Given that for every one kilometer there are 1,000,000 millimeters, which unit of measurement should be used to best represent the lengths of the sun and Mar's diameters?
Part II: Use estimation to approximate how many times greater the sun’s diameter is than planet Mars’s
The best unit of measurement to represent the diameters of Mars and the Sun is millimeters.
How to explain the measurement1 kilometer = 1,000,000 millimeters
Therefore, the Sun's diameter in millimeters can be calculated as:
1.391 × 10⁶ km × 1,000,000 mm/km = 1.391 × 10¹² mm
Sun's diameter / Mars's diameter = (1.391 × 10¹² mm) / (6.794 × 10⁹ mm)
This simplifies to:
Sun's diameter / Mars's diameter ≈ 204,474
Therefore, the Sun's diameter is approximately 204,474 times greater than Mars's diameter.
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