A level 0.95 confidence interval is a range of values computed from sample data that will contain the true value of the parameter of interest 95% of the time. So, the correct answer is C).
A level 0.95 confidence interval is a statistical measure used to estimate the true value of a population parameter based on a sample of data. It provides a range of values that is likely to contain the true value of the parameter with a certain degree of confidence.
The level of confidence, in this case 0.95, means that if the same sampling method and data analysis were repeated multiple times, the resulting confidence intervals would contain the true population parameter in 95% of cases.
The width of the interval, or margin of error, is influenced by factors such as sample size, variability, and level of confidence. So, the correct option is C).
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In IJK, j=530 cm, i=740 cm and
In the given triangle IJK, the measure of angle J is approximately 32°
Law of Sines: Calculating the measure of angle in a triangleFrom the question, we are to determine the measure of angle J in the given triangle
From the Law of Sines,
We can write that
sin (I) / i = sin (J) / j
From the given information,
j = 530 cm
i = 740 cm
∠I = 133°
Substituting the parameters into the formula,
sin (I) / i = sin (J) / j
sin (133°) / 740 = sin (J) / 530
sin (J) = (530 × sin (133°)) / 740
sin (J) = 0.5238
J = sin⁻¹ (0.5238)
J = 31.59°
J ≈ 32° (to the nearest degree)
Hence,
The measure of angle J is approximately 32°
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The figure below is a net for a right rectangular prism. Its surface area is 416 m² and the area of some of the faces are filled in below. Find the area of the missing faces, and the missing dimension.
The area of each of the missing faces is 40 m².
The length of each of the missing faces is 10 m.
The missing dimension is 10 m by 4 m.
What is area?Area is the region bounded by a plane shape.
To calculate the area of each missing face, we use the formula below.
Formula:
a = [A-2(48+120)]/2.............. Equation 1Where:
a = Area of each missing facesA = Total surface area of the rectangular prismFrom the question,
Given:
A = 416 m²Substitute these values into equation 1
a = [416-2(48+120)]/2a = (416-336)/2a = 40 m²And the length of each of the missing edge can be calculated using the formula below
Formula:
l = a/w.................Equation 2Where:
l = Length of each of the missing edgew = width of each of the missing edgeFrom the diagram in the question,
Given:
w = 4 ma = 40 m²Substitute into equation 2
l = 40/4l = 10 mHence, the length is 10 m.
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50.12 in word form
PLEASE HELP ME I WILL DO WHATEVER
Suppose that Leni and Thom are lawyers and each has a taxable income of $230,000. They can't decide if they should be married in December or in January. If they marry in December, then they are considered married for the entire tax year and could file a joint return. If they get married in January of the next year, they would file a separate return each as a single taxpayer. Examine Schedules X and Y-1. Which filing status would yield the lower tax? If so, by how much? is there really a marriage penalty?
Getting married in December and filing a joint return would result in a lower tax liability by: $65,917.
Based on the given tax schedules, if Leni and Thom get married in December and file a joint return, their total tax liability would be:
$4,220 for the first $19,900 of taxable income
$20,227 for the remaining $210,100 of taxable income ($230,000 - $19,900)
Total tax liability: $24,447
If they get married in January of the next year and file separate returns, each as a single taxpayer, their total tax liability would be:
Leni's tax liability: $45,182
Thom's tax liability: $45,182
Total tax liability: $90,364
Therefore, getting married in December and filing a joint return would result in a lower tax liability by: $90,364 - $24,447 = $65,917.
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18PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST ALL FAKE ANSWERS WILL BE REPORTED AND PLS PLS PLS EXPLAIN THE ANSWER OR HOW U GOT IT PLEASE AND TY
The exact lengths of the missing sides for the right triangle using trigonometric ratio of the respective angles are: a = 4, b = 4√3, c = 4√3, and d = 4√6
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
sin 30 = a/8 {opposite/hypotenuse}
a = 8 × 1/2 {sin 30 = 1/2}
a = 4
cos 30 = b/8 {adjacent/hypotenuse}
b = 8 × √3/2 {cos 30 = √3/2}
b = 4√3
sin 45 = 4√3/d
d = 4√3 × 2/√2 {sin45 = √2/2}
d = 4√6
cos 45 = c/4√6
c = 4√6 × √2/2
c = 2√12
c = 4√3
Therefore, the exact lengths of the missing sides for the right triangle using trigonometric ratio of the respective angles are: a = 4, b = 4√3, c = 4√3, and d = 4√6
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Which of the following best describes the graph below?
Answer:
B. It is not a function.
This graph is a circle.
How do you find the equation?
The equation of the line CD obtained from the slope of the line AB, and the coordinates of the point C is; 7·y - 3·x = 2
What is the slope of a line?The slope of a line is the ratio of the rise to the run of the line.
The specified information indicates;
AB ║ CD
The coordinates of the point A is (-3, 2), the coordinates of the point B is (4, 5)
The slope of the segment AB is therefore; (5 - 2)/(4 - (-3)) = 3/7
The coordinates of the point C is; (4 , 5 - 3) = (4, 2)
The equation of the line CD is therefore; y - 2 = (3/7)·(x - 4)
7·y - 14 = 3·x - 12
7·y - 3·x = 14 - 12 = 2
The equation of the segment CD is; 7·y - 3·x = 2
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If I have this sequence 2, 4, 6, . . . I can describe the rule as add 2
For each sequence below, describe the rule and write the
next two terms.
a)
b)
2, 5, 8,
The rule is
23, 18, 13,
The rule is
Hey can anyone solve these questions. Thanks
1. $.50 is what fraction of a dollar? Reduce the fraction to lowest terms.
2. If Sue's batting average is .250, what fraction of her times at bat does she get a hit?
1. $0.5 is 1/2 of a dollar
2. The fraction of her times at a bat that she get a hit is 1/4
What is decimal and fraction?Decimals are the numbers, which consist of two parts namely, a whole number part and a fractional part separated by a decimal point.
For example, 0.4 is 0 + 4/10 = 4/10,/. This means the conversion of 0.4 to fraction is 4/10.
1. The fraction of $0.5 to $1 is calculated as;
representing the fraction by x
x of 1 = 0.5
0.5 = 5/10
therefore
x= 5/10 = 1/2
Therefore the fraction of $1 that gives $0.5 is 1/2
2. converting 0.250 to fraction
= 0 + 250/1000
= 250/1000
= 25/100 = 5/20 = 1/4
therefore the fraction of Sue's hit is 1/4.
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we can use a normal probability model to represent the distribution of sample means for which of the following reasons? check all that apply. group of answer choices the sample is randomly selected the distribution of the variable in the population is normally distributed the sample size is large enough to ensure that sample means will be normally distributed flag question: question 2 question 23 pts what is the standard error for the distribution of sample means? [ select ] what is the z-score for the observed sample? [ select ] what is the probability that a random sample of 100 bags has a mean weight less than 33.6 grams? [ select ] flag question: question 3 question 31 pts does the sample provide strong evidence that the mean weight of the bags is lower than the 35.6 grams listed on the package? group of answer choices yes, because a random sample of 100 bags with a mean weight below 33.6 grams is very unlikely if the individual bags have a mean weight of 35.6 grams. no, because random samples of 100 bags will have mean weights that vary. a mean weight around 33.6 grams is not unusual. no, because the mean weight of the sample is only off by 2 grams. yes, because 33.6 is less than 35.6 grams flag question: spacer the annual salary of teachers in a certain state has a mean of $ 54,000 and standard deviation of $ 5,000 . use this information to answer the questions below. flag question: question 4 question 41 pts what is the probability that a randomly selected teacher from this state has an annual salary of $55,500 or more. group of answer choices we cannot find the probability with the given information. flag question: question 5 question 51 pts what is the probability that the mean annual salary of a random sample of 5 teachers from this state is more than $60,000? group of answer choices it is impossible to tell because normality conditions are not met flag question: question 6 question 61 pts what is the probability that the mean annual salary of a random sample of
We can use a normal probability model to represent the distribution of sample means when the sample size is large enough to ensure that sample means will be normally distributed, option (C) is correct.
The central limit theorem (CLT) states that when sample sizes are sufficiently large (typically, n > 30), the distribution of sample means will be approximately normal, regardless of the distribution of the variable in the population.
This is because as the probability of sample size increases, the sample mean becomes a more reliable estimate of the population mean, and the variability in the sample means decreases. This results in a distribution that is bell-shaped and symmetric, similar to a normal distribution, option (C) is correct.
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– The question is inappropriate, The correct question is:
We can use a normal probability model to represent the distribution of sample means for which of the following reasons? check all that apply.
A) the sample is randomly selected
B) the distribution of the variable in the population is normally distributed
C) the sample size is large enough to ensure that sample means will be normally distributed flag –
PLEASE HELP ME!!!!!!!
The number of lattes sold daily by two coffee shops is shown in the table.
Shop A Shop B
55 36
52 40
50 34
47 39
51 44
48 41
53 40
53 38
Based on these data, is it better to describe the centers of distribution in terms of the mean or the median?
a. Mean for both coffee shops because the data distribution is symmetric
b. Median for both coffee shops because the data distribution is not symmetric
c. Mean for shop B because the data distribution is symmetric; median for shop A because the data distribution is not symmetric
d. Mean for shop A because the data distribution is symmetric; median for shop B because the data distribution is not symmetric
Based on data, it is better to describe the centers of distribution in terms of median because the data distribution is not symmetric. The Option B is correct.
What is a better measure of center for the given data?To determine a better measure of center, we must examine the symmetry of the data distribution. We can do it by constructing box plots or dot plots but because we have small data set, we will examine the data visually.
By looking at the data, we see that those distributions are not perfectly symmetric with some values have more spread out than the others. So, it is better to describe the centers of distribution in median rather than in mean.
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Mr. Howard surveyed his students about their favorite flavor of ice cream. In his second period class, 725 preferred vanilla. In his fourth period class, 8 out of 27 students preferred vanilla. In his sixth period class, 30% preferred vanilla. In which class did the greatest fraction of the students prefer vanilla ice cream?
Answer:
8/27.
Step-by-step explanation:
To find out which class had the greatest fraction of students who preferred vanilla ice cream, we need to compare the ratios of students who preferred vanilla to the total number of students in each class.
For second period class:
Number of students who preferred vanilla = 725
Total number of students = unknown
Ratio of students who preferred vanilla to total number of students = unknown/unknown = undefined
For fourth period class:
Number of students who preferred vanilla = 8
Total number of students = 27
Ratio of students who preferred vanilla to total number of students = 8/27
For sixth period class:
Number of students who preferred vanilla = 30% of total number of students
Total number of students = unknown
Ratio of students who preferred vanilla to total number of students = 0.3*unknown/unknown = 0.3
Therefore, the fourth period class had the greatest fraction of students who preferred vanilla ice cream, with a ratio of 8/27.
. Joe has 784 one-centimetre cubes.
He arranges all of the cubes into a cuboid.
The perimeter of the top of the cuboid is 30 cm.
Each side of the cuboid has a length greater than 2 cm.
Find the height of the cuboid.
The height of the cuboid is 14cm.
What is the perimeter?
A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are numerous uses in real life for perimeter calculations.
Here, we have
Given: Joe has 784 one-centimeter cubes.
He arranges all of the cubes into a cuboid.
The perimeter of the top of the cuboid is 30 cm.
Each side of the cuboid has a length greater than 2 cm.
We have to find the height of the cuboid.
1. a = 7, b = 8
V = 784
We know that
height = V/s
h = 784/56
h = 14cm
Hence, the height of the cuboid is 14cm.
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Oakwood Inc. Is a public enterprise whose shares are traded in the over-the-counter market. At December 31, 2018, Oakwood had 6,000,000 authorized shares of $10 par value common stock, of which 2,000,000 shares were issued and outstanding. The shareholders' equity accounts at December 31, 2018, had the following balances: Common stock $20,000,000 Additional paid-in capital on common stock 7,500,000 Retained earnings 6,470,000 Transactions during 2019 and other information relating to the shareholders' equity accounts were as follows: On January 5, 2019, Oakwood issued at $54 per share, 100,000 shares of $50 par value, 9%, cumulative convertible preferred stock. Each share of preferred stock is convertible, at the option of the holder, into 2 shares of common stock. Oakwood had 600,000 authorized shares of preferred stock. On February 2, 2019, Oakwood reacquired 20,000 shares of its common stock for $16 per share. Oakwood uses the cost method to account for treasury stock. On April 27, 2019, Oakwood sold 500,000 shares (previously unissued) of $10 par value common stock to the public at $17 per share. On June 18, 2019, Oakwood declared a cash dividend of $1 per share of common stock, payable on July 13, 2019, to shareholders of record on July 2, 2019. On November 9, 2019, Oakwood sold 10,000 shares of treasury stock for $21 per share. On December 14, 2019, Oakwood declared the yearly cash dividend on preferred stock, payable on January 14, 2020, to shareholders of record on December 31, 2019. On January 18, 2020, before the books were closed for 2019, Oakwood became aware that the ending inventories at December 31, 2018, were understated by $300,000 (the after-tax effect on 2018 net income was $210,000). The appropriate correcting entry was recorded the same day. After correcting the beginning inventory, net income for 2019 was $4,500,000. Required: Question Content Area 1. Prepare a statement of retained earnings for Oakwood for the year ended December 31, 2019. Assume that only single-period financial stat
Retained earnings, December 31, 2018 $6,470,000
Add: Net income December 31, 2019 $4,500,000
Less: Preferred stock dividends declared and paid $4,500,000
Less: Common stock dividends declared and paid $1,000,000
Total adjustments $3,500,000
Retained earnings, December 31, 2019 $9,970,000
How do we compute the statement of retained earnings?The statement shows changes in the balance of retained earnings account during the year. The retained earnings balance at the beginning of the year is adjusted for the net income earned during the year and for the dividends declared and paid to the shareholders.
In this case:
retained earnings balance at December 31, 2018 was $6,470,000,net income for the year ended December 31, 2019 was $4,500,000, declared and paid preferred stock dividends of $4,500,000,common stock dividends of $1,000,000 during the year.So, total adjustments to the retained earnings balance:
= $4,500,000 + $1,000,000 - $4,500,000.
= $3,500,000
After adjustment on net income and dividends, the retained earnings balance at December 31 2019 is:
= $6,470,000 + $4,500,000 - $3,500,000
= $9,970,000
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Right Angle Trigonometry
Answer: The answer to
sinΘ = 7/7√2
cosΘ = 7/7√2
tanΘ = 7/7
cosecΘ = 7√2/7
secΘ = 7√2/7
cotΘ = 7/7
Step-by-step explanation:
The given triangle consists of three sides namely, hypotenuse, opposite and adjacent.
The value of the hypotenuse is 7√2 and the value of the adjacent is 7.
We will calculate the value of the adjacent.
By Pythagoras' theorem, (hypotenuse)^2=(opposite)^2+(adjacent)^2
Putting the given values, (7√2)^2=(opposite)^2+(7)^2
(opposite)^2=(7√2)^2-(7)^2
(opposite)^2=98-49
(opposite)^2=49
Therefore, the value of the opposite is 7.
Now, we can put the following values in the trigonometric table.
sinΘ = opposite/hypotenuse = 7/7√2
cosΘ = adjacent/hypotenuse = 7/7√2
tanΘ = opposite/adjacent = 7/7
cosecΘ = hypotenuse/opposite = 7√2/7
secΘ = hypotenuse/adjacent = 7√2/7
cotΘ = adjacent/opposite = 7/7
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Use the photo below to help me with this problem
The domain and the range of the function are given as follows:
Domain: (-6, 1].Range: [-2, 4).What are the domain and range of a function?The domain of a function is the set that contains all possible input values of the function, that is, all the values assumed by the independent variable x in the function.The range of a function is the set that contains all possible output values of the function, that is, all the values assumed by the dependent variable y in the function.The values of x of the function are from an open circle at x = -6 to a closed circle at x = 1, hence the domain is given as follows:
(-6, 1].
The minimum value of the function is y = -2, while the maximum value is an open circle at y = 4, hence the range of the function is given as follows:
[-2, 4).
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what percentage of 2-digit positive integers have a tens digit that is one greater than the ones digit?
10% of 2-digit positive integers have a tens digit that is one greater than the ones digit.
To solve this problem, we first need to determine how many 2-digit positive integers there are. Since the smallest 2-digit integer is 10 and the largest is 99, we have a total of 90 integers (99-10+1).
Next, we need to determine how many of these integers have a tens digit that is one greater than the ones digit. To do this, we can create a chart and list out all possible combinations:
10, 21, 32, 43, 54, 65, 76, 87, 98
There are a total of 9 such integers. Therefore, the percentage of 2-digit positive integers that have a tens digit that is one greater than the ones digit is:
9/90 * 100% = 10%
So, 10% of 2-digit positive integers have a tens digit that is one greater than the ones digit.
To answer your question, let's first identify the range of 2-digit positive integers and determine the number of combinations where the tens digit is one greater than the ones digit.
The range of 2-digit positive integers is from 10 to 99. Now, we need to find the pairs of digits where the tens digit is one greater than the ones digit. The possible pairs are:
(1,0), (2,1), (3,2), (4,3), (5,4), (6,5), (7,6), (8,7), and (9,8)
There are 9 pairs that meet the condition. Now we need to find the total number of 2-digit positive integers:
99 (the last 2-digit integer) - 10 (the first 2-digit integer) + 1 = 90
So, there are 90 two-digit positive integers in total.
Now, we can calculate the percentage of the 2-digit positive integers that have a tens digit one greater than the ones digit:
(9 / 90) * 100 = 10%
Therefore, 10% of 2-digit positive integers have a tens digit that is one greater than the ones digit.
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Approximately 4.44% of 2-digit positive integers have a tens digit that is one greater than the ones digit.
Let's consider the possible pairs of tens digit and ones digit that satisfy the condition. There are 4 such pairs: [tex](1, 0)$, $(2, 1)$, $(3, 2)$[/tex], and [tex](4, 3)$.[/tex] For each tens digit, there is exactly one ones digit that satisfies the condition. So, out of the 90 possible two-digit positive integers (ranging from 10 to 99), only 4 of them have a tens digit that is one greater than the ones digit.
Therefore, the percentage of 2-digit positive integers that have a tens digit that is one greater than the ones digit is:
[tex]$\frac{4}{90} \cdot 100% \approx 4.44%$[/tex]
So, approximately 4.44% of 2-digit positive integers have a tens digit that is one greater than the ones digit.
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As Almay walks through a local park, she happens to pass an old man who is lying on a bench, clutching his stomach, and moaning in pain. The presence of many other walkers in the park will most likely increase the probability that Almay will
As Almay walks through a local park and passes an old man in pain, the presence of many other walkers in the park will most likely increase the probability that Almay will experience the "bystander effect."
As Almay walks through the local park and comes across an old man who is in pain, the presence of many other walkers in the park will most likely increase the probability that Almay will seek help for the man.
This is because the bystander effect, which is the tendency for individuals to be less likely to intervene in an emergency situation when others are present, is less likely to occur when there are more people around. With more people present, Almay may feel a greater sense of responsibility to act and seek help for the man.
Additionally, the presence of other walkers may also make it easier for Almay to quickly locate someone who can assist with medical attention or call for emergency services.
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How do I rewrite the equation y=-2x^2+8x-5
Answer:
Y= (x+4)(x+4)-21
Step-by-step explanation:
If you are factoring It out:
Y=-2x^2+8x-5 is the same as Y= (x+4)(x+4)-21
Let me know if it is incorrect!
-a friendly 8th grader
Find the exact value of cos (2theta), given tan A = -8/15, and theta lies in Quadrant II.
Please show steps and thank you in advance!
The value of cos (2theta) will be; 161/289
We are given that tan(A) = -8/15, therefore opposite is 8 and adj is 15
hyp = √8²+15²
= √ 64+225
= √ 289
= 17
Thus, cos (theta) = 8/17 and since theta is in second quadrant, cos tetha will be negative
cos (theta) = -15/17
cos²(theta) = 225/289
sin(theta) = 8/17
sin²(theta) = 64/289
cos(2theta) = cos²(theta) -sin²(theta)
= 225/289 - 64/289
= 161/289
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What is the median of the data in this stem-and-leaf plot?
Responses
31.0
31.0
31.5
31.5
32.0
32.0
32.5
Answer:
32.5
Step-by-step explanation:
hope this helps
Expand. Your answer should be a polynomial in standard form. (-p^2+4p-3)(p^2+2)=(−p 2 +4p−3)(p 2 +2)=left parenthesis, minus, p, squared, plus, 4, p, minus, 3, right parenthesis, left parenthesis, p, squared, plus, 2, right parenthesis, equals
The expansion of the polynomial (-p²+4p-3)(p²+2) would be is -p⁴ + 4p³ - 5p² + 8p - 6
Here we need to expand the polynomial (-p²+4p-3)(p²+2)
To do so we need to multiply each of the term with the first bracketby the each term of second bracket.
So, the expansion of the polynomial (-p²+4p-3)(p²+2) would be,
(-p² + 4p - 3)(p² + 2)
= [p² × (-p² + 4p - 3)] + [2 × (-p² + 4p - 3)]
= [p² × (-p²) + p² × 4p - p² × 3] + (-2p² + 8p - 6)
= (-p⁴ + 4p³ - 3p²) + (-2p² + 8p - 6)
= -p⁴ + 4p³ - (3 + 2)p² + 8p - 6 .......(add like terms)
= -p⁴ + 4p³ - 5p² + 8p - 6
Therefore, the required polynomial is -p⁴ + 4p³ - 5p² + 8p - 6
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In the figure below, find the exact value of x. (Do not approximate your answer.)
6
The value of x is given as follows:
x = 2.25.
What is the geometric mean theorem?The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.
From the image at the end of the answer, we have that 3 is the geometric mean of 4 and x, hence the value of x is obtained as follows:
4x = 3²
4x = 9
x = 9/4
x = 2.25.
Missing InformationThe image is given at the end of the answer.
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PLSSS help XX
Find the man median mode and range for this set of data : 29,20,15,13,35,20
For the data set 29, 20, 15, 13, 35, 20. the mean, median, mode and range are 22, 20, 20, and 22, respectively.
The mean (arithmetic mean), denoted by μ, is a single value defined as the sum of the data values divided by the total number of data values.
[tex]\text{Mean} =\dfrac{x_1+x_2+...+x_n}{\text{N}}[/tex]
[tex]\text{Mean} = \dfrac{29+20+15+13+35+20}{6}[/tex]
[tex]\text{Mean} = 22[/tex]
The median, denoted by , is the single value at the middle of an ordered arrangement of data values according to increasing or decreasing magnitude.
[tex]\text{M}_{\text{d}}=x_{\dfrac{\text{N}+1}{2} }[/tex] if N is odd, and
[tex]\text{M}_{\text{d}}=\dfrac{^x\frac{\text{N}}{2}^{+x} \frac{\text{N}}{2} +1}{y}[/tex] if N is even
[tex]\text{N = 8}[/tex]
Data : 13, 15, 20, 20, 29, 35
[tex]\text{M}_{\text{d}}=\dfrac{^x\frac{\text{N}}{2}^{+x} \frac{\text{N}}{2} +1}{y}[/tex]
where [tex]x_\frac{\text{N}}{2}[/tex] = [tex]x_\frac{8}{2}[/tex] = [tex]x_4[/tex] = 20 and [tex]x_\frac{\text{N}}{2}_{+1}=x_\frac{8}{2}_{+1}=x_4_{+1}=x^5[/tex] = 20
[tex]\text{M}_{\text{d}}=\dfrac{20+20}{2}[/tex]
[tex]\text{M}_{\text{d}}=20[/tex]
The mode, denoted by , refers to the most frequent value in the data set.
[tex]\text{Mode = 20}[/tex]
The range (R) is defined as the difference between the maximum and minimum values of a data set.
[tex]\text{R} = \text{MAX} - \text{MIN}[/tex]
[tex]\text{R} = 35- 13[/tex]
[tex]\text{R} = 22[/tex]
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The variables x and y vary inversely. Use the given values to write an equation relating x and y. Then find y when x = −3.
x = −4, y = −6
The equation is y =
The value of y for the inverse variation when x = -3 is derived to be equal to -8, and the equation that relating x and y is: y = 24/x.
What is inverse variationInverse variation is a mathematical relationship between two variables, in which an increase in one variable leads to a proportional decrease in the other variable. Mathematically, inverse variation can be expressed as y = k/x, where y and x are the two variables, k is a constant of proportionality, and the product of y and x is always equal to k.
when x = -4 and y = -6, then k is derived as:
-6 = k/-4
k = 24 {cross multiplication}
equation relating x and y is:
y = 24/x
when x = -3, y is derived as:
y = 24/-3
y = -8
Therefore, the value of y for the inverse variation when x = -3 is derived to be equal to -8, and the equation that relating x and y is: y = 24/x.
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PLEASE HELP ME THIS IS DUE ANY MINUTE
Answer: (7, 1)
Step-by-step explanation:
To find the coordinates of Q' which is the image of point Q(0, 6) under the translation (x, y) → (x + 7, y − 5), we can apply the translation to the coordinates of Q as follows:
x-coordinate of Q' = x-coordinate of Q + 7
= 0 + 7
= 7
y-coordinate of Q' = y-coordinate of Q - 5
= 6 - 5
= 1
Therefore, the coordinates of Q' are (7, 1).
a scientist was interested in studying if students religious beliefs change as they go through college. one hundred randomly selected students were asked before they entered college if they would consider themselves religious, yes or no. four years later, the same one hundred students were asked if they would consider themselves religious, yes or no. the scientist decided to perform mcnemar's test. the data is below. what is the test statistic? after college before college yes no yes 55 23 no 11 11 group of answer choices 1.96 or -1.96 1.35 or -1.35 55 or -55 32 or -32 2.05 or -2.05
Answer:
To perform McNemar's test, we need to find the number of discordant pairs, i.e., the pairs of individuals who change their response from before to after college. In this case, there are 23 students who said "yes" before college but "no" after college, and 11 students who said "no" before college but "yes" after college. Therefore, there are 23 discordant pairs.
The test statistic for McNemar's test is calculated as:
z = (|b-c| - 1) / √(b+c)
where b is the number of discordant pairs who responded "yes" before college, and c is the number of discordant pairs who responded "no" before college.
In this case, b = 23 and c = 11, so:
z = (|23-11| - 1) / √(23+11)
z = 1.96
Therefore, the test statistic is 1.96
The binomial probability model is useful in many situations with variables of whatâ kind?
âDiscrete-valued numerical variables
Categorical variables
âContinuous-valued numerical variables
Bothâ discrete-valued andâ continuous-valued variables
The binomial probability model is useful in situations with discrete-valued numerical variables. Hence, the answer is option (a) discrete-valued numerical variables.
The binomial distribution is a probability model that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (e.g., success or failure, heads or tails, etc.).
The binomial distribution can be used to model a wide range of real-world scenarios, such as the number of defective products in a batch of goods, the number of heads in a series of coin flips, or the number of people who respond positively to a survey question.
Therefore, the correct option is (a) discrete-valued numerical variables.
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a rectangular pool is 9 meters wide and 12 meters long. if you swim diagonally across the pool, how many meters would you be swimming?
if you swim diagonally across the pool, you would be swimming for 15 meters.
Define rectangleA rectangle is a 2-dimensional shape with four straight sides and four right angles. It is a type of quadrilateral where opposite sides are parallel and congruent, and all angles are 90 degrees (right angles). The length of a rectangle is typically defined as the longer side, and the width is the shorter side.
We can use the Pythagorean theorem to find the length of the diagonal:
diagonal² = width² + length²
Substituting the given values, we get:
diagonal² = 9² + 12²
diagonal² = 81 + 144
diagonal² = 225
diagonal = √(225)
diagonal = 15 meters
Therefore, if you swim diagonally across the pool, you would be swimming for 15 meters.
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Kira deposit $2000 into an account that pays simple interest at a rate of 3% per year. How much interest will she be paid in the first two years
Kira will be paid $120 in interest in the first two years.
How much interest will Kira be paid in the first two years?Simple interest is expressed as;
I = P × r × t
Where I is the interest, P is the principal amount, r is the interest rate per year, and t is the time in years.
Given that:
Principal P = $2000Elapsed time t = 2 yearsInterest rate r = 30% = = 3/100 = 0.003Interest I = ?Substituting the given values, we get:
I = P × r × t
I = 2000 × 0.03 × 2
I = $120
Therefore, the interest in the first two years is $120.
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