The probability that a person has a disease given that they test positive, when 0.4% of the population has the disease and the test is positive with probability 0.99 if they have the disease and 0.03 if they don't have it, is 0.116 or about 11.6%.
Let D be the event that the person has the disease and T be the event that the person tests positive. We need to calculate P(D|T), the probability that the person has the disease given that they test positive.
Using Bayes' theorem, we have
P(D|T) = P(T|D) * P(D) / P(T)
where P(T|D) is the probability of testing positive given that the person has the disease, P(D) is the prior probability of having the disease, and P(T) is the total probability of testing positive, which can be calculated as
P(T) = P(T|D) * P(D) + P(T|D') * P(D')
where P(T|D') is the probability of testing positive given that the person does not have the disease, and P(D') is the complement of P(D), which is the probability of not having the disease.
Substituting the given values, we get
P(D|T) = (0.99 * 0.004) / [(0.99 * 0.004) + (0.03 * 0.996)]
= 0.116
Therefore, the probability that the person has the disease given that they test positive is 0.116 or about 11.6%.
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We collected data from 9th and 10th. 9th grade students were 45% of the responses and 10th grade were the
rest. Of the 9th graders 31% said they did like the school lunches and 42% of the 10th graders said they did like
the school lunches. Find the probability that if we chose a student at random that they would not like the school
lunches.
Answer is 64.05% probability that if we chose a student at random
To find the probability that a randomly chosen student would not like the school lunches, we need to find the complement of the probability that they do like the school lunches.
The proportion of 9th graders in the sample is 45%, so the proportion of 10th graders is 100% - 45% = 55%.
Of the 9th graders, 31% said they liked the school lunches, so the proportion that did not like them is 100% - 31% = 69%.
Of the 10th graders, 42% said they liked the school lunches, so the proportion that did not like them is 100% - 42% = 58%.
So, the probability that a randomly chosen student would not like the school lunches is:
(0.45 * 0.69) + (0.55 * 0.58) = 0.6405 or 64.05% (rounded to two decimal places).
Therefore, there is a 64.05% probability that if we chose a student at random, they would not like the school lunches.
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please solve for each
Use a calculator or program to compute the first 10 iterations of Newton's method for the given function and initial approximation f(x)=2 sin x + 3x +3.x = 15 Complete the table (Do not found until th
The first 10 iterations of Newton's method for f(x) = 2 sin x + 3x + 3, with initial approximation x₀ = 15, are approximately 8.156, 6.099, 5.091, 4.941, 4.929, 4.929, 4.929, 4.929, 4.929, 4.929
The first 10 iterations of Newton's method for the given function and initial approximation
x₁ = x₀ - f(x₀)/f'(x₀) = 15 - (2sin(15) + 45) / (2cos(15) + 3) ≈ 8.156
x₂ = x₁ - f(x₁)/f'(x₁) ≈ 6.099
x₃ = x₂ - f(x₂)/f'(x₂) ≈ 5.091
x₄ = x₃ - f(x₃)/f'(x₃) ≈ 4.941
x₅ = x₄ - f(x₄)/f'(x₄) ≈ 4.929
x₆ = x₅ - f(x₅)/f'(x₅) ≈ 4.929
x₇ = x₆ - f(x₆)/f'(x₆) ≈ 4.929
x₈ = x₇ - f(x₇)/f'(x₇) ≈ 4.929
x₉ = x₈ - f(x₈)/f'(x₈) ≈ 4.929
x₁₀ = x₉ - f(x₉)/f'(x₉) ≈ 4.929
Therefore, the first 10 iterations are 8.156, 6.099, 5.091, 4.941, 4.929, 4.929, 4.929, 4.929, 4.929, 4.929
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Part A
Alex has \$ 30,000$30,000 in his savings account that earns 10\%10% annually.
How much interest will he earn in one year?
Interest == \$$
Part B
If Alex spends 20\%20% of the interest received on buying furniture for his new house, what amount did he spent on furniture?
A) The amount of interest he will earn in a year is $3,000.
B) The amount he spent on furniture is $600.
Part A: To calculate the interest Alex will earn in one year, use the formula for simple interest:
Interest = Principal × Rate × Time.
In this case, Principal = $30,000, Rate = 10% (0.10), and Time = 1 year. So,
Interest = $30,000 × 0.10 × 1 = $3,000.
Part B: Alex spends 20% of the interest on furniture. To calculate this amount, multiply the interest by 20% (0.20): $3,000 × 0.20 = $600.
Therefore, in one year, Alex will earn $3,000 in interest. He will spend $600 on furniture for his new house.
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Baking company wants to know how many muffins it made in one night if it made b muffins in the first hour then threw half of them away on the second hour due to sour milk. on the third hour they made 3 times as much as the first two hours and then on last hour made 7 more. write an expression of how many they made in total and simplify.
The expression is (5/2)b + 7 for muffins is made by the baking company in total in one night.
To find the total number of muffins the baking company made in one night, we can use the following expression:
Total = b - (b/2) + 3b + 7
Let's break it down by each hour:
- In the first hour, the company made b muffins.
- In the second hour, they threw away half of the muffins made in the first hour, which is b/2. So, they only have b - (b/2) muffins left.
- In the third hour, they made 3 times as much as the first two hours, which is 3b.
- In the last hour, they made 7 more muffins.
If we simplify the expression by combining like terms, we get:
Total = (5/2)b + 7
Therefore, the baking company made (5/2)b + 7 muffins in total in one night.
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Which inequalities are true when m= -4
The inequailty y < m + 4 would be true when m = -4 and all values of y are less than 0
Which inequalities are true when m= -4From the question, we have the following parameters that can be used in our computation:
The statement that m = -4
The above value implies that we substitute -4 for m in an inequality and solve for the other variable (say y)
Take for instance, we have
y < m + 4
Substitute the known values in the above equation, so, we have the following representation
y < -4 + 4
Evaluate
y < 0
This means that the inequailty y < m + 4 would be true when m = -4 and all values of y are less than 0
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Question 4(Multiple Choice Worth 2 points) (Identifying Transformations LC) Use the image to determine the type of transformation shown. Graph of polygon VWXYZ with W at point 3 comma negative 2. A second polygon V prime W prime X prime Y prime Z prime with W prime at point negative 3 comma negative 2. 270° counterclockwise rotation Horizontal translation Reflection across the x-axis Reflection across the y-axis
Reflection across the y-axis is the transformation used to the polygon ABCD. The type of transformation shown is a horizontal translation.
What is Polygon?A polygon is closed geometric shape that is made up of straight line segments connected end to end. It is two-dimensional shape that has three or more sides, angles, and vertices.
In a polygon, sides do not cross each other and vertices are points where two sides meet.
1) The type of transformation shown in the image is a Horizontal translation, because the second polygon A'B'C'D' is moved horizontally to the right of the original polygon ABCD while maintaining its size and shape.
2) 90° clockwise rotation
3) 90° counterclockwise rotation.
4) Reflection across the x-axis.
5) Reflection across the y-axis.
6) Reflection across the y-axis
7) the correct answer is 180° clockwise rotation.
The type of transformation shown is a horizontal translation, since the image has been shifted horizontally from the original position.
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complete question -
I just need help on B PLS :)
The data modeled by the box plots represent the battery life of two different brands of batteries that Mary
tested.
(a) What is the median value of each data set? (just fyi I know the answer to this already) it's Brand X 13 and Brand Y 16
(b) Compare the median values of the data sets. What does this comparison tell you in terms of the
situation the data represent?
Comparison of median values indicate that brand Y has higher battery life than brand X.
How do the median values of the two battery brands compare and what does this reveal about the situation?Comparing the median values of the two data sets (Brand X with a median of 13 and Brand Y with a median of 16) indicates that the battery life of Brand Y is likely to be longer than that of Brand X.
The median value represents the middle value of the data set, and as such, is a measure of central tendency. Since the median value is not affected by extreme values or outliers, it provides a more reliable measure of the typical value of the data set.
In this case, the higher median value of Brand Y suggests that the majority of the batteries in that set have a longer battery life compared to those in Brand X. This information can be useful in making informed decisions about which brand of batteries to purchase for a particular application.
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#1 - The value of y varies directly with x. When y = 75, x = 4. What is the value of y when x = 2? **For your response, enter the numerical value ONLY. NO Letters & NO Spaces. ** *
The answer is 37.5.
What is the value of y when x = 2 if y varies directly with x and when y = 75, x = 4?The problem provides the information that "the value of y varies directly with x", which means that there is a constant of proportionality between y and x, denoted by k. This can be written as an equation: y = kx. To find the value of k, we can use the information given in the problem. When y = 75 and x = 4, we have 75 = k(4), which means k = 75/4. Now, we can use this value of k to find the value of y when x = 2: y = (75/4)(2) = 37.5.
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Find the Circumference and area of the circle with the center C=(-1, 6) and a point on the circle A(3, 9). Round to the nearest tenth
Circumference of circle is 31.4 and area of circle is 78.6
Given, C(-1,6) is center and A(3, 9) is a point on circle.
CA is the radius of the circle.
Using Distance Formula
[tex]r=\sqrt{(3-(-1))^2+(9-6)^2}[/tex]
[tex]r=\sqrt{(4)^2+(3)^2}[/tex]
[tex]r=\sqrt{16+9}[/tex]
[tex]r=\sqrt{25}=5[/tex]
We know the the formula for circumference of circle C = 2πr
C = 2*22/7*5
= 31.428
Rounding to nearest tenth
C = 31.4
Area of the circle = [tex]\pi r^2[/tex]
[tex]A=\frac{22}{7}(5)^2[/tex]
= 78.571
Rounding to nearest tenth
A = 78.6
Hence, circumference of circle is 31.4 and area of circle is 78.6.
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a.
Volume measured in cups (c) vs. the same volume measured in ounces
(z): c = 1/8 z
The equations a-d all represent proportional relationships, meaning that the ratio between the two measurements is constant. This means that for any given area, perimeter, or volume, the two measurements can be determined by simply multiplying or dividing by the constant.
What is equation?An equation is a mathematical expression that relates two or more variables in such a way that the values of the variables satisfy the equation. In other words, an equation is a statement of equality between two expressions, usually involving numbers and symbols. Equations are used to describe physical principles, solve problems, and uncover relationships between different parts of an equation.
a. Volume measured in cups (Vc) vs. the same volume measured in ounces (Vo): Yes, this equation represents a proportional relationship. The ratio between Vc and Vo is constant, meaning that for any given volume, the number of cups is equal to the number of ounces multiplied by the same constant. For example, if Vc = 4 cups and Vo = 32 ounces, then 4 cups = 32 ounces * 1/8, meaning that 1 cup = 8 ounces.
b. Area of a square (A) vs. the side length of the square (s): Yes, this equation represents a proportional relationship. The ratio between A and s is constant, meaning that for any given area, the side length of the square is equal to the area divided by the same constant. For example, if A = 36 square units and s = 6 units, then 36 square units = 6 units * 6, meaning that 1 square unit = 1 unit.
c. Perimeter of an equilateral triangle (P) vs. the side length of the triangle (s): Yes, this equation represents a proportional relationship. The ratio between P and s is constant, meaning that for any given perimeter, the side length of the triangle is equal to the perimeter divided by the same constant. For example, if P = 18 units and s = 3 units, then 18 units = 3 units * 6, meaning that 1 unit = 1/6 of the perimeter.
d. Length (L) vs. width (W) for a rectangle whose area is 60 square units: Yes, this equation represents a proportional relationship. The ratio between L and W is constant, meaning that for any given area, the length of the rectangle is equal to the width multiplied by the same constant. For example, if L = 8 units and W = 5 units, then 8 units = 5 units * 1.6, meaning that 1 unit = 1.6 of the width.
In conclusion, the equations a-d all represent proportional relationships, meaning that the ratio between the two measurements is constant. This means that for any given area, perimeter, or volume, the two measurements can be determined by simply multiplying or dividing by the constant.
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Complete questions as follows-
Decide whether or not each equation represents a proportional relationship. a. Volume measured in cups ( ) vs. the same volume measured in ounces ( ): b. Area of a square ( ) vs. the side length of the square ( ): c. Perimeter of an equilateral triangle ( ) vs. the side length of the triangle ( ): d. Length ( ) vs. width ( ) for a rectangle whose area is 60 square units:
State how many terms are in each algebraic expression:
(a) -112y2 ____________________ [1mark]
(b) 7x2 + 5y – 9xy + 3 __________________ [1mark]
(A) There is only one term in the expression:[tex]-112y^2.[/tex]
(B) There are four terms in the expression[tex]: 7x^2, 5y, -9xy, and 3.[/tex]
In A option, There is only one term within the algebraic expression [tex]-112y^2.[/tex]A term is a single numerical or variable expression this is separated from other expressions through addition or subtraction.
In B option, There are 4 terms within the algebraic expression[tex]7x^2 + 5y - 9xy +[/tex] 3. A time period is a single numerical or variable expression that is separated from other expressions through addition or subtraction.
In this situation, the primary term is[tex]7x^2[/tex], the second time period is 5y, the 0.33 time period is -9xy, and the fourth term is 3.
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Please upload a picture of a piece of paper with the problem worked out, and draw the graph for extra points, there will be 6 of these, so go to my profile and find the rest, and do the same, for extra points. solve the system using the ELIMINATION method.
The solution to this system of equations are x = 7 and y = -3.
How to solve these system of linear equations?In order to determine the solution to a system of two linear equations, we would have to evaluate and eliminate each of the variables one after the other, especially by selecting a pair of linear equations at each step and then applying the elimination method.
Given the following system of linear equations:
3y = 26 - 5x .........equation 1.
6x + 7y = 21 .........equation 2.
Rewriting in standard form, we have:
5x + 3y = 26
6x + 7y = 21
By multiplying equation 1 by 6 and dividing by 5, we have:
6x + 3.6y = 31.2 .........equation 3.
By subtracting equation 3 from equation 2, we have:
3.4y = -10.2
y = -3.
x = (26 - 3y)/5
x = (26 - 3(-3))/5
x = 7
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i need help its due in 2 hours
Answer:
C. The product of two irrational numbers is irrational.
Example: √3•√3=3
11 term of 7 -28 112
The 11th term of this geometric sequence 7 -28, 112, .... include the following: 7,340,032.
How to calculate the nth term of a geometric sequence?In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical equation (formula):
aₙ = a₁rⁿ⁻¹
Where:
aₙ represents the nth term of a geometric sequence.r represents the common ratio.a₁ represents the first term of a geometric sequence.Next, we would determine the common ratio as follows;
Common ratio, r = a₂/a₁
Common ratio, r = -28/7
Common ratio, r = -4
For the 11th term, we have:
a₁₁ = 7(-4)¹¹⁻¹
a₁₁ = 7,340,032.
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A figure with parallel Lines m and n is shown.
The measure of angles A, B, and C for the given parallel lines will be 53°,90°, and 143° corresponding.
What is an example of a parallel line?
In terms of geometry, parallel lines are two separate lines that never cross each other and are located in the same plane. Both vertical and horizontal can be used. A zebra crossing, rows of notebooks and nearby railway tracks are just a few instances of parallel lines that we encounter every day.
As per the parallel lines m and n.
The adjacent angle of B = 37° (corresponding angle same)
m∠B = 180° - (53° + 37°) = 90°
m∠A = 53° (corresponding angle same)
m∠C = 180° - 37° = 143°
Hence "The measure of angles A, B, and C for the given parallel lines will be 53°,90°, and 143° corresponding".
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Which is an expression in terms of π that represents the area of the shaded part of ⊙R
The expression in terms of π that represents the area of the shaded part of ⊙R is 3πR²/4, obtained by subtracting the area of the smaller circle from the larger circle.
How to find the area of the shaded region in terms of π?To find the area of circle of the shaded part of ⊙R, we need to subtract the area of the smaller circle from the area of the larger circle.
The area of a circle is given by the formula A = πr², where r is the radius of the circle.
Let the radius of the larger circle be R and the radius of the smaller circle be r. Then the area of the shaded part can be expressed as:
A(shaded) = A(large circle) - A(small circle)
= πR² - πr²
We can simplify this expression further by noticing that the radius of the smaller circle is half the radius of the larger circle, so r = R/2. Substituting this into the equation gives:
A(shaded) = πR² - π(R/2)²
= πR² - πR²/4
= 3πR²/4
Therefore, the area of the shaded part of ⊙R can be expressed as 3πR²/4. This expression represents the difference in the area between the larger and smaller circles, which gives us the area of the shaded region.
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The expression in terms of π that represents the area of the shaded part of ⊙R is 3πR²/4, obtained by subtracting the area of the smaller circle from the larger circle.
How to find the area of the shaded region in terms of π?To find the area of circle of the shaded part of ⊙R, we need to subtract the area of the smaller circle from the area of the larger circle.
The area of a circle is given by the formula A = πr², where r is the radius of the circle.
Let the radius of the larger circle be R and the radius of the smaller circle be r. Then the area of the shaded part can be expressed as:
A(shaded) = A(large circle) - A(small circle)
= πR² - πr²
We can simplify this expression further by noticing that the radius of the smaller circle is half the radius of the larger circle, so r = R/2. Substituting this into the equation gives:
A(shaded) = πR² - π(R/2)²
= πR² - πR²/4
= 3πR²/4
Therefore, the area of the shaded part of ⊙R can be expressed as 3πR²/4. This expression represents the difference in the area between the larger and smaller circles, which gives us the area of the shaded region.
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How do I fill this chart with the information given?
Fill the two-way frequency table as shown in the image attached.
How to fill the chart with the information given?A two-way frequency table is a way of displaying frequencies for two different categories collected from a single group of people. One category is represented by the rows and the other is represented by the columns.
For the frequency table:
Total = 82
Apple
Total = 24
Students = 22
Teachers = 24 - 22 = 2
Grape
Total = 82 - 25 -24 = 33
Students = 33 - 4 = 29
Orange
Teachers = 25 - 24 = 1
Students
Total = 22 + 29 + 24 = 75
Teachers
Total = 2 + 4 + 1 = 7
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An educational psychologist wants to check claims that regular physical exercise improves academic achievement. To control for academic aptitude, pairs of college students with similar GPAs are randomly assigned to either a treatment group that attends daily exercise classes or a control group. At the end of the experiment, the following scores were reported for the six pairs of participants:
GPAs Pair number Physical Exercise No Physical exercise
1 4 3. 75
2 2. 67 2. 74
3 3. 65 3. 42
4 2. 11 1. 67
5 3. 21 3
6 3. 6 3. 25
7 2. 8 2. 65
Using t, test the null hypothesis at the. 01 level of significance Specify the p-value for this test result. If appropriate (because the test result is statistically significant), use Cohen’s d to estimate the effect size. How might this test result be reported in the literature?
The calculated t-value of 1.100 is less than the critical t-value of 2.718, we fail to reject the null hypothesis.
To test the hypothesis that regular physical exercise improves academic achievement, we will conduct a two-sample t-test for independent samples. The null hypothesis is that there is no difference in the mean academic achievement scores between the treatment group (physical exercise) and the control group (no physical exercise).
Let's calculate the mean and standard deviation for each group:
Treatment group (physical exercise):
mean = (4 + 2.67 + 3.65 + 2.11 + 3.21 + 3.6) / 6 = 3.3833
standard deviation = 0.7589
Control group (no physical exercise):
mean = (3.75 + 2.74 + 3.42 + 1.67 + 3 + 3.25 + 2.65) / 7 = 3.0071
standard deviation = 0.7037
We can now calculate the t-statistic:
t = (3.3833 - 3.0071) / sqrt((0.7589^2 / 6) + (0.7037^2 / 7)) = 1.100
The degrees of freedom for this test are 6 + 7 - 2 = 11 (assuming equal variances).
Using a t-table or a t-distribution calculator with 11 degrees of freedom and a significance level of 0.01, we find that the critical t-value is ±2.718.
Since the calculated t-value of 1.100 is less than the critical t-value of 2.718, we fail to reject the null hypothesis. We do not have enough evidence to conclude that regular physical exercise improves academic achievement.
The p-value for this test can be calculated as the probability of getting a t-value as extreme as 1.100, assuming the null hypothesis is true. Using a t-distribution calculator with 11 degrees of freedom, we find that the p-value is 0.294 (rounded to three decimal places).
Since the test result is not statistically significant (p > 0.01), we do not need to report an effect size using Cohen's d.
This test result could be reported in the literature as follows: "A two-sample t-test for independent samples was conducted to examine the effect of regular physical exercise on academic achievement, while controlling for academic aptitude. Six pairs of college students with similar GPAs were randomly assigned to either a treatment group that attended daily exercise classes or a control group. The mean academic achievement score for the treatment group was 3.3833 with a standard deviation of 0.7589, while the mean academic achievement score for the control group was 3.0071 with a standard deviation of 0.7037. The t-test result was not statistically significant (t(11) = 1.100, p = 0.294), indicating that there is not enough evidence to conclude that regular physical exercise improves academic achievement."
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a beverage company published the probabilities of winning in a bottle-top prize promotion as 5% win a free beverage and 15% win a free music download, while the remaining 80% are non-winners. a consumer plans to sample 200 bottles and conduct a chi-square goodness of fit test to see whether this distribution claimed by the company fits the observed data. what is the expected cell count for music downloads in this study?
The expected cell count for free music downloads in a sample of 200 bottles from a beverage company's prize promotion is 30, based on the company's claimed probabilities of winning.
To find the expected cell count for music downloads in this study, we first need to calculate the total expected counts for each category of the prize promotion.
Given that the company claims that 5% of the bottle-tops will win a free beverage and 15% will win a free music download, the expected counts for each category in a sample of 200 bottles are
Expected count for free beverages = 0.05 * 200 = 10
Expected count for free music downloads = 0.15 * 200 = 30
Expected count for non-winners = 0.80 * 200 = 160
The expected count for music downloads is 30, which is calculated by multiplying the probability of winning a free music download (0.15) by the sample size (200). Therefore, the expected cell count for music downloads in this study is 30.
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Mandy bought a desktop computer system to start her business from home for $4,995. It is expected to depreciate at a rate of 10% per year. How much will her home computer system be worth after 9 years? Round to the nearest hundredth
Mandy's home computer system is expected to be worth $1,576.11.
Mandy's home computer system is expected to depreciate at a rate of 10% per year. After 1 year, the value of the computer system will be 90% of its original value.
After 2 years, it will be worth 90% of that value, or 0.9 × 0.9 = 0.81 times the original value. Continuing in this way, we can write the value of the computer system after n years as [tex]0.9^n[/tex] times its original value. Thus, after 9 years, the computer system will be worth [tex]0.9^n[/tex] times its original value:
Value after 9 years = 4995 × [tex]0.9^n[/tex]
Using a calculator, we find that the value is approximately $1,576.11 when rounded to the nearest hundredth. Therefore, after 9 years, Mandy's home computer system is expected to be worth $1,576.11.
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Mean Mode 42 X X X X 43 X X X - 44 Median Range X X 45 X X 46 47 48
The mean, median, mode and the range of the data given is 44.21, 44, 44 and 3 respectively.
Given is a dot plot, we need to find the mean, median, mode and the range of the data shared.
So, the data is = 43, 43, 43, 43, 44, 44, 44, 44, 44, 45, 45, 45, 46, 46
So, mean = 43×4+44×5+45×3+46×2 / 14
= 619/14 = 44.21
Median = 44+44/2 = 44
Mode = 44
Range = 46-43 = 3
Hence, the mean, median, mode and the range of the data given is 44.21, 44, 44 and 3 respectively.
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4. A person wants to buy a car from Toyota Company. If the price of car
including VAT is Birr 5,000,000 then,
a) What is the price of car before VAT?
b) What is the value of VAT?
Answer:
Step-by-step explanation:a) To find the price of the car before VAT, we need to first calculate the percentage of VAT included in the price:
VAT% = (VAT / Total Price) x 100
where VAT% is the percentage of VAT, VAT is the value of VAT, and Total Price is the price of the car including VAT.
From the given information, we have:
Total Price = Birr 5,000,000
VAT% = 15% (assuming a VAT rate of 15% in Ethiopia)
Therefore, we can solve for the value of the car before VAT as follows:
Total Price = Car Price + VAT
Birr 5,000,000 = Car Price + 0.15Car Price
Birr 5,000,000 = 1.15Car Price
Car Price = Birr 4,347,826.09
So the price of the car before VAT is Birr 4,347,826.09.
b) To find the value of VAT, we can use the same formula as above and solve for VAT:
Total Price = Car Price + VAT
Birr 5,000,000 = Birr 4,347,826.09 + VAT
VAT = Birr 652,173.91
Therefore, the value of VAT is Birr 652,173.91.
Pairs of twins are numbered 1, 1, 2, 2, 3, 3, and so on. They are seated
in a circle so that the least number of gaps between two twins always
equals their assigned number. This is called a twin circle. Note that this
means there is no person between the twins numbered 1 and 1, there is
just one person between the twins numbered 2 and 2, and so on.
Reflections (flips) and rotations (turns) of a twin circle are regarded as
the same. For example, the following are the same twin circles for 4
pairs of twins
a) Two different twin circles for five pair of twins are ( 5,2,4,2,3,5,4,3,1,1,3) and ( 3,1,1,3,4,5,3,2,4,2,5).
b) No twin circles in 3 pair of twins because any of arrangement of them cannot fulfil the condition of twin circle.
c) The partial twin circle ( third circle) present in above figure can't be completed because 4 positions are fixed there and after that number of persons more than seats.
We have a pair twins are numbered 1, 1, 2, 2, 3, 3, and so on. They all seated in a circle so that the least number of gaps between two twins always
equals their assigned number. This is called a twin circle. That is Number of persons between 1 and 1 twins = 0
Number of persons between 2 and 2 twins = 1,
so on.. Reflections (flips) and rotations (turns) of a twin circle are regarded as the same.
a) We have to make two twin circles for five pair twins. The arrangement of pair twins in two different ways with the satisfaction of conditions. So, first arrangement is ( 5,2,4,2,3,5,4,3,1,1,3) and
other arrangement is ( 3,1,1,3,4,5,3,2,4,2,5).
b) There is no twin circle between the arrangement of 3 twin pairs. Because in case of 3 twin pair total members = 3×2 = 6 and number of members can be seat between pairs are 3( 1+2+0). As we know, it is fixed that no person between (1,1). So, we cannot be arrange the 2 pairs with desirable 3 gaps that is 1 person between (2,2) and 2 persons between (3,3).
c) There is total 12 positions to seat in circles. The position of 6 and 1 is fixed. According to above scenario, position next to 1 is for 1 (clockwise) and 5th position from given 1 position in (clockwise) is other member of twin 6. Now, four positions are fixed. Eight positions are left and 4 twin pairs (2,2) , (3,3), (4,4),(5,5). Number of persons seat between 4 pairs are 10 in counts ( greater than position ) so, no such arrangement is possible. Hence, this partial circle can't be completed.
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Complete question:
The above figure complete question.
Pairs of twins are numbered 1, 1, 2, 2, 3, 3, and so on. They are seated in a circle so that the least number of gaps between two twins always
equals their assigned number. This is called a twin circle. Note that this means there is no person between the twins numbered 1 and 1, there is just one person between the twins numbered 2 and 2, and so on. Reflections (flips) and rotations (turns) of a twin circle are regarded as the same. For example, the following are the same twin circles for 4 pairs of twin.
a) Find two twin circles for five pairs of twin
b) Explain why no twin circles in 3 pairs of twin
c) explain why this partial twin circle can't be completed ? ( third circle)
Evaluate (8 + 2)^3 - 6
Step-by-step explanation:
First you need to do of bracket
(8+2)
=10
Second you need to do of exponential sign ^
10^3=1000(note this sign is also called cube)
Now,
1000-6
=994
Answer:
994
Step-by-step explanation:
We need to use order of operations to solve this problem.
( 8 + 2 ) ^ 3 - 6
According to PEMDAS, Parenthesis must be resolved first.
So we get:
10 ^ 3 - 6
Secondly, PEMDAS states that Exponents go next
1000 - 6
Finally, we only have one operation left, subtraction, so we can go ahead and do that.
994 is your answer.
I put a lot of thought and effort into my answers, so a brainliest would be much appreciated!
Nolan is following his family's macaroni and and cheese recipe. The recipe calls 6 cups of shredded cheese 4 tablespoons of milk. He wants to make a smaller batch, so he uses only 3 cups of shredded cheese
Nolan is making a smaller batch of his family's macaroni and cheese recipe, and as a result, he has reduced the amount of shredded cheese to 3 cups. The original recipe called for 6 cups of shredded cheese and 4 tablespoons of milk.
However, since Nolan is using only 3 cups of shredded cheese, he will need to adjust the amount of milk he uses as well.
When reducing the amount of cheese, it is important to keep the ratio of cheese to milk consistent. Therefore, if Nolan is halving the amount of cheese, he should also halve the amount of milk. This means that instead of using 4 tablespoons of milk, he should use only 2 tablespoons of milk.
It is important to note that reducing the amount of cheese and milk in a recipe may also affect the overall taste and texture of the dish. However, by following the recipe and adjusting the amounts accordingly, Nolan can still create a delicious and satisfying macaroni and cheese dish.
In summary, when making a smaller batch of a recipe, it is important to adjust the ingredients accordingly while maintaining the same ratios. Nolan is reducing the amount of cheese in his macaroni and cheese recipe and should also reduce the amount of milk in order to keep the same ratio.
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If the an average American makes around $ 40,000 per year for his or her lifetime and works from age 22 to 65, what amount will he or she pay in taxes for their entire lifetime?
We can see here that the amount he or she will pay in taxes for their entire lifetime is: $344,000
What is tax?Tax is a financial obligation that all people, businesses, and other types of entities must fulfill for a government organization.
Let us say that an average American makes $40,000 for his or her lifetime and works from age 22 to 65, and pays a combined federal and state income tax rate of 20%, the amount of taxes paid per year would be:
$40,000 x 0.20 = $8,000
Over a 43-year period (from age 22 to 65), the total amount of taxes paid would be: $8,000 x 43 = $344,000
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A basket contains a red, a yellow, and a green apple. A second basket contains an orange, a lemon, and a peach. Use an organized list to show all the outcomes in sample space
There are 9 different outcomes in the sample space when selecting one fruit from each basket.
Using an organized list, we can represent all the possible outcomes in the sample space for the two baskets of fruit:
1. Red Apple, Orange
2. Red Apple, Lemon
3. Red Apple, Peach
4. Yellow Apple, Orange
5. Yellow Apple, Lemon
6. Yellow Apple, Peach
7. Green Apple, Orange
8. Green Apple, Lemon
9. Green Apple, Peach
In total, there are 9 different outcomes in the sample space when selecting one fruit from each basket.
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A styrofoam model of a volcano is in the shape of a cone. The model has a circular base with a diameter of 48 centimeters and a height of 12 centimeters. Find the volume of foam in the model to the nearest tenth. Use 3. 14 for TT.
The volume of foam in the model is approximately 27,211.5 cubic centimeters
The radius of the circular base can be found by dividing the diameter by 2:
radius = diameter / 2 = 48 cm / 2 = 24 cm
The formula for the volume of a cone is:
V = (1/3) * π * r² * h
where π is approximately 3.14, r is the radius of the circular base, and h is the height of the cone.
Substituting the values we have:
V = (1/3) * 3.14 * 24² * 12
V = 27,211.52 cm³
Rounding this to the nearest tenth, we get:
V ≈ 27,211.5 cm³
Therefore, the volume of foam in the model is approximately 27,211.5 cubic centimeters
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When calculating the price (p) of an item that has been marked down by 25%, Denise states that the expression
p - 0. 25p will calculate the
sale price. Kristal says that a shorter way to calculate the sale price would be to use the expression 0. 75p. Who is correct
A Denise is correct.
B Kristal is correct. .
C Both Denise and Kristal are correct.
D Neither Denise nor Kristal are correct.

Both Denise and Kristal are correct. The expression "p - 0.25p" is equivalent to "0.75p," which represents the sale price after a 25% markdown. Therefore, option C is the correct answer.
Denise's expression, "p - 0.25p," represents the original price (p) minus the 25% markdown (0.25p). This simplifies to 0.75p, which is indeed the sale price.
On the other hand, Kristal's expression, "0.75p," directly represents the sale price after applying a 25% discount. This expression skips the intermediate step of subtracting the markdown from the original price.
Both expressions, "p - 0.25p" and "0.75p," yield the same result, which is the sale price after a 25% markdown. Therefore, both Denise and Kristal are correct in their calculations.
The choice between the two expressions comes down to personal preference or convenience. Some individuals may find it easier to directly calculate the sale price using a percentage of the original price, while others may prefer subtracting the markdown amount from the original price.
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Let D be the smaller cap cut from a solid ball of radius 6 units by a plane 3 units from the center of the sphere. Express the volume of D as an iterated triple integral in (a) spherical, (b) cylindrical
To express the volume of D as an iterated triple integral in (a) spherical, (b) cylindrical coordinates, we can use the following formulas:
(a) Spherical Coordinates:
We know that the equation of a sphere with radius 6 units is given by:
x^2 + y^2 + z^2 = 6^2
The equation of the plane 3 units from the center of the sphere is given by:
z = 3
To find the equation of the smaller cap cut from the sphere by this plane, we need to find the upper limit of the radial coordinate. This can be found by solving the equation of the sphere for z, and substituting z = 3:
z = sqrt(6^2 - x^2 - y^2)
3 = sqrt(6^2 - x^2 - y^2)
x^2 + y^2 = 27
Thus, the smaller cap D is the region of the sphere bounded by the plane z = 3 and the surface x^2 + y^2 + z^2 = 6^2, with x^2 + y^2 <= 27.
To express the volume of D as an iterated triple integral in spherical coordinates, we can use the following limits:
0 <= r <= sqrt(27)
0 <= θ <= 2π
arcsin(3/6) <= φ <= π
The volume of D can be expressed as the triple integral:
∫∫∫ D r^2 sin φ dr dφ dθ
(b) Cylindrical Coordinates:
To express the volume of D as an iterated triple integral in cylindrical coordinates, we can use the following limits:
0 <= r <= sqrt(27)
0 <= θ <= 2π
3 <= z <= sqrt(6^2 - r^2)
The volume of D can be expressed as the triple integral:
∫∫∫ D r dz dr dθ
(a) In spherical coordinates, the volume element is given by dV = ρ²sin(φ)dρdθdφ. To find the limits of integration, note that the radius of the smaller cap ranges from 0 to 3 units, the angle θ ranges from 0 to 2π, and the angle φ ranges from 0 to φ₀, where φ₀ is the angle between the plane and the line from the sphere's center to the plane's intersection with the sphere.
Using the cosine rule, we can find φ₀ as follows:
cos(φ₀) = (6² + 3² - 3²) / (2 × 6 × 3) = 1/2
φ₀ = π/3
Now, we can express the volume of D as an iterated triple integral in spherical coordinates:
∫(ρ=0 to 3) ∫(θ=0 to 2π) ∫(φ=0 to π/3) ρ²sin(φ)dρdθdφ
(b) In cylindrical coordinates, the volume element is given by dV = rdzdrdθ. To find the limits of integration, note that the height z ranges from 3 to 6 units, the radius r ranges from 0 to √((6 - z)²), and the angle θ ranges from 0 to 2π.
Now, we can express the volume of D as an iterated triple integral in cylindrical coordinates:
∫(z=3 to 6) ∫(θ=0 to 2π) ∫(r=0 to √((6 - z)²)) rdzdrdθ
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