The coefficient of determination is 0.49. This means that approximately 49% of the variation in the dependent variable can be explained by the variation in the independent variable.
What is coefficient of determination?
The coefficient of determination, also known as R-squared (R²), quantifies the extent to which the variation in the dependent variable can be accounted for or attributed to the independent variable(s) in a regression model.
On the other hand, the coefficient of correlation, represented as r, measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where a value of 1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and 0 suggests no linear relationship.
In order to assess the percentage of variability in the dependent variable (y) that can be explained by the independent variable (x), we calculate the coefficient of determination (r²). This value indicates the proportion of the variance in the dependent variable that can be understood based on the variation in the independent variable.
To calculate [tex]r^2[/tex], we square the coefficient of correlation (r):
[tex]r^2 = (0.7)^2 = 0.49[/tex]
So, the coefficient of determination is 0.49. This means that approximately 49% of the variation in the dependent variable can be explained by the variation in the independent variable.
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in the year 2018, it was estimated that approximately 28,000 floridians were homeless. a social worker estimates that 78% of these people were age 18 and up. in the distribution of ages of homeless floridians, an 18 year old would be considered what percentile? group of answer choices 22nd percentile 78th percentile 28th percentile 18th percentile
The an 18-year-old homeless Floridian would be considered at the 22nd percentile in the distribution of ages of homeless Floridians.
the social worker estimated that 78% of the homeless population in Florida in 2018 were age 18 and up, which means that 22% of the homeless population were under 18 years old. Therefore, an 18-year-old would be at the 22nd percentile in the age distribution of homeless Floridians.
based on the given information, an 18-year-old homeless Floridian would be at the 22nd percentile in the age distribution of homeless Floridians.
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biologists want to determine the number of raccoons in a particular area. they captured 16 raccoons, tagged them, and released them back into the area. the next week, 40 raccoons were caught, of which 9 were tagged. what is the best estimate of the number of raccoons in the area?
The best estimate of the number of raccoons in the area is approximately 71.
The best estimate of the number of raccoons in the area can be obtained using the mark and recapture method, also known as the Lincoln-Petersen index.
The formula for the Lincoln-Petersen index is:
Estimated population size = (Number of marked individuals in first sample * Total number of individuals in second sample) / Number of marked individuals recaptured in second sample
In this case, 16 raccoons were initially captured and tagged, and in the subsequent sample of 40 raccoons, 9 were found to be tagged.
Using the formula, the estimated population size would be:
Estimated population size = (16 * 40) / 9 = 71.11
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A photographer had to change the size of his cover photo. He increased the length by 30% and decreased the width by 10%. By what percent was the area of the final photo changed?
Answer:
17%---------------------
Let the dimensions be x and y.
The area is:
A = xyWhen sides have changed we get:
x + 30% = x + 0.3x = 1.3xy - 10% = y - 0.1y = 0.9yThe new area is:
A = 1.3x * 0.9y = 1.17xyThe difference in areas is:
1.17xy - xy = 0.17xyIt represents 17% increase.
HELP!!! Please solve this logarithmic equation for the value of the equation. Be sure to check for extraneous solutions. Thank you!
[tex]D:2x > 0\wedge x+2 > 0\\D:x > 0 \wedge x > -2\\D: x > 0[/tex]
[tex]\log_42x+\log_4(x+2)=2\\\log_4(2x(x+2))=2\\2x^2+4x=4^2\\2x^2+4x-16=0\\x^2+2x-8=0\\x^2+2x+1-9=0\\(x+1)^2=9\\x+1=3 \vee x+1=-3\\x=2 \vee x=-4[/tex]
[tex]-4\not\in D[/tex]
Therefore [tex]x=2[/tex].
Given that P(A|B)=0.22 and P(B)=0.46, what is P(A AND B)?
Round your answer to three decimal places.
P(A AND B) is approximately 0.101 (rounded to three decimal places).
Conditional probability is defined as the likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome. Conditional probability is calculated by multiplying the probability of the preceding event by the updated probability of the succeeding, or conditional, event.
To find P(A AND B), we can use the conditional probability formula:
P(A AND B) = P(A|B) * P(B)
Given:
P(A|B) = 0.22
P(B) = 0.46
Plugging in the values:
P(A AND B) = 0.22 * 0.46
Calculating the result:
P(A AND B) = 0.1012
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In a regular polygon (all sides and angles are equal-sized), the measure of each exterior angle is 12.5%
of the measure of each Interior angle.
Write and solve an equation to find m, the measure of each exterior angle.
Equation
Answer
Using the given information, the measure of each exterior angle in the polygon is 20°
Measure of angles in a polygon
From the question, we are to determine the measure of each exterior angle in the polygon
Let the number of sides in the polygon be n.
Sum of exterior angles in a polygon = 360°
Thus,
Measure of one exterior angle = 360°/n
From the given information,
The measure of each exterior angle is 12.5% of the measure of each interior angle
The measure of each interior angle = (n - 2)180° / n
Thus,
360°/n = 12.5% of (n - 2)180° / n
360° = 12.5% of (n - 2)180°
Solve for n
360° = 0.125 × (n - 2)180°
360° = (n - 2)22.5°
360° = 22.5n° - 45°
22.5n° = 360° + 45°
22.5n° = 405°
n = 405°/22.5°
n = 18
Then,
Measure of each exterior angle = 360° / 18
Measure of each exterior angle = 20°
Hence, the measure of each exterior angle is 20°
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Given: △STQ,
ST = TQ,
SD ⊥ TQ ,
m∠1=32°
Find: m∠S, m∠T, m∠Q
The angles in the triangle are as follows:
m∠S = m∠Q = 58°
m∠T = 64°
How to find the angles of a triangle?The unknown angles in the triangle can be found as follows:
In the triangle STQ, ST = TQ and SD is perpendicular to TQ.
Therefore, let's find the unknown angles as follows:
Hence, base on ST = TQ, STQ is an isosceles triangle. Therefore,
m∠S = m∠Q
Therefore,
m∠Q = 180 - 90 - 32
m∠Q = 58 degrees
m∠S = m∠Q = 58 degrees
Finally,
m∠T = 180 - 58 - 58
m∠T = 64 degrees
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The pack burro race is the biggest event at Rockyville's annual Burro Days. Participants run the race with a burro, or donkey, running alongside. This year, there is a crack across the road before the finish line that some burros think is the finish line. So far, 3 of the burros stopped at the crack before finishing the race, while 5 burros finished without stopping. Based on the data, estimate how many of the remaining 85 burros will stop before the finish line. If necessary, round your answer to the nearest whole number.
Out of the remaining 85 burros, 32 burros are expected to stop before the finish line.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
3 out of the 5 + 3 = 8 burros stopped before the finishing line, hence the probability is given as follows:
p = 3/8.
Out of 85 burros, the expected number to stop before the finish line is given as follows:
3/8 x 85 = 32 burros. (rounded up).
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30 = 2(x + 6) solve for x
Answer:
x = 9
Step-by-step explanation:
30 = 2(x +6)
30 = 2x +12
Subtract 12 from both sides.
18 = 2x
divide both sides by 2.
9 = x
First, we can simplify the equation by dividing both sides by 2:
30/2 = x + 6
This gives us:
15 = x + 6
Now we can solve for x by subtracting 6 from both sides:
15 - 6 = x
Therefore, the solution is:
x = 9.
Why did the congruent triangles get caught cheating?
because their sides were corresponding.
answers:
1. aas (g).
2. sas (h).
3. sss (n).
4. asa (s).
5. hl (c).
6. none - aaa (t).
7. asa (0).
8. none - ssa (d).
9. aas (i).
10. sas (w).
11. sss (p).
12. hl (r).
13. asa (e).
In a math class with 27 students, a test was given the same day that an assignment was due. There were 18 students who passed the test and 17 students who completed the assignment. There were 15 students who passed the test and also completed the assignment. What is the probability that a student who passed the test did not complete the homework?
The probability that a student who passed the test did not complete the homework is 1 / 6.
How to find the probability ?This is a conditional probability problem and we are looking for the probability that a student who passed the test did not complete the homework.
Assuming event A is the event that a student passed the test and B is event that a student completed the assignment.
We have :
P ( B' | A ) = P ( A ∩ B ' ) / P (A)
P ( B' | A ) = ( 3 / 27 ) / ( 18 / 27 )
P ( B' | A ) = 3 / 18
P (B' | A ) = 1 / 6
In conclusion, the probability that a student who passed the test did not complete the assignment is 1/6.
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sometimes two variables are statistically correlated, but there is actualy a third variable that is driving this relationship. an example provided in class was the correlation between ice cream sales and violent crimes, where the third variable was temperature. what is the name of this type of correlation
The type of correlation that occurs when two variables are statistically correlated due to the influence of a third variable is called a spurious correlation.
A spurious correlation is a type of correlation that occurs when two variables are statistically related to each other, but the relationship is not causal. Instead, the relationship is driven by the influence of a third variable that is related to both variables. This type of correlation can be misleading and can lead to incorrect conclusions if not properly understood.
For example, consider the relationship between ice cream sales and violent crime. Studies have found a positive correlation between these two variables, meaning that as ice cream sales increase, so do violent crimes. However, it is unlikely that there is a causal relationship between these two variables. Instead, the real cause of the correlation is likely the temperature. As the temperature increases, people are more likely to buy ice cream and to be out and about, which increases the opportunity for violent crime to occur. Thus, the temperature is the third variable that is driving the spurious correlation between ice cream sales and violent crime.
It is a type of correlation where there is no causal relationship between the two variables that are correlated. Instead, the correlation is driven by the influence of a third variable that is related to both variables. In the example given, the correlation between ice cream sales and violent crimes is spurious, as the real cause of the correlation is the temperature, which influences both variables.
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Kelly can drive 45 miles on 5 gallons of gas. If Kelly keeps driving at this same rate, how far can she travel on 33 gallons of gas.
(A) 279
(B) 345
(C) 297
(D) 927
Answer:
(C) 297
Step-by-step explanation:
Write a proportion. 45 miles is to 5 gallons as x miles is to 33 gallons.
45 / 5 = x / 33
9 = x / 33
x = 297
A force of 60 newtons is applied to a 10 cm² surface. The force applied is then increased by 15 newtons and the surface area is increased by 15 cm². Shayna says "The pressure decreases by more than 40%" Is Shayna correct? Yes/No yes, You must show how you get your answer. Show your working h pressure = force area
7 + x to the fifth power =
Answer:
Step-by-step explanation:
[tex](7+x)^5[/tex]
What is the range of the following: 68, 56, 40, 10, 51, 15
Answer:58
Step-by-step explanation:
The range of a set of numbers is the difference between the largest and smallest numbers in the set.
To find the range of the following set of numbers: 68, 56, 40, 10, 51, 15
First, we need to find the largest and smallest numbers in the set.
The largest number is 68 and the smallest number is 10.
So, the range is:
68 - 10 = 58
Therefore, the range of the set of numbers is 58.
amazon claims that if you are a prime member, 85% of your packages will arrive within two business days. you have decided that you want to know if this claim is true. you take a simple random sample of 25 students at your school and 19 of the students claim that their packages arrived within two business days of ordering. a. what is the population proportion? what is the sample proportion? please use correct symbols in your answer.
Population proportion (claim): p = 0.85
Sample proportion: [tex]\hat p[/tex]= 19/25
What is proportion?
In statistics, proportion typically refers to the proportion or percentage of individuals or items in a population that have a specific characteristic or belong to a certain category.
In this scenario, the population proportion refers to the proportion of all Prime members' packages that arrive within two business days. The claim made by Amazon is that this population proportion is 85%.
Let's denote the population proportion as p.
a. The population proportion:
p = 0.85
The sample proportion, on the other hand, refers to the proportion of packages that arrived within two business days among the 25 students in the random sample. We can calculate the sample proportion using the number of students who claimed their packages arrived within two business days.
Let's denote the sample proportion as [tex]\hat p[/tex] (pronounced "p-hat").
Given:
Number of students in the sample (n) = 25
Number of students who claimed their packages arrived within two business days (x) = 19
b. The sample proportion:
[tex]\hat p[/tex] = x / n
[tex]\hat p[/tex] = 19 / 25
Therefore, the sample proportion is 19/25.
To summarize:
Population proportion (claim): p = 0.85
Sample proportion: [tex]\hat p[/tex] = 19/25
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The mean weight for a typical bunch of bananas in grocery stores is 3.54 pounds. The owner of a grocery store will reject a shipment of bananas if the mean weight of the banana bunches is less than 3.54 pounds. The owner randomly selects and weighs 30 bunches of bananas. A significance test at an alpha level of tests the hypotheses H 0: Mu = 3.54 pounds; pounds. What is a Type II error in this situation?
Answer: Based on the sample mean, the owner concludes that the mean weight of all of the bunches of bananas is not less than 3.54 pounds when the true mean weight is actually less than 3.54 pounds.
The fourth choice in this scenario is the Type II error: (d) Using the sample mean, the owner determines that the average weight of all the banana bunches is more than 3.54 pounds even though the real average weight is lower.
When the null hypothesis—in this case,
The average weight of the banana bunches is 3.54 pounds—is not accepted despite being erroneous, a Type II mistake takes place.
In other words, despite the cargo of bananas not meeting the requisite weight criteria, the owner fails to reject it. In this case, the owner may experience a loss in sales or reputation as a result of the poor quality of the bananas, as well as losses from selling the underweight bananas at a loss or even throwing them away.
The probability of making a Type II error can be minimized by increasing the sample size or decreasing the significance level (alpha level) of the test. However, a Type II error can never be completely eliminated.
Therefore, the correct option is d.
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Volumes of a Composite Solid
12.
10 cm
4 cm
4cm
The volume of composite solid is 418.67 cm³.
We have to find the volume of Cone and cylinder.
First, Volume of Cone
= (1/3)πr²h
Given that the radius (r) of the cone is 5 cm and the height (h) is 4 cm, we can substitute these values into the formula:
= (1/3) (3.14) (5)² (4)
= 104.67 cm³
Second, Volume of cylinder
= πr²h
Given that the radius (r) of the cylinder is 5 cm and the height (h) is 4 cm, we can substitute these values into the formula:
= π (5)² (4)
= 3.14 x 100
= 314 cm³
Thus, the volume of composite solid
= 314 + 104.67
= 418.67 cm³
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consider the following solution of 9x-7= -70
what properties of equality can justify the two steps in the solution
A.addition and division property
B. addition and multiply property
C. subrtraction and mutiply property
D. subtraction and division property
Answer:
A. Addition and division property--------------------------
The first step involves addition of 7 to both sides and the second step involves division of both sides by 9.
They indicate the addition and division property of equality respectively.
Therefore correct choice is A.
At first, a tank was completely filled with water. A pump was turned on for some time to drain water from the tank. The line graph shows the volume of water in the tank over 40 minutes.
a)how much water was drained out of the tankin one minute
b)how long will it take for the water to be drained out of the tank completely?
see the attachment below.
10 liters of water was drained out of the tank in one minute and it would take 80 minutes to completely drain the water
How much water was drained out of the tankin one minuteThis is the slope of the graph
From the graph, we have
(x, y) = (0, 800) and (40, 400)
So, we have
Slope = (400 - 800)/(40 - 0)
Evaluate
Slope = -10
This means that 10 liters of water was drained out of the tank in one minute
How long for the water to be drained out of the tank completely?From (a), the equation of the line would be
y = -10x + 800
When the water is completely out, we have
-10x + 800 = 0
So, we have
x = 80
This means that it would take 80 minutes
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a bicycle wheel has a diameter of 2.8 ft if it rotates at 40 rpm how far will it travel in 2 hours
A map of three airstrips labeled
A, B, and C is shown below. About
how far is airstrip C from airstrip A
Answer:
192.17 mi
Step-by-step explanation:
three fire hydrants in a neighborhood are represented on a map. the coordinates of the fire hydrants are (0,0) , (2,5) , and (7,y) . the fire hydrants are arranged in a right triangle, where y is a natural number less than 10 . find y .
We can use the distance formula to find the distances between the fire hydrants and determine whether they form a right triangle. The value of y is 4.
The distance between (0,0) and (2,5) is:
√((2-0)² + (5-0)²) = √29
The distance between (0,0) and (7,y) is:
√((7-0)² + (y-0)²) = √(49 + y²)
The distance between (2,5) and (7,y) is:
√((7-2)² + (y-5)²) = √(25 + (y-5)²)
If these distances form a right triangle, then the Pythagorean theorem must be satisfied:
(√29)² + (√(49 + y²))² = (√(25 + (y-5)²))²
Simplifying this expression, we get:
29 + 49 + y² = 25 + (y-5)²
Expanding the square on the right-hand side, we get:
29 + 49 + y² = 25 + y² - 10y + 25
Simplifying this expression, we get:
y = 4
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Mrs. B tutors outside of her normal
teaching job. She charges $60 for one
hour sessions and $40 for half hour
sessions. One week she can work a
maximum of 12 hours, but hopes to make
more than $800 tutoring. Graph a system
of inequalities below to determine how
many one hour sessions (x) and half hour
sessions (y) she could possibly teach to
reach her goals. Is it possible for Mrs.
Keesler to teach 5 one hour sessions and
14 half hour sessions? Explain.
Let x be the number of one hour sessions that Mrs. B teaches and let y be the number of half hour sessions that she teaches per week. Then we can write the following system of inequalities to represent her goals:
60x + 40y > 800 (She hopes to make more than $800 tutoring)
x + y <= 12 (She can work a maximum of 12 hours per week)
To determine how many one hour sessions and half hour sessions she can teach, we need to graph these inequalities on a coordinate plane. The graph should show the shaded region that satisfies both inequalities.
To graph the inequality 60x + 40y > 800, we can first rewrite it as:
3x + 2y > 40
Then we can graph the line 3x + 2y = 40 by plotting the points (0,20) and (13.33,0) and drawing a line through them. Since we want to graph the inequality 3x + 2y > 40, we need to shade the region above the line.
To graph the inequality x + y <= 12, we can simply graph the line x + y = 12 by plotting the points (0,12) and (12,0) and drawing a line through them. Since we want to graph the inequality x + y <= 12, we need to shade the region below the line.
The shaded region that satisfies both inequalities is the region that is above the line 3x + 2y = 40 and below the line x + y = 12. This region is a triangle with vertices at (0,12), (8,4), and (13.33,0).
To determine if Mrs. B can teach 5 one hour sessions and 14 half hour sessions, we can plug these values into the inequalities and see if they are satisfied:
60(5) + 40(14) = 860 > 800 (This inequality is satisfied)
5 + 14 = 19 <= 12 (This inequality is not satisfied)
Since the second inequality is not satisfied, it is not possible for Mrs. B to teach 5 one hour sessions and 14 half hour sessions.
a sample of n sludge specimens is selected and the ph of each one is determined. the one-sample t test will then be used to see if there is compelling evidence for concluding that true average ph is less than 7.0. what conclusion is
For the sample of n sludge specimens is selected and the conclusion and the pH of each one is determined.
Null hypothesis:The null hypothesis will be rejected in favour of the alternative hypothesis only if sample evidence suggests that H0 is false. If the sample does not strongly contradict H0, we will continue to believe in the plausibility of the null hypothesis. The two possible conclusions from a hypothesis-testing analysis are then reject H0 or fail to reject H0.
A) Reject the null hypothesis. There is sufficient evidence that the true average pH is less than 7.0.
B) Reject the null hypothesis. There is sufficient evidence that the true average pH is less than 7.0.
C) Reject the null hypothesis. There is sufficient evidence that the true average pH is less than 7.0.
D) Reject the null hypothesis. There is sufficient evidence that the true average pH is less than 7.0.
E) Reject the null hypothesis. There is sufficient evidence that the true average pH is less than 7.0.
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cody builds mailboxes. if he charges $20 for each mailbox, his total revenue will be
To determine Cody's total revenue if he charges $20 for each mailbox, we need to know the number of mailboxes he sells. Let's denote the number of mailboxes as 'n'.
Cody's total revenue can be calculated by multiplying the price per mailbox ($20) by the number of mailboxes sold (n):
Total revenue = Price per mailbox × Number of mailboxes sold
Total revenue = $20 × n
Therefore, Cody's total revenue will be $20n, where 'n' represents the number of mailboxes he sells.
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what factor should -8-7i be multiplied by to find the quotient? enter any complex numbers in the form .
The factor that -8 - 7i should be multiplied by to find the quotient is 1 + 2i and the quotient is (-22 - 23i) / 5.
When dividing complex numbers of the form a + bi by another complex number of the form c + di, we use the following method:
Multiplying both the numerator and denominator by the conjugate of the denominator, c - di, we get:
(a + bi)(c - di)/(c + di)(c - di) = [(ac + bd) + (bc - ad)i]/(c² + d²)
where a, b, c, and d are real numbers and i is the imaginary unit with the property i² = -1.
In the given question, the denominator is 1 - 2i, so its complex conjugate would be 1 + 2i. Therefore, we need to multiply -8 - 7i by 1 + 2i in both numerator and denominator to get the quotient: (-8 - 7i)(1 + 2i) / (1 - 2i)(1 + 2i) = (-8 - 23i - 14) / (1 + 4) = (-22 - 23i) / 5
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An urn contains 6 red beads, 4 blue beads, and 2 green beads. If a single bead is picked at random, what is the probability that the bead is blue?
Give your answer as a fraction.
[tex]|\Omega|=6+4+2=12\\|A|=4\\\\P(A)=\dfrac{4}{12}=\dfrac{1}{3}\approx33.3\%[/tex]
Answer:
Step-by-step explanation: 6 + 4 + 2 = 12 (denominator)
Put 4 (blue beads) in numerator
4/12 reduces to 1/3
Final answer is 1/3
Biologists studying horseshoe crabs want to estimate the percent of crabs in a certain area that are longer than 35 centimeters. The biologists will select a random sample of crabs to measure.
Which of the following is the most appropriate method to use for such an estimate?
a A one sampe z-interval for a population proportion
b A one sampe z-interval for a sample proportion
c A one sampe z-interval for a population proportion
d A one sampe z-interval for a difference between population proportions
e A one sampe z-interval for a difference between sample proportins
The most appropriate method to use for estimating the percent of horseshoe crabs longer than 35 centimeters in a certain area would be a one-sample z-interval for a population proportion (Option C).
In this scenario, the biologists want to estimate a percentage or proportion (percent of crabs longer than 35 centimeters) for a specific population (horseshoe crabs in a certain area). A one-sample z-interval for a population proportion is used when estimating a single population proportion based on a random sample. It allows for determining a confidence interval for the true proportion in the population using the sample data.
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