The angle G is (1/18) th {or (20/360)th } fraction of complete circle.
The angle G is measured to be 20°.
We know, the total angle of a complete circle is 360°.
Thus, by simple fraction we can say,
The angle G fraction of complete circle is = 20° / 360°
Simplifying we get, the angle G fraction of complete circle is = 1/18
Hence the angle G is (1/18 )th fraction of a complete circle.
In mathematical term, fractions are defined as a part of the whole. In other words, fraction is referred to the ratio of the value observing to the whole set of values.
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Determine whether ▰ABCD with vertices A(-4,6), B(-1,7), C(0,4), and D(-3,3) is a rhombus, a rectangle, a square, or none. Select all the apply.
~a.) Rhombus
~b.) Rectangle
~c.) Square
~d.) None
The only statement that is true is b, which states that the quadrilateral is a rectangle.
What is quadrilateral?A quadrilateral is a polygon with four sides and four vertices. The sum of the interior angles of a quadrilateral is always 360 degrees. Quadrilaterals can have sides of different lengths and angles of different measures, giving rise to many different types of quadrilaterals with different properties.
According to the given informationFirst, we find the lengths of the sides of the quadrilateral:
AB = √[(7-6)² + (-1+4)²] = √10
BC = √[(4-7)² + (0-0)²] = 3
CD = √[(3-4)² + (-3+0)²] = √10
AD = √[(6-3)² + (-4+1)²] = √26
Then, we find the slopes of each pair of opposite sides:
AB: (7-6)/(−1+4) = 1/3
BC: (4-0)/(0-(-1)) = 4/1 = 4
CD: (-3-(-4))/(0-(-3)) = 1/3
AD: (6-3)/(-4-(-1)) = -1/5
Now we can analyze each statement:
a.) Rhombus
A rhombus is a quadrilateral with all sides of equal length. We found that AB = CD and AD ≠ BC, so not all sides are of equal length. Therefore, statement a is false.
b.) Rectangle
A rectangle is a quadrilateral with all angles equal to 90 degrees. We can find the slopes of adjacent sides and check if they are opposite reciprocals:
AB: 1/3
BC: 4
CD: 1/3
AD: -1/5
We can see that AB and CD have slopes of 1/3 and are opposite reciprocals, and BC and AD have slopes of 4 and -1/5, respectively, and are also opposite reciprocals. Therefore, all angles of the quadrilateral are 90 degrees. Also, since AB = CD and AD ≠ BC, the quadrilateral is a rectangle. Therefore, statement b is true.
c.) Square
A square is a special type of rectangle with all sides of equal length. We found that AB ≠ AD, so not all sides are of equal length. Therefore, statement c is false.
d.) None
We have determined that the quadrilateral is a rectangle, so it is not "none". Therefore, statement d is false.
Therefore, the only statement that is true is b, which states that the quadrilateral is a rectangle.
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The radius of a circle is 10 cm. Find the diameter, circumference and area of the circle. Show your working.
A researcher administers a treatment to a sample from a population with a mean of m = 60. If the treatment is expected to increase scores and a one-tailed test is used to evaluate the treatment effect, then the null hypothesis would state that m ³ 60.A) TrueB) False
For the given statement after evaluating both the options the correct option is true under the condition that scores increase and null hypothesis is used to find out Treatment effect.
Here, null hypothesis clearly states that there is no significant difference is observed in comparison of sample mean and population mean.
Null hypothesis refers to statistical process which takes certain assumptions regarding two sets of different variables. In the branch of science it is used to find credibility regarding a sample data.
For the given case, the null hypothesis presents that the population mean remains unchanged (m = 60) post treatment, doesn't matter if it is greater than or equal to 60. The alternative hypothesis will be increases the mean for the treatment (m > 60).
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True. Your statement is: A researcher administers a treatment to a sample from a population with a mean of m = 60. If the treatment is expected to increase scores and a one-tailed test is used to evaluate the treatment effect, then the null hypothesis would state that m ≥ 60.
The null hypothesis typically represents no effect or no difference. In this case, the null hypothesis would state that the population mean remains unchanged (m = 60) after the treatment, not that it is greater than or equal to 60. The alternative hypothesis would be that the treatment increases the mean (m > 60).
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a clinical trial is conducted studying the time it takes a certain allergy medication to be effective. a sample of patients in the trial report that it takes 23 minutes, on average, for them to feel the effects of the medication. the researchers report that their 99% confidence interval is: (19.728,26.272) what is the margin of error? round your answer to three decimal places.
Margin of error is equal to half of this width:
6.544 / 2 = 3.272
What is the margin of error?In a confidence interval, the margin of error is half of the width of the interval.
So, the width of the confidence interval is:
26.272 - 19.728 = 6.544
Margin of error is equal to half of this width:
6.544 / 2 = 3.272
Rounding to three decimal places, the margin of error is 3.272.
This means that the researchers are 99% confident that the true mean time for the medication to take effect falls between 19.728 and 26.272 minutes.
The margin of error tells us how much we can expect the sample mean (23 minutes) to differ from the true mean. So, we can say with 99% confidence that the true mean time it takes for the medication to take effect is within 3.272 minutes of the sample mean.
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Question 2
The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.
Which of the following is the appropriate measure of center for the data, and what is its value?
The mean is the best measure of center, and it equals 19.
The median is the best measure of center, and it equals 4.
The median is the best measure of center, and it equals 19.
The mean is the best measure of center, and it equals 4.
Question 5
A recent conference had 900 people in attendance. In one exhibit room of 80 people, there were 65 teachers and 15 principals. What prediction can you make about the number of principals in attendance at the conference?
There were about 820 principals in attendance.
There were about 731 principals in attendance.
There were about 208 principals in attendance.
There were about 169 principals in attendance.
Question 6
A teacher was interested in the subject that students preferred in a particular school. He gathered data from a random sample of 100 students in the school and wanted to create an appropriate graphical representation for the data.
Which graphical representation would be best for his data?
Stem-and-leaf plot
Histogram
Circle graph
Box plot
Question 7
A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.
Sports Basketball Baseball Soccer Tennis
Number of Students 17 12 27 44
Which of the following graphs correctly displays the data?
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
Question 8
A New York City hotel surveyed its visitors to determine which type of transportation they used to get around the city. The hotel created a table of the data it gathered.
Type of Transportation Number of Visitors
Walk 120
Bicycle 24
Car Service 45
Bus 30
Subway 81
Which of the following circle graphs correctly represents the data in the table?
circle graph titled New York City visitor's transportation, with five sections labeled walk 80 percent, bus 16 percent, car service 30 percent, bicycle 20 percent, and subway 54 percent
circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 40 percent, bus 8 percent, car service 15 percent, bicycle 10 percent, and walk 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 80 percent, bicycle 20 percent, car service 30 percent, bus 16 percent, and walk 54 percent
Question 9
A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.
Ice Cream Candy Cake Pie Cookies
81 9 72 36 27
Which statement is the best prediction about the scoops of ice cream the college will need?
The college will have about 480 students who prefer ice cream.
The college will have about 640 students who prefer ice cream.
The college will have about 1,280 students who prefer ice cream.
The college will have about 1,440 students who prefer ice cream.
The measure of the center is 19.
we can predict that about 169 principals
A pie chart shows how the whole is divided into parts
A bar graph with the title favorite sport and the x-axis labeled sport and the y-axis labeled the number of students,
the proportion of students in the sample who prefer ice cream:
81/225 = 0.36
we can predict that about 1440 students prefer ice cream.
What is proportion?
The size, number, or amount of one thing or group as compared to the size, number, or amount of another. The proportion of boys to girls in our class is three to one.
Answer to Question 2:
The appropriate measure of the center for the given box plot is the median, and its value is 19.
Answer to Question 5:
Since 15 out of 80 people in the exhibit room are principals, we can estimate that 15/80 of the total attendees are principals. To estimate the total number of attendees who are principals, we can multiply this fraction by the total number of attendees:
15/80 x 900 = 168.75
So, we can predict that about 169 principals were in attendance at the conference.
Answer to Question 6:
Since the teacher gathered data on the subject that students preferred, a pie chart would be the best graphical representation of the data. A pie chart shows how the whole is divided into parts, which is exactly what the teacher is trying to show.
Answer to Question 7:
A bar graph with the title favorite sport and the x-axis labeled sport and the y-axis labeled the number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44 correctly displays the data.
Answer to Question 8:
A circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent correctly represents the data in the table.
Answer to Question 9:
To estimate the number of students who prefer ice cream, we can use the proportion of students in the sample who prefer ice cream:
81/225 = 0.36
We can estimate the total number of students who prefer ice cream by multiplying this proportion by the total number of students:
0.36 x 4000 = 1440
So, we can predict that about 1440 students prefer ice cream.
Hence, the answers to all question are:
the measure of the center is 19.
we can predict that about 169 principals
A pie chart shows how the whole is divided into parts
A bar graph with the title favorite sport and the x-axis labeled sport and the y-axis labeled the number of students,
the proportion of students in the sample who prefer ice cream:
81/225 = 0.36
we can predict that about 1440 students prefer ice cream.
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a random sample of n equal to 64 scores is selected from a normally distributed population with mu equal to 77 and sigma equal to 21. what is the probability that the sample mean will be less than 79? hint: this is a z-score for a sample.
The probability of the sample mean being less than 79 is 77.64%
In order to solve the given problem we have to take the help of Standard error mean
SEM = ∑/√(n)
here,
∑ = population standard deviation
n = sample size
hence, the z-score can be calculated as
z = ( x' - μ)/σ/√(n)
here,
x' = sample mean
μ = population mean
σ = population standard deviation
n = sample size
adding the values into the formula
SEM = σ / √(n)
= 21/√64
= 2.625
z = (x' - μ)/SEM
= (79-77)/2.625
= 0.76
now, using standard distribution table we find that probability of a z-score is less than 0.77 then converting it into percentage
0.77 x 100
= 77%
The probability of the sample mean being less than 79 is 77.64%
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What is the surface area? * W 17' l 21' h 19
To find the surface area of an object, we need to calculate the area of all its faces and add them up.
Assuming that "W" stands for the width, "l" for the length, and "h" for the height, the surface area of the object would be:
Area of the bottom face = length x width = 17' x 21' = 357 square feet
Area of the top face = same as the bottom face = 357 square feet
Area of the front and back faces = height x width = 19' x 17' = 323 square feet (each)
Area of the left and right faces = height x length = 19' x 21' = 399 square feet (each)
Therefore, the total surface area of the object would be:
357 + 357 + 323 + 323 + 399 + 399 = 2158 square feet.
So, the surface area of the object is 2158 square feet.
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The probability that the golfer will hit at least 6 times in his next 10 attempts is A. 20 %
How to find the probability ?To estimate the probability of the golfer hitting at least 6 times in his next 10 attempts using a table of random numbers, we can perform a simulation.
Let's use the given table of random numbers to simulate 10 attempts for each trial. We can consider each pair of digits as one attempt. We will perform 10 trials and count how many times the golfer hits at least 6 times in 10 attempts.
Now count the number of trials with at least 6 hits:
Trial 2, Trial 5, and Trial 9 have at least 6 hits. That's 3 out of 10 trials.
To estimate the probability, divide the number of successful trials (at least 6 hits) by the total number of trials:
Probability = (Number of successful trials) / (Total number of trials)
Probability = 3 / 10 = 0.3
The estimated probability that the golfer will hit at least 6 times in his next 10 attempts is 30%. There is no exact match among the possible answers, but the closest one is 20%.
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Find the total amount of money in an account at the end of the given time period. compounded monthly, P = $2,000, r = 3%, t = 5 years
The total amount of money in the account at the end of 5 years, compounded monthly, is $2,329.48.
What is statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.
To find the total amount of money in the account, we can use the formula for compound interest:
A = [tex]P*(1 + r/n)^{(n*t)}[/tex]
where:
A is the total amount of money in the account
P is the principal or initial amount of money in the account
r is the annual interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the time period in years
In this case, P = $2,000, r = 0.03 (since 3% is equivalent to 0.03), n = 12 (since the interest is compounded monthly), and t = 5.
So, plugging in the values, we get:
A = [tex]2000*(1 + 0.03/12)^{(125)}[/tex]
A = [tex]2000(1.0025)^{60}[/tex]
A = $2,329.48 (rounded to the nearest cent)
Therefore, the total amount of money in the account at the end of 5 years, compounded monthly, is $2,329.48.
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the mean number of words per minute (wpm) read by sixth graders is 90 with a variance of 529 . if 94 sixth graders are randomly selected, what is the probability that the sample mean would be greater than 87.78 wpm? round your answer to four decimal places.
The probability that the sample mean would be greater than 87.78 wpm is 0.8933.
The problem provides information on the mean and variation of the amount of words per minute (wpm) read by sixth graders, and it asks for the likelihood of receiving a sample mean wpm bigger than a particular value if a random sample of 94 sixth graders is collected.
By using a standard normal distribution table or calculator and estimating the sampling distribution of the sample means as being normal using the central limit theorem, we can find the standard deviation of the sampling distribution and calculate the probability of obtaining a sample mean wpm that is less than or equal to the given value by subtracting this value from 1.
Calculations result in a likelihood of 0.8933, which means there is a good chance the sample mean wpm will be higher than the value provided.
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a researcher wants to determine if zinc levels are different between the top of a glass of water and the bottom of a glass of water. many samples of water are taken. from half, the zinc level at the top is measured and from half, the zinc level at the bottom is measured. would this be a valid matched pair test?
Yes, this would be a valid matched pair test. In a matched pair test, two samples are taken from the same group or individual, and the samples are matched on some criteria such as age, sex, or in this case, location in the glass of water.
The researcher is using a matched pair test, which is an acceptable method to account for individual variations and boost the statistical power of the test, by collecting samples from the top and bottom of the glass of water and matching them according to the position. Due to the fact that any additional changes (such as in the source of the water or pollution) should be uniformly distributed across the two groups, this design also enables the researcher to ascertain whether there is a substantial difference in zinc levels between the top and bottom of the glass of water.
A paired t-test will be used to conduct the test in order to see if there is a significant difference between the zinc levels at the top and bottom of the water glass.
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Red=10
blue=8
yellow=5
what is the ratio of red balls to blue balls?
Answer:1.25
Step-by-step explanation:
it just math
The following table shows Jace's earnings based on the number of hours that he works.
Number of hours 111 222 333
Jace's Earnings \$20$20dollar sign, 20 \$30$30dollar sign, 30 \$40$40dollar sign, 40
Are Jace's earnings proportional to the number of hours that he works?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Yes
(Choice B)
B
No
The correct answer to the given problem is choice B - No.
Jace's earnings are not proportional to the number of hours that he works because if he worked twice as many hours, he would earn twice as much but he is not earning twice the amount.
Jace's earnings are not proportional to the number of hours that he works. Proportional means that one quantity is a constant multiple of the other. In this case, if Jace's earnings were proportional to the number of hours he works, we would expect that if he worked twice as many hours, he would earn twice as much. However, we can see from the table that this is not the case.
For example, when Jace works 1 hour, he earns $20, but when he works 2 hours, he earns $30, which is not double his earnings for 1 hour of work.
Therefore, Jace's earnings are not proportional to the number of hours that he works.
Hence, the correct option is "B".
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To determine whether 2126.5
and 58158
are in a proportional relationship, write each ratio as a fraction in simplest form.
What is 2126.5
as a fraction in simplest form?
Enter your answer in the box.
Answer:
both are 5/13the relationship is proportionalStep-by-step explanation:
You want to know if the fractions (2 1/2)/(6.5) and (5/8)/(1 5/8) are in a proportional relationship, and the simplest form of each.
FractionsEquivalent fractions can be found by multiplying numerator and denominator by the same number.
(2 1/2)/(6.5) = 2·(2 1/2)/(2·6.5) = 5/13
(5/8)/(1 5/8) = 8(5/8)/(8·(1 5/8)) = 5/(8+5) = 5/13
Both fractions are equivalent to 5/13, so their relationship is proportional.
A container built for transatlantic shipping is constructed in the shape of a right
rectangular prism. Its dimensions are 4 ft by 9.5 ft by 13 ft. If the container is entirely
full and, on average, its contents weigh 0.05 pounds per cubic foot, find the total
weight of the contents. Round your answer to the nearest pound if necessary
Thus, the on average the contents weight for the transatlantic shipping is found as 24.7 pounds.
Explain about the rectangular prism:a solid, three-dimensional object with six rectangular faces.It is a prism due to its uniform cross-section along its whole length.Volume is a unit of measurement for the amount of 3-dimensional space a thing occupies. Cubic units are used to measure volume.Given dimension of rectangular prism
Length l = 4ft
width w = 9.5 ft
height h = 13 ft
Volume of rectangular prism = l*w*h
V = 4*9.5*13
V = 494 ft³
Now,
1 ft³ = 0.05 pounds
So,
weight of 494 ft³ = 494*0.05 pounds
weight of 494 ft³ = 24.7 pounds
Thus, the on average the contents weigh for the transatlantic shipping is found as 24.7 pounds.
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a medical researcher wants to estimate , the mean weight of babies born to women over the age of 40. the researcher chooses a random sample of 100 pregnant women who are over 40. using the mean birth weight of the 100 babies in the sample, the researcher calculates the 95% confidence interval for . with 95% confidence, the researcher estimates the mean birth weight of all babies born to women who are over the age of 40 to be between 2935 and 3135 grams. the researcher wants to maintain the 95% level of confidence but report a confidence interval with a smaller margin of error. what should she do? group of answer choices redo the study and choose a different sample of size 100.
Maintain the 95% level of confidence but report a confidence interval with a smaller margin of error, the medical researcher should increase the sample size.
This will provide a more precise estimate of the mean birth weight of babies born to women over the age of 40.
Maintain the 95% level of confidence but report a confidence interval with a smaller margin of error, the researcher should increase the sample size.
The larger the sample size, the smaller the margin of error, which means that the estimated mean birth weight of all babies born to women over the age of 40 will be more precise.
Redoing the study and choosing a different sample of size 100 will not necessarily reduce the margin of error, as the variability in the sample may be the same.
To achieve a smaller margin of error, the researcher needs to increase the sample size.
With a larger sample size, the researcher will have a more representative sample of the population, which will lead to a more accurate estimate of the mean birth weight of all babies born to women over the age of 40.
However, the larger sample size may require more resources and time to collect the data.
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19.
Solve the problem.
2
Find the critical value XR corresponding to a sample size of 5 and a confidence
level of 98%.
(1 point)
O11.143
00.297
13.277
00.484
The critical value of the chi-square distribution corresponding to a sample size of 5 and a confidence level of 98% is given as follows:
0.297 and 13.277.
How to obtain the critical value?To obtain a critical value, we need three parameters, given as follows:
Distribution.Significance level.Degrees of freedom.Then, with the parameters, the critical value is found using a calculator.
The parameters for this problem are given as follows:
Chi-square distribution.1 - 0.98 = 0.02 significance level.5 - 1 = 4 degrees of freedom.Using a chi-square distribution calculator, the critical values are given as follows:
0.297 and 13.277.
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a rectangular prism has a square base with edge length . its volume is . what does the expression represent?
The expression represents the height of the, rectangular prism has a square base with edge length, which is 3 cm.
Explain in detail about what does the expression represent?The expression represents the height of the rectangular prism with a square base of edge length and volume .
To make this more concrete, let's assume some values for and . Let's say that the edge length of the square base is 4 cm, and the volume of the rectangular prism is 48 cubic cm.
Using the formula for the volume of a rectangular prism, we can write:
Volume = Base Area x Height
Since the base of the rectangular prism is a square with edge length 4 cm, its area is:
Base Area = 4 x 4 = 16 square cm
Substituting the given values into the formula for volume, we get:
48 cubic cm = 16 square cm x Height
To solve for the height, we can isolate it on one side of the equation by dividing both sides by 16 square cm:
48 cubic cm ÷ 16 square cm = Height
3 cm = Height
Therefore, in this scenario, the expression represents the height of the rectangular prism, which is 3 cm.
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Of all rectangles with a perimeter of 10 meters, which one has the maximum area? (Give both the dimensions and the area enclosed)
Zone(area) = L x W = 2.5 x 2.5 = 6.25 square meters.
Of all rectangles with an edge of 10 meters, the one that has the greatest zone(area) could be a square.
To see why, let's assume that a rectangle with a border of 10 meters has measurements of length L and width W.
At that point, we know that:
2L + 2W = 10
Rearranging this condition, we get:
L + W = 5
Presently, we need to discover the most extreme range encased by the rectangle, which is given by:
Area = L x W
Able to illuminate for one variable in terms of the other utilizing the condition L + W = 5:
L = 5 - W
Substituting this expression for L into the condition for the zone, we get:
Zone = (5 - W) x W
Extending and disentangling this expression, we get:
Area = 5W - W²
To discover the most extreme esteem of this quadratic expression, we will take its subsidiary with regard to W and set it to break even with zero:
dArea/dW = 5 - 2W =
Tackling for W, we get:
W = 2.5
Substituting this esteem back into the condition for the edge, we get:
L = 2.5
Hence, the measurements of the rectangle that has the greatest region are L = 2.5 meters and W = 2.5 meters, which implies it could be a square. The most extreme zone enclosed by the rectangle is:
Zone(area) = L x W = 2.5 x 2.5 = 6.25 square meters.
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a large sample of x-y data values are analyzed and reveal a correlation coefficient of-.88. which statement is correct? group of answer choices a weak negative relationship exists. the correlation is weak because r is less than -1. if r had been .88, the correlation would have been much stronger. there is no relation. a fairly strong negative linear relationship exists. *
The correct statement is that a fairly strong negative linear relationship exists between the x and y variables.
How to find the relationship between the x and y variables of correlation coefficient?The correlation coefficient is a measure of 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 negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation.
In this case, the correlation coefficient is -0.88, which indicates a strong negative linear relationship between the x and y variables. This means that as the value of x increases, the value of y decreases in a predictable manner.
The negative sign of the correlation coefficient indicates that the relationship is negative, meaning that as one variable increases, the other variable tends to decrease. The absolute value of the correlation coefficient, 0.88, indicates a strong relationship, meaning that the values of the two variables are closely related and can be used to predict each other's values.
Therefore, the correct statement is that a fairly strong negative linear relationship exists between the x and y variables.
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STRUCTURE The ratio of circumference to diameter is the same for every circle. Is the ratio of circumference to radius the same for every circle? Make sure to explain!
No, the ratio of circumference to radius is not the same for every circle.
What is ratio?Ratio refers to the quantitative relation between two or more values, typically expressed in the form of a fraction or a proportion.
According to given information:No, the ratio of circumference to radius is not the same for every circle. The ratio of circumference to diameter, also known as pi (π), is a constant value that remains the same for every circle. It is approximately equal to 3.14 or 22/7. However, the ratio of circumference to radius varies depending on the size of the circle.
The formula for circumference of a circle is C=2πr, where C is the circumference and r is the radius. Therefore, the ratio of circumference to radius is C/r = 2π. This means that for circles of different sizes, the ratio of circumference to radius will differ since the value of pi remains the same while the radius changes.
For example, if we consider two circles, one with a radius of 2 cm and the other with a radius of 4 cm, the ratio of circumference to radius for the first circle will be 2π (since C = 2πr = 2π x 2 = 4π) and for the second circle, it will be 2π (since C = 2πr = 2π x 4 = 8π). Thus, the ratio of circumference to radius is not the same for every circle.
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During a flood, there were 6000 acres of land under water. After 2 days, only 3375 acres of land were under water. Assume that the water receded at an exponential rate. Write a function to model this situation that has a B-value of 1.
where t is measured in days, and A(t) represents the amount of flooded land at time t. This function has a B-value of -0.3118.
To model the situation of the flood, we can use an exponential decay function, which represents the decreasing amount of flooded land over time. The function can be written as:
[tex]A(t) = A0 * e^{(-kt)}[/tex]
where A(t) is the amount of flooded land at time t, A0 is the initial amount of flooded land, k is a constant representing the rate of decay, and e is the mathematical constant approximately equal to 2.718.
To determine the value of k, we can use the given information that after 2 days, only 3375 acres of land were under water. Substituting t = 2 and A(t) = 3375 into the equation above, we get:
[tex]3375 = A0 * e^{(-2k)[/tex]
We also know that initially, there were 6000 acres of land under water. Substituting A0 = 6000 into the equation above, we get:
Dividing both sides by 6000, we get:
ln(0.5625) = -2k[tex]ln(0.5625) = -2k[/tex]
Taking the natural logarithm of both sides, we get:
[tex]ln(0.5625) = -2k[/tex]
Solving for k, we get:
[tex]k = -ln(0.5625)/2[/tex]
k ≈ 0.3118
Therefore, the function to model the situation of the flood is:
[tex]A(t) = 6000 * e^{(-0.3118t)}[/tex]
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Solve for x to make A||B.
A = x + 12
B = x + 48
X = [?]
Answer:
Step-by-step explanation:= x+48=180 ( linier pair )
= x=180-48
= x=132
= x+12=180 (liner pair)
= x=180-12
= x=168
Find the missing value to the nearest hundredth. sin(____) =3/16
1. 10.81°
2. 31.72°
3. 9.29°
4. 34.23°
The value of the angle is 10.81° ( nearest hundredth). ( optionA)
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
The value of sin(tetha) = opposite/hypotenuse.
This means that if sin x = 3/16 , then 3 is the opposite and 16 is the hypotenuse. and the inverse of sin is sin^-1 . Same thing is applied to other functions like cos and tan.
If sinx = 3/16
sin x = 0.1875
x = sin^-1(0.1875)
x = 10.81° ( nearest hundredth)
therefore the missing value is 10.81°.
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if there are no other feasible solutions with a larger objective function value in the immediate neighborhood, then the feasible solution is known as
The feasible solution is known as a locally optimal solution.
It may not be the best possible solution for the entire optimization problem.
If there are no other feasible solutions with a larger objective function value.
The immediate neighborhood, then the feasible solution is known as a locally optimal solution.
This means that the solution is optimal within a particular region of the feasible space but may not necessarily be the globally optimal solution. Bhe best possible solution over the entire feasible space.
In other words, a locally optimal solution is the best possible solution. Among all feasible solutions in its immediate neighborhood or region.
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4. Given the equation (x - 11) ^ 2 + (y + 4) ^ 2 = 15 what is the center and radius of the circle?
6. What is the centerradius form of the circle with center (- 3, 5) that passes through the point \{0, 1\}
The center-radius form of the circle is:
(x + 3)² + (y - 5)² = 25
What is a circle?
It is the center of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
Given the equation (x - 11)² + (y + 4)² = 15, we can see that the equation is in standard form:
(x - h)² + (y - k)² = r²
where (h, k) is the center of the circle, and r is the radius. Comparing the given equation with the standard form, we can see that:
h = 11, k = -4, and r² = 15
Taking the square root on both sides, we get:
r = √15
Therefore, the center of the circle is (11, -4) and the radius is √15.
The center-radius form of the circle with center (-3, 5) that passes through the point (0, 1) can be found using the formula:
(x - h)² + (y - k)² = r²
where (h, k) is the center of the circle and r is the radius. We are given that the center of the circle is (-3, 5), so we can substitute these values into the formula:
(x - (-3))² + (y - 5)² = r²
Simplifying the expression on the left-hand side, we get:
(x + 3)² + (y - 5)² = r²
Now, we need to find the value of r. Since the circle passes through the point (0, 1), we can substitute these values into the equation above:
(0 + 3)² + (1 - 5)² = r²
Simplifying the expression on the left-hand side, we get:
9 + 16 = r²
25 = r²
Taking the square root on both sides, we get:
r = 5
Therefore, the center-radius form of the circle is:
(x + 3)² + (y - 5)² = 25
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Compare the numbers using <, >, or =. 0. 78 ___ 0. 708 < > =
For the given numbers, 78 < 0. 708
To compare two numbers, we need to look at their values and determine which one is larger or smaller. In this case, we have 78 and 0.708. We can start by comparing their whole number parts, which are 78 and 0, respectively. Since 78 is greater than 0, we know that 78 is a larger number.
But what about the decimal parts of these numbers? To compare them, we need to look at the place value of each digit. The first digit after the decimal point in 78 is 0, and the first digit after the decimal point in 0.708 is 7. Since 7 is greater than 0, we know that 0.708 is a larger number than 0.78 in terms of their decimal parts.
Now that we have compared the whole number parts and decimal parts separately, we can combine the results to determine the final comparison. Since 78 is larger than 0 and 0.708 is larger than 0.78 in terms of their decimal parts, we can conclude that:
78 < 0.708
We use the symbol "<" here because 78 is smaller than 0.708.
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If triangle PQR is has a right angle at Q and m<R is 45°, what is the length of PR is PQ is 3?
1. 3
2. 2
3. 2√3
4. 3√2
The length of PR of the triangle is 3√2 units
How to determine the length of PR?Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.
The triangle PQR can be drawn as shown in the attached image. Thus, we can say:
sin 45° = 3/PR (sine = opposite/hypotenuse)
1/√2 = 3/PR (Remember: sin 45° = 1/√2)
PR = 3 * √2
PR = 3√2 units
Thus, the length of PR is 3√2 units
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Please help.
If the radius of the clock is 24 cm and the distance from the top of the clock at point D to the hanger at point B is 2 cm, what is the length from point A to point B?
2 cm
10 cm
12 cm
24 cm
The length from point A to point B on the clock is approximately 24.083 cm, which is closest to 24 cm. This is calculated using the Pythagorean theorem.
Using the Pythagorean theorem, we can calculate the length from point A to point B as follows
First, we need to find the length of the vertical line segment from point D to point A. This is equal to the radius of the clock, which is 24 cm.
Next, we can find the length of the horizontal line segment from point D to point B. This is equal to the distance from the top of the clock at point D to the hanger at point B, which is given as 2 cm.
Now, we can use the Pythagorean theorem to find the length from point A to point B
AB² = AD² + DB²
AB² = (24 cm)² + (2 cm)²
AB² = 576 cm² + 4 cm²
AB² = 580 cm²
AB ≈ 24.083 cm
Therefore, the length from point A to point B is approximately 24.083 cm, which is closest to 24 cm.
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Answer:
The length from point A to point B on the clock is approximately 24.083 cm, which is closest to 24 cm. This is calculated using the Pythagorean theorem.
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true or false: a linear programming problem can have an optimal solution that is not a corner point. select one: true false
It is true that a linear programming problem can have an optimal solution that is not a corner point.
How given statement is true? Explain further?In linear programming, the optimal solution represents the point where the objective function is optimized while still satisfying all the constraints.
In some cases, the optimal solution may occur at a corner point of the feasible region, where two or more of the constraints intersect.
However, it is possible for the optimal solution to occur at a point that is not a corner point, but rather lies on an edge or a line segment of the feasible region.
This can occur when the objective function is parallel to one of the constraint lines or when there are redundant constraints that limit the feasible region.
Therefore, it is true that a linear programming problem can have an optimal solution that is not a corner point.
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