Answer:
6 x 10^7.
Step-by-step explanation:
If you want to compare the biggest and the tiniest algae, you have to do some math. Don't worry, it's not hard. Just follow these steps:
- First, change the big algae's length from feet to inches. You know that one foot is 12 inches, right? So just multiply 200 feet by 12 inches and you get 2400 inches. Easy peasy.- Second, divide the big algae's length by the small algae's length. The small algae is super tiny, only 0.00004 inches long. So just divide 2400 inches by 0.00004 inches and you get 60000000. That's a lot of zeros!- Third, write this huge number in a simpler way using scientific notation. That means you move the decimal point until there is only one number before it, and then you write how many places you moved it as a power of 10. If you move it to the left, the power is positive; if you move it to the right, the power is negative. Here, you move it seven places to the left, so the power is positive 7: 60000000 = 6 x 10⁷.And that's it! The ratio of the big algae to the small algae in scientific notation is 6 x 10⁷. Isn't math fun?
Write Yes if the situation is an example of random sampling. Write No if the situation is not. State your reason for your answer.
1. The teacher asked the first 5 students on her class seating chart to write down where the class should go on a field trip.
2. Clara surveyed more than half the teachers at her school and then, without looking, selected the responses for her sample.
3. To get a random sampling of every student in her school, Cheryl surveyed all the students in her math class.
4. A company sent e-mails to its customers asking them to e-mail back their opinion of the company’s products. Only 10 of them e-mailed back.
The teacher asked the first 5 students on her class seating chart to write down where the class should go on a field trip is yes
Clara surveyed more than half the teachers at her school and then, without looking, selected the responses for her sample is no
To get a random sampling of every student in her school, Cheryl surveyed all the students in her math class is no
A company sent e-mails to its customers asking them to e-mail back their opinion of the company’s products. Only 10 of them e-mailed back is no
1) Yes, this is an example of random sampling.
The teacher used a systematic method of selecting the first 5 students on her seating chart to ensure that the sample is representative of the class.
2) No, this is not an example of random sampling.
Clara did not use a random selection method to choose the responses for her sample, which can result in a biased sample.
3) No, this is not an example of random sampling.
Cheryl only surveyed the students in her math class, which is not a representative sample of the entire school population.
4) No, this is not an example of random sampling.
The sample is not representative of the entire customer population since only 10 customers responded.
This may lead to biased results if the 10 customers who responded have different opinions than those who did not respond.
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a rectangular restaurant kitchen has an area of 91 square meters. its perimeter is 40 meters. what are the dimensions of the kitchen?
Let's assume that the length of the rectangular kitchen is L and the width is W. We know that the area of the kitchen is 91 square meters, so we can write:
L x W = 91
We also know that the perimeter of the kitchen is 40 meters, which means:
2L + 2W = 40
We can simplify this equation by dividing both sides by 2:
L + W = 20
Now we have two equations:
L x W = 91
L + W = 20
We can use substitution to solve for one of the variables. Let's solve for L:
L = 20 - W
Now we can substitute this expression for L in the first equation:
(20 - W) x W = 91
Expanding this equation gives us a quadratic equation:
W^2 - 20W + 91 = 0
We can solve for W using the quadratic formula:
W = (20 ± √(20^2 - 4 x 1 x 91)) / (2 x 1)
W = (20 ± 3) / 2
W = 11 or W = 9
If W is 11, then L is 9. If W is 9, then L is 11. Therefore, the dimensions of the kitchen are either 9 meters by 11 meters or 11 meters by 9 meters.
In summary, we can use the area and perimeter of a rectangular shape to find its dimensions by setting up equations and solving for the variables. In this case, we used substitution and the quadratic formula to find the possible dimensions of a rectangular kitchen with an area of 91 square meters and a perimeter of 40 metres.
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the lower class limit represents the smallest data value that can be included in the class.True/False
the lower class limit represents the smallest data value that can be included in the classThe statement is true.
The lower class limit is the smallest value that can be included in a class interval.
Therefore, the statement is correct.
The lower class limit represents the smallest data value that can be included in a particular class. In a frequency distribution table, data values are grouped into classes, and each class has a lower and upper class limit. The lower class limit denotes the lowest value within that class, and any data value equal to or greater than the lower limit but less than the upper limit falls into that class.
The statement is true, as the lower-class limit indeed represents the smallest data value that can be included in the class.
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Use the given minimum and maximum data entries, and the number of classes, to find the class width, the lower class limits, and the upper class limits. minimum = 8, maximum=79, 7 classes
The upper class limits are- 29, 39, 49, 59, 69, 79, 89
The lower class limits are- 20, 30, 40, 50, 60, 70, 80
The class midpoints are- 24.5, 24.5, 44.5, 54.5, 64.5, 74.5, 84.5
The class boundaries are- 29.5, 39.5, 49.5, 59.5, 69.5, 79.5
And the number of individuals included in the summary is 84.
Here, we are given the following dataset-
Age (yr) when Frequency
award was won
20-29 27
30-39 32
40-49 15
50-59 3
60-69 5
70-79 1
80-89 1
Upper class limit is the largest data value that can go in a class.
Thus, the upper class limits are- 29, 39, 49, 59, 69, 79, 89
Lower class limit is the smallest data value that can go in a class.
Thus, the lower class limits are- 20, 30, 40, 50, 60, 70, 80
The class midpoint is the average of the upper and lower limits of a class. Class midpoint = (upper limit + lower limit)/ 2
Thus, the class midpoints are- 24.5, 24.5, 44.5, 54.5, 64.5, 74.5, 84.5
Class boundary is the midpoint of the upper class limit of a class and the lower class limit of the previous class.
Thus, the class boundaries are- 29.5, 39.5, 49.5, 59.5, 69.5, 79.5
Frequency gives us the number of individuals/ objects belonging to a particular class.
Thus, the number of individuals included in the summary = 27 + 32 + 15 + 3 + 5 + 1 + 1 = 84
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complete question:
Identify the lower class limits, upper class limits,
class width, class midpoints, and class boundaries for
the given frequency distribution. Also identify the
number of individuals included in the summary.
Age (yr) when
award was won
20-29
30-39
40-49
50-59
60-69
70-79
80-89
Frequency
27
32
15
3
5
1
1
A photo of a beetle in a science book is increased to 555% as large as the actual size. If the beetle is 14 millimeters, what is the size of the beetle in the photo?
A photo of a beetle in a science book is increased to 555% as large as the actual size. If the beetle is 14 millimeters. The size of the beetle in the photo is 77.7 millimeters.
To determine the size of the beetle in the photo, we can multiply its actual size by the percentage increase in size. 555% can also be expressed as a decimal, 5.55. Therefore, to find the size of the beetle in the photo, we multiply 14 millimeters by 5.55, which gives us 77.7 millimeters. This means that the beetle appears to be almost six times larger in the photo than its actual size. It's important to note that the size of the beetle in the photo may vary depending on the size of the book it's printed in or the resolution of the image.
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verify that f = ∇f and evaluate the line integral of f over the given path. f(x, y, z) = z x i j ln(x)k, f(x, y, z) = y z ln(x); circle (x − 6)2 y2 = 1 in the clockwise direction
To verify that f = ∇f, we need to find the gradient of f and compare it to f.
The line integral of f over the given path = 0
The gradient of f is given by:
∇f = (∂f/∂x) i + (∂f/∂y) j + (∂f/∂z) k
= (z/x) i j + 0 j k + (x ln(x)) k
Now, we can see that f = ∇f, since the corresponding components match:
f(x, y, z) = z x i j ln(x)k
= (z/x) i j x ln(x)k
= (z/x) i j + 0 j k + (x ln(x)) k
= (∂f/∂x) i + (∂f/∂y) j + (∂f/∂z) k
= ∇f
To evaluate the line integral of f over the given path, we need to parameterize the path and then compute the integral. The given path is a circle with center (6,0) and radius 1, so we can parameterize it as:
r(t) = <6 + cos(t), sin(t), 0>, 0 ≤ t ≤ 2π
Using this parameterization, we can compute the line integral as:
∫f(r(t)) ⋅ r'(t) dt from 0 to 2π
where r'(t) is the derivative of r(t) with respect to t.
We have:
r'(t) = <-sin(t), cos(t), 0>
f(r(t)) = y z ln(x) = sin(t) ⋅ 0 ⋅ ln(6 + cos(t)) = 0
So the line integral simplifies to:
∫0 dt from 0 to 2π
The integral of 0 over any interval is 0, so the final result is:
0
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a boat is pulled by a winch on a dock, and the winch is 12 feet above the deck of the boat (see figure). the winch pulls the rope at a rate of 4 feet per second. find the speed of the boat when 15 feet of rope is out. what happens to the speed of the boat as it gets closer and closer to the dock?
Answer is Speed of boat = 4 * 3.75 = 15 feet per second
To find the speed of the boat when 15 feet of rope is out, we can use the formula:
Speed of boat = rate of rope being pulled * time
We know that the rate of rope being pulled is 4 feet per second, and the amount of rope out is 15 feet. So, we can calculate the time it takes for 15 feet of rope to be pulled out, the equation is:
Time = distance / rate = 15 / 4 = 3.75 seconds
Now that we have the time, we can use the formula above to find the speed of the boat:
Speed of boat = 4 * 3.75 = 15 feet per second
As the boat gets closer and closer to the dock, the speed of the boat will decrease. This is because the angle of the rope pulling the boat towards the dock becomes sharper and sharper, causing more and more of the pulling force to be directed upwards instead of forwards. Additionally, the winch itself will be pulling at a sharper angle, reducing its effective force. This means that the boat will slow down as it approaches the dock, eventually coming to a stop when the pulling force is no longer sufficient to overcome the resistance of the water.
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Polynomial Long Division: Problem Type 1
-Your answer should be given the quotient and remainder-
**Algebra 1**
For the given polynomials after solving the long division, the quotient of the polynomial is x+3 and the remainder of the polynomial is 0.
Long Division: Long division is the method of performing division operations on the polynomials. In the given polynomial the divisor is 3x+7 and the dividend is 3x²+16x+21.
To know the quotient and remainder we have to perform the long division. It is almost likely normal division only but, only we can perform it with polynomials.
The long division for the given polynomial is performed below:
3x + 7 ) 3x²+16x+21 ( x + 3
3x² + 7x
-------------------------
9x + 21
9x + 21
----------------------------
0
From the above analysis, we can conclude that the quotient is x+3 and the remainder is 0.
For, clear understanding attaching the handwritten solution.
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the appropriate chi-square test will be performed to test the claim. what is the contribution of the monday absences to the calculation of the chi-square test statistic?
The contribution of the Monday absences to the calculation of the chi-square test statistic would depend on the size of the observed and expected frequencies in that cell relative to the other cells in the table.
Without more information about the specific claim being tested and the data being analyzed, it is difficult to provide a precise answer. However, in general, if the claim being tested involves a comparison of the frequency of absences on Mondays to the frequency of absences on other days of the week, then the number of Monday absences would likely be one of the variables included in the calculation of the chi-square test statistic.
The chi-square test is a statistical test that is used to determine if there is a significant association between two categorical variables. In order to perform the test, the observed frequencies of each category of each variable are compared to the expected frequencies, which are calculated based on the assumption of independence between the variables. The difference between the observed and expected frequencies is then squared, divided by the expected frequency, and summed across all categories of both variables to obtain the chi-square test statistic.
If the claim being tested involves a comparison of the frequency of absences on Mondays to the frequency of absences on other days of the week, then the number of Monday absences would likely be one of the categories of one of the variables included in the calculation of the chi-square test statistic. For example, if the data were organized into a contingency table with one variable representing the day of the week and the other variable representing the frequency of absences on that day, then the number of Monday absences would be one of the cells in the table. The contribution of the Monday absences to the calculation of the chi-square test statistic would depend on the size of the observed and expected frequencies in that cell relative to the other cells in the table.
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Let X1,…,Xn be an independent trials process, and S∗n be their standardized sum. What is limn→[infinity]P(−0.28
If X1,…,Xn be an independent trials process, and S∗n be their standardized sum then,
limn→[infinity]P(S∗n > -0.28) = 0.6103
To answer this question, we need to use the central limit theorem. The central limit theorem states that if we have a large enough sample size, the distribution of the standardized sum (S∗n) approaches a normal distribution.
In this case, we want to find the limit of the probability that S∗n is greater than -0.28 as n approaches infinity.
Let Z be a standard normal random variable, then:
P(S∗n > -0.28) = P((S∗n - E[S∗n]) / sqrt(Var[S∗n]) > (-0.28 - E[S∗n]) / sqrt(Var[S∗n]))
= P(Z > (-0.28 - 0) / 1)
= P(Z > -0.28)
Using a standard normal distribution table, we can find that P(Z > -0.28) is approximately 0.6103.
Therefore, limn→[infinity]P(S∗n > -0.28) = 0.6103, since as n approaches infinity, S∗n approaches a standard normal distribution.
The correct question should be :
Let X1,…,Xn be an independent trials process, and S∗n be their standardized sum. What is limn→[infinity]P(S∗n > -0.28)?
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a similar extra-large protein bar company has a manufacturing process that creates snack bars with a process mean of 18 ounces and standard deviation of 2.5 ounces. according to cpk is this process capable of meeting an 17.5 ounce -2.5 requirement?
The given manufacturing process has a CpK value of 0.4, which indicates that it is not capable of meeting the requirement of producing protein bars with a weight of 17.5 ounces.
Explanation:
The CpK (Process Capability Index) value is a measure of how well a process is capable of meeting the specifications or requirements. It takes into account both the process mean and the variability of the process. A CpK value of 1 indicates that the process is capable of meeting the requirement, while a CpK value less than 1 indicates that the process is not capable of meeting the requirement.
In this case, the process mean is 18 ounces and the standard deviation is 2.5 ounces. To find the CpK value, we need to calculate the upper and lower specification limits. Since the requirement is to produce protein bars with a weight of 17.5 ounces, and the requirement is at -2.5 from the process mean, the lower specification limit would be 18 - 2.5 = 15.5 ounces. The upper specification limit would be 18 + 2.5 = 20.5 ounces.
The CpK value can be calculated using the formula:
CpK = min((USL - mean)/3σ, (mean - LSL)/3σ)
where USL is the upper specification limit, LSL is the lower specification limit, σ is the standard deviation, and mean is the process mean.
Substituting the values, we get:
CpK = min((20.5 - 18)/(3 × 2.5), (18 - 15.5)/(3 × 2.5))
= min(0.4, 0.4)
= 0.4
Since the CpK value is less than 1, the process is not capable of meeting the requirement of producing protein bars with a weight of 17.5 ounces. Therefore, the company needs to improve its manufacturing process to meet the requirements.
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Find two positive numbers whose squares have a sum of 74 and a difference of 24.
Answer:
Step-by-step explanation:
Given,
Two positive number whose squares have a sum of 74 and a difference of 24
To Find:
The two positive number.
Explanation
Let the two positive numbers be x and y.
Then according to the question, we have two equations:
[tex]x^2 + y^2 = 74[/tex] (equation 1)
[tex]x^2 - y^2 = 24[/tex] (equation 2)
Now, use equation 2 to solve for one of the variables in terms of the other.
Adding [tex]y^2[/tex] to both sides gives:
[tex]x^2 = y^2 + 24[/tex]
Taking the square root of both sides gives:
[tex]x = \sqrt{(y^2 + 24)}[/tex]
Now substitute this expression for x into equation 1 and solve for y:
[tex](y^2 + 24) + y^2 = 74[/tex]
[tex]2y^2 + 24 = 74[/tex]
[tex]2y^2 = 50[/tex]
[tex]y^2 = 25[/tex]
[tex]y = 5[/tex] (since we're looking for a positive number)
Now we can use the expression we found for x to get:
[tex]x = \sqrt{(y^2 + 24)} = \sqrt{25 + 24} = \sqrt{49} = 7[/tex]
So the two positive numbers are x = 7 and y = 5.
Therefore, the solution is x = 7 and y = 5.
Answer:
7 and 5
Step-by-step explanation:
Let x and y be the two unknown positive numbers.
Set up a system of equations using the defined variables and the given information:
[tex]\begin{cases}x^2 + y^2 = 74\\x^2 - y^2 = 24 \end{cases}[/tex]
Solve the system of equations by the method of elimination.
Add the two equations to eliminate the terms in y:
[tex]\begin{array}{crcccc}&x^2&+&y^2&=&74\\\vphantom{\dfrac12}+&x^2&-&y^2&=&24\\\cline{2-6}\vphantom{\dfrac12}&2x^2&&&=&98\end{array}[/tex]
Solve for x:
[tex]\begin{aligned}2x^2&=98\\2x^2 \div 2&=98 \div 2\\x^2&=49\\\sqrt{x^2}&=\sqrt{49}\\x&=\pm7\end{aligned}[/tex]
As x is positive, x = 7 only.
To find the value of y, substitute x = 7 into one of the equations:
[tex]\begin{aligned}x^2+y^2&=74\\(7)^2+y^2&=74\\49+y^2&=74\\49+y^2-49&=74-49\\y^2&=25\\\sqrt{y^2}&=\sqrt{25}\\y&=\pm 5\end{aligned}[/tex]
As y is positive, y = 5 only.
Therefore, the two positive numbers whose squares have a sum of 74 and a difference of 24 are 7 and 5.
a department store carries different cotton bed sheets, which vary by threadcount (the number of horizontal and vertical threads per square inch). the correlation between threadcount and cost of the bed sheets is moderate and positive. suppose a particular sheet is at the 90th percentile of both threadcount and cost. relative to all the sheets at the 90th percentile of threadcount, this means that this sheet is...
A department store carries different cotton bed sheets, for a particular sheet is at the 90th percentile of both threadcount and cost, means that this sheet is about what we'd except from regression relationship. So, option(a) is right one.
There is a moderate, positive correlation between threadcount of a bed sheet, and its price. If considering a regression relationship between the two variables, it is reasonable to assume that the threadcount is the independent or predictor variable, and its cost is the dependent or response variable- as more the resources involved in a production (here, threadcount), more expensive it will be, and usually not the other way round.
Since the correlation is positive, higher threadcount will be associated with higher cost.
When a bed sheet is at the 90th percentile of threadcount, it can be said that this particular bed sheet has threadcount greater than about 90% of all the bed sheets at the store.
When a bed sheet is at the 90th percentile of cost, it can be said that this particular bed sheet is costlier than about 90% of all the bed sheets at the store.
Due to the moderate positive correlation, a bed sheet at the 90th percentile of threadcount would be expected to have a cost that is also around the 90th percentile of cost- a slightly lesser or a slightly greater value is also acceptable. Thus, a bed sheet at the 90th percentile of both threadcount and cost, relative to all the sheets at the 90th percentile of threadcount, is "about what we'd expect from the regression relationship", and not lower or higher than what is expected from the regression relationship. Hence, the first option is correct.
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Complete question:
a department store carries different cotton bed sheets, which vary by threadcount (the number of horizontal and vertical threads per square inch). the correlation between threadcount and cost of the bed sheets is moderate and positive. suppose a particular sheet is at the 90th percentile of both threadcount and cost. relative to all the sheets at the 90th percentile of threadcount, this means that this sheet is.....
a) about what we'd except from regression relationship
b) lower cost than we'd except from regression relationship
c) higher cost than we'd except from regression relationship.
Indicate below weather the equation in the box is true or false
Answer:
False
Step-by-step explanation:
4/8 equals to 1/2 but 6/10 equals to 3/5. Correct would be if it was 5/10
On a test that has a normal distribution, a score of 53 falls two standard deviations above the mean, and a score of 33 falls two standard deviations below the mean. Determine the mean of this test.
The solution is: A score of approximately 38.2 separates the top 53% from the bottom 47% on this English test.
Here, we have,
We can use the inverse normal distribution function to find the z-score corresponding to the desired percentile, and then use the formula for standardizing a normal variable to find the corresponding raw score.
The score that separates the top 53% from the bottom 47% on an English test with a normal distribution, mean of 37.6, and standard deviation of 7.6 can be found using the inverse normal distribution function.
We need to find the z-score that corresponds to the 53rd percentile. We can do this using a standard normal distribution table or a calculator. The z-score corresponding to the 53rd percentile is approximately 0.07.
We can use the formula for standardizing a normal variable to find the corresponding raw score: z = (X - mean) / standard deviation Rearranging this formula, we get: X = z * standard deviation + mean
Plugging in the values we have: X = 0.07 * 7.6 + 37.6 X ≈ 38.2
A score of approximately 38.2 separates the top 53% from the bottom 47% on this English test.
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complete question:
scores on an english test are normally distributed with a mean of 37.6 and a standard deviation of 7.6. find the score that separates the top 53% from the bottom 47%
show that if a ⊆ c and b ⊆ d, then a × b ⊆ c × d
(x, y) is an element of the set c × d, since x is an element of c and y is an element of d.
Since (x, y) was an arbitrary element in a × b, we can conclude that every element in a × b is also in c × d. Thus, we have shown that if a ⊆ c and b ⊆ d, then a × b ⊆ c × d.
To show that if a ⊆ c and b ⊆ d, then a × b ⊆ c × d, follow these steps:
Step 1: Understand the notation.
a ⊆ c means that every element in set a is also in set c.
b ⊆ d means that every element in set b is also in set d.
Step 2: Consider the Cartesian products.
a × b is the set of all ordered pairs (x, y) where x ∈ a and y ∈ b.
c × d is the set of all ordered pairs (x, y) where x ∈ c and y ∈ d.
Step 3: Show that a × b ⊆ c × d.
To prove this, we need to show that any ordered pair (x, y) in a × b is also in c × d.
Let (x, y) be an arbitrary ordered pair in a × b. This means that x ∈ a and y ∈ b.
Since a ⊆ c, we know that x ∈ c because every element in set a is also in set c.
Similarly, since b ⊆ d, we know that y ∈ d because every element in set b is also in set d.
Now, we have x ∈ c and y ∈ d, so the ordered pair (x, y) belongs to c × d.
Step 4: Conclusion
Since any arbitrary ordered pair (x, y) in a × b also belongs to c × d, we can conclude that a × b ⊆ c × d.
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george has (-2x 5) dollars. evan has (6x 77) dollars. george and evan have the same amount of money. how much do they each have?
By setting up some equations, George and Evan each have 23 dollars.
To find how much money George and Evan each have, we can set up the equation:
-2x + 5 = 6x + 77
First, we can simplify by subtracting 5 from both sides:
-2x = 6x + 72
Next, we can subtract 6x from both sides:
-8x = 72
Finally, we can solve for x by dividing both sides by -8:
x = -9
Now that we have found the value of x, we can substitute it back into one of the original expressions to find how much money George and Evan each have. Let's use the expression for George:
-2x + 5 = (-2)(-9) + 5 = 23
So, George has 23 dollars. To find how much Evan has, we can substitute x = -9 into his expression:
6x + 77 = 6(-9) + 77 = 23
So, Evan also has 23 dollars. Therefore, George and Evan each have 23 dollars.
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−3(x+1)(x−3) in standard form
Answer: [tex]-3x^{2} +6x+9[/tex]
Step-by-step explanation:
andre and mai are discussing how to solve for side . andre thinks he can use the equation to solve for . mai thinks she can use the equation to solve for . do you agree with either of them? show or explain your reasoning.
It is important to carefully consider the given information and the specific equation being used in order to determine the appropriate method for solving for a specific side of a shape.
Without knowing the specific equation mentioned in the question, it is difficult to determine whether Andre or Mai's approach is correct. However, in general, the equation used to solve for a specific side of a shape depends on the information given about the other sides and angles of the shape.
If the equation involves the known values of angles and/or sides that are not the one being solved for, then either Andre or Mai's approach may be valid, depending on which side or angle is known.
However, if the equation only involves the unknown side and no other information about the shape is given, then neither approach would be correct. In such a case, additional information or equations would be needed to solve for the unknown side.
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ABCD is a quadrilateral in which the angles at A and C are right angle Prove that /AB/² - / CD/2= /BC/2 - [AD) ²
In any right-angled triangle, the square of the longest side of it (i.e., the hypotenuse) is equal to the sum of the squares of the other two sides
How to solveFrom the above question, by applying Pythagoras' theorem, we can say :
AB² + CD²
= OB²+OA²+OD²+OC²
= OB²+OC²+OA²+OD²
= BC²+AD² [PROVED]
(Thus, OB²+OC² = BC² and OA²+OD² = AD², by pythagoras theorem)
_______________________________
PYTHAGORAS THEOREM
_______________________________
In any right-angled triangle, the square of the longest side of it (i.e., the hypotenuse) is equal to the sum of the squares of the other two sides (i.e., its height and base).
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Which of the following statements about the mean absolute deviation (MAD) is the most accurate? A. It is the square root of the standard deviation. B. It can be a positive number or a negative number. C. It is measured in the same units as the original data. D. It is the arithmetic mean of the squared deviations from the mean.
The most accurate statement about the mean absolute deviation (MAD) is that it is measured in the same units as the original data. MAD is the arithmetic mean of the absolute deviations from the mean, which means that it measures the average distance between each data point and the mean. It is different from standard deviation, which measures the spread of the data around the mean, and is calculated by taking the square root of the arithmetic mean of the squared deviations from the mean. MAD can only be a positive number, as it measures distances. Therefore, the correct answer is C.
C. It is measured in the same units as the original data.
The mean absolute deviation (MAD) is a measure of dispersion or variability in a dataset. It is calculated by finding the arithmetic mean of the absolute deviations from the mean of the dataset. Since the absolute deviations are in the same units as the original data, the MAD is also measured in the same units as the original data.
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(a) If sup A < sup B, show that there exists an element b ∈ B that is an upper bound for A.
(b) Give an example to show that this is not always the case if we only assume sup A ≤ sup B.
(a) We have shown that there exists an element b ∈ B that is an upper bound for A.
(b) The statement in part (a) is not always the case if we only assume sup A ≤ sup B.
(a) If sup A < sup B, show that there exists an element b ∈ B that is an upper bound for A.
Proof:
1. By definition, sup A is the least upper bound for set A, and sup B is the least upper bound for set B.
2. Since sup A < sup B, there must be a value between sup A and sup B.
3. Let's call this value x, where sup A < x < sup B.
4. Now, since x < sup B and sup B is the least upper bound of set B, there must be an element b ∈ B such that b > x (otherwise, x would be the least upper bound for B, which contradicts the definition of sup B).
5. Since x > sup A and b > x, it follows that b > sup A.
6. As sup A is an upper bound for A, it implies that b is also an upper bound for A (b > sup A ≥ every element in A).
Thus, we have shown that there exists an element b ∈ B that is an upper bound for A.
(b) Give an example to show that this is not always the case if we only assume sup A ≤ sup B.
Example:
Let A = {1, 2, 3} and B = {3, 4, 5}.
Here, sup A = 3 and sup B = 5. We can see that sup A ≤ sup B, but there is no element b ∈ B that is an upper bound for A, as the smallest element in B (3) is equal to the largest element in A, but not greater than it.
This example shows that the statement in part (a) is not always the case if we only assume sup A ≤ sup B.
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8. Parkinson's disease: A survey was conducted of patients
with Parkinson's disease. Of 164 patients who said they
exercised regularly, 76 reported falling within the previous
six months. Of 96 patients who said they did not exercise regularly, 48 reported falling within the previous six months.
Can you conclude that the proportion of patients who fall is
less for those who exercise than for those who do not? Use
the a= 0.05 level of significance.
consider a device with 7 parts. for the device to work properly, at least one of the parts need to work. if each part works with probability p=0.216, what is the probability that the device will work?
Therefore, The probability that the device will work is 0.634 or 63.4%.
This problem can be solved using the complement rule. The complement of the device working is all the parts failing. Therefore, the probability of the device not working is (1 - 0.216)^7 = 0.366. To find the probability of the device working, we subtract this from 1:
1 - 0.366 = 0.634.
To find the probability that the device will work, we'll use the complementary probability. This means we'll first find the probability that all parts fail and then subtract it from 1. Let's denote the probability of a part failing as q, which is equal to 1 - p.
Step 1: Calculate q.
q = 1 - p = 1 - 0.216 = 0.784
Step 2: Calculate the probability of all parts failing.
P(all parts fail) = q^7 = 0.784^7 ≈ 0.1278
Step 3: Calculate the probability that the device will work.
P(device works) = 1 - P(all parts fail) = 1 - 0.1278 ≈ 0.8722
In conclusion, the probability that the device will work is approximately 0.8722.
Therefore, The probability that the device will work is 0.634 or 63.4%.
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Most large companies rely on one person to evaluate systems requests instead of relying on a systems review committee.
true or false
Most large companies rely on one person to evaluate system time requests instead of relying on a systems review committee. The above statement is true.
Most large companies do not rely on just one person to evaluate system requests. They typically rely on a systems review committee, which consists of multiple individuals with diverse expertise, to make more informed and balanced decisions regarding their systems.
Many small companies rely on a single person rather than a group of people to evaluate demand. The request is reasonable if possible. Attaching a report required by new federal law is an example of a blank check project. Limitations may include hardware, software, time, authorization, rights or cost.
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Brandon bought 3 hot dogs and 2 sodas for $14.50 Carson bought 4 hot dogs and 1 soda for $16 how much did each cost?
what is a percentage?
Answer: A percentage is a way of expressing a number as a fraction of 100. It is denoted by the symbol % and is used to indicate a proportion or a part of a whole. For example, 50% means 50 out of 100, or half of a whole. Percentages are commonly used in a variety of contexts, including finance, mathematics, statistics, and everyday life. They are used to express changes in quantity or value, to calculate interest rates, to compare different amounts or values, and to represent probabilities and percentages in statistics.
Step-by-step explanation:
Answer:
Sure, here's a longer and cooler explanation of percentages:
In our everyday lives, we often encounter situations where we need to compare one quantity to another. For example, we might want to know what percentage of a pizza we've eaten, or what percentage of our salary goes towards taxes. That's where percentages come in – they allow us to express one quantity as a fraction of another, using a common base of 100.
So, what is a percentage, exactly? At its most basic level, a percentage is simply a way of expressing a fraction with a denominator of 100. For example, if we say that 25 out of 100 people like pizza, we can also say that 25% of people like pizza. The symbol "%" is used to represent a percentage, so we would write this as "25%".
But percentages are more than just a shorthand way of writing fractions – they also allow us to easily compare different quantities, even if they have different units. For example, if we know that a product has a 20% discount, we can easily calculate the sale price without needing to know the original price. Similarly, if we know that a city's population has increased by 10%, we can compare this to the population of another city, even if the actual numbers are different.
Percentages are used in a wide range of fields, from finance to science to sports. In finance, percentages are used to calculate interest rates, inflation, and stock market returns. In science, percentages are used to express probabilities, error margins, and experimental results. And in sports, percentages are used to compare player statistics and determine playoff rankings.
In short, percentages are a powerful tool for expressing and comparing quantities. Whether you're calculating a discount, measuring your golf handicap, or analyzing data from a scientific experiment, percentages are an essential part of the process. So next time you see a percentage sign, remember that it's not just a symbol – it's a gateway to a whole world of numerical comparisons and insights.
Step-by-step explanation:
What do 5x+35 degrees equal?
Answer:
Factor 5 out of 5x+35 deg.
5 (x+7 deg)
Step-by-step explanation:
use spherical coordinates to evaluate the integral ∫ ∫ ∫ dzdydx/√(2 x^2 y^2 z^2)
The value of the integral ∫ ∫ ∫ dzdydx/√(2 x^2 y^2 z^2) in spherical coordinates is 4π.
To evaluate the integral ∫ ∫ ∫ dzdydx/√(2 x^2 y^2 z^2) using spherical coordinates, we need to express the integrand and the volume element in terms of spherical coordinates.
First, let's express the integrand in terms of spherical coordinates. We have:
√(2 x^2 y^2 z^2) = √(2 r^2 sin^2θ cos^2ϕ r^2 sin^2θ sin^2ϕ r^2 cos^2θ)
= r^2 sinθ cosϕ sinθ sinϕ cosθ = r^2 sinθ cosθ sinϕ cosϕ
So the integrand becomes:
1/√(2 x^2 y^2 z^2) = 1/r^2 sinθ cosθ sinϕ cosϕ
Next, let's express the volume element in terms of spherical coordinates. We have:
dV = dz dy dx = r^2 sinθ dr dθ dϕ
Now we can write the integral in spherical coordinates as:
∫ ∫ ∫ dzdydx/√(2 x^2 y^2 z^2)
= ∫₀²π ∫₀ⁿπ ∫₀^∞ (1/r^2 sinθ cosθ sinϕ cosϕ) r^2 sinθ dr dθ dϕ
Simplifying this expression, we get:
∫₀²π ∫₀ⁿπ ∫₀^∞ sinϕ dϕ dθ dr/2
= ∫₀²π ∫₀ⁿπ (-cosϕ) dθ dr
= 4π
Therefore, the value of the integral ∫ ∫ ∫ dzdydx/√(2 x^2 y^2 z^2) in spherical coordinates is 4π.
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If y = 4 find slope, X-intercept and y-intercept.
Answer:
An equation in the form y = mx + b is in the 'slope y-intercept' form where m is the slope and b is the y-intercept. We can rewrite our equation, y = 4, in slope y-intercept form as follows: y = 0x + 4. Here, it is clear that the slope, or m, is zero. Therefore, the slope of the horizontal line y = 4 is zero
