The expression that is equivalent to 135−−−√5–√ is: 131.764.
What is the equivalent expression?An equivalent expression is one that has the same value as another. To evaluate the given expression, the three minus signs all equate to -. So, the question is asking that we subtract the root of 5 from 135.
Also, the root of minus 1 will be subtracted from the answer that we arrive at.
135−−−√5 = 132.764
132.764 - √1 = 131.764
So, the decimal equivalent of this expression is 131.764.
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The stem-and-leaf plot displays data collected on the size of 15 classes at two different schools.
Sky View School Riverside School
0 5, 6, 9
9, 7, 2, 0 1 0, 2, 4, 5, 6, 7
8, 7, 6, 5, 5, 5, 4, 3, 1, 0 2 0, 0, 2, 3, 5
0 3
4 2
Key: 2 | 1 | 0 means 12 for Sky View and 10 for Riverside
Part A: Calculate the measures of center. Show all work. (5 points)
Part B: Calculate the measures of variability. Show all work. (5 points)
Part C: If you are interested in a larger class size, which school is a better choice for you? Explain your reasoning. (2 points)
I really need help on these
The correct option is b, the statement is false because the leading coefficient is -2, which is negative.
Does the parabola opens upwards?
Here we have the quadratic function:
f(x) = -2x² - 4x + 7
Remember that if the leading coefficient is positive, then the parabola opens up, while if the leading coefficient is negative, the parabola opens down.
Here the leading coefficient is -2, is negative, then the parabola opens down.
Then the correct option is the second one, the statement is false because the leading coefficient is negative.
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15)
If f(x) = x³ - 11x² + 34x 24 and x- 4 is a factor of f(x), then find
all of the zeros of f(x) algebraically.
For the a factor of f(x) expression, the zeros of f(x) are x = 1, x = 4, and x = 6.
How to determine all of the zeros?To find all the zeros of the function f(x) algebraically, determine the values of x that make f(x) equal to zero.
Here are the steps on how to find the zeros of f(x) algebraically.
Since x-4 is a factor of f(x), factor it out to get:
f(x) = (x - 4)(x² - 7x + 6)
Factor the quadratic expression in the parenthesis to get:
f(x) = (x-4)(x-1)(x-6)
This means that the zeros of f(x) are 4, 1, and 6.
Therefore, the answer is:
4, 1, 6
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[70, 73) c− [67, 70) d [63, 67) d [0, 63) f is this grading function a one-to-one correspondence? prove or disprove.
Therefore, The grading function is not a one-to-one correspondence since two numerical ranges, [70, 73) and [67, 70), have the same grade assigned to them.
Explanation:
A one-to-one correspondence means that each input has a unique output and vice versa. In this case, the grading function assigns a grade to a numerical range.
To determine if it is a one-to-one correspondence, we need to check if any two numerical ranges have the same grade assigned to them.
Looking at the given ranges, we can see that there is an overlap between [70, 73) and [67, 70) since they share the grade. Therefore, this grading function is not a one-to-one correspondence.
Therefore, The grading function is not a one-to-one correspondence since two numerical ranges, [70, 73) and [67, 70), have the same grade assigned to them.
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A container holds 0.7 liters of oil and vinegar.
3
4
of the mixture is vinegar.
How many liters of oil are in the container? Express your answer as both a fraction and a decimal
Using the given fraction we can see that there are 0.175 liters of oil in the container.
How many liters of oil are in the container?We know that 3/4 of the total volume in the container is vinegar, then the remaining fraction must be oil.
The remaining fraction is given by:
1 - 3/4
4/4 - 3/4 = 1/4
Then 1/4 of the total volume is oil (because the mix is only oil and vinegar), and we know that the total volume is 0.7 liters, then the amount of oil is:
(1/4)*0.7 L =0.175 L
There are 0.175 liters of oil in the mix in the container.
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evaluate the integral. (use c for the constant of integration.) 6 tan2(x) dx
The value of the integral ∫ 6 tan^2(x) dx is 6tan(x) - 6x + c.
We can start by using the identity tan^2(x) = sec^2(x) - 1 to rewrite the integral as:
6 tan^2(x) dx = 6(sec^2(x) - 1) dx
Now we can integrate each term separately:
∫ 6(sec^2(x) - 1) dx = 6∫sec^2(x) dx - 6∫dx
The antiderivative of sec^2(x) is tan(x), so:
6∫sec^2(x) dx - 6∫dx = 6tan(x) - 6x + c
where c is the constant of integration.
Therefore, the value of the integral ∫ 6 tan^2(x) dx is 6tan(x) - 6x + c.
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a random sample of students who took the sat college entrance examination twice found that 427 of the respondents had paid for coaching courses and the remaining 2733 had not. construct and interpret a 99% confidence interval for the proportion of coaching among students who retake the sat. what is the margin of error for this confidence interval? interpret the 99% confidence level. if the college board wanted guarantee no more than 1% margin of error at 99% confidence, what sample size would it have to use?
The 99% confidence interval for the proportion of coaching among students who retake the SAT is 0.130 to 0.176. The margin of error is 0.023. This means we are 99% confident that the true proportion of students who paid for coaching falls within this range.
A 99% confidence level means that if we were to repeat this study multiple times, 99% of the intervals we construct would contain the true proportion of students who paid for coaching. This level of confidence is commonly used in academic research to ensure that the results are reliable.
To guarantee a maximum margin of error of 1% at a 99% confidence level, the sample size needed would be approximately 15,823. This calculation can be done using the formula: n = (z^2 * p * q) / E^2, where z is the z-score for the desired confidence level, p is the estimated proportion of students who paid for coaching (0.135 in this case), q is 1-p, and E is the maximum margin of error (0.01 in this case).
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students who get help from the professor during office hours are 18x more likely to get an a on the exam than students who do not get help from the professor during office hours. about 11.7% of students get help from the professor during office hours. if you learn that a student got an a on the exam, what are the odds that they got help from the professor during office hours? put your answer in percentage form and round to two decimal places.
The odds that a student who got an A on the exam got help from the professor during office hours is about 41.77%.
To solve this problem, we can use Bayes' theorem, which is a way to calculate conditional probabilities. Let A be the event that a student got an A on the exam, and B be the event that a student got help from the professor during office hours.
We want to find P(B|A), the probability that a student got help from the professor during office hours given that they got an A on the exam.
Bayes' theorem states that:
P(B|A) = P(A|B) * P(B) / P(A)
We are given that students who get help from the professor during office hours are 18 times more likely to get an A on the exam than students who do not get help, so:
P(A|B) = 18 * P(A|B')
where B' is the complement of B (i.e., not getting help from the professor during office hours).
We are also given that about 11.7% of students get help from the professor during office hours, so:
P(B) = 0.117
We can calculate P(A) by using the law of total probability:
P(A) = P(A|B) * P(B) + P(A|B') * P(B')
Since P(B') = 1 - P(B), we have:
P(A) = 18 * P(A|B') * 0.883 + P(A|B) * 0.117
Now we can plug in the values we have and solve for P(B|A):
P(B|A) = (18 * P(A|B') * P(B)) / (18 * P(A|B') * 0.883 + P(A|B) * 0.117)
Using a calculator, we can find that P(B|A) is approximately 41.77%.
In other words, if we randomly select a student who got an A on the exam, there is a 41.77% chance that they got help from the professor during office hours.
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Suppose that the function f is defined on the interval (-2.5, 1.5) as follows. f(x) = {-2 if -2.5 < x lessthanorequalto -1.5 -1 if -1.5 < x lessthanorequalto -0.5 0 if -0.5 < x < 0.5 1 if 0.5 lessthanorequalto x < 1.5 Find f(-0.5), f(0.3), and f(0.5). f(-0.5) = f(0.3) = f(0.5) =
To find the values of f(-0.5), f(0.3), and f(0.5), we need to evaluate the function f(x) at those specific points.
f(-0.5) = -1, f(0.3) = 0, and f(0.5) = 1.
Explanation:
The function f is defined on the interval (-2.5, 1.5) with different values for different sub-intervals. We can evaluate the function at a specific point by finding the sub-interval that contains that point and using the corresponding value of f.
For f(-0.5), the point -0.5 lies in the sub-interval (-0.5, 0.5), where f(x) = 0. Therefore, f(-0.5) = 0.
For f(0.3), the point 0.3 also lies in the sub-interval (-0.5, 0.5), where f(x) = 0. Therefore, f(0.3) = 0.
For f(0.5), the point 0.5 lies in the sub-interval (0.5, 1.5), where f(x) = 1. Therefore, f(0.5) = 1.
Thus, we have f(-0.5) = -1, f(0.3) = 0, and f(0.5) = 1, which are the values of the function at those specific points.
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ASNER RN PLSS (15 POINTS) show wrk step by step
Last year, there were 1,500 people who attended the homecoming football game at a local high school. This year, there is expected to be a 16% increase in attendance. Based on the equation, approximately how many people will attend homecoming next year? (Round to the nearest person)
Answer:
1740 people
Step-by-step explanation:
A 16% increase is 0.16 as a decimal.
1500 * 0.16 = 240 more people expected next year
Add that 240 to the 1500 for the total number expected next year:
1500+240 = 1740 people
Answer: Approximately 1,740 people are expected to attend the homecoming football game this year, which is a 16% increase from last year's attendance of 1,500 people. This value is already rounded to the nearest person.
Step-by-step explanation:
Sure, let's calculate the expected attendance for this year's homecoming football game.
Step 1: Understand the problem
The problem states that there was an attendance of 1,500 people last year and this year there is expected to be a 16% increase in attendance. We need to find out the expected attendance for this year.
Step 2: Set up the equation
We can calculate the increase in attendance by multiplying last year's attendance by the percentage increase. The equation for this is:
New Attendance = Old Attendance + (Old Attendance * Percentage Increase)
Step 3: Substitute the given values into the equation
In this case, the Old Attendance is 1,500 and the Percentage Increase is 16% or 0.16 in decimal form. Substituting these values into the equation gives:
New Attendance = 1,500 + (1,500 * 0.16)
Step 4: Solve the equation
Let's calculate the result.
The calculation gives us:
New Attendance = 1,740
So, approximately 1,740 people are expected to attend the homecoming football game this year, which is a 16% increase from last year's attendance of 1,500 people. This value is already rounded to the nearest person.
M
P
E
2.
T
M
y coloring tin
Trapezoid: Find the Hidden Word
There is one traped in each line denly which one
Use the letter in each trapezoid to spell out the hidden word
*Remember: Atrapazed has only one pair of
Paralel sides.
P
S
O
C
S
S
Y R
The Hidden Word:
A T
C
S
R
E
E
M
R
P
Answer: YOU have to put the answer
Step-by-step explanation:
Using Pythagoras' theorem, calculate the length of XY. Give your answer in centimetres (cm) to 1 d.p. 16 cm X Z 5 cm
By using Pythagoras' theorem, the length of XY is equal to 14.4 centimeters.
How to calculate the length of XY?In Mathematics and Geometry, Pythagorean's theorem is modeled or represented by the following mathematical equation (formula):
x² + y² = z²
Where:
x, y, and z represents the length of sides or side lengths of any right-angled triangle.
Based on the information provided about the side lengths of this right-angled triangle, we have the following equation:
XZ² = ZY² + XY²
16² = 7² + XY²
256 = 49 + XY²
XY² = 256 - 49
XY² = 207
XY = √207
XY = 14.4 centimeters.
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why are t statistics more variable than z-scores? group of answer choices
T-statistics are more variable than z-scores because the standard error of the mean is more uncertain in small sample sizes. In a smaller sample size, there is less data to draw from which makes the estimate of the population mean less accurate. Therefore, the t-distribution takes into account the additional variability caused by the uncertainty of the sample size. In contrast, the z-score assumes that the population standard deviation is known, which is only true in large sample sizes. As a result, the t-distribution has fatter tails than the z-distribution, indicating a greater likelihood of extreme values.
The variability of t-statistics and z-scores is due to the differences in the distributions they come from. Z-scores are calculated from a standard normal distribution, which assumes that the sample size is infinite and the population standard deviation is known. However, in real-life situations, it is rare to have access to an infinite sample size or knowledge of the population standard deviation. In contrast, t-statistics are calculated from a t-distribution, which assumes that the sample size is small and the population standard deviation is unknown.
In summary, t-statistics are more variable than z-scores due to the additional uncertainty of the standard error of the mean in smaller sample sizes. The t-distribution is used to account for this additional variability, while the z-score assumes a known population standard deviation and an infinite sample size. Understanding the differences between these two distributions is essential for accurate statistical analysis in real-world situations.
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T statistics are more variable than z-scores because they are based on smaller sample sizes and have larger degrees of freedom.
T statistics are used when the sample size is small and the population standard deviation is unknown. In such cases, the standard error of the mean is estimated using the sample standard deviation and the degrees of freedom, which are calculated as n-1. As the sample size decreases, the degrees of freedom increase, which leads to greater variability in the t distribution.
On the other hand, z-scores are used when the sample size is large and the population standard deviation is known. In this case, the standard error of the mean is estimated using the population standard deviation, which leads to a smaller variability in the z distribution. Therefore, t statistics are more variable than z-scores due to their dependence on smaller sample sizes and larger degrees of freedom.
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jim places $ in a bank account that pays ompounded . after years, will he have enough money to buy a car that costs $? if another bank will pay jim ompounded , is this a better deal?
Main Answer: The second bank's offer is a slightly better deal compared to the first bank's offer.
Supporting Question and Answer:
How can we compare different bank offers to determine which one provides a better deal?
To compare different bank offers, we can consider the interest rates and compounding frequencies offered by each bank. By calculating the future value of an investment using the provided interest rate and compounding frequency, we can determine which bank will yield a higher return over a given time period. Additionally, considering other factors such as fees, terms and conditions, and the reputation of the banks can help in making an informed decision about which offer is a better deal.
Body of the Solution:To determine if Jim will have enough money to buy a car that costs $12,160 after 2 years with an interest rate of 9.8% compounded annually, we can calculate the future value of his initial investment of $10,000.
The formula to calculate the future value (FV) of an investment with compound interest is:
FV = P(1 + r/n)^(nt);Where, P = Principal amount (initial investment) ,r = Annual interest rate (as a decimal) ,n = Number of times interest is
compounded per year and t = Number of years
Using the given information, we have:
P = $10,000
r = 9.8% = 0.098 (as a decimal)
n = 1 (compounded annually)
t = 2 years
Plugging in these values into the formula:
FV = 10,000(1 + 0.098/1)^(1×2)
FV = 10,000(1.098)^2
FV = 10,000(1.206)
FV = 12,060
The future value of Jim's investment after 2 years would be approximately $12,060. Therefore, he would not have enough money to buy the car that costs $12,160.
Now, let's consider the second bank offering an interest rate of 10% compounded semiannually. To determine if this is a better deal, we need to calculate the future value using the same formula, but with the new interest rate.
r = 10% = 0.10 (as a decimal)
n = 2 (compounded semiannually, meaning twice a year)
FV = 10,000(1 + 0.10/2)^(2×2)
FV = 10,000(1.05)^4
FV = 10,000(1.2155)
FV = 12,155
The future value of Jim's investment after 2 years with the second bank would be approximately $12,155. Therefore, the second bank offering an interest rate of 10% compounded semiannually would be a slightly better deal as Jim would have more money by the end of the 2-year period compared to the first bank's offer.
Final Answer:Therefore, the second bank's offer is a slightly better deal compared to the first bank's offer.
Question:Jim places $10,000 in a bank account that pays 9.8% compounded. After 2 years, will he have enough money to buy a car that costs $12,160? If another bank will pay Jim 10% compounded semiannually, is this a better deal?
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The second bank's offer is a slightly better deal compared to the first bank's offer.
To compare different bank offers, we can consider the interest rates and compounding frequencies offered by each bank. By calculating the future value of an investment using the provided interest rate and compounding frequency, we can determine which bank will yield a higher return over a given time period. Additionally, considering other factors such as fees, terms and conditions, and the reputation of the banks can help in making an informed decision about which offer is a better deal.
To determine if Jim will have enough money to buy a car that costs $12,160 after 2 years with an interest rate of 9.8% compounded annually, we can calculate the future value of his initial investment of $10,000.
The formula to calculate the future value (FV) of an investment with compound interest is:
FV = P(1 + r/n)^(nt);Where, P = Principal amount (initial investment) ,r = Annual interest rate (as a decimal) ,n = Number of times interest is
compounded per year and t = Number of years
Using the given information, we have:
P = $10,000
r = 9.8% = 0.098 (as a decimal)
n = 1 (compounded annually)
t = 2 years
Plugging in these values into the formula:
FV = 10,000(1 + 0.098/1)[tex]^(1×2)[/tex]
FV = 10,000(1.098[tex])^2[/tex]
FV = 10,000(1.206)
FV = 12,060
The future value of Jim's investment after 2 years would be approximately $12,060. Therefore, he would not have enough money to buy the car that costs $12,160.
Now, let's consider the second bank offering an interest rate of 10% compounded semiannually. To determine if this is a better deal, we need to calculate the future value using the same formula, but with the new interest rate.
r = 10% = 0.10 (as a decimal)
n = 2 (compounded semiannually, meaning twice a year)
FV = 10,000(1 + 0.10/2)^(2×2)
FV = 10,000(1.05)^4
FV = 10,000(1.2155)
FV = 12,155
The future value of Jim's investment after 2 years with the second bank would be approximately $12,155. Therefore, the second bank offering an interest rate of 10% compounded semiannually would be a slightly better deal as Jim would have more money by the end of the 2-year period compared to the first bank's offer.
Therefore, the second bank's offer is a slightly better deal compared to the first bank's offer.
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Determine if the set of ordered pairs is a relation or a function. {(–5,2), (–4,1), (–3,0), (–3,–1)} neither
relation
function
The set of ordered pairs {(–5,2), (–4,1), (–3,0), (–3,–1)} is a relation but not a function.
The set of ordered pairs are {(–5,2), (–4,1), (–3,0), (–3,–1)}
We have to check whether the set is a relation or a function.
We know that a relation is a set of ordered pairs that relate inputs (x-values) to outputs (y-values).
So the set of ordered pairs is a relation.
We know that in a function, each input (x-value) is associated with exactly one output (y-value).
In this set of ordered pairs, the input –3 is associated with two different outputs: 0 and –1.
Therefore, it does not satisfy the criteria for a function, it is not a function.
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Bill wants to earn at least 33 trimming trees.He charges 7 per hour and pays 9 in equipment fees. What are the possible numbers of hours Bill could trim trees? Use t for the number of house
Write your answer as an inequality solved for t
Bill must trim trees for at least 6 hours to earn at least 33 dollars.
The inequality solved for t is t ≥ 6.
We have,
Bill's earnings for t hours of trimming trees is 7t dollars, and his expenses are 9 dollars.
Now,
Profit = 7t - 9
To earn at least 33 dollars, the profit must be greater than or equal to 33:
7t - 9 ≥ 33
Adding 9 to both sides, we get:
7t ≥ 42
Dividing both sides by 7, we get:
t ≥ 6
Therefore,
Bill must trim trees for at least 6 hours to earn at least 33 dollars.
The inequality solved for t is t ≥ 6.
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What is an equation of the line that passes through the point
(−3,−5) and is parallel to the line
2x+3y=15
Therefore, the equation of the line passing through (-3, -5) and parallel to the line 2x + 3y = 15, in slope-intercept form, is y = (-2/3)x - 7.
What is the Equation of Parallel Lines?To find the equation of a line parallel to the line 2x + 3y = 15 and passing through the point (-3, -5), we need to determine the slope of the given line and use it to construct the equation in slope-intercept form (y = mx + b).
The given line is in the form Ax + By = C, where A = 2, B = 3, and C = 15. To find the slope of this line, we can rearrange the equation to isolate y:
2x + 3y = 15
3y = -2x + 15
y = (-2/3)x + 5
The slope of the given line is -2/3.
Since the line we want to find is parallel to this line, it will have the same slope. Therefore, the slope of the line passing through (-3, -5) will also be -2/3.
Now, we can use the point-slope form of a linear equation to write the equation of the line:
y - y1 = m(x - x1)
Substituting the values of (-3, -5) and -2/3 for (x1, y1) and m, respectively:
y - (-5) = (-2/3)(x - (-3))
y + 5 = (-2/3)(x + 3)
To convert this equation into slope-intercept form, we can simplify and rearrange:
y + 5 = (-2/3)x - 2
y = (-2/3)x - 2 - 5
y = (-2/3)x - 7
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PLEASE HELP
dont mind the extra letters
Answer:
D
Step-by-step explanation:
1/5*12x/1=
12x/5
1/5*-10=
-2
D=12x/5-2
ind the radius of convergence, r, of the series. [infinity] n!xn 3 · 7 · 11 · ⋯ · (4n − 1) n = 1
Thus, the radius of convergence of the series is 4. That shows that the series converges absolutely for all values of x such that |x| < 4, and diverges for all values of x such that |x| > 4.
To find the radius of convergence of the given series, we can use the ratio test.
The ratio test states that for a series ∑an, if the limit of |an+1/an| as n approaches infinity is L, then the series converges absolutely if L < 1, diverges if L > 1, and inconclusive if L = 1.
So, applying the ratio test to the given series, we get:
|a(n+1)/an| = |(n+1)!x^(n+1) 3 · 7 · 11 · ⋯ · (4n + 3) / n!x^n 3 · 7 · 11 · ⋯ · (4n − 1)|
= |(n+1)x / (4n+3)|
= |x/(4 + 3/n)|
Taking the limit as n approaches infinity, we get:
lim n→∞ |a(n+1)/an| = |x/4|
Since we want this limit to be less than 1, we have:
|x/4| < 1
Solving for x, we get:
-1 < x < 4
Therefore, the radius of convergence of the series is 4. This means that the series converges absolutely for all values of x such that |x| < 4, and diverges for all values of x such that |x| > 4. When |x| = 4, the series may converge or diverge, and further analysis is needed to determine this.
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real life problem that can be solved by statistical
Answer: Weather Forecasting
Step-by-step explanation:
a 15 ¾ in. board is cut in a single cut from a 38 ¼ in board. the saw cut takes 3/8 in. how much of the 38 ¼ in board is left after cutting?
A 15 ¾ in. board is cut in a single cut from a 38 ¼ in board. The saw cut takes 3/8 in. 21 ¾ inches of the 38 ¼ inch board is left.
To find out how much of the 38 ¼ inch board is left after cutting, follow these steps:
1. Determine the total length of the cut: The cut takes 3/8 inch and removes a 15 ¾ inch board, so the total length of the cut is 15 ¾ inches + 3/8 inch.
2. Convert mixed numbers to improper fractions: 15 ¾ = (15 × 4 + 3)/4 = 63/4; 38 ¼ = (38 × 4 + 1)/4 = 153/4
3. Add the improper fractions: (63/4) + (3/8) = (63/4) + (3/8 × 2/2) = (63/4) + (6/8) = (126/8) + (6/8) = 132/8 = 16 ½ inches
4. Subtract the cut length from the original board length: (153/4) - (132/8) = (153/4) - (16 ½ × 4/4) = (153/4) - (66/4) = 87/4 = 21 ¾ inches
After cutting, 21 ¾ inches of the 38 ¼ inch board is left.
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BRAINIEST TO WHOEVER CAN ANSWER THIS QUESTION!
Answer:
x=72
y=92
Sum of Opposite angles of a cyclic quadrilateral is 180°
RESPUESTAS
A)4.5
B)5.45
C)9.1
D)10.9
AYUDAA
The value of the PQ is 5.452 when the PR value is 7 and the ∠PRQ value is 50°. Option B is the correct answer.
We need to find the value of the PQ. To determine the value of PQ we need to use the trigonometry functions which are,
Sinθ = opposite side / hypotenuse
Cosθ = Adjacent side / hypotenuse
Tanθ = opposite side / Adjacent side
Given data:
PR = 7
∠PRQ = 50°
We can determine the PQ by using the formula,
Sin θ = opposite side / hypotenuse
Sin θ = P Q / PR
0.766044 = P Q / 7
P Q = 0.766044 × 7
P Q = 5.452
Therefore, The value of the PQ is 5.45.
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The question is,
use one of the triangles to approximate PQ in the following triangle Answers
suppose that x and y are random variables with the same variance. show that x - y and x y are uncorrelated.
= 0 - Var(y) = 0 Thus, we have shown that x - y and xy are uncorrelated.
To show that x - y and xy are uncorrelated, we need to show that their covariance is zero.
Covariance is defined as Cov(x,y) = E[(x - E[x])(y - E[y])].
We can expand the covariance of x-y and xy as follows:
Cov(x - y, xy) = E[(x - y - E[x - y])(xy - E[xy])]
= E[((x - E[x]) - (y - E[y]))(xy - E[x]E[y])]
= E[(x - E[x])xy - (x - E[x])E[y] - (y - E[y])E[x] + (y - E[y])E[x]E[y]]
= E[(x - E[x])xy] - E[(x - E[x])E[y]] - E[(y - E[y])E[x]] + E[(y - E[y])E[x]E[y]]
= E[(x - E[x])xy] - E[x - E[x]]E[y - E[y]] - E[y - E[y]]E[x - E[x]] + E[x - E[x]]E[y - E[y]]
= E[(x - E[x])xy] - (Var(x) - 0)
= E[(x - E[x])xy] - Var(x)
Since x and y have the same variance, Var(x) = Var(y). Therefore:
Cov(x - y, xy) = E[(x - E[x])xy] - Var(x) = E[(x - E[x])xy] - Var(y)
To show that this is equal to zero, we can use the fact that E[xy] = E[x]E[y] since x and y are independent.
Therefore:
Cov(x - y, xy) = E[(x - E[x])xy] - Var(y)
= E[(x - E[x])y]E[x] - E[(x - E[x])E[y]] - Var(y)
= E[(x - E[x])](E[xy] - E[x]E[y]) - Var(y)
= 0 - Var(y) = 0
Thus, we have shown that x - y and xy are uncorrelated.
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A hydraulic lift system is needed to lift a school bus which weights 10,000 lbs. The system runs at 2000 lb/in. 2 and each cylinder will be 2 inches in diameter. How many cylinders will the hydraulic system require, in order to lift the bus?
One cylinder with a 2-inch diameter is sufficient to lift the school bus using the given hydraulic lift system.
To determine how many cylinders are required to lift the school bus using a hydraulic lift system, we need to use the formula:
force = pressure x area
where force is the weight of the bus (10,000 lbs), pressure is the operating pressure of the system (2000 lb/in²), and area is the cross-sectional area of the cylinder (pi x radius²).
First, we need to calculate the area of each cylinder:
radius = diameter/2 = 1 inch
area = pi x (1 inch)² = pi square inches
Next, we can calculate the force required to lift the bus:
force = 10,000 lbs
Finally, we can calculate the number of cylinders needed:
force = pressure x area x number of cylinders
number of cylinders = force / (pressure x area)
Substituting the values we calculated, we get:
number of cylinders = 10,000 lbs / (2000 lb/in² x pi square inches x (2 inches)²)
number of cylinders = 10,000 / (2000 x 4 x pi)
number of cylinders = 0.397
Since we cannot have a fractional number of cylinders, we round up to the nearest integer:
number of cylinders = 1
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Jake built a skateboard ramp that covers a horizontal distance of 10 ft. The ramp rises a total of 3. 5 ft. What angle does the ramp make with the ground? Round to the nearest degree.
19 degrees
20 degrees
28 degrees
35 degrees
The angle that the ramp makes with the ground is approximately 19 degrees.
the angle that the ramp makes with the ground can be found using trigonometry. the tangent of the angle is equal to the height of the ramp divided by the horizontal distance it covers:
tan(θ) = height / distance
where θ is the angle, height is 3.5 ft, and distance is 10 ft.
tan(θ) = 3.5 / 10θ = arctan(3.5 / 10)
θ = 19.1 degrees (rounded to the nearest degree)
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107. 6 is 75% of what
number?
the number is really "x", which oddly enough is the 100%, but we also know that 15% of that is 107.6.
[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} x & 100\\ 107.6& 75 \end{array} \implies \cfrac{x}{107.6}~~=~~\cfrac{100}{75} \implies\cfrac{x}{107.6} ~~=~~ \cfrac{4}{3} \\\\\\ 3x=430.4\implies x=\cfrac{430.4}{3}\implies x=\cfrac{2152}{15}\implies x=143\frac{7}{15}\implies x=143.4\overline{66}[/tex]
Sally finds that the correlation between high school gpa and performance ratings at work 5 years later have a correlation ofr = .09, p<.01. She concludes that high school gpa is an excellent and useful predictor of performance ratings at work: Is she right?
Sally's conclusion that high school GPA is an excellent and useful predictor of performance ratings at work is not entirely supported by the correlation coefficient of 0.09 with a significance level of p<.01.
Although a significant correlation suggests a positive association between high school GPA and performance ratings, the strength of the relationship is weak. The practical significance of such a weak correlation may be limited in real-world scenarios where multiple factors can influence job performance.
It is also important to note that correlation does not imply causation.
Therefore, even if high school GPA is significantly correlated with performance ratings at work, it does not necessarily mean that high school GPA is a causative factor in better job performance. Other variables such as work experience, motivation, and personality may also contribute to predicting job performance, and their effects should also be taken into account when assessing the usefulness of high school GPA as a predictor.
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The figure below shows a circular courtyard.
Its diameter is 96 m.
(a) Use the calculator to find the circumference and area of the courtyard.
Use 3.14 for it in your calculations, and do not round your answers.
Make sure to include the correct units.
Circumference:
Area:
(b) The courtyard will be covered with gravel.
Which measure would be used in finding the amount of gravel needed?
- Circumference
- Area
(c) The courtyard will be paved.
Which measure would be used in finding the amount of pavement needed?
- Circumference
- Area
The circumference and area of the courtyard are:
Circumference = 301.44 m
Area = 7234.56 m²
How to find the circumference and area of the courtyard?a) Circumference = πd
Circumference = 3.14 × 96 m
Circumference = 301.44 m
Area = πr²
Area = 3.14 × (96/2)²
Area = 7234.56 m²
(b)The measure that would be used in finding the amount of gravel needed is the area. Because the amount of gravel depends on the area of the courtyard.
(c) The measure that would be used in finding the amount of pavement needed is the area. Because the pavement size depends on area of the courtyard.
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which of the following pairs of triangles can be proven similar through SSS similarity
Among the following pairs of triangles, the triangle in option D can be proven through SSS similarity.
Similar triangles are the pair of triangles with corresponding angles of the same magnitude and the corresponding sides are proportional. The following are the criteria for proving similarities:
SSS criterion is applicable when all the corresponding sides are proportional to each other.AA or AAA criterion is applicable when all or any of the two corresponding angles are equal.SAS criterion is the case when the corresponding sides are proportional and the angles between the sides are equal.In the given question,
In option A,
Given:
DF / JK = FG / KL
∠F = ∠K
Therefore, ΔDFG ≈ ΔJKL by SAS criterion
In option B,
Given:
∠G = ∠L
∠F = ∠K
Therefore, ΔDFG ≈ ΔJKL by AA criterion
In option C,
Given:
∠G = ∠L
∠F = ∠K
Therefore, ΔDFG ≈ ΔJKL by AA criterion
In option A,
Given:
DF / JK = FG / KL = GD / LJ
Therefore, ΔDFG ≈ ΔJKL by SSS criterion
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