Answer:
Part A:
Assuming that Morgan kicks the ball at an angle that will allow it to clear the crossbar, we can use the following formula to determine how far she must kick the ball:
Distance = Height / tan(θ)
where θ is the angle at which the ball is kicked.
Since the field goal is 16 feet off the ground and we want the ball to clear the crossbar, we can assume that Morgan needs to kick the ball at an angle of approximately 45 degrees. Therefore, plugging in the given values, we get:
Distance = 16 / tan(45)
Simplifying the equation, we get:
Distance = 16 / 1
Therefore, Morgan must kick the ball a distance of 16 feet to make the extra point if she stands 30 feet from the field goal.
Part B:
To arrive at this conclusion, we used the formula for the distance of a projectile when given the initial velocity, angle, and height of the object. However, since we were not given the initial velocity, we assumed that Morgan would need to kick the ball at an angle of approximately 45 degrees to clear the crossbar. This is a common assumption in football, as it allows for the ball to travel the farthest distance possible while still clearing the crossbar. Additionally, we assumed that there was no wind or other external factors that could affect the trajectory of the ball. With these assumptions, we were able to determine that Morgan would need to kick the ball a distance of 16 feet to make the extra point if she stood 30 feet from the field goal.
exploraton in math suppose a principal amount of $15,400 is borrowed at a simple interest rate 15% for a period of 13 years. determine the amount of simple interest owed for the use of this loan. round the solution to the nearest cent, if necessary. the amount of simple interest owed is
The amount of simple interest owed for the loan is $30,010.00.
A method for determining the proportion of interest paid on a sum over a predetermined period of time at a predetermined rate is called simple interest. In simple interest, the principal amount remains unchanged. A straightforward and simple method for calculating money interest is simple interest.
To calculate the simple interest, we use the formula:
Simple Interest = P * r * t
where P is the principal amount, r is the interest rate as a decimal, and t is the time period in years.
Substituting the given values, we get:
Simple Interest = $15,400 * 0.15 * 13
= $30,010.00
Therefore, the amount of simple interest owed for the use of the loan is $30,010.00.
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Which of the following is the fourth vertex needed to create a rectangle with vertices located at (5, 6), (9, 6), and (5, 3)? (5, –6) (5, –3) (9, –6) (9, 3)
PLSSS ANYONEEEE
what happens to the sector area of a circle if you double its radius? what happens to the arc length of a circle if you double its radius? why do you think that happens?
The sector area of a circle is quadrupled when the radius is doubled. When the radius is doubled, the arc length of a circle is also doubled. This happens because the sector area and arc length are both dependent on the radius of a circle. Therefore, any change in the radius of a circle affects both its sector area and arc length.
Let us understand both these concepts in detail:
Sector area of a circle: A sector is a region of a circle, and the area enclosed by two radii and an arc is known as a sector area. The formula for the sector area of a circle is given by:
Sector Area = (θ/360)πr²
where θ is the central angle in degrees,
r is the radius of the circle,
and is a constant value.
If we double the radius of a circle, the sector area increases by a factor of 4. This is because the sector area is directly proportional to the square of the radius.
Hence, doubling the radius of a circle results in an increase in the sector area by a factor of 22 (four).
Arc length of a circle: The length of an arc is the distance between two points on a circle. The formula for the arc length of a circle is given:
Arc Length = (θ/360)2πr
where θ is the central angle in degrees,
r is the radius of the circle,
and 2pie is a constant value.
If we double the radius of a circle, the arc length also doubles.
This is because the arc length is directly proportional to the radius.
Hence, doubling the radius of a circle results in an increase in the arc length by a factor of 2.
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Evaluate. Write your answer as a fraction or whole number without exponents.
6^–3 =
Answer:
i'm pretty sure it's 33
Step-by-step explanation:
6^= 36
36-3= 33
what is the approximate distribution of the sample mean copper content if we sample 16 pads? include the mean and standard error of this distribution.
a) Approximately 29.50% of brake pads will contain less than 32.5% copper. b) The approximate distribution of the sample mean copper percentage is a normal distribution with mean 34 and standard error 0.7.
a)To solve this problem, we can use the z-score formula to standardize the value of 32.5 using the mean and standard deviation given:
z = (x - μ) / σ
where x is the value we are interested in (32.5), μ is the mean (34), and σ is the standard deviation (2.8).
Substituting these values, we get:
z = (32.5 - 34) / 2.8 = -0.536
Using a standard normal distribution table or calculator, we can find the probability of a z-score less than -0.536, which is approximately 0.2950 or 29.50%. Therefore, approximately 29.50% of brake pads will contain less than 32.5% copper.
b) The sample mean copper percentage of 16 pads will also follow an approximate normal distribution with mean μ = 34 and standard deviation σ/√n = 2.8/√16 = 0.7, where n is the sample size.
Therefore, the approximate distribution of the sample mean copper percentage can be expressed as:
X ~ N(34, 0.7)
where X is the sample mean copper percentage.
The mean of this distribution is equal to the population mean μ, which is 34. The standard error of the mean (also known as the standard deviation of the sampling distribution) is given by σ/√n, which is 0.7 in this case.
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Your question is incomplete, but probably the complete question is :
Assume the distribution of copper content (%) in sintered brake pads follows an approximate normal distribution with a mean of 34 and a standard deviation of 2.8
a.) What percentage of brake pads will contain less than 32.5% copper?
b.) What is the approximate distribution of the sample mean copper percentage if we sample 16 pads? Include the mean and standard error of this distribution
If 3 to the power a is equal to 21 to the power b and 7 to the power c is also equal to 21 to the power b, prove that b is equal to (ac)÷(a+b) where a+b is not equal to 0
According to the given exponential equations it is proved that b = (ac) / (a+b) where a+b ≠ 0.
We are given the first equation as [tex]3^{a} = 21^{b}[/tex] ----(1) i.e 3 to the power a is equal to 21 to the power b.
The next exponential equation is [tex]7^{c} = 21^{b}[/tex] ----(2)
We know, 21 can be written as 3*7 because they are the factors of 21. Therefore, [tex]21^{b} = (3*7)^{b} = 3^{b}7^{b}[/tex]
Substituting equations (1) and (2), we get:
[tex]3^{a}= 3^{b} *7^{b}[/tex]
Taking logarithm base 3 on both sides:
a = blog3(37)
a = b*(log3(3) + log3(7))
a = b*(1 + log3(7))
b = a / (1 + log3(7)) ------ (3)
Similarly, taking logarithm base 7 on both sides of equation (2):
c = b*log7(21)
c = b*(log7(3) + log7(7))
c = b*(1 + log7(3/7))
b = c / (1 + log7(3/7)) ------ (4)
Substituting (3) and (4) in the given equation, we get:
a / (1 + log3(7)) = (ac) / (a+b) * (1 + log7(3/7))
After cross-multiplying and simplifying the equations,
b = (ac) / (a+b)
Hence,b = (ac) / (a+b)
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You wish to compute the 90% confidence interval for the population proportion. How large a sample should you draw to ensure that the sample proportion does not deviate from the population proportion by more than 0. 08? No prior estimate for the population proportion is available
To compute a 90% confidence interval for the population proportion with a margin of error of 0.08 and no prior estimate for the population proportion, a sample size of 181 is needed.
To determine the sample size needed to compute the 90% confidence interval for the population proportion with a margin of error of 0.08, we can use the formula:
n = (z^2 * p * (1 - p)) / E^2
where n is the sample size needed, z is the z-score for the desired confidence level (90% confidence level has a z-score of 1.645), p is the estimated proportion (since no prior estimate is available, we use 0.5 as a conservative estimate), E is the margin of error (0.08)
Substituting the given values, we get:
n = (1.645^2 * 0.5 * (1 - 0.5)) / 0.08^2
n = 180.99
Rounding up to the nearest whole number, we get:
n = 181
Therefore, a sample size of 181 is needed to compute the 90% confidence interval for the population proportion with a margin of error of 0.08, when no prior estimate for the population proportion is available.
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what is the problem with this question item that appeared in a survey? was your phone purchased in the last two years and have you recently updated it?
Option B, The fact that this survey question is a double-barreled question makes it problematic.
A survey question known as a double-barreled question has two questions inside one, making it challenging for respondents to give truthful and insightful responses.
The offered inquiry, in this instance, combines two distinct inquiries: if the phone was acquired within the last two years and whether it has recently had an upgrade.
Inconsistent answers might result from a person who bought their phone more than two years ago but only recently upgraded it, or vice versa. In order to prevent double-barreled questions and guarantee that responders can give precise and complete replies, each question should be isolated and posed independently.
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The question is -
What is the problem with this question item that appeared in a survey? was your phone purchased in the last two years and have you recently updated it?
a. It is a leading question
b. It involves negative wording
c. It is a double-barreled question
d. It is not on a Likert Scale
In a class of students, the following data table summarizes the gender of the students
and whether they have an A in the class. What is the probability that a female student
does not have an A?
Has an A
Does not have an A
Female Male
4
8
5
11
A female student's probability of not receiving an A is 0.56, or 56%.
What makes probability so special?Probability and probability, as well as its cognates in various modern languages, come from the educated Latin of the Middle Ages called probabilis, which Cicero used to refer to a viewpoint as being plausible or generally accepted. Ancient French probabilite is where the word probability came from (14 c.)
We must utilise the data in the table to determine the likelihood that a female student will not receive an A.
There are 16 male students and 9 female students in the class, according to the table. Of the nine female students, four received As compared to five Bs.
Hence, the The likelihood that a female student won't receive an A is: P (Female student does not have an A) = Total number of female students / Number of female students without an A
P
Female student does not have an A (Female student does not have an A) = 5/9 P(Female student does not have an A) = 0.56 or 56%.
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the income i of a computer analyst varies directly as the number of hours h worked. if the analyst earns $352 for working 8 h, how much will the analy
Triangles 1 and 2 are similar. what ratio relates a side length of triangle 1 to the corresponding side length of triangle 2? fill in the box to complete the ratio. triangle a b c is labeled triangle 1. side a c is 17, c b is 15, a b is 8. angle c is 28 degrees and angle a is 62 degrees. triangle d e f is labeled triangle 2. side d f is 25.5, f e is 22.5 and d e is 12. angle d is 62 degrees, f is 28 degrees, and e is 90 degrees. to 12
If triangles 1 and 2 are similar, the ratio relates a side length of triangle 1 to the corresponding side length of triangle 2 is 2:3.
Since Triangles 1 and 2 are similar, their corresponding sides are proportional. This means that the ratio of the length of any corresponding pair of sides in the two triangles will be equal.
To determine the ratio of the side lengths of triangle 1 to the corresponding side lengths of triangle 2, we can choose any two corresponding sides and divide their lengths.
Let's choose side AC of triangle 1 and side DF of triangle 2. We know that these two sides are corresponding because they are both opposite angles that have the same measure.
The length of side AC in triangle 1 is given as 17, and the length of side DF in triangle 2 is given as 25.5. Therefore, the ratio of the length of side AC to side DF is:
AC/DF = 17/25.5 = 0.6667 or 2/3
So the ratio of the length of a side in triangle 1 to the corresponding side in triangle 2 is 2:3. This means that if we multiply any side length in triangle 1 by 2, we will get the length of the corresponding side in triangle 2.
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how would you interpret the finding of a correlation study that reported a linear correlation coefficient of 21.34?
A correlation coefficient of 21.34 is an impossible value.
In statistics, correlation is defined as the degree of association between two or more variables. Correlation research helps to establish whether a relationship exists between two variables, and if so, to what extent. The correlation coefficient is a statistical measure used to quantify the degree of association between two variables.
The correlation coefficient, which ranges from -1 to +1, indicates the strength of the relationship between the two variables. When the correlation coefficient is 0, it indicates that there is no correlation between the two variables. When the correlation coefficient is positive, it indicates that the two variables are directly related, whereas when the correlation coefficient is negative, it indicates that the two variables are inversely related.
In this case, a correlation study reported a linear correlation coefficient of 21.34, which is not possible. Correlation coefficients range from -1 to +1. The value of the correlation coefficient ranges from -1 to +1, where a value of 0 indicates no correlation, a value of 1 indicates perfect positive correlation, and a value of -1 indicates perfect negative correlation. Therefore, a correlation coefficient of 21.34 is an impossible value.
In this case, it is likely that the correlation coefficient was misreported or that a different statistical measure was used. It is important to carefully examine and verify statistical findings before drawing any conclusions or making decisions based on the results.
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suppose that x is the number of cars per minute that pass through a certain intersection, and that x has the poisson distribution. what can be the smallest value of x? enter your answer in accordance to the question statemententer your answer in accordance to the question statement
The smallest value of x in the Poisson distribution is 0, which means that no cars can pass through the intersection in a given minute.
For explain further, a Poisson distribution is a statistical model that describes the probability of a given number of events occurring in a fixed period of time, such as cars passing through an intersection in a minute.
In a Poisson distribution, the probability of x events occurring in a given minute is given by the equation P(x) = e-λλx/x!, where λ is the average number of events in a given minute. In this case, λ would be the average number of cars that pass through the intersection per minute.
The probability of 0 cars passing through the intersection in a given minute is e-λλ0/0! = 1, which is the highest probability in the distribution. Therefore, the smallest value of x in a Poisson distribution is 0.
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answer two questions about the following rational division.
1. The quotient in lowest terms of the given rational division is (x+2)/(3x-9).
2. The values of r is A. x=-2 and B. x=0.
What is factor?Factor is a quantity which when multiplied by another quantity, produces a given product. Factors are used to simplify and solve equations, as well as in other areas of mathematics. Factors can be numbers, variables, and expressions.
To find the lowest terms, we must divide the numerator and denominator by the same number. The largest common factor of the numerator and denominator is 3. Dividing both the numerator and denominator by 3, we get (x+2)/(3x-9) = (x+2)/(x-3).
The values of r that must be excluded from the domains of the expressions are x=0 and x=3. x=0 must be excluded because it will create a zero in the denominator which is not allowed. x=3 must also be excluded because it will create a zero in the numerator, and thus make the entire expression equal to 0. Thus, the correct answer is A. x=-2 and B. x=0.
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a 336-m long fence is to be cut into pieces to make three enclosures, each of which is square. how should the fence be cut up in order to minimize the total area enclosed by the fence?
The fence ought to be cut into 12 pieces, every one of length 28 m, to make three squares, each with a side length of 28 m. This will limit the total area encased by the fence.
To limit the total area encased by the fence, the three squares ought to have equivalent areas. Let x be the length of each side of the squares. Then the perimeter of each square is 4x, and the total length of the fence is 3(4x) = 12x. Since the total length of the fence is given to be 336 m, we have:
12x = 336
Addressing for x, we get:
x = 28
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3. if you measure an interval of 5 seconds between seeing a lighting flash and hearing the thunder, how far away was the lighting? assume the temperature of the air was 20 degree celsius.
It took 5 seconds for the thunder to be heard, the lightning was 343 * 5 = 1715 meters away.
The distance between the lightning flash and hearing the thunder can be calculated using the speed of sound. The speed of sound in air at 20°C is 343 meters/second.
Explanation: When lightning strikes, the initial flash travels at the speed of light, which is 299,792,458 meters per second. The sound wave created by the flash, however, travels at a much slower speed.
The speed of sound in air at 20°C is 343 meters per second.
To calculate the distance of the lightning, we multiply the speed of sound by the amount of time it took to hear the thunder. In this case, the amount of time was 5 seconds, so the lightning was 1715 meters away (343 * 5 = 1715).
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when a person standing in neutral flexes their right shoulder so that their arm is horizontal with the ground, the center of gravity (mass) will
When a person standing in neutral flexes their right shoulder so that their arm is horizontal with the ground, the center of gravity (mass) will shift towards the left side of the body.
Explanation:
What is center of gravity?The point at which the weight of a body or an object is concentrated, that is, the point at which the mass of the body or the object is focused is known as the center of gravity. The center of gravity (CG) is the point where the weight of the body is supposed to act, which is the point about which the body remains in balance. The body's center of gravity is important because it affects its balance and stability
.When a person is standing in a neutral position, the center of gravity is in the midline of the body. When the person flexes their right shoulder and holds their arm horizontally, the center of gravity will shift towards the left side of the body. This is because the weight of the arm is now being supported by the left side of the body. The shift in the center of gravity will cause the person to adjust their posture to maintain balance and stability.
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which of the following is a requirement of a random sample? group of answer choices every individual has an equal chance of being selected all of the other choices are correct. all scores must be equally represented in the population the sample must contain at least five individuals
A requirement of a random sample is that every individual has an equal chance of being selected.
What is a random sample? A random sample is a process of selecting members from a population, that each member has an equal chance of being chosen. In a random sample, each member of the population has an equal chance of being selected.
Therefore, every individual has an equal chance of being selected is a requirement of a random sample. So, option A is the correct answer. It is the most essential part of random sampling.
There are various types of random sampling techniques, including simple random sampling, stratified sampling, cluster sampling, and systematic sampling.
The objective of random sampling is to acquire an unbiased sample that represents the entire population fairly. The primary purpose of random sampling is to minimize bias while selecting the members of a population.
Hence, most essential part of Random Sampling is that every individual has an equal chance of being selected.
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GM is tangent to circle O at point G, and GS
is a secant line. If mGS = 84°, find
m/SGM.
Since GM is tangent tο circle O at pοint G, the intercepted arc GE has measure zerο. ,then ∠SGM = 84°.
What is secant line?Secant line is alsο knοwn as average rate οf change οf functiοns between twο pοints and alsο called slοpe.
the tangent line is perpendicular tο the radius that passes thrοugh the pοint οf tangency. Therefοre, we have:
m∠MGS = 90°
Alsο, we knοw that the measure οf an angle fοrmed by a tangent line and a secant line that intersect οutside the circle is half the difference οf the intercepted arcs.
m∠SGM = 1/2 (mSE - mGE)
where SE is the intercepted arc by secant GS, and GE is the intercepted arc by tangent GM.
Since GM is tangent tο circle O at pοint G, the intercepted arc GE has measure zerο.
mSE = 2mGS
mSE = 2(84°) = 168°
m∠SGM = 1/2 (mSE - mGE) = 1/2 (168° - 0°) = 84°
Therefοre, m∠SGM = 84°.
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PL3ASE HELP - WORTH 40 POINTS
Answer:
What is the probability of rolling an odd product? 1/4
What is the probability of rolling a product that is greater than or equal to 20? 2/9
What is the probability of rolling a product that is less than 10? 17/36
What is the probability of rolling a product that is a multiple of 10? 1/6
A first-year teacher wants to retire in 40 years. The teacher plans to invest in an account with a 6.95% annual interest rate compounded continuously. If the teacher wants to retire with at least $125,000 in the account, how much money must be initially invested? Round your answer to the nearest dollar.
Therefore, the teacher must initially invest at least $7,725 to retire with at least $125,000 in the account after 40 years at a 6.95% annual interest rate compounded continuously.
What is percent?Percent is a way of expressing a number as a fraction of 100. It is often denoted by the symbol "%". Percentages are commonly used to describe proportions or rates, such as the percentage of students who passed a test, the percentage of a population that belongs to a certain group, or the percentage increase or decrease in a quantity over time. Percentages are also used in calculations involving discounts, taxes, interest rates, and other financial applications.
Here,
The formula for the continuous compounding interest is given by:
[tex]A = Pe^{rt}[/tex]
where A is the final amount, P is the principal amount (initial investment), e is the constant 2.71828..., r is the annual interest rate as a decimal, and t is the time in years.
In this case, we want to solve for the initial investment P, given that the teacher wants to retire with at least $125,000 in the account after 40 years, and the annual interest rate is 6.95% compounded continuously. Therefore, we have:
A = $125,000
r = 0.0695 (annual interest rate as a decimal)
t = 40 years
Substituting these values into the formula, we get:
$125,000 = [tex]Pe^{0.0695*40}[/tex]
Dividing both sides by [tex]e^{0.0695*40}[/tex], we get:
P = $125,000 / [tex]e^{0.0695*40}[/tex]
Using a calculator, we find that [tex]e^{0.0695*40}[/tex] is approximately 16.173, so:
P = $125,000 / 16.173
P ≈ $7,725.32
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the pharmacy sends the nurse the following coreg tablets. the order is to administer 9.375 mg po daily. how many tablets will the nurse administer? enter only the numeral (not the unit of measurement) in your answer.
The nurse will administer 3 tablets of Coreg to meet the prescribed dosage of 9.375 mg PO daily.
The prescription order is for the nurse to administer 9.375mg of Coreg tablets orally each day. The Coreg tablets have a dosage strength of 3.125mg per tablet. To calculate the number of tablets the nurse needs to administer, we can divide the total dosage needed (9.375mg) by the dosage strength per tablet (3.125mg per tablet).
This results in the nurse administering 3 tablets to meet the prescribed dosage. Therefore, the nurse should give 3 tablets of Coreg to the patient each day to ensure they receive the correct amount of medication.
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The given question is incomplete, the complete question is:
the pharmacy sends the nurse the following coreg tablets. the order is to administer 9.375 mg po daily. how many tablets will the nurse administer? enter only the numeral (not the unit of measurement) in your answer.
Neal buys a board game. He pays for the board game and pays
$
1.54
$1.54dollar sign, 1, point, 54 in sales tax. The sales tax rate is
5.5
%
5.5
Proportionately, the cost of the board game without the sales tax is $28.00.
What is the sales tax?The sales tax is the levy imposed by the government on the consumption and production of certain goods and services.
The purposes of imposing sales taxes are to discourage consumption and to increase governmental revenue.
Proportion refers to the equation of two ratios.
In this situation, we can equate the value of the sales tax with its percentage to determine the cost of the board game.
The sales tax in dollars = $1.54
The sales tax rate = 5.5%
Proportionately, the value of the board game without the sales tax = $28.00 ($1.54/5.5%).
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Question Completion:How how is the cost?
the population of chicago is about 3 million. how does that compare to the total number of dead and wounded in world war i? (give your answer as a fraction)
if a sample of 5 lightbulbs is selected, find the probability that none in the sample are defective.
The probability of selecting a sample of 5 lightbulbs without any defective bulbs is then given by p^5, where p is the probability of not having a defective bulb.
In this situation, the probability of selecting a sample of 5 lightbulbs without any defective bulbs is calculated using the binomial distribution. The probability of success, p, is the probability that a single lightbulb is not defective, and the probability of failure, q, is the probability that a single lightbulb is defective. The probability of selecting 5 lightbulbs with no defective bulbs is then given by the equation:
P(x=0) = (p^5)*(q^0) = p^5
In this case, p is the probability of not having a defective bulb, and q is the probability of having a defective bulb. The probability of selecting 5 lightbulbs without any defective bulbs is then given by p^5.
For example, if the probability of not having a defective bulb is 0.95 and the probability of having a defective bulb is 0.05, then the probability of selecting a sample of 5 lightbulbs without any defective bulbs is 0.95^5 = 0.7737. This means that there is a 77.37% chance of selecting a sample of 5 lightbulbs without any defective bulbs.
To sum up, the probability of selecting a sample of 5 lightbulbs without any defective bulbs is calculated using the binomial distribution. The probability of success is the probability of not having a defective bulb, and the probability of failure is the probability of having a defective bulb. The probability of selecting a sample of 5 lightbulbs without any defective bulbs is then given by p^5, where p is the probability of not having a defective bulb.
The correct question is:
A box contains 100 bulbs, out of which 10 are defective. If a sample of 5 lightbulbs is selected, find the probability that none in the sample are defective
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In an election, there were three candidates;⅔ of the electors voted for the first candidates,¼ for the second candidate and the rest for the third candidate. If the third candidate got 3290 votes, how many votes did the winner get? Solve this and show All your workings
The winner of the election got 26320 votes.
Let's first find the total number of votes cast in the election. We know that 2/3 fraction of the electors voted for the first candidate and 1/4 of the electors voted for the second candidate. Therefore, the remaining 1/12 of the electors voted for the third candidate. So, we have:
2/3 + 1/4 + 1/12 = 8/12 + 3/12 + 1/12 = 12/12 = 1
This means that all the electors voted, and the total number of votes cast is equal to the total number of electors.
Now, let's find the number of votes the third candidate got, which is 1/12 of the total number of votes. We know that this is equal to 3290. So, we have
1/12 x Total Number of Votes = 3290
Multiplying both sides by 12, we get:
Total Number of Votes = 3290 x 12 = 39480
Now, we can find the number of votes the first candidate got, which is 2/3 of the total number of votes. We have:
2/3 x Total Number of Votes = 2/3 x 39480 = 26320 votes
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A chain that has a negligible mass is draped over the sprocket which has a mass of 2 kg and a radius of gyration of k_0 = 50 mm. If the 4-kg block A is released from rest in the position s = 2 m. Using energy methods, determine the angular velocity of the sprocket at the instant s = 4 m. Draw FBD at both states and clearly label datum.
The given chain which has a negligible mass is draped over the sprocket which has a mass of 2 kg and a radius of gyration of k0=50 mm.
If the 4-kg block A is released from rest in the position s=2 m. Using energy methods, determine the angular velocity of the sprocket at the instant s=4 m.First of all, draw a FBD of the system at s=2 m and at s=4 m.At s=2 m Let the velocity of the block A be v2m/s.At s=4 m Let the velocity of the block A be v4m/s.Let the angular velocity of the sprocket be ω rad/s. Draw FBD at both states and clearly label datum.For the block A at s=2 m Velocity of the block A, v=0 (Initial velocity)
Kinetic energy of the block A,KE1=12mv²=12×4×(0)²=0Potential energy of the block A,PE1=mgh=4×9.81×2=78.48JFor the block A at s=4 mLet h be the height by which the [tex],KE1=12mv²=12×4×(0)²=0[/tex]block A falls. Velocity of the block A, [tex]v=√2gh=√2×9.81×h[/tex]Kinetic energy of the block A,KE2=[tex]12mv²=12×4×[√2gh]²=8gh[/tex] Joule (J)Total potential energy of the system at s=2 m,PE1=2×g×k0 Joule (J)When the block falls from s=2 m to s=4 m, the change in the potential energy of the system is,ΔPE=PE2-PE1Where,PE2=2×g×(2k0) Joule (J)Let the change in the potential energy of the system be ΔPE1 Joule (J).
So,ΔPE1=PE2-PE1=2gk0 Joule (J)The total energy of the system is conserved.
So,ΔPE1=KE2ω²+Iω²Where,ΔPE1 is the change in the potential energy of the systemKE2 is the kinetic energy of the block A when it is at s=4 mI is the moment of inertia of the sprocket about its axisω is the angular velocity of the sprocket at s=4 mSo,ω²=ΔPE1KE2+Iω²Substitute the values of ΔPE1, KE2 and I in the above equation.
[tex]ω²=(2gk0)8gh+mr²ω²=(2×9.81×50×10⁻³)8×h×h+2×1×(50×10⁻³)²ω²=0.7848h²+2.5×10⁻³[/tex]
Therefore,ω=√(0.7848h²+2.5×10⁻³) rad/s.
Substitute the value of h=2 m in the above equation.ω=2.808 rad/s.So, the angular velocity of the sprocket at the instant s=4 m is 2.808 rad/s.
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A line passes through the point (2, 3) and has a slope of 5.
Write an equation in slope-intercept form for this line.
Answer:
y=5x-7
Step-by-step explanation:
Disha states that the circumference and the area of the larger circle are both double the
circumference and the area of the smaller circle. Is she correct? Explain why or why not.
D
10
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the volume of a ice cube is decreasting at a rate of 1.5cm cubed per second at what rate is a side of the ice cube decreasing when the side is 6cm
The rate of decrease of the side of the cube with a side of 6 cm is 0.25 cm per second.
The rate of decrease of the side of an ice cube can be calculated by considering the volume of the cube. The volume of the cube is decreasing at a rate of 1.5 cm3 per second. Therefore, the rate of decrease of the side of the cube is proportional to the cube's volume.
To calculate the rate of decrease of the side of the cube, we need to use the formula for the volume of a cube, which is: V = s3, where V is the volume and s is the side of the cube.
Since we know that the volume of the cube is decreasing at a rate of 1.5 cm3 per second, we can calculate the rate of decrease of the side of the cube by substituting the value of the rate of decrease of the volume and the current side of the cube (6 cm) into the formula.
Therefore, the rate of decrease of the side of the cube is equal to 1.5 cm3 per second divided by 6 cm3, which is equal to 0.25 cm per second.
In conclusion, the rate of decrease of the side of the cube with a side of 6 cm is 0.25 cm per second.
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