the question is that as we increase the sample size in a one sample test for the population mean, the size of the rejection region decreases. This means that the probability of rejecting the null hypothesis when it is actually true, also known as a Type I error, decreases.
The t critical value is a constant value determined by the sample size and the significance level. It is the point at which we decide to reject or fail to reject the null hypothesis. As we increase the sample size, the t critical value moves closer to zero, but this does not have a direct impact on the probability of a Type I error.
The size of the rejection region, on the other hand, is determined by the t critical value and the variability of the sample. As the sample size increases, the variability decreases, leading to a smaller rejection region. This means that it is less likely to reject the null hypothesis when it is actually true, resulting in a lower probability of a Type I error.
Therefore, we can conclude that increasing the sample size in a one sample test for the population mean decreases the size of the rejection region and the probability of a Type I error.
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Please please help please please
Answer:
G(9, -5)
Step-by-step explanation:
Point G is not shown in the figure, but I assume point G is on the bottom side of the square, directly below point F.
We are told each side of the square is 8 units long.
Starting at point E, to get to point G, go 8 units right and 8 units down.
Start at E(1, 3).
Then go 8 units right to point F(9, 3).
Now go 8 units down to point G(9, -5).
7 1/4 divided by 3/8
Answer:
14/3
Step-by-step explanation:
Answer:
58/3
Step-by-step explanation:
7 1/4 ÷ 3/8
= 29/4 x 8/3
= 29 x 2/3
= 58/3
Suppose that the number of miles that a car can run before it's battery wears out is exponentially distributed with an average value of 10000 miles.if a person desires to take a 5000 mile trip,what is the probability that he or she will be able to complete the trip without having to replace the car battery?
The probability that a person will be able to complete a 5000 mile trip without having to replace the car battery can be calculated using the cumulative distribution function (CDF) of the exponential distribution. The answer is approximately 60.7%.
To explain further, we know that the average value of the exponential distribution is 10000 miles. This means that the expected value of the number of miles a car can run before its battery wears out is 10000 miles. The probability that the car's battery will last for at least 5000 miles can be calculated using the CDF of the exponential distribution. The CDF of the exponential distribution is given by F(x) = 1 - e^(-x/μ), where x is the number of miles and μ is the average value of the distribution.
Substituting x = 5000 and μ = 10000, we get F(5000) = 1 - e^(-0.5) ≈ 0.607. Therefore, the probability that a person will be able to complete a 5000 mile trip without having to replace the car battery is approximately 60.7%. This means that there is a 60.7% chance that the car's battery will last for at least 5000 miles, and the person will not have to replace it during the trip.
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find the radius of convergence, r, of the series. [infinity] xn 3 5n! n = 2
The limit of the ratio is infinity, the series diverges for all values of x except x = 0 and the radius of convergence is r = 0.
To find the radius of convergence of the series, we can use the ratio test.
The ratio of the (n+1)th and the nth term of the series is:
|(x(n+1)) / (x(n))| = ((n+1)^3) / (5(n+1))
We take the limit of this ratio as n approaches infinity:
lim |(x(n+1)) / (x(n))| = lim (((n+1)^3) / (5(n+1))) = lim ((n^3 + 3n^2 + 3n + 1) / (5n)) = ∞
Since the limit of the ratio is infinity, the series diverges for all values of x except x = 0. Hence, the radius of convergence is r = 0.
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Determine whether a triangle with the given side lengths is a right triangle.
3,9,10 >>> not a right triangle. because 3^2 + 9^2 is not equal to 10^2
27, 36, 45 >>> yes, a right triangle bc 27^2 + 36^2 = 45^2
11,13,17 >>>
11^2 + 13^2 = 290
The sqrt of 290 = 17.0293863659.
If you are in the lower grades, probably your teacher expects you to round this to 17. I honestly don't know how to answer bc I don't know what your teacher's expectations are for rounding.
I am a precise person, but I could see a teacher accepting YES RIGHT TRIANGLE bc it's basically 17.
4, 8, 9 >>> NOT a right triangle.
4^2 + 8^2 = 80
The sqrt of 80 = 8.94427191
I would say NO because this does not equal 9!
what is the probability that a student chosen at random from this school will be enrolled in a both a foreign language course and a psychology course
Probability that a student chosen at random from class is not a psychology major = 0.82
Probability:Probability is a branch of mathematics which tells about the occurrence of any event.
The sum of the probability of an event to occur and the probability of the same event not to occur is always equal to 1.
Mathematically, we can represent it as mentioned below:
P(E) + P(E') = 1
where P(E) = Probability of an event to occur.
And P(E') = Probability of an event not to occur.
According to the question,
The probability that a student chosen at random from class is a psychology major = P(E) = 0.18
As we know,
P(E) + P(E') = 1
Hence, Probability that a student chosen at random from class is not a psychology major = P(E') = 1 - P(E) = 1 - 0.18 = 0.82
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The given question is incomplete, complete question is:
The probability that a student chosen at random from your class is a psychology major is 0.18.
What is the probability that a student chosen at random from your class is not a psychology major?
at a lunch stand, each hamburger has 50 5050 more calories than each order of fries. if 2 22 hamburgers and 3 33 orders of fries have a total of 1700 17001700 calories, how many calories does a hamburger have?
A hamburger has 350 calories. So an order of fries has 320 calories, and a hamburger has 50 + 320 = 370 calories.
To solve the problem, you can use algebraic equations. Let x be the number of calories in an order of fries. Then, the number of calories in a hamburger is 50 + x. The problem tells us that 2 hamburgers and 3 orders of fries have a total of 1700 calories. This can be written as:
2(50 + x) + 3x = 1700
Simplifying and solving for x, we get:
100 + 2x + 3x = 1700
5x = 1600
x = 320
So an order of fries has 320 calories, and a hamburger has 50 + 320 = 370 calories.
Explanation:
To solve the problem, we need to set up an equation that relates the number of hamburgers and fries to the total number of calories. We can use algebraic variables to represent the unknown quantities. Let x be the number of calories in an order of fries, and let y be the number of calories in a hamburger.
The problem tells us that each hamburger has 50 + x more calories than each order of fries. This means that the number of calories in a hamburger is equal to the number of calories in an order of fries plus 50:
y = x + 50
We also know that 2 hamburgers and 3 orders of fries have a total of 1700 calories. This can be written as:
2y + 3x = 1700
Now we can substitute the first equation into the second equation to eliminate y:
2(x + 50) + 3x = 1700
Simplifying and solving for x, we get:
2x + 100 + 3x = 1700
5x = 1600
x = 320
So an order of fries has 320 calories. We can substitute this value back into the first equation to find the number of calories in a hamburger:
y = x + 50
y = 320 + 50
y = 370
Therefore, a hamburger has 370 calories.
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in order to take a survey a sample of 90 members of a local gym, i first divide the members into men and women, and then take a srs of 45 men and a separate srs of 45 women. this is an example of:
The sampling technique used in this scenario is stratified random sampling. Stratified random sampling is a useful technique for obtaining a representative sample from a population with identifiable subgroups, and can improve the validity and generalizability of survey results.
Stratified random sampling involves dividing the population into homogeneous groups, or strata, based on a specific characteristic, and then taking a random sample from each stratum. In this case, the population of gym members was divided into men and women, which are two distinct and easily identifiable strata. A simple random sample was then taken from each stratum to obtain a representative sample of both genders.
The use of stratified random sampling can increase the precision and accuracy of the sample by ensuring that each stratum is represented proportionally in the sample. This technique is commonly used when the population of interest exhibits a significant characteristic that may impact the outcome of the survey. For example, if the survey was investigating the effectiveness of a new exercise program, it would be important to ensure that both men and women were represented equally in the sample, as their physiological differences may impact their response to the program.
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leo ate 3/5 cup of strawberries and jack ate 7/10 cup of strawberries. how much more did jack eat than leo?
Jack ate 1/10 cup more strawberries than Leo
The problem states that Leo ate 3/5 cup of strawberries, and Jack ate 7/10 cup of strawberries. We need to find out how much more Jack ate than Leo.
To solve this problem, we first need to find a common denominator for the two fractions. The denominator is the bottom number of a fraction, which represents the total number of equal parts that make up a whole.
The smallest common denominator for 5 and 10 is 10. We can convert the fraction 3/5 into an equivalent fraction with a denominator of 10 by multiplying both the numerator and denominator by 2. This gives us 6/10.
Now, we have two fractions with the same denominator: 6/10 and 7/10. To find out how much more Jack ate than Leo, we can subtract the fraction representing what Leo ate from the fraction representing what Jack ate:
7/10 - 6/10 = 1/10
Therefore, Jack ate 1/10 cup more strawberries than Leo did.
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What are the advantages of an open question? Select all that apply.
-An open question allows for new solutions to be introduced.
-An open question allows the respondent to go in-depth with their answer.
The advantages of an open question include:
An open question allows for new solutions to be introduced.An open question allows the respondent to go in-depth with their answer.An open question is designed to elicit a broad and unrestricted response from the respondent. It encourages them to think creatively and explore various possibilities, which can lead to the introduction of new solutions. Unlike closed-ended questions that limit respondents to predefined options, an open question provides the freedom to express ideas, perspectives, and insights that may not have been considered before.
Furthermore, an open question allows the respondent to go in-depth with their answer. It prompts them to provide detailed explanations, examples, and personal experiences, allowing for a richer and more nuanced understanding of their thoughts and perspectives. This depth of response can unveil valuable insights, uncover underlying motivations, and provide context that may not have been captured with closed-ended questions. It also encourages active engagement and reflection from the respondent, as they are encouraged to express their thoughts and feelings in a more comprehensive manner.
Overall, open questions promote creativity, critical thinking, and a deeper exploration of ideas, making them advantageous in various contexts such as research, interviews, surveys, and problem-solving discussions.
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a baseball collides with a baseball glove. which equation is used to calculate the force the glove exerts on the ball during the collision?(1 point)
Therefore, the force the glove exerts on the ball during the collision can be calculated by measuring the change in momentum of the ball and dividing it by the time of the collision.
The equation used to calculate the force the glove exerts on the ball during the collision is the impulse-momentum equation. This equation states that the force applied to an object is equal to the change in momentum of the object over time. Therefore, the force the glove exerts on the ball during the collision can be calculated by measuring the change in momentum of the ball and dividing it by the time of the collision.
To calculate the force the glove exerts on the ball during the collision, you can use Newton's second law of motion, which states:
Force (F) = Mass (m) × Acceleration (a)
In this scenario, the mass (m) refers to the mass of the baseball, and the acceleration (a) is the change in the baseball's velocity divided by the time it takes for the collision to occur. Keep in mind that the acceleration will have a negative value, as the ball is decelerating during the collision.
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if the sixth term of a geometric sequence is 224, and the eleventh term is 7168, what is the first term?
Answer:
Step-by-step explanation:
ajns
4. if you draw three cards from a deck of 52 cards one at a time without replacement, what is the probability that all three cards are diamonds?
The probability of drawing three cards from a deck of 52 cards one at a time without replacement and having all three cards be diamonds is 0.0026, or approximately 0.26%.
To calculate this probability, we can use the formula for conditional probability. The probability of drawing the first diamond is 13/52, since there are 13 diamonds in the deck. Once the first diamond has been drawn, there are 12 diamonds left out of 51 cards. So the probability of drawing a second diamond, given that the first card was a diamond, is 12/51. Finally, once two diamonds have been drawn, there are 11 diamonds left out of 50 cards. So the probability of drawing a third diamond, given that the first two cards were diamonds, is 11/50. Multiplying these three probabilities together gives us the probability of drawing three diamonds in a row, which is approximately 0.0026.
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i need help asap plsssss
Answer:
'x' only has one solution
Step-by-step explanation:
First multiply both sides by 'x^2'
40x = -5x^2
(bring both values to one side and factorize to solve for 'x')
5x^2 +40x=0
5x(x+8)=0
5x= 0 ; x+8 = 0
x=0 ; x=-8
x cannot equal to '0' as zero cannot be a denominator.
Hence, x=-8 is the only correct solution.
So, 'x' only has one solution.
The circle below is centred at O.
What is the size of angle x?
Write a justification for your answer.
o =146°
Not drawn accurately
The value of angle x is 107°
What is circle geometry?A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.
There is a theorem in circle geometry that states that : The angle subtended at the centre of a circle is twice the angle at the circumference.
This means if the angle at the circumference is 50, the angle at the center is 100.
The angle at the center = 360 - 146( angle at a point)
= 214°
2x = 214
x = 214/2
x = 107°
therefore the value of x is 107°
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The table shows the projected population of the United States through 2050. Does
this table show an arithmetic sequence, a geometric sequence or neither? Explain
year projected population
2000 282,125,000
2010 308.936,000
2020 335,805,000
2030 363,584,000
2040 391,946,000
2050 419,854,000
The table shows neither an arithmetic sequence nor a geometric sequence because it doesn't have a common difference and common ratio.
How to calculate an arithmetic sequence?In Mathematics and Geometry, the nth term of an arithmetic sequence can be calculated by using this expression:
aₙ = a₁ + (n - 1)d
Where:
d represents the common difference.a₁ represents the first term of an arithmetic sequence.n represents the total number of terms.Next, we would determine the common difference as follows.
Common difference, d = a₂ - a₁
Common difference, d = 308,936,000 - 282,125,000 = 363,584,000 - 335,805,000
Common difference, d = 26,811,000 ≠ 27,779,000
Next, we would determine the common ratio as follows;
Common ratio, r = a₂/a₁
Common ratio, r = 308,936,000/282,125,000 ≠ 335,805,000/363,584,000
Common ratio, r = 1.095 ≠ 0.924
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35°
46"
65"
30"
2x
What is the perimeter? This is a little tougher problem,
and to solve it you'll need to know the lengths of the
segments on either side of the perpendicular height
(which is whyt I gave you the numbers in smaller font).
Submit
The perimeter of the triangle is 170 inches.
How to calculate the valueTo solve for the perimeter, we first need to find the length of the perpendicular height. We can do this using the sine function:
sin(35°) = 46/x
x = 46/sin(35°) = 65 inches
Now that we know the length of the perpendicular height, we can find the length of the base of the triangle using the cosine function:
cos(35°) = 65/x
x = 65/cos(35°) = 75 inches
The perimeter of the triangle is the sum of the lengths of the three sides, so the perimeter is:
P = 65 + 75 + 30
= 170 inches
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Find the mean of 8,9,1
Answer:
6
Step-by-step explanation:
8+9+1 is 18, and since there are 3 numbers, we must divide 18 by 3, 2 which is 6
Answer: 6
Step-by-step explanation:
8+9+1 = 18
3 numbers
18/3 = 6
Calculate the size of angle x.
x
240°
x
x
Answer:
280 degrees.
Step-by-step explanation:
The way you work this out is by:
1) Work out 240-360
2) Subtract the answer from 360
3) Divide the answer of step 2 into however many angles you have (in this instance 4).
4) Then use one of these angles and subtract it from 360. This will give you a reflex angle.
5) That's it.
Answer:
Angle x is 280°----------------------
We know that the sum of interior angles of a quadrilateral is 360°.
Show this as a sum using angle measures in the diagram:
3(360 - x) + (360 - 240) = 3603*360 - 3x + 120 = 360360 - x + 40 = 120x = 400 - 120x = 280can sb help me with this question
Answer:
-18
Step-by-step explanation:
suppose an economy can be described by the consumption function c = 75 0.80yd and i = $50. what is the multiplier? a. 0.20. b. 5. c. 1.25. d. 0.80.
The multiplier is 5. To find the multiplier, we use the formula: Multiplier = 1 / (1 - MPC), where MPC is the marginal propensity to consume.
In this case, the consumption function is c = 75 + 0.80yd, which implies that MPC = 0.80. Therefore, the multiplier is 1 / (1 - 0.80) = 5. This means that an initial change in investment spending of $50 will lead to a total change in output (GDP) of $250, assuming no other changes in the economy.
The multiplier effect occurs because the initial injection of spending leads to an increase in income, which in turn leads to an increase in consumption, and so on, in a multiplier process.
It is important to note that the multiplier effect assumes that there are no leakages (such as taxes or imports) in the economy, which can reduce the size of the multiplier.
Additionally, the multiplier effect assumes that the economy is operating below full capacity, so that there is room for output to expand.
If the economy is already operating at full capacity, the multiplier effect may be limited, as additional spending may lead to inflationary pressures rather than an increase in output.
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pls answer this question brainliest will be given
√8/98
A dietitian was interested in the heights of 13-year-olds in the state. He gathered data from a random sample of 400 pediatricians in the state and wanted to create an appropriate graphical representation for the data. Which graphical representation would be best for the data?
Bar graph
Circle graph
Histogram
Line plot
A Histogram would be the best for the data representation of the girls by dietitian.
What is histogram?Histogram, it is an approximate representation of the distribution of numerical data. The most popular graph for showing frequency distributions is a histogram. Though it also closely resembles a bar chart, there are significant differences. One of the seven basic quality tools is this useful gathering and analyzing information tool.
Variable = the height of 13-year-olds in the state of Texas.
Where the height of each bar represents the frequency of observations.
[tex]\sf (2-2.5) \ feet[/tex]
[tex]\sf (2.6-3) \ feet[/tex]
[tex]\sf (3.1-3.5) \ feet[/tex]
[tex]\sf (4.1-4.5) \ feet[/tex]
So, The best graphical representation of the dietitian's data would be a histogram.
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Find the next row of Pascal's triangle given the row 1 7 21 35 35 21 7 1.
The next row of Pascal's triangle for the given row 1 7 21 35 35 21 7 1 is equal to 1 8 28 56 70 56 28 1.
Row of Pascal's triangle is equal to,
1 7 21 35 35 21 7 1
To find the next row of Pascal's triangle given the row 1 7 21 35 35 21 7 1,
Use the property that each element in Pascal's triangle is the sum of the two elements directly above it.
Let us calculate the next row,
Row = 1 7 21 35 35 21 7 1
Next row = 1 _ _ _ _ _ _ 1
To fill in the missing values,
Start by writing down the first and last elements, which are always 1,
Row = 1 7 21 35 35 21 7 1
Next row= 1 _ _ _ _ _ _ 1
Next, we can calculate the remaining elements by adding the two elements directly above each empty space,
Row = 1 7 21 35 35 21 7 1
Next row = 1 8 _ _ _ _ 8 1
Continuing the process,
Row = 1 7 21 35 35 21 7 1
Next row = 1 8 28 _ _ 28 8 1
Row = 1 7 21 35 35 21 7 1
Next row = 1 8 28 56 _ 56 28 1
Row = 1 7 21 35 35 21 7 1
Next row = 1 8 28 56 70 56 28 1
Therefore, the next row of Pascal's triangle is 1 8 28 56 70 56 28 1.
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if 95% of a drink is real fruit juice, what percent is not real fruit juice
Answer:
5%
Step-by-step explanation:
100 - 95 = 5
which of the following bit arrays below is the correct 4-bit combination for the decimal number 9?
The correct 4-bit combination for the decimal number 9 is 1001. To explain it in a long answer, we need to understand binary representation. In binary, each digit can either be 0 or 1, and the value of the digit depends on its position.
The rightmost digit represents the value 2^0 (which is 1), the next digit to the left represents the value 2^1 (which is 2), the next represents 2^2 (which is 4), and so on. To convert decimal number 9 to binary, we can start by finding the highest power of 2 that is less than or equal to 9, which is 2^3 (which is 8). We can subtract 8 from 9, and the remainder is 1. This means the leftmost digit in the binary representation is 1.
We repeat the same process with the remainder, which is 1, and find the highest power of 2 that is less than or equal to 1, which is 2^0 (which is 1). We subtract 1 from 1, and the remainder is 0. This means the rightmost digit in the binary representation is 0. Thus, the binary representation of decimal number 9 is 1001, which is the correct 4-bit combination.
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Out of 160 workers surveyed at a company, 29 walk to work. a. What is the experimental probability that a randomly selected worker at that company walks to work? b. Predict about how many of the 3800 workers at the company walk to work.
The experimental probability is 29/100 and the number of workers that walk is 1102
What is Experimental Probability?The experimental probability of an event is based on the number of times the event has occurred during the experiment and the total number of times the experiment was conducted. Each possible outcome is uncertain and the set of all the possible outcomes is called the sample space.
The formula for this is given as;
P(E) = Number of occurrence of an event / Total number of times experiment is carried out.
a. Experimental probability = 29/100
b. To predict the total number of workers that walk, we can go as;
(29/100) * 3800 = 1102
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what growth model is appropriate for the number of arrests grew for several years, but now has been decreasing
The appropriate growth model for the given scenario would be a logistic growth model where the growth rate slows down as the variable approaches its carrying capacity, which is the maximum value it can reach.
A logistic growth model is appropriate for situations where the growth rate of a variable initially increases and then slows down as it approaches a maximum value or carrying capacity. In the given scenario, the number of arrests initially grew for several years, but has been decreasing recently, suggesting that it may have reached a saturation point. Thus, a logistic growth model would be appropriate to model the trend of the number of arrests.
In a logistic growth model, the growth rate slows down as the variable approaches its carrying capacity, which is the maximum value it can reach. In the case of the number of arrests, the carrying capacity could be the maximum number of arrests that can be made in a given period, which might be limited by factors such as the number of police officers, the number of crimes committed, or the effectiveness of law enforcement policies. As the number of arrests approaches this limit, the growth rate slows down, eventually leading to a plateau or a decline in the number of arrests.
Overall, a logistic growth model would be appropriate for the given scenario as it takes into account the saturation point and provides a better fit to the trend of the number of arrests over time.
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What is the area of the regular hexagon shown below?
Hint:
Central angle = 360/n where n is the number of sides
Area= (n) 1/2 (r2)sin(central angle)
A flu vaccine was developed, and testing was conducted to prove its effectiveness. Normally 4% of the population get this flu strain 700 people participated in the study with 12 getting the flu. What is a good point estimate to use for the population proportion to test the effectiveness of the flu vaccine? a. 0.3333 6.0.23541 OC 0.0400 d. 0.01714
A good point estimate for the population proportion is 0.01714. Option D is correct.
A good point estimate to use for the population proportion to test the effectiveness of the flu vaccine can be calculated by dividing the number of people who got the flu (12) by the total number of participants in the study (700).
Point Estimate = Number of people who got the flu / Total number of participants
Point Estimate = 12 / 700
Using a calculator, the approximate value of the point estimate is 0.01714 (rounded to five decimal places).
Therefore, the good point estimate to use for the population proportion to test the effectiveness of the flu vaccine is 0.01714. Option D is correct.
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