Answer:
a tangent is never a secant
Step-by-step explanation:
the secant is in the circle
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The correct statement is A: 'A tangent is never a secant.' because it accurately describes that a tangent only touches the circle at one point and does not cross the circle's interior unlike a secant.
Explanation:The question you've asked pertains to the geometric definitions of a tangent, secant, chord, and diameter in relation to a circle. Reviewing the options provided:
A tangent is a line that touches a circle at exactly one point and never enters the circle's interior, so it's distinct from a secant, which does enter the interior. Therefore, option A ('A tangent is never a secant.') is true.A secant is a line that intersects a circle at two points and always includes a chord, the segment between these two points, which makes option B ('A secant is always a chord.') incorrect as a secant is not a chord, it includes a chord.A chord is a segment whose endpoints lie on a circle, and it could be any length up to the length of the diameter; hence, option C ('A chord is always a radius.') is incorrect.A diameter is a special type of chord that passes through the center of the circle and its longest possible chord. So, option D ('A diameter is never a chord.') is incorrect.Given these explanations, the best answer from the choices provided is in fact option A.
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HELP PLSS Solve: e2x + 5 = 4
Answer:
x = 1/2( ln(4) -5)
Step-by-step explanation:
e ^ 2x+5 =4
Take the natural log of each side
ln(e ^ 2x+5) =ln(4)
2x+5 = ln(4)
Subtract 5 from each side
2x = ln(4) - 5
Divide by 2
2x/2 = (ln(4) -5)/2
x = 1/2( ln(4) -5)
Answer:
its c on edge.
Arlin has 9 dollars and 37 cents. Lauren has 6 dollars and 63 cents. How much money does Arlin need to give Lauren so that each of them has the same amount of money?
Answer:
Arlin has to give lauren 1.37
Step-by-step explanation:
9.37 + 6.63 / 2 = 16 / 2 = 8
9.37 - 8 = 1.37
Answer:
$1.37
Step-by-step explanation:
I would start by adding up the total money between them. $9.37 + $6.63 = $16.00. They want the same amount of money, so divide the total by two.
$16.00/2 = $8.00.
Now take the difference between how much Arlin had ($9.37) and how much she has now ($8.00).
$9.37 - $8.00 = $1.37
Joyce saved $140 on an item that was 40% off. What was the original price?
Answer: $350 because you multiply 140 and 100 then divide 40
What is the equation of the line that goes through the points (1,2) and (2,1)?
Answer:
y = -x+3
Step-by-step explanation:
We have two points so we can find the slope
m =(y2-y1)/(x2-x1)
(1-2)/(2-1)
-1/1
The slope is -1
We can use the slope intercept form of the equation
y = mx+b where m is the slope and b is the y intercept
y = -x+b
Substitute a point into the equation to find b
2 = -1 +b
Add 1 to each side
2+1 =-1+1 +b
3 =b
y = -x+3
The mean of the sample is 9.771 km/h , and the standard deviation is 0.944 km/h . Construct and interpret a 95 percent confidence interval for the mean swimming speed of all emperor penguins in the population.
Answer:
Step-by-step explanation:
The confidence interval for the mean swimming speed of all emperor penguins in the sampled population is (9.4248, 10.1172).
Given the following data:
Mean of a sample = 9.771 km/hStandard deviation = 0.944 km/hConfidence interval = 95% = 0.95Sample size = 31What is a confidence interval?In Statistics, a confidence interval can be defined as the degree of uncertainty that is associated with a given statistical population.
How to calculate confidence intervalFirst of all, we would subtract one from the given sample size for penguins.
[tex]n=31-1=30[/tex]
Next, we would subtract the confidence interval from 1 and then divide by 2:
[tex]\frac{(1-0.95)}{2} =\frac{0.05}{2} =0.025[/tex]
From the t-distribution table, a 30 degree of freedom (df) with 0.025 is equal to 2.042.
Divide the standard deviation by the square root of penguin's population size and then multiply by the t-interval.
[tex]\frac{0.944}{\sqrt{30} } \times 2.042=0.3462[/tex]
For the lower end:
[tex]9.771-0.3462=9.4248[/tex]
For the upper end:
[tex]9.771+0.3462=10.1172[/tex]
Therefore, the confidence interval for the mean swimming speed of all emperor penguins in the sampled population is (9.4248, 10.1172).
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A college admissions director wishes to estimate the mean age of all students currently enrolled. In a random sample of 20 students, the mean age is found to be 22.9 years. From past studies, the standard deviation is known to be 1.5 years, and the population is normally distributed. Construct a 90% confidence interval of the population mean age.
Answer:
90% confidence interval: (22.35,23.45)
Step-by-step explanation:
We are given the following in the question:
Sample mean, [tex]\bar{x}[/tex] = 22.9 years
Sample size, n = 20
Alpha, α = 0.10
Population standard deviation, σ = 1.5 years
90% Confidence interval:
[tex]\bar{x} \pm z_{critical}\dfrac{\sigma}{\sqrt{n}}[/tex]
Putting the values, we get,
[tex]z_{critical}\text{ at}~\alpha_{0.05} = \pm 1.64[/tex]
[tex]22.9 \pm 1.64(\dfrac{1.5}{\sqrt{20}} )\\\\ = 22.9 \pm 0.55 \\\\= (22.35,23.45)[/tex]
(22.35,23.45) is the required 90% confidence interval for population mean age.
The 90% confidence interval for the population mean age, from the given data, is approximated to be between 22.46 years and 23.34 years.
Explanation:To construct a 90% confidence interval of the population mean age, we will use the formula for the confidence interval, which is sample mean ± Z-score * (Standard deviation/ sqrt (sample size)), where the Z-score is based on the confidence level. For 90%, the Z-score is 1.645.
So in this case, the sample mean is 22.9 years, the known standard deviation is 1.5 years, and the sample size (n) is 20. Plugging these values into the formula gives:
22.9 ± 1.645 * (1.5 / sqrt (20))
When you calculate, it will give an interval of about 22.46 years to 23.34 years. Hence the 90% confidence interval for the population mean age is 22.46 years to 23.34 years.
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A professor believes that students at her large university who exercise daily perform better in statistics classes. Since all students at the university are required to take Introduction to Statistics, she randomly selects 17 students who exercise daily and 22 students who exercise at most once per week. She obtains their scores in the final exam in Introduction to Statistics and finds that the students who did not exercise daily primarily produced scores in the 90s, with some scores in the 80s and a very few scores in the 70s and 60s. The students who did exercise daily also had a large number of scores in the 90s and an almost equal number in the 60s, with very few scores in between.
Would it be valid for the professor to use the independent-measures t test to test whether students at her large university who exercise daily perform better in statistics classes?
a. Yes, because the two populations from which the samples are selected have equal variances.
b. Yes, because none of the assumptions of the independent-measures t test are violated.
c. No, because the two populations studied are not independent.
d. No, because the two populations from which the samples are selected do not appear to be normally distributed.
Answer:
d. No, because the two populations from which the samples are selected do not appear to be normally distributed.
Step-by-step explanation:
First, the assumptions of an independent-measures t test are as follows:
1. The data is continuous
2. Only two groups are compared
3. The two groups should be independent
4. The groups should have equal variance
5. The data should be normally distributed
In this case, the 5th assumption has been violated because scores in the two samples are distributed in different ranges in two samples. So the outliers in the scores may be exist. Therefore, it would not be valid for the professor to use the independent-measures t test because the two populations from which the samples are selected do not appear to be normally distributed.
what is 210% as a fraction?
Answer:
21/10
Step-by-step explanation:
Answer:
21/10
Step-by-step explanation:
if i have 5 blue pens and 3 black pens, What fraction of the number of black pens is the number of blue pens?
Answer:
the answer to the question is 3/5
suppose you deposit $3000 in a savings account that pays interest at an annual rate of 4%. if no other money is added or withdrawn from the account how much will be in the account after 10 years?
If no other money is added or withdrawn from the account how much will be in the account after 10 years is $4,440.73.
Simple interestUsing this formula
Amount=Principla(1+Interest rate)^ Time
Let plugm in the formula]
Amount=$3,000(1+0.04)^10
Amount=$3,000(1.04)^10
Amount-$3,000(1.4802442849)
Amount=$4,440.73
Therefore how much will be in the account after 10 years is $4,440.73.
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I have 3 Sisters each
Sister has 3 sisters. How
many of us are there?
Answer:
4 sisters
Step-by-step explanation:
-This is a logic question.
-Given that she has 3 sisters, it only means that the 4 are siblings of the same family.
-As such, eaxh sister can correctly claim to have 3 sisters.
Hence, there is a total of 4 sisters.
Luke puts 3 apples in each bag. How many apples does he put in 4 bags
Answer:
12
Step-by-step explanation:
3x4=12
Answer:
12
Step-by-step explanation:
Multiply the number of bags times the apples per bag
4*3 = 12
He needs 12 apples
What does this mean 31>28
Answer:
What does this mean 31>28
Step-by-step explanation:
Final answer:
The expression 31>28 means that 31 is greater than 28, which is a basic mathematical comparison used widely across various contexts, from simple arithmetic to data analysis and the mnemonic for remembering the number of days in each month.
Explanation:
The expression 31>28 is a mathematical comparison indicating that the number 31 is greater than the number 28. This can be applied in various contexts, such as comparing quantities, ages, temperatures, or even the number of days in different months. For example, using the knuckle mnemonic, months with 31 days are more than those with 28 days (February, typically), illustrating a practical application of this comparison.
In statistics and data analysis, understanding comparative values like this is crucial. It helps in analyzing data intervals, as in the provided reference, where different age intervals are being compared based on the number of data values they contain. This fundamental concept of comparison underpins much of mathematical reasoning and data analysis.
A study was to be undertaken to determine if a particular training program would improve physical fitness. A simple random sample of 35 university students was selected to be enrolled in the training program. After the training program was completed, the maximum oxygen uptake of the students was measured to indicate their fitness level. The researchers wished to determine if there was evidence that their sample of students differed from the general population of untrained subjects, whose maximum oxygen uptake is known to be 45 mL/kg/min on average. Based on the sample of 35 students, the maximum oxygen uptake was found to have slight skewness but no strong outliers. Why can we safely use a t procedure in this testing situation
Answer:
The t-test for one mean can be safely used for this situation.
Step-by-step explanation:
A statistical experiment is conducted to determine if a particular training program would improve physical fitness.
The objective of the experiment was to determine if there is some evidence that the maximum oxygen uptake of the sample of students differed from the general population of untrained subjects, whose maximum oxygen uptake is known to be 45 ml/kg/min on average.
The hypothesis is defined as:
H₀: The population mean is 45 ml/kg/min, i.e. μ = 45.
Hₐ: The population mean is different from 45 ml/kg/min, i.e. μ ≠ 45.
The test for single mean can be either using the z-distribution or the t-distribution.
The z-distribution is used if it provided that:
The population from which the sample is drawn is normally distributedThe population standard deviation is known.The t-distribution is used if :
The population standard deviation is not known.The sample size is not quite large.To use a t-distribution for a single mean test the following assumptions are to made:
The parent population is normally distributed.The sample selected is a simple random sample.There are no outliers in the sample.The observations are independent of each other.In this case we will use a t-distribution since there is no information about the population standard deviation.
The sample of 35 students are randomly selected for the training program.
The maximum oxygen uptake of every student is independent of the others.
Thus, the t-test for one mean can be safely used for this situation.
What is the volume of this rectangular prism? 2 cm 1/4 cm 2 cm
Answer:
1 cm cubed
Step-by-step explanation:
The volume of a rectangular prism is found by the equation: [tex]V=lwh[/tex] , where [tex]l[/tex] is the length, w is the width, and h is the height.
Here, our dimensions are 2 by 1/4 by 2. So: [tex]l=2,w=1/4,h=2[/tex].
Substituting these into the equation, we have:
[tex]V=2*(1/4)*2=1[/tex]
Thus, the volume is 1 cm cubed.
Hope this helps!
Answer:
1
Step-by-step explanation:
2*2=4
4*1/4=1
multiplying 1/4 is the same as dividing by 4
What is the effect of visualizing the hole as bigger A taking longer to play golf B worse golf scores C selecting larger circles D better golf score
Answer:
better golf scores
Step-by-step explanation:
i did the quiz just a few secs ago
According to the excerpt, seeing the "hole as bigger" has the benefit of improving gold scores. The right answer is D.
How can imagining larger gaps in scores help?Visualization is the capacity to create mental images of situations and things using one's imagination.
Visualization enhanced results in the excerpt provided.
Golfers typically earned better gold scores when they saw the golf hole as larger circles.
The result of seeing the "hole as greater" is that you will receive better gold scores.
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true or false The typical measurement of hotel demand is the room night (RN). When we say that each room night is perishable , we mean that once each room goes unoccupied/unsold for any night, it cannot be "stored away" and then sold on another date.
Answer:
True
Step-by-step explanation:
Perishable is a term for a product that has limited time to sell. A product like meat, fruit, and most fresh food will have a shelf life and you have to sell the product before the shelf life expires. Some preservation techniques can help to extend food products like freezing or curing them.
Room night of a hotel or any rent product is also considered as perishable since you can't store the rent time and sell it another day. So, every unoccupied room is treated as expired food. Unlike food products, room nights for the hotel can't be preserved. There are other strategies to maximize the revenue of rent products such as overselling or selling promise/reservation.
Solve
A lady buys grocery worth Rs.350 from a shop. (shopkeeper selling the goods with zero profit)
The lady gives him 2000 rs note. The shopkeeper gets the *change* from next shop, keeps 350 for himself and returns Rs.1650 to d lady.
Later the shopkeeper of the next shop comes with the Rs.2000 note saying "duplicate" *and takes his money back.*
"How much LOSS did the shopkeeper face ?"
A. 350
B. 1650
C. 2000
D. 2350
E. 3650
F. 4000
G. Other(Specify Amount)
Simple yet confusing n challenging.
D : 2350
Step-by-step explanation:
Given,
The grocery price: 350
The amount lady gave: 2000
The amount returned to the lady: 1650
Also, given that the shopkeeper of the next shop comes with the Rs.2000 note saying "duplicate" *and takes his money back.
Therefore, the loss would be the sum of two items:
1) The shopkeeper have to return the 2000 rupees to the next shopkeeper. Therefore, he suffers the loss of 2000.
2) He also sold the grocery worth 350 rupees. Therefore, it would be the extra loss of 350 rupees.
Hence, the shopkeeper faced the loss of 2000 + 350 = 2350 rupees.
Graph each inequality in a numerical line
[tex]x\ \textless \ -1[/tex]
[tex]y\geq 5[/tex]
[tex]w\ \textless \ 9[/tex]
[tex]z\leq 2[/tex]
See the attached picture
An oil exploration company currently has two active projects, one in Asia and the other in Europe. Let A be the event that the Asian project is successful and B be the event that the European project is successful. Suppose that A and B are independent events with P(A) ¼ .4 and P(B) ¼ .7. (a) If the Asian project is not successful, what is the probability that the European project is also not successful? Explain your reasoning. (b) What is the probability that at least one of the two projects will be successful? (c) Given that at least one of the tw
Answer:
a) 0.75
b) 0.4375
c) 0.5714
Step-by-step explanation:
Solution:-
- The events are defined as follows:
Event A : The Asian project is successful
Event B : The European project is successful
- The two given events are independent. Their respective probabilities are:
P ( A ) = 0.25
P ( B ) = 0.25
- The conditional probability for European project to fail given that asian project also failed.
- The probability can be expressed as:
P ( B ' / A ' ) = P ( A' & B' ) / P ( A' )
- According to the property of independent events we have:
P ( A ' & B ' ) = ( 1 - P ( A ) )* ( 1 - P ( B ) )
Therefore,
P ( B ' / A ' ) = [ ( 1 - P ( A ) )* ( 1 - P ( B ) ) ] / ( 1 - P ( A ) )
P ( B ' / A ' ) = 1 - P ( B )
Answer: The probability is simply the failure of event (B) : The european project fails = 0.75.
b) The probability that at-least one of the two projects will successful consists of (either A or B is successful) or ( Both are successful). We can mathematically express it as:
P ( At-least 1 project is success ) = P ( A U B ) + P ( A & B )
P ( At-least 1 project is success ) = P ( A )*(1 - P ( B )) + P ( B )*(1 - P ( A )]+ P ( A ) * P ( B )
= 2*0.25*0.75 + 0.25^2
= 0.4375
c ) Given that at least one of the two projects is successful, what is the probability that only the Asian project is successful?
- We can mathematically express the required conditional probability as follows with help of part b):
P ( A / At-least 1 project is success ) = P ( A & any at-least 1 is success) / P ( At-least 1 project is success )
- The probability of P ( A & any at-least 1 is success), consists of event A success and event B fails or both are a success:
P ( A & any at-least 1 is success) = P ( A )*( 1 - P ( B ) ) + P ( A )*P ( B )
= 0.25*0.75 + 0.25^2
= 0.25
- The conditional probability can now be evaluated:
= P ( A & any at-least 1 is success) / P ( At-least 1 project is success )
= 0.25 / 0.4375
= 0.5714
2. A two-stage rocket is in development. The required probability is for the overall rocket to be a minimum of 97% reliable for a successful mission. The first stage is a previously developed design with a known reliability of 99%. The reliability measures for the two stages are independent. What must the minimum reliability for the second stage be
Answer: The minimum reliability for the second stage be 0.979.
Step-by-step explanation:
Since we have given that
Probability for the overall rocket reliable for a successful mission = 97%
Probability for the first stage = 99%
We need to find the minimum reliability for the second stage :
So, it becomes:
P(overall reliability) = P(first stage ) × P(second stage)
[tex]0.97=0.99\times x\\\\\dfrac{0.97}{0.99}=x\\\\0.979=x[/tex]
Hence, the minimum reliability for the second stage be 0.979.
Using probability of independent events, it is found that the minimum reliability for the second stage must be of 97.98%.
If two events, A and B, are independent, the probability of both events happening is the multiplication of the probability of each happening, that is:
[tex]P(A \cap B) = P(A)P(B)[/tex]
In this problem:
There are 2 stages, A and B.The first stage is 99% reliable, hence [tex]P(A) = 0.99[/tex].The system has to be 97% reliable, hence [tex]P(A \cap B) = 0.97[/tex].Then:
[tex]P(A \cap B) = P(A)P(B)[/tex]
[tex]0.97 = 0.99P(B)[/tex]
[tex]P(B) = \frac{0.97}{0.99}[/tex]
[tex]P(B) = 0.9798[/tex]
Hence, the minimum reliability for the second stage must be of 97.98%.
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Paco plans to attend college. He has estimated the costs for his first year.
Tuition = $1,600
Other educational expenses = $400
Housing and living expenses = $1,400
The college financial aid counselor estimates that Paco will receive $1,900 that year in grant money. He also has a scholarship that awards him $1,000 a year.
How much money does Paco need to save to pay for his first year of college?
$300
$500
$800
$1,100
please an thank you!
Wow. That is a nice tuition.
The question is asking, how much money does he need to pay after taking consideration of the grant money and scholarship.
We need to add up the estimated costs for his first year. 1,600+400+1,400=3,400.
Subtract both 1,900 and 1,000 (2,900) because he does not need to pay that amount from the original estimated costs.
3,400-2,900=500
This means that aside from the financial aid help, he will need to pay an additional 500 dollars to pay for his first year of college.
Answer:$500
Step-by-step explanation:
1. 1,600+400+1,400=3,400
2. 1,900+1,000=2,900
3. 3,400-2,900=500
A cup shaped like a hemisphere has a radius of approximately 2.125 inches. Which of the following is the best estimate of the volume of the cup?
The volume of the cup is 20 cubic inches.
Step-by-step explanation:
Given that the cup is in the hemispherical shape.
Radius of the cup = 2.125 inches
Volume of the cup = (2/3) π(r x r x r)
= (2/3) (3.14) (2.125 x 2.125 x 2.125)
= (2/3) (3.14) ( 9.59)
= (2/3) (30.13)
= 20 cubic inches
The volume of the cup is 20 cubic inches.
Find the coordinates of the intersection of the diagonals of parallelogram QRST with vertices Q(−8, 1), R(2, 1), S(4,−3), and T(−6,−3).
Answer:
(-2,1)
Step-by-step explanation:
To find the coordinates of the intersection of the diagonals of parallelogram QRST, we first need to find the midpoints of the diagonals. The midpoint of diagonal QR is (-3, 1) and the midpoint of diagonal ST is (-1, -3). We can find the equation of the line passing through these midpoints, and then find the x and y coordinates of the intersection point.
Explanation:Detailed Answer:To find the coordinates of the intersection of the diagonals of parallelogram QRST, we first need to find the midpoints of the diagonals. The midpoint of diagonal QR can be found by averaging the x-coordinates of Q and R, and the y-coordinates of Q and R. Therefore, the midpoint of QR is ((-8 + 2)/2, (1 + 1)/2) = (-3, 1). Similarly, the midpoint of diagonal ST is ((4 - 6)/2, (-3 - 3)/2) = (-1, -3).
Now that we have the midpoints, we can find the equation of the line passing through these two points. Using the slope-intercept form, we have y - 1 = (1 - (-3))/(-3 - (-1))(x - (-3)). Simplifying, we get y - 1 = 2(x + 3). Rearranging the equation gives us y = 2x + 5.
Substituting this equation into the equation of diagonal QR, we can find the x-coordinate of the intersection point. Plugging in y = 2x + 5 into the equation of QR, we get 1 = -x + 5. Solving for x, we get x = 4. Substituting the value of x into the equation of ST, we find the y-coordinate to be y = 2(4) + 5 = 13. Therefore, the coordinates of the intersection point are (4, 13).
g Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. A sample of 3000 bacteria selected from this population reached the size of 3145 bacteria in one and a half hours. Find the hourly growth rate parameter. Note: This is a continuous exponential growth model. Write your answer as a percentage. Do not round any intermediate computations, and round your percentage to the nearest hundredth.
Answer:
The hourly growth rate is of 3.15%
Step-by-step explanation:
The population of bacteria after t hours can be modeled by the following formula:
[tex]P(t) = P(0)e^{rt}[/tex]
In which P(0) is the initial population and r is the hourly growth parameter, as a decimal.
A sample of 3000 bacteria selected from this population reached the size of 3145 bacteria in one and a half hours. Find the hourly growth rate parameter.
This means that [tex]P(0) = 3000, P(1.5) = 3145[/tex]
We use this to find r.
[tex]P(t) = P(0)e^{rt}[/tex]
[tex]3145 = 3000e^{1.5r}[/tex]
[tex]e^{1.5r} = \frac{3145}{3000}[/tex]
[tex]\ln{e^{1.5r}} = \ln{\frac{3145}{3000}}[/tex]
[tex]1.5r = \ln{\frac{3145}{3000}}[/tex]
[tex]r = \frac{\ln{\frac{3145}{3000}}}{1.5}[/tex]
[tex]r = 0.0315[/tex]
The hourly growth rate is of 3.15%
Danika is making pizza. She has 1/3 cup of cheese and knows this is only enough for 2/5 of the recipe. How much cheese does the recipe call for?
Answer:
2/15 cups of cheese
Step-by-step explanation:
Because you are eating 2/5 of the recipe you have to multiply the values
2/5*1/3 = 2/15
Jamie places fifteen 1 inch cubes in the bottom of a box. She adds 4 more layers of the same number of cubes to completely fill the box. What is the volume of the box?
Answer:
60
Step-by-step explanation:
15cubes assuming 3rows of 5 cubes in one layer so volume of first layer is 3x5x1 =15
4 layers means 4 times or 4 inch in height, either way 4x15 = 60
Answer:
75
Step-by-step explanation:
Classify the following polynomials by degree and number of terms
3. x3-8
4. 24
5. 2x^4-x^3+5x^2+x-7
6. 10x
For each question answered I’ll answer two of your questions so a total of 8 questions answered also will give top answer thank you
Polynomials are classified by their degree and number of terms. x³-8 is a 3rd degree binomial, 24 is a 0th degree monomial, 2x⁴-x³+5x²+x-7 is a 4th degree quintic, and 10x is a 1st degree monomial.
Explanation:Polynomials can be classified by their degree (the highest power of the variable) and by the number of terms they contain. This classification is done as follows:
x3-8: This is a binomial (two terms) of 3rd degree, because the highest power of the variable is 3. 24: This is a monomial (one term) of 0th degree, because there is no variable present. 2x4-x3+5x2+x-7: This is a polynomial of 4th degree (due to the highest power of variable) with five terms, so it is also called a quintic. 10x: This is a monomial of 1st degree because the power of the variable is 1. Learn more about Polynomials here:
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Polynomials are classified by degree and number of terms: [tex]x^3[/tex]- 8 is a cubic binomial, 24 is a zero-degree monomial, [tex]2x^4 - x^3 + 5x^2[/tex] + x - 7 is a quartic quintic, and 10x is a linear monomial.
To classify polynomials by degree and number of terms, we check its highest exponent and count its terms:
[tex]x^3[/tex] - 8: This is a binomial (two terms) and its degree is 3 because the highest exponent of x is 3.
24: This is a monomial (one term) and its degree is 0 since it is a constant.
[tex]2x^4 - x^3 + 5x^2[/tex] + x - 7: This is a polynomial of five terms, so it's called a quintic. Its degree is 4 because the highest exponent of x is 4.
10x: This is a monomial (one term) and its degree is 1 because x is to the first power.
The classification is based on the degree of the polynomial, which is determined by the highest power of the variable x present in the equation, and the number of terms present in the polynomial (monomial for one term, binomial for two terms, and so on).
A sample of 100 workers located in Atlanta has an average daily work time of 6.5 hours with a standard deviation of 0.5 hours. A sample of 110 workers located in Chicago has an average daily work time of 6.7 hours with a standard deviation of 0.7 hours. With 95% confidence, can you say that the average hours worked daily in Atlanta is different than Chicago?
Answer:
[tex]t=\frac{6.5-6.7}{\sqrt{\frac{0.5^2}{100}+\frac{0.7^2}{110}}}}=-2.398[/tex]
[tex] df = n_1 +n_2 -2= 100+110-2= 208[/tex]
Since is a bilateral test the p value would be:
[tex]p_v =2*P(t_{208}<-2.398)=0.01110[/tex]
Comparing the p value with the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we can reject the null hypothesis, and we have significant differences between the two groups at 5% of significance.
Step-by-step explanation:
Data given and notation
[tex]\bar X_{1}=6.5[/tex] represent the sample mean for Atlanta
[tex]\bar X_{2}=6.7[/tex] represent the sample mean for Chicago
[tex]s_{1}=0.5[/tex] represent the sample deviation for Atlanta
[tex]s_{2}=0.7[/tex] represent the sample standard deviation for Chicago
[tex]n_{1}=100[/tex] sample size for the group Atlanta
[tex]n_{2}=110[/tex] sample size for the group Chicago
t would represent the statistic (variable of interest)
[tex]\alpha=0.01[/tex] significance level provided
Develop the null and alternative hypotheses for this study?
We need to conduct a hypothesis in order to check if the meanfor atlanta is different from the mean of Chicago, the system of hypothesis would be:
Null hypothesis:[tex]\mu_{1}=\mu_{2}[/tex]
Alternative hypothesis:[tex]\mu_{1} \neq \mu_{2}[/tex]
Since we don't know the population deviations for each group, for this case is better apply a t test to compare means, and the statistic is given by:
[tex]t=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}}[/tex] (1)
t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.
Calculate the value of the test statistic for this hypothesis testing.
Since we have all the values we can replace in formula (1) like this:
[tex]t=\frac{6.5-6.7}{\sqrt{\frac{0.5^2}{100}+\frac{0.7^2}{110}}}}=-2.398[/tex]
What is the p-value for this hypothesis test?
The degrees of freedom are given by:
[tex] df = n_1 +n_2 -2= 100+110-2= 208[/tex]
Since is a bilateral test the p value would be:
[tex]p_v =2*P(t_{208}<-2.398)=0.01110[/tex]
Based on the p-value, what is your conclusion?
Comparing the p value with the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we can reject the null hypothesis, and we have significant differences between the two groups at 5% of significance.
Answer:
No, I can't say precisely that. Because there are common values within both working hours intervals.
Step-by-step explanation:
1)Let's do it by parts. For a Confidence Interval of 95%, i.e. covering 95% of the area of the Graph of this distribution, with known mean and Standard Deviation we have to plug it in the formula below.
Notice that in the formula the part:
[tex]Z\frac{s}{\sqrt{n}}[/tex]
2)We can find the margin of error.
Atlanta:
Average Daily Work Time
100 workers
[tex]\bar{x}=6.5[/tex]
[tex]s=0.5[/tex]
[tex]\bar{x}\pm Z\frac{s}{\sqrt{n}}\\6.5\pm 1.96\frac{0.5}{\sqrt{100}}\\6.5 \pm 0.098\\6.40\: to\: 6.59[/tex]
Atlanta workers may have a an average of 6.4 to 6.59 daily working hours
Chicago
110 workers (observations)
[tex]\bar{x}:6.7\\s=0.7[/tex]
[tex]\bar{x}\pm Z\frac{s}{\sqrt{n}}\\6.7\pm 1.96\frac{0.7}{\sqrt{110}}\\6.7\pm 0.13\\6.57\: to\: 6.83[/tex]
Chicago workers may have worked an average of 6.57 to 6.83 daily working hours
It is believed that the average starting salary for a 21-25 year old college grad exceeds $52,000 per year. Hence, it is desired to test H0: µ ≤ 52,000 versus H1 : µ > 52,000. Assume σ = $5,745 and a SRS of size 65 is taken. We reject H0 when X > 53,460. The significance level α is:
Answer:
The significance level α is 0.02.
Step-by-step explanation:
A hypothesis test for single mean can be performed to determine whether the average starting salary for a 21-25 year old college grad exceeds $52,000 per year.
The hypothesis is defined as follows:
H₀: The average starting salary for a 21-25 year old college grad does not exceeds $52,000 per year, i.e. µ ≤ 52,000.
Hₐ: The average starting salary for a 21-25 year old college grad exceeds $52,000 per year, i.e. µ > 52,000.
The information provided is:
σ = $5,745
n = 65
Also, if [tex]\bar X>\$53,460[/tex] then the null hypothesis will be rejected.
Here, we need to compute the value of significance level α, the type I error probability.
A type I error occurs when we reject a true null hypothesis (H₀).
That is:
α = P (type I error)
α = P (Rejecting H₀| H₀ is true)
[tex]=P(\bar X>53460|\mu \leq 52000)[/tex]
[tex]=P[\frac{\bar X-\mu_{0}}{\sigma/\sqrt{n}}>\frac{53460-52000}{5745/\sqrt{65}}][/tex]
[tex]=P(Z>2.05)\\=1-P(Z<2.05)\\=1-0.97982\\=0.02018\\\approx0.02[/tex]
*Use a z-table for the probability.
Thus, the significance level α is 0.02.