Describe the center of the dot plot. What single dot would best represent the data?
Answers
The center, 6, is less frequent than the neighbor values, but the single dot that best represents the data still is 6.
What can we say about the center?Each point on the dot plot over each number represents the amount of times that we have that value in the data set.
Here the center is 6, and we can see that we have only one point in 6, while in the neighbors we can see more points, then we can see that the center is less populated than the neighbor values.
Now, what single dot would best represent the data?
To answer that we need to get the mean of the data set,
Counting the values in the graph, and dividing by the number of points, we have:
mean = (3 + 4 + 4 + 5 + 5 + 6 + 7 + 7 + 8 + 8+ 8+ 9)/12 = 6.16
Which we can round to 6.
So that is the single dot that best represents the data.
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Related Questions
Pls help me I will make u brainest
How many different numbers can be obtained from multiplying 2 distinct integer divisors of 10?
3
4
5
6
7
8
9
Answers
We can obtain 6 different numbers by multiplying 2 distinct integer divisors of 10.
How many different numbers can be obtained from multiplying 2 distinct integer divisors of 10?The divisors of 10 are 1, 2, 5, and 10.
To determine how many different numbers can be obtained from multiplying 2 distinct integer divisors.
We need to select 2 distinct divisors and find their product.
The possible pairs are:
1 and 2, product = 21 and 5, product = 51 and 10, product = 102 and 5, product = 102 and 10, product = 205 and 10, product = 50Therefoore, we can obtain 6 different numbers.
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use the formula for the sum of a geometric series to find the sum or state that the series diverges. (use symbolic notation and fractions where needed. enter dne if the series diverges.) (4^3 / 5^3) + (4^4 / 5^4) + (4^5 / 5^5) = ________--
Answers
The sum of the geometric series is 3904/3125.
By using the formula for the sum of a geometric series, we'll have to identify the first term, the common ratio, and the number of terms.
Let's identify the first term, the common ratio, and the number of terms in the given series as shown below;
The first term, a = 4³/5³
Common ratio, r = 4/5
The number of terms, n = 3
We have identified the values of a, r, and n, we can now substitute them into the formula for the sum of a geometric series, shown below;
S_n = a(1 - rⁿ) / (1 - r)
S₃ = {(4³/5³) [1 - (4/5)³]} / [1 - (4/5)]
S₃ = {(64/125) [1 - (64/125)]} / [1/5]
S₃ = (64/125) [(125-64)/125] [5/1]
S₃ = (64/125) (61/125) (5)
Therefore, S₃ = 3904/3125.
Thus, the sum of the geometric series (4³/5³) + (4⁴/5⁴) + (4⁵/5⁵) is equal to 3904/3125.
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I need help please
Answers
Answer:
64 sq cm
Step-by-step explanation:
triangle area = 1/2*b*h (×4 because 4 triangles)
square area = lw
Juanita’s Social Security full monthly retirement benefit is $2,128. She started collecting Social Security at age 65. Her benefit is reduced since she started collecting before age 67. Using the reduction percents from Example 1, find her approximate monthly Social Security benefit to the nearest dollar.EXAMPLE 1Marissa from Example 2. What will her monthly benefit be, since she did not wait until age 67 to receive full retirement benefits?SOLUTION Age 67 is considered to be full retirement age if you were born in 1945. If you start collecting Social Security before age 67, your full retirement benefit is reduced, according to the following schedule.• If you start at collecting benefits at 62, the reduction is about 30%.• If you start at collecting benefits at 63, the reduction is about 25%.• If you start at collecting benefits at 64, the reduction is about 20%.• If you start at collecting benefits at 65, the reduction is about 13.3%.• If you start at collecting benefits at 66, the reduction is about 6.7%.Marissa’s full retirement benefit was $1,130.40. Since she retired at age 65, the benefit will be reduced about 13.3%.Find 13.3% of $1,130.40, and round to the nearest cent.0.133 x 1,130.40Subtract to find the benefit Marissa would receive.1,130.40 x 150.34Marissa’s benefit would be about $980.06.EXAMPLE 2Marissa reached age 62 in 2007. She did not retire until years later. Over her life, she earned an average of $2,300 per month after her earnings were adjusted for inflation. What is her Social Security full retirement benefit?
Answers
Juanita's approximate monthly Social Security benefit is $1,844.90 to the nearest dollar.
What is social security benefits retirement age?The age at which a person is qualified to receive their full retirement payment under Social Security is determined by their lifetime earnings history. The complete retirement age for anybody born in 1960 or later is 67. The complete retirement age is steadily lowered for people born before 1960, and is 65 for those born in 1937 or before.
Given that, Juanita started collecting benefits at age 65.
Thus, her benefits reduced by 13.3%.
0.133 x $2,128 = $283.10
Deducting the reduction amount from the total:
$2,128 - $283.10 = $1,844.90
Hence, Juanita's approximate monthly Social Security benefit is $1,844.90 to the nearest dollar.
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Can i get assistance with this?
Answers
Answer:
see attached
Step-by-step explanation:
You want the given triangle dilated by a factor of -3 about point A.
DilationTo find the image point corresponding to a pre-image point, multiply the pre-image point's distance from A by the dilation factor. The negative sign means the distance to the image point is measured in the opposite direction.
In the attached figure, the chosen point is 4 units up and 5 units right of A. Its image in the dilated figure is 3·4 = 12 units down, and 3·5 = 15 units left of A.
This same process can be used to locate the other vertices of the triangle's image.
Find the slope-intercept form of the line with the slope m= 1/7 which passes through the point (-1, 4).
Answers
Answer:
y = 1/7x + 29/7
Step-by-step explanation:
Slope intercept form is y = mx + b
m = the slope
b = y-intercept
m = 1/7
Y-intercept is located at (0, 29/7)
So, the equation is y = 1/7x + 29/7
A random variable is normally distributed. It has a mean of 228 and a standard deviation of 16. If you take a sample of size 12, can you say what the shape of the sampling distribution for the sample mean is? Why?
A. If the sample size is 12, then you can say the sampling distribution of the sample mean is not normally distributed since the sample size is less than 30.
B. If the sample size is 12, then you can say the sampling distribution of the sample mean is normally distributed since the variable is normally distributed.
C. If the sample size is 12, then you can't say anything about the sampling distribution of the sample mean, since the population of the random variable is not normally distributed and the sample size is less than 30.
Answers
If a random variable is normally distributed, and has a mean of 228 and
a standard deviation of 16. If a sample of size 12 is taken, then the shape
of the sampling distribution for the sample mean is normally distributed
since the variable is normally distributed. Hence, option B is correct.
A normal distribution is a type of probability distribution in which the
value of the mean, standard deviation, and random variables are well
known. Sampling distribution refers to the probability distribution of the
statistics that have been derived from a sample taken from a population.
As per the Central Limit Theorem, if the sample size is large enough,
then the sampling distribution of the sample means will be normally
distributed, no matter how the population looks. If the random variable is
normally distributed, then the sampling distribution of the sample mean
will also be normally distributed, no matter what the size of the sample is.
Hence, option B is the correct answer as the sampling distribution of the
sample mean is normally distributed since the variable is normally distributed.
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Maths work …………………………
Answers
Answer:
by similarity
as these questions are usually solve by similarity
Serenity and her children went into a restaurant and will buy hamburgers and tacos. Each hamburger costs $5.50 and each taco costs $2. Serenity has a total of $45 to spend on hamburgers and tacos. Write an inequality that would represent the possible values for the number of hamburgers purchased, ℎ h, and the number of tacos purchased, � . t.
Answers
Answer: Less than or equal to 45
Step-by-step explanation:
Let's use algebra to write the inequality.
Let h be the number of hamburgers purchased and t be the number of tacos purchased.
Each hamburger costs $5.50 and each taco costs $2, so the total cost of h hamburgers and t tacos is:
5.5h + 2t
Serenity has a total of $45 to spend, so we can write:
5.5h + 2t ≤ 45
This is the inequality that represents the possible values for the number of hamburgers purchased, h, and the number of tacos purchased, t.
Note that the inequality is less than or equal to 45, since Serenity cannot spend more than $45.
To represent the possible values for the number of hamburgers and tacos purchased, an Inequality can be written as 5.5x + 2y ≤ 45.
To write an inequality to represent the possible values for the number of hamburgers purchased (h) and the number of tacos purchased (t), we need to consider the cost of each item and the total amount Serenity has to spend.
Let's assume Serenity buys x hamburgers and y tacos. Each hamburger costs $5.50, so the total cost of hamburgers purchased would be 5.5x. Each taco costs $2, so the total cost of tacos purchased would be 2y.
The total amount Serenity has to spend is $45. Therefore, the inequality that represents the possible values for h and t is: 5.5x + 2y ≤ 45.
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if a measure that is in 4/4 time has a half note, a quarter note, and an eighth note, whatn ote value is missing
Answers
If a measure that is in 4/4 time has a half note, a quarter note, and an eighth note, a sixteenth note value is missing.
4/4 time signature is also known as a common time signature. In a 4/4 measure, we have four beats or counts, and each quarter note takes one beat or count. A half note gets two beats or counts, a quarter note gets one beat, and an eighth note gets half a beat.
Therefore, if a measure in 4/4 time has a half note, a quarter note, and an eighth note, then a sixteenth note value is missing because a sixteenth note gets one-quarter of a beat or count.
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The shipping container shown is a rectangular prism. Write a polynomial in standard form that represents the volume of the container.
Answers
Answer:
V = (4y³ + 6y² - 4y - 6) ft³
Step-by-step explanation:
Its a rectangular prism so its Volume is its lenght * its width* its height:
V = l * w * h
V = (4y - 3) ft * (y + 2) ft * (y + 1) ft
V = (4y² + 8y - 6y - 6) ft² * (y + 1) ft
V = (4y² + 2y - 6) ft² * (y + 1) ft
V = (4y³ + 2y² - 6y + 4y² + 2y - 6) ft³
V = (4y³ + 6y² - 4y - 6) ft³
I think it’s to do with Pythagoras theorm
Answers
8.6cm is the hypotenuse and 8.6/2 is the length of base.
The Pythagorean theorem: a^2+b^2=c^2
So that means 8.6^2-4.3^2=height
= 73.96 - 18.49 = 55.47
So the square root of 55.47 is the height of the triangle.
The area of a triangle is h * b/2
So the base is 8.6 and the height is the square root of 55.47. 8.6/2=4.3
So 4.3 times the square root of 55.47 is the area.
Please answer,
Consider a simple AD-AS model. The MPC = 0.8, the net tax rate t = 0.2, the marginal propensity to import m = 0.14. The aggregate demand function is given by P = 80 - Y, where P is the price level (GDP deflator) and Y is real GDP (billion). The aggregate supply function is given by P = 20 + Y. If the government increased its purchases G by $1 billion, ceteris paribus, what is the increase in equilibrium Y*?
Answers
Answer:
fFind the sum of
4
4
and
4
8
4
8
in simplest form. Also, determine whether the result is rational or irrational and explain your answer.
Step-by-step explanation:
At a basketball game, an air cannon launches T-shirts into the crowd. The function y=−18x2+4x
represents the path of a T-shirt. The function 3y=2x−14
represents the height of the bleachers. In both functions, y
represents vertical height (in feet) and x
represents horizontal distance (in feet). At what height does the T-shirt land in the bleachers?
Answers
The height that the T-short lands on the bleachers is x = 0.65.
What is quadratic formula?The quadratic equation may be solved by adding and subtracting the same number within the parenthesis to get a perfect square trinomial, which is how the quadratic formula is obtained. A version of the equation that can be solved using the square root function is the result of this method.
Given that it can be used to solve any quadratic equation regardless of the values of the variables a, b, and c, the quadratic formula is an effective tool for solving quadratic equations.
The equation of the path of T-shirt is y = -18x² + 4x and that of the height of bleachers is 3y=2x−14 or y = 2/3x - 14/3
To find the height of the T-shirt landing we find the intersection of the two equations as follows:
-18x² + 4x = (2x - 14)/3
-54x² + 12x = 2x - 14
54x² - 10x - 14 = 0
27x² - 5x - 7 = 0
Using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
Substitute the values;
x = (-(-5) ± √((-5)² - 4(27)(-7))) / 2(27)
x = (5 ± √(925)) / 54
x = (5 ± 5√37) / 54
x = (5 + 5√37) / 54 = 0.65 and
x = (5 - 5√37) / 54 = -0.47
Hence, the height that the T-short lands on the bleachers is x = 0.65.
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Goods with a cost price of R200 are sold at a mark-up of 100%. The selling price is:
Answers
If the cost price of the goods is R200 and they are sold at a mark-up of 100%, then the selling price is equal to the cost price plus the mark-up, or:
Selling price = Cost price + Mark-up
Mark-up = 100% x Cost price
= 100% x R200
= R200
So the mark-up is R200.
Selling price = Cost price + Mark-up
= R200 + R200
= R400
Therefore, the selling price of the goods is R400.
f² + 7f + 10 = (ƒ +_)(ƒ +_)
Whats this answer i dont get it pls domeone help me <33
Answers
Answer:
To factorize the quadratic expression f² + 7f + 10, we need to find two numbers that multiply to 10 and add up to 7. These numbers are 2 and 5. So, we can write:
f² + 7f + 10 = (f + 2)(f + 5)
Therefore, the answer is (f + 2)(f + 5).
Answer:
Step-by-step explanation:
[tex]f^2+7f+10=f^2+2f+5f+10=f(f+2)+5(f+2)=(f+5)(f+2)[/tex]
By grouping, we can factor the polynomial. We know that 2+5=7 and 2*5=10, so this is why (f+5) and (f+2) are factors of f²+7f+10.
Card 2 of 8
Alg2.2.17 Practice 1
Clare is planning a sailing trip. She finds an expression for time, T (s), in hours it takes her to sail 6 miles in terms of s, the speed
of the current tailwind in miles per hour. This is the graph Clare gets if she allows s to take on any value between 0 and 10.
a. What does the y-intercept tell you in this situation?
Type your response in the space below.
Answers
The y-intercept for this situation shows that the speed of the ship sailing is 0 miles per second during the time t = 4 seconds, after that the speed keeps on decreasing.
Explain about the negative acceleration?Look into the fact that the vector of acceleration points in the same general direction as the vector of velocity change. This indicates that whether you add to or subtract from the velocity depends on the direction of the acceleration.
According to mathematics, a negative acceleration indicates that the velocity will be subtracted from, while a positive acceleration indicates that the velocity will be increased. If the velocity had become negative to begin with, subtracting as from value may make an object move faster since the magnitude would grow.The graph is shown for the distance travelled by the ship with time by Clare.
Thus, the y-intercept for this situation shows that the speed of the ship sailing is 0 miles per second during the time t = 4 seconds, after that the speed keeps on decreasing.
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In the morning 134 books were checked out from the library.in the afternoon 254 books were checked out and 188 books were checked out in the evening.how many books were checked out in the library that day?
Answers
Answer:
576 books.
Step-by-step explanation:
134+254+188=576 books in total.
Answer:
576
Step-by-step explanation:
This is literally easy!
Checked books are 134 + 254 + 188 = 576
Describe the possible echelon forms of the following matrix. A is a 2x2 matrix with linearly dependent columns Select all that apply (Note that leading entries marked with an X may have any nonzero value and starred entries (*) may have any value including zero)
a. 0 0
0 0
b. 0 x
0 0
c. x *
0 0
d. x *
0 x
Answers
The possible echelon forms of the given matrix are:
0 0c. x *
0 0d. x *
0 x
A matrix is in echelon form when it has leading nonzero entries in each row, with each row starting further to the right than the row above it. In the given matrix, the first row does not have any nonzero entries, so it does not meet this criterion. The second row does have a nonzero entry (x) so it can meet the criterion, provided that it is the leading entry.
This is the case for b. 0 x
0 0, c. x *
0 0, and d. x *
0 x.
The other criterion for echelon form is that all starred entries (*) may have any value including zero. This criterion is met in all three cases.
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Find the surface area of the regular pyramid. Round your answer to two decimal places.
Answers
Which retirement plan(s) do not come with a guaranteed benefit at retirement?
401(k)
Fixed annuity
Roth IRA
Traditional IRA
II, III
III, IV
I, III, IV
I, II
Answers
The retirement plans that do not come with a guaranteed benefit at retirement are C) I, III, and IV.
What is a guaranteed benefit?A guaranteed benefits refers to the fact that the retiree will be paid a certain amount at retirement.
The 401(k) is an employer-offered retirement plan with defined contributions from the employees. The employee bears the investment risks and there is no guarantee of benefits.
With fixed annuity, there is a guarantee of an annual payment by the insurance company to the beneficiary or insured.
The Roth IRA does not offer guaranteed benefit just like the traditional IRA.
Thus, only the fixed annuity, an insurance contract, offers a guaranteed benefit at retirement.
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what is the expected count for women for the presence of aortic stenosis? a. 49.7 b. 59.3 c. 109 d. 57.7
Answers
The expected count for women for the presence of aortic stenosis is 57.7. The correct option is D.
What is aortic stenosis?Aortic stenosis is a cardiovascular ailment that causes the aortic valve in the heart to narrow, reducing blood flow from the heart to the rest of the body. Aortic stenosis usually progresses gradually and, in the beginning, may not produce any symptoms.
The severity of aortic stenosis is divided into four categories, ranging from mild to severe. People who are asymptomatic may require monitoring, whereas those who are symptomatic may need to undergo surgery or other procedures.
The expected count for women for the presence of aortic stenosis in this question refers to the number of women who have this condition according to a particular study or statistic.
Therefore, the correct option is D.
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solve the proportion 7/11=18/x+1
Answers
Solve the equation [tex]7/11=18/x+1[/tex] we find the solution is [tex]x = 27.2857[/tex]
What is a formula or equation?Your example is an equation since an equation is any statement with an equals sign. Equations are frequently utilized for mathematical equations since mathematicians like equal signs. A set of instructions for achieving a certain result is called an equation.
A formula is it an expression?A number, a constant, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by such an assignment operator form an equation.
we can cross-multiply,
[tex]7(x+1) = 11(18)[/tex]
Expanding the left side,
[tex]7x + 7 = 198[/tex]
Subtracting [tex]7[/tex] from both sides,
[tex]7x = 191[/tex]
Dividing both sides by [tex]7[/tex],
[tex]x = 191/7[/tex]
Therefore, the solution to the proportion is
[tex]x = 27.2857[/tex]
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5) Is the following list of ordered pair a
function?
{(-3,4),(-4,3),(-1,4)}
Answers
WILL GIVE BRAINLIEST 15 POINTS PLEASEE Fill in the blanks pleaseee
Answers
Therefore, we have the values of:
a = -g(x) for -10 < x < -8
b = lower limit of the range where g(x) = -6
c = -C for -1 < x < 1
d = upper limit of the range where g(x) = 4
e = we cannot determine the value of e based on the given information.
What is function?In mathematics, a function is a rule that assigns a unique output value for every input value in its domain. It is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. Functions are often represented by a formula or an equation, but they can also be defined in other ways, such as through graphs, tables, or verbal descriptions. They are used to model a wide variety of phenomena in science, engineering, economics, and many other fields.
Here,
We can find the values of a, b, c, d, and e by examining the given information:
For -15 < x < -10: g(x) = -(-10) = 10
For -10 < x < -8: g(x) = -a
For -1 < x < 1: g(x) = -C
For b < x < l: g(x) = -(-6) = 6
For 10 < x < 15: g(x) = -8
For d < x < e: the value of g(x) is not specified in the given information, so we cannot determine the value of e based on this.
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how long will a car take to travel 140km averaging a speed of 35km/h
Answers
Answer:
Step-by-step explanation:
To calculate the time it will take a car to travel 140km at an average speed of 35km/h, we can use the formula:
time = distance ÷ speed
Plugging in the given values, we get:
time = 140km ÷ 35km/h
time = 4 hours
Therefore, it will take a car 4 hours to travel 140km at an average speed of 35km/h.
Answer:
ㅤ
Car will take 4 hours
ㅤ
Step-by-step explanation:
ㅤ
[tex]\large{\blue{\star} \: {\underline{\boxed{\pmb{\tt{Time = \dfrac{Distance}{Speed}}}}}}}[/tex]
ㅤ
[tex]\large{\leadsto{\sf{Given_{(Distance)} = 140 \: km}}}[/tex]
ㅤ
[tex]\large{\leadsto{\sf{Given_{(Speed)} = 35 \: km/hr}}}[/tex]
ㅤ
[tex]\large{\underline{\underline{\sf{Applying \: Formula:-}}}}[/tex]
ㅤ
[tex]\large{\leadsto{\sf{Required_{(Time)} = \bigg(\dfrac{\cancel{140}}{\cancel{35}}\bigg)} \: hr}}[/tex]
ㅤ
[tex]\large{\purple{\boxed{\leadsto{\sf{Required_{(Time)} = 4 \: hr}}}}}[/tex]
ㅤ
━━━━━━━━━━━━━━━━━━━━━━
[tex]\star \: {\large{\underline{\underline{\pink{\mathfrak{More:-}}}}}} \: \star[/tex]
ㅤ
[tex]\large{\dashrightarrow{\sf{Time = \dfrac{Distance}{Speed}}}}[/tex]
ㅤ
[tex]\large{\dashrightarrow{\sf{Speed = \dfrac{Distance}{Time}}}}[/tex]
ㅤ
[tex]\large{\dashrightarrow{\sf{Distance = Speed \times Time}}}[/tex]
please help!!
4.
Two bikers meet at a park. Biker A needs to stop at the store that is 12 miles east of the park. Biker B heads southeast at a 61° angle at the same time for 24 miles. Once biker A leaves the store he heads southwest at an angle of 89° for 21 miles. Do NOT use the law of cosines, use your knowledge from the content of this course.
a. Use your knowledge of triangles to figure out if the two bikers will be able to meet up if each biker travels the distance given.
b. If they do not meet up, how much farther would one of the bikers have to travel to meet the other?
c. What is the measure of the angle between the bikers?
d. What is the relationship between the measure of the angles and the paths the bikers took?
e. Classify the triangle the paths created.
f. How many miles did they travel together?
Answers
a) Biker A follows the hypotenuse of the triangle on a straight path.
It is probable that the bikers will meet at the vertex located at the base of the triangle.
How to solve:The bikers have created a triangle with sides measuring 12, 21, and 24 miles and angles measuring 61, 89, and 30 degrees, respectively.
a) Biker A follows the hypotenuse of the triangle on a straight path.
It is probable that the bikers will meet at the vertex located at the base of the triangle.
They cover almost equal distances from their starting points:
24 miles ≈ √12²+21² miles
b) They encounter each other.
c) The angle at one vertex measures 30 degrees.
d) e) As shown in the attached picture, it is an almost right triangle.
f) Together, they cover a total distance of 57 miles (12+21+24).
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A researcher claims to have found a drug that causes people to grow taller. The coach of the basketball team at Brandon University has expressed interest but demands evidence. Over 1000 Brandon students volunteer to participate in an experiment to test this new drug. Fifty of the volunteers are randomly selected, their heights are measured, and they are given the drug. Two weeks later, their heights are measured again. The power of the test to detect an average increase in height of 1 inch could be increased by
a. using only volunteers from the basketball team in the experiment.
b. using ἁ =0.05 instead of ἁ =0.05
c. using ἁ =0.05 instead of ἁ =0.01
d. giving the drug to 25 randomly selected students instead of 50.
e. using a two-sided test instead of a one-sided test.
Answers
The power of the test to detect an average increase in height of 1 inch could be increased by d. giving the drug to 25 randomly selected students instead of 50.
The power of a test is the probability of correctly rejecting the null hypothesis when it is false. In this case, the null hypothesis is that the drug does not cause people to grow taller, and the alternative hypothesis is that the drug causes an average increase in height of 1 inch.
To increase the power of the test, we want to increase the probability of correctly rejecting the null hypothesis when it is false. One way to do this is to increase the sample size, which will reduce the standard error of the mean and increase the t-statistic, making it more likely to reject the null hypothesis.
However, in this case, we can increase the power of the test by giving the drug to a smaller sample size of 25 instead of 50. This is because the effect size of the drug is not known, and giving the drug to a larger sample size will increase the variance of the data, making it harder to detect a significant difference. By reducing the sample size, we can increase the power of the test while still maintaining a reasonable sample size.
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C(1)=-20 c(n)=c(n-1)+0 find the second term in the sequence
Answers
The second term in the sequence is equal to the first term, which is -20. Hence, the answer is -20.
The given sequence starts with C(1) = -20. Each subsequent term is obtained by adding 0 to the previous term, which means that the sequence is constant.
The recursive formula for this sequence is given as:
c(1) = -20 and c(n) = c(n-1) + 0
This means that the first term of the sequence is -20, and each subsequent term is obtained by adding 0 to the previous term
Therefore, the second term in the sequence is equal to the first term, which is -20. Hence, the answer is -20.
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[amc10b.2011.7] the sum of two angles of a triangle is $\frac{6}{5}$ of a right angle, and one of these two angles is $30^{\circ}$ larger than the other. what is the degree measure of the largest angle in the triangle?
Answers
The degree measure of the largest angle is 72° in the triangle.
We have, The sum of two angles of a triangle is 6/5 of a right angle.
One of these two angles is 30° larger than the other.
Let A and B be the two angles of the triangle such that A = B + 30°.
We know that the sum of three angles in a triangle is 180°.
⇒ A + B + C = 180°
⇒ B + 30° + B + C = 180°
⇒ 2B + C = 150°
We also know that the sum of two angles of a triangle is 6/5 of a right angle.
⇒ A + B = 6/5 × 90°
⇒ B + 30° + B = 108°
⇒ 2B = 78°
⇒ B = 39°
C = 150° - 2B ⇒ 72°
A = B + 30° ⇒ 39° + 30° ⇒ 69°
Therefore, the degree measure of the largest angle in the triangle is 72°.
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