Answer:
5,6,7 because they are in line with the letter
Determine if the expressions are equivalent.
when w = 11:
2w + 3 + 4 4 + 2w + 3
2(11) + 3 + 4 4 + 2(11) + 3
22 + 3 + 4 4 + 22 + 3
25 + 4 26 + 3
29 29
Complete the statements.
Answer:
Determine if the expressions are equivalent.
when w = 11:
2w + 3 + 4 4 + 2w + 3
2(11) + 3 + 4 4 + 2(11) + 3
22 + 3 + 4 4 + 22 + 3
25 + 4 26 + 3
29 29
Complete the statements.
Now, check another value for the variable.
When w = 2, the first expression is
11
.
When w = 2, the second expression is
11
.
Therefore, the expressions are
equivalent
.
Step-by-step explanation:
i did the math hope this helps
Answer:
Hii its Nat here to help! :)
Step-by-step explanation: A is 11 and b is 11.
C is Equal
Screenshot included.
SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answer:
38 units
Step-by-step explanation:
We can find the perimeter of the shaded figure be finding out the number of unit lengths we have along the boundary of the given figure.
Thus, see attachment below for the number of units of each length of the figure that we have counted.
The perimeter of the figure = sum of all the lengths = 7 + 7 + 10 + 2 + 2 + 6 + 2 + 2 = 38
Perimeter of the shaded figure = 38 units
What is the rule for the geometric sequence ?
Answer:
Option 3 or 4 is correct depending on the first term and common ratio
aₙ= a₁rⁿ⁻¹
Option 3 in case the first term is 1/2 and common ratio is 972
Option 4 in case the first term is 972 and common ratio is 1/2
Answer:
its D & the next is 7.594
Step-by-step explanation:
just got it on edge2020
combine like terms to create an equivalent expression -1/2(-3y+10)
Answer:
3/2y - 5
Step-by-step explanation:
-1/2(-3y+10)
Expand the brackets.
-1/2(-3y) -1/2(10)
Multiply.
3/2y - 5
Answer:
[tex]= \frac{ 3y}{2} - 5 \\ [/tex]
Step-by-step explanation:
we know that,
[tex]( - ) \times ( - ) = ( + ) \\ ( - ) \times ( + ) = ( - )[/tex]
Let's solve now,
[tex] - \frac{1}{2} ( - 3y + 10) \\ \frac{3y}{2} - \frac{10}{2} \\ = \frac{ 3y}{2} - 5[/tex]
what solid 3D object is produced by rotating the triangle about line m with a height of 8 and radius 4
Answer:
The diagram of the question is missing, I found a matching diagram, and it is attached to this answer
The 3D object produced is a cone with height 8 and diameter 8 (radius 4)
Step-by-step explanation:
A 3 dimensional solid figure can be formed when a 2 dimensional object is rotated about a line without displacing the object.
when the object in the diagram is rotated about line m, the rotation forms an object with a circular base of diameter 8 units (radius 4) from the base of the triangle and height 8 units, and the 3D object formed is called a cone.
Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. (Assume that n begins with 1.) 1, 1 3 , 1 5 , 1 7 , 1 9 , ...
Answer:
The general term for the sequence can be given by the following formula:
[tex]a_n=2\,n+9[/tex]
Step-by-step explanation:
If the sequence you typed starts with first term 11 and continues with terms 13, 15, 17, 19, We understand that the sequence is formed by adding 2 units to the previous term. So we are in the case of an arithmetic sequence with constant difference (d) = 2, and with first term 11.
Therefore, the nth term of this arithmetic sequence can be expressed by using the general form for an arithmetic sequence as:
[tex]a_n=a_1\,+\,(n-1)\,d\\a_n=11\,+\,(n-1)\,2\\a_n=11+2\,n-2\\a_n=2\,n+9[/tex]
Which statement represents a true conclusion, based on the Venn diagram? All real numbers are even numbers. All numbers that are multiples of three are even numbers. Some numbers that are multiples of three are also even numbers. No numbers that are multiples of three are also even numbers.
Answer:
Some number that are multiples of three are also even numbers
Step-by-step explanation:
In the picture
The statement represents a true conclusion, based on the Venn diagram is option A) Some numbers that are multiples of three are also even numbers
What are real numbers?The numbers which are not imaginary and can be quantified are real numbers.Real numbers can be positive or negative, and include the number zero. Imaginary numbers are numbers that cannot be quantified, like the square root of -1-2,-1.1 etc.What are even numbers?They are whole numbers that can be be divided by two into two equal value. examples 2,4,6,8 etc.
According to the question:-
A) All real numbers are even numbers.
B) All numbers that are multiples of three are even numbers.
C) Some numbers that are multiples of three are also even numbers
D) No numbers that are multiples of three are also even numbers.
OPTION C is the answer of the given question example 4*3,6*3 etc.
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A triangular window has an area of 594 square meters. The base is 54 meters. What is the height?
Answer:
22 m
Step-by-step explanation:
Use the formula for the area of a triangle. Fill in the known values and solve for the unknown.
A = (1/2)bh
594 m^2 = (1/2)(54 m)h
h = (594 m^2)/(27 m) = 22 m
The height of the window is 22 meters.
Bill buys and sells laptops. Last month Bill bought 50 laptops. He paid £400 for each laptop. He sold 40 of these laptops at a profit of 30% on each laptop and 10 of these laptops at a profit of 15% on each laptop. Bill’s target last month was to sell all 50 laptops for a total of at least £25 000. Did Bill reach this target?
Answer:
As Bill's sales is £25400, which is greater than £25000, he achieved his target.
Step-by-step explanation:
Cost of each laptop = £400
lets calculate for 40 laptops first
Given, he sold 40 of these at 30% profit
30% of cost price = 30% of £400 = 30/100 * 400 = 120
Therefore, selling price of these laptops = £400 + £120 = £520
Total sales generated from selling 40 of these laptop = 40*£520
= £520 =£20,800
lets calculate for 10 laptops now
Given, he sold 10 of these at 15% profit
15% of cost price = 15% of £400 = 15/100 * 400 = 60
Therefore, selling price of these laptops = £400 + £60 = £460
Total sales generated from selling 10 of these laptop = 10*£460
= £4600
Total sales generated from selling all the 50 laptop =
Total sales generated from selling 40 of these laptop + Total, sales generated from selling 10 of these laptop = £20,800 + £4600 = £25,400
Target for Bill = £25000
As his sales is £25400, which is greater than £25000, he achieved his target.
Find the sum and choose the correct answer 2n^3 + 4n^2 -7 and -n^3 - 8n - 2
Answer:
n³ + 4n² - 8n -9
Step-by-step explanation:
Just combine like terms while you add the 2 expressions together.
In the questions below nine people (Ann, Ben, Cal, Dot, Ed, Fran, Gail, Hal, and Ida) are in a room. Five of them stand in a row for a picture. In how many ways can this be done if a) Ben is to be in the picture? b) Both Ed and Gail are in the picture? 4200 c) Neither Ed nor Fran are in the picture? 5040 d) Dot is on the left end and Ed is on the right end? 210 e) Hal or Ida (but not both) are in the picture? 4200 f) Ed and Gail are in the picture, standing next to each other? 960 g) Ann and Ben are in the picture, but not standing next to each other?
Answer:
Step-by-step explanation:
Ben is present in all pictures so rest of 4 persons to be selected from 8 persons , no of ways to do it is
⁸C₄ = 8 x 7 x 6 x 5 / 4 x 3 x 2 x 1
= 70 .
In one of these combination , we can get 5 ! ( five factorial )
Total no of permutations
= 70 x 5 !
= 8400 .
b ) Both Ed and Gail are present
The above derivation changes to the following .
Total no of permutations
= ⁷C₃ x 5 !
= 35 x 120
= 4200
c )
exclude 2 person from 9 to be selected
permutation
= ⁷C₅ x 5 !
= 21 x 120
= 2520
d )
rest of 3 person from 7 persons , no of permutations
⁷P₃ = 7 x 6 x 5 = 210
e )
Hal or Ida can occupy any of the 5 position which can be done in 5 ways .
when one position is occupied , the rest of 4 position can be occupied by 7 persons which can be done in
⁷P₄ ways
Total ways = 5 x ⁷P₄
= 5 x 840
= 4200
f )
They can occupy position like 1,2 or 2,3 or 3,4 or 4,5
Rest of the position can be occupied in ⁷P₃ ways
Total ways = 4 x ⁷P₃
= 4 x 210
= 840
They can also be exchanged mutually so no of ways
= 840 x 2 = 1680 .
g ) No of pictures in which Ann and Ben are present
two position to be selected out of 5 = ⁵P₂
Rest of position that can be shuffled = ⁷P₃
Total no of pictures in which both are present
= ⁵P₂ x ⁷P₃
= 20 x 210
= 4200
out of which they will be standing next to each other = 1680
no of pictures in which they will not be standing next to each other
= 4200 - 1680 = 2520. .
A study conducted at a certain college shows that "53%" of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that among 6 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating. 0.989 0.978 0.927 0.167 0.530
Answer:
0.989
Step-by-step explanation:
For each graduate, there are only two possible outcomes. Either they find a job in their chosen field within a year after graduation, or they do not. The probability of a graduate finding a job is independent of other graduates. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A study conducted at a certain college shows that "53%" of the school's graduates find a job in their chosen field within a year after graduation.
This means that [tex]p = 0.53[/tex]
6 randomly selected graduates
This means that [tex]n = 6[/tex]
Probability that at least one finds a job in his or her chosen field within a year of graduating:
Either none find a job, or at least one does. The sum of the probabilities of these outcomes is 1. So
[tex]P(X = 0) + P(X \geq 1) = 1[/tex]
We want [tex]P(X \geq 1)[/tex]
So
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{6,0}.(0.53)^{0}.(0.47)^{6} = 0.011[/tex]
So
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.011 = 0.989[/tex]
Help plssss
Stephn says that the numbers 38 and 40 are relatively prime. explain why he is incorrect in making this statement.
Answer:
When you say that two numbers are relatively prime, it means that both numbers do not have a common factor except 1. Stephen is incorrect because 38 and 40 are both multiples of 2.
Answer:
Prime numbers are number that has its factors to be 1 and itself
38 and 40 are not prime because they have more than one factor
38 = { 1 , 2 , 19 , 38} and
40 = { 1 , 2 , 4 , 5 , 8 , 10 , 20 , 40 }
This make his statement incorrect.
Hope this helps.
Given z = 4x – 6y, solve for y.
Answer:
Step-by-step explanation:
-6y+4x=z
-6y=z-4x
y=(z-4x)/-6
Answer:
[tex]y=\frac{z-4x}{-6}[/tex]
Step-by-step explanation:
plz help me divide and simplify
Answer:
Step-by-step explanation:
The period of a simple pendulum of length L feet is given by T=2πLg−−√~seconds. We assume that g, the acceleration due to gravity on the surface of the earth, is 32 feet per second per second. If the pendulum is that of a clock that keeps good time when L=4 feet, how much time will the clock gain in 24 hours if the length of the pendulum is decreased to 3.97 feet? (Use differentials and evaluate the necessary derivative at L=4 feet.)
Given that,
The acceleration due to gravity on the surface of the earth = 32 feet/s²
We need to calculate the time
Using formula of time period
[tex]T=2\pi\sqrt{\dfrac{l}{g}}[/tex]
On differentiating with respect to l
[tex]\dfrac{dT}{dL}=2\pi\times\dfrac{1}{2}(\dfrac{l}{g})^{-\frac{1}{2}}\times\dfrac{1}{g}[/tex]
[tex]\dfrac{dT}{dL}=\dfrac{\pi}{g}\times(\dfrac{g}{L})^{\frac{1}{2}}[/tex]
Put the value into the formula
[tex]\dfrac{dT}{dL}=\dfrac{\pi}{32}\times(\dfrac{32}{4})^{\frac{1}{2}}[/tex]
[tex]\dfrac{dT}{dL}=0.277\ sec[/tex]
If the length of the pendulum is decreased to 3.97 feet.
We need to calculate the time
Using formula of time period
[tex]\dfrac{dT'}{dL}=\dfrac{\pi}{g}\times(\dfrac{g}{L})^{\frac{1}{2}}[/tex]
Put the value into the formula
[tex]\dfrac{dT'}{dL}=\dfrac{\pi}{32}\times(\dfrac{32}{3.97})^{\frac{1}{2}}[/tex]
[tex]\dfrac{dT'}{dL}=0.278\ sec[/tex]
We need to calculate the gain time
Using formula for time
[tex]\dfrac{dT''}{dL}=\dfrac{dT'}{dL}-\dfrac{dT}{dL}[/tex]
Put the value into the formula
[tex]\dfrac{dT''}{dL}=0.278-0.277[/tex]
[tex]\dfrac{dT''}{dL}=0.001\ sec[/tex]
Hence, The clock gain the time in 24 hours is 0.001 sec.
The pie chart to the right shows how adults rate their financial shape. Suppose 4 people are chosen at random from a group of 1400. What is the probability that all four would rate their financial shape as excellent? (Make the assumption that the 1400 people are represented by the pie chart.)
Question Completion
PIE CHART NUMBERS:
Excellent 9% Good 41% Fair 36% Poor 13% Other 1%Answer:
0.000063
Step-by-step explanation:
Number of Respondents, n=1400
Probability that they would rate their financial shape as excellent = 0.09
Number of Those who would rate their financial shape as excellent
=0.09 X 1400
=126
Therefore:
The probability that 4 people chosen at random would rate their financial shape as excellent
[tex]=\dfrac{^{126}C_4 \times ^{1400-126}C_0}{^{1400}C_4} \\=\dfrac{^{126}C_4 \times ^{1274}C_0}{^{1400}C_4}\\=0.000063 $(correct to 6 decimal places)[/tex]
The table shows some values of x and y that satisfy the equation y = acosxº + b
Х
0
30
180
60
90
120
150
y
10
4 + 373
7
4
1
4-373
-2
Find the value of y when x = 45
Answer:
Y = 3√2 +4
Step-by-step explanation:
y = acosxº + b
Let's look for the values of a and b first.
Let's get values of x and y and solve simultaneously
When x= 0 ,y=10
When x = 120, y= 1
10 =acos0 + b
10 = a +b..... equation 1
1 = acos120 + b
1= -0.5a + b ..... equation 2
10 = a +b
1= -0.5a + b
10-1= a +0.5a
9 = 1.5a
9/1.5 = a
6 = a
1= -0.5a + b ..... equation 2
1 = -0.5(6) +b
1= -3 + b
1+3 = b
4 =b
So
y = acosxº + b equal to
Y = 6cosx° + 4
So value of y when x= 45 is
Y= 6cos45° +4
Y =6(√2/2) +4
Y = 3√2 +4
The value of y when x = 45 degree is, [tex]y=3\sqrt{2}+4[/tex]
Given function is,
[tex]y = a cos(x)+ b[/tex]
From given table, It is observed that,
x = 0, y = 10 and x = 90, y = 4
Substitute above values in above equation.
[tex]a+b=10\\\\b=4[/tex]
[tex]a=10-b=10-4=6[/tex]
Now, our equation become,
[tex]y = 6 cos(x)+ 4[/tex]
Substitute x = 45 in above equation.
[tex]y=6cos(45)+4\\\\y=6*(\frac{\sqrt{2} }{2} )+4\\\\y=3\sqrt{2} +4[/tex]
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Find f(x) - g(x) when f(x) = 2x^2 - 4x g(x) = x^2 + 6x
3x^2
x^2 + 2x
x^2 - 10x
3x^2 + 2x
Answer:
x^2 - 10x
Step-by-step explanation:
2x^2 - 4x - x^2 +6x
You subtract x^2 from 2x^2 and you get x^2
Then you add 6x and 4x together and get 10x
So then you have x^2 - 10x
(plus I took the test and this was the correct answer.)
Find the scale ratio for the map described below. 1 mm(map) equals 500 m (actual) The scale ratio is 1 to ? .
Answer:
1 : 500,000
Step-by-step explanation:
The scale of a map scale refers to the relationship (or ratio) between the distance on a map and the corresponding distance on the ground.
In the given map:
1 mm(map) = 500 m (actual)
1 meter = 1000 millimeter
Therefore:
500 meters = 1000 X 500 =500,000 millimeter
Therefore, the scale ratio of the map is:
1:500,000
hey guys please help
Answer:
[tex]7.98 \:m[/tex]
Step-by-step explanation:
Area of a triangle is base times height divided by 2.
[tex]A= \frac{bh}{2}[/tex]
[tex]69.6= \frac{b \times 17.45}{2}[/tex]
[tex]69.6 \times 2= b \times 17.45[/tex]
[tex]139.2=b \times 17.45[/tex]
[tex]\frac{17.45b}{17.45}=\frac{139.2}{17.45}[/tex]
[tex]b=\frac{2784}{349}[/tex]
[tex]b=7.97707[/tex]
The appropriate unit is meters.
Answer:
7.98 m
Step-by-step explanation:
People were surveyed worldwide, being asked the question "How important is acquiring wealth to you?" of 1500 respondents in country A, 1185 said that it was of more than average importance. In country B, of 1302 respondents, 613 said it was of more than average importance.
1) (Round to three decimal places as needed):
a. The sample proportions for country A are: ___
b. The sample proportions for country B are: ___
2) What is the confidence interval for country A? Select the correct choice below and, if necessary, fill in the answer boxes within your choice.
a. The 90% confidence interval for country A is (__%, ___%) [Round to one decimal place as needed.]
b. The conditions for constructing a confidence interval are not satisfied.
3) Compare to the confidence interval for country B. Choose the correct answer below.
a. It is not possible to make a comparaison because the conditions for creating a confidence interval are not satisfied.
b. It appears that the proportion of adults who feel this way in country A is more than those in country B.
c. It appears that the proportion of adults who feel this way in country A is about the same as those in country B.
d. it appears that the proportion of adults who feel this way in country B is more than those in country A.
Answer:
1) A = 0.79
B = 0.4708
2) CI = (0.7728, 0.8072)
3) CI = (0.4481, 0.4935)
b. It appears that the proportion of adults who feel this way in country A is more than those in country B.
Step-by-step explanation:
1) Sample proportions for both Population A and B
For country A:
Sample size,n = 1500
Sample proportion = [tex] \frac{1185}{1500} = 0.79 [/tex]
For Country B:
Sample size,n = 1302
Sample proportion = [tex] \frac{613}{1302} = 0.4708 [/tex]
2) Confidence interval for country A:
Given:
Mean,x = 1185
Sample size = 1500
Sample proportion, p = 0.79
q = 1 - 0.79 = 0.21
Using z table,
90% confidence interval, [tex] Z _\alpha /2 = 1.64 [/tex]
Confidence interval, CI:
[tex] \frac{p +/- Z_\alpha_/2}{\sqrt{(p * q)/n}} [/tex]
[tex] = \frac{0.79 - 1.64}{\sqrt{(0.79 * 0.21)/1500}}, \frac{0.79 + 1.64}{\sqrt{(0.79 * 0.21)/1500}} [/tex]
[tex] CI = (0.7728, 0.8072) [/tex]
3) Confidence interval for country A:
Given:
Mean,x = 613
Sample size = 1302
Sample proportion, p = 0.4708
q = 1 - 0.4708 = 0.5292
Using z table,
90% confidence interval, [tex] Z _\alpha /2 = 1.64 [/tex]
Confidence interval, CI:
[tex] \frac{p +/- Z_\alpha_/2}{\sqrt{(p * q)/n}} [/tex]
[tex] = \frac{0.4708 - 1.64}{\sqrt{(0.4708 * 0.5292)/1302}}, \frac{0.4708 + 1.64}{\sqrt{(0.4708 * 0.5295)/1302}} [/tex]
[tex] CI = (0.4481, 0.4935) [/tex]
From both confidence interval, we could see that that the proportion of adults who feel this way in country A is more than those in country B.
Option B is correct.
Explain why fishers index is called ideal index number
Answer:
This is because it contains the PAASCHE and the LASPEYRES index, the index satisfies the time reversal test.
Step-by-step explanation:
if cos theta < 0 and cot theta > 0, then the terminal point determined by theta is in:
A. Quadrant 1
B. Quadrant 3
C. Quadrant 4
D. Quadrant 2
please help me !
Answer:
If cosine theta < 0 and cotangent theta > 0, then the terminal point determined by theta is in: quadrant 3.
Step-by-step explanation:
hope this helps you :) my answer is the Step-by-step explanation: and the answer :)
Considering the signals of the sine and the cosine of the trigonometric function, it is found that it's quadrant is given by:
B. Quadrant 3
What are the signals of the sine and the cosine in each quadrant?Q1: cos > 0, sin > 0.Q2: cos < 0, sin > 0.Q3: cos < 0, sin <0.Q4: cos > 0, sin < 0.In this problem, we have that the cosine is negative, and the cotangent is positive. Cotangent is cosine divided by sine, hence if it is positive, both cosine and sine have the same signal, since cos < 0, sine is negative, they are in third quadrant and option B is correct.
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f(x)
9 - 4x
8x - 1
INVERSE??
Answer:
(x+9)/(8x+4)
Step-by-step explanation:
what are the formulas for right triangles
Answer:
The Pythagorean theorem is
a^2 + b^2 = c^2
where a and b are the lengths of the legs (the sides that form the right angle), and c is the length of the hypotenuse (the side opposite the right angle.)
Answer: Attached
Step-by-step explanation:
An insurance company examines its pool of auto insurance customers and gathers the following information: (i) All customers insure at least one car. (ii) 70% of the customers insure more than one car. (iii) 20% of the customers insure a sports car. (iv) Of those customers who insure more than one car, 15% insure a sports car. Calculate the probability that a randomly se
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
An insurance company examines its pool of auto insurance customers and gathers the following information: (i) All customers insure at least one car. (ii) 70% of the customers insure more than one car. (iii) 20% of the customers insure a sports car. (iv) Of those customers who insure more than one car, 15% insure a sports car. Calculate the probability that a randomly selected customer insures exactly one car, and that car is not a sports car?
Answer:
P( X' ∩ Y' ) = 0.205
Step-by-step explanation:
Let X is the event that the customer insures more than one car.
Let X' is the event that the customer insures exactly one car.
Let Y is the event that customer insures a sport car.
Let Y' is the event that customer insures not a sport car.
From the given information we have
70% of customers insure more than one car.
P(X) = 0.70
20% of customers insure a sports car.
P(Y) = 0.20
Of those customers who insure more than one car, 15% insure a sports car.
P(Y | X) = 0.15
We want to find out the probability that a randomly selected customer insures exactly one car, and that car is not a sports car.
P( X' ∩ Y' ) = ?
Which can be found by
P( X' ∩ Y' ) = 1 - P( X ∪ Y )
From the rules of probability we know that,
P( X ∪ Y ) = P(X) + P(Y) - P( X ∩ Y ) (Additive Law)
First, we have to find out P( X ∩ Y )
From the rules of probability we know that,
P( X ∩ Y ) = P(Y | X) × P(X) (Multiplicative law)
P( X ∩ Y ) = 0.15 × 0.70
P( X ∩ Y ) = 0.105
So,
P( X ∪ Y ) = P(X) + P(Y) - P( X ∩ Y )
P( X ∪ Y ) = 0.70 + 0.20 - 0.105
P( X ∪ Y ) = 0.795
Finally,
P( X' ∩ Y' ) = 1 - P( X ∪ Y )
P( X' ∩ Y' ) = 1 - 0.795
P( X' ∩ Y' ) = 0.205
Therefore, there is 0.205 probability that a randomly selected customer insures exactly one car, and that car is not a sports car.
An economist at Vanderbilt University devised a study to compare different types of online auctions. In one experiment he compared a Dutch auction to a first-place sealed bid auction. In the Dutch auction the item for sale starts at a very high price and is lowered gradually until someone finds the price low enough to buy. In the first-price sealed bid auction each bidder submits a single sealed bid before a particular deadline. After the deadline, the person with the highest bid wins. The researcher auctioned off collectible trading cards from the game Magic: The Gathering. He placed pairs of identical cards up for auction; one would go into Dutch auction and the other to the first-price sealed bid auction. He then looked at the difference in the prices he received on the pair. He repeated this for a total of 88 pairs.
[a] Explained why the data should be analyzed using paired samples as opposed to two independent samples.
[b] What makes a pair?
[c] What is the explanatory variable? Is it categorical or quantitative?
[d] What is the response variable? Is it categorical or quantitative?
[e] State the relevant hypotheses in words:
Null hypothesis:
Alternative hypothesis:
[f] Define the parameter of interest and give the symbol that should be assigned to it.
[g] State the relevant hypotheses in symbols (using a parameter):
Null hypothesis:
Alternative hypothesis:
[h] Assume the p-value is 0.17 (write a conclusion).
Answer:
Step-by-step explanation:
a. The data should be analyzed using paired samples because the economist made two measurements (samples) drawn from the same pair of identical cards. Each data point in one sample is uniquely paired to a data point in the second sample.
b. A pair is made up of two identical cards where one would go into Dutch auction and the other to the first-price sealed bid auction.
c. The explanatory variables are the types of online auction which are the Dutch auction and the first price sealed bid auction. The explanation variable here is categorical: the Dutch auction and the first price sealed bid auction.
d. The response variable which is also known as the outcome variable is prices for the 2 different auction for each pair of identical cards. This variable is quantitative.
e. Null Hypothesis in words: There is no difference in the prices obtained in the two different online auction.
Alternative hypothesis: There is a difference in the prices obtained in the two different online auction.
f. The parameter of interest in this case is the mean prices of pairs of identical cards for both auction and is assigned p.
g. Null hypothesis: p(dutch) = p(first-price sealed auction)
Alternative hypothesis: p(dutch) =/ p(first-price sealed auction)
h. Assuming the p-value is 0.17 at an assed standard 0.05 significance level, our conclusion would be to fail to reject the null hypothesis as 0.17 is greater than 0.05 or even 0.01 and we can conclude that, there is no statistically significant evidence to prove that there is a difference in the prices obtained in the two different online auction.
A basketball coach is looking over the possessions per game during last season. Assume that the possessions per game follows an unknown distribution with a mean of 56 points and a standard deviation of 12 points. The basketball coach believes it is unusual to score less than 50 points per game. To test this, she randomly selects 36 games. Use a calculator to find the probability that the sample mean is less than 50 points. Round your answer to three decimal places if necessary.
Answer:
The probability that the sample mean is less than 50 points = 0.002
Step-by-step explanation:
Step(i):-
Given mean of the normal distribution = 56 points
Given standard deviation of the normal distribution = 12 points
Random sample size 'n' = 36 games
Step(ii):-
Let x⁻ be the random variable of normal distribution
Let x⁻ = 50
[tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{50-56 }{\frac{12}{\sqrt{36} } }= -3[/tex]
The probability that the sample mean is less than 50 points
P( x⁻≤ 50) = P( Z≤-3)
= 0.5 - P(-3 <z<0)
= 0.5 -P(0<z<3)
= 0.5 - 0.498
= 0.002
Final answer:-
The probability that the sample mean is less than 50 points = 0.002
Answer:
56
2
.001
Step-by-step explanation:
The Central Limit Theorem for Means states that the mean of any sampling distribution of the means is equal to the mean of the population distribution. The standard deviation is equal to the standard deviation of the population divided by the square root of the sample size. So, the mean of this sampling distribution of the means with sample size 36 is 56 points and the standard deviation is 1236√=2 points. The z-score for 50 using the formula z=x¯¯¯−μσ is −3.
z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
-3.0 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001
-2.9 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.001 0.001 0.001
-2.8 0.003 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002
-2.7 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003
-2.6 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004
-2.5 0.006 0.006 0.006 0.006 0.006 0.005 0.005 0.005 0.005 0.005
Using the Standard Normal Table, the area to the left of −3 is approximately 0.001. Therefore, the probability that the sample mean will be less than 50 points is approximately 0.001.
Please answer this correctly
Answer:
1/2
Step-by-step explanation:
There is a 50/50 chance for the coin to land either heads or tails. Convert that to probability and it is 1/2.
The only time a coin would not be 50/50 chance is if the coin is weighted.
Answer:
1/2 is probability
becoz one side is head or one is tail