25/250 = 1/10
I do not know that much english. I an spanish so I might have done it wrong.
the probability that the horse is at least 25 feet away from all boundary lines is 0.5
To calculate the probability that the horse is at least 25 feet away from all boundary lines in an enclosed pasture that is 150 feet by 200 feet, we need to consider the available space for the horse to roam.
The area of the pasture is given by:
Area = Length * Width = 150 feet * 200 feet = 30,000 square feet
Now, let's consider the area where the horse must stay within at least 25 feet away from all boundary lines. We can imagine this as a rectangular strip along the inner boundary of the pasture, with dimensions reduced by 50 feet on each side.
The dimensions of this rectangular strip would be:
Length = 150 feet - 2 * 25 feet = 100 feet
Width = 200 feet - 2 * 25 feet = 150 feet
The area of this rectangular strip is given by:
Area_strip = Length * Width = 100 feet * 150 feet = 15,000 square feet
Therefore, the probability that the horse is at least 25 feet away from all boundary lines is:
Probability = Area_strip / Area = 15,000 square feet / 30,000 square feet = 0.5
The probability is 0.5 or 50%.
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-5/2x-3 is less than or equal to 2 what is the solution.
Answer: 1/4≤x
Step-by-step explanation:
-5/(2x-3)≤2
Multiply by (2x-3)
-5≤4x-6
Add 6
1≤4x
1/4≤x
Hope it helps <3
Answer:
[tex]x \geq 1/4[/tex]
Step-by-step explanation:
=> [tex]\frac{-5}{2x-3} \leq 2[/tex]
Multiplying both sides by (2x-3)
=> [tex]-5 \leq 2(2x-3)[/tex]
=> [tex]-5 \leq 4x-6[/tex]
Adding 6 to both sides
=> [tex]-5+6 \leq 4x[/tex]
=> [tex]4x\geq 1[/tex]
Dividing both sides by 4
=> [tex]x \geq 1/4[/tex]
What's the common denominator of this equation?
3 - b = 6-7
Answer:
b = 4
Step-by-step explanation:
3 - b = 6 - 7
3 - b = -1
-b = -1 -3
-b = -4
b = 4
Suppose Mr. Pink is 28 years old right now and puts away $1,800 per quarter in an account that returns 6% interest. a.) How much will be in the account when he turns 68? b.)What is his total contribution to the account?
Answer: (a) When he turns 68 , the account will have = $1,179,415.39
(b) $ 288,000
Step-by-step explanation:
Formula: Future value of annuity =[tex]P[\dfrac{(1+r)^n-1}{r}][/tex], where P+ periodic payment, r = rate of interest per period, n= number of periods.
As per given, we have
P= $1800
rate of interest = 6% = 0.06
(a) n= 68-28 = 40
Rate per period : r= [tex]\dfrac{0.06}{4}=0.015[/tex]
Number of periods: n = 4x 40 =160
Now, Future value of amount when Mr. Pink turns 28 years = [tex]1800(\dfrac{(1+0.015)^{160}-1}{0.015})[/tex]
[tex]=1800(\dfrac{10.8284615777-1}{0.015})\\\\=1800\times\dfrac{9.8284615777}{0.015}\\\\\approx\$1179415.39[/tex]
Hence, when he turns 68 , the account will have = $1,179,415.39
(b) Total contribution = P × n
=1800 × 160
=$ 288,000
Hence, Total contribution =$ 288,000
my number is the first multiple of 3,6, and 9 what is my number
Answer:
18 is the first multiple of 3,6, and 9.
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
We need to find the LCM (lowest common multiple) of 3, 6, and 9. Let's count by multiples of 3 to find it.
3 (not a multiple of 6 or 9), 6 (not a multiple of 9), 9 (not a multiple of 6), 12 (not a multiple of 9), 15 (not a multiple of 6 or 9), 18.
Since 18 is the first number that is a multiple of 3, 6, and 9, that is the answer.
Select the correct option.
In a game, bonus points are awarded based on the number of the level that is cleared. The bonus points are calculated by a function
that is 15 times the cube root of the level cleared and rounded to the closest integer value.
Which of the following options represents the bonus points scored as the levels advance?
Answer:
Graph A.
Step-by-step explanation:
Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g. A. g(0) = 2 B. g(7) = -1 C. g(-13) = 20 D. g(-4) = -11
Answer:
C. g(-13) = 20
Step-by-step explanation:
Let's check the offered statements:
A. g(0) = 2 . . . . . . doesn't match g(0) = -2
B. g(7) = -1 . . . . . . 7 is not in the domain of g
C. g(-13) = 20 . . . could be true
D. g(-4) = -11 . . . . -11 is not in the range of g
What is the equation of the following graph in vertex form? Courtesy of Texas Instruments A. y = (x − 4)2 − 4 B. y = (x + 4)2 − 4 C. y = (x + 2)2 + 6 D. y = (x + 2)2 + 12
Answer:
A: y = (x − 4)^2 − 4
Step-by-step explanation:
vertex=(4.-4)
A: y = (x − 4)^2 − 4
y=x^2-8x+16-4
y=x^2-8x+12 (a=1,b=-8,c=12)
the y intercept is (0,12)
vertex ( h, k)
h=-b/2a ⇒ h=-(-8)/2=4
plug the value of h in the equation y=x^2-8x+12
k=4²-8(4)+12
k=16-32+12
k=-4
v(4,-4)
The required equation of the given graph in vertex form is y = (x − 4)² − 4. which is the correct answer would be option (A).
What is Parabola?A parabola is a U-shaped curve this is drawn for a quadratic function,
f(x) = ax² + b x + c.
The parabola equation into the vertex form:
(y-k) = a(x-h)²
Where (h,k) are the x and y-coordinates of the vertex.
The vertex = (4, -4) is given in the shown graph.
As per option (A),
y = (x − 4)² − 4
y = x²-8x+16-4
y = x²-8x+12 (a=1,b=-8,c=12)
the y-intercept is (0,12)
vertex ( h, k)
h = -b/2a ⇒ h=-(-8)/2=4
Substitute the value of h in the equation y = x²-8x+12
k = 4²- 8(4) + 12
k =16 - 32 + 12
k = -4
Thus, the vertex is (4,-4)
Hence, the correct answer would be option (A).
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find the product of .42 and 7/20
To make it easier, you can convert 7/20 to a decimal, and as a decimal it is 0.35. 0.42*0.35=0.147, so .42*7/20=0.147.
Answer:
0.147
Step-by-step explanation:
0.42 * 7/20
Well, 0.42 = 42/100. Now we have both numbers as fractions.
We can simplify 42/100 to 21/50
Therefore we have 7/20 * 21/50
To multiply fractions multiply the numerators together and multiply the denominators together.
This gives: 147 / 1000
Which is equal to 0.147
Therefore 0.42 * 7/20 = 0.147
Please help with 4d.
Answer:
(Hemingway, The Old Man and the Sea)(Orwell, 1984)Step-by-step explanation:
A short web search will turn up the authors of the given titles:
The Old Man and the Sea - Hemingway
Huckleberry Finn - Twain
Moby D.ick - Melville
1984 - Orwell
Crime and Punishment - Dostoevsky
A 6 foot person casts a 26 foot shadow. What is the angle of elevation of the sun? (nearest whole degree)
Answer:
13°
Step-by-step explanation:
The trigonometric ratio formula can be used in calculating the angle of elevation (x°) of the sun, as the person makes a right angle with the ground.
The height of the person would be the opposite length = 6 ft, the shadow of the person would be the adjacent length = 26 ft
Therefore, according to the trigonometric ratio formula, we would calculate angle of elevation (x°) as follows:
[tex] tan x = \frac{opposite}{adjacent} [/tex]
[tex] tan x = \frac{6}{26} [/tex]
[tex] tan x = 0.2308 [/tex]
x = tan-¹(0.2308)
x = 12.996
x ≈ 13° (to the nearest whole degree)
The angle of elevation of the sun = 13°
Hypothesis Testing
Problem 1. Adults saving for retirement
In a recent survey conducted by Pew Research, it was found that 156 of 295 adult Americans without a high school diploma were worried about having enough saved for retirement. Does
the sample evidence suggest that a majority of adult Americans without a high school diploma are worried about having enough saved for retirement? Use a 0.05 level of significance
1. State the null and alternative hypothesis.
2. What type of hypothesis test is to be used?
3. What distribution should be used and why?
4. Is this a right, left, or two-tailed test?
5. Compute the test statistic.
6. Compute the p-value.
7. Do you reject or not reject the null hypothesis? Explain why.
8. What do you conclude?
Problem 2: Google Stock
Google became a publicly traded company in August 2004. Initially, the stock traded over 10 million shares each day! Since the initial offering, the volume of stock traded daily has
decreased substantially. In 2010, the mean daily volume in Google stock was 5.44 million shares, according to Yahoo!Enance. A random sample of 35 trading days in 2014 resulted in a
sample mean of 3.28 million shares with a standard deviation of 1.68 million shares. Does the evidence suggest that the volume of Google stock has changed since 2007? Use a 0.05 level of
significance
1. State the null and alternative hypothesis.
2. What type of hypothesis test is to be used?
3. What distribution should be used and why?
4. Is this a right, left, or two-tailed test?
5. Compute the test statistic.
6. Compute the p-value.
7. Do you reject or not reject the null hypothesis? Explain why
8. What do you conclude?
Answer:
Problem 1: We conclude that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement.
Problem 2: We conclude that the volume of Google stock has changed.
Step-by-step explanation:
Problem 1:
We are given that in a recent survey conducted by Pew Research, it was found that 156 of 295 adult Americans without a high school diploma were worried about having enough saved for retirement.
Let p = proportion of adult Americans without a high school diploma who are worried about having enough saved for retirement
So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 50% {means that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement}
Alternate Hypothesis, [tex]H_A[/tex] : p > 50% {means that a majority of adult Americans without a high school diploma are worried about having enough saved for retirement}
This is a right-tailed test.
The test statistics that would be used here is One-sample z-test for proportions;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of adult Americans who were worried about having enough saved for retirement = [tex]\frac{156}{295}[/tex] = 0.53
n = sample of adult Americans = 295
So, the test statistics = [tex]\frac{0.53-0.50}{\sqrt{\frac{0.50(1-0.50)}{295} } }[/tex]
= 1.03
The value of z-test statistics is 1.03.
Also, the P-value of the test statistics is given by;
P-value = P(Z > 1.03) = 1 - P(Z [tex]\leq[/tex] 1.03)
= 1 - 0.8485 = 0.1515
Now, at a 0.05 level of significance, the z table gives a critical value of 1.645 for the right-tailed test.
Since the value of our test statistics is less than the critical value of z as 1.03 < 1.645, so we insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
Therefore, we conclude that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement.
Problem 2:
We are given that a random sample of 35 trading days in 2014 resulted in a sample mean of 3.28 million shares with a standard deviation of 1.68 million shares.
Let [tex]\mu[/tex] = mean daily volume in Google stock
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 5.44 million shares {means that the volume of Google stock has not changed}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 5.44 million shares {means that the volume of Google stock has changed}
This is a two-tailed test.
The test statistics that would be used here is One-sample t-test statistics because we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean volume in Google stock = 3.28 million shares
s = sample standard deviation = 1.68 million shares
n = sample of trading days = 35
So, the test statistics = [tex]\frac{3.28-5.44}{\frac{1.68}{\sqrt{35} } }[/tex] ~ [tex]t_3_4[/tex]
= -7.606
The value of t-test statistics is -7.606.
Also, the P-value of the test statistics is given by;
P-value = P([tex]t_3_4[/tex] < -7.606) = Less than 0.05%
Now, at a 0.05 level of significance, the t table gives a critical value of -2.032 and 2.032 at 34 degrees of freedom for the two-tailed test.
Since the value of our test statistics doesn't lie within the range of critical values of t, so we sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the volume of Google stock has changed.
Scores turned in by an amateur golfer at the Bonita Fairways Golf Course in Bonita Springs, Florida, during and are as follows: Season: 7377787674727476 Season: 7069747684797078a. Calculate the mean (to the nearest whole number) and the standard deviation (to decimals) of the golfer's scores, for both years.MeanStandard deviationMeanStandard deviationb. What is the primary difference in performance between and
Complete question is;
Scores turned in by an amateur golfer at the Bonita Fairways Golf Course in Bonita Springs, Florida, during 2005 and 2006 are as follows:
2005 Season: 73 77 78 76 74 72 74 76
2006 Season: 70 69 74 76 84 79 70 78
A) Calculate the mean (to the nearest whole number) and the standard deviation (to decimals) of the golfer's scores, for both years.
B) What is the primary difference in performance between 2005 and 2006? What improvement,
if any, can be seen in the 2006 scores?
Answer:
A) 2006 mean = 75
2005 mean = 75
2006 standard deviation = 5.2644
2005 standard deviation = 2.0702
B)The primary difference is that variation is higher in the 2006 season than the 2005 season.
Step-by-step explanation:
A) Mean is the sum of all scores divided by the number of scores.
Thus;
μ_2005 = (73 + 77 + 78 + 76 + 74 + 72 +74 + 76)/8 = 75
Similarly;
μ_2006 = (70 + 69 + 74 + 76 + 84 + 79 + 70 + 78)/8 = 75
Now, variance is calculated by the sum of the square of mean deviations divided by (n - 1)
Thus;
2005 Variance = ((73-75)² + (77-75)² + (78-75)² + (76-75)² + (74-75)² + (72-75)² + (74-75)² + (76-75)²)/(8-1) = 4.2857
2006 Variance = ((70-75)² + (69-75)² + (74-75)² + (76-75)² + (84-75)² + (79-75)² + (70-75)² + (78-75)²)/(8 - 1) = 27.7143
Now, standard deviation is the square root of variance.
Thus;
2005 standard deviation = √4.2857 = 2.0702
2006 standard deviation = √27.7143 = 5.2644
B) The primary difference is that variation is higher in the 2006 season than the 2005 season.
Also,
Which of the following shapes can NOT be created by revolving a two-dimensional figure around an axis? There can be more than 1. A. come B. cube C. Rectangular pyramid D. Rectangular Prism E. Cylinder F. Sphere
PLEASE HELP
Answer:
A. Cone
D. Rectangular Prism
E. Cylinder
F. Sphere
Step-by-step explanation:
Rectangular Prism is a solid three dimensional shape. It has six faces which are sides of a rectangle. It is also known as Cuboid. The rectangular prism cannot be formed with two dimensional shapes. Sphere is a geometrical object which is a three dimensional circle. This shape has a circumference so this shape cannot be formed with two dimensional shapes.
the mean cost of domestic airfares is RS 385 per ticket. Airfares were based on the total ticket value, which consisted of the price charged by the airlines plus any additional taxes and fees. Assume domestic airfares are normally distributed with a standard deviation of RS 110. What is the probability that a domestic airfare is RS 550 or more?
Answer: 0.0668
Step-by-step explanation:
Given the following :
Mean (m) Cost = RS385
Standard deviation (s) = RS110
Assume a normal distribution, Probability that domestic airfare is RS550 or more?
P(x > 550)
Find the z - score
Z - score = (x - m) / s
Where x = 550
Z = (550 - 385) / 110
Z = 165 / 110 = 1.5
P(Z > 1.5) = 1 - P(Z ≤1.5)
Using the z table : 1.5 = 0.9332
Therefore,
1 - P(Z ≤1.5) = 1 - 0.9332 = 0.0668
P(x > 550) = 0.0668
Kite LMNO is shown below.
What is the measure of angle M
Answer:
<M = 78°
Step-by-step explanation:
The sum of angles in a kite is 360°.
One of the properties of a kite is that one pair of opposite angles are equal.
Since it is not <L and <N, it must be <O and <M
Therefore:
<O = <M = x
=> x + x + 130 + 74 = 360
2x + 204 = 360
2x = 360 - 204
2x = 156
x = 156/2 = 78°
This means that <M = 78°
A polynomial function is shown below:
f(x) = x3 - 4x2 - x + 4
Which graph best represents the function? (5 points)
Answer:
Simply plug in the polynomial into a graphing calc.
Step-by-step explanation:
A market trader has 100 oranges for sale, 4 of them are unripe, what is the
probability that an orange chosen at random is ripe?
4/100?
90/100?
2/5?
24/25?
[tex]\bold{Answer}:\quad \dfrac{24}{25}[/tex]
Step-by-step explanation:
There are 100 oranges. 4 of them are unripe which means 96 are ripe.
[tex]\dfrac{ripe}{total}=\dfrac{96}{100}\quad \div \dfrac{4}{4}=\large\boxed{\dfrac{24}{25}}[/tex]
Amy have 398.5 L of apple juice . Avery have 40098 ml of apple juice how many do they have all together
Answer: 438.5L = 438000ml
Step-by-step explanation:
The perimeter of an equilateral triangle with a side length of 12 units is:
Answer:
Hey there!
An equilateral triangle has all sides equal to each other, so the perimeter would be 3x, where x is the length of one side.
Thus, the perimeter for this equilateral triangle would be 3(12)=36
Hope this helps :)
Answer:
[tex]\boxed{Perimeter = 36 \ units}[/tex]
Step-by-step explanation:
Perimeter = sum of all sides
Perimeter = 12 +12 + 12
Perimeter = 36 units
Someone help me with this, please!
Answer:
B = 26.4
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp/ hyp
sin B = 4/9
Take the inverse sin of each side
sin ^-1 sin ( B) = sin ^-1 ( 4/9)
B = 26.38779996
B = 26.4
Answer:
[tex]26.4\º[/tex]
Step-by-step explanation:
[tex]\theta=?[/tex]
[tex]$\sin(\theta)=\frac{opp}{hyp} = \frac{4}{9} $[/tex]
[tex]$\theta=\sin^{-1}\frac{4}{9} =\arcsin\frac{4}{9} \approx 26.4\º$[/tex]
5x - y = -7
4x + 2y = – 14
Answer:
[tex]\boxed{\sf \ \ x=-2, \ y=-3 \ \ }[/tex]
Step-by-step explanation:
Hello,
I assume that you want to solve this system of two equations
(1) 5x - y = -7
(2) 4x + 2y = -14
We will multiply (1) by 2 and add to (2) so that we can eliminate the terms in y
2*(1)+(2) gives
10x - 2y + 4x + 2y = -7*2 -14 = -14 - 14 = -28
<=>
14x = - 28 we can divide by 14 both parts
x = -28/14 = -2
and then we replace x in (1)
5*(-2)-y=-7
-10-y=-7 add 7
-10-y+7=0
-3-y=0 add y
-3 = y
which is equivalent to y = -3
do not hesitate if you have any question
Answer:
x = -2, y = -3
Step-by-step explanation:
5x - y = -7
4x + 2y = – 14
Multiply the first equation by 2
2(5x - y) = 2*-7
10x -2y = -14
Add this to the second equation to eliminate y
10x -2y = -14
4x + 2y = – 14
---------------------------
14x = -28
Divide by 14
14x/14 = -28/14
x = -2
Now find y
4x+2y = -14
4*-2 +2y = -14
-8+2y = -14
Add 8 to each side
2y = -6
Divide by 2
2y/2 = -6/2
y = -3
Imagine a man in the Chicago suburbs went outside to shovel his driveway after the Feb 10, 2018 snowstorm and had a heart attack while shoveling. When the police discovered the body later that day at 4PM, his body temperature had dropped from 98.6°F to 42°F. The environmental air temperature was 10°F. What time did he die from the heart attack?
Answer:
I did my best with the information! The Man died at around 11:20 am.
Step-by-step explanation:
So due to the algus mortis process, after death, a body can stay at its regulated temperature for up to 2 to 3 hours postmortem. But after that, the body soon drops at about 1 degrees celsius each hour. 1 degrees celsius is about -33 . So he was found at 42 degrees fahrenheit, which means he died somewhere around 11 o-clock. We do not know how long the postmortem process had his temperature delayed, so it would be roughly I say around 11: 20 am.
Rachel Plant has $28,000 invested in stock A and stock B. Stock A currently sells for $20 a share and stock B sells for $80 a share. If stock B doubles in value and stock A goes up 50%, her stock will be worth $54,000. How many shares of each stock does she own?
Answer:
A= 66.6667
B = 333.3333
Step-by-step explanation:
Initial value of A = $20
Initial value of B = $80
Initial total=$ 28000
A moves up 50%= 20+(0.5*20)
A moves up 50% = 20+10
A moves up 50% =$ 30
B double it values = $80*2
B double it values = $160
Now total value is = $54000
A20+B80= 28000... equation 1
A30+B160= 54000.... equation 2
Multiplying equation 1 * 2
Multiplying equation 2 * 1
A40 +B160 = 56000
A30+B160= 54000
A30 = 2000
A= 2000/30
A= 200/3
A= 66.6667
A20+B80= 28000
Substituting A
200/3 (20) +B80= 28000
B80= 28000-4000/3
B80= 80000/3
B= 80000/240
B = 333.3333
a sample of bacteria is growing at an hourly rate of 14% according to the exponential growth function.the sa
Answer:
pleasse elaborate more
Step-by-step explanation:
6th grade math help me, please :)))
85% x 1600/100 = 1360 number of seats sold
Evaluate the following geometric sum.
1/2 + 1/10 + ( 1/50) + (1/250 ) + midline ellipsis + (1/31,250)
Answer:
39062/62,500Step-by-step explanation:
Given the following geometric progression; 1/2 + 1/10 + ( 1/50) + (1/250 ) + ... + (1/31,250),the sum of the arithmetic geometric progression is expressed using the formula below;
Sn = a(1-rⁿ)/1-r for r less than 1
r is the common ratio
n is the number of terms
a is the first term of the series
In between the mid-line ellipsis there are 2 more terms, making the total number of terms n to be 7]
common ratio = (1/10)/(1/2) = (1/50)/(1/10) = (1/250)/(1/50) = 1/5
a = 1/2
Substituting the given values into the equation above
S7 = 1/2{1 - (1/5)⁷}/1 - 1/5
S7 = 1/2(1- 1/78125)/(4/5)
S7 = 1/2 (78124/78125)/(4/5)
S7 = 78124/156,250 * 5/4
S7 = 390,620/625000
S7 = 39062/62,500
Hence the geometric sum is 39062/62,500
Find the hcf of 15a²b² and -24ab | plzzz solve
Answer:
[tex]\large \boxed{\sf \ \ \ 3\cdot a \cdot b \ \ \ }[/tex]
Step-by-step explanation:
Hello,
First of all, let's find the factors of these two numbers and I will put in boxes the common factors.
[tex]15a^2b^2=\boxed{3}\cdot 5\cdot \boxed{a} \cdot a \cdot \boxed{b} \cdot b \\ \\ \\-24ab=(-1)\cdot 2 \cdot \boxed{3} \cdot 4 \cdot \boxed{a} \cdot \boxed{b}[/tex]
The Highest Common Factor (HCF) is found by finding all common factors and selecting the largest one. So, in this case, it gives
[tex]\large \boxed{\sf \ \ \ 3\cdot a \cdot b \ \ \ }[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Use the accompanying data set to complete the following actions. a. Find the quartiles. b. Find the interquartile range. c. Identify any outliers. 41 52 37 44 42 38 41 48 43 39 36 55 42 35 15 52 39 50 29 30
Answer:
(a) [tex]Q_1=36.5,M=Q_2=41,Q_3=46[/tex]
(b) [tex]IQR=9.5[/tex]
(c) 15
Step-by-step explanation:
The given data set is
41, 52, 37, 44, 42, 38, 41, 48, 43, 39, 36, 55, 42, 35, 15, 52, 39, 50, 29, 30
Arrange the data in ascending order.
15, 29, 30, 35, 36, 37, 38, 39, 39, 41, 41, 42, 42, 43, 44, 48, 50, 52, 52, 55
Divide the data in four equal parts.
(15, 29, 30, 35, 36), (37, 38, 39, 39, 41), (41, 42, 42, 43, 44), (48, 50, 52, 52, 55)
Now,
[tex]Q_1=\dfrac{36+37}{2}=36.5[/tex]
[tex]M=Q_2=\dfrac{41+41}{2}=41[/tex]
[tex]Q_3=\dfrac{44+48}{2}=46[/tex]
[tex]IQR=Q_3-Q_1=46-36.5=9.5[/tex]
Range for outlier is
[tex][Q_1-1.5IQR,Q_3+1.5IQR]=[36.5-1.5(9.5),46+1.5(9.5)][/tex]
[tex]=[22.25,60.25][/tex]
Since, 15 lies outside the interval [22.25,60.25], therefore 15 is an outlier.
Consider the following scores. (i) a score of 40 from a distribution with mean 50 and standard deviation 10 (ii) a score of 45 from a distribution with mean 50 and standard deviation 5 How do the two scores compare relative to their respective distributions
Answer:
The scores are equal
Step-by-step explanation:
The z-score for any normal distribution is:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
(i) Score (X) = 40
Mean (μ)= 50
Standard deviation (σ) = 10
[tex]z=\frac{40-50}{10}\\ z=-1[/tex]
(ii) Score (X) = 45
Mean (μ)= 50
Standard deviation (σ) = 5
[tex]z=\frac{45-50}{5}\\ z=-1[/tex]
Both scores have the same z-score, which means that, relative to their respective distributions, the scores are equal.
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Answer:
50% of 100<75% of 104
50% of 100>75% of 60
Step-by-step explanation:
For the inequality to support the statement, we can use 50% of 100 which is 50
Now we need to find "any other number" that is greater. I'll use 104 since it divides evenly. 75% of 104 is 78, 50<78
Now for the second one, we can use 50% of 100 again which is 50.
This time we need to find another number that is less than. I'll use 60. 75% of 60 is 45. 50>45