Answer:
Means:
1.55
1.73
Standard Deviation:
0.1434
0.1338
Coefficient of variation:
9.2
7.7
the limited data listed here shows evidence of stealing by the security service company's employees.
Step-by-step explanation:
Given data:
security Service Company Other Companies
x₁ x₂
1.5 1.8
1.7 1.9
1.6 1.6
1.4 1.7
1.7 1.8
1.5 1.9
1.8 1.6
1.4 1.5
1.4 1.7
1.5 1.8
n₁ = 10 n₂ = 10
To find:
coefficient of variation for each of the two samples
Solution:
The formula for calculating coefficient of variation of sample is:
Coefficient of Variation (CV) = (Standard Deviation / Mean) * 100%
Calculate Mean for Security Service Company data:
Mean = (Σ x₁) / n₁
= (1.5 + 1.7 + 1.6 + 1.4 + 1.7 + 1.5 + 1.8 + 1.4 + 1.4 + 1.5) / 10
= 15.5 / 10
Mean = 1.55
Calculate Standard Deviation for Security Service Company data:
Standard Deviation = √∑(x₁ - Mean)²/n₁-1
= √∑(1.5-1.55)² + (1.7-1.55)² + (1.6-1.55)² + (1.4-1.55)² + (1.7-1.55)² + (1.5-1.55)² + (1.8-1.55)² + (1.4-1.55)² + (1.4-1.55)² + (1.5-1.55)² / 10-1
=√∑ (−0.05)² + (0.15)² + (0.05)² + (−0.15)² + (0.15)² + (−0.05)² + (0.25)² + (−0.15)² + (−0.15)² + (−0.05)² / 10 - 1
= √∑0.0025 + 0.0225 + 0.0025 + 0.0225 + 0.0225 + 0.0025 + 0.0625 + 0.0225 + 0.0225 + 0.0025 / 9
= √0.185 / 9
= √0.020555555555556
= 0.14337208778404
= 0.143374
Standard Deviation = 0.143374
Coefficient of Variation for Security Service Company:
CV = (Standard Deviation / Mean) * 100%
= (0.143374 / 1.55) * 100
= 0.09249935 * 100
= 9.249935
CV = 9.2
CV = 9.2%
Calculate Mean for Other Companies data:
Mean = (Σ x₂) / n₂
= (1.8 + 1.9 + 1.6 + 1.7 + 1.8 + 1.9 + 1.6 + 1.5 + 1.7 + 1.8) / 10
= 17.3 / 10
Mean = 1.73
Calculate Standard Deviation for Other Companies data:
Standard Deviation = √∑(x₂-Mean)²/n₂-1
= √∑[(1.8-1.73)² + (1.9-1.73)² + (1.6-1.73)² + (1.7-1.73)² + (1.8-1.73)² + (1.9-1.73)² + (1.6-1.73)² + (1.5-1.73)² + (1.7-1.73)² + (1.8-1.73)²] / 10 - 1
= √∑ [(0.07)² + (0.17)² + (-0.13)² + (-0.03)² + (0.07)² + (0.17)² + (-0.13)² + (-0.23)² + (-0.03)² + (0.07)²] / 9
= √∑ (0.0049 + 0.0289 + 0.0169 + 0.0009 + 0.0049 + 0.0289 + 0.0169 + 0.0529 + 0.0009 + 0.0049) / 9
= √(0.161 / 9)
= √0.017888888888889
= 0.13374935098493
= 0.13375
Standard Deviation = 0.13375
Coefficient of Variation for Other Companies:
CV = (Standard Deviation / Mean) * 100%
= (0.13375 / 1.73) * 100
= 0.077312 * 100
= 7.7312
CV = 7.7
CV = 7.7%
Yes, the limited data listed here shows evidence of stealing by the security service company's employees because there is a significant difference in the variation.
The size of a television is the length of the diagonal of its screen in inches. The aspect ratio of the screens of older televisions is 4:3, while the aspect ratio of newer wide-screen televisions is 16:9. Find the width and height of an newer 75-inch television whose screen has an aspect ratio of 16:9
Answer:
The Width = 65.44 inches
The Height = 36.81 inches
Step-by-step explanation:
We are told in the question that:
The width and height of an newer 75-inch television whose screen has an aspect ratio of 16:9
Using Pythagoras Theorem we known that:
Width² + Height² = Diagonal²
Since we known that the size of a television is the length of the diagonal of its screen in inches.
Hence, for this new TV
Width² + Height² = 75²
We are given ratio: 16:9 as aspect ratio
Width = 16x
Height = 9x
(16x)² +(9x)² = 75²
= 256x² + 81x² = 75²
337x² = 5625
x² = 5625/337
x² = 16.691394659
x = √16.691394659
x = 4.0855103303
Approximately x = 4.09
For the newer 75 inch tv set
The Height = 9x
= 9 × 4.09
= 36.81 inches
The Width = 16x
= 16 × 4.09
= 65.44 inches.
more math questions if you would
Answer:
A.
Step-by-step explanation:
So we are given the function:
[tex]f(x)=7x+8[/tex]
To find the inverse of the function, we simply need to flip f(x) and x and then solve for f(x). Thus:
[tex]x=7f^{-1}(x)+8\\x-8=7f^{-1}(x)\\f^{-1}(x)=\frac{x-8}{7}[/tex]
So the answer is A.
Answer:
[tex]\large \boxed{\mathrm{Option \ A}}[/tex]
Step-by-step explanation:
f(x) = 7x+8
Write f(x) as y.
y = 7x + 8
Switch variables.
x = 7y + 8
Solve for y to find the inverse.
x - 8 = 7y
[tex]\frac{x-8}{7}[/tex] = y
Why would a linear function be an appropriate model?
Answer:
I know the answer
Step-by-step explanation:
Linear functions are those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.
what is ap in math abreviation and explain my math teacher was drunk so he couldn't teach nothing
Step-by-step explanation:
n mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. ... For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with common difference of 2.
PLEASE HELP!!!
Evaluate the expression when b=4 and y= -3
-b+2y
Answer: -10
Step-by-step explanation: All you have to do is plug the values into the equation. -4+2(-3). Then you solve the equation using PEDMAS.
1. -4+2(-3)
2. -4+(-6)
3.-4-6
4.-10
Answer:
8
Step-by-step explanation:
-b + 2y
if
b = 4
and
y = 3
then:
-b + 2y = -4 + 2*6 = -4 + 12
= 8
Based on this plot, which one of the following statements is not correct? The median room rate is $150 per night. There is one outlier in this data set. The 25th percentile in this data set is $130 per night. The second quartile in the data set is $160 per night.
Answer:
The second quartile in the data set is $130 per night.
Step-by-step explanation:
Quartile is a type of quantile which divides the number of data set into even numbered sub groups. The second quartile is median of data set. This means that 5% of data lies within this point. The middle value between the median and highest value of data set. The second quartile in the data set must be 50% so the statement is not correct.
The length of the sides of the triangle are in the ratio 3:4:5 and it’s perimeter is 144 cm find its area and height corresponding to the longest side
Which phrase represents t times 33 he quotient of a number and 33 the product of a number and 33 the quotient of 33 and a number the difference of a number and 33
Answer:
the product of a number and 33
Step-by-step explanation:
The operation "times" is what is used to form the product of two operands.
"t times 33" is "the product of t and 33"
Let x represent the number of times a student visits a gym in a one month period. Assume that the probability distribution of X is as follows:
x 0 1 2 3
p(x) 0.37 0.29 0.22 0.12
Find the mean, of this distribution. Report your answer to two decimal places.
Answer:
1.86
Step-by-step explanation:
Given the following :
X : - - - - 0 - - - - 1 - - - - 2 - - - - - 3 - - - - 4
P(x) - 0.37 - - 0.28 - - 0.22 - - 0.22 - - 0.12
The mean of the distribution can be calculated by evaluated by determining the expected value of the distribution given that the data above is a discrete random variable. The mean value can be deduced multiplying each possible outcome by the probability of it's occurrence.
Summation of [P(x) * X] :
(0.37 * 0) + (0.28 * 1) + (0.22 * 2) + (0.22 * 3) + (0.12 * 4)
= 0 + 0.28 + 0.44 + 0.66 + 0.48
= 1.86
According to a study, the probability that a randomly selected teenagar shopped at a mall at least once during a week was 0.61. Let X be the number of students in a randomly selected group of 50 that will shop at a mall during the next week. (a) Compute the expected value and standard deviation of X. expected value standard deviation (b) Fill in the missing quantity. (Round your answer to the nearest whole number.)There is an approximately 2.5% chance that _____ or more teenagers in the group will shop at the mall during the next week.
Answer:
Step-by-step explanation:
Given that:
p = 0.61
If X is the the number of students in a randomly selected group of a sample size n = 50
The expected value and the standard deviation can be computed as follows:
The expected value E(X) = np
The expected value E(X) = 50 × 0.61
The expected value E(X) = 30.5
The required standard deviation = [tex]\sqrt{np(1-p)}[/tex]
The required standard deviation = [tex]\sqrt{30.5(1-0.61)}[/tex]
The required standard deviation = [tex]\sqrt{30.5(0.39)}[/tex]
The required standard deviation = [tex]\sqrt{11.895}[/tex]
The required standard deviation = 3.4489
The required standard deviation = 3.45
(b) Fill in the missing quantity. (Round your answer to the nearest whole number.)
There is an approximately 2.5% chance that _____ or more teenagers in the group will shop at the mall during the next week.
From the given information:
Now, we can deduce that:
the mean = 30.5
standard deviation = 3.45
Using the empirical rule:
At 95% confidence interval;
[μ - 2σ, μ + 2σ] = [ 30.5 - 2(3.45) , 30.5 + 2(3.45)]
[μ - 2σ, μ + 2σ] = [ 30.5 - 6.9 , 30.5 + 6.9]
[μ - 2σ, μ + 2σ] = [ 23.6, 37.4]
The 2.5% of the observations are less than 95% confidence interval and 2.5% observations are greater than 95% confidence interval.
The required number of teenagers is = the upper limit of the 95% confidence interval = 37
There is an approximately 2.5% chance that __37___ or more teenagers in the group will shop at the mall during the next week.
Kelly bought a cup of coffee and drank 58 of it. Write an addition equation to represent how much coffee is remaining.
Answer:
[tex]L + \frac{5}{8} = 1[/tex]
Step-by-step explanation:
Given
A cup of coffee
Kelly drank 5/8 of the coffee
Required
Determine how much is left
Start by representing the amount of coffee left with L
Because the amount of coffee Kelly drank is in fraction (5/8), the total cup of coffee will equate to 1;
Hence, the addition equation as requested in the question to represent the scenario is
[tex]L + \frac{5}{8} = 1[/tex]
The average price of a college math textbook is $158 and the standard deviation is $26. Suppose that 40 textbooks are randomly chosen. Round all answers to 4 decimal places where possible.
What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
For the group of 48, find the probability that the average price is between $153 and $155.
Find the first quartile for the average textbook price for this sample size. $ (round to the nearest cent)
For part b), is the assumption that the distribution is normal necessary? Yes No
Please only answer if you are able to answer correctly and entirely.
The probability that the average price is between $153 and $155 is 0.04.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The average price of a math textbook =$158
The standard deviation =$26
The mean= 158
n =number of textbooks randomly chosen which is 40
n=10
Then
σ = 26
σₓ = σₓ/√n
= 26/√40
Therefore. σₓ² = 16.90
For the group of 48, find the probability that the average price is between $153 and $155.
The probability that the average price is between $153 and $155
= 0.04
Learn more about probability here;
https://brainly.com/question/11234923
#SPJ1
janice is buying paint to paint her new apartment
Answer:
I canot answer this
Step-by-step explanation:
Find the missing length.
A. 25
B. 12
C. 20
D. 100
Answer:
25 Answer A
Step-by-step explanation:
Use similar triangles, and the proportion derived from the quotient of a leg to the hypotenuse:
[tex]\frac{15}{9} =\frac{x}{15} \\x=\frac{15^2}{9} \\x=25[/tex]
A baseball player has a batting average (probability of getting on base per time at bat) of 0.215. Based on this: What is the probability that they will get on base more than 6 of the next 15 at bats
Answer:
[tex]\mathbf{P(x>6) = 0.0265}[/tex]
Step-by-step explanation:
Given that:
A baseball player has a batting average (probability of getting on base per time at bat) of 0.215
i.e
let x to be the random variable,
consider [tex]x_1 = \left \{ {{1} \atop {0}} \right.[/tex] to be if the baseball player has a batting average or otherwise.
Then
p(x₁ = 1) = 0.125
What is the probability that they will get on base more than 6 of the next 15 at bats
So
[tex]\mathtt{x_i \sim Binomial (n,p)}[/tex]
where; n = 15 and p = 0.125
P(x>6) = P(x ≥ 7)
[tex]P(x>6) = \sum \limits ^{15}_{x=7} ( ^{15 }_x ) \ (0.215)^x \ (1 - 0.215)^{15-x}[/tex]
[tex]P(x>6) = 1 - \sum \limits ^{6}_{x=7} ( ^{15 }_x ) \ (0.215)^x \ (1 - 0.215)^{15-x}[/tex]
[tex]P(x>6) = 1 - \sum \limits ^{6}_{x=0} ( ^{15 }_x ) \ (0.215)^x \ (1 - 0.215)^{15-x}[/tex]
[tex]P(x>6) = 1 -0.9735[/tex]
[tex]\mathbf{P(x>6) = 0.0265}[/tex]
find the circle through (-4,sqrt(5) with center (0,0)
Answer:
Circle Equation : x² + y² = 21
Step-by-step explanation:
So we know that this circle goes through the point ( - 4, √5 ), with a center being the origin. Therefore, this makes the circle equation a bit simpler.
The first step in determining the circle equation is the length of the radius. Applying the distance formula, the radius would be the length between the given points. Another approach would be creating a right triangle such that the radius is the hypotenuse. Knowing the length of the legs as √5 and 4, we can calculate the radius,
( √5 )² + ( 4 )² = r²,
5 + 16 = r²,
r = √21
In general, a circle equation is represented by the formula ( x - a )² + ( y - b )² = r², with radius r centered at point ( a, b ). Therefore our circle equation will be represented by the following -
( x - 0 )² + ( y - 0 )² = (√21 )²
Circle Equation : x² + y² = 21
60 is x% of 12. Find the value of x.
Answer:
20
Step-by-step explanation:
We can set up a percentage proportion to find the value of x.
[tex]\frac{12}{x} = \frac{60}{100}[/tex]
Now we cross multiply:
[tex]100\cdot12=1200\\\\1200\div60=20[/tex]
Hope this helped!
Find the work done by the force field F(x,y,z)=6xi+6yj+6k on a particle that moves along the helix r(t)=3 cos(t)i+3sin(t)j+2 tk,0≤t≤2π.
Answer:
the work done by the force field = 24 π
Step-by-step explanation:
From the information given:
r(t) = 3 cos (t)i + 3 sin (t) j + 2 tk
= xi + yj + zk
∴
x = 3 cos (t)
y = 3 sin (t)
z = 2t
dr = (-3 sin (t)i + 3 cos (t) j + 2 k ) dt
Also F(x,y,z) = 6xi + 6yj + 6k
∴ F(t) = 18 cos (t) i + 18 sin (t) j +6 k
Workdone = 0 to 2π ∫ F(t) dr
[tex]\mathbf{= \int \limits ^{2 \pi} _{0} (18 cos (t) i + 18 sin (t) j +6k)(-3 sin (t)i+3cos (t) j +2k)\ dt}[/tex]
[tex]\mathbf{= \int \limits ^{2 \pi} _{0} (-54 \ cos (t).sin(t) + 54 \ sin (t).cos (t) + 12 ) \ dt}[/tex]
[tex]\mathbf{= \int \limits ^{2 \pi} _{0} 12 \ dt}[/tex]
[tex]\mathbf{= 12 \times 2 \pi}[/tex]
= 24 π
se pueden calcular las edades de Juanita y de su madre si se sabe que:
1) actualmente la suma de sus edades es 44 años
2) dentro de 11 años la edad de juanita será la mitad de la edad de su mamá
Responder:
Juanita = 11, madre = 33
Explicación paso a paso:
Dado lo siguiente:
Suma de sus edades = 44
En 11 años, Juanita tendrá la mitad de la edad de su madre
Sea la edad de la madre = my la edad de juanita = j
m + j = 44 - - - - (1)
(j + 11) = 1/2 (m + 11)
j + 11 = 1/2 m + 5,5; j - 1/2 m = - 5,5; 2j - m = - 11
2j - m = - 11 - - - - (2)
Desde (1): m = 44 - j
Sustituyendo m = 44- j en (2)
2j - (44 - j) = - 11
2j - 44 + j = - 11
3j = - 11 + 44
3j = 33
j = 11
De 1)
m + j = 44
m + 11 = 44
m = 44 - 11
m = 33
Given that a random variable X is normally distributed with a mean of 2 and a variance of 4, find the value of x such that P(X < x)
Given that a random variable X is normally distributed with a mean of 2 and a variance of 4, find the value of x such that P(X < x)=0.99 using the cumulative standard normal distribution table
Answer:
6.642
Step-by-step explanation:
Given that mean = 2
standard deviation = 2
Let X be the random Variable
Then X [tex]\sim[/tex] N(n,[tex]\sigma[/tex])
X [tex]\sim[/tex] N(2,2)
By Central limit theorem;
[tex]z = \dfrac{X - \mu}{\sigma} \sim N(0,1)[/tex]
[tex]z = \dfrac{X - 2}{2} \sim N(0,1)[/tex]
P(X<x) = 0.09
[tex]P(Z < \dfrac{X-\mu}{\sigma })= 0.99[/tex]
[tex]P(Z < \dfrac{X-2}{2})= 0.99[/tex]
P(X < x) = 0.99
[tex]P(\dfrac{X-2}{2}< \dfrac{X-2}{2})=0.99[/tex]
[tex]P(Z< \dfrac{X-2}{2})=0.99[/tex]
[tex]\phi ( \dfrac{X-2}{2})=0.99[/tex]
[tex]( \dfrac{X-2}{2})= \phi^{-1} (0.99)[/tex]
[tex]( \dfrac{X-2}{2})= 2.321[/tex]
X -2 = 2.321 × 2
X -2 = 4.642
X = 4.642 +2
X = 6.642
what does 7g equal in like a verbal form
Answer:
see below
Step-by-step explanation:
7g can be "split" as 7 * g. The "*" means multiplication so a verbal form of this expression could be "7 times a number g" or "The product of 7 and a number g".
PLEASE HELP!!! Determine the domain and range of the following function. Record your answers in set notation.
Answer:
Ok so to help you out, first, off you need to be sure that the sets domain and range use the proper variable. After that, you are going to want to just plug it into the equation. I am going to link a screenshot to the correct answer if you are still have trouble finding it.
Anyways hoped this helped and I got to this question in time c:
15 < −5x can someone please solve for x?
Answer:
x <-3
Step-by-step explanation:
15 <-5x
divide both sides by 5 but since the coefficient of x is negative after dividing the sign changes.
x <-3
Answer:
x < −3
I hope this helps!
GCF/LCM of 8 and 24 the reduce 8/24
Answer:
GCF(8, 24) = 8LCM(8, 24) = 248/24 = 1/3Step-by-step explanation:
Since 8 is a factor of 24, 8 is the GCF of the pair, and 24 is the LCM of the pair.
__
The ratio 8/24 is reduced by observing that 24 = 8·3:
8/24 = 8/(8·3) = (8/8)·(1/3)
8/24 = 1/3
(a) Find the standard error of the mean for each sampling situation (assuming a normal population). (Round your answers to 2 decimal places.) (a) σ = 18, n = 9 (b) σ = 18, n = 36 (c) σ = 18, n = 144
Answer:
a) 6.00
b) 3.00
c) 1.50
Step-by-step explanation:
Sample error of the mean is expressed mathematically using the formula;
SE = σ /√n where;
σ is the standard deviation and n is the sample size.
a) Given σ = 18, n = 9
Standard error of the mean = σ /√n
Standard error of the mean = 18/√9
Standard error of the mean = 18/3
Standard error of the mean = 6.00
b) Given σ = 18, n = 36
Standard error of the mean = σ /√n
Standard error of the mean = 18/√36
Standard error of the mean = 18/6
Standard error of the mean = 3.00
c) Given σ = 18, n = 144
Standard error of the mean = σ /√n
Standard error of the mean = 18/√144
Standard error of the mean = 18/12
Standard error of the mean = 3/2
Standard error of the mean = 1.50
Using only four 4's and any operational sign find the value of 8
Answer:
The answer is 4 + 4 + 4 - 4 = 8
Step-by-step explanation:
The four fours problem is one of the problems given in the book "The Man Who Calculated" by Malba Tahan, a Brazilian-born professor of mathematical sciences.
There are many complicated problems in this book made with the intention of using logic to find a value.
The 4 fours problem is based on using these numbers and using any operation to result in the numbers 1 through 10.
Can anyone help me please??
Answer:
-20x / (x-12) = y
Step-by-step explanation:
3/x - 5/y = 1/4
Multiply each side by 4xy to clear the fractions
4xy ( 3/x - 5/y = 1/4)
Distribute
12y - 20x = xy
Subtract 12y from each side
-20x = xy -12y
Factor out y
-20x = y(x-12)
Divide each side by (x-12)
-20x / (x-12) = y
Find the sum. 1. -7+(-5)
O-12
O-2
0 2
0 12
Answer:
-12
Step-by-step explanation:
-7+(-5)=
-7-5=
-12
Please answer this correctly without making mistakes
Answer:
1,377/2 and 688 1/17
Step-by-step explanation:
A mail truck traveled 82 miles in 4 1/2 hours. The distance is the product of the rate and the time. To the nearest tenth, what was the average speed of the mail truck?
Answer:
= 18.2 miles per hour
Step-by-step explanation:
Speed = distance / time
=82 miles / 4.5 hours
=18.22222222 miles per hour
Rounding
= 18.2 miles per hour
Answer:
Given that
Distance = rate × time
82 = r × 4½
r = 18.2 mph
