Answer:
0.0284Step-by-step explanation:
The formula for calculating the Margin of error of a dataset is expressed as;
Margin of error = [tex]Z*\sqrt{\frac{p(1-p)}{n} } \\\\[/tex] where;
Z is the z-score of 95% confidence interval = 1.96
p is the sample proportion/mean = 0.75
n is the sample size = total number of people = 1000
Note that when the confidence interval is not given, it is always safe to use 95% confidence.
Substituting this values into the formula we have;
[tex]ME = 1.96*\sqrt{\frac{0.7(1-0.7)}{1000} } \\\\ME = 1.96*\sqrt{\frac{0.7(0.3)}{1000} } \\\\ME = 1.96*\sqrt{0.00021} } \\\\ME = 1.96*0.01449\\\\ME = 0.0284[/tex]
Hence the margin error for the dataset is 0.0284
A manufacturer of paper coffee cups would like to estimate the proportion of cups that are defective (tears, broken seems, etc.) from a large batch of cups. They take a random sample of 200 cups from the batch of a few thousand cups and found 18 to be defective. The goal is to perform a hypothesis test to determine if the proportion of defective cups made by this machine is more than 8%.
Required:
a. Calculate a 95% confidence interval for the true proportion of defective cups made by this machine.
b. What is the sample proportion?
c. What is the critical value for this problem?
d. What is the standard error for this problem?
Answer:
a
The 95% confidence interval is [tex]0.0503 < p < 0.1297[/tex]
b
The sample proportion is [tex]\r p = 0.09[/tex]
c
The critical value is [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
d
The standard error is [tex]SE =0.020[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 200
The number of defective is k = 18
The null hypothesis is [tex]H_o : p = 0.08[/tex]
The alternative hypothesis is [tex]H_a : p > 0.08[/tex]
Generally the sample proportion is mathematically evaluated as
[tex]\r p = \frac{18}{200}[/tex]
[tex]\r p = 0.09[/tex]
Given that the confidence level is 95% then the level of significance is mathematically evaluated as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table, the value is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the standard of error is mathematically represented as
[tex]SE = \sqrt{\frac{\r p (1 - \r p)}{n} }[/tex]
substituting values
[tex]SE = \sqrt{\frac{0.09 (1 - 0.09)}{200} }[/tex]
[tex]SE =0.020[/tex]
The margin of error is
[tex]E = Z_{\frac{ \alpha }{2} } * SE[/tex]
=> [tex]E = 1.96 * 0.020[/tex]
=> [tex]E = 0.0397[/tex]
The 95% confidence interval is mathematically represented as
[tex]\r p - E < \mu < p < \r p + E[/tex]
=> [tex]0.09 - 0.0397 < \mu < p < 0.09 + 0.0397[/tex]
=> [tex]0.0503 < p < 0.1297[/tex]
a college entrance exam company determined that a score of 25 on the mathematics portion of the exam suggests that a student is ready for
Answer:
Student is ready for college level mathematics.
The null hypothesis will be H0 = 25
The alternative hypothesis is Ha > 25
Step-by-step explanation:
The correct order of the steps of a hypothesis test is given following
1. Determine the null and alternative hypothesis.
2. Select a sample and compute the z - score for the sample mean.
3. Determine the probability at which you will conclude that the sample outcome is very unlikely.
4. Make a decision about the unknown population.
These steps are performed in the given sequence to test a hypothesis.
In which set(s) of numbers would you find the number -832 a. whole number b. irrational number c. integer d. rational number e. real number f. natural number
Answer:
integer of course
Step-by-step explanation:
an integer can either be negative or positive.
The bowling scores for six people are:
27, 142, 145, 146, 154, 162
What is the most appropriate measure of center?
O A. The standard deviation
O B. The range
O C. The median
O D. The mean
Answer: Option D. will be the answer.
Explanation: The bowling scores for six persons have been given as 27, 142, 145, 146, 154, 162.
The most appropriate measure of the center of these scores will be the median.
Here median will be mean of 146 and 146 because number of persons are 6 which is an even number.
So there are two center scores those are 145 and 146 and median =
Option D. will be the answer.
Solve the equation 3(2x + 2) = 3x − 15.
Hi there! :)
Answer:
x = -7.
Step-by-step explanation:
Starting with:
3(2x + 2) = 3x - 15
Begin by distributing '3' with the terms inside of the parenthesis:
3(2x) + 3(2) = 3x - 15
Simplify:
6x + 6 = 3x - 15
Isolate the variable by subtracting '3x' from both sides:
6x - 3x + 6 = 3x - 3x - 15
3x + 6 = -15
Subtract 6 from both sides:
3x + 6 - 6 = -15 - 6
3x = -21
Divide both sides by 3:
3x/3 = -21/3
x = -7.
Answer:
x = -7
Step-by-step explanation:
3(2x+2) = 3x - 15
First, we should simplify on the left side.
6x + 6 = 3x - 15 ; Now we subtract six from both sides.
-6 -6
6x = 3x - 21 ; next we just subtract 3x from both sides.
-3x -3x
3x = -21
Finally, we divide 3 from both sides to separate the three from the x.
x = -7
Hope this helps!! <3 :)
It is known that 80% of all brand A external hard drives work in a satisfactory manner throughout the warranty period (are "successes"). Suppose that n= 15 drives are randomly selected. Let X = the number of successes in the sample. The statistic X/n is the sample proportion (fraction) of successes. Obtain the sampling distribution of this statistic.
Answer:
P (x= 5) = 0.0001
P(x=3) = 0.008699
Step-by-step explanation:
This is a binomial distribution .
Here p = 0.8 q= 1-p = 1-0.8 = 0.2
n= 15
So we find the probability for x taking different values from 0 - 15.
The formula used will be
n Cx p^x q^n-x
Suppose we want to find the value of x= 5
P (x= 5) = 15C5*(0.2)^10*(0.8)^5 = 0.0001
P(x=3) = 15C3*(0.2)^12*(0.8)^3 = 9.54 e ^-7= 0.008699
Similarly we can find the values for all the trials from 0 -15 by substituting the values of x =0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15.
The value for p(x = 5) is 0.0001 and the value for p(x = 3) is 0.008699.
It is given that the 80% of all brand A external hard drives work in a satisfactory manner throughout the warranty period.
It is required to find the sampling distribution if n =15 samples.
What is sampling distribution?It is defined as the probability distribution for the definite sample size the sample is the random data.
We have p =80% = 0.8 and q = 1 - p ⇒ 1 -0.8 ⇒ 0.2
n = 15
We can find the probability for the given x by taking different values from 0 to 15
the formula can be used:
[tex]\rm _{n}^{}\textrm{C}_x p^xq^{n-x}[/tex]
If we find the value for p(x = 5)
[tex]\rm _{15}^{}\textrm{C}_5 p^5q^{15-5}\\\\\rm _{15}^{}\textrm{C}_5 0.8^50.2^{10}[/tex]⇒ 0.0001
If we find the value for p(x = 3)
[tex]\rm _{15}^{}\textrm{C}_3 0.8^30.2^{12}\\[/tex] ⇒
Similarly, we can find the values for all the trials from 0 to 15 by putting the values of x = 0 to 15.
Thus, the value for p(x = 5) is 0.0001 and the value for p(x = 3) is 0.008699.
Learn more about the sampling distribution here:
https://brainly.com/question/10554762
Simplify: 9h-12h=54-23
A. 3h=-77
B.3h= 31
C.-3h= -31
D.-3h= 31
Answer:
c is the answer
Step-by-step explanation:
-3h = 31
-9h-12h = -3h
54-23= 31
Answer:
[tex]\boxed{C. -3h = 31}[/tex]
Step-by-step explanation:
Hey there!
9h - 12h = 54 - 23
Simplify
-3h = 31
C. -3h = 31
Hope this helps :)
The number of values of xx in the interval [0,5π][0,5π] satisfying the equation 3sin2x−7sinx+2=03sin2x-7sinx+2=0 is/are
Answer:
6
Step-by-step explanation:
Given, 3sin2x−7sinx+2=03sin2x-7sinx+2=0
⇒(3sinx−1)(sinx−2)=0⇒3sinx-1sinx-2=0
⇒sinx=13 or 2⇒sinx=13 or 2
⇒sinx=13 [∵sinx≠2]⇒sinx=13 [∵sinx≠2]
Let sinα=13,0<α<π2,sinα=13,0<α<π2, then sinx=sinαsinx=sinα
now x=nπ+(−1)nα(n∈I)x=nπ+(−1)nα(n∈I)
⇒x=α,π−α,2π+α,3π−α,4π+α,5π−α⇒x=α,π−α,2π+α,3π−α,4π+α,5π−α Are the solution in [0,5π][0,5π]
Hence, required number of solutions are 6
This is the ASVAB question If 500 people are at a concert and 70% are adults. How many children are there?
Answer:
150
Step-by-step explanation:
70% of 500 people are adults and the remainder are children.
30% of 500 are children30*500/100= 150There are 150 children
Lauren is a college sophomore majoring in business. This semester Lauren is taking courses in accounting, economics, management information systems, public speaking, and statistics. The sizes of these classes are, respectively, 375, 35, 45, 25, and 60.Required:Find the mean and the median of the class sizes. What is a better measure of Lauren's "typical class size"—the mean or the median?
Answer:
Mean = 108
Median = 45
The better measure of Lauren's "typical class size" is the Mean
Step-by-step explanation:
1. Calculating mean and median.
The mean is an important measure of central tendency, and it is the average of the measurement of a given set of data. It is calculated as follows:
[tex]Mean\ (\overline {X}) &= \frac{\sum X}{N}[/tex]
where X = individual data sets
N = total number of data
[tex]Mean= \frac{375\; +\ 35\ +\ 45\ +\ 25\ +\ 60}{5} \\=\frac{540}{5} \\= 108[/tex]
The Median divides the measurements into two equal parts, and in order to calculate the median, the distribution has to first be arranged in ascending or descending order. Arranging this series in descending order:
375, 60, 45, 35, 25
The formula for calculating median is given by:
[tex]M_{d} = \frac{N\ +\ 1}{2} th\ data\\\\=\frac{5\ +\ 1}{2}th\ data\\\\=\frac{6}{2} th\ data\\= 3rd\ data\\M_{d} = 45[/tex]
from the list or arranged data in descending order (375, 60, 45, 35, 25), the third data is 45.
Therefore, Median = 45
2. The better measure of typical class size is Mean because the mean depends on all the values of the data sets, whereas the median does not. When there are extreme values (outliers) the effect on the median is very small, whereas it is effectively captured by the mean.
If the area of the square is A(s) = s², find the formula for the area as a function of time, and then determine A(s(3)).
A(t) = 100t^2 + 500t + 625
3,025 square pixels
Answer:
A(t) equals 100t²+ 500t + 625.
The area of the square image after 3 seconds is 3,025 square pixels.
the point p(-3,4) is reflected in the line x +2=0. find the coordinate of the image x
Answer:
(- 1, 4 )
Step-by-step explanation:
The line x + 2 = 0 can be expressed as
x + 2 = 0 ( subtract 2 from both sides )
x = - 2
This is the equation of a vertical line parallel to the y- axis and passing through all points with an x- coordinate of - 2
Thus (- 3, 4 ) is 1 unit to the left of - 2
Under a reflection in the line x = - 2
The x- coordinate will be the same distance from x = - 2 but on the other side while the y- coordinate remains unchanged.
Thus
(- 3, 4 ) → (- 1, 4 )
i will rate you brainliest
Answer:
D) 3/2(X-4)
Step-by-step explanation:
Invert and multiply to get:
3(x+4)/2(x²-16)
factor the bottom
3(x+4)/2(x+4)(x-4)
The (x+4)’s cancel out, and you’re left with
3/2(X-4)
[tex]\dfrac{{x+4\over2}}{{x^2-16\over3}}[/tex]
[tex]=\dfrac{3(x+4)}{2(x+4)(x-4)}=\frac{3}{2(x-4)} [/tex]
but in original fraction, denominator can't be zero so we have to exclude x=±4
do that answer is D
About % of babies born with a certain ailment recover fully. A hospital is caring for babies born with this ailment. The random variable represents the number of babies that recover fully. Decide whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x. Is the experiment a binomial experiment?
Answer:
This is a binomial experiment .
Step-by-step explanation:
As the percent is not indicated the success is the amount of percent (if given) say it is 10 % . So p will be equal to = 0.1 and q will be = 1-0.1= 0.9
and n would be five or any number as a binomial experiment is repeated for a fixed number of times.
And x would take any value of n i.e.
X= 0,1,2,3,4,5
If it is 20 % . So p will be equal to = 0.2 and q will be = 1-0.2= 0.8
The probability is the number of the percent indicated. But as it is not indicated we assume it to be 10 % or 20 % .Or suppose any number for it to be a binomial experiment.
The number of trials n would be fixed .
The success remains constant for all trials.
All trials are independent.
Find the area of the shape shown below.
2
2
nd
2
Need help Plz hurry and answer!!!
Answer:
=6 units squared
Step-by-step explanation:
area=1/2h(a+b)
=1/2×2(4+2)
=6
Which is an example of a situation that is in equilibrium?
A. The amount of air in a room increases quickly when the door is
opened.
B. The amount of money in a bank account never changes
C. The amount of water in a cup decreases as it evaporates
D. A flower slowly grows taller
Answer:B the amount of money in a bank account never changes.
Step-by-step explanation:
Answer:
B. The amount of money in a bank account never changes.
Step-by-step explanation:
Equilibrium is achieved when the state of a reversible reaction of opposing forces cancel each other out. While in a state of equilibrium, the competing influences are balanced out. Imagine a cup with a hole in it being filled with water from a tap. The level of water in this cup would stay the same if the rate at which the water that flows inside is the same as the water that flows outside. Option B will be the correct answer because the amount of money going into the account is at the same rate of money coming out of the account.
Solve the following system of eq ions. Express your answer as an ordered
pair in the format (a,b), with no spaces between the numbers or symbols.
3x + 4y=17
- 4x – 3y= - 18
Answer here
Answer:
(3,2)
Step-by-step explanation:
3x + 4y=17
- 4x – 3y= - 18
Multiply the first equation by 4
4(3x + 4y=17 )
12x +16y = 68
Multiply the second equation by 3
3( - 4x – 3y= - 18)
-12x -9y = -54
Add the new equations together to eliminate x
12x +16y = 68
-12x -9y = -54
-----------------------
7y = 14
Divide by 7
7y/7 = 14/7
y=2
Now find x
3x+4(2) = 17
3x+8 = 17
Subtract 8 from each side
3x+8-8 = 17-8
3x = 9
Divide by 3
x = 3
Fill in the blanks and explain the pattern.
4.25, 4.5,__,__,__,5.5,__,6.0
Answer:
4.25, 4.5, 4.75, 5.00, 5.25, 5.5, 5.75, 6.00
Step-by-step explanation:
it is an arithmetic sequence with common difference 0.25
Dan weighs 205 pounds but is only 5 feet 8 inches tall. Evan is 6 feet tall. How much would you expect Evan to weigh if they have the same height/weight ratio? WILL MARK BRAINLIST
Answer:
Around 217 pounds
Step-by-step explanation:
Let's convert the height into inches.
5 feet 8 = [tex]5\cdot12 + 8 = 60 + 8 = 68[/tex]
6 feet [tex]= 6\cdot12 = 72[/tex].
We can set up a proportion
[tex]\frac{205}{68} = \frac{x}{72}[/tex]
We can use the cross products property to find x.
[tex]205\cdot72=14760\\\\\\14760\div68\approx217[/tex]
Hope this helped!
Answer:
217.0588235 lbs
Step-by-step explanation:
Convert ft inches to inches
5 ft = 5*12 = 60 inches
5 ft 8 inches = 68 inches
6 ft = 6*12 = 72 inches
We can use ratios to solve
205 lbs x lbs
------------- = ----------------
68 inches 72 inches
Using cross products
205 * 72 = 68x
Divide by 68
205 *72/68 = x
217.0588235 lbs
i will rate you brainliest
Answer:
First option
Step-by-step explanation:
Common ratio is greater than 1
Which of the following statements are true? Select all that apply.
If the equation were graphed, it would be a horizontal line.
Both functions have the same slope.
The origin is the y-intercept for the function expressed in the table.
The linear equation does not have a y-intercept.
The table and the graph express an equivalent function.
Answer:
Both functions have the same slope.The origin is the y-intercept for the function expressed in the table.The table and the graph express an equivalent function.Step-by-step explanation:
Both functions have the same slope
The slope is m in the equation; y =mx+c which is the formula for a straight line.
m = change in Y/change in x
Using 2 points: (1,3/4) and ( 4,3) from the table;
= (3 - 3/4) / ( 4 - 1)
= 2.25/3
= 0.75 which is 3/4 which is the same as the slope of the function in the equation.
The origin is the y-intercept for the function expressed in the table.
Slope of function in table is known to be 0.75. Find c to complete equation.
3 = 0.75 ( 4) + c
3 = 3 + c
c = 0
c is the y-intercept. The origin of a line is 0 so if c is 0 then the origin is the y intercept.
The table and the graph express an equivalent function.
The function for the table as calculated is;
y = 0.75x + 0
y = 0.75x
This is the same as the function for the equation for the graph which is y = 3/4x.
Answer:Both functions have the same slope.
The origin is the y-intercept for the function expressed in the table.
The table and the graph express an equivalent function.
Step-by-step explanation:
Compare the linear functions expressed below by data in a table and by an equation.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 6, negative four-thirds, 1, 4. Column 2 is labeled y with entries negative StartFraction 9 Over 2 EndFraction, negative 1, three-fourths, 3. y = three-fourths x.
Which of the following statements are true? Select all that apply.
If the equation were graphed, it would be a horizontal line.
Both functions have the same slope.
The origin is the y-intercept for the function expressed in the table.
The linear equation does not have a y-intercept.
The table and the graph express an equivalent function.
Find the union and interesection of each of the following A={3,6,9,12}, B ={6,8,9}
Answer:
Hello,
The answer would be,
A union B = {3,6,9,12}
and A intersection B= {6,9}
Answer:
[tex]\huge\boxed{ A\ union \ B = \{3,6,8,9,12\}}[/tex]
[tex]\huge\boxed{A\ intersection \ B = \{6,9\}}[/tex]
Step-by-step explanation:
A = {3,6,9,12}
B = {6,8,9}
A∪B = {3,6,9,12} ∪ { 6,8,9} [Union means all of the elements should be included in the set of A∪B]
=> A∪B = {3,6,8,9,12}
Now,
A∩B = {3,6,9,12} ∩ {6,8,9} [Intersection means common elements of the set]
=> A∩B = {6,9}
A number is chosen at random from the set of consecutive natural numbers $\{1, 2, 3, \ldots, 24\}$. What is the probability that the number chosen is a factor of $4!$? Express your answer as a common fraction.
Answer:
[tex]Probability = \frac{1}{3}[/tex]
Step-by-step explanation:
Given
[tex]Set:\ \{1, 2, 3, \ldots, 24\}[/tex]
[tex]n(Set) = 24[/tex]
Required
Determine the probability of selecting a factor of 4!
First, we have to calculate 4!
[tex]4! = 4 * 3 * 2 * 1[/tex]
[tex]4! = 24[/tex]
Then, we list set of all factors of 24
[tex]Factors:\ \{1, 2, 3, 4, 6, 8, 12, 24\}[/tex]
[tex]n(Factors) = 8[/tex]
The probability of selecting a factor if 24 is calculated as:
[tex]Probability = \frac{n(Factor)}{n(Set)}[/tex]
Substitute values for n(Set) and n(Factors)
[tex]Probability = \frac{8}{24}[/tex]
Simplify to lowest term
[tex]Probability = \frac{1}{3}[/tex]
The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 229 customers on the number of hours cars are parked and the amount they are charged.
Number of Hours Frequency Amount Charged 1 16 $ 3 2 34 6 3 51 12 4 39 16 5 34 21 6 16 24 7 9 27 8 30 29 229
a. Convert the information on the number of hours parked to a probability distribution. (Round your answers to 3 decimal places.) Hours Probability 1 2 3 4 5 6 7 8
a-2. Is this a discrete or a continuous probability distribution?
b-1. Find the mean and the standard deviation of the number of hours parked. (Do not round intermediate calculations. Round your final answers to 3 decimal places.)
b-2. How long is a typical customer parked? (Do not round intermediate calculations. Round your final answers to 3 decimal places.)
c. Find the mean and the standard deviation of the amount charged. (Do not round intermediate calculations. Round your final answers to 3 decimal places.)
Answer:
a
See in the explanation
a-2.
Discrete
b-1.
Mean = 4.201
Standard Deviation = 2.069
b-2.
4.201
c.
Mean = 16.153
Standard Deviation = 8.079
Step-by-step explanation:
Given Data:
Number of Hours Frequency Amount Charged
1 16 $3
2 34 6
3 51 12
4 39 16
5 34 21
6 16 24
7 9 27
8 30 29
∑f = 229
a. Convert the information on the number of hours parked to a probability distribution:
The probability is calculated by dividing each frequency by 229. For example probability of Hour 1 is calculated as:
16 / 229 = 0.06987
This way all the hours probabilities are computed. The probability distribution is given below
Hours Probability
1 0.06987
2 0.14847
3 0.2227
4 0.1703
5 0.1485
6 0.0699
7 0.0393
8 0.1310
∑ 1
a-2. Is this a discrete or a continuous probability distribution?
This is a discrete probability distribution as the probability of each hour of between 0 and 1 and the sum of all the probabilities of hours is 1.
b-1. Find the mean and the standard deviation of the number of hours parked.
First multiply each value of Number of hours by the corresponding frequency. Let x represents the number of hours and f represents frequency. Then:
Number of Hours Parked
fx
16
68
153
156
170
96
63
240
Now add the above computed products.
∑fx = 16+68+153+156+170+96+63+240 = 962
Compute Mean:
Now the formula to calculate mean:
Mean = Sum of the value / Number of value
= ∑fx / ∑f
= 962 / 229
Mean = 4.201
Compute Standard Deviation:
Let x be the Number of hours.
Let f be the frequency
First calculate (x-x_bar) where x is each number of hours and x_bar is mean. The value of x_bar i.e. [tex]\frac{}{x}[/tex] = 4.201
For example for the Hour = 1 , and mean = 4.201
Then (x-[tex]\frac{}{x}[/tex]) = 1 - 4.201 = -3.201
So calculating this for every number of hour we get:
(x-[tex]\frac{}{x}[/tex])
-3.201
-2.201
-1.201
-0.201
0.799
1.799
2.799
3.799
Next calculate (x-[tex]\frac{}{x}[/tex])². Just take the squares of the above column (x-[tex]\frac{}{x}[/tex])
For example the first entry of below calculation is computed by:
(x-[tex]\frac{}{x}[/tex])² = (-3.201 )² = 10.246401
(x-[tex]\frac{}{x}[/tex])²
10.246401
4.844401
1.442401
0.040401
0.638401
3.236401
7.834401
14.432401
Next multiply each entry of (x-[tex]\frac{}{x}[/tex])² with frequency f. For example the first entry below is computed by:
(x-[tex]\frac{}{x}[/tex])² * f = 10.246401 * 16 = 163.942416
(x-[tex]\frac{}{x}[/tex])² * f
163.942416
164.709634
73.562451
1.575639
21.705634
51.782416
70.509609
432.97203
Now the formula to calculate standard deviation is:
S = √∑(x-[tex]\frac{}{x}[/tex])² * f/n
Here
n = ∑f = 229
∑(x-[tex]\frac{}{x}[/tex])² * f is the sum of all entries of (x-[tex]\frac{}{x}[/tex])² * f
∑(x-[tex]\frac{}{x}[/tex])² * f = 980.759829
S = √∑(x-[tex]\frac{}{x}[/tex])² * f/n
= √980.759829 / 229
= √4.2827940131004
= 2.0694912449924
S = 2.069
b-2) How long is a typical customer parked?
That is the value of mean calculated in part b-1. Hence
Typical Customer Parked for 4.201 hours
c) Find the mean and the standard deviation of the amount charged.
First multiply each value of Amount Charged by the corresponding frequency. Let x represents the number of hours and f represents frequency. Then:
fx
48
204
612
624
714
384
243
870
Now add the above computed products.
∑fx = 48+204+612+624+714+384+243+870 = 3699
Compute Mean:
Now the formula to calculate mean:
Mean = Sum of the value / Number of value
= ∑fx / ∑f
= 3699 / 229
Mean = 16.153
Compute Standard Deviation:
Let x be the Amount Charged.
Let f be the frequency.
First calculate (x-x_bar) where x is each value of Amount charged and x_bar is mean. The value of x_bar i.e. [tex]\frac{}{x}[/tex] = 16.153
For example for the Amount Charged = 3 , and mean = 16.153
Then (x-[tex]\frac{}{x}[/tex]) = 3 - 16.153 = -13.153
So calculating this for every number of hour we get:
(x-[tex]\frac{}{x}[/tex])
-13.153
-10.153
-4.153
-0.153
4.847
7.847
10.847
12.847
Next calculate (x-[tex]\frac{}{x}[/tex])². Just take the squares of the above column (x-[tex]\frac{}{x}[/tex])
For example the first entry of below calculation is computed by:
(x-[tex]\frac{}{x}[/tex])² = (-13.153 )² = 173.001409
(x-[tex]\frac{}{x}[/tex])²
173.001409
103.083409
17.247409
0.023409
23.493409
61.575409
117.657409
165.045409
Next multiply each entry of (x-[tex]\frac{}{x}[/tex])² with frequency f. For example the first entry below is computed by:
(x-[tex]\frac{}{x}[/tex])² * f = 173.001409 * 16 =
(x-[tex]\frac{}{x}[/tex])² * f
2768.022544
3504.835906
879.617859
0.912951
798.775906
985.206544
1058.916681
4951.36227
∑(x-[tex]\frac{}{x}[/tex])² = 14947.65066
Now the formula to calculate standard deviation is:
S = √∑(x-[tex]\frac{}{x}[/tex])² * f/n
Here
n = ∑f = 229
∑(x-[tex]\frac{}{x}[/tex])² * f is the sum of all entries of (x-[tex]\frac{}{x}[/tex])² * f
∑(x-[tex]\frac{}{x}[/tex])² * f = 14947.65066
S = √∑(x-[tex]\frac{}{x}[/tex])² * f/ ∑f
= √65.273583668122
= 8.0792068712295
S = 8.079
Evaluate cosA/2 given cosA=-1/3 and tanA >0
Answer:
[tex]\bold{cos\dfrac{A}{2} = -\dfrac{1}{\sqrt3}}[/tex]
Step-by-step explanation:
Given that:
[tex]cosA=-\dfrac{1}3[/tex]
and
[tex]tanA > 0[/tex]
To find:
[tex]cos\dfrac{A}{2} = ?[/tex]
Solution:
First of all,we have cos value as negative and tan value as positive.
It is possible in the 3rd quadrant only.
[tex]\dfrac{A}{2}[/tex] will lie in the 2nd quadrant so [tex]cos\dfrac{A}{2}[/tex] will be negative again.
Because Cosine is positive in 1st and 4th quadrant.
Formula:
[tex]cos2\theta =2cos^2(\theta) - 1[/tex]
Here [tex]\theta = \frac{A}{2}[/tex]
[tex]cosA =2cos^2(\dfrac{A}{2}) - 1\\\Rightarrow 2cos^2(\dfrac{A}{2}) =cosA+1\\\Rightarrow 2cos^2(\dfrac{A}{2}) =-\dfrac{1}3+1\\\Rightarrow 2cos^2(\dfrac{A}{2}) =\dfrac{2}3\\\Rightarrow cos(\dfrac{A}{2}) = \pm \dfrac{1}{\sqrt3}[/tex]
But as we have discussed, [tex]cos\dfrac{A}{2}[/tex] will be negative.
So, answer is:
[tex]\bold{cos\dfrac{A}{2} = -\dfrac{1}{\sqrt3}}[/tex]
An octagonal pyramid ... how many faces does it have, how many vertices and how many edges? A triangular prism ... how many faces does it have, how many vertices and how many edges? a triangular pyramid ... how many faces does it have, how many vertices and how many edges?
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Hope this can help you.
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Find the intervals on which the function f(x) = ax2 + bx + c (where "a" doesn't = 0) is increasing and decreasing. Describe the reasoning behind your answer.
Answer:
Step-by-step explanation:
Given that:
[tex]\mathtt{f(x) = ax^2 + bx + c}[/tex]
The derivative of the function of x is [tex]\mathtt{f'(x) = 2ax + b}[/tex]
Thus; f(x) is increasing when f'(x) > 0
f(x) is decreasing when f'(x) < 0
i.e
f'(x) > 0 , when b > 0 and a < 0
∴
2ax + b < 0
2ax < - b
[tex]\mathtt{x < \dfrac{-b}{2a}}[/tex]
f'(x) < 0 , when b < 0 and a > 0
2ax + b > 0
2ax > - b
[tex]\mathtt{x > \dfrac{-b}{2a}}[/tex]
Give the domain and range of each relation using set notation
Answer:
See below.
Step-by-step explanation:
First, recall the meanings of the domain and range.
The domain is the span of x-values covered by the graph.
And the range is the span of y-values covered by the graph.
1)
So, we have here an absolute value function.
As we can see, the domain of the function is all real numbers because the graph stretches left and right infinitely. Therefore, the domain of the function is:
[tex]\{x|x\in\textbb{R}\}[/tex]
(You are correct!)
For the range, notice how the function stops at y=7. The highest point of the function is (-2,7). There graph doesn't and won't ever reach above y=7. Therefore, the range of the graph is all values less than or equal to 7. In set notation, this is:
[tex]\{y|y\leq 7\}[/tex]
2)
We have here an ellipse.
First, for the domain. We can see the the span of x-values covered by the ellipse is from x=-4 to x=6. In other words, the domain is all values in between these two numbers and including them. Therefore, we can write it as such:
[tex]-4\leq x\leq 6[/tex]
So x is all numbers greater than or equal to -4 but less than or equal to 6. This describes the span of x-values. In set notation, this is:
[tex]\{x|-4\leq x\leq 6\}[/tex]
For the range, we can see that the span of x values covered by the ellipse is from y=-5 to y=1. Just like the domain, we can write it like this:
[tex]-5\leq y\leq 1[/tex]
This represents all the y-values between -5 and 1, including -5 and 1.
In set notation, thi is:
[tex]\{y|-5\leq y\leq 1\}[/tex]
Can somebody help me please?
Answer:
[tex]\boxed{x \geq 353}[/tex]
Step-by-step explanation:
Hey there!
Info Given
- Dot is solid
- Line goes to the right
- Dot is at 353
So by using the given info we can conclude that the inequality is,
x ≥ 353
Hope this helps :)
Answer:
Inequality: 100 + 50w ≥ 18000
What to put on graph: w ≥ 358
The price of a technology stock was $ 9.56 yesterday. Today, the price rose to $ 9.69 . Find the percentage increase. Round your answer to the nearest tenth of a percent.
Answer and Step-by-Step explanation:
% increase = 100 x [(new price) - (original price)] / (original price)] = 100 (9.67 - 9.56) / 9.56
% increase ≅ 1.2% (to the nearest tenth)
