Answer:
It will take them both 24 minutes to mow the lawn if they are working together.
Step-by-step explanation:
Given that Sam can mow a lawn in 40 minutes, and Melissa can mow the same lawn in 80 minutes, to determine how long does it take for both Sam and Melissa to mow the lawn if they are working together, the following calculation must be performed:
1/40 + 1/60 = 1 / X
3X + 2X = 120
X = 120/5
X = 24
Thus, it will take them both 24 minutes to mow the lawn if they are working together.
A random sample of n1 = 296 voters registered in the state of California showed that 146 voted in the last general election. A random sample of n2 = 215 registered voters in the state of Colorado showed that 127 voted in the most recent general election. Do these data indicate that the population proportion of voter turnout in Colorado is higher than that in California? Use a 5% level of significance.
Answer:
The p-value of the test is 0.0139 < 0.05, which means that these data indicates that the population proportion of voter turnout in Colorado is higher than that in California.
Step-by-step explanation:
Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
California:
Sample of 296 voters, 146 voted. This means that:
[tex]p_{Ca} = \frac{146}{296} = 0.4932[/tex]
[tex]s_{Ca} = \sqrt{\frac{0.4932*0.5068}{296}} = 0.0291[/tex]
Colorado:
Sample of 215 voters, 127 voted. This means that:
[tex]p_{Co} = \frac{127}{215} = 0.5907[/tex]
[tex]s_{Co} = \sqrt{\frac{0.5907*0.4093}{215}} = 0.0335[/tex]
Test if the population proportion of voter turnout in Colorado is higher than that in California:
At the null hypothesis, we test if it is not higher, that is, the subtraction of the proportions is at most 0. So
[tex]H_0: p_{Co} - p_{Ca} \leq 0[/tex]
At the alternative hypothesis, we test if it is higher, that is, the subtraction of the proportions is greater than 0. So
[tex]H_1: p_{Co} - p_{Ca} > 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the two samples:
[tex]X = p_{Co} - p_{Ca} = 0.5907 - 0.4932 = 0.0975[/tex]
[tex]s = \sqrt{s_{Co}^2+s_{Ca}^2} = \sqrt{0.0291^2+0.0335^2} = 0.0444[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{0.0975 - 0}{0.0444}[/tex]
[tex]z = 2.2[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a difference above 0.0975, which is 1 subtracted by the p-value of z = 2.2.
Looking at the z-table, z = 2.2 has a p-value of 0.9861.
1 - 0.9861 = 0.0139.
The p-value of the test is 0.0139 < 0.05, which means that these data indicates that the population proportion of voter turnout in Colorado is higher than that in California.
Given a set of data that is skewed-left, there is at least _____ % of the data within 2 standard deviations.
Answer:
75
Step-by-step explanation:
For non-normal distributions, we use Chebyshev's Theorem.
Chebyshev Theorem
The Chebyshev Theorem states that:
At least 75% of the measures are within 2 standard deviations of the mean.
At least 89% of the measures are within 3 standard deviations of the mean.
An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].
In this question:
Within 2 standard deviations of the mean, so 75%.
A teacher calculates for the test grades in
Class A, mean = 32 and sd = 4
Class B, mean = 32 and sd = 8
a. If the teacher was going to guess what any student in his/her class would earn, what is the best score
to guess?
b. Which of the classes has more consistency in their scores? Why?
Answer:
a. best score to guess would be 33
b. Standard deviation simplifies the square root of the mean so makes it closer to 1 has more consistency as the mean of 32 when squared is sqrt 32 is Class A as class a = 4 and is closer to 5.65685425
as 5.65685425^2 = 32
Step-by-step explanation:
If you are comparing two normally-distributed variables on the same measurement scale then yes, you can regard the standard deviation as an indicator of how reliable the mean is--the smaller the standard deviation, the better able you are to "zero in" on the actual population mean.
a. proofs;
We find 32/6 = 5.333 and 32/5 = 6.4 and 6.4 is closer to both sd 4 and 8 than 5.33 is. As 6.4 it is closer to 6
But when we use 33/6 = 5.5 and therefore shows close range 6
therefore the two sd proves it is slightly high 32 score average for both classes A + B when joined and high 32 = 33 mean when classes A+B are joined or you could say 32/8 = 4 is class B becomes lower tests scores as 32/4 = 8 of class A that has higher test scores.
In this exercise we have to use probability and statistics to organize the students' grades, so we have:
A) best score is 33
B) Class A
In the first part of the exercise we have to analyze the grades of each class, like this:
A)Class A: 32/4
Class B: 32/8
Dividing each of them we have:
[tex]32/4=8 \\32/8=4[/tex]
B) With the information given above, we can say that the best class is A.
See more about statistics at brainly.com/question/10951564
Can someone please do these three and number them? -Numbers: 10,11,12-
Answer:
10. Option: c11. Option: a12. Option: aCan someone please help me?
you have to read the bottom link for the answer key
Find the range from the ordered pair {(1, 2), (2, 3), (3, 4), (4, 5)}
Answer:
Range { 2,3,4,5}
Step-by-step explanation:
The range is the output values
Range { 2,3,4,5}
Does anyone know these?
Answer:
1 = - 4 - 14 √3
2 = 9 - 11 √3
Step-by-step explanation:
Question 1
(-4√3 + 2)(√3 + 4)
Apply FOIL method
= (-4√3) √3 + (-4√3) . 4 + 2 √3 + 2 . 4
Apply minus-plus rules: + (-a) = -a
= -4 √3 √3 - 4 . 4 √3 + 2 √3 + 2 . 4
Simplify
= - 4 - 14 √3
Question 2
(-3 + √3)(1 + 4 √3)
Apply FOIL method
= (-3) . 1 + (-3) . 4 √3 + √3 . 1 + √3 . 4 √3
Apply minus-plus rules: + (-a) = -a
= -3 . 1 - 3 . 4 √3 + 1 . √3 + 4 √3 √3
Simplify
= 9 - 11 √3
a study of patients who were overweight found that 53% also had elevated blood pressure. If 3 overweight patients are selected find the probability that all three have elevated blood pressure
Answer:
14.8%
Step-by-step explanation:
53/100*53/100*53/100
The director of research and development is testing a new medicine. She wants to know if there is evidence at the 0.02 level that the medicine relieves pain in more than 384 seconds. For a sample of 41 patients, the mean time in which the medicine relieved pain was 387 seconds. Assume the population standard deviation is 23. Find the P-value of the test statistic.
Answer:
The p-value of the test statistic is 0.2019.
Step-by-step explanation:
Test if there is evidence at the 0.02 level that the medicine relieves pain in more than 384 seconds.
At the null hypothesis, we test if it relieves pain in at most 384 seconds, that is:
[tex]H_0: \mu \leq 384[/tex]
At the alternative hypothesis, we test if it relieves pain in more than 384 seconds, that is:
[tex]H_1: \mu > 384[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
384 is tested at the null hypothesis:
This means that [tex]\mu = 384[/tex]
For a sample of 41 patients, the mean time in which the medicine relieved pain was 387 seconds. Assume the population standard deviation is 23.
This means that [tex]n = 41, X = 387, \sigma = 23[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{387 - 384}{\frac{23}{\sqrt{41}}}[/tex]
[tex]z = 0.835[/tex]
P-value of the test:
The p-value of the test is the probability of finding a sample mean above 387, which is 1 subtracted by the p-value of z = 0.835.
Looking at the z-table, z = 0.835 has a p-value of 0.7981.
1 - 0.7981 = 0.2019
The p-value of the test statistic is 0.2019.
The wholesale price of 6 oz plastic bottles is 6 cents how many plastic bottles can be purchased for $98.41
Answer:
1640
Step-by-step explanation:
Take the total amount and divide by the amount for one
Make sure to write 6 cent in dollar form (.06)
98.41 / .06
1640.1666
Round down since we need to buy whole bottles
1640
What is the value of the expression (2x + y) (2x - y) when x = 4 and y = -5?
Answer:
39
Step-by-step explanation:
1. (2(4)-5)(2(4)+5)
2.(3)(13)
3.39
Answer:
Step-by-step explanation:
This is a difference of squares question. You should 64 = 25 = 39 Let's see if that happens.
Difference of squares
(2x - y) ( 2x + y) = 4x^2 - y^2
4(4)^2 - (5)^2
64 - 25 = 39
Now do the question exactly as it is written.
(2*4 - -5)(2*4 + -5)
(8 +5)(8 - 5)
3 * 13
39
They really do give the same answer.
20 students were asked “How many pets do you have in your household?” and the following data was collected:
2 1 0 3 1 2 1 3 4 0
0 2 2 0 1 1 0 1 0 1
Select the type of the data ?
Discrete
Continuous
Categorical
Qualitative
NO FAKE ANS
FRIST MARKED BRAINLIST
CHOOSE ONE ANS
Answer:
qualitative
Step-by-step explanation:
bcos the question is in quality format
Answer:
we are armysss!!!!\
hiiiiiiiiii
yoooooooo
heyyyyyy
brainlist meeee!
Michael drove 210 miles in 3 1/2. Jordan drove 330 miles in 6 hours. Which is an accurate comparison of the rates at which the two people drove?
Michael = 210 / 3.5 = 60 miles per hour
Jordan = 330/ 6 =55 miles per hour
Jordan drove 5 miles per hour slower than michael
Select the correct statement about what data scientists do during the Data Preparation stage.
a. During the Data Preparation stage, data scientists define the variables to be used in the model.
b. During the Data Preparation stage, data scientists determine the timing of events.
c. During the Data Preparation stage, data scientists aggregate the data and merge them from different sources.
d. During the Data Preparation stage, data scientists identify missing data.
e. All of the above statements are correct.
Answer:
e. All of the above statements are correct.
Option e is correct. All of the above statements are correct.
What is Data science?Data science is an interdisciplinary academic field that uses statistics, scientific computing, scientific methods, processes, algorithms and systems to extract or extrapolate knowledge and insights from noisy, structured and unstructured data
Data Scientist makes value out of data, he is expert in various tools and technologies like machine learning, deep learning, artificial intelligence and he solve business problems by presenting a model to predict business future.
During data preparation, data scientists and DBAs aggregate the data and merge them from different sources. During data preparation, data scientists and DBAs define the variables to be used in the model.
Hence, All of the above statements are correct, Option e is correct.
To learn more on Data science click:
https://brainly.com/question/20815848
#SPJ5
find m∠H
What does m∠H happened to equal
Answer:
[tex]m\angle H = 30^o[/tex]
Step-by-step explanation:
Given
See attachment
Required
Find [tex]m\angle H[/tex]
To calculate [tex]m\angle H[/tex], we make use of:
[tex]\cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]
So, we have:
[tex]\cos(H) = \frac{GH}{HI}[/tex]
This gives:
[tex]\cos(H) = \frac{10\sqrt3}{20}[/tex]
[tex]\cos(H) = \frac{\sqrt3}{2}[/tex]
Take arccos of both sides
[tex]m\angle H = cos^{-1}(\frac{\sqrt3}{2})[/tex]
[tex]m\angle H = 30^o[/tex]
The theoretical mean of a distribution is also known as its ______________.
Answer:
skewness
Step-by-step explanation:
Average.
The average of a set of observations is the most important and useful measure of statistics and is a position measure, as it shows the positions of the numbers to which it refers. The average value is involved in several types of statistics and is examined in almost all statistical distributions. It is generally defined as the sum of the observations by their number. That is, it is the mathematical operation of finding the "mean distance" between two or more numbers.
Learn more about averages in https://brainly.com/question/22390452
Which graph represents y = |xl?
A
B
C
D
Answer:
B
Step-by-step explanation:
The equation represented in the question is the parent absolute value question. If you know the different parent functions, then the answer is obvious because absolute value equations always form a V. However, if you do not do this then you can create a table and plugin values. Plugin numbers like 0, -1, and 1 for X and solve for Y. Finally, graph these points and see what graph best fits. If needed you can also plug in more points.
Answer:
B.
Step-by-step explanation:
I got it correct on the warm up
Suppose 50.7 liters of water came out of a faucet today. If 2.6 liters of water come out each minute, for how many minutes was the faucet on?
i’ll make brainliest
look at the photo and check my work?
also tell me the answer to the ones i didn’t do
thanks :)
A trough has ends shaped like isosceles triangles, with width 2 m and height 5 m, and the trough is 18 m long. Water is being pumped into the trough at a rate of 8 m3/min. At what rate (in m/min) does the height of the water change when the water is 2 m deep
9514 1404 393
Answer:
5/9 m/min
Step-by-step explanation:
The depth of the water is 2/5 of the depth of the trough, so the width of the surface will be 2/5 of the width of the trough:
2/5 × 2 m = 4/5 m
Then the surface area of the water is ...
A = LW = (18 m)(4/5 m) = 14.4 m²
The rate of change of height multiplied by the area gives the rate of change of volume:
8 m³/min = (14.4 m²)(h')
h' = (8 m³/min)/(14.4 m²) = 5/9 m/min
What is the value of y?
9514 1404 393
Answer:
(d) 2
Step-by-step explanation:
The parallel lines divide the transversals proportionally, so we have ...
3y/3 = 2y/y
y = 2 . . . . . . . . . simplify (assuming y ≠ 0)
Find the slope of the line #67
Solve this equation for x. Round your answer to the nearest hundredth. 0.77 = log x
Answer:
x ≈ 5.89
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra II
Exponential to Logarithmic: [tex]\displaystyle b^m=x \rightarrow log_bx=m[/tex]Step-by-step explanation:
Step 1: Define
Identify
0.77 = log(x)
Step 2: Solve for x
[Equality Property] Raise both sides to the 10th power: [tex]\displaysytle 10^{0.77} = 10^{logx}[/tex]Simplify: [tex]\displaysytle x = 10^{0.77}[/tex]Evaluate: [tex]\displaysytle x = 5.88844[/tex]An industrial psychologist consulting with a chain of music stores knows that the average number of complaints management receives each month throughout the industry is 4, but the variance is unknown. Nine of the chain's stores were randomly selected to record complaints for one month; they received 2, 4, 3, 5, 0, 2, 5, 1, and 5 complaints. Using the .05 significance level, is the number of complaints received by the chain different from the number of complaints received by music stores in general?
1. Use the five steps of hypothesis testing.
2. Sketch the distributions involved
3. Explain the logic of what you did to a person who is familiar with hypothesis testing, but knows nothing about t tests of any kind. Be sure to explain how this problem differs from a problem with a known population variance and a single sample.
Answer: See explanation
Step-by-step explanation:
1. Use the five steps of hypothesis testing.
Step 1: The aim of the research is to conduct the five steps of hypothesis testing.
Step 2:
Null hypothesis: H0 u= 4
Population mean: H1 u = 4
Alternate hypothesis: u ≠ 4
Population mean: u ≠ 4
Step 3 and step 4 are attached.
Step 5: Based on the calculation, the calculated value of t is less than the t critical value, therefore, the null hypothesis will be failed to be rejected.
2. Sketch the distributions involved
This has been attached.
3. Explain the logic of what you did to a person who is familiar with hypothesis testing, but knows nothing about t tests of any kind.
The distribution is "t".
The means is tested by using T-test.
Chi-square is used to test the single variance.
A group of 120 students were surveyed about their interest in a new International Studies program. Interest was measured in terms of high, medium, or low. 30 students responded high interest; 50 students responded medium interest; 40 students responded low interest. What is the relative frequency of students with high interest? A. 30% B. 36.4% C. 25% D. Cannot be determined. Group of answer choices
Answer:
Option C (25%) is the correct answer.
Step-by-step explanation:
Given:
Number of students,
= 120
Students responded high interest,
= 30
Students responded medium interest,
= 50
Students responded low interest,
= 40
Now,
The relative frequency will be:
= [tex]\frac{30}{120}[/tex]
= [tex]0.25[/tex]
or,
= [tex]25[/tex]%
57 117find x triangle
Answer:
60
Step-by-step explanation:
x = 180 - [ 57 + ( 180 - 117 ) ]
= 180 - [ 57 + 63 ]
= 180 - 120
x = 60
HELPPPP
what is this
Answer:
Pls be specific with your question
annual cost of 35,000 expected to save 40,000 during the first year how many months will the take to recover investment
Answer:
500000
Step-by-step explanation:
Perimeter (numerical)
Answer:
270 m
Step-by-step explanation:
Add up all the sides
P = 19 +18.8+18.8 +18.8+18.8+40.8+19+40.8+18.8+18.8+18.8+18.8
P = 270 m
Draw clearly the graph of the linear equation. y=1/2x, where x= (-4 -2, 0, 2, 4)
Answer:
(in attachment)
Step-by-step explanation:
you can find the points by inputting the x-values into the equation to solve for the y-values, then connecting the plotted points to create the line.
When x=-4
y=1/2(-4)
y=-2
(-4,-2)
Repeat for all values.
