Certify Completion Icon Tries remaining:2 A town recently dismissed 10 employees in order to meet their new budget reductions. The town had 7 employees over 50 years of age and 18 under 50. If the dismissed employees were selected at random, what is the probability that exactly 5 employees were over 50
Answer:
0.055 = 5.5% probability that exactly 5 employees were over 50.
Step-by-step explanation:
The employees are removed from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[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]
In this question:
7 + 18 = 25 employees, which means that [tex]N = 25[/tex]
7 over 50, which means that [tex]k = 7[/tex]
10 dismissed, which means that [tex]n = 10[/tex]
What is the probability that exactly 5 employees were over 50?
This is P(X = 5). So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 5) = h(5,25,10,7) = \frac{C_{7,5}*C_{18,5}}{C_{25,10}} = 0.055[/tex]
0.055 = 5.5% probability that exactly 5 employees were over 50.
write the equation of a line of a line passing through the points (3,1) and (6,3).
Answer:
i think its 2 1
Step-by-step explanation:
Answer:
y =2/3x-1
Step-by-step explanation:
First find the slope
m = ( y2-y1)/(x2-x1)
= ( 3-1)/ (6-3)
= 2/3
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = 2/3x +b
Using a point
3 = 2/3(6)+b
3 = 4+b
3-4 =b
-1=b
y =2/3x-1
a rectangle has an area of 186m2
one of the sides is 3m in length
work out the perimeter of the rectangle
seriously need help
Step-by-step explanation:
here is the ans
the perimeter= 130m
hope so this might help you
Paul baked 208 brown loaves. If the ratio of white loaves to brown loaves is 3:2, how many loaves did he bake in total?
Paul baked 520
loaves.
The owner of a restaurant is placing an order for bread.
On Friday there were 300 customers in the restaurant and 100 bread rolls were served.
On Saturday he is expecting 540 customers.
What would be a good estimate of how many bread rolls should he order? I
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Answer:
A. Total=520 loaves
B. Estimate= 180 rolls
Step-by-step explanation:
7(x-9y) need an answer
Answer:
7x - 63y
Step-by-step explanation:
Given
7(x - 9y) ← multiply each term in the parenthesis by 7
= 7x - 63y
A university professor asked his class of 42 students when they had studied for his class the previous weekend. There responses were. please answer part a, b and c
ANSWERS:
a) 16 students
b) 25 students
c) 2 students
STEP BY STEP:
There are 42 students in total. This question can be solved by "Principal of Inclusion and Exclusion"
Question a)
The students that studied on Sunday in total with overlaps is 30. To figure out the students that ONLY studied on Sunday you need to first minus the overlaps in the combos:
the combos:
3, 10, 6, 2
Since the last combo included all of the other dates, we need to minus it:
1, 8, 4, 2
Now we can use the total of Sunday and minus the combos that includes Sunday:
30 - (4 + 2 + 8) = 16 students
Question b)
To figure out all the students that only studied on ONE day, not 2 not 3, just one day. We need to figure out the students that studied for Saturday and Friday using the same method before for figuring out Sunday:
Friday: 9 - 4 - 1 -2 = 2 students
Saturday: 18 - 1 - 2- 8 = 7 students
and now add them all together: 2 + 7 + 16 = 25 students
That is the total number of students that studied on one day.
Question c)
Now for the numbers of students that didn't study... We can just use the total to minus everything else!
42 - (25 + 1 + 4 + 8 + 2) = 2 students!!!
And thats all done! If you still don't get it, please ask!
...............................................................
Under which transformation can the image be a different size than the original
figure?
A. translation
B. rotation
C. dilation
D. reflection
C. Dilation.
Dilation can resize the image.
Translation will shift the imagine's position but won't change its actual size.
Rotation will mangle with image's orientation but also won't change its size.
Reflection is just a type of rotation which as established, also won't change its size.
Hope this helps.
(c³d)a(cd⁷)a
Simplify
Answer:
= c^4 d^8 a^2
Step-by-step explanation:
Apply exponent rule: aa= a^2
= c^3 da^2 cd^7
= c^4 da^2 d^7
= c^4 d^8 a^2
Anthony steps on a bathroom scale that records his weight at 195 pounds. He immediately steps back onto the same scale, which records his weight at 205 pounds. It is MOST accurate to describe these scales as:
Answer:
Moving upwards with an acceleration.
Step-by-step explanation:
weight of the person = 195 pounds
Apparent weight = 205 pounds
As the weight increases so the scale is moving upwards with some acceleration.
The scale is in elevator which is moving upwards.
Engineers are designing a large elevator that will accommodate 44 people. The maximum weight the elevator can hold safely is 8228 pounds. According to the National Health Statistics Reports, the weights of adult U.S. men have mean 186 pounds and standard deviation 60 pounds, and the weights of adult U.S. women have mean 157 pounds and standard deviation 69 pounds.
a. If 44 people are on the elevator, and their total weight is 8228 pounds, what is their average weight?
b. If a random sample of 44 adult men ride the elevator, what is the probability that the maximum safe weight will be exceeded?
c. If a random sample of 44 adult women ride the elevator, what is the probability that the maximum safe weight will be exceeded?
Answer:
a) Their average weight is of 187 pounds.
b) 0.4562 = 45.62% probability that the maximum safe weight will be exceeded.
c) 0.002 = 0.2% probability that the maximum safe weight will be exceeded
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
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.
a. If 44 people are on the elevator, and their total weight is 8228 pounds, what is their average weight?
8228/44 = 187
Their average weight is of 187 pounds.
b. If a random sample of 44 adult men ride the elevator, what is the probability that the maximum safe weight will be exceeded?
For men, we have that [tex]\mu = 186, \sigma = 60[/tex]
Sample of 44 means that [tex]n = 44, s = \frac{60}{\sqrt{44}}[/tex]
This probability is 1 subtracted by the p-value of Z when X = 187. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{187 - 186}{\frac{60}{\sqrt{44}}}[/tex]
[tex]Z = 0.11[/tex]
[tex]Z = 0.11[/tex] has a p-value of 0.5438.
1 - 0.5438 = 0.4562
0.4562 = 45.62% probability that the maximum safe weight will be exceeded.
c. If a random sample of 44 adult women ride the elevator, what is the probability that the maximum safe weight will be exceeded?
For women, we have that [tex]\mu = 157, \sigma = 69[/tex]
Sample of 44 means that [tex]n = 44, s = \frac{69}{\sqrt{44}}[/tex]
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{187 - 157}{\frac{69}{\sqrt{44}}}[/tex]
[tex]Z = 2.88[/tex]
[tex]Z = 2.88[/tex] has a p-value of 0.998.
1 - 0.998 = 0.002.
0.002 = 0.2% probability that the maximum safe weight will be exceeded
I need help.
You are interested in finding a 95% confidence interval for the average commute that non-residential students have to their college. The data below show the number of commute miles for 12 randomly selected non-residential college students. Round answers to 3 decimal places where possible.
Answer:
(11.847 ; 15.813)
Step-by-step explanation:
We are given 12 samples which are :
8, 20, 20, 11, 18, 12, 6, 5, 7, 22, 12, 25
We use a T-distribution to find the confidence interval since the sample size. is small, n < 30
Using a calculator :
The sample mean, xbar = 13.83
Sample standard deviation, s = 6.87
The confidence interval, C.I
C.I = xbar ± Tcritical * s/√n)
Tcritical at 95%, df = n - 1, 12 - 1 = 11
Tcritical(0.05, 11) = 2.20
Hence,
C.I = 13.83 ± 2.20(6.87/√12)
C.I = 13.83 ± 1.9831981
C. I = (13.83 - 1.983 ; 13.83 + 1.983)
C. I = (11.847 ; 15.813)
Matthew Travels 42/50 Meters In 26/30 Minutes. Find The Speed of Mathew In Meters Per Second.
Answer:
Matthew travels 0.0161 meters per second.
Step-by-step explanation:
Given that Matthew travels 42/50 meters In 26/30 minutes, to find the speed of Mathew in meters per second the following calculation must be performed:
42/50 = 0.84
26/30 = 0.86
0.86 x 60 = 52
0.84 meters in 52 seconds
0.84 / 52 = 0.01615
Therefore, Matthew travels 0.0161 meters per second.
Which ratio expresses the scale used to create this drawing?
1 square=10 yards
Answer:
option B
Step-by-step explanation:
option B
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A television stand at Wiles' Discount Mart is $187, and the sales tax is 6%. What is the amount of tax to be paid for the TV?
Answer:
$11.22
Step-by-step explanation:
100% = 187
1% = 187/100 = $1.87
6% = 1%×6 = 1.87×6 = $11.22
Answer:
In this case, you need to calculate the 6% of the price, which is 187 $.
We only need to multiply the price (187) by the percentage (6%):
187 * 0.06 = 11.22
So the tax would be $11.22
PLEASE i need the answers!!!!!!!!!
I have no time please if you know the answer please tell MEEE!!!!!!!!!!!
Answer:
5x^2(2-3x)
(n+4)(x+y)
Step-by-step explanation:
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]
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
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
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
HELPPPP
what is this
Answer:
Pls be specific with your question
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.
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?
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.
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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.
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 :)
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.
wrote the terms below.
–8, –4, 0, 4, 8, 12
What do these terms represent?
an arithmetic series
an arithmetic sequence
a geometric series
a geometric sequence
Answer:
an arithmetic sequence
Step-by-step explanation:
an arithmetic series is wrong also heres an example i found of an arithmetic sequence
The terms in the given sequence represents an arithmetic sequence.
What is Arithmetic Sequence?Arithmetic sequence is a sequence of numbers where the numbers are arranged ion a definite order such that the difference of two consecutive numbers is a constant. This constant of difference is called common difference which is commonly denoted by the letter 'd'.
Given sequence of numbers is,
-8, -4, 0, 4, 8, 12, ......
We have to find which sequence does it represent.
This is not a series since they are not represented as the sum.
If the sequence is a geometric sequence, then the ratio of consecutive numbers will be same.
If it is arithmetic sequence, then the difference of consecutive numbers will be same.
Here, ratio is not same.
Difference are same.
-4 - -8 = 4, 0 - -4 = 4, 4 - 0 = 4, 8 - 4 = 4, ........
Common difference is 4.
Hence it is an arithmetic sequence.
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Answer this please~!!!!
Answer:
12
Step-by-step explanation:
113.04=3.14 x 3^2 x h/3
