Answer:
C
Step-by-step explanation:
Given
[tex]\frac{x}{3}[/tex] < 5 ( multiply both sides by 3 to clear the fraction )
x < 15 → C
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]%
Which of the following tables represent valid functions?
Answer:
Step-by-step explanation:
A relation may or may not represent a function.
Table (a), (c) and (d) represent a function
The tables represent a relation
For a relation to be a function, then:
The y values must have unique (or distinct) x-values.
From the list of tables, we have the following observations
All y values in table (a), have different corresponding x valuesy values 3 and 6 in table (b), point to the same x value (2)All y values in table (c), have different corresponding x valuesAll y values in table (d), have different corresponding x valuesHence, all the tables represent a valid function, except table (b)
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Which of these are related functions. Plato
Answer:
◦•●◉these are related functions
Consider points a, b, and c in the graph. Determine which of these points is relative minima on the interval x = –1 and x = –2 in the graph.
Answer:
C.
Step-by-step explanation:
1) note, the point "а" belongs to the given interval only, then
2) the correct answer is C) a.
Answer:
as we can see here point {\color{Red}a} lies on the interval (-2, -1)
so option A is correct
Step-by-step explanation:
A vegetable garden and a surrounding as a shaped like a square that together a 11 ft wide. The path is 2 feet wide. If one bag of gravel covers 10 square feet, how many bags are needed to cover the path? Round your answer to the nearest tenth. NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW.
Answer:
[tex] \displaystyle 4[/tex]
Step-by-step explanation:
we are given that A vegetable garden and a surrounding as a shaped like a square that together a 11 ft wide. The path is 2 feet wide.since together the width of Vegetable garden and path is 11 ft, the width of the vegetables garden will be the difference between the total width and the width of path Thus,
[tex] \displaystyle \rm W _{ garden} = 11 - 2[/tex]
simplify substraction:
[tex] \displaystyle \rm W _{ garden} = 9[/tex]
recall that, every single side of a square is equal to each other therefore the the area of the garden will be
[tex] \displaystyle {9}^{2} [/tex]
simplify square:
[tex] \displaystyle 81[/tex]
together the garden and path makes a square of every side length 11 ft saying that the area will be:
[tex] \displaystyle {11}^{2} [/tex]
simplify square:
[tex] \displaystyle 121[/tex]
the area of path will be the difference between the total area and the garden area therefore,
[tex] \displaystyle 121 - 81[/tex]
simplify addition:
[tex] \displaystyle 40[/tex]
to figure out how many bags are needed to cover the path. we just need to divide the area of the path by the area of a bag of gravel and that yields:
[tex] \displaystyle \frac{40}{10} [/tex]
simplify division:
[tex] \displaystyle \boxed{\rm4}[/tex]
hence,
4 bags are needed to cover the path.
whats the correct answer?
Answer:
its the 4 one
Step-by-step explanation:
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.
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.
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Help I’ll mark you!!
Answer:
A.
Step-by-step explanation:
Each mark is worth two. We are inbetween the first mark and 0 on the left. Half of two is one. and since we are in the left quadrant we know it to be negative. Looking down, we see that we are exactly one mark down. As a mark is two, ans that we are going down, this will be a negative two. That leaves us with the answer of (-1, -2)
Answer:
A. (-1,-2)
Step-by-step explanation:
just trust me...I promise it right
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?
According to records from a large public university, 88% of students who graduate from the university successfully find employment in their chosen field within three months of graduation. What is the probability that of nine randomly selected students who have graduated from this university, at least six of them find employment in their chosen field within three months
Answer:
0.9842 = 98.42% probability that at least six of them find employment in their chosen field within three months.
Step-by-step explanation:
For each student, there are only two possible outcomes. Either they found employment, or they did not. The probability of a student finding employment is independent of any other student, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [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]
And p is the probability of X happening.
88% of students who graduate from the university successfully find employment in their chosen field within three months of graduation.
This means that [tex]p = 0.88[/tex]
Nine randomly selected students
This means that [tex]n = 9[/tex]
What is the probability that of nine randomly selected students who have graduated from this university, at least six of them find employment in their chosen field within three months?
This is:
[tex]P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 6) = C_{9,6}.(0.88)^{6}.(0.12)^{3} = 0.0674[/tex]
[tex]P(X = 7) = C_{9,7}.(0.88)^{7}.(0.12)^{2} = 0.2119[/tex]
[tex]P(X = 8) = C_{9,8}.(0.88)^{8}.(0.12)^{1} = 0.3884[/tex]
[tex]P(X = 9) = C_{9,9}.(0.88)^{9}.(0.12)^{0} = 0.3165[/tex]
Then
[tex]P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) = 0.0674 + 0.2119 + 0.3884 + 0.3165 = 0.9842[/tex]
0.9842 = 98.42% probability that at least six of them find employment in their chosen field within three months.
Alex and Morgan or ask to solve 2x-5=5x+7+3x X equal 5
Answer:
no solution?
Step-by-step explanation:
2(5)-5=5(5)+7+3(5) <-- plug in 5
10−5=25+7+15
5=32+15
5=47
Two classes have a total of 50 students. One of the classes has 6 more students than the other. How many students are in the larger class.
14
19
28
31
Answer:
28 are in the larger class.
Step-by-step explanation:
50/2 = 25 xy
25+ 3 = 28 larger
25-3 = 22 smaller
x = 28
The larger class has 28 students, and the correct option is 28.
Let's assume the number of students in one class is x.
According to the given information, the other class has 6 more students than this class, which means the number of students in the other class is x + 6.
To find the total number of students, we add the number of students in both classes: x + (x + 6) = 50.
Combining like terms, we have: 2x + 6 = 50.
Next, we subtract 6 from both sides of the equation: 2x = 44.
Finally, we divide both sides of the equation by 2 to solve for x: x = 22.
So, there are 22 students in one class, and the other class has 22 + 6 = 28 students.
Therefore, the larger class has 28 students, and the correct option is 28.
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g From a distribution with mean 38 and variance 52, a sample of size 16 is taken. Let X be the mean of the sample. Show that the probability is at least 0.87 that X is in (33, 43)
Answer:
[tex]P=8.869[/tex]
Step-by-step explanation:
From the question we are told that:
Mean [tex]\=x =38[/tex]
Variance [tex]\sigma=52[/tex]
Sample size [tex]n=16[/tex]
[tex]X=(33, 43)[/tex]
Generally the equation for Chebyshev's Rule is mathematically given by
[tex]A=(1-\frac{1}{k^2})*100\%[/tex]
Where
[tex]k=\frac{\=x-\mu}{\frac{\sigma}{\sqrt n}}}}[/tex]
[tex]k=\frac{43-38}{\frac{52}{\sqrt 16}}}}[/tex]
[tex]k=2.77[/tex]
Therefore
Probability
[tex]P=(1-\frac{1}{2.77^2})[/tex]
[tex]P=8.869[/tex]
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%.
if the average of b and c is 8, and d=3b-4, what is the average of c and d in terms of b?
[tex] \underline{ \huge \mathcal{ Ànswér} } \huge: - [/tex]
Average of b and c is 8, that is
[tex]➢ \: \: \dfrac{b + c}{2} = 8[/tex]
[tex]➢ \: \: b + c = 16[/tex]
[tex]➢ \: \: c = 16 - b[/tex]
now let's solve for average of c and d :
[tex]➢ \: \: \dfrac{c + d}{2} [/tex]
[tex]➢ \: \: \dfrac{16 - b + 3b - 4}{2} [/tex]
[tex]➢ \: \: \dfrac{12 + 2b}{2} [/tex]
[tex]➢ \: \: \dfrac{2(6 + b)}{2} [/tex]
[tex]➢ \: \: b + 6[/tex]
Therefore, the average of c and d, in terms of b is : -
[tex] \large \boxed{ \boxed{b + 6}}[/tex]
[tex]\mathrm{✌TeeNForeveR✌}[/tex]
Answer:
b+6
Problem:
If the average of b and c is 8, and d=3b-4, what is the average of c and d in terms of b?
Step-by-step explanation:
We are given (b+c)/2=8 and d=3b-4.
We are asked to find (c+d)/2 in terms of variable, b.
We need to first solve (b+c)/2=8 for c.
Multiply both sides by 2: b+c=16.
Subtract b on both sides: c=16-b
Now let's plug in c=16-b and d=3b-4 into (c+d)/2:
([16-b]+[3b-4])/2
Combine like terms:
(12+2b)/2
Divide top and bottom by 2:
(6+1b)/1
Multiplicative identity property applied:
(6+b)/1
Anything divided by 1 is that anything:
(6+b)
6+b
b+6
Eight students are running for three positions in
the student council: president, vice president,
and secretary. Which represents the total
number of ways that three students can be
selected if each student can be elected to only
one position?
Answer:
Step-by-step explanation:
Total number of outcome are
1320
.
Explanation:
It is apparent that there are
12
ways in which the post of President can be filled. Once President's post is filled, there are
11
ways to fill the post of Vice President and then
10
ways to fill the post of Secretary,
Hence a total of
12
⋅
11
⋅
10
or
1320
ways or outcomes.
Answer:
1320
Step-by-step explanation:
what is the ratio of the two values and what new value do they produce? $280 in 7m
what is the ratio of the two values and what new value do they produce? 105 miles in 2 hours
what is the ratio of the two values and what new value do they produce? $33 for 5lb
what is the ratio of the two values and what new value do they produce? 50 pages in 2 hours
Answer:
The ratio between two values A and B is just the quotient between these two values:
ratio = A/B
a) $280 in 7m
Here the ratio is:
$280/7m = $40/m
This also can be read as:
$40 per meter.
b) 105 miles in 2 hours
Here the ratio is:
105mi/2h = 52.5 mi/h
This also can be read as:
52.5 miles per hour
c) $33 for 5lb
The ratio is:
$33/5lb = $6.6/lb
This can be read as:
$6.6 per pound.
d) 50 pages in 2 hours
the ratio is:
(50 pages)/2h = 25 pages/h
this can be read as:
25 pages per hour.
If a quadrilateral is a square, then all sides are the same. What part is the conclusion
Bill works for a large food service company. In one hour he can make 19 sandwiches or he can make 40 salads. Bill works 7 hours per day. If Bill needs to make 30 sandwiches then how many salads can he make
Answer:
[tex]x=216 salads[/tex]
Step-by-step explanation:
One Hour:
Salad=40
Sandwich=19
Total work time[tex]T=7[/tex]
Generally
Time to make 30 sandwiches is
[tex]T_s=\frac{30}{19}[/tex]
[tex]T-s=1.6hours[/tex]
Therefore
Bill has 7-1.6 hours to make salads and can make x about of salads in
[tex]x=(7-1.6)*40[/tex]
[tex]x=5.4*40[/tex]
[tex]x=216 salads[/tex]
Select the correct answer. Solve the equation using the method of completing the square. 2r2 + 16r - 8 = 0
Answer:
r=-4+2[tex]\sqrt{5}[/tex], r=-4-2[tex]\sqrt{5}[/tex]
Answer:
r=-4+2[tex]\sqrt{5}[/tex], r=-4-2[tex]\sqrt{5}[/tex]
Step-by-step explanation:
It was right for me
In how many ways can a committee of 3 men and 4 boys be chosen from 7 men and 6 boys so as not to include the youngest boy if the eldest man is serving?
Answer:
There are 75 ways to form the committee.
Step-by-step explanation:
The order in which the people are chosen is not important, which means that the combinations formula is used to solve this question.
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:
Considering the eldest has to be there, 2 men from a set of 6 and 4 boys from a set of 5(excluding the youngest), so:
[tex]T = C_{6,2}C_{5,4} = \frac{6!}{2!4!} \times \frac{5!}{1!4!} = 3*5*5 = 75[/tex]
There are 75 ways to form the committee.
Can I have help I am stuck on this problem It would mean the world if u helped me and tysm!! =-)
Answer:
1. >
2. <
3. =
4. <
Step-by-step explanation:
23.197 > 23.179
3 2/10 which is the same as,
3.2 < 3.243
30.423 = 30 423/1000
18.546 < 18 56/100
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.
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.
Which expression is equivalent to cos120°?
The expression cos240 degrees is equivalent to cos120 degrees
Answer: B. cos240°
Step-by-step explanation:
Took the Test/Exam on Edge
Suki makes and sells denim jackets in a small store at the mall. She has found that
the following system of equations represents the expenses and the revenue for
running her store.
C = 520 + 31n
C = 96n
Determine the minimum number of jackets she must sell to make a profit.
Answer:
8
Step-by-step explanation:
96n = 520 + 31n
65n=520
n=8
Hope this helps :)
What is the area of the given triangle? Round to the nearest tenth
Answer:
28.0125 cm^2 rounded to 28.0 cm^2
Step-by-step explanation:
Area = a*b*sin(c)*1/2
Area = 7 * 13 * sin(38) * 1/2
Area = 91/2 * 0.61566...
Area = 28.0125...
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 :)
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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