Multiple choice: According to the central limit theorem, the standard deviation of the sample means is:
a) less than the population standard deviation
b) the same as the population standard deviation
c) more than the population standard deviation
According to the central limit theorem, the standard deviation of the sample means is a) less than the population standard deviation.
What is a central limit theorem?According to the central limit theorem, as long as the sample size is large enough, the sampling distribution of the mean will always be normally distributed. The sampling distribution of the mean will be normal regardless of whether the population has a normal, Poisson, binomial, or other distribution.
The sample means' standard deviation (also known as the standard error of the mean) will be less than the population standard deviation and equal to the population standard deviation divided by the square root of the sample size.
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A theater is presenting a program on drinking and driving for students and their
parents or other responsible adults. The proceeds will be donated to a local alcohol
information center. Admission is $2.00 for adults and $1.00 for students. However,
this situation has two constraints: The theater can hold no more than 240 people
and for every two adults, there must be at least one student. How many adults and
students should attend to raise the maximum amount of money?
To raise the maximum amount of money,
attend.
adults and
students should
Using equations, to raise the maximum amount of money, 160 adults and 80 students should attend the theater program on drinking and driving.
What is an equation?An equation is a mathematical statement of the equality of two or more mathematical expressions, using the equation symbol (=).
In this situation, we form a system of equations, to show the maximum number of adults and students allowed for the program.
We also form an objective constraint of inequality to show the limit of the allowed number of people for the program.
Admission fee for adults = $2.00
Admission fee for students = $1.00
Equations:The total number allowed in the theater = 240 persons
The ratio of adults to students = 2:1
The sum of ratios is 3
The number of adults = 2x, where, the number of students = x.
2x + x = 240 ... Equation 1
3x ≤ 240 ... Equation 2
If 3x = 240
x = 80
Check:
3x ≤ 240
3(80) ≤ 240
240 = 240
Allowed Admission:Adults = 160 (2 x 80)
Students = 80 (1 x 80), which meet the second requirement or constraint.
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Karen can read 10 pages and complete 15 math problems in 30 minutes. How long will it take her to do her homework if she has 30 pages to read and 45 math problems to complete? Your answer should refer to the amount of time in minutes.
1 hour 30 minutes take her to do her homework if she has 30 pages to read and 45 math problems to complete.
What is Unitary Method?
The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Karen can read 10 pages and complete 15 math problems in 30 minutes.
So, if she reads 30 pages which is 3 times of 10.
Also, solve 45 maths problem which is 3 times of 15.
So, the time taken to complete 30 pages to read and 45 math problem
= 30 x 3
= 90 minutes
= 1 hour 30 minutes
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Question 3(Multiple Choice Worth 2 points)
(Proportional Relationships MC)
A wheat farmer plows 5 acres of land and collects 135 bushels of wheat. The next day, the farmer plows 8 acres of land and collects 216 bushels of wheat.
Is there a proportional relationship between the number of bushels of wheat collected and the number of acres plowed over the two days? Explain.
Yes, it is proportional because the farmer collected 7 bushels for every 1 acre plowed.
Yes, it is proportional because the farmer collected 27 bushels for every 1 acre plowed.
No, it is not proportional because both variables cannot be zero at the same time.
No, it is not proportional because all ratios between the number of bushels collected and the number of acres plowed are not equivalent.
Yes, it is proportional because the farmer collected 27 bushels for every 1 acre plowed.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given,
A wheat farmer plows 5 acres of land and collects 135 bushels of wheat
The next day, the farmer plows 8 acres of land and collects 216 bushels of wheat.
Let us create a equation
Bushels/Acres
For first day:
Number of bushels of wheat=135
Number of acres of land=5
135/5=27
Next day:
Number of bushels of wheat=216
Number of acres of land=8
216/8=27
The proportional relation between 1st day and next day is same. It is proportional because the farmer collected 27 bushels for every 1 acre plowed.
Hence, Yes, it is proportional because the farmer collected 27 bushels for every 1 acre plowed.
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Give an example of bounded sequence that are not conregent?
Answer The sequence {an = (−a)n}
Step-by-step explanation: The sequence {an = (−a)n} is bounded below by −1 and bounded above by 1, and so is bounded. This sequence does not converge, though; since |an − an+1| = 2 for all n, this sequence fails the Cauchy criterion, and hence diverges.
6. The number of nickels in Bart's piggy bank is 1 less than twice the number of dimes. If the total value of the coins in the piggy bank is at least $4.35, find the smallest possible number of coins in the bank.
If the number of nickels in a piggy bank is 1 less than twice that of dimes and the total value of the coins is at least $4.35, then the smallest possible number of Nickels and Dimes is 43 and 22, respectively.
As per the question statement, The number of nickels in Bart's piggy bank is 1 less than twice the number of dimes, and the total value of the coins in this piggy bank is at least $4.35,
Then, we are required to determine the smallest possible number of individual coins in the bank.
To answer this question, first we will need to know the monetary values of nickels and dimes, that is,
(1 dime = 10 cents = $0.1), and (1 Nickel = 5 cents = $0.05).
Now let us assume that, there are "x" nickels and "y" dimes in that bank, Then as per the condition that, the number of nickels in Bart's piggy bank is 1 less than twice the number of dimes, we can write an equation with the above assumed two variables, which is, [x = (2y - 1)]...(i)
And as per the other condition that, the total value of the coins in this piggy bank is at least $4.35, we can write another equation, which is,
[(0.1y + 0.05x) = 4.35]
Or, [100(0.1y + 0.05x) = (100 * 4.35)]
Or, [(10y + 5x) = 435]...(ii)
Now substituting eqn (i) in eqn (ii), we get,
[{10y + 5(2y - 1)} = 435]
Or, [(10y + 10y - 5) = 435]
Or, [(10y + 10y) = (435 + 5)]
Or, (20y = 440)
Or, [y = (440/20)]
Or, (y = 22)
Therefore, [x = {(2 * 22) - 1}]
Or, [x = (44 - 1)]
Or, [x = 43]
That is, If the number of nickels in a piggy bank is 1 less than twice that of dimes and the total value of the coins is at least $4.35, then the smallest possible number of Nickels and Dimes is 43 and 22, respectively.
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please help 3
what is(fog)(3)if f(x)=3x-1 and g(x)=4x2+9
The value of (fоg)(3) = 134.
What is composition of functions?
A function is composed in mathematics when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a function is essentially applied to the output of another function.
Consider, the given functions
f(x) = 3x - 1, g(x) = 4x^2 + 9
First to find f(g(x)).
Let,
f(g(x)) = 3(4x^2 + 9) - 1
= 12x^2 + 27 - 1
f(g(x)) = 12x^2 + 26
Now, to find f(g(3)).
Plug x = 3 in the above equation,
f(g(3)) = 12(3)^2 + 26
= 12(9) + 26
f(g(3)) = 134
Hence, (fоg)(3) = 134.
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IXL Please Help Fast!, Thank you guys for the help!
Answer:
FROM YOUR IXL I GOT IT FOR YOU
Step-by-step explanation:
Write an equation in slope-intercept form for the line with slope 5 and y-intercept -5 . Then graph the line.
Answer:
Step-by-step explanation: The equation for slope-intercept is y=mx+b
m= slope of the equation, b= y-intercept(what y is when x is zero)
there for the equation is y=5x-5
0000000036 * 000000716
Answer:
your answer is 25776
Step-by-step explanation:
Answer: 25776 is your answer
Graphing and Solving Inequalities
m-1<-3. -4y <-20. 5+b>1. -18
Solutions for the given equalities:
m < - 2
y > 5
b > -4
What is inequality in mathematics?
An inequality in mathematics is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line.
The given inequalities are
1) m - 1 < -3
Adding 3 on both sides, we get
m - 1 + 3 < -3 + 3
m + 2 < 0
Subtracting 2 from both the side, we get
m + 2 - 2 < 0 - 2
m < - 2
The graph of this inequality is shown below
2) -4y < -20
Dividing by -4, we get
y > 5
The graph of this inequality is shown below
3) 5 + b > 1
Subtracting 1 from both the side, we get
b + 4 > 0
b > -4
The graph of this inequality is shown below
4) y = -18
This is a point on a number line, and it can be shown as
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What word sentence represents this inequality?
A number is at least as large as 8.9
A number is no more than 8.9
A number is greater that 8.9
The word sentence which is used to represent the given inequality
p ≥ 8.9 is a number is at least as large as 8.9.
As given in the question,
Given inequality is equal to :
p ≥ 8.9
In the given inequality sign of greater than and equals to is used.
Explanation for the given word sentences:
A number is at least as large as 8.9.Meaning of at least is minimum this much.
At least as large means ( ≥) greater than or equal to
Option is correct.
A number is no more than 8.9.It represents the symbol (≤ )less than or equal to.
Incorrect option.
A number is greater than 8.9.It represents the symbol of > greater than only.
Incorrect option.
Therefore, the word sentence which is used to represent the given inequality p ≥ 8.9 is a number is at least as large as 8.9.
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Which is the graph of g(x) = [x + 3]?
Answer:
Step-by-step explanation:
................ x2
what is the round figure of 2089.17
2089.17 rounded off to nearest tenths(1 decimal place) is 2089.2
2089.17 rounded off to the nearest one is 2089
When you "round to the nearest _____" regardless of what is in the blank the steps are nearly always the same:
Identify which place value you are rounding off a number. The smaller the place value, the more accurate the final result shall be.
Find the next smallest place value, the digit to the right of the place value you're rounding off to. For example, if you want to round to the nearest ten you would have to find the number at the one's place.
If the digit in the next smallest place value is less than five (0, 1, 2, 3, or 4), you leave the digit you want to round off. Any digits after that number become zeros, or drop-offs if they're located after the decimal point. This is called rounding down a number or a sequence of numbers.
If the smallest place value is greater than or equal to five (5, 6, 7, 8, or 9), you increase the value of the digit you're rounding off to by one place (+1). Any remaining digits before the decimal point become zeroes, and any digits that are after the decimal point are dropped. This is called rounding up of numbers.
For example, for rounding off a number 838.274, depending on which place value you'll round to, the final rounded-off answer will vary. Rounding off 838.274:
Rounding off the nearest hundred is 800
Rounding off the nearest ten is 840
Rounding off the nearest one is 838
Rounding off the nearest tenth is 838.3
Rounding off the nearest hundredth is 838.27
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Evaluate y + (-32.577) for the following values of y.
value of y value of expression
-12.975 -45.552
-41.08
-74.003
-10.304
It would be much appreciated if someone could aid me in solving question B for this problem. I have been unable to calculate the correct answer. Thank you so much in advance : )
A floating rate mortgage loan is made for $125,000 for a 30-year period at an initial rate of 12 percent interest. However, the borrower
and lender have negotiated a monthly payment of $1,000.
Required:
a. What will be the loan balance at the end of year 1?
b. If the interest rate increases to 13 percent at the end of year 2, how much is the payment plus negative amortization in year 2 and
year 5 if the payment remains at $1,000?
Complete this question by entering your answers in the tabs below.
Required A Required B
If the interest rate increases to 13 percent at the end of year 2, how much is the payment plus negative amortization in year
2 and year 5 if the payment remains at $1,000?
Note: Do not round intermediate calculations. Round your final answers to 2 decimal places.
Loan balance in year 2:
Interest accrued-Year 2:
Interest accrued - Years 2-Year 5:
The negative amortization at the end of year 1 is $2536.50
For the year 1 there will be still 12% rate of interest going on. There is a negative balance of $200 after payment of 1st month installment.
Thus negative amortization = FV(0.01x12 - 200)
Here 0.01 is the interest per month, 12 is the number of months in a year and -200 is the negative balance in first month
negative amortization = FV(0.01x12 - 200)
The negative amortization at the end of year 1 = $2536.50
The negative amortization at the end of year 5
The loan balance at the end of year 4 = FV(0.13x12x36x800 - 102536)
The loan balance at the end of year 4 = $16132.46
The negative amortization at the end of year 1 is $2536.50
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The Data: Statistics about smoking and lung cancer for adults (age 18 and older) in the U.S:
⦁ Researchers estimate that 21.5% of men and 17% of women smoke cigarettes.1
⦁ The rate of new cases in 2008 showed that men develop lung cancer more often than women (70.2 and 50.5 cases per 100,000 persons, respectively).2
⦁ Smoking, a main cause of small cell and non-small cell lung cancer, correlates to 90% and 80% of lung cancer deaths in men and women, respectively.3 That is, 90% of men who are diagnosed with lung cancer are active smokers, and 80% of women who are diagnosed with lung cancer are active smokers.
Analyze the Conjecture:
1. What answer do you predict? Why? (2 points)
I predict 90% All the probabilities are given for the three different scenarios in men and women: people who smoke, people who develop lung cancer, and people who develop lung cancer who are also smokers. Then, these are even classified in terms of gender.
2. Given what you know about probability, how can you determine if smoking and lung cancer are related? (2 points)
Analyze the Data:
3. What is the probability that a randomly chosen man is a smoker? (1 point)
4. What is the probability that a randomly chosen man will be diagnosed with lung cancer? (1 point)
5. Given that a man has lung cancer, what is the probability that he is a smoker? Write this event with the correct conditional notation. (2 points)
6. What is the probability that a randomly selected man will be a smoker and be diagnosed with lung cancer? (2 points)
7. For a randomly selected man, are the events diagnosed with lung cancer and smoker independent events? Support your answer with probabilities. (2 points)
Consider the Case for Women:
8. For a randomly selected woman, are the events diagnosed with lung cancer and smoker independent or conditional? Support your answer with probabilities. (4 points)
Making a Decision:
9. What can you conclude about smoking and lung cancer? Are they conditional or independent events? (2 point)
10. Some people who have never smoked develop lung cancer. Does this disprove the evidence? (1 point)
All the probabilities are provided for the three situations involving men and women: smoking, developing lung cancer, and developing lung cancer while simultaneously smoking. Then, these are even divided into gender categories.
However, the last query is limited to males who smoke who develop lung cancer. Therefore, I believe that all of the other information is merely a red herring. You just need to search through the other options to locate the answer, which is already there. You should first disregard any possibilities involving ladies because we are only interested in men. The likelihood that males with lung cancer smoke is the next statistic you discover. The solution is 90%.
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The quantity x plus 3, multiplied by negative 7
Step-by-step explanation:
(x + 3) × -7 = -7x - 7×3 = -7x - 21
Sketch the graph of the exponential function. Label the y-intercept and at least two other points on the graph using both
positive and negative values of x.
f(x) = 5e^x
Answer:
Take a look at the attachment...
Hope this helps! :)
On a construction site, the amount of hours needed to do a job is
inversely proportional to the number of men working. If it takes 10 men
18 hours to repair a road, how long will it take 15 men to do the same
job if they work at the same rate?
It will take 12 hours for 15 men to do same job.
How to determine this?
When amount of hour ∝ 1/number of men
When H represent Hour
And M represent the number of men
k to represent the constant
H = k/M as it is inversely proportional
It takes 10 men 18 hours to repair a road
18 = k/10
k = 18 × 10
k = 180
How long will it take 15 men?
When k = 180
H = k/M
H = 180/15
H = 12 hours
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1) A local fast food restaurant takes in $9000 in a 4 hour
period. Estimate how many hours it would take the same
restaurant to earn $20,250.
Answer: 9 hours
Step-by-step explanation:
Assuming they keep earning money at the same rate, we will set up a proportion to help us solve.
[tex]\displaystyle \frac{\$9,000}{4\;\text{hours}} =\frac{\$20,250}{x\;\text{hours}}[/tex]
Next, we will cross-multiply.
$9,000 * x = $20,250 * 4
$9,000x = $81,000
x = 9 hours
It will take the same restaurant about 9 hours to earn $20,250.
A salesman earns 40% commission on all the merchandise that he sells. Last month he sold $800 worth of merchandise. How much commission (in dollars) did he earn last month?
The commission when the salesman earns 40% commission on all the merchandise that he sells is $320.
What is percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In this case, the salesman earns 40% commission on all the merchandise that he sells and last month he sold $800 worth of merchandise.
The amount in commission will be:
= Commission percentage × Sales
= 40% × $800
= $320
The commission is $320.
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When firefighters are trying to put out a fire, the rate at
which they can spray water on the fire depends on the
water pressure. You can find the flow rate f in gallons
per minute using the equation, f = √120p, where p
is the nozzle pressure in pounds per square inch.
What pressure would be required to have a flow rate of
62 gal/min? show work
The pressure that would be required to have a flow rate of 62 gal/min is f=86.25
What is meant by nozzle pressure?The velocity of the stream is exactly proportional to nozzle pressure. In the given scenario, instead of a stream moving at 80 mph through the fire's super-heated gases, it moves at 60 mph.
The velocity increases as the pressure decreases in a convergent nozzle, but we know that pressure is inversely related to area.
The following formula can be used to compute the flow rate for a given nozzle. Q represents the flow rate. K = Nozzle K factor. P = Nozzle pressure differential. n = Is a constant that is determined by the type of spray pattern.
Given equation is,
f = √120p
Here p denotes the nozzle pressure in pounds per square inch
Also given that p=62 gal/min
f = √120p
Then,
f= √120(62)
f=√7440
f= 86.25
The pressure that would be required to have a flow rate of 62 gal/min is f=86.25
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A library had 32 shelves of books. The books were placed either on the right or left side of the shelves. Each shelf had 21 books. There were 301 books on the left, how many books were there on the right?
Answer:
371
Step-by-step explanation:
hope it helped :)
Answer:
there are books on the right
371
Step-by-step explanation:
each shelves is 21
there are 32
books on the left 301
so the rest are on the right
21*32-301=371
so find how many are there and minus it by the books on the left side
[tex]21 \times 32 - 301[/tex]
80% of what number is 280
Using the percentages formula, we know that 80% of 350 is 280.
What is the percentage?A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.So, let the number be x:
Then, 80% of x is 280:Now, calculate as follows:
x/100 × 80 = 28080x = 280 × 10080x = 28000x = 28000/80x = 2800/8x = 350Therefore, using the percentages formula, we know that 80% of 350 is 280.
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Please I need some help understanding this
The values are given below,
Left Hand Limit i.e. lim x -> 1- f(x) = 3 ,
Right Hand Limit i.e. lim x -> 1+ f(x) = 1 ,
Function value at x = 1 i.e. f(1) = 1 ,
Left Hand Derivative lim x -> 1- f'(x)= -6 and
Right Hand Derivative lim -> 1+ f'(x) = -6.
So, the function f(x) is neither continuous nor differentiable at x = 1.
Given, a piecewise function
3㏑(3 - 2x) + 3 for x < 1
f(x) =
-3x² + 4 for x ≥ 1
Now, for lim x -> 1- f(x) we will consider the function 3㏑(3 - 2x) + 3, as we have to find the Left Hand Limit of the function, at x = 1.
lim x -> 1 3㏑(3 - 2x) + 3 = 3㏑(3 - 2(1)) + 3
= 3 ㏑(1) + 3
= 0 + 3
= 3
Now, for lim x -> 1+ f(x) we will consider the function -3x² + 4, as we have to find the Right Hand Limit of the function, at x = 1.
lim x -> 1 -3x² + 4 = -3(1)² + 4
= -3 + 4
= 1
Now, for f( 1 ) we will consider the function -3x² + 4,
f(1) = -3(1)² + 4
= -3 + 4
= 1
Now, for lim x -> 1- f'(x) we will consider the derivative of the function
3㏑(3 - 2x) + 3,
lim x -> 1 -6/(3 - 2x) = -6/(3 - 2(1))
= -6
Now, for lim -> 1+ f'(x) we will consider the derivative of the function
-3x² + 4,
lim x -> 1 -6x = -6(1)
= -6
So, the function f(x) is neither continuous nor differentiable at x = 1.
Hence, lim x -> 1- f(x) = 3 , lim x -> 1+ f(x) = 1 , f( 1 ) = 1 , lim x -> 1- f'(x) = -6 and lim -> 1+ f'(x) = -6.
The function is neither continuous nor differentiable at x = 1.
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A pizza restaurant used 1/2 of a liter of pizza sauce to make some pizzas. They put 1/8 of a liter of sauce on each pizza. How many pizzas did they make?
Answer:
4
Step-by-step explanation:
you can convert 1 half to 20/40 and 1/8 to 5/40 5,10,15,20 you can make 4 pizzas
A container has the shape of an open right circular cone, as shown in the figure above. The container has a radius of 4 feet at the top, and its height is 12 feet. If water flows into the container at a constant rate of 6 cubic feet per minute, how fast is the water level rising when the height of the water is 5 feet?
If water flows into the container at a constant rate of 6 cubic feet per minute, the rate at which the water level rising when the height of the water is 5 feet is; 0.688 ft/min
How to find the rate of change?When we are given an equation that gives the relationship between two or more variables, then by differentiating the equation with respect to time would give us a new equation that involves the rate of change of each of the given variables.
We are given the dimensions of the tank as;
Radius; r = 4 feet
Height; h = 12 feet.
The water in the tank will also have a conical shape.
By similar triangles, we know that;
r/h = 4/12
r = h/3
Now the volume of the water is;
V = ¹/₃πr²h
Put h/3 for r in this volume equation to get;
V = ¹/₃π(h/3)²h
V = (1/27)πh³
Differentiating with respect to time gives;
dV/dt = (3/27)πh²(dh/dt)
We are given;
dV/dt = 6 cubic feet per minute
h = 5
Thus;
6 = (3/27)π(5²)(dh/dt)
dh/dt = 0.688 ft/min
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Arrange the following polynomials in order of their degree from least to greatest.
The polynomials in order of their degree from least to greatest are x, -3x² - 1, 4c² + c - 3, -8y³ + 5y - 2, y¹⁰
How to order the polynomials?The list of options represents the given parameters
The degree of a polynomial is the highest power of the polynomial
Take for instance, a polynomial ax^n has a degree of n
This means that the degrees of the given polynomials are:
Degree of x = 1Degree of -3x² - 1 = 2Degree of 4c² + c - 3 = 2Degree of -8y³ + 5y - 2 = 3Degree of y¹⁰ = 10The above represents the order of the polynomials
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A bag contains 10 red balls, 8 green balls, and 6 blue balls. 2 balls are drawn at random at the bag. What is the probability that both balls are red?
Answer:
Assuming every single ball has an equal chance of being drawn, then if B is the probability of drawing a blue ball and R is the probability of drawing a red ball:
B + R = 1,
since either a red or blue ball will be drawn. Since each ball has an equal chance of being drawn:
16 p = 1, or
p = 1/16
where p is the chance to draw a single ball. Since there are 10 red balls, there are ten independent and different ways to draw a red ball, which means that
R = 10 p = 10/16 = 5/8.
You can either apply the first equation to find that
B = 1 - R = 3/8
or state directly that
B = 6 p = 6/16 = 3/8
since there are six independent and different ways to draw a blue ball from the bag.
Answer:
41.67%
Step-by-step explanation:
10+8+6= 24
10/24
First, you need to calculate your grade in percentages. The total answers count 24 - it's 100%, so we to get a 1% value, divide 24 by 100 to get 0.24. Next, calculate the percentage of 10: divide 10 by 1% value (0.24), and you get 41.67% - it's your percentage grade
