According to the central limit theorem, when n=9, the variance of the distribution of means is equal to the population variance divided by the sample size.
Let σ^2 be the population variance. Then, the variance of the distribution of means (also known as the standard error) is σ^2/n.
The central limit theorem states that as the sample size increases, the distribution of sample means approaches a normal distribution with mean μ and variance σ^2/n, where μ is the population mean. Therefore, when n=9, the variance of the distribution of means is σ^2/9.
In summary, when n=9, the variance of the distribution of means is equal to the population variance divided by the sample size, which is σ^2/9.
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A card is randomly chosen from the cards in the image. Find the probability of choosing the cards with either Q or R on them.
P(Q or R) = ________
The probability of choosing cards either Q or R when a card is drawn from a deck of 8 cards is 0.25.
Given that a card is randomly chosen from 8 cards shown in figure.
We have to calculate the probability of choosing either Q or R when a card is drawn from those 8 cards.
Probability means calculating the likeliness of happening an event among all the events possible. It lies between 0 and 1. It cannot be negative.
Number of cards=8
Number of repeated cards=0
Number of cards showing Q and R =1 each.
Probability of getting Q or R is P(X=Q)+P(X=R)
= 1/8+1/8
=2/8
=1/4
=0.25
Hence the probability of getting either P or Q when a card is drawn from 8 cards is 0.25.
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From Andys house to Billys hometown you can travel by 3 roads. And to get from Billys hometown to Willies's house you can travel by 5 roads. How many possible wats are there to travel from andys house to willies house?
Using the Fundamental Counting Theorem, there are 15 ways to travel from Andy's house to Willie's house.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For this problem, the parameters are:
[tex]n_1 = 3, n_2 = 5[/tex].
Hence the number of ways is:
N = 3 x 5 = 15.
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solve each equation round to the nearest ten-thousandth in (x+21)=7
The solution to the equation (x+21)=7 is x = -14
How to solve the equation?The equation is given as:
(x+21)=7
Remove the brackets
x + 21 = 7
Subtract 21 from both sides
x + 21 - 21 = 7 - 21
Evaluate the expression
x = -14
Hence, the solution to the equation (x+21)=7 is x = -14
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Solve F=gm1*m2/d2 for g
The expression for g in terms of other variables is g = Fd^2/m1m2
Subject of formulaGiven the expression below as shown
F=gm1*m2/d2
We are to make g the subject of the formula
F=gm1*m2/d2
Cross multiply
Fd2 = gm1m2
Divide both sides by m1m2
Fd^2/m1m2 = g
g = Fd^2/m1m2
Hence the expression for g in terms of other variables is g = Fd^2/m1m2
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Help me solve this problem on arithmetic and geométrica sequences
Answer:
math math math math math math math math math math
Solve this system of equations using the substitution method
y = 2x + 17
y = 6x - 3
Step-by-step explanation:
well, as you can witness both of the equations are equal to y, so you're free to reckon that they are equal as well
[tex]6x - 3 = 2x + 17 = = = > \\ 4x = 20 = = = > x = 5 \: and \: \\ y = 6(5) - 3= = = > y = 27[/tex]
Answer:
<3
Step-by-step explanation:
5, 27 is right on acellus
x=5
y=27
You’re catering a banquet and want to use a delicious chicken recipe that was a success with a previous client. However, the recipe makes 10, 4-oz portions, and you need to serve 60 people with 3-oz portions. Calculate the recipe conversion factor.
The conversion factor of the chicken recipe used at the banquet is 4.5.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Conversion factor = (new amount * portion size) / (old amount * portion size)
Hence:
Conversion factor = (60 * 3) / (10 * 4) = 4.5
The conversion factor of the chicken recipe used at the banquet is 4.5.
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Given that zQ =zR and pv= PT, show that PQ = PR
Answer:
We have,
According to given figure.
PQ=PR(giventhat)
QS=SR(Bydefinationofmidpoint)
PS=PS(Commonline)
Then,
ΔSPQ≅ΔSPR (BY congruency S.S.S.)
Hence, PS bisects ∠PQR by definition of angle bisector.
A worker at a shoe factory is required to box at least
8
pairs of shoes per minute, but is not allowed to box more than
12
pairs of shoes per minute. According to this information, what is a possible amount of time, in minutes, that it could take the worker to box
168
pairs of shoes?
The possible amount of time, in minutes, that it could take the worker to box 168 pairs of shoes is between 14 minutes to 21 minutes.
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
A worker at a shoe factory is required to box at least 8 pairs of shoes per minute, and not more than 12 pairs of shoes per minute.
For 168 pairs of shoe:
Maximum time = 168 pair / 8 pairs per minute = 21 minutes
Minimum time = 168 pair / 12 pairs per minute = 14 minutes
The possible amount of time, in minutes, that it could take the worker to box 168 pairs of shoes is between 14 minutes to 21 minutes.
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Given the following system of equations for n≥2, find a5.
a1=2
an=3⋅an−1−1
Select one:
a. 41
b. 122
c. 365
d. 2,094
Answer:
b
Step-by-step explanation:
using the recursive rule [tex]a_{n}[/tex] = 3[tex]a_{n-1}[/tex] - 1 and a₁ = 2 , then
a₂ = 3a₁ - 1 = (3 × 2) - 1 = 6 - 1 = 5
a₃ = 3a₂ - 1 = (3 × 5) - 1 = 15 - 1 = 14
a₄ = 3a₃ - 1 = (3 × 14) - 1 = 42 - 1 = 41
a₅ = 3a₄ - 1 = (3 × 41) - 1 = 123 - 1 = 122
What is the nature of the solution set to the following system of equations?
4x + 3y = 2
3x − 2y = 10
The solution to the system of equations is one solution at (2, -2)
How to determine the solution set?The system of equations is given as:
4x + 3y = 2
3x − 2y = 10
Multiply (1) by 2 and (2) by 3.
So, we have:
8x + 6y = 4
9x − 6y = 30
Add both equations
17x = 34
Divide by 17
x = 2
Substitute x = 2 in 3x − 2y = 10
3(2) − 2y = 10
Solve for y
y = -2
Hence, the solution to the system of equations is one solution at (2, -2)
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Which expression could help you find the distance between –1 and 3 on the number line?
Answer:
|-1| + |3|
Step-by-step explanation:
We can use absolute values to find the distance between positive and negative numbers on a number line.
|-1| + |3| =
Keep in mind that
- the absolute value of a positive number is positive and
- the absolute value of a negative number is positive
1 + 3 =
4 units
Sketch the curve y = \sqrt{x+3} .
Find the area bounded by the curve, X-axis and Y-axis.
I get the first part but not the second part.
The area bounded by the curve, x-axis and y-axis of the function y = √(x + 3) is 2√3
How to determine the area bounded by the curve, x-axis and y-axis?The curve is given as:
y = √(x + 3)
The area bounded by the curve, x-axis and y-axis is when x = 0 and y = 0
When y = 0, we have:
0 = √(x + 3)
This gives
x = -3
So, we set up the following integral
A = ∫ f(x) d(x) (Interval a to b)
This gives
A = ∫ √(x + 3) d(x) (Interval -3 to 0)
When the above is integrated, we have:
A = 1/3 * [2(x + 3)^(3/2)] (Interval -3 to 0)
Expand
A = 1/3 * [2(0 + 3)^3/2 - 2(-3 + 3)^3/2]
This gives
A = 1/3 * 2(3)^3/2
Apply the law of indices
A = 2(3)^1/2
Rewrite as:
A = 2√3 or 3.46
Hence, the area bounded by the curve, x-axis and y-axis of the function y = √(x + 3) is 2√3
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A customer who sees a pair of boots online but then decides to buy the same pair at Macy's after trying them on would be best classified as a(n)
The term used to describe a customer who sees a pair of boots online but then decides to buy the same pair at Macy's after trying them on would be best classified as a cross-channel shopper.
Who is a cross-channel shopper?A cross-channel shopper is a consumer who uses various combination of both several channels for the same purchase.
The customer has checked the pair of boots online but rather purchased the same boots at Macy's instead of purchasing online.
Therefore, a cross-channel shopper uses different purchasing channel to purchase a product.
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There were 50,000 bacteria in a petri dish yesterday at noon, and 40,000 bacteria at noon today. if the trend continues, on what day at noon can you expect to find less than 5,000 bacteria?
Answer:
900
Step-by-step explanation:
The equation -2x − y = -4 shows the budget for spending on supplies over the next few weeks. If the total money (y) decreases every week (x), how many weeks will it take for the budget money to run out?
The number of weeks it will take for the budget money to run out is; 2 weeks.
How many weeks will it take for the money to run out?The number of weeks it would take for the budget money to decrease till it runs out as required in the task can be interpreted as the x-value which corresponds to a Y-value of zero.
Hence, by setting y=0; we have;
-2x -0 = -4
-2x = -4
Divide both sides of the equation by; -2.
x = 2
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PLEASE HELP NOW
Which formula can be used to find the volume of the cylinder? Check all that apply. A = ( d )( h ) V = B( h ) V = ( l )( w )( h ) V = 2( r )( h ) V = (pi) (r squared) (h)
Answer:
V= (pi) (r squared) (h)
Step-by-step explanation:
Find the smallest perimeter and the dimensions for a rectangle with an area of 169 in2. Question content area bottom Part 1 The smallest perimeter for a rectangle with an area of 169 in2 is enter your response here in.
The smallest perimeter and dimensions of rectangle having area of 169 [tex]inches^{2}[/tex] is 52 inches , length 16 inches and breadth also 16 inches.
Given that the area of rectangle is 169 [tex]inches^{2}[/tex].
We have to find the smallest perimeter and dimensions of the rectangle.
let the length of rectangle be x inches and breadth be y inches.
We know that area of rectangle is the product of its length and breadth. So,
Area=xy
169=xy
y=169/x
Perimeter of rectangle =2(x+y)
Put the value of y=169/x in the perimeter.
P=2(x+169/x)
P=2x+338/x
Differentiate both sides with respect to x.
dP/dx=2-338/[tex]x^{2}[/tex]
Again differentiate it with respect to x.
[tex]d^{2} P/dP^{2}[/tex]=676/[tex]x^{3}[/tex]
Because the second derivative is greater than 0 so the perimeter is minimum.
Put dP/dx=0 to get the value of x.
dP/dx=0
2-338/[tex]x^{2}[/tex]=0
2=338/[tex]x^{2}[/tex]
[tex]x^{2}[/tex]=169
x=[tex]\sqrt{169}[/tex]
x=13
Put the value of x in y=169/x
y=169/13
=13
To calculate the perimeter, put the values of x and y in P=2(x+y)
P=2(13+13)
=2*26
=52 inches.
Hence The smallest perimeter and dimensions of rectangle having area of 169 [tex]inches^{2}[/tex] is 52 inches , length 16 inches and breadth also 16 inches.
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which unit of measure would be appropriate for the volume of a sphere with aradius of 2 meters?
Answer:
The unit of measuring volume of the sphere is cubic meters.
This is confusing me please someone help
Answer:
The distance from the plane to the observer tower is 7.7 kmStep-by-step explanation:
We are given two sides and one angle opposite to one of the known sides.
In order to find the missing side we need to use the law of sines.
Step 1Find the angle opposite to the second known side, let it be x.
sin 68°/7.5 = sin x /5.2sin x = 5.2 sin 68°/7.5sin x = 0.64 (rounded)x = arcsin 0.64x = 39.8°Step 2Find the missing third angle y, using angle sum theorem:
68° + 39.8° + y = 180°107.8° + y = 180°y = 180° - 107.8°y = 72.2°Step 3Find the required side length z, the distance from the plane to the observer tower, using the law of sines again.
Note. At this point you can use the law of cosines as we have found the angle between the known sides.
sin 68°/7.5 = sin 72.2°/zz = 7.5 sin 72.2°/sin 68°z = 7.7 km (rounded)
So the required distance is 7.7 km
Can someone please help
Solving the given equation, the value of v that makes the statement true is:
A. v = 8.
What is the given equation?The equation is:
[tex]12 = 12 + \frac{v - 8}{2}[/tex]
Hence:
[tex]\frac{v - 8}{2} = 0[/tex]
Applying cross multiplication:
v - 8 = 0
v = 8.
Hence option A is correct.
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Leigh has information on how many customers purchase bagels at her coffee shop. With the bagel sales numbers from the past four months, she wants to
To predict the bagel sales numbers for the next month, Leigh could use Predict trend.
Given that Leigh has information on how many customers purchase bagel at her coffee shop.
We are required to answer the spreadsheet Leigh could use to predict bagel sales number for the next month.
Spreadsheet is developed for windows, macOS, Android and iOS.It features calculation through functions. In this we can use mathematical functions,logical functions, etc.
Leigh could use predict trend to predict the sales number of bagels of next month.
Hence predict trend could be used by Leigh to predict the sales for the next month.
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Question is incomplete as question should include the following:
What spreadsheet could Leigh use to predict the sales of next month?
PLS HELP ASAP
whats relationship between a and b
The correct answer is none of the above.
What is a line?A line is defined as the shortest distance between two points and the point where two lines meet is known as an angle.
From the given figure, the measure of angle a and b are supplementary since the sum of the angles is not 180 degrees.
They are not vertical angles since they do not meet at a point of intersection
The measure of angle a and b are complementary since the sum of the angles is not 90 degrees. Hence the correct answer is none of the above.
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A zoologist researched the feeding habits of lemurs. she collected data by studying the lemurs in a zoo exhibit for a one-month period and drew conclusions based on her data. what kind of statistical study did the zoologist conduct?
The kind of statistical study the zoologist conducted was D. observational study.
What is observational study in research?An observational study serves as a study whereby the researcher simply observes the subjects without interfering with it.
This is different from carrying out experiment on them or just a theoretical approach.
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CHECK THE COMPLETE QUESTION BELOW:
A zoologist researched the feeding habits of lemurs. She collected data by studying the lemurs in a zoo exhibit for a one-month period and drew conclusions based on her data. What kind of statistical study did the zoologist conduct? A. survey B. theoretical study C. experiment D. observational study
1.rani was selling flowers. each day she made 7 bouquets by arranging 8 roses and 6 marigolds in each bouquet. each bouquet was sold for rs.85. a) find the number of marigolds used in a day. b) find the total number of flowers used by using suitable property of whole numbers. c) if she sold 42 bouquets in a whole week, find the amount she earned. 2. by suitable rearrangement, find the value of a) 819 + 364 + 181 + 436 b) 20 x 348 x 50 3. using suitable property find the value of 492 x 13 + 492 x 37 4. a) name the property 86 + 65 = 65 + 83 b) the multiplicative identity of whole numbers is ______ 5. find the next two numbers in the pattern 1,1,2, 3,5,8, ______, ________
1.(a) The number of marigolds used in a day is 42.
(b) The total number of flowers used by using suitable property of whole numbers is 98.
(c) She earned Rs. 3570
2.(a) The value of [tex]819 + 364 + 181 + 436[/tex] is 1800.
(b) The value of [tex]20 \times 348 \times 50[/tex] is 348000.
3. The value of [tex]492 \times 13 + 492 \times 37[/tex] is 24600.
4.(a) Name the property 86 + 65 = 65 + 86 is commutative property.
(b) The multiplicative identity of whole numbers is 1.
5. The next two numbers in the pattern 1,1,2, 3,5,8 are 13 and 21.
1. (a) The number of marigolds used in a day is 42.
Rani made 7 bouquets on each day by arranging 8 roses and 6 marigolds in each bouquet. So number of marigolds used in a day is 7×6 = 42.
(b) The total number of flowers used by using suitable property of whole numbers is 98 flowers used by using distributive property.
What is distributive property of whole numbers?
The distributive property of multiplication states that when multiplying a number by the sum/difference of 2 numbers, the final value is equal to the sum/difference of each addend multiplied by the third number.
Distributive property = a×(b+c) = a×b+a×c
Total number of flowers = 7×(8+6) = 7×14 = 98.
(c) If she sold 42 bouquets in a whole week, find the amount she earned is rs.3570.
Each bouquet was sold for Rs.85. Then she earned a whole week off = 42×85 = rs.3570.
2. (a) By suitable rearrangement, the value of 819 + 364 + 181 + 436 is 1800.
Rearrangement of the given numbers = (819+181)+(364+436)
= 1000+800
= 1800
(b) By suitable rearrangement, the value of 20 x 348 x 50 is 348000.
Rearrangement of the given numbers = 348×(50×20)
= 348×1000
= 348000
3. Using suitable property find the value of 492 x 13 + 492 x 37 is 24600 by using distributive property.
By using distributive property = 492 x 13 + 492 x 37
= 492×(13+37)
= 492×50
= 24600
4. (a) Name the property 86 + 65 = 65 + 86 is commutative property.
What is commutative property?
This law simply states that with addition and multiplication of numbers, you can change the order of the numbers in the problem and it will not affect the answer.
By using commutative property, a+b = b+a
86 + 65 = 65 + 86
151 = 151
(b) The multiplicative identity of whole numbers is 1.
Multiplying a whole number by 1 equals that identical number, the whole number 1 is called the multiplicative identity.
5. The next two numbers in the pattern 1,1,2, 3,5,8,?,? are 13 and 21.
Just add the no before the given no then you will get the pattern. example first no=1 and no before it is 0
1+0=1
1+1=2
2+1=3
3+2=5
5+3=8
8+5=13
Hence, The next two numbers for the given series are 13 and 21.
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Meg plotted the graph below to show the relationship between the temperature of her city and the number of sweaters sold at a store:
Part A: In your own words, describe the relationship between the temperature of the city and the sale of sweaters in the city. (5 points)
Part B: Describe how you can make the line of best fit. Write the approximate slope and y-intercept of the line of best fit. Show your work, including the points that you use to calculate slope and y-intercept. (5 points)
PLEASE HELP WITH PART B ASAP
The explanation about the graph is illustrated below.
How to illustrate the graph?The graph shows 0 to 30 on the x-axis at increments of 5 and 0 to 12 on the y-axis at increments of 1. The label on the x-axis is Temperature in degrees C, and the label on the y axis is the Number of Sweaters Sold.
If you will draw lines through, (12.5,6) and (15,4), it will best represent a line of best fit, because most of the points on the same and opposite sides of line are equidistant from each other.
Equation of line passing through (12.5,6) and (15,4) A line of best is the line that passes through all or some points or only through a single point, which describes the relationship between x and y values of data set
4x + 5y = 80
5y = -4x + 80.
y = -4x/5 + 16
Slope = -4/5 and y intercept is 16.
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Calculate the mean and standard deviation for the average yards rushed by
each player. Then graph the data (use the mean for each player and SD for error bars).
Compare and contrast the mean rushing yards Dillon and Corey.
What does the SD indicate about the mean rushing yards for each player?
Question:
A sample of cans of peaches was taken from a warehouse, and the content of each can mearsed for weight. the sample means was 486g with stand deviation 6g. state the weight percentage of cans with weight:
Draw normal curve to help - split into 8 section ( i can't draw it here)
a) 34.13% of cans will be between 480g and 486g.
b) 13.59 + 2.15 + 0.13= 15.87% of cans greater than 492g.
Look at the Stand Dev Graph where the give you the number
Step-by-step explanation:
Let me give you a different question and i will answer it, which you help you answer your question.
36 fifth graders are on a team with the same number on students on each team, if there are more then then 1 but less then 20 teams, how many students can be on each team?
Depending on the number of teams, the possible numbers of students per team are in the set:
{2, 3, 4, 6, 9, 12, 18}
How many students can be on each team?
We know that there are 36 students divided equally into N teams.
Such that the number of teams is larger than 1 and smaller than 20.
Then we could have 2 teams, such that the number of students in each team is given by the quotient between the total number of students and the number of teams.
36/2 = 18
There are 18 students in each team.
Notice that the numbers of teams can only be factors of 36, where:
36 = 6*6 = 2*2*3*3
So the factors are:
2, 3, 2*3, 3*3, etc...
If there are 3 teams we have:
36/3 = 12 students per team.
If there are 6 teams we have:
36/6 = 6 students per team.
if there are 9 teams:
36/9 = 4 students per team.
If there are 12 teams:
36/12 = 3 students per team.
If there are 18 teams:
36/18 = 2 students per team.
These are all the possibilities.
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Agents J and K work in a long hallway with 4000 equally-spaced, consecutive offices. The agents decide to walk toward each other so they can meet and have lunch together. Agent J has recently been relocated from office 2013 to office 1. His former office neighbor, Agent K, is still in office 2014. Assuming that Agent J can walk at a rate of 25 offices per minute, and Agent K walks at 36 offices per minute, what office will they meet at if they leave at the same time
At office 826 they will meet if they leave at the same time.
How many offices are there between agents J and K?It is given that,
Agent J has recently been relocated from office 2013 to office 1. But his former office neighbor, Agent K is still in office 2014.
So, there are (2014 - 1) - 1 = 2012 offices in between them.
How much time is required for them to walk the whole distance?It is given that,
Agent J can walk at a rate of 25 offices per minute, and Agent K walks at 36 offices per minute.
So,
Per minute they cross
= 25 + 36
= 61 offices.
Thus, the time required for crossing all the 2012 offices is,
= 2012/61
= 32.9 ≅ 33 minutes
Then,
They will meet at
1 + 25(33) = 826 office (or)
2014 - 36(33) = 826 office (Negative since opposite direction)
Therefore, both of them meet at office 826.
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In a recent poll, 230 people were asked if they liked dogs, and 90% said they did. Find the margin of error of this poll, at the 99% confidence level.
The margin of error of this poll is
Given that 230 people were asked if they liked dogs, and 90% said they did.
In a random sample, a margin of error is a statistical measure that takes into account the discrepancy between actual and expected results.
Sample size (N)=230
Sample proportion [tex](\hat{p})[/tex] = 90% = 0.90 and
confidence interval = 99%
The critical value at 99% confidence interval with α=0.01 is
[tex]\begin{aligned}Z_{c}&=Z_{1-\frac{\alpha}{2}}\\ &=Z_{1-\frac{0.01}{2}}\\ &=Z_{0.995}\\ &=2.576\end[/tex]
This value is taken from the Standard normal distribution table.
Now, we will calculate the margin of error (E) by using the formula
[tex]E=Z_{c}\sqrt{\frac{\hat{p}(1-\hat{p})}{N}}[/tex]
Substituting the values in the formula, we get
[tex]\begin{aligned}E &=2.576\times \sqrt{\frac{0.90(1-0.90)}{230}}\\ &=2.576\times \sqrt{\frac{0.09}{230}}\\ &=2.576\times\sqrt{0.00039}\\ &=2.576\times 0.0197\\ &=0.0507\end[/tex]
Hence, the margin of error when 230 people were asked if they liked dogs, and 90% said they did is 0.0507.
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