a) SS = {HHH, THH, HTH, HHT, THT, TTH, HTT, TTT} i) P(1 head) = 0.375 ii) P(at least 2 heads) = 0.5 iii) P(no heads) = 0.125.
Suppose that a coin is tossed three times and the side showing face up on each toss is noted. Suppose also that on each toss heads and tails are equally likely. Let HHT indicate the outcome heads on the first two tosses and tails on the third, THT the outcome tails on the first and third tosses and heads on the second, and so forth.
Given that
a) A coin is tossed three times and the side showing face up on each toss is noted.
The total number of possible outcome are 2³ = 8
The sample space is given by
SS = {HHH, THH, HTH, HHT, THT, TTH, HTT, TTT}
b) Write each of the following events as a set, in set-roster notation, and find its probability.
(i)The event that exactly one toss results in a head.
In this case we need to include only those outcomes where we have exactly on head,
E(1 head) = {THT, TTH, HTT}
So there are 3 such outcomes, the probability is
P(1 head) = no. of desired outcomes/total number of outcomes
P(1 head) = 3/8
P(1 head) = 0.375
(ii) The event that at least two tosses result in a head
In this case we need to include only those outcomes where we have at least two heads which means two or greater than two,
E(at least 2 heads) = {HHH, THH, HTH, HHT}
So there are 4 such outcomes, the probability is
P(at least 2 heads) = 4/8
P(at least 2 heads) = 0.5
(iii) The event that no head is obtained.
In this case we need to include only those outcomes where we have no heads at all.
E(no heads) = {TTT}
So there is only 1 such outcome, the probability is
P(no heads) = 1/8
P(no heads) = 0.125
Hence the answer is a) SS = {HHH, THH, HTH, HHT, THT, TTH, HTT, TTT} i) P(1 head) = 0.375 ii) P(at least 2 heads) = 0.5 iii) P(no heads) = 0.125.
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Use elimination to solve the equations
1. x - 2y = 4
-x + y = -2
2. -x + y = 3
3x + y = 11
3. -4x - 2y = -12
4x + 8y = -24
Answer:
Step-by-step explanation:
1. x=5
2. xy7
a measure of the long-run average value of a random variable used to represent the central location of a probability distribution is called a(n) .
The measure of the long -run average value of a random variable used to represent the central location of a probability distribution is called an expected value E(x).
As given in the question,
Reason with explanation :
The Mean represents the central location of the random variable.It represent the weighted average of the value taken by X.Weight represents the probability distribution.The expected average value of the many distributed value.The average value of a random variable to represents the central location is called expected value.Therefore, the measure of the long run average value of a random variable representing central location of the probability distribution is called the expected value.
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scores from the sit and reach test weren't normally distributed. what is the likely cause for this lack of normal distribution?
A normal distribution can appear utterly erratic due to a lack of data. Results from tests taken in class, for instance, are often regularly distributed.
Given information;
Scores from the sit and reach test weren't normally distributed.
To find what is the likely cause for this lack of normal distribution,
⇒ A normal distribution can appear utterly dispersed due to Insufficient Data. For instance, test scores in the classroom are often regularly distributed.
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when a truckload of apples arrives at a packing plant, a random sample of 150 is selected and examined for bruises, discolouration, and other defects. the whole truckload will be rejected if more than 5% of the sample is unsatisfactory. suppose that 8% of the apples on the truck do not meet the desired standard. what is the probability that the shipment will be accepted anyway? remember to check if the sample size is large enough!
The probability that the shipment will be accepted anyway is 0.0885.
Given,
In the question:
A random sample of 150 is selected and examined for bruises, discoloration, and other defects. The whole truckload will be rejected if more than 5% of the sample is unsatisfactory. Suppose that 8% of the apples on the truck do not meet the desired standard.
To find the probability that the shipment will be accepted anyway.
Now, According to the question:
The sample size, n = 150.
The population proportion, p = 0.08.
The shipment is accepted of the sample proportion is less than 5%.
Now, to find the required probability the listed conditions to verified.
Randomization: It was stated that a random sample is chosen.
Independence: It can be supposed that the fact that a sample is satisfactory is independent of the other apple's condition.
10% condition: It can be supposed that the population size is larger than 150 (sample size).
Normality: This condition requires that np and n (1 − p) must be at least 10, so it can be verified as,
np = (150 x 0.08)
np = 12 [tex]\geq[/tex] 10
The mean of the sample proportion can be estimated as:
μ[tex]_p[/tex] = p
= 0.08
Similarly, The standard deviation of the sample proportion can be estimated as:
σ[tex]_p[/tex] = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]
= [tex]\sqrt{\frac{0.08(1-0.08)}{150} }[/tex]
= 0.02215
Thus, the sampling distribution of sample proportion can be approximated as,
p ~ N(0.08 ~ 0.0222)
The required probability is given as:
P(p < 0.05) = P (p - μ[tex]_p[/tex] /σ[tex]_p[/tex] < 0.05 - 0.08/ 0.0222)
= P(Z < -1.35)
= 1 - P (Z < 1.35)
= 0.0885
Note: The probability value corresponding to the Z score is obtained from the unit normal table.
Thus, the probability that the shipment will be accepted anyway is 0.0885.
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judy selected ten states and then calculated statistics on them. which statement best describes the resulting statistics?
The statement best describing is only statistics for the ten states are reported
The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data. Statistics can be used to make future predictions calculate the likelihood that a given event will occur, or provide information about a survey. It primarily serves to convey knowledge, compute probabilities, and store records. In essence, it improves our understanding of the world by using numbers and other quantitative data.
In the given case, a total of ten states were selected by Judy and then the statical analysis was made. As per the given options, the correct option is that only statistics for the ten states are reported. This is because the number of terms, which are the states is ten.
Complete Question
Judy selected ten states and then calculated statistics on them. Which statement best describes the resulting statistics?
Only statistics for the ten states are reported.
No statistics are reported.
Statistics for all fifty U.S. states are reported.
The number of states included in the report depends on whether an attribute, interactive or spatial query was used to make the selection.
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Pls help!! Trying to do asap! First answer will get brainleist
Answer:
84
Step-by-step explanation:
Answer:
Step-by-step explanation:
Let, the dimension of cuboid are l=5x,b=4x and h=2x
Now, the surface area of cuboid =2(5x×4x+4x×2x+2x×5x)=76x2
Now,
76x2=1216
x2=16
x=4
Dimensions of cuboid are,
l=5x=5×4=20cm,b=4x=4×4=16cm
h=2x=2×4=8cm
Volume of cuboid=l×b×h=20×16×8=2560cm3
Hence, this is the answer.
one morning, ms. simon drove directly from her home to her workplace in 242424 minutes. what was her average speed, in miles per hour, during her drive that morning?
The average speed in miles per hour during her drive that morning is 43.5 miles per hour .
In the question ,
it is given that ,
the distance between home to freeway entrance is = 0.6 miles
the distance between freeway entrance to freeway exit is = 15.4 miles
the distance between freeway exit to workplace is = 1.4 miles
So , the distance from home to work place = 0.6 + 15.4 + 1.4 = 17.4 miles
we know that 24 minutes = 24/60 = 0.4 hours ,
the average speed = total distance / total time
= 17.4/0.4
= 43.5 miles per hour
Therefore , the average speed is 43.5 miles per hour .
The given question is incomplete , the complete question is
One morning, Ms. Simon drove directly from her home to her workplace in 24 minutes. what was her average speed, in miles per hour, during her drive that morning ?
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an electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 40 hours. how large a sample is needed if we wish to be 96% confident that our sample mean will be within 10 hours of the true mean?
A sample of at least 68 bulbs is needed to be 96% confident that our sample mean will be within 10 hours of the true mean.
What do you mean by sampling?
Sampling is the process of choosing the group from which you will actually collect data for your study. For instance, you could interview a sample of 100 students if you were examining the viewpoints of students at your university. With the help of sampling, you can test a statistical hypothesis on the features of a population.
According to the question,
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha =\frac{1-0.96}{2} =0.02[/tex]
Now, we have to find z in the Z table as such z has a p value of [tex]1-\alpha[/tex].
So it is z with a p value of [tex]1-0.02=0.98[/tex], so z= 2.055
Now, find the margin M as such
M = z*σ/√n
In which σ is the standard deviation of the population and n is the size of the sample.
In this problem, we have that:
σ = 40, M = 10,
M = z*σ/√n
[tex]10=2.055*\frac{40}{\sqrt{n} } \\10\sqrt{n}=82.2\\ \sqrt{n}=8.22\\ n=67.6[/tex]
Therefore, a sample of at least 68 bulbs is needed to be 96% confident that our sample mean will be within 10 hours of the true mean.
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Select all the prime numbers.
3
9
13
23
33
Answer:
Prime Numbers: 3,13,23,33
Composite Number: 9
Step-by-step explanation:
If a number has only 2 factors 1 and itself, then the number is prime
if you have string of length 50 cm, what are the dimension
of the rectangle of maximum area that you can enclose with your string?
expline your reasoning. what about string of length K cm?
The dimension of the rectangle of maximum area that you can enclose with the string is 12.5 x 12.5
n let x = the length of one side of the rectangle and y = the length of the other side of the rectangle.
The area is:
A = xy
and the perimetere is the string of length 50 cm
50 = 2(x + y) Solve this in terms of y. Divide both sides by 2.
25 = x + y By Subtract x from both sides.
25-x = y Now substitute this into the equation for the area.
A = x (25 - x) Simplify.
A = 25x - x²
the general form of quadratic equation: ax² + bx + c
x is given by -b/2a
Here the equation is A = -x² + 25x
, a = -1, b = 25, and c = 0
so we can find the x-coordinate of the vertex by -25/2(-1) = 12.5
So the length (x) of the rectangle must be 12.5 cm to get the maximum area.
But what about the width (y)?
Since the perimeter is 50 cm and this is twice the (length + width), the (length + width) is 25 cm, so the width is 25 cm - the length.
x + y = 25
12.5 + y = 25
y = 12.5
So, we end up with x (the length) = 12.5 cm and y (the width) = 12.5 cm.
And this, of course, is a square whose sides are 12.5 cm
If the perimeter were k cm,
2(x + y) = k
x + y = k/2
x + x = k/2 (as x = y)
x = k/4
x = k/4, y = k/4
Therefore, the dimension of the rectangle of maximum area that you can enclose with the string is 12.5 x 12.5
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PLEASE I NEED HELP I WILL GIVE YOU BRAINLIEST
in the graph of the inequality x-2y (less than or equal too) 4, which is a value for x on the boundary line and the x axis
4
-2
2
-4
The value of x on the boundary line and the x axis is found as 4.
Explain the term inequality?In mathematics, "inequality" refers to a relationship among two expressions and values that is not equivalent to each other. Therefore, inequality emerges from a lack of balance.When two components are equal, we use the sign "=," and if they are not equal, we use the symbol "," which stands for "not equal."For the given question,
The graph of inequality x-2y ≤ 4 is drawn.
Consider the graph,
The straight lien formed by the graph touches the x coordinate axis at (4,0).
Thus, the value of x on the boundary line and the x axis is found as 4.
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Which of these relations is a function?
Graph D is a function because it passes the vertical line test
Vertical Line TestA vertical line test helps to find if the graph is a function or not. The vertical line in a coordinate system represents a set of infinite points having the same x coordinate values and different y coordinate values for each of its points. The vertical line is drawn parallel to the y-axis, if it cuts the curve at one distinct point then it has one y-value for the given x value and it follows the basic definition of a function.
Applying the vertical line test in the graphs given, only graph D is a function.
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You have $10,000 to invest in a stock portfolio. Your choices are Stock X with an expected return of 13 percent and Stock Y with an expected return of 8 percent. Your goal is to create a portfolio with an expected return of 12.4 percent. All money must be invested. How much will you invest in stock X? A. $800B. $1,200C. $4,600D. $8,800E. $9,200
The money invested in stock X is $8,800.
Given,
Total investment in stock portfolio=$10000
Expected return from stock X=13%=0.13
Expected return from stock Y=8%=0.08
Expected return from portfolio=12.4%=0.124
The portfolio return is calculated by taking the weighted average of individual stock returns.
Let x represent the portfolio weightage of stock X.
1-x is the portfolio weightage of stock Y.
money invested in stock X be
0.124=0.13x+0.08(1-x)
0.124=0.13x+0.08-0.08x
0.124-0.08=0.05x
0.044=0.05x
x=0.88
money invested in stock X=0.88*10000=$8800
Thus, the money invested in stock X is $8,800.
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The probability that a marksman will hit a target each time he shoots is 0. 89. If he fires 15 times, what is the probability that he hits the target at most 13 times?.
Answer:
Step-by-step explanation:
Correct option is A)
Determine the degree measure of one angle of a 36-sided regular polygon. 170° 180° 6,120° 6,480°
Answer:
170 Degrees.
Step-by-step explanation:
If an interior angle is 170 degrees, that's your best bet.
a bin contains 4 items: 1 a, 1 b, 2 c and 6 d. a person randomly selects 3. how many different types of items will be selected
Using combinations, we know that 4 different types of items will be selected.
What are combinations?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.
We can choose the components of combos in any order.
Permutations and combinations can be mixed up.
Combination formula: [tex]n C r=\frac{n !}{(n-r) ! r !}[/tex]
So, this formula, commonly known as the NCR formula, determines the number of combinations that may be made with r items out of the n available options.
We, therefore, have 4 objects, and a person chooses 3 at random.
[tex]\begin{aligned}& n C r=(n, r)=(4,3) \\& =\frac{4 !}{3 !(4-3) !} \\& =4 ! / 3 ! \\& =4\end{aligned}[/tex]
Therefore, using combinations, we know that 4 different types of items will be selected.
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Marko has $22. He needs at least $42 to go to a concert. How much more money does Marko need?
Marko needs the amount of money which would be $20 to go to a concert.
What is the Subtraction operation?Subtraction is a mathematical operation that deducts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
We have been given that Marko has $22. He needs at least $42 to go to a concert.
We have to determine the required amount of money Marko
the required amount of money = cost of the concert - he has the amount
the required amount of money = $42 - $22
Apply the subtraction operation, and we get
the required amount of money = $20
Therefore, Marko needs the amount of money that would be $20.
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Factorise the following: a) x² + 6x + 8 b) x²-9x + 18 c) x² - 8x-9 d) x² + 6x-27
a) To factorize this expression, we need to find two numbers that multiply to give 8 and add to give 6. The two numbers that fit this description are 4 and 2, so we can write the expression as x² + 6x + 8 = (x + 4)(x + 2).
b) To factorize this expression, we need to find two numbers that multiply to give 18 and add to give -9. The two numbers that fit this description are -6 and -3, so we can write the expression as x²-9x + 18 = (x - 6)(x - 3).
c) To factorize this expression, we need to find two numbers that multiply to give -9 and add to give -8. The two numbers that fit this description are -3 and 3, so we can write the expression as x² - 8x-9 = (x - 3)(x + 3).
d) To factorize this expression, we need to find two numbers that multiply to give -27 and add to give 6. The two numbers that fit this description are -9 and 3, so we can write the expression as x² + 6x-27 = (x + 9)(x - 3).
Grayson owns a food truck that sells tacos and burritos. He only has enough supplies
to make 110 tacos or burritos. He sells each taco for $3.25 and each burrito for $7.
Grayson must sell a minimum of $560 worth of tacos and burritos each day. If x
represents the number of tacos sold and y represents the number of burritos sold,
write and solve a system of inequalities graphically and determine one possible
solution.
Using system of linear inequality, the number of tacos and burrito he sold was 56 and 54 respectively
System of Linear InequalityA system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system.
To solve this problem, we have to write two system of inequality and then graph the inequalities to show the solution.
Let;
x = tacosy = burritosx + y = 110 ...eq(i)
7x + 3.25y ≥ 560 ..eq(ii)
From eq(i)
x + y 110
x = 110 - y ..eq(iii)
Put eq(iii) into eq(ii)
7(110 - y) + 3.25y ≥ 560
770 - 7y + 3.25y ≥ 560
770 - 3.75y ≥ 560
-3.75y ≥ 560 - 770
-3.75y ≥ -210
y ≤ 56
Assuming y is less than or equal to 56, x will be
x + 56 = 110
x = 54
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in a science classroom, when labs are performed, students are seated at lab tables. if the teacher assigns 2 students to each lab table, 4 additional lab tables will be needed to seat all of the studetnds. if the teacher assigns 4 students to each lab table, 4 lab tables will not be used. how many students are in the science clas
Answer: 16 students
Step-by-step explanation:
2x + (2•4) = 4x
2x + 8 = 4x
-2x -2x
8 = 2x
(Divide by 2 on both sides)
vvv
2x/2= x
8/2 = 4
x = 4
(substitute 4 in for x)
2(4) + 8 = 4(4)
8+8 = 16
16 = 16
A final exam in Math 160 has a mean of 73 with standard deviation 7.8. If 24 students are randomly selected, find the probability that the mean of their test scores is greater than 78. A) 0.0103 B) 0.0008 C) 0.8962 D) 0.0036
The probability that the mean of their test scores is greater than 78 is 0.0301.
Given,
Mean = 73
Standard Deviation σ = 7.8
Number of students randomly selected = 24
Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x.
The formula to calculate the probability of an event is as follows.
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n
The number of standard deviations from the mean is called the z - score and can be found by the formula
Z = (x - μ)/σ.
Z = (70 - 73)/(7.8/√24) = -1.88442228
P(z < -1.88) = 0.0301
Therefore, P(z < -1.88) = 0.0301
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Linear relationship.
The slope value of the linear relationship tells us how much Austin pays to his friend weekly, which is: $8.
How to Find the Slope of a Linear Relationship?A linear relationship between two variables, x and y, can be defined by the equation, y = mx + b, where the value of m is the slope and b is the y-intercept or starting value.
If we have a table that represents a linear relationship between two variables, x and y, what we need to do is to use two pairs of values from the table to find the change in y / change in x.
In this context, L = amount Austin owes his friend for t weeks, so the slope will be the amount Austin pays to his friend every week = change in L / change in t.
Using two pair of values from the table, (1, 32) and (4, 8):
Slope (m) = change in L / change in t = (32 - 8) / (1 - 4)
Slope (m) = 24/-3
m = -8
Therefore, the amount Austin will be paying to his friend weekly would be $8.
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What does the equation look like after you combine like terms?
−3x + 2 − 4x = 16
7x+2=16
x+2=16
−x+2=16
−7x+2=16
Answer:
it'll look like the last one -7x + 2 = 16
Please answer quickly :) If wrong i will report
Answer:
(0,2)
Step-by-step explanation:
plug in 0 for x
can you help me find the points for this question? And how to solve it?
The line segment has a length of 13 units. (Correct choice: D)
How to determine the length of a line segment
According to Euclidean geometry, any line can be constructed by the locations of two distinct points on Cartesian plane. In this question we must determine the length of the line segment by means of Pythagorean theorem, whose formula is shown below:
l = √(x² + y²)
Where:
l - Length of the line segment.x - Horizontal length of the line segment.y - Vertical length of the line segment.First, determine the horizontal and vertical lengths of the line segment:
x = 12, y = 5
Second, determine the length of the line segment:
l = √(12² + 5²)
l = √169
l = 13
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Sadio tart with aving of £15. Thoma tart with no aving. Each week from now,
Sadio will ave £3. 50 and Thoma will ave £3
in how many week will Sadio and Thoma have aving in the ratio 2:1?
In total 6 weeks, the saved money by both Sadio and Thoma will be in the ratio of 2:1.
Define the term ratios?When two or so more numbers are compared, the ratio shows how big one is in relation to the other. The dividend and number being divided is referred to as the antecedent, and the divisor for number that also is dividing is referred to as the consequent. A ratio compares two numbers by division.For the given question.
Initial money owned by each is-
Sadio = $15
Thoma = $0.
Let the number of weeks passed be 'x'.
Then, present money after x weeks.
Sadio = $3.50x + 15
Thoma = $3x
The number of weeks , when ratio becomes 2:1
(3.50x + 15)/3x = 2/1
3.50x + 15 = 6x
6x - 3.5x = 15
x = 15/2.5
x = 6
Thus, in total 6 weeks, the money held by both Sadio and Thoma will be in the ratio of 2:1.
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A.) 5/4
B.) 1/2
C.) -5
D.) 3
Answer: A
Step-by-step explanation:
4y=5x-16
divide each side by 4
y=5/4x-4
Answer:
Step-by-step explanation:
5/4 is the answer
cause you add =4y to other side and -16 to left side
divide by 4 on both sides to get
5/4x -4 = y
back to assignment attempts keep the highest no score out of 2/ 2 10. missing data which of the following are valid reasons for why there may be missing data in a well-designed study? check all that apply. some respondents didn’t know the answer to the question. some respondents refused to answer the question. data for some respondents were lost or misrecorded. researchers always have access to all values of all variables in the data set of a well-designed study. why might eliminating respondents with missing data compromise the results of a study? a random sample may no longer be random if you eliminate some members of the sample. statistical software is not equipped to handle eliminating responses. continue without saving
There may be missing data in a well-designed study because some respondents didn’t know the answer to the question, some respondents refused to answer the question and data for some respondents were lost or misrecorded. A random sample may no longer be random if you eliminate some members of the sample so eliminating might respondents with missing data compromise the results of a study
The first question is:
Missing data which of the following are valid reasons for why there may be missing data in a well-designed study? check all that apply.
some respondents didn’t know the answer to the question. some respondents refused to answer the question. data for some respondents were lost or misrecorded. researchers always have access to all values of all variables in the data set of a well-designed study.The option 1, 2 and 3 may be possible reasons.
It is possible that some respondants did not know the answer of the question. Because it is not neccesary that every respondants know the answer of the quesions that are asked. So they can provide the wrong data and also not give the answer.
Some may refuse to answer because they don't want to answer or may be it is deficult to answer of those questions.
It may also possible that the the record were lost or misrecorded. Because there is lot of data that they have to organize and also possible there have many same detalis in the respondants that leads to the misrecoding.
The second question is:
Why might eliminating respondents with missing data compromise the results of a study?
a random sample may no longer be random if you eliminate some members of the sample. statistical software is not equipped to handle eliminating responses. continue without savingIf we eliminate a random sample then it is possible that the data may be biased and didn't involve the all factors. So it leads to wrong result and may harm the all process. So it directly effect the result of a study.
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explain how the is related to the standard error of the estimated difference in average birth weight for smoking and nonsmoking mothers.
The average birthweight of a nonsmoker was between 1,000 and 5,000 grams. Babies born to smokers frequently weighed between 500 and 4500 grams.
Given,
What is the newborn's weight?
A newborn's body weight is referred to as birth weight. At birth, babies of European descent typically weigh between 2.5 and 4.5 kilograms, or about 3.5 kilograms on average. South Asian and Chinese babies typically weigh 3.26 kg.
Here,
Babies born to nonsmokers typically weighed between 1,000 and 5,000 grams. Babies of smokers typically ranged in weight from 500 to 4500 grams.
However, there are some obvious disparities between the two groups' typical ranges of birth weights. Since there are fewer newborns in the lower weight groups, over half of neonates among nonsmokers (56 out of 115, 48.7%) had birth weights between 3,000 and 4,000 grams. Less infants are born in the heavier weight categories; 40 of the 74 newborns delivered to smokers, or 54% of them, had birth weights between 2,000 and 3,000 grams.
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Your team has 17 kickballs to store in baskets.
Each basket can hold 5 kickballs.
How many baskets do you need to store all the kickballs?
Answer:
85baskets
Step-by-step explanation:
17*5=85 baskets,if each basket hold 5kickballs 17*5.