Answer:
To answer these, we can use the standard normal distribution & z-scores. A z-score represents the number of standard deviations a value is from the mean. The formula to calculate a z-score is: z = (x - μ) / σ, where x is the value, μ is the mean and σ is the standard deviation.
A) To find the proportion of pregnancies that last more than 278 days, we first calculate the z-score for 278 days: z = (278 - 272) / 12 = 0.5. Using a standard normal distribution table, we find that the proportion of values above a z-score of 0.5 is approximately 0.3085. So, about 30.85% of pregnancies last more than 278 days.
B) To find the proportion of pregnancies that last between 257 and 275 days, we first calculate the z-scores for both values: z1 = (257 - 272) / 12 = -1.25 and z2 = (275 - 272) / 12 = 0.25. Using a standard normal distribution table, we find that the proportion of values between z-scores of -1.25 and 0.25 is approximately 0.3944. So, about 39.44% of pregnancies last between 257 and 275 days.
C) To find the probability that a randomly selected pregnancy lasts no more than 266 days, we first calculate the z-score for 266 days: z = (266 - 272) / 12 = -0.5. Using a standard normal distribution table, we find that the proportion of values below a z-score of -0.5 is approximately 0.3085. So, there is about a 30.85% chance that a randomly selected pregnancy lasts no more than 266 days.
D) To determine if very preterm babies are unusual, we first calculate the z-score for 242 days: z = (242 - 272) / 12 = -2.5. Using a standard normal distribution table, we find that the proportion of values below a z-score of -2.5 is approximately 0.0062. Since this value is less than 0.05, we can conclude that very preterm babies are unusual.
what is the
quotient of 62.72+4.9
Answer:
12.8
Step-by-step explanation:
Quotient means the answer of two things divided.
62.72/4.9=12.8
A school purchases boxes of paints for the annual painting competition. The expression below represents the total price for the order including delivery to the school. $11.75x + $20
Answer:
The expression $11.75x + $20 represents the total price for the order, including delivery to the school.
In this expression, 'x' represents the number of boxes of paints being purchased, and $11.75 represents the cost of each box. The term $11.75x represents the total cost of the boxes of paints based on the number of boxes being purchased.
The term $20 represents the delivery cost to the school, which is added to the total cost of the boxes of paints.
By multiplying the cost per box ($11.75) by the number of boxes (x) and adding the delivery cost ($20), you can calculate the total price for the order, including delivery.
suppose that the function G is defined for all real numbers as follows. Find g(-5), g(-2) and g(-1)
If "function-g" defined for all real numbers as g(x) = x² + 6, then the value of g(-5) = 31, g(-2) = 10 and g(-1) = 7.
In mathematics, a function is generally denoted by a symbol such as "f" or "g", and its definition is given by an equation or formula that specifies the relationship between the input and output values.
The function "g" is given as : g(x) = x² + 6;, which is defined for all "real-numbers",
So, to find g(-5), g(-2), and g(-1), we simply substitute these values of x into the function "g" and simplify the resulting expressions:
⇒ g(-5) = (-5)² + 6 = 25 + 6 = 31,
⇒ g(-2) = (-2)² + 6 = 4 + 6 = 10,
⇒ g(-1) = (-1)² + 6 = 1 + 6 = 7.
Therefore, g(-5) = 31, g(-2) = 10, and g(-1) = 7.
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The given question is incomplete, the complete question is
Suppose that the function G is defined for all real numbers as g(x) = x² + 6. Find g(-5), g(-2) and g(-1).
a train will travel 300 kilometers at a constant rate. write an equation that represents the trains rate in kilometers per hour (r) based on how mant hours the trip takes (t).
Answer:
distance = rate x time
where distance is 300 kilometers and time is t hours. Rearranging this formula to solve for rate, we get:
rate = distance / time
Substituting the given values, we get:
r = 300 / t
Therefore, the equation that represents the train's rate in kilometers per hour based on how many hours the trip takes is r = 300/t.
Step-by-step explanation:
A regular heptagon has a side of approximately 3.9 yd and an apothem of approximately 4.0 yd.
Find the area of the heptagon
Answer:
54.6 square yards
Step-by-step explanation:
For any regular polygon, the area of the polygon is given by:
[tex]A_{regular~polygon}=\frac{1}{2}nsa[/tex], where
n is the number of sides of the polygon, s is the side length of the polygon, and a is the length of the apothem.Heptagons are 7-sided polygons, so n=7.
The length of a side and the apothem are given, so substitute and calculate:
[tex]A_{heptagon}=\frac{1}{2}(7)sa[/tex]
[tex]A_{heptagon}=\frac{1}{2}(7)(3.9~yd)(4.0~yd)[/tex]
[tex]A_{heptagon}=54.6 ~yd^2[/tex]
Determine the solution to the equation shown below.
3.2 - 1/2 (x+4) = 4.8x + 2 - 5.2x
Answer:x=-8
Step-by-step explanation:
3.2+(−1/2)x−2=4.8x+2−5.2x
−0.1x=0.8
x=-8
Answer:
x=-8
Step-by-step explanation:
x=-8
Shape of sampling, distribution, CLT application and proportion
1. normally distributed if the sample size is 30 or larger.
2. Not always normally distributed.
3. Skewed to the right is still normally distributed
4. normally distributed.
1. normally distributed if the sample size is 30 or larger.
2. If the population from which samples are drawn is not normally distributed, then the sampling distribution of the sample mean is not always normally distributed. It depends on the sample size and the shape of the population distribution.
3. The sampling distribution of the sample mean for a sample of 10 elements taken from a population with a bell-shaped distribution that is skewed to the right is still normally distributed, by the central limit theorem, as long as the sample size is sufficiently large (typically at least 30) or the population distribution is approximately normal. Therefore, the answer is normally distributed.
4. The sampling distribution of the sample mean for a sample of 36 elements taken from a population with a bell-shaped distribution is normally distributed regardless of the population's skewness. Therefore, the answer is "normally distributed".
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Help with math problems
The surd forms are simplified to give;
21. 10√6 - 12√10
23. -56a - 5√2a - 25
25. -4√15x - 25x + 3
What are surds?Surds are described as values in square root that can no longer be simplified into whole numbers or integers
They are also seen as irrational numbers.
From the information given, we have that;
√15(2√10 - 4√6)
Expand the bracket and multiply the surd forms
2√150 - 4√90
Factorize the forms
2√25 ×√6 - 4√9 × √10
find the square root
10√6 - 12√10
23. (√2a - 5)(7√2a - 5)
expand the bracket
7√4a² - 5√2a - 35√4a² + 25
find the square root, we have;
7×2a - 5√2a - 35×2a + 25
collect the like terms
14a - 70a - 5√2a - 25
-56a - 5√2a - 25
25. (√3 + √5x)(√3 - 5√5x)
expand the bracket
3 - 5√15x + √15x - 5√25x²
find the square root
3 - 5√15x + √15x - 25x
collect the like terms
-4√15x - 25x + 3
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Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation.
United States Birth Rate (per 1000)
Birth Rate
A graph titled United States Birth Rate (per 1000) has year on the x-axis and birthrate on the y-axis. Points trend in a negative line.
Year
Source: National Center for Health Statistics, U.S. Dept. of Health and Human Services
a.
no correlation
b.
positive correlation; as time passes, the birth rate increases.
c.
positive correlation; as time passes, the birth rate decreases.
d.
negative correlation; as time passes, the birth rate decreases.
A negative correlation may be seen on the graph. The birth rate declines over time. This indicates that the number of births per 1000 persons in the US has been declining over time.
(40 POINTS)
Data based on past observations can sometimes predict future performance.
a. Give an example where past performance does predict future performance. Explain your reasoning.
b. Give an example where past performance does not predict future performance. Explain your reasoning.
An example of where past performance does predict future performance would be Mt. Kīlauea's eruption in 2018.
An example of where past performance does not predict future performance would be the eruption of Hualālai last happening in 1801.
What does the data show on volcanoes ?Using past data, there was a prediction that Mt. Kīlauea would erupt in the year 2018 and it did happen ( even though it was not very serious ) at the Lower East rift zone of the volcano. Past performance therefore predicted the future.
However, the same prediction said that Hualālai would erupt in 1854 and yet the volcano has not erupted since 1801 which shows that the prediction was wrong.
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Suppose that diameters of a new species of apple have a bell-shaped distribution with a mean of 7.42cm
7.42cm and a standard deviation of 0.36cm. Using the empirical rule, what percentage of the apples have diameters that are between 6.34cm and 8.5cm
The percentage of percentage of the apples have diameters that are between 6.34cm and 8.5cm is given as follows:
99.7%.
What does the Empirical Rule state?The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:
The percentage of scores within one standard deviation of the mean of the distribution is of approximately 68%.The percentage of scores within two standard deviations of the mean of the distribution is of approximately 95%.The percentage of scores within three standard deviations of the mean off the distribution is of approximately 99.7%.The measures of 6.34 cm and 8.50 cm are the bounds exactly within three standard deviations of the mean, hence the percentage is given as follows:
99.7%.
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Find the perimeter of the triangle below.
31 cm
36.8 cm
9.73 cm
Answer:
77.53
Step-by-step explanation:
You just have to sum them up
Answer:
i think the answer is 77.53
Step-by-step explanation:
pls help with this geometry asap
Area of sector XYZ is 81.45 feet².
Define area of sectorThe area of a sector is a measure of the size of a portion of a circle enclosed by two radii and an arc between them. It is expressed in square units, such as square centimeters, square meters, or square inches.
To find the area of a sector, you need to know the radius of the circle and the central angle of the sector.
The formula for the area of a sector is:
Area of sector = (central angle / 360°) x π x r²
where r is the radius of the circle, π is the mathematical constant pi (approximately 3.14), and the central angle is measured in degrees.
n is the area of sector XYZ
n/360=115/255(X)
n/255=115/360(V)
(The same elements are proportional)
n=115/360×255
n=81.4583≈81.45 feet²
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A spherical balloon has a 20-in. diameter when it is fully inflated. Half of the air is let out of the balloon. What is the volume of the fully-inflated balloon?
The volume of the fully - inflated balloon is 4186.67 cubic inches. The solution has been obtained by using the formula for sphere.
What is a sphere?
The geometric equivalent of a circle in two dimensions in three dimensions is a sphere. A collection of three-dimensional points with the same r separation between them are referred to as a sphere.
We are given diameter as 20 inches.
So, the radius is half of the diameter which comes out to be 10 inches.
From this, we get the volume as
⇒ Volume = [tex]\frac{4}{3}[/tex] π [tex]r^{3}[/tex]
⇒ Volume = [tex]\frac{4}{3}[/tex] π [tex]10^{3}[/tex]
⇒ Volume = [tex]\frac{4000}{3}[/tex] π
⇒ Volume = 4186.67 cubic inches
Hence, the volume of the fully - inflated balloon is 4186.67 cubic inches.
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Write as a product 4x^2+y^2-4xy-16
PLEASEEE Help :')
Need by TONIGHT 11:59 EDT
Will give brainliest (need 2+ ppl to answer to give brainliest, I will give the first answer branliest)
Answer:
We can write 4x^2 + y^2 - 4xy - 16 as the product:
(2x - y + 4)(2x - y - 4)
Step-by-step explanation:
To write 4x^2 + y^2 - 4xy - 16 as a product, we can use the technique of completing the square. First, we can rearrange the terms to group the x terms and the y terms:
4x^2 - 4xy + y^2 - 16
Next, we can complete the square for the x terms and the y terms separately. For the x terms, we can add and subtract (2x)^2:
4x^2 - 4xy + (2x)^2 - (2x)^2 + y^2 - 16
Simplifying the first three terms gives:
(2x - y)^2 - (2x)^2 + y^2 - 16
For the y terms, we can add and subtract 16:
(2x - y)^2 - (2x)^2 + (y - 4)^2 - 16^2
Simplifying the second term gives:
-(4x^2) + 16x - (y^2) + 16y - 16^2
Therefore, we can write 4x^2 + y^2 - 4xy - 16 as the product:
(2x - y + 4)(2x - y - 4)
ACTIVITY 1: Complete the table below by computing the unknown component of simple interest.
Answer:
what arecrosses on line 2
5. Find x and y of a , b and c
The value of x and y will be
a) x= 48 y= 72
b) x= 10 y= 3
c) x= 18 y= 3
What is triangle proportionality theorem ?
Triangle Proportionality Theorem Statement
If a line is drawn parallel to any one side of a triangle so that it intersects the other two sides in two distinct points, then the other two sides of the triangle are divided in the same ratio.
DA/BD = EC/BE
How we can calculate the value of x and y from the figure ?
The value of x and y can be calculated as
a ) x/4 + 5 =x/2-7 y/3-6=66-2/3y
x/4- x/2 = -7-5 y/3+ 2y/3= 66 + 6
x-2x/4=-12 3y/3= 72
x= 48 y=72
b) x/5 +3 = 4x-35 2y + 1 = 5y-8
x/5 - 4x = -35-3 2y-5y= -8-1
x-20x/5 = -38 -3y=-9
-1 9x/5 = -38 y=3
x= 10
c) x/3 + 2= 2x/3-4 5y=7y/3+8
x/3-2x/3= -4-2 5y-7y/3=8
-x/3 = -6 15y-7y=8x3
x= 18 y=3
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In Tasheena's Anthropology class Quizzes are worth 15% of the final grade, Exams are worth 55%, Projects are worth 25%, and Attendance is worth 5%.
At mid-semester Tasheena scored 117 out of 150 points on quizzes, 74, 86, and 91 on the first three exams,each worth 100 points. She got extra credit on her project with a score of 29 out of 25 possible points, and she had perfect attendance to class. Compute Tasheena's grade percentage in the class so far.
Tasheena's grade percentage in the class so far is approximately 71.00935%.
How do you find percentages?The percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.
To compute Tasheena's grade percentage in the class so far, we can calculate the weighted average of her scores based on the weightage of each component of the final grade.
Given:
Quizzes: 15% weightage
Exams: 55% weightage
Projects: 25% weightage
Attendance: 5% weightage
Tasheena's scores:
Quizzes: 117 out of 150 points
Exams: 74, 86, and 91 on the first three exams (each worth 100 points)
Projects: 29 out of 25 possible points
Attendance: Perfect attendance
Let's calculate Tasheena's grade percentage:
Quizzes:
Tasheena's quiz score percentage = (117 / 150) * 100 = 78%
Exams:
Tasheena's exam average = (74 + 86 + 91) / 3 = 83.67
Tasheena's exam score percentage = (83.67 / 100) * 55 = 46.017%
Projects:
Tasheena's project score percentage = (29 / 25) * 100 = 116%
Attendance:
Tasheena's attendance score percentage = 100% (since she had perfect attendance)
Now, let's calculate the weighted average of Tasheena's scores:
Weighted average = (Quizzes weightage * Quiz score percentage) + (Exams weightage * Exam score percentage) + (Projects weightage * Project score percentage) + (Attendance weightage * Attendance score percentage)
= (15% * 78%) + (55% * 46.017%) + (25% * 116%) + (5% * 100%)
= 11.7% + 25.30935% + 29% + 5%
= 71.00935%
Hence, Tasheena's grade percentage in the class so far is approximately 71.00935%.
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A manager of Furniture store has compiled a list of written complaints during the past three months. The complaints were categorized as follows. Type and Frequency Error in billing, Rudeness by store personnel, Late delivery, Questions not answered during telephone inquiry,and Other 42 14 8 6 5 Total 75 Present the above data using pie-chart(put the relative frequencyand the central angle measure toeach categoryon a table)
We can conclude that there is significant evidence that the number of complaints received by Lara music store is different from number of complaints received by music stores in general.
Here, we have,
H0 : μ ≥ 6
H1 : μ < 6
Test statistic :
n = 20
Sample Mean, x = 3
σ = 1.5
Test statistic = (x - μ) ÷ σ/sqrt(n)
Test statistic = (3 - 6) ÷ 1.5/sqrt(20)
Test statistic = - 3 / 0.3354101
Test statistic = −8.944271
Since, sample size is < 30 ;
Obtaining the Critical value using the from T;
Tcritical at 0.05, df = 19 = - 1.729
Tstatistic < Tcritical
−8.944271 < - 1.729
Hence, we reject the Null:
We can conclude that there is significant evidence that the number of complaints received by Lara music store is different from number of complaints received by music stores in general.
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2. You have graduated and landed a good stable job (congratulations!) which requires a commute by car (meh). Your daily drive to work takes about 20 minutes or so with plenty of stoplights and left turns, so it varies day to day. Just out of curiosity you want to find out how long it usually takes to get from home to work, so you accurately time for four weeks. On four of those mornings you stopped for gas or coffee and a bagel or whatever, so you recorded 16 usable results. The mean of these results is 21.4 minutes and the standard deviation is 1.8 minutes. your commute Given these results find a 95% confidence interval for your true average commute time. Assume that these four weeks are a representative sample of your overall commuting experience.
Therefore , the solution of the given problem of unitary method comes out to be a 95% degree of certainty that the genuine average commute time falls within this range.
An unitary method is defined as what?To complete the work, the well-known straightforward strategy, actual variables, and any essential components from the very first and specialised inquiries can all be utilised. In response, customers might be given another opportunity to sample the product. Otherwise, important advancements in our comprehension of algorithms will be lost.
Here,
We may use the following calculation to determine the 95% confidence interval for the actual average commute time:
=> CI = x' ± t*(s/√n)
Finding the essential t-value is the first step. We can apply a two-tailed t-test with a significance level of = 0.05/2 = 0.025 because we have 16 useable findings (sample size: n = 16) and
we require a 95% confidence interval. The crucial t-value, which we determine using a t-distribution table or calculator, is roughly 2.131.
=> CI = 21.4 ± 2.131*(1.8/√16)
=> 21.4 ± 0.95
The genuine average commute time has a 95% confidence interval of 20.45 to 22.35 minutes.
Based on our sample of 16 travel times, we can thus say with a 95% degree of certainty that the genuine average commute time falls within this range.
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99 Points! Algebra question. Photo attached. Please show as much work as possible. Thank you!
The solution to the exponential equation is given as follows:
x = 0.8.
How to solve the exponential equation?The exponential equation in the context of this problem is defined as follows:
[tex]\left(\frac{1}{64}\right)^{0.5x - 3} = 8^{9x - 2}[/tex]
64 is the sixth power of two, while 8 is the third power of two, hence:
[tex]\frac{1}{64} = 2^6[/tex][tex]8 = 2^3[/tex]Applying the power of power rule, the equation can be given as follows:
[tex]2^{-6(0.5x - 3)} = 2^{3(9x - 2)}[/tex]
[tex]2^{-3x + 18} = 2^{27x - 6}[/tex]
Exponential functions are one-to-one, meaning that the solution is obtained as follows:
-3x + 18 = 27x - 6
30x = 24
x = 0.8.
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Will give brainliest if correct
explain reason
Therefore , the solution of the given problem of parallel lines comes out to be parallel lines stay parallel option C is correct.
What applications do parallel lines have?A parallelogram in Euclidean geometry is essentially a straightforward hexagon with two different groups & equal distances. When both sets of sides evenly share a horizontal path, a particular type of quadrilateral known as a parallelogram is created. There are four distinct types of parallelograms, three of them being incompatible. The four distinct forms are slightly parallelograms, rectangular shapes, squares, and parallelograms.
Here,
C. It is untrue that a line may be translated into two parallel lines.
A line can be translated into another line that runs parallel to the first line, but not into two parallel lines.
Every point on the line is rigidly transformed by a translation, which moves all of the points along the line uniformly and in one direction.
After a translation, parallel lines stay parallel.
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8
Jonah is decorating a cake. He uses vanilla frosting on 1/5of the cake, lemon
frosting on 2/5 of the cake, and chocolate frosting on the rest of the cake.
Write and solve an equation to show the part of the cake with vanilla or
lemon frosting.
Show your work.
Answer
The part of the cake with vanilla or lemon frosting is 1/5 by using arithmetic and algebraic expression.
Let's start by defining the variable "x" as the part of the cake with vanilla or lemon frosting.
According to the problem, Jonah uses vanilla frosting on 1/5 of the cake, which can also be written as x = 1/5.
Similarly, he uses lemon frosting on 2/5 of the cake, which can be written as x = 2/5.
We know that the sum of the parts of the cake with vanilla, lemon, and chocolate frosting should equal the whole cake. Since there are only three types of frosting, we can write:
x + x + chocolate frosting = 1
2x + chocolate frosting = 1
We also know that chocolate frosting covers the remaining part of the cake, which is 3/5. Therefore, we can write:
chocolate frosting = 3/5
Substituting this value into the previous algebraic expression, we get:
2x + 3/5 = 1
Subtracting 3/5 from both sides of the equation, we get:
2x = 2/5
x = 1/5
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Liz opened a savings account and deposited $1,000.00 as principal. The account earns 8% interest, compounded quarterly. What is the balance after 4 years?
After the first quarter, the interest earned would be:
$1,000.00 * 0.02 = $20.00
So the new balance would be:
$1,000.00 + $20.00 = $1,020.00
After the second quarter, the interest earned would be:
$1,020.00 * 0.02 = $20.40
So the new balance would be:
$1,020.00 + $20.40 = $1,040.40
After the third quarter, the interest earned would be:
$1,040.40 * 0.02 = $20.81
So the new balance would be:
$1,040.40 + $20.81 = $1,061.21
After the fourth quarter, the interest earned would be:
$1,061.21 * 0.02 = $21.22
So the final balance after 4 years would be:
$1,061.21 + $21.22 = $1,082.43
Therefore, the balance after 4 years would be $1,082.43.
A date in March is chosen at random, then the spinner below is spun once. Find the probability of an odd number, and then blue. Use the counting principle to find the probability.
The probability of randomly selecting a date in March and spinning the spinner once, resulting in an odd number and then blue, is 1/6.
To find the probability of an odd number and then blue, we need to consider the number of favorable outcomes for each event and the total number of possible outcomes.
Probability of an odd number:
The spinner has 6 equally likely outcomes (numbers 1 to 6), and out of these, 3 are odd numbers (1, 3, and 5).
Therefore, the probability of getting an odd number is 3/6, which simplifies to 1/2.
Probability of blue:
The spinner has 6 equally likely outcomes, and out of these, 2 are blue. Therefore, the probability of getting blue is 2/6, which simplifies to 1/3.
To find the probability of both events occurring, we multiply the probabilities of each event:
Probability of an odd number and then blue [tex]= Probability $ of an odd number \times Probability $ of blue[/tex]
[tex]= (1/2) \times (1/3)[/tex]
= 1/6.
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Question: A date in March is chosen at random, then the spinner below is spun once. Find the probability of an odd number, and then blue. Use the counting principle to find the probability.
The standard deviation of test scores on a certain achievement test is 11.4. A random sample of 50 scores on this test had a mean of 75.3. Based on this
sample, find a 95% confidence interval for the true mean of all scores. Then give its lower limit and upper limit.
Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)
Lower limit:
Upper limit:
X
Ś
The lower limit is 72.1 and the upper limit is 78.5.
The sample mean is 75.3, and the standard error is 1.613.
What is standard deviation?The standard deviation is a measurement of how differently distributed a set of data values are from their mean or average. Finding the square root of the variance, which is the sum of the squared deviations between each data point and the mean, is how it is determined.
To find the confidence interval, we can use the formula:
Confidence interval = sample mean ± (critical value) x (standard error)
where the standard error is the standard deviation of the sample mean and the critical value is based on the desired confidence level and the sample size.
Since we want a 95% confidence interval and the sample size is 50, we can find the critical value from a t-distribution with 49 degrees of freedom (n-1). Using a t-distribution instead of a normal distribution is appropriate here because the population standard deviation is not known.
From a t-distribution table or calculator, the critical value for a 95% confidence interval with 49 degrees of freedom is approximately 2.009.
The standard error can be found using the formula:
standard error = standard deviation / sqrt(sample size)
Substituting the given values, we get:
standard error = 11.4 / sqrt(50) = 1.613
Now we can plug in the values into the formula for the confidence interval:
Confidence interval = 75.3 ± 2.009 x 1.613 = (72.14, 78.46)
Therefore, the lower limit is 72.1 and the upper limit is 78.5. The sample mean is 75.3, denoted by X-bar and the standard error is 1.613, denoted by Ś.
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Which scenario can be represented using the inequalities below?
1.25 < x < 1.5
A container of milk costs at least $1.25 but less than $1.50.
A student spends at least 1 hour 15 minutes, but no more than 1 hour 30 minutes on homework.
A tip added to a restaurant bill is less than or equal to 25% or less than or equal to 50%.
The point value of a test item is more than 1.25 points and less than 1.5 points.
The scenario that can be represented by the inequalities 1.25 < x < 1.5 is: A. A container of milk costs at least $1.25 but less than $1.50
How to Represent a Scenario Using Inequalities?The inequality 1.25 < x < 1.5 represents a range of values between 1.25 and 1.5, where x falls within that range.
Option A, which states that a container of milk costs at least $1.25 but less than $1.50, fits this range.
Option B, which states that a student spends at least 1 hour 15 minutes, but no more than 1 hour 30 minutes on homework, does not fit this range, as it represents a range of time values and not a range of numerical values.
Option C, which states that a tip added to a restaurant bill is less than or equal to 25% or less than or equal to 50%, does not fit this range either, as it represents two separate ranges of values.
Option D, which states that the point value of a test item is more than 1.25 points and less than 1.5 points, fits this range as well.
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The temperature is dropping at 3 degrees per hour. At noon it was 0 degrees, what was the temperature at 1pm? 2pm? 3pm? 6pm? What was the temperature t hours after noon?
The temperature at 1pm is -3°C, at 2pm it's -6°C, at 3pm it's -9°C, and at 6pm it's -18°C. The temperature t hours after noon is T = 0 - 3t
If the temperature is dropping at a rate of 3 degrees per hour, then the temperature t hours after noon can be represented by the equation T = 0 - 3t, where T is the temperature in degrees Celsius.
To find the temperature at a specific time after noon, we need to substitute the corresponding value of t into the equation and solve for T. For example:
At 1pm (t = 1), T = 0 - 3(1) = -3°C
At 2pm (t = 2), T = 0 - 3(2) = -6°C
At 3pm (t = 3), T = 0 - 3(3) = -9°C
At 6pm (t = 6), T = 0 - 3(6) = -18°C
To find the temperature t hours after noon, we can use the same equation: T = 0 - 3t. For example, if we want to find the temperature 4 hours after noon, we can substitute t = 4 into the equation: T = 0 - 3(4) = -12°C. So the temperature 4 hours after noon is -12°C.
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Help me pleaseeeee :(
I'm taking linear algebra right now so this one hits home :)
Elementary Row Operations (EROs) are very important and not too difficult, so let's dive into the problem!
You're given the matrix below and asked to perform a single ERO to produce a matrix with a 1 at the position (1,1):
[tex]\begin{bmatrix}3 & 10 & 5\\2 & -1 & 1\end{bmatrix}[/tex]
Think of the two rows as separate entities in the matrix. Ultimately we want to have the index (1,1) currently holding the number 3 to become the number 1. To do this, logically you just need to subtract 2. Now, looking at the rows we have, a simple row operation is quite apparent.
Simply subtract row 2 from row 1, shown below:
[tex]\begin{bmatrix}3-2 & 10-(-1) & 5-1\\2 & -1 & 1\end{bmatrix}[/tex]
Now, simplify and you will have the answer:
[tex]\begin{bmatrix}1 & 11 & 4\\2 & -1 & 1\end{bmatrix}[/tex]
Notice that our matrix now has the required number 1 in row 1 and column 1, therefore, the matrix above is our answer! Let me know if you have any questions!
An individual makes five annual deposits of $2000 in a savings account that
pays interest at a rate of 4% per year. One year after making the last deposit, the
interest rate changes to 6% per year. Five years after the last deposit, the accumulated
money is withdrawn from the account. How much is withdrawn?
could you solve this problem?
The total amount withdrawn from the account after five years is $24,927.38.
How do we calculate?The future value of a series of annual deposits of $2000) can be calculated using the following formula:
FV = [tex]PMT x (((1 + r)^n^-^ 1) / r)[/tex]
where FV = the future value, PMT= the payment amount = $2000 r = the interest rate per period = 4% n = the number of periods = 5
the interest rate and the number of periods are the same.
[tex]FV1 = $2000 x (((1 + 0.04)^5^-^ 1) / 0.04) = $11,025.52[/tex]
This is the amount that the deposits will grow to one year after the last deposit, at an interest rate of 4% per year.
We use compound interest:
FV = [tex]PV x (1 + r)^n[/tex]
we apply this formula with a present value of $11,025.52, an interest rate of 6%, and 4 periods, we get:
FV2 = [tex]$11,025.52 * (1 + 0.06)^4 = $13,901.86[/tex]
Therefore the total amount withdrawn = FV1 + FV2 = $11,025.52 + $13,901.86 = $24,927.38
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