we need to understand the concept of probability and how it is related to the mean and emissions. Probability is the likelihood or chance of an event occurring.
In this case, the event is the number of alpha particle emissions of carbon-14 counted by a Geiger counter per second. The mean is the average value of these emissions. The question asks us to find the probability that it takes no longer than 1 second for the second count.
This means that we need to find the probability of observing a count of alpha particle emissions equal to or less than the mean value of 25 in one second.
We can use the Poisson distribution to calculate this probability. The Poisson distribution is used to model the number of occurrences of an event in a given time period or space.
It assumes that the occurrences are independent and random, and that the mean and variance of the distribution are equal. In this case, the mean and variance are both 25.
Using the Poisson distribution formula, we can calculate the probability of observing a count of alpha particle emissions equal to or less than 25 in one second.
The formula is: P(X ≤ 25) = e^(-λ) * Σ(λ^k / k!), where λ is the mean value, k is the number of occurrences, and Σ is the sum from k=0 to k=25. Plugging in the values, we get: P(X ≤ 25) = e^(-25) * Σ(25^k / k!) Using a calculator, we can evaluate this sum and get: P(X ≤ 25) = 0.3841.
Therefore, the probability of observing a count of alpha particle emissions equal to or less than 25 in one second is 0.3841 or 38.41%. In conclusion,
the probability of observing a count of alpha particle emissions equal to or less than the mean value of 25 in one second is 0.3841. This means that there is a 38.41% chance of observing this event in one second.
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A random sample of 40 adults was chosen (22 of whom were women and 18 of whom were men). At the end of the week, each of the 40 subjects reported the total amount of time (in minutes) that he/she watched TV during that week. Click here (Links to an external site.)Links to an external site. if you would like to see the histograms of the data. We cannot use the T-test for this situation for which of the following reasons? choose all that apply.
The samples are not randomly selected. The samples are not independent. The samples are too small and the variable's distribution is heavily skewed in at least one sample.
The t-test cannot be used in this situation because the samples are not independent, and the variable's distribution is heavily skewed in at least one sample, violating the assumptions of normality and independence.
We cannot use the t-test for this situation for two reasons. Firstly, the samples are not independent as the same 40 subjects are used for both the men and women groups. Secondly, the variable's distribution is heavily skewed in at least one sample and the sample size is relatively small. These factors violate the assumptions of normality and independence that are required for the t-test to be valid. Therefore, alternative non-parametric tests should be considered, such as the Mann-Whitney U test or Wilcoxon rank-sum test, which do not require normality assumptions and can handle non-independent samples.
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In 2012, gallup asked participants if they had exercised more than 30 minutes a day for three days out of the week. Suppose that random samples of 100 respondents were selected from both vermont and hawaii. From the survey, vermont had 65. 3% who said yes and hawaii had 62. 2% who said yes. What is the value of the sample proportion of people from vermont who exercised for at least 30 minutes a day 3 days a week?.
in the sample of 100 respondents from Vermont, 65.3% of them reported exercising for at least 30 minutes a day for three days out of the week.
The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day 3 days a week can be calculated as:
sample proportion = 65.3% = 0.653
what is minute?
In this context, "minute" likely refers to the amount of time spent exercising per day. Specifically, the survey asked if participants had exercised "more than 30 minutes a day for three days out of the week."
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Find the measure of x. (Geometry) please help me, i need to get this extra credit done! :(
a researcher interested in a data matrix that displays the frequency of some combination of possible responses to multiple categorical variables should construct a: a. marginal table b. perceptual map c. regression table d. contingency table
The researcher interested in analyzing the frequency of some combination of possible responses to multiple categorical variables should construct a contingency table.
A contingency table is a two-way table that displays the frequency of observations or counts for two or more categorical variables. The table is constructed by tabulating the counts or percentages of the variables in rows and columns. The contingency table can be used to identify relationships between variables and can be helpful in analyzing data and developing hypotheses.
In a contingency table, the frequency of observations is summarized in rows and columns, as well as in the margins. The marginal totals represent the total counts or percentages for each variable, and they are typically displayed at the bottom or the right side of the table.
The marginal totals provide an overview of the overall distribution of the variables and can be helpful in identifying patterns or trends. A researcher interested in analyzing multiple categorical variables may need to construct a multiple contingency table. This type of table displays the frequency of observations for more than two categorical variables.
The table is constructed by tabulating the counts or percentages of the variables in rows and columns, as well as in the margins. In summary, a researcher interested in analyzing the frequency of some combination of possible responses to multiple categorical variables should construct a contingency table.
The contingency table summarizes the frequency of observations in rows, columns, and margins, providing a comprehensive overview of the distribution of the variables. The table can be helpful in identifying relationships between variables and developing hypotheses.
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After deducting grants based on need, the average cost to attend the University of Southern California (USC) is $27,175. Assume the population standard deviation is $7,400. Suppose that a random sample of 69 USC students will be taken from this population.
(a)
What is the value of the standard error of the mean? (Round your answer to the nearest whole number.)
$
(b)
What is the probability that the sample mean will be more than $27,175?
(c)
What is the probability that the sample mean will be within $1,000 of the population mean? (Round your answer to four decimal places.)
(d)
What is the probability that the sample mean will be within $1,000 of the population mean if the sample size were increased to 100? (Round your answer to four decimal places.)
a) The standard error of the mean value is 890.
b) 0.5 is the probability that the sample mean will be more than $27,175.
c) [tex]11%[/tex] of the population means being within [tex]$1,000[/tex] of the sample mean.
d) The population mean is [tex]71%.[/tex] .
(a) The formula for calculating the standard error of the mean (SE) is as follows:[tex]SE = / sq rt(n),[/tex] where n is the sample size and is the population standard-deviation.
Inputting the values provided yields:
[tex]SE = 7,400 sq/69 890[/tex]
The standard error of the mean, rounded to the closest whole number, is [tex]890.[/tex]
[tex]= 890[/tex]
(b) We must standardize the sample mean using the following method in order to determine the likelihood that the sample mean will exceed [tex]$27,175:[/tex]
z is equal to[tex](x - ) / ( / sort(n)).[/tex]
where n is the sample size, x is the sample mean, is the population standard deviation, and is the population mean (which is assumed to be equal to the sample mean because it is not provided).
We obtain the following by substituting the above values: [tex]z = (27,175 - 27,175) / (7,400 / sqrt(69)) = 0.[/tex]
Obtaining a z-score of [tex]0[/tex] or above has a [tex]0.5[/tex] percent chance. As a result, there is a [tex]0.5[/tex] percent chance that the sample mean will be higher than [tex]$27,175.[/tex]
[tex]= 0.5%[/tex]
(c) To determine the likelihood that the sample-mean will be within [tex]$1,000[/tex] of the population mean, we must determine the z-scores for the interval's upper and lower boundaries, which are:
[tex]Z1[/tex] is equal to[tex](27,175 - 27,175) / (7,400 / sqrt(69)) = 0 Z2[/tex]is equal to [tex](27,175 + 1,000 - 27,175) / (7,400 / sqrt(69)) 0.14[/tex] [tex]Z3[/tex] is equal to[tex](27,175 - 1,000 - 27,175) / (7,400 / sqrt(69)) -0.14[/tex]
The area under the curve between[tex]z2[/tex] and [tex]z3[/tex] can be calculated or found using a basic normal distribution table or calculator:
[tex]P(z2 z3 z2) = P(-0.14 z 0.14) 0.1096[/tex]
Therefore,[tex]0.1096[/tex], or about [tex]11%[/tex], of the population means being within [tex]$1,000[/tex] of the sample mean.
[tex]= 11%[/tex]
(d) If the sample-size were raised to [tex]100[/tex], we would need to recalculate the standard error of the mean to determine the likelihood that the sample mean will be within [tex]$1,000[/tex] of the population mean:
[tex]SE = 7,400/7,400/sqrt(100) = 740.[/tex]
We determine the z-scores for the upper and lower boundaries of the interval using the same technique as in (c)
[tex]z2 = (27,175 + 1,000 - 27,175) / (740) ≈ 1.35[/tex]
[tex]z3 = (27,175 - 1,000 - 27,175) / (740) ≈ -1.35[/tex]
Once more, we can calculate or use a conventional normal distribution table to get the area under the curve between[tex]z2[/tex]and[tex]z3[/tex]:
[tex]P(z2+z+z3) = P(-1.35+z+1.35) = 0.7146[/tex]
Therefore, if the sample size were increased to 100, the likelihood that the sample mean will be within[tex]$1,000[/tex] of the population mean is[tex]0.7146,[/tex]or roughly [tex]71%.[/tex]
[tex]= 71%[/tex]
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Complete Question:
(a) What is the value of the standard error of the mean? (Round your answer to the nearest whole number.)
(b) What is the probability that the sample mean will be more than $27,175?
(c)What is the probability that the sample mean will be within $1,000 of the population mean? (Round your answer to four decimal places.)
(d) What is the probability that the sample mean will be within $1,000 of the population mean if the sample size were increased to 100? (Round your answer to four decimal places.)
How can you decompose the composite figure to determine its area? as a circle, three rectangles, and a triangle as a circle, a trapezoid, and four triangles as a semicircle, three rectangles, and a square as a semicircle, a trapezoid, and two rectangles.
Answer:
The best way to decompose the composite figure to determine its area is as a semicircle, a trapezoid, and two rectangles. This way, we can use the following formulas to find the area of each part:
Area of a semicircle = 21πr2, where r is the radius of the circle.
Area of a trapezoid = 21(b1+b2)h, where b1 and b2 are the bases and h is the height of the trapezoid.
Area of a rectangle = l×w, where l is the length and w is the width of the rectangle.
Then, we can add up the areas of each part to find the total area of the composite figure. The other options are not as convenient because they either involve more parts or more complicated shapes. For example, option A would require finding the area of a triangle, which involves using trigonometry or the Pythagorean theorem. Option B would require finding the area of four triangles, which is more tedious than finding the area of two rectangles. Option C would require finding the area of a square, which is redundant because a square is a special case of a rectangle.
Step-by-step explanation:
The composite figure can be decomposed into a semicircle, a trapezoid, and two rectangles.
Option D is the correct answer.
What is a trapezium?It is a quadrilateral that has one pair of parallel sides and a height.
The area is calculated as: 1/2 x sum of the parallel sides x height.
Examples:
Area of a trapezium that has the parallel sides as 3 cm and 4 cm and a heght o 5 cm.
Area = 1/2 x (3 + 4) x 5
Area = 1/2 x 7 x 5
Area = 35/2 = 17.5 cm^2
We have,
The given figure can be decomposed into the following figure.
- Semicircle
- Trapezoid
- Two rectangles
Thus,
A semicircle, a trapezoid, and two rectangles.
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(d) two adults are selected at random. find the probability that at least one of the two smokes.round your answer to 4 decimal places.leave your answer in decimal form.
The probability that at least one of the two adults smokes is 0.64, rounded to 4 decimal places.
What are Smoking rates. ?Smoking rates refer to the percentage of people in a given population who smoke tobacco products such as cigarettes, cigars, or pipes. Smoking rates can be calculated for different age groups, genders, socioeconomic backgrounds, and geographic regions. Smoking rates are an important indicator of public health because smoking is a leading cause of preventable death worldwide,
The smoking rates for the population are 40% smoke, 30% used to smoke, and 30% have never smoked.
To find the probability that at least one of the two adults smokes, we can use the complement rule, which states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring.
The probability that neither of the two adults smokes can be found by multiplying the probability that each of them does not smoke:
P(neither smoke) = 0.6 × 0.6 = 0.36
Therefore, the probability that at least one of the two adults smokes is:
P(at least one smokes) = 1 - P(neither smoke)
P(at least one smokes) = 1 - 0.36
P(at least one smokes) = 0.64
So the probability that at least one of the two adults smokes is 0.64, rounded to 4 decimal places.
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Complete Question:
Two adults are selected at random. The smoking rates for the population are such that 40% of adults smoke, 30% used to smoke, and 30% have never smoked. What is the probability that at least one of the two adults smokes? Round your answer to 4 decimal places and leave it in decimal form.
help me with this please
Answer:
Here is the sample space:
(1, 1), (1, 2) (1, 3), (2, 1), (2, 2), (2, 3), (3, 1),
(3, 2), (3, 3)
Assuming all conditions for inference are met, what defines a 95 percent confidence interval for the slope of the least-squares regression line?
Assuming all conditions for inference are met, a 95 per cent confidence interval for the slope of the least-squares regression line is defined as the range of values within which we are 95 per cent confident that the true population slope lies.
It is calculated as the point estimate (the slope of the least-squares regression line) plus or minus the margin of error, which is determined by multiplying the standard error of the slope by the critical value from the t-distribution with n-2 degrees of freedom (where n is the sample size). This critical value is chosen such that 95 per cent of the t-distribution falls within the interval. Therefore, a larger sample size or a smaller standard error will result in a narrower confidence interval, while a smaller sample size or a larger standard error will result in a wider confidence interval.
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Find the area of the shape.
The area of the given shape above would be = 228
How to calculate the area of the given shape above?To calculate the area of the shape above, the shape is divided into three separate shapes and then added up together. This would be calculated using area of rectangle = length×width.
First shape; length = 15; width = 9
Area = 15×9 = 135
Second shape; Length = 17; width = 3
Area = 17×3 = 51
Third shape ; length = 14 width = 3
Area = 14×3 = 42
Therefore, area of the shape = 135+51+42 = 228
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Simplify [tex]\frac{9}{8 - \sqrt 3}[/tex]
Step-by-step explanation:
[tex] \frac{9}{8 - \sqrt{3} } [/tex]
[tex] \frac{9}{8 - \sqrt{3} } \times \frac{8 + \sqrt{3} }{8 + \sqrt{3} } [/tex]
[tex] \frac{72 + 9 \sqrt{3} }{64 - 9} [/tex]
[tex] \frac{72 + 9 \sqrt{3} }{55} [/tex]
Let X = number of red Skittles in a fun size Skittles package. Then X is...
Let X = number of red Skittles in a fun size Skittles package. Then X is a random variable, which means its value is uncertain and subject to chance.
The possible values of X range from 0 (if there are no red Skittles in the package) to the total number of Skittles in the package (if all Skittles are red). The probability distribution of X describes the likelihood of each possible value occurring.
The terms you've mentioned relate to the number of red Skittles in a fun size package. In this context, X represents a discrete random variable, as it can take on a finite number of distinct values (i.e., the possible counts of red Skittles in each package).
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the measure of location which is the most likely to be influenced by extreme values in the data set is the group of answer choices range. median. mode. mean.
The measure of location which is the most likely to be influenced by extreme values in the data set is mean.
The measure of location which is the most likely to be influenced by extreme values in the data set is the mean. The range is a measure of dispersion and is calculated as the difference between the highest and lowest values in the data set.
The median, on the other hand, is the middle value in a sorted list of data and is not affected by extreme values. The mode is the most frequently occurring value and is also not affected by extreme values. Therefore, the answer is the mean.
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suppose that eight workers can manufacture 70 radios per day and that nine workers can manufacture 90 radios per day. if radios can be sold for $20 each, the value of marginal product of the ninth worker is
Answer: The value of the marginal product of the ninth worker is $400
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In circle E with the measure of minor arc � � ⌢ = 4 8 ∘ , DF ⌢ =48 ∘ , find m ∠ � � �. M∠DGF
The measure of the central angle of the circle is m∠DGF = 24°
Given data ,
Let the measure of the minor arc of the circle be DF = 48°
Let the measure of the central angle be ∠DGF
And , Central Angle = 2 x Angle in other segment
On simplifying , we get
m∠DGF = ( 1/2 ) ( 48 )°
So , the measure of m∠DGF = 24°
Hence , the angle is m∠DGF = 24°
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(L7) a=3 cm, b=5 cm, c=6 cmThe triangle is a(n) _____ triangle.
Based on the given side lengths a=3 cm, b=5 cm, and c=6 cm, the triangle is a(n) scalene triangle. A scalene triangle has all sides of different lengths, which applies to this triangle with sides 3 cm, 5 cm, and 6 cm.
Triangles are described in terms of their sides and angles in geometry. A closed planar three-sided polygon shape with three sides and three angles is known as a triangle. The lengths of the sides of a scalene triangle vary. They are not equal, and the angles have three measurements. However, it still has a 180° angle sum, just like all triangles.
A scalene triangle is a triangle with three different side lengths and three different angle measurements. The total of all internal angles, however, is always equal to 180 degrees. As a result, it satisfies the triangle's condition of angle sum.
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Need help!
Find the perimeter and area of the triangle.
Thanks! :)
Answer:
A= 1320 u^2 P= 176 u
Step-by-step explanation
A= 1/2 (b)(h)
A=1/2 (48)(55)= 1320
P= a+b+c
48+55+73=176
Answer:
A= 1320 u^2 P= 176 u
Step-by-step explanation
A= 1/2 (b)(h)
A=1/2 (48)(55)= 1320
P= a+b+c
48+55+73=176
Step-by-step explanation:
Suppose a bond with no expiration date annually pays a fixed amount of interest of $700.
a. In the table provided below, calculate and enter either the interest rate that the bond would yield to a bond buyer at each of the bond prices listed below or the bond price at each of the interest yields shown.
Instructions: Enter your answers in the gray-shaded cells. For bond prices, round your answers to the nearest hundred dollars. For interest yields, round your answers to 2 decimal places.
Answer:
Bond Price / Interest Yield, %
$8,500 / 8.24%
$9,500 / 7.37%
$10,500 / 6.67%
$11,500 / 6.09%
$13,500 / 5.19%
Step-by-step explanation:
To calculate the interest rate or bond price, we can use the following formula:
Bond price = Annual interest payment / Interest rate
For a bond price of $8,500:
Interest rate = Annual interest payment / Bond price
Interest rate = $700 / $8,500
Interest rate = 0.0824 or 8.24%
For an interest yield of 7.37%:
Bond price = Annual interest payment / Interest rate
$8,500 = $700 / 0.0737
Bond price = $9,500.20 or $9,500 (rounded to the nearest hundred dollars)
For a bond price of $10,500:
Interest rate = Annual interest payment / Bond price
Interest rate = $700 / $10,500
Interest rate = 0.0667 or 6.67%
For a bond price of $11,500:
Interest rate = Annual interest payment / Bond price
Interest rate = $700 / $11,500
Interest rate = 0.0609 or 6.09%
For an interest yield of 5.19%:
Bond price = Annual interest payment / Interest rate
$8,500 = $700 / 0.0519
Bond price = $13,481.86 or $13,500 (rounded to the nearest hundred dollars)
So the completed table is:
Bond Price / Interest Yield, %
$8,500 / 8.24%
$9,500 / 7.37%
$10,500 / 6.67%
$11,500 / 6.09%
$13,500 / 5.19%
On a map of Arizona, 2 inches represents 52 miles. The distance between Yuma and Sentinel is 3.5 inches on the map. What is the actual distance, in miles, between these two cities?
Answer:
Step-by-step explanation:
On a map of Arizona, 2 inches represents 52 miles. The distance between Yuma and Sentinel is 3.5 inches on the map. What is the actual distance, in miles, between these two cities?
you can solve with a proportion between the real measurements and those on the map
52 : 2 = x : 3.5
x = 52 x 3.5 : 2
x = 182 : 2
x = 91 miles
------------------------- check
52 : 2 = 91 : 3.5
26 = 26
the answer is good
Help I don't understand.
Answer:
[tex](2x - 1)(x + 3) = [/tex]
[tex]2 {x}^{2} + 5x - 3[/tex]
A = 2, B = 5, C = -3
a spinner for a board-game is divided into four equal-sized sections colored red, green, yellow, and blue. if you land on a line between the colors, you keep spinning until you land on a color. william's turn is next. which word or phrase describes the probability that he will land on red or blue?
The word or phrase that describes the probability that William will land on red or blue is "50-50" or "even chance."
What is probability?
Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.
The probability that William will land on red or blue is the sum of the individual probabilities of landing on red and blue.
Since the spinner is divided into four equal-sized sections, each section has an equal probability of being landed on, which is 1/4 or 0.25 as a decimal.
To find the probability of landing on red or blue, we add the probabilities of landing on each color:
P(red or blue) = P(red) + P(blue) = 0.25 + 0.25 = 0.5
Therefore, the word or phrase that describes the probability that William will land on red or blue is "50-50" or "even chance."
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if is an invertible matrix that is orthogonally diagonalizable, show that is orthogonally diagonalizable.
If A is invertible and orthogonally diagonalizable, then A is also orthogonally diagonalizable using the same orthogonal matrix Q that diagonalizes A.
If a matrix A is invertible and orthogonally diagonalizable, it means that there exists an orthogonal matrix Q and a diagonal matrix D such that
A = QDQT∧.
To show that A is orthogonally diagonalizable, we need to find an orthogonal matrix P and a diagonal matrix B such that
A = PBP∧T.
Since A is invertible, it has an inverse A∧-1. Using the property
A∧-1 = (QDQ∧T)∧-1 = QD∧-1Q∧T
we can write
A∧-1 = QD∧-1Q∧T.
We can also rewrite the equation
A = QDQ∧T as D = Q∧TAQ.
Multiplying both sides of
D = Q∧TAQ
by Q from the right, we get
DQ = Q∧TAQQ = Q∧TA,
since
Q∧TQ = I (Q is orthogonal). Similarly, multiplying both sides of
DQ = Q∧TA by Q∧T from the left, we get
Q∧TDQ = AQ∧T.
Now we have
A = QDQ∧T = (Q∧T)∧T D Q∧T = (QQ∧T)∧T D (QQ∧T)
where QQ∧T is an orthogonal matrix. Letting
P = QQ∧T
and B = D, we have
A = PBP∧T, which shows that A is also orthogonally diagonalizable.
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(d) what is the probability that a vehicle will weigh more than 4,000 pounds? (round your answer to 2 decimal places.)
The probability that a vehicle will weigh more than 4,000 pounds is 0.20 or 20%.
(a) The mean weight of a randomly chosen vehicle can be calculated as the average of the minimum and maximum weights:
Mean = (2500 + 4500)/(2)
= 3500$ pounds
Therefore, the mean weight of a randomly chosen vehicle is 3500 pounds.
(b) The standard deviation of a uniformly distributed random variable is given by:
SD = (b-a)/√12
where a is the minimum value and b is the maximum value of the distribution. Substituting the given values, we get:
SD = 4500- 2500/ √12
= 433.01$ pounds
Therefore, the standard deviation of a randomly chosen vehicle is approximately 433.01 pounds.
(c) To find the probability that a vehicle will weigh less than 3,000 pounds, we need to calculate the proportion of the total area under the probability density function (PDF) that lies to the left of 3,000 pounds. Since the distribution is uniform, the PDF is a horizontal line with a height of (b-a) over the interval from a to b. Therefore, the probability can be calculated as:
P(X < 3000) = (3000-2500)(4500-2500)
= 1/4
= 0.25$
Therefore, the probability that a vehicle will weigh less than 3,000 pounds is 0.25 or 25%.
(d) To find the probability that a vehicle will weigh more than 4,000 pounds, we need to calculate the proportion of the total area under the PDF that lies to the right of 4,000 pounds. Again, since the distribution is uniform, the PDF is a horizontal line with a height of 1/(b-a) over the interval from a to b. Therefore, the probability can be calculated as:
P(X > 4000) = 1 - P(X >= 4000)
= 1 / (4000-2500)(4500-2500)
= 1/5
= 0.20$
Therefore, the probability that a vehicle will weigh more than 4,000 pounds is 0.20 or 20%.
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Complete question:
Assume the weight of a randomly chosen American passenger car is a uniformly distributed random variable ranging from 2,500 pounds to 4,500 pounds.
(a) What is the mean weight of a randomly chosen vehicle?
(b) What is the standard deviation of a randomly chosen vehicle? (Round your answer to 4 decimal places.)
(c) What is the probability that a vehicle will weigh less than 3,000 pounds? (Round your answer to 2 decimal places.)
(d) What is the probability that a vehicle will weigh more than 4,000 pounds? (Round your answer to 2 decimal places.)
find the order of the matrix product ab and the product ba, whenever the products exist. a is 4 x 2, b is 2 x 4.A) AB is 2 x 2, BA is 4 x 4. B) AB is nonexistent, BA is 2x2. C) AB is 4 x 4, BA is nonexistent. D) AB is 4 x 4, BA is 2 x 2
The correct answer is (D) AB is 4 x 4, BA is 2 x 2.
What is order of a matrix?
The order of a matrix refers to the number of rows and columns in the matrix. If a matrix has m rows and n columns, we say that it is an m x n matrix. The order of the matrix is written as "m x n".
In general, if A is an m x n matrix and B is an n x p matrix, then the product AB is an m x p matrix and the product BA is an n x n matrix.
In this case, A is a 4 x 2 matrix and B is a 2 x 4 matrix. Therefore, the product AB is a 4 x 4 matrix, and the product BA is a 2 x 2 matrix.
So the answer is (D) AB is 4 x 4, BA is 2 x 2.
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x = ±4
When there's an exponent, take the root of both sides
√x² = √16
x = ±4
*The even root of any number is ±* How do you solve x² = 16?
The solutions to the equation x² = 16 are x = 4 and x = -4.
What is equation?
An equation is a statement in mathematics that states the equality of two expressions. It usually consists of variables, which are represented by letters and can take on different values, as well as constants and mathematical operations like addition, subtraction, multiplication, division, and exponentiation.
To solve x² = 16, we need to find the value of x that makes the equation true.
One way to solve this equation is to take the square root of both sides. However, it's important to remember that the square root of a number can be positive or negative, so we need to include both solutions:
√x² = √16
|x| = 4
x = ±4
Therefore, the solutions to the equation x² = 16 are x = 4 and x = -4.
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Problem 3 (10 points) You are analyzing a dataset and have fit a multiple regression with 12 continuous explanatory variables and one intercept. You are given the following:
Sum of square of errors = 618
The 10th diagonal entry of the hat matrix: h10,10 = 0.35
The 10th residual value: e10 = 9.5
Cook’s Distance for 10th observation: D10 = 5.0
Calculate the number of data points this model was fit to.
Answer:
the answer is B
Step-by-step explanation:
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Because i would love for you to bounce that
Definition of a derivative (alternate form)
The derivative of a function is a measure of how much the function changes with respect to its input. An alternate form of the definition of a derivative is based on the concept of limits.
If f(x) is a function, then the derivative of f(x) at a point x=a is defined as the limit of the difference quotient (f(x)-f(a))/(x-a) as x approaches a. Geometrically, this corresponds to the slope of the tangent line to the graph of f(x) at x=a. The derivative provides important information about the behavior of the function, such as the location of maximum and minimum values and the concavity of the curve.
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The mean weight of a breed of yearling cattle is 1150 pounds. Suppose that weights of all such animals can be described by a normal model with a standard deviation of 54 pounds
A) a steer weighing 1000 pounds is ___ standard deviations below the mean
B) which would be more unusual, a steer weighing 1000 pounds or one weighing 1250 pounds?
A) A steer weighing 1000 pounds is 2.78 standard deviations below the mean.
B) A z-score of 1.85 is closer to the mean than a z-score of -2.78, we can conclude that a steer weighing 1000 pounds is more unusual than one weighing 1250 pounds.
A) To find how many standard deviations below the mean a steer weighing 1000 pounds is, we need to use the formula for standard score (or z-score):
z = (x - μ) / σ
where x is the weight of the steer, μ is the mean weight, and σ is the standard deviation. Substituting the values we have:
z = (1000 - 1150) / 54
z = -2.78
B) To determine which is more unusual, we need to compare the z-scores for a steer weighing 1000 pounds and one weighing 1250 pounds. Using the same formula as before:
For a steer weighing 1000 pounds:
z1 = (1000 - 1150) / 54
z1 = -2.78
For a steer weighing 1250 pounds:
z2 = (1250 - 1150) / 54
z2 = 1.85
A positive z-score means the weight is above the mean, while a negative z-score means the weight is below the mean. Therefore, a steer weighing 1250 pounds is 1.85 standard deviations above the mean, while a steer weighing 1000 pounds is 2.78 standard deviations below the mean.
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Haley is trying to save $8000 to put a down payment on a car. If she starts with $2000 saved and saves an additional $200 each month, which equation represents how far Haley is from her goal of reaching $8000? Let x stand for months and y stand for dollars.
Answer: The equation that represents how far Haley is from her goal of reaching $8000 is y = 8000 - 2000 - 200x.
Step-by-step explanation:
Haley starts with $2000 and saves an additional $200 each month. Therefore, after x months, she will have saved:
2000 + 200x dollars
To find how far Haley is from her goal of reaching $8000, we need to subtract her savings from her goal:
8000 - (2000 + 200x) = 6000 - 200x
This gives us the value of y, which represents how far Haley is from her goal.
Therefore, the equation that represents how far Haley is from her goal of reaching $8000 is:
y = 6000 - 200x
Alternatively, we can simplify this equation to:
y = 8000 - 2000 - 200x
y = 8000 - 2000 - 200x represents how much more money Haley needs to save to reach her goal of $8000 after x months.
he base of a triangle exceeds the height by 7 yards. if the area is 372 square yards, find the length of the base and the height of the triangle.
The length of the base is approximately 34.28 yards and the height is approximately 27.28 yards.
Let's use the formula for the area of a triangle:
A = (1/2) × b × h, where A is the area, b is the length of the base, and h is the height of the triangle.
From the problem statement, we know that:
b = h + 7 (the base exceeds the height by 7 yards)
A = 372 (the area is 372 square yards)
Substituting the first equation into the formula for the area, we get:
A = (1/2) × (h+7) × h = 372
Multiplying both sides by 2, we get:
(h+7) × h = 744
Expanding the left side and rearranging, we get:
[tex]$h^2 + 7h - 744 = 0$[/tex]
This is a quadratic equation that we can solve using the quadratic formula:
[tex]h = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
where a = 1, b = 7, and c = -744.
Plugging in these values, we get:
[tex]h &= \frac{-7 \pm \sqrt{7^2 - 4(1)(-744)}}{2(1)} \\ &= \frac{-7 \pm \sqrt{7^2 + 4\cdot 744}}{2} \\ &= \frac{-7 \pm \sqrt{5969}}{2} \end{align*}[/tex]
We can ignore the negative root since h must be positive, so:
h = (-7 + sqrt(5969)) / 2 ≈ 27.28
Now we can use the first equation to find the length of the base:
b = h + 7 ≈ 34.28
Therefore, the length of the base is approximately 34.28 yards and the height is approximately 27.28 yards.
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Answer:
Step-by-step explanation:
Let's call the height of the triangle "h" and the length of the base "b".
We are given that the base exceeds the height by 7 yards, so we can write:
b=h+7
We are also given that the area of the triangle is 372 square yards, so we can write:
(1/2)bh=372
Now we can substitute the expression for b from the first equation into the second equation:
(1/2)(h+7)h=372
Multiplying out the left-hand side:
(1/2)(h^2+7h)=372
Multiplying both sides by 2 to eliminate the fraction:
h^2+7h=744
Bringing all the terms to one side of the equation:
h^2+7h-744=0
Now we can solve the quadratic equation for h using the quadratic formula:
h=(-b±sqrt(b^2-4ac))/2a
In this case, a=1, b=7, c=-744
h=(-7±sqrt(7^2-4(1)(-744)))/2(1)
h=(-7±sqrt(7^2+2976))/2
We can discard the negative solution since the height can't be negative. So, we have:
h=(-7+sqrt(2985))/2
h≈24.2 yards
Now, we can use the first equation to find the length of the base:
b=h+7
b≈31.2 yards
If asked to round to the nearest whole number:
h=24 yards
b=31 yards
