The least likely event from given events is Option B: A randomly selected student who is freshmen owns a skateboard.
The event whose occurence is minimum is least likely event.
Suppose there are finite elementary events in sample space of considered experiment and all are equally likely.
Then, we want to find the probability of an event E.
Then, its probability is given as
P(E) = Number of favourable cases/ Number of total cases = n(E)/n(S)
where favorable cases are the elementary events who belong to E, and total cases are size of sample space.
For two events A and B, by chain rule, we have:
P(A∩B) = P(B)P(A|B) = P(A)P(A|B)
How to find the conditional probability:
Suppose that there are two events A and B. Then suppose the conditional probability are:
P(A|B) = probability of occurrence of A given B has already occurred.
P(B|A) = probability of occurrence of B given A has already occurred.
We can then use the chain rule to find them, or Bayes theorem also helps in finding these probabilities.
We are given the table of joint relative frequency:
We take events as A, A' and B and B'
Important probabilities which will be used are evaluated as:
P(A) = n(A)/n(S) = 150/1200 = 1/8
P(B) = n(B)/n(S) = 250/1200 = 5/24
P(A') = 1 - P(A) = 7/8
P(B') = 1 - P(B) = 1 - 5/24 = 19/24
P(A∩B) = n(A∩B) / n(S) = 40/1200 = 1/30
P(A'∩B') = n(A'∩B') / n(S) = 840/1200 = 7/10
P(A'∩B) = n(A'∩B) / n(S) = 210/1200 = 7/40
Evaluating probabilities of choices given, we get:
Case 1: E = A random selected student who owns skateboard is freshmen
P(E) = ?
P(E) = P(B|A) = P(A∩B) / P(A) = 1/30 ÷ 1/8 = 4/15
Case 2: E = A random selected student who is freshmen owns skateboard:
P(E) = P(A|B) = P(A∩B) / P(B) = 1/30 ÷ 5/24 = 4/25
Case 3: E = A random selected student who doesn't owns skateboard is freshmen
P(E) = P(B|A') = P(A'∩B) / P(A') = 7/40 ÷ 19/24 = 21/95
Case 4: E = A randomly selected student who doesn't owns skateboard is not freshmen
P(E) = P(B'|A') = P(A'∩B') / P(A') = 7/10 ÷ 19/24 = 84/95
So, the least probability is for second case.
Question - Seth is analyzing number of students in class and high school who own skateboards. He puts the data in table shown. Given information in table, which event is least likely?
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A cylindrical glass with a radius of 5 cm and a height of 20 cm is half full of milk. How
many milliliters of milk are in the glass? (1cm3
= 1ml)
There is 78.54 mI of miIk in the gIass.
What is VoIume of a cyIinder ?The voIume of a cyIinder means the space inside the cyIinder that can hoId a specific amount of materiaI quantity. In simpIer words, the capacity of a cyIinder to hoId a thing is its voIume. Inside the space of a cyIinder, you can hoId either of the three types of matter – soIid, Iiquid, or gas. This capacity can onIy be witnessed in a three-dimensionaI cyIinder, i.e., you cannot hoId any Iiquid, soIid, or gas in a two-dimensionaI cyIinder.
The equation for the voIume of a cyIinder is V = Ah,
where A is the area of the base and h is the height.
Thus, the voIume can aIso be expressed as V = πr2h.
Find capacity of the gIass :
VoIume of the gIass = πr²h
Given radius = 5 ; Height = 2
VoIume of the gIass = π(5)²(2)
VoIume of the gIass = 157.08cm³
Find the voIume of the miIk :
If the gIass is haIf fuII,
VoIume of the miIk = 177.08 ÷ 2
VoIume of the miIk = 78.54 cm³
Convert cm³ to mI :
1 mI = 1000 cm³
78.54cm³ = 78.54 mI
There is 78.54 mI of miIk in the gIass.
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Halla m∆1 y m∆2.
ayuda porfaa
Hi! I understand that you want help finding the values of m∆1 and m∆2. To provide a step-by-step explanation, I need more information about the problem, such as the type of triangles, angles, or side lengths involved. Please provide more context or details, and I will be happy to help you.
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A person places $398 in an investment account earning an annual rate of 9.7%, compounded continuously. Using the formula V = Pe^{rt}V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 7 years.
A person has $785.35 after 7 years in the account.
What is continuous compound interest?Interest that is compounded continuously to the principal amount. This interest rate provides exponential growth for a period of time.
The formula of continuous compound interest rate;
[tex]V = Pe^{rt}[/tex],
Where P is the principal amount, r is the interest rate and t is the time period.
A person places $398 in an investment account earning an annual rate of 9.7%, compounded continuously.
Using the formula:
[tex]V = Pe^{rt}[/tex], where P = $398, r = 0.097 (9.7% as a decimal), and t = 7 years, we can calculate the value of the account after 7 years as:
V = 398[tex]e^(0.0977)[/tex]
V = 398[tex]e^{0.679}[/tex]
V = 784.818126761
V = $785.35 (rounded to the nearest cent)
Therefore, the amount of money in the account after 7 years is $785.35.
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PLEASE HELP WITH EXPLANATION PLEASE PLEASE PLEASE NO SCAMMING FOR THE COINS OR I WILL REPORT YOU
The correct solutions for the given equation is given by table in option 3.
Explain about the solution of linear equation?A straight line is produced when a linear equation, which is a two-variable equation, is graphed. The intersection of corresponding values which satisfy the equation results in the line.
The variables x and y are most frequently used in linear equations, hence the associated values can be shown as (x,y) on the coordinate plane, pairs. A collection of two maybe more linear equations is known as a system of linear equations.
The given equation is-
y = x - 6
Put the value of 'x' from the options and check for 'y', if its correct.
The option are the solution of the equation.
option 1:
y = x - 6
x = --5
y = -5 - 6 = -11 (incorrect)
option 2:
y = x - 6
Put x = -8
y = -8 - 6 = -14 (incorrect)
option 3:
y = x - 6
Put x = -7
y = -7 - 6 = -13 (correct)
Thus, the correct solutions for the given linear equation is given by table in option 3.
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Name 2 figures for which all cross sections taken at a particular orientation
are congruent.
Answer: Rectangular prism & Cylinder
Step-by-step explanation: In geometry, a rectangular prism is a polyhedron with two congruent and parallel bases. It is also called a cuboid. A rectangular prism has six faces, and all the faces are in a rectangle shape and have twelve edges. Because of its cross-section along the length, it is said to be a prism.
A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The line segment joining the two centers is the axis, that denotes the height of the cylinder.
in cluster analysis, a method can be used to reduce bias due to the difference in units of measurement. one such method is called
In cluster analysis, a method can be used to reduce bias due to the difference in units of measurement. One such method is called standardization.
Cluster analysis is a data mining approach that is widely utilized in data processing, image analysis, and other data-based analytics applications. It groups items that have comparable characteristics into clusters by separating them from other objects that do not share the same features.
Standardization is the process of converting variables with various scales to a common scale so that they can be compared fairly.
Standardization involves transforming all of the variables into comparable units of measurement by converting them into z-scores. This allows for the comparison of values without being affected by the different units of measurement.
The method that can be used to reduce bias due to the difference in units of measurement in cluster analysis is standardization, which converts variables with various scales to a common scale so that they can be compared fairly. This ensures that each variable contributes equally to the distance between the clusters.
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a camper attaches a rope from the top of her tent, feet above the ground, to give it more support. if she takes the rope to the ground feet from the middle of her tent, about how long is the rope from the ground to the tent?
4 feet.
The length of the rope from the ground to the top of the tent is 4 feet.
To calculate this, subtract the distance from the tent to the ground (2 feet) from the height of the tent (6 feet), and you will get the length of the rope (4 feet).
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Angle PQR is isosocles with PQ=PR= 7. 5cm and QR = 9cm. The height PS from P to QR,is 6cm. Find the area of Angle PQR. What will be the height from R to PQ that is RT
The height RT from R to PQ is approximately 3.16 cm.
To find the area of triangle PQR, we can use the formula:
Area = 1/2 * base * height
Since PQR is isosceles with PQ = PR, the base is PQ or PR. We can choose PQ as the base. Then the height is PS.
Area of PQR = 1/2 * PQ * PS
Since PQ = PR = 7.5 cm and PS = 6 cm, we can substitute these values into the formula and simplify:
[tex]Area of PQR = 1/2 * 7.5 cm * 6 cm[/tex]
[tex]Area of PQR = 22.5 cm^2[/tex]
Therefore, the area of triangle PQR is [tex]22.5 cm^2[/tex].
To find the height RT from R to PQ, we can use the Pythagorean theorem.
Let's draw a perpendicular line from R to PQ, intersecting at T. Then we have a right triangle PRT with hypotenuse PR and legs PT and RT.
Since PQR is isosceles, we can also see that angle PQR is equal to angle PRQ. Therefore, angles PQR and PRQ are equal and each is approximately 69.3 degrees (using inverse cosine function).
Using the sine function, we can find the length of PT:
sin(69.3) = PT / 7.5
PT = 7.5 * sin(69.3)
PT ≈ 6.93 cm
Using the Pythagorean theorem, we can find the length of RT:
[tex]RT^2 + PT^2 = PR^2[/tex]
[tex]RT^2 = PR^2 - PT^2[/tex]
[tex]RT^2 = 7.5^2 - 6.93^2[/tex]
RT ≈ 3.16 cm
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Find the area of the following
rhombus:
10 cm
6 cm
8 cm
A = [?] cm²
Answer:96
Step-by-step explanation:
[tex]Area=\frac{d1 d2}{2}[/tex]
[tex]Area=\frac{(6+6)(8+8)}{2}[/tex]
[tex]Area=96[/tex]
need help to this what would the variance be?
The variance of the set of data is 10. Option A
What is variance?Variance can be defined as a statistical measurement of the spread of numbers in a data set.
It is used to measure how far each number in the set is distant from the mean and from every other number in the set.
It is sometimes described as the measure of variability.
It is denoted with the mathematical symbol,'σ²'
The formula for calculating the variance of a set of data is;
Variance = ∑(x-x⁻)²/n - 1
Substitute the values, we have;
Variance = 16 + 4 + 4 + 16 + 0/5 - 1
Add the values
Variance = 40/4
Divide the values
Variance = 10
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PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP
Answer: 35 Millimeters
Step-by-step explanation: Add all the numbers around your shape and you got the perimeter :)
Answer: 35 mm
Step-by-step explanation:
Add all sides together: 4+13+13+5 = 35
the top of an l-shaped desk has the dimensions shown. what volume of wood is needed to make the top of the desk? complete the explanation of how you solved this problem.
The volume of wood needed to make the top of the l-shaped desk is 0.728 cubic feet
The top of an l-shaped desk has the dimensions shown in the diagram. To determine the volume of wood needed to make the top of the desk, we must use the formula for volume. The formula for volume is length times width times height, or V = lwh. In this case, the length of the top is 28 inches, the width is 45 inches, and the height is 0.75 inches.
Plugging these values into the volume formula gives us V = 28 x 45 x 0.75, which equals 1260 cubic inches. Since wood is typically sold in cubic feet, we must convert this volume to cubic feet by dividing it by 1728, the number of cubic inches in one cubic foot. 1260/1728 = 0.728, so the volume of wood needed to make the top of the desk is 0.728 cubic feet.
To summarize, the volume of wood needed to make the top of the l-shaped desk is 0.728 cubic feet. This was determined by using the volume formula, which is V = lwh, where l is the length, w is the width, and h is the height. The length, width, and height of the desk top were 28 inches, 45 inches, and 0.75 inches, respectively. By plugging these values into the volume formula and converting to cubic feet, we determined the volume of wood needed is 0.728 cubic feet.
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What is 102.5% of 80?
Answer:
Step-by-step explanation:
102.5/80=
82
Answer: 82
Step-by-step explanation:
FirstMove the percent 2 times to the right to get a decimal.
102.5% ——> 1.025
Secondly
You’re dividing the part with the whole always to get the percent. So if we have the precent (converted into a decimal) and the whole. So we are finding the part. So to find the part we multiple 1.025 and 80.
Third
You solve now. So 1.025 x 80 = 82
What is the value of angle h?
How do you know (what type of angle pairs are they)?
The value of h is 34.
What is the angle formed when two lines intersect?
Intersecting lines are two or more lines that have precisely one point in common. The point of junction is this central location that connects all of these lines. It should be observed that the intersecting lines only come together at one point, regardless of the angle at which they do so.The vertical angles are the opposing angle pairs created by two intersecting lines. Non-adjacent angles created by two crossing lines are known as opposite angles. Angles at opposite sides are equal. (equal in measure)According to the Vertically opposite angle theorem, opposite angles are equal.
So, h = 34.
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there are 20 rows of seats on a concert hall: 25 seats are in the 1st row, 27 seats on the 2nd row, 29 seats on the 3rd row, and so on. if the price per ticket is $2,300, how much will be the total sales for a one-night concert if all seats are taken?
The total sales for a one-night concert with all seats taken will be $2,024,000.
To solve this problem, we need to find the total number of seats in the concert hall. We know that the first row has 25 seats, the second row has 27 seats, and the third row has 29 seats.
We can represent the number of seats in each row using an arithmetic sequence with a first term of 25 and a common difference of 2. The nth term of this sequence can be found using the formula:
a_n = a_1 + (n - 1)d
where a_1 is the first term (25), d is the common difference (2), and n is the number of the row.
Using this formula, we can find the number of seats in the 20th row
a_20 = 25 + (20 - 1)2
a_20 = 25 + 38
a_20 = 63
Therefore, the total number of seats in the concert hall is the sum of the seats in all 20 rows:
total seats = 25 + 27 + 29 + ... + 63
To find this sum, we can use the formula for the sum of an arithmetic sequence
S_n = (n/2)(a_1 + a_n)
where S_n is the sum of the first n terms of the sequence. In this case, n = 20, a_1 = 25, and a_n = 63.
S_20 = (20/2)(25 + 63)
S_20 = 10(88)
S_20 = 880
Therefore, there are a total of 880 seats in the concert hall. If all seats are taken, the total sales for the one-night concert will be
total sales = number of seats x price per ticket
total sales = 880 x $2,300
total sales = $2,024,000
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suppose that a conveyor used to sort packages by size does not work properly. we test the conveyor on several packages (with h0:incorrect sort) and our data results in a p-value of 0.016. what probably happens as a result of our testing?
If the p-value of a hypothesis test is 0.016, it means that the probability of observing the data or more extreme data assuming the null hypothesis (i.e., the conveyor works properly) is 0.016. So, we reject the null hypothesis.
This p-value is relatively small and falls below the conventional significance level of 0.05. Therefore, we can reject the null hypothesis that the conveyor works properly and conclude that the conveyor is not sorting packages correctly.
However, we cannot determine the cause of the problem with the conveyor from this hypothesis test alone. Further investigation is necessary to identify the root cause of the issue and determine the appropriate corrective actions.
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Answer this for points
2.40 in a certain binary communication channel, it is equally likely to send a 1 or a 0 (both probabilities are equal to 1/2). the probability of an error given that a 1 is sent is 2/9, while the probability of an error given a 0 is sent is 1/9. (a) what is the probability that a 1 is received? (b) what is the (unconditional) probability that an error occurs? (c) what is the probability that a 1 was sent, given a 1 was received?
(a) The probability that a 1 is received is 4/9.
(b) The (unconditional) probability that an error occurs is 1/6.
(c) The probability that a 1 was sent, given that a 1 was received, is 7/8.
To solve this problem, we can use Bayes' theorem and conditional probability.
(a) The probability that a 1 is received can be found using the law of total probability. We can calculate it by considering the probabilities of two mutually exclusive events: receiving a 1 when a 1 is sent and receiving a 1 when a 0 is sent.
Let P(1) be the probability that a 1 is sent and P(0) be the probability that a 0 is sent. Both probabilities are equal to 1/2 since they are equally likely.
The probability of receiving a 1 when a 1 is sent is 1 minus the probability of an error when a 1 is sent, which is 1 - (2/9) = 7/9.
The probability of receiving a 1 when a 0 is sent is the probability of an error when a 0 is sent, which is 1/9.
Using the law of total probability:
P(1 received) = P(1 sent) x P(1 received | 1 sent) + P(0 sent) x P(1 received | 0 sent)
P(1 received) = (1/2) x (7/9) + (1/2) x (1/9)
P(1 received) = 7/18 + 1/18
P(1 received) = 8/18
P(1 received) = 4/9
Therefore, the probability that a 1 is received is 4/9.
(b) The (unconditional) probability that an error occurs can be calculated by considering the probabilities of two mutually exclusive events: an error occurs when a 1 is sent and an error occurs when a 0 is sent.
Using the law of total probability:
P(Error) = P(1 sent) x P(Error | 1 sent) + P(0 sent) x P(Error | 0 sent)
P(Error) = (1/2) x (2/9) + (1/2) x (1/9)
P(Error) = 2/18 + 1/18
P(Error) = 3/18
P(Error) = 1/6
Therefore, the (unconditional) probability that an error occurs is 1/6.
(c) The probability that a 1 was sent, given that a 1 was received, can be calculated using Bayes' theorem:
P(1 sent | 1 received) = (P(1 sent) x P(1 received | 1 sent)) / P(1 received)
P(1 sent | 1 received )= (1/2) x (7/9) / (4/9)
P(1 sent | 1 received) = (1/2) x (7/9) * (9/4)
P(1 sent | 1 received) = 7/8
Therefore, the probability that a 1 was sent, given that a 1 was received, is 7/8.
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what central idea about mathematical instruction does the author express in passage 1?
An all-night study session can help you catch up on school assignments. The only way to become a straight-A student is efficient study habits.
Most students pseudo-work and end up wasting valuable time.
The correct option is (C)
This is based on an article about pseudo-working which is something that students do where they read for long hours and appear very serious in reading when in fact they do not focus on the reading and therefore end up not grasping much.
The author was trying to express that most students do this and that it is simply a waste of time which could have been spent actually studying.
The correct option is (C).
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The given question is incomplete, complete question is:
What central idea about studying does the author express in Passage 1?
A Straight-A students know how to work harder than other students.
B The only way to become a straight-A student is efficient study habits.
C Most students pseudo-work and end up wasting valuable time.
D An all-night study session can help you catch up on school assignments.
in general, which point size would you use if you wanted each character to be approximately one inch in size? a.) 1 pt b.) 72 pts c.) 24 pts d.) 36 pts
If you want each character to be approximately one inch in size, you would use a point size of 72 pts.
Point size is a unit of measurement used to determine the size of typefaces. It represents the height of the characters in a font. One point is equal to 1/72 of an inch, which means there are 72 points in one inch.
Therefore, if you want each character to be approximately one inch in size, you would need to use a font size of 72 points. This would ensure that the characters are roughly one inch tall, assuming that the font is designed to be proportional and not condensed or expanded.
Choosing a smaller point size, such as 1 pt or 24 pts, would result in characters that are much smaller than one inch. Choosing a larger point size, such as 36 pts, would result in characters that are larger than one inch.
Therefore the correct answer is option b.) 72 pts.
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Find the area of each of the regular polygon below.
Round non-terminating decimals to the nearest hundredth.
nonagon (9 sided figure)
apothem = 16.5
side = 12
Rοunding tο the nearest hundredth, the area οf the nοnagοn is 891.00 square units.
What is the regular pοlygοn?A regular pοlygοn is a pοlygοn that has all sides οf equal length and all angles οf equal measure.
Tο find the area οf a regular pοlygοn, we use the fοrmula:
Area = (1/2) × Perimeter × Apοthem
The perimeter οf a nοnagοn (9-sided figure) with a side length οf 12 is:
Perimeter = 9 × 12 = 108
Therefοre, the area οf the nοnagοn is:
Area = (1/2) × 108 × 16.5
Area = 891
Hence, Rοunding tο the nearest hundredth, the area οf the nοnagοn is 891.00 square units.
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define "area "in the context
Therefore, the area of the object or surface in this context would be 2 square meters.
What is length?Length is a measure of the distance between two points. It is a physical quantity that describes the extent of an object or space in one dimension, usually measured in units such as meters, centimeters, feet, inches, etc. Length can also refer to the size or duration of something, such as the length of a book, the length of a movie, or the length of a period of time. In mathematics, length is also used to describe the size of a curve or a line segment, as well as the perimeter of a polygon or the circumference of a circle.
by the question.
In the context of length 2m and breadth 1m, the area refers to the measurement of the total amount of space that is covered by a two-dimensional object or surface within those dimensions.
The formula for calculating the area is:
Area = length x breadth
Substituting the given values, we get:
Area = 2m x 1m = 2 square meters
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what is 9 divided by 2.5
Answer: 3.6
Step-by-step explanation:
It's 3.6, hope it helped! :D
Liam has 11/4 packets of red clay.If he crafts a sculpture using 5/3 packets, how much clay does he have left?
Answer:
Step-by-step explanation:
Liam has 11/4 packets of red clay, which is equal to 33/12 packets of clay.
If he uses 5/3 packets of clay for crafting, he would have used 20/12 packets of clay.
To find how much clay he has left, we need to subtract the used amount from the original amount:
33/12 - 20/12 = 13/12
Therefore, Liam has 13/12 packets of clay left.
Which three side length best describes the triangle in the diagram
Answer:
i think that it is d or c just guessing
if you have minimums and maximums that are far away (several standard deviations away from the mean) from the rest of the data observations, medians would be the best measure of central tendency?
Yes, if you have minimums and maximums that are several standard deviations away from the rest of the data observations, medians would be the best measure of central tendency.
Having minimums and maximums that are far away (several standard deviations away from the mean) from the rest of the data observations, medians would be the best measure of central tendency. This is because, when there are outliers or extreme values in a dataset, the mean can be influenced and it may not be an accurate representation of the central tendency.
However, the median is not affected by extreme values or outliers since it only depends on the middle value of the dataset. Therefore, if the dataset has outliers, it is better to use the median as a measure of central tendency to provide a more accurate representation of the data.
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i have no idea abt any of this
Answer:
201.06 [tex]in^{2}[/tex]
Step-by-step explanation:
A = [tex]\frac{1}{4} \pi d^{2}[/tex]
A = [tex]\frac{1}{4} \pi (16)^{2}[/tex]
A = 201.06 [tex]in^{2}[/tex]
Answer:
divide 16 and use pi
pi is this π
π always equally 3.14
Write and solve an inequality Diego family tank
Answer:
please make me brainalist and keep smiling dude I hope you will
Step-by-step explanation:
The inequality represents the number of days Diego's father can drive the car without the warning light coming on is, The remaining fuel is greater than 1.5 gallons Diego's father can drive the car without the warning light coming on.
in january , the temperature in parts of minnesota fell from f to f over a -hour period. what was the average temperature change per hour?
The average temperature change per hour was -2.708 degrees Fahrenheit.
To calculate the average temperature change per hour, we need to find the total temperature change over the 24-hour period and then divide by the number of hours.
The total temperature change is the difference between the starting temperature (41 degrees Fahrenheit) and the ending temperature (-13 degrees Fahrenheit), which is -54 degrees Fahrenheit.
Dividing the total temperature change by the number of hours, we get:
-54 degrees Fahrenheit / 24 hours = -2.25 degrees Fahrenheit per hour.
Rounding to three decimal places, we get an average temperature change per hour of -2.708 degrees Fahrenheit per hour.
The complete question is: In January 2008, the temperature in parts of Minnesota fell from 41∘41∘F to −13∘-13∘F over a 24-hour period. What was the average temperature change per hour?
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Using laws of logarithms, write the given expressions usingsums and/or differences of logarithmic expressions which donot contain the logarithms of products, quotients, or powers.a. log(45x) = log(45)+log(x). Previewb. log (x⁵⁵) = 55log(x). Previewc. 10 log(⁵√x) = 1/5log(x)^10. Preview2/5 log(x)¹⁰ syntax ok
Additionally, you should focus on answering the specific question being asked and ignore any typos or irrelevant parts of the question.
Using laws of logarithms, the given expressions can be written using sums and/or differences of logarithmic expressions which do not contain the logarithms of products, quotients, or powers as follows:
a.[tex] log(45x) = log(45) + log(x)b. log(x⁵⁵) = 55log(x)c. 10 log(⁵√x) = log(x)^(10/5) = log(x)^2 = 2log(x)2/5 log(x¹⁰) = (2/5)log(x) + (2/5)log(x) + ... + (2/5)log(x) (10 times)= 2log(x^10)[/tex]
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