In bayes theorem, you have some starting information, then you collect some new information so that you can UPDATE the original probabilities so you now have better information.
What is Baye's theorm ?The Bayes' theorem, commonly referred to as the Bayes' rule, is a mathematical formula used in statistics and probability theory to calculate the conditional probability of events. The Bayes theorem essentially describes the likelihood of an event based on prior knowledge of any circumstances that might be relevant to the event.
P(A|B) = [tex]\frac{ P(A) P(B|A)}{P(B)}[/tex]
How often A happens given that B already happens, written as P(A|B),How often B happens given that A already happens, written as P(B|A)How likely A is on its own, written as P(A)How likely B is on its own, written as P(B)So it is always the case of conditional probability.
Hence, the original probability is always updated in case of Baye's theorm.
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If Bob produces 36 or fewer items in a week, he is paid X dollars per item. If Bob produces more than 36 items in a week, he is paid X dollars per item for the first 36 items and 3/2 times that amount for each additional item. How many items did Bob produce last week?
Last week Bob was paid total of $480 for the items that he produced that week and this week Bob produced 2 items more than last week and was paid a total of $510 for the items that he produced this week.
Let's start with the simplest case:
he produced 36 or less items this week.
In this case he produced less than 36 items last week too.
So he was paid the same amount of dollar per item. Using assumptions (1) and (2), we have:
$480 + 2X = $510
⇒2X=510-480$
⇒2X=$30
⇒2X=$30/2
⇒X=$15
He was paid $15 per item.
Last week he received his $480.
480/15= 32 items.
This week he received his $510.
510/15=34 items. Other cases have no solution.
seems your question is incomplete., but most probably the complete question was
If Bob produces 36 or fewer items in a week, he is paid X dollars per item. If Bob produces more than 36 items in a week, he is paid X dollars per item for the first 36 items and 3/2 times that amount for each additional item. How many items did Bob produce last week?(1) Last week Bob was paid total of $480 for the items that he produced that week.(2) This week Bob produced 2 items more than last week and was paid a total of $510 for the items that he produced this week.
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Shopping While shopping for clothes,
Tracy spent $29 less than 3 times what
Curtis spent. Tracy spent $13. Write and
solve an equation to find how much
Curtis spent. Let x represent how much
Curtis spent.
The equation that can be used to
determine how much Curtis has spent is
X-
-
=
Answer:
Curtis spent 14 dollars
Step-by-step explanation:
3x-29=13
+29. +29
3x=42
/3. /3
x=14
Hopes this helps please mark brainliest
Find the equation of a line that passes through the point (0,-1) and has a gradient of -3. Leave your answer in the form y = m x + c
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{-1})\hspace{10em} \stackrel{slope}{m} ~=~ - 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{- 3}(x-\stackrel{x_1}{0}) \implies y +1= -3 (x -0) \\\\\\ y+1=-3x\implies {\Large \begin{array}{llll} y=-3x-1 \end{array}}[/tex]
Solve the following exponential equation by first writing it in the logarithmic form and then using a calculator to solve it to 2 decimal places. 6 = 170 2 = log T =
The value of x from the exponential equation is 2.866.
Logarithm:
A logarithm is a power to which a number must be raised to get some other number.
Here we have to find the value of x.
The equation is given:
[tex]6^{x}[/tex] = 170
Taking logarithms on both sides, we have:
log [tex]6^{x}[/tex] = log 170
x log 6 = log 170
x = log 170 / log 6
= 2.230/ 0.778
= 2.866
Therefore the value of x is 2.866.
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The box plots show the weights, in pounds, of the dogs in two different animal shelters. Weights of dogs in shelter a 2 box plots. The number line goes from 6 to 30. For the weights of dogs in shelter a, the whiskers range from 8 to 30, and the box ranges from 17 to 28. A line divides the box at 21. For shelter b, the whiskers range from 10 to 28, and the box ranges from 16 to 20. A line divides the box at 18. Weights of dogs in shelter b which correctly compares the ranges of the data? the range in shelter a is 11, and the range in shelter b is 4. The range in shelter a is 20, and the range in shelter b is 10. The range in shelter a is 13, and the range in shelter b is 8. The range in shelter a is 22, and the range in shelter b is 18.
A line divides the box at 18. Weights of dogs in shelter b which correctly compares the ranges in shelter a is 11, and the range in shelter b is 4.
Define interquartile range .The IQR describes the middle 50% of values when ordered from lowest to highest. To find the interquartile range (IQR), first find the median (middle value) of the lower and upper half of the data. These values are quartile 1 (Q1) and quartile 3 (Q3). The IQR is the difference between Q3 and Q1.
Given:
For Shelter A: The whiskers range from 8 to 30
The minimum weight of Shelter A is 8 pounds.
For Shelter B: The whiskers range from 10 to 28
The minimum weight of Shelter B is 10 pounds.
Thus, the animal shelter has the dog that weighs the least is Shelter A. The animal shelter has the dog that weighs the least is Shelter A
Infact, whiskers are plotted are from the minimum to Q1 and from Q2 to the max.
Q1 stands here for low quartile and
Q2 stands here for upper quartile .
Median is the point between Q1 and Q3 .Interquartile range is the range from Q1 to Q3 .
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Alton estimated that 230 people attended the band concert. The actual count for attendance was 200 people. Find the percent of error.
The percentage of error in the estimation of Alton is:
13.04%
Given:
Alton estimated that 230 people attended the band concert.
The actual count for attendance was 200 people.
we are asked to determine the percent of error = ?
Percent error
Using this formula
Percent error=Actual attendance -Estimated attendance/Actual attendance
Let plug in the formula
Percent error=230-200/230
Percent error=30/230
Percent error=0.1304×100
Percent error=13.04%
Hence we get the percentage error as 13.04%.
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P(A)=2/3, P(B)=3/5, and P(AB)=11/15, Find P(B|A)
Based on the probability values, the value of the probability notation P(B|A) is 9/11
How to evaluate the probability?The given parameters from the question are given as
P(A) = 2/3
P(B) = 3/5
P(AB) = 11/15
Before solving the probability notation P(B|A), we start by calculating the probability expression
This is represented as
P(B|A) = P(AB)/P(A)
Substitute the known values in the above equation, so, we have the following representation
P(B|A) = (3/5)/(11/15)
Express the quotient expression as products
So, we have the following representation
P(B|A) = 3/5 * 15/11
Divide 15 and 5 by 5
This gives
P(B|A) = 3/1 * 3/11
So, we have
P(B|A) = 3 * 3/11
Multiply 3 and 3
P(B|A) = 9/11
Hence, the value of the probability is 9/11
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Annie was given two pieces of information and must write the equation of a line. She knows the line crosses the y-axis at the point (0,6) and has a slope of 7. What is the equation of the line?.
The correct answer is the equation of line is y = 7x + 6 when the point is (0,6) and the slope is 7.
We know a point which is (0,6) and a slope which is 7. It's a unique point, where we have to find its equation. Firstly, it is the y intercept because
x = 0. We can use the equation for a line in the form of slope-intercept
The required equation of line formula is y= mx+c where m is the slope that is 7 and c is the y intercept that is 6.
where y = 7x + 6
The general equation of a straight line is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis.
On the y-axis, this value c is referred to as the intercept, it represents the equation of a straight line with gradient m and intercept c on the y-axis.
Hence, the equation of line is y = 7x + 6 when the point is (0,6) and the slope is 7.
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A newsletter publisher believes that over 63 % of their readers own a Rolls Royce. For marketing purposes, a potential advertiser wants to confirm this claim. After performing a test at the 0.10 level of significance, the advertiser failed to reject the null hypothesis. What is the conclusion regarding the publisher's claim? Answer 2 Points m Tables Keypad There is sufficient evidence at the 0.10 level of significance that the percentage is over 63 %. There is not sufficient evidence at the 0.10 level of significance to say that the percentage is over 63 % .
Answer:
Step-by-step explanation:
The conclusion is that the null hypothesis is not true
How do you prove the SSS congruence theorem?.
When one triangle's three sides are equal to the corresponding three sides of another triangle, two triangles are said to be congruent.
Triangle ABC and triangle PQR, where AB = PQ, BC = QR, and AC = PR.
Triangle ABC is comparable to PQR, therefore proving
Assuming triangle ABC's longest side is BC, triangle PQR's longest side is QR.
As a result, the angles RQS = angle CBA, QRS = angle BCA, and they combine at SQ and SR.
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Ciphers, such as the enigma machine, that rearrange the sequence of characters based on a fixed rule are known as ______________.
Ciphers, such as the enigma machine, that rearrange the sequence of characters based on a fixed rule are known as substitution cipher.
A type of encryption known as a replacement cypher employs a key to substitute certain plaintext chunks with the ciphertext in a predetermined manner.
Single letters, pairs of letters, triplets of letters, combinations of the aforementioned, etc. are all acceptable "units." The receiver decodes the text using the inverse substitution technique to ascertain what the original message was.
Cyphers for transposition and substitution are similar. In a transposition cypher, the plaintext's units are not changed; instead, they are rearranged in a brand-new, frequently extremely complex pattern. A substitution cypher modifies the units themselves while preserving the order of the units from the plaintext in the ciphertext.
The substitution cypher can take many different shapes. If a cypher only functions with single letters, it is referred to as a simple substitution cypher; a polytrophic cypher, on the other hand, functions with larger groups of letters.
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A multiple is a number
that is the ____
of
a given number and
some other number.
The correct statement will be;
''A multiple is a number that is the product of a given number and some other number.''
What is Greatest common factors?
The highest number that divides exactly into two more numbers, is called Greatest common factors.
Given that;
The statement is,
A multiple is a number that is the ____ of a given number and some other number.
Now,
We know that;
A multiple is a number that is the product of a given number and some other number.
Thus, The correct statement will be;
''A multiple is a number that is the product of a given number and some other number.''
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In March 2015, the Public Policy Institute of California (PPIC) surveyed 7,525 likely voters living in California. In the survey, respondents were asked about global warming. PPIC results show that 47% of adults age 55 and older view global warming as a serious problem, and 65% of adults age 18 to 34 view global warming as a serious problem. PPIC researchers are interested in the difference in proportions of adults age 55 and over and adults age 18 to 34. The standard error for the difference in proportions is 0.011.
Researchers want to decrease the margin of error by adjusting the confidence level. Which confidence interval will have the smallest margin of error (MOE)?
a) 90% confidence interval
b) 95% confidence interval
c) 99% confidence interval
90% confidence interval will have the smallest margin of error.
What is global warming?
Long-term changes in temperature and weather patterns are referred to as climate change. These changes may be organic, but since the 1800s, human activity has been the primary cause of climate change. This is primarily because burning fossil fuels, such as coal, oil, and gas, releases gases that trap heat.
In March 2015, the Public Policy Institute of California (PPIC) surveyed 7,525 likely voters living in California.
In the survey, respondents were asked about global warming. PPIC results show that 47% of adults age 55 and older view global warming as a serious problem, and 65% of adults age 18 to 34 view global warming as a serious problem.
PPIC researchers are interested in the difference in proportions of adults age 55 and over and adults age 18 to 34.
The standard error for the difference in proportions is 0.011.
The correct option is (a).
As the confidence level decreases margin of error decreases.
So 90% confidence interval will have the smallest margin of error.
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Between which two consecutive whole numbers does v87 lie?
The number square root of 87 which is √87 lies between the two consecutive integers are 9 and 10.
Given that,
The number is square root of 87 which is√87.
We have to find the two consecutive whole numbers does √87 lies.
We know that,
What is an whole number?In the category of numbers known as "whole numbers," all natural numbers and 0 are included. They are a subset of "real numbers," which are those that don't contain fractions, decimals, or negative numbers.
The √87 lies between √81 and √100
Which we can write as
√81<√87<√100
9<√87<10
Therefore, The number square root of 87 which is √87 lies between the two consecutive integers are 9 and 10.
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in multiple regression analysis, there can be any number of dependent variables but only one independent variable there must be only one independent variable the coefficient of determination must be larger than 1 there can be several independent variables, but only one dependent variable
In multiple regression analysis, there can be several independent variables, but only one dependent variable
The link between several independent or predictor variables and one dependent or criterion variable is typically explained using multiple regression. The constant term, along with a number of independent variables and their corresponding coefficients, are used to model a dependent variable. Thus, it refers to a regression model that uses two or more predictor variables.
It is a statistical method that can be used to examine the relationship among a single dependent variable and a number of independent variables. The variables are quantified because an equation is used to represent the model. Although the independent variables are almost always positive, their coefficients occasionally aren't.
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suppose you want to distribute 10 candies among 5 kids such that each kid gets atleast one candy. in how many ways can you distribute the candies? (all 10 pieces of candies are identical, but the kids are distinct.)
There are a total of 126 ways to distribute the 10 identical candies among the 5 distinct kids.
A combination is also called a selection. A combination corresponds to a selection of things from a given set of things. It is Denoted by
ⁿCᵣ = n!/r!(n-r)!
the number of unique r selections fromaset of n objects.
We have given that,
Total number of candies for distribution = 10
number of kids who take the candies = 5
Candies are distributed among the kids such that each kid has atleast one candy.
Here, candies are identical and kids are distinct.
Number of ways in which 10 identical candies can be divided among 5 kids if each kid must get at least one candy. The problem can be solved using the combination formula with
n = 5, k = 10.
= ⁽ᵏ⁻¹⁾Cₙ₋₁· = ⁹C₄ = 126 ways to do this.
So, there are 126 ways to distribute the candies among the five kids.
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No matter which brand he chooses, gareth will pay for the freezer on his credit card, which has an apr of 9. 31%, compounded monthly. It takes gareth eighteen months to pay off a brand s freezer and four years to pay off a brand r freezer. Assuming that gareth makes no other purchases or payments with his credit card, over the next ten years, which brand of freezer will have a lower lifetime cost, and how much lower will it be? (round all dollar values to the nearest cent. ).
The correct option is (a) Gareth will choose the Brand R credit card for the freezer because it is $548.18 less expensive than the Brand S.
An annual percentage rate, or APR, is used to express the interest rate that is applied to the principal amount of a loan.
The credit card's yearly percentage rate is 9.31%.
Gareth takes four years to pay off a Brand R freezer compared to just 18 months for a Brand S freezer.
Overall, ten years have gone.
To determine which credit card has the lowest lifetime cost for a freezer, we must compare the APRs of the two cards.
Let's say there are 1000 freezers. As a result, the APR for 18 months will be lower because the interest rate's duration is shorter.
The B and R will therefore be $548.18 less expensive than Brand S, according to a comparison of the APR.
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x² = 5x + 6 = 0 if and only if x = 2. True False
Answer:
Did you mean x^2 + 5x + 6?
Step-by-step explanation:
If so, then the answer would be x=-2 or x=-3
Step 1: Factor left side of equation.
(x+2)(x+3)=0
Step 2: Set factors equal to 0.
x+2=0 or x+3=0
x=−2 or x=−3
Hi! Can you guys help me with this
Q:
Dora opened a saving account and deposited $50. After she gets her paycheck each week, she plans to deposit $20 into the saving account
1. Describe the initial value in this situation.
2. Then, find the rate of change for the account.
3. Will the rate of change over time change values? Explain.
The rate of change for the first week is 40%, and it changes values over the time.
Rate is a measurement to determine the change in one quantity with respect to another quantity.
It shows are the changing
The amount deposit by Dora in account = $50.
Also, amount planned by Dora to deposit each week = $20
The rate of change for first week = (20/50)×100 %
= 40 %
The rate of change for the first week is 40%.
The rate of change will change the value, as principal amount increases every week, therefore, rate of change will decrease over the time.
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a diesel-powered tractor with a cost of $136,700 and estimated residual value of $14,500 is expected to have a useful operating life of 18,800 hours. during november, the tractor was operated 160 hours. determine the depreciation for the month. carry out any division to two decimal places.
For the month of November, there has been a depreciation of almost $1,089.60.
By deducting the expected residual value from the cost of the tractor and dividing the result by the total projected operational life in hours, let's first get the depreciation per hour:
A tractor's depreciation per hour is calculated by deducting the residual value from the purchase price, and multiplying the result by the number of hours the tractor will be in use.
[tex]\rm D = \dfrac {136,700 - 14,500} { 18,800}\\D = \$6.81[/tex]
Multiplying the depreciation per hour by the number of hours the tractor was used to get the depreciation for the month of November
[tex]D_m = 6.81 \times 160\\D_m = \$1,089.60[/tex]
Therefore, for the month of November, there has been a depreciation of almost $1,089.60.
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What is a central angle part of?.
In Circles the central angle is the angle measures between two radii of the circle.
As shown in the figure:
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Does the altitude of an isosceles triangle bisect the vertex angle?.
Yes, the altitude of an isosceles triangle bisect the vertex angle as ∠BAD = ∠CAD (by CPCT) in isosceles triangle ABC.
Given, an isosceles triangle ABC
now, the two sides are equal
AB = AC
now, drawing an altitude AD in the triangle.
So, in triangles ADB and ADC
AB = AC (given)
AD = AD (common)
∠ADB = ∠ADC (90°)
So, by RHS congruence rule
ΔADB ≅ ΔADC
and therefore ∠BAD = ∠CAD (by CPCT)
Hence, Yes the altitude of an isosceles triangle bisect the vertex angle as ∠BAD = ∠CAD (by CPCT) in isosceles triangle ABC.
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If she made the last free throw; then her probability of making the next one is 0.7 . On the other hand, If she missed the last free throw, then her probability of making the next one is 0.3. Assume that state is Makes the Free Throw and that state 2 is Misses the Free Throw: (1) Find the transition matrix for this Markov process_
The transition matrix for Markovian is,
[ 0.7 0.3 ]
[ 0.3 0.7 ]
What is meant by probability?Probability is an area of mathematics that deals with numerical descriptions of the likelihood of an event happening or a proposition being true. An event's probability is a number between 0 and 1, where 0 indicates impossibility and 1 represents certainty.
Probability is simply the possibility of something happening. When we are confused about the outcome of an event, we might discuss the probabilities of certain outcomes—how likely they are. Statistics is the study of occurrences based on probability.
Let [tex]S_{i}[/tex], i = 1, 2, is denoted for state i.
If [tex]T_{ij}[/tex] is denoted for the transition from [tex]S_{j}[/tex] to [tex]S_{i}[/tex],
The transition probabilities are given by:
Probability(T₁₁) = 0.7
Probability(T₂₁) = 1- Probability(T₁₁) = 1 - 0.7 = 0.3
Probability(T₁₂) = 0.3
Probability(T₂₂) = 1- Prob(T₁₂) = 1 - 0.3 = 0.7
So, the transition matrix for Markovian is,
[ 0.7 0.3 ]
[ 0.3 0.7 ]
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If you are conducting a survey to determine the public opinion on whether hockey is too dangerous, which of the following samples would be the least biased and most not useful ?
B: shoppers at the mall
The shoppers at the mall would be the least biased and the hockey fans would be most not useful for the survey
For avoiding bias the best option would be one that most diverse individuals. If we are evaluating violence in hockey we should avoid hockey fans, as the probably would think that violence is something bad and they do not want their sport to be bad.
The hockey fans would be most not useful for the survey
If there is a correlation between football fans and hockey fans, for example, that most of hockey fans also watch football games (which is very likely because sports fans tend to watch more than one sport), we will have the same kind of bias than above.
A similar reasoning can be thought with sportscasters, as they are peole that are very interested in sports and their opinion can be biased. Also, as mos sportscasters are men, you got a gender bias.
However, in a shopping mall we can have the most random sample. There will be interviewed people that love hockey, people that do not love hockey. we avoid age bias, as in a shopping there are people of every age. we can expect to find women and men, differently to the other options. So, this is the best option to run a survey about violence/danger in hockey.
Therefore, the shoppers at the mall would be the least biased and the hockey fans would be most not useful for the survey.
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what is y=2x-14 and y=-5x
The unknown value x = 2 after substitution for the value y = -5x for y = 2x - 4.
What is SubstitutionSubstitution in mathematics is the process for solving systems of equations that include solving for one variable and using that solution to find the other (or unknown) variable.
For y = 2x - 14 and y = -5x, we substitute the value -5x for y in the equation y = 2x - 4 to find the unknown value x;
-5x = 2x - 14
add 5x to both sides of the equation
5x - 5x= 2x + 5x - 14
0 = 7x - 14
add 14 to both sides of the equation
14 = 7x - 14 + 14
14 = 7x
also 7x = 14 {divide through by 7}
x = 14/7
x = 2.
Thus, the value of the unknown x is 2 after proper substitution.
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A race track has a diameter of 350 ft. How far does a car drive if it completes one lap
around the track?
1) 843 ft
2) 1,099 ft
3) 1,653 ft
4) 2,198 ft
The required distance that a car can drive in one lap is 1099 ft. Option 2 is correct.
Given that,
A race track has a diameter of 350 ft. how far a car drive if it completes one lap is to be determined.
Perimeter is the measure of the figure on its circumference.
Here,
Diameter = 350 ft
Circumference = πD
Circumference = 3.14 × 350 = 1099ft
Thus, the required distance that a car can drive in one lap is 1099 ft. Option 2 is correct.
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the short-run quantity of output supplied by firms will exceed the natural level of output when the actual price level the price level that people expected.
The price level that people expected rise above.
What is the term for price increases?
The rate at which prices rise over a given time is called inflation. A country's cost of living or overall increase in prices are two examples of broad measures of inflation.
What happens when the price level rises above expectations?
The economy's leading indicators are price levels; Inflation occurs when prices rise in response to increased demand, while deflation occurs when prices fall in response to decreased demand.
What happens when the price rises?
The average price of all goods and services sold rises when an economy's price level rises. The percentage increase in a nation's price level over some time, typically a year, is what is used to calculate inflation. This indicates that inflation is taking place during the time when prices rise.
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How do you find the length and width of a rectangle when given the area?.
if you additionally recognize the perimeter of the rectangle, you could use that data to locate possible values for length and width. The area of a rectangle (A) is related to the length (L) and width (W) of its facets by the following relationship: A = L × W
ShapeIn Euclidean aircraft geometry, a rectangle is a quadrilateral with four right angles. it may additionally be defined as an equiangular quadrilateral, given that equiangular method that all of its angles are identical (360°/4 = 90°); or a parallelogram containing a right angle. A rectangle with 4 facets of an equal period is a square. The term rectangular is sometimes used to refer to a non-square rectangle. A rectangle with vertices ABCD might be denoted as Rectangle ABCD.
The phrase rectangle comes from the Latin rectangles, which is a mixture of rectus (as an adjective, right, proper) and angelus (attitude).
A crossed rectangle is a crossed (self-intersecting) quadrilateral that consists of two opposite aspects of a rectangle in conjunction with the two diagonals (consequently simplest aspects are parallel). it's miles a special case of an antiparallelogram, and its angles aren't right angles and now not all same, although opposite angles are the same. different geometries, along with spherical, elliptic, and hyperbolic, have so-called rectangles with opposite facets same in the period, and the same angles that aren't right angles.
Rectangles are worried in many tiling issues, including tiling the aircraft by means of rectangles or tiling a rectangle through polygons.
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A baseball dropped from the roof of a tall building takes 3. 1 seconds to hit the ground. How tall is the building? [neglect friction. ].
After solving, the height of the building is 15.19 m tall.
In the given question, a baseball dropped from the roof of a tall building takes 3. 1 seconds to hit the ground.
We have to find the height of the building.
Initial Velocity, denoted as u, is the velocity at time interval t = 0. It is the speed at which motion first occurs.
Initial velocity u=0
Time t=3.1 seconds
Let height of the cliff is h.
So s=ut+at^2/2
Now putting the value
s = 0+(9.8×3.1)/2
s = 30.38/2
s = 15.19 m
Hence, the height of the building is 15.19 m tall.
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Combine like terms to create an equivalent expression.
Enter any coefficients as simplified proper or improper fractions or integers.
By combining like terms, the equivalent of the given expression, [tex]-\frac{2}{3}a + \frac{5}{6}a-\frac{1}{6}[/tex] , is [tex]\frac{a}{6} -\frac{1}{6}[/tex] or [tex]\frac{a-1}{6}[/tex]
Determining an Equivalent expression by combining like termsFrom the question, we are to combine like terms to create an equivalent expression of the given expression.
The given expression is
[tex]-\frac{2}{3}a + \frac{5}{6}a-\frac{1}{6}[/tex]
Combining like terms
[tex]\frac{2(-2a) + 1(5a)}{6} -\frac{1}{6}[/tex]
[tex]\frac{-4a + 5a}{6} -\frac{1}{6}[/tex]
[tex]\frac{a}{6} -\frac{1}{6}[/tex]
= [tex]\frac{a-1}{6}[/tex]
Hence, the equivalent expression is [tex]\frac{a}{6} -\frac{1}{6}[/tex] or [tex]\frac{a-1}{6}[/tex].
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