Triangle ABC is indeed similar to Triangle CDE by the SAS (Side-Angle-Side) Congruence Postulate.
How are the triangles congruent ?Assume that we have the following to prove congruence:
AB/DC = AC/CE (proportional sides)
AB || CD (parallel lines)
This means that angle ABC is congruent to angle CDE.
Looking at this, we can infer that Side AB is proportional to side DC. We also see that Angle ABC is the same as Angle CDE.
Going by the SAS Congruence theorem, Triangle ABC is indeed similar to Triangle CDE because two sides of the triangle are similar and one angle is congruent.
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Radioactive decay tends to follow an exponential distribution; the half-life of an isotope is the time by which there is a 50% probability that decay has occurred. Cobalt-60 has a half-life of 5.27 years. (a) What is the mean time to decay? (b) What is the standard deviation of the decay time? (c) What is the 99th percentile? (d) You are conducting an experiment which first involves obtaining a single cobalt-60 atom, then observing it over time until it decays. You then obtain a second cobalt-60 atom, and observe it until it decays; and then repeat this a third time. What is the mean and standard deviation of the total time the experiment will last?
The exponential distribution is a probability distribution that models the time between events in a Poisson process, where events occur randomly and independently at a constant average rate.
It is commonly used in reliability theory, queuing theory, and other fields to model the failure or waiting times of systems.
(a) The mean time to decay for Cobalt-60 is 5.27 years.
(b) The standard deviation of the decay time is 2.6355 years.
(c) The 99th percentile is 13.6825 years.
(d) The mean time of the experiment is 15.8175 years and the standard deviation is 4.86788 years.
Note: The answers are calculated based on the exponential distribution of radioactive decay with a half-life of 5.27 years for Cobalt-60.
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Need help ASAP!!!!
Triangle ABC is a right triangle with sides that
measure 3, 4, and 5 units. If point A is located
at (1,2) and point B is located at (1,-1), give the
coordinates for point C.
Answer:
I think it would be (5,2)
please graph y≤ 2x-3
Inverse Functions, graphs
Answer:
a.
inverse
of
(0,1)=(1,0)
(1,0)=(0,1)
(2,-1)=(-1,2)
(3,0)=(0,3)
(4,1)=(1,4)
Step-by-step explanation:
b.
yes the function are inverse
as
(-1,2)=(2,-1)
(0,1)=(1,0)
Take any one point .
(-2,-1)For inverse
(x,y) should be (y,-x)
Apply
(-(-2),-1)(-1,2)Yes the functions are inverses of each other
use logarithm table to evaluate (3.68)2 x 6.705
Answer:
Step-by-step explanation:
49.3488
Which expressions are equivalent to -6n+(-12)+4
A 4(n - 3) - 6n
B 2(2n - 6)
C None of the above
Aerin's friend Fritz gives her a riddle to solve about the ages of the people in his family. There are 5 people in Fritz's family: Mom, Dad, his sisters Adele and Erika, and Fritz. Here are the clues to the puzzle. 1) Mom is 8 years younger than Dad. 2) Dad is 2 times as old as Fritz. 3) Adele is 4 years old. 4) Fritz's age plus Adele's age equals Erika's age. 5) Mom was 24 when Erika was born. 6) In 9 years, Mom will be twice as old as Erika will be. All the ages are whole numbers. Aerin decides to use variable for the unknown ages and write equations to express the information. M
Answer:
Dad = 47, Mom = 39, Fritz = 11, Erika = 15 and Adele = 4
Step-by-step explanation:
Let M = Mom's age, D = Dad's age, F = Fritz's age, A = Adele's age and E = Erika's age.
Given that
1) Mom is 8 years younger than Dad, we have D = M + 8 (1)
2) Dad is 2 times as old as Fritz. D = 2F (2)
3) Adele is 4 years old. A = 4 (3)
4) Fritz's age plus Adele's age equals Erika's age. F + A = E (4)
5) Mom was 24 when Erika was born. M = E + 24 (5)
6) In 9 years, Mom will be twice as old as Erika will be. M + 9 = 2(E + 9) (6)
Substituting (5) into (6), we have
E + 24 + 9 = 2(E + 9)
E + 33 = 2E + 18
subtracting E from both sides, we have
2E - E + 18 = 33 + E - E
E + 18 = 33
subtracting 18 from both sides, we have
E + 18 - 18 = 33 - 18
E = 15
M = 15 + 24 = 15 + 24 = 39
From (4) F = E - A = 15 - 4 = 11
From (1) D = M + 8 = 39 + 8 = 47
So, their ages are Dad = 47, Mom = 39, Fritz = 11, Erika = 15 and Adele = 4
what is 14/7 into improper fraction
Answer: 2 and 0/7
MATH
need help with this NO BOTS OR LINKS
Answer:
946
Step-by-step explanation:
To find the area, you can split the figure into 2 rectangles. The one on the left has a width of 7 and a height of 28. Multiply 28 * 7 to get the area of the first rectangle, which is 196 in.
The second rectangle has a width of 25 and a length of 30. Multiply 30 by 25 to get the area, which is 750 in.
To find the area of the entire figure, add the areas of both rectangles.
196 + 750 = 946 square inches.
Describe how to compare the two ratios 5:8 to 7:9. Tell each step to set up the ratios, then explain what to do to be able to compare the ratios. Finally make sure to answer how the ratios compare.
Answer:
5/8 is smaller.
Step-by-step explanation:
A ratio is just a different type of fraction, a 5:8 ratio means 5/8 which is 0.625. A 7:9 ratio equals 7/9 which is 0.777777
Then to compare them you see which is smaller or bigger.
0.77777 is bigger than 0.625 so we know that 0.77777777 which was the 7:9 ratio is the bigger one.
What is the value of x in the equation?
5 5/6x+2 2/3=12
A)
2/3
B)
1 2/3
C)
1 5/6
D
1 3/5
A stream of crude oil has a molecular weight of 4.5x10² kg/mol and a mean average boiling point of 370 °C. Estimate the followings: 1. The crude specific gravity at 60 °F? 2. The crude gravity (API°) at 60 °F? 3. Watson characterization factor? 4. Refractive index? 5. Surface tension? 6. Is this crude oil paraffinic, naphthenic or aromatic? Explain, briefly and qualitatively.
The crude oil is likely to be paraffinic. Paraffinic crude oils are characterized by having a high API°, low Watson characterization factor, and low refractive index. They also tend to have a high surface tension.
Specific gravity at 60 °F: 0.88
API° at 60 °F: 28
Watson characterization factor: 1.014
Refractive index: 1.44
Surface tension: 20 dyne/cm
Paraffinic, naphthenic, or aromatic: Paraffinic
Specific gravity at 60 °F the specific gravity of a liquid is its density relative to the density of water. The specific gravity of crude oil is typically between 0.8 and 1.0. A specific gravity of 0.88 means that the crude oil is 88% as dense as water.
API° at 60 °F: The API°, or American Petroleum Institute gravity, is a measure of the lightness or darkness of crude oil. A higher API° indicates a lighter crude oil. A crude oil with an API° of 28 is considered to be a medium-heavy crude oil.
Watson characterization factor the Watson characterization factor is a measure of the aromaticity of crude oil. A higher Watson characterization factor indicates a more aromatic crude oil. A crude oil with a Watson characterization factor of 1.014 is considered to be a paraffinic crude oil.
Refractive index the refractive index of a liquid is a measure of how much light is bent when it passes through the liquid. The refractive index of crude oil is typically between 1.4 and 1.5. A refractive index of 1.44 indicates that the crude oil is slightly more refractive than water.
Surface tension the surface tension of a liquid is a measure of the force that acts at the surface of the liquid, tending to minimize the surface area. The surface tension of crude oil is typically between 20 and 30 dyne/cm. A surface tension of 20 dyne/cm indicates that the crude oil has a relatively high surface tension.
Based on the estimated values, the crude oil is likely to be paraffinic. Paraffinic crude oils are characterized by having a high API°, low Watson characterization factor, and low refractive index. They also tend to have a high surface tension.
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Please help im in math right now and im about to leave to go to my next class
Answer:
rlkgj3ypihjepvwr'kg3tyhjl3jofj 'y4ujk
Step-by-step explanation:
epoijreohrj3oewmydwlmh5lu6jm;s,dky608jp
Answer: #3 is 156.86
Step-by-step explanation:
First you Multiply 136.40 by .15. It comes out to 20.46. Then add 136.40 and 20.46 together
when you multiply a three-digit number by a four-digit number, what is the greatest number of digits the product can have? Explain
Answer:
7 digits
Step-by-step explanation:
When we multiply a two digit number like 17 by another 2 digit
The highest number of digits we can get as answer is 4 digits
This can be seen in the case of 10 * 10
So what this mean is that at any point in time, we can sum the numbers to get the digits
3 + 4 will give 7
And that is the greatest number we can get
Which of the following is a radical equation?
A. x StartRoot 3 EndRoot = 13
B. x + StartRoot 3 EndRoot = 13
C. StartRoot x EndRoot + 3 = 13
D. x + 3 = StartRoot 13 EndRoot
Answer:
C. StartRoot x Endroot + 3 = 13
Step-by-step explanation:
the x variable under the root is what makes it a radical. all of the others dont have an x variable under the root. hope this helps !
HELP PLEASE
Mitchell earns $14 for each hour of mowing lawns. How many hours in all will it take Mitchell to earn a total of $56?
Answer: 4 hours in total
Step-by-step explanation:
$56 divided by $14 per hour is equal to 4 hours.
Please help please! No fake answers pls
Answer:
3,8,11
Step-by-step explanation:
if line d was parallel there might be more but it is not so the only ones that are congruent are 3,8 and 11
Negative air pressure created by an air pump makes a vacuum cleaner able to collect air and dirt into a bag or other container. Below are several readings from a pressure gauge. Write rational numbers to represent each of the readings, and then order the rational numbers from least to greatest.
Gauge Readings ( pounds per square inch )
25 psi pressure
13 psi vacuum
6.3 psi vacuum
7.8 psi vacuum
1.9 psi vacuum
2 psi pressure
7.8 psi pressure
Pressure readings ( pounds per inch) answers:
The ordered rational numbers representing the gauge readings from least to greatest are 19/10, 63/10, 78/10, 78/10, 13/1, 25/1, 2/1.
To represent the gauge readings as rational numbers, we can express them as fractions with a common denominator.
Given readings:
25 psi pressure
13 psi vacuum
6.3 psi vacuum
7.8 psi vacuum
1.9 psi vacuum
2 psi pressure
7.8 psi pressure
Expressed as rational numbers with a common denominator:
25 psi = 25/1
13 psi = 13/1
6.3 psi = 63/10
7.8 psi = 78/10
1.9 psi = 19/10
2 psi = 2/1
7.8 psi = 78/10
Now, let's order these rational numbers from least to greatest:
1.9 psi = 19/10
6.3 psi = 63/10
7.8 psi = 78/10
7.8 psi = 78/10
13 psi = 13/1
25 psi = 25/1
2 psi = 2/1
Ordered from least to greatest:
19/10, 63/10, 78/10, 78/10, 13/1, 25/1, 2/1
Therefore, the ordered rational numbers representing the gauge readings from least to greatest are 19/10, 63/10, 78/10, 78/10, 13/1, 25/1, 2/1.
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Plxzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz helpe me if you can
Write an expression for the sequence of operations described below.
multiply 9 by the difference of 6 and 4
Answer:
not sure
Step-by-step explanation:
6-4 =2
2*9=18??
I'm not sure, since that was simple math, can you clarify by what you meant the difference of 6 and 4.
Four points are labeled on the number line.
Answer:
What does it mean? Also I think the picture didn't go through
Step-by-step explanation:
But I found its L or Point Q -0.5
Sorry if this doesn't help ;-;
Have a nice day
Answer:
I don’t know
Step-by-step explanation:
What is the length of AB?
1. Square root 53
2. 5
3. 2 square root 10
4. 2 square root 6
Answer:
Step-by-step explanation:
where is the figure of this
V = √3 3-x² S -√√3-√3-x²1 4-x²-y² dzdydx
The value of the given integral is: v = [(4√(3) - 5)π/3]
To evaluate the given integral, let's calculate it step by step:
First, let's integrate with respect to z from 1 to √(4 - x² - y²):
∫[1, √(4 - x² - y²)] dz = √(4 - x² - y²) - 1
Next, let's integrate the above expression with respect to y from -√(3 - x²) to √(3 - x²):
∫[-√(3 - x²), √(3 - x²)] (√(4 - x² - y²) - 1) dy
To simplify the integration, let's convert to polar coordinates:
x = r cosθ
y = r sinθ
The bounds of integration in polar coordinates will be:
r: 0 to √(3)
θ: 0 to 2π
Now, we can rewrite the integral in terms of polar coordinates:
∫[0, 2π] ∫[0, √(3)] (√(4 - r²) - 1) r dr dθ
Evaluating the inner integral with respect to r:
∫[0, 2π] [(-1/3) (4 - r²)\(^{3/2}\) - (1/2) r²] | [0, √(3)] dθ
∫[0, 2π] [(2√(3)/3) - (1/3)(4 - 3)\(^{3/2}\) - (1/2)(√(3))²] dθ
Simplifying further:
∫[0, 2π] [(2√(3)/3) - (1/3) - (3/2)] dθ
∫[0, 2π] [(2√(3)/3) - (5/6)] dθ
Now, integrating with respect to θ:
[(2√(3)/3)θ - (5/6)θ] | [0, 2π]
[(2√(3)/3)(2π) - (5/6)(2π)] - [(2√(3)/3)(0) - (5/6)(0)]
[(4√(3)/3)π - (5/3)π] = [(4√(3) - 5)π/3]
Therefore, the value of the given integral is: v = [(4√(3) - 5)π/3]
Complete Question:
Evaluate the integral:
v = ∫∫∫ [−√3, √3] [−√(3−x²), √(3−x²)] [1, √(4−x²−y²)] dz dy dx
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Johanna graphed the number of calls she made during one day. How many calls were made before 6 p.m.?
A histogram titled Cell Phone Calls has time of day on the x-axis and number of calls on the y-axis. From 10 to 12 pm there were 2 calls; from 12 to 2 pm there were 8 calls; from 2 to 4 pm there were 0 calls; from 4 to 6 pm there were 10 calls; from 6 to 8 there were 4 calls; from 8 to 10 pm there were 2 calls.
Answer:
i think it was 20
Step-by-step explanation:
i took the quiz
Answer:
20
Step-by-step explanation:
By The Way You Matter Dont Give Up
Kiera and Roger each made a bowl of punch. Roger used 8 7/10 times as much lemonade as Kiera did. If Kiera used 1/5 of a cup of lemonade, how many cups of lemonade did Roger use? HEEELP ASAP!
Roger used 87/10 times as much lemonade as Kiera did, and the number of cup is 87/50.
What is an improper fraction?An improper fraction is one where the numerator is more than or equal to the denominator.
Given, Kiera and Roger each made a bowl of punch.
Roger used 8 7/10 times as much lemonade as Kiera did.
First, we convert mixed fraction to improper fraction,
\(8\frac{7}{10}\) = 87 / 10
To find the number of cups of lemonade, Roger used;
\(8\frac{7}{10}\) x number of cups Kiera used
= \(8\frac{7}{10}\) x 1/5
= 87/10 x 1/5
= 87/50
Therefore, Roger used 87/50 cups of lemonade.
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pls help me quick erg
The distance Chyna ran is 7 1 / 2 kilometres.
How to find the distance Chyna ran?Ronaldo ran 9 / 10 fewer kilometres than Chyna ran. Ronaldo ran 6 3 / 5
kilometres
Therefore, the distance Chyna ran in kilometres can be calculated as follows:
Therefore,
Distance Ronaldo ran = 6 3 / 5 = 33 / 5 kilometres
Hence,
Distance Chyna ran = 33 / 5 + 9 / 10
Distance Chyna ran = 66 + 9 / 10
Distance Chyna ran = 75 / 10
Therefore,
Distance Chyna ran = 7 5 / 10
Distance Chyna ran = 7 1 / 2 kilometres
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PLEASE HELP WILL MARK BRANLIEST
If f(x)= 4x-12 and the value of f(2)= -4, find f(5). *
WILL GIVE BRAINLIEST.
Find the equation of the line. Use the exact numbers.
Equation: y = __ x + __
Answer:
y=1/2x+4
Step-by-step explanation:
Answer:
y=2x+4
Step-by-step explanation:
the perimeter of a triangle is 14x - 4. if two sides measure 3x - 2 and 5x + 3, then how long is the third side?
Answer:
6x-5
Step-by-step explanation:
14x-4- (3x-2)-(5x+3)= 14x-4-3x+2-5x-3= 6x-5
I need help with number two
Answer:
?
Step-by-step explanation:
Please help meeeee !!!
Answer:
its c
Step-by-step explanation: