Using logarithm properties, the expression written as a single term is:
[tex]\ln{\left(\frac{(x - 1)^6(x+1)}{x^3}\right)}[/tex]
What is the expression and how the write it as a single term?Researching the problem on a search engine, the expression is given by:
3[2ln(x - 1) - ln(x)] + ln(x + 1).
Applying the distributive property, we have that:
6ln(x - 1) - 3ln(x) + ln(x + 1).
Applying the exponential property of logarithms, we have that the expression is:
[tex]\ln{(x - 1)^6} - \ln{(x)^3} + \ln{(x + 1)}[/tex]
The adding terms can be placed inside multiplying, the subtracting dividing, hence:
[tex]\ln{(x - 1)^6} - \ln{(x)^3} + \ln{(x + 1)} = \ln{\left(\frac{(x - 1)^6(x+1)}{x^3}\right)}[/tex]
Hence the expression written as a single term is:
[tex]\ln{\left(\frac{(x - 1)^6(x+1)}{x^3}\right)}[/tex]
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kurt busch won the daytona 500 (mile) race with a rate of 143.187 mph in 2017. find his time to the nearest thousandth
The time taken to finish the race is 3.49 hours
Speed is defined as. The rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered.
Given,
The total distance = 500 miles
The speed = 143.187 mph
We know, Speed = Distance / Time
Time = Distance / Speed
Substitute the values
Time = [tex]\frac{500}{143.187}=3.49[/tex] hours
Hence, the time taken to finish the race is 3.49 hours
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Simplify 5 · P · 2.
A. 10P
B. 52P
C. 7P
Answer:
Step-by-step explanation:
5 x 2 = 10
Pretty sure this is right but I'm not 100 percent sure!
Answer: 10P ==> A
Step-by-step explanation:
5 · P · 2= 5 · 2 · P ==> Commutative property of multiplication
5 · 2 · P=
10 · P=10P ==> A
suppose that the probability that a randomly selected person who has recently married for the first time will be divorced within 5 years is 0.2, and that the probability that a randomly selected person who has recently married for the second time will be divorced within 5 years is 0.30. take a random sample of 10 people married for the first time and 10 people married for the second time. the sample is chosen such that no one in the sample is married to anyone else in the sample. why is the binomial model inappropriate for finding the probability that exactly 4 of the 20 people in the sample will be divorced within 5 years? list all of the binomial conditions that are not met.
The binomial is a unique type of discrete random variable. If ALL four of the following conditions are met, our experiment is a binomial experiment: it consists of n identical trials.
What do you mean by the term binomial condition?One of the two outcomes, known as success or failure, arises from every try. From trial to trial, the likelihood of success, given by the symbol, stays constant. There are n independent trials. The binomial distribution is a probability distribution that summarizes the possibility that a value will take one of two independent values under a given set of parameters or assumptions, which means the result of each trial has no bearing on the results of the others. The fundamental presumptions of the binomial distribution are that there is only one possible result for each trial, that each trial has the same success probability, and that each trial is independent of the others or mutually exclusive.
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The table shows the numbers y of students absent from school x days after a flu outbreak.
Write a function that models the data.
Use the model to approximate the number of students absent 10 days after the outbreak.
A scatter plot is also referred to as scatter chart, scatter diagram or scattergram and it can be defined as a type of graph which is used for the graphical representation of the values of two (2) variables, with the resulting points showing any association (correlation) between the data set.
What is a quadratic function?A quadratic function can be defined as a mathematical expression (equation) that can be used to define and represent the relationship that exists between two or more variable on a graph.
In Mathematics, the standard form of a quadratic equation is given by;
ax² + bx + c = 0
By critically observing the graph (see attachment) which models the data in the given table, we can infer and logically deduce that the polynomial function is given by:
y = -0.4908x² + 5.8845x + 1.3572
For the number of students that are absent 10 days after the outbreak, we have:
y = -0.4908(10)² + 5.8845(10) + 1.3572
y = -0.4908(100) + 58.845 + 1.3572
y = -49.08 + 58.845 + 1.3572
y = 11.12 ≈ 11 students.
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A group of students is asked if they travel; to school by car, students travelling by car = 14 students not travelling by car=11 what percentage of these students do not travel to school by car?????
Answer: 44%
Step-by-step explanation:
To find the percentage of students who do not travel by car, we first need to find the total number of students.
14 + 11 = 25
So out of the total of 25 students, 11 do not travel by car, so to find that percentage we will divide the number that do not travel by car by the total number.
11/25 = 0.44
We have the percentage as a decimal. To convert the decimal to a percent we multiply it by 100.
0.44 x 100 = 44%
Simplify 3x-2y+7-2x-2x -y-5
Answer:
-x - 3y + 2
Step-by-step explanation:
sorry explain to long if you want it here a pic
7 of 107 of 10 items question ben went to the hardware store and bought 15 pieces of rope of equal length. the total length of the ropes was 326.7 meters. how long was each rope?
Answer:
The Correct answer is 21.78 meters
Step-by-step explanation:
Simply divide 326.7 ÷ 15 and it will leave you with 21.78
A prize at an arcade costs 545 tickets. You have 435 tickets, and your friend has
690 tickets. Can you buy the prize when your friend gives you 1/6 of their tickets?
Explain.
Create a function that has been:
Shifted right 3 units
Shifted up 2 units
Reflected about the x-axis
A function that has been transformed by the given transformations is y = -f(x - 3) + 2
How to create a function that has been transformed?The transformation are given as:
Shifted right 3 unitsShifted up 2 unitsReflected about the x-axisLet the equation of the parent function be
y = f(x)
So, we have the following transformations
Shifted right 3 units
The transformation rule is
(x, y) = (x - 3, y)
So, we have:
y = f(x - 3)
Shifted up 2 units
The transformation rule is
(x, y) = (x, y + 2)
So, we have:
y = f(x - 3) + 2
Reflected about the x-axis
The transformation rule is
(x, y) = (x, -y)
So, we have:
y = -f(x - 3) + 2
Hence, a function that has been transformed by the given transformations is y = -f(x - 3) + 2
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since 1900, the percentage of americans over the age of 65 has while the percentage of americans under the age of 18 has .
The percentage of Americans over the age of 65 has increased while the percentage of Americans under the age of 18 has decreased .
What happened to the population in America?The United Stats of America is one of the countries that is known to have a very good health care system. This implies that, there has ben a very huge improvement in the health care of the population of the United States.
As a result of this improvement in the healthcare of the people of the United States, the percentage of Americans over the age of 65 has increased while the percentage of Americans under the age of 18 has decreased .
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Use prime factors to find the H.C. F and
L.C.M
-168 and 196
-150 and 180
(Refer to the table given below)
So,
LCM of 168 and 196: 1176LCM of 150 and 180: 900Then,
HCF of 168 and 196: 28HCF of 150 and 180: 30Therefore,
LCM of 168 and 196: 1176LCM of 150 and 180: 900HCF of 168 and 196: 28HCF of 150 and 180: 30Know more about LCM here:
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Solve for x, given the equation square root of x plus 9 − 4 = 1. (2 points)
Answer:
x = 16
Step-by-step explanation:
(-12c⁵) (3c⁴)
Sensitive fr
Simplify: (-12c⁵) (3c⁴)=36c⁹.
Simplification of (-12c^5) (3c^4) is -36c⁹.Given that
(-12c⁵) (3c⁴)To find
Simplification form of (-12c⁵) (3c⁴) = .........?So, according to the question
We have,
(-12c⁵) (3c⁴)To convert it in simplest form we have to use mathematically operations of powers.
= (-12c⁵) (3c⁴)
Now, separate the numerical and variable parts from equation
= (-12 ×3) c⁵× c⁴
Now, from using the mathematically operations of powers, to add powers, and multiply 12 with 3.
∵ [tex]a^m\times a^n = a^{m+n}[/tex]
∴[tex]c^5\times c^4 = c^{5+4}[/tex]
= (-36) c⁵⁺⁴
= (-36) c⁹
Simplification form of (-12c⁵) (3c⁴) = (-36) c⁹.
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(-1)⁵, 3`⁶, 3⁶, 5¹, 10°, 0.1
the 3⁶ is a negative exponent
What is this least to greatest?
The least to greatest will [ ( - 1 ) ^ 5 ] < [ 3 ^ ( - 6 ) < 0.1 < ( 10 ^ 0 ) < ( 5 ^ 1 ) < ( 3 ^ 6 ) .
( - 1 ) ^ 5 , 3 ^ ( - 6 ) , 3 ^ 6 , 5 ^ 1 , 10 ^ 0 , 0.1
Simplifying each of them
( - 1 ) ^ 5 = - 1
3 ^ ( - 6 ) = 0.001
3 ^ 6 = 729
5 ^ 1 = 5
10 ^ 0 = 1
0.1 = 0.1
Least to greatest = - 1 < 0.001 < 0.1 < 1 < 5 < 729
= [ ( - 1 ) ^ 5 ] < [ 3 ^ ( - 6 ) < 0.1 < ( 10 ^ 0 ) < ( 5 ^ 1 ) < ( 3 ^ 6 )
Hence , least to greatest will [ ( - 1 ) ^ 5 ] < [ 3 ^ ( - 6 ) < 0.1 < ( 10 ^ 0 ) < ( 5 ^ 1 ) < ( 3 ^ 6 ) .
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At 6am, the temperature started
at -2°F. At 10am the temperature
increased by 8°. The last recorded
temperature of the day at 4pm
was 11°F. What was the recorded
temperature at 10am?
Answer:
6°
Step-by-step explanation:
It started at -2°f and increased b 8° so 2 of those degrees get you back to 0°f and the remains is 6 so 6°
a positive five-digit integer is in the form $ab,cba$; where $a$, $b$ and $c$ are each distinct digits. what is the greatest possible value of $ab,cba$ that is divisible by eleven?
The required positive five-digit integer of the form ab,cba; which should be divisible by 11 is 87,978
Explain the divisibility test of 11.
For a number to be divisible by 11, the difference between the sum of its odd digits (1st, 3rd, 5th...) and the sum of its even digits (2nd, 4th...) must be divisible by 11.
Calculation for the positive five-digit integer of the form ab,cba to be divisible by 11
Required 5 digit number is of the form, ab,cba
Using the divisibility test of 11, we get
(b + b) - (a + c + a) to be divisible by 11
i.e. 2b - (2a + c) to be divisible by 11
Replacing ab,cba using the greatest numbers, such as 7, 8 and 9 and checking its divisibility with 11
78,987 = 2*8 - (2*7 + 9) = 16 - (14 + 9) = 16 - 23 = -7 NO
87,978 = 2*7 - (2*8 + 9) = 14 - (16 + 9) = 14 - 25 = -11 YES
79,897 = 2*9 - (2*7 + 8) = 18 - (14 + 8) = 18 - 22 = -4 NO
97,879 = 2*7 - (2*9 + 8) = 14 - (18 + 8) = 14 - 26 = -12 NO
89,798 = 2*9 - (2*8 + 7) = 18 - (16 + 7) = 18 - 23 = -5 NO
98,789 = 2*8 - (2*9 + 7) = 16 - (18 + 7) = 16 - 25 = -9 NO
Thus, a positive 5-digit number is 87,978
Hence, the required positive five-digit integer of the form ab,cba; which should be divisible by 11 is 87,978
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50% don't smoke, 20% light smokers, 30% heavy smokers heavy smokers twice as likely to die as light smokers, light smokers twice as likely to die as nonsmokers probability of being a heavy smoker given person died?
The probability of person being a heavy smoker given person died is 0.57 .
Baye's Theorem helps in finding the probability of any event A given that event B has already occurred.
For Example the probability of event A given that event B has already occurred is denoted by
[tex]P(A/B)=\frac{P(B/A)P(A)}{P(B)}[/tex]
In the given question
Let H denoted heavy smokers , L denote Light smokers , N denote Non smokers.
Given the probability of non smokers P(N) = 50%=0.5
the probability of light smokers P(L)=20%=0.2
the probability of heavy smokers P(H)=30%=0.3
let P(D/H) denoted the person died given he was a heavy smoker.
let P(D/L) denoted the person died given he was a light smoker.
let P(D/N) denoted the person died given that he was a non smoker.
According to question
"heavy smokers twice as likely to die as light smokers" means
P(D/H)=2P(D/L)......(1)
and "light smokers twice as likely to die as nonsmokers" means
P(D/L)=2P(D/N)
On simplifying we get
[tex]P(D/N)=\frac{1}{2} P(D/L)\\ \\ P(D/N)=0.5 P(D/L)[/tex].....(2)
According to Baye's Theorem
[tex]P(H/D)=\frac{P(D/H)P(H)}{P(D/N)P(N)+P(D/L)P(L)+P(D/H)P(H)}[/tex]
Substituting values of P(D/H) from ...(1) and values of P(D/N) from ....(2)
we get [tex]P(H/D)=\frac{2*P(D/L)P(H)}{0.5*P(D/L)P(N)+P(D/L)P(L)+2*P(D/L)P(H)}[/tex]
taking P(D/L) common from each term
[tex]P(H/D)=\frac{P(D/L)}{P(D/L)} (\frac{2*P(H)}{0.5*P(N)+P(L)+2*P(H)})[/tex]
[tex]P(H/D)= (\frac{2*P(H)}{0.5*P(N)+P(L)+2*P(H)})[/tex]
Substituting the values of P(N), P(H), P(L) from above we get
[tex]P(H/D)= (\frac{2*(0.3)}{0.5*(0.5)+(0.2)+2*(0.3)})[/tex]
[tex]P(H/D)= (\frac{0.6}{0.25+0.2+0.6})[/tex]
=[tex]\frac{0.6}{1.05}=0.57[/tex]
Therefore , the probability of person being a heavy smoker given person died is 0.57 .
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If the points A, B, and C are clinear with B between A and C, and if AC = 21 and AB = 7, what is the
length of line segment BC?
BC=
Answer: BC=14
Subtract AC by AB. Just learned this in Geomatry.
Draw the line of reflection that reflects \triangle ABC△ABCtriangle, A, B, C onto \triangle A'B'C'△A
′
B
′
C
′
triangle, A, prime, B, prime, C, prime.
Thus, the equation of the line of reflection,
x=2 and x=4
When a point on a line segment divides it into two segments, the formula used to determine the coordinates of that point is known as the section formula.
It is given that,
A=(7,6)
A'=(-1,6),
B=(5,5)
and B'=(1,5),
As, the mid point of vertices of figure to the corresponding vertices of reflected figure should lie on reflected line.
Since, Δ ABC is reflected to Δ A'B'C' through this line,
Let, Q be the mid point of line AA', using section formula
Coordinate of Q = ((7-(-1))/2 , (6-6)/2 )
Q = (4,0)
and R be the mid point of line BB', using section formula
Coordinate of R = Q = ((5-1)/2 , (5-5)/2 )
Q = (2,0)
Q and R lies on the line of the reflection,
Thus, the equation of the line of reflection,
x=2 and x=4
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I have a math question, try not to get it wrong
Answer: c
Step-by-step explanation: it is a rational number because it repeats
help me please
(2a+3)(3a-4)
Answer: 6[tex]a^{2}[/tex]+a-12
Step-by-step explanation:
First, you want to distribute (2a+3)(3a-4) ---> 2a(3a-4) + 3a(3a-4)
That will get you 6[tex]a^{2}[/tex]-8a+9a-12
Next, you will want to combine like terms to get 6[tex]a^{2}[/tex]+a-12
Since you cannot simplify that any further, 6[tex]a^{2}[/tex]+a-12 is your answer.
What is the value of (3.5)3?
9.15
10.5
17.9
42.875
Answer:Your answer is 10.5
Step-by-step explanation:Multiply 3.5 by 3 and you get 10.5.
A test has twenty questions
worth 100 points. Some
questions are worth three points,
some are worth eleven points.
How many three-point questions
are there? How many eleven
point questions are there?
There are 5 11 pointer questions and 15 3 pointer questions
We are given that total points of the test is 100
The test contains questions of two markings 3 points and 11 points
It is given that the total number of questions is 20
Let the number of three pointer questions be 'x' and the number of 11 pointer questions be 'y'
Thus total number of questions=x + y =20
Now the total sum of all the points comes to 100
Therefore,
3x+11y =100
x + y =20
x= 20-y
Now putting the value of x in the other question,
3(20-y) +11y =100
60-3y +11y=100
8y=100-60
8y=40
y=5
Thus x=20-y=20-5=15
Thus there are 5 11 pointer questions and 15 3 pointer questions
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4x = 16
Step by step please
Pre algebra
Answer:
Step-by-step explanation:
Just divide four into sixteen. You should get x=4. To check, multiply 4 by 4 (4 x 4), and you should get 16.
What is the value of 2|2-9|-3(5+2)2∣2−9∣−3(5+2) ? A. -35 B. -27 C. -18 D. -8 E. -7
Answer:
Step-by-step explanation:
ygjhyjvnvbuh
kjhbhyjg';pjpo jiou; mnhbgvdfhj9y fgxjibt f drztf dd hj bvgdana walk 350 meter to school enevy day how many kio
Answer:
2.1
Step-by-step explanation:
A frame 2 inches wide surrounds a painting that is 18 inches wide and 14 inches tall. What is the area of the frame?
A 68 in²
B 84 in²
C 144 in²
D 252 in²
E 396 in²
The area of the frame is D. 252 in².
How to calculate the area?It should be noted that the frame 2 inches wide surrounds a painting that is 18 inches wide and 14 inches tall.
The area will be:
= Length × Width
= 18 × 14
= 252 in²
The area is 252 inches².
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5p+4p=7 how do I solve the equation with two variables
Answer:
7/9
Step-by-step explanation:
Combine the two variables: 9p = 7
Then do 7 / 9
Gabrielle is 7 years younger than Mikhail. The sum of their ages is 67. What is Mikhail‘a age
Answer:
Step-by-step explanation
Mikhail is 37
Gabrielle is 30
37+30= 67
NEED THIS DONE ASAP !! PLEASE
A: All real numbers greater than 0
B: All real numbers
C: All real numbers between -5 and 4
D : All real numbers greater than -2
Answer:
B: All real numbers
Step-by-step explanation:
Check the attached image for explanation.
Hope it helps.