suppose that ln(x) = f and ln(y) = m. write each expression in terms of f and m. (a) ln(eln(x)) (b) eln(ln(xy)) (c) ln ex y − ln y ex (d) (ln(x))3 − ln(x4) ln x e2 ln(xe2)
Answers
(a) ln(eln(x)) = x
(b) eln(ln(xy)) = xy
(c) ln(exy) - ln(yex) = xy - yx
(d) \((ln(x))^3 - ln(x^4) ln(x) e^2 ln(xe^2) = ln(x)(ln(x)^2 - 4) - x^2\)
(a) ln(eln(x)): Using the property of logarithms that ln(e^a) = a, we can rewrite ln(eln(x)) as x. Therefore, the expression ln(eln(x)) can be written as x in terms of f and m.
(b) eln(ln(xy)): Using the property of exponentials that e^ln(a) = a, we can rewrite eln(ln(xy)) as xy. Therefore, the expression eln(ln(xy)) can be written as xy in terms of f and m.
(c) ln(exy) - ln(yex): Using the property of logarithms that ln(a) - ln(b) = ln(a/b), we can rewrite ln(exy) - ln(yex) as ln((exy)/(yex)). Simplifying further, we can cancel out the exponential terms, as exy / yex = (e^x)^y / (e^y)^x = e^(xy - yx). Therefore, the expression ln(exy) - ln(yex) can be written as ln(e^(xy - yx)) or simply xy - yx in terms of f and m.
(d) (ln(x))^3 - ln(x^4) ln(x) e^2 ln(xe^2): Expanding the expression, we have (ln(x))^3 - ln(x^4) = ln(x)^3 - 4ln(x). Rearranging, we can factor out ln(x) to obtain ln(x)(ln(x)^2 - 4). Additionally, e^2ln(xe^2) simplifies to x^2. Therefore, the expression (ln(x))^3 - ln(x^4) ln(x) e^2 ln(xe^2) can be written as ln(x)(ln(x)^2 - 4) - x^2 in terms of f and m.
In summary, we can rewrite the expressions in terms of f and m as follows:
(a) ln(eln(x)) = x
(b) eln(ln(xy)) = xy
(c) ln(exy) - ln(yex) = xy - yx
(d) (ln(x))^3 - ln(x^4) ln(x) e^2 ln(xe^2) = ln(x)(ln(x)^2 - 4) - x^2
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Related Questions
which of the following applies to sampling plan? a. objectives of the sampling activity b. population frame c. statistical tools that will be used to analyze the data d. method of sampling
Answers
Objectives of the sampling activity apply to the sampling plan.
So, the correct option is A.
A certain number of observations are chosen at random from a larger population as part of the sampling process in statistical analysis. Depending on what kind of study is being done, the sampling technique may be systematic or just random. An Examination of Population Characteristics is the basic goal of sample research is to quickly, cheaply, and accurately identify all of the features of the population. Sampling allows for the collection of additional data on the entire population.
In order to obtain the same results from the sample as they would from the population, random population, random sampling helps researchers save money. Due to decreased costs involved with recruiting data collectors, non-random sampling is much less expensive than random sampling.
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Find the surface area of D
Answers
Answer:
151 cm² (i don't know what unit you were given so im going to use cm)
Step-by-step explanation:
Part One: finding the missing side (h)
h = a² = b² + c²
13² = 12² + c²
169 = 144 + c²
169 - 145 = c²
= 25
square root of 25 = c
5 = c
area of top triangular area = ½ b × h
= ½ × 12 × 5
= 30 cm²
Part Two
area of rectangle = l × b
= 12 × 8
= 96 cm²
Part Three
area of square = l × l
= 5 × 5
= 25 cm²
total surface area = (30 + 96 + 25) cm²
= 151 cm²
In a right triangle, if the length of the hypotenuse is 10 and the length of one of the other sides is 6, what is the length of the third side? (Simplify Answer)
Answers
Answer:
8
Step-by-step explanation:
10^2=100 6^2=36 100-36=64 sqrt64=8
How many times will the following loop execute?
int x = 0;
do {
x++;
cout << x << endl;
}while(x < 5)
Answers:
a. - 5 times
b. - 4 times
c. - It doesn't
d. - Infinite times
e. - 6 times
Answers
Answer:
Step-by-step explanation:
The loop will run an infinite number of times
how many seconds are in 5 hours abs 30 minutes
Answers
Answer:
19800 seconds
Step-by-step explanation:
6 (8j - 3l + 9 ) 12l + 14j
Answers
Answer:
5822j-15972
Step-by-step explanation:
Answer:
5822j-15972
Step-by-step explanation:
i have no idea how to do this ha
Answers
Answer:
30
Step-by-step explanation:
If they are parallel then the 2 labelled angles sum to 180.
2x+50+5x-80=180
7x-30=180
7x=210
x=30
Answer:
X=30
Step-by-step explanation:
2x+50+5x-80=180
7x-30=180
7x=210
×=30
Write the prime factorization of 21. Use exponents when appropriate and order the factors from least to greatest (for example, 2235).
Answers
The prime factorization of the number 21 is:
21 = 3*7
How to write the prime factorization?We want to write the prime factorization of 21.
To do so, we just need to divide the number by prime numbers.
The first prime number we can try is 2, if we divide by 2 we get:
21/2 = 10.5
This is not an integer, so 2 is not a factor.
The next one is 3:
21/3 = 7
Now we can rewrite:
21 = 3*7
Where 3 and 7 are prime numbers, so that is the prime factorization.
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.18 g = ___ kg ANSWER IF YOU KNOW PLEASE :(
Answers
Answer:
.18 grams equals .00018 kilograms
Answer:
.00018 kg
Step-by-step explanation:
To get from grams to kilograms, you divide by 1000, so you have to divide .18 by 1000. 0.18/1000 = .00018, so the answer is .00018 kg
Each base in this right figure is a semicircle with a radius of
7
cm
7 cm7, start text, space, c, m, end text. A cylinder-like figure where the bases are semicircles instead of circles. The radius of the semicircle is 7 centimeters. The height of the figure is twenty centimeters. A cylinder-like figure where the bases are semicircles instead of circles. The radius of the semicircle is 7 centimeters. The height of the figure is twenty centimeters. What is the volume of the figure?
Give an exact answer in terms of pi
Answers
The volume of the figure is 1538.6 cm³.
We have,
The area of a semicircle.
= 1/2 x πr²
Now,
Radius = r = 7 cm
So,
The area of a semicircle.
= 1/2 x πr²
= 1/2 x 3.14 x 7²
= 1/2 x 3.14 x 49
= 76.93 cm²
Now,
Height = 20 cm
The volume of the figure.
= Area of the semicircle x height
= 76.93 x 20
= 1538.6 cm³
Thus,
The volume of the figure is 1538.6 cm³.
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A line has a slope of –7 and a y-intercept of –1/5 Write its equation in slope-intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
Answer:
y= -7x-1/5
Step-by-step explanation:
The slope intercept form is expressed as y=mx+b
M is the slope while b is the Y-intercept.
The given line has a slope of -7 which fulfills the m spot in the formula.
-1/5 is the Y-Intercept which also fulfills the B spot in the formula
y= -7x-1/5
hey question,
2/9×3/5=??
Thank you!
Answers
Answer:
2/15
or
0.13
Step by step:
2/9×3/5
multiply the numerators together
2×3= 6
then
multiply the denominators together
9×5= 45
so now you have 6/45
we cab simply this to 2/15 by dividing top and bottom by 3
therefore your answer is 2/15
or in decimal form: 0.13
Hope this helped you- have a good day bro cya)
~
given a drug administered 50 mg every three hours and the drug decays 12% per hour, then what is the limiting value? give two decimals past the decimal point.
Answers
A drug administered 50 mg every three hours and the drug decays 12% per hour, the limiting value is approximately 416.67 mg.
To find the limiting value, we need to determine the amount of the drug remaining after each administration and observe how it approaches a stable value over time.
First, let's calculate the decay factor per hour. The drug decays by 12% per hour, which means it retains 88% of its previous value after each hour.
Decay factor = 1 - 0.12 = 0.88
Now, let's calculate the amount of drug remaining after each administration:
After 1st administration: 50 mg
After 2nd administration: 50 mg * 0.88 = 44 mg
After 3rd administration: 44 mg * 0.88 = 38.72 mg
After 4th administration: 38.72 mg * 0.88 = 34.04 mg
After 5th administration: 34.04 mg * 0.88 = 29.92 mg
As we can see, the amount of drug remaining decreases with each administration, approaching a limiting value. To find this limiting value, we can continue the pattern or use a formula.
The formula for the limiting value of a drug administered every three hours is:
Limiting value = dosage / (1 - decay factor)
In this case, the dosage is 50 mg, and the decay factor is 0.88.
Limiting value = 50 mg / (1 - 0.88) = 50 mg / 0.12 ≈ 416.67 mg (rounded to two decimal places)
Therefore, the limiting value is approximately 416.67 mg.
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Question- A circle has a circumference of 10π inches and a center of (9, 2). What is the standard form equation of this circle?
Answers:
A. (x-9)^2 + (y-2)^2 = 10
B. (x-9)^2 + (y-2)^2 = 25
C. (x-9)^2 + (y-2)^2 = 3.14
D. (x-9)^2 + (y-2)^2 = 100
Answers
Answer:
\(\sf{Choice \;B.\;\; (x-9)^2 + (y-2)^2 = 25\)
Step-by-step explanation:
The standard form equation of a circle with center (a, b) and radius r is
\((x-a)^2 + (y-b)^2 = r^2\)
where (a, b) is the center of the circle.
Here we are given that the circle has center (9, 2)
So the equation becomes
\((x-9)^2 + (y-2)^2 = r^2\cdots(1)\)
All we have to do is find the radius and we are done
Circumference of a circle with radius r
\(= 2 \pi r\\\)
Given circumference \(= 10\pi\)
\(10\pi = 2\pi r\\\implies r = 10/2 = 5\)
Substitute this into equation (1):
\((x-9)^2 + (y-2)^2 = 5^2\\\\(x-9)^2 + (y-2)^2 = 25\\\)
This corresponds to option B.
The equation of a circle is (x - 9) + (y - 2) = 25.
Option B is the correct answer.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2πr.
We have,
The equation of a circle is (x - h) + (y - k) = r² _____(A)
Where (h, k) is the center and r is the radius.
Now,
Centre = (9, 2)
This means,
(h, k) = (9, 2) _____(1)
Circumference = 10π
This means,
2πr = 10π
2r = 10
r = 5 in ____(2)
Now,
Substituting (1) and (2) in (A).
(x - h) + (y - k) = r²
(x - 9) + (y - 2) = 5²
(x - 9) + (y - 2) = 25
Thus,
The equation of a circle is (x - 9) + (y - 2) = 25.
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Which polynomial function has a root of 1 with
multiplicity 2 and a root of 6 with multiplicity 1?
Of(x) = (x - 1)(x – 6)
O f(x) = 2(x - 1)(x – 6)
O f(x) = (x - 1)(x - 1)(x – 6)
O f(x) = (x - 1)(x - 6)(x-6)
Answers
Answer:
The 3rd:
f(x) = (x - 1)(x - 1)(x – 6)
Step-by-step explanation:
Its roots are the x-values for which f(x)=0, that are:
x1=1
x2=1
x3=6
What is the solution to the following equation? 4(3x − 11) + 23 = 5x − 14 a 0 b 1 c 10 d 14
Answers
Answer:
b 1
Step-by-step explanation:
Listen Rachel babysat three children for five hours if they were paid $2.50 per hour for each child and divided their earnings equally how much did each girl receive
Answers
Answer: Each girl will receive $18.75.
Step-by-step explanation:
Given: Two girls babysat three children for five hours.
Hourly pay for each child = $2.50
Payment for 5 hours per child = \(5\times\$2.50=\$12.5\)
Payment to 3 children for 5 hours = \(3\times \$12.5=\$37.5\)
So, the amount received by each girl = \(\dfrac{\text{Payment to 3 children for 5 hours}}{2}\)
\(=\dfrac{37.5}{2}=\$18.75\)
Hence, each girl will receive $18.75.
A rancher wants to fence in an area of 1500000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?.
Answers
The shortest length of fence that the rancher can use is 6000 ft.
What is meant by length?
The measuring of one thing from finish to finish or on its longest aspect, or a measuring of a selected a part of one thing is known as length.
Main Body:
x = width of rectangle
y = length of rectangle
A = area of rectangle = xy = 1500000 ft^2
L = length of fencing needed = 2(x + y) + x = 3x + 2y
L = 3x + 2(1500000/x) = 3x + 3(10^6)x^(-1)
As x –> 0+, L –> +inf.
As x –> +inf, L –> (3x)+.
Sketch and see that there will be a minimum in Quadrant I.
dL/dx = 3 - 3(10^6)x^(-2)
Extrema occur when dL/dx = 0:
3 - 3(10^6)x^(-2) = 0
(10^6)x^(-2) = 1
x^2 = 10^6
x > 0, so x = 1000 feet for shortest length.
Hence,Shortest L = 3000 + 3(10^6)(10^3)^(-1) = 6000 feet.
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A stack of Magic cards consists of 4 land cards and 6 creature cards. You draw 4 cards from the shuffled stack of 10 cards. Find the probability that you pull 4 creature cards. (give answer as a fraction or a decimal to 3 decimal places)
Find the probability that you pull 3 land cards and 1 creature card.
(give answer as a fraction or a decimal to 3 decimal places)
Answers
Answer:
1/14 ; 1/35
Step-by-step explanation:
A
6/10 x 5/9 x 4/8 x 3/7
3/5 x 5/9 x 1/2 x 3/7
1 x 1/3 x 3/14
1/14
B
4/10 x 3/9 x 2/8 x 6/7
2/5 x 1/3 x 1/4 x 6/7
2/15 x 3/14
1/5 x 1/7
1/35
The probability that 4 creature cards is pulled is 1/14 and the probability that 3 land cards and 1 creature card is pulled is 4/35
What is probability?Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.
Given here there are 4 land cards and 6 creature cards
thus selecting four cards at random from 10 cards is ¹⁰C₄=210
and the event of selecting 4 creature cards from a total of 6 cards is ⁶C₄ =15
Therefore probability of pulling 4 creature cards is = 15/210
= 1/14
The probability of pulling 3 land cards and 1 creature cards is
= ⁴C₃ × ⁶C₁ / ¹⁰C₄
= 4/35
Hence 1/14 and 4/35 are the respective probabilities.
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write these ratios using fraction notation and reduce 10 inches to 1 foot
Answers
We know that 1 inch = 0.083 feet
Therefore,
\(\frac{10\text{ inches}}{1\text{ foot}}=\frac{10\text{ inch}\times\frac{0.083\text{ f}eet}{1\text{ inch}}}{1\text{ foot}}=0.83\)Thus the ratio is 0.83
Find general solution of the equation
y" – 2y' + y = 4 sin(t) + e^t/1 + t^2
Answers
The general solution of the given second-order linear homogeneous ordinary differential equation (ODE) y" - 2y' + y = 0 can be found by solving its characteristic equation and applying the appropriate method for solving linear ODEs. However, the equation provided includes a non-homogeneous term, making it a non-homogeneous ODE. To solve this type of equation, we use the method of undetermined coefficients or variation of parameters.
To find the general solution, we first consider the homogeneous part of the equation, which is y" - 2y' + y = 0. The characteristic equation is r^2 - 2r + 1 = 0, which can be factored as \((r - 1)^2\) = 0. This yields a repeated root of r = 1, giving us the complementary solution\(y_c(t) = c1e^t + c2te^t,\)where c1 and c2 are arbitrary constants. Next, we consider the non-homogeneous part of the equation, which consists of the terms 4sin(t) and \(e^t/(1 + t^2).\) We assume a particular solution in the form of yp(t) = A sin(t) + B cos(t) + C e^t, where A, B, and C are constants to be determined. Plugging this particular solution into the original equation and solving for the coefficients, we find A = -4/5, B = 0, and C = 4/5. Therefore, the particular solution is yp(t) = (-4/5)sin(t) + (4/5)e^t. The general solution of the non-homogeneous equation is y(t) = y_c(t) + yp(t), which can be written as y(t) =\(c1e^t + c2te^t - (4/5)sin(t) + (4/5)e^t.\) In summary, the general solution of the given non-homogeneous ODE y" - 2y' + y = \(4sin(t) + e^t/(1 + t^2) is y(t) = c1e^t + c2te^t - (4/5)sin(t) + (4/5)e^t,\)where c1 and c2 are arbitrary constants.
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canbon-14 is used to determite the age of artificats in carbon sating. it has a half-life of 5730 years. write the exponential decay function for a 24-mg sample. find the amount of carbon-14 remaining after 20 millennia
Answers
The amount of carbon-14 remaining after 20 millennia is 0.912 mg.
The exponential decay function for a 24-mg sample of carbon-14 can be represented by the equation:
y = 24e^(-kt)
where:
y is the amount of carbon-14 remaining
e is the base of the natural logarithm
k is the decay constant, calculated by dividing the natural logarithm of 2 by the half-life of carbon-14 (5730 years)
t is the time elapsed
So, k = ln(2)/5730
To find the amount of carbon-14 remaining after 20 millennia (20,000 years), we can plug in the values:
t = 20,000 years
y = 24e^(-k * 20,000)
Substituting the value of k:
y = 24e^(-ln(2)/5730 * 20,000)
y = 24 * e^(-0.000011 * 20,000)
y = 24 * 0.038
y = 0.912 mg
So, the amount of carbon-14 remaining after 20 millennia is 0.912 mg.
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suppose we want to estimate family size, where family is defined as one or more parents living with children. if we select students at random at an elementary school and ask them what their family size is, will our average be biased? if so, will it overestimate or underestimate the true value?
Answers
Yes, the average family size obtained from asking students at an elementary school would likely be biased. The average is likely to underestimate the true value of the family size for the population.
This is because a student’s family size only includes individuals who are living in the same household as the student and not everyone in the family.
For example, the student's siblings who have left the household to attend college or have moved out for other reasons would not be included in the student's family size estimate. Additionally, grandparents, uncles, aunts, and cousins who may also be part of the family are not included. Thus, the average family size obtained from asking students would be lower than the true average family size for the population.
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3. The talent show committee sold a total of 522 tickets. Student tickets cost $3 each and adult tickets
cost $4 each. They made a total of $1873 off of ticket sales. How many student tickets were sold?
How many adult tickets were sold?
Answers
Answer:
Step-by-step explanation:
If student ticket = 215 then 215 x 3 = 645$
Remaining tickets = 522 - 215 = 307
So adult tickets = 307 x 4 = 1228$
Total amount = 1228 + 645 = $1873
A line has a slope of -3 and passes through the point
passes through the point (-2, -3/2)
By substituting into the equation y = mx + b, find the value of b for this line
Answers
Answer:
If I am not mistaking it should be -7.5
Step-by-step explanation:
Answer:
b = -15/2
y = -3x -15/2
Step-by-step explanation:
The value of the y-intercept can be found from a point and the slope of the line by solving the slope-intercept equation for the intercept.
__
intercepty = mx + b . . . . . . . equation of a line with slope m and y-intercept b
y -mx = b . . . . . . . . subtract mx from both sides
For the point (x, y) = (-2, -3/2) and slope m = -3, the value of b is ...
b = -3/2 -(-3)(-2) = -3/2 -6
b = -15/2 . . . . . the value of b for this line
__
equation of the lineThen the equation for the line is ...
y = mx +b
y = -3x -15/2
you you have 80¢ in your backpack and dimes and quarters let's represent the number of times in white representing number of quarters
Answers
1.
T = Total money in your backpack = $0.80
x = Number of dimes
y = Number of quarters = 2
T = $0.1x + $0.25y
Replacing the data provided:
0.8 = 0.1x + 0.25(2)
0.8 = 0.1x + 0.5
Solving for x:
Subtract 0.5 from both sides:
0.8 - 0.5 = 0.1x + 0.5 - 0.5
0.3 = 0.1x
Divide both sides by 0.1:
0.3/0.1 = 0.1x/0.1
3 = x
So, you have 3 dimes
-calculati
5+2
7
7
-
3
8
8
13
8
52
5+1
3
7
3
1
ام اس
2
5
32
5
اران
3
7
2
3 5
1
4
41
Answers
Answer:
Step-by-step explanation:
Use this calculator to add or subtract time (days, hours, minutes, seconds) from a starting time and date. The result will be the new time and date based on the ...
Missing: ام اس اران 41
The table below shows the heights of students in a group. Student Height (in inches) A 54 B 48 C 52 D 56 E 55 What is the mean height of the students in the group? (1 point) Group of answer choices 48 inches 49 inches 52 inches 53 inches
Answers
53 inches is the mean height of the students in the group.
Given data: \(54,48,52,56,55\)
We know that mean of the heights = \(\frac{Sum of all the heights}{No. of students}\)
\(= \frac{54+48+52+56+55}{5}\)
\(= \frac{265}{5}\)
\(= 53\) inches
Thus, the mean height of the students is 53 inches
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Which one is the vertical axis?
Answers
Answer:
Step-by-step explanation:
Vertical by definition means up and down. The y-axis fits this description. Look at a picture of a Cartesian coordinate system
Answer:
the y-axis
Step-by-step explanation:
vertical is up and down
horizontal is side to side or left and right
y is up and down
The weekly amount of money spent on maintenance and repairs by a company was observed, over a long period of time, to be approximately normally distributed with mean $400 and standard deviation $20. How much should be budgeted for weekly repairs and maintenance to provide that the probability the budgeted amount will be exceeded in a given week is only 0.1?
Answers
Answer:
$425.6 should be budgeted for weekly repairs and maintenance.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean $400 and standard deviation $20.
This means that \(\mu = 400, \sigma = 20\)
How much should be budgeted for weekly repairs and maintenance to provide that the probability the budgeted amount will be exceeded in a given week is only 0.1?
This is the 100 - 10 = 90th percentile, which is X when Z has a p-value of 0.9, so X when Z = 1.28.
\(Z = \frac{X - \mu}{\sigma}\)
\(1.28 = \frac{X - 400}{20}\)
\(X - 400 = 20*1.28\)
\(X = 425.6\)
$425.6 should be budgeted for weekly repairs and maintenance.