Given:
The equation is:
[tex]\ln e^{\ln x}+\ln e^{\ln x^2}=2\ln 8[/tex]
To find:
The solution for the given equation.
Solution:
We have,
[tex]\ln e^{\ln x}+\ln e^{\ln x^2}=2\ln 8[/tex]
It can be written as:
[tex]\ln x+\ln x^2=2\ln 8[/tex] [tex][\because \ln e^x=x][/tex]
[tex]\ln (x\cdot x^2)=2\ln 8[/tex] [tex][\because \ln a+\ln b=\ln (ab)][/tex]
[tex]\ln (x^3)=\ln 8^2[/tex] [tex][\because \ln x^n=n\ln x ][/tex]
On comparing both sides, we get
[tex]x^3=8^2[/tex]
[tex]x^3=64[/tex]
Taking cube root, we get
[tex]x=\sqrt[3]{64}[/tex]
[tex]x=4[/tex]
Therefore, the required solution is [tex]x=4[/tex].
Answer:
x=4
Step-by-step explanation:
What is the true solution to the equation below?
ln e Superscript ln x Baseline + ln e Superscript ln x squared Baseline = 2 ln 8
x = 2
x = 4
x = 8
84 percent of students athletes attend a preseason meeting. If there are 175 students athletes how many attend the meeting
Answer:
Total no. of students =175
percent of students athletes who attend a preseason meeting =84
No. of students who attend the meeting
= 84% of 175
=147
Ngân hàng rơi vào tình trạng vỡ nợ khi nào
Answer:
.
Step-by-step explanation:
.
How can Paige share 11 identical apples among 30 of her friends evenly so that no apple is sliced into more than 10 pieces?
Answer: Paige can slice _ apples into _ pieces each and _ apples into _ pieces each.
Answer:
7 apples into 2 pieces and 4 apples into 4 pieces
Step-by-step explanation:
if you split 7 apples into 2 pieces each than you'l have 14 slices. You need 30 though which means you need 16 more. so you split 4 into 4 pieces. and the number of apples we used is 7 and 4 which make up 11. So this answer works
Please help how to do this
Answer:
Frumpyton
Step-by-step explanation:
Since the standard deviation of Frumpyton is a lower number, this means a higher percentage of outcomes (job salaries) will be within a closer range to the mean salary. Since Frumpyton's standard deviation is $2,000 and the window your looking for is $32,000 to $36,000, if you go one interval up or down from the mean of $34,000, it falls in that range. Whereas, Dirtballville's standard deviation is $3,000 so it's more likely to fall outside of that range.
Determine which diagram could be used to prove triangle ABC is congruent to triangle EDC using similarity transformations
Answer:
A
Step-by-step explanation:
edge 2021
Select all of the following statments that are true
Answer:
A. -¾ + 0 = -¾
B. -¾ - ¾ = -(¾ + ¾)
C. ¾ - ¾ = ¾ + (-¾)
E. -¾ + ¾ = ¾ + (-¾)
F. -¾ + ¾ = 0
Step-by-step explanation:
Let's check each equation to determine whether they are true or false.
If what we have in the both sides are equal, then the equation is true, if they're not, them it is false.
✔️-¾ + 0 = -¾
Add everything on your left together
-¾ = -¾ (TRUE)
✔️-¾ - ¾ = -(¾ + ¾)
Add everything on both sides together respectively
(-3 - 3)/4 = -(3 + 3)/4
-6/4 = -6/4 (TRUE)
✔️¾ - ¾ = ¾ + (-¾)
0 = ¾ - ¾ (+ × - = -)
0 = 0 (TRUE)
✔️-¾ + ¾ = ¾ - (-¾)
0 = ¾ + ¾ (- × - = +)
0 = 6/4 (FALSE)
✔️-¾ + ¾ = ¾ + (-¾)
0 = ¾ - ¾ (+ × - = -)
0 = 0 (TRUE)
✔️-¾ + ¾ = 0
0 = 0 (TRUE)
Each of the 8 cats in a pet store was weighed. Here are their weights (in pounds): 6,6, 10, 6, 8, 7, 14, 12 Find the median and mean weights of these cats. If necessary, round your answers to the nearest tenth. Median: pounds Х X ? Mean: pounds
Answer:
Median: 7.5
Mean: 8.6
Step-by-step explanation:
Median = the average of the 2 middle numbers of the set in ascending order, 6, 6, 6, 7, 8, 10, 12, 14
(7+8)/2 = 2
Mean = the sum of the numbers divided by the number of values
6 + 6+ 6+ 7 +8 +10 +12 +14/8
69/8
8.625
Imagine that you need to compute e^0.4 but you have no calculator or other aid to enable you to compute it exactly, only paper and pencil. You decide to use a third-degree Taylor polynomial expanded around x = 0. Use the fact that e^0.4 < e < 3 and the Error Bound for Taylor Polynomials to find an upper bound for the error in your approximation.
I error l ≤
Answer:
upper bound for the error, | Error | ≤ 0.0032
Step-by-step explanation:
Given the data in the question;
[tex]e^{0.4[/tex] < e < 3
Using Taylor's Error bound formula
| Error | ≤ ( m / ( N + 1 )! ) [tex]| x-a |^{N+1[/tex]
where m = [tex]| f^{N+1 }(x) |[/tex]
so we have
| Error | ≤ ( 3 / ( 3 + 1 )! ) [tex]|[/tex] -0.4 [tex]|[/tex]⁴
| Error | ≤ ( 3 / 4! ) [tex]|[/tex] -0.4 [tex]|[/tex]⁴
| Error | ≤ ( 3 / 24 ) [tex]|[/tex] -0.4 [tex]|[/tex]⁴
| Error | ≤ ( 0.125 ) [tex]|[/tex] -0.0256 [tex]|[/tex]
| Error | ≤ ( 0.125 ) 0.0256
| Error | ≤ 0.0032
Therefore, upper bound for the error, | Error | ≤ 0.0032
A total of $20,000 is invested at an annual interest rate of 6%. No matter how many years this
money is invested, what is the best investment plan to earn the most money in the end?
Compounded continuously
Compounded daily
Compounded quarterly
Compounded monthly
Which line is parallel to the line that passes through the points (1,7) and (-3, 4)? A. y=--x-5 B. y=+*+1 y=-x-8 O c. D. 11 v==x+3 4
Answer:
B
Step-by-step explanation:
because
Cole biked at 5 mph for 1 1/2 hours. Which of the following choices show how far he biked?
Answer:
Should be 5 1/2 if thats on there
Step-by-step explanation:
u take 11/2 and take out the 1 u get 10/2 so u cut 10 in half get 5 then add the one and make it 5 1/2
There are 4 white and 5 red (indistinguishable) balls in a bag. Suppose you draw one ballout at a time without replacement and stop when you have drawn all the white (4 white) orall the red (5 red) balls. What is the probability that the last ball you drawn was a whiteball?
Answer:
5/9
Step-by-step explanation:
What we have in this question are four white balls and 5 red balls.
This is the sample space
[(4w,0R) (4w,1R)(4w,2R)(4w,3R)(4w,4R)(0w,5R)(1w,5R)(2w,5R)
So we have 9 possible sets of events
The event number with the last ball being white = 5
Probability of the last ball drawn being white = 5/9
= 0.56
the shorter side of a rectangle is 60% of the longer side and the perimeter of the rectangle is 96 inches. find the side lengths
Answer:length 30, width 18
Step-by-step explanation:
60% +100%=160%
160% × 2 = 320 %
96/320 = 0.3 ×100 =30 ( length)
30 × 0.6 =18 (width)
Check: (18 + 30) 2 = 96
Please help me quick
Answer:
I belive it has no x intercepts
it looks weird, but it can be a function. the x-intercept and the y-intercept can also be found in the table above.
to draw a line that can represent a function with these point, we would need to cross y=0 multiple times, so it will have more then one x-intercept.
option A
key takeaway: just draw stuff you find complicated:)
48. What is the volume of the cuboid below? 3cm 2cm 2cm
Answer:
Cuboid = width*height*length
Cuboid = 24 cm^2
5. What is the value of x if the quadrilateral is a kite? B X+2 C С 13 A Xth12 D
Answer: just had this problem! X = 11
find the equation of the line
Answer:
y = x + 6
Step-by-step explanation:
rise = 1
run = 1
slope = rise/run = 1
y-intercept = 6
y = mx + b
y = x + 6
Write the equation of the line with the given conditions. passing through (-1, -7) and perpendicular to the line with equation 4x + 5y = 31
Answer:
y = 5/4 x - 23/4
Step-by-step explanation:
4x + 5y = 31
5y = - 4x +31
y = -4/5 x + 31/5
⊥ slope = 5/4
-7 = 5/4 (-1) + B
-28 = -5 + 4b
-23 = 4B
b = -23/4
SCALCET8 3.11.501.XP. Find the numerical value of each expression. (Round your answers to five decimal places.) (a) sinh(ln(4)) (b) sinh(4)
sinh(ln(4)) = (exp(ln(4)) - exp(-ln(4)))/2 = (4 - 1/4)/2 = 15/8 = 1.875
sinh(4) = (exp(4) - exp(-4))/2 ≈ 27.28992
HELP HELP QUICK QUICK
Answer:
multiplication by -1 will reflect over the x-axis
multiplication by a positive number will "scale" or "stretch" the function
Step-by-step explanation:
Which of the following lists of ordered pairs is a function? A. (1,8), (2, 9), (3, 10), (3, 11) B. (-1,4), (1,7), (2, 10) C. (3,7),(4, 5), (3, 8) D. (-2,3), (1, 3), (3, 7), (1, 4)
Answer:
B
Step-by-step explanation:
B is the only one that doesnt share x-values
The manager of a fast-food restaurant determines that the average time that her customers wait for service is 2.5 minutes. (a) Find the probability that a customer has to wait more than 4 minutes. (Round your answer to three decimal places.)
Answer:
0.758
explaination
using poisson distribution
0.08208+0.2052+0.2565+0.2138
0 .758
The mean per capita consumption of milk per year is 131 liters with a variance of 841. If a sample of 132 people is randomly selected, what is the probability that the sample mean would be less than 133.5 liters
Answer:
0.8389 = 83.89% probability that the sample mean would be less than 133.5 liters.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The mean per capita consumption of milk per year is 131 liters with a variance of 841.
This means that [tex]\mu = 131, \sigma = \sqrt{841} = 29[/tex]
Sample of 132 people
This means that [tex]n = 132, s = \frac{29}{\sqrt{132}}[/tex]
What is the probability that the sample mean would be less than 133.5 liters?
This is the p-value of Z when X = 133.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{133.5 - 131}{\frac{29}{\sqrt{132}}}[/tex]
[tex]Z = 0.99[/tex]
[tex]Z = 0.99[/tex] has a p-value of 0.8389
0.8389 = 83.89% probability that the sample mean would be less than 133.5 liters.
A bank gives you a loan of 1,500,000 Baht to buy a house. The interest rate of the loan is 0.01% per day (Using 1 year = 365 days)
How much interest you pay after 10 years
Answer:
15.000 is cost so relate it with 265..hope it is help u.
the percentage of people under the age of 18 was 23.5% in New York City, 25.8% in Chicago, and 26% in Los Angeles.
If one person is selected from each city, what is the probability that all of them are under 18?
Answer:
0.0158 = 1.58% probability that all of them are under 18.
Step-by-step explanation:
Probability of independent events:
If three events, A, B and C are independent, the probability of all happening is the multiplication of the probabilities of each happening, that is:
[tex]P(A \cap B \cap C) = P(A)P(B)P(C)[/tex]
The percentage of people under the age of 18 was 23.5% in New York City, 25.8% in Chicago, and 26% in Los Angeles.
This means that [tex]P(A) = 0.235, P(B) = 0.258, P(C) = 0.26[/tex]
If one person is selected from each city, what is the probability that all of them are under 18?
Since the three people are independent:
[tex]P(A \cap B \cap C) = 0.235*0.258*0.26 = 0.0158[/tex]
0.0158 = 1.58% probability that all of them are under 18.
Few drivers realize that steel is used to keep the road surface flat despite the weight of buses and trucks. Steel bars, deeply embedded in the concrete, are sinews to take the stresses so that the stresses cannot crack the slab or make it wavy. The passage best supports the statement that a concrete road
Answer: Is reinforced with other material
Step-by-step explanation:
The options are:
A is expensive to build.
B usually cracks under heavy weights.
C looks like any other road.
D is reinforced with other material.
The passage best supports the statement that a concrete road are reinforced with other material. According to the information given in the passage, steel plays a vital role in keeping the road surface flat.
Steel bars are embedded in concrete so that the stresses cannot crack the slab. Therefore, it indicates that concrete road is reinforced with other material.
(a) Find the average rate of change of the area of a circle with respect to its radius r as r changes from 2 to each of the following.
(i) 2 to 3
(ii) 2 to 2.5
(iii) 2 to 2.1
(b) Find the instantaneous rate of change when r =2.
Answer:
ai) 5pi
aii) 4.5pi
aiii) 4.1pi
b) 4pi
Step-by-step explanation:
a) Area of a circle is given by pi×r^2.
The average rate of change of the area of a circle from r=b to r=a is (pi×b^2-pi×a^2)/(b-a).
Let's simplify this.
Factor pi from the terms in the numerator:
pi(b^2-a^2)/(b-a)
Factor the difference of squares in the numerator:
pi(b-a)(b+a)/(b-a)
"Cancel" common factor (b-a):
pi(b+a).
So let's write a conclusive statement about what we just came up with:
The average rate of change of the area of a circle from r=b to r=a is pi(b+a).
i) from 2 to 3 the average rate of change is pi(2+3)=5pi.
ii) from 2 to 2.5 the average rate of change is pi(2+2.5)=4.5pi.
from 2 to 2.1 the average rate of change is pi(2+2.1)=4.1pi.
b) It looks like a good guess at the instantaneous rate of change is 4pi following what the average rate of change of the area approached in parts i) through iii) as we got closer to making the other number 2.
Let's confirm by differentiating and then plugging in 2 for r.
A=pi×r^2
A'=pi×2r
At r=2, we have A'=pi×2(2)=4pi. It has been confirmed.
SOMEONE HELP PLEASE! So for this problem the answer I got is $4000. Is that the correct or incorrect answer? Can someone please help me if it is the incorrect answer. Thank you for your time.
Answer:
You're correct
Step-by-step explanation:
Please help ASAP. No links
Hello my dear friend of USA !!!
DB/AD = BE/EC
=> 6/4 = x+1/x
=> 6x = 4x + 4
=> 2x = 4
=> x = 2
So x = 2
I am from INDIA.
Lots of love ❤️!!!
Have a great day ahead!
Answer:
x = 2
Step-by-step explanation:
[tex]\frac{6}{4} = \frac{x+1}{x}[/tex]
6x = 4x + 4
2x = 4
x = 2
Rajah 1 menunjukkan lukisan pelan berskala bagi sebuah rumah
lantainya berbentuk dua segi empat sama.
Skala yang digunakan adalah 1:200. Jika
kos memasang jubin jalah Rm 30 per m3
berapakah jumlah kos memasang jubin bagi
rumah tersebut?
Answer:
RM 1200 kalau ada gambar cuba insert
