PLEASE HELP 40 POINTS
Express each logarithm in terms of ln 3 and ln 5.
ln 81 / 125
Answers
The solution is 4ln3 - 3ln5, which is correct option(C).
What are the properties of logarithms?There are four basic properties of logarithms:
logₐ(xy) = logₐx + logₐy.
logₐ(x/y) = logₐx - logₐy.
logₐ(xⁿ) = n logₐx.
logₐx = logₓa / logₓb.
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
The operator that perform arithmatic operation are called arithmatic operators .
Operators which let do basic mathematical calculation
+ Addition operation : Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation : Subtracts right hand operand from left hand operand.
for example 4 -2 = 2
* Multiplication operation : Multiplies values on either side of the operator
For example 4*2 = 8
/ Division operation : Divides left hand operand by right hand operand
For example 4/2 = 2
According to the problem, we will use some of the basic logarithmic properties,
Given expression,
⇒ ln81/125
⇒ ln81 - ln125 [used property : logₐ(x/y) = logₐx - logₐy]
⇒ ln3⁴ - ln5³ [ 81 =3⁴ and 125 = 5³ ]
⇒ 4ln3 - 3ln5 [used property : logₐ(xⁿ) = nlogₐx]
Hence, the solution is 4ln3 - 3ln5
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Related Questions
If K = (AB)/(A+B) , then B = ?
(a) (A)/(1−A)
(b) (AK)/(A−K)
(c) (AK)/(K−A)
(d) (A+K)/(A)
(e) (A−K)/(AK)
Answers
Lets do
[tex]\\ \sf\longmapsto K=\dfrac{AB}{A+B}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{K}=\dfrac{A+B}{AB}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{K}=\dfrac{1}{A}+\dfrac{1}{B}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{B}=\dfrac{1}{K}-\dfrac{1}{A}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{B}=\dfrac{K-A}{AK}[/tex]
[tex]\\ \sf\longmapsto B=\dfrac{AK}{K-A}[/tex]
If there are 43,560 square feet in an acre, and there are 7.5 gallons in a cubic foot, calculate gallons of irrigation water per square foot?
Answers
The following information related to irrigation is as follows:
It is the water application that should be artificial via different sprays, pumps systems.It could be found from the groundwater via springs, surface water, etcThe gallons of irrigation water per square foot is [tex]326,700\ gallons\ per\ square\ foot[/tex]
For determining the gallons of irrigation water we have to multiply the square foot by the number of gallons in a cubic foot.
Given that,
There are 43,560 square feet in an acre i.e. 1 acre = 43,560.
And, there are 7.5 gallons in a cubic foot i.e. 1 cubic foot = 7.5 gallons.
So, the gallons of irrigation water per square foot is
[tex]= 43,560 \times 7.5\ gallons \\\\= 326,700\ gallons\ per\ square\ foot[/tex]
Therefore we can conclude that the gallons per square foot of irrigation water is [tex]326,700\ gallons\ per\ square\ foot[/tex]
Learn more about per square foot here: brainly.com/question/5991264
Answer:
326,700 gallons
Step-by-step explanation:
1 acre = 43,560 square feet
1 acre-foot of irrigation is an acre irrigated 1 foot deep with water.
Since thee are approximately 7.5 gallons in 1 cubic foot,
1 acre-foot of irrigation = 43,560 * 7.5 gallons
1 acre-foot = 326,700 gallons
This is the number of gallons in one acre-foot, not gallons per square foot.
(20/2 + 4)/2
^^^ I NEED A EQUATION LIKE THAT BUT FOR IT TO EQUAL 16
Answers
Answer:
Here are a few examples.
(30/2 + 1)/2
(26/2 + 3)/2
(28/2 + 2)/2
How do I solve for y:
x²y² = 12/z²
Answers
Answer:
Y=Srt(12xs^2/z^2)
Step-by-step explanation:
Firstly
We multiply both sides with 1/x^2
We get
Y^2=12/z^2*1/x^2
Y^2=12x^2/z^2
Next: introduce a srt root
We have
Y=srt(12x^2/z^2)
Is u=−12 a solution of 8u−1=6u?
Answers
Answer:
No, -12 is not a solution.
Step-by-step explanation:
8u-1=6u
8(-12)-1=6(-12)
-96-1=-72
-97=-72
Untrue, to it’s not a solution
Which of the following factorizations is correct?
O x3 + 27 = (x - 3)(x2 + 3x – 9)
O x - 27 = (x - 3)(x2 + 3x +9)
O x3 - 27 = (x - 3)(x2 +9)
O x3 + 27 = (x - 3)(x2 - 9)
Answers
Answer:
first one is correct bro
The correct factorization of x³ - 27 is (x - 3)(x² + 3x + 9).
What are the formulas for a³ + b³ and a³ - b³?a³ + b³ = (a + b)(a² -ab + b²) and a³ - b³ = (a - b)(a² + ab + b²).
If we know the formula of these two we can conclude by observing that
the second option x³ - 27 = (x - 3)(x² + 3x +9) is correct.
As x³ - 27
= x³ - 3³.
= (x - 3)(x² + 3x + 9).
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A.60
B.40
C.24
D.20
Please help me on this
Answers
Answer:
The answer is 20
Step-by-step explanation:
3 times 2 is 6, and 120 divided by six is 20%.
10a+5(a-3)=15 I don’t know the answer I keep checking and it’s wrong
Answers
Answer:
[tex]10a + 5(a - 3) = 15 \\ 10a + 5a - 15 = 15 \\ 15a = 30 \\ a = \frac{30}{15} \\ a = 2 \\ 10 \times 2 + 5(2 - 3) = 15 \\ 20 + - 5 = 15 \\ 15 = 15 \\ lhs = rhs\\ thank \: you[/tex]
Answer: a = 2
Solve:
Given
10a + 5 (a - 3) = 15
Expand parentheses and apply the distributive property
10a + 5 · a - 5 · 3 = 15
10a + 5a - 15 = 15
Combine like terms
(10a + 5a) - 15 = 15
15a - 15 = 15
Add 15 on both sides
15a - 15 + 15 = 15 + 15
15a = 30
Divide 15 on both sides
15a / 15 = 30 / 15
[tex]\boxed{a=2}[/tex]
Check:
Left-hand side = 10a + 5 (a - 3)
Left-hand side = 10(2) + 5 (2 - 3)
Left-hand side = 20 + 5(-1)
Left-hand side = 20 - 5
Left-hand side = 15
Right-hand side = 15
15 = 15, therefore, [tex]\boxed{a=2}[/tex] would make the equation true.
Hope this helps!! :)
Please let me know if you have any questions
Solve the system of equations.
6x−y=−14
2x−3y=6
whats the answer please C:
Answers
Answer:
Step-by-step explanation:
If the prism has 3 layers, what would the volume of the
prism be in cubic centimeters?
OA) 4 cubic centimeters
OB) 8 cubic centimeters
OC) 12 cubic centimeters
OD) 16 cubic centimeters
Answers
Answer:
OD) 16 cubic centimeters
8 millions =
how many hundred thousands
Answers
Answer:
100000
Step-by-step explanation:
100000x80=8m
Paul bought a student discount card for the bus. The card allows him to buy daily bus passes for $1.70.
After one month, Paul bought 16 passes and spent a total of $35.20.
How much did he spend on the student discount card?
Answers
He spent $22.5 on the student discount card.
This question is solved using proportions.
The cost of each card is of $1.50.
Paul bought 15 passes, that is, 15 cards.
Considering that he bought 15 cards, each for $1.50, his spending was of:
He spent $22.5 on the student discount card.
5404 buttons are produced by a factory in Jebel Ali in a week. If the factory produced same number of buttons every day of the week, buttons produced in a day is _________________
Answers
We need to find the number of buttons the company produced per day
The company produced 772 buttons per day
Total bottons produced in a week = 5404
There are 7 days in a week
If the factory produced same number of buttons every day of the week
Then,
Buttons produced per day = Total bottons produced in a week / Total number of days in a week
= 5404 / 7
= 772 buttons
The company produced 772 buttons per day
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area of a triangle 5cm base and 4 cm height
Answers
Answer:
1/2 base×height
1/2 .5×4
1/2.20
20 divided by 2 is 10
1/1×10
10cm2
ans
please solve asap thanks
Answers
Answer:
6x+36=180
6x=144
x=24
Step-by-step explanation:
this is the correct answer
Find the shortest distance from A
to C
in the diagram below.
Answers
9514 1404 393
Answer:
5√13 m
Step-by-step explanation:
The length of the space diagonal is the "Pythagorean sum" of the lengths of the edges of the cuboid.
AC = √(8² +6² +15²) = √325 = √(13·25)
AC = 5√13 . . . meters
__
AB is the hypotenuse of the right triangle with legs 6 and 8, so is 10 units. AC is the hypotenuse of right triangle ABC, so is ...
AC = √(AB² +BC²) = √(10² +15²)
Fewer and fewer customers have been coming into the restaurant, so Bill, the manager, decides to change the entire menu. After he does this, he finds out that people loved the food, but the service has been driving people away. This represents what kind of problem in the decision-making process? O a) Failure to develop enough options O b) Failure to correctly define the problem c) Failure to act on a decision O d) Failure to evaluate the decision
Answers
Answer:
failure to correctly define the problem
Step-by-step explanation:
He changes the menu without identify that the real problem was the service.
120 students, 41 for maths, 48 for chemistry, 42 for physics. 16 study both chemistry and maths, 14 study maths and physics, 18 study chemistry and physics, 9 study the three subjects, 1) how many of them study exactly one subject. 2) At least one subject. 3) None of the Subject
Answers
Answers:
number who study exactly one subject = 62number who study at least one subject = 92number who study none of the subjects = 28The venn diagram is shown below.
========================================================
Explanation:
M = set of people studying math
C = set of people studying chemistry
P = set of people studying physics
Something like the notation n(C) refers to the count of items in set C, aka the number of people who study chemistry. Similar ideas apply to n(M) and n(P) to refer to the counts of math and physics respectively.
Something like n(C and M) is the number of people who study chemistry and math. Same idea applies to something like n(C and P) or n(M and P)
With all that in mind, we have these 7 facts
n(M) = 41 n(C) = 48 n(P) = 42 n(C and M) = 16 n(M and P) = 14 n(C and P) = 18 n(C and M and P) = 9We'll start with fact 7. This value goes in the very center of the 3 overlapping circles of the venn diagram. Refer to the diagram below.
Since 9 people study all three subjects, and 16 study chemistry and math, this must mean 16-9 = 7 people study chemistry and math without physics involved. We'll write 7 in the region between circles C and M, but outside of circle P.
Since 9 people study all three subjects, and 14 study math and physics, we know that 14-9 = 5 people study only math and physics without chemistry. We'll write 5 in the region between circles M and P, but outside circle C.
Since 9 people study all three subjects, and 18 study chemistry and physics, we know that 18-9 = 9 people study only chemistry and physics without math. We'll write 9 in the region between circles C and P but outside circle M.
If you're lost, then refer the diagram below. So far, we have filled in the very center "9" and the closest three values surrounding it (the 7, 9 and 5).
-------------------------
Focus your attention on circle M for now. The values in this circle add to: 7+9+5 = 21
Since n(M) = 41, this must mean the missing value must be 20. This goes in circle M but outside the other two circles.
Note how 7+9+5+20 = 41 when we add everything in circle M. This circle is completely filled out. We'll follow a similar path for the other circles.
Move onto circle C. Adding everything in it so far gets us 9+9+7 = 25. We want to get to n(C) = 48 which means we need to have 48-25 = 23 in circle C but outside the other circles. Circle C is now done.
Lastly, focus on circle P. The values we found so far in this circle add to 9+9+5 = 23. The missing value must be 19 because 42-23 = 19, and n(P) = 42.
-------------------------
At this point, all three circles are filled out. The only thing missing is the number outside the circles, but inside the rectangle.
Add up everything in the circles: 23+7+20+9+9+5+19 = 92
This tells us that we have 92 people who studied at least one subject (i.e. one or more subjects). There are 120 people surveyed, meaning that 120-92 = 28 people study neither of these subjects. We write 28 outside the circles.
-------------------------
The venn diagram is done by this point. To address the questions, we'll just read from the diagram (and at most do an addition problem).
To find the number of people who study exactly one subject, we will add up the numbers that are in one circle but not in any other circle. Those values are: 23, 20, and 19. So 23+20+19 = 62 people study exactly one subject.
We already found the number of people who study at least one subject, and that was 92 people. This was when we added every number in the circles.
For the last question, we already found this value as well. This answer is 28 people which is found outside all three circles.
The venn diagram is shown below to visually summarize and organize all of the data. Hopefully it clears up any confusion you may have about the previous steps.
Total number of students who exactly one subject is 62
No of students who study at least one subject is 92
No of students who do not study any subject is 28
let us do this problem by set theory.
in the attached figure
three circles have been drawn representing the number of students studying maths, physics and chemistry.
from the diagram
1) Number of students who study exactly one subject=no of students who study maths + number of students who study chemistry+number of students who study physics- 2*[number of students who study both physics and chemistry-number of students who study both physics and maths-number of students who study both maths and chemistry ]+3*number of students who study all three subjects
from the attached figure,
2) Total number of students who exactly one subject = 20+19+23 = 62
3) No of students who study at least one subject will be the sum of each data in the attached figure i.e union of all three sets.
no of students who study at least one subject = 20+7+5+9+19+9+23=92
no of students who do not study any subject = total students- the union of all three sets.
no of students who do not study any subject = 120-92 = 28
therefore,
total number of students who exactly one subject is 62
no of students who study at least one subject is 92
no of students who do not study any subject is 28
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the factor of 12 are ...............
Answers
Answer:
1, 2, 3, 4, 6, and 12
Step-by-step explanation:
Answer:
1,2,3,4,6,12
Step-by-step explanation:
because they divide the numbers without any remainder.
Find the area of the figure
A =
Answers
207 m
Step-by-step explanation:
17 x 6 = 102
15 + 6 = 21
5 x 21 = 105
105 + 102 = 207 m^2
Answer:
207m
Step-by-step explanation:
(17+5)*6=132
(15*5)=75
132+75=207
For a particular event, 669 tickets were sold for a total of $4293. If students paid $5 per ticket and nonstudents paid $8 per ticket, how many student tickets were sold?
Answers
Answer:
353 tickets.
Step-by-step explanation:
Let's say that there are s student tickets and n nonstudent tickets.
s + n = 669
5s + 8n = 4293
Multiply -5 by the entire first equation to get...
-5s - 5n = -3345
Combine the two equations.
5s - 5s + 8n - 5n = 4293 - 3345
3n = 948
n = 316
Now, put the number of nonstudent tickets sold back into the first equation.
s + 316 = 669
s = 353 tickets.
Hope this helps!
Picking a card and spinning a spinner are independent events.
True
False
Answers
Answer:
True
Step-by-step explanation:
Both happened in different times and are seprate events
Quadrilateral ABCD has vertices A(–1, –2), B(–1, 3), C(4, 3) and D(4, –2). It’s dilated by a factor of 2 with the center of dilation at the origin. What are the coordinates of the resulting quadrilateral A’B’C’D
Answers
9514 1404 393
Answer:
A'(-2, -4)B'(-2, 6)C'(8, 6)D'(8, -4)Step-by-step explanation:
Dilation about the origin multiplies each coordinate value by the dilation factor.
A' = 2A = 2(-1, -2) = (-2, -4)
B' = 2B = 2(-1, 3) = (-2, 6)
C' = 2C = 2(4, 3) = (8, 6)
D' = 2D = 2(4, -2) = (8, -4)
what is the tan invers of 3i/-1-i
Answers
z = 3i / (-1 - i )
z = 3i / (-1 - i ) × (-1 + i ) / (-1 + i )
z = (3i × (-1 + i )) / ((-1)² - i ²)
z = (-3i + 3i ²) / ((-1)² - i ²)
z = (-3 - 3i ) / (1 - (-1))
z = (-3 - 3i ) / 2
Note that this number lies in the third quadrant of the complex plane, where both Re(z) and Im(z) are negative. But arctan only returns angles between -π/2 and π/2. So we have
arg(z) = arctan((-3/2)/(-3/2)) - π
arg(z) = arctan(1) - π
arg(z) = π/4 - π
arg(z) = -3π/4
where I'm taking arg(z) to have a range of -π < arg(z) ≤ π.
look at the image below
Answers
Answer:
272 yd²
Step-by-step explanation:
Surface area = base area + lateral area
= (10×10)+(8.6×10×2)
= 100+172
= 272 yd²
While organizing the magazines at the doctor's office, Camille put 12 magazines in the first pile, 15 magazines in the second pile, 18 magazines in the third pile, 21 magazines in the fourth pile, and 24 magazines in the fifth pile. If this pattern continues, how many magazines will Camille put in the sixth pile?
Answers
Answer:
27
Step-by-step explanation:
since you are adding 3 to the pile each time, on the 6th pile you would have 27 because 24 + 3 = 27
The sum of two numbers is 41. The larger number is 17 more than the smaller number. What are the numbers?
Larger number:
Smaller number:
Answers
Let x - 17 = the smaller number
x + x + 17 = 41
2x + 17 = 41
2x = 58
x = 29
x - 17 = 29 - 17 = 12
What is 10,000,000 + 700,000,000 + 2,000,000 + 9,000 + 4 + 400,000 + 10,000 + 70 + 700 in standard form?
Answers
please mark this answer as brainlist
solve the equation
0.09w+1.8
Answers
Step-by-step explanation:
0.09w + 1.8 = 0
0.09w = 0 - 1.8
0.09w = - 1.8
0.09w ÷ 0.09 = - 1.8/ 0.09
w = - 20
Subtract the integers. 22−(−10)
Answers
Answer:
32
Step-by-step explanation:
Step 1: change 22 - ( - 10) into 22 + 10
Step 2: solve it like normal
