Answer:
Below.
Step-by-step explanation:
Prove that if
a^x = b^y = (ab)^(xy) then x + y = 1.
From the second equation:
y = 1 - x
So we have:
a^x = b^y = b^(1-x)
Taking logs:
x ln a = (1-x)ln b
x ln a + x ln b = ln b
x = ln b / ( ln a + ln b)
x = ln b / ln ab.
This is true if x + y = 1.
Now consider b^y = (ab)^(xy):
b^(1 - x) = (ab)^(x(1- x)
ln b - x ln b = x(1 - x)ln ab
ln b - x ln b = x ln ab - x^2 ln ab
Now we substitute for x = ln b / ln ab in this expression.
If left side = right side then we have proved this identity and therefore the original one.
Left side = ln b - (ln b / ln ab) * ln b = ln b - (ln b)^2 / ln ab.
Right side = (ln b / ln ab) * ln ab - [(ln b)^2 / (ln ab)^2] * ln ab
= ln b - (ln b)^2 / ln ab.
Left side = right side so this identity is true, and so the original one
( x + y = 1) is true also.
How many solutions does -2 + 5p + 10 = 10 + 3p have?
Answer:
Only 1 solution
Step-by-step explanation:
-2 + 5p + 10 = 10 + 3p
Subtract 10 from both sides:
-2 + 5p + 10 -10 = 10 + 3p- 10
Simplify:
-2+5p=3p
Add 2 to both sides:
-2+5p+2=3p+2
Subtract 3p from both sides:
5p-3p=3p+2-3p
simplify:
2p=2
Divide both sides by 2:
2p/2=2/2
Simplify:
p=1
Zaid spent AED 61.50 for 15 LITERS of premium PETROL. What was the price per LITER?
Answer:
4.1
Step-by-step explanation:
61.50/15 = 4.1
per liter= AED 4.1
In degrees what is the measure of MFE
HELP PLS I AM TIMED
Answer:
ADD THEM AND THEN SUBSTRACT THE RWO NUMBER AND DIVIDE YOUR X!!
Step-by-step explanation:
A sandwich shop sells 4 veggie subs for every 5 turkey subs. The shop sold 27 subs today. How many of each kind
did they sell?
Answer:
4+5=9
27÷9=3
they sold 3 types of each because if you do 3×5=15 and 3×4=12 and add 12 and 15 you get 27.
50 points
tan⁻¹(√3) − cot⁻¹(−√3) is equal to ???
Can anyone solve this?
Answer:
I think it -pie/2 but I could be wrong
if anyone know the answers to this question i really need help.
Answer:
b.) 6
Step-by-step explanation:
2^6 = 64 because 2 * 2 * 2 * 2 * 2 * 2 = 64.
Can you help me with this if you’re a smart person
If 15×5 equals what what times five equals what
Answer:
15 x 5 = 75 x 5 = 375
Step-by-step explanation:
Not sure what you were saying but its just some spelling errors but i think i did what you said. You multiply the product of it to 5.
Find the vertex and focus of the
parabola.
y2 – 12y + 4x + 4 = 0
Answer:
t y = 6 and x = 8, or the vertex is at (8,6).
Step-by-step explanation:
Answer:
Step-by-step explanation:
Vertex: (8,6) Focus (7,6)
Step-by-step explanation:
32/4=8
Half of 12=6
For the function: f(x) = 12 + 10x − 5x2
Find f(-6)
Answer:
-228
Step-by-step explanation:
I Used the given functions to set up and simplify f(-6)
Hope this helps:)
17 apples for $3.91 what is the unit rate per apple
9514 1404 393
Answer:
$0.23 per apple
Step-by-step explanation:
The cost per apple is found by dividing the cost by the number of apples. (You can think of "per" as meaning "divided by".)
cost/apple = $3.91/(17 apples) = $0.23 /apple
Write the rule for the nth term of the sequence 2, 6, 18, 54, ... Then find a8.
Answer:
Multiply by 3
a8 = 4,374
Step-by-step explanation:
Consider the following question.
"Do you watch television every day?"
Which of the following statements BEST explains why the question is NOT a statistical question?
A The question does not anticipate variability in the answers
B The question results in a single absolute answer.
C The question may be answered differently by different people.
D. The question does not require an explanation
Answer:
a
Step-by-step explanation:
Answer:
C, the only info for the question is about yourself which is a survery question
Step-by-step explanation:
If diana spends 25 minutes running at the gym how many minutes does she spend lifting weight
Answer:
0
Step-by-step explanation:
The question doesn’t say that she lifted weights
If Diana spends 25 minutes running at the gym, then she spend lifting weight for 13 minutes.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given that,
At the gym, Diana always spends more minutes running than lifting weights.
If r represents the number of minutes Diana runs and w represents the number of minutes Diana lifts weights, then, r must be greater than w.
Possible equations are,
12 + w = r
r - 12 = w
In both cases, r is greater than w.
If Diana spends 25 minutes running at the gym, r = 25.
w = r - 12 = 25 - 12 = 13
Hence the number of minutes that Diana spends lifting weights is 13 minutes.
Learn more about Equations here :
https://brainly.com/question/29657983
#SPJ3
Your question is incomplete. The complete question is as given below.
Im a game with 10 floating ducks,there are 2 ducks with a green dot on the bottom,3with a blue dot and 5 with a red dot.What is the probability of selecting a green duck
Answer:
2/10 or 1/5
Step-by-step explanation:
There are a total of 10 ducks, and only 2 have green dots.
So the probability would be 2 / 10, which simplifies to 1 / 5.
Greatest common factor of 2 and 10: 2
So: 2 ÷ 2 = 1
10 ÷ 2 = 5
Determine whether each sequence appears to be an arithmetic
sequence. If so, find the common difference and the next three terms
in the sequence.
1) 3,9,26,81 ...
2) 5,6.5,8,9.5...
Help plz right answer only help me
IT'S A TIME SENSITIVE EMERGENCY!!!
2. Mai, Clare, and Tyler are hiking from a parking lot to the summit of a mountain. They pass a sign that gives distances. Parking lot: mile Summit: 1 miles Mai says: "We are one third of the way there." Clare says: "We have to go twice as far as we have already gone." Tyler says: "The total hike is three times as long as what we have already gone." Can they all be correct? Explain how you know.
Complete question is missing, so i have attached it.
Answer:
Yes, they are all correct
Step-by-step explanation:
From the attached image, we see that the sign is showing;
Parking lot: ¾ miles
Summit: 1½ miles
Summit distance can also be expressed as an improper fraction = 3/2 miles
Now, since they started hiking from the park to the summit, it means that they had moved ¾ mile from the parking lot and had 3/2 miles left to get to the summit.
Thus, total distance from parking lot to summit = ¾ + 3/2 = 9/4 miles
Now, let's analyze each of their statements;
Mai said they are a third of their way there.
They had covered 3/4 mile and the total distance is 9/4 miles.
Thus, fraction of total distance covered is;
9/4 ÷ 3/4 = 1/3.
So, Mai is correct
Clare said they have to go twice as far as they had already gone.
They had covered 3/4 miles.
Therefore, twice this = 2 × 3/4 = 6/4 = 3/2 which is same as the sign distance left to the summit.
Thus, Clare is correct
Tyler said that the total hike is three times as long as what we have already gone.
They had gone 3/4 miles
3 times this = 3 × 3/4 = 9/4 miles.
This tallies with the total distance calculated earlier.
Thus, they are all correct
A local school is holding a fundraising event. Everyone that attends receives a raffle ticket. At the end of the night the raffle is held.
Assume 1,000 people attend the event, and hence there are 1,000 tickets in the raffle.
There will be
• 85 tickets that each win $10
• 60 tickets that each win $20
• 20 tickets that each win $50
• 10 tickets that each win $100
• and the rest of the tickets win nothing
What is the variance of the winnings from this raffle?
Do not round until you have your answer. Round your answer to 2 decimal places.
Find the coordinates of the midpoint between the two
points on the graph.
Answer:
(0,2)
Step-by-step explanation:
Cords are ( 0, 4 ) and ( 4, -4)
x1 + x2 / 2 , y1 +y2/2
0 + 4 / 2 , 4 - 4 / 2
4/2,0/2
(2,0)
PLEASE HELP ASAP! thank you!
4x + y=7
2x - 7y=1
If (x,y) is the solution to the given system of equations, what is the Value of X?
Answer:
[tex]x = \frac{5}{3} [/tex]
Factorise the following.
Answer:
iii. (l + m - n)(l - m + n)
vi. (5a -b) ( 5b - a)
Step-by-step explanation:
iii. l² - (m - n)²
= (l + m - n)(l - m + n)
vi. 4(a+b)² - 9(a-b)²
= (2(a+b))² - (3(a-b))²
= (2(a+b) + 3(a-b)) (2(a+b) - 3(a-b))
= (2a+2b + 3a - 3b) (2a+2b - 3a + 3b)
= (5a -b) ( 5b - a)
Q. 1) l²- (m - n)²
=(l - m + n)(l + m - n)
Q.2) 4(a+b)²- 9(a-b)²
= [(2(a+b))²- (3(a-b))²]
=[2(a+b)+3(a-b)][ 2(a+b)-3(a-b)]
=[2a+2b+3a-3b][2a+2b-3a+3b]
=[5a-b][5b-a] ]
need help on edge 6th grade math
Answer: a, 7ft
Step-by-step explanation:
Answer:
Answer A
Step-by-step explanation:
Help please!!!!!!!!!!
Answer:
6/8,
12/16,
24/32
48/64
96/128
192/256
384/512
Step-by-step explanation:
-.25z=-1.25 What is Z?
Answer:
z=5
Step-by-step explanation:
A.The Murray family has produced 8 children.
What is the probability that there are an equal number of boys and girls?
B.Margie has the uncanny ability of being able to guess the correct answer to TRUE/FALSE questions with an 80% accuracy rate. Tomorrow’s test has 7 questions on it and she needs to answer 5 questions correctly in order to make the Honor Roll. If she guesses on every question, what is the probability that she’ll answer exactly 5 questions correctly?
Answer:
A. 0.2734 = 27.34% probability that there are an equal number of boys and girls
B. 0.2753 = 27.53% probability that she’ll answer exactly 5 questions correctly
Step-by-step explanation:
In each of these questions, the binomial probability distribution is used.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A.The Murray family has produced 8 children.
What is the probability that there are an equal number of boys and girls?
8 children means that [tex]n = 8[/tex]
Each children is equally as likely to be a boy or a girl, which means that [tex]p = 0.5[/tex]
This probability is P(X = 4). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{8,4}.(0.5)^{4}.(0.5)^{4} = 0.2734[/tex]
0.2734 = 27.34% probability that there are an equal number of boys and girls
B.Margie has the uncanny ability of being able to guess the correct answer to TRUE/FALSE questions with an 80% accuracy rate. Tomorrow’s test has 7 questions on it and she needs to answer 5 questions correctly in order to make the Honor Roll. If she guesses on every question, what is the probability that she’ll answer exactly 5 questions correctly?
80% accurracy rate means that [tex]p = 0.8[/tex]
7 questions means that [tex]n = 7[/tex]
The probability is P(X = 5). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{7,5}.(0.8)^{5}.(0.2)^{2} = 0.2753[/tex]
0.2753 = 27.53% probability that she’ll answer exactly 5 questions correctly
Which of the following is the MOST reasonable equation for the line of best fit?
Answer:
either c or b that's what I think
The amount C in grams of carbon-14 present in a certain substance after t years is given by
C = 52e-0.0001097
a. What is the initial amount of carbon-14 present?
Answer:
987e-628479.9079083
Step-by-step explanation:
Answer:
maybe 7
Step-by-step explanation:
2028.863 rounded to the nearest hundredth
Answer:
2028.863 to the nearest hundredth
The Number In The Hundredth Place Is 6 And The The Number Following Is 3 And Because Its Less Than 5, The 6 Will Remain.
So Its 2028.86
Answer:
2,028.86
Step-by-step explanation:
this is the correct answer to your question