1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
jasenka [17]
2 years ago
8

2•log(x – 3) = log 25

Mathematics
1 answer:
AfilCa [17]2 years ago
8 0

Answer:

Step-by-step explanation:

2log(x-3)=log25

log(x-3)²=log25 cancel out log on both sides

(x-3)²=25

x²-6x+9=25

x²-6x+9-25=0

x²-6x-16=0 factorize

x²+2x-8x-16=0

x(x+2)-8(x+2)

(x-8)(x+2)=0

x-8=0 or x+2=0

x=8 or x=-2

x=-2 cannot be considered because of the -ve sign.

x=8.

check

2log(x-3)

2log(8-3)

2log5

log5²=25

therefore LHS=RHS

You might be interested in
A poker deck consists of cards ranked 2,3,4,5,6,7,8,9,10,J,Q,K,A, (13 different ranks) each in four suits, for a total of 52 dis
snow_lady [41]

Answer:

1) The probability to be given a Poker hand from a Pinochle deck is 0.7943

2) The probability that a hand that could be either a Poker hand or a Pinochle hand was given from a Pinochle deck is 0,3675

Step-by-step explanation:

Letc denote some events:

X = The hand i receive is from a Pinochle deck.

Y = The hand i receive is from a Poker deck

Z = The hand i receive is a Poker hand (from any deck)

Note that Y is the complementary event of X, therefore P(Y) = 1-P(X). Also, if Y is true so is Z, thus

P(Z | Y) = 1

we want to know P(Z | X) in order to resolve item 1)

The first card i receive from the five card hand can be anything, the second one can be anything different from the first card, and there is one copy of that card remaining in the deck, thus, 46 cards from the deck works, from a total of 47. After the second card was given, if it was different from the first card, we will have 2 cards that are copies of the 2 cards i receive, thus, there are, from the 46 remaining cases, only 44 are favourable. For the fourth card we will have 3 cards we dont want to draw, therefore we have 42 cases favourable over 45, and for the last card from a total of 44 cards, only 40 can help us.

With all this information, we have that the probability that a hand dealt from a Pinochle deck is a Poker hand is

P(Z | X) = 46/47* 44/46 * 42/45 * 40/44 = 112/141 = 0.7943

2) Since rach deck has a 1/2 probability of being selected, then

P(X) = P(Y) = 1/2.

In order to compute the probability that i draw a hand that could be either kind from a Pinochle deck, i will calculate first the probability that i draw a 'Pinochle hand' from a poker deck, in other words, if we call W the event that i drew a Pinochle hand, then we want P(W | Y)

Since a Poker deck has 52 cards and only 24 works for us, then P(W | Y) = 24/52 = 6/13 = 0.4615.

Note that P(W | X) = 1

Now, lets calculate what the problem wants, and that is P(X | W∩Z) (The probability to have drawn from a Pinochle deck a hand that could be either Poker or Pinochle. For that we use the Bayes Theorem

P(X | W \cap Z) = \frac{P(W \cap Z |X) * P(X)}{P(W \cap Z |X) * P(X) + P(W \cap Z |Y) * P(Y)} = \frac{P(Z | X) * 1/2}{P(Z |X)*1/2+P(W|Y)*1/2} = \frac{6/26}{6/26+56/141} = \frac{423}{1151} = 0.3675

[ Note that if X is given, then W always holds, thats why p(W∩Z|X) = P(Z|X). In a similar way P(W∩Z|Y) = P(W|Y), because given Y, Z always happens (a hand given from a Poker deck is always a poker hand). ]

We conclude that the probability that a hand that can be from any deck is in fact given from a Pinochle deck is 0.3675.

3 0
3 years ago
Solve for x 2/5 x = 6/5 <br><br> answer choices<br><br> 12/15<br><br> 12/5<br><br> 3<br><br> 6
SIZIF [17.4K]
The answer is 3. 
<span><span>65</span>÷<span>25</span></span><span>=
<span>(6 × 5) (5 × 2)</span></span><span>=<span>30
10</span></span><span>=<span>30 ÷ 10
10 ÷ 10</span></span><span>=<span>3</span></span>
5 0
3 years ago
HELP ASAP!!! There are 18 girls and 12 boys in an 8th grade class. Two students are chosen to go on the field trip. What is the
noname [10]

Answer:

12/30

Step-by-step explanation:

3 0
3 years ago
Solve the equation for a.
katrin [286]

Answer:

a= \frac{k}{9b+4}

Step-by-step explanation:

In this question, you would solve for "a".

Solve:

K = 4a + 9ab

Since we have our "a" on the same side, we can factor it out from the variables:

K = a(9b + 4)

To get "a" by itself, we would have to divide both sides by 9b + 4:

K/9b+ 4 = a

Your answer would be K/9b+ 4 = a

It would look like this: a= \frac{k}{9b+4}

8 0
2 years ago
Read 2 more answers
Use the tables to complete the statements,
Blababa [14]

Answer:

Short term Capital gain and $1200

Step-by-step explanation:

Any investment held under a year falls under short term capital gain

5,000 X 0.24 = 1,200

6 0
2 years ago
Other questions:
  • Perimeter and area of a rectangle 11 cm by 19.3cm
    10·1 answer
  • Write a linear Write a linear function f with f(−9)=10 and f(−1)=−2.function f with f(−9)=10 and f(−1)=−2.
    9·1 answer
  • A single trip on a toll road costs $1.20. Frequent users can get a monthly pass that costs $25. How many times must a person use
    9·2 answers
  • What is the relationship between turning points of a graph and its derivative function​
    15·1 answer
  • How many 5 person squads can a basketball coach send out on an 11 person team
    5·2 answers
  • What is the constant rate of change shown in the table?
    9·1 answer
  • ASAP kinda need help atm if anyone can solve this?
    12·1 answer
  • Simplify (6 + 4i) + (3 - 3i)
    11·1 answer
  • Which relation is a function?
    10·1 answer
  • Find the sequence 5n+1
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!