We can use the logarithmic identity log_a(b) + log_a(c) = log_a(bc) to simplify the left side of the equation:
log_2(x) + log_4(x+1) = log_2(x) + log_2((x+1)^(1/2))
Using the rule log_a(b^c) = c*log_a(b), we can simplify further:
log_2(x) + log_2((x+1)^(1/2)) = log_2(x(x+1)^(1/2))
Now we can rewrite the equation as:
log_2(x(x+1)^(1/2)) = 3
Using the rule log_a(b^c) = c*log_a(b), we can rewrite this as:
x(x+1)^(1/2) = 2^3
Squaring both sides, we get:
x^2 + x - 8 = 0
This is a quadratic equation that can be solved using the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 1, b = 1, and c = -8. Plugging in these values, we get:
x = (-1 ± sqrt(1^2 - 4(1)(-8))) / 2(1)
x = (-1 ± sqrt(33)) / 2
x ≈ -2.54 or x ≈ 3.54
However, we must check our solutions to make sure they are valid. Plugging in x = -2.54 to the original equation results in an invalid logarithm, so this solution is extraneous. Plugging in x = 3.54 yields:
log_2(3.54) + log_4(4.54) = 3
0.847 + 0.847 = 3
So x = 3.54 is the valid solution to the equation.
Need help alegbra!!! Look at photo for question!!
Answer
74+2
Step-by-step explanation:
Find the measure of the inscribed angle(real answers only please)
Answer:
46
Step-by-step explanation:
Sum of all the Arcs of a circle = 360.
So, the angle of the 3 arcs is
153 + 115 + x =360
=>268+x=360
=> x = 92
*** x = Arc FG
We know that the inscribed angle is 1/2 times the amount that of the intercepted arc.
=> Inscribed Angle = 1/2 * Intercepted Arc
=> ? = 1/2* Arc FG
=> ? = 1/2 * 92
=> Angle E = 46
most adult medication doses are for a person weighing 150 pounds. for a 45 pound child, the adult dose should be multiplied by 0.3. if the child's dose of a decongestant is 18 milligrams, what is the adult dose?
Can someone help with this question
what is 21 5/8% as a decimal
Answer: 21.625
Step-by-step explanation:
The percentage of 21 (5/8)% in decimal form is 173/800.
We have,
The percentage means the required value out of 100.
It is calculated by dividing the required value by the total value and multiplying by 100.
The given percentage expression.
21(5/8) %
Divide by 100 to remove the %.
This can be written as,
21(5/8) / 100
Now,
21(5/8)
= (21 x 8 + 5) / 8
Simply the fraction.
= 173/8
Now,
173/8 / 100
Simplify the fraction.
= 173/800
Thus,
The percentage of 21 (5/8)% in decimal form is 173/800.
Learn more about percentages here:
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Consider the following scenarios, where we apply probability to a game of flipping coins. In the game, we flip one coin each round. The game will not stop until two consecutive heads appear. (a) What is the probability that the game ends by flipping exactly five coins? (b) Given that the game ends after flipping the fifth coin, what is the probability that three heads appear in the sequence?
Answer:
3.125%
0%
Step-by-step explanation:
A regular coin has two sides, meaning that each side has the same probability of landing which is 50%. Therefore, for the game to end exactly on the fifth flip it would need to land 3 times in a row on tails and the last 2 times on heads. Therefore, to get this probability we need to multiply 0.50 (50%) 5 times
0.5 * 0.5 * 0.5 * 0.5 * 0.5 = 0.03125 or 3.125%
Now the probability of three heads appearing in a sequence is 0% because after the second head in a row the game will automatically end.
Part(a): The probability that the game ends by flipping exactly five coins is [tex]0.5[/tex]
Part(b): The probability that three heads appear in the sequence is [tex]0.5[/tex].
Probability:Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e. How likely they are to happen, using it.
Part(a):
The Probability of games ends by flipping exactly five coins is,
[tex]P((TTTHH),(HTTHH),(THTHH),(HHTHH))=(1-p)^3p^2+2(1-p)^2p^3+(1-p)p^4[/tex]
Where [tex]p=P(H)[/tex]
When the coin is fair so the probability is,
[tex]P(H)=\frac{1}{2}[/tex]
P(game ends by flipping exactly five coins)=[tex]\frac{2^2}{2^5} =0.125[/tex]
Part(b):
The Probability of games ends by flipping exactly three heads is,
[tex]\frac{2(1-p)^2p^3}{(1-p)^3p^2+2(1-p)^2p^3+(1-p)p^4}[/tex]
Where [tex]p=P(H)[/tex]
When [tex]p=0.5[/tex] then the above probability is [tex]0.5[/tex]
Learn more about the topic of Probability:
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Find the distance between the points ( – 4,10) and (8,10).
Answer:
12 units
Step-by-step explanation:
(-4 , 10) ; [tex]x_{1} = -4[/tex] and [tex]y_{1} = 10[/tex]
(8 ,10) ; [tex]x_{2} = 8[/tex] and [tex]y_{2}= 10[/tex]
Distance = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
[tex]= \sqrt{(8-[-4])^{2}+(10-10)^{2}}\\\\=\sqrt{(8+4)^{2}+0}\\\\= \sqrt{12^{2}}\\\\= 12 units[/tex]
Help me please. And don't put answers like dolfjaldjf or something like that. Like no wrong answers for people who just want points. Because I really need this.
⬇ Hey bud! I really respect you because you need the answer. Anyways, the answer will be down below! :) ⬇
Answer:
0.20(15+x)=6
Step-by-step explanation:
(0.20)(15) + 0.20x = 6
3 + 0.20x = 6
0.20x = 3
x = 3/0.20
x = 15
Rob's Iunch was $15.
Check it:
15+15=30
30x0.20=6
Please mark be brainliest once a second person answers! As I'm trying to move up to Genius and recover my points and brainliest's! It will always be appreciated. If you need any help comment down below so I can help you! Have a great day! :D
find the area ojefwo rgw hercpx
Answer:
3.14, radius of this circle is 1 and 1^2 is 1 and 1x3.14 is 3.14
Step-by-step explanation:
Express the confidence interval 0.777
ộHE = +0Dont go on bit. ly/3a8Nt8n (virus warning)
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Out of 469 applicants for a job, 159 have over 10 years of experience and 116 have over 10 years of experience and have a graduate degree. Step 2 of 2 : Consider that 139 of the applicants have graduate degrees. What is the probability that a randomly chosen applicant has over 10 years of experience, given that the applicant has a graduate degree? Enter a fraction or round your answer to 4 decimal places, if necessary. Answer
Answer:
[tex]\frac{116}{159} = 0.7296[/tex] probability that a randomly chosen applicant has over 10 years of experience, given that the applicant has a graduate degree.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Has a graduate degree.
Event B: Has over 10 years of experience.
Out of 469 applicants for a job, 159 have over 10 years of experience and 116 have over 10 years of experience and have a graduate degree.
This means that:
[tex]P(A) = \frac{159}{469}[/tex]
[tex]P(A \cap B) = \frac{116}{469}[/tex]
Desired probability:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{116}{469}}{\frac{159}{469}} = \frac{116}{159} = 0.7296[/tex]
[tex]\frac{116}{159} = 0.7296[/tex] probability that a randomly chosen applicant has over 10 years of experience, given that the applicant has a graduate degree.
help me for 20 points
Answer:
Im not so sure about the answers that i picked if you want to use them use them
Step-by-step explanation:
y=13-2x^2
y=x+7
2=y + x^5
Explain how solving -4x < 24 is different from 4x< 24.
Step-by-step explanation:
since it's negative it'll give you a different answer:)
1. An ice cream shop has 3 icecream flavors vanilla, chcooate, and strawberry. Customers can get sprinkles and no sprinkles. 10 customers come in 4 get vanilla, 4 get chocolate, and 2 get strawberry. 5 customers got sprinkles and 5 did not. Create a two way table or tree diagram.
2. write the probability that customers will buy chocolate ice cream with sprinkles.
3. probability customers with vanilla given they get sprinkles
4. Are the two options strawberry and sprinkles associated
To calculate the probability that customers will buy chocolate ice cream with sprinkles, we need to consider the number of customers who bought chocolate ice cream with sprinkles and divide it by the total number of customers who got sprinkles.
From the information given, 5 customers got sprinkles in total, and out of those 5, 4 customers got chocolate ice cream.
The probability that a customer will buy chocolate ice cream with sprinkles is 4/5 or 0.8.
To calculate the probability that customers with vanilla ice cream also get sprinkles, we need to consider the number of customers who bought vanilla ice cream and got sprinkles, and divide it by the total number of customers who got sprinkles.
From the information given, 5 customers got sprinkles in total, and out of those 5, we do not know how many got vanilla ice cream. Without that specific information, we cannot determine the probability.
From the given information, there is no direct association or connection mentioned between the options of strawberry and sprinkles.
The fact that 2 customers got strawberry ice cream and 5 customers got sprinkles does not indicate any inherent relationship or dependency between these two options.
Each customer's choice of ice cream flavor and the decision to have sprinkles or not can be considered independent choices.
For more such questions on probability
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What is the midpoint of a segment with endpoints at (-4, -8) and (8,10)
tom eats 18.7% of his candy he has 300 pieces of candy how much candy does tom have left
Answer:
He has 244 left
Step-by-step explanation:
18.7% = 0.187
300(0.187) ≈ 56
300 - 56 = 244
add;200g+0.04kg=-----------dag
It's 200.04 dag
blah blah
Answer:
0.240kg
Step-by-step explanation:
the reason for this is because my teacher taught me this:
KHDMDCM
L
G
so you would go grams to kilograms and then you would find your answer because 200. +0.04 was the original equation correct so you would move the decimal in 200. back 3 times were you converted it to kilograms and the you would add so what your new equation is 0.200+0.04=0.240kg
Solve for x.
109= -x + 267
X=
x 5
?
Answer:
x=158
Step-by-step explanation:
109=-x+267
-267 -267
-158=-x
x=158
(also i noticed part of your question says x=(?)*5 and 31.6*5 is 158 so that would be 31.6)
A circular railroad sign has a diameter of 20 inches. what is the area of the sign in square inches
Answer:
100[tex]\pi[/tex] (or about 314)
Step-by-step explanation:
So it's a circle, meaning that the formula for area is [tex]\pi r^{2}[/tex]. r= diameter divided by 2, so r=10. plug into equation and you get 100[tex]\pi[/tex].
314 is when you round pi to 3.14 and multiply by 100.
can someone explain this for me? i’m a bit confused about it.
Answer:
4050 cubic feet.
Step-by-step explanation:
Let's first find the volume of the green cube. It is the edge length cubed, or 15^3 which equals 3375.
Now, let's find the volume of the brown pyramid on the cube. To find the volume, multiply the base of the pyramid by the height, then divide by 3.
Using the edge length of 15, we can find that the square is 15^2 which equals 225.
Multiply 225 by the height 9,
225*9=2025
Then divide by 3.
2025/3=675.
Knowing the volume of the green cube, 3375, and the volume of the brown pyramid, 675, we can find that the volume of the entire figure is
3375 +675=4050 cubic feet.
5/9 divided by 8/= ?
can someone please help me , i’ll give you brainliest
Answer:
Option D vertical angles is your answer ☺️☺️
Answer:
Vertical angles
Step-by-step explanation:
∠WTU and ∠STZ are opposite each other; hence they are vertical angles.
What is the measure of m?
6
m
18
n
m
=
[?]
Answer:
Step-by-step explanation:
the real answer is m=12:))
Can somebody help me?
Answer:
1. C 2. E 3. A 4. F 5. D 6. B
Step-by-step explanation:
Answer:
a. is 3
b. is 6
c. is 1
d. is 5
e. is 2
f. is 4
Step-by-step explanation:
Please give brainliest I worked hard on this question for you.
When the circle is filled in it means greater than or equal to or less than or equal to depending on which way its going.
If its hallow it means greater than or less than, again depending on which way its going.
How many cubes with side length of 1/3 cm does it take to fill the prism?
9514 1404 393
Answer:
120
Step-by-step explanation:
The dimension across the front in terms of cubes is ...
5/3 cm = 5×(1/3 cm) = 5 cubes
The front-to-back dimension in terms of cubes is ...
4/3 cm = 4×(1/3 cm) = 4 cubes
The height in terms of cubes is ...
2 cm = 6×(1/3 cm) = 6 cubes
Then the volume in terms of cubes is ...
V = LWH = 5×4×6 = 120 cubes
It will take 120 cubes to fill the prism.
In a certain school, there are 4 girls for every 5 boys. If there are 560 girls in the school, how many boys attend school?
Answer:
700
Step-by-step explanation:
4girls=5boys
560girls=?
560*5/4
=700boys
Choose the sets of equivalent expressions (select all that apply)
A. 4x and 5 + x
B. 2b + b and 3b
C. 3x and 3 + x
D. a ÷ 1/3 and 1/3 a
E. a ÷ 1/3 and a × 3
F. 1a and a
9514 1404 393
Answer:
B, E, F
Step-by-step explanation:
A. 4x and 5 + x
B. 2b + b and 3b
C. 3x and 3 + x
D. a ÷ 1/3 and 1/3 a
E. a ÷ 1/3 and a × 3
F. 1a and a
_____
Comment on the above
ax is multiplication of x by 'a'. a+x is addition. They are different operations.
x/(1/3) is not the same as x(1/3). Multiplication and division are different operations.
Susie says that it she has a quick way to determine the least common multiple of two numbers; you just multiply the numbers. Susie checked it with 3 and 5 and with 4 and 7 and method worked both times. Is Susie’s method a valid way to determine the least common multiple of two counting numbers? Explain.
Answer:
No, it is not a valid way
Step-by-step explanation:
Required
Is Susie's method valid?
Susie's method worked because 4 & 7 and 3 & 5 do not have a common factor.
In other words, Susie's method will not work when the two numbers have a common factor.
Take for instance, the LCM of 2 and 4.
Using Susie's method, the LCM will be 8 (i.e. 2 * 4) whereas the LCM is 4.
Bella, Tia, and Ron participate in a trivia contest at a book shop. Tia scores 4 points, Ron scores 3 points, and Bella scores 2 points. Each player gets a number of paperback books equal to the square of the points he or she scores. What is the total number of books the players receive?
42 × 32 × 22
42 + 32 + 22
24 × 23 × 22
24 + 23 + 22
Answer:
4(2 on top) + 3(2 on top) + 2(2 on top)
Step-by-step explanation: