To evaluate [tex]\log _{\frac{1}{3}}27[/tex] note that:
[tex]\dfrac{1}{3}=3^{-1};[/tex][tex]27=3^3.[/tex]Use following properties:
1) [tex]\log_ab^k=k\log_ab;[/tex]
2) [tex]\log_{a^k}b=\dfrac{1}{k}\log_ab.[/tex]
Then
[tex]\log _{\frac{1}{3}}27=\log_{3^{-1}}3^3=3\log_{3^{-1}}3=3\cdot \dfrac{1}{-1}\log_33=-3\log_33.[/tex]
Since [tex]\log_aa=1,[/tex] you have
[tex]\log _{\frac{1}{3}}27=-3.[/tex]
Answer:
a on edge
Step-by-step explanation:
Mark and his friends Byron were watching a superhero movies. During the movie mark ate 5 pieces of candy . Byron ate 7 times as much candy as mark. How much candy did Byron eat.?
Final answer:
To find out how much candy Byron ate, we multiply the number of candies Mark ate, which is 5, by 7. Byron ate a total of 35 pieces of candy.
Explanation:
The question involves solving a basic multiplication problem to determine how much candy Byron ate if Mark ate 5 pieces of candy and Byron ate 7 times as much. According to the given scenario, we can represent this mathematically as:
Mark ate 5 pieces of candy. Byron ate 7 times as much candy as Mark did. To find out the total pieces of candy Byron ate, we multiply the number of candies Mark ate by 7. Therefore, Byron ate 5 pieces × 7 = 35 pieces of candy.
This arithmetic calculation shows us Byron's total candy consumption during the movie.
A portable CD player costs $48. How much is a payment of 25% of the cost
25% is the same is 1/4 of something. So you have to find what 1/4th of 48 is. To do that, just divide 48 by 4. and you get 12.
A 25% payment on a CD player that costs $48 would be $12. Hope that helps!
ANIME BRAINLY PLEASE HELP!
4. Tom decided to join Platinum Gym because of its new equipment. At the grand opening, the manager announced that 124 people had signed up for gym membership. As part of the grand opening event, the manager waived the registration fee for 50 random people.
(a) Write an expression to represent how much money Platinum Gym will make from the grand opening memberships. Simplify the expression and label any variables.
(b) After 6 months, how much money will Platinum Gym have made from the original 124 people who joined at the grand opening, assuming that all 124 people are still members? Show your work.
Answer:
Remark
Question B is a bit of a guess, but A is pretty straight forward.
A
Let P = Platinum Gym's income (total)
Let M = Platinum Gym's Registration Fee.
Number of people who received free membership registrations = 50
The total income from anyone who had to register was
P = (124 - 50)*M
P = 74 * M
B
Monthly Fee = MF
n = number of months = 6
c = customer base = 124
Equation
P = Registration Fee (found in A) + n * c * MF
Solution
P = 74*M + 6*124*MC
P = 74M + 744*MC
The question is, do you count the registration fee at the beginning or not? I would.
wx + yz = h, solve for z
Wx + yz = h
yz = h - wx
z = (h - wx) / y
Answer
z = (h - wx) / y
The sum of three consecutive odd integers is 17 less than four times the smallest integer
The three consecutive odd integers are 23, 25,27
What is Algebraic expression ?
Algebraic expressions are numbers expressed using letters or alphabets without specifying their values. Algebra taught us how to express unknown values using letters such as x, y, and z. There can also be a single value that is placed before and multiplied by a variable in an algebraic expression in addition to these letters, which are called variables.
Let the three consecutive odd integers be x , x + 2 , x+ 4 then,
the sum of these three odd integers is 17 less than four times the smallest integer that is :
x + (x+2) + (x+4) = 4x -17
3x + 6 = 4x -17
4x - 3x = 6 + 17
x = 23
x + 2 = 25
x + 4 = 27
Therefore, the three consecutive odd integers are 23, 25,27
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Which recursive formula can be used to generate the sequence shown, where f(1) = 5 and n > 1?
5,–1, –7, –13, –19, ...
5, -1, -7, -13, -19
-6 -6 -6 -6 the difference between the numbers is -6
[tex]a_{n} = a_{1} + d(n - 1)[/tex] ; where a₁ is the first term, d is the difference, and n is the term
[tex]a_{n} = 5 - 6(n - 1)[/tex]
[tex]a_{n} = 5 - 6n + 6)[/tex]
[tex]a_{n} = 11 - 6n[/tex]
f(1) = 5
[tex]a_{1} = 11 - 6(1)[/tex]
= 11 - 6
= 5
TRUE
what is 0.012 as a fraction
To convert 0.012 to a fraction, you multiply by 1000 to get 12/1000 and then simplify it to 3/250. Therefore, 0.012 as a fraction is 3/250.
To convert the decimal 0.012 into a fraction, follow these simple steps:
Write down 0.012 as 0.012/1.
Multiply both the numerator and the denominator by 1000 to get rid of the decimal point:
0.012 x 1000 / 1 x 1000 = 12 / 1000.
Simplify the fraction by finding the greatest common divisor (GCD) of 12 and 1000, which is 4:
(12 ÷ 4) / (1000 ÷ 4) = 3 / 250.
Thus, 0.012 as a fraction is 3/250.
Which expression can be used to convert 22 Australian dollars to US dollars
The expression is
[tex]AUD/1.38 = USD[/tex]
ExplanationStep by step conversion is as following;
1 USD = 1.38 AUD, or its reciprocal
Where,
1.38 recent currency rate
AUD = Australian dollar
USD = US dollar
So, by rearranging
[tex]1 AUD = 1/1.38 USD[/tex]
Then
[tex]22AUD/1.38 = 15.94 USD[/tex]
The answer is
[tex]22A UD = 15.94 USD[/tex]
A garage door opener has a ten number keypad. Codes to open the door must consist of 5 digits with no adjecent digits the sane. How many codes are possible?
1st slot: 10 possibilities
2nd slot: 9 possibilities
3rd slot: 9 possibilities
4th slot: 9 possibilities
5th slot: 9 possibilities
10 * 9 * 9 * 9 * 9 = 65610 Possibilities
The total number of possible 5-digit codes for the garage door opener, where no two adjacent digits are the same, is 59,049.
Explanation:This is a combinatorics problem in mathematics. A simple way to solve this problem is to calculate the total number of 5-digit code combinations possible without any constraint, which is 10^5 = 100,000.
However, the condition given in the problem is that no two adjacent digits can be the same. The possible codes for the first digit are 10 (0-9). For the second digit, because it cannot be the same as the first, there are 9 possibilities, the third digit also has 9 possibilities because it cannot be the same as the second, and so on.
Therefore, the total number of possible codes is 10 * 9 * 9 * 9 * 9 = 59,049. Hence, the garage door opener can have 59,049 different codes.
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The length of a rectangle is 2 centimeters longer than its width,if the perimeter of the rectangle is 60cm,find its width and length?
Let the width of rectangle= x centimeter
According to condition length = (x+2) centimeter
As accoding to formula
perimeter of rectangle = 2( lenght +width)
so Perimeter = 2{(x+2) +(x)} equation 1
Give perimeter = 60cm equation 2
comparing equation 1 and equation 2
2{(x+2) +(x)} = 60
Solving 2{2x+2} =60
4x+4 =60
subtracting 4 both sides
4x= 56
dividing 4 both sides.
x=14 width of rectangle
AS we have assume length = x+2 ⇒ 14 +2
Length =16
divide by 1-digit divisors~~~ help me with 3, 7 please!!!
well I think it is 7.214 give me brainiest if i got it right plz
To divide a number by a 1-digit divisor, simply divide the number by the divisor. For example, 15 divided by 3 is 5, and 21 divided by 7 is 3. Practice makes perfect in this fundamental aspect of mathematics.
Explanation:I understand you are trying to learn how to divide by 1-digit divisors. It is a fundamental topic in mathematics that you will use many times in the future.
Let's take the numbers 3 and 7 as examples. To divide by 3 or 7, simply take the number you are wanting to divide and divide it by either 3 or 7. For example, if we want to divide 15 by 3, you would simply perform 15 ÷ 3, which results in 5.
Now, if we want to divide 21 by 7, you would do 21 ÷ 7, which gives you a result of 3. It's that simple! Remember, the biggest key to success here is practice. The more you practice these divisions, the better you'll get at them.
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Help me with number one please !! What’s the answer ? Please please help
Hey guys not sure which one plz help
Hey mate!!
Answer
4/7 and 8/14 are equivalent fractions, because they are both equal to 4/7 when they are simplified.
Correct answer is D. 8/14
Hope it helps you!
PLEASE HELP!!! A container holds 80,000 ounces of water. There is a small leak in the the container. Every 96 minutes, 1.9 ounces of water leak out. What is the total change in water after 8 hours?
What does 9/11 × 4/15 equal?
The product for these two fractions is equal to 12/55
(1.)
|x| + 5 = 18
(2.)
|y + 4| < 1
(3.)
|2t| - 5 = 7
(4.)
|a| - 3/4 = - 5/8
Gotcha!
The 1st answer is x=-13 or x=13
The 2nd answer is -5<y<-3
The 3rd answer is t=-6 or t=6
The 4th answer is a=-1/8 or a=1/8
What is 12:64 In lowest terms
The lowest terms would be 3/16 because you could divide top and bottom by 4
The lowest it vould be is 4:16
This is because the BCF is 4.
Ashley’s math average decreased 12 points to 78.
Then she completed an extra credit assignment and raised her final average by 5 points.
How did Ashley’s average change? What was her starting average? What was her final average?
Answer
83
Step-by-step explanation:
she had 90.
turned in to 78.
now she has 83
75=3(-6n-5)
Having troubles with this one too!! XD. I’m going to fail math this year, I swear ;((
Order the numbers from least to greatest -7/6,-2.8,-5/4,4/3,1.3
To order the numbers from least to greatest: -2.8, -1.25 (-5/4), -1.17 (-7/6), 1.3, 1.33 (4/3). Decimal conversion helps compare their values, with negative numbers being smaller than positive ones.
To order the numbers from least to greatest, we need to compare their values. Negative numbers are less than positive numbers, and among negative numbers, the one with the smaller absolute value is greater. We can convert the fractions to decimals to make it easier to compare all the numbers:
-7/6 is approximately -1.17-2.8 is already a decimal-5/4 is -1.254/3 is approximately 1.331.3 is already a decimalNow we order them from least to greatest:
-2.8 (since it's the smallest)-1.25 (-5/4)-1.17 (-7/6)1.31.33 (4/3)
Factor the expression completely.
-9.75 + 3.25x
A.
-3.25(3 - x)
B.
-0.25(39 + 13x)
C.
-3.25(6.5 + x)
D.
-0.25(-9.5 - 3x)
-9.75 + 3.25x
= -3.25(3) + 3.25(x)
= -3.25(3) - -3.25(x) notice they have the same factor of -3.25
= -3.25(3 - x)
Answer: A
What value of x makes the equation true?
12(4x−5)+52=10
Drag and drop the correct number in the box.
x =
5 8 12 20
Answer:
The answer is 5
Step-by-step explanation:
I had the test, and what you meant was probably: 1/2(4x-5)+5/2=10
but yes, the answer is 5
write and solve an equation based off the verbal phrase: the difference between 7 and the product of 3x is 23
what is 4 to the -5th power
Answer: [tex]\frac{1}{4^5}[/tex] because any exponent that is a negative has to be brought down.
hope that helps :)
Answer:
The answer is 1/45
Step-by-step explanation:
81x-27, apply the distributive property to factor our of the greatest common factor
The greatest common factor of the expression 81x - 27 is;
⇒ 27 (3x - 1)
What is Greatest common factors?
The highest number that divides exactly into two more numbers, is called Greatest common factors.
Given that;
The expression is;
⇒ 81x - 27
Now,
Solve the expression for the greatest common factor as;
Since, The greatest common factor of the numbers 81 and 27 = 27
So, We take common 27 as;
⇒ 81x - 27
= 3 × 3 × 3 × 3x - 3 × 3 × 3
= 3 × 3 × 3 (3x - 1)
= 27 (3x - 1)
Thus, The greatest common factor of the expression 81x - 27 is;
⇒ 27 (3x - 1)
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20 more than half a number is at least 45 find the smallest number that means this condition
.5x>=25
x>=50
50 is the least number for x; it makes the equation equal 45
50 is the least number for x it makes the equation equal 45
what is the answer to
-1 times 2
Answer:
Negative 2.
Step-by-step explanation:
2x -1 would have an outcome of a negative number since 2 is positive and one is negative. if they were both positive numbers or negative numbers then the answer would be positive
You saw on the previous page that 2/11=0.18. Show how you can use what you know about the decimal for 2/11 to find the decimal for 1/11
1/11 is half of 2/11. (1/11 + 1/11 = 2/11)
As 2/11 = 0.18, 1/11 must equal half of 0.18.
Half of 0.18 is 0.09. Thus the decimal for 1/11 is 0.09.
Answer:
The decimal for 1/11 is 0.09
Step-by-step explanation:
We have two options to get the answer, the first one is when we know that 1/11 is half of 2/11, so 1/11 will be half of 0.18. We have to divide 0.18 by 2:
0.18÷2 = 0.09
The other way to do it is to divide 1÷11 = 1/11
The answer is 0.09
simplify the expression -9fgh/f, f
What even is this ???
Which expression can be used to find 80% of 120?
120*0.8 is the expression, because you can put 80% as 80/100 and that is equal to .8 so you just put that in a calculator and thats your answer. Hope that helped :)
Answer:
[tex](0.80)120[/tex]
Step-by-step explanation:
We are asked to find an expression that represents 80% of 120.
We know that % means per hundred. 80% would be 80 divided by 100.
[tex]80\%\text{ of }120=\frac{80}{100}\times 120=(0.80)120[/tex]
Therefore, the expression [tex](0.80)120[/tex] represent 80% of 120.