Answer:
Students will usually not want their name written because they believe it is humiliating.
A) Convert the exponential function, 12^3=x^4 y^3 z^6, to its corresponding logarithmic function.
B) Write the log form from Part A into the expanded log form. **expression must be fully expanded for full credit**
The logarithmic function is ㏒ 12³ = ㏒ x⁴ · y³ · z⁶. The equation into the expanded logarithmic form is 3 · ㏒ 12 = 4 · ㏒ x + 3 · ㏒ y + 6 · ㏒ z.
How to apply logarithms on a exponential function
Logarithms are the reciprocal of exponential functions. In this question we must apply logarithms and its properties to obtain a linear-like expression in the following lines. The logarithm properties are summarized below:
㏒ₐ (b/c) = ㏒ₐ b - ㏒ₐ c (1)
㏒ₐ (b · c) = ㏒ₐ b + ㏒ₐ c (2)
㏒ₐ bⁿ = n · ㏒ₐ b (3)
a) To obtain the corresponding logarithmic function we apply logarithms on both sides of the expression:
㏒ 12³ = ㏒ x⁴ · y³ · z⁶ (4)
The logarithmic function is ㏒ 12³ = ㏒ x⁴ · y³ · z⁶. [tex]\blacksquare[/tex]
b) The expanded logaritmic form of (4) consists in the addition and subtraction of logarithms of non-power numbers, whose formed could be found, if possible, by logarithm properties:
㏒ 12³ = ㏒ x⁴ · y³ · z⁶
㏒ 12³ = ㏒ x⁴ + ㏒ y³ + ㏒ z⁶
3 · ㏒ 12 = 4 · ㏒ x + 3 · ㏒ y + 6 · ㏒ z
The equation into the expanded logarithmic form is 3 · ㏒ 12 = 4 · ㏒ x + 3 · ㏒ y + 6 · ㏒ z. [tex]\blacksquare[/tex]
To learn more on logarithms, we kindly invite to check this verified question: https://brainly.com/question/24211708
The baseball team in your community is playing for the championship. They will play seven games against the opposing team.
a. If the probability for your team to win is 74%, what is the probability for the other team to win?
b. Is this a binomial distribution? Why or why not?
c. What is the probability that your team will win 4 of the 7 games?
Answer:
a. 26%
b. It's a binomial distribution because the competition will only have two outcomes, win or lose.
c. 4/7 or 57%
Step-by-step explanation:
Hope this helps :)
The function, f(n) = 70n – 400, models the profit of the instructor of a guitar class per month, where n is
e number of students enrolled in the class.
How many students must be enrolled in the class for the instructor to make a profit?
ow many students must be enrolled in the class if the instructor needs to make $1,000.00 profit per
onth?
Using the given function, it is found that:
6 students need to be enrolled for the instructor to make a profit.20 students must be enrolled for the instructor to make a profit of $1,000 a month.What is the profit function?The profit when n students are enrolled in the class is given by:
f(n) = 70n - 400.
A profit is made when f(n) > 0, hence:
70n - 400 > 0
70n > 400
n > 5.71.
6 students need to be enrolled for the instructor to make a profit.
A profit of $1,000 is made when f(n) = 1000, hence:
70n - 400 = 1000
70n = 1400.
n = 20.
20 students must be enrolled for the instructor to make a profit of $1,000 a month.
More can be learned about functions at https://brainly.com/question/25537936
Atleast 6 students must be enrolled to make a profit and 20 student are needed to make $1,000.00 profit per month.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Given the function:
f(n) = 70n - 400
To make a profit, f(n) > 0, hence:
70n - 400 > 0
n > 6
For a profit of $1000:
70n - 400 = 1000
n= 20
Atleast 6 students must be enrolled to make a profit and 20 student are needed to make $1,000.00 profit per month.
Find out more on equation at: https://brainly.com/question/2972832
pls explain why and how the answer u got is proportional
Answer:
A
Step-by-step explanation:
This is because to find out if a table is proportional you have to do y divided by x. Whatever table has the same answer on all of the table sections when you divide y by x, that is proportional.
Which term describes the red curve in the figure below?
A. Hyperbola
B. Parabola
C. Ellipse
D. Circle
Answer:
Hyperbola
Step-by-step explanation:
Sorry if incorect
Hope this helps
help me with this
forgot how to do it
Answer:
C =113.04 ft
Step-by-step explanation:
[tex]C = 2\pi \: r \\ \\ \implies C =2(3.14)(18) \\ \\ \implies C =113.04 \: ft[/tex]
Gina rolls a six-sided die, numbered 1 to 6. She wants to find the probability of
rolling a number less than 6. The size of the sample space is 6, because Gina can
roll any of the six numbers on the die. What is the size of the event space?
The size of the event space is
The solution is
Answer:
5/6
Step-by-step explanation:
thats what it is
3. Triangle ABC with AB = 3 cm, LABC = 40°,
=
and Z BAC = 70°.
Construct a triangle with the given conditions
Answer: Right angled triangle
Step-by-step explanation: Find attached in the picture
My sister is 13 years old. My brother says that his age minus 14 is equal to my sisters age. How old is my brother?
Answer:
Brother's age = 13 years
Step-by-step explanation:
Sister's age = 13 year
Brother's age = x
Brother's age will be equal to the Sister's age when x-14
According To The Question
[tex]x - 14 = 13 \\ x = 13 + 14 \\ x = 27[/tex]
Therefore, Brother's age will be 27 years
!!PLEASE PLEASE PLEASE MARK ME THE BRAINLIEST!!
The State Board of Education has $1,742 to buy new calculators. If each calculator costs $2, how many calculators can the board buy?
Answer:
871
Step-by-step explanation:
The State Board of Education can buy 871 calculators with the available budget.
Here, we have to find out how many calculators the State Board of Education can buy,
We have to divide the total amount they have ($1,742) by the cost of each calculator ($2):
So, we get,
Number of calculators = Total amount / Cost per calculator
Number of calculators = $1,742 / $2
Number of calculators = 871
So, the State Board of Education can buy 871 calculators with the available budget.
To learn more on division click:
brainly.com/question/21416852
#SPJ3
For what values of a make each expression true. |a|=-a
Answer:
a=0
Step-by-step explanation:
Aaron has a dime, a penny, and a nickel in both of his pockets. If Aaron chooses a coin randomly from his left pocket and then from his right pocket, how many possible outcomes are in the sample space?
A: 27 outcomes
B: 9 outcomes
C: 3 outcomes
D: 18 outcomes
Answer:
B: 9 outcomes
Step-by-step explanation:
you have 3 possibilites in the left pocket, and 3 in the right. Multiply the number of possibilites in each pocket to find how many total possibilites there are.
Select all that apply
Answer:
B, C, D, F
Step-by-step explanation:
if you know the length and width of the traffic jam is (F and C) you can start to calculate how many cars are stuck in it. then by using how long the vehicles are and how long the space between them is you can find out how many cars would fit in this area. (B and D)
A and F are irrelevant because the question is simply asking how many vehicles in the jam not how many people or what cuased it.
hope this helps :]
Assume there are 365 days in a year. (40 points!!!) NEED HELP ASAP will mark brainlist
-What is the probability that ten students in a class have different birthdays?
-What is the probability that at least ten students in a class share their birthday?
check out brainly.com/question/7567074, same question, verified answer
7. Square numbers, such as 1, 4, 9, etc., can be formed by adding consecutive add made beginning with 1. Which is NOT an example of this fact? 1 + 3 + 5 1 +3 + 5 + 7 1+3 + 5 + 7 +9
A rectangle has vertices (–1, 1), (–4, 1), (–1, 3), and (–4, 3). If the rectangle is reflected over the y-axis, what algebraic rule can be used to find each of the new vertices?
Select one:
A. (x,y)→(−x,−y)
B. (x,y)→(–y,–x)
C. (x,y)→(y,−x)
D. (x,y)→(−x,y)
Answer:
D. (x,y)→(−x,y)
Step-by-step explanation:
Reflecting OVER the Y axis means it will end up on the other side of the Y axis line. The Y coordinates remain unchanged while the X coordinates invert. Attaching a crude diagram to help you picture it.
For problem 8, find the area of the shaded region. The polygon is a regular polygon. please show work.
Answer:
34.7791 [unit²].
Step-by-step explanation:
1) area of the circle is:
πr²;
2) area of the regular polygon is:
6*r²√3*0.25=1.5√3r²;
3) the required area:
πr²-1.5√3r²=r²(π-1.5*√3)=64*(3.1415-1.5*1.7321)=34.7791
how would I rewrite, 7x - 14y= -56 into slope-intercept form?
Answer:
[tex]y =\dfrac{1}{2}x+4[/tex]
Step-by-step explanation:
Slope-intercept form: y =mx +b
7x - 14y = -56
Step1 : subtract 7x from both sides
[tex]-14y = -7x - 56[/tex]
Step2: now divide both sides by (-14)
[tex]y =\dfrac{-7}{-14}x -\dfrac{56}{-14}\\\\y = \dfrac{1}{2}x+ 4[/tex]
Answer:
y = [tex]\frac{1}{2}[/tex] x + 4
Step-by-step explanation:
7x - 14y = - 56 ( subtract 7x from both sides )
- 14y = - 7x - 56 ( divide through by - 14 )
y = [tex]\frac{-7}{-14}[/tex] x - [tex]\frac{56}{-14}[/tex]
y = [tex]\frac{1}{2}[/tex] x + 4 ← in slope- intercept form
In this figure, 12.2% of the area is painted blue.
How much of the area is painted blue?
1.22 cm²
3.05 cm²
4.27 cm²
5.49 cm²
The area of the figure painted blue, which is 12.2% of the total area is: 4.27 cm².
What is the Area of a Triangle and Square?Area of triangle = 1/2(b)(h)Area of Square = s²The figure is composed of a triangle and a square. Find the area of the figure.
Area of the figure = 1/2(b)(h) + s² = 1/2(5)(4) + 5² = 35 cm²
12.2% of the area of the figure = 12.2/100 × 35 = 4.27 cm²
Therefore, the area of the figure painted blue, which is 12.2% of the total area is: 4.27 cm².
Learn more about area of square and triangle on:
https://brainly.com/question/21735282
how many days are in 3 weeks??
Answer:
21
Step-by-step explanation:
because 7 day or in a week so 7 time 3 = 21
Answer:
21
Step-by-step explanation:
Becasue there are 7 days in a week, So use and time 7x3 and you will get 21 multiplication.
plewse help me i need help!!?
Answer:
A
Step-by-step explanation:
[tex] - \frac{4}{3} \times \frac{4}{1} = - \frac{1}{3} [/tex]
Hope this helps
Can two obtuse angles be supplementary? Why or why not?
Answer:
No.
Step-by-step explanation:
Two Angles are Supplementary when they add up to 180.
Let us consider the least obtuse angle, i.e., >90
Say 91 and add it to itself.
91+91 =182
This is >180
Hence, two obtuse angles can never be supplementary.
PLS HELP!!! No links pls and Ty <333
Sid is making a pizza. The diameter of the pizza is 15 inches.
What is the area of the pizza (use 3.14 for pi and round to the nearest
tenth)?
Step-by-step explanation:
Your diameter is 15 and a diameter is a whole line, what your going to do it divide the 15 by 2, than mutiply the answer by 3.14 and than round ur answer :)
What is the common denominator of 2/5 and 3/10
Answer:
Answer:
10
Step-by-step explanation:
3/10~3/10
2/5
5x2=10
2x2=4
2/5=4/*10*
Frank is 6 years older than his brother Joe. The sum of their ages is 38. How old is Joe AND Frank?
Answer:
Joe is 16, Frank is 22
Step-by-step explanation:
To find the solution to this problem, we first divide 38 by two.
38 / 2 = 19.
Then, we subtract 6 from 19 and have 19 and 13. Obviously, 19 is 6 more than 13 (19 - 13 = 6). Now, we need to make sure our number on the left is always 6 more than the number on the right. 19 + 3 = 22, 13 + 3 = 16. Since Frank is older than Joe by 6 years, we get 22 and 16 as their ages.
PLEASE HELP 75 POINTS
Answer:
Volume of larger box: 480
Length of small box: 5
Width of small box: 4
Height of small box: 3
Volume of small box: 60
Ratio of small box to large box: 1/8
Find the GCF of 60, 96, and 156.
Answer:
GCF = 12
for the values 60, 96, 156
Step-by-step explanation:
Solution by Factorization:
The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The factors of 96 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
The factors of 156 are: 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156
Then the greatest common factor is 12.
340 to nearest hundred
Answer:
300 - hope this helped :)
Step-by-step explanation:
340 to the nearest hundred
is 300 since thats the closest
4x^2- 4x-1=0 i need the awnser
Answer:
See below
Step-by-step explanation:
Do you know how to use the Quadratic Formula with
a = 4 b = -4 c = -1
results in x = 1/2 +- sqrt(2) / 2
Three friends decide to rent an apartment and split the cost evenly. they each paid $640 towards the total move in cost of first and last month's rent and a security deposit. if rent is $650 per month, how much was the security deposit? a. $10 b. $207 c. $620 d. $1,270
The total amount of security deposit, deposited by three friends after paying the rent is $620.01. Option C is the correct option.
What is a monthly payment?The monthly payment is the amount which is required to pay each month to pay off the borrowed principal amount or the rent of a service charged monthly.
The rent of the apartment is $650 per month. The rent for the two months (first and last) is,
[tex]\rm M = 2\times 650\\\\M =1300[/tex]
This rent is paid by three friends. Thus, the amount which is paid by an individual friend is,
[tex]\rm P=\dfrac{1300}{3}\\\\P=433.33[/tex]
They each paid $640 towards the total move-in cost of first and last month's rent and a security deposit. Therefore,
[tex]\rm P=640-433P=206.67\\\\[/tex]
Thus, $206.67 is paid by each of them towards security deposits. The total amount of security deposit, deposited by 3 of them, is,
[tex]\rm SD=206.67\times 3\\\\SD=620.01[/tex]
Hence, the total amount of security deposit, deposited by three friends after paying the rent is $620.01. Option C is the correct option.
Learn more about the monthly payment here;
brainly.com/question/25599836
Answer:
Option C
Step-by-step explanation:
I got it right on the test