After expanding logarithm equation is : [tex]3.log_3(xy^\frac{1}{3} + z^2)[/tex]
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as .
[tex]log_ax=N[/tex]
where, a is the base of function or equation
x define expression
Mathematically, if [tex]a^N=x[/tex] is an exponential function then, this can be converted to logarithmic function as [tex]log_ax=N[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.
Some important formulas of logarithms are :
log_c a × b = log_c a + log_c b , c is the baselog a/b = log a - log blog a^x = x log alog a^a = 1log (√x) = 1/2 log (x)The given expression can be written as,
[tex]log_3[xy^\frac{1}{3} + z^2]^3[/tex]
apply formulas log a^x = x log a
=> [tex]3.log_3(xy^\frac{1}{3} + z^2)[/tex]
Thus, after expanding the logarithm equation is : [tex]3.log_3(xy^\frac{1}{3} + z^2)[/tex]
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Two financial institutions offer different deals to new customers. The first bank offers an interest rate of 3 % for the first year and 2 % for the next two years. The second bank offers an interest rate of 2.49 % for three years. You decide to invest the same amount of principal in each bank. To answer the following, assume you make no withdrawal or deposits during the three-year period.
c. Write a function that represents the total amount of money in both accounts at the end of three years.
The function that represents the total amount of money in both accounts at the end of three years as
First Bank - 107 P / 100
Second Bank - 10747 P / 10000
Simple interest :
Simple interest can be calculated as follows
S.I = PRT / 100
Let the amount invested in two banks be 'P'
First Bank :
Given the first bank offers an interest rate of 3% for the first year and 2% for the next two years as
R₁ = 3%, R₂ = 2% T₁ = 1, T₂ = 2
Now the simple interest for the first bank is
S. I = PR₁T₁ / 100 + PR₂T₂ / 100
= P(3*1 / 100 + 2*2 / 100)
= P(3 / 100 + 4 / 100)
= 7P/100
The total amount of money in the first bank at the end of three years is
= S.I + P
= 7P / 100 + P
= 107 P / 100
Second Bank:
Given the second bank offers an interest rate of 2.49% for the three years as
R = 2.49, T = 3
Now the simple interest for the second bank is
S. I = PRT / 100
= P(2.49 * 3 / 100 )
= P(7.47 / 100)
= 7.47P/100
The total amount of money in the second bank at the end of three years is
= S.I + P
= 7.47P / 100 + P
= 107.47 P / 100
= 10747 P / 10000
Therefore, the function that represents the total amount of money in both accounts at the end of three years as
First - 107 P / 100
Second - 10747 P / 10000
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to determine the number of cashiers needed when a grocery store opens each
morning, the manager of the store wanted to estimate the typical number of items each
customer purchased. the manager took all the receipts from the first 30 minutes the
store was open on a particular day and recorded the number of items purchased by
each customer. the manager constructed the following boxplot from the information
on the receipts.
From the box-and-whisker plot of the distribution, we have that:
The center of the distribution is the median of 32.The range of the distribution is described by two measures, the IQR of 35 - 22 = 13 and the range of 62 - 17 = 45.The distribution is left skewed.What is the missing information?The plot of the distribution is missing, as is given at the end of the answer.
It asks to describe:
The center of the distribution.The variability of the distribution.The shape of the distribution.What does a box-and-whisker plot shows?A box and whisker plot shows five things:
The minimum value.The 25th percentile, which is the median of the bottom 50%.The median, which splits the entire data-set into two halfs, the bottom 50% and the upper 50%.The 75th percentile, which is the median of the upper 50%.The maximum value.For the plot in this problem, we have that:
Minimum: 17.Q1: 22.Median: 32.Q3: 35.Maximum: 62.Hence:
The center of the distribution is the median of 32.The range of the distribution is described by two measures, the IQR of 35 - 22 = 13 and the range of 62 - 17 = 45.The distribution is left skewed, as Q3 - Q2 < Q2 - Q1.More can be learned about box-and-whisker plots at https://brainly.com/question/12343132
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Written as a simplified polynomial in standard form, what is the result when (3x-3)^2 is subtarcted from 4xr^2
The resulting polynomial after subtracting will be -5x² +18x -9
In the given question, we have two polynomials. We have to Subtract (3x-3)² from 4x². Firstly we will have to calculate (3x-3)².
Calculating, (3x-3)²
=> (3x - 3)² = 9x² -18x +9
After evaluating (3x - 3)² we get 9x² -18x +9.
Subtracting 4x² by 9x² -18x +9 we get:
=> 4x² - (9x² -18x +9) => 4x² - 9x² +18x -9
=> -5x² + 18x -9
We get a resultant answer after subtracting -5x² + 18x -9
Hence, the equation after subtracting the two numbers will be
-5x² + 18x -9
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The function g is defined as follows.
g(x)=3x² +5
If the graph of g is translated vertically downward by 6 units, it becomes the graph of a function f.
Find the expression for f(x).
Answer: graph the function defined by the formula g(x) = f(x)+2. To graph y = f(x) - k, shift the graph of y = f(x) down k units by subtracting k from.
Step-by-step explanation:
If x=10, find m∠WYZ
Will choose brainliest
Answer:
23˚
Step-by-step explanation:
If x = 10, then angle VYZ = 157 by basic algebra. Knowing that VYZ and WYZ are supplementary angles, we can do 180-157 to find angle WYZ. 180-157 = 23˚
Write the phrase as an expression. Twice a number w
Answer: w2
Step-by-step explanation:
It is just w2, or w*2, or w x 2. You just have the number w twice.
which pairs of equations produce parallel lines
pls help giving brainliest answers!! :)
Answer: A. 3x+y=-6 y=-3x+6
Step-by-step explanation:
Rewrite the expression as the sum of two numbers. 7(2 + 6)
Answer: First you used distribute property
7(2+6) bring 7 into the parentheses
14+42 Then you just add
56 that’s the sum
Step-by-step explanation: hope this helps
0.6r = 4.5
giving brainlest n a lot of points
[ Brainliest ] please answer the question in the photo!
Answer:
angle v
please take a look at the gif
Answer:
v
Step-by-step explanation:
Find the amount in a continuously compounded account for the given conditions.principal: $ 950 annual interest rate: 6.5% time: 10 years
The amount in a continuously compounded account for the given conditions is $1819.76 .
Compound interest is interest calculated on the principal and the interest accrued in previous periods. Compound interest is interest based on principal and interest accumulated over a period of time.If we specifically state that the quantity in question is "continuously composed", we must use the continuous constitutive formula which is given by [tex]A=Pe^{rt}[/tex] ..... (1) where, P = initial amount , A = final amount , r = interest rate , t = time , e is a mathematical constant with e ≈ 2.7183.
It is given that principal is 950 , annual interest rate is 6.5% , time is 10 years
Putting [tex]P=\$950 , \ r= 6.5\% , \ t=10 \ years[/tex] in equation (1) , we get
[tex]A=950\times 2.71^{0.065 \times 10}\\A=950\times 2.71^{0..65}\\\A=950\times1.9155\\A =$1819.76[/tex]
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What is the longest side of a right triangle
A right angle
B leg B
C leg A
Hypotenuse
Answer:
Hypotenuse
Step-by-step explanation:
The longest side of a triangle is opposite the largest angle, which is the right angle in a right triangle.
Answer:
Hypotenuse.
Step-by-step explanation:
Discussion
A: says it is a right angle. It can't be the answer to the longest side.
B: Usually B and A might be the hypotenuse, but that is generally not the way they are displayed.
C: Neither B nor A can be chosen.
D: Answer:
y 3x + 6
y>-1/3x-6
y>x
Answer:y x
Step-by-step explanation:
calculator
There are 75 men at a party and 60 women. How many more percent more men are there then women?
Need help, had a brain fart
There are 11.2% more men than women
How to calculate the percentage ?The First step is to calculate the percentage of men in attendance
There are 75 men and 60 women
Total number of people in attendance= 75 +60
= 135
75/135 × 100
= 0.556 × 100
= 55.6
The percentage of women in attendance
= 60/135 × 100
= 0.444 × 100
= 44.4
Next step is to subtract both percentages
= 55.6 - 44.4
= 11.2
Hence there are 11.2% more men that women
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Simplify each expression.
[tex](y-3)(y^2+9)(y+3) - (2y^2 -y)^2 - 19[/tex]
The simplified expression of the expression given as (y - 3)(y^2 + 9)(y + 3) - (2y^2 - y)^2 - 19 is (y^4 - 81) - (2y^2 - y)^2 - 19
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to simplify the expression?The expression is given as
(y - 3)(y^2 + 9)(y + 3) - (2y^2 - y)^2 - 19
Rewrite the above expression as
(y + 3)(y - 3)(y^2 + 9) - (2y^2 - y)^2 - 19
Apply the difference of two squares formula
So, we have
(y^2 - 9)(y^2 + 9) - (2y^2 - y)^2 - 19
Evaluate the product
So, we have
(y^4 - 81) - (2y^2 - y)^2 - 19
Hence, the simplified expression of the expression given as (y - 3)(y^2 + 9)(y + 3) - (2y^2 - y)^2 - 19 is (y^4 - 81) - (2y^2 - y)^2 - 19
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For each function, find the inverse and the domain and range of the function and its inverse. Determine whether the inverse is a function. f(x)=x²/2
Answer to this question is:
Domain of given function is (-∞,∞),{x|x∈R}
Range of given function is [0,∞),{y|y≥0}
Inverse of given function is √2x,-√2x
The domain is all values of x that make the expression defined.The entire range of independent variable values is the domain of a function.
This definition can be stated simply as follows: The domain is the collection of all x-values that can be used to make the function "work" and produce actual y-values.
When choosing the domain, keep in mind that a fraction's denominator (bottom) cannot be 0.
Interval Notation:(-∞,∞)
Set-Builder Notation:{x|x∈R}
The set of all valid y values constitutes the range.Graph may be used to find the values.
Interval Notation:[0,∞)
Set-Builder Notation:{y|y≥0}
For calculation of inverse:
Interchange the variables x=y²/2Solve for yy=√2x,-√2xReplace y with f^-1(x)f^-1(x)=√2x,-√2x∴Domain of given function is (-∞,∞),{x|x∈R}
Range of given function is [0,∞),{y|y≥0}
Inverse of given function is √2x,-√2x
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Which table shows a constant of proportionality of 2 for the ratio of string instruments to percussion instruments?
Table with proportionality 2 is table 3
Percussion string
1 2
2 4
3 6
What is proportionality?A proportion is an equation in which two ratios are set equal to each other.
from first table
2/3
4/6=3/2
6/9=3/2
from second table
2/5
4/10=5/2
6/15=5/2
From the third table
2/1=2
4/2=2
6/3=2
and from fourth table
2/4=1/2
4/8=1/2
6/12=1/2
hence, the table with proportionality 2 is table 3.
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pls helpp
does m^2-4 equal to (m-2)(m+2)?
and does m^2+4 equal to (m-2)(m+2) also then??when simplified
Answer:(m+2)(m+2)
Step-by-step explanation:
The difference of two squares takes the form
[tex](x^{2} -y^{2} ) =(x-y)(x+y)[/tex]
[tex](x^{2} +y^{2} ) =(x+y)(x+y)[/tex]
[tex](m^{2} -4)=(m^{2} -2^{2} )=(m-2)(m+2)\\\\(m^{2} +4)=(m^{2} +2^{2} )=(m+2)(m+2)[/tex]
I hope you understand!
In a book store,60 books of the same kind occupy 1.4m of shelf length . how much shelf length is required for 300 such books ? if a shelf is 84cm long,how many books are needed to fill the shelf?
7m shelf length is required for 300 such books, and 36 books are needed to fill the 84cm long shelf. So option (a). 7m,36 books is the correct option.
here in the question we need to apply concept of division.
what is division ?
Division is kind of mathematical operation where we find out equals parts of a number, by applying it a number can cut into many equal parts. It is opposite to multiplication.
As 60 books occupy 1.4 m of shelf ,
S0, 1 books occupies = 1.4/60 m of shelf
Then, 300 books occupy {(1.4/60)×300} m of shelf=
7m of shelf
Now, 7m=700cm is occupied by 300 books,
So,1cm is occupied by (300/700) books
Then, 84cm is occupied by (300/700)×84 books=36 books.
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The question was incomplete.
Check below the full question.
In a book store,60 books of the same kind occupy 1.4m of shelf length . how much shelf length is required for 300 such books ? if a shelf is 84cm long, how many books are needed to fill the shelf?
a. 7m,36 books
b. 5m,32 books
c. 10m,16 books
d. 3m,9 books
help please i dont know
Denote by x the number of miles traveled.
Denote by p(x) the price paid
[tex]p(x) = 2 + 0.75x[/tex]
B.[tex]p(12) = 2 + 0.75(12) \\ p(12) = 2 + 9 \\ p(12) = 11 \: dollars[/tex]
C.No he is not, since they stated that the price is equal to two more than the product of 0.75 and the distance traveled, in this case represented by the variable m
A math test is worth 100 points. There are a total of 26 questions. There are equation questions that are worth 2 points each and vocabulary questions are 5 points each. Use a system of equations to solve for the number of equation questions and vocabulary questions on the math test.
Answer:
Let the number of equations be x and the number of vocabulary questions be y.
x + y = 26 (total num of questions)So, y = 26 - x (eliminate one variable to solve for one first)2x + 5y = 100 (total points)2x + 5 (26 - x) = 100 (substituting 26 - x in place of y)
2x + 130 - 5x = 100 (distributing the 5)-3x = -30x = 10
Since there are 10 equation questions, there must be 16 vocabulary questions to satisfy the total number of questions in the test
Hope this helps!
Explain how you can tell if y=ab x represents exponential growth or exponential decay.
In the form y = ab^x, if b is a number between 0 and 1, the function represents exponential decay.
The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)x, where x is the amount of time that has passed, an is the initial amount, b is the decay factor, and y is the final amount.
Radioactive decay and population decline are two examples of exponential decay. The data collected can be used to forecast future population trends for cities and colonies as well as the half-life of radioactive materials.
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if f(x) is the height in cm of a sunflower plant that is x days old which of the following statements best describes the meaning of f(60) = 210
What is the five-number summary for the data 2, 2, 4, 4, 5, 5, 6, 7, 9, 15
The five-number summary for the data 2, 2, 4, 4, 5, 5, 6, 7, 9, 15 is 2, 4, 5, 7, 15
The given data is 2, 2, 4, 4, 5, 5, 6, 7, 9, 15
The first step is to arrange the data in ascending order.
The given data is already in ascending order.
Lowest value = 2
Q1 = 4 (Median of first part i.e., 2, 2, 4, 4, 5)
Q2 = 5 (Median of full data i.e., 2, 2, 4, 4, 5, 5, 6, 7, 9, 15)
Q3 = 7 (Median of second part i.e., 5, 6, 7, 9, 15)
Highest value = 15
So, the five number summary of the data is 2, 4, 5, 7, 15
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Shaniece has a points card for a movie theater.
• She receives 50 rewards points just for signing up.
• She earns 14.5 points for each visit to the movie theater.
• She needs at least 195 points for a free movie ticket.
Write and solve an inequality which can be used to determine x, the number of visits
Shaniece can make to earn her first free movie ticket.
(this is due in 9 minutes someone pleaseeee help)
The inequality which can be used to determine x, the number of visits Shaniece can make to earn her first free movie ticket is 50 + 14.5x >= 195 and the solution is x >= 10
How to write and solve an inequality which can be used to determine x, the number of visits Shaniece can make to earn her first free movie ticketThe given parameters are:
Reward point = 50Visit = 14.5 points per visitPoints needed = At least 195The inequality is calculated as
Reward point + Visit * Number of visits >= Points needed
So, we have
50 + 14.5x >= 195
Solve the inequality
14.5 >= 145
Divide by 14.5
x >= 10
Hence, the inequality which can be used to determine x, the number of visits Shaniece can make to earn her first free movie ticket is 50 + 14.5x >= 195 and the solution is x >= 10
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The inequality which can be used to determine x, the number of visits Shaniece can make to earn her first free movie ticket is 50 + 14.5x >= 195 and the solution is x >= 10
How to write and solve an inequality which can be used to determine x, the number of visits Shaniece can make to earn her first free movie ticket
The given parameters are:
Reward point = 50
Visit = 14.5 points per visit
Points needed = At least 195
The inequality is calculated as
Reward point + Visit * Number of visits >= Points needed
So, we have
50 + 14.5x >= 195
Solve the inequality
14.5 >= 145
Divide by 14.5
x >= 10
Hence, the inequality which can be used to determine x, the number of visits Shaniece can make to earn her first free movie ticket is 50 + 14.5x >= 195 and the solution is x >= 10
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A ball is thrown upward and outward from a height of 5 feet. The height of the ball, y, in feet, can be modeled by y=-0.4x^2+1.6x+5 where x is the ball's horizontal distance, in feet, from where it was thrown.
a. What is the maximum height of the ball and how far from where it was thrown does this occur?
b. How far does the ball travel horizontally before hitting the ground?
c. Graph the equation that models the ball's parabolic path.
The maximum height of the ball is 9.8 feet.
The distance the ball travels horizontally before hitting the ground is 2.
The graph that model the parabolic path is given below.
What is a parabolic path?Parabolic path is defined as the angle of trajectory of a projectile.
We have,
y = 0.4x² + 1.6x + 5 _____(1)
Where,
x = balls horizontal distance
y = height of the ball
To find the maximum height we need to differentiate y and set y = 0.
y' = 0
0.4 x (2x) + 1.6 + 0 = 0
0.8x + 1.6 = 0
-0.8x = -1.6
x = 1.6 / 0.8
x = 2
Now the maximum height of the ball is:
Put x = 2 in (1)
y = -0.4 x (2)² + 1.6 x (2) + 5
y = 0.4 x 4 + 3.2 + 5
y = 1.6 + 3.2 + 5
y = 9.8
The distance the ball travels horizontally before hitting the ground:
x = 2
The equation that models the ball's parabolic path is given below:
Thus,
The maximum height of the ball is 9.8 feet.
The distance the ball travels horizontally before hitting the ground is 2.
The graph that model the parabolic path is given below.
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butterfly population at Glen Arbor farms was 250 last year. this year there are 100 butterflies. what is the percent increase or decrease.
Answer:
250% decrease
Step-by-step explanation:
How many times does 100 go into 250. 2.5 times. Thus it is 250%
Bentley drove 329 miles in 7 hours. On average, how fast did he drive, in miles
hour?
per
Answer:
47mph
Step-by-step explanation:
329/7=47
6
Susan is using 0.5 acres of land for organic farming.
If she divides the land into 6 equal-sized plots for the
6 vegetables she is planting, what will be the size of
each plot? (1 acre = 43,560 square feet)
A) 3,630 square feet
B) 6,700 square feet
C)
7,260 square feet
D) 14,520 square feet
The size of each plot is 3630 square feet to plant six vegetables.
Given, Susan is using 0.5 acres of land.
we know that 1 acre = 43,560 square feet
0.5 acre = 1/2 acre = 1/2 × 43,560
= 21780 square feet.
we need to divide the land into 6 equal sized plots.
divide 21780 into six equal parts.
= 21780/6
= 3630 square feet
the land is being divided into 3630 square feet to plant 6 equal sized plots.
Hence susan plants six vegetables in 3630 square feet each.
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Scott is making pizzas for everyone at a party.
He has 644 pepperonis. How many pizzas can
Scott make with 9 pepperonis on each?
Answer:
71.5556 but since you cant have half a pizza its only 71
Step-by-step explanation: