The options that are equivalent to the given function are;
Option A
Option B
Option E
The correct options are;
A) f(x) = [tex]162^{x/4}[/tex]
B) f(x) = (3∜2[tex])^{x}[/tex]
C) f(x) = [tex]9\sqrt[4]{2^{x} }[/tex]
D) f(x) = [tex]162^{4/x}[/tex]
E) f(x) = [tex](3(2^{1/4}))^{x}[/tex]
We are given the function; f(x) = [tex](\sqrt[4]{162})^{x}[/tex]
Now, when we have something like; [tex]\sqrt[b]{2}^{a}[/tex]
This expression can also be expressed as; [tex]2^{a/b}[/tex]
Therefore our function can also be expressed as; f(x) = [tex]162^{x/4}[/tex]
Option A; This is correct because it is equal to our function gotten
Option B; f(x) = (3∜2[tex])^{x}[/tex]
From earlier, we will have; (3 × [tex]2^{1/4}[/tex][tex])^{x}[/tex]
Now, 3 can also be expressed as [tex]81^{1/4}[/tex]
Thus, we now have;
([tex]81^{1/4}[/tex] × [tex]2^{1/4}[/tex][tex])^{x}[/tex]
Factorizing out the 1/4 exponent gives;
(81 × 2[tex])^{x/4}[/tex]
⇒ = [tex]162^{x/4}[/tex]
This is same with our function and it is correct
Option C; f(x) = (9∜2[tex])^{x}[/tex]
This is similar to our equation in option B which was correct but the difference here is 9 instead of 3 and clearly this option is not correct.
Option D; f(x) = [tex]162^{4/x}[/tex]
This is not the same with our function and so it is wrong
Option E; f(x) = [tex](3(2^{1/4}))^{x}[/tex]
As seen in option B;
3 can also be expressed as [tex]81^{1/4}[/tex]
Thus, we now have;
;([tex]81^{1/4}[/tex] × [tex]2^{1/4}[/tex][tex])^{x}[/tex]
Factorizing out the 1/4 exponent gives;
(81 × 2[tex])^{x/4}[/tex]
⇒ = [tex]162^{x/4}[/tex]
This is same with our function and it is correct
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You have 2,500 square feet of selling space. You want to reserve at least 125 square feet for each product category you will carry. 30% of the space will be used for aisles. How many categories can you carry?
Examine the two functions below. Use the equation and table given to answer the question below.
Which of the following statements is true?
A.
Both functions have the same y-intercept.
B.
f(x) has a negative slope while g(x) has a positive slope.
C.
Both functions are linear functions.
D.
g(x) has a common ratio of 4.
Find the value of the following expression:
(3^8 ⋅ 2^-5 ⋅ 9^0)^-2 ⋅ (2^ -2 / 3^3) ^4 ⋅ 3^28
Write your answer in simplified form. Show all of the steps.
(3^8 ⋅ 2^-5 ⋅ 9^0)^-2 ⋅ (2^ -2 / 3^3) ^4 ⋅ 3^28 =
(6561 * 0.03125 * 1)^2 * (0.00925)^4 * 22876792454961 =
42037.81348 * 0.00000000732094 * 22876792454961 =
7040477235.56798349
round answer as needed
A restaurant uses 4 pounds of potatoes for a party of 12 people. If they are cooking potatoes for a party of 60 people, what should they do?
A person standing close to the edge on top of a 56-foot building throws a ball vertically upward. The quadratic function h ( t ) = − 16 t 2 + 104 t + 56 h(t)=-16t2+104t+56 models the ball's height about the ground, h ( t ) h(t), in feet, t t seconds after it was thrown. a) What is the maximum height of the ball?
The maximum height of the ball at a time of 3.25 seconds will be 275 feet.
What are the maxima and minima of a function?For the maximum value of the function if f''(x) < 0 and for the minimum value of the function if f''(x) > 0.
The maximum and minimum value of the function is at f'(x) = 0.
An individual standing near the edge on top of a 56-foot building tosses a ball upward vertically.
The quadratic function is given below.
h(t) = - 16t² + 104t + 56
The value of 't' at which the ball is at its maximum height. Then we have
h'(t) = 0
-32t + 104 = 0
32t = 104
t = 3.25 seconds
Then the maximum height of the ball is given as,
h(t) = - 16(3.25)² + 104(3.25) + 56
h(t) = -16 x 10.5625 + 338 + 56
h(t) = - 169 + 444
h(t) = 275 feet
The maximum height of the ball at a time of 3.25 seconds will be 275 feet.
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Who should fill out the W-2 form?
a.
the taxpayer’s employer
b.
the taxpayer
c.
a qualified tax professional
d.
the IRS
The correct answer is A. The taxpayer's employer
Explanation:
In the U.S. the W-2 form is a special format that should be filled by employers to report payments to employees and the taxes derived from these. This form is part of the IRS or the Internal Revenue System and therefore it is mandatory for taxpayer's employers to fill the form every year. Additionally, employers need to fill the form by each worker and then send it to them. According to this, the person that should fill out the W-2 form is the taxpayer's employer.
Maude sees 3 more foxes than Henry. Henry see 4 foxes. How many foxes did Maude see?
Maude sees 3 more foxes than Henry and Henry sees 4 foxes then Maude
sees 7 foxes.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, Henry sees 4 foxes and Maude sees 3 more foxes than Henry.
∴ Maude sees (4 + 3) = 7 foxes.
Some more insights:
Addition is also known as the sum, subtraction is also known as the difference, multiplication is also known as the product, and division is also known as the factor.
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Find the state that has the largest number for the execution variable in 1993. (the variable exec is total executions in 1991, 1992, and 1993.) how much bigger is this value than the next highest value?
the ratio of number of miles walked by fernando in a week to the number walked by julia in a week is 4 to 3. julia waled 15 miles. how many miles did fernando walked in a week?
which function has no horizontal asymptote?
A) f(x)=2x-1/3x^2,
B) f(x)=x-1/3x,
C) f(x)=2x^2/3x-1
D)f(x)=3x^2/x^2-1
Function has no horizontal asymptote is C) f(x)=2x^2/3x-1
Further explanationThe rational functions graphs can be recognised by the fact that they often break into two or more parts. These parts go out of the coordinate system along an imaginary straight line called an asymptote.
Vertical asymptotes can be found by solve the equation n(x) = 0, where n(x) is the function denominator. This only applies if the numerator t(x) is not zero for the same x value. The graph has a vertical asymptote with the equation x = 1.
The three rules that horizontal asymptotes are based on the degree of the numerator, n, and the degree of the denominator, m.
If n < m, the horizontal asymptote is y = 0. If n = m, the horizontal asymptote is y = a/b. If n > m, there is no horizontal asymptote.A rational function has no horizontal asymptote when the degree of the numerator is greater than the denominator.
A) f(x)=2x-1/3x^2, the degree of the numerator is lower than the denominator.B) f(x)=x-1/3x, the degree of the numerator is lower than the denominator.C) f(x)=2x^2/3x-1 , the degree of the numerator is greater than the denominator.D)f(x)=3x^2/x^2-1 , the degree of the numerator is lower than the denominator.Learn moreLearn more about asymptote https://brainly.com/question/2914025Learn more about function https://brainly.com/question/12397187Learn more about horizontal asymptote https://brainly.com/question/4221615Answer details
Grade: 9
Subject: mathematics
Chapter: Graphs of rational functions
Keywords: asymptote, function, horizontal asymptote, horizontal, mathematics
list the partial products of 42 x 28
Answer:
The partial product of [tex]42\times 28[/tex] are 800,320,40,16 and their sum is 1176.
Step-by-step explanation:
The given expression is,
[tex]42\times 28[/tex]
In number 42 the place value of 4 is 40 and the place value of 2 is 2. In number 28 the place value of 2 is 20 and the place value of 8 is 8.
To find the partial product, we have multiply the place values of first number with the place values of second number.
Place values of 42 are 40 and 2. Place values of 28 are 20 and 8.
[tex]40\times 20=800[/tex]
[tex]40\times 8=320[/tex]
[tex]2\times 20=40[/tex]
[tex]2\times 8=16[/tex]
Therefore the partial product of [tex]42\times 28[/tex] are 800,320,40 and 16.
To find the total product, we have add all partial products.
[tex]T=800+320+40+16=1176[/tex]
The value of given expression is 1176.
A negative correlation between two variables x and y usually yields a negative p-value for r.
a. True
b. False
Two-fifths of the fish in Gary's fish tank are guppies.One-fourth of the guppies are red.What fraction of the fish in Gary's tank are red guppies?Show your work.
Answer:
[tex]\frac{1}{10}[/tex]
Step-by-step explanation:
Given: Two-fifths of the fish in Gary's fish tank are guppies.One-fourth of the guppies are red.
To Find: What fraction of the fish in Gary's tank are red guppies.
Solution:
Let total number of fish in tank be [tex]=\text{x}[/tex]
Number of guppies in tank are [tex]=\frac{2}{5}\text{of total fish}[/tex]
Number of guppies in tank are [tex]=\frac{2}{5}\text{x}[/tex]
Number of red guppies in tank are [tex]=\frac{1}{4}\text{of total guppies}[/tex]
[tex]\frac{1}{4}\times\frac{2}{5}\text{x}[/tex]
[tex]\frac{1}{10}\text{x}[/tex]
Now,
fraction of the fish in Gary's tank that are red guppies
[tex]=\frac{\text{red guppies}}{\text{total fish in Gary's tank}}[/tex]
[tex]\frac{\frac{1}{10}\text{x}}{\text{x}}[/tex]
[tex]\frac{1}{10}[/tex]
Hence [tex]\frac{1}{10}[/tex] of total fish are red guppies.
Brian drove 120 miles at a speed of 60 mph. He drove the same distance back home at an average speed of 40 mph. Brian adds the speeds and divides by two to come up with an average speed of 50 mph what is wrong with his reasoning? Find his average speed
Use the graph to find the x-intercept for the equation y + 2 = 2(x + 3). The x-intercept is
Answer:
(-2,0)
Step-by-step explanation:
I just did the assignment
Mark bought a double oven electric range for 1350 he made a 15% down payment and finance the balance paying 150 a month for 10 months how much did mark pay for all the range
I believe it's 1702.5, but I'm not the best at math.
15% of 1350 is 202.5.
Then 150 dollars is paid every 10 months, so 150*10 is 1500. Then you just add the two together!
Good luck!
The rectangular box shown in the figure has dimensions 8" × 7" × 4" (a = 8, b = 7, c = 4). Approximate the angle θ formed by a diagonal of the base and a diagonal of the 7" × 4" side. (Round your answer to two decimal places.)
Answer:
Rectangle
four
Length and width
Step-by-step explanation:
How many ounces of honey dew melons are needed to make 400 ounces of fruit salsa using a ratio of 8 ounces to make 32 ounces of salsa?
Step by step ways to solve 3.4 x 4.72
Final answer:
To solve 3.4 x 4.72, multiply the numbers as if they are whole, then place the decimal in the product so that it has the same number of decimal places as the sum of the decimal places in the factors, resulting in 16.048.
Explanation:
To solve the multiplication of 3.4 x 4.72, follow these steps:
Write down the numbers to be multiplied, one below the other, aligning the decimal points: 3.4The final result of multiplying 3.4 by 4.72 is 16.048.
Write a real-life situation that can be modeled by the expression 1 1/3 x 2.
1 1/3 is a mixed number
Which word best describes the range of a function?
A. input
B. output
C. independent
D. relation
Answer:
It is actually B output
Step-by-step explanation:
The choir club at a local school is running a field to a waterpark. There are 6 parks the club is considering. The director has asked the members to each pick three to narrow down the list of possibilities before making a final decision. How many different possibilities are there for the list of three?
A. 20
B. 150
C. 30
D. 120
The formula [tex]C(n, r)= \frac{n!}{r!(n-r)!} [/tex], where r! is 1*2*3*...r
is the formula which gives us the total number of ways of forming groups of r objects out of n objects.
for example, given 10 objects, there are C(10,6) ways of forming groups of 6, out of the 10 objects.
Thus, there are C(6, 3) many ways of forming different triples out of 6.
[tex]C(6, 3)= \frac{6!}{3!(6-3)!}=\frac{6!}{3!3!}=\frac{6\cdot5\cdot4\cdot3!}{3!3!}=\frac{6\cdot5\cdot4}{3!}=\frac{6\cdot5\cdot4}{3\cdot2\cdot1}=5\cdot4=20[/tex]
Answer: A.20
Answer20:
Step-by-step explanation:
The point P(8, 6) is on the terminal side of θ. Evaluate sin θ.
A pine tree grows at a rate of 1.5 feet per year. James plants a 2-foot tall pine tree in his yard. How many years will it take for the tree to be at least 14 feet tall?
Let hh be the set of all points in the second quadrant in the plane v=ℝ2v=r2. that is, h={(x,y)∣x≤0,y≥0}h={(x,y)∣x≤0,y≥0}. is hh a subspace of the vector space vv?
The set hh, which represents all points in the second quadrant of the Cartesian plane, is not a subspace of the vector space vv, because it does not contain the zero vector and is not closed under scalar multiplication.
Explanation:In vector space theory, a subset of a vector space forms a subspace if it satisfies three key properties: it contains the zero vector of the larger vector space, it is closed under vector addition, and it is closed under scalar multiplication.
In our case, the set hh represents all points in the second quadrant of the Cartesian plane, that is, hh={(x, y)∣x≤0, y≥0}. Since the zero vector is not included in this set of vectors, it does not meet the first requirement. Therefore, hh is not a subspace of the vector space vv.
To illustrate, let's consider the vectors A=(0, 1) and B=(-1, 0) that belong to set hh. The sum of these vectors is A + B = (0 - 1, 1 + 0) = (-1, 1), which also belongs to set hh. However, if we multiply vector A by the scalar -1, the result is -A = (0, -1), a vector that does not belong to set hh. Hence, the set hh is not closed under scalar multiplication.
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A bus timetable states that the next bus leaving for holmfirth is at 16:40 what time is this in 12 hours time
The cartesian coordinates of a point are given. (a) (2, −2) (i) find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π.
5×143=use distributive property
Hypatia has read 13 chapters of a 22 chapter book what percent has she read
Answer:
59.09%
Step-by-step explanation:
We can calculate it with a direct rule of 3. If 22 chapters are the 100% of the book, what percent is 13 chapters?
[tex]\text{22 chapters} -\!\!\!-\!\!\!- 100\%\\ \\\text{13 chapters} -\!\!\!-\!\!\!- x\%[/tex]
We use the formula of the direct rule of 3:
[tex]x = \frac {13* 100}{22} \\ \\ x = \frac {1300}{22}[/tex]
x = 59.09
She has read the 59.09% of the book.
In a standard deck of cards, the jack, queen, and king are "face cards." you draw a card from a standard deck. your friend peeks and lets you know that your card is a face card. what is the probability that it is not a king given that it is a face card? leave your answer as a fraction
Answer: [tex]\dfrac{2}{3}[/tex]
Step-by-step explanation:
Total number of cards in a deck = 52
Number of face cards = 12 ( 4 King + 8 others)
The probability that a card is face card P(Face card)= [tex]\dfrac{\text{Number of face cards }}{\text{Total cards}}[/tex]
[tex]\\\\=\dfrac{12}{52}=\dfrac{3}{13}[/tex]
Number of cards are not king = 8
The probability that a card is face card are not King :
P( Face card and not king )= [tex]\dfrac{\text{Number of face cards are not King}}{\text{Total cards}}[/tex]
[tex]\\\\=\dfrac{8}{52}=\dfrac{2}{13}[/tex]
Using conditional probability formula ,
[tex]\text{P(Not king}|\text{ Face card})=\dfrac{\text{P( Face card and not king )}}{\text{ P(Face card)}}[/tex]
[tex]=\dfrac{\dfrac{2}{13}}{\dfrac{3}{13}}=\dfrac{2}{3}[/tex]
Hence, the probability that it is not a king given that it is a face card [tex]=\dfrac{2}{3}[/tex]