Answer:
the answers are
1/3
27
All real numbers
y>0
Step-by-step explanation:
To simplify the function f(x) = 1/3(81)^3x/4, we identify 81 as 3^4 and then apply exponent rules which lead to the simplified form f(x)=3^(3x-1). The base indicates exponential growth, and the exponent determines the growth rate and vertical scaling. Additional analysis would involve graphing to observe its behavior.
Explanation:To simplify the function f(x)=1/3(81)^3x/4, we must first recognize that 81 is a power of 3, specifically 3^4. Thus, when raised to the 3x/4 power, we multiply these exponents to get 3^(4*3x/4) which simplifies to 3^(3x). Our function now looks like f(x)=(1/3)*3^(3x). By properties of exponents, this can further simplify to f(x)=3^(3x-1).
Key aspects of this function include the base of the exponential (which is 3), indicating that the growth is exponential, and the exponents indicate how quickly this growth occurs. The term '-1' in the exponent shows a vertical scaling factor of 1/3 on the base function 3^x.
To analyze the function in more detail, one could use a graphing calculator or computer software to visualize the growth pattern. However, it should be noted that in this case, a graphing calculator can't solve for x using the zero function as we don't have an equation set to zero.
Hans needs to make a total of 80 deliveries this week. So far he has completed 32 of them. What percentage of his total deliveries has Hans completed?
Explain how you round the weights of fruits?
A student takes a 10-question true-or-false quiz and randomly guesses the answer to each question. Suppose that a correct answer is worth 1 point and an incorrect answer is worth -.5 points. Find the probability that
estimate the value of 97.5 square rated divided by 1.96
Find a formula for a function of the form y=bxe^−ax with local maximum at (1,2.2073). y=________
The required formula is y = 6x e⁻ˣ for a function of the form y=bxe^−ax with the local maximum at (1,2.2073).
What are Maxima of a Function?A function curve has peaks known as maxima. There can be an unlimited number of peaks.
The given function of the form as:
y = bxe⁻ᵃˣ y' = be⁻ᵃˣ (1-ax)
Plug point (x,y) = (1, 2.2073) into equation: 2.2073 = 6be⁻ᵃ
Now plug in y' = 0 at the same x value: 0 = be-6ᵃ(1-6a) or a = 1
and y' = be⁻ᵃ(-a + 1) = 0 giving a = 1
From first equation 2.2073 = b e⁻¹ so b = 2.2073e = 6
So the required formula is y = 6x e⁻ˣ
To find b, plug an into the first equation. The sign of the first derivative shifts from + to -, indicating that it is a maximum critical point.
You may graph the equation using your constants and observe that the point (1, 2.2073) is the maximum.
Therefore, the required formula is y = 6x e⁻ˣ.
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The registration fee for a used car is 0.8% of the sale price of $5,700. How much is the fee?
The registration fee for a used car is 0.8% of the sale price of $5,700 as a result the registration fee is $ 45.60.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages. For comprehending the financial elements of daily life, percentages are crucial.
It is given that the registration fee for a used car is 0.8% of the sale price of $5,700,
The value of the registration fee is found as,
Registration fee = 0.8% of $5,700
Registration fee = (0.8/100) × $5,700
Registration fee = $ 45.6
Thus, the registration fee for a used car is 0.8% of the sale price of $5,700 as a result the registration fee is $ 45.60.
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4th grade homework.
Write an equation that represents this comparison sentence..
32 is 8 times as many as 4
NEED HELP FAST!!!!
Solve the equation.
3x/5 - 0.5 = 1.9
A. 2.3
B. 0.16
C. 4
D. 16
Please explain your answer.
1)The range of the following relation: R {(3, -5), (1, 2), (-1, -4), (-1, 2)} is
{-1, 1, 3}
{-5, -4, 2}
{-1, -1, 1, 3}
{-4, -5, 2, 2}
2) The domain of the following relation: R {(3, -2), (1, 2), (-1, -4), (-1, 2)} is
{-1, 1, 3}
{-1, -1, 1, 3}
{-4, -2, 2, 2}
{-4, -2, 2}
The range of the first relation is {-5, -4, 2}, and the domain of the second relation is {-1, 1, 3}.
The range of a relation is the set of all second elements in each ordered pair. For the relation R = {(3, -5), (1, 2), (-1, -4), (-1, 2)}, the range is the set of second elements {-5, 2, -4, 2}. When we list the unique values, we get the range as {-5,-4, 2}.
The domain of a relation consists of all the first elements in each ordered pair. Given the relation R = {(3, -2), (1, 2), (-1, -4), (-1, 2)}, the domain is the set of first elements {3, 1, -1, -1}. The domain with unique values is {-1, 1, 3}.
what is 5-2y=3x in standard form?
To write 5 - 2y = 3x in standard form, you rearrange it to Ax + By = C, resulting in the equation 3x - 2y = -5, which is in standard form as requested.
To write the equation 5 - 2y = 3x in standard form, you want to arrange it to Ax + By = C, where A, B, and C are integers, and A should not be negative. Here's how you can do it:
First, we will move the term involving x to the left side of the equation by subtracting 3x from both sides:3x - (5 - 2y) = 3x - 3xThis simplifies to:-3x + 2y = 5Finally, to keep A positive, if necessary, multiply the entire equation by -1:3x - 2y = -5Thus, the standard form of the equation is 3x - 2y = -5.
What is the answer to 6= a/4 + 2
what is the value of x in the equation -6/7= -×/84?
Answer:
x=7.
Step-by-step explanation:
To solve this you just hace to clear x from the equation and multipliead the other part of the equation by -84:
[tex]\frac{-6}{7} =\frac{-x}{84} \\x=\frac{6*-84}{7} \\x=\frac{504}{7}\\ x= 72[/tex]
So we know that the value of x in the equation will be 72,
Which distribution has a mean of 5? poisson with λ = 25 binomial with n = 200, π = .05 hypergeometric with n = 100, n = 10, s = 50?
If I drive 70 miles per hour for eight and a half hours, how far will I have driven
multiply speed by time to get distance
70 *8.5 = 595 miles
What is green and famous for running away from jail?
Escape peas. It is a joke (cause someone to laugh/cause amusement), an example of a joke in English. Jokes are popular because children learn them. Jokes can be an element of mood change for adults. The peas mean the "green" and the escape is related to the "famous for running away from jail" part.
Simplify the expression where possible. (3b 3) 4
To simplify the expression (3b^3)^4, raise the base to the fourth power and simplify the exponent.
Explanation:To simplify the expression (3b^3)^4, we need to raise the base, 3b^3, to the fourth power. This can be done by multiplying the exponents. The result is 3^4 * (b^3)^4, which simplifies to 81b^12.
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The function h(t) = 210 – 15t models the altitude of a hot air balloon over time t, in minutes. Explain what h(10) means in the context of the real-world scenario, and how to find its value.
li started a pool cleaning business. She purchased cleaning supplies and charged the same amount for each pool cleaned. The expression −243+24x−243+24x represents the profit Tali has earned from cleaning pools. Which expression represents the total amount Tali earns from pool cleaning?
answer is one of these (x , 24, -243 , 24x )
While sailing toward a statue, a sailor in a boat observed that at a certain point, the angle of elevation of the tip of the torch was 25 degrees 25°. after sailing another 110 110 meters toward the statue, the angle of elevation became 43 degrees 50 prime 43°50′. how tall is the statue?
The height of the statue is 97.6 meters
The Breakdown
To determine the height of the statue, we can use trigonometry and create a right triangle with the sailor, the tip of the torch, and the top of the statue.
Assuming the height of the statue is "h" (in meters). The distance between the sailor and the statue is the sum of the initial distance and the additional distance sailed, which is 110 meters.
In the first observation, the angle of elevation is 25 degrees. This means that the tangent of the angle is equal to the height of the statue divided by the initial distance between the sailor and the statue:
tan(25°) = h / initial distance
Similarly, in the second observation, the angle of elevation is 43 degrees and 50 minutes. We need to convert this angle to decimal degrees before using it in calculations. 50 minutes is equal to 50/60 = 5/6 degrees.
So, the angle of elevation in decimal degrees is 43 + 5/6 = 43.8333 degrees.
Now, we can use the tangent function again to relate the height of the statue to the new distance between the sailor and the statue:
tan(43.8333°) = h / (initial distance + 110)
We have two equations with two unknowns (h and initial distance). We can solve this system of equations to find the height of the statue.
Solving the first equation for the initial distance:
initial distance = h / tan(25°)
Substituting this value into the second equation, we get:
tan(43.8333°) = h / (h / tan(25°) + 110)
Now, we can solve this equation for h:
h = (tan(43.8333°) × 110) / (1 - tan(43.8333°) / tan(25°))
Using a calculator, we find that:
tan(43.8333°) ≈ 0.957
tan(25°) ≈ 0.466
Substituting these values into the equation:
h = (0.957 × 110) / (1 - 0.957 / 0.466)
h ≈ 97.6 meters
Therefore, the height of the statue is 97.6 meters.
What is r, the common ratio, in the geometric sequence 2, −14, 98, −686
Answer:
The common ratio r is -7.
Step-by-step explanation:
The common ratio of a geometric sequence is the division of the term [tex]a_{n+1}[/tex] by the term [tex]a_{n}[/tex].
In this problem, we have that:
[tex]a_{1} = 2, a_{2} = -14, a_{3} = 98, a_{4} = -686[/tex].
So the common ratio r is:
[tex]r = \frac{-14}{2} = \frac{98}{-14} = \frac{-686}{98} = -7[/tex]
The common ratio r is -7.
A researcher sends out a survey to 740 subjects by mail and receives completed surveys from 65% of the subjects. How many surveys did the researcher receive?
You buy a container of cat litter for $11.50 and a bag of cat food for x dollars. The total purchase is $16.80, which includes 5% sales tax. Write and solve an equation to find the cost of the cat food.
let cat food = x
total plus 5% = 105% = 1.05
1.05 * (11.50 + X) = 16.80
12.075 + 1.05x = 16.80
1.05x = 16.80-12.075
1.05x = 4.725
x = 4.725 / 1.05
x= 4.50
the cat food cost $4.50
11.50 +4.50 = 16.00
16.00 * 0.05 = 0.80
16.00 + 0.80 = 16.80
When water freezes, its volume increases by 9.05% (that is, δv/v0 = 9.05 10-2). what force per unit area is water capable of exerting on a container when it freezes? (the bulk modulus of water is 2.2 109 n/m2. enter the magnitude only.)?
Carlos wants to add two more bags of apples to his order. What is the new total?
Answer:
Hi! The answer to this question is 9.10
Step-by-step explanation:
All of the Items added up equals 9.10
Answer:I thought it was 4.34 but its 9.10
Step-by-step explanation:
G verify that the divergence theorem is true for the vector field f on the region
e. f(x, y, z) = z, y, x , e is the solid ball x2 + y2 + z2 ≤ 36
sixty-two percent of pet owners say they consider their pet to be their best friend. you randomly select 12 pet owners and ask them if they consider their pet to be their best friend. find the probability that the number who say their pet is their best friend is (a) exactly nine, (b) at least eight, and (c) at most three.
Ruth sets out to visit her friend ward, who lives 20 mi north and 100 mi east of her. she starts by driving east, but after 70 mi she comes to a detour that takes her 15 mi south before going east again. she then drives east for 8 mi and runs out of gas, so ward flies there in his small plane to get her.
Solution:
Distance between Ruth House and Ruth Friend House =20 Meter north and 100 meter east of Ruth
Now , Ruth Starts Driving,
but after 70 mi she comes to a detour that takes her 15 mi south before going east again. she then drives east for 8 mi and runs out of gas.
The Diagram of Ruth Driving is depicted below.
Now , when ward flies in small plane to get Ruth,
So, Distance between Ruth and Ward , when Ruth is at Point S=SM
In Right Δ SVM, By Using Pythagoras theorem
SM²=SV² + VM²
DT=VS=15 m
VM=100 - (70+8)
= 100 -78
=22 meter
SM²=(15)² + (22)²
= 225 + 484
= 709
[tex]SM=\sqrt{709}=26.62[/tex]
So, Ward has to travel 26.62 miles east north to reach Ruth.
Ryan is a software salesman. His base salary is $2500 , and he makes an additional $90 for every copy of History is Fun he sells. Let P represent his total pay (in dollars), and let N represent the number of copies of History is Fun he sells. Write an equation relating P to N . Then use this equation to find his total pay if he sells 21 copies of History is Fun.
equation:
total pay if 21 copies are sold?
write the algebraic expression for the verbal statement. Let x represent the unknown number. 3 less than twice the sum of a number and 4
The algebraic expression for '3 less than twice the sum of a number and 4' where x is the unknown number is
'2(x + 4) - 3'.
The algebraic expression for the verbal statement "3 less than twice the sum of a number and 4" can be written as follows:
First, let's represent the unknown number by x. The phrase 'the sum of a number and 4' translates to x + 4. 'Twice this sum' means we multiply the expression by 2, resulting in 2(x + 4). Finally, '3 less than' indicates that we need to subtract 3 from this expression. Therefore, the complete algebraic expression is 2(x + 4) - 3.
There are 8 people fishing at Lake Connor: 5 have fishing licenses, and 3 do not. An inspector chooses two of the people at random. What is the probability that the first person chosen has a license and the second one does not? Write your answer as a fraction in simplest form.
Answer:3/28
Step-by-step explanation:
The probability that the first person chosen has a license and the second one does not is 15/56
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur.
Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
Given that, there are 8 people fishing at lake 5 have fishing licenses, and 3 do not. An inspector chooses two of the people at random. we need to find the probability that the first person chosen has a license and the second one does not
Let us consider the possibility of the first person not having a license, which is:
3/7
Now, after a person has been chosen, there will be 7 people remaining. Assuming that the first person chosen did not have a license, there will be 2 people left in the group without a license.
So, the probability of choosing a person without a license the second time will be:
3/7
In probability, when two events occur together (the word "and" is used), multiplication is carried out.
Therefore, we multiply the two probabilities to get:
5/8 x 3/7 = 15/56
Hence, The probability of choosing two people without a license is 15/56
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