Answers
Answer:
5)
The inverse of the function f(x) = x^7 can be found by following these steps:
Step 1: Replace f(x) with y. The equation becomes y = x^7.
Step 2: Interchange x and y in the equation, so it becomes x = y^7.
Step 3: Solve the equation for y by taking the seventh root of both sides. This yields y = x^(1/7).
Therefore, the inverse function of f(x) = x^7 is g(x) = x^(1/7), which maps any given value of x to its seventh root.
It's important to note that the domain and range of the inverse function are the opposite of those of the original function. The domain of the inverse function is all real numbers, while the range is only positive real numbers. The domain of the original function is all real numbers, while the range is also all real numbers.
6)
To find the inverse of the function f(x) = (-2/5)x^3, we can follow these steps:
Step 1: Replace f(x) with y. The equation becomes y = (-2/5)x^3.
Step 2: Solve the equation for x in terms of y.
Multiply both sides by -5/2:
(-5/2) y = x^3
Take the cube root of both sides:
x = [(-5/2) y]^(1/3)
Step 3: Replace x with f^-1(y) to obtain the inverse function.
f^-1(y) = [(-5/2) y]^(1/3)
Therefore, the inverse function of f(x) = (-2/5)x^3 is f^-1(y) = [(-5/2) y]^(1/3).
It is important to note that the domain and range of the inverse function are the opposite of those of the original function. The domain of the inverse function is all real numbers, while the range is also all real numbers. The domain of the original function is all real numbers, while the range is only negative real numbers if x is negative and only positive real numbers if x is positive.
Related Questions
Suppose that the function g is defined, for all real numbers, as follows.
Answers
The graph of the piecewise function is given by the image presented at the end of the answer.
What is a piece-wise function?A piece-wise function is a function that has different definitions, depending on the input of the function.
All the three definitions of the function in this problem are constant, hence the graph will be composed by horizontal lines.
The definitions are given as follows:
y = 2 to the left of x = 0.y = -1 at x = 0.y = -3 to the right of x = 0.More can be learned about piece-wise functions at brainly.com/question/19358926
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HELP PLEASE
at big 5, the percent of sales tax is 6 percent. you want to buy a skateboard that costs 98 dollars. you have 100 dollars to spend. do you have enough money? if you don't, how much more money would you need in order to buy the skateboard.
Answers
You would need an additional $3.88 to buy the skateboard.
To find out if you have enough money to buy the skateboardWe need to calculate the total cost, including sales tax.
The sales tax rate is 6%, so the tax on a skateboard costing $98 would be as follows:
tax = 0.06 x $98 = $5.88
Consequently, the skateboard would have a total cost of:
total cost = $98 + $5.88 = $103.88
Since you have $100 to spend, you do not have enough money to buy the skateboard. You would need:
additional money = $103.88 - $100 = $3.88
Therefore, you would need an additional $3.88 to buy the skateboard.
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Find the perimeter of each figure
Answers
Answer: 53 ft
Step-by-step explanation:
The perimeter of a polygon is the sum of all sides. In this example, the sides are 4 ft, 20 ft, 18 ft, and 11 ft, so the perimeter is
4+20+18+11=53 ft
can some one help me
Caleb is selecting cards from a set of 12 cards numbered 1-2-4-4-5-5-5-5-6-9-10-13.
What is the probability that Caleb selects a 5 on the first selection, returns the card to the deck, shuffles the cards, and then draws a 5 on the second selection?
Answers
The probability of Caleb selecting a 5 on the first selection and then selecting a 5 on the second selection after returning the card to the deck and shuffling is 1/9.
There are a total of 12 cards, out of which 4 are 5s. Since Caleb returns the card to the deck and shuffles it, the selection of the first card does not affect the probability of selecting a 5 on the second selection.
Therefore, the probability of selecting a 5 on the first selection is 4/12 = 1/3, and the probability of selecting a 5 on the second selection is also 4/12 = 1/3.
Since the events are independent, we can multiply the probabilities to find the probability of both events occurring:
P(selecting a 5 on first selection and selecting a 5 on second selection) = P(selecting a 5 on first selection) x P(selecting a 5 on second selection)
= (1/3) x (1/3)
= 1/9
Therefore, the probability that Caleb selects a 5 on the first selection, returns the card to the deck, shuffles the cards, and then draws a 5 on the second selection is 1/9.
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7. The towns of Washington, Franklin, and Springfield are
connected by straight roads. The towns wish to build an
airport to be shared by all of them.
a. Where should they build the airport if they want it to be the same distance from
each town's center? Describe how to find the precise location.
b. Where should they build the airport if they want it to be the same distance from
each of the roads connecting the towns? Describe how to find the precise
location.
They should build the airport at the
They should build the airport at the
n be found by locating the intersection of at least
which can be found by locating the intersection of a
a circumcenter
medians
Answers
b. To build the airport at the same distance from each road connecting the towns, they should locate the intersection of the angle bisectors of the angles formed by the roads at each town. The precise location of the airport will be the point where these angle bisectors intersect. This point will be equidistant from each road connecting the towns.
Alternatively, they could locate the intersection of the medians of the triangle formed by the three towns. The medians are the segments connecting each vertex of the triangle with the midpoint of the opposite side. The precise location of the airport will be the point where these medians intersect, which is also the centroid of the triangle. This point will be equidistant from each of the three towns.
Ilana is training for a half marathon. For the first three days of her training plan, she will need to run 4.125 miles each day. For the next two days she will increase her mileage to 5.675 miles per day. How many miles total did Ilana run during her first training week?
Answers
Ilana ran a total distance of 23.725 miles during her first week of training for a half marathon.
What does distance mean?Distance refers to the amount of space or physical separation between two points or objects. It is a measure of how far apart two objects or points are from each other.
According to the given informationIlana will run 4.125 miles each day for the first three days, which gives a total distance of:
4.125 miles/day × 3 days = 12.375 miles
For the next two days, she will run 5.675 miles per day, which gives a total distance of:
5.675 miles/day × 2 days = 11.35 miles
To find the total distance that Ilana ran during her first training week, we simply add the distances from the first three days and the next two days:
12.375 miles + 11.35 miles = 23.725 miles
Therefore, Ilana ran a total of 23.725 miles during her first week of training.
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A researcher is analyzing bacteria on a door handle after cleaning it with antibacterial disinfectant. Initially there were 15 bacteria, but the researcher noticed that the number of bacteria quadruples every hour,t. Write a function B(t) to represent the number of bacteria t hours after the initial measurement. Write a exponential function
Answers
The exponential function representing the number of bacteria t hours after the initial measurement is B(t) = 15 (4[tex])^t[/tex].
The function B(t) can be represented by an exponential function of the form:
B(t) = a[tex]b^t[/tex]
where 'a' is the initial number of bacteria and 'b' is the growth factor or rate at which the number of bacteria quadruples.
Given that the initial number of bacteria is 15 and the number of bacteria quadruples every hour, we can express 'b' as:
b = 4¹ = 4
Substituting the values of 'a' and 'b' in the general form of exponential function, we get:
B(t) = 15 (4[tex])^t[/tex]
Therefore, the exponential function representing the number of bacteria t hours after the initial measurement is B(t) = 15 (4[tex])^t[/tex].
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Element X decays radioactivity with a half-life in 10 minutes if there are 660 g of element X how long to the nearest 10th of a minute would it take for the element to decay to 58 g
Answers
Step-by-step explanation:
58 g = 660 g * ( 1/2)^n
58 / 660 = (1/2) ^n LOG both sides
-1.056 = n log 1/2
n = 3.508 half lives
3. 508 x 10 min = ~ 35.1 min
[tex]\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\dotfill & 58\\ P=\textit{initial amount}\dotfill &660\\ t=minutes\dotfill &t\\ h=\textit{half-life}\dotfill &10 \end{cases} \\\\\\ 58 = 660\left( \cfrac{1}{2} \right)^{\frac{t}{10}} \implies \cfrac{58}{660}=\left( \cfrac{1}{2} \right)^{\frac{t}{10}}\implies \cfrac{29}{330}=\left( \cfrac{1}{2} \right)^{\frac{1}{10}\cdot t}[/tex]
[tex]\log\left( \cfrac{29}{330} \right)=\log\left[ \left( \cfrac{1}{2} \right)^{\frac{1}{10}\cdot t} \right]\implies \log\left( \cfrac{29}{330} \right)=t\log\left[ \left( \cfrac{1}{2} \right)^{\frac{1}{10}} \right] \\\\\\ \cfrac{ ~~ \log\left( \frac{29}{330} \right) ~~ }{\log\left[ \left( \frac{1}{2} \right)^{\frac{1}{10}} \right]}=t\implies 35.1\approx t[/tex]
Which expression is equivalent to (4.3x + 4)(−1.8x)?
A. −4.14x2 + 0.08x
B. −7.74x2 − 7.2
C. −7.74x2 − 7.2x
D. −7.74x2 + 7.2x
Answers
The expression that is equivalent to (4.3x + 4)(−1.8x) is -7.74x² -7.2x (optionC)
What is equivalent of expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value.
For example, 2a+6 is equivalent to 2(a+3) and will surely have thesame value when a value is substituted for a.
Similar (4.3x + 4)(−1.8x) can be simplified by multiplying -1.8x with both 4.3x and 4
= -7.74x²-7.2x
therefore the equivalent of (4.3x + 4)(−1.8x) is -7.74x²-7.2x.
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ERROR ANALYSIS Describe and correct the error in finding the area of sector XZY when the area of
OZ is 255 square feet.
X
W
Z
X
115°
Let n be the area
of sector XZY.
115
255
n≈ 162.35 ft²
n
360
=
Answers
The wrong formula was used. The correct method is: area of sector = 115/360 * 255 ≈ 81.46 square feet.
How to Find the Area of a Sector?The area of a sector is calculated by using the formula:
Area of sector = ∅/360 * πr², where:
r is the radius of the circle
∅ is the central angle measure.
The error made was that a wrong method/formula was used in finding the area of sector.
Given the following:
Area of circle = 255 square feet (πr²)
∅ = 115°
Note that πr² represents the area of a circle, therefore, substituting the values into the formula, we have:
Area of sector = 115/360 * 255
Area of sector ≈ 81.46 square feet
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Solve the following equation by completing square 15x^2-2ax=a^2
Answers
Answer:
Step-by-step explanation:
Answer: x=a/3 x=a/5
Step-by-step explanation:
15x²-2ax = a² subtract a² from both sides
15x²- 2ax - a² = 0
You would solve this like you would any quadratic. Factor.
Start my multiplying the first and last coefficients
15(-a²) = -15a² =>find 2 numbers that multiply to this but add to middle
term (-2a)
-5a and +3a multiply to -15a² and adds to -2a
Substitute the middle term with the numbers we just found, keeping the x
15x²- 2ax - a² = 0
15x²- 5ax+3ax - a² = 0 > group the first 2 terms and last 2
(15x²- 5ax)(+3ax - a²)= 0 > this is not your factors, you need to take
GCF out of each grouping
5x(3x-a)+a(3x-a)=0 >if the parenthesis is same, you did good
now the parenthesis is your GCF and one of
your factors, whatever is left is your other
factor
(3x-a)(5x-a)=0 > set each factor = 0 and solve for x
(3x-a)=0 and (5x-a)=0
x=a/3 x=a/5
The population of a small town of 29,000 people is expected to grow exponentially at a rate of 1.9% per year. Estimate the population in 2 years' time.
Answers
Answer:
Step-by-step explanation:
A number rounded to the nearest thousand is 47,000 which number could be the number that was rounded
Answers
Answer:
Anything greater than or equal to 46,500, and less than or equal to 47,499 could be the answer.
For example, a number, let's say 46,589 falls within that range and may have been the number that was rounded.
Lines and Angles
10) In the figure below BD is the perpendicular bisector of AC. Find the value of x.
3(2x-8)
4425
Enter your answer in the box.
x=
Answers
The value of x if the line BD is the perpendicular bisector of AC is 11.5
Calculating the value of xFrom the question, we have the following parameters that can be used in our computation:
The figure where the line BD is the perpendicular bisector of AC.
To calculate the value of x, we use the following equation by setting the line segments equal to each other
3(2x - 8) = 45
Divide both sides of the above equation by 3
2x - 8 = 15
So, we have the following equation
2x = 23
Divide both sides of the above equation by 2
x = 11.5
Hence, the calculated value of x is 11.5
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Are low elevation, high precipitation areas close or far from the ocean.
Answers
Answer:
low lying areas
Given the equations of two lines, describe how to determine if the lines are parallel.
Answers
Hi! To determine if two lines are parallel given their equations, follow these steps:
1. Identify the slopes of the lines from their equations.
If the equations are in the slope-intercept form (y = mx + b), the slope is the coefficient of x (m). If the equations are in standard form (Ax + By = C), you can find the slope by rearranging the equation to the slope-intercept form.
2. Compare the slopes of both lines. If the slopes are equal, the lines are parallel.
In summary, given their math equations, you need to describe their slopes and check if they are equal to determine if the lines are parallel.
Hi to confirm that two lines are parallel lines given their equation you the gradient which is the value of x in the equation y=mx + c. Where m is the gradient
Please help will mark Brainly
Answers
The number of tickets day and evening combined should be more then 8 since it says at least 8 tickets. However the cost of the tickets which is 15x+30y (multiply the amount of tickets bought by the cost) should be less then 300 bucks since they have a budget. Hope this helps!
El perímetro de un campo rectangular es 300 m . Si la longitud del campo es 88 , ¿cuál es su anchura?
Answers
Based on the above, the width of the field is 62 meters.
What is the width?Based on the question, Let's say that the width of the field is denoted with 'w'.
Note that the formula for the perimeter (P) of a rectangle is:
P = 2(l + w)
where"
l = length
w = width.
Fixing the values into the equation, it will be:
300 = 2(88 + w)
So, Divide both sides by 2:
150 = 88 + w
Subtract 88 from both sides:
w = 150 - 88
w = 62
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Se text below
The perimeter of a rectangular field is 300 m. If the length of the field is 88 , what is its width?
Factor the polynomial, if possible. Check your answer using foil.
y² + 49
Answers
Answer:
its prime
Step-by-step explanation:
it can not be factored using foil
A vehicle use 2 gallons of gasoline to travel 18 1⁄2 miles. At this rate, how many miles can 2 3 the vehicle travel per gallon of gasoline?
Answers
If a vehicle uses 2 gallons of gasoline to travel 18¹/₂ miles, at this rate, the vehicle can travel 9¹/₄ miles per gallon of gasoline.
What is the rate?The rate refers to the average speed of the vehicle.
The rate also describes the unit rate or the rate expressed as a percentage or in terms of speed.
The number of gallons of gasoline used to travel 18¹/₂ miles = 2 gallons
The total distance traveled using two gallons of gasoline = 18¹/₂ miles
The average distance traveled per gallon of gasoline = 9¹/₄ miles (18¹/₂ ÷ 2)
Thus, on the average, the vehicle can travel 9¹/₄ miles miles per gallon of gasoline.
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Correct Question:A vehicle uses 2 gallons of gasoline to travel 18 1⁄2 miles. At this rate, how many miles can the vehicle travel per gallon of gasoline?
2. You have graduated and landed a good stable job (congratulations!) which requires a commute by car (meh). Your daily drive to work takes about 20 minutes or so with plenty of stoplights and left turns, so it varies day to day. Just out of curiosity you want to find out how long it usually takes to get from home to work, so you accurately time for four weeks. On four of those mornings you stopped for gas or coffee and a bagel or whatever, so you recorded 16 usable results. The mean of these results is 21.4 minutes and the standard deviation is 1.8 minutes. your commute Given these results find a 95% confidence interval for your true average commute time. Assume that these four weeks are a representative sample of your overall commuting experience.
Answers
Therefore , the solution of the given problem of unitary method comes out to be a 95% degree of certainty that the genuine average commute time falls within this range.
An unitary method is defined as what?To complete the work, the well-known straightforward strategy, actual variables, and any essential components from the very first and specialised inquiries can all be utilised. In response, customers might be given another opportunity to sample the product. Otherwise, important advancements in our comprehension of algorithms will be lost.
Here,
We may use the following calculation to determine the 95% confidence interval for the actual average commute time:
=> CI = x' ± t*(s/√n)
Finding the essential t-value is the first step. We can apply a two-tailed t-test with a significance level of = 0.05/2 = 0.025 because we have 16 useable findings (sample size: n = 16) and
we require a 95% confidence interval. The crucial t-value, which we determine using a t-distribution table or calculator, is roughly 2.131.
=> CI = 21.4 ± 2.131*(1.8/√16)
=> 21.4 ± 0.95
The genuine average commute time has a 95% confidence interval of 20.45 to 22.35 minutes.
Based on our sample of 16 travel times, we can thus say with a 95% degree of certainty that the genuine average commute time falls within this range.
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100 POINTS
Question:
Answers
read the paragraph and then you’d have all the information that you need
Answer:
First braclets coast 3$ and necklaces coast 6$ so now in the box you can put 3in the first one then 6 in the next and keep going its like multiples of 3 and 6 :) Hope this helps.
Step-by-step explanation:
what is the sum of 14, 12, 8, and 6
Answers
Answer:
Step-by-step explanation:
14+12 = 26+8 = 34 + 6 is 40
the answer is 40.
Answer:
[tex]2\sqrt{10[/tex]
Step-by-step explanation:
Add all the numbers together on your calculator
a train will travel 300 kilometers at a constant rate. write an equation that represents the trains rate in kilometers per hour (r) based on how mant hours the trip takes (t).
Answers
Answer:
distance = rate x time
where distance is 300 kilometers and time is t hours. Rearranging this formula to solve for rate, we get:
rate = distance / time
Substituting the given values, we get:
r = 300 / t
Therefore, the equation that represents the train's rate in kilometers per hour based on how many hours the trip takes is r = 300/t.
Step-by-step explanation:
During an experiment, 2 mL of solution evaporates from a beaker each minute. After 5 minutes, there are 50.25 ml of the solution remaining. Write an equation in slope-intercept form that represents the amount of solution y in the beaker x minutes after the start of the experiment.
Answers
An equation in slope-intercept form that represents the amount of solution y in the beaker x minutes after the start of the experiment is y = 9.65x + 2.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would find the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (50.25 - 2)/(5 - 0)
Slope (m) = 48.25/5
Slope (m) = 9.65.
At data point (0, 2) and a slope of 9.65, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 2 = 9.65(x - 0)
y = 9.65x + 2
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Find the principal needed now to get the given amount; that is, find the present value.
To get $100 after 3 years at 9% compounded quarterly
The present value of $100 is $
(Round to the nearest cent as needed.)
Answers
The present value of $100 to be received after 3 years at 9% compounded quarterly is $73.67.
The formula for the present value of a future amount under quarterly compounding is:
PV = FV / (1 + r/4)⁴ⁿ
where PV is the present value,
FV is the future value, r is the interest rate per year, and n is the number of years.
In this case, FV = $100, r = 0.09 (9%), n = 3 years, and the interest is compounded quarterly
so the interest rate per quarter is r/4 = 0.0225.
Plugging these values into the formula, we get:
PV = $100 / (1 + 0.0225)¹² = $73.67
Therefore, the present value of $100 to be received after 3 years at 9% compounded quarterly is $73.67.
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Find x. Simplify completely.
X
8
C
17
x = [?] √ [
Enter the number that belongs in the green box.
Enter
Answers
Answer:
17/x = x/8
x^2 = 136, so x = 2√34
Suppose that the function f is defined as follows.
Answers
Answer:
Step-by-step explanation:
Please help discrete math question.
Answers
The number of ways you can tile your walkway if you choose single tiles and double tiles is 3,992,781,803 ways.
How to find the number of ways ?To tile a 1x20 walkway using red, blue, and yellow single tiles (1x1) and green and white double tiles (1x2), we can consider the number of ways to combine the single and double tiles to fill the entire 1x20 space.
The exact number of ways to tile the 1x20 walkway using red, blue, and yellow single tiles and green and white double tiles:
= 3^20 + 3^18 x 2 + 3^16 x 4 + 3^14 x 8 + 3^12 x 16 + 3^10 x 32 + 3^8 x 64 + 3^6 x 128 + 3^4 x 256 + 3^2 x 512 + 1, 024
= 3486784401 + 258280326 + 172186884 + 38263752 + 8503056 + 1889568 + 419904 + 93456 + 20736 + 4608 + 1024
= 3,992,781,803 ways
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Confusing Calculus Parametric Equations Question
Answers
Rounding to the nearest meter, we get that the bullet will hit the ground 18603 meters away from the gun.
what is acceleration?The rate at which an object's velocity varies with respect to time is known as its acceleration. It is a vector quantity whose definition is the product of the velocity change and the time period during which the change takes place. Depending on the direction and size of the velocity change, acceleration may be positive, negative, or zero. Acceleration in physics is frequently represented by the letter "a," and its SI unit is metres per second squared (m/s2).
To find when the bullet will hit the ground, we need to find the time at which y = 0.
y = vo sin(a) t - (1/2)g[tex]t^2[/tex], where g is the acceleration due to gravity (9.8 m/s^2).
Setting y = 0, we get:
0 = vo sin(a) t - (1/2)g[tex]t^2[/tex]
Solving for t using the quadratic formula, we get:
Since we want the time when the bullet hits the ground, we take the positive root:
t = (vo sin(a) + √((vo sin(a))^2 + 2gy)) / g
Plugging in the values given, we get:
t = (550 m/s * sin(a) + √((550 m/s * sin(a))^2 + 2 * 9.8 m/s^2 * 0)) / 9.8 m/s^2
Simplifying, we get:
t = (550 m/s * sin(a)) / 9.8 m/s^2
t = 35.27 seconds (rounded to two decimal places)
To find how far from the gun the bullet will hit the ground, we need to find the value of x at this time:
x = vo cos(a) t
Plugging in the values given, we get:
x = 550 m/s * cos(a) * 35.27 s
x = 18602.57 meters
Rounding to the nearest meter, we get that the bullet will hit the ground 18603 meters away from the gun.
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