Answers
Answer:
x = -9
Step-by-step explanation:
As this is an absolute value function, the line of symmetry is the x-value of the maximum/minimum point. An absolute value function can be denoted as y = |x - h| + k, where (h, k) is the maximum/minimum point. We only need the x-value of the maximum/minimum point, so we only have to look at "h". Now, we can use y = |x - h| + k and turn it into g(x):
y = |x - h| + k
g(x) = |x - -9| + -11 --> this means h = -9, and the line of symmetry is at x = -9
g(x) = |x + 9| - 11
Answer:
I think x equals --9
Related Questions
Examples of geometric transformations can be found throughout the real world. Think about some places where you might use or se transformations. Give at least three examples for each type of transformation. Make use of the Internet, books, magazines, newspapers, and everyday life experiences to come up with your examples.
Answers
Geometric transformations can be found in everyday life, such as moving furniture (translation), opening a door (rotation), using mirrors (reflection), zooming in and out of maps (scaling), skewing images in Photoshop (shearing), and stretching a rubber band (stretching).
Here are some examples of different types of transformations and their applications:
Translation:
Moving furniture in a room
Moving a vehicle on a map
Shifting a picture on a wall
Rotation:
Swinging a pendulum
Turning a key in a lock
Opening a door
Reflection:
Mirrors reflecting images
Water reflections of a landscape
Reflective surfaces on cars and buildings
Scaling:
Enlarging or reducing a picture on a screen
Adjusting the size of a printout
Shearing:
Skewing an image in Photoshop
Tilting a picture frame on a wall
Slanting the roof of a building for better drainage
Stretching:
Stretching a rubber band
Stretching a balloon before inflating it
Stretching a canvas for painting
These are just a few examples of the many ways geometric transformations are used in our everyday lives. By understanding these concepts, we can appreciate the beauty and functionality of the world around us.
To know more about geometric transformations refer here:
https://brainly.com/question/29987040
#SPJ11
In a discussion between Modise and Benjamin about functions, Benjamin said that the diagram below represents a function, but Modise argued that it does not. Who is right? Motivate your answer. x - Input value C 5 8 y-Output value 2 5 1 9
Answers
Answer:
Modise is right.
This diagram does not represent a function because each input value does not correspond to exactly one output value. The input value 5 corresponds to two outputs, 2 and 9.
Choose the correct answer.
Find the quadratic equation given the points (6,0), (-1,0), and (7,4).
h(x) = 1/2(x + 1)(x − 6)
h(x) = 2(x+6)(x − 1)
h(x) = 2(x + 1)(x - 6)
h(x):1/2(x+6) (x - 1)
Answers
The quadratic equation given the points (6,0), (-1,0), and (7,4).
The correct answer is h(x) = 1/2(x + 1)(x - 6).
To find the quadratic equation given the points (6,0), (-1,0), and (7,4), we can use the general form of a quadratic equation, which is [tex]h(x) = ax^2 + bx + c.[/tex]
First, let's substitute the coordinates of the given points into the equation to create a system of equations:
For the point (6,0):
[tex]0 = a(6)^2 + b(6) + c ---- (1)[/tex]
For the point (-1,0):
[tex]0 = a(-1)^2 + b(-1) + c ---- (2)[/tex]
For the point (7,4):
[tex]4 = a(7)^2 + b(7) + c ---- (3)[/tex]
We now have a system of three equations with three unknowns (a, b, c). We can solve this system to find the values of a, b, and c.
Solving the system of equations (1), (2), and (3), we find:
a = 1/2
b = -3/2
c = 0
Thus, the quadratic equation that satisfies the given points is:
h(x) = 1/2(x + 1)(x - 6).
For similar question on quadratic equation.
https://brainly.com/question/30916775
#SPJ11
At an abandoned home, there is a septic tank with a capacity of 5000 ???????????????????????? which was left near full when the homeowner left. Due to deterioration and ground shifting, the tank cracked along the bottom and began leaking on October 10th, 2021. The rate at which the contents spill out over time is modeled by 200???? −.075???? ???????????????????????? ????????y , where ???? is measured in days since the leak began. If left to leak at this rate indefinitely, will the tank empty all of its contents as a result of this crack?
Answers
If left to leak at this rate indefinitely, the tank will not empty all of its contents as a result of this crack, as it would take approximately 853.33 days for the tank to reach zero capacity
To determine whether the tank will empty all of its contents as a result of the crack,
we need to find out how long it will take for the tank to reach zero capacity.
Using the given model, the rate at which the contents spill out over time is 200 - 0.075t,
where t is the number of days since the leak began on October 10th, 2021.
We can set up an equation to find out when the tank will reach zero capacity:
5000 - (200 - 0.075t) = 0
Simplifying this equation, we get:
0.075t = 4800
t = 64000/75
t = 853.33
Therefore, if left to leak at this rate indefinitely, the tank will not empty all of its contents as a result of this crack, as it would take approximately 853.33 days for the tank to reach zero capacity.
To know more about capacity deterioration model:
https://brainly.com/question/28168721
#SPJ11
whats the answer!???????
Answers
3 + v = 2 (2v -1) -----------
Answers
4v-v =-2-3
3v=-5
V=-5 over 3
Next Problem (1 point) Suppose f"(x) = -(sin(x)), f'(0) = 0, and f(0) = -3. - Find f(1/4). f(1/4) = 1
Answers
f(1/4) is approximately equal to -2.9974. The problem states that f"(x) = -(sin(x)), which means that the second derivative of the function f(x) is equal to the negative of the sine of x. We are also given that f'(0) = 0 and f(0) = -3.
To find f(1/4), we need to use the information given to us and apply the process of integration. We know that the first derivative of f(x) is f'(x), so we need to integrate f"(x) to find f'(x). Integrating the negative sine function will give us the cosine function, so:
f'(x) = -cos(x) + C
Where C is a constant of integration. To find the value of C, we use the fact that f'(0) = 0:
0 = -cos(0) + C
C = 1
So now we have:
f'(x) = -cos(x) + 1
Next, we integrate f'(x) to find f(x):
f(x) = -sin(x) + x + D
Where D is another constant of integration. We can find the value of D by using the fact that f(0) = -3:
-3 = -sin(0) + 0 + D
D = -3
So finally, we have:
f(x) = -sin(x) + x - 3
Now we can find f(1/4):
f(1/4) = -sin(1/4) + (1/4) - 3
f(1/4) = -0.2474 + 0.25 - 3
f(1/4) = -2.9974
Therefore, f(1/4) is approximately equal to -2.9974.
Learn more about function here:
brainly.com/question/13514866
#SPJ11
Determine the location and value of the absolute extreme values off on the given interval, if they exist f(x) = 8x^3 / 3 +11x^2 - 6x on (-4,1)
Answers
Answer:
Calculate X at -4,-3 ,1/4 and 1.You can get 4 values.
Respectively.62.33,45,-0.77,4.6
The absolute maximum value is 123.333 at x = -4, and the absolute minimum value is -11.779 at x ≈ -1.135.
How to find bthe location and value of the absolute extreme valuesTo determine the location and value of the absolute extreme values of the function f(x) = (8/3)x³ + 11x² - 6x on the interval (-4, 1), follow these steps:
1. Find the critical points by taking the first derivative and setting it to zero:
f'(x) = (8/3)(3)x² + 11(2)x - 6 f'(x) = 8x² + 22x - 6
2. Solve for x: 8x² + 22x - 6 = 0
Using a quadratic formula or factoring, we get:
x ≈ -1.135 and x ≈ 0.634 3.
Check the endpoints and critical points for absolute extreme values:
f(-4) = (8/3)(-4)³ + 11(-4)² - 6(-4) ≈ 123.333
f(-1.135) ≈ -11.779 f(0.634) ≈ -0.981
f(1) = (8/3)(1)³ + 11(1)² - 6(1) = 5
The absolute maximum value is 123.333 at x = -4, and the absolute minimum value is -11.779 at x ≈ -1.135.
Learn more about absolute extreme value at
https://brainly.com/question/29017602
#SPJ11
Ayo can people who read team katsudon sus mangas rate my favorite ones. Number 1 : life with my cat kacchan. Number 2: whatever my pets say. Rn rate them only if you read then
Answers
The quality of a manga is subjective and it varies from person to person.
Quality of a manga is depending on their interests, preferences, and tastes.
Therefore,If anything favourite of one person that not mean another person also like the thing.
Manga ratings can be found on various online platforms such as MyAnimeList, MangaUpdates and Goodreads.
These all websites have a community of users who rate and review manga based on their own opinions and experiences.
If we want to get a rating for our favorite manga,
We can try posting your question on manga-related forums, social media groups, or other online communities where manga enthusiasts gather.
We can also ask your friends who are into manga to share their thoughts on the series we like.
Learn more about manga here,
https://brainly.com/question/19620744
#SPJ4
Whats the difference between correlation coefficient and determination coefficient?
Answers
Answer: The correlation coefficient (r) and determination coefficient (r²) are both measures of the strength and direction of the linear relationship between two variables in a dataset.
The correlation coefficient (r) is a measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, with -1 indicating a perfect negative correlation, 0 indicating no correlation, and 1 indicating a perfect positive correlation. The correlation coefficient only tells us the strength and direction of the relationship; it does not tell us anything about the proportion of variation in one variable that is explained by the variation in the other variable.
The determination coefficient (r²), also known as the coefficient of determination, is a measure of the proportion of variation in one variable that is explained by the variation in the other variable. It ranges from 0 to 1, with 0 indicating that none of the variation in one variable is explained by the variation in the other variable, and 1 indicating that all of the variation in one variable is explained by the variation in the other variable. The determination coefficient is calculated as the square of the correlation coefficient, so r² always has the same sign as r. A value of r² close to 1 indicates that the relationship between the variables is strong and that a large proportion of the variation in one variable can be explained by the variation in the other variable.
In summary, the correlation coefficient tells us about the strength and direction of the linear relationship between two variables, while the determination coefficient tells us about the proportion of variation in one variable that is explained by the variation in the other variable.
While correlation coefficient measures the strength and direction of the relationship between two variables, determination coefficient measures how much of the variability in one variable can be explained by the other variable.
The correlation coefficient and determination coefficient are two related statistical measures that help us understand the strength and direction of a relationship between two variables. The correlation coefficient (denoted as r) measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, with -1 indicating a strong negative relationship, 1 indicating a strong positive relationship, and 0 suggesting no relationship.
On the other hand, the determination coefficient (represented as R²) quantifies the proportion of variance in the dependent variable that is predictable from the independent variable. It ranges from 0 to 1, with 0 indicating no explanatory power and 1 indicating perfect prediction. R² is simply the square of the correlation coefficient (r²).
In summary, while the correlation coefficient shows the strength and direction of a linear relationship, the determination coefficient indicates the extent to which one variable can predict the other. Both are important in determining the nature of relationships between variables in a data set.
Learn more about determination coefficient here: https://brainly.com/question/17237825
#SPJ11
The mean test score of 12 students is 42. A student joins the class and the mean becomes 43. Find the test score of the student who joined the class
Answers
The test score of the student who joined the class is 55.
To find the test score of the student who joined the class, we can use the formula for calculating the mean:
Mean = (Sum of all values) / (Number of values)
We know that the mean test score of the original 12 students was 42. This means that the sum of their test scores was:
Sum of scores = Mean x Number of students = 42 x 12 = 504
Now, when the new student joins the class, the mean test score becomes 43. This means that the sum of all 13 students' test scores is:
Sum of scores = Mean x Number of students = 43 x 13 = 559
We can subtract the sum of the original 12 students' test scores from the sum of all 13 students' test scores to find the test score of the student who joined the class:
Test score of new student = Sum of all scores - Sum of original scores
Test score of new student = 559 - 504
Test score of new student = 55
Therefore, the test score of the student who joined the class is 55.
To know more about mean refer here:
https://brainly.com/question/31101410?#
SPJ11
Mario had 40 shares of stock that each lost $75 during the half of the year. He also had 24 shares of a different stock that gained $50 each. What was his net change during this time period on these stocks?
Answers
The net change in the stock is $1800
How to calculate the net change ?Mario has 40 shares of stick that each lost $75 during half of the year
He also had 24 shares of a different stock that gained $50
The net change can be calculated as follows
-40 × 75
= -3000
= 24 × 50
= 1200
Net change
-3000 + 1200
= -1800
Hence the net change in the stocks is $1800
Read more on stocks here
https://brainly.com/question/11237105
#SPJ1
Room and board charges for on-campus students at the local college have increased 3.1% each year since 2000. In 2000, students paid $4,291for room and board.
Write a function to model the cost C after t years since 2000.
If the trend continues, how much would a student expect to pay for room and board in 2017? Express your answer as a decimal rounded to the nearest hundredth.
Answers
A student would expect to pay approximately $7,096.47 for room and board in 2017. Rounded to the nearest hundredth, this is $7,096.47 rounded to $7,096.50.
What is Function ?
In mathematics, a function is a rule that assigns each element in a set (the domain) to a unique element in another set (the range). The domain and range can be any sets, but they are typically sets of real numbers.
The cost of room and board after t years since 2000 can be modeled by the equation:
C(t) = 4291[tex](1 + 0.031)^{t}[/tex]
where C(t) is the cost after t years.
To find out how much a student would expect to pay in 2017, we need to plug in t = 17 (since 2017 is 17 years after 2000) into the equation:
C(17) = 4291[tex](1 + 0.031)^{17}[/tex]
≈ 7,096.47
Therefore, a student would expect to pay approximately $7,096.47 for room and board in 2017. Rounded to the nearest hundredth, this is $7,096.47 rounded to $7,096.50.
To learn more about Function from given link.
https://brainly.com/question/29120892
#SPJ1
HELP PLEASE I’m struggling
Answers
A) we can forecast that 15,007 will attend this year's county fair.
B) we can expect approximately 1,001 people to receive a prize.
How did we get the above conclusions?Using the attendance data given, we can find the %increase in attendance from year to year as follows
From year 1 to year 2 - (10,365 - 9,278)/9,278
≈ 0.117 or 11.7%
From year 2 to year 3 - (12,128 - 10,365)/10,365
≈ 0.170 or 17.0%
From year 3 to year 4 - (13,304 - 12,128)/12,128
≈ 0.097 or 9.7%
finding the average of the tree percentages, we have
(11.7% + 17.0% + 9.7%)/3 ≈ 12.8 %
So applying this to the last years attenance we have:
1.129 x 13,304 = 15020.216
Or 15,020 since people cannot be in decimal format.
2)
Since the first 20% of people attending the fair will receive a raffle ticket, we can estimate the number of raffle tickets as follows ....
15,007 ×0.20 = 3, 001.4
Now we can estimate the number of people who will receive a prize by taking one-third of the number of raffle tickets...
3,002 ÷ 3 ≈1 ,000.7
which is approximatly 1001 people.
Learn more about forecasting:
https://brainly.com/question/30167588
#SPJ1
The diagram shows a pyramid with a square base.
The triangular faces are congruent isosceles triangles.
(a) Write down the number of planes of symmetry of this pyramid.
Answers
Answer:
4
Step-by-step explanation:
You can cut it 4 ways to obtain equal parts on both sides. It's along the same as the symmetry of a square.
An animal reserve is home to 8 meerkats. It costs the reserve $1.50 per day to feed each meerkat. Write an equation with two variables that can be used to determine the total cost of feeding the reserve's meerkats for any number of days.
Answers
Answer:
y = 12x
Step-by-step explanation:
First let's find the total cost of feeding all the meerkats per day:
8*1.5 = 12
That means it costs $12 to feed all the meerkats each day. Now we can construct our equation
Let y = cost
Let x = days
y = 12x
This equation tells us the cost for feeding the meerkats an x number of days
Find dy/dx implicitly. X^2e^{-x } + 3y^2 – xy = 0 dy/dx = ?
Answers
To find dy/dx implicitly, we need to differentiate both sides of the equation with respect to x, treating y as a function of x and using the chain rule.
In this problem, we are given the equation X^2e^{-x} + 3y^2 - xy = 0, and we need to find dy/dx. To do this, we first differentiate each term with respect to x, using the product rule for the xy term and the chain rule for the y^2 term. Then we can solve for dy/dx by isolating the derivative term on one side of the equation. Implicit differentiation is a powerful technique used in calculus to find derivatives of functions that are not easily expressed in terms of a single variable. This technique is used extensively in many areas of mathematics, science, and engineering, including optimization, physics, and economics.
For more similar questions on topic Derivatives calculation.
https://brainly.com/question/25324584
#SPJ11
pleasee helppp!!!!!!
Answers
The volume of the cone with a radius of 8cm and height of 15 cm is V = 1005.3 cm³, so the correct option is C.
How to get the volume of the cone?Remember that for a cone of radius R, and height H, the volume is given by the formula below:
V = (1/3)*pi*R²*H
Where pi = 3.1416
In this case, we know that the radius of the cone is 8cm and the height is 15cm, replacing that in the volume formula we will get:
V = (1/3)*3.1416*(8cm)²*15cm = 1,005.3 cm³
Then the correct option is c.
Learn more about cones at:
https://brainly.com/question/6613758
#SPJ1
A farmer of a large apple orchard would like to estimate the true mean number of suitable apples produced per tree. He selects a random sample of 40 trees from his large orchard and determines with 95% confidence that the true mean number of suitable apples produced per tree is between 375 and 520. Which of these statements is a correct interpretation of the confidence level?
Answers
The correct interpretation of the 95% confidence level is that if we were to repeat this sampling process multiple times and construct confidence intervals in the same way, about 95% of the intervals would contain the true mean number of suitable apples produced per tree.
In other words, we are 95% confident that the true mean number of suitable apples produced per tree is between 375 and 520 based on this particular sample of 40 trees. However, we cannot say with certainty that the true mean falls within this interval, nor can we say that it falls outside of this interval with 95% confidence.
It's important to note that the confidence level refers to the long-run behavior of the method of constructing confidence intervals, rather than the probability that the true mean falls within the specific interval calculated from this one sample.
Learn more about confidence level at https://brainly.com/question/23229423
#SPJ11
Auto Loans ~ George works for a credit union that serves a large, urban area. For his annual report, he wants to estimate the mean interest rate for 60-month fixed-rate auto loans at lending institutions (banks, credit unions, auto dealers, etc. ) in his area. George selects a random sample of 12 lending institutions and obtains the following rates:
Answers
The estimated mean interest rate for 60-month fixed-rate auto loans at lending institutions in the urban area is 3.59% (the calculated mean from the given data).
To calculate the estimated mean interest rate, we need to find the average of the interest rates provided by the 12 lending institutions. The given data is as follows:
3.25%, 3.50%, 3.75%, 3.25%, 3.80%, 3.90%, 3.95%, 3.75%, 3.40%, 3.50%, 3.60%, 3.65%
The mean is calculated by adding up all the interest rates and then dividing by the total number of rates. Therefore,
Mean = (3.25 + 3.50 + 3.75 + 3.25 + 3.80 + 3.90 + 3.95 + 3.75 + 3.40 + 3.50 + 3.60 + 3.65)/12
Mean = 3.59%
Hence, the estimated mean interest rate for 60-month fixed-rate auto loans at lending institutions in the urban area is 3.59%.
For more questions like Interest click the link below:
https://brainly.com/question/13324776
#SPJ11
A rectangular square prism cage with a side that measures 10 inches will hold 5 basketballs. The height of the basketballs, when stacked on top of each other, measures 48 3/4 inches. (a) What is the volume of the cage?
Answers
The volume of the rectangular square prism cage is 12,000 cubic inches.
Let the dimensions of the rectangular square prism cage be l x w x h, where l = w = 10 inches (since it's a square prism), and h is the height of the basketballs when stacked on top of each other. We can find the value of h using the given information as follows:
h = 5 basketballs x 48 3/4 inches/basketball = 243 3/4 inches
Therefore, the volume of the cage can be calculated as:
Volume = l x w x h = 10 in x 10 in x 243 3/4 in = 12,000 cubic inches.
Hence, the volume of the cage is 12,000 cubic inches.
For more questions like Volume click the link below:
https://brainly.com/question/1578538
#SPJ11
find the area of a triangle point
Answers
To find the area of a triangle , you'll need to use the
following formula: A = 12 b h A is the area, b is the
base of the triangle (usually the bottom side), and h is the height (a straight perpendicular line drawn from the base to the highest point of the triangle).
Harvey won some money on a
scratch-and-win ticket. Then, he won a
$2 bonus. When he arrived at the counter,
he noticed that he had also won a "triple
your winnings" ticket. As Harvey was
cashing in his prize, the cashier told him
he was the 100th customer, so his total
winnings were automatically doubled. Write two algebraic expressions to
describe Harvey’s winnings
Answers
First algebraic expression: x + 2. Second algebraic expression: 6x + 12.
We can represent Harvey's winnings using algebraic expressions.
Let's use the variable 'x' to represent the amount Harvey won on the scratch-and-win ticket. Harvey then won a $2 bonus, so we add 2 to 'x':
1) x + 2
Next, Harvey won a "triple your winnings" ticket, so we need to multiply the current winnings by 3:
2) 3(x + 2)
Finally, as the 100th customer, Harvey's total winnings were doubled:
3) 2 * 3(x + 2)
So, the two algebraic expressions to describe Harvey's winnings are:
1) x + 2 (initial winnings with the $2 bonus)
2) 2 * 3(x + 2) (total winnings after tripling and doubling)
Know more about algebraic here:
https://brainly.com/question/4344214
#SPJ11
In two or more complete sentences, describe the transformation(s) that take place on the parent function F=f(x)=log(x) to achieve the graph of g(x)=log(-3x-6)-2
Answers
The transformations that take place on the parent function F=f(x)=log(x) to achieve the graph of g(x)=log(-3x-6)-2 are horizontal compression and vertical shift.
What transformations took place in the function?The transformations are a horizontal compression and a vertical shift.
Horizontal compression: The factor of 3 in the argument of the logarithm function causes a horizontal compression by a factor of 1/3. This means that the graph of g(x) is narrower than the graph of f(x) and it is shifted to the left.Vertical shift: The constant term of -2 is subtracted from the logarithm function, causing a vertical shift downwards by 2 units.Therefore, the transformations can be expressed mathematically as follows:
g(x) = log(-3x - 6) - 2
= log(-3(x + 2)) - 2
= log(1/3)log(-3(x + 2)) - 2
Therefore, the transformations are a horizontal compression by a factor of 1/3 and a vertical shift downwards by 2 units.
Learn more about transformations at brainly.com/question/29788009
#SPJ1
Cassie wants to buy a shirt for $15. 75 and some shoes for $10. 25. If the sales tax is 8. 25%, what is the TOTAL amount Cassie will pay?
Answers
The sales tax is 8.25% of the total cost of the shirt and shoes, so we need to add this to the cost of the items:
Cost of shirt = $15.75
Cost of shoes = $10.25
Total cost before tax = $15.75 + $10.25 = $26.00
Sales tax = 8.25% of $26.00 = 0.0825 x $26.00 = $2.15
Therefore, the TOTAL amount Cassie will pay is:
Total cost after tax = $26.00 + $2.15 = $28.15
So, Cassie will pay $28.15 in total.
To know more about sales tax refer here
https://brainly.com/question/29442509#
#SPJ11
Your friends, Fernando and Amelia, each own a video game designer company. They both want you to join their company. You currently have a part-time job making $8. 00 per hour. Fernando offers to pay you $15 per hour for the first month and then increase your hourly rate by $1. 00 each month. Amelia says she will start your pay at $8. 00 per hour but she will increase your hourly rate by 10% each month. In order to make the best decision, you decide to use the mathematics to choose the best offer based on the best hourly wage per month.
Write the equations to represent Fernando’s job offer and Amelia’s job offer. Let x = number of months, y = hourly wage.
Under what time period would you accept Fernando’s offer? Use mathematics to support your reasoning.
Under what time period would you prefer Amelia’s offer? Use mathematics to support your reasoning.
Now that we have looked at the different figures for Fernando and Amelia, which job would you take for the long run? Use mathematics to justify your answer
Answers
Answer:
The equation to represent Fernando's job offer is:
y = 15 + x
Where y is the hourly wage and x is the number of months worked.
The equation to represent Amelia's job offer is:
y = 8(1 + 0.1)^x
Where y is the hourly wage and x is the number of months worked.
To determine the time period for which Fernando's offer is better, we need to find the point where his hourly wage is greater than Amelia's. We can set the two equations equal to each other and solve for x:
15 + x = 8(1 + 0.1)^x
15 + x = 8(1.1)^x
x ≈ 20.44
Therefore, Fernando's offer is better for any time period greater than 20.44 months.
To determine the time period for which Amelia's offer is better, we need to find the point where her hourly wage is greater than Fernando's. We can set the two equations equal to each other and solve for x:
8(1 + 0.1)^x = 15 + x
8(1.1)^x = 15 + x
x ≈ 14.45
Therefore, Amelia's offer is better for any time period less than 14.45 months.
For the long run, we need to determine which offer has a higher hourly wage after a certain number of months. We can compare the two equations by finding their limits as x approaches infinity:
lim (y = 15 + x) as x → ∞ = ∞
lim (y = 8(1 + 0.1)^x) as x → ∞ = ∞
Therefore, both offers have the same long-term hourly wage of infinity. However, Fernando's offer has a faster rate of increase, so it may be more beneficial in the long run.
To know more about hourly wage refer here
https://brainly.com/question/1582269#
#SPJ11
Sara reduced the time it takes her to run a mile from 12 minutes to 8 minutes. Which is closest to Sara's
percent decrease in the time it takes her to run a mile?
A. 14%
B. 25%
C. 33%
D. 75%
Answers
The closest answer is C. 33%.
We can use the percent decrease formula to calculate Sara's percent decrease in the time it takes her to run a mile:
percent decrease = [(original value - new value) / original value] x 100%
In this case, Sara's original time was 12 minutes and her new time is 8 minutes, so we have:
percent decrease = [(12 - 8) / 12] x 100%
percent decrease = (4 / 12) x 100%
percent decrease = 0.33 x 100%
percent decrease = 33%
Therefore, the closest answer is C. 33%.
To know more about percent decrease refer here:
https://brainly.com/question/12930236
#SPJ11
please help asap!!, the image is attached, 30 points !!
Answers
I need help. Assume the base is 2
Answers
a = 5
b = 4
c= 0
Therefore, the equation for graph C is Y = a ^b + c
Y = 5 ^4 + 0
What is a graph?A graph is described as a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.
Graphs are a popular tool for graphically illuminating data relationships.
A graph serves the purpose of presenting data that are either too numerous or complex to be properly described in the text while taking up less room.
Learn more about graphs at: https://brainly.com/question/25184007
#PJ1
Determine an equation for an exponential that model this data set in form p=a(b)^t justify both your values of a and b round b to the nearest hundredth
Answers
The equation for an exponential that models this data set is: p = 10(2)^t
To determine an equation for an exponential that models the given data set in the form p = a(b)^t, we first need to identify the values of a and b. To do this, we can use two points from the data set and solve for a and b. Let's choose the points (0, 10) and (2, 40):
When t = 0, p = 10: 10 = a(b)^0 = a
When t = 2, p = 40: 40 = a(b)²
Dividing the second equation by the first, we get:
4 = (b)²
Taking the square root of both sides, we get:
b = 2
Now that we have the value of b, we can use one of the original equations to solve for a:
10 = a(2)^0 = a
So, a = 10.
Therefore, the equation for an exponential that models this data set is:
p = 10(2)^t
We can check this equation by plugging in the other data points and verifying that they satisfy the equation. And rounding b to the nearest hundredth gives us b = 2.00.
More on exponentials: https://brainly.com/question/28916668
#SPJ11
