The function notation formula is given as g(x) = f(x/2)
Function notation explained.
Function notation is a way of representing a mathematical function using symbols and variables. It is a shorthand way of writing the rule or formula for a function, which specifies how the input values (usually denoted by x) are transformed into output values (usually denoted by y or f(x)).
In function notation, a function is typically represented by a letter (usually f, g, or h) followed by parentheses that enclose the input value or variable, such as f(x), g(t), or h(y). This notation indicates that the function takes an input value (x, t, or y) and produces a corresponding output value (f(x), g(t), or h(y)).
Assuming we want to horizontally stretch the graph of f(x) by a factor of 2 to obtain the graph of g(x), the function notation for g(x) can be written as:
g(x) = f(x/2)
In other words, we plug in x/2 instead of x in the formula for f(x) to get the corresponding value of g(x) that is horizontally stretched by a factor of 2. This is because when we substitute x/2 in f(x), it effectively multiplies the input (x) by 2, which horizontally stretches the graph by a factor of 2.
Learn more about function notation below.
https://brainly.com/question/27915724
#SPJ1
What is the value of x in the figure?
Enter your answer in the box.
50 points HELP me please
Answer:
4-2(16x+8)^1/3=-8
-2(16x+8)^1/3=-12
(16x+8)^1/3=6
16x+8=216
16x=208
x=13
Checking if x=13 is an extraneous solution:
4-2[16(13)+8]^1/3=-8
4-2(208+8]^1/3=-8
4-2(216)^1/3=-8
4-2(6)=-8
4-12=-8
-8=-8
Not an extraneous solution.
A taxi ride costs $1.25 plus 50 cents for each mile, and 30 cents for each minute for waiting time. How much does a 6 mile ride costs if 2.5 minutes are spent eating at stoplights?
Answer: $5.00
Step-by-step explanation:
The cost of a 6-mile ride is made up of three components: a base fare of $1.25, a distance charge of 50 cents per mile, and a waiting charge of 30 cents per minute for the time spent eating at stoplights.
The distance charge for a 6-mile ride is:
6 miles x $0.50/mile = $3.00
The waiting charge for 2.5 minutes at 30 cents per minute is:
2.5 minutes x $0.30/minute = $0.75
So the total cost of the ride is:
$1.25 (base fare) + $3.00 (distance charge) + $0.75 (waiting charge) = $5.00
Therefore, a 6-mile taxi ride with 2.5 minutes of waiting time at stoplights costs $5.00.
At a recent football game of 8,450 in attendance, 150 people were asked what they prefer on a hot dog. The results are shown.
Ketchup Relish Chili
54 36 60
Based on the data in this sample, how many of the people in attendance would prefer relish on a hot dog?
4,479
3,380
2,028
2,016
Answer: Out of the 150 people surveyed, 36 preferred relish on a hot dog.
To estimate how many people in attendance would prefer relish on a hot dog, we can use the proportion of people in the sample who preferred relish:
36/150 = x/8,450
Solving for x, we get:
x = (36/150) * 8,450 = 2,028
Therefore, an estimated 2,028 people in attendance would prefer relish on a hot dog.
The answer is option C: 2,028.
Step-by-step explanation:
The contents of a tin choclates weigh 6500 grams. The choclates are divided up into packets of 250 grams. How many packets are there?
What is your yearly median income if you are a male with an associate’s degree?
(Other question has been asked.)
The male with an associate degree has a yearly median income of $36,432.
What is median income?The median income means an income amount that divides a population into two equal groups, half having an income above that amount, and half having an income below that amount
The weekly income of a male with an associate degree is $759. We have 4 weeks in a month, and 12 months in a year. So, the yearly median income is:
= 4 *12 * $759
= $36,432
Therefore, the male with an associate degree has a yearly median income of $36,432.
Read more about median income
brainly.com/question/16488054
#SPJ1
Write down the power set of {9,11}
Answer:
(9), (11), ( ) and (9,11) is your correct answer.
The sales force at a certain company successfully closed 92 out of 200 sales calls. What was their percent success rate?
if we take 200(origin amount) as the 100%, what's 92 off of it in percentage?
[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} 200 & 100\\ 92& x \end{array} \implies \cfrac{200}{92}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 50 }{ 23 } ~~=~~ \cfrac{ 100 }{ x }\implies 50x=2300\implies x=\cfrac{2300}{50}\implies x=46[/tex]
Find the sum of the first 19 terms of the arithmetic sequence 2, 3, 4, 5, ...
The sum of the first 19 terms of the arithmetic sequence 2, 3, 4, 5, ... is 209.
To find the sum of the first 19 terms of the arithmetic sequence 2, 3, 4, 5, ..., we need to use the formula for the sum of an arithmetic sequence:
Sₙ = n/2 (a₁ + aₙ)
where Sₙ is the sum of the first n terms of the sequence, a₁ is the first term of the sequence, aₙ is the nth term of the sequence, and n is the number of terms we want to sum.
In this case, a₁ = 2 (the first term of the sequence), aₙ = 2 + (n - 1) = n + 1 (the nth term of the sequence), and n = 19 (we want to sum the first 19 terms of the sequence).
Therefore, we can plug these values into the formula and get:
S₁₉ = 19/2 ˣ (2 + 19 + 1)
= 19/2 ˣ 22
= 209
So the sum of the first 19 terms of the arithmetic sequence 2, 3, 4, 5, ... is 209.
To know more about sum visit:
https://brainly.com/question/13013054?
#SPJ1
$195,000 25/7 balloon 7.2% annual rate Monthly Payment: $1,403.20 Balloon Payment: $170,644.33 What is the total cost of this balloon mortgage? (4 points) $179,287.28 $420,960.00 $288,513.13 $172,047.53
The total cost of this balloon mortgage is $288,513.13.
What is a mortgage?
When you and a lender enter into a mortgage, the lender is granted the power to seize your property if you are unable to pay back the loan amount plus interest. To purchase a property or borrow money against the value of a home you currently own, you can use a mortgage loan.
Here, we have
Given: $195,000 25/7 balloon 7.2% annual rate Monthly Payment: $1,403.20 Balloon Payment: $170,644.33
We have to find the total cost of this balloon mortgage.
Monthly payment = 1403.20 which happens for 7 years (7*12 Months)
The total monthly payment for 7 years = 1403.20*7*12 = 117,868.80
Ballon payment =170,644.33 (Given)
Total cost of the balloon payment = 117,868.80 + 170,644.33 = 288,513.13
Hence, the total cost of this balloon mortgage is $288,513.13.
To learn more about the mortgage the given link
https://brainly.com/question/28472132
#SPJ1
How many modes are in the data set?
1.50, 1.70, 2.30, 2.30, 1.70, 2.00, 1.50, 1.50, 1.70, 2.00, 2.00
0
1
2
3
1. Add the following three vectors to find the resultant vector, XR:
X1 (-2,0)m, X2= (0,-5,)m, x3 = (3,0)m
We must add the relevant components of each of the three vectors, X1, X2, and X3, in order to resultant vector the final vector XR, which has the components (1, -5)m.
How can a resultant vector be located?R = A + B. Equation 2 To create the resultant vector, opposing vectors are subtracted from one another. R is the resulting vector in this case, and the column B is directed in the opposite direction to a vector A.
We must add the relevant components of each of the three vectors, X1, X2, and X3, in order to resultant vector the final vector XR, which has the components (1, -5)m.
To find the resultant vector, we need to add the corresponding components of the three given vectors. So, we have:
XR = X1 + X2 + X3
XR = (-2,0) m + (0,-5) m + (3,0) m
XR = (-2+0+3, 0+(-5)+0) m
XR = (1, -5) m
Therefore, the resultant vector XR is (1, -5) meters.
To know more about resultant vector visit:
brainly.com/question/20426452
#SPJ1
Complete question -
Add the following three vectors to find the resultant vector, XR:
X1 = (-2,0)m, X2= (0,-5,)m, x3 = (3,0)m
Height (m)
1000
800
600-
400
200
0
3
4
h=f(t)
6
Time (min)
8 9 10
(a) State the vertical intercept and clearly explain what this means, in the context of this
The vertical intercept in this context refers to the height at which the object is positioned when time is equal to zero.
Based on the information,, we can see that the vertical intercept is at a height of 1000 meters.
What is the intercept about?In terms of the context, this means that at the beginning of the experiment or measurement, the object was positioned at a height of 1000 meters above the ground.
This could represent the initial position of an object that is being dropped or launched from a certain height, or the starting altitude of an aircraft or spacecraft.
In this case, the vertical intercept in this context refers to the height at which the object is positioned when time is equal to zero.
Learn more about intercept on;
https://brainly.com/question/29155562
#SPJ1
How can plot and character development help you predict a novel’s theme?
by leading you to believe that the story is about one thing when it’s about something else
by creating empathy for the characters and the situations they are facing
by hinting at ideas about what the conflict is and how the main characters are likely to deal with it
by helping you understand where the story is set and why the characters behave the way they do
Plot and character development can help you predict a novel’s theme by hinting at ideas about what the conflict is and how the main characters are likely to deal with it.
What is plot?
The sequence of events in a book, movie, or other narrative where each event has an influence on the subsequent one in accordance with the law of cause and effect is known as the plot. The causal events of a narrative can be conceived of as a collection of occurrences linked together by the connector "and so." Plots can be simple—like in a traditional ballad—or complicated and intertwined, with each element occasionally referred to as a subplot or imbroglio.
To learn more about plot from the given link
https://brainly.com/question/1345709
#SPJ1
The casino manager anticipates that, during the next week, 25000 bets of the same type ($1 bet on red color) will be placed at all the (American) roulette tables. Assume independence for the corresponding roulette spins, and that the Central Limit Theorem provides an accurate approximation to the distribution of the casino’s total profit from the 25000 bets. What is the probability that the casino’s total profit will exceed $1000?
The probability that the casino's total profit will exceed $1000 is very close to zero.
What is the probability that the casino’s total profit will exceed $1000?The probability of winning a bet on red in American roulette is 18/38, and the probability of losing is 20/38.
Therefore, the expected profit for the casino on each bet is:
E(profit per bet) = (18/38) x ($1) + (20/38) x (-$1) = -$0.0526
The variance of the profit per bet can be calculated as follows:
Var(profit per bet) = (18/38) x ($1 - (-$0.0526))^2 + (20/38) x (-$1 - (-$0.0526))^2 = $0.921
The standard deviation of the profit per bet is the square root of the variance, which is approximately $0.960.
The expected profit for the casino from 25000 bets is:
E(total profit) = 25000 x (-$0.0526) = -$1315
The standard deviation of the total profit is the square root of the variance multiplied by the number of bets, which is approximately $305.46.
To find the probability that the casino's total profit will exceed $1000, we can standardize the distribution of the total profit as follows:
z = (1000 - (-$1315)) / $305.46 = 9.48
Using a standard normal table or calculator, we can find that the probability of a standard normal variable exceeding 9.48 is essentially zero.
Learn more about probability here: https://brainly.com/question/24756209
#SPJ1
I need help on this one too
Supplementary angles are a pair of angles that add up to 180 degrees. In other words, if you have two angles that are supplementary, the sum of their measures is 180 degrees.
What are supplementary angles?Supplementary angles can be adjacent or non-adjacent. Adjacent supplementary angles are two angles that share a common vertex and side, but whose non-shared sides form a straight line. Non-adjacent supplementary angles are two angles that are not next to each other, but whose sum is equal to 180 degrees.
Given that x + y = 180
If y = 56 degrees
x = 180 - 56
x = 124
Learn more about supplementary angles:https://brainly.com/question/13045673
#SPJ1
What are the coordinates of the point on
the directed line segment from (1, 2) to
(8,9) that partitions the segment into a
ratio of 6 to 1?
Answer:
Step-by-step explanation:
=√((x2 – x1)² + (y2 – y1)²)
=√((8 – 1)² + (9 – 2)²)
=√((7)² + (7)²)
=√(49 + 49)
=√(2 • 49)
=7√2
Divide the line segment into 7 parts equally:
=(7√2)/7
=1√2
Multiply to 6 and 1 to get 6:1 ratio:
= 6(1√2)
= 6√2
Final Answer: 6√2 and √2.
A ballet class has 40 dancers. If I collect all of the dancer's heights, is it a census or sample?
Answer:
Census
Step-by-step explanation:
It's a census because it provides meaningful information to the person who is collecting it. The meaningful information being the height
Answer:
Census
Step-by-step explanation:
The other guy already said it.
Suppose we want to choose 6 objects without replacement from 14 distinct objects
If we want to choose 6 objects out of 14 objects and the order does not matter, then the number of ways we can do this is 3003.
How to calculate the number of ways the objects can be selected?The number of ways you can select or organize objects is defined by formulas of permutation and combination. Choosing one or the other depends on whether the order matters (permutation) or not (combination). In this case, as the order does not matter, the general formula is:
C = n! / r! (n-r)!
In this formula, n is the total of items and r is the total I need to select. Let's then solve it:
C= 14! / 6! (14! - 6!)
C = 14! / 6! 8!
C= 14 x 13 x 12 x 11 x 10 x 9 / 6 x 5 x 4 x 3 x 2
C= 7 x 13 x 11 x 3
C= 3003
Note: This question is incomplete; here is the missing section;
How many ways can this be done, if the order of the choices does not matter?
Learn more about combinations in https://brainly.com/question/19692242
#SPJ1
Assuming all parabolas are of the form y = ax² + bx + c, drag and drop the graphs to match the appropriate a-value (if necessary).
A -4
a = 4
a = -1
Answer:a=4
Step-by-step explanation:
Alan found the distance between point A(-8, -4) and point B(3, -4). His worn is shown below. -8 to the y-axis=8 units. 3 to the y-axis=3 units. |-8| - |3| = 5 units from A to B. What error did Alan make? What is the actual distance from point A to point B?
Answer:
Step-by-step explanation:
Alan made an error in assuming that the distance between -8 and 3 on the x-axis is the same as the distance between -8 and the y-axis, and between 3 and the y-axis. This is not necessarily true, as the distance between two points on a coordinate plane is given by the Pythagorean theorem:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, we can find the actual distance between points A and B:
distance = sqrt((3 - (-8))^2 + (-4 - (-4))^2)
distance = sqrt(11^2 + 0^2)
distance = sqrt(121)
distance = 11
So the actual distance between points A and B is 11 units.
Therefore, Alan's error was assuming that the distance between A and B is simply the difference in the x-coordinates, which is not the case.
Standard Deviation. Find the Standard Deviation of the following set of data. You must fill out the table and show the ending calculations in order to get full credit here.
7.2, 8.9, 2.7, 11.6, 5.8, 10.2
A. 51.75
B. 2.93
C. 8.62
D. 7.73
show all steps
Answer:
Option B
Step-by-step explanation:
To find the standard deviation, we need to follow these steps:
1) Find the mean of the data set.
2) Calculate the difference between each data point and the mean.
3) Square each difference.
4) Find the average of the squared differences.
5) Take the square root of the average to get the standard deviation.
First, we find the mean of the data set:
Mean = (7.2 + 8.9 + 2.7 + 11.6 + 5.8 + 10.2) / 6 = 46.4 / 6 = 7.73
Next, we calculate the difference between each data point and the mean:
| 7.2 - 7.73 | = 0.53
| 8.9 - 7.73 | = 1.17
| 2.7 - 7.73 | = 5.03
| 11.6 - 7.73 | = 3.87
| 5.8 - 7.73 | = 1.93
| 10.2 - 7.73 | = 2.47
Then, we square each difference:
0.53^2 = 0.2809
1.17^2 = 1.3689
5.03^2 = 25.3009
3.87^2 = 14.9569
1.93^2 = 3.7249
2.47^2 = 6.1009
Next, we find the average of the squared differences:
(0.2809 + 1.3689 + 25.3009 + 14.9569 + 3.7249 + 6.1009) / 6 = 8.62
Finally, we take the square root of the average to get the standard deviation:
sqrt(8.62) = 2.93
Therefore, the standard deviation of the data set is 2.93, which is option B.
Which expression is equivalent to 6(4w+7)?
Kara and Michael both spent 1 hour and 20 minutes doing their homework. Kara spent 1 of the time on her math homework. Michael spent ! of the time on his math homework. Write a sentence comparing the amount of time that Kara and Michael spent on math homework. Explain how you know.
I will give 40 points to who answer nicely
Answer:
if you have to compare then 1/2=2/4 which means 1/4 is half of 1/22/3 of a class are girls. What is the ratio girls to boys in the class? What is the ratio boys to girls in the class?
Answer:
If a class has 2/3 girls.
Lets ask ourselves, what does this mean?
It means that 2/3 of the class are girls and therefore 1/3 of the class are boys. I.e. for every 2 girls in the class there is 1 boy in the class.
Therefore the ratio of girls to boys is
2 : 1
Are the terms 2x and -5x like or unlike terms?
Answer:
The terms 2x and -5x are like terms.
Step-by-step explanation:
Like terms are terms that have the same variable(s) raised to the same power(s). In this case, both 2x and -5x have the same variable "x" raised to the same power "1". The only difference between them is the coefficient, which is 2 for 2x and -5 for -5x. However, the coefficients do not affect whether two terms are like or unlike terms.
So, because 2x and -5x have the same variable raised to the same power, they are like terms.
Emanuel eats three eggs each day for breakfast during the month of November. How many eggs in total does he eat in November?
Answer:
90
Step-by-step explanation:
There are 30 days in November, so 3 x 30 = 90.
There is a 20% chance that a particular volcano will erupt during any given decade. A random number generator generated 10 sets of random numbers from 1 to 5 as shown. The number 1 represents the volcano erupting. Find the experimental probability that the volcano will erupt in 1 or 2 of the next 5 decades
A rough estimate of the actual probability is [tex]0.43[/tex], or [tex]43[/tex]%.
What is the probability synthesis?When compared to a collection of possible occurrences that do not occur, probability may be thought of as a numerical indicator of how likely it is that an event will occur. All potential outcomes must be known as a set.
What makes probability significant?Information about the possibility that a certain thing will happen is provided by probability. For instance, meteorologists utilise weather patterns to forecast the likelihood of rain. Probability theory is utilised in epidemiology to comprehend the connection between exposures as well as the risk of health outcomes.
In three of the seven experiments, the volcano erupted once or twice throughout the course of the next half century (trial 1, 3, and 7).
Trial 1: 1 eruption
Trial 2: 0 eruptions
Trial 3: 1 eruption
Trial 4: 0 eruptions
Trial 5: 0 eruptions
Trial 6: 0 eruptions
Trial 7: 2 eruptions
Therefore, the experimental probability that the volcano will erupt in [tex]1[/tex] or [tex]2[/tex] of the next [tex]5[/tex] decades is:
experimental probability [tex]=[/tex] number of successful trials / total number of trials
experimental probability [tex]= 3 / 7[/tex]
experimental probability [tex]= 0.4286[/tex]
So the experimental probability is approximately [tex]0.43[/tex] or [tex]43[/tex]%.
To know more about probability visit:
https://brainly.com/question/11234923
#SPJ1
Identify the function family to which g belongs.
G(x)=-x3
The cubic function family includes the function G(x).
A collection of functions known as the cubic function family may be written as [tex]f(x) = ax3 + bx2 + cx + d,[/tex] where a, b, c, and d are constants. Cubic functions can have one, two, or three real roots because of their odd degree (3). Real-world phenomena like population growth and decline are frequently modelled using these functions. The coefficient of x3 in the following function [tex]G(x) = -x3 is -1,[/tex] which is a constant. This function belongs to the family of cubic functions since it may be written in the typical form of a cubic function. As a result, G(x) has a single real root and is a cubic function.
learn more about functions here:
https://brainly.com/question/12431044
#SPJ11
1.2.5 Quiz: Solving Problems by Dividing Fractions
Question 2 of 5
It takes Saraday to make a birdhouse. How much of the
birdhouse will be built after day?
As It takes Sara 1/2 day to make a birdhouse, the number of birdhouse which will be built after 2/5 day is 4/5 of a birdhouse.
How many birdhouse will be built after 2/5 day?Since it takes Sara 1/2 day to make a birdhouse, we can say that she can make 2 birdhouses in one day.
So, after 1/2 day, Sara will complete 1 birdhouse.
Now, let's see how much of the birdhouse Sara can build after 2/5 day:
2/5 day is equivalent to (2/5) x (1/2) = 1/5 day.
Since Sara can build 1 birdhouse in 1/2 day, she can build 1/2 of a birdhouse in 1/4 day (half of 1/2 day).
Therefore, in 1/5 day, she can build:
= (1/5) / (1/4)
= (1/5) x (4/1)
= 4/5 of a birdhouse.
Full question "It takes Sara 1/2 day to make a birdhouse. How much of the birdhouse will be built after 2/5 day"
Read more about birdhouse
brainly.com/question/10497596
#SPJ1