The value of (f o g)(3) using composite function is 35
What is composite function?Composite function refers to the combining of functions in a manner where the output from one function becomes the input for the next function.
To calculate the composite function (f o g)(3), we use the techniques below.
From the question,
Given:
f(x) = 3x-1g(x) = x²+3Note that,
(f o g)(3) = f(g)(3)Step 1: Find g(3)
To find g(3) we suebtitute the value of x in g(x) by 3Therefore,
g(3) = 3²+3g(3) = 12Step 2: To find f(g)(3), we subetitute the value of x in f(x) by 12
f(g)(3) = 3(12)-1 f(g)(3) = 36-1f(g)(3) = 35Hence, (f o g)(3) is 35
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What is the distance between the points (-2,1) and (5,-4)
Considering the definition of distance between two points, the distance between the points (-2,1) and (5,-4) is √74= 8.6023.
Distance between two pointsThe distance between two points is equal to the length of the segment that joins them. Therefore, to determine the distance between two different points, you must calculate the squares of the differences between their coordinates and then find the root of the sum of said squares.
In other words, the distance between two points in space is the magnitude of the vector formed by said points.
So, given the coordinates of two distinct points (x1, y1) and (x2, y2), the distance between two points is the square root of the sum of the squares of the difference of the coordinates of the points:
distance= \(\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }\)
Distance between the points (-2,1) and (5,-4)In this case, you know:
(x1, y1): (-2,1)(x2, y2): (5,-4)Replacing in the definition of distance:
distance= \(\sqrt{(5-(-2))^{2} +(-4-1)^{2} }\)
distance= \(\sqrt{(5+2)^{2} +(-5)^{2} }\)
distance= \(\sqrt{7^{2} +(-5)^{2} }\)
distance= \(\sqrt{49+25 }\)
distance= √74= 8.6023
Finally, the distance between the points (-2,1) and (5,-4) is √74= 8.6023.
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what is the y-intercept of the line?
Answer:
the answer would be 1/2 I believe
Answer:
y-intercept is 1
Step-by-step explanation:
The y-intercept of the line is the value of y at the point where the line crosses the y axis.
If R, S, and T are collinear and RS + ST = RT, which of the following is true?
T is between R and S.
RS = RT
S is between R and T.
S is the midpoint of ./rt
Answer:
\(S \: is \: between \: R \: and \: T.\)
Answer:
S is between R and T.
Step-by-step explanation:
Jillian is making accessories for the soccer team. She uses 677.46 inches of fabric on headbands for 38 players and 4 coaches. She also uses 366.32 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?
The amount of fabric used to make the headband is 16.13 inches. The amount of fabric used to make the wristband is 9.64 inches.
In order to determine the amount of fabric used to make the accessories, the total inches used would be divided by the total number of people the accessory was made for.
The amount of fabric used to make headband for a player = total quantity of fabrics used / total number of people
677.46 / (38 + 4)
677.46 / 42
= 16.13 inches
The amount of fabric used to make wristband for a player = total quantity of fabrics used / total number of players
366.32 / 38 = 9.64 inches
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- 16 + ( - 12 ) - ( - 40 )
Answer:
12
Step-by-step explanation:
Its 12 because when you do -16 + - 40.... then -12 you get =12 There you go
Step-by-step explanation:
Solution ,
Firstly we need to understand that
( - ) × ( - ) = ( + )
( + ) × ( + ) = ( - )
( - ) × ( + ) = ( - )
( + ) × ( - ) = ( - )
Question:
- 16 + ( - 12 ) - ( - 40 )
here ( + ) × ( - ) = ( - )
= - 16 - 12 - ( - 40 )
here ( - ) × ( - ) = ( + )
= - 28 + 40
here the ( + ) has greater variable so....
= + 12
hence 12 is the answer....
160.7 is what percent of 128?
Answer:
125.54%
Step-by-step explanation:
160.7/128 = 1.2554
1.2554 *100 = 125.54%
Tori rented a car and drove 325 miles. She decided to fill up the tank before returning the car to the rental company.
She put 11 gallons of gas in the car to fill the tank. She paid $2.85 per gallon for gas. The rental company would have
charged $3.50 per gallon to fill the tank. How much did she save by filling the tank herself?
O $3.50
O $0.65
O $7.15
$29.54
Answer:
C. $7.15
Step-by-step explanation:
3.5(11)= 38.5
2.85(11)= 31.35
38.5-31.35=7.15
You model your investment account using the formula y = 20000(1.035)x where x represents the
number of years and y represents the account balance after x years. What is the growth rate of your
investment?
Answer:
Step-by-step explanation:
The growth rate of the investment is represented by the constant multiplier in the exponential term of the formula y = 20000(1.035)x. In this case, the constant multiplier is 1.035, which represents the annual growth rate of the investment account.
To calculate the growth rate as a percentage, we can subtract 1 from the constant multiplier, and then multiply the result by 100.
So, the growth rate of the investment is:
1.035 - 1 = 0.035
0.035 * 100 = 3.5%
Therefore, the growth rate of the investment is 3.5%.
What is 2/3 divided by 4 in the Simplest form?
Answer:
2/3 divided by 4 = .16
Step-by-step explanation:
This problem is pretty simple. Since we cannot divide this we can change the division sign into a multiplication, but to do this we need to also take the reciprocal of 2/3, which means we flip th number so it becomes 3/2. Now we can simply multiply. (1/4)*(3/2) which should give you 3/8
If each quadrilateral below is a kite, find the missing measures.
Answer:
F and H are both 121 degrees
Step-by-step explanation:
"A kite has 4 interior angles and the sum of these interior angles is 360°. In these angles, it has one pair of opposite angles that are obtuse angles and are equal." - Cue math
Ok, so the two acute angles add up to 118 degrees, and in order to find the remaining angles we need, subtract 118 from 360 to get 242. Because the two obtuse angles are equivalent, divide 242 by 2 to get the measure of each.
transistors are used to build computer chips. The size of the earliest transistors
The number of times that the old transistor is bigger than the new ones in the computer is 1 × 10^6.
How to illustrate the information?It should be noted that the the side of the earliest form of transistors for computer was 1 × 10⁴.
Now, the size of the transistor today was illustrated as 1 × 10^-².
Therefore, the difference in size will be about:
= 1 × 10⁴ / 1 × 10^-²
= 1 × 10^6
Therefore, the number of times that the old transistor is bigger than the new ones in the computer is 1 × 10^6.
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A boat travels 336 miles in 67
hours (with a constant speed).
How far can it travel in 58 hours
(with the same speed)?
Answer:
290.87 miles
Step-by-step explanation:
336 miles - 67 hours
x miles - 58 hours
Cross multiply
67x = 336 x 58
67x = 19488.
Divide both sides by 67
x = 19488/67
x = 290.87 miles
This exponential function has a base of 1.4 and an initial amount of 17. Its graph
is shifted 3 units left and 5 units up.
Answer:
-2.4 and 22
Step-by-step explanation:
Find the value of x and y
Answer:
x = 30, y = 15
Step-by-step explanation:
x = 2*15 = 30
(Central angle is twice the inscribed angle standing on the same arc.)
Similarly,
y = 15
(Base angles of isosceles triangle are equal)
ASAP! equation of the line in slope-intercept form
Line through (2,6) and perpendicular to y+4=3x
Answer:
y = -1/3x + 6\(\frac{2}{3}\)
Step-by-step explanation:
First, change the original equation to slope intercept form:
y + 4 = 3x
y = 3x - 4
Now, find the slope of the perpendicular line. It will be the opposite reciprocal:
The opposite reciprocal of 3 is -1/3.
Next, plug this into the slope intercept equation along with the given point, so we can solve for b:
y = mx + b
6 = -1/3(2) + b
6 = -2/3 + b
6.67 = b
So, the equation will be y = -1/3x + 6\(\frac{2}{3}\)
Smallest to largest. 1/4,1/16,1/2,7/16,3/16,5/16?
Find x
X + 50
X + 10
Answer:
x = 60
Step-by-step explanation:
(x + 50)° + (x + 10)° = 180° (interior angles on the same side of transversal)
(2x + 60)° = 180°
2x + 60 = 180
2x = 180 - 60
2x = 120
x = 120/2
x = 60
Identify the solution to the system of equations
4x-y=7
-12x+3y=-21
Answer:
Step-by-step explanation:
The equations are not independent. They represent the same graph.
There are an infinite number of solutions.
Question 2 The current report quantitatively analyzes three variables - load factors, revenue passenger mile, and available seat miles for American Airlines. The data retrieved for the analysis was extracted from the Bureau of Transportation Statistics, focusing on domestic flights from January 2006 to December 2012. The quantitative analysis focused on finding critical statistical values like mean, median, mode, standard deviation, variance, and minimum/maximum variables. Table 2: Summary Statistics of American Airlines (Domestic) Revenue Passenger Miles Mean 6,624,897 Median 6,522,230 Mode NONE Minimum 5,208,159 Maximum 8,277,155 Standard Dev 720,158.571 Variance 518,628,367,282.42 Load Factors Mean 82.934 Median 83.355 Mode 84.56 Minimum 74.91 Maximum 89.94 Standard Dev 3.972 Variance 15.762 Revenue Passenger Miles 9000000 8000000 7000000 6000000 5000000 4000000 3000000 2000000 1000000 0 0 10 American Airlines (Domestic) Performance 20 30 ● Revenue Passenger Miles 40 50 Load Factors Available Seat Miles 60 Mean 7,984,735 Median 7,753,372 Mode NONE Minimum 6,734,620 Maximum 9,424,489 Standard Dev 744,469.8849 Variance 554,235,409,510.06 70 80 Linear (Revenue Passenger Miles) 90 100 Figure 1: American Airlines (Domestic) Performance Write a report based on the given data. Please include additional tests such as hypothesis testing, skewness, z statistic, level of significance, and other necessary tests, as well as a discussion of the results obtained.
The z-statistic test was conducted to determine the Deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.
Report on the Analysis of American Airlines (Domestic) PerformanceThe quantitative analysis focused on three variables- load factors, revenue passenger miles, and available seat miles for American Airlines.
The Bureau of Transportation Statistics data for domestic flights from January 2006 to December 2012 was retrieved for the analysis. The quantitative analysis also focused on finding critical statistical values like mean, median, mode, standard deviation, variance, and minimum/maximum variables. The results of the data are summarized in Table 2. Revenue Passenger Miles (RPM) mean is 6,624,897, the median is 6,522,230, and mode is NONE. The minimum is 5,208,159 and the maximum is 8,277,155. The standard deviation is 720,158.571, and the variance is 518,628,367,282.42.
Load Factors (LF) mean is 82.934, the median is 83.355, and mode is 84.56. The minimum is 74.91, and the maximum is 89.94. The standard deviation is 3.972, and the variance is 15.762. The Available Seat Miles (ASM) mean is 7,984,735, the median is 7,753,372, and mode is NONE. The minimum is 6,734,620, and the maximum is 9,424,489. The standard deviation is 744,469.8849, and the variance is 554,235,409,510.06.Figure 1 above displays the performance of American Airlines (Domestic).
The mean RPM is 7,984,735, and the linear regression line is y = 50584x - 2.53E+8. The linear regression line indicates a positive relationship between RPM and year, with a coefficient of determination, R² = 0.6806. A coefficient of determination indicates the proportion of the variance in the dependent variable that is predictable from the independent variable. Therefore, 68.06% of the variance in RPM is predictable from the year. A one-way ANOVA analysis of variance test was conducted to determine the equality of means of three groups of variables; RPM, ASM, and LF. The null hypothesis is that the means of RPM, ASM, and LF are equal.
The alternative hypothesis is that the means of RPM, ASM, and LF are not equal. The level of significance is 0.05. The ANOVA results indicate that there is a significant difference in means of RPM, ASM, and LF (F = 17335.276, p < 0.05). Furthermore, a post-hoc Tukey's test was conducted to determine which variable means differ significantly. The test indicates that RPM, ASM, and LF means differ significantly.
The skewness test was conducted to determine the symmetry of the distribution of RPM, ASM, and LF. The test indicates that the distribution of RPM, ASM, and LF is not symmetrical (Skewness > 0).
Additionally, the z-statistic test was conducted to determine the deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.
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Find the x- and y-intercepts of the linear function.
-8 - 2x + 4y = 0
Answer: x-2y=-4
Step-by-step explanation:
Move the constant to the righthand side and change its sign (-2x=4y+8)Change the signs on both sides of the equation (x-2y=-4)Divide both sides of the equation by 2 (-x+2y=4)Solution: x-2y=-4Translate the sentence into a
Twice the difference of a number and 8 is 2.
Use the variable c for the unknown number.
Answer: 16 - C
Step-by-step explanation:
So basicly, what it is asking is to solve this problem. I would like to call it a puzzle because there is a missing part that we have to find. Let's get this started!
Here is the equaiton: 2 x (8 - C)
First, we will multiply 8 by 2.
8 x 2 = 16
Now the equation is: 16 - C
We don't know what C is, so this equation is as done as we can do it.
Marco wants to know how much the other students in his mathematics class study. He recorded the data he collected in
the following table.
Time spent studying per week (in hours)
2.0
5.0
1.0
2.5
2.5
3.5
0.0
4.5
2.5
4.0
3.5
3.0
2.0
1.5
4.0
2.0
0.5
3.0
1.0
3.0
3.5
1.5
1. Construct a histogram for the data.
Answer:
Step-by-step explanation:
This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.
Which function models the relationship shown by the line?
A
y = -3.3 + 2
B
y
= 12 + 2
с
y= -3x + 6
D
y=-3x + 6
Consider the two triangles. How can the triangles be proven similar by the SSS similarity theorem?
Answer:if their corresponding sides are proportional.
Step-by-step explanation:
What percent of the front page is taken up by the
prom story, including the prom photograph?
A. 20%
B. 22%
C. 25%
D. 45%
E. 60%
The percent of the front page taken up by the prom story is 20%
Calculating the percent of the front page taken up by the prom storyFrom the question, we have the following parameters that can be used in our computation:
The front page
From the front page, we have
Area front page = 5 * 4
Area front page = 20
Also, we have
Prom = 2 * 2
Prom = 4
So, we have
Percentage = 4/20 * 100%
Evaluate
Percentage = 20%
Hence, the percent of the front page taken up by the prom story is 20%
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Question 8 » Our galaxy, the Milky Way, has a diameter of about 1* 1021 meters. The largest galaxy known to man, the IC 1101, has a diameter of 5 * 1022 meters. The diameter of the IC 1101 is about how many times greater than the diameter of the Milky Way? Milky Way: 1x 1021 m IC 1101: 5 x 1022 m 5 50 5,000 500
Answer:
the Milky Way, has a diameter of about 1x10^21 meters. the largest galaxy known to man, the ic 1101, has a diameter of 5x10^22 meters.
Step-by-step explanation:
The graphs below have the same shape the equation of the bluegrass is f(x)=x^3 what is the equation of the red graph
Answer:
g(x) = x^3 - 2
Step-by-step explanation:
As you can see on the graph, the line has been translated down 2 units.
If the graph of f has the same shape as the graph of g, then the slope remains the same. The y intercept (k) changes by -2 units, so the k value is -2
g(x) = x^3 - 2
Hope this helps!!
Select the correct answer.
Each statement describes a transformation of the graph of f(x) = x. Which statement correctly describes the graph of g(x) if g(x) = f(x - 11)?
A. It is the graph of f(x) where the slope is increased by 11.
It is the graph of f(x) translated 11 units to the left.
It is the graph of f(x) translated 11 units up.
It is the graph of f(x) translated 11 units to the right.
B.
C.
OD.
The correct answer is C. It is the graph of f(x) translated 11 units to the left.
The correct answer is:
C. It is the graph of f(x) translated 11 units to the left.
When we have a function of the form g(x) = f(x - a), it represents a horizontal translation of the graph of f(x) by 'a' units to the right if 'a' is positive and to the left if 'a' is negative.
In this case, g(x) = f(x - 11), which means that the graph of f(x) is being translated 11 units to the right. However, the answer options do not include this specific transformation. The closest option is option C, which states that the graph of g(x) is translated 11 units to the left.
The graph of f(x) = x is a straight line passing through the origin with a slope of 1. If we apply the transformation g(x) = f(x - 11), it means that we are shifting the graph of f(x) 11 units to the right. This results in a new function g(x) that has the same shape and slope as f(x), but is shifted to the right by 11 units.
Therefore, the correct answer is C. It is the graph of f(x) translated 11 units to the left.
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A dog shelter is giving away 19 different dogs, but you have room for only 4 of them. How many different dog families could you create?
The 19 tykes given away by the Shelter, that have room for only 4 tykes per family.
The number of different canine families that could be created from the 19 tykes given away by the sanctum, we need to calculate the number of combinations. room for only 4 tykes , we need to choose 4 tykes from the aggregate of 19 tykes . The order of the tykes in the family doesn't count, as long as we choose different tykes for each family. The number of combinations can be calculated using the formula for combinations C( n, r) = n!/( r!( n- r)!) Where C( n, r) represents the number of combinations of choosing r particulars from a set of n particulars. In this case, we've n = 19( total number of tykes ) and r = 4( number of tykes per family). Plugging these values into the formula, we get C( 19, 4) = 19!/( 4!( 19- 4)!) Calculating the factorial values 19! = 19 × 18 × 17 × 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = ! = 4 × 3 × 2 × 1 = 24 15! = 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = Substituting these values into the formula C( 19, 4) = /( 24 ×) ≈ 91,390 The 19 tykes given away by the sanctum, considering that you have room for only 4 tykes per family.
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PLEASE HELP!!!!!!! IM STRUGGLING