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If f(x) = 2x - 8 and g(x) = square root of x - 5, what is (f ^ g)(30).
The output of the function (f ^ g)(30) in this context refers to first calculating the output of the g function given x = 30, then substituting this output into the f function. With g(30) = sqrt(x - 5) and f(x) = 2x - 8, we find that (f ^ g)(30) = 2.
Explanation:To find (f ^ g)(30), we first need to find the output of the g function when x = 30 and then substitute this output into the f function. This is also known as the composition of functions.
First, let's find the output of the g function when x = 30. Given that g(x) = sqrt(x - 5), for x = 30, g(30) = sqrt(30 - 5) = sqrt(25) = 5.
Next, we substitute this output into the f function. Given that f(x) = 2x - 8, when x = 5, f(5) = 2(5) - 8 = 10 - 8 = 2.
Therefore, (f ^ g)(30) = 2.
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To find the value of [tex](f ^ g)(30)[/tex], substitute 30 into both f(x) and g(x) to find f(30) and g(30). Then substitute g(30) into f(x) to find the final value.
Explanation:In this mathematics question, you're asked to find the value of [tex](f ^ g)(30)[/tex]where [tex]f(x) = 2x - 8[/tex]and g(x) = square root of x - 5. To calculate (f ^ g)(x), we first need to find the value x in both functions f and g. So, let's find f(30) and g(30) first.
Firstly, substitute x = 30 into f(x). So, [tex]f(30) = 2*30 - 8 = 52[/tex]. Now, substitute x = 30 into g(x). So, g(30) = square root of (30 - 5) = square root of 25 = 5.
Now, f ^ g(30) means we substitute the output of g(30) = 5 into f(x) which gives us [tex]f(5) = 2*5 - 8 = 2.[/tex]
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{ x - y = 4 3x - 6y = -12 graph
List all integers between -15 and 25 that are congruent to 3 mod (11)
The base of an isosceles triangle is 7 cm longer than the legs. Find the legs if the perimeter of the triangle is 43 cm.
(Giving Brainliest)
what is the solution to...
[tex]|x| +19 \leqslant 3[/tex]
Tangerine trees yield 50 pounds of fruit per acre and grapefruit trees yield 75 pounds of fruit per acre. John's orchard produced a maximum total of 1,500 pounds of fruit. Is it possible for John to have 25 acres of tangerine trees and 15 acres of grapefruit trees?
No, because 50(25) + 75(15) ≠ 1500 No, because (50 + 75)(20 + 15) ≠ 1500 Yes, because 50(25) + 75(15) ≥ 1500 Yes, because 50 + 75 + 25 + 15 ≤ 1500
HELP FAST ILL MAKE BRAINIEST Mr. McClellan compared the weights (in pounds) of pairs of elk antlers dropped at Mount St Helens NVM and Rocky Mountain NP. He tabulated them in the following colored data tables. Purple: Weight of elk antler pairs at Mount St Helens NVM: {34, 34, 30, 30, 30, 28, 28, 26} Red: Weight of elk antler pairs at Rocky Mountain NP: {40, 38, 36, 36, 36, 36, 34, 32}
(a) Create a line plot for each data set.
(b) Calculate the following for each set of data: a. Purple Mean: b. Red Mean: c. Purple Median: d. Red Median: e. Purple MAD: f. Red MAD:
(c) Calculate the means-to-MAD ratio for the two areas of collection. (
d) What inference can be made about the areas in regard to weight of dropped elk antlers? Explain. Answer:
MAD tells us how far, on average, all values are from the middle. So, in the example weight of elk antler pairs at Mount St Helens NVM are, on average, 2 away from the middle. On the other hand, weight of elk antler pairs at Rocky Mountain NP are, on average, 1.5 away from the middle. So, we can assure that elk antler pairs at Rocky Mountain NP weighs more than elk antler pairs at Mount St Helens NVM.
If the mean waiting time for the next arrival is 12 minutes, what is the median waiting time? 8.3 minutes 12 minutes 9.1 minutes 7.2 minutes
Since the mean waiting time is 12 minutes, the median waiting time would also be 12 minutes.
Here's how we can find the median waiting time:
Since the mean waiting time is 12 minutes, it means that if you were to add up all the waiting times of different arrivals and divide by the number of arrivals, you would get 12 minutes.
Now, for the median waiting time, we're looking for the value that falls exactly in the middle of all the waiting times.
If the distribution is symmetrical, which is often the case with waiting times, the mean and median will be the same.
Show that the vector field f(x,y,z)=⟨ycos(−2x),−2xsin(y),0⟩f(x,y,z)=⟨ycos(−2x),−2xsin(y),0⟩ is not a gradient vector field by computing its curl. how does this show what you intended?
Final answer:
To show that the given vector field is not a gradient vector field, we need to compute its curl. The curl is computed by taking the cross product of the gradient operator with the vector field. By computing the partial derivatives and simplifying, we find that the curl of the given vector field is not zero, which indicates that it is not a gradient vector field.
Explanation:
To show that the vector field is not a gradient vector field, we need to compute its curl. The given vector field is f(x,y,z) = <ycos(-2x), -2xsin(y), 0>. The curl of a vector field is defined as the cross product of the gradient operator with the vector field. In this case, the curl of f(x,y,z) is computed as:
curl(f) = ∇ × f = (∂f_z/∂y - ∂f_y/∂z)i + (∂f_x/∂z - ∂f_z/∂x)j + (∂f_y/∂x - ∂f_x/∂y)k
By computing the partial derivatives and simplifying, we find that:
∂f_z/∂y = 0∂f_y/∂z = 0∂f_x/∂z = 0∂f_z/∂x = 2ycos(-2x)∂f_y/∂x = 0∂f_x/∂y = -2sin(y)Substituting these values back into the curl formula, we get:
curl(f) = (2ycos(-2x))i + 0j + (-2sin(y))k
This shows that the curl of the vector field is not zero, which means the vector field is not a gradient vector field.
The price of a pair of jeans at a store increased by 25% to $40. Find the price of the pair of jeans before the increase
Two people started from the same point at the same time and traveled in opposite directions. One traveled at 60 mph and the other at 50 mph. How long will it take before the two people are 440 miles apart?
When the sample size and sample standard deviation remain the same, a 99% confidence interval for a population mean, µ will be narrower than the 95% confidence interval for µ?
Using the equation for the margin of error, it is found that the 99% confidence interval will be wider than the 95% confidence interval for µ.
What is the margin of error of a confidence interval?The margin of error of a confidence interval is given by an equation in the following format:
[tex]M = t\frac{s}{\sqrt{n}}[/tex]
In which:
t is the critical value, which increases as the confidence level increases.s is the standard deviation of the sample.n is the sample size.In this problem, a 99% confidence interval will have a higher value of t than a 95% confidence interval, hence a higher margin of error, and thus will be wider.
You can learn more about the margin of error of a confidence interval at https://brainly.com/question/25779324
A cylindrical can of cat food has a diameter of 3.5 inches and a height of 1.25 inches. A second brand of cat food is packaged in a cylindrical can with a radius of 1.2 inches and a height of 1.25 inches. What is the difference between the volumes of the cans? Show your work.
If you wanted to vertically stretch the graph of F(x) = |x| by five units, what would the equation of the new function, G(x), be?
A. G(x)=|x|-5
B. G(x)=|x+5|
C. G(x)=5|x|
D.G(x)=|5x|
mcr apex
Solution:
The Preimage function is , F(x)=|x|
Consider a point (a,b) on the function, F(x)=|x|. it means
b=|a|-----(1) satisfies the function.
Now the function F(x)=|x| is vertically stretched by 5 units.It means
x=a , y= b+5
x=a, b=y-5
So, putting the value of a and b in equation (1).
y-5=|x|
y= |x| + 5 is vertical stretch of y= |x| by 5 units.
Evaluate C(7, 7).
A: 0
B: 1
C: 7
If you can, could you please explain how you got your answer. These problems honestly don't make any sense to me and I'm turning towards here as a last resort. Thanks in advance.
Answer:
Answer = 1
Step-by-step explanation:
Michael has $1.95 totally in his collection, consisting of quarters and nickels. The number of nickels is three more than the number of quarters. How many nickels and how many quarters does Michael have?
Which of these points does not change its location when it is reflected across the y-axis? (2, 0) (0, 6) (3, 3) (–5, 5)
Answer:
-5,5
Step-by-step explanation:
hey can you please help me posted picture of question
Choose the equation of a line in standard form that satisfies the given conditions. perpendicular to 4x + y = 8 through (4, 3) A. x − 4y = −8 B. x + 4y = 16 C. 4x − y = 11 D. 4x + y = 19
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An oil company fills 1 over 10 of a tank in 1 over 5 hour. At this rate, which expression can be used to determine how long will it take for the tank to fill completely?
1 over 5 ⋅ 10 hours
1 over 10 ⋅ 5 hours
1 over 5 ⋅ 1 over 10 hours
5 ⋅ 10 hours
Answer:
Option A. 1 over 5. 10 hours
Step-by-step explanation:
This question can be solved by the unitary method.
∵ Oil company fills [tex]\frac{1}{10}[/tex] of a tank in the time = [tex]\frac{1}{5}[/tex] hurs
∴ Full tank can be filled in the time = [tex]\frac{\frac{1}{5} }{\frac{1}{10} }[/tex] hours.
= [tex]\frac{1}{5}\times 10[/tex]
Therefore, the expression that can be used to determine the time that it will take to fill the tank completely will be Option A.
Which statements correctly describe the solid figure? Check all that apply.
It is an octagonal prism.
It is an octahedron.
It is oblique.
It is a Platonic solid.
It is a convex polyhedron.
Fill in the blank 300mm =___m
Final answer:
To convert 300mm to meters, divide 300 by 1000 because there are 1000 mm in a meter, resulting in 0.3 meters.
Explanation:
To convert millimeters to meters, we use the conversion factor that 1000 mm equals 1 m. Therefore, to convert 300mm to meters, you divide 300 mm by 1000 because there are 1000 mm in a single meter. So, let's carry out the calculation:
300 mm ÷ 1000 = 0.3 m
Thus, 300 mm is equal to 0.3 meters.
The numbers of rooms for 15 homes recently sold were: 8, 8, 8, 5, 9, 8, 7, 6, 6, 7, 7, 7, 7, 9, 9. what is the sample standard deviation?
Hence, the sample standard deviation is:
1.1832
Step-by-step explanation:The data is given by:
8, 8, 8, 5, 9, 8, 7, 6, 6, 7, 7, 7, 7, 9, 9.
The mean of these data points is given by:
[tex]Mean(x')=\dfrac{8+8+8+5+9+8+7+6+6+7+7+7+7+9+9}{15}\\\\i.e.\\\\Mean(x')=\dfrac{111}{15}\\\\i.e.\\\\Mean(x')=7.4[/tex]
Now,
x x-x' (x-x')²
8 8-7.4=0.6 0.36
8 8-7.4=0.6 0.36
8 8-7.4=0.6 0.36
5 5-7.4= -2.4 5.76
9 9-7.4=1.6 2.56
8 8-7.4=0.6 0.36
7 7-7.4= -0.4 0.16
6 6-7.4= -1.4 1.96
6 6-7.4= -1.4 1.96
7 7-7.4= -0.4 0.16
7 7-7.4= -0.4 0.16
7 7-7.4= -0.4 0.16
7 7-7.4= -0.4 0.16
9 9-7.4=1.6 2.56
9 9-7.4=1.6 2.56
∑(x-x')²=19.69
Now the variance of the sample population is given by:
[tex]Variance=\dfrac{\sum (x-x')^2}{n-1}[/tex]
where n is the number of data points.
Here n= 15
Hence, n-1=14
Hence, we get:
[tex]Variance=\dfrac{19.6}{14}\\\\i.e.\\\\Variance=1.4[/tex]
We know that the standard deviation is the square root of the variance.
i.e.
[tex]Standard\ deviation=\sqrt{1.4}\\\\i.e.\\\\Standard\ deviation=1.1832[/tex]
Express Express 0.45 as a percent
To change 0.45 to a percent, we can move the decimal point 2 places to the right and add the percent sign.
If we move the decimal 2 places to the right, we will end up with 45 and then we will add the percent sign and it will become 45%
Therefore, 0.45 to a percent is 45%
This is a priority! The equation of a parabola is 1/16 (y+3)^=x+4 what are the coordinates of the focus?
(4k^4 + 2 - 3k) + (5k^4 + k - 8)
What is the formula for margin of error?
Answer:
ME=z×s/√n
Step-by-step explanation:
Basically the answer is C.
A cylinder has a height of 16 cm and a radius of 5 cm. A cone has a height of 12 cm and a radius of 4 cm. If the cone is placed inside the cylinder as shown, what is the volume of the air space surrounding the cone inside the cylinder? (Use 3.14 as an approximation of .) 452.16 cm3 840.54 cm3 1,055.04 cm3 1,456.96 cm3 NextReset
all real cube roots of 27