The expressions for · f g x and g f x and evaluate − f g 3 is 1716
How to write the expressions for · f g x and g f x and evaluate − f g 3Given the functions[tex]\(f(x) = x - x^3\) and \(g(x) = 4x^2\)[/tex],
we can write the expressions for [tex]\(f \circ g(x)\) and \(g \circ f(x)\)[/tex]as follows:
[tex]\(f \circ g(x) = f(g(x)) = f(4x^2)\\ \\= 4x^2 - (4x^2)^3\)\(g \circ f(x)\\ \\= g(f(x)) = g(x - x^3)\\ \\= 4(x - x^3)^2\)[/tex]
To evaluate[tex]\(-f \circ g(3)\),[/tex]
we substitute[tex]\(x = 3\)[/tex] into the expression [tex]\(f \circ g(x)\):[/tex]
[tex]\(-f \circ g(3)\\ = -(4(3) - (4(3))^3) \\= -(12 - 12^3)\\= -(12 - 1728) \\= -(-1716)\\= 1716\)[/tex]
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PLEASE ANSWER QUICKLY
Answer:
x = 90 and 20 x 4 = 6x9 = k2 over -2
If I drive at `70` miles per hour, my journey will take `2.5` hours. How long will my journey take if I drive at `60` miles per hour? Explain your answer
Answer:
It'll take 25 more minutes
Step-by-step explanation:
Please show me step by step how to do this
Answer:
You know that the beginning salary is $32,000, and it is raised by $1,000 per year.
a) We want to find a recursive relation, let's try to find a pattern:
S₁ = salary on the first year = $32,000
S₂ = salary on the second year = $32,000 + $1,000 = $33,000
S₃ = salary on the third year = $33,000 + $1,000 = $34,000
and so on.
We already can see that the recursive relation is: "the salary of the previous year plus $1,000", this can be written as:
Sₙ = Sₙ₋₁ + $1,000
Such that S₁ = $32,000
b) Your salary in the fifth year is S₅
Let's construct it:
S₃ = $34,000
S₄ = $34,000 + $1,000 = $35,000
S₅ = $35,000 + $1,000 = $36,000
Your salary on the fifth year is $36,000
c) When we have a recursive relation like:
Aₙ = Aₙ₋₁ + d
The sum of the first N elements is given by:
Sum(N) = N*(2*A₁ + (N - 1)*d)/2
Then the sum of your salary for the first 20 years is:
S(20) = 20*(2*$32,000 + (20 - 1)*$1,000)/2
S(20) = $830,000
Two parallel lines, I and m, are cut by a transversal, t, as shown below.
1
(17x + 14)
((48-2°
m
What is the value of z?
Answer:
x = 8
Step-by-step explanation:
alternate-interior angles equal 180°
17x + 14 + 4x - 2 = 180
21x + 12 = 180
21x = 168
x = 8
Suppose you measured a boiling temperature (in Cº) for a liquid 6 times and observed. the following results:
Sample mean: 101.82, sample variance (biased): 0.81
a. You are given that σ^2 = 1.2 for the population distribution. What is the confidence interval for the mean at 95% confidence level?
b. Assuming σ is unknown, what is the confidence interval for the population mean at 95% confidence level?
Please round your answers to 2 decimal digits.
The confidence interval for the mean at 95% confidence level with the variance known and unknown are (101.17, 102.47), (101.06, 102.58) respectively
A.)
Known VarianceConfidence interval is related by the formula:
CI = μ ± t * s * √(1/n)Where :
μ = population mean
t = critical value for the confidence level
s = sample standard deviation
n = sample size
The critical value for a 95% confidence level is 1.96.
C.I = 101.82 ± 1.96 * 0.81 * √(1/6)
C.I = 101.82 ± 0.648
C.I = (101.172, 102.468)
Hence, the confidence interval is (101.17, 102.47)
B.)
Assuming variance is Unknown
We use the t-distribition; The critical value at 95% confidence and (6-1) degree of freedom = 2.306
CI = μ ± t * s * √(1/n)
C.I = 101.82 ± 2.306 * 0.81 * √(1/6)
C.I = 101.82 ± 0.763
C.I = 101.057, 102.583
Hence, the confidence interval is (101.06, 102.58)
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Find the missing side lengths. Leave your answers as radicals in simplest form
Answer:
i think the answer is c but im not sure sorry if im wrong
Step-by-step explanation:
A discrete random variable X is said to be uniformly distributed over the numbers 1. 2. 3......,n, if
P(X=i) =1/n, i=1,2....,n
Find EX and Var(X).
For a discrete random variable X that is uniformly distributed over the numbers 1, 2, 3, ..., n, the expected value (EX) can be calculated as the average of all possible values of X. The variance (Var(X)) measures the spread or variability of the distribution.
The expected value and variance, we need to use the formulas for the mean and variance of a uniform distribution.
The expected value (EX) for a uniform distribution can be calculated as the average of all possible values of X. In this case, since X is uniformly distributed over the numbers 1, 2, 3, ..., n, the expected value can be found using the formula:
EX = (1 + 2 + 3 + ... + n) / n
Simplifying this expression, we get:
EX = (n + 1) / 2
The variance (Var(X)) of a uniform distribution can be calculated using the formula:
Var(X) = (n^2 - 1) / 12
where n is the total number of possible values.
Therefore, for a discrete random variable X that is uniformly distributed over the numbers 1, 2, 3, ..., n, the expected value is (n + 1) / 2, and the variance is (n^2 - 1) / 12. These formulas allow us to calculate the average and measure the spread of the distribution.
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please help easy math!! 8th grade math Storypromblem answer number 9
Answer: Chris's Gym pays $2.75
Step-by-step explanation:
So i was glancing at this question wondering how I was gonna figure it out then flipped it upside down in my head and figred out what I was missing
So basically we know that Tyrell pays $2.00 for court reservations
Chris on the other hand according to the table pays $52.75 for court reservation in addition to his monthly fee. Now we have to find out how much is just the court fee. So if we look at the next box I realized that a second court recomendation costs $55.5 and I realized that to find the court reservation costs I needed to subtract so 55.5-52.755= 2.75 which means Chis has a monthly costs of 50 and pays $2.75 for a court holding
The approximation of 1 = integral cos(x3 + 10) dx using composite Simpson's rule with n= 3 is: When approximating Sof(x)dx using Romberg integration, R3,3 gives an approximation of order:
The approximation of the integral ∫cos(x³ + 10) dx using composite Simpson's rule with n = 3 is 0.126. When approximating the integral using Romberg integration, R₃,₃ gives an approximation of order h⁶.
To calculate the approximation using composite Simpson's rule, we divide the interval of integration into subintervals and apply Simpson's rule to each subinterval. The formula for Simpson's rule is:
S = h/3 * (f(x₀) + 4f(x₁) + 2f(x₂) + 4f(x₃) + ... + 2f(x_{n-2}) + 4f(x_{n-1}) + f(xₙ))
where h is the step size and n is the number of subintervals. In this case, we have n = 3, so we divide the interval into three equal subintervals, and the step size is h = (b - a) / n = (π - 0) / 3 = π/3.
Evaluating the function cos(x³ + 10) at the points x₀ = 0, x₁ = π/3, x₂ = 2π/3, and x₃ = π, we get:
f(x₀) = cos((0)³ + 10) = cos(10) ≈ -0.8391
f(x₁) = cos((π/3)³ + 10) = cos(π³/27 + 10) ≈ -0.4586
f(x₂) = cos((2π/3)³ + 10) = cos(8π³/27 + 10) ≈ -0.8391
f(x₃) = cos((π)³ + 10) = cos(π³ + 10) ≈ -0.3473
Using the Simpson's rule formula, we can now calculate the approximation:
S ≈ π/3 * (f(x₀) + 4f(x₁) + 2f(x₂) + 4f(x₃))
≈ π/3 * (-0.8391 + 4(-0.4586) + 2(-0.8391) + 4(-0.3473))
≈ 0.126
To calculate the order of approximation using Romberg integration, we use the formula:
Rₙ,ₖ = Rₙ₋₁,ₖ₋₁ + (Rₙ₋₁,ₖ₋₁ - Rₙ,ₖ₋₁) / (4ₖ - 1)
where Rₙ,ₖ represents the Romberg approximation at level n and column k. The order of approximation is determined by the highest power of h in the error term. In this case, we have R₃,₃, so the order is h⁶.
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PLEASE HELP ME OUT AND MAKE SURE TO SHOW YOUR WORK!!!! PLEASEEEEE
Answer:
1. 15
2. 16
3. 46
4. 59
Step-by-step explanation:
1. 44+30=74, 89-74=15
2. 90-74=16
3. 180-134=46
4. angles like that are the same
Answer:
1. x=5
2. x=16
3.x=46
4.x=59
Step-by-step explanation:
1. It says that the angle in total is 89 degrees (faded). then it shows the degrees 44 and 30. add them together to get 74 degrees. next subtract 89 by 74 to get the answer 5.
2. it shows a box at the corner of the angle (box means its a perfect 90 degree angle) so you need to subtract 90 by 74 to get the answer 16.
3. the whole entire angle is 180. so you need to subtract 134 from 180 to get the answer 46.
4. look focus on the one line that shows 59 degrees and right above it there is a blank. that arrow line represents 180 degrees. subtract 180 by 59 to get 121. next focus on the second line (the one that faces downward to the right) you then subtract 180 by 121 to get 59.
1. 44+30=74 89-74=5 x=5
2. box=90 90-74=16 x=16
3. 180-134=46 x=46
4. 180-59=121 180-121=59 x=59
I need help with math.
Step-by-step explanation:
Circumference of a circle= 2πr
where r=6
and π=22/7
C=2πr
=2×22/7×6
=44/7×6
=264/7
=37.71cm
plzz hurryyyy its for my mathhhh classss
Answer:
A
Step-by-step explanation:
4x+2 = 10
=> 2x+2 = 10-2x
HELP ASAP PLZ!!! Question in picture!
Answer:YOUR ANSWER IS C
Step-by-step explanation:
Answer:
y=11/2x-10
20 character minimum
pls help asap this is too hard helpme
Which equation is equivalent to 3 = 87 ÷ h? A. 3 = (87 ÷ h) – 9 B. 3 × 9 = (87 ÷ h) ÷ 9 C. 3 + 9 = (87 ÷ h) + 9 D. 3 – 9 = (87 ÷ h)
Answer:
3= (87÷h)
Step-by-step explanation:
The question is to pick among the option the solutions that will be equal to 3= (87÷h)
Therefore the most suitable and correct option is
3×9= (87÷h)÷9
27= (87÷h)÷9
Divide by 9
3= (87÷h)
Hence the answer is 3=(87÷h)
18,8. Assuming the tree shown below is perpendicular to the base distance, use trigonometry
to calculate its height to 1 decimal place. Dimensions are in feet.
I
32°
150
Answer:
x = 93.7ft or x = 94ft
Step-by-step explanation:
Hope that helps :)
Look at the triangle: A right angle triangle is shown with hypotenuse equal to 17 centimeters. An acute angle of the triangle is labeled as x degrees What is the value of cos x°? (1 point) 8 ÷ 17 17 ÷ 8 15 ÷ 17 8 ÷ 15 I can't put in the photo. So, description. h- 17cm o- 8cm a- 15cm. This is a right triangle btw. (this is 9th grade work)
Answer:
15 ÷ 17
Step-by-step explanation:
Since our hypotenuse side is 17 cm, our opposite side is 8 cm and our adjacent side is 15 cm. Since the acute angle is x degrees,
From trigonometric ratios, cosx° = adjacent/hypotenuse
= 15 cm/17 cm
= 15/17
= 15 ÷ 17
what is the ratio for 0.875?
The simplified ratio for 0.875 is 7:8 .
To express the ratio for 0.875, we need to convert the decimal value to a ratio form.
0.875 can be written as 875 / 1000 because the decimal value is equivalent to the fraction obtained by dividing the numerator by the denominator.
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 125 in this case.
Dividing 875 and 1000 by 125, we get:
875 / 125 = 7
1000 / 125 = 8
So, the simplified ratio for 0.875 is 7:8 .
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Compare the probability that a student will pass the test in the morning with
the probability that a student will pass the test in the afternoon. Draw a
conclusion based on your results.
A. P(pass morning) = 0.24
P(pass afternoon) = 0.41
Conclusion: A student taking the test in the morning has a greater
chance of passing it than a student taking it in the afternoon
O B. P(pass morning) = 0.24
P(pass | afternoon) = 0.41
Conclusion: A student taking the test in the afternoon has a
greater chance of passing it than a student taking it in the
morning.
O c. P(pass morning) = 0.48
P(pass | afternoon) = 0.82
Conclusion: A student taking the test in the afternoon has a
greater chance of passing it than a student taking it in the
morning.
D. P(pass morning) = 0.48
P(pass afternoon) = 0.82
Conclusion: A student taking the test in the morning has a greater
chance of passing it than a student taking it in the afternoon.
Answer: C
Step-by-step explanation:
just took the quiz
The conclusion based on the statement would be option C. Conclusion: A student taking the test in the afternoon has a greater chance of passing it than a student taking it in the morning.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
We need to Compare the probability that a student will pass the test in the morning with the probability that a student will pass the test in the afternoon.
The conclusion based on the statement would be;
C. P(pass morning) = 0.48
P(pass | afternoon) = 0.82
Conclusion: A student taking the test in the afternoon has a greater chance of passing it than a student taking it in the morning.
Therefore, the correct option is C.
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Find the area of the following
triangle:
5 cm
10 cm
A= [?] cm?
Answer:
25
Step-by-step explanation:
A=1/2×b×h
A=1/2×5cm×10cm
A=25cm
Which of the numbers listed below are solutions to the equation?
Check all that apply.
x2 = 49
A. -7
B. 14
C. 24.5
D. 7
E. -14
F. 2401
If I have 2(2.5)³, is it 2.5 to the power of 3? Or is it 2 to the power of 3?
Points that two lines pass through are given in the table. Match each point of intersection to the correct pair of lines.
(2, 0)
(-1, 3)
(1, 0)
(-1, -3)
(0, 2)
(-3, -1)
Answer:
(2,0)(0,2
(-1,-3)(-3,-1)
(-1,3) (1,0)
Step-by-step explanation:
Consider the function f(x)=6x+5
(A) find it’s average rate of change by changing x=1 to x=5
Answer: I really don’t know
Step-by-step explanation: I need help with this as well. I’m really sorry if you were looking for a real answer
the perimeter of the triangle is ___ units.
Answer:
29 units
Step-by-step explanation:
12 + 12 + 5
29
Questions (a,b), 1 (a,b)
a )
First of all we need to find the value of x ,
because the angles are written in terms of the variable x .
______________________________________
Let's find the value of x :STV angle & SUV angle have same measure because both of them are the front angle of SV arc .
[tex]STV angle \: = SUV angle \: \: = \frac{SV \: arc}{2} \\ [/tex]
So :
[tex]3x - 5 = 2x + 15[/tex]
Add sides 5
[tex]3x - 5 + 5 = 2x + 15 + 5[/tex]
[tex]3x = 2x + 20[/tex]
Subtract sides minus 2x
[tex]3x - 2x = 2x + 20 - 2x[/tex]
Collect like terms
[tex]x = 2x - 2x + 20[/tex]
[tex]x = 20[/tex]
Thus the measure of angle T equals :
[tex]measure \: of \: angle \: T = 3x - 5 \\ [/tex]
Now just need to put the value of x which we found :
[tex]measure \: of \: angle \: T \: = 3 \times (20) - 5 \\ [/tex]
[tex]measure \: of \: angle \: T \: = 60 - 5[/tex]
[tex]measure \: of \: angle \: T \: = 55°[/tex]
♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡
b )
angle S & angle V are also have same measure because they both are the front angles to the TU arc .
And we need to find the value of x again in this part exactly like we did for a .
[tex]angle \: \: S = angle \: \: V[/tex]
As the question told :
[tex]angle \: \: S = 3x[/tex]
and ,
[tex]angle \: \: V = x + 16[/tex]
Thus :
[tex]3x = x + 16[/tex]
Subtract sides minus x
[tex]3x - x = x + 16 - x[/tex]
Collect like terms
[tex]2x = x - x + 16[/tex]
[tex]2x = 16[/tex]
Divide sides by 2
[tex] \frac{2x}{2} = \frac{16}{2} \\ [/tex]
Simplification
[tex]x = 8[/tex]
So ;
[tex]measure \: \: of \: \: angle \: \: S = 3x[/tex]
[tex]measure \: \: of \: \: angle \: \: S = 3(8)[/tex]
[tex]measure \: \: of \: \: angle \: \: S = 24°[/tex]
And we're done.
Q10.
Prove algebraically that the recurring decimal 0.178 can be written as the fraction 59/330
Answer:
bbv
Step-by-step explanation:
Recurring decimal is decimal representation of a number whose digits are periodic and infinite. Proved algebraically that the recurring decimal 0.178 can be written as the fraction 59/330 below.
Given information;Given number in the decimal form is [tex]0. 1 \overline 7 \overline 8[/tex]
Suppose the number is equal to the x,
[tex]x=0. 1 \overline 7 \overline 8[/tex]
Recurring decimalRecurring decimal is decimal representation of a number whose digits are periodic and infinite.
As the number 78 is the recurring number. Thus the recurring number can be written as,
[tex]x=0.1787878.....[/tex] .......equation 1.
Suppose this is equation number 1.
Multiply the above equation with 100 both the sides,
[tex]100\times x=100\times0. 1 787878....[/tex]
[tex]100x=100\times0.1787878...[/tex]
[tex]100x=17.87878...[/tex]
Subtract the above equation from equation number 1. Thus,
[tex]\begin{aligned}\ 100x-x&=17.87878-0.1787878\\ 99x&=17.7\\ \end[/tex]
Solve for x ,
[tex]x=\dfrac{17.7}{99} [/tex]
Multiply with 10 in both numerator and denominator,
[tex]x=\dfrac{177}{990} \\ x=\dfrac{59}{330} \\[/tex]
Hence proved algebraically that the recurring decimal 0.178 can be written as the fraction 59/330
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Adults in various groups were they voted in recent section. The wind be. ARE Yotel der 30 30 50 Over 30 Yes 16 77 27 Nie 24 23 11 Alest is conduct the 0.090 kcalve to whether and voting independent Finthectable for this independence et Ae 10 der Over the value of the forthco AX Which the cont concerned OM-0.050 The water The wash 0.006 the A random sample of 950 Democrats included 817 that consider protecting the environment to be a top priority. A random sample of 800 Republicans included 384 that consider protecting the environment to be a top priority. Construct a 90% confidence interval estimate of the overall difference in the percentages of Democrats and Republicans that prioritize protecting the environment. (Give your answers as percentages, rounded to the nearest tenth of a percent.) Answers The margin of error is 3. We are 90% confident that the difference between the percentage of Democrats and Republicans who prioritize protecting the environment lies between % and 9
The 90% confidence interval estimate for the overall difference in the percentages of Democrats and Republicans who prioritize protecting the environment is between X% and Y%.
To estimate the overall difference in the percentages of Democrats and Republicans who consider protecting the environment a top priority, we can use the concept of confidence intervals.
Confidence intervals provide a range of values within which we can be reasonably confident that the true population parameter lies. In this case, we want to estimate the difference in the proportions of Democrats and Republicans who prioritize protecting the environment.
The provided information states that in a random sample of 950 Democrats, 817 consider protecting the environment a top priority, while in a random sample of 800 Republicans, 384 share the same view. To construct a 90% confidence interval, we need to calculate the margin of error, which is determined by the sample sizes and proportions.
Using the formulas for the margin of error, we find that the margin of error is 3. With this information, we can state that we are 90% confident that the difference between the percentage of Democrats and Republicans who prioritize protecting the environment lies between X% and Y%.
The confidence interval estimate gives us a range within which we can reasonably expect the true difference to fall. However, it does not provide an exact value for the difference. The range allows for some uncertainty due to the sampling variability inherent in survey data.
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A woman bought a bag of rice for 5,700 naira and in three weeks later,she could only buy 3/4 of a bag for 5,700 find the percentage increase
y=-3x + 4
y = 3x - 2
What solution does this system have? How do you
know? Justify(explain).