Answers
Answer:
D) [tex]\frac{1}{6}[/tex]
g¹(1) = [tex]\frac{1}{6}[/tex]
The inverse of the function [tex]g(x) = \frac{x^{\frac{1}{3} }-1 }{2}[/tex]
Step-by-step explanation:
Step(i):-
Given that f(x) = (2x+1)³
Let y = (2x+1)³
[tex]y^{\frac{1}{3} } =2x+1[/tex]
[tex]2x = y^{\frac{1}{3} } -1[/tex]
[tex]x = \frac{y^{\frac{1}{3} }-1 }{2}[/tex]
Step(ii):-
y = f(x) ⇒ x = f⁻¹ (y)
⇒ [tex]f^{-1} (y) = \frac{y^{\frac{1}{3} }-1 }{2}[/tex]
[tex]f^{-1} (x) = \frac{x^{\frac{1}{3} }-1 }{2}[/tex]
The inverse of the given function
[tex]g(x) = \frac{x^{\frac{1}{3} }-1 }{2}[/tex]
Differentiating equation (i) with respective to 'x', we get
[tex]g^{l} (x) = \frac{1}{2} X \frac{1}{3} x^{\frac{1}{3} -1}[/tex]
[tex]g^{l} (x) = \frac{1}{6} x^{\frac{-2}{3} }[/tex]
Final answer:-
Put x=1
[tex]g^{l} (1) = \frac{1}{6} 1^{\frac{-2}{3} } = \frac{1}{6}[/tex]
Related Questions
Select the correct answer.
Which expression in factored form is equivalent to this expression?
4(x2 – 2x) – 2(x2 – 3)
A. (2x − 3)(x + 1)
B. 2(x + 1)(x + 3)
C. (2x + 3)(x + 1)
D. 2(x - 1)(x – 3)
Took the test. This is the answer.
Answers
Answer:
D. 2(x - 1)(x – 3)
Step-by-step explanation:
4(x2 – 2x) – 2(x2 – 3)
We would first of all expand the expression given
This becomes
= 4x2 - 8x - 2x2 + 6
Rearrange to enable us simplify
4x2 - 2x2 - 8x + 6
= 2x2 - 8x + 6
Factorize
2 (x2 - 4x + 3)
factorizing further using the factors of 3 that add up to -4
2(x2 - x - 3x + 3)
pick out the common factors
2(x(x-1) -3(x-1)
2(x-1)(x-3)
Option D. 2(x - 1)(x – 3) is right
Using the Factor Theorem, the factored form equivalent to this expression is:
[tex]2(x - 1)(x - 3)[/tex], given by option D.
The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.In this problem, the expression is:
[tex]4(x^2 - 2x) - 2(x^2 - 3) = 0[/tex]
[tex]4x^2 - 8x - 2x^2 + 6 = 0[/tex]
[tex]2x^2 - 8x + 6 = 0[/tex]
Which is a quadratic equation with coefficients [tex]a = 2, b = -8, c = 6[/tex].
Hence:
[tex]\Delta = b^2 - 4ac = (-8)^2 - 4(2)(6) = 16[/tex]
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{8 + 4}{4} = 3[/tex]
[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{8 - 4}{4} = 1[/tex]
Hence, the expression is:
[tex]2(x - 1)(x - 3)[/tex], given by option D.
You can learn more about the Factor Theorem at https://brainly.com/question/24380382
The null and alternative hypotheses for a hypothesis test of the difference in two population means are: Null Hypothesis:mu 1 equals mu 2 Alternative Hypothesis: mu 1 is less than mu 2 Notice that the alternative hypothesis is a one-tailed test. Suppose ttest_ind method from scipy module is used to perform the test and the output is (3.25, 0.0043). What is the P-value for this hypothesis test
Answers
Answer:
the P-value for this hypothesis test is 0.00215
Step-by-step explanation:
Given that;
Null Hypothesis: mu1 = mu2
Alternative Hypothesis: mu1 < mu2
Notice that the alternative hypothesis is a one-tailed test
Now, when when a one-tailed alternative hypothesis is used, To obtain a one-tailed alternative probability value i.e p-value, we divide the result by two (2).
so, given output ( z=3.25, p[tex]_{value}[/tex]=0.0043)
since its one-tailed test
P-value for this hypothesis test = 0.0043 / 2 = 0.00215
Therefore, the P-value for this hypothesis test is 0.00215
find the percentage increase of a rectangle
Answers
Answer:
your question is quite different. I do not understand properly
Find the equation of the line parallel to the line g(x) = -0.01x + 2.01 through the point (1, 2).
Answers
Answer:
Baka renejay to HAHAHHA
In the supply-and-demand schedule shown above, at the equilibrium price, the quantity supplied is _____ and the quantity demanded is _____. 0, 500 200, 200 400, 0
Answers
Answer:
200, 200
Step-by-step explanation:
Please answer and explain for 15 points
Answers
Answer:
55% or 27.2 ounces
Out of 40 times at bat, Raul got 15 hits. Find Raul’s batting average.
Answers
Answer:
.375
Step-by-step explanation:
To find the batting average, do 15/40. And 15/40=.375
Alyssa's cat weighs 12 pounds, which is 3/8 of the weight of her dog. Use the equation 3/8d=12 to find the weight of Alyssa's dog.
Answers
Answer:
0.5 pounds!
Step-by-step explanation:
12/0.375=32
Her dog is 32 pounds
Each of 16 students measured the circumference of a tennis ball by four different methods, which were: A: Estimate the circumference by eye B: Measure the diameter with a ruler, then compute the circumference C: Measure the circumference with ruler and string D: Measure the circumference by rolling the ball along a ruler
Answers
Answer:
Following are the solution to the given equation:
Step-by-step explanation:
Please find the complete question in the attachment file.
In point a:
[tex]\to \mu=\frac{\sum xi}{n}[/tex]
[tex]=22.8[/tex]
[tex]\to \sigma=\sqrt{\frac{\sum (xi-\mu)^2}{n-1}}[/tex]
[tex]=\sqrt{\frac{119.18}{16-1}}\\\\ =\sqrt{\frac{119.18}{15}}\\\\ = \sqrt{7.94533333}\\\\=2.8187[/tex]
In point b:
[tex]\to \mu=\frac{\sum xi}{n}[/tex]
[tex]=20.6875[/tex]
[tex]\to \sigma=\sqrt{\frac{\sum (xi-\mu)^2}{n-1}}[/tex]
[tex]=\sqrt{\frac{26.3375}{16-1}}\\\\=\sqrt{\frac{26.3375}{15}}\\\\ =\sqrt{1.75583333}\\\\ =1.3251[/tex]
In point c:
[tex]\to \mu=\frac{\sum xi}{n}[/tex]
[tex]=21[/tex]
[tex]\to \sigma=\sqrt{\frac{\sum (xi-\mu)^2}{n-1}}[/tex]
[tex]=\sqrt{\frac{2.62}{16-1}}\\\\ =\sqrt{\frac{2.62}{15}} \\\\= \sqrt{0.174666667}\\\\=0.4179[/tex]
In point d:
[tex]\to \mu=\frac{\sum xi}{n}[/tex]
[tex]=20.8375[/tex]
[tex]\to \sigma=\sqrt{\frac{\sum (xi-\mu)^2}{n-1}}[/tex]
[tex]=\sqrt{\frac{8.2975}{16-1}}\\\\ =\sqrt{\frac{8.2975}{15}} \\\\ =\sqrt{0.553166667} \\\\ =0.7438[/tex]
On Wednesday, how many total kilograms of flour were prodľiced at plant #1 and
plant #2 combined?
Answers
Answer:
110,000 kg
Step-by-step explanation:
Just look at the kilos of flour produced on Wednesday from both plants and add them together :)
A random survey of enrollment at 35 community colleges across the United States yielded the following figures:
6,416; 1,550; 2,110; 9,351; 21,830; 4,299; 5,945; 5,722; 2,827; 2,046; 5,481; 5,202; 5,855; 2,749; 10,011;
6,356; 27,000; 9,415; 7,683; 3,202; 17,502; 9,200; 7,380; 18,315; 6,557; 13,714; 17,767; 7,491; 2,769;
2,861; 1,264; 7,284; 28,165; 5,081; 11,624.
Assume the underlying population is normal.
a. Which distribution should you use for this problem? Explain your choice.
b. Construct a 95% confidence interval for the population mean enrollment at community colleges in the United States.
i. State the confidence interval.
ii. Sketch the graph.
Iii. Calculate the error bound.
c. What will happen to the error bound and confidence interval if 500 community colleges were surveyed? Why?
Answers
Answer:
(6243.99, 11014.53) ; 2385.27 ; (7998.17, 9260.34) ;
Step-by-step explanation:
Given the data:
6416; 1550; 2110; 9351; 21830; 4299; 5945; 5722; 2827; 2046; 5481; 5202; 5855; 2749; 10011; 6356; 27000; 9415; 7683; 3202; 17502; 9200; 7380; 18315; 6557; 13714; 17767; 7491; 2769; 2861; 1264; 7284; 28165; 5081; 11624
Using calculator :
Sample mean, m= 8629.25714
Sample standard deviation, s = 6943.92362
1.) T test distribution ;
Sample size, n = 35
Confidence interval (C. I) : m ± Zcritical * s/sqrt(n)
n = sample size = 35
Tn-1,0.025 = t34, 0.025 = 2.0322
C.I = 8629.25714 ± 2.0322 * (6943.92362 / sqrt(35))
C.I = 8629.25714 ± 2385.2689
Lower bound = 8629.25714 - 2385.2689 = 6243.98824
Upper bound = 8629.25714 + 2385.2689 = 11014.52604
(6243.99, 11014.53)
Error bound :
E = t34, 0.025 * (s/sqrt(n))
E = 2.0322 * 6943.92362 / sqrt(35)
E = 2.0322 * 1173.7373
E = 2385.27
C.)
If n = 500
C.I = 8629.25714 ± 2.0322 * (6943.92362 / sqrt(500))
C.I = 8629.25714 ± 631.08285
Lower bound = 8629.25714 - 631.08285 = 7998.17429
Upper bound = 8629.25714 + 631.08285 = 9260.33999
(7998.17, 9260.34)
Error bound :
E = t34, 0.025 * (s/sqrt(n))
E = 2.0322 * 6943.92362 / sqrt(500)
E = 2.0322 * 310.54170
E = 631.08
Both the error margin and the confidence interval reduces due to large sample size.
Which is the equation of a line perpendicular to the line with the equation:
y = -3x + 5
A. Y= -3x -7
B. Y= 3x + 2
C. Y= -1/3x - 1/2
D. Y= 1/3x - 1/2
Answers
Answer:
D- y=1/3x-1/2
Step-by-step explanation:
I believe that the slope needs to be opposite and the reciprocal
a sequence of payment made at equal time period is a/an'????
Answers
Answer:
Annuity.
Step-by-step explanation:
A sequence of payment made at equal time period is called an annuity.
Basically, annuity can be calculated using the compound interest formula. It is given by the mathematical expression;
[tex] A = P(1 + \frac{r}{n})^{nt}[/tex]
Where;
A is the future value.
P is the principal or starting amount.
r is annual interest rate.
n is the number of times the interest is compounded in a year.
t is the number of years for the compound interest.
Additionally, the time period between each payment is called payment period.
The term of an annuity refers to the time from the beginning of the first payment made by an individual to the end of the last payment period.
Max walks 10 meters in 4 seconds what is his walking rate in meters per second
Answers
Answer:
2.5 m/s
Step-by-step explanation:
10/4 gets the answer. it is just distance over time
Answer: 2.5 m/s
Step-by-step explanation:
How is Solve this equation
M + A = 68 and M = A + 24
Answers
Hi there! :)
[tex]\large\boxed{A = 22 \text{ , } M = 46 }[/tex]
We can solve by setting both equations equal to the same variable.
We are given that M + A = 68 and M = A + 24. The easiest variable to set both equal to would be M.
Rearrange the first equation by subtracting A from both sides:
M = -A + 68
Now that both equations equal to M, we can set the two equal to each other:
-A + 68 = A + 24
Add A to both sides:
68 = 2A + 24
Subtract 24 from both sides:
44 = 2A
Divide both sides by 2:
A = 22.
Plug this back into an equation to solve for M:
M + 22 = 68
M = 68 - 22
M = 46.
9+4f-7z use f=6 and z=5
Answers
Answer:
-2
Step-by-step explanation:
9 + 4f - 7z
Use what they have given you
f = 6
z = 5
Now that you have those, all you need to do is substitute them into the expression
9 + 4f - 7z
9 + 4 (6) - 7 (5)
9 + 24 - 35
33 - 35
-2
Hope this helped!
Have a supercalifragilisticexpialidocious day!
Answer: -2
9 + 4f - 7z
Use what they have given you
f = 6
z = 5
Now that you have those, all you need to do is substitute them into the expression
9 + 4f - 7z
9 + 4 (6) - 7 (5)
9 + 24 - 35
33 - 35
-2
Find the slope of the line graphed below.
Answers
Answer: 3/2
Step-by-step explanation:
To find the slope, you want to take the two points and plug it into the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]. That will find the slope. The points are (-5,-4) and (-1,2).[tex]m=\frac{2-(-4)}{-1-(-5)} =\frac{6}{4}=\frac{3}{2}[/tex]
Now, we know that the slope is [tex]m=\frac{3}{2}[/tex].
PLEASE HELP! Will give brainliest! Worth 30 points!
Answers
9514 1404 393
Answer:
a) 102.4
b) 72.6
c) 87.5
Step-by-step explanation:
The average value of a function over an interval is the integral of that function over the interval, divided by the width of the interval.
(a) The summer average is ...
[tex]\text{summer average}=\displaystyle\dfrac{1}{(\frac{1}{4})}\int_\frac{1}{2}^\frac{3}{4}{T(x)}}\,dx=87.5+23.4\cdot\dfrac{2}{\pi}\approx 102.4[/tex]
__
(b) The winter average is similar:
[tex]\text{winter average}=87.5-23.4\cdot\dfrac{2}{\pi}\approx 72.6[/tex]
__
(c) The annual average is the value added to the cosine function: 87.5
_____
Additional comment
The integral of the cosine function over the period of interest is ...
∫cos(2πx)dx = 1/(2π)sin(2πx)
For the limits x=1/2 and x=3/4, this becomes 1/(2π)(-1 -0) = -1/(2π).
When multiplied by -23.4(1/(1/4)), we get +23.4(2/π).
A recreational court is twice as long as it is wide. if the perimeter is 210 feet, find the width and length .
Answers
Answer:
The court has a length of 70 feet, and a width of 35 feet.
Step-by-step explanation:
We know two things:
the the length is twice the width
l = 2w
We also know that the perimeter is 210 feet. Noting that the perimeter of a rectangle is equal to twice its length plus twice its width, we can say:
210 = 2w + 2l
Now we can substitute the first definition of l into the second equation:
210 = 2w + 2(2w)
And now we can solve for w:
210 = 2w + 2(2w)
210 = 2w = 4w
210 = 6w
w = 210 / 6
w = 35
Now that we have w, we can plug that into our first little equation to find l:
l = 2w
l = 2 × 35
l = 70
So the width of the court is 35 feet, and it's length is 70.
Ally made 60 donuts on Friday. She made 3x donuts on Wednesday and 2x donuts on Thursday. How much donuts did she make in all?
Answers
Answer:
Step-by-step explanation: 60 x 3= 380
2 x 60= 270
270 + 380= 810
If two angles are supplementary do they form a straight angle ?
Answers
Answer:
Yes. A linear pair forms a straight angle which contains 180º, so you have 2 angles whose measures add to 180, which means they are supplementary.
X-8-3X-10
Use distributive property
Answers
Answer:
5x-10
Step-by-step explanation:
8x-3x-10
first you subtract 3from 8 and get 5 just add the x so your left with 10
Answer:
-2(x+9)
Step-by-step explanation:
x-8-3x-10
-4x-18
-2(x+9)
Hope it helps you
What is the perimeter of the figure
Answers
Answer:
61cm
Step-by-step explanation:
23 + 23 + 5 + 5 + 5 = 61
hope this helps...
Answer:
The perimeter of the figure is 61 cm
Step-by-step explanation:
The Perimeter of a Shape
It's the sum of all the external side lengths of the shape.
The figure shows a compound shape made of an equilateral triangle and a rectangle.
The external sides are two sides of the triangle and three sides of the rectangle:
P = 5 cm + 5 cm + 23 cm + 23 cm + 5 cm =61 cm
The perimeter of the figure is 61 cm
a red knot is flying at the average speed of 37 miles per hour. the red knot has flown 296 miles. how many hours has it been tracked
Answers
Answer:
time = distance / rate
time = 296 miles / 37 mile per hour
time = 8 hours
Step-by-step explanation:
350 kilometers in 5 hours i dont get it
Answers
Answer:
I cant see the question
Step-by-step explanation:
5. Murphy obtains a 15/5 balloon mortgage to finance $113,500 at 4.95%. How much principal and interest will he have already pald when his balloon payment is due? (2 points)
$85,433.10
O $70,863.13
O $52,781.40
O $53,676.00
Answers
Answer:
$278.15×60= $16688.969
Step-by-step explanation:
Murphy has a 15/5 balloon mortgage plan therefore he would make constant payments monthly for five years and then pay the balance of the loan/balloon payment for the 10 years left in bulk
To calculate principal+interest on loan before balloon payment is due, we simply calculate Murphy's constant/monthly payments for the 15 year loan amortization and multiply by number of payments before balloon payment is due:
Formula for monthly payments
A= P×r×r(1+r)^n/(1+r)^n-1
Where A= monthly payments
P= mortgage loan value
r= interest rate on loan
n= number of payments = 15×12= 180 monthly payments
Substitute :
A= $113500×0.0495×0.0495(1+0.0495)^180/(1+0.0495)^180-1
A= $113500×0.0495×296.104/5980.90
A= $113500×0.0495×0.049508
A= $278.15
To calculate our principal and interest before balloon payment, we multiply by number of payments(5×12=60 payments) before due balloon payment
60×$278.15= $16688.969
Which organism does not produce an external egg as part of its life cycle? *
1 point
A dog
B turtle
C parrot
D insect
Answers
Answer:
dog
Step-by-step explanation:
What is the value of p2 + r3, when p = 2 & r = 3?
Answers
answer is 13
I hope it helpful
Answer:
The value of p² + r³, when p = 2 & r = 3
(2)²+(3)³=4+27=31
31 is the right answer.100 points for answer
Answers
As far as I can tell, your graph is correct.
If you look at the x-axis of the graph, you'll see that the graph crosses it when x is 0, 1, 2, 3, and 4. The asymptotes are halfway in between these points, so if you find the midpoints between each set of points, you'll get 0.5, 1.5, 2.5, and 3.5. These are your answers.
Step-by-step explanation:
The answer of this questions is 0.5,1.5,2.5,3.5Which set of ordered pairs represents y as a function of X?
A {(-3,-1), (2, -1),(5,2)}
® {(-3,-1), (2, 2), (-3,2)}
© {(-3,-1),(5,2), (-3,2)}
D {(-3,-1), (2, 2), (2,5)}
Answers
Answer:
A
Step-by-step explanation:
A. Here is why:
In a function, each x maps to exactly one value of y.
In B and C, x = -3 maps to both -1 and 2, is they are not functions.