9514 1404 393
Answer:
B.
Step-by-step explanation:
The relation between a function f(x) and its inverse g(x) is ...
f(g(x)) = g(f(x)) = x
On can compute these functions of functions, or take an easier route and do the computation with a couple of numbers. It is often easiest to use x=0 or x=1. If we find g(f(x)) ≠ x, then we know the functions are not inverses. If we find g(f(x)) = x for one particular value of x, then we need to try at least one more to verify the relation.
__
If we call the two given functions f and g, then we have ...
A. f(0) = -2/3, g(-2/3) ≠ 0 . . . . not inverses
__
B. f(0) = -3/2, g(-3/2) = 0 . . . . possible inverses
f(1) = 4/2 = 2, g(2) = 7/7 = 1 . . . . probable inverses
__
C. f(0) = -2, g(-2) = 0 . . . . possible inverses
f(1) = 1/2, g(1/2) = -5/3 . . . . not inverses
__
D. f(0) = 5, g(5) = 27 . . . . not inverses
_____
Additional comment
Our assessment above is sufficiently convincing to let us choose an answer. If we want to verify the functions are inverses, we need to graph them or compute f(g(x)). The graph in the second attachment shows each appears to be the reflection of the other in the line y=x, as required of function inverses.
Find the area If you get this correct i WILL GIVE YOU 100 POINTS
Answer:
Area of yellow portion =54 in
On the first day of a two-day meeting, 10 coffees and 10 doughnuts were purchased for a total of $20.00. Since nobody drank the coffee and all the doughnuts were eaten, the next day only 2 coffees and 14 doughnuts were purchased for a total of $13.00. How much did each coffee and each doughnut cost?
Answer:
1.25 dollars- the value of each coffee
0.75 dollars- the value of each doughnut
Step-by-step explanation:
Suppose that value of one coffee is x dollars, when one doughnut costs y dollars. The value o 10 coffee is 10x, when 10 doughnuts cost 10y. The sum is 10x+10y and it is 20.
10x+10y= 20 (we can divide each part by 10)
x+y=2
2coffee cost 2x, 14 doughnuts cost 14y
2x+14y=13 (it can be divided by two)
x+7y=6.5
We have the system of equations x+y=2, x+7y=6.5
Subtract the first equation from the second one (the left side of the first equation from the left side
x+7y - (x+y)= 6.5-2
6y=4.5
y=4.5/6= 3/4 = 0.75 dollars- the value of each doughnut
x=2-0.75=1.25 dollars- the value of each coffee
For what numbers is f(0) = sec 0 not defined?
Answer:
stundeez
Step-by-step explanation:
Nicki Minaj hdhsbskdhsnsk
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On Melissa's 6th birthday, she gets a $2000 CD that earns 5% interest, compounded semiannually. If the
CD matures on her 16th birthday, how much money will be available?
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$
(S
9514 1404 393
Answer:
$3277.23
Step-by-step explanation:
The future value of the CD with interest at rate r compounded semiannually for t years will be given by ...
A = P(1 +r/2)^(2t)
where P is the principal value.
For the given rate and time, this is ...
A = $2000(1 +0.05/2)^(2·10) = $2000(1.025^20) ≈ $3277.23
The value of the CD at maturity will be $3277.23.
If 2x - 5y – 7 = 0 is perpendicular to the line ax - y - 3 = 0 what is the value of a ?
A) a =2/3
B) a =5/2
C) a = -2/3
D) a = -5/2
Answer:
D) a = - 5/2
Step-by-step explanation:
2x -5y - 7 = 0
5y = 2x - 7
y = 2/5 x - 7
the slope of this line is therefore 2/5 (factor of x).
the perpendicular slope is then (exchange y and x and flip the sign) -5/2, which is then a and the factor of x.
Consider this equation. √x - 1 - 5 = x - 8 The equation has(two valid solutions, one valid solution) and(one extraneous solution, no extraneous solutions) A valid solution for x is(0, 4, 2, 5)
The equation has 2 valid solutions; no extraneous solutions
The given equation is:
[tex]\sqrt{x - 1} - 5= x - 8[/tex]
First, we determine the solutions
[tex]\sqrt{x - 1} - 5= x - 8[/tex]
Add 5 to both sides
[tex]\sqrt{x - 1} = x - 8 + 5[/tex]
[tex]\sqrt{x - 1} = x - 3[/tex]
Square both sides
[tex]x - 1 = (x - 3)^2[/tex]
Expand
[tex]x - 1 = x^2- 3x - 3x + 9[/tex]
[tex]x - 1 = x^2- 6x + 9[/tex]
Collect like terms
[tex]x^2 - 6x - x + 9 + 1 = 0[/tex]
[tex]x^2 - 7x + 10 = 0[/tex]
Expand again
[tex]x^2 - 2x-5x + 10 = 0[/tex]
Factorize
[tex]x(x - 2) -5(x -2)= 0[/tex]
Factor out x - 2
[tex](x - 5)(x -2)= 0[/tex]
Split
[tex]x - 5=0[/tex] or [tex]x - 2 = 0[/tex]
[tex]x= 5[/tex] or [tex]x = 2[/tex]
The above values are valid values of x.
Hence, the equation has 2 valid solutions; no extraneous solutions
Read more about equations at:
https://brainly.com/question/2396830
Answer:
That person is wrong, First blank is : one valid solution , Second blank is : one extraneous solution, and I'm not sure what the 3rd blank is but I think It's 4.
Step-by-step explanation:
for plato users
Nasa is building a satellite that is roughly the shape of a sphere. If the satellite weighs 14.25 pounds per cubic foot before the launch and has a diameter of 4.7 feet. What is the total weight in pounds?
Answer:
Step-by-step explanation:
What is the product of 2/5 × 3/4?
Answer:
3/10
Step-by-step explanation:
2/5*3*4
=6/20
=3/10
IV. Round to the nearest ten thousand
31. 41,876
32. 260,098
33. 91,975
34. 207,865
35. 462,876
please help me I need help
Answer:
This is so hard for me. I can't understand. I am in grade 9 now.
What is the volume of this rectangular pyramid?
_____ cubic millimeters
Answer:
Step-by-step explanation:
L = 9 mm
W = 9 mm
H = 10 mm
volume = LWH/3 = 9·9·10/3 = 270 mm³
CHứng minh rằng trong hệ g - phân với 2
How do you write it in digits
27 million, 200
Answer:
27,000,200
Step-by-step explanation:
Going by basic math you know a million has six 0's.
So; one million is represented as 1,000,000.
Hence twenty-seven million as 27,000,000.
Using you tens, hundreds and thousands you'll know 200 will fall into the last area.
Use the confidence level and sample data to find a confidence interval for estimating the population μ. Round your answer to the same number of decimal places as the sample mean.
Test scores: n = 92, = 90.6, σ = 8.9; 99% confidence
Options:
A.) 88.2 < μ < 93.0
B.) 88.4 < μ < 92.8
C.) 89.1 < μ < 92.1
D.) 88.8 < μ < 92.4
Answer: Choice A.) 88.2 < μ < 93.0
=============================================================
Explanation:
We have this given info:
n = 92 = sample sizexbar = 90.6 = sample meansigma = 8.9 = population standard deviationC = 99% = confidence levelBecause n > 30 and because we know sigma, this allows us to use the Z distribution (aka standard normal distribution).
At 99% confidence, the z critical value is roughly z = 2.576; use a reference sheet, table, or calculator to determine this.
The lower bound of the confidence interval (L) is roughly
L = xbar - z*sigma/sqrt(n)
L = 90.6 - 2.576*8.9/sqrt(92)
L = 88.209757568781
L = 88.2
The upper bound (U) of this confidence interval is roughly
U = xbar + z*sigma/sqrt(n)
U = 90.6 + 2.576*8.9/sqrt(92)
U = 92.990242431219
U = 93.0
Therefore, the confidence interval in the format (L, U) is approximately (88.2, 93.0)
When converted to L < μ < U format, then we get approximately 88.2 < μ < 93.0 which shows that the final answer is choice A.
We're 99% confident that the population mean mu is somewhere between 88.2 and 93.0
can someone help me pls
Answer:
D NO IS THE WRITE ANSWER .
Answer:
D)
Step-by-step explanation:
One angle of an isosceles triangle is 16 what are the other 2 angles
Answer:
other two angle will be
82
as 82+82+16 = 180'
Which points are also part of this set of equivalent ratios? Select all that apply.
a. (3, 2)
b. (4, 2)
c. (4, 8)
d. (8, 4)
e. (12, 6)
Answer:
Option b, (4,2)
Option d, (8,4)
Option e, (12,6)
Answered by GAUTHMATH
Answer:
Option b, (4,2)
Option d, (8,4)
Option e, (12,6)
Step-by-step explanation:
the person above me is correct
The population of a city increased from 23,400 to 27,800 between 2008 and 2012. Find the change of population per year if we assume the change was constant from 2008 to 2012.
Find the amount of the increase:
27800 - 23400 = 4,400
Find number of years: 2012 - 2008 = 4 years
Divide amount of change by number of years:
4,400 / 4 = 1,100 people per year.
Simplify: −4(b+6)−2b(1−4b
Step-by-step explanation:
-4b-24-2b+8b2
8b2-6b-24=0
Find the equation of the midline of the function y = 2 sin(1∕4x) – 3.
A) y = –3
B) y = 3
C) y = 2
D) y = 1∕4
Explanation:
The general sine equation is
y = A*sin(B(x-C)) + D
where the D variable directly determines the midline. In this case, D = -3, so that corresponds to a midline of y = -3
The sine curve oscillates going up and down, passing through this middle horizontal line infinitely many times. See the graph below.
Answer:
A) y = –3
Step-by-step explanation:I took the test
Which of the following choices is equivalent to the equation below?
5(2x−1) = 5(5x−14)
A 2x − 1 = 5x − 14
B 5(2x − 1) = 5x − 14
C 2x − 1 = 5
D None of these choices are correct.
Answer:
2x-1 = 5x-14
Step-by-step explanation:
5(2x−1) = 5(5x−14)
Divide each side by 5
5/5(2x−1) = 5/5(5x−14)
2x-1 = 5x-14
Answer:
A.
Step-by-step explanation:
5(2x−1) = 5(5x−14)
10x - 5 = 25x - 70
65 = 15x
x = 13/3.
Take Option A.
2x - 1 = 5x - 14
3x = 13
x = 13/3 so its this one.
B: 10x - 5 = 5x - 14
5x = -9
x = -9/5 so NOT B.
C. simplifies to x = 3. so NOT C.
A consumer advocate agency is concerned about reported failures of two brands of MP3 players, which we will label Brand A and Brand B. In a random sample of 197 Brand A players, 33 units failed within 1 year of purchase. Of the 290 Brand B players, 25 units were reported to have failed within the first year following purchase. The agency is interested in the difference between the population proportions, , for the two brands. Using the data from the two brands, what would be the standard error of the estimated difference, Dp = A – B, if it were believed that the two population proportions were, in fact, equal (i.e., )?
Answer:
The standard error of the estimated difference is of 0.0313.
Step-by-step explanation:
To solve this question, we need to understand the central limit theorem, and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Brand A:
33 out of 197, so:
[tex]p_A = \frac{33}{197} = 0.1675[/tex]
[tex]s_A = \sqrt{\frac{0.1675*0.8325}{197}} = 0.0266[/tex]
Brand B:
25 out of 290, so:
[tex]p_B = \frac{25}{290} = 0.0862[/tex]
[tex]s_B = \sqrt{\frac{0.0862*0.9138}{290}} = 0.0165[/tex]
What would be the standard error of the estimated difference?
[tex]s = \sqrt{s_A^2+s_B^2} = \sqrt{0.0266^2+0.0165^2} = 0.0313[/tex]
The standard error of the estimated difference is of 0.0313.
Show why (2×3×7)^4 = 2^4 × 3^4 × 7^4 show work
[tex] {a}^{m} \times {b}^{m} = ( {ab)}^{m} [/tex]
(2×3×7)⁴=(2×3)⁴×7⁴(2×3×7)⁴=(2×3×7)⁴RHS=LHSplease mark this answer as brainlist
-36 = 6(2-8n) please
Answer:
n=1
Step-by-step explanation:
-36 = 6(2-8n)
-36=12-48n
-36-12=-48n
-48=-48n
n=1
- Mean test score was 200 with a standard deviation of 40- Mean number of years of service was 20 years with a standard deviation of 2 years.In comparing the relative dispersion of the two distributions, what are the coefficients of variation
Answer:
The correct answer is "Test 20%, Service 10%".
Step-by-step explanation:
As we know,
The coefficient of variation (CV) is:
⇒ [tex]CV=\frac{Standard \ deviation}{Mean}\times 100[/tex]
Now,
CV of test will be:
= [tex]\frac{40}{200}\times 100[/tex]
= [tex]20[/tex] (%)
CV of service will be:
= [tex]\frac{2}{20}\times 100[/tex]
= [tex]10[/tex] (%)
HELP ME PLEASE I NEED HELP
Answer:
1. 3-5
2. 5-3
3. 3-5
4. 5-3
Step-by-step explanation:
This is simple! Just get rid of the parenthesis for each of the expressions shown.
3 + (-5)
the plus sign is next to the negative which is in the parenthesis. Negative times positive is equal to negative. The expression then becomes
3 - 5
Now do the same for the rest!
For things like 3 and 4, you can just flip it like 3-5 and 5-3 because it will all equal the same :]
Hope this helps !!
-Ketifa
The speed of the light is approximately 3x10^14 centimeters per second.how much will it take light to Tavel 9x10^14 centimeters
Answer:
3 seconds
Step-by-step explanation:
First, let's calculate the approximate speed of light.
3 · 10^14 = 3 · 100,000,000,000,000
= 300,000,000,000,000
Approximately, light travels 300,000,000,000,000 centimeters per second.
Now, let's simplify 9x10^14.
9 · 10^14 = 9 · 100,000,000,000,000
= 900,000,000,000,000
To find out how many seconds light takes to travel 900,000,000,000,000 centimeters, we have to divide this number by 300,000,000,000,000, the approximate speed of light.
900,000,000,000,000/300,000,000,000,000 = 3
Therefore, it will take 3 seconds for light to travel 900,000,000,000,000 centimeters.
It will take 3 seconds to cover the distance of 9×10¹⁴ cm.
What is scientific notation?We use the scientific notation of numbers to write very large numbers in compact form.
In the scientific form, we write a number in the form of base×10ⁿ.
Where 0 ≤ base < 10 and n can be any rational number.
Given the speed of light s approximately 3×10¹⁴ cm/sec.
∴ It will take (9×10¹⁴/3×10¹⁴) = 3 seconds.
We know that exponents are added when the same base is multiplied and exponents are subtracted when the same base or integral multiple of the same base is divided.
learn more about scientific notation here :
https://brainly.com/question/18073768
#SPJ2
What number increased by 30% is 34.5
Answer:
44.85
Step-by-step explanation:
There are two ways to do it, you can either multiply 0.3 by 34.5 and then add it to 34.5 to get 44.85, or you can add the 30% to 100% and get 1.3 which you multiply by 34.5 and that gets you 44.85
a jet flew 2660 miles in 4.75 hours. what is the rate of speed in miles per hour? (the proportion would be 2660:4.75::x:1 set the proportion in fractional form and proceed to find x.)
Set the proportion as shown:
2660/4.75 = x/1
Cross multiply:
4.75x = 2660
Divide both sides by 4.75
x = 560
Answer: 560 miles per hour
modeled by a cylinder with diameter 15 feet
