Answers
Given that f(x) = x/(x - 3) and g(x) = 1/x and the application of function operators, f ° g (x) = 1/(1 - 3 · x) and the domain of the resulting function is any real number except x = 1/3.
How to analyze a composed function
Let be f and g functions. Composition is a binary function operation where the variable of the former function (f) is substituted by the latter function (g). If we know that f(x) = x/(x - 3) and g(x) = 1/x, then the composed function is:
[tex]f\,\circ\,g \,(x) = \frac{\frac{1}{x} }{\frac{1}{x}-3}[/tex]
[tex]f\,\circ\,g\,(x) = \frac{\frac{1}{x} }{\frac{1-3\cdot x}{x} }[/tex]
[tex]f\,\circ\,g\,(x) = \frac{1}{1-3\cdot x}[/tex]
The domain of the function is the set of x-values such that f ° g (x) exists. In the case of rational functions of the form p(x)/q(x), the domain is the set of x-values such that q(x) ≠ 0. Thus, the domain of f ° g (x) is [tex]\mathbb{R} - \{\frac{1}{3} \}[/tex].
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Related Questions
The domain of the piecewise function is (-infinity,infinity).
a. Graph the function.
b. Use your graph to determine the function's range.
f(x) =
3x if x≤0
3 if x>0
Answers
Answer:
The condantrnirte will be 3x if x is 0 (underfined)
Step-by-step explanation:
In the standard Normal distribution, which z-score represents the 99th percentile?
Find the z-table here.
–3.00
–2.33
2.33
3.00
Picture posted below
Answers
The Z- score representing the 99th percentile is given by 2.33
Problems of commonly distributed samples can be solved using the z-score formula.
For a set with a standard deviation, the z-score scale X is provided by:
Z = ( x- mean )/ standard deviation
Z-score measures how many standard deviations are derived from the description. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the scale is less than X, that is, the X percentage. Subtract 1 with p-value, we get the chance that the average value is greater than X.
To Find the z-result corresponding to P99, 99 percent of the normal distribution curve.
This is the Z value where X has a p-value of 0.99. This is between 2.32 and 2.33, so the answer is Z = 2.33
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What is the slope of the line y = 3? O A. 3 O B. 1 O C. O O D. Undefined
Answers
Answer:
C
Step-by-step explanation:
The slope of a horizontal line, such as that of y= 3, is equal to 0.
This can be proved using the slope formula.
[tex]\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]
Let's choose 2 points on the line y= 3:
(0, 3) and (2, 3)
Slope
[tex] = \frac{3 - 3}{2 - 0} [/tex]
[tex] = \frac{0}{2} [/tex]
= 0
Thus, the line has a slope of zero.
On the other hand, vertical lines have an undefined slope.
Additional:
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https://brainly.com/question/12528289If a soup recipe yields 20 gallons, how many 5 fluid ounce portions will the recipe yield?
Answers
The total number of 512 portions will be made the recipe that contains 5 fluid ounces each.
The soup recipe gives 20 gallons.
As we know one gallon produces 128 fluid ounces.
There are 20 gallons produced.
So the number of fluid ounces produced will be 20*128= 2560
Given in the question each portion contains 5 fluid ounces.
Then there is a total of 2560 numbers of fluid ounces.
So the number of portions will be = number of fluid ounces/ number of fluid ounces in each portion= 2560/5= 512
Therefore the total number of 512 portions will be made the recipe that contains 5 fluid ounces each.
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An object’s position in meters and motion in meters per second can be described by x = −12 − 5t + 3t^2 during the time interval 0[tex]\leq[/tex]t[tex]\leq[/tex]1.
Which of the following statements is the best description of the object’s motion?
A
The acceleration of the object is zero.
B
The initial position of the object is −12 meters.
C
The object’s speed is increasing.
D
The average velocity of the object is −5 m/s.
Answers
Answer:
B
Step-by-step explanation:
Comment
Thank you for editing the choices.
The reason the answer is B is because the object begins to move when t = 0. Only - 12 will be left after that.
The acceleration is 3. I don't know how to explain that because I'm using calculus and I don't know if you have taken that or not. I assume not by the right answer you are not in a calculus class. You'll have to ask your instructor about the actual answer. Not A
The same is true of D. The answer is - 5 m/s. It is - 4 Not D
All the minus signs indicate a decrease during that interval. Not C
I'm a kid. and I'm starting 4th grade so I lied to the computer, Anyhoo. Can anyone PLS help me comvert 6/7.
Answers
6/7 converted to a decimal is 0.8571
Conversion to decimalsFrom the question, we are to convert the given fraction to a decimal
The given fraction is
6/7
6/7 = 0.8571
Thus,
6/7 expressed as a decimal is 0.8571
Hence, 6/7 converted to a decimal is 0.8571
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Which of the following is another name for a proof by contradiction?
Answers
There are a few possibilities:
Indirect proofreductio ad absurdumThe second term refers to the idea of simplifying a claim down to an impossible absurd one.
Each of the integers 1-25 is written on an individual card and placed in a hat. You
randomly draw a card. How many favorable outcomes are there for choosing a card
with an odd number?
Ο Α. 2
OB. 11
O C. 13
OD. 25
Answers
Answer:
Step-by-step explanation:
Comment
If you know this formula
tn = t1 + (n - 1)*d then you don't even have to count how many odd numbers there are. If you don't know the formula, then you have to count how many odds there are between 1 and 25 inclusive. Just to save you the trouble, there are 13.
Givens
1 = t1
25 = tn
d = 2
Solution
25 = 1 + (n - 1)*2 Subtract 1 from both sides?
25-1 = 1-1 + (n - 1)*2 Combine
24 = (n - 1) * 2 Divide by 2
24/2 = (n - 1)*2/2
12 = n - 1 Add 1 to both sides
12 + 1 = n - 1 + 1 Combine
13 = n
Answer
So you have 13 cards that will bring success.
The volume of a cylinder is given by the formula V = 3.14rh, where r is the radius of the cylinder and h is the height. Suppose a cylindrical can has radius (x+8) and height (2x+3). Which expression represents the volume of the can?
O (pi)x^3 + 19(pi)x^2 + 112(pi)x + 192(pi)
O 2(pi)x^3 + 35(pi)x^2 + 80(pi)x + 48(pi)
O 2(pi)x^3 + 35(pi)x^2 + 176(pi)x + 192(pi)
O 4(pi)x^3 + 44(pi)x^2 + 105(pi)x + 72(pi)
Answers
The expression which represents the volume of the cane will be 2(pi)x^3 + 35(pi)x^2 + 176(pi)x + 192(pi)
The most fundamental of curvilinear geometric forms, a cylinder has historically been a three-dimensional solid. From a geometric perspective, it may be compared to a prism with a circle as its basis.
Given the volume of a cylinder is given by the formula V = 3.14r^2h, where r is the radius of the cylinder and h is the height and suppose a cylindrical cane has radius (x+8) and height (2x+3)
We have to find expression which represents the volume of the cane
So as per given,
r = x+8
h = 2x + 3
v = πr²h
v = π(x+8)²(2x+3)
v = π(x²+64+16x)(2x+3)
v = π(2x³+128x+32x²+3x²+192+48x)
v = π(2x³+35x²+176x+192)
v = π2x³+π35x²+π176x+π192
Hence the expression which represents the volume of the cane will be 2(pi)x^3 + 35(pi)x^2 + 176(pi)x + 192(pi)
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An object is thrown upward from the top of a 144-foot building with an initial velocity of 128 feet per second. The height h of the object after t seconds is given by the quadratic equation h= -16t^2 + 128t + 144. After how many seconds will the ball pass the top of the building
Answers
The time for the ball to pass the top of the building is determined as 4 s.
Time of motion of the ballThe time for the ball to pass the top of the building is obtained when the velocity of the ball is zero.
h = -16t² + 128t + 144
v = dh/dt
v = -32t + 128
at maximum height, v = 0
0 = -32t + 128
32t = 128
t = 128/32
t = 4 s
Thus, the time for the ball to pass the top of the building is determined as 4 s.
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After 8 seconds, the ball will pass the top of the building if the object is thrown upward from the top of a 144-foot building with an initial velocity of 128 feet per second.
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
We have:
An object is thrown upward from the top of a 144-foot building with an initial velocity of 128 feet per second.
When the ball pass the top of the building, h = 144 foot
Plug h = 144 foot in h= -16t² + 128t + 144
144 = -16t² + 128t + 144
[tex]\rm -16t^2+128t=0[/tex]
t = 0 or t = 8 seconds
At t = 0, initially, the ball was thrown upward.
At t = 8 seconds, the ball passes the top of the building
Thus, after 8 seconds, the ball will pass the top of the building if the object is thrown upward from the top of a 144-foot building with an initial velocity of 128 feet per second.
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a number is tripled and then increased by four. the result is seventy-nine. what is the original number?
Answers
Answer:
3x+4=79
Step-by-step explanation:
3x+4=79
3x=79-4
3x=75
Divide both sides by three
3x/3 = 75/3
x=25
Therefore the original number is 25.
Hope it helps.✨✨
answer this 14+20-48
t
Answers
Which of the following best describes the slope of the line below?
A. Negative
B. Undefined
C. Positive
D. Zero
PLEASE HELP
Answers
Answer:
A. negative
Step-by-step explanation:
It is clear from the accompanying graph that the value of y decreases as the value of x grows. The line has a negative slope, and the right answer is C, as shown by the inverse connection between the values of x and y.
Reasoning for other incorrect options:
The slope is positive if the connection between x and y is positive (y rises as x rises, and vice versa). As a result, choice A is incorrect.It is an undefined slope if the value of y varies without the value of x changing. A horizontal line is used to symbolize it. Option B is thus untrue.The slope of a line is zero and is determined by a vertical line if the value of x varies but the value of y stays the same. So, the option D is incorrect.If slope is denoted by m, then the line with various slopes is depicted in the picture below.Complete the table for the given rule. Rule: Y = X + 8
X | Y
2. _
0. _
4. _
Answers
Y=x+8
Table
[tex]\boxed{\begin{array}{c|c}\bf x&\bf y\\ \rm 2&\rm 10\\ \rm 0&\rm 8\\ \rm 4&\rm 12\end{array}}[/tex]
How?
x=2
y=2+8=10x=0
y=0+8=8x=4
y=4+8=12Answer:
[tex]\large\begin{array}{| c | c |}\cline{1-2} x & y \\\cline{1-2} 2 & 10 \\\cline{1-2} 0 & 8 \\\cline{1-2} 4 & 12 \\\cline{1-2}\end{array}[/tex]
Step-by-step explanation:
Given rule:
[tex]y=x+8[/tex]
The rule tells us that to the corresponding y-values, simply substitute the given value of x into the given rule:
[tex]x=2 \implies y=2+8=10[/tex]
[tex]x=0 \implies y=0+8=8[/tex]
[tex]x=4 \implies y=4+8=12[/tex]
Therefore, the completed table is:
[tex]\large\begin{array}{| c | c |}\cline{1-2} x & y \\\cline{1-2} 2 & 10 \\\cline{1-2} 0 & 8 \\\cline{1-2} 4 & 12 \\\cline{1-2}\end{array}[/tex]
Find domain and range of
f(x) = -x2 - 4x + 2
Answers
Answer:
domain is all reals
Step-by-step explanation:
sorry I couldn't find the range
Help me with this math problem
Answers
The required probabilities are as follows:
a) P(X=5) = 0.123
b) P(X6) = P(X=6+X=7+X=8+X=9+X=10)
c) P(X4)=P(X=0), P(X=1), P(X=2), and P(X=3)
Using a binomial random variable, the following is modeled:
There are always ten (10) persons that are being questioned.
From trial to trial, the likelihood of success (i.e., very little faith in newspapers) remains consistent (p=0.68).
The trials are impartial (a reasonable assumption, since the response of 1 of the people should not affect the response of any other)
There are just two possible results for each trial: low faith in newspapers or not.
X counts how many of the 10 trials were successful.
P(X=k) = is the probability mass function for the binomial random variable.
= [tex]^nC_k\times(p^k)\times(1-p)^{n-k}[/tex]
a) P(X=5) =[tex]^{10}C_5\times(0.68)^5\times(0.32)^5[/tex]≈ 0.123
b) P(X6) = P(X=6+X=7+X=8+X=9+X=10)
These may all be calculated individually, then summed together.
c) P(X4)=P(X=0), P(X=1), P(X=2), and P(X=3)
the same concept as in (b) above.
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Cells B1, C1, and D1 contain the values Seat1Row1, Seat2Row1, and Seat3Row1. If cells B1, C1, and D1 were selected, and autofill
used to fill E1, F1, and G1, what would be the auto-filled values?
Seat1Row2, Seat2Row2, Seat3Row2
Seat 2Row2, Seat3Row3, Seat4Row4
Seat 1Row1, Seat2Row2, Seat3Row2
Seat 2Row2, Seat3Row2, Seat4Row2
Answers
In the event that cells B1, C1, and D1 were highlighted and then used to fill E1, F1, and G1, the values we would see are A. Seat1Row2, Seat2Row2, Seat3Row2.
What values would be in E1, F1, and G1?When using a spreadsheet, you can autofill succeeding cells if you highlight the preceding ones and then drag the cursor.
If Seat1Row1, Seat2Row1, and Seat3Row1 are in the cells B1, C1, and D1, then the spreadsheet would take note of the "1s" at the end of the values.
When it is then used to autofill the next cells, it would make this a 2 such that we see Seat1Row2, Seat2Row2, Seat3Row2.
If cells H1, I1, and J1 are filled, we would then see Seat1Row3, Seat2Row3, Seat3Row3.
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What is the answer to the question
Answers
Answer:
180 cm squared
Step-by-step explanation:
Area Of A Rectangle is Length times Width, so 20 times 9, which equals 180.
Find the perimeter of a rectangle whose leath in 223 and width is 3/2. Find the perimeter of a rectangle whose leath in 223 and width is 3/2 .
Answers
Answer:
449 units
Step-by-step explanation:
Perimeter of a rectangle = 2(a+b)
= 2(223+3/2)
=449 units
Determine the value of x.
Answers
Answer: 75
Step-by-step explanation:
For the lines to be parallel, this means the given angles have to be congruent (because then the lines will be parallel by the converse of the corresponding angles theorem)
2x - 45 = x + 30 [congruent angles have equal measure]x - 45 = 30 [subtract x from both sides]x = 75 [add 45 to both sides]pleaseee answer people good at math
Answers
Car averages x miles per gallon means that 1 gallon is enough to drive 36 miles.
We are asked to find average miles per gallon (miles/gallon) --> average miles per gallon would be total miles driven divided by total gallons used (miles/gallon).
Total miles driven is 10+50=60.
As a car averages 25 miles per gallon in the city for 10 miles in the city it will use 10/25=0.4 gallons
What is the average value?
A data set, the arithmetic mean, also known as arithmetic average, is a measure of the central tendency of a finite set of numbers: specifically, the sum of the values divided by the number of values.
As a car averages 40 miles per gallon on the highway for 50 miles on the highway it will use
50/40=1.25 gallons;
So average miles per gallon equals to
[tex]=\frac{10+50}{0.4+1.25}\\=36[/tex]
Therefore option D is correct.
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I will give BRAINLIEST! ANSWER QUESTION! I NEED IT ASAP
Out of a sample of 500 high school students, 376 said they would prefer to have computers in every classroom. Construct a 95% confidence interval for the population mean of high school students who would prefer to have computers in every classroom.
CI = (71.41%, 78.99%)
CI = (71.98%, 79.45%)
CI = (70.23%, 80.17%)
CI = (72.02%, 78.38%)
Answers
Answer:
CI = (71.41%, 78.99%)
Step-by-step explanation:
[tex] \frac{376}{500} - 1.96 \sqrt{ \frac{ (\frac{376}{500} )( \frac{124}{500} )}{500} } = 71.415\%[/tex]
[tex] \frac{376}{500} + 1.96 \sqrt{ \frac{ (\frac{376}{500} )( \frac{124}{500}) }{500} } = 78.985\%[/tex]
If 500 high school students, 376 said they would prefer to have computers in every classroom then the confidence interval at 95% is (71.41%,78.99%) Since option (a) is correct.
Given x= 376, n = 500
The (71.41%,78.99%)
[tex]\hat{p}=\frac{x}{n}\\ =\frac{376}{500} \\=0.752[/tex]
Critical values
Using the z-table the z-critical value at the given significance level at α=0.05 is,[tex]z_{a/2} =1.96[/tex]
Construct a 95% confidence interval
That is,
[tex]\hat{p}= z_{a/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n} }[/tex]
[tex]=0.752\pm 1.96\sqrt{\frac{0.752(1-0.752)}{500} }[/tex]
[tex]=0.752\pm 0.0379[/tex]
= (71.41%,78.99%)
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Camacho is buying a monster truck. The price of the truck is x dollars, and he also has to pay a 13%, percent monster truck tax. Which of the following expressions could represent how much Camacho pays in total for the truck?
Answers
The total price of the truck =$x + $ 0.13x
We have given that,
Camacho is buying a monster truck. The price of the truck is x dollars, and he also has to pay a 13%, percent monster truck tax.
We have to determine the expressions that could represent how much Camacho pays in total for the truck.
We will consider the price of the truck to be $x
What is the tax?And the amount of tax in the percentage would be 13%
13/100 = $ 0.13x (this is the actual amount of the tax)
Now we will calculate the total price of the truck =$x + $ 0.13x
= $ x(1 + 0.13)
If there is any confusion please leave a comment below.
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What is the ratio of the weight of two castings that weigh 32 lbs. and 38 lbs
Answers
Answer:
16 : 19
Step-by-step explanation:
Given weights of the two castings : 32 lbs and 38 lbs respectively.
Now,
Ratio of the weights of the two castings ;
= 32 : 38
= 16 : 19
32:38
16:19
Answer:
this is my answer
A boat traveled north for 28 miles, then turned x° southwest and traveled for 25 miles before stopping. When it stopped, the boat was 18 miles from its starting point.
A triangle shows the course of a boat. Starting at the dock, it travels 18 miles to the left, then 25 miles up and to the right, and then 28 miles down and back to the dock. The angle between 25 miles and 28 miles is x degrees.
Law of cosines:
By how many degrees did the direction of the boat change when it made its first turn? Round to the nearest degree.
30 degrees
39 degrees
46 degrees
50 degrees
Answers
Answer:
Option B :39 degrees is the correct.
The nearest degree is 39°
Step-by-step explanation:
Laws of cosines relates each side with its opposite angle.
Formula for this is :
[tex]c^{2} =a^{2} +b^{2} - 2abcosC[/tex]
[tex]a^{2} = b^{2}+c^{2} - 2bccosA[/tex]
[tex]b^{2} =a^{2}+c^{2} -2accosB[/tex]
in figure a=28
b=18
c=25
Here we have to find angle between a and c that is B
So [tex]18^{2} = 25^{2} +28^{2} -2*25*28cosB[/tex]
324 = 625 + 784 - 1400cosB
1400cosB = 625 + 784 - 324
1400cosB = 1085
cosB = 0.775
∠B = 39.195° ≈ 39°
The boat change 39° when it made its first turn.
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Answer:
B 39 degrees
Step-by-step explanation:
The person above me is correct and I got proof for the people with trust issues. : )
A manpaid rs 510 as income tax when it was 5 paisa per rupee what was his income?
Answers
The income of the man in discuss as in the task content is; rs 10,200.
What is the income of the man?Since, it follows that 100 paisas make one rupee. This insinuates that the income tax rate which corresponds to 5 paisa per rupee is; 5%.
Hence, the amount earned by the man in discuss can be evaluated as follows;
(5/100) × Income = 510
Hence, Income = 510/0.05 = rs 10,200.
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Yolanda invests $30,000 in an account that offers a compound interest rate of 7.9% per year. Which of the following is the correct equation for how much Yolanda will have in year 10?
Answers
The correct option will be Option D: [tex]P_{10} =30000(1+0.079)^{10[/tex]
The compounds interest can be estimated by using the following formula
[tex]A =P(1+r/n)^{nt[/tex]
where
A: the final amount
P: the initial investment
r: the interest rate (in decimal)
n: the number of times the interest will be compounded per year
t: the time (in year)
Given in the problem that
the initial investment is $30,000 and the time period is 10 years,
so P=30000 and
t=10
As we know The interest will be compounded one time per year
n=1.
now for converting the interest rate into decimal form, we will divide the rate of interest by 100.
r=7.9/100
⇒r=0.079
putting above values in the above formula
[tex]A =P(1+r/n)^{nt[/tex]
⇒ [tex]A =30000(1+0.079/1)^{(1)(10)[/tex]
⇒ [tex]A =30000(1+0.079)^{10[/tex]
⇒[tex]P_{10} =30000(1+0.079)^{10[/tex]
Therefore correct option is Option D: [tex]P_{10} =30000(1+0.079)^{10[/tex]
By completing the above equation to find the total amount
[tex]P_{10} =30000(1+0.079)^{10[/tex]
⇒[tex]P_{10} =30000(1.079)^{10[/tex]
⇒[tex]P_{10} =64170.54[/tex]
Yolanda will have to pay $64,170.54 in her account after ten years.
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Raj’s bathtub is clogged and is draining at a rate of 1.5 gallons of water per minute. The table shows that the amount of water remaining in the bathtub, y, is a function of the time in minutes, x, that it has been draining.
A 2-column table with 4 rows. The first column is labeled x with entries 0, 0.5, 1, 1.5. The second column is labeled y with entries 40, 39.25, 38.5, 37.75.
Answers
The range would be all real numbers such that 0 ≤ y ≤ 40.
The complete question is
Raj’s bathtub is clogged and is draining at a rate of 1.5 gallons of water per minute. The table shows that the amount of water remaining in the bathtub, y, is a function of the time in minutes, x, that it has been draining. What is the range of this function? all real numbers such that y ≤ 40 all real numbers such that y ≥ 0 all real numbers such that 0 ≤ y ≤ 40 all real numbers such that 37.75 ≤ y ≤ 40\
What is a function ?A function is an algebraic expression which relates an independent variable with a dependent variable.
It always comes with a defined range and domain.
Draining rate is at 1.5 gallons per minute
That would be y = 1.5x +c
at x = 0 , y = 40
Therefore the equation is y = 1.5x + 40
and from the data
It can be interpreted that as the time increases the water is draining
The range would be all real numbers such that 0 ≤ y ≤ 40.
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C would be the correct answer, I just did the test and got the answer correct.
What are the rotations that will carry this equilateral triangle onto itself?
A
B
90° counterclockwise rotation about its center P
270° counterclockwise rotation about its center P
120° counterclockwise rotation about its center P
240° clockwise rotation about its center P
O225 clockwise rotation about its center P
O200 counterclockwise rotation about its center P
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Answers
The rotations that will carry the equilateral triangle in discuss onto itself are;
90° counterclockwise rotation about its center P.270° counterclockwise rotation about its center P.Which rotations will carry this equilateral triangle onto itself?It follows from the task content that the rotation which produces the desired output in which case, the rotation maps exactly unto the equilateral triangle is required.
On this note, when the rotation is 90° and 270° about the center P in which case, the rotation can be clockwise or anticlockwise, the desired result is obtained.
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Answer: 240 and 120
Step-by-step explanation:
plot the point A(-1,1) B(-3,2) and C (-1,2) in a cartesian plane name the figure so obtained by join A , B and C Also find is area
Answers
The area of the right angle triangle is 1 square unit and the figure is a right angle triangle after plotting the points on a cartesian plane.
What is a right-angle triangle?It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
We have three point A(-1,1) B(-3,2) and C (-1,2) in a cartesian plan.
After plotting the points on the cartesian plane.
We will get a right-angle triangle,
The area of the right angle triangle = (1/2)height×base
Base length from the graph = 1 units
The height of the triangle = 2 units
= (1/2)(2)(1)
= 1 square units
Thus, the area of the right angle triangle is 1 square unit and the figure is a right angle triangle after plotting the points on a cartesian plane.
Learn more about the right-angle triangle here:
brainly.com/question/3770177
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