The solution to the given composite function is; C: 4x² - 4x - 2
How to solve composite functions?From the question, we are given the individual functions as;
f(x) = x² - 3
g(x) = 2x - 1
Now when it comes to composite functions, we know that;
(f ° g)(x) = f[g(x)]
Substitute the known values in the above equation, so, we have the following representation
(f ° g)(x) = f(2x - 1) = (2x - 1)² - 3 = 4x² - 2x - 2x + 1 - 3 = 4x² - 4x - 2
This is the final solution of the composite function expression.
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The solution to the given composite function is; Option D: 2x² - 7
How to solve composite functions?Composite functions are defined as functions where the output of one function is used as the input of another. Wheb we have a function f and another function g, then the function fg(x), said as “ f of g of x”, is the composition of the two functions.
The given functions are:
f(x) = x² - 3
g(x) = 2x - 1
We want to find (g ° f)(x) . We know that:
(g ° f)(x) = g[f(x)]
Thus:
(g ° f)(x) = g(x² - 3)
= 2(x² - 3) - 1
= 2x² - 6 - 1
= 2x² - 7
This is the final result of the composite function expression.
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The numerator of a fraction is 9 and the denominator is 6. All of the following numbers are equivalent except ____.
○ 2/3
○ 3/2
○ 1 ½
○ 18/12
Answer:
2/3
Step-by-step explanation:
When writing a proof, how do you construct the first statement?
A) By writing the justification for the first statement in the right column.
B) By copying the “prove” statement(s) from the original problem.
C) By writing the next logical statement from the current one.
D) By copying the “given” statement(s) from the original problem.
When writing a proof , by copying the “given” statement(s) from the original problem
Given data ,
A true assertion that is provided in the problem or is known to be true should be the first statement in a proof. The subsequent logical argument has this as its foundation.
We can provide the groundwork for the proof and proceed to the desired conclusion by duplicating the "given" statement(s) from the original problem.
Once the first statement is established, we can move on to writing additional statements that are each logically supported by the first statement.
The logical evolution of the preceding assertions demonstrates that the last statement should be the intended conclusion.
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f(x)=x3 −4x even odd or neither
Answer:
The function would be odd
The answer is neither.
Let's take an odd number and substitute.
f(3) = 3³ - 4(3)f(3) = 27 - 12f(3) = 15 (odd)Now, let's take an even number.
f(4) = 4³ - 4(4)f(4) = 64 - 16f(4) = 48 (even)Since both even and odd numbers are possible, it is neither.
Simplify the expression.
4f8 +39) + 5g
Answer:4f^8+5g+39
Step-by-step explanation:
Quadratic Transformations (photo down below)
Answer: b
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Because the transformation of the quadratic equation is outside of parentheses, it can be concluded that the line is either above or below each other. Next, since we are determining how much higher of lower f(x) is according to g(x), we can determine that it is above since the f(x) is a + and g(x) is a -.
What is the inverse of function f?
f(x)=64x^3-1
The inverse function of f(x) is:
\(g(x) = \sqrt[3]{(x +1)/64}\)
How to find the inverse function?
Here we have the function:
\(f(x) = 64*x^3 -1\)
We want to find the inverse, we will say that is of the form:
\(g(x) = \sqrt[3]{a*x + b}\)
If we evaluate f(x) on g(x), we get:
\(f(g(x)) = 64*(\sqrt[3]{ax + b})^3 - 1\\ \\f(g(x)) = 64*(ax + b) - 1\)
If these are inverses, that must be equal to x:
\(64*(ax + b) - 1 = x\\\\64*a*x + 64*b - 1 = x\\\)
Then:
64*a = 1
a = 1/64
64*b - 1 = 0
b = 1/64
So the inverse function is:
\(g(x) = \sqrt[3]{(x +1)/64}\)
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Helpppp!! This is wayyyy overdue and i only have a couple more questions on this paper.
Answer:
10.2a+3+3a-1+a
= 6a+2
=2(3a+1)
11)2y-1+3y-2+2y+2+2y-2+y
=10y-3
x 16 28 44
y 8 14 22
determine whether y varies directly with x. if so find the constant of variation and write the function rule.
simple formula for that is y×2=x
9. A candle has an initial height of12 inches. Sara lights the candle and it begins to melt at an average rate of 0.5
inch per hour. Which function can be used to find the height of the candle inches after x hours?
A) H(X) = 0.5(x +12) B) H(x) = -0.5(x +12) C)H(x) = 12 +0.5x
+
D) H(X) = 12 -0.5x
1 Pt
А.
B
D
E
Answer:
D
Step-by-step explanation:
h(x)=12-0.5x
x=hour
Jane bought 6 boxes of beads. She used 14 of it to make face mask holders and also gave 12 of the boxes to her sister. How many boxes of beads were left?
Jane has 6 - 14 - 12 = -20 boxes of beads left.
Jane initially had 6 boxes of beads.
She used 14 of those boxes to make face mask holders and gave 12 boxes to her sister.
To find out how many boxes of beads she has left, we need to subtract the boxes used and given away from the initial number.
First, let's calculate the total number of boxes used and given away:
Total boxes used and given away = Boxes used for face mask holders + Boxes given to sister
Total boxes used and given away = 14 + 12
Total boxes used and given away = 26
Next, we can subtract the total boxes used and given away from the initial number of boxes Jane had:
Boxes left = Initial number of boxes - Total boxes used and given away
Boxes left = 6 - 26
Boxes left = -20
The result is -20, which implies that Jane has a deficit of 20 boxes of beads.
This means she doesn't have any boxes of beads left; she has a shortage of 20 boxes based on the activities she performed.
It's important to note that having a negative value indicates that Jane doesn't have enough boxes to fulfill her activities.
If the result were positive, it would represent the number of boxes remaining.
However, in this case, Jane has used and given away more boxes than she initially had, resulting in a negative value.
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express 2 cos 35 sin 67 as a sum
2 cos 35 sin 67 can be expressed as the sum of sin(102) and -sin(32).
To express 2 cos 35 sin 67 as a sum, we can use the trigonometric identity for the product of two sine or cosine functions.
Specifically, the identity states that 2 cos A sin B can be written as
sin(A + B) + sin(A - B).
Applying this identity, we have:
2 cos 35 sin 67 = sin(35 + 67) + sin(35 - 67)
Simplifying the expressions inside the sine functions:
sin(102) + sin(-32)
Since the sine function is an odd function,
sin(-x) = -sin(x),
so we can rewrite the equation as:
sin(102) - sin(32)
Therefore, 2 cos 35 sin 67 can be expressed as the sum of sin(102) and -sin(32).
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1.2 for each of the following 14 functions list the parent function variety parent equation and describe the transformation
A motorist travels 228 kilometers in 6 hours. At that rate, how long will it take him to travel and additional 247 kilometers?
Answer:
The motorist's rate is:
rate = distance / time
where distance is measured in kilometers and time is measured in hours.
We are given that the motorist travels 228 kilometers in 6 hours, so we can use this information to find the rate:
rate = distance / time = 228 km / 6 hours = 38 km/hour
To find how long it will take the motorist to travel an additional 247 kilometers at this rate, we can use the same formula and solve for time:
time = distance / rate = 247 km / 38 km/hour ≈ 6.5 hours
Therefore, it will take the motorist approximately 6.5 hours to travel an additional 247 kilometers at the same rate of 38 km/hour.
Helpppp plzzzzzzzzz !!!!!!
Answer:
the 3rd box
Step-by-step explanation:
Answer:
\(5^{-1}\)
Step-by-step explanation:
5⁻⁴ ÷ 5³
Since they have the same base we can combine the exponents. Since we have a division sign, we add the exponents
5⁻⁴⁻³
5⁻¹
A company makes chocolate candies in a shape of a solid sphere. Each piece of candy has a diameter of 9 centimeters. If a box contains 10 pieces of candy, how much chocolate does the box contain?
Answer:
10
Step-by-step explanation:
the answer is in the question
Round 0.25773438 to the nearest hundredth
Answer:
The answer is 0.26.
I wish you luck on your assignments.
Answer: 0.26
Step-by-step explanation:
1. The hundredths place is two digits from the decimal point
2. Look at the thousandths place and if it is larger or equal to 5 then we round up, otherwise we round down and the hundredths digit remains the same
3. 7 is larger than 5 therefore the hundredths place digit of 5 rounds to a 6
4. Our final answer is 0.26
What is a perfect square 6^1
A perfect square refers to a number that is the result of multiplying an integer by itself. In this case, 6^1 is equal to 6.
However, 6 is not a perfect square because it cannot be obtained by multiplying an integer by itself. The perfect squares up to 6^1 would be 1^2 = 1 and 2^2 = 4.
The respiratory rate (in breaths per minute) in newborns varies according to a distribution that is approximately Normal, with a mean of 50 and a standard deviation of 5. Use Excel to answer this question: What is the probability that a randomly chosen newborn has a respiratory rate between 40 and 55 breaths per minute
Answer:
\(P(40<X<55)\)
And since we need to use excel the code in order to find the answer would be:
=NORM.DIST(55,50,5,TRUE)-NORM.DIST(40,50,5,TRUE)
And the answer would be:
\(P(40<X<55)=0.819\)
Step-by-step explanation:
Let X the random variable that represent the respiratory rate of a population, and for this case we know the distribution for X is given by:
\(X \sim N(50,5)\)
Where \(\mu=50\) and \(\sigma=5\)
We are interested on this probability
\(P(40<X<55)\)
And since we need to use excel the code in order to find the answer would be:
=NORM.DIST(55,50,5,TRUE)-NORM.DIST(40,50,5,TRUE)
And the answer would be:
\(P(40<X<55)=0.819\)
Could i get some help with this problem. 7(x-3)=49
Answer:
x = 10
Step-by-step explanation:
- The first thing to do is open parentheses:
7 (x - 3) = 49
7x - 21 = 49
- Then add 21 to each side:
7x - 21 = 49
7x = 70
- Now divide each side by 7:
7x = 70
x = 10
Calculator
A computer generates 90 integers from 1 to 8 at random. The results are recorded in this table.
Outcome
Number of times outcome occurred
9%
What is the experimental probability of the computer generating a 3 or a 5?
O 20%
O 18%
1
O 40%
26
2 3
8
10
4
12
ស
5
8
6
6
7
9
8
11
The experimental probability of the computer generating a 3 or a 5 is given as follows:
20%.
How to calculate a probability?The parameters that are needed to calculate a probability are given as follows:
Number of desired outcomes in the context of a problem/experiment.Number of total outcomes in the context of a problem/experiment.Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
The total number of outcomes in the table is given as follows:
90.
The desired number of outcomes is given as follows:
10 + 8 = 18.
Hence the experimental probability is given as follows:
p = 18/90 = 0.2 = 20%.
Missing InformationThe problem is given by the image presented at the end of the answer.
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Which term of the sequence 1/4;-1;-21/4;...is equal to -131/2
11, - 6, -1, 4, 9, 14, 19, ... are mapped onto 4. ... A;-l = (-ltQn (mod N),. (A5.34) ... 131 2, 14, 34, 38, 42, 78, 90, 178, 778, 974(1000).
Step-by-step explanation:
the nearest .1/2 incp, we say the 'unit 131/2 incl. 1.4 a measUrement is-stated tp- be 546 inch, this UM= the
GIVING GOOD POINTS FOR THIS PLS HELP
Answer:
x≈1.75
Step-by-step explanation:
Answer: ...
Step-by-step explanation: ...
If interest is compounded once every 12 months, how often is it compounded?
A) Monthly
B) Annually
C) Semiannually
D) Quarterly
Answer:
B) Annually
Step-by-step explanation:
If interest is compounded once every 12 months, it is compounded annually.
Answer:
B) Annually
Step-by-step explanation:
What does compounded mean?Compounded means to calculate interest on the borrowed amount and on previous interest.
What does monthly mean?Monthly means to be done one every month.
What does annually mean?Annually means to be done yearly or every year.
What does semiannually mean?Let's break this down. Semi means half or a partial of something. Annually, as we already discussed, means yearly or every year. Now, when we put it together, it creates half a year. So, semiannually means half a year.
What does quarterly mean?We know a quarter, as in, the coin, is 25 cent. if we multiply 25 cents by four, we get a dollar. So a quarter coin is one fourth, or, a quarter of a dollar. Now, applying that to years, since a year is twelve months and a quarter is one fourth, we can divide twelve by four to get three. Three months is one quarter of a year.
With this in mind, twelve months is equal to a year. So, the interest is compounded every year.
A is incorrect because it says monthly. We have already figured out that the interest is compounded yearly, so it is incorrect.
B is correct because the definition of Annually is yearly or every twelve months.
C is incorrect because semiannually means half or part of a year, not a full year.
D is incorrect because quarterly means one fourth of a year, or, three months.
It took gigi 1 hour and 20 minutes to complete a bicycle race It took Johnny twice as long because he got a flat tire. How many minutes did it take Johnny to finish the race?
You expect to receive $10,000 at graduation in two years. You plan on investing it at 11% until you have $75,000. How long will you wait from now?
Answer:
about 19.31 years
Step-by-step explanation:
\(10000( {1.11}^{x} ) = 75000\)
\( {1.11}^{x} = 7.5\)
\(x ln(1.11) = ln(7.5) \)
\(x = \frac{ ln(7.5) }{ ln(1.11) } = 19.31\)
Daisy cream is sold in a bulk of 76 cups of cream. Kremlin cream is sold in a bulk of 4 1/2 gallons of cream. Marble cream is sold in a bulk of 40 pints of cream. Which one has the most cream?
Therefore , the solution of the given problem of unitary method comes out to be Daisy cream and Kremlin cream both have less cream per bulk 1 gallon and 4.5 gallons, respectively than Marble cream.
An unitary method is what?The objective can be accomplished by utilising what has already been discovered, taking advantage of this worldwide access, and including all essential components from earlier changeable study who employed a certain technique. If the anticipated claim outcome actually occurs, it will either be possible to contact the variable again or both important processes will undoubtedly miss the statement.
Here,
We must convert cups to gallons because daisy cream is sold in bulks of cups. Since a gallon of Daisy cream comprises 16 cups, one quantity of Daisy cream contains:
=> 16 cups per bulk = 1 gallon 16 cups per bulk = 1 gallon
Moscow cream is offered in bulk quantities of 4 1/2 gallons, which is one gallon.
Thus, we must convert pints to gallons. A gallon of Marble cream comprises eight pints, hence one quantity of Marble cream contains:
=> 40 pints in a bulk equal 1 gallon, 8 pints, or 5 gallons.
As a result, we can see that Marble cream, with 5 gallons per bulk, has the most cream.
Daisy cream and Kremlin cream both have less cream per bulk (1 gallon and 4.5 gallons, respectively) than Marble cream.
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Can you please tell me the sum of the question
Answer:
B) \(4i\sqrt{2}\)
Step-by-step explanation:
\(\sqrt{-2}=i\sqrt{2}\\\sqrt{-18}=i\sqrt{18}=i\sqrt{9*2}=3i\sqrt{2}\\\\\sqrt{-2}+\sqrt{-18}=i\sqrt{2}+3i\sqrt{2}=4i\sqrt{2}\)
I do not have an answer to this question: Keith buys a bad of dog food. The bag contains 16 1/2 cups of food. If his dog eats 1 3/8 cups a day, how long will the bag last?
Answer:
12 days
Step-by-step explanation:
3/8=.375
16.5 divided by 1.375 equals to 12. I hope that helps.
Question 4 Score on last try: 0.67 of 2 pts. See Details for more. WIT > Next question Suppose you roll a pair of six-sided dice and add their totals. (a) What is the probability that the sum of the numbers on your dice is 9 or 8? نا است Get a similar question You can retry this question below X (b) What is the probability that the sum of the numbers on your dice is an even number or a num! than 6? (c) What is the probability that the sum of the numbers on y than 5?
The probability that the sum of the numbers on your dice is 9 or 8 is 1/4.
How to calculate the probabilityIt should be noted that to calculate the probability of rolling a 9 or 8, we can first list all the possible outcomes of rolling two six-sided dice:
1 + 1 = 2
1 + 2 = 3
1 + 3 = 4
1 + 4 = 5
1 + 5 = 6
1 + 6 = 7
2 + 1 = 3
2 + 2 = 4
2 + 3 = 5
2 + 4 = 6
2 + 5 = 7
2 + 6 = 8
3 + 1 = 4
3 + 2 = 5
3 + 3 = 6
3 + 4 = 7
3 + 5 = 8
3 + 6 = 9
4 + 1 = 5
4 + 2 = 6
4 + 3 = 7
4 + 4 = 8
4 + 5 = 9
4 + 6 = 10
5 + 1 = 6
5 + 2 = 7
5 + 3 = 8
5 + 4 = 9
5 + 5 = 10
5 + 6 = 11
6 + 1 = 7
6 + 2 = 8
6 + 3 = 9
6 + 4 = 10
6 + 5 = 11
6 + 6 = 12
There are a total of 36 possible outcomes, and we need to find the probability of rolling a 9 or 8, which corresponds 9 outcomes.
This will be;
= 9 / 36
= 1/4
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Maria purchased a car for $8599. If the rate of depreciation is 2.5%, what will the value of the car be after four years? Round your answer to the nearest hundredth.
Answer:
$ 7770.81
Step-by-step explanation:
2.5 % each year means the car retains 97.5 % ( or .975 in decimal) of its value per year
8599 ( .975) ^4 = $ 7770.81