The solution of the function is as follows:
(f o g)(x) = 16x² + 17x + 1
(g o f)(x) = 4x² + 36x + 1
How to solve composite function?Composite functions are when the output of one function is used as the input of another.
Therefore, let's solve the composite functions as follows:
f(x) = x² + 9x
g(x) = 4x + 1
Therefore,
(f o g)(x) = f(g(x))
Therefore,
f(g(x)) = (4x + 1)² + 9x = (4x + 1)(4x + 1) + 9x = 16x² + 4x + 4x + 1 + 9x = 16x² + 17x + 1
(g o f)(x) = g(f(x))
g(f(x)) = 4(x² + 9x) + 1 = 4x² + 36x + 1
Therefore,
(f o g)(x) = 16x² + 17x + 1
(g o f)(x) = 4x² + 36x + 1
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How much WORK is done when you push on a wall with 500 N, and the wall moves 0.5 m?
Answer:
the amount of work that is done when the wall is moving 0.5 m is 250 jewels
Step-by-step explanation:
1) write out the equation
(W=F×d)
2) plug in the numbers into the equation
W= F×d= 500 ×0.5 m
3) solve the problem
W=F×d=500 × 0.5m =250 jewels
What is the coefficient in the following expression
5+3x+ (-3)
Answer:
The coefficient is 3.
Step-by-step explanation:
The coefficient is the number that is grouped with an unknown number represented by a letter.
6(3y + 2) + 8(4y + 3) + 6y =
6(3y+2) + 8(4y+3) + 6y =
Distribute:
18y + 12 + 32y + 24 + 6y =
Combine like terms:
56y + 36
Is 1/3 less than or greater than 5?
Answer: Less than 5
Step-by-step explanation: 1/3 is less than one its .33 so 5 is bigger
Answer: 5
Step-by-step explanation: 1/3 is smaller than 5 therefore 5 is bigger
Carsen loves to run. She runs 4 miles each day. If she wants to run a total of 56 miles how many days should she run? Write an equation to show this problem along with the answer. *Please click on "show your work" to set up the problem and show your work. Then, enter your answer in the box to the right. You must complete both of these steps.
Answer:
4 miles/1 day=56 miles/X days
X=56/4=14
Step-by-step explanation:
Answer:
She runs 14 miles.
explanation:
I got it right on my test (before I saw the other answer).
Which is greater? 12.045 or 12.54
Answer:
12.54
Step-by-step explanation:
which state ment correctly identifies the line of reflection
Which do the following options represent the measure of arc RA
A.38.6
B.65.6
C.71.4
D.77.2
Answer:
77.2°
Step-by-step explanation:
Consider the triangle JKR.
∠KJR=108.6 (lies on the same line as ∠RJA, angles on a straight line add up to 180)
All the angles in a triangle add up to 180, so:
∠JKR+∠KJR+∠JRK=180
∠JKR+108.6+32.8=180
∠JKR=38.6=∠RKA
Consider ∠RKA. This angle stands on the same arc as ∠RCA.
Since the angle at centre is twice the angle at circumference, 2(∠RKA) = ∠RCA.
2(∠RKA) = ∠RCA
2(38.6)=∠RCA
∠RCA=77.2°
Determine if the finite correction factor should be used. If so, use it in your calculations when you find the probability. In a sample of 800 gas stations, the mean price for regular gasoline at the pump was $2.816 per gallon and the standard deviation was $0.008 per gallon. A random sample of size 45 is drawn from this population. What is the probability that the mean price per gallon is less than $2.812?
Answer:
0.0003 = 0.03% probability that the mean price per gallon is less than $2.812
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. 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 measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes 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.
Finite correction factor:
If the sample is more than 5% of the population, instead of Central Limit Theorem, we use the finite correction factor, as the standard deviation of the sampling distribution would be too big.
The mean price for regular gasoline at the pump was $2.816 per gallon and the standard deviation was $0.008 per gallon.
Large sample, so this can be treated as the population data. Then [tex]\mu = 2.816, \sigma = 0.008[/tex]
Sample of 45:
45/800 = 0.056 = 5.6% -> Sample more than 5% of the population, so we use the finite correction factor. This means that s will be multiplied by:
[tex]FCF = \sqrt{\frac{N-n}{N-1}}[/tex]
In which n is the size of the sample(45) and N is the size of the population (800). So
[tex]FCF = \sqrt{\frac{755}{799}} = 0.9721[/tex]
By the Central Limit Theorem, [tex]n = 45, s = 0.9721*\frac{0.008}{\sqrt{45}} = 0.00116[/tex]
What is the probability that the mean price per gallon is less than $2.812?
This is the pvalue of Z when X = 2.812. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2.812 - 2.816}{0.00116}[/tex]
[tex]Z = -3.45[/tex]
[tex]Z = -3.45[/tex] has a pvalue of 0.0003
0.0003 = 0.03% probability that the mean price per gallon is less than $2.812
Please help!! I will give you brain list
Answer:
It will take you at least 17 full weeks to make twice what you spend on the arcade.
Step-by-step explanation:
The inequality will look like this: 10,153x ≥ 170,978
After 17 weeks, you'll have made $172,601, one week less you'll only make $162,448, so it will take you at least 17 full weeks to make twice what you spent on the arcade.
y=ax with a>1
im very confused on what to do
Answer:
Step-by-step explanation:
‘a’ in this question is the slope of the line. Slope is (y2-y1)/(x2-x1) for any two points. We can see the line intersects the point (0,0) and (-10/9) so the slope is -10/9 which is less than -1 so
a<-1
what is 3,000 + 200 + .4 + .06 in standard from
Answer:
3,200.406
I think
Step-by-step explanation:
Answer:
Hello! :) have a good day!
3000 + 200 + .4 + 0.6 in standard form is 3201
PLEASE HELP ITS OVERDUE PLEASE I NEED HELP!!
Answer:
B
Step-by-step explanation:
it has a line of 1/12 so every shirt is $12
simplify your answer
Answer:
51
Step-by-step explanation:
Simplify: (3x - 4x^2 + 8x^3) + ( - 6x + 2x^4 - 5x^2)
Answer:
−x(3−9x+8x^2+2x^3)
That's the answer simplified. Not simplified is −3x−9x^2+8x^3+2x^4
Step-by-step explanation:
James has $25 to spend at the concession stand. He buys nachos for $8.50, a soda for $2.50 and some Sour Straws for $1.25 each. How many Sour Straws can James purchase with the money he has?
A. 1.25x + 11 > 25
B. 1.25x + 11 < 25
C. 11x + 1.25 > 25
D. 1.25x + 11 < 25
E. 11x + 1.25 > 25
F. 25x - 1.25 > 11
The distance from New York City to Riverhead is approximately 150 miles. On a map whose scale is 24mi= 2inch, what is the distance between the two locations in inches?
Answer:
12.5 inches
Step-by-step explanation:
Given
[tex]Distance = 150\ miles[/tex]
[tex]Scale:= 24\ miles : 2\ inches[/tex]
Required
Determine the measurement in inches
Represent the inches equivalent with d.
So, the scale can also be calculated as:
[tex]Scale:= 150\ miles: d[/tex]
Equate both scales
[tex]150\ miles: d = 24\ miles ; 2\ inches[/tex]
Convert to fraction
[tex]\frac{d}{150\ miles} = \frac{2\ inches}{24\ miles}[/tex]
[tex]\frac{d}{150} = \frac{2\ inches}{24}[/tex]
Multiply both sides by 150
[tex]150 * \frac{d}{150} = \frac{2\ inches}{24} * 150[/tex]
[tex]d = \frac{2\ inches}{24} * 150[/tex]
[tex]d = \frac{2\ inches * 150}{24}[/tex]
[tex]d = \frac{300\ inches}{24}[/tex]
[tex]d =12.5\ inches[/tex]
Write an equation using “x” and then solve the equation. The rate charged for a standard room is $250 dollars. A couple stayed in a standard room for x nights and their total room charge is $750.
Answer:
3 nights
Step-by-step explanation:
total charge = rate times time interval
Here, time interval = total charge / rate
$750 = ($250/night)(n nights)
Solving for n, we get n = 3 (nights)
An equation for a couple stayed in a standard room for x nights and their total room charge is $750 is, 250x = 750
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given that,
The rate charged for a standard room is $250 dollars
A couple stayed in a standard room for x nights
Total room charge = $750
Equation = ?
Total charge = 250 × x
Total charge = 750
So,
250x = 750
Thus, an equation is 250x = 750
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The ratio of children to adults at a movie theater was 8:5. The theater sold 120 children tickets
that evening. How many adults attended the theater that night? How many tickets did the theater
sell altogether?
Answer:
75 adults
195 total tickets
Step-by-step explanation:
8:5
120:x
Skylas research Shows at eight empty cans make 1/ 4th pound of aluminum
she
wants to know how many cans it takes to make 5 pounds of aluminum how many kids are there per pound of aluminum
Answer:
160 cans for 5 pounds of aluminum
Step-by-step explanation:
Is this a parallelogram? If so, please explain why.
Answer:
the answer is no
Step-by-step explanation:
It only shows that one pair of lines are parallel but not both are. Parallelograms have two pairs of parallel lines.
I WILL GIVE BRAINLIST PLEASE HELP
Is the set of rational expressions closed under subtraction? Explain p(x) - r(x) = ______________
q(x) s(x)
2. Is the set of rational expressions closed under multiplication? Explain ( p(x) ) ( r(x) ) = _______________
q(x) s(x)
3. Is the set of rational expressions closed under division? Explain
p(x) ÷ r(x) = ________________ q(x) s(x)
Answer:
so where is the equation
Please help me with this question what’s 84 + 6 1/3
Answer:
90 1/3
Step-by-step explanation:
Answer: Mixed number form = 90 1/3
Decimal form = 90.3 with a repation bar
Actual Form = 271 / 3
Step-by-step explanation:
find the area of a rectangular carpet the measures 3 1/3 feet by 3 feet
Answer:
area = 4
Step-by-step explanation:
area = length × width
length= 3 1/3 =3/3 = 1 and width= 3
area = 1 × 3
= 4
SOLVE FOR w
-3(w + 5) = -6
Answer:
Step-by-step explanation:
-3w - 15 = -6
-3w = 9
w = -3
Answer:
w = -3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
-3(w + 5) = -6
Step 2: Solve for w
[Division Property of Equality] Divide -3 on both sides: w + 5 = 2[Subtraction Property of Equality] Subtract 5 on both sides: w = -3I don't get this part can somebody help pls?
Answer:
the ground level is -2
Step-by-step explanation:
hope this helps
What is the solution to the equation 9 ^-3x ≈ 7?
Answer:
Press the png
Step-by-step explanation:
4/5 = 28/x
x=
i need to know what x =
Answer:
Hello! :) have a good day!
x = 35
4/5 = 28/35
Need number 11 and 10 all parts
Write 1/4 as a fraction with 8 as the denominator. Then add the fraction to 3/8. What is the sum? Write the fractions and the answer.
Answer:
2/8, 5/8
Step-by-step explanation:
[tex]\frac{1}{4}*\frac{2}{2} =\frac{2}{8} \\\\\frac{3}{8} +\frac{2}{8} =\frac{5}{8}[/tex]
Multiplying by 2/2 is like multiplying by 1, so it doesn't affect the value.
To add fractions with the same denominator just add the numerator, the denominator stays the same.
The fraction is 2/8 and the sum is 5/8.
What is Fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
let the numerator be x when denominator is 8.
so, 1/4 = x /8
8 = 4x
x= 8/4
x= 2
Now, fraction resulted above is added with 3/8
2/8 + 3/8
= (2+3)/8
= 5/8
Hence, the sum is 5/8.
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