Answer:
(f o g)(x) = x + 5
General Formulas and Concepts:
Algebra I
Combining Like TermsAlgebra II
Function CompositionStep-by-step explanation:
Step 1: Define
f(x) = x + 2
g(x) = x + 3
(f o g)(x) = f(g(x))
Step 2: Find
Substitute: (f o g)(x) = (x + 3) + 2Combine like terms: (f o g)(x) = x + 5Answer:
f(x+3)=x+5
Goodluck to you
The amounts a soft drink machine is designed to dispense for each drink are normally distributed, with a mean of 12.1 fluid ounces and a standard deviation of 0.3 fluid ounce. A drink is randomly selected.
Required:
a. Find the probability that the drink is less than fluid ounces.
b. Find the probability that the drink is between and fluid ounces.
c. Find the probability that the drink is more than fluid ounces. Can this be considered an unusual event? Explain your reasoning.
Complete Question
The amounts a soft drink machine is designed to dispense for each drink are normally distributed, with a mean of 12.1 fluid ounces and a standard deviation of 0.3 fluid ounce. A drink is randomly selected.
Required:
a) Find the probability that the drink is less than 11.9 fluid ounces
b) Find the probability that the drink is between 11.6 and 11.9 fluid ounces
c) Find the probability that the drink is more than 12.6 fluid ounces. Can this be considered an unusual event? Explain your reasoning.
Answer:
a
[tex] P(X < 11.9 ) = 0.25239 [/tex ]
b
[tex]P( 11.6 < X < 11.9 ) = 0.20463 [/tex]
c
[tex] P(X > 12.6 ) = 0.047757 [/tex ]
Yes It is an unusual event
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 12.1[/tex]
The standard deviation is [tex]\sigma =0.3[/tex]
Generally the probability that the drink is less than 11.9 fluid ounces is mathematically represented as
P(X < 11.9 ) = P(\frac{X -\mu}{\sigma } < \frac{11.9 - 12.1}{0.3} )
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
[tex] P(X < 11.9 ) = P(Z< -0.667 ) [/tex ]
From the z table the area under the normal curve to the left corresponding to -0.667 is
P(Z< -0.667 ) = 0.25239
So
[tex] P(X < 11.9 ) = 0.25239 [/tex ]
Generally the probability that the drink is between 11.6 and 11.9 fluid ounces is mathematically represented as
[tex] P( 11.6 < X < 11.9 ) = P( \frac{11.6 -12.1}{0.3} < \frac{X -\mu}{\sigma } < \frac{11.9 - 12.1}{0.3} ) [/tex]
[tex]P( 11.6 < X < 11.9 ) = P( -1.667 < Z < -0.667 ) [/tex]
=> [tex]P( 11.6 < X < 11.9 ) = P( Z < -0.667) - P ( Z < -1.667 ) [/tex]
From the z table the area under the normal curve to the left corresponding to -1.667 is
P(Z< -1.667 ) = 0.047757
So
[tex]P( 11.6 < X < 11.9 ) = 0.25239 - 0.047757 [/tex]
=> [tex]P( 11.6 < X < 11.9 ) = 0.20463 [/tex]
Generally the probability that the drink is more than 12.6 fluid ounces is mathematically represented as
P(X > 12.6 ) = P(\frac{X -\mu}{\sigma } > \frac{12.6 - 12.1}{0.3} )
[tex] P(X >12.6 ) = P(Z> 1.667 ) [/tex ]
From the z table the area under the normal curve to the right corresponding to 1.667 is
P(Z> 1.667 ) = 0.047757
So
[tex] P(X > 12.6 ) = 0.047757 [/tex ]
Given that this probability is less than 0.05 , it mean it is an unusual event
which of the following are properties of all rectangles? Select all that apply.
Answer:
see explanation
Step-by-step explanation:
The rectangle has the following properties
• Opposite sides are parallel and congruent
• All angles are right angles
• The diagonals are congruent
• The diagonals bisect each other
Thus
They are quadrilaterals
Opposite sides are equal in length
All angles are 90°
Opposite sides are parallel
Rectangles are not parallelograms ( the angles of a parallelogram are not necessarily right and diagonals are not congruent )
Please help, this chapter was on derivatives...
(3) Differentiating both sides of
[tex]2x^{3/2} + y^{3/2} = 29[/tex]
with respect to x gives
[tex]3x^{1/2} + \dfrac32 y^{1/2} \dfrac{\mathrm dy}{\mathrm dx} = 0[/tex]
Solve for dy/dx :
[tex]\dfrac32 y^{1/2} \dfrac{\mathrm dy}{\mathrm dx} = -3x^{1/2} \\\\ \dfrac{\mathrm dy}{\mathrm dx} = \dfrac{-3x^{1/2}}{\frac32y^{1/2}} = \dfrac{-2x^{1/2}}{y^{1/2}} = -2\sqrt{\dfrac xy}[/tex]
Then the slope of the tangent line to the curve at (1, 9) is
[tex]\dfrac{\mathrm dy}{\mathrm dx} = -2\sqrt{\dfrac19} = -\dfrac23[/tex]
The equation of the tangent line would then be
y - 9 = -2/3 (x - 1) ==> y = -2/3 x + 29/3
(4) The slope of the tangent line to
[tex]y=\dfrac{ax+1}{x-2}[/tex]
at a point (x, y) on the curve is
[tex]\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{a(x-2)-(ax+1)}{(x-2)^2} = -\dfrac{2a+1}{(x-2)^2}[/tex]
When x = -1, we have a slope of 2/3, so
-(2a + 1)/(-1 - 2)² = 2/3
Solve for a :
-(2a + 1)/9 = 2/3
2a + 1 = -18/3 = -6
2a = -7
a = -7/2
The entrance for the amusement park is $40, visitors purchase additional $2
tickets for rides, games and food. How many tickets can you buy if you
brought $100 to spend at the park?
Answer:
2 tickets because round
Step-by-step explanation:
make an equation: 100=40x+2 and solve
2.45 tickets so only two
40+40 =80
100-80=20
but 100-2=98 so there is only 18$ left so not enough for another ticket
Answer:
30 Tickets
Step-by-step explanation:
In the question, it said that $40 is the entrance fee. Then, it said that visitors purchase additional tickets for rides, games, and food. This means that EACH ticket is 2 dollars.
Hence, $40 (entrance fee) + $2 (each ticket price) x (the number of tickets spent) = 100 (total amount of money).
So, the equation should be 40 + 2x = 100, which means x = 30.
100 - 40 = 60
60/2 = 30
30 tickets can be purchased
There are 31 guests at your home for a dinner party. In how many ways could the guests arrange themselves on a four person couch?
Answer:
7.75
Step-by-step explanation:
The total number of ways could the guests be arranged on a four person couch is 31465.
What is a function? What is equation modelling? What is a mathematical equation and expression?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the functionEquation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Given is that there are 31 guests at your home for a dinner party.
The total number of ways could the guests be arranged on a four person couch is -
C{31, 4} = 31!/{(31 - 4)!4!}
C{31, 4} = (31 x 30 x 29 x 28 x 27!/27! x 4!) = (31 x 30 x 29 x 28)/24 = 31465
C{31, 4} = 31465
Therefore, the total number of ways could the guests be arranged on a four person couch is 31465.
To solve more questions on equations, expressions and polynomials, visit the link below -
brainly.com/question/17421223
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HELP
Describe any similarities or differences in the following equations: y = 4x and y = -4x -3
Answer:
Step-by-step explanation:
y = 4x is proportional and linear ( y = coffienient(x) )
y = -4x - 3 is not proportional because it has a costant ( -3 )
They are both an equation, they have a coffienient, and a value like (x)
9514 1404 393
Answer:
the lines have opposite slopeseach is a mirror of the other in the line y = -1.5the point (-3/8, -3/2) is common to both linesStep-by-step explanation:
The slope of the first line is 4; the slope of the second line is -4, so the slopes are opposites of each other. (The lines are not perpendicular.)
The y-intercept of the first line is 0; that of the second line is -3, so they cross the y-axis in different places.
Since the slopes are opposites of each other, one line is a reflection of the other about the horizontal line through the point where the lines meet. That point is ...
4x = -4x -3
8x = -3
x = -3/8
y = 4x = -3/2
The point of intersection (common to both lines) is (-3/8, -3/2).
This is for the roller coaster design packet, I need the graph, I’ll give Brainliest and give a handsome amount of 100 points
Answer:
i am going to work it out
Step-by-step explanation:
i am to ask my mom for help and tell you the answer
44% x 205???????????????????????????????
Answer: 90.2
Step-by-step explanation:
evaluate (distributive property)
9*6= ? sixes + 4 sixes
=30 + ?
=???
Answer:
Step-by-step explanation:
If A, B and C are integers, according to distributive property;
A(B+C) = AB+AB
A is distributed over B and C
Given
9×6 = 5 sixes +4 sixes
5 sixes = 5(6) =30
4 sixes = 4(6) =24
9×6 = 5(6)+4(6)
9×6 = 30+24
9×6 = 54
Hence ? =5,?? =24 ??? = 54
What is the value of 12 (2b-4) when b=16
Answer:
this is the answer
Step-by-step explanation:
[tex]12(2(16) - 4) =336 [/tex]
336
Step-by-step explanation:
12(2×16-4) =12(32-4)=12×28=336
If x = 4 and y = 3, then xy – 2x = A 4 B 6 C 19 D 40
Answer:
A) 4
Step-by-step explanation:
Plug in the value for x and y.
(4 x 3) - 2(4)
12 - 8 = 4
Which of these numbers is greater than 2.25 but less than 1? Is it 1 or 1.5 or 0 or 2.5....
I think the answer is 1.5 but can someone tell me how I came up with this answer. He has to write it down.
Answer:
the answer is 1.5 of course because converting them into their fractional form indeed informs u that 1.5 is the solely answer
To visit his grandmother, Michael takes a motorcycle 3.85 kilometers and a horse 3.32 kilometers. In total, the
journey takes 50.54 minutes.
How many kilometers is Michael's journey in total?
Answer:
7.17
Step-by-step explanation:
sorry for the first answer
7.17 kilometres is Michael's journey in total.
Given that, the number of kilometres Michael travelled on motorcycle =3.85 kilometres and on a horse 3.32=kilometers.
How to find the total distance travelled?Total distance means the actual distance between the places from which the material is transported to the destination place.
The total distance travelled is the path taken by a body to get from an initial point to an endpoint in a given period of time.
Now, total distance travelled=3.85+3.32=7.17 kilometres.
Therefore, the distance travelled is 7.17 kilometres.
To learn more about distance visit:
https://brainly.com/question/15172156.
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Write the improper fraction 62/9 as a mixed number.
Answer:
62/9
Step-by-step explanation:
help me asap please!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
D. should be the answer
Ha, Asa and Aas are correct because there is only one known side, and two known angles, making these postulates correct.
For the following quadratic equation, find the discriminant.
5x^2– 10x – 255 = 0
please help meee
Answer:
5200
Step-by-step explanation:
STEP 1: The discriminant of a quadratic is the expression inside the radical of the quadratic formula.
[tex]b^2-4(ac)[/tex]
STEP 2: Substitute in the values of a, b, and c.
[tex](-10)^2-4(5)(-255)[/tex]
STEP 3: Evaluate the result to find the discriminant.
[tex]5200[/tex]
Given: BD is perpendicular to AC, measure DBA = 7x+6. Find x
Answer:
x = 12
Step-by-step explanation:
[tex] \because BD \perp AC... (given) \\\\
\therefore m\angle DBA =90\degree... (1)\\\\
\because m\angle DBA=(7x + 6)\degree... (2)\\[/tex]
From equations (1) & (2)
[tex](7x + 6)\degree= 90\degree \\\\
7x + 6 =90\\\\
7x = 90 - 6\\\\
7x = 84\\\\
x = \frac{84}{7}\\\\
\huge \orange {\boxed {x = 12}} [/tex]
simplify the following boolean expression (A+B) (A+B)
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[tex](A + B)(A + B) = [/tex]
[tex] {A}^{2} + 2AB + {B}^{2} [/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
IF YOU ANSWER THIS YOU WILL HAVE BRAINLIEST AND FRIEND REQUEST
Answer:
Uhm answer what? there is no picture nor question.
Step-by-step explanation:
theres nothing there
Step-by-step explanation:
do u play among us
pls help 19 points !!
Answer:
(3,-2), (-3,-7), 2nd one is x2,y2
Step-by-step explanation:
Which is not a terminating decimal? -3/9, 6/36, 12/28, 7/8
Answer: 12/28
Explanation: I got this right years ago my man.
The graph shows y as a function of x:
y
B
А
D
In which segment is the function increasing?
Answer:
The correct answer (B)
Mrs. jones bought 25 mangoes for $7.50. she sold 12 mangoes for 60 cents each and the remaining for 55 cents each. a. state whether she made a profit or loss b. calculate the profit loss c. calculate the percentage profit or loss
Answer:
when u search it one by one
A random sample of 2,500 people was selected, and the people were asked to give their favorite season. Their responses, along with their age group, are summarized in the two-way table below.
Among those whose favorite season is spring, what proportion are adults?
1.)250/1000
2.)250/2500
3.)475/2500
4.)250/475
5.)225/475
Answer:
250/475
Step-by-step explanation:
write the slope intercept
Answer:
b = 4,
m = 4/3,
y = 4x/3 + 4
Step-by-step explanation:
We can see the line intercepts the x-axis in (-3,0) and the y-axis in (0,4). So, using the fact that the line equation in the slope-intercept form is:
[tex]y = mx+b[/tex]
We can substitute the points we know:
→ (0,4):
[tex]y = mx+b\\\\4 = m\cdot0+b\\\\4 = 0+b\\\\\boxed{b=4}[/tex]
→ (-3,0):
[tex]y = mx+b\\\\0 = -3m + 4\\\\3m = 4\\\\\boxed{m = \dfrac{4}{3}}[/tex]
So, the line equation in form requested is:
[tex]\boxed{y=\dfrac{4}{3}x+4}[/tex]
Tall Mountain is 8,678.37 feet higher than Mt. Might. What is the elevation of Tall Mountain?
The elevation of Tall Mountain is
feet.
Answer:
i wont give u a direct answer but i will tell u this.. Look up Mt. Mights height and subtract 8,678.37 with a cauculator. The answer will tell you
Answer: 28,979.87
Step by step explanation: I GOT THE ANSWER CORRECT!!!!!! For any one wondering I am doing this question right no and what the other guy said about subtracting is wrong because i tried doing tat and it said it was wrong.
A quadrilateral has no pairs of parallel sides, what two shapes could it be?
Answer:
Kite
Step-by-step explanation:
Def of kite has no parallel sides
Answer:
Kite and TrapeziumStep-by-step explanation:
Each of them do not have any parallel lines or sides
Kim received a discount of $8.60 when she purchased an item for $20. What was the percent of the discount?
Can someone help me??
Answer:
24 i think if im wrong im sorry :(
Step-by-step explanation:
How long would 8 thousand trillion trillion trillion trillion trillion trillion trillion trillion years be if typed out?
Answer:
100 digits
Step-by-step explanation:
One trillion is 10¹², so it adds 12 zeros.
8000 adds 4 digits.
8 trillions add 8·12 = 96 zeros.
So in total you have 96+4 = 100 digits
This number would also be called 8 googol, since 1 googol is 10¹⁰⁰