We have to find the expression for the composition
[tex]g\circ\text{ g\lparen x\rparen}[/tex]Where
[tex]g(x)=\frac{6}{x}[/tex]And express its domain in set notation. We will start by finding the expression for the composition
[tex]g\circ\text{ }g(x)=g(g(x))=g(\frac{6}{x})[/tex]that is we firsts evaluate the inner functions that in this case is g, now taking as argument y=6/x, we evaluate the outer function that in this case also is g, as follows:
[tex]g\text{ \lparen }\frac{6}{x})=\frac{6}{\frac{6}{x}}=\frac{6}{6}=x[/tex]That is, the composition g*g is equal to x, the identity.
Now we will find the domain of g*g:
Note that the domain of a composition is an interception, as follows:
[tex]Domain\text{ }g\circ\text{ g=\textbraceleft Domain of }g\text{ \textbraceright }\cap\text{ \textbraceleft Image of }g\text{ \textbraceright}[/tex]Therefore, we have to find the domain and image of g, and intercept both sets. We start with the domain of g_
[tex]Domain\text{ of }g\text{ }=\text{ }\mathbb{R}\text{ - \textbraceleft0\textbraceright}[/tex]That is all the real numbers except the 0. Now note that the image of g is
[tex]Image\text{ g= }\mathbb{R}\text{ - \textbraceleft0\textbraceright}[/tex]Finally, the domain of the composition g*g, can be obtained by the formula above:
[tex]Domain\text{ of }g\circ\text{ g=}\mathbb{R}\text{ -\textbraceleft0\textbraceright }\cap\text{ }\mathbb{R}\text{ - \textbraceleft0\textbraceright= }\mathbb{R}\text{ - \textbraceleft0\textbraceright=}(-\infty\text{ },0)\text{ }\cup\text{ }(0,\infty)\text{ }[/tex]Therefore, the domain of the composition are all the real numbers excluding the 0.
-
. Find an ordered pair that represents a solution to the equation x + 2y = 20
we have
x + 2y = 20
The linear equation represent the equation of a line
If a ordered pair is a solution of the equation, that means that the ordered pair lies on the line
so
Find a ordered pair that represents a solution
Assume the value of x
so
For x=1
substitute in the equation
(1)+2y=20
solve for y
2y=20-1
2y=19
y=19/2
y=9.5
therefore
The ordered pair (1,9.5) represents a solutionWhich equation has (1,1),(2,4),(3,7) and (4,10) as solutions?A)y=2x - 1.B)y= 2x+3.C)y=3x-2.D)y=3x+1.
Answer:
y=3x-2
Explanation:
The equation that has the given solutions is the equation that satisfies all the given (x, y) pairs.
From the given options:
[tex]\begin{gathered} \text{When x=1} \\ y=3x-2 \\ y=3(1)-2=1 \\ \implies(1,1) \end{gathered}[/tex]Likewise:
[tex]\begin{gathered} \text{When x=}2 \\ y=3x-2 \\ y=3(2)-2=4 \\ \implies(2,4) \end{gathered}[/tex]Also when x=3:
[tex]\begin{gathered} y=3\mleft(3\mright)-2=7 \\ \implies(3,7) \end{gathered}[/tex]Finally, when x=4
[tex]\begin{gathered} y=3\mleft(4\mright)-2=10 \\ \implies(4,10) \end{gathered}[/tex]Thus, since y=3x-2 satisfies all four points, it is the right equation.
an object is thrown upward from the top of a 160 foots building with an initial velocity of 48 feet per second .solve the equation -16^2 + 48t + 160=0 find the time(t) in seconds at which the object hits the ground.
The given equation represents the distance travelled by the object at time t.
The given equation is expressed as
-16t^2 + 48t + 160
At the point where it hits the ground, the distance woule be 0. Thus, we would so;ve the equation,
-16t^2 + 48t + 160=0
We would divide through by - 16. We have
t^2 - 3t - 10 = 0
We would find two terms such that their sum or difference is - 3t and their product is - 10t^2. They are 2t and - 5t. We have
t^2 + 2t - 5t - 10 = 0
By factorising, we have
t(t + 2) - 5(t + 2) = 0
(t + 2)(t - 5) = 0
t + 2 = 0 or t - 5 = 0
t = - 2 or t = 5
Since the time cannot be negative, the correct answer is
time = 5 seconds
6 cm Find the missing dimension of each figure. Round your answer to the nearest tenth. 5. V=252 ft 4. V=100 in 6 ft 12 in 14 ft rin. eft Find the volume of each composite figure. Round your answer to the nearest tenth. 6. 6 in. 7. A cylindrical-shaped hole is cut from 11 in. the center of a cube. 2.5 cm 15 in.solve #5 please
The volume of cuboid is V = 252 ft^3.
The width of cuboid is w = 14 ft.
The height of cuboid is h = 6 ft.
The formula for the volume of cuboid is,
[tex]V=l\cdot w\cdot h[/tex]Substitute the values in the formula to determine the length of cuboid.
[tex]\begin{gathered} 252=l\cdot14\cdot6 \\ l=\frac{252}{84} \\ =3 \end{gathered}[/tex]So length (missing dimension) of the cuboid is 3 ft.
I think I got the two that I did but I’m not sure and really need help
b) You have the following expression:
[tex]x^3=\frac{27}{64}[/tex]Take into account that 27/64 can be written as follow:
[tex]\frac{27}{64}=\frac{3}{4}\cdot\frac{3}{4}\cdot\frac{3}{4}[/tex]Then, x = 3/4
c) For the following expression:
[tex]x^3=\frac{1}{8}[/tex]you can write it as follow:
[tex]\frac{1}{8}=\frac{1}{2}\cdot\frac{1}{2}\cdot\frac{1}{2}[/tex]Then, x = 1/2
Select the correct choice and fill in the blank if necessary
Given
[tex]f(x)=\frac{x+6}{x-7}[/tex]Recall
The horizontal line test can be used to determine if a function is one-to-one given a graph. Simply superimpose a horizontal line onto a graph and see if it intersects the graph at more than one point. If it does, the graph is not one-to-one and if it only intersects at one point, it will be one-to-one.
The graph
It passed the horizontal line test, therefore is one to one function
Part B
[tex]f(x)=\frac{x+6}{x-7}[/tex]Step 1
Replace f(x) with y
[tex]y=\frac{x+6}{x-7}[/tex]Step 2
Inter change y and x
[tex]x=\frac{y+6}{y-7}[/tex]Step 3
Make y the subject
[tex]\begin{gathered} x=\frac{y+6}{y-7} \\ x(y-7)=y+6 \\ xy-7x=y+6 \\ xy-y=6+7x \\ y(x-1)=6+7x \\ divide\text{ both sides by x-1} \\ y=\frac{6+7x}{x-1} \end{gathered}[/tex]Step 4
Replace y with f^-1
[tex]f^{-1}(x)=\frac{6+7x}{x-1}[/tex]The final answer
[tex]f^{-1}(x)=\frac{6+7x}{x-1}[/tex]A manufacturer knows that their items have a normally distributed lifespan, with a mean of 3.5 years, and standarddeviation of 0.6 years.The 10% of items with the shortest lifespan will last less than how many years?[1])])1)Give your answer to one decimal place.
1) In this question, we need to make use of a standard normal table to check which is the value (in terms of Z-score) for that 10%.
2) Checking that out, we can see that the Z-score is -1.282. So now, let's plug that into the Z-score formula so that we get the corresponding raw value:
[tex]\begin{gathered} Z=\frac{X-\mu}{\sigma} \\ -1.282=\frac{X-3.5}{0.6} \\ X=2.73\approx2.7 \end{gathered}[/tex]Thus, this is the answer: 2.7 years
The ratio of short to pants is 1:2 if there are eight shorts how many pants are there? 16,4,6,or 8
There are 16 pants
Explanation:Ratio of short to pants = 1:2
There are 8 shorts
Let x be the number of pants, then
8/x = 1/2
x = 8 * 2
= 16
There are 16 pants
Which one of the following equations could describe the above graph?OA. Y=1.5^(x+2)-3OB. Y=2^x+6Oc. = y=(1/2)^x+6D. Y= 3^(x-1)
Given:
The points lie on the graph are (1,1) and (2,3).
Required:
We need to find the equation of the given graph.
Explanation:
Consider the individual equation.
A.
[tex]y=1.5^{(x+2)}-3[/tex]Substitute x =1 and y =1 in the equation.
[tex]1=1.5^{(1+2)}-3[/tex][tex]1=0.375[/tex]This is not true,
This is not a required equation.
B.
[tex]y=2^x+6[/tex]Substitute x =1 and y =1 in the equation.
[tex]1=2^1+6[/tex][tex]1=8[/tex]This is not true,
This is not a required equation.
C.
[tex]y=(\frac{1}{2})^x+6[/tex]Substitute x =1 and y =1 in the equation.
[tex]1=(\frac{1}{2})^1+6[/tex][tex]1=6.5[/tex]This is not true,
This is not a required equation.
D.
[tex]y=3^{(x-1)}[/tex]Substitute x =1 and y =1 in the equation.
[tex]1=3^{(1-1)}[/tex][tex]1=1[/tex]This is true.
Substitute x =2 and y =3 in the equation.
[tex]3=3^{(2-1)}[/tex][tex]3=3[/tex]This is true.
This is a required equation.
Final answer:
[tex]y=3^{(x-1)}[/tex]Which additional piece of information would you need to prove these two triangles are congruent using the side-side-side or SSS triangle congruence postulate?
By using congruency of triangles, the result obtained is
The additional information needed to make [tex]\Delta STU \cong \Delta SHU[/tex] by SSS axiom is
TU = SH
Side SH is congruent to side TU
Third option is correct
What is Congruency of triangles?
Two triangles are said to be congruent if the corrosponding sides and corrosponding angles are same.
The different axioms of congruency are SSS axiom, SAS axiom, ASA axiom, AAS axiom, RHS axiom
In [tex]\Delta STU[/tex] and [tex]\Delta SHU[/tex]
ST = HU [Given]
SU is common.
The additional information needed to make [tex]\Delta STU \cong \Delta SHU[/tex] by SSS axiom is
TU = SH
Side SH is congruent to side TU
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15x+3x^2+55x^2+3x+155+3x+15x^2which is written in standard form.
ANSWER
[tex]5x^{2}+3x+15[/tex]EXPLANATION
A standard quadratic equation must be of the form;
[tex]ax^2+bx+c=0[/tex]Hence, the standard equation is;
[tex]5x^2+3x+15[/tex]Select the correct answer. Describes the zeros of the graphed function.
Answer
The function has 3 distinct roots (OPTION A)
SOLUTION
Problem Statement
The question gives us a graph and we are required to find the number of zeros the function has.
Method
- The number of zeros a function has corresponds to the number of times the graph crosses the x-axis. If the graph crosses the x-axis once then there is one zero. If it crosses the x-axis twice, then it has 2 zeros.
- The number of zeros a function has also depends on the way the graph touches the x-axis. If the graph touches the x-axis like a quadratic, then there are 2 zeros or zeros that are multiples of 2, that have the same value.
Implementation
The following can be observed from the figure given to us:
- The graph crosses the x-axis twice at x = -2 and x = 2. This means that the graph has at least 2 zeros.
- The graph curves like a quadratic at x = 0. This means that there are at least 2 zeros of the same value or zeros of the same value.
Thus, we can predict that the function must be:
[tex]x^2\mleft(x-2\mright)\mleft(x+2\mright)[/tex]
Final Answer
The answer is:
The function has 3 distinct roots (OPTION A)
Line segment EF is shown on the coordinate grid:A coordinate grid is shown from positive 6 to negative 6 on the x-axis and from positive 6 to negative 6 on the y-axis. A line segment EF is shown with E as ordered pair 1, negative 4 and F as ordered pair 5, negative 4.The line segment is rotated by 270 degrees counterclockwise about the origin to form E′F′. Which statement describes E′F′? (1 point)E′F′ is equal in length to EF.E′F′ is half the length of EF.E′F′ is parallel to EF.E′F′ is twice the length of EF.
the initial coordinates of EF are:
[tex](1,-4),(5,-4)[/tex]then the segment is rotate 270 degrees counterclockwise so:
In a rotation the length do not change so the answer is A) E'F' is equal in length to EF
In a lottery, the top cash prize was $629 million, going to three lucky winners. Players pick four different numbers from 1 to 56 and one number from 1 to 41.A player wins a minimum award of$525 by correctly matching three numbers drawn from the white balls (1 through 56) and matching the number on the gold ball (1 through 41).What is the probability of winning the minimum award?
Step 1
Given;
[tex]\begin{gathered} Top\text{ cash prize is \$629} \\ Players\text{ pick four different numbers from 1 to 56 and 1 to 41} \end{gathered}[/tex]Step 2
Probability is given as;
[tex]undefined[/tex]The sale Price of a swing set is $90. What is the original price?Sale:75% Round your answer to the whole dollar
To solve this problem we can use the expression that defines percents. What price has a 75% of $90?
[tex]\text{Total}\cdot\frac{\text{percent}}{100}=\text{equivalent number to the percent}[/tex]With the information given, we know that the equivalent number to the percent is $90 and the percent is 75%.
Then, substitute and solve for the total variable:
[tex]\begin{gathered} \text{Total}\cdot\frac{75}{100}=90 \\ \text{Total}=\frac{90\cdot100}{75} \\ \text{Total}=120 \end{gathered}[/tex]The original price of the swing set is $120.
Both customers spent same amount of money. customer one bought 8 chicken wings and left a tip of four dollars. second customer bought 10 chicken wings and left a tip of $2.50. how much is each chicken wing?
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the representation of the chicken wings
Let the chicken wing be represented by x
[tex]\begin{gathered} For\text{ Customer 1, he spent;} \\ 8x+4 \\ From\text{ second customer, he spent} \\ 10x+2.50 \end{gathered}[/tex]STEP 2: Equate the two amounts
Since they both spent same amount of money, this means that;
[tex]8x+4=10x+2.50[/tex]STEP 3: Solve for x
[tex]\begin{gathered} Collecting\text{ like terms:} \\ 8x-10x=2.50-4 \\ -2x=-1.5 \\ Divide\text{ both sides by -2} \\ \frac{-2x}{-2}=\frac{-1.5}{-2} \\ x=0.75 \end{gathered}[/tex]Hence, each chicken wing costs $0.75
What was the median price of new home in 1981
1) In this question, let's spot in the graph the median price given by the blue curve on the graph.
2) Examining it we can see that the y-axis point that corresponds to the Median Price in 1981 is:
[tex]\$70,000[/tex]
There are 30 boys in a sporting club, 20 of them play hockey and 15 play volleyball. Each play at least one 9f the two games. Illustrate this using:
A. The Venn diagram.
B. Only volleyball
C. Both games
The students who play both hockey and volleyball 5 and the Venn diagram is shown below.
What are Venn diagrams?A Venn diagram uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items. Often, they serve to graphically organize things, highlighting how the items are similar and different.A Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things. Circles that overlap have a commonality while circles that do not overlap do not share those traits. Venn diagrams help to visually represent the similarities and differences between two concepts.So, the Venn digram will be:
The total number of boys are 30.Boys playing hockey are 20.The boys playing volleyball are 15.A Number of students who play both:
(20+15) - 3035 - 305So, the Venn diagram will be:
(Refer to the Venn diagram attached below)Therefore, the students who play both hockey and volleyball 5 and the Venn diagram is shown below.
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3SpointsWhich is the image of vertex C after the triangle is rotated 180 degrees about the origin?
T' (3,0) A' (5,-1) and C' (2,-4)
1) Considering that the Pre-image coordinates are :T(-3,0), A (-5,1) C(-2,4)
and there was a rotation 180º about the origin, then
2) In the Rotation, the rules for 180º rotation Counterclockwise and clockwise is
Pre-image Image
(x,y) ---- (-x, -y)
3)
Thus,
T' (3,0) A' (5,-1) and C' (2,-4)
Gary and his four friends wish to share 45 cards equally. how many cards will each person get
The number of persons including Gary and four friends is 5.
Determine the number of cards that each person get.
[tex]\begin{gathered} n=\frac{45}{5} \\ =9 \end{gathered}[/tex]So each person get 9 cards.
Scores on a standardized reading test for fourth-gradestudents form a normal distribution with µ = 60 ando = 20. What is the probability of obtaining a sample mean greater than M = 65 for each of the following?a. A sample of n = 16 studentsb. A sample of n = 25 studentsc. A sample of n = 100 students
If scores on a standardized reading test form a normal distribution with (µ = 60) and (σ = 20), then the probability of obtaining a sample mean greater than (M = 65) for a sample size of (n = 16) will be .
As per the question statement, Scores on a standardized reading test for fourth-grade students form a normal distribution with (µ = 60) and (σ = 20),
And we are required to calculate the probability of obtaining a sample mean greater than (M = 65) for a sample size of (n = 16).
To solve this question, let us assume that, a random variable "X" follows normal distribution with mean (μ = 60), standard deviation (σ = 20) and a sample size of (n = 16).
Then the probability that a sample of size (n = 16) is randomly selected with a mean greater than 65 can be calculated as follows:
P(M > 65) = [1 - P(M < 65)]
= [1 - P{(M - μ)/(σ/√n) < (65 - 60/(20/√16)}]
= [1 - P{(M - μ)/(σ/√n) < (65-60)/(20/4)}]
= [1 - P{Z < (5/5)}]
= [1 - P(Z < 1)]
= (1 - 0.841344746069)...[Using Excel Function "NORMSDIST (1)]
= 0.158655253931
≈ 0.16
Probability: Probability is the branch of mathematics that deals with the numerical descriptions on the extent to which an event is likely to occur, or how likely it is, that a proposition is true, being calculated by the ratio of the favorable cases to the total number of cases possible.To learn more about Samples and Probability, click on the link below.
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In a circle of radius 10 cm, there are two parallel chords (in different sides of a circle) of lengths 16 cm and 12 cm. Calculate the distance between the chords.
The distance between the chords is 14 cm
Given that AB=16 cm and CD=12 cm
So, AL=8 cm and CM=6 cm (⊥ from the centre to the chord bisect the chord)
In right triangles OLA and OMC,
By Pythagoras theorem,
OA² = OL²+AL²
and OC² = OM²+CM²
⇒ 10² = OL²+8²
and 10² = OM²+6²
⇒ OL²=100-64
and OM² = 100 - 36
⇒ OL² = 36 and OM² = 64
⇒ OL = 6 cm
and OM = 8 cm
In the second case distance between AB and CD is:
LM=OM+OL
= 8+6
= 14 cm
Hence distance between the chords is 14 cm,
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Evaluate the expression when a=-5 and c=27c-a
Given:
7c - a
a=-5 and c = 2
Substitute the values into the expression
7(2) - (-5)
=14 + 5
= 19
In a game, 2 players each flip a coin. If both land on heads, player A gets 2points and player B loses 1 points. If both land on tails, player B gets 2 points andplayer A loses 1 point. Find the expected value of the game for each player.
The expected value for player A is:
[tex]\begin{gathered} (\frac{1}{2}\times\frac{1}{2}\times2)-(1\times\frac{1}{2}\times\frac{1}{2}) \\ =(\frac{1}{4}\times2)-(1\times\frac{1}{4}) \\ =(\frac{1}{2})-(\frac{1}{4}) \\ =\frac{1}{4} \end{gathered}[/tex]The expected value of player B is:
[tex]\begin{gathered} (\frac{1}{2}\times\frac{1}{2}\times2)-(1\times\frac{1}{2}\times\frac{1}{2}) \\ =(\frac{1}{4}\times2)-(1\times\frac{1}{4}) \\ =(\frac{1}{2})-(\frac{1}{4}) \\ =\frac{1}{4} \end{gathered}[/tex]A group have in their families. The bar graph of adults were asked how many children they below shows the number of adults who indicated each number of children.How many adults were questioned?
If we add the frequencies of the histogram ( vertical axis), we get that the number of adults questioned is:
[tex]4+7+5+3+1=20.[/tex]Now, out of those 20, only 5 have 2 children, therefore:
[tex]\frac{5}{20}*100=25\%[/tex]have 2 children.
Answer:
20 adults were questioned,
25% have 2 children.
I need help with this practice I am having trouble with it The subject is trig
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given range
[tex](-\infty,-9\rbrack\cup\lbrack5,\infty)[/tex]STEP 2: Find the cosecant function
[tex]\begin{gathered} \text{The range of a cosecant function normally excludes the interval }(-1,1)\text{.} \\ The\text{ range in the question excludes the interval }(-9,5)\text{, which has a width 7 times as great.} \\ \text{Thus, we know the vertical factor is 7.} \\ \\ T\text{he midpoint of the excluded interval of the given function is }\frac{(-9+5)}{2}=-\frac{4}{2}=-2 \\ so\text{ that is the vertical translation.} \\ \text{The cosecant function normally has vertical asymptotes at }x=0\text{ and }x=\pi\text{ so the function is } \\ \text{expanded horizontally by a factor of }2. \end{gathered}[/tex]Hence, the cosecant function is
[tex]undefined[/tex]What was the total length of all the scarves put together?
ANSWER :
37.8 feet
EXPLANATION :
From the problem, each scarf is 50.4 inches long.
Since there's a total of 9 scarfs.
The total length will be :
[tex]9(50.4)=453.6\text{ }in[/tex]There are 12 inches in 1 foot.
Divide the result by 12 to get the number of feet.
[tex]\frac{453.6}{12}=37.8\text{ }feet[/tex]Ryan earns $20 for every lawn that he mows. Which equation can be used to find t, the total amount Ryan will earn after mowing n lawns?
Ryan earns $20 for every lawn that he mows.
Let t represents the total amount Ryan will earn.
Let n repreents the number of laws Ryan will mow.
So, the equation becomes
[tex]t=20n[/tex]For example:
How much Ryan will earn if he mows 5 lawns?
Let us substitute n = 5 into the equation
[tex]\begin{gathered} t=20n \\ t=20(5) \\ t=\$100 \end{gathered}[/tex]Therefore, Ryan will earn $100 if he mows 5 lawns.
1. Predict what will happen when a tape diagram has a large number of squares, some squares are removed, and thenthe same amount of squares are added back on.Build a tana diagram mit 10
When some squares are removed, the number of squares in the tape diagram are reduced but when the same number of squares are added back, then we will find out that the number of squares in the tape diagram remain the same.
Solve by substitution method. a) x + y = 8 and x - y = 4
Answer:
x = 6
y = 2
Step-by-step explanation:
x + y = 8 ---> (1)
x - y = 4 ---> (2)
First, let us find the value of x.
For that, add both equations.
(1) + (2)
x + y + ( x - y ) = 8 + 4
Solve the brackets.
x + y + x - y = 8 + 4
2x = 12
Divide both sides by 2.
x = 6
Now let us find the value of y.
For that, let us use equation 1 and replace x with 6.
x + y = 8
6 + y = 8
Subtract 6 from both sides.
y = 8 - 6
y = 2