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To find the inverse of a function:
[tex]f(x)=\frac{2}{x-5}[/tex]We will follow the steps below
Step 1: Replace f(x) witth y
[tex]y=\frac{2}{x-5}[/tex]Step 2: interchange x with y
[tex]x=\frac{2}{y-5}[/tex]Step 3: Make y the subject of the formula
[tex]\begin{gathered} y-5=\frac{2}{x} \\ \\ y=\frac{2}{x}+5 \end{gathered}[/tex]Thus, the inverse of the function is:
[tex]y=\frac{2}{x}+5[/tex]Related Questions
A tub of theater popcorn has 247.5 grams of popcorn, which is 275% larger than a regular bag of popcorn. How many grams of popcorn would be in a regular sized bag.
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Let's begin by listing out the information given to us:
A tub has this: 247.5 grams of popcorn = 275%
regular-sized bag: x grams = 100%
We will solve using simple proportion
[tex]\begin{gathered} 247.5g=275 \\ xg=100 \\ \text{Cross Multiply, we have:} \\ 247.5\cdot100\cdot g=275\cdot x\cdot g \\ \text{Make x the subject of formula (divide by 275g)} \\ \frac{247.5\cdot100\cdot g}{275\cdot g}=\frac{275\cdot x\cdot g}{275\cdot g} \\ 0.9\cdot100=x\Rightarrow x=900 \\ x=900g \end{gathered}[/tex]Triangle BCA is similar to Triangle STR . What is the value of x?
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Sin the triangles are similar the ratio 4 to 6 should hold for any side, this means that:
[tex]\frac{4}{6}=\frac{x}{9}[/tex]Solving for x we have:
[tex]\begin{gathered} \frac{4}{6}=\frac{x}{9} \\ x=9(\frac{4}{6}) \\ x=\frac{36}{6} \\ x=6 \end{gathered}[/tex]Therefore. x=6.
In the diagram below of AGJK, H is a point onGJ, HJ = JK, m2 = 28, and mZGJK = 76.What is mZGKH?2870H
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Problem
Solution
For the triangle GKJ we can find the angle K on this way:
28 +70 + Now we know that HJ= JK so then the triangle HJK is an isosceles triangle so then < JHK = < HKJ and we can do this:
70+ 2x = 180
2x= 110
x= 55
And then we can find the angle < GKH with the following equation:
28+70 + (55+y) = 180
y= 180-55 -28-70= 27
give the coordinates of the image of each point under a reflection across to given line.(0,8); y=x
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Answer:
(8, 0)
Explanation:
Whenever a point (x,y) is reflected across the line y=x, the transformation rule is given below:
[tex](x,y)\to(y,x)[/tex]That is, the x-coordinate and y-coordinate change places.
Therefore, the image of the point (0,8) when reflected across the line y=x is:
[tex](8,0)[/tex]The correct answer is (8,0).
Here is a system of equations.y=-3x+3y=-x-1Graph the system. Then write its solution. Note that you can also answer "No solution" or "Infinitely many solutions.-6
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From the given system, we can observe that the y intercepts of the equations are 3 and -1 respectively.
Also we can find the x intercepts by replacing y for 0 and solving for x:
[tex]\begin{gathered} 0=-3x+3 \\ -3=-3x \\ x=\frac{-3}{-3} \\ x=1 \end{gathered}[/tex][tex]\begin{gathered} 0=-x-1 \\ 1=-x \\ x=-1 \end{gathered}[/tex]It means that the x intercepts of the lines are 1 and -1 respectively.
Using these points we can graph both lines, this way:
According to this graph, the intersection of these lines is at (2, -3). This represent the solution of the system, therefore, the solution of the system is x=2 and y=-3.
A basketball player scored 24 times during one game. she scored a total of 38 points, two for each two-point shot and one for each free throw. How many two-point shots did she make? How many free throws?
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The number of two-points shots made is 14
The number of free throws made is 10
What is the number of two-points shots and free throws made?The first step is to formulate a set of linear equations that represent the information in the question:
x + y = 24 equation 1
2x + y = 38 equation 2
Where:
x = number of two-point shots made y = number of free throws madeThe linear equations would be solved using the elimination method.
In order to determine the value of x, take the following steps:
Subtract equation 1 from equation 2
x = 14
Substitute for x in equation 1
14 + y = 24
Combine similar terms:
y = 24 - 14
Add similar terms together
y = 10
To learn more about linear equations, please check: https://brainly.com/question/25875552
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Answer:
Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables are studied under the supposition or demand that they depend, by some law or rule, on the values of other variables.
Step-by-step explanation:
If the m< P is 65 degrees, then what is the measure of Arc XY
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Answer:
[tex]\text{ArcXY}=115\text{ degrees}[/tex]Step by step explanation:
We can solve this situation by the theorem of the angle formed outside of a circle by intersection:
*For two tangents:
[tex]mThen, if m
[tex]\begin{gathered} 65=\frac{1}{2}((360-mXY)-mXY) \\ 65=\frac{1}{2}(360-\text{mXY-mXY)} \\ 65=\frac{1}{2}(360-2\text{mXY)} \\ 65=180-\text{mXY} \\ \text{mXY}=180-65 \\ \text{mXY}=115 \end{gathered}[/tex]
A country with 16 states and a population of 615529 contains 128 seats in a House of Representatives.What is the average number of seats assigned per state?
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Since there are 128 seats available and these 128 seats will be filled in by people from 16 states, we will divide 128 by 16 to get the average number of seats assigned per state.
[tex]128\div16=8[/tex]Therefore, the average number of seats assigned per state is 8.
A triangle has angle measurements of 15°, 90°, and 75°. What kind of triangle is it?
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The triangle has one angle of 90 degrees, so it is a rigth triangle.
As the other two angles are different between them, the triangle is also scalene (all sides are different)
.
Can you please help me solve this and the test statistics and p value
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The claim is that the population mean for the smartphone carrier's data speed at airports is less than 4.00 Mbps
The parameter of the study is the population mean, symbolized by the Greek letter mu "μ"
The researchers believe is that his value is less than 4, you can symbolize this as:
[tex]\mu<4[/tex]This expression does not include the "=" symbol, which indicates that it represents the alternative hypothesis. The null and alternative hypotheses are complementary, so if the alternative hypothesis represents the values of μ less than 4, then the null hypothesis, as its complement, should represent all other possible values, which are those greater than and equal to 4. You can represent this as:
[tex]\mu\ge4\text{ or simply }\mu=4[/tex]The statistical hypotheses for this test are:
[tex]\begin{gathered} H_0\colon\mu=4 \\ H_1\colon\mu<4 \end{gathered}[/tex]Option A.
In the display of technology, you can see the data calculated for the test.
The second value shown in the display corresponds to the value of the test statistic under the null hypothesis, you have to round it to two decimal places:
[tex]t_{H0}=-2.432925\approx-2.43[/tex]The value of the test statistic is -2.43
The p-value corresponds to the third value shown in the display.
The p-value is 0.009337
To make a decision over the hypothesis test using the p-value you have to follow the decision rule:
- If p-value ≥ α, do not reject the null hypotheses.
- If p-value < α, reject the null hypotheses.
The significance level is α= 0.05
Since the p-value (0.009337) is less than the significance level of 0.05, the decision is to reject the null hypothesis.
Conclusion
So, at a 5% significance level, you can conclude that there is significant evidence to reject the null hypothesis (H₀: μ=4), which means that the population mean of the smartphone carrier's data speed at the airport is less than 4.00 Mbps.
AABC - ADEF? Explain your reasoning. E 6 units C 40° 9 units 4 units 6 units er your answer and explanation.
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Side-Angle-Side Theorem states that triangles are congruent if any pair of corresponding sides and their included angle are congruent.
How do we know that their sides are congruent, by similarity ratios, means a ratio of the lengths of the sides to see if they have the same ratio or scale factor:
[tex]\begin{gathered} \frac{9}{6}=1.5 \\ \frac{6}{4}=1.5 \end{gathered}[/tex]Then, since their sides are congruent and they have the same angle, they are congruent by SAS.
3.50 divide by 24.50
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Answer:
1/7 or 0.143
Step-by-step explanation:
i hope this helps
Describe the correlation in the scatter plot below.----------------The scatter plot shows (positive linear, positive linear with one outlier, negative linear, negative linear with one outlier, nonlinear, or no) correlation because as the plotted values of x increase, the values of y generally (decrease, increase, show no pattern or follow a nonlinear pattern).
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A scatter plot shows a positive correlation when the values of y tend to increase as the values of x increases.
From this scatter plot, we can see that as the values of x increase, the values of y also increase. Therefore, this scatter plot shows a positive linear correlation.
An outlier is the the dot which doesn't fit with other dots or is far away from the rest of the dots. Here, we have one outlier.
Therefore, we can say the scatter plot shows positive linear with one outlier correlation because as the plotted values of x increase, the values of y generally increase.
ANSWER:
The scatter plot shows positive linear with one outlier correlation because as the plotted values of x increase, the values of y generally increase.
write the slope intercept form:through: (2, 5), perp. to y= -5
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If the original line is y = -5, then the perpendicular line would be x = a, where a is the x value of the point where it passes through, then the line is x = 2
Answer:
x = 2
a diver takes a dive in the red sea. He initially descends 100 feet. Then rises 28 before descending another 33. What is his final position
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Descending: subtraction
Rises: Addition
The diver descends 100ft: Position -100 (the 0 is the sea level)
Then rises 28: Add 28 to the previous position: Position -72
[tex]-100+28=-72[/tex]...before descending another 33: Subtract 33 to the previous position:
[tex]-72-33=-105[/tex]Then, the final position is -105ft (105 ft under the sea level)
1 pointThe 5 consecutive integers below add up to 175. What is the value of x?x-3x-2X - 1ХX + 1
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Then x=36.
The first three terms of a sequence are given. Round to the nearest thousandth (ifnecessary).15, 18, 108/5. find the 8th term
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SOLUTION
The following is a geometric series
We will use the formula
[tex]T_n=ar^{n-1}[/tex]Where Tn is the nth term of the series,
n is the number of terms = 8,
a is the first term = 15
And r is the common ratio = 1.2 (to find r, divide the second term, 18 by the first term which is 15
Now let's solve
[tex]\begin{gathered} T_n=ar^{n-1} \\ T_8=15\times1.2^{8-1} \\ T_8=15\times1.2^7 \\ T_8=15\times3.583 \\ T_8=53.748 \end{gathered}[/tex]So the 8th term = 53.748
I can't solve them 15 here and 15 on another post
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6. Measure of angle 1 is 60 degrees because it congruent to angle 4 because they are opposed by the vertex
7. Measure of angle 3 is equal to 180 - angle 1 - angle 2 = 180 - 60 - 40 = 80 because these three angles sum 180 degrees
8. Measure of angle 5 is 40 degrees because it congruent to angle 2 because they are opposed by the vertex
9. Measure of angle 6 is equal to angle 3, because they are congruent, so it measures 80 degrees
10. Mesure of angle 7 is equal to the sum of angles 1 and 2 because they are congruent, so measure of angle 7 is 100
11. 80
12. 60
13. 120
14. 60
15. 120
How do you convert 313313 yards to inches? Use the drop-down menus to explain your answer.Since there are inches in 11 yard, 313313 by .So, 313313 yards = inches.
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Given:
[tex]3\frac{1}{3}\text{yards}[/tex]Aim:
We need to convert yards into inches.
Explanation:
[tex]3\frac{1}{3}\text{yards}=\frac{3\times3+1}{3}\text{ yards}[/tex]
[tex]3\frac{1}{3}\text{yards}=\frac{10}{3}\text{ yards}[/tex]
Recall that
[tex]1\text{ yard =}36\text{ inches}[/tex]Multiply 10/3 on both sides, we get
[tex]\frac{10}{3}\text{ yards =}\frac{10}{3}\times36\text{ inches}[/tex][tex]\frac{10}{3}\text{ yards=}120\text{ inches}[/tex][tex]3\frac{1}{3}\text{ yards =}120\text{ inches}[/tex]We know that
[tex]3\frac{1}{3}\times36=120[/tex]Final answer:
Since there are 36 inches in 1 yard.
[tex]\text{ multiply 3}\frac{1}{3}\text{ by 36.}[/tex][tex]\text{ So, }3\frac{1}{3}\text{ yards =}120\text{ inches}[/tex]a. A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 45 months and a standard deviation of 3 months. Using the empirical rule (as presented in the book), what is the approximate percentage of cars that remain in service between 48 and 51 months?b. The physical plant at the main campus of a large state university recieves daily requests to replace fluorescent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 64 and a standard deviation of 7. Using the empirical rule (as presented in the book), what is the approximate percentage of lightbulb replacement requests numbering between 57 and 64?
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In this case
[tex]\begin{gathered} 48=45+3 \\ 51=45+2(3) \end{gathered}[/tex]Therefore, the percentage that lies between 45 and 48 is given by
[tex]\frac{68}{2}=34\text{ \%}[/tex]And, the percentage that lies between 45 and 51 is given by
[tex]\frac{68}{2}=34\text{ \%}[/tex]Each face of a pyramid is an isosceles triangle with a 70 degree vertex angle. What are the measures of the base angles?
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We are given that each face of a pyramid is an isosceles triangle and that its vertex angle is 70 degrees. This problem can be exemplified in the following diagram:
Since the triangle is isosceles, its base angles are the same, and the sum of the interior angles must be equal to 180 degrees. Therefore, we have the following relationship:
[tex]70+x+x=180[/tex]Adding like terms, we get:
[tex]70+2x=180[/tex]Now we solve for "x", first by subtracting 70 on both sides:
[tex]\begin{gathered} 70-70+2x=180-70 \\ 2x=110 \end{gathered}[/tex]Now we divide both sides by 2
[tex]x=\frac{110}{2}=55[/tex]Therefore, the base angles of the pyramid are 55 degrees.
Answer this question and show me how to check it
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We write numbers that are very small or very large in standard form. Any number that we can write as a decimal number, between 1.0 and 10.0, multiplied by a power of 10, is said to be in standard form
Given that the length and thickness as
[tex]\begin{gathered} l=8\times10^4 \\ t=5\times10^{-6} \end{gathered}[/tex]The ordinary form of the wire is
[tex]\begin{gathered} l=8\times10^4m=8\times10000m=80000m \\ t=5\times10^{-6}m=5\times\frac{1}{1000000}m=0.000005m \end{gathered}[/tex]From the defination of standard form, taking the length, 8 is a number between 1.0 and 10.0 and 10⁴m is a power of 10.
Also, the width, 5 is a number between 1.0 and 10.0 and 10 ⁻⁶ is a power of 10.
Hence, the standard form of the length and thickness of the wire is
length = 8.0 x 10⁴m
thickness = 5.0 x 10 ⁻⁶m
A loaded S-sided de is loaded so that the number 4 occurs 3/10 of the time while the other numbers occur with equal frequency. What is the expected value of this die? CASS 08.44 OC.48 Next O My
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The probablity of obtain a 4 is= 3/10
The probablity of obtain a 1,2,3,5,6,7,8= 1-3/10=7/10
The expect value is:
[tex]E(p)=X1*p1+X2*p2+X3*p3+...+X8*p8[/tex]And p(1)=p(2)=p(3)=p(5)=p(6)=7/10
All have the same frequency, therefore
p(1,2,3,5,6,7,8)=7/10*1/5=7/50=1/10
Where x=1, 2 ,3,4,5,6 and p=3/10 if is 4 and 7/10 for any other number.
Replacing:
[tex]\begin{gathered} E=(1+2+3+5+6)*\frac{7}{50}+4*\frac{3}{10} \\ \\ E=2.38+1.2=3.58\approx4 \end{gathered}[/tex]Number 5 need help I really forgot how to solve this problem
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Line Segments and Rays
A line segment has two endpoints. It contains these endpoints and all the points of the line between them,
A ray is a part of a line that has one endpoint and goes on infinitely in only one direction. You cannot measure the length of a ray.
The figure shows a line that starts in B and goes infinitely to the left side, passing through A, thus the correct choice is B. Ray BA
Andre is looking at apartments with 1 of his friends. They want the monthly rent to be no more than $1000. If the roommates split the rent evenly among the two of them, what is the maximum rent each will pay?
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We have the next inequality
[tex]2x\le1000[/tex]where x is the rent of each person
[tex]\begin{gathered} x\le\frac{1000}{2} \\ x\le500 \end{gathered}[/tex]The maximum rent each will pay is $500
WITHOUT using a graphing device, find the x- and y-intercepts of the graph:y = 3x^3 - 9x^2
Answers
Given:
The function is,
[tex]y=3x^3-9x^2[/tex]To find the x intercept set y=0,
[tex]\begin{gathered} y=3x^3-9x^2 \\ 3x^3-9x^2=0 \\ x^2(3x-9)=0 \\ \Rightarrow x^2=0,3x-9=0 \\ x=0,3x=9 \\ x=0,x=\frac{9}{3} \\ x=0,x=3 \end{gathered}[/tex]So, x-intercepts are ( 0 , 0 ), ( 3, 0 ).
Now to find y-intercepts set x=0.
[tex]\begin{gathered} y=3x^3-9x^2 \\ y=3(0)-9(0) \\ y=0 \end{gathered}[/tex]y- intercept is ( 0 ,0 )
Answer: option e)
The given diagram shows the steps for constructing a parallel line to line AB and passing through point P, but an error has occurred in the construction
Answers
Given:
Constructing a parallel line to line AB and passing through point P.
To find:
The error occurred in the construction.
Explanation:
The procedure is,
The first arc must be drawn centred at C.
The second must be drawn centred at P.
Finally, the third arc must be drawn centred at F.
But here, the third arc is drawn centred at D. This is wrong.
Therefore, the correct step is that the third arc must be centred at F.
Final answer:
The third arc should be drawn centred at F.
A golf course charges you $54 for a round of golf using a set of their clubs, and $42 if you have your own clubs. You decide to buy a set of clubs for $280 and your friend wants to just use the course's clubs.a. Write an equation to describe the cost for x number of rounds for you.b. write an equation to describe the cost for x number of rounds for your friend.c. How many rounds must you play to recover the cost of the clubs? (Find the break-even point).
Answers
Answer
You must play 24 rounds to recover the cost of the club
Step-by-step explanation:
The amount golf charged for using their set clubs = $54
They charged $42 for using personal course
let x be the number of rounds played
let y be the total cost of the clubs
Since you will be buying a set of clubs worth $280
Then, the first equation is
a. y = 280 + 42x
b. y = 54x
c . Calculate the number of rounds that must be played to recover the cost of the clubs
To calculate this, we need to equate equations a and b together
280 + 42x = 54x
Collect the like terms
280 = 54x - 42x
280 = 12x
Isolate x by dividing through by 12
280/12 = 12x/12
x = 23.3333
Hence, you must play 24 rounds to recover the cost of the club
Which expression is equivalent to (6 – 3x) + 9x ? 1 A. 8x + 2 B. 8x + 3 C. 10x-2 D. 10x - 6
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Given to solve the expression:
[tex]\frac{1}{3}(6-3x)+9x[/tex]step 1: Expand the bracket by multiplying each term by the factor outside
[tex]\begin{gathered} (\frac{1}{3}\times6)-(\frac{1}{3}\times3x)+9x \\ 2-x+9x \end{gathered}[/tex]step 2: Simplify the expression obtained in step 1
[tex]\begin{gathered} 2-x+9x\text{ } \\ =2+8x \\ =8x+2 \\ \\ \text{The answer is \lbrack{}Option }A\rbrack \end{gathered}[/tex]Not sure on how to do this. Would really like some help.
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Given:
[tex]\cos60^{\circ}[/tex]To find:
The value
Explanation:
We know that,
[tex]\cos\theta=\sin(90-\theta)[/tex]So, we write,
[tex]\begin{gathered} \cos60^{\circ}=\sin(90-60) \\ =\sin30^{\circ} \\ =\frac{1}{2} \end{gathered}[/tex]Final answer:
[tex]\cos60^{\circ}=\frac{1}{2}[/tex]