Each pair has the inverse points corresponding to the points in the original set.
To match the sets of points representing one-to-one functions with the sets of points representing their inverse functions, we need to find the pairs where each point in one set corresponds to the inverse point in the other set.
Here are the matches:
1. Set of Points Representing Function: [tex]\( h = \{(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)\} \)[/tex]
Set of Points Representing Inverse Function: [tex]\( h^{-1} = \{(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)\} \)[/tex]
2. Set of Points Representing Function: [tex]\( g = \{(1,3), (2,6), (3,9), (4,12), (5,15), (6,18)\} \)[/tex]
Set of Points Representing Inverse Function: [tex]\( g^{-1} = \{(3,1), (6,2), (9,3), (12,4), (15,5), (18,6)\} \)[/tex]
3. Set of Points Representing Function: [tex]\( f = \{(1,2), (2,3), (3,4), (4,5), (5,6), (6,7)\} \)[/tex]
Set of Points Representing Inverse Function: [tex]\( f^{-1} = \{(2,1), (3,2), (4,3), (5,4), (6,5), (7,6)\} \)[/tex]
4. Set of Points Representing Function: [tex]\( i = \{(1,1), (2,3), (3,5), (4,7), (5,9), (6,11)\} \)[/tex]
Set of Points Representing Inverse Function: [tex]\( i^{-1} = \{(1,1), (3,2), (5,3), (7,4), (9,5), (11,6)\} \)[/tex]
Each pair has the inverse points corresponding to the points in the original set.
State how many imaginary and real zeros the function has. f(x) = x^5+7x^4+2x^3+14x^2+x+7
Since the degree of the equation is 5, then the number of zeros is also equal to 5. We can find for the 1st value of the root by trial and error. To do this, we find for the value of x which makes the equation equal to zero, that is:
x^5 + 7x^4 + 2x^3 + 14x^2 + x + 7 = 0 (find x)
By trial and error I made (which I will not show anymore), the possible root is -7. This is equivalent to x + 7.
To find more roots, we divide x^5 + 7x^4 + 2x^3 + 14x^2 + x + 7 by x + 7. The answer of the division results in x^4 + 2x^2 + 1 which is a perfect square trinomial in the form of:
(x^2 + 1)^2
Therefore the other 4 roots are:
x^2 + 1 = 0 ---> i, -i
and
x^2 + 1 = 0 ---> i, -i
Therefore the answer is:
1 real and 4 imaginary zeros
Oq is a diagonal of quadrilateral nopq. if noq=pqo, no = 5x + 12, and pq = 7x – 8, find the length of no for which nopq is a parallelogram.
a. 10
b. 24
c. 47
d. 62
Since it is a parallelogram, NO = PQ
5 x + 12 = 7 x - 8
12 + 8 = 7 x - 5 x
20 = 2 x
x = 20 : 2
x = 10
NO = 5 * 10 + 12 = 50 + 12 = 62
Answer: 62
Hope this helps, have a BLESSED and wonderful day, as well as a safe one! Also, have a merry Christmas! :-)
-Cutiepatutie
Twelve employees were sick. If the company has 360 employees, what percent of the employees were sick on Monday? Round to the nearest tenth.
The lengths of the sides of a triangle are in the extended ratio 1:2:5. The perimeter of the triangle is 32 ft. The length of the longest side is?
PLEASE HELP! (8)/(5x) - (4)/(x^2) Show your work :)
The graph below shows the height of a tunnel f(x), in feet, depending on the distance from one side of the tunnel x, in feet:
Graph of quadratic function f of x having x intercepts at ordered pairs 0, 0 and 120, 0. The vertex is at 60, 35.
Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the distance and height?
Part B: What is an approximate average rate of change of the graph from x = 20 to x = 35, and what does this rate represent?
Answer:
i have the image of the tunnel and here is my work
Part B: x=20 y=20 x=35 y=60 so {60-20}/{35-20}=40/15=2.6
hope this helps
A real estate agent received a 6% commission on the selling price of a house. If his commission was $8,880, what was the selling price of the house?
If 2+2=4 why is the answer fish
The empty gas tank of a truck needs to be completely filled. The tank is shaped like a cylinder that is 3 ft long with a diameter of 2.4 ft . Suppose gas is poured into the tank at a rate of 2.5 ft 3 per minute. How many minutes does it take to fill the empty tank? Use the value 3.14 for π , and round your answer to the nearest minute. Do not round any intermediate computations.
Find the truth set of each of these predicates where the domain is the set of integers.
a.p(x): x3 ≥ 1
b.q(x): x2 =2
c.r(x): x < x2
Please help me on this one
south America = 2.2%
2.2% = 0.022
0.022 = 22/1000 which reduces to 11/500
A mail distribution center processes as many as 150,000 pieces of mail each day. The mail is sent via ground and air. Each land carrier takes 1800 pieces per load and each air carrier 1500 pieces per load. The loading equipment is able to handle as many as 150 loads per day. Let x be the number of loads by land carriers and y the number of loads by air carriers. Which system of inequalities represents this situation? Click on the correct answer. 1500x + 1800y ≥ 150,000 x + y ≤ 150 1800x + 1500y ≤ 150,000 x + y ≤ 150 1800x + 1500y ≥ 150,000 x + y ≥ 150 1500x + 1800y ≤ 150,000 x + y ≤ 150
x = land carriers = 1800x
y = air carries = 1500y
as many as means up to that amount so <=150000 and <= 150
so equation is:
1800x + 1500y ≤ 150,000 x + y ≤ 150
The correct system of inequalities for this problem is: 1500x + 1800y ≤ 150,000 and x + y ≤ 150 - representing mail distribution limitations of a center.
Explanation:In order for the mail distribution center to process the maximum amount of mail (150,000 pieces) with the available resources, the inequalities should be framed as follows:
The total pieces of mail loaded should be equal to or less than 150,000: 1500x + 1800y ≤ 150,000The total loads done by air and land carriers should not exceed the limit of 150: x + y ≤ 150This mathematical model sets the limitations of the mail distribution process and can be used to predict the optimal allocation of mail to air and land carriers.
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Solve the equation for x and round your answer to the nearest hundreth. 5 = ln(x + 1)
18 thousands times 10=
Answer:
180,000.
Step-by-step explanation:
Given : 18 thousands times 10.
To find : Solve .
Solution : We have given
18 thousands times 10.
According to question :
18 thousand = 18000.
10 Times of 18 thousand .
18000 *10 .
180,000.
Number would be 180,000
Therefore, 180,000.
The probability that a train leaves on time is 0.4. The probability that the train arrives on time and leaves on time is 0.28. What is the probability that the train arrives on time, given that it leaves on time?
0.4
0.12
0.28
0.7
The probability that the train arrives on time, given that it leaves on time is 0.7
Explanation:The question asks for the probability that the train arrives on time, given that it leaves on time. This is a conditional probability problem, and we can use the formula for conditional probability, which is P(A|B) = P(A and B)/P(B).
In this case, event A is the train arrives on time, event B is the train leaves on time. We know that P(A and B) = 0.28 (the probability that the train arrives on time and leaves on time) and P(B) = 0.4 (the probability that the train leaves on time).
By substituting these values into the formula, we get P(A|B) = 0.28/0.4 = 0.7. So, the probability that the train arrives on time, given that it leaves on time is 0.7.
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A man travels from town x to town y at an average rate of 60 mph and returns at an average rate of 50 mph. He takes a 1/2 hour longer than he would take if he mage the round trip at an average of 55 mph. What is the distance from town x to town y
D/60 + D/50 = 2D/55 - 1/2
find common denominator ( 3300)
3300/60 = 55
3300/50 = 66
3300/55=60
so then you get 55D +66D= 60(2D)-1650
121D=120D-1650
D=1650 miles
check
1650/60 =27.5, 1650/50 = 33, 27.5 + 33 = 60.5 hours total
1650/55 = 30, 30 x 2 = 60
60.5-60 = 0.5 longer
so distance = 1650 miles
Matt is five years older than twice his cousin andy’s age. the sum of their ages is less than 35. what is the greatest age that andy could be?
2|x+1/4|=6
Can someone help me please, I'm so confused
How many different id cards can be made if there are 5 digits on a card and no digit can be repeated?
if no numbers can repeat then you have
1st digit = 10 numbers
2nd digit = 9 numbers
3rd digit = 8 numbers
4th digit = 7 numbers
5th digit = 6 numbers
10 * 9 * 8 * 7 *6 =30,240 different combinations
There are 30,240 different ID cards that can be made with 5 digits where no digit can be repeated, calculated as a permutation of 10 choices taken 5 at a time without replacement.
Explanation:The question asks us to determine how many different ID cards can be made with 5 digits where no digit can be repeated. This is a problem of permutations where the order of the digits matters. We have 10 possible digits (0-9), and we need to choose 5 of them without repetition.
For the first digit, we have 10 choices (0-9). Once we choose the first digit, we have 9 choices left for the second digit (since one digit is already used and can't be repeated). Continuing this pattern, we have 8 choices for the third digit, 7 choices for the fourth digit, and 6 choices for the fifth digit.
The total number of different ID cards is calculated by multiplying these choices:
10 choices for the first digit9 choices for the second digit8 choices for the third digit7 choices for the fourth digit6 choices for the fifth digitThe calculation is 10 x 9 x 8 x 7 x 6, which equals 30,240 different ID cards.
A seamstress is paid $9.55 for every pair of pants made. how many pants would have to be made to receive $525.00 a week?
To receive $525.00 a week, a seamstress being paid $9.55 per pair of pants made would need to make approximately 55 pairs of pants.
Let’s denote the number of pairs of pants that need to be made as x.
The seamstress is paid $9.55 for every pair of pants.
We want to find the number of pairs of pants needed to earn $525.00, so we set up the equation:
[tex]9.55 \times x = 525.00[/tex]
Solve for x:
[tex]x = \frac{525.00}{9.55} \approx 54.97[/tex]
Since we can’t make a fraction of a pair, we round up to the nearest whole number:
The seamstress would need to make 55 pairs of pants (which means a total of 110 pants) to receive $525.00 a week.
Use the student's t distribution to find tc for a 0.95 confidence level when the sample is 29. (round your answer to three decimal places.)
Using a t distribution table you can easily find the t critical value in a very easy way just look for the confidence level which is 95% or the 5% significance level and look for the degrees of freedom which is 28 (just to remind you degrees of freedom is always -1, so if you have 29 – 1 you will get 28 and it is the degrees of freedom), then the t distribution should give you 2.048 for your t critical value. When you use the significance level here you need to subtract the 100% by your confidence level of 95% you will get the 5% then you should divide it to 2, you will get the .025 if it only a two-tailed test you will use the significance level.
Solve for number 9 please:)
Which statement is correct when a scatterplot is constructed? A.The independent variable is the input variable and should be represented by the x-axis. B.The independent variable is the input variable and should be represented by the y-axis. C.The dependent variable is the input variable and should be represented by the x-axis. D.The dependent variable is the input variable and should be represented by the y-axis.
Answer:- A.The independent variable is the input variable and should be represented by the x-axis.
Explanation:-
A. Correct.
B. Not correct.
Reason:- The independent variable is the input variable and should be represented by the x-axis.
C. Not correct.
Reason:- The dependent variable is the output variable and should be represented by y-axis.
D. Not correct.
Reason:-The dependent variable is the output variable and should be represented by y-axis.
Answer:
A.The independent variable is the input variable and should be represented by the x-axis.
Step-by-step explanation:
It was right on the test.
the product of 18 and q
The product of 18 and q is expressed as 18q in an algebraic expression, representing the multiplication of 18 by a variable, q. The value of the expression depends on what value q has.
Explanation:The phrase 'the product of 18 and q' is a mathematical term used in algebra. It represents the multiplication of 18 and a variable 'q'. In algebraic expression, it can be written as 18q, where 18 is the constant multiplicand, and 'q' is the variable multiplier. The value of this product depends on the value of 'q'. For example, if q is 2, the product of 18 and q would be 36.
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Which positive integers less than 12 are relatively prime to 12?
Final answer:
To find the positive integers less than 12 that are relatively prime to 12, we need to find the positive integers that do not share any common factors with 12 other than 1. The positive integers less than 12 that are relatively prime to 12 are 1, 5, 7, and 11.
Explanation:
Two positive integers are relatively prime if their greatest common divisor (GCD) is 1. To find the positive integers less than 12 that are relatively prime to 12, we need to find the positive integers that do not share any common factors with 12 other than 1.
The prime factors of 12 are 2 and 3. Therefore, any positive integer less than 12 that is not divisible by 2 or 3 will be relatively prime to 12.
Therefore, the positive integers less than 12 that are relatively prime to 12 are 1, 5, 7, and 11.
Kite WXYZ is graphed on a coordinate plane. What is the area of the kite? 7 square units 8 square units 14 square units 16 square units
The area of the kite will be equal to 14 sq. units
What is an area?
The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the Kite in a two-dimensional plane is called the area of the kite.
The area of the kite can be found as follows;
Area = [area of XWY] + [areaYWZ]
Area XWY = 1/2 x b x h
Area XWY = 1/2 x 4 x 3 = 6 sq units
Area YWZ = 1/2 x b x h
Area YWZ = 1/2 x 4 x 4 = 8 sq units
Hence the area of the kite will be:
Area = 6 + 8 = 14 sq. units
Therefore the area of the kite will be equal to 14 sq. units
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Find the indicated critical z value. Find zα/2 for α = 0.08
To find the critical z value for α = 0.08, we first divide α by 2 to get 0.04. This value corresponds to the tail regions in a two-tailed test. We then lookup or calculate the z value associated with a cumulative probability of 0.04, which gives us a z value of approximately 1.75.
Explanation:The question is about finding the indicated critical z value. In statistics, critical values are used to make decisions about the null hypothesis in hypothesis testing. When α = 0.08, α/2 = 0.04 which refers to the tail regions in a two-tailed test.
First, we find the z value associated with α/2=0.04. This is found by looking at a standard z-table, or using a statistical calculator or a software tool that can calculate the inverse of the standard normal cumulative distribution function. For α/2=0.04, the z value is approximately 1.75.
Therefore, the critical z value (zα/2) is approximately 1.75.
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HELP PLEASE!!!! :((((((((
Jorani flips two standard American quarters. How many ways can she get at least one head?
Let f( x)= sin(x) Let g(x)=cos(x) a) Sketch the graph of f^2 b) Sketch the graph of g^2 c) Sketch the graph of f^2+g^2
To sketch the graphs, square the y-values of sin(x) and cos(x) to get f^2(x) and g^2(x), respectively. Then, add the squared y-values of f(x) and g(x) to get f^2(x)+g^2(x). Plot the points obtained for each function and sketch the graphs.
Explanation:a) To sketch the graph of f^2, we need to square every y-value of the function f(x)=sin(x). This means finding the square of the sine of each angle. For example, f^2(0)=sin^2(0)=0^2=0. By repeating this process for multiple angles, we can plot the points and sketch the graph.
b) Similarly, to sketch the graph of g^2, we need to square every y-value of the function g(x)=cos(x). This means finding the square of the cosine of each angle. For example, g^2(0)=cos^2(0)=1^2=1. By repeating this process for multiple angles, we can plot the points and sketch the graph.
c) To sketch the graph of f^2+g^2, we need to add the squared y-values of f(x) and g(x) at each angle. For example, f^2+g^2(0)=sin^2(0)+cos^2(0)=0^2+1^2=1. By repeating this process for multiple angles, we can plot the points and sketch the graph.