Each of the following tables defines a relationship between an input x and an output y. Which of the relationships represent functions? Table A x -8 -3 0 6 y 24 4 9 72 Table B x 9 15 24 38 y -14 -16 53 29 Table C x 15 24 24 100 y -16 53 29 7 Table D x -8 6 0 6 y 24 4 9 72 a. Table A and Table C b. Table A and Table B c. Table B and Table C d. Table C and Table D Please select the best answer from the choices provided

Answers

Answer 1

Answer:

The relationship representing the function as per the input and output value is given by option b. Table A and Table B.

In order for a relationship between an input x and an output y to represent a function,

each input value x must be associated with exactly one output value y. Let's analyze the given tables:

Table A:

x -8 -3 0 6

y 24 4 9 72

Table B:

x 9 15 24 38

y -14 -16 53 29

Table C:

x 15 24 24 100

y -16 53 29 7

Table D:

x -8 6 0 6

y 24 4 9 72

Let's examine the options:

a. Table A and Table C: Table A represents a function because each x value corresponds to a unique y value.

Table C has duplicate x values, which means it doesn't represent a function.

b. Table A and Table B: Both Table A and Table B represent functions because each x value is associated with a single unique y value in both tables.

c. Table B and Table C: Table B does not represent a function

because the x value 24 is associated with two different y values (-16 and 53) in Table B.

Table C does not represent a function either because of the duplicate x value 24.

d. Table C and Table D: Similar to options a and c,

Table C does not represent a function due to duplicate x values.

Table D represents a function as each x value is associated with a unique y value.

Therefore, based on the analysis above, the correct answer for the function is option b. Table A and Table B.

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Answer 2

Answer:

Answer: is B. table A and Table B

Step-by-step explanation:

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Classify the angle as acute, right, obtuse, or straight.

Find the surface area of the triangular prism.5 ft
5 ft
13 ft
4 ft
6 ft

Answers

Answer:

234ft²

Step-by-step explanation:

Surface of the triangular prism

= ab+3bh

= (6ft×13ft)+(3×13ft×4ft)

= 78ft²+156ft²

= 234ft²

Hence, the surface area of the given triangular prism is 234ft².

The volume V of an ideal gas varies directly with the temperature T and inversely with thepressure P. A cylinder contains oxygen at a temperature of 320 degrees Kelvin and a pressure of

25 atmospheres in a volume of 120 liters. Find the pressure if the volume is decreased to 110

liters and the temperature is increased to 335 degrees Kelvin.

Hint: Look at the equation V = k* Then use the initial values to solve for k. Then plug in the

values you know for the second set of values and solve for your unknown.

Answers

Answer:

Pressure=22.55 atmospheres

Step-by-step explanation:

Let

V=volume of the ideal gas

P=pressure

T=temperature

Volume varies directly with temperature and inversely with pressure

V=kT/P

t=320°K

P=25 atmospheres

V=120 liters

V=kT/P

120=k*320/25

120=320k/25

120×25=320k

3000=320k

k=300/320

=9.375

k=9.375

V=110 liters

p=?

t=335°K

V=kT/P

110=9.375*335/p

110=3,140.625/p

110p=3,140.625

P=3,140.625/110

=28.55

P=22.55 atmospheres

1. Julia's goal is to run faster than two of her friends in an upcoming6.2-mile race. The table shows the results of the last race that each
runner finished. Assume they each run the race at the same rate
they ran their last race. Complete the table. Who will finish first
among the three friends, and by how much time will she beat the
second-place finisher?
Runner
Julia
Hazel
Mekena
Last Race
Distance
(mi)
8
5
6
Last Race
Time
(min: sec)
62:00
39:10
46:00
Rate
(min:sec
per mi)
Time for
6.2 Miles
(min: sec)

Answers

It was a good choice to ask Toni to join the team as she would be able to contribute to the team's success in the race.

What is the ratio and proportion ?

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as 1 : 3 (for every one boy there are 3 girls).

To complete the 1-mile relay race in 4:34, each runner must run their quarter-mile leg of the race in a total time of 1:08 (68 seconds).

We can use this information to fill in the missing information in the table:

Runner Rate(min:sec per mi) Time for 1/4mile (min:sec)

Julia 4:40 1:10

Hazel 4:48 1:12

Mekena 4:32 1:08

Toni 4:18 1:04

Based on the table, Toni's rate is faster than the other runners, and her time for a quarter-mile leg of the race is also faster.

Therefore, it was a good choice to ask Toni to join the team as she would be able to contribute to the team's success in the race.

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HELP!! Monette began heating a liquid with a starting temperature of 62.5°F. The temperature increased by 5° per minute.

What is the recursive rule that represents this situation?\
an=
a1=

Answers

Greetings!

Answer:

an = 65 + 5 $_(n - 1)$

a1 = 65

Step-by-step explanation:

If the begining value is 65, then a1 has to be itL

a1 = 65

Then, if this amount increased every minute then 5 has to be added to this value each time:

an = 65 + 5

But this means that 5 is added to 65 every time with no increase, so the five must me multiplied by the n value:

an = 65 + 5 $_(n)$

a2 = 65 + 10 = 75

But this value should be 70 because it is the first point after 65 so it should be +5 not +10

To do this we can simply subtract one from the n value that is being multiplied by 5:

an = 65 + 5 $_(n - 1)$

Which is the recursive rule!

Hope this helps!

The number of potholes on 30 randomly selected 1 mile stretch of highways in the City of Chicago is given below 2, 7, 4, 7, 2, 7, 2, 2, 2, 3, 4, 3, 1, 2, 3, 2, 1, 4, 2, 2, 5, 2, 3, 4, 4, 1, 7, 6, 3, 5 (a) Complete the frequency distribution for the data. Make sure to enter your answers for the relative frequency as decimals, rounded to the nearest tenth.

Answers

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

2, 7, 4, 7, 2, 7, 2, 2, 2, 3, 4, 3, 1, 2, 3, 2, 1, 4, 2, 2, 5, 2, 3, 4, 4, 1, 7, 6, 3, 5

Value __ Frequency ___ relative frequency

1 ___ 3 ______ 3/30 ____ 0.1

2 __ 10 ______ 10/30 ___ 0.3

3 __ 5 _______ 5/30____0.2

4 __ 5 ________ 5 / 30 __0.2

5 __ 2 _________ 2/30 __ 0.1

6 __ 1 _________ 1/30 ___0.0

7 __ 4 ________ 4/30 ___0.1

Kindly note that relative frequencies were rounded to the nearest tenth.

While on vacation, Rosa stopped at a souvenir shop to buykeychains and refrigerator magnets for family members and
friends. Keychains cost $2 each, and refrigerator magnets cost $1
each. Let x represent the number of keychains that Rosa bought,
and let y represent the number of refrigerator magnets.
Rosa bought 12 items and paid $18 more for the keychains than
for the refrigerator magnets.