Give the domain and range of each relation using set notation​

Give The Domain And Range Of Each Relation Using Set Notation

Answers

Answer 1

Answer:

See below.

Step-by-step explanation:

First, recall the meanings of the domain and range.

The domain is the span of x-values covered by the graph.

And the range is the span of y-values covered by the graph.

1)

So, we have here an absolute value function.

As we can see, the domain of the function is all real numbers because the graph stretches left and right infinitely. Therefore, the domain of the function is:

[tex]\{x|x\in\textbb{R}\}[/tex]

(You are correct!)

For the range, notice how the function stops at y=7. The highest point of the function is (-2,7). There graph doesn't and won't ever reach above y=7. Therefore, the range of the graph is all values less than or equal to 7. In set notation, this is:

[tex]\{y|y\leq 7\}[/tex]

2)

We have here an ellipse.

First, for the domain. We can see the the span of x-values covered by the ellipse is from x=-4 to x=6. In other words, the domain is all values in between these two numbers and including them. Therefore, we can write it as such:

[tex]-4\leq x\leq 6[/tex]

So x is all numbers greater than or equal to -4 but less than or equal to 6. This describes the span of x-values. In set notation, this is:

[tex]\{x|-4\leq x\leq 6\}[/tex]

For the range, we can see that the span of x values covered by the ellipse is from y=-5 to y=1. Just like the domain, we can write it like this:

[tex]-5\leq y\leq 1[/tex]

This represents all the y-values between -5 and 1, including -5 and 1.

In set notation, thi is:

[tex]\{y|-5\leq y\leq 1\}[/tex]


Related Questions

It used to take 20 hours to get to Los Angeles, now it takes 12 hours, how much shorter was it?​

Answers

Step-by-step explanation:

It takes 20 Hours to get to Los Angeles

Now it takes 12 hours....

Therefore we subtract 20 from 12

which becomes

20 - 12= 8.

So it's 8 hours shorter

Find the product of the roots of the equation
xl-5x - 36 = 0

Answers

Answer:

Step-by-step explanation:

Hello, I assume that you mean

[tex]x^2-5x-36[/tex]

The product is -36.

[tex]x_1 \text{ and } x_2 \text{ are the two roots, we can write}\\\\(x-x_1)(x-x_2)=x^2-(x_1+x_2)x+x_1\cdot x_2[/tex]

So in this example, it means that the sum is 5 and the product is -36.

Thank you

find out what's wrong with this graph

Answers

Answer:

The y-axis is upside down, meaning that instead of the values increasing as they go up, they decrease.

Compare –3.5 and . Use <, >, or =.

–3.5 >

–3.5 <

–3.5 =

Answers

Answer:

-3.5 > -4.5-3.5 < -1.5-3.5 = -3.5

Step-by-step explanation:

Give any integer that suits the expression:-3.5 > -4.5-3.5 < -1.5-3.5 = -3.5• The farther a negative integer from 0, the smaller its value.

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]


What is the inverse of the function a(x)=1/x-2

Answers

Answer:

x = 1/x - 2

Step-by-step explanation:

The joint density function for a pair of random variables X and Y is given. f(x, y) = Cx(1 + y) if 0 ≤ x ≤ 4, 0 ≤ y ≤ 4 0 otherwise f(x,y) = 0
A) Find the value of the constant C. I already have 1/24.
B) Find P(X < = 1, Y < = 1)
C) Find P(X + Y < = 1).

Answers

Answer:

A) C = 1/96

B) P(x<=1, y<=1) = 1/128 or 0.0078125 to 7 places

C) P(x+y<=1) = 5/2305, or 0.0021701 to 7 places

Step-by-step explanation:

f(x,y) = C x (1+y)

A)

To find C, we need to integrate the volume under region bound by

0 <= x <= 4, and

0 <= y <= 4

This volume equals 1.0.

Find integral,

int( int(f(x,y),x=0,4), y = 0,4) = 96C

therefore C = 1/96

or

F(x,y) = x (1+y) / 96  ............................(1)

B)

P(x<=1, y<=1)

Repeat the integral, substitute the appropriate limits,

P = int( int(F(x,y),x=0,1), y = 0,1)

= 1/128 or 0.0078125

P(x<=1, y<=1) = 1/128 or 0.0078125 to 7 places

C)

P(x+y<=1)

From the function, we know that this is going to be less than one half of the probability in (B), closer to 1/4 of the previous.

It will be again a double integral, as follows:

P = int( int(F(x,y),x=0,1-y), y = 0,1)

= 5/2304

= 0.0021701 (to 7 decimals)

P(x+y<=1) = 5/2305, or 0.0021701 to 7 places

The cost in dollars y of producing x computer
desks is given by y = 40x + 4000
X
100
200
300
a. Complete the table
y
b. Find the number of computer desks that can be produced for $6200. (Hint: Find x when y = 6200.)
a. Complete the table.
х
100
200
300
y
b. For $6200,_ computer desks can be produced

Answers

Answer:

a.

y= 40x +4000

x= 100 --> y= 40(100)+4000= 4000+4000=8000

x=200 --> y= 40(200)+4000= 6000+4000= 10000

x=300 --> y= 40(300)+4000= 12000+4000= 16000

(in $)

b.

y= 40x+4000

6200= 40x+4000

6200-4000= 40x

2200= 40x

2200/40= x

55= x

(in unit)

Step-by-step explanation:

I hope this helps

if u have question let me know in comments ^_^

Can some body write a word problem using these numbers

Answers

Answer:

Mr Singh was travelling from England to Punjab, India. He arrived 5 hours after 0:00. When he was on the plane, there was a delay which caused the whole flight to be pushed 4 hours ahead. This would mean that he would arrive 9 hours after 0:00. Mr Singh was also with his son and he had some homework to do. He had to order the numbers   [tex]-4,-2\frac{1}{3} ,0, \frac{3}{4} ,\sqrt{5},5[/tex]  from lowest to highest.

A ball is released at a height of 16 inches to roll inside a half-cylinder. It rolls
to a height of 8 inches on the other side of the cylinder on roll 1. Each time it
rolls up a side of the cylinder, the ball reaches a point that is as high as it
had reached on the other side.
-lo
This explicit formula models the height of the ball, in inches, the nth time it
rolls up a side of the cylinder.

How high does the ball roll on its 5th time up the cylinder's side?​

Answers

Answer:

Step-by-step explanation:

Using the given formula, we put n = 5

[tex]h = 8* {(\frac{1}{2}) ^{n-1}[/tex]

h = 8 / 16

h = 1 / 2 inches

Describe the following sequence using an algebraic expression as a rule 0; 2,4; 6​

Answers

Answer:

Step-by-step explanation:

I assume the sequence is 0, 2, 4, 6

nth term = 2(n-1)

One time Maria took 27 minutes to walk 1.8km to school. She left home at 07:48 . Write down the time Maria arrived at school

Answers

Answer:

8:15

Step-by-step explanation:

the time would be 8:15 7:48 + 27 = 8:15

A new soft drink is being market tested. A sample of 400 individuals participated in the taste test and 80 indicated they like the taste. At 95% confidence, test to determine if at least 22% of the population will like the new soft drink.


Required:

Determine the p-value.

Answers

Answer: p-value of the test  = 0.167

Step-by-step explanation:

Given that,

sample size n = 400

sample success X = 80

confidence = 95%

significance level = 1 - (95/100) = 0.05

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.22

Hₐ : p < 0.22

P = x/n = 80/400 = 0.2

Standard deviation of proportion α = √{  (p ( 1 - p ) / n }

α = √ { ( 0.22 ( 1 - 0.22 ) / 400 }

α = √ { 0.1716 / 400 }

α = √0.000429

α = 0.0207

Test statistic

z = (p - p₀) / α

z = ( 0.2 - 0.22 ) / 0.0207

z = - 0.02 / 0.0207

z = - 0.9661

fail to reject null hypothesis.

P-value Approach

P-value = 0.167

As P-value >= 0.05, fail to reject null hypothesis.

Since test is left tailed so p-value of the test is 0.167. Since p-value is greater than 0.05 so we fail to reject the null hypothesis.

_____, as a defense mechanism, is the unconscious act of keeping threatening or disturbingthoughts, feelings, or impulses out of consciousness.

a. Sublimation
b. Projection
c. Reaction formation
d. Repression

Answers

_____, as a defense mechanism, is the unconscious act of keeping threatening or disturbing thoughts, feelings, or impulses out of consciousness.



Answer is: REPRESSION.

trigonometric identities

Answers

1/tan x = cot x

Cot x + tan x = 1/ sin x cos x

The answer is D.

Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.
a^2-2a-224=0

Answers

Answer:

{-14, 16}

Step-by-step explanation:

The coefficients of this quadratic are a = 1, b = -2 and c = -224.

Thus, the discriminant is b^2 - 4ac, or (-2)^2 - 4(1)(-224), or 900, whose square root is 30.

Thus, the roots (solutions) are

      -(-2) ± 30

x = -----------------  =  {-14, 16}

             2

f(x) = 3x + 2
What is f(5)?

Answers

Answer:

17

Step-by-step explanation:

f(x) = 3x + 2

f(5) = 3(5) + 2

f(5) = 15 + 2

f(5) = 17

Answer:

17

Step-by-step explanation:

f(x) = 3x + 2

Plug in:

3(5) + 2

15 + 2 = 17

Hope this helped.

1
2
3
4
Which value of a in the exponential function below would cause the function
f(x)
=a
Tln wilt ml
4
o

Answers

Answer:

Step-by-step explanation: sajkdkdksskkcfd

Find the distance between (8,4) and (8,8).

Answers

Answer:

From the given points above, the distance between them is 4 units.

Step-by-step explanation:

In order to find the distance between the two points, we must know the distance formula.

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Now, we plug in our numbers from the coordinate points that we are given to their respectful places.

[tex]d=\sqrt{(8-8)^2+(8-4)^2}[/tex]

Now, we solve. First, simplify the terms in parentheses. So, subtract 8 from 8 and subtract 4 from 8.

[tex]d=\sqrt{(0)^2+(4)^2}[/tex]

Next, solve for the exponents.

[tex]d=\sqrt{0+16}[/tex]

Add the numbers in the radical.  

[tex]d=\sqrt{16}[/tex]

Solve the radical.

[tex]d=4[/tex]

So, the distance  between the two given points is 4 units.

A researcher is interested in finding a 90% confidence interval for the mean number of times per

day that college students text. The study included 147 students who averaged 44.7 texts per

day. The standard deviation was 17.9 texts. Round answers to 3 decimal places where possible.

a. To compute the confidence interval use a tv distribution.

b. With 90% confidence the population mean number of texts per day is between

and

texts.

Answers

Answer:

90% confidence the Population mean number of texts per day

(42.2561 ,47.1439)

Step-by-step explanation:

Step(i):-  

Given sample size 'n' = 147

mean of the sample size x⁻ = 44.7

standard deviation of the sample 'S' = 17.9

90% confidence the Population mean number of texts per day

[tex](x^{-} - t_{\alpha } \frac{S}{\sqrt{n} } ,(x^{-} + t_{\alpha } \frac{S}{\sqrt{n} })[/tex]

Step(ii):-

Degrees of freedom

       ν=n-1=147-1=146

t₀.₁₀ =  1.6554

[tex](x^{-} - t_{\alpha } \frac{S}{\sqrt{n} } ,(x^{-} + t_{\alpha } \frac{S}{\sqrt{n} })[/tex]

[tex](44.7 - 1.6554 \frac{17.9}{\sqrt{147} } ,(44.7 + 1.6554 \frac{17.9}{\sqrt{147} })[/tex]

(44.7 - 2.4439 ,44.7 + 2.4439 )

(42.2561 ,47.1439)

Conclusion:-

90% confidence the Population mean number of texts per day

(42.2561 ,47.1439)

mortician math word problem

Answers

Answer:

wat do u want me to do

Step-by-step explanation:

I need help on this question ASAP please?

Answers

Answer:

B.

Step-by-step explanation:

10c + 5 ≤ 45

10c ≤ 40

c ≤ 4

Since the inequality uses the less than or equal to sign, we use a shaded circle on the number line. Since c is less than or equal to 4, your answer will be B, since the line extends infinitely to the left of 4.

Hope this helps!

Answer:

B

Step-by-step explanation:

To get the answer, you need to simplify or re-write the equation given:

10c + 5 ≤ 45 = 10 × c + 5 - (45) ≤ 0

Next, group the like terms together:

10c - 40

Now, we can apply algebra to simplify the equation further:

(10c ÷ 10) ≤ (40 ÷ 10)c ≤ 4

Now, look at your options. Only option B matches our equations. Therefore, B is the correct answer.

Natalie's team needs to make a decision on how to handle a big product recall. People on the team have a lot of strong opinions. Management wants everyone to come to a consensus and to find a solution that everyone can support. What's the best way to get to a consensus?
a) Everyone on the team talks until the entire team agrees on one decision. O b) Everyone on the team discusses options and then votes. Oc) The team passes the decision-making responsibility to an outside person. O di The team leader makes a decision without input from the other members.

Answers

Answer:

a) Everyone on the team talks until the entire team agrees on one decision.

Step-by-step explanation:

Option B consists of voting and not everyone would like the outcome. Option C is making an outsider the decision maker, which can't be helpful since he / she won't have as strong opinions as the team itself. Option D is just plain wrong as it defeats the purpose of team work and deciding as one team. So, I believe option A makes the most sense

represent -√2.3 and +√2.3 on number line​

Answers

Answer:

-√2.3 on left of number line and zero and +√2.3 on right side of number line and zero

Step-by-step explanation:

List the stem numbers below!!

Answers

Answer:

see below

Step-by-step explanation:

The stems are in the middle and the leaves are on the left and right

Stems are 0,1,2,3,4,5

The Junior class has raised
4/7
of the amount of money that is needed for the Junior-Senior

Prom, and the Senior class has raised 3/11 of the amount of money that is needed. Estimate
what portion of the money the two classes have already raised of the money
A.1/4 of the money
B.all of the money
C.1/2 of the money
D.3/4 of the money

Answers

Answer:

B. all of the money this is my answer

Write an equation for a line perpendicular to y = − 5 x + 5 and passing through the point (5,5)

Answers

Answer:

The answer is

[tex]y = \frac{1}{5} x + 4[/tex]

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the line perpendicular to

y = -5x + 5 we must first find the slope of

Comparing with the general equation above

Slope = - 5

The slope of the perpendicular line is the negative inverse of the slope of the original line

Slope of perpendicular line = 1/5

Equation of the line using point (5,5) and slope 1/5 is

[tex]y - 5 = \frac{1}{5} (x - 5)[/tex][tex]y - 5 = \frac{1}{5} x - 1[/tex][tex]y = \frac{1}{5} x - 1 + 5[/tex]

We have the final answer as

[tex]y = \frac{1}{5} x + 4[/tex]

Hope this helps you

Answer:

y=0.2x+4 or y=1/5 x+4.

Step-by-step explanation:

When one line is perpendicular to another, you have to find the opposite reciprocal for the slope of the given equation.

For instance, if you have the number 5, the reciprocal of 5 is 1/5 or 0.2. The opposite of positive is negative. Therefore, it is -0.2.

Therefore, if the slope of the first equation is -5, the slope for the next equation is 1/5. Reciprocal of -5 is -1/5. The opposite of -1/5 is positive 1/5. Or, the opposite of negative is positive. Therefore, it would be 1/5x.

However, we are not done.

Since we are given that the line passes through the point (5,5), we need to find the y-intercept of this equation.

The formula for slope-intercept is y=mx+b.

M is your slope

B is your y-intercept.

We can find the y-intercept by actually plugging in the point (5,5) into the new equation.

5=0.2(5)+b.

5 is x and 5 is also y.

(x,y).

Simplify the equation by multiplying 0.2 times 5. That is equal to 1.

We now have 5=1+b.

Isolate for the letter "b" by subtracting 1 from both sides.

1-1 is 0.

5-1 is 4.

Therefore, b=4.

Finally, we can plug in the y-intercept into the new equation.

y=0.2 or 1/5x+4.

I hope this helps! I also hope you have a great rest of your day!

Solve for x: −3|2x + 6| = −12.

Answers

Answer:

x = -1 or x = -5

Step-by-step explanation:

−3 * |2x + 6| = −12 / -3

|2x + 6| = 4

because this is an absolute value equation there are 2 solutions:

2x + 6 = 4 or 2x + 6 = -4

2x = -2 or 2x = -10

x = -1 or x = -5

Answer:

x = -1 or x = -5

Step-by-step explanation:

cuz it is

The general manager, marketing director, and 3 other employees of CompanyAare hosting a visitby the vice president and 2 other employees of CompanyB. The eight people line up in a randomorder to take a photo. Every way of lining up the people is equally likely.Required:a. What is the probability that the bride is next to the groom?b. What is the probability that the maid of honor is in the leftmost position?c. Determine whether the two events are independent. Prove your answer by showing that one of the conditions for independence is either true or false.

Answers

Answer:

Following are the answer to this question:

Step-by-step explanation:

Let, In the Bth place there are 8 values.

In point a:

There is no case, where it generally manages its next groom is = 7 and it will be arranged in the 2, that can be arranged in 2! ways. So, the total number of ways are: [tex]\to 7 \times 2= 14\\\\ \{(1,2),(2,1),(2,3),(3,2),(3,4),(4,3),(4,5),(5,4),(5,6),(6,5),(6,7),(7,8),(8,7),(7,6)\}\\[/tex][tex]\therefore[/tex] required probability:

[tex]= \frac{14}{8!}\\\\= \frac{14}{8\times7 \times6 \times 5 \times 4 \times 3\times 2 \times 1 }\\\\= \frac{1}{8\times6 \times5 \times 4 \times 3}\\\\= \frac{1}{8\times6 \times5 \times 4 \times 3}\\\\=\frac{1}{2880}\\\\=0.00034[/tex]

In point b:

Calculating the leftmost position:

[tex]\to \frac{7!}{8!}\\\\\to \frac{7!}{8 \times 7!}\\\\\to \frac{1}{8}\\\\\to 0.125[/tex]

In point c:

This option is false because

[tex]\to P(A \cap B) \neq P(A) \times P(B)\\\\\to \frac{12}{8!} \neq \frac{14}{8!}\times \frac{1}{8}\\\\\to \frac{12}{8!} \neq \frac{7}{8!}\times \frac{1}{4}\\\\[/tex]

The equation 8(y-3)= -40 is solved in several steps below. For each step, choose the reason that best justifies it.

Addition property of Equality
Subtraction Property of Equality
Multiplication property of equality
Division property of equality
simplifying
distributive property

Answers

Answer:

Step-by-step explanation:

The steps and their reasons for the equation 8(y - 3) = - 40 are given below.

What is the solution to the equation?

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The equation is given below.

8(y - 3) = - 40

            Steps                                               Reason

       8(y - 3) = - 40                                          Given

       8y - 24 = - 40                                Distributive property

8y - 24 + 24 = - 24 + 24                 Addition Property of Equality

               8y = - 16                                      Simplifying

          8y / 8 = - 16/8                       Division property of equality

                  y = - 2                                       Simplifying

More about the solution of the equation link is given below.

https://brainly.com/question/545403

#SPJ2

find the value of X from the given picture ​

Answers

Answer:

x = 108

Step-by-step explanation:

The sum of a circle is 360

90 + x/2 + x+x = 360

Combine like terms

90 + 2x+x/2 = 360

90 + 5/2 x = 360

Subtract 90 from each side

5/2x = 270

Multiply each side by 2/5

5/2x * 2/5 = 270*2/5

x =108

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