Exercise 1.6.3: Translating mathematical statements in English into logical expressions. info About Consider the following statements in English. Write a logical expression with the same meaning. The domain is the set of all real numbers. (a) There is a number whose cube is equal to 2. (b) The square of every number is at least 0. (c) There is a number that is equal to its square. (d) Every number is less than or equal to its square..

Answers

Answer 1

Answer:

a)  Эx ∈ R   ⊇  x³ = 2

b) ∀x ∈ R, x² ≥ 0

c)  Эx ∈ R   ⊇  x³ = x

d) ∀x ∈ R, x ≤ x²

Step-by-step explanation:

Given the data in the question;

let us first go through some symbols and their possible meanings;

Э  ⇒ there exists

∀ ⇒ for all

∈ ⇒ belongs to or set membership or element of the set

⊇ ⇒ such that

now;

a) There is a number whose cube is equal to 2

let x represent the number; so

Эx ∈ R   ⊇  x³ = 2

b) The square of every number is at least 0

x² ≥ 0, ∀x ∈ R

∀x ∈ R, x² ≥ 0

c) There is a number that is equal to its square

Эx ∈ R   ⊇  x³ = x

d) Every number is less than or equal to its square.

x ≤ x², ∀x ∈ R

∀x ∈ R, x ≤ x²


Related Questions

Bob built birdhouses to sell at the craft fair for $8.00 each. He had to spend $40 for materials . Which inequality represents the number of bird houses he must sell to make more than $ 200?

Answers

Answer:

8x - 40 > 200

Step-by-step explanation:

PLZ HELP ME What shape is this cross-section?

Answers

Answer:

i'm not sure if i'm right but think is cube

A quality assurance check is 91% accurate for non-defective devices and 97% accurate for defective devices. Of the devices checked, 84% are not defective. What is the probability of an incorrect conclusion? Round your answer to the nearest tenth of a percent.

Answers

The probability of an incorrect conclusion is,

In 84 % of inspection,  [tex]7.56\%[/tex]  of them labeled as not defective but they are actually defective

Probability :

It is given that,

A quality assurance check is 91% accurate for non-defective devices and 97% accurate for defective devices.

Of the devices checked, 84% are not defective.

Actual not defective is,

            [tex]\frac{91*84}{100} = 76.44\%[/tex]

In  [tex]84\%[/tex] of inspection,[tex]76.44\%[/tex] are actually not defective

But [tex]84- 76.44 = 7.56\%[/tex]  of them labeled as not defective but they are actually defective

Learn more about Probability here:

https://brainly.com/question/24756209

What’s the answer pls

Answers

Answer:

Step-by-step explanation:

There is no bird on the spinner. therefore the answer is impossible because there is no bird.

Answer:

Impossible - There's no bird on the wheel.

Step-by-step explanation:

Photo attached please help

Answers

it’s a

hope this helped!:)
I’m pretty sure it’s a

What is the measure of angle M?

Answers

Answer:

35°

Step-by-step explanation:

4x+11 = 5x-24

5x-4x=x

x=24+11

x=35

Prior to hosting an international soccer match, the local soccer club needs to replace the artificial turf on their field with grass turf. The grass turf will cost $ 6.75 per square meter. If the field is 0.101 km by 0.065 km, how much will it cost the club to add the grass turf to their field

Answers

Answer:

$44,313.75

Step-by-step explanation:

First, we need to turn the km into meters. There are 1000 meters in a km meaning we need to multiply each of these values by 1000.

0.101 km * 1000= 101 meters

0.065 km * 1000 =  65 meters

Now we need to multiply these values together to find the area of the field

101m * 65m = 6,565[tex]m^{2}[/tex]

Finally, we need to multiply this area by the cost per square meter

6,565[tex]m^{2}[/tex] / 6.75 = $44,313.75

The total repair will cost $44,313.75

Jacob spent 24% of his allowance last week. What fraction of his allowance did Jacob spend? Write the answer in simplest form.

Answers

6/25

Step-by-step explanation:

24/100

both can be multiplyed or divided by 4 and that is the lowest.

so

24÷4=6

100÷4=25

State the average rate of change for the situation. Be sure to include units.

The population of Felton was 2400 in 2013 and 2800 in 2017.

The population of Felton grew by

Answers

In 4 years is grew by 400 people averaging to 100 per year

1. In a 30-60-90 triangle, the length of the hypotenuse is 6. What is the length of the shortest side?



A2
B3
C [tex]3\sqrt{2}[/tex]
D[tex]3\sqrt{3}[/tex]
F[tex]6\sqrt{2}[/tex]

Answers

Answer:

i think it’s b

if sarah has 800 marbles and her teacher gave her 3,00 more and she have 100 to her 2 friends how much will sarah have??

Answers

Answer:

3600

Step-by-step explanation:

If she has 800 her teacher gives her 3000= 3800 and she gave 100 to both of her friends - 200 then she will have 3600.

Hope this helps! Please consider marking brainliest! I hope you have an amazing day. Always remember, your smart and you got this! -Alycia

Estimate the value of 50.
O A. between 5 and 6
O B. between 6 and 7
C. between 7 and 8
<
D. between 8 and 9
PLEASE HELPP

Answers

Answer: c

Step-by-step explanation: because 7 squared is 49 and 8 squared is 64

nvm i read the question wrong

Step-by-step explanation:

the person above is correct

Mr. Jones charged Roberta $105 for parts and $25 per hour for labor to repair her bicycle. He spent 2 hours repairing her bike. Which expression would be used to correctly calculate the amount Roberta owes him?

a.(2 × 25) + 105

b.(105 x 2) + (25 x 2)

c.2 x (25 + 105)

d.2 x 25 × 105

Answers

Answer:

a.(2 × 25) + 105

Step-by-step explanation:

Let the number of hours spent repairing the bike = x

Mr. Jones charged Roberta $105 for parts and $25 per hour for labor to repair her bicycle.

Therefore, our algebraic expression

= $25× x + $105

= 25x + 105

We were told in the question that He spent 2 hours repairing her bike.

Hence:

25 × 2 + 105

Therefore, the correct option is option a

a.(2 × 25) + 105

5/= 1.5 x 25

What is 1.5 × 25

A. 22.5

B. 37.5

c. 52.5

D. 85.5​

Answers

Answer:

37.5 is the answer

Step-by-step explanation:

all you do is just multiply the 2 numbers

A professor in one city earns $61,000 a year. A bioengineer earns $95,750. A nurse earns $50,600. What is the difference in salary between the professor and nurse?

Answers

Answer:

The difference is 10,400$.

Step-by-step explanation:

$61,000-$50,600=$10,400

List all factors of 72

Answers

Answer:

1,2,3,4,6,8,9,12,18,24,36,72.

Step-by-step explanation:

What you are looking for are numbers that multiply by each other to equal 72, like 1 and 72 or 8 and 9. Factor tree may help, search it up :)

Which type of interest will earn you more money in a savings account?

Answers

Answer:

a compound interest that has the lowest interest rate .  

Step-by-step explanation:

I need help with this.​

Answers

Answer:

D=4

C=12.56

Step-by-step explanation:

D=2r

d=2×2

D=4

C=pi ×D

C=3.14×4

C=12.56

Please please please help ill do anything ​

Answers

Answer:

Anything??

Step-by-step explanation: (Im joing btw didnt want to offend anyone lol)

x=40

three and two forths - one and two thirds =
3 2/4 - 1 2/3 =

Answers

Answer:

1.83333333333

Step-by-step explanation:

pls mark me brainliest

ok thanks :) :) :) :)

Use the exchange rate £1 = $1.38 to convert $276 into £.

Answers

Answer:

£200

Step-by-step explanation:

$276*(1/$138)=200 pounds

How do you graph y=−x−2.

Answers

Y=-x-2 that is how you graph it
Isn’t that how you graph it? I’m confused about the question sorry!

Helppppppppppppp meeeeee

Answers

Answer:

9

Step-by-step explanation:

because 9 in a third is 3

3 + 12 is 15

9x2 is 18

and 15 is 3 less than 18

What is the equation in slope-intercept form for the line that passes through the points (–1, 3) and (–2, –3)?

Answers

Answer:

The answer is y = 6x + 9.

-

Step-by-step explanation:

☆Remember: [tex]m =  \frac{y_2 - y_1}{x_2 - x_1} [/tex]

☆Slope-intercept: [tex]y = mx + b[/tex]

---

☆We need to find the slope first. So just plug in according to the slope formula!

[tex]m =  \frac{ - 3 - 3}{ - 2 - ( - 1)} = \frac{ - 6}{ - 1} = 6[/tex]

---

☆Now we need to find the y-intercept. We are going to plug in the slope and a set of coordinates to find the y-intercept.

[tex]y = mx + b \\ 3 = 6( -1 ) + b \\ 3 = - 6 + b \\ \frac{ + 6 = + 6 \: \: \: \: \: \: \: \: \: \: }{9 = b \: \: \: \: \: \: \: \: \: \: \: } [/tex]

---

☆Now all we need to do is plug in and we are done!

[tex]y = 6x + 9[/tex]

▪Happy To Help <3

Promise Easy Points
Calculate the average monthly expenses for these individuals?

Kelsey spent $350 in May, $432 in June and $420 in July. Her average monthly expenses are:____

Michael spent $700 in April and May and $800 in June and July. His average monthly expenses are:____

Answers

$420+$350+$432=kelsey's monthly expenses  

$700+$800=Micheal's Monthly expenses

Michael's average monthly expenses are $750.

What is the average?

The average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.

Given that, Kelsey spent $350 in May, $432 in June and $420 in July.

Now, average monthly expenses are

(350+432+420)/3

= 1202/3

= 400.67

Michael spent $700 in April and May and $800 in June and July.

Here, (700×2+800×2)/4

= (1400+1600)/4

= 3000/4

= $750

Therefore, Michael's average monthly expenses are $750.

To learn more about an average visit:

https://brainly.com/question/11195029.

#SPJ2

PLEASE HELP




Consider the expressions (3m+2n−6) and (−4−6m+7n).

Part A


What is the sum of the expressions for n=−2 and m=5?


The sum is

Answers

Answer:

5, -20

Step-by-step explanation:

Given the equation (3m+2n−6) and (−4−6m+7n).

Also, given that we're told that

n = -2 and

m = 5, if we take a rather direct approach by substituting like for like, we have

(3m+2n−6) = (3 * 5 + 2 * -2 - 6)

(3m+2n−6) = 15 - 4 - 6

(3m+2n−6) = 15 - 10

(3m+2n−6) = 5

(−4−6m+7n) = (-4 - 6 * 5 + 7 * 2)

(−4−6m+7n) = -4 - 30 + 14

(−4−6m+7n) = -34 + 14

(−4−6m+7n) = -20

Therefore, we proceed to conclude that the answers are 5 and -20 respectively

At a restaurant, the bill comes to $30. If you decide to leave a 10% tip, how much total do you need to pay? Give your answer to the nearest dollar.

Answers

Answer:

33dollors if I'm not mistakin

my friend needs help with this can someone help

Answers

Answer:Sorry

Step-by-step explanation:

Hi would help but i dont know and im not in collage sorry.

Tickets for a concert cost $4.00 for a balcony seat and $7.50 for an orchestra seat. If ticket sales totaled $1,585 for 300 tickets sold, how many more tickets for balcony seats were sold than tickets for orchestra seats? - thanks

Answers

Answer:there were 80 more tickets sold for balcony seats than for orchestra seats

Step-by-step explanation:

Step 1

Let number of tIcket for balcony be represented as x

and

Number of tickets for orchestra seat be represented as y such that the total number pf tickets sol;d would be

X+ Y = 300--- equation 1

And the cost for $4.00 for a balcony seat and $7.50 for an orchestra seat totalling ticket sales of $1,585 be represented as

4x + 7.50y = 1585----- equation 2

Step 2

X+ Y = 300--- equation 1

4x + 7.50y = 1585----- equation 2

Multiplying equation 1 by 4 and subtracting from equation2

4x + 7.50y = 1585

-4x+4y= 1200

3.50y =385

y =385/3.50

y=110

To find x, when y=110

X+ Y = 300--- equation 1

x+110=300

x= 300-110= 190 tickets

balcony seats  tickets = 190

orchestra seats tickets = 110

Therefore, there were 80 more tickets sold for balcony seats than for orchestra seats

Summarize the process of solving a two-step equation.

Answers

Answer:

Solving Two-Step Equations

1) First, add or subtract both sides of the linear equation by the same number.

2) Secondly, multiply or divide both sides of the linear equation by the same number.

3)* Instead of step #2, always multiply both sides of the equation by the reciprocal of the coefficient of the variable

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