Write each of these propositions in the form "p if and only if q" in English.
a) If it is hot outside you buy an ice cream cone, and if you buy an ice cream cone it is hot outside.
b) For you to win the contest it is necessary and sufficient that you have the only winning ticket.
c) You get promoted only if you have connections, and you have connections only if you get promoted.
d) If you watch television your mind will decay, and conversely.
e) The trains run late on exactly those days when I take it.

Answers

Answer 1

Answer:

The "p if and only if q" statement is equivalent to "q if and only if p", then let's rewrite all the propositions in this way.

a) "If it is hot outside you buy an ice cream cone, and if you buy an ice cream cone it is hot outside."

We can define:

q = is hot outside

p = you buy an ice cream cone

Then we can rewrite this as:

"You buy an ice cream cone if and only if is hot outside"

b)  "For you to win the contest it is necessary and sufficient that you have the only winning ticket."

We can define:

p = you winning the contest

q = have the winning ticket

Then we can rewrite (changing some words) this as:

"You will win the contest if and only if you have the winning ticke"

c) "You get promoted only if you have connections, and you have connections only if you get promoted."

We can define:

p = you get promoted

q = you have connections

We can rewrite the proposition as:

"You can get promoted if and only if you have connections"

d) " If you watch television your mind will decay, and conversely."

We can define:

p = you watch television

q = your mind will decay

We can rewrite it as:

"You can watch television if and only if your mind decays"

e) " The trains run late on exactly those days when I take it."

We can define:

p = The train runs late

q = I take it.

We can rewrite the proposition as:

"The train runs late if and only if I take it"


Related Questions

Javier built a skateboard ramp by elevating one end of an 8-foot piece of plywood so that it makes a 20 degree angle with the ground.

Answers

Answer:

2.74feet

Step-by-step explanation:

Since we are not told what to find, we can find the height of the plywood

Given the following

length of ramp = 8feet

angle of elevation = 20degrees

Required

Height of the plywood

Using the SOH CAH TOA identity

Sin theta = opposite/hypotenuse

Sin 20 = H/8

H = 8sin20

H = 8(0.3420)

H = 2.74 feet

Hence the height of the plywood is 2.74feet

What is the answer and how do you get it?

Answers

Y^5*2^7 bc you have to had the exponents if you see a multiple sign but if you see a division sign you subtract

Answer:

it would D, when you simplify both expressions, they get the same result which is 1024y^6

Match the cube roots and square roots with their values.
V4
327
64
364
49
31,000
2
10
3
4
8
7

Answers

2= sqrt 4
10= cube root of 1000
3= cube root of 27
4= cube root of 64
8= sqrt 64
7= sqrt 49

Select ALL the expressions that are equivalent to -4(8x-3)

A) -20X
B) 4(3-8x)
C) -32x-12
D) 2(-16x+6)
E) 5-9(8x-3)

Answers

Answer:

dddddStep-by-step explanation:

The diameter of a circle is 19 ft. Find the circumference to the nearest tenth.

Answers

Answer:

Half of 19 = 9.5(new radius)

2 x 3.4 x 9.5 = 64.6 ft is your answer.

Formula of circumference:

2 x 3.14(pi or 22/7 depending on what they tell you to use for pi) x radius(half of diameter or given radius)

Answer:

C = 59.7

Step-by-step explanation:

The formula for the circumference of a circle is C = 2πr

R = radius

The radius is the half of a diameter, so 19/2 is 9.5.

C = 2π(9.5)

C = 59.69026041

Help Me And If ITs Right Ill Give Brainliest to you

Answers

Answer: I thınk so aswer ıs B

Step-by-step explanation:

MARKING BRAINLIEST ..Please

Answers

Answer:

B

Step-by-step explanation:

Have a good day :)

Answer: I think D.

Step-by-step explanation:

9 Sam earns $54 275 in a year.
He pays no income tax on the first $8200.
He pays 18% income tax on everything he earns over $8200.
a Work out how much income tax he pays.
b Work out what percentage of his income he pays in tax.
c If the income tax rate is increased to 21%, how much more tax will Sam pay?

Answers

Answer:

See all three answers below

Step-by-step explanation:

Given data

Amount Earned= $54275

Income Tax= 18%

a Work out how much income tax he pays.

Amount of income tax

=18/100*54275

=0.18*54275

=$9769.5

b Work out what percentage of his income he pays in tax.

=9769.5/54275*100

=0.18*100

=18%

c. If the income tax rate is increased to 21%, how much more tax will Sam pay?

=21/100*54275

=0.21*54275

=$11397.75

help plzzzzzzzzzzzzzzzzzzzzzzzzzzz

Answers

Answer:

I think I just posted that last time. Check my timeline


1) Bruce L. Sprouts had to take a loan worth $5,000.
The loan has a 3.5% interest rate.
He has to pay the loan off in 6 years.
A) How much will he have to pay for the interest?
B) How much will he have to pay total? Please answer fast show your work you will be marked as brain

Answers

Answer:

A) $1,050

B) $6,050

Step-by-step explanation:

We solve using the Simple Interest formula

Simple Interest (I) = Principal × Rate × Time

From that above question, we have the parameters

Principal = $5000

Rate = 3.5 % = 0.035

Time = 6 years

A) How much will he have to pay for the interest?

Hence,

Interest = $5,000 × 0.035 × 6

= $1,050

Therefore, the amount of interest he will have to pay is $1,050

B) How much will he have to pay total?

The amount he will have to pay in contact =

Principal + Interest paid on loan

= $5,000 + $1,050

= $6,050

The length of a rectangle is 8feet less than the width. The perimeter is 64 feet. Find the length and the width

Answers

Answer:

Length = 4 feet

Width = 4 feet

Step-by-step explanation:

The perimeter of a rectangle formula = 2L + 2W

Where L = Length

W = Width

The length of a rectangle is 8feet less than the width.

Hence,

L = 8 - W

The perimeter is 64 feet.

Hence,

64 = 2(8 - W) × 2W

64 =( 16 - 2W )2W

64 = -4W² + 32W

4W² - 32W + 64 = 0

Factorise

4W² - 16W - 16W + 64 = 0

4W (W - 4) - 16(W - 4) = 0

W - 4 = 0

W = 4

Width = 4

Solving for L

L = 8 - W

L = 8 - 4

L = 4

Therefore,

Length = 4 feet

Width = 4 feet

At cracker barrel there are 15 side items to choose from. You order a variety plate that consists of 5
sides. In how many different ways can you choose your plate?

Answers

Answer:

3003

Step-by-step explanation:

It is going to be 15C5

PLS HELP ASAP!!

50 POINTS!

Answers

Answer:

135

Step-by-step explanation:

3³· (12 - 2) ÷ 2 = 3³ · 10 ÷ 2 = 27 · 10 ÷ 2 = 270 ÷ 2 = 135

Find the MEDIAN of the data set. (Hint: the numbers must be in order first!) 40 76 40 63 47 57 49 55 50 53

Answers

Given:

The data set is:

40, 76, 40, 63, 47, 57, 49, 55, 50, 53

To find:

The median of the given data set.

Solution:

We have,

40, 76, 40, 63, 47, 57, 49, 55, 50, 53

Arrange the data values in ascending order.

40, 40, 47, 49, 50, 53, 55, 57, 63, 76

Here, the number of observations is 10 which is an even number. So, the median is:

[tex]Median=\dfrac{(\dfrac{n}{2})\text{th term}+(\dfrac{n}{2}+1)\text{th term}}{2}[/tex]

Putting n=10, we get

[tex]Median=\dfrac{(\dfrac{10}{2})\text{th term}+(\dfrac{10}{2}+1)\text{th term}}{2}[/tex]

[tex]Median=\dfrac{5\text{th term}+6\text{th term}}{2}[/tex]

From the arranged terms, it is clear that the the 5th term is 50 and the 6th term is 53.

[tex]Median=\dfrac{50+53}{2}[/tex]

[tex]Median=\dfrac{103}{2}[/tex]

[tex]Median=51.5[/tex]

Therefore, the median of the given data set is 51.5.

Christopher the barber did 8 haircuts. One of the 8 was a walk-in. Express the amount
of walk-ins as a percent.

Answers

It’s 12.5% I hope this helps but that’s the correct answer :)

The price of an item yesterday was $130. Today, the price rose to $351. Find the percentage increase.​

please help and I will mark you braniest!

Answers

Answer: The percentage increase is 170%

Step-by-step explanation:

Increase= $351 - $130

Increase= 221

Percent increase = 221/ 130

Percent increase= 170%

I'm not sure if I'm right, but I hope that this helped:)

Answer:

170%

Step-by-step explanation:

130 = 100%

65 = 50%

13 = 10%

351 - 130 = 221 (doesnt count)

221 - 130 = 91

91 - 65 = 26

26 - (13 + 13) = 0

100 +  50 + 20 = 170%

What is the range of the function f(x)=2x+4f⁢(x)=2x+4 when the domain is {-2, 0, 3}?

A. {0, 4, 10}

B. {4.25, 5, 12}

C. {4.25, 4, 12}

D. All real numbers

Answers

D. All real numbers is the answers

Determine whether the triangles are similar. If they are, write a similarity statement. Explain your reasoning.

Answers

Answer:

yes

Step-by-step explanation:

angle XZY = GHF (given)

zxy =48° And ghf =48°

same no of angle are equql

Tatum walks her dog 2/3 of a mile every day after school how many miles does she walk her dog in 5 days

Answers

Answer:

i think it is 3 miles but dunno

Step-by-step explanation:

Which table represents a nonlinear function?

Answers

Answer:C

Step-by-step explanation: When a table represents a nonlinear function, the rate of change is not constant. A wouldn't be the answer because the rate of change is always +10 (you would add 10 to get from -9 to 1; you would add 10 to get from 1 to 10) . It wouldn't be B because the rate of change is always -2, and the rate of change for D is always +3. For C, however, the rate of change is not constant all the way through (to get from 0 to 6, you would add 6, but to get from 6 to 16 you add 10).

It’s about solving systems of equations...

Answers

Answer:

(-1,-1)

Step-by-step explanation:

A school eacher took some student to the amusement park. 1/2 of them has 3 rides on the merry-go-round. 3/5 of the remainder had two rides and the rest of the children had one ride. If 8 students had one ride. How many students did she take to the amusement park?

Answers

Answer:

40 students

Step-by-step explanation:

Total students in the amusement park = x

Students who had 3 rides = 1/2x

Remainder = x - 1/2x

= 1/2x

Students who had two rides = 3/5 of 1/2x

= 3/5 * 1/2x

= 3/10x

Students who had one ride = 8 students

x = 1/2x + 3/10x + 8

x = (5x+3x) / 10 + 8

x = 8/10x + 8

x = 4/5x + 8

x - 4/5x = 8

(5x-4x) / 5 = 8

1/5x = 8

x = 8 ÷ 1/5

x = 8 × 5/1

x = 40 students

Total students in the amusement park = x = 40 students

For any number, y
Add one third of the number
Then subtract _____________ of the result.
The answer is y

Answers

Answer:

y/3

Step-by-step explanation:

According to the conditions :

y + y/3 - x = y

y + y/3 - y = x

(3y + y - 3y )/3 = x

y/3 = x

Answer:

[tex]\frac{3}{12}[/tex]

Step-by-step explanation:

Create an equation and solve for x:

[tex]y + \frac{1}{3} y = \frac{4}{3} y\\\frac{4}{3}y - x(\frac{4}{3}y) = y\\x = \frac{3}{12}[/tex]

Which of the following is a dilation?​

Answers

Answer:

A) image is being doubled in size in A

Step-by-step explanation:

B and C are rotations

D is a translation

The product of -3 and -7 is positive.


True False

Answers

True!! If you multiply -3 x -7 you get 21!!

Answer:

True

Step-by-step explanation:

[tex] - 3 \times - 7 \\ = {}^{ + } 21[/tex]

I need help on this equation

Answers

45 degree angle :))
Angle abc is 90 and half of that is 45 degrees

There are 4 portable classrooms at Glynn High School. Four teachers will be assigned to the rooms. In how many ways can these assignments be made?

Answers

Answer:

24

Step-by-step explanation:

In the first classroom, there are 4 possibilities of teachers to be assigned.

In the second classroom, 1 teacher has already been assigned, so there are 3 possibilities.

In the third classroom, 2 teachers have already been assigned, so there are only 2 possibilities.

Finally, there is only 1 possible teacher for the fourth classroom, since 3 teachers have already been assigned to other classrooms.

We can find the total number of possibilities using the product rule.

N = 4 × 3 × 2 × 1 = 24

What is the equation of the line that passes through the point (-4, 2) and has a slope of -5/4?​

Answers

Answer:

y = -5/4 x - 3   is the slope-intercept form

5x + 4y = -12    is the standard form

Step-by-step explanation:

Use the point-slope form:  [tex]y - y_{1} = m(x - x_{1})[/tex]

[tex](x_{1}, y_{1})[/tex] = (-4, 2)

y - 2 = -5/4(x + 4)       Multiply by 4 to remove the fraction

4y - 8 = -5(x + 4)

4y - 8 = -5x - 20

4y = -5x - 12

y = -5/4 x - 3   is the slope-intercept form

5x + 4y = -12    is the standard form

Jose has a bag of 6 blue marbles, 3 white marbles, and 8 black marbles. What is the probability that he pulls a blue marble out of the bag?

Answers

First you add all marbles so you know how many there are:

6+3+8= 17

Then, to find the probability you put the number of marbles which you want to find the probability of being pulled out on top of the fraction and make it out of 17

6/17

Wait what about this one

Answers

Answer:

I believe it is 7/20

Step-by-step explanation:

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