The question involves using logical quantifiers to express the statements "Many people love A" and "A loves many people" and their negations. The formulas are ∃x (p(x, A)) and ∃y (p(A, y)) for the original statements, and the negations are ¬∃x (p(x, A)) and ¬∃y (p(A, y)).
The question involves expressing statements about relationships using logical quantifiers and then finding their negations. Given S as the domain of humans and p(x, y) representing the statement "x loves y", we can write the formulas for the following statements:
a) Many people love A: ∃x (p(x, A))
b) A loves many people: ∃y (p(A, y))
The negation of these statements can be written as:
a) It is not the case that many people love A: ¬∃x (p(x, A)), which means no one loves A or everyone does not love A.
b) A does not love many people: ¬∃y (p(A, y)), implying A loves no one or A does not love everyone.
Answer:
Step-by-step explanation:
Answer:
Sale price of video game with tax = $20.3775
Yes, they both have enough money to purchase the video game.
Step-by-step explanation:
Given that:
Original price of video game = $28.50
Discount on original price = 35%
Sales tax = 10%
Money available with Pat and Henri = $21 each
First of all, let us find out the price as per Pat's method.
Step 1:
Taking 35% of $28.50
Step 2:
Subtract from $28.50 to find the sale price:
$28.50 - $9.975 = $18.525
Step 3:
Take 10% of sale price:
Step 4:
Add to sale price to get the final amount to be paid:
$18.525 + $1.8525 = $20.3775
Now, let us use Henri's method:
Step 1:
Find 65% of original price:
Step 2:
Find 110%:
Sale price of video game with tax = $20.3775
Yes, they both have enough money to purchase the video game.
Answer:
The answer is 6x
Step-by-step explanation:
Step-by-step explanation:
I think common factors are
18 = 1 2 3 6 9 18
30 = 1 2 3 10 15 30
So highest common factor is 3
18x + 30x2
3x (6 + 10x)
Answer: 7a+3
Step-by-step explanation:
9a and 2a are two like terms that we can combine. Because there is a minus sign in front of the 2a, we should subtract 9a from 2a to get
7a. Then because the 3 has plus sign in front of it, we add 7a to 3. BUT because 3 a is NOT a like term, you don’t actually add it, so it looks like this: 7a+3. Hope this helped!
and
B. are between 37.25 and 101.75
The height of the television set would be 21.6 inches to the nearest inch.
If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
where |AB| = length of line segment AB. (AB and BC are the rest of the two sides of that triangle ABC, AC being the hypotenuse).
We have been given that the television set is 36 inches wide and has a diagonal length of 42 inches.
Let b represent the height of the television set.
We will use the Pythagorean theorem;
36² + b² = 42²
1296 + b² = 1764
-1296. -1296
b² = 468
√ b² =√ 468
b = height
b = 21.6 inches
Therefore, the height of the television set would be 21.6 inches to the nearest inch.
Learn more about Pythagoras' theorem here:
#SPJ5
Answer:
g
Step-by-step explanation:
a) A good method to convert a decimal number to binary is dividing it by 2 and using the remainder of the division as the converted number, starting by the most significant bit (the right one). We we can't divide anymore. So we have:
217/2 = 108 + 1
108/2 = 54 + 0
54/2 = 27 + 0
27/2 = 13 + 1
13/2 = 6 + 1
6/2 = 3 + 0
3/2 = 2 +1
2/2 = 1
The binary equivalent to 217 is 11011001
b) To convert a number from decimal to hex we can divide the number by 16, taking out the decimal part and multiplying it by 16 using that as our most significant number while using the result of the original division to continue our conversion. So we have:
99/16 = 6.1875
The decimal part is 0.1875, we multiply it by 16 and obtain 3 as our most significant number. Since we can't divide 6 by 16 we have that as our least significant number then the hexadecimal equivalent is 63.
c) We follow the same steps as in item b:
344/16 = 21.5
The most significant number is 0.5*16 = 8
21/16 = 1.3125
The next number is 0.3125*16 = 5
Since we can't divide it anymore we have our result wich is 158 in hex.
d) To convert from decimal to base 7 we'll use the same method as to hex, but this time dividing and multiplying by 7.
136/7 = 19.428571
The most significant number is 0.428571 * 7 = 3
19/7 = 2.71428571
The next number is 0.71428571*7 = 5
Since we can't divide it anymore we have our result wich is 253.
e) To convert from decimal to a base 5 we'll use the same method as before but dividing and multiplying by 5.
542/5 = 108.4
The most significant number is 0.4*5 = 2
108/5 = 21.6
The next number is 0.6*5 = 3
21/5 = 4.2
The next number is 0.2*5 = 1
Since we can't divide it anymore we have our result that is 4132.
f) To convert from decimal to a base 8 we'll use the same method as before but dividing and multiplying by 8.
727/8 = 90.875
The most significant number is 0.875*8 = 7
90/8 = 11.25
The next number is 0.25*8 = 2
11/8 = 1.375
The next number is 0.375*8 = 3
Since we can't divide anymore we have our result wich is 1327
g) Following the same steps as before:
171/16 = 10.6875
The most significant number is 0.6875*16 = 11
Since we can't divide anymore we have our result wich is 1011
h) Following the same steps as before:
91/3 = 30.333333333
The most significant number is 0.333333*3 = 1
30/3 = 10
The next number is 0
10/3 = 3.3333333333
The next number is 0.333333*3 = 1
3/3 = 1
Since we have the final value remainder as 0 the least significant number is 1
Since we can't divide anymore we have our result that is 10101.
i) Following the same steps as before:
840/9 = 93.333333
The most significant number is 0.33333*9 = 3
93/9 = 10.3333333
The next number is 0.333333*9 = 3
10/9 = 1.11111111
The next number is 0.11111111*9 = 1
Since we cant divide anymore we have our result that is 1133
To convert decimal numbers to non-decimal bases, divide the number by the base, note the remainders, and read the remainders in reverse order to get the converted number. This applies to binary, hexadecimal, and other bases like base 7 or base 5. The process continues until the quotient is zero.
The process of converting numbers from decimal to non-decimal bases involves division for integer parts and multiplication for fractional parts, using the target base until the dividends are zero or an acceptable level of fractional precision is reached. For whole numbers, divide the number by the new base, note the remainder, and continue dividing the quotient until it equals zero. The remainders noted, read in reverse order (from last to first), give the resulting non-decimal number.
To convert 217 to binary, you would start by dividing 217 by 2, the base for binary numbers, and noting the remainders. This division continues until the quotient is zero. Read the remainders backwards to get the binary representation.
For conversion to hexadecimal, which is base 16, you divide the number by 16, note the remainders, continue with the quotient, and read the remainders in reverse order to get the hexadecimal equivalent. Alphabetic characters are used for remainders of 10-15, representing 'A' to 'F'.
When converting to other bases like base 7 or base 5, you follow a similar division method but use the base you're converting to. For example, in base 7, you divide by 7 and use the remainders to construct the new base representation. Always read the remainders in reverse to obtain the correct number in the new base.
In cases like base 8 or base 9, the same principles apply. Dividing the number by 8 or 9, respectively, and noting the remainders until you reach a quotient of zero will give you the representation in the new base.
#SPJ3