Which of the following are valid (necessarily true) sentences? a. (∃x x = x) ⇒ (∀ y ∃z y = z). b. ∀ x P(x) ∨ ¬P(x). c. ∀ x Smart(x) ∨ (x = x)
Answer:
b; ∀x P(x) ∨ ¬P(x)
Step-by-step explanation:
Suppose that we have a proposition p
Such that p can be true or false.
We can define the negation of p as:
¬p
Such that, if p is false, then ¬p is true
if p is true, then ¬p is false.
Also remember that a proposition like:
p ∨ q
is true when, at least one, p or q, is true.
Then if we write:
p ∨ ¬p
Always one of these will be true (and the other false)
Then the statement is true.
And if the statement depends on some variable, then we will have that:
p(x) ∨ ¬p(x)
is true for all the allowed values of x.
from this, we can conclude that the statement that is always true is:
b; ∀x P(x) ∨ ¬P(x)
Where here we have:
For all the values of x, P(x) ∨ ¬P(x)
Micheal is selling lemonade.He sold 6 large lemonades at $3 each and 5 small lemonades at $2 each. How much money did he earn ?
Answer:
$28
Step-by-step explanation:
Answer:
6=$3
5=$2
6x3=18
5x2=10
18+10= 28
=$28
Step-by-step explanation:
What are equivalent expressions please explain
Answer:
Equivalent expressions are expressions that are the same, even though they may look a little different. If you plug in the same variable value into equivalent expressions, they will each give you the same value when you simplify.
Step-by-step explanation:
The following are the last 10 run scores Colin got in cricket:
28, 13, 4, 12, 32, 22, 13, 22, 26, 32
a) Work out Colin's mean score.
b) Colin plays cricket again on Sunday. He gets 16 runs.
What is his new mean score?
Give your answers as decimals.
Answers:
a) Mean = 20.4b) New mean = 20==================================================
Explanation:
To get the mean, we add up the scores and divide by 10 (because there are 10 scores at first)
28+13+4+12+32+22+13+22+26+32 = 204
204/10 = 20.4
The mean is 20.4
------------
For part b), we redo those steps shown above, but tack 16 onto the list. So we'll add up all the values (including that 16 at the end) and divide by 11 this time.
28+13+4+12+32+22+13+22+26+32+16 = 220
220/11 = 20
The new mean is 20.
The new mean is slightly smaller than the old mean. Notice how 16 is smaller than 20.4, so this new score pulls down the mean just a little bit.
Surveying Indiana high school students about virtual learning or e-learning by sampling all of the students from only some of the online schools in Indiana would be a type of sampling known as cluster sampling.
True
False
Each high school in Indiana is considered a cluster. Let's say there are 1000 high schools in that state. That would mean there are 1000 clusters.
You would then randomly select say 5 clusters. Once those selections are made, you would then survey every student at those five schools selected. The number of clusters selected will depend on the situation of course.
plz hellppp 10 points!!
Select the correct difference.
5d^2 + 4d-3 less 3d^2-2d+4
answers:
a. 2d^2+2d+1
b. 2d^2+6d+7
c. 2d^2+6d-7
d. -2d^2-6d+1
Answer:
(c)
Step-by-step explanation:
Put all numbers in the same side
5d^2-3d^2+4d+2d-4-3=0
2d^2+6d-7
does this table represent a function? why or why not 2,1 3,4 4,4 5,2 5,5
Helppppp and explain tooo pls and thankyouuu
Answer:
--- ---
| -5 -2 |
| 4 12 |
--- ----
Step-by-step explanation:
A matrix can only be added to (or subtracted from) another matrix if the two matrices have the same dimensions . To add two matrices, just add the corresponding entries, and place this sum in the corresponding position in the matrix which results.
(a+1)(b+2)
please help me!!!
Answer:
(a + 1) (b + 2 ) = 2a + b + ab + 2
Step-by-step explanation:
[tex](a +1 )(b + 2) \\\\= a( b+ 2) + 1 (b +2) \\\\= ab + 2a + b + 2\\\\=2a + b + ab + 2[/tex]
[tex](a + 1)(b + 2) \\ = a(b + 2) + 1(b + 2) \\ = ab + 2a + b + 2[/tex]
Answer ↦ [tex]\boxed{\tt{ab + 2a + b + 2}}[/tex]
Method Used:↦ Distributive Property.
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐
Why is lowering the interest rate on reserves considered an expansionary monetary policy? A. It encourages banks to lend money instead of keeping it in reserve.
B. It pressures investors to spend more money on treasury securities.
C. It prevents investors from withdrawing too much money from banks.
D. It causes banks to increase their prime interest rate in response.
Step-by-step explanation:
The reserve ratio is the central bank's mandate for banks to keep a certain reserve requirements, which are excess cash deposits that must be kept on hand and not loaned out.
Raising the ratio is contractionary since less loans can be made, but this also solidifies banks' balance sheets.
If the Federal Reserve instead lowers the reserve ratio through an expansionary monetary policy, commercial banks are required to hold less cash on hand and can make more loans.
The lowering of the interest rate on reserves, considered an expansionary monetary policy, as it encourages banks to lend money instead of keeping it in reserve.
Hence, option 1 is correct.
Lowering the interest rate on reserves is considered an expansionary monetary policy because it incentivizes banks to lend out their excess reserves rather than keeping them idle in reserve accounts. When the central bank reduces the interest rate on reserves, it effectively lowers the opportunity cost for banks to hold reserves.
As a result, banks are more inclined to lend money to consumers and businesses at lower interest rates, which stimulates borrowing and spending in the economy. Increased lending and spending contribute to economic expansion and growth, making it an expansionary monetary policy.
Thus, lowering the interest rate encourages banks to lend money instead of keeping it in reserve.
Learn more about monetary policy here:https://brainly.com/question/28199887
#SPJ4
Whats the mean, modian, mode, and range, of these five?
6) 35, 74, 76, 93, 84, 22
Mean=
Median=
Mode=
Range=
7) 72, 55, 11, 55, 42, 25, 79, 69
Mean=
Median=
Mode=
Range=
8) 93, 15, 11, 58, 94, 87, 73, 16, 21
Mean=
Median=
Mode=
Range=
9) 17, 45, 12, 74, 89, 57
Mean=
Median=
Mode=
Range=
10) 52, 35, 55, 23, 30
Mean=
Median=
Mode=
Range=
Answer:
Step-by-step explanation:
mean:64
median: (74+76)/2=75
mode: no mode
Range: 71
#2
mean:51
median:(55+55)/2=55
mode:55
Range; 68
Answer:
6)
Mean = 35+ 74+ 76+ 93+ 84+ 22 = 384
mean = total amount/total numbers
384/6 = 64
Median = 76 + 93/2 = 169/2 = 84.5
Mode = there is no mode (there are no numbers repeated)
Range = (biggest - smallest) = 93 - 22 = 71.
7)
Mean = total amount/total numbers
72+ 55 +11+ 55 + 42 + 25 + 79 + 69 = 408/8 = 51
Median = 55 + 42/2 = 97/2 = 48.5
Mode = 55
Range = 79 - 25 = 54
8) Mean = 93 + 15 + 11+ 58+ 94+ 87 + 73+ 16+ 21 = 468/9 = 52
Median = 94
Mode = nothing
Range = 93 - 11 = 82
9)
Mean = 17+45+ 12+ 74+ 89 + 57 = 294/6 = 49
Median = 12 + 74/2 = 43
Mode = nothing
Range = 89 - 12 = 77
10)
Mean = 52+ 35+ 55+ 23+ 30 = 195/5 = 39
Median = 55
Mode = nothing
Range = 55 - 23 = 32
Step-by-step explanation:
I rlly hope this helped i took soooo long(sry for that btw)
rization
Vhat is the prime factorization of 180?
Select a composite number to break into factors. Continue
factoring until all factors are prime.
22•2•3•3.5
2.2.45
2.3.3.5
480
2.9.5
Answer:
5 3 3 2 2
Step-by-step explanation:
180
90 2
45 2 2
15 3 2 2
5 3 3 2 2
Answer:
180 = 5 × 3² × 2²
Step-by-step explanation:
Starting with 180, the prime factors are in bold
180 = 90 × 2
= 45 × 2 × 2
= 15 × 3 × 2 × 2
= 5 × 3 × 3 × 2 × 2
Then
180 = 5 × 3 × 3 × 2 × 2 = 5 × 3² × 2²
What is the measure of Arc E B C?
The midpoint, M , of segment AB has coordinates (2,−1) . If endpoint A of the segment has coordinates (−3,5) , what are the coordinates of endpoint B ?
The coordinates of endpoint B are?
the coordinates of endpoint B are (7,7)
Answer:
Solution given:
M(x,y)=(2,-1)
A[tex](x_{1},y_{1})=(-3,5)[/tex]
Let
B[tex](x_{2},y_{2})=(a,b)[/tex]
now
by using mid point formula
x=[tex]\frac{x_{1}+x_{2}}{2}[/tex]
$ubstituting value
2*2=-3+a
a=4+3
a=7
again
y=[tex]\frac{y_{1}+y_{2}}{2}[/tex]
$ubstituting value
-1*2=5-b
b=5+2
b=7
the coordinates of endpoint B are (7,7)
SOMEONE PLEASE HELP ME! IM SO CONFUSED, NEED THIS VERY BADLY!
Answer:
115°
Step-by-step explanation:
in a parallelogram vertically opposite angles are equal.
m∠MNK=m∠KLM=115°
they help me ? is the last someone please
Determine the period
Answer:
It's 10, on acellus :)
Step-by-step explanation:
yeaaaaaaaaaa help plzzzzzzzzzz
Answer:
See Explanation
Step-by-step explanation:
Given
The attached graph
Required
Point on the line
The options are not given. So, I will provide general answers.
To do this, we simply write out the coordinates that lie on the line.
Some of them are:
[tex](0.5,3)[/tex]
[tex](1.25,8)[/tex]
[tex](1.5,10)[/tex]
what is the measure of < B ? help !!
The choose (C) 60
The measure of the angles of a triangle is 180, and this triangle is equilateral, so 180/3=60, each angle is 60°
Find the equation of the line through the points (6, -9) and (-2, -1).
If a^2 -b^2 =12 and a-b=4 what is the bay of a +b
Answer:
a+b = 3
Step-by-step explanation:
a = b+4
a^2 = (b+4)(b+4) = b^2 + 8b +16=-b^2 = 12
8b=-4
b = - 1/2
a = 3.5
If 'a' is a number lying between 0 and 1. then which of the following is in increasing order? a) a², a, √a b) a √a ,a² c) a²,√a,a d) a, a², √a
Hello,
[tex]0\leq a\leq 1 \Longrightarrow 0*a\leq a*a\leq 1*a \Longrightarrow 0 \leq a^2 \leq a\\\\0\leq a^2\leq a \Longrightarrow \sqrt{0} \leq \sqrt{a^2} \leq \sqrt{a} \\\\The\ function\ y=x^2\ is\ increasing\\\\Answer A\\\\ex: a=0.5 \\\\a^2=0.25\\\\\sqrt{a}=\dfrac{\sqrt{2}}{2}\approx{0.7071...}\\\\and\ 0.25\leq 0.5 \leq 0.7071...[/tex]
I really need some help with this question also.
A) 2/5
B) 3/5
C) 11/25
D) 14/25
In ΔEFG, the measure of ∠G=90°, GF = 33, FE = 65, and EG = 56. What ratio represents the sine of ∠F?
Which of the following describes point D?
The coordinates that describe the point D are: Option C: (0, 4)
How to find the coordinates of the graph?The graph shows that the vertical axis is labelled as the y-axis while the horizontal axis is labelled as the x -axis.
Normally, the coordinate system of writing the given points of the graph is (x, y)
Thus, the point D on the graph is seem to be 4 units on the positive y-axis and 0 units on the positive x-axis and as such, we can say that the coordinates of point D are:
D(0, 4)
Read more about Graph Coordinates at: https://brainly.com/question/11337174
Complete question is:
Which of the following describes point D?
(-4, 0)
(0, -4)
(0, 4)
(4, 0)
If AABC IS REFLECTED across the y axis what are the coordinates of A
Answer:
A. (-1, 3)
Step-by-step explanation:
When reflecting across the y-axis: (x, y) ⇒ (-x, y).
Therefore, A(1, 3) ⇒ A'(-1, 3).
According to general equation for conditional probability, if P(A^B) = 2/3 and P(B) = 3/4, what is P(A|B)?
Answer:
a
Step-by-step explanation:
ok
Answer:
D. 8/9
Step-by-step explanation:
Jing jing works in a store and she spends some of her time organizing the stationary section. If there are nine different items on the rack, how many ways can she organize the rack so that the two most expensive items are not together?
Answer:
282240 ways
Step-by-step explanation:
number of items = 9 different items
Ranking based on worth
determine number of ways to arrange the 9 items such that the 2 most expensive are apart
first step: consider the 2expensive items as 1
∴ number of permutation = [ ( 9 - 2 ) + 1 ]! * 2!
= [ 8 ] ! * 2! = 80640
Total number of permutation/arrangement = 9! = 362880
hence to arrange the 9 items without having the two most expensive items together
= 362,880 - 80640
= 282240 ways
PLEASE HELP! Use the substitution method to solve the system of equations.
A. (-30,11)
B. (5,-3)
C. (10,-5)
D. (0,1)
Hello,
[tex]\left\{\begin{array}{ccc}2x+5y&=&-5\\x+3y&=&3\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x&=&3-3y\\6-6y+5y&=&-5\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x&=&3-3y\\y&=&11\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x&=&-30\\y&=&11\\\end{array}\right.\\\\[/tex]
Answer A
What should be done first to evaluate the expression?
3 + (5 - 3)2 × 4
Answer:
19
Step-by-step explanation:
19 is the answer I think so