Answer:
a. Negation of ∃x ∀y(P(x,y) → Q(x,y)) = ∀x ∃y P(x,y) ∧ ¬Q(x,y) ]
b. Negation of ∃x ∀y(P(x,y) → P(y,x)) = ∀x ∃y [ ¬P(x,y) ∨ ¬P(y,x) ] ∧ [P(x,y) ∨ P(y,x)]
c. Negation of ∃x ∃y P(x,y) ∧ ∀x ∀y Q(x,y) = ∀x ∀y ¬ [P(x,y)] ∨ ∃x ∃y ¬ [Q(x,y)]
Step-by-step explanation:
a.∃x ∀y(P(x,y) → Q(x,y))
Negation = ¬ [ ∃x ∀y(P(x,y) → Q(x,y)) ]
= ∀x ¬ [ ∀y(P(x,y) → Q(x,y)) ]
= ∀x ∃y ¬ [ (P(x,y) → Q(x,y)) ]
= ∀x ∃y ¬ [ ¬P(x,y) ∨ Q(x,y) ]
= ∀x ∃y P(x,y) ∧ ¬Q(x,y) ]
Negation of ∃x ∀y(P(x,y) → Q(x,y)) = ∀x ∃y P(x,y) ∧ ¬Q(x,y) ]
b. ∃x ∀y(P(x,y) → P(y,x))
Negation = ¬ [ ∃x ∀y(P(x,y) → P(y,x)) ]
= ∀x ¬ [ ∀y(P(x,y) → P(y,x)) ]
= ∀x ∃y ¬ [ (P(x,y) → P(y,x)) ]
= ∀x ∃y ¬ [ ( P(x,y) ∧ P(y,x) ) ∨ ( ¬P(x,y) ∧ ¬P(y,x) )]
= ∀x ∃y ¬ [ P(x,y) ∧ P(y,x) ] ∧ ¬[ ¬P(x,y) ∧ ¬P(y,x) ]
= ∀x ∃y [ ¬P(x,y) ∨ ¬P(y,x) ] ∧ [ P(x,y) ∨ P(y,x) ]
∴ we get
Negation of ∃x ∀y(P(x,y) → P(y,x)) = ∀x ∃y [ ¬P(x,y) ∨ ¬P(y,x) ] ∧ [P(x,y) ∨ P(y,x)]
c. ∃x ∃y P(x,y) ∧ ∀x ∀y Q(x,y)
Negation = ¬ [ ∃x ∃y P(x,y) ∧ ∀x ∀y Q(x,y) ]
= ¬ [ ∃x ∃y P(x,y) ] ∨ ¬ [ ∀x ∀y Q(x,y) ]
= ∀x¬ [ ∃y P(x,y) ] ∨ ∃x ¬ [ ∀y Q(x,y) ]
= ∀x ∀y ¬ [ P(x,y) ] ∨ ∃x ∃y ¬ [ Q(x,y) ]
∴ we get
Negation of ∃x ∃y P(x,y) ∧ ∀x ∀y Q(x,y) = ∀x ∀y ¬ [ P(x,y) ] ∨ ∃x ∃y ¬ [ Q(x,y) ]
Evaluate the expression.
(-7) + (-3)
Answer:
-10
Step-by-step explanation:
Answer:
= -10
Step-by-step explanation:
-7 + (-3)
=
-7 - 3
-10
plz hurry
How many faces does the solid made from the net below have?
A shape has a pentagon base. There are 5 triangles on the sides.
5
6
10
15
Answer:
6
Step-by-step explanation:
I
did quiz.
The net of the solid is a plane shape, and The net of the solid is made from 6 faces
How to determine the number of faces?From the question, we understand that:
Sides = 5 trianglesBase = 1 pentagonSo, the number of faces is:
Face = Triangle + Pentagon
This gives
Face = 5 + 1
Face = 6
Hence, the net of the solid is made from 6 faces
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Plllllwaaaaasseeee hellollll
Suppose you are given two quadrilaterals, ABCD EFGH. If the similarity ratio of ABCD to EFGH is 4:3, and it EH =
60, find AD
a. 45
0.90
b. 40
d. 80
Please select the best answer from the choices provided
B
Look at image^^^
Answer:
d. 80
Step-by-step explanation:
Similarity ratio of ABCD to EFGH = 4:3.
This implies that the ratio of AD to EH = 4:3
If EH = 60, then:
AD:60 = 4:3
AD/60 = 4/3
Multiply both sides by 60
AD = ⁴/3 × 60
AD = 80
how to solve the volume formula for cylinders using pi
The formula for the volume of a cylinder is V=Bh or V=πr2h . The radius of the cylinder is 8 cm and the height is 15 cm. Substitute 8 for r and 15 for h in the formula V=πr2h . i think the answer is this
Darius has a 6-month loan for $500. He must pay 5.6% annual interest on the loan. Using the formula for simple interest, I = Prt, where I is interest owed, P is the amount borrowed, r is the rate as a decimal, and t is time in years, find the amount of interest owed by Darius after 6 months.
The amount of interest that's owed by Darius after 6 months will be $14
Principal = $500
Rate = 5.6%
Time = 6 months.
Based on the information given, the simple interest will be calculated as:
Simple Interest = PRT/100
Simple Interest = ($500 × 5.6 × 1/2) / 100
Simple Interest = $1400/100
Simple Interest = $14
Therefore, the amount of interest that's owed by Darius after 6 months will be $14
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solve the inequality and graph the solution on the line provided.
Answer:
x [tex]\geq[/tex] 5
Step-by-step explanation:
step 1: subtract 6 from both sides
step 2: divide both sides by 7
answer: x [tex]\geq[/tex] 5
interval notation: [5,∞)
Mae Ling earns a weekly salary of $325 plus a 7.5% commission
on sales at a gift shop. How much would she make in a work week if she sold
$5,800 worth of merchandise? Write in money format.
Answer:
$760
Step-by-step explanation:
Given data
weekly = $325
commission= 7.5%
if she sold $5,800 worth of merchandise
Her earnings will be
Week earning= base salary+ 7.5% of sales
Week earning= 325+ 7.5/100*5800
Week earning= 325+ 0.075*5800
Week earning= 325+ 435
Week earning= $760
What is the simplified form of each expression?
21. 2x + 5x + 4x
A. 11 + 3x
B. 7x
C. 11x
D. 7x + 4x
Answer:
C
Step-by-step explanation:
They all share a common variable so you can add them all together to get the simpliest form.
Can I get help on C plz
Answer:
the answer would be 6...
i need help
(64-4) / 2-7^2
Answer:
-19
Step-by-step explanation:
60/2-7²
30-49
-19
Let R be the triangular region in the first quadrant with vertices at points (0,0), (a,0), and (0,b), where a and b are positive constants. Write dow the volume of the solid generated when region R is revolved about the x-axis?
Answer:
volume of the solid generated when region R is revolved about the x-axis is π ₀∫^a ( [tex]\frac{-b}{a}[/tex]x + b )² dx
Step-by-step explanation:
Given the data in the question and as illustrated in the image below;
R is in the region first quadrant with vertices; 0(0,0), A(a,0) and B(0,b)
from the image;
the equation of AB will be;
y-b / b-0 = x-0 / 0-a
(y-b)(0-a) = (b-0)(x-0)
0 - ay -0 + ba = bx - 0 - 0 + 0
-ay + ba = bx
ay = -bx + ba
divide through by a
y = [tex]\frac{-b}{a}[/tex]x + ba/a
y = [tex]\frac{-b}{a}[/tex]x + b
so R is bounded by y = [tex]\frac{-b}{a}[/tex]x + b and y =0, 0 ≤ x ≤ a
The volume of the solid revolving R about x axis is;
dv = Area × thickness
= π( Radius)² dx
= π ( [tex]\frac{-b}{a}[/tex]x + b )² dx
V = π ₀∫^a ( [tex]\frac{-b}{a}[/tex]x + b )² dx
Therefore, volume of the solid generated when region R is revolved about the x-axis is π ₀∫^a ( [tex]\frac{-b}{a}[/tex]x + b )² dx
The volume of the solid generated when region R is revolved about the x-axis is [tex]\frac{b^{5} }{3a^{2} }[/tex].
Equation of the line AB
[tex]y-0 = \frac{b-0}{0-a} (x-a)[/tex]
[tex]y = \frac{-b}{a} (x-a)[/tex]
What is the volume generated when a curve f(x) is generated about the x-axis?The volume generated when a curve f(x) is rotated about the x-axis in x∈(c,d) is given by:
[tex]V=\int\limits^d_c {y^2} \, dx[/tex]
So, the volume generated when line AB is rotated about the x-axis will be [tex]V=\int\limits^b_0 ({\frac{-b}{a} (x-a))^2} \, dx[/tex]
[tex]V=\frac{b^{5} }{3a^{2} }[/tex]
Therefore, the volume of the solid generated when region R is revolved about the x-axis is [tex]\frac{b^{5} }{3a^{2} }[/tex].
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SIMPLIFY -3/4( 8/9Y - 18) - 3/5(5/6Y + 25)?
Answer:
I believe the answer is
-7y+9/6
Answer:
-7/6 y -3/2
Step-by-step explanation:
How many births occur among women under the age of 20?
Answer:
what do you mean?
Step-by-step explanation:
Evaluate the expression: (10) -3x (-2) +5
Answer:
-3x(-2)+15
Step-by-step explanation:
add the numbers
Please help me I don’t get it
Answer:
x=8°
Step-by-step explanation:
If two sides are equal than there angles are also equal.
2x+40+5x+22+5x+22=180
12x+84=180
12x=180-84
12x=96
x=96/12
x=8°
Someone please help and thank you
Answer:
8:3
Step-by-step explanation:
The GCF of each of them is 8. Divide both of them by it you'll get the ratio
in equivalence the answer is 8 3
Simplify the expression.
21 + 49 divided by 7 + 1
Answer:
60 divided by 8
Step-by-step explanation:
60 divided by 8
GUYS I NEED HELP PLSSSSSS! Ive been working on this ALL day!
First, let's write what we know.
We can represent the number of students in the play from each class as L, G, and C. We know that L = 7, and if Gardener has 4 more students than Cho, then G = C + 4.
Then, taking the third line, we can write an inequality:
C < L < G
C < 7 < C + 4
C - 4 < 3 < C
3 < C < 7
If C is greater than 3 and less than 7 and is an integer, than means C is 4, 5, or 6.
Then, we need to find how many students are in the play.
C + L + G
C + 7 + C + 4
2C + 11
So we have our expression for the number of students in the play. Then, we need to find the total number of students. We know that 2C + 11 will be 30% of the total, so if T is the total, we can find T.
0.3T = 2C + 11
(Divide by 3/10 or multiply by 10/3 on both sides)
T = 20/3 C + 110/3
We know from before that C is 4, 5 or 6. We can plug these into our equation here to find which one produces a whole number.
T = 20/3 * 4 + 110/3
T = 190/3
T = 20/3 * 5 + 110/3
T = 210/3
T = 70
T = 20/3 * 6 + 110/3
T = 230/3
We can see here that only when C is 5 will the total be a whole number. That means Mrs. Cho has 5 students in the play. If Mrs. Gardner has 4 more than that, she has 9 students in the play in her class. We now need to figure out the number of student in her class.
The total students are Cho's, Logan's, and Gardner's classes added together. We know that Logan's class is 23 students, so if we subtract that from the total, we can see that Cho's and Gardner's class have 47 students. If Mrs. Cho has 24 students in her class, we can subtract that from the 47, so we know that Mrs. Gardner has 23 students in her class.
NEED FAST HURRY
A candy store sells caramels and milk chocolate by the pound the table below shows the total cost in dollars for a pound of each type of candy the store sells
Caramels: $9.28
Milk Chocolate: $12.80
How much more is the cost for 1 3/4 pounds of milk chocolate than the cost for 1 3/4 pounds of caramels?
Answer:
$6.16
Step-by-step explanation:
Answer:
Caramels=$16.24
Milk chocolate=$22.40
All together= $29.04
Step-by-step explanation:
64 + (5 ÷ 3) - 2^3
help me plz
Answer:
57.67
Step-by-step explanation:
64+1.67-8
65.67-8
57.67
Ms. Hagan invested twice as much money in an account that pays 7% interest as she did in an account that pays 6% in interest. Her total investment pays her $1,000 a year in interest. How much did she invest at each rate?
Answer: She invested $5000 in an account that pays 6% interest and $10000 in an account that pays 7% interest.
Step-by-step explanation:
Let P be the initial amount she invested in an account that pays 6% interest.
Then, amount invested in other account = 2P
Simple interest = Principal x rate x time
After one year, for the first account,
Interest = P(0.06)(1) = 0.06P
For second account,
Interest = (2P)(0.07)(1)=0.14P
Total interest = [tex]0.06P+0.14P=1000[/tex]
[tex]\Rightarrow\ 0.20P=1000\\\\\Rightarrow\ P=\dfrac{1000}{0.20}\\\\\Rightarrow\ P=5000[/tex]
2P = 2(5000)=10000
Hence, She invested $5000 in an account that pays 6% interest and $10000 in an account that pays 7% interest.
At the interest rate of 6%, amount invested is; $5000
At interest rate of 7%, amount invested is; $10000
Let P be the initial amount that Ms. Hagan invested in the 6% interest account that
Since she invested twice as much in the 7% interest account as in the 6% interest account, then;
Initial amount invested in the 7% interest account = 2P
Formula for Simple interest is;
I = Principal × rate × time
Interest after 1 year for the 6% interest account is,
I_1 = P × 0.06 × 1
I_1 = 0.06P
Interest after 1 year for the 7% interest account is,
I_2 = 2P × 0.07 × 1
I_2 = 0.14P
Total investment pays her $1000 after a year. Thus;
0.06P + 0.14P = 1000
0.2P = 1000
P = 1000/0.2
P = $5000
Then amount initially invested in the 7% interest account = 2P = $10000
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NOTE: Angles not necessarily drawn to size . what is x?
Answer: 45
Step-by-step explanation: 160-115= 45 you do this because the angles are across the vertex from each other.
Answer:
X=45
Step-by-step explanation:
Method 1 ( the long one)
So AED and CEB are vertical angles, that means that the are the same and have the same value.
So 115 plus x equal 160.
115 + x = 160
from there we just have to subtract 115 from both sides to get x by itself.
115 + x = 160
-115 -115
_________________
x=45
Method 2 (short one
If you know that those are vertical angles, then just subtract 115 from 160 and there you go. You get 45.
Tucker's bedroom is a rectangle that measures 3
5
6
yards by 4
1
6
yards. His dad buys two area rugs that each have a length of 4 yards. Rug one has an area of 16
35
36
square yards. Rug two is 15 square yards.
Which rug will fit Tucker's room?
Answer:
my teacher has cancer please help her at #snowmanchallenge
Step-by-step explanation:
try to spread the help every snowman is ten dollars for her
A group of friends hiked 7 miles in 2 hours at this same rate what is the total number of miles they can hike in 8 hours
Domesticated animals were primarily valued for meat.
true or false
Answer:
False
Step-by-step explanation:
Hope this helps :)
WORTH 30 POINTS *will give you brainliest*
Answer:
x = 3
Step-by-step explanation:
MN is exactly half of 6x + 2 (midpoint theorem)
2(2x + 4) = 6x + 2
4x + 8 = 6x + 2
-2x + 8 = 2
-2x = -6
x = 3
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7. Write an equation of the line that passes through the points (1, 4) and (-2, 10), in point-slope form.
Answer:
y = -2x + 6
Step-by-step explanation:
This has sort of the same concept as your earlier question
Use the equation y = mx + b
To find the slope, take the second y value and subtract the first y value. Then take the second x value and subtract the first x value. Divide the answers. You'd get -2 in this case. -2 would be your slope (m).
The substitute any set of x and y values (either (1, 4) or (-2, 10)) and the slope into y = mx + b. You'd get 6 as your y-intercept (b).
One alloy is 2 parts iron and 3 parts silver and another alloy is 7 parts iron to 3 parts silver. How much of each should be combined to produce a 30 pound alloy that is one part iron to one part silver
Answer:
Let x be your first alloy
2/5x+7/10(30-x)=1/2(30)
4x+210-7x=150
3x=60
x=20
So, you need 20 lbs of the first alloy, and 10 parts of the second to make 30 lbs of half iron and half silver alloy
Answer:
20 pounds for first 10 for second.
Step-by-step explanation:
can anyone help me i dont understand this