I'll use text forms of the logical symbols because copying/pasting on mobile is annoying.
⊕ = XOR
∨ = OR
∧ = AND
~ = NOT
↔ = IFF (meaning "if and only if")
→ = IMP (short for "implies")
and for logical equivalence I'll use a regular equal sign.
Then
p XOR q = (p OR q) AND NOT (p AND q)
(a) By definition of XOR, we have
p XOR p = (p OR p) AND NOT (p AND p)
= p AND NOT p
and this is tautologically FALSE.
(b) To rewrite XOR, first distribute the NOT over the AND using DeMorgan's law:
NOT (p AND q) = NOT p OR NOT q
Then we can interchange the AND and ORs using their respective distributive properties. That is,
p XOR q = (p OR q) AND (NOT p OR NOT q)
= (p AND (NOT p OR NOT q)) OR (q AND (NOT p OR NOT q))
= ((p AND NOT p) OR (p AND NOT q)) OR ((q AND NOT p) OR (q AND NOT q))
Both (p AND NOT p) and (q AND NOT q) are tautologically FALSE, so the truth value of either OR depends only on the other statements, so we have
p XOR q = (p AND NOT q) OR (q AND NOT p)
Recall the definition of IFF:
p IFF q = (p IMP q) AND (q IMP p)
Also recall that IMP is logically equivalent to
p IMP q = p OR NOT q
Then we have
p IFF q = (p OR NOT q) AND (q OR NOT p)
so that its negation is
NOT (p IFF q) = NOT ((p OR NOT q) AND (q OR NOT p))
= NOT (p OR NOT q) OR NOT (q OR NOT p)
= (NOT p AND q) OR (NOT q AND p)
The statements in bold match, so p XOR q is indeed equivalent to NOT (p IFF q).
Arrange the following numbers in descending order: 50,101 501,100 51,150 500,101
Answer:
Step-by-step explanation:
Hope it helps,view the image:
If an apple and 3 bananas cost $2.50, but 2 apples and 5 bananas cost $4.50, then how many dollars do 3 apples and 6 bananas cost?
Answer:
See below:
Step-by-step explanation:
So we know that an apple and 3 bannans are dollar 2.50
We also know that 2 apples and 5 bannanas are dollar 4.50.
Therefore, if we subtract 2 apples and 5 bannanas from 1 apple and 3 bannanas we will get a price.
Therefore, 1 apple and 2 bannanas are 2 dollars. (4.50 - 2.50 = 2)
Now, we can multiply by 3 to get it for 3 apples and 6 bannanas.
3*1 + 3*2 = 2*3
3a + 6b = 6 dollars.
The cost of 3 apples and 6 bananas is $7 and this can be determined by forming the linear equation in two variables.
Given :
An apple and 3 bananas cost $2.50.2 apples and 5 bananas cost $4.50.Let the cost of one apple be 'x' and the cost of one banana be 'y'. Then the cost of an apple and 3 bananas is given by the equation:
x + 3y = 2.5 --- (1)
The cost of 2 apples and 5 bananas is given by the equation:
2x + 5y = 4.5 ---- (2)
Now, solve the equation (1) for 'x'.
x = 2.5 - 3y --- (3)
Now, put the value of 'x' in equation (2).
2(2.5 - 3y) + 3y = 4.5
5 - 6y + 3y = 4.5
0.5 = 3y
[tex]y = \dfrac{1}{6}[/tex]
Now, put the value of 'y' in the equation (3).
[tex]\rm x = 2.5-3\times \dfrac{1}{6}[/tex]
x = 2
Now, the cost of 3 apples and 6 bananas will be:
[tex]3 \times 2 + 6 \times \dfrac{1}{6} = 7[/tex]
So, the cost of 3 apples and 6 bananas is $7.
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PLEASE HELP DUE NOW!!!
WILL MARK BRAINLIEST!!!!
Answer:
In point form, the answer is (1, -7) and in equation form, x = 1, y = -7.
Step-by-step explanation:
I hope this helps!
These triangles
are congruent by
the triangle
congruence
postulate [? ].
A. ASA
B. Neither, they are not congruent
C. AAS
Since in the two triangles,
2 angles and the side between them is given and equal, the triangles are congruent using the Criteria ASA.
Option A is the correct answer.
can anyone help with this equation?
Simplify the expression √((8x^5 y^2)/z^3 ).
[tex]\sqrt{\dfrac{8x^5 y^2}{z^3}}\\\\\\=\dfrac{\sqrt{8x^5 y^2}}{\sqrt{z^3}}\\\\\\=\dfrac{\left( y\sqrt{8}\right) \sqrt{x^5}}{\sqrt{z^2 \cdot z}}\\\\\\=\dfrac{\left(y\sqrt{4\cdot 2} \right) \sqrt{x^2 \cdot x^2 \cdot x}}{z\sqrt z}\\\\\\=\dfrac{\left(2\sqrt 2 \right) y x^2\sqrt{x}}{z\sqrt z}\\[/tex]
For f(x)= 1/x^2-3 substitute 3 for x in the function to solve for f(3)
Answer:
f(3) = 1/(3)^2-3
Step-by-step explanation:
To solve for when x=3, we simple replace x with 3
f(3) = 1/(3)^2-3
i'll mark brainliest thanks
Answer:
Transitive
Step-by-step explanation:
Match the function to the graph.
Answer:
[tex]a) \ sin(x - \frac{\pi }{2})[/tex]
Step-by-step explanation:
You can does a horizontal shift to the [tex]sin[/tex] function.
[tex]f(x - c)[/tex] shift the graph [tex]c[/tex] units to the right[tex]f(x + c)[/tex] shift the graph [tex]c[/tex] units to the leftBeside we know that when [tex]sin(0) = -1[/tex] then the only option that produce the desire result is the [tex]a[/tex] option because
Order from greatest to least. 5.249; 5.43; 5.340; 5.209
Answer:
5.43 > 5.340 > 5.249 > 5.209
Step-by-step explanation:
Answer:
5.43, 5.340, 5.249, 5.209,
Step-by-step explanation:
im in high school this is very easy for me. its right
The more numbers the more exact it is. Just because it has more numbers doesn’t mean it’s bigger. all decimals have infinite zeros after it. So if you have two twos after a decimal you have to go to the next number and see which one is less.
There is a line that includes the point(10, 5)and has a slope of 1 What
is its equation in slope-intercept form?So far I have y=1x+what's the y?
Answer:
y = x - 5
Step-by-step explanation:
Given the point, (10, 5), and the slope, m = 1:
Substitute these values into the slope-intercept form to solve for the y-intercept, b:
y = mx + b
5 = 1(10) + b
5 = 10 + b
Subtract 10 from both sides to isolate b:
5 - 10 = 10 - 10 + b
-5 = b
The y-intercept of the line is: b = -5. This represents the y-coordinate of the y-intercept, (0, -5), which represents the point on the graph where it crosses the y-axis. Along the y-axis, the value of x = 0. Hence, the y-intercept is (0, -5).
Therefore, given the slope, m = 1, and the y-intercept, b = -5:
The equation of the line in slope-intercept form is: y = x - 5.
An employee earns $480 per week. They are entitled to 4% vacation pay. How much vacation pay should they receive per week?
Answer:
480 * 0.04 = 19.2
$19.20
A bike take 56 minutes to travel 8 km? How many minutes will take to travel 15?
Answer:
1 hour 45 mins
Step-by-step explanation:
56÷8=7
7x15=105mins
105mins=1hr 45mins
HIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
Answer:
HIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
Farmer Bob is planting a garden this spring. He wants to plant squash, pumpkins, corn, beans, and potatoes. His plan for the field layout in feet is shown in the figure below. Use the figure and your knowledge of polynomials, perimeter, and area to solve the following:
For your initial response, answer the two questions below:
1. The farmer needs to spread hay under all the squash plants. Write an expression, using x, that represents the amount of the area of the field just for the squash.
2. The farmer needs a small fence for just around the potato patch. Write an expression, using x, that represents the perimeter of the part of the field just for potatoes. (simplify)
3. Challenge question! Write an expression, using x, that represents the perimeter of the entire garden, should the farmer want a bigger fence. (simplify)
Be sure to explain/show your work on how you determined your answers. Feel free to upload a picture of work or a video explanation to the discussion board.
Answer:
1.
The farmer needs to spread hay under all the squash plants. Write an expression, using x, that represents the amount of the area of the field just for the squash.
solution
area of rectangle is L x W,
let L =4x and and W = x
therefore Area (A) = 4x(x) = 4x2
2
The farmer needs a small fence for just around the potato patch. Write an expression, using x, that represents the perimeter of the part of the field just for potatoes. (simplify)
solution
parameter(P) = 2( L + W )
let L=x2 - 7x +12 and W = x +6
therefore
P = 2(x2 -7x +12 + x + 6)
= 2( x2 -6x + 18)
P = 2x2 -12x +36
3.
Challenge question! Write an expression, using x, that represents the perimeter of the entire garden, should the farmer want a bigger fence. (simplify)
solution
P= L1+L2+W1+W2
when
L1 = x + 6x +xy -1 = 7x +xy -1
L = 5x + 2 + x2 - 9 +x2 -7x + 12 = 2x2 5x + 2
w1 4x + 5x -2
w2 = xy + x 7
p = 7x +xy -1 + 2x2 5x + 2 + 4x + 5x -2 + xy + x 7
p = 2xy + 2x2 +16x +9
Step-by-step explanation:
Riddle me this: You're always right, what is your sine?
Answer: #1
What does that even mean??
Step-by-step explanation:
"You're always right" means that you're a right angle (90°) and [tex]\sin{90°} = 1.[/tex]
Answer of the riddle is 1.
What is right angle?
A right angle is an angle that is exactly equal to 90 degrees (or π/2) in measure.
What is the value of Sine 90 degree?The exact value of sine 90 degree.
What is sine of an angle?The sine (sin) of an acute angle in a right angled triangle is the ratio between the side opposite the angle and the hypotenuse of the triangle.
According to the given question
We have a riddle " You're always right, what is your sine?".
So, you're always right means you are always at 90 degrees.
What is your sine means, what is sin 90 degrees.
And we know that
[tex]sin90=1[/tex]
Hence, the answer of the riddle is 1.
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1 + 1 = 22
Explain why it equals 22.
What expressions areequalivent to 6 x 4 1/2
Answer: 32 + 1 and 5 x 2
x=4y-7
2x+9y=-31
What be the answer
Answer:
x=-11
y=-1
Step-by-step explanation:
x=4y-7
2x+9y=-31
2(4y-7)+9y=-31
8y-14+9y=-31
17=-31+14
17y=-17
y=-1
x=4(-1)-7
x=-11
Answer:
x = -11, y = -1
Step-by-step explanation:
solving simultaneously,
2(4y-7) + 9y = -31
17y = 14 - 31
17y = -17
y = -1
back sub, we get:
x = 4(-1)-7
x = -11
so x = -11, y = -1
I WILL MARK BRAINLIEST, PLEASE HURRY
Suppose radius CA is 12 meters long. What is the diameter of the circle?
Answer:
24 meters
Step-by-step explanation:
a radius is half the diameter of the circle. hence, the diameter is 24 meters.
Can someone please help me?
7x7x7x7
Answer:
2401
Step-by-step explanation:
use a calculator and this can also be written as 7^4
Answer:
2401
Figure out 7x7 then just multiply the answer by 2.
What will it cost to carpet a rectangular floor measuring 21 feet by 9 feet if the carpet costs $31. 29 per square yard?
Answer:
$657.09
Step-by-step explanation:
The area of the carpet is:
21 × 9 = 189 Square foot
189 foot² = 21 yard²
We know 1 yard² = $31.29
So 21 yard² = 21 × $31.29 = $657.09
72 boxes sold out of 90 boxes what percent sold
Answer:
80%
Step-by-step explanation:
Answer:
80%
Step-by-step explanation:
90 boxes = 100%
72 boxes = ?
=> (72 * 100)/ 90 = 80%
Find the Simple Linear Regression Formula of the data set shown below: (10pts)
Where the monthly e-commerce sales is Y and online advertising costs X.
Note: Round off your answers to two decimal places. No spaces in between characters.
Example format for the Final answer: y=36.11x+23.22
Uisng technology, such as a linear regression calculator or excel , the linear equation in slope - intercept format which models the data is 171.47x - 125.83
The relationship between advertising cost and e-commerce sales is positive which can be inferred from the positive value of the slope which models the data. Also, since, the correlation Coefficient is high, we can expect to have a high e-commerce sales whenever, the advertising cost is high.
Therefore, the linear regression equation is 171.47x - 125.83
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Jade and Juliette are riding their bikes across the country to promote autism awareness. They rode their bikes 45.4 miles on the first day and 56.3 miles on the second day. From now on, Jade and Juliette plan to ride their bikes 62 miles per day. If the entire trip is 2,878 miles, how many more days do they need to ride?
Can someone please find a way to solve this using a graph, table, or diagram? Plssss Urgent
Answer:
about 46
Step-by-step explanation
Cheryl is planning to spend $75 on a Christmas gift for her father. He needs new socks and ties. A store has socks s and ties t on sale for $4 and $11, respectively. Which equation models this situation?
Answer:
4s + 11t = 75
Step-by-step explanation:
Assuming you are asking for an equation to find how many socks and ties Cheryl could get with $75, then the equation 4s + 11t = 75 would represent that.
s is the number of socks that are bought (assuming s = 1 means that 1 pair of socks is bought).
t is the number of ties that are bought.
4s represents the total cost of the socks that are bought (if you plug in 4 for s, then the total cost of the socks is 4(4) = 16+
11t represents the total cost of the ties that are bought
Give the coordinates and quadrant of Point Z.
Number graph ranging from negative ten to ten on the x and y axes. Point C is drawn at (negative four, five), point D is drawn at (negative nine, nine), point E is drawn at (five, zero), point I is drawn at (zero, nine), point J is drawn at (negative nine, zero), point L is drawn at (nine, negative nine), point P is drawn at (zero, negative nine), point X is drawn at (zero, five) and point Z is drawn at (nine, ten).
(9, 10) Quadrant II
(10, 9) Quadrant I
(9, 10) Quadrant I
(10, 9) Quadrant II
The coordinates and quadrant of Point Z is (9, 10) Quadrant I.
Which four quadrants of graph?The X and Y axes divide the graph plane into four quadrants:
The first quarter is at the upper right corner of the plane. In this quadrant, the x and y coordinates are both positive. The second quadrant is situated in the top left corner of the plane. In this quadrant, the x-coordinate is negative while the y-coordinate is positive. The third quarter lies at the lower left-hand corner of the plane. In this quadrant, the x and y coordinates are both negative. The fourth quarter is at the lower right corner of the aircraft. In this quadrant, the x-coordinate is positive while the y-coordinate is negative.Given:
Coordinates:
C( -4, 5), D(-9, 9), E(5, 0), I(0, 9), J(-9, 0), L(9, -9), P(0, -9), X(0, 5) and
Z(9, 10).
As, we know The upper right corner of the plane is where the first quarter is located. The x and y coordinates in this quadrant are both positive.
Hence, Z lies in Quadrant !.
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Kate is competing in a 200 m race.
She runs at a constant speed of 4.8 m/s for the first 50 m, then 3.8 m/s for 20 seconds.
The remainder of the race takes her 22 seconds to complete.
What is Kate's average speed for the entire race to 1 dp?
Answer:
3.816 m/s
Step-by-step explanation:
Answer:
3.816 m/s
Step-by-step explanation:
In pic
(Hope this helps can I pls have brainlist (crown)☺️)
Evaluate. 10/1·(−4) Enter your answer in the box.
I’ll give brainliest if its correct on the test! (And if i can figure out how)
Step-by-step explanation:
10/1(-4)
10(-4)
=-2.5 or 5/-2
Question 10 of 10
Which of the following is the solution to the inequality below?
-2/6(4-x)<4(x+1/2
Answer:
x > -11/10
Step-by-step explanation:
-2/6(4-x) < 4(x+1/2)
-1/3(4-x) < 4x + 2
-4/3 + 1/3x < 4x + 2
-4 +x < 12x + 6
x - 12 x < 6 + 4
-11x < 10
x > -11/10
From first principles, find the indicated derivatives
By definition of the derivative,
[tex]\displaystyle\frac{dr}{ds} = \lim_{h\to0} \frac{\left(\frac{(s + h)^3}2 + 1\right) - \left(\frac{s^3}2 + 1\right)}{h}[/tex]
[tex]\displaystyle\frac{dr}{ds} = \lim_{h\to0} \frac{\left(\frac{s^3+3s^2h+3sh^2+h^3}2 + 1\right) - \left(\frac{s^3}2 + 1\right)}{h}[/tex]
[tex]\displaystyle\frac{dr}{ds} = \lim_{h\to0} \frac{\frac{3s^2h+3sh^2+h^3}2}{h}[/tex]
[tex]\displaystyle\frac{dr}{ds} = \lim_{h\to0} \frac12 \frac{3s^2h+3sh^2+h^3}{h}[/tex]
[tex]\displaystyle\frac{dr}{ds} = \lim_{h\to0} \frac12 (3s^2+3sh+h^2)[/tex]
[tex]\displaystyle\frac{dr}{ds} = \frac{3s^2}2[/tex]
