Answer:
A) ∀ real numbers x and y, if xy = 0 then x = 0 or y = 0.
B) ∀ real numbers x and y, if xy ≠ 0 then x ≠ 0 and y ≠ 0.
c) If neither of two real numbers is zero, then their product is nonzero
Step-by-step explanation:
A) Expression of zero product property using quantifiers and variables
∀ real numbers x and y, if xy = 0 then x = 0 or y = 0.
B) Contrapositive of the zero product property
∀ real numbers x and y, if xy ≠ 0 then x ≠ 0 and y ≠ 0.
C) The Informal version (without quantifier symbols or variables) for the contrapositive of the zero product property is : If neither of two real numbers is zero, then their product is nonzero
g(x) = 30x + 5
h(x) = 10x – 15
Find h(–3) + g(–5)
Answer:
The answer is: -190
Step-by-step explanation:
First, you need to input the -3 into the h(x) equation as follows:
h(-3) = 10(-3) - 15, then solve.
h(-3) = -30 - 15
h(-3) = -45.
Then you do the same for g(-5).
So, g(-5) = 30(-5) + 5
g(-5) = -150 + 5
g(-5) = -145.
Now you add the -45 and -145.
h(-3) + g(-5) = -45 - 145
h(-3) + g(-5) = -190.
According to Boyle's Law, if the temperature of a confined gas is held fixed, then the product of the pressure P and the volume V is a constant, suppose that, for a certain gas, PV=800 where P is measured in pounds per square inch and V is measured in cubic inches. Answer the following: (this is calculus)
A) Find the average rate of change of P as V increases from 200in^3 to 250in^3.
B) Express V as a function of P and show that the instantaneous rate of change of V with respect to P is inversely proportional to the square of P.
If PV = 800, then P can be written as a function of V,
P(V) = 800 / V
(a) The average rate of change of P as V increases from 200 to 250 in³ is then
(P (250) - P (200)) / (250 in³ - 200 in³) = (3.2 lb/in² - 4lb/in²) / (50 in³)
... = -0.016 (lb/in²)/in³
(Or -0.016 lb/in⁵, but I figure writing the rate as (units of pressure) per (unit volume) makes more sense.)
(b) We can also write V as a function of P :
V(P) = 800 / P
Take the derivative:
V'(P) = - 800 / P²
which immediately demonstrates that V'(P) ∝ 1 / P², as required. (The fish-looking symbol, ∝, means "is proportional to".)
If differentiating is supposed to be more involved, you can use the limit definition:
[tex]V'(P)=\displaystyle\lim_{h\to0}\frac{V(P+h)-V(P)}h[/tex]
[tex]V'(P)=\displaystyle\lim_{h\to0}\frac{\frac{800}{P+h}-\frac{800}P}h[/tex]
[tex]V'(P)=\displaystyle\lim_{h\to0}\frac{\frac{800P-800(P+h)}{P(P+h)}}h[/tex]
[tex]V'(P)=\displaystyle800\lim_{h\to0}\frac{-\frac h{P(P+h)}}h[/tex]
[tex]V'(P)=\displaystyle-800\lim_{h\to0}\frac1{P(P+h)}=-\dfrac{800}{P^2}[/tex]
Part(a): The average rate of change of [tex]\frac{dP}{dV}[/tex] is [tex]-0.0164 lb/in^{2}[/tex]
Part(b): The required answer is [tex]\frac{dV}{dP} \infty \frac{1}{P^{2}}[/tex]
Part(a):
Given,
[tex]PV=800[/tex]
Differentiating the above equation with respect to [tex]V[/tex].
[tex]\frac{dP}{dV}=-\frac{P}{V}[/tex]
Now, at [tex]V=200 in^{3}[/tex] and [tex]P=4 lb/in^2[/tex]
At [tex]V=250 in^3[/tex] and [tex]P=\frac{80}{25} lb/in^2[/tex]
Hence, we can write,
[tex]\frac{dP}{dV}[/tex] at [tex]V=200[/tex] we get,
[tex]\frac{-1}{200}=\frac{-1}{50}[/tex]
Again [tex]\frac{dP}{dV}[/tex] at [tex]V=250[/tex] we get,
[tex]\frac{-80}{25\times 250}[/tex]
So, the average rate of change of [tex]\frac{dP}{dV}[/tex] is,
[tex]\frac{-\frac{1}{50}- \frac{8}{25\times25} }2\\=-\frac{1}{100}-\frac{1}{625}\\=-0.0164 lb/in^2[/tex]
Part(b):
Given,[tex]PV=800[/tex] then,
[tex]V=\frac{800}{P}[/tex]
Now,[tex]\frac{dV}{dP} =-\frac{800}{P^2}[/tex]
Then the above implies,
[tex]\frac{dV}{dP} \infty \frac{1}{P^{2}}[/tex]
Learn more:https://brainly.com/question/12817429
Solve for x:3(x+1)=-6
Answer:
x=-3
Step-by-step explanation:
Answer:
-3
Step-by-step explanation:
3(x +1) =-6
3x +3 =-6
3x =-6 - 3
3x=-9
x=-9:3
x=-3
Joe has $800 to spend on a new dining room table and chairs. If the sales tax is 8%, how much can he afford to spend on the table and chairs?
Answer:
no
Step-by-step explanation:
800x8%=64
64+800=864
Answer:
$736
Step-by-step explanation:
800 x (100% - 8%)
800 x 92%
=736
For the following exercises, rewrite the quadratic functions in standard form and give the vertex. Standard form is y=a(x-h)²+k
6.) f(x) = x² – 12x + 32
8. f(x) = x² - x
10. h(x) = 2x² + 8x - 10
g Explain why x is a discrete random variable. A. The event x is a discrete random variable because the values of the random variable are countable and each possible outcome is equally likely. B. The event x is a discrete random variable because the values of the random variable are contained in one or more intervals and each possible outcome is not equally likely. C. The event x is a discrete random variable because the values of the random variable are countable. D. The event x is a discrete
Answer:
Correct option: C
Step-by-step explanation:
A random variable, denote by X, is a variable whose probable values are numeric and are of a random occurrence. There are two types of random variables, discrete and continuous.
A discrete random variable is the one which takes on only a finite number of distinct values such as 0, 1, 2, 3, 4... For example, the number of female members in a family, the daily attendance at a yoga class, the number of defective light bulbs in a box of five bulbs.
The probability distribution of a discrete random variable consist of a list of probabilities related with the respective possible values. It is also known as the probability mass function.
The correct statement describing X is:
C. The event x is a discrete random variable because the values of the random variable are countable.
3x - 15 = 7 - 8x how do you solve this
Answer:
X=2
Step-by-step explanation:
3x-15=7-8x
3x+8x=7+15
11x=22
x=[tex]\frac{22}{11}[/tex]
x=2
Answer:
324
Step-by-step explanation:
3x3 = 9
9-15 = -6
8x8=64
7-64=-54
-54 x -6 = 324
Adding/Subtracting Rational Expressions
9514 1404 393
Answer:
(4x^2 +21x +18)/(3x^2 +34x -24)
Step-by-step explanation:
I find it helpful to keep in mind the form ...
a/b + c/d = (ad +bc)/(bd)
When we apply that to this case, we get ...
[tex]\dfrac{x+3}{x+12}+\dfrac{x+2}{3x-2}=\dfrac{(x+3)(3x-2)+(x+12)(x+2)}{(x+12)(3x-2)}\\\\=\dfrac{(3x^2+7x-6)+(x^2+14x+24)}{(x+12)(3x-2)}=\boxed{\dfrac{4x^2+21x+18}{3x^2+34x-24}}[/tex]
Can someone help
Please
Answer:
Step-by-step explanation:
.
You have 8 quarts of brown stock. You need 3 cups to make one serving of braised short ribs. How many servings can you make? (don't include partial portions)
Answer:
You can make 2 servings.
Step-by-step explanation:
Hi there!
3 cups makes one serving, so 2 servings require 6 cups. Since you don't have 9 cups to make 3 servings, and you don't want partial portions, you can only make 2 servings with 6 cups and have 2 cups left over.
Have a great day!
(I'd also appreicate it if I got a rating and maybe a Thanks please!)
A gardener has 27 pansies and 36 daisies. He planted an equal number of each type of flower in each row. What is the greatest possible number of pansies in each row? I need the answer quick
Answer:
There will be 3 rows of pansies
Step-by-step explanation:
Let p = log10 x, q = log10 y, and r = log10 z. (The 10s are base numbers.)
Write the expression log10 (x / y^2 √z) in terms of p, q, and r.
Please show work! I have the answer ( p- (2q + 1/2 r) ), but I need to show my work.
Answer:
(p / q^2 √r)
Just make x, y, z into p, q, r.
Very simple!
factorise x squared - 42 squared
Answer:
42 squared is 1764
Step-by-step explanation:
Answer: (x + 42)(x - 42)
Step-by-step explanation:
factorise: x^2 - 42^2
. x^2 - 42^2 have ^2 in common (so you can ignore that).
. put in brackets (x - 42)(x + 42)
. +/- any order really doesn't matter :D
Find the difference: 34.14 - 67.42
Answer:
the answer is -33.28
Step-by-step explanation:
Click on the correct answer.
\(\frac{2}{5}\div2\frac{1}{4}\)
a:\(\frac{8}{45}\)
b:\(\frac{9}{10}\)
c:\(1\frac{1}{9}\)
d:\(5\frac{5}{8}\)
Answer:
A
Step-by-step explanation:
i am smart
Rewrite the statement as an equation. $10
for each x plus $5 for each y equals $1500
Answer:
10x+5y=1500
Step-by-step explanation:
I don't know how to explain this but i think this is right.
Can someone help me
Answer:
Su=10
Explaination:
So from s to u on the nunebr line is worth 2x-12. So what is s to u worth? Well. S to t on the number line = x-7. T to u =6. And 2 x is worth 12 more than s to u, using th e expression. X has to be at least 8 because otherwise the x-7 wouldn't work, and u might get s to u = 0 or a negative number.
Say x was 13, then 13 - 7 =6. So S to t =6. And r to u =6. So s to u =12. (6+6). Then check if the expression fits this answer of 12. 2x - 12. 2x = 26. 26-12=14, which doesn't match.
Let's try 14. 14-7=7. Then s to u = 7+6=13. The expression: 2x= 28. 28-12=16. 13 and 16 dont match. So we have got further away from what we need. Why don't we try going in the opposite direction. Rather than testing 13 and +1, let's now - 1 and try 12.
If x=12, then s to t =12-7=5. And s to u =6+5=11. The expression: 2x=24.-12=12. We are very close now with 11 and 12.
Lets test x=11!
S to t = 11-7=4. 4+6=10. So s to u =10.
2x=22. 22-12=10. So the expression works and the number line measurements.
The answer is su=10 and x=11.
Find the 84th term of the arithmetic sequence -5,15,35, ...
The 84th term of the sequence is 1655
How to determine the 84th term?The arithmetic sequence is given as:
-5, 15, 35, .....
The above sequence has the following parameters:
Initial value, a = -5Common difference, d = 20The nth term of the sequence is:
Tn = a + (n - 1) * d
So, we have:
T84 = -5 + (84 - 1) * 20
Evaluate
T84 = 1655
Hence, the 84th term of the sequence is 1655
Read more about sequence at:
https://brainly.com/question/7882626
Rick invest $5,830 into a retirement saving account. The account compounds at 3.2% monthly for. How much money will Rick have in 4 years? Show work. Use comma and dollar signs in the final answer.
Answer:
$746.24
Step-by-step explanation:
3.2/100 = 0.032
5,830 X 4 = 23,320
23,320 X 0.032 = 746.24
I WILL GIVE EXTRA POINTS!!! HELPPPPP PLEASE!!!! SHOW ALL WORK!!!
Answer: 2x+52=2(x+26)
3x-35=-105
Step-by-step explanation:
Referring to the methods for calculating average atomic mass, which one is 'incorrect' ?
Mary
Jack
Alan
Alan's method is correct coz to find we add all the given value and divide by the numbers present
The length of rectangle is 5 cm greater than its width. The perimeter is 106cm. Find the dimensions of the rectangle.
Width-24 Length-29
Two sides of the rectangle are 5 cm bigger than the other two. So you would add the two 5 cm together (10cm). If you take the 10 cm off you (106-10) you will get a square. Then all you have to do is divide 96 by 4 (24), and add back on the two 5cm from the beginning to the length (29).
Evaluate -9x-2 when x=-4
Answer:
34
Step-by-step explanation:
76 divided by 12 in a lixed fraction
6 or. 1/3
hopethishelp
Answer:
6 1/3
Step-by-step explanation:
72/12 = 6.3333 = 6
76 - (12 x 6) = 4
6 4/12
6 1/3
Find the slope of a line graphed below
Answer:
Slope is 2/5x
Step-by-step explanation:
Which number set correctly represents the range of the given data?
{(0, 0), (2, 0), (3, 0), (5, 0)}
{0, 2, 3,5)
{0, 2, 3)
{0,2)
(0)
Answer:
I would assume {0, 2, 3, 5}
Step-by-step explanation:
I would assume that answer because all three are given in the range of the given data set.
Answer:
The answer is [0] (D)
Step-by-step explanation:
Given the fact that the Range is Y value, we see 0,0,0,0
So its 0
Norman answered the following question below lilith brought 20 cans to the food drive marcus brought 7 cans to the food drive if Paulina brought 8 more cans than lilith and marcus Combined, how many cans did Paulina bring. explain you answer
Answer:
100 is a cool number
Step-by-step explanation:
i also ate a rock
at the zoo there are 3 times
Answer:
at the zoo there are 3 times what?
Step-by-step explanation:
2. Which of the following uses the Distributive Property?
A. 0.4 x (2a-0.3b) = 0.4 + (2a-0.3b)
B. 0.4 x (2a-0.3b) = 0.8a - 0.12b
C. 0.4 x (2a -0.3b) = 0.8ax 0.12b
Answer:
B
Step-by-step explanation:
It is B because 0.4 times 2 would be 0.8 and 0.3 times 0.4 would be 0.12b.
A farmer wanted to distribute 36 mangoes in paper bags, how many ways he can contribute the mangoes equally in paper bags?? Solve this using Factoring, Finding multiples and Divisibility Rules.
Answer:
36 = 2 x 2 x 3 x 3
Step-by-step explanation:
Given:
Number of mangoes = 36
Computation:
Factor of 36
36 = 2 x 2 x 3 x 3
Number of packing = 2 and number of mangoes in each = 18
Number of packing = 4 and number of mangoes in each = 9
Number of packing = 12 and number of mangoes in each = 3
Number of packing = 6 and number of mangoes in each = 6
Number of packing = 36 and number of mangoes in each = 1