Answer:
A) З x,y : ( x/y < 1, y/x < 1 )
B) ∀ Y : ( Y > 0 = 1/Y > 0 )
C) з x,y : ( x+y = xy )
D) ∀ x,y : [ ( x>0 ) ∧( y > 0 ) = (( x/y > 0 ) ∧ ( y/x > 0 ))
E ) ∀ y : [ ( y > 0 ) ∧ ( y < 1) = ( 1 / y > 1 )
F) n ( ( з x ∀ y ( x <y ) )
G) ∀x (( x ≠ 0 ) = ( зy ( xy = 1 ) ))
H) ∀x ( (x≠0) = ( з! y (xy = 1))
Step-by-step explanation:
since the domain of discourse is a set of all real numbers the logical expressions of the English statements are expressed with respect to real number:
A) З x,y : ( x/y < 1, y/x < 1 )
B) ∀ Y : ( Y > 0 = 1/Y > 0 )
C) з x,y : ( x+y = xy )
D) ∀ x,y : [ ( x>0 ) ∧( y > 0 ) = (( x/y > 0 ) ∧ ( y/x > 0 ))
E ) ∀ y : [ ( y > 0 ) ∧ ( y < 1) = ( 1 / y > 1 )
F) n ( ( з x ∀ y ( x <y ) )
G) ∀x (( x ≠ 0 ) = ( зy ( xy = 1 ) ))
H) ∀x ( (x≠0) = ( з! y (xy = 1))
In translating English written expressions to logical expressions, we have to know the domain of the discourse. The domain of discourse can be said to be a set of all real numbers that the logical expressions of the English statements are expressed with respect to their real numbers. And as such, we arrive at each of this.
A) З x,y : ( x/y < 1, y/x < 1 )
B) ∀ Y : ( Y > 0 = 1/Y > 0 )
C) з x,y : ( x+y = xy )
D) ∀ x,y : [ ( x>0 ) ∧( y > 0 ) = (( x/y > 0 ) ∧ ( y/x > 0 ))
E ) ∀ y : [ ( y > 0 ) ∧ ( y < 1) = ( 1 / y > 1 )
F) n ( ( з x ∀ y ( x <y ) )
G) ∀x (( x ≠ 0 ) = ( зy ( xy = 1 ) ))
H) ∀x ( (x≠0) = ( з! y (xy = 1))
read more about logic here https://brainly.com/question/7581378
What is twice a number divided by 5
Answer:
4
just go with it the explaining would take to long
Step-by-step explanation:
Rachel, Hong, and Manuel have a total of 95 in their wallets. Hong has 3 times what Manuel has. Rachel has $10 more than Manuel. How much does each have?
Answer:
Rachel has 27
Hong has 51
Manuel has 17
Step-by-step explanation:
Let R represent Rachel, H represent Hong, and M represent Manuel.
They combined have a total of 95. Thus:
[tex]R+H+M=95[/tex]
Hong has 3 times what Manuel has. Therefore:
[tex]H=3M[/tex]
Rachel has 10 more than Manuel. Therefore:
[tex]R=10+M[/tex]
Substitute:
[tex]R+H+M=95\\(10+M)+(3M)+M=95[/tex]
Combine like terms:
[tex]5M+10=95[/tex]
Subtract 10 from both sides:
[tex]5M=85[/tex]
Divide by 5:
[tex]M=17[/tex]
Therefore, Manuel has 17.
Now, find Rachel and Hong's money.
[tex]H=3M\\H=3(17)=51[/tex]
So, Hong has 51.
And for Rachel:
[tex]R=10+M\\R=10+17=27[/tex]
Rachel has 27.
POSSIBLE POINTS: 10
The midpoint of QR is M(2, 1.5). One endpoint is R(1, -1). Find the coordinates of endpoint Q. {Write as an ordered pair (X, Y).} Q
Answer:
Q (3.4)
Step-by-step explanation:
Midpoint for point (x1,y1) and (x2,y2) is given by
(x1+x2)/2, (y1+y2)/2.
__________________________________________________________
Given
one endpoint ( R(1, -1)
midpoint is M(2,1.5)
we have to find coordinates of endpoint Q
let Q(x,y)
Thus, for x coordinate of midpoint
2 = (1+x)/2
=> 2*2 = 1+x
=> 4 = 1+x
=> x = 4-1 = 3
x coordinate of midpoint m is 3
________________________
for y coordinate of midpoint
1.5 = (-1+y)/2
=> 2*1.5 = -1+y
=> 3 = -1+ y
=> y = 3 + 1 = 4
y coordinate of midpoint m is 4
Thus, the coordinates of endpoint Q (3.4)
You take thirty measurements in order to find the length of a rod, you calculate the average and obtain the value L0. Supposed that now a different person takes twenty measurements as well of the same rod, then calculates the average and obtains the same L0 as you. Does it mean that both of you obtain a result with the same precision and accuracy
Answer:
Yes, it means that both of you obtain a result with the same precision and accuracy.
Step-by-step explanation:
It is provided that two different people took measurements in order to find the length of a rod.
The first person took 30 measurements.
The second person took 20 measurements.
Both the people got the same average length, i.e. L₀.
In statistics, a larger sample leads to an error free result.
So, for the first person the larger sample helped reducing the chance of any sort of error that may be present.
For the second person, the average is same as the first even when their sample size is less than the first.
This may happen because the sample was selected with a certain precision and accuracy.
Thus, both of them obtain a result with the same precision and accuracy.
A Women making $29 an hour gets a 15% raise. How much money will she make after 4 hours of working with the increased hourly pay?
Answer:
$133.4
Step-by-step explanation:
1. Find the increased pay:
29 * 1.15 = 33.35
2. Find how much she makes in 4 hrs
33.35 * 4 = 133.4
y varies directly with x. If x = 16 and y = 2 find y when x = 96
Answer:
y = 12
Step-by-step explanation:
Use the equation y = kx
Plug in x and y to find k:
2 = k(16)
1/8 = k
Then, plug in 1/8 as k and 96 as x to find y:
y = 1/8(96)
y = 12
Simplify: power with a power 5^8*7^8
Answer:
35^8
Step-by-step explanation:
5^8 x 7^8
(5 x 7)^8
=35^8
ax + by = c, bx + ay = (1 + c)
Answer:
( x - y ) ( a - b ) = -1
Step-by-step explanation:
ax + by = c and bx + ay = 1 + c
ax + by = c and bx + ay - 1 = c
And now we set c equivalent
ax + by = bx + ay - 1
ax - bx + by - ay = -1
x (a - b) + -y (a - b) = -1
(x - y) ( a - b) = -1
So we can leave it like that, or we can solve for one of the variables.
If we solve for y:
(x - y) ( a - b) = -1
(x - y) = -1 / (a - b)
-y = (-1 / (a - b)) - x
y = (1 / (a-b)) + x
Cheers.
if y varies directly as x, and y is 6 when x is 72, what is the value of y when x is 8
Answer:
Y varies directly as X.
y=kx.
6=K72.
x=6/72.
x=0.08.
Y=0.08x.
when y=?, x=8.
y=0.08×8=0.64.
The quality control manager of a light bulb factory needs to estimate the average life of a large shipment of light bulbs. The process standard deviation is known to be 100 hours. A random sample of 64 light bulbs indicated a sample average life of 350 hours. Given the confidence interval calculated above. do you think the manufacturer has the right to state that the light bulbs last on average 400 hours?
a. No.
b. Yes.
c. Maybe.
d. Do not know
Answer:
b) yes
The manufacturer has the right to state that the light bulbs last on average 400 hours
Step-by-step explanation:
Explanation:-
Given sample size 'n' = 64
Given standard deviation of the Population (σ)=100
Mean of the sample (x⁻) = 350 hours
95% of confidence interval is determined by
[tex](x^{-} -Z_{0.95} \frac{S.D}{\sqrt{n} } , x^{-} +Z_{0.95} \frac{S.D}{\sqrt{n} } )[/tex]
([tex](350 -1.96 \frac{100}{\sqrt{64} } , 350+1.96\frac{100}{\sqrt{64} } )[/tex]
(350-24.5 , 350+24.5)
(325.5 , 374.5)
Conclusion:-
Yes
The manufacturer has the right to state that the light bulbs last on average 400 hours
The GCF of 30 and 45 is
3
8
1
2
15
Answer:
The GCF of 30 and 45 is
15.
Hope it helps.
Find the area in blue.
Answer: The area is 13[tex]\pi[/tex]ft^2 or 40.84 ft^2
Step-by-step explanation:
First find the area of the square and subtract it from the area of the circle.
The area of a square is one of the side length squared.
A= 6^2
A = 36
Now find the area of the whole circle.As it indicates that the diameter is 14ft and to find the area of a circle,we need square the radius and multiply it by pi.
Since the diameter is 14 divide it by 2 to find the radius. 14/2 = 7
A= 7^2*[tex]\pi[/tex]
A = 49[tex]\pi[/tex] We will leave the area in terms of pi.
49[tex]\pi[/tex] - 36 = 13[tex]\pi[/tex]
A set of three scores consists of the values 3, 7, and 2.
Σ2X – 2 =
Σ(X – 1)² =
Answer:
Step-by-step explanation:
Given the set of datas 3, 7 and 2, we are to evaluate the folowing;
Σ2X – 2 and Σ(X – 1)² =where X are the individual datas.
We will substitute each of the data as value of X and ten take the sum as shown;
For Σ2X – 2
Σ2X – 2 = [2(3)-2]+[2(7)-2]+[2(2)-2]
Σ2X – 2 = (6-2)+(14-2)+(4-2)
Σ2X – 2 = 4+12+2
Σ2X – 2 = 18
For Σ(X – 1)² where x values are also 3, 7 and 2 we will have;
Σ(X – 1)² = (3 – 1)²+(7 – 1)²+(2 – 1)²
Σ(X – 1)² = 2²+6²+1²
Σ(X – 1)² = 4+36+1
Σ(X – 1)² = 41
32 POINTS! WILL MAKE BRAINLIEST. ANSWER ASAP
trough: (2,2) parallel to y=x+4
Answer:
y = x
Step-by-step explanation:
The slopes of parallel lines are the same, so we know the equation will be ...
y = x + constant
We can find the constant by using the given point's values for x and y:
2 = 2 + constant
Obviously, the constant is zero.
The equation of the parallel line through (2, 2) is y = x.
Solve the inequality
The solution is....
Answer:
x ≤ -7
Step-by-step explanation:
Eliminate parentheses using the distributive property.
-8 -2x ≥ 40 +6x +8
-8 ≥ 48 +8x . . . . . . . . . add 2x
-56 ≥ 8x . . . . . . . . . . . subtract 48
-7 ≥ x . . . . . . . . . . . . . . divide by 8
The solution is x ≤ -7.
For what positive values of k does the function y=sin(kt) satisfy the differential equation y''+144y=0 ?
Answer:
The positive value of k that the function y = sin(kt) satisfies the differential equation y'' + 144y = 0 is +12
Step-by-step explanation:
To determine the positive values of k that the function y = sin(kt) satisfy the differential equation y''+144y=0.
First, we will determine y''.
From y = sin(kt)
y' = [tex]\frac{d}{dt}(y)[/tex]
y' = [tex]\frac{d}{dt}(sin(kt))\\[/tex]
y' = kcos(kt)
Now for y''
y'' = [tex]\frac{d}{dt}(y')[/tex]
y'' = [tex]\frac{d}{dt}(kcos(kt))[/tex]
y'' = [tex]-k^{2}sin(kt)[/tex]
Hence, the equation y'' + 144y = becomes
[tex]-k^{2}sin(kt)[/tex] + [tex]144(sin(kt))[/tex] [tex]= 0[/tex]
[tex](144 - k^{2})(sin(kt)) = 0[/tex]
[tex](144 - k^{2})= 0[/tex]
∴ [tex]k^{2} = 144\\[/tex]
[tex]k =[/tex] ±[tex]\sqrt{144}\\[/tex]
[tex]k =[/tex] ± [tex]12[/tex]
∴ [tex]k = +12[/tex] or [tex]-12[/tex]
Hence, the positive value of k that the function y = sin(kt) satisfies the differential equation y'' + 144y = 0 is +12
The positive value of k that satisfies the differential equation is k = 12.
To find the value of k that satisfies the equation, we differentiate the function y = sin(kt) twice to obtain y" and we insert it into the differential equation y" + 144y = 0.
So, y' = dy/dt
= dsin(kt)/dt
= kcos(kt)
y" = dy'/dt
y" = dkcos(kt)/dt
y" = -k²sin(kt)
So, substituting y and y" into the differential equation, we have
y" + 144y = 0
-k²sin(kt) + 144sin(kt) = 0
-k²sin(kt) = -144sin(kt)
k² = 144
k = ±√144
k = ±12
Since we require a positive value, k = 12
So, the positive value of k that satisfies the differential equation is k = 12.
Learn more about differential equations here:
https://brainly.com/question/18760518
In a local election, 16,000 people voted. This was an increase of 4% over the last election.
How many people voted in the last election? If necessary, round to the nearest whole
number
Answer:
Hey!
Your answer is 15,360!
Step-by-step explanation:
4% of 16,000 is 640
SO...
To find out the last year's amount of voters we have to minus 640 from 16,000...
16,000 - 640 = 15,360
HOPE THIS HELPED!!
Please help me it’s in my math class
Answer:
1-70: Purple- 9/10= 0.18= 2 marbles
Orange- 16/50= 0.32= 3 marbles
Yellow- 6/50= 0.12= 1 marble
Green- 19/50= 0.38= 4 marbles
1-71: Part A. 3/6= 1/2
Part B. 4/6= 2/3
What is the equation when y=5x+4 is reflected over the x-axis, y-axis & y=x?
Answer:
A) [tex]y=-5x-4[/tex]
B) [tex]y=-5x+4[/tex]
C) [tex]y=\frac{x-4}{5}[/tex]
Step-by-step explanation:
So we have the equation:
[tex]y=5x+4[/tex]
Let's write this in function notation. Thus:
[tex]y=f(x)=5x+4[/tex]
A)
To flip a function over the x-axis, multiply the function by -1. Thus:
[tex]f(x)=5x+4\\-(f(x))=-(5x+4)[/tex]
Simplify:
[tex]-f(x)=-5x-4[/tex]
B) To flip a function over the y-axis, change the variable x to -x. Thus:
[tex]f(x)=5x+4\\f(-x)=5(-x)+4[/tex]
Simplify:
[tex]f(-x)=-5x+4[/tex]
C) A reflection over the line y=x is synonymous with finding the inverse of the function.
To find the inverse, switch x and f(x) and solve for f(x):
[tex]f(x)=5x+4[/tex]
Switch:
[tex]x=5f^{-1}(x)+4[/tex]
Subtract 4 from both sides:
[tex]x-4=5f^{-1}(x)[/tex]
Divide both sides by 5:
[tex]f^{-1}(x)=\frac{x-4}{5}[/tex]
And we're done :)
Assume that the two polygons are similiar, with the same orientation.
Write a proportion to determine the lengths of the sides labeled by variables.
(DO NOT SOLVE. You will solve the proportion in the next question.)
Answer:
4/6=t/(t+1)
Step-by-step explanation:
4/6=t/(t+1)
A line has a slope of 3 and passes through the point (2,31). Write the equation of the line in slope-intercept form
Answer:
y=3x+25
Step-by-step explanation:
So to find the slope-intercept we need to find the slope and the y intercept. we already know the slope so to find the y intercept you subtract 2 from the x coordinate and 6 from the y, because the slope is 3. So the answer is y=3x+23
Answer:
y=3x+25
Step-by-step explanation:
We are given a point and the slope, so let's use the slope-intercept equation.
[tex]y-y_{1}=m(x-x_{1})[/tex]
where m is the slope and (x₁, y₁) is the point given. The slope is 3 and the point is (2,31). Therefore,
[tex]m= 3 \\x_{1}=2\\y_{1}=31[/tex]
Substitute the values into the equation.
[tex]y-31=3(x-2)[/tex]
We want the equation in slope intercept form: y=mx+b. We must isolate y on the left side of the equation.
First, distribute the 3. Multiply each term inside the parentheses by 3.
[tex]y-31= (3*x)+(3*-2)[/tex]
[tex]y-31=(3x)+(-6)[/tex]
[tex]y-31=3x-6[/tex]
Next, add 31 to both sides of the equation.
[tex]y-31+31=3x-6+31[/tex]
[tex]y=3x-6+31[/tex]
[tex]y=3x+25[/tex]
This equation is in slope intercept form, so our final answer is:
y= 3x+25 (slope⇒3 , y-intercept ⇒25)
Given m parallel to I, and m2 7 = 94, find the measure of angle 5
O 10
045
O 97
O 120
Answer:
97
Step-by-step explanation:
What would be the first step you do to solve the equation below? 2x - 4 = 12 Question 1 options: Add 4 Subtract 4 Divide by 2 Multiply by 2
Answer:
ADD 4
Step-by-step explanation:
you want to get 2x by itself so you want to do opposite of -4 so you would do +4 and they cancel out, and what you do to one side you do to the other so
2x = 12 +4
2x = 16
and then you would divide the 2 on both sides so
x = 8 ... just in case you later need to know what x is :)
Is 1/4 greater than 4/5, 2/4, 1/10, 2/10, 1/5?
Answer:
1/4 is greater than 1/10, 2/10, and 1/5 but not 4/5, and 2/4
Step-by-step explanation:
1/4 = 25%
4/5 = 80%
2/4 = 50%
1/10 = 10%
2/10 = 20%
1/5 = 20%
explain how you can rename 5,400 as hundreds.
Answer:
The correct answer would be 54 hundreds
Step-by-step explanation:
If we are considering how many hundreds something has, we can simply take away two 0's and use that number. We take the two 0's off and then we have the right number of hundreds
Answer:
Hey there!
Five-thousand four-hundred can be expressed as fifty-four hundred.
Let me know if this helps :)
g What is the probability that a randomly selected person with adequate lung capacity is a non-exerciser?
Answer:
Step-by-step explanation:
What is the probability that a randomly selected person with adequate lung capacity is a non-exerciser?
This depends on statistics given in the prior part of the question.
From this question, i can pick that there is an assumption or statement (in the full question) that exercisers have adequate lung capacity, in a population of both exercisers and non-exercisers.
Data that will help solve this include:
- Population Count or Total number of subjects in the population
- Number of exercisers
- Number of non-exercisers
- Number of subjects with adequate lung capacity
- Number of subjects with inadequate lung capacity
The formula to get the desired answer would be:
Number of non-exercisers
Number of persons with adequate lung capacity
The figure you get from this computation is the answer you seek!
Since it is a probability figure, it must lie between the values of 0 and 1.
A card is selected at random from a standard 52-card deck. (a) What is the probability that it is an ace
Answer:
4/52 = 1/13
Step-by-step explanation:
Which set of data do you believe to be better? Your data or your friend's data?
Answer:
Your friends data
Step-by-step explanation:
The rule of statistics is: the more exact the data, the better.
It looks like you just rounded your data to the nearest tenth. This is good, but not nearly as good as rounding it to the nearest hundredth.
This is because when you have data that is more exact, you get a better estimation for mean, median, etc. This can help make patterns in your data.
This means that your friend had better data than you.
Hope this helped!
what substitution should be used to rewrite 4x^12-5x^6-14=0 as a quadratic equation?
Answer:
Step-by-step explanation:
4x12-5x6-14=0, the highest power of the variable in this equation is 12 so to make it a quadratic equation we should replace x12 by y2. Hence to rewrite the given equation as quadratic just substitute x6=y.