Answers
The truth set for each predicate are:
a) d ∈ { -6, -3, -2, -1, 1, 2, 3, 6}
b) d ∈ { 1, 2, 3, 6}
c) x ∈ { [-2, -1] U [1, 2]}
d) x ∈ {-2, -1, 1, 2}
How to find the truth set of each predicate?
We only need to find the sets of values such that the statements are true.
a)
We want to find vales of d, such that d is an integer, and 6/d is an integer.
Here the possible values of d will be:
d ∈ { -6, -3, -2, -1, 1, 2, 3, 6}
Which are all the factors of 6, so all these integers divide 6.
b) Same as before, but this time the domain is a positive integer, so now the truth set will be:
d ∈ { 1, 2, 3, 6}
c) We want to find real values of x such that:
1 ≤ x² ≤ 4
If we apply the square root to the 3 sides, we get two inequalities:
-√1 ≥ x ≥ -√4
√1 ≤ x ≤ √4
Simplifying:
-1 ≥ x ≥ -2
1 ≤ x ≤ 2
So the truth set is:
x ∈ { [-2, -1] U [1, 2]}
c) Same as before, but now we only have integer solutions, so the truth set is:
x ∈ {-2, -1, 1, 2}
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Related Questions
A recipe says to use 3 cups of flour to make 48 cookies. What is the constant of proportionality that relates the number of cookies made, y , to the number of cups of flour used, x ?
Answers
Answer: 3cups
Step-by-step explanation:
List all of the solutions.
3cups = 48 = y = cups = x =
Answer:
3cups
Step-by-step explanation:
What should be the third row in the following series of shapes
Answers
Answer:
The answer is number 2
Factor as the product of two binomials 81 + 18x + x*2
Answers
Answer:
(x+9)(x+9)
Step-by-step explanation:
Factor 81+18x+x^2
x^2+18x+81
=(x+9)(x+9)
what are the features of the function g if g(x)= f(x+4) +8
Answers
The domain, range, x-intercept, or y-intercept of g(x) = f(x + 4) + 8. The features of g depend on the corresponding features of f.
Given the function g(x) = f(x + 4) + 8, let's examine its features:
Domain:
The domain of the function g will be the same as the domain of the function f, which depends on the restrictions or constraints of f. However, it is important to note that shifting the input by 4 units (x + 4) does not inherently change the domain unless there are specific restrictions imposed by f.
Range:
Similar to the domain, the range of the function g will depend on the range of the function f.
x-intercept:
The x-intercept of a function is the point where the graph intersects the x-axis, meaning the y-coordinate is zero (y = 0). To find the x-intercept of g(x), we set g(x) = 0 and solve for x.
0 = f(x + 4) + 8
By subtracting 8 from both sides:
-8 = f(x + 4)
Since the exact value of x that makes f(x + 4) equal to -8. The x-intercept will depend on the behavior of f.
y-intercept:
The y-intercept of a function is the point where the graph intersects the y-axis, meaning the x-coordinate is zero (x = 0). To find the y-intercept of g(x), we substitute x = 0 into the function:
g(0) = f(0 + 4) + 8
g(0) = f(4) + 8
Again, the specific value of f(4) will depend on the behavior of the function f.
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You deposit $400 in an account earning 8% interest compounded annually. How much will you have in the account in 15 years?
Answers
Answer:
you will gain 280,462.92 in peso.but you convert in in dollar you will gain $5,520.00
You have 2 jars of marbles. The first jar contains a blue marble, a yellow marble, and a purple marble. The second jar contains a green marble, a blue marble, and a pink marble. Write out the sets that represent all the colors of the marbles.
Answers
The set containing all the colors of the marbles is given as follows:
{blue, yellow, purple, green, pink}.
What is the set of elements?A set of elements is composed by elements that respect a given characteristic, or are present in an experiment.
In this problem, we need to find the colors present in each marble, which are given as follows:
First jar: Blue marble, yellow marble and purple marble.Second jar: Green marble, blue marble and pink marble.Then we have to list all these colors in a set, which are opened and closed by the brackets {}.
The color blue appears in both sets, however, it will appear only once in the set of the colors, as the elements are not repeated.
Thus, the set containing all the colors of the marbles is given by the set presented as follows:
{blue, yellow, purple, green, pink}.
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Evaluate the following for x=5 and y=5
y^3-3x
Answers
Answer:
110
Step-by-step explanation:
5^3-3x5
=125-15
=110
x = 5 and y = 5
y³ - 3x = 5³ - 3 · 5 = 125 - 15 = 110
In 1995, wolves were introduced into Yellowstone Park.
The function `w\left(x\right)=14\cdot1.08^{x}` models the number of wolves, `w`, in the years since 1995, `x`.
Determine the value of `w(25)`.
What does this value say about the wolf population?
Answers
Answer:
w(25) = 96
There are 96 wolves in the year 2020
Step-by-step explanation:
Given:
\(w(x)=14\cdot 1.08^{x}\)
w(25) =
\(w(25)=14\cdot 1.08^{25}\\\\= 14 * (6.848)\\\\=95.872\\\\\approx 96\)
Number of years : 1995 + 25 = 2020
In 2020, there are 96 wolves
Find the area of the parallelogram
Answers
Answer:
1191 cm²
Step-by-step explanation:
Area of parallelogram = base X vertical height.
Call the vertical line h.
h/ sin 80 = 7/ sin 10
h = (7 sin 80) / sin 10
= 39.7.
Area of parallelogram = 30 X 39.7
= 1191 cm²
The Area of Parallelogram whose side length is 30 cm is 1,190.952 square cm.
Given:
Side length = 30 cm
Using Trigonometry
tan 80 = P / Base
5.6712 = P / 7
P = 39.6984 cm
Using the formula for Area of parallelogram
= Base x height
= 30 x 39.6984
= 1,190.952 square cm.
Therefore, the area is 1,190.952 square cm.
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In an ESP experiment subjects must predict whether a number randomly generated by a computer will be odd or even. (Round your answer to four decimal places.) (b) What is the probability that a subject would guess more than 20 correct in a series of 36 trials?
Answers
The probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001
How to find the pobability that a subject would guess more than 20 correct in a series of 36 trialsIn a series of 36 trials, if the subject is guessing randomly, then the probability of correctly guessing odd or even is 1/2.
Let X be the number of correct guesses in a series of 36 trials. X follows a binomial distribution with parameters n = 36 and p = 1/2.
The probability of guessing more than 20 correct is:
P(X > 20) = 1 - P(X ≤ 20)
Using a binomial distribution table, we can find that P(X ≤ 20) = 0.9999 (rounded to four decimal places).
Therefore: P(X > 20) = 1 - 0.9999 = 0.0001
So the probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001 (rounded to four decimal places).
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tic is an isosceles triangle with a vertex angle i if the measure of i90
Answers
Applying the definition of an Isosceles triangle, given that isosceles triangle TIC has a vertex angle I of 90 degrees, the measure of angle T is 45 degrees.
In geometry, an isosceles triangle is a triangle that has at least two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case. Examples of isosceles triangles include the isosceles right triangle, the golden triangle, and the faces of bipyramids and certain Catalan solids.
The two equal sides are called the legs and the third side is called the base of the triangle. The other dimensions of the triangle, such as its height, area, and perimeter, can be calculated by simple formulas from the lengths of the legs and base. Every isosceles triangle has an axis of symmetry along the perpendicular bisector of its base. The two angles opposite the legs are equal and are always acute, so the classification of the triangle as acute, right, or obtuse depends only on the angle between its two legs.
An Isosceles triangle has a vertex angle and two equal base angles.
Given that triangle TIC is an isosceles triangle:
angle I is the vertex angle = 90 degrees
angle T is a base angle
angle C is also a base angle
Thus:
angle C and angle T are congruent or equal to each other.
Therefore,
Angle T = (180 - 90)/2
⇒ Angle T = 90/2
⇒ Angle T = 45 degrees.
applying the definition of an isosceles triangle, given that isosceles triangle TIC has a vertex angle I of 90 degrees, the measure of angle T is 45 degrees.
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What’s the distance between 15,-17 and -20, -5
Answers
The distance will be in the decimal form is :41.34
Pythagoras Theorem Formula:Consider the triangle :
Where “a” is the perpendicular,
“b” is the base,
“c” is the hypotenuse.
According to the definition, the Pythagoras Theorem formula is given as:
\(Hypotenuse^2 = Perpendicular^2 + Base^2\)
\(c^2 = a^2 + b^2\)
We have the points are:
15,-17 and -20, -5
To find the distance between them.
The distance of x- axis is:
15 - (-20)
= 15 + 20
= 35
The distance of y- axis is:
|17 - 5| = |-22| = 22
We can now use the Pythagorean theorem (a²+b²=c²) with our imaginary triangle:
\(x^2+y^2=(distance)^2\)
\(35^2+22^2=distance^2\)
\(1709= distance^2\\Distance = \sqrt{1709}\)
In decimal form the distance would be around 41.34.
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write your answer as an integer or as a decimal rounded to the nearest tenth
Answers
Answer:
8.6
Step-by-step explanation:
VW = WX / cos (36°)
= 7 / 0.81
= 8.6
Answer:
8.65
Step-by-step explanation:
cos 36° = 7 / VW
VW = 7 / cos 36°
VW = 8.65
How many times can 1/5 go into nine
Answers
Answer:
1.8
Step-by-step explanation:
Shania wants to purchase a book bag with an original price of $28.00. She also bought a necklace for $35.75. There is a storewide sale of 20% off and a tax of 7%. What would be the total price after discount and tax?
A.
$54.57
B.
$68.21
C.
$51.00
D.
$63.75
Answers
Answer:
Step-by-step explanation:
An exterior angle of a regular convex polygon is 40°. What is the number of sides of the polygon?
A. 8
B. 9
C. 10
D.11
Answers
Answer:
option B
Step-by-step explanation:
Sum of interior angles of a polygon with n sides:
\(= (n - 2 )\times 180\)
\(Therefore, Each \ interior \ angle = (\frac{n - 2}{n} )\times 180\)
\(Sum \ of \ one \ of \ the \ interior \ angle \ with \ its \ exterior \ angle \ is \ 180^\circ\)
\([ \ because \ straight \ line \ angle = 180^\circ \ ]\)
That is ,
\(Exterior \ angle + Interior \ angle = 180^\circ\\\\40^ \circ + (\frac{n-2}{n}) \times 180 = 180^\circ\\\\40 n + 180n - 360 = 180n\\\\40n = 180n - 180n + 360 \\\\40n = 360 \\\\n = 9\)
OR
Sum of exterior angles of a regular polygon = 360
Given 1 exterior angle of the regular polygon is 40
Therefore ,
\(n \times 40 = 360\\\\n = \frac{360}{40} \\\\n = 9\)
Answer:
9
Step-by-step explanation:
in a science experiment, Judah is tracking the height of a small tree. At the beginning, the tree measured 32 inches. Six weeks later, The tree measures 36 inches. What is the percent increase in the tree's height? Please help!.
Answers
We can say that the tree's height increased by 12.5% over the course of the six-week experiment.
To calculate the percent increase in the tree's height, we need to find the difference between its new height and its old height, and then express that difference as a percentage of the old height.
We start with the formula:
percent increase = (new value - old value) / old value * 100%
In this case, the old value is the height of the tree at the beginning of the experiment, which is 32 inches. The new value is the height of the tree six weeks later, which is 36 inches.
So, plugging in those values, we get:
percent increase = (36 - 32) / 32 * 100%
Simplifying this expression gives us:
percent increase = 4 / 32 * 100%
And when we evaluate that expression, we get:
percent increase = 12.5%
Therefore, the percent increase in the tree's height is 12.5%.
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A package of 25 fishing hooks costs $9.95 , while a package with 40 hooks costs $13.99 . Which is the better buy? Round your answer to the nearest cent if necessary.
Answers
Therefore, the package with 40 hooks is the better buy in terms of cost efficiency.
To determine which package is the better buy, we need to compare the cost per hook for each package.
For the package of 25 hooks costing $9.95, we divide the total cost by the number of hooks:
Cost per hook = $9.95 / 25 = $0.398
Rounding to the nearest cent, the cost per hook is $0.40.
For the package of 40 hooks costing $13.99, we divide the total cost by the number of hooks:
Cost per hook = $13.99 / 40 = $0.3498
Rounding to the nearest cent, the cost per hook is $0.35.
Comparing the two costs per hook, we can see that the package with 40 hooks for $13.99 offers a better deal, as the cost per hook is lower at $0.35.
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If the radius of a circle is 31.2 cm, what is the approximate area if you use 3.14 for pi and the area is rounded to the nearest tenth?
Answers
Answer:
3056.6 cm^2
Step-by-step explanation:
A = (pi)r^2 = 3.14 * 31.2 cm * 31.2 cm = 3056.6 cm^2
Answer: 3056.60 sq. cm.
Step-by-step explanation:
Area of a circle = π x r^2
= 3.14 x 31.2^2
= 3056.60
I need some help with this problem
Answers
Answer:(-(3x^(3)-x-1))/((x^(2)+1)^(2))
43.18 divide by 3.4 equal
Answers
Answer:
12.7
Step-by-step explanation:
43.18 divided by 3.4 equals 12.7
Computer systems analysts
Database administrators
Computer software engineers,
systems software
Gaming and sports book writers
and runners
Environmental science and
protection technicians, including
health
Manicurists and pedicurists
Physical therapists
Physician assistants
504
650
119 154
350 449
18 24
36
78
47
100
220
29.0
28.6
28.2
28.0
28.0
27,6
27.1
146
34
99
5
10
22
47
18
Bachelor's degree
Bachelor's degree
Bachelor's degree
Short-term on-thi
Associate degree
Postsecondary vocational award
Master's degree
Master's degree
173
66
83
27.0
Based on the above table, what is the fastest growing listed occupation for those without a college degree?
a. Gaming and sports book writers and runners
b. Dental assistants
c. Marriage and family therapists
d. Manicurists and pedicurists
Answers
Based on the above table , the fastest growing listed occupation for those without a college degree is Gaming and sports book writers and runners.
Therefore option A is correct.
What is a college degree?The college degree is described as a qualification awarded to students after completing the requirements for a specific course of study of which the two most common types of degrees are the Bachelor of Arts and Bachelor of Science.
With reference to the table, the occupations that do not require a college degree are:
Gaming and sports book writers and runnersEnvironmental science and protection technicians, including healthManicurists and pedicuristsWe were able to conclude that Based on the above table , the fastest growing listed occupation for those without a college degree is Gaming and sports book writers and runners with a rate of 24.6%.
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Hello everyone please Can u help
Answers
Answer:
the second one is x= -1
*this stuff is genuinely easy. I'm in 10th grade and all you have to do is put it in the calculator. If you have a tinspire like me you could make the x into a 1 in the calculator, put the whole thing in graph and it'll trace the answer for you. If your teacher wants to see work then maybe don't do that but let me know and I'll send the work for you.
What is the approximate area of the circle shown below
Answers
A = πr²
Given:
r = 14 cm
Solve:
A = π(14)²
A = 196π
A = 615.7521601035995
A ≈ 616 cm²
Answer: Choice D
A point in the table for the transformed function is
Answers
Answer:
linear function
Step-by-step explanation:
straight line then add up
Jane received a $80 gift card for a coffee store. She used it in buying some coffee that cost $7.56 per pound. After buying the coffee, she had $49.76 left on
her card. How many pounds of coffee did she buy?
Answers
Answer:
Jane spent on coffee.
She started with $80 on her gift card and ended with $49.76, so she spent:
80 - 49.76 = $30.24
We know that she bought coffee that cost $7.56 per pound, so we can set up an equation to find how many pounds of coffee she bought:
7.56x = 30.24
where x is the number of pounds of coffee she bought.
Solving for x, we get:
x = 30.24 / 7.56 = 4
So Jane bought 4 pounds of coffee with her gift card.
It’s D right? Let me know if I’m wrong.
Answers
Answer:
yes D is right... brainliest plz
graph y = 6/5x - 6/5
Answers
The ordered pairs are (1,0), (2,6/5),(3,12/5)
What is the solution to a linear equation?The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.
Given here: The equation as y = 6x/5 - 6/5
putting (1,0) in the equation we get 6×1/5-6/5=0
Similarly we can find the ordered pair as y = 6/5x - 6/5
Hence, The ordered pairs are (1,0), (2,6/5),(3,12/5)
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Question 3
A group of 5 people went to the movies and spent $44 on food and drink. The total amount spent, including
tickets, was $98.50.
What was the price, in dollars, of one ticket?
Answers
Answer:
One ticket cost $10.90.
Step-by-step explanation:
The total spent was $98.50--food, drinks, admission--everything.
$44.00 was for food and drinks.
We can take the 44 away from the total.
98.50 - 44.00
= 54.50
They spent 54.50 on 5 tickets to get in. Divide to find the cost of one tickets. This assumes that all 5 tickets were the same price.
54.50 ÷ 5 = 10.90
The price of one ticket was $10.90
To make this look like algebra class...
let x = the price of one ticket
5x = the price of 5 tickets
5x + 44 = 98.50
subtract 44
5x = 54.50
divide by 5
x = 10.90
the If the area of a square shape paper is 96.04 cm?, find its a side.
Answers
Answer:
9.8 cm
Step-by-step explanation:
let side be L
AREA OF SQUARE PAPER =96.04 CM^2
L^2 = 96.04 CM^2
L = square root 96.04 CM^2
L = 9.8 cm
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