The proposition with three variable p, q and r are as -
C = (p∧q∧¬r)∨(p∧¬q∧r)∨(¬p∧q∧r)
What is compound proposition?A proposition is defined as a statement that expresses an idea, suggestion, or plan. A proposition is the notion that death penalty is an effective way to reduce crime.
Now, as per the given question-
This compound proposition C employs the outer disjunction (∨), and it is true if and only if any one of finally three propositions is true, (p∧q∧¬r),(p∧¬q∧r),(¬p∧q∧r) is true.First, it is impossible for two or three of these propositions to be true at the same time. As an example, suppose (p∧q∧¬r) and (p∧¬q∧r) are both true, then ¬r is true (from the first conjunction) & r is true (from the second), resulting in a contradiction. All other possible options can be ruled out using the same logic.Because these propositions have become mutually exclusive, C is true if and only if one of the three is true (and false otherwise).
This is only possible if two of p,q, & r are true while the third is false.For instance, (p∧q∧¬r) is true once p and q are true but r is false.
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Scores
14
8
13
10
20
12
11
Find the students median quiz score
Answer:
In ascending order:8,10,11,12,13,14,20
N=7
Step-by-step explanation:
Position of median=(N+1/2)th item
=(7+1/2)th item
(8/2)th item
4th item
=:4th item =12
So,12is median quiz score.
Hope this helpful for you.
∠ABC and ∠DEF are complementary. If m∠ABC = (2x+4)∘ and m∠DEF = (3x−5)∘, find the measure of each angle.
m∠ABC =
m∠DEF =
The measure of each angle are m∠ABC = 40.4 and m∠DEF = 49.6
How to determine the measure of each angle?The given parameters are
m∠ABC = (2x+4)∘ and m∠DEF = (3x−5)∘,
Complementary angles add up to 90 degrees
So, we have
2x + 4 + 3x - 5 = 90
Evaluate the like terms
5x = 91
Divide by 5
x = 18.2
Substitute x = 18.2 in m∠ABC = (2x+4)∘ and m∠DEF = (3x−5)∘,
m∠ABC = (2 x 18.2 + 4) = 40.4
m∠DEF = (3 x 18.2 − 5)∘ = 49.6
Hence, the measure of each angle are m∠ABC = 40.4 and m∠DEF = 49.6
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Austin is mailing packages. Each small package costs him $2.60 to send. Each large package costs him $3.50. How much will it cost him to send 1 small package and 5 large packages?
Answer:
$20.1
Step-by-step explanation:
1 small package is $2.60
1 large package is $3.50
We multiply 3.5 * 5 since there are 5 large packages and we add 1 small package to get $20.1
Answer:
$20.10
Step-by-step explanation:
Let s = the cost of a small package and
l = the cost of a large package
1 small pakcage and 5 large package
1s+5l
Substitute s = $2.60 and l = $3.50
1($2.60) + 5(3.50)
= $20.10
What is the line of symmetry for the parabola whose equation is y=x²-12x + 7?
Ox=12
Ox=6
Ox=-6
Answer:
x = 6
Explanation:
completing square:
[tex]y=x^2-12x+7[/tex]
[tex]y=(x^2-12x)+7[/tex]
[tex]y=(x-6)^2+7-(-6)^2[/tex]
[tex]y=(x-6)^2+7-36[/tex]
[tex]y=(x-6)^2-29[/tex]
Comparing with quadratic equation [tex]y=ax^2 + bx+c[/tex], in vertex form where [tex]y = a(x-h)^2+k[/tex]. In this x - h = 0, x = h defines the symmetry of equation.
So here the symmetry for parabola:
x - 6 = 0
x = 6
Answer:
x = 6
Step-by-step explanation:
The axis of symmetry of a parabola is the x-value of its vertex.
For a quadratic function in the form [tex]y=ax^2+bx+c[/tex], the x-value of the vertex is:
[tex]x=-\dfrac{b}{2a}[/tex]
Given function:
[tex]y=x^2-12x+7[/tex]
Therefore:
[tex]a=1, \quad b=-12, \quad c=7[/tex]
So the axis of symmetry of the given quadratic function is:
[tex]\implies x=-\dfrac{b}{2a}=-\dfrac{-12}{2(1)}=\dfrac{12}{2}=6[/tex]
2(b + 5) = 3(b - 2) + 23
Answer:
b = -7
Step-by-step explanation:
2(b + 5) = 3(b - 2) + 23
2b + 10 = 3b - 6 + 23
10 + 6 -23 = 3b - 2b
-7 = b
Answer:
b = -7
Step-by-step explanation:
[tex]2(b+5) = 3(b-2) + 23[/tex]
for the left side of the equation: [tex]2*b + 2*5 = 2b + 10[/tex]
for the right side of the equation: [tex]3*b + 3*-2 = 3b - 6 + 23 = 3b + 17[/tex]
[tex]2b + 10 = 3b + 17[/tex]
to isolate b, subtract 2b from both sides
[tex]10 = b + 17[/tex]
subtract 17 from both sides
[tex]-7 = b\\b = -7[/tex]
an amusement park charges 18 dollars for 4 rides. how much will 7 rides cost
If a process improvement has changed the mean observed time for element 6 to 1.50 minutes, what is the new standard time for the navigator iii?.
9 minutes is the new standard time for the navigator iii.
What is statistics and example?
Statistics is the branch of mathematics that deals with the gathering, tabulating, and analysis of numerical data. Statistics is defined as numerical data. A report of data indicating the number of adherents of each religion in a specific nation is an example of statistics.If a process improvement has changed the mean observed time for element 6 to 1.50 minutes, then
Element 1 2 3 4 5 6
Mean obs. Time(t) 1.11 3.1 0.895 1.283333 1.565 1.5
Normal time 1.0545 1.395 0.93975 1.283333 1.33025 1.65 Sum
Standard time 1.240588 1.641176 1.105588 1.509804 1.565 1.941176
Sum 9.003333
New standard time = 9 minutes
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Monica has a goal to complete a triathlon. The race consists of a 2.4-mile swim, a 112-mile bike ride, and a 26.2-mile run. In training, Monica can swim at an average pace of 1.8mph. She rides her bike at an average of 19.2mph and runs at 4.8mph. Estimate how long it will take her to complete the triathlon.
Taking into account the definition of speed, Monica will complete the triathlon in 12.62 hours.
Definition of speedSpeed can be defined as the amount of space traveled per unit of time with which a body moves and can be calculated using the expression:
speed= distance traveled÷ time
Time to complete the triathlonIn this case, you know
Swim:speed= 1.8 mphdistance traveled= 2.4 milesRide a bikespeed= 19.2 mphdistance traveled= 112 milesRun:speed= 4.8 mphdistance traveled= 26.2 milesReplacing these values in the speed definition:
Swim: 1.8 mph= 2.4 miles÷ time to swimRide a bike: 19.2 mph= 112 miles÷ time to ride a bikeRun: 4.8 mph= 26.2 miles÷ time to runSolving:
Swim: 1.8 mph×time to swim= 2.4 miles
time to swim= 2.4 miles÷ 1.8 mph
time to swim= 1.33 h
Ride a bike: 19.2 mph× time to ride a bike = 112 miles
time to ride a bike= 112 miles÷ 19.2 mph
time to ride a bike=5.83 h
Run: 4.8 mph× time to run= 26.2 miles
time tu run= 26.2 miles÷ 4.8 mph
time to run= 5.46 h
The time to complete the triathlon is the sum of each of the stages:
Total time= time to swim + time to ride a bike + time to run
Total time= 1.33 h + 5.83 h + 5.46 h
Total time= 12.62 h
In summary, Monica will complete the triathlon in 12.62 hours.
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PLEASE HELP!!
30 POINTS + BRAINLIEST!
GEOMETRY A
An executive invests 28,000 some at 7% and the rest at 4% annual interest if he receives an annual return of $1,570 how much is invested at each rate
we get that the amount invested at 7 % interest rate is $ 15,000 and at 4 % interest rate is $ 13,000.
We are given that:
the total amount invested is = $ 28,000
Let the amount invested at 7 % interest rate be x
Amount invested at 4 % interest rate = 28,000 - x
Interest received at the end of year = $ 1570
ATQ:
7 % x + 4 % ( 28,000 - x) = 1570
7 x + 4 (28,000 - x) = 157000
7 x + 112,000 - 4 x = 157,000
3 x = 157,000 - 112,000
3 x = 45,000
x = 45,000 / 3
x = 15,000
Amount invested at 7 % interest rate = x = $ 15,000
Amount invested at 4 % interest rate = 28,000 - x = $ 13,000
Therefore, we get that the amount invested at 7 % interest rate is $ 15,000 and at 4 % interest rate is $ 13,000.
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find the derivative of f(x)=3x+5
Answer: Derivative of f(x) =3x+5=3
Step-by-step explanation:
By the Sum Rule, the derivative of 3x+5 with respect to x is d/dx[3x]+d/dx[5]
d/dx[3x]+d/dx[5]
evaluate: d/dx[3x]
Since 3 is constant with respect to x, the derivative of 3x with respect to x is 3d/dx[x].
3d/dx[x]+d/dx[5]
Differentiate using the power rule
which states that d/dx[[tex]x^{n}[/tex]] is [tex]nx^{n-1}[/tex] where n=1.
3⋅1+d/dx[5]
Multiply 3 by 1.
3+d/dx[5]
Differentiate using the Constant Rule.
Since 5 is constant with respect to x, the derivative of 5 with respect to x is 0.
3+0
Add 3 and 0 = 3
So, derivative of f(x) =3x+5=3
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Which expression is equivalent to quantity y raised to the negative second power times z raised to the third power end quantity over quantity z raised to the negative fourth power times y raised to the fifth power end quantity all raised to the negative second power?
NEED ASAP HURRY UP
The simplification of the given expression using laws of Indices is; y³z⁷
How to use Laws of Indices?
We want to simplify the expression y raised to the negative second power times z raised to the third power end quantity over quantity z raised to the negative fourth power times y raised to the fifth power end quantity all raised to the negative second power.
The above can be expressed as;
(y⁻² * z³)/(z⁻⁴ * y⁵)
Collecting like terms gives;
(y⁻²/y⁵) * (z³/z⁻⁴)
= y⁻² ⁺ ⁵ * z³ ⁺ ⁴
= y³z⁷
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Answer:
y^18/z^18
Step-by-step explanation:
Which expression is equivalent to the quantity seven raised to the negative second power times three raised to the fifth power end quantity all raised to the negative second power?
seven raised to the fourth power divided by three raised to the tenth power
negative seven raised to the fourth power divided by three raised to the tenth power
three raised to the third power divided by seven raised to the fourth power
negative three raised to the third power divided by seven raised to the fourth power
The expression that is equivalent to the quantity seven raised to the negative second power times three raised to the fifth power end quantity all raised to the negative second power is negative seven raised to the fourth power divided by three raised to the tenth power.
What is power in mathematics?power in mathematics can be described as the the expression which help to give the representation of repeated multiplication by the use of same factor.
We can open the bracket, for each term as [tex]\frac{1}{7^{-2}( ^{2}) }[/tex] and [tex]\frac{1}{3^{10} }[/tex]
Therefore, the second option is correct because they are the option that correct with the description in the question.
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Which best describes the triangle?
Apply the rule for negative exponents to select the equivalent expression. 8-1 08 8X -8
The equivalent expression of 8^-1 is 1/8
How to apply the rule for negative exponents?The expression is given as
8^-1
The above represents 8 exponent -1
The rule for negative exponents states that
a^-1 = 1/a
This means that
8^-1 = 1/8
Hence, the equivalent expression of 8^-1 is 1/8
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What are the three principles of describing data?
dispersion, range and standard deviation mean, median and mode
Mean, median and mode are the three principles of describing data.
Describing data:- Describing data is also called descriptive statistics, that describes the data through several methods such as graphical representations, central tendency, variability. It summarizes the data efficiently, which helps to make any conclusion on that dataset.
The three principles of describing data are-
Mean:- The summation of all the values divided by the total number of values, is called mean. It is also called as average.Median:- The middle value is called median.Mode:- The value, which occurs most often in a set of all values, is called mode.Thus we can conclude that, mean, median and mode are the three principles of describing data.
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(I didnt put the full question on acident please ignore this :') )
Answer:
k but pls put the question so you that will get support:-)
The median of a quanitive data set is always one of the infiviual data values. True or false
The given statement "The median of a quantitative data set is always one of the individual data values" is false.
What is a median?When a given data set is arranged in ascending order the observation which at the between of the data is the median of that data set. It is a value in the set whose left and right both have the same number of observations.
The given statement is not true, this is because the median is the mid-value of any data set.
If the number of data observations is odd then the median of a quantitative data set is always one of the individual data values.But if the number of data observations is even then the median is the average of the two numbers present in between the data observations.Hence, the given statement "The median of a quantitative data set is always one of the individual data values" is false.
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Pleaseeeee I really need some help here
Answer:
a) 17 b)22
Step-by-step explanation:
a) 3 - (-14)
Negative minus Negative is positive so we get
3+14
which is
17
drawing that on the number line:
<-20---------------0-------------17--20>
b) -36 + 58
we can rearrange the numbers to get
58-36
which is equal to
22
drawing that on the number line:
<-20---------------0---------------20--22>
if this was helpful pls give me brainliest <3
Histograms, tables, and pie charts are examples of
A. Data organization
B. Data analysis
C. Data Gathering
D. Data Creation
Answer:
B.DATA ANALYSIS
Step-by-step explanation:
uahvaishsbdiisbd hi isjsbbssihsbsbs
The function ƒ(x) = e2x+1 when graphed could be described as
The function ƒ(x) = e^(2x + 1) when graphed could be described as; an increasing exponential graph.
How to Interpret Exponential Graphs?The graphs of exponential functions are nonlinear—because their slopes are always changing, they look like curves, not straight lines.
Now, we are given the exponential function as; ƒ(x) = e^(2x + 1)
Now, as the exponent increases, the curves get steeper and the rate of growth increases respectively. Thus, we can see that the exponent we are given increases as seen in the exponent attached to it.
Thus, we can conclude that The function ƒ(x) = e^(2x + 1) when graphed could be described as; an increasing exponential graph.
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For f(x) = 3x+1 and g(x)=x2-6, find (f- g)(x).
The simplified equation of the given Arithmetic function (f- g)(x) is:
-x² + 3x + 7.
Arithmetic function describe as:Arithmetic is a fundamental branch of mathematics that studies the properties of classical operations on numbers such as addition, subtraction, multiplication, division, exponentiation, and root extraction.
Which of the following is not an arithmetic function?Addition, subtraction, multiplication, as well as division are the four basic arithmetic operations. There are additional arithmetic operators, such as exponentiation, modulus operations, increment, decrement, and so on. * - The operator for multiplication. As a result, the And operator is not an arithmetic operator.
According to the given information:Given:
f(x) = 3x+1
g(x)=x²-6
(f- g)(x) =
Substituting the value we get:
(f - g)(x) = (3x + 1) - (x² - 6)
= 3x + 1 - x² + 6
= -x² + 3x + 7
The simplified equation of the given Arithmetic function (f- g)(x) is = -x² + 3x + 7.
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Please help with algebra!
Answer: x=-10
Step-by-step explanation:
LMN=LMF+FMN
125=x+48+x+97
125=2x+48+97
125=2x+145
2x=-20
x=-10
Question 2 of 10
Which situation shows a constant rate of change?
A. The amount raised by a booster club compared with the number
of raffle tickets sold
B. The weight of a kitten compared with its age in months
C. The number of goals scored in a soccer game compared with the
minutes played
D. The height of a paper airplane over time
The amount raised by a booster club compared with the number of raffle tickets sold shows a constant rate of change;
A constant rate of change is realized when a change in one situation always results in a change in another. In the scenario of a booster club that regularly sells raffle tickets, the more tickets it sells, the higher the club gets.
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Tyler solves an equation. His work is shown.
Step
Original equation 10x = -4(2x-9)
10x = -8x +36
2
X=2
1
2
In step 2, Tyler uses the addition property of equality.
Create the equation that could show the missing step.
The equation which could show the missing step in Tyler's solution to the equation as requested in the task content is; 10x + 8x = 36.
What is the solution that could show the missing step in Tyler's solution to the equation as requested in the task content?It follows from the task content that the missing step in the solution steps is to be determined.
Given an equation;
10x = -4(2x-9)
By distributing -4 on the right hand side, we have;
10x = -8x + 36
The next step which is therefore the missing step is;
Add 8x to both sides of the equation so that we have;
10x + 8x = 36
18x = 36
Divide both sides by 18, so that we have;
x = 2 as obtained in the task content.
Ultimately, the equation which could show the missing step in Tyler's solution to the equation as requested in the task content is; 10x + 8x = 36.
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100 Points Please Help Quick
Which function has a constant additive rate of change of –1/4?
A coordinate plane with a straight line with a negative slope. The line passes through (negative 2, 2) and (2, 1).
A coordinate plane with a curved line passing through (negative 1, 2), (0, negative 1), the minimum (2, negative 2), and (4, negative 1).
A two-column table with five rows. The first column, x, has the entries, 20, 21, 22, and 23. The second column, y, has the entries negative 1, negative 1.5, negative 2, and negative 2.5.
A two-column table with five rows. The first column, x, has the entries, negative 12, negative 11, negative 10, and negative 9. The second column, y, has the entries, 7, 11, 14, and 17.
Answer:
(A) is correct.
Step-by-step explanation:
As we know,
The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
From the first graph:
The line goes through the points:
(-2, 2) and (2, 1)
y - 1 = (1-2)/(2+2)[x -2]
y - 1 = (-1/4)[x -2]
y = -x/4 + 1/2 + 1
y = -x/4 + 3/2
The constant additive rate of change = -1/4
Thus, the function shown in graph (A) has a constant additive rate of change is -1/4 option (A) is correct.
martin can read 4 pages in 7 minutes. at this rate,how long will it take him to read 9 pages
Answer:
5.14 minutes
Step-by-step explanation:
4 pages / 7 minutes = 0.57 minutes per page
0.57 minutes/pg * 9 pages = 5.14 minutes
what is 3-5b=-32 in algebra
Answer:
b=7
Step-by-step explanation:
3-5b=-32
-5b=-32-3
-5b=-35
Divide both sides by -5
b=7
( I also had trouble with these kind of expressions)
(x+2, y+3)
help please
Answer:
is that the equation ? is that all they gave you
im going to answer but do you mean
(x +2y+3)
Step-by-step explanation:
The data set represents the number of pages in the last book read by each of 20 students over the summer. 163, 170, 171, 173, 175, 205, 220, 220, 220, 253, 267, 281, 305, 305, 305, 355, 371, 388, 402, 431 Create a histogram to represent the distribution of the data.
The required histogram is attached as a picture.
Given the information on how many pages each of the 20 pupils read throughout the summer.
163, 170, 171, 173, 175, 205, 220, 220, 220, 253, 267, 281, 305, 305, 305, 355, 371, 388, 402, 431
With frequency on the y axis and class on the x axis.
we observe the histogram and make out that:
class 160 - 220 has the highest frequency of 6 students whereas
400 - 460 has the least with 2 students.
The classes between them range as follows:
220 - 280 has 5 students
280 - 340 has 4 students
340 - 400 has 3 students.
Hence the required histogram is created .
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