Identify p, q, and r if necessary. Then translate each argument to symbals and use a truth table to decide if the argument is valid or invalid.
Answers
Let p denote the statement "It snows", and q denote tthe statement "I can go snowboarding"
The we need to draw a table for
(p => q)v(-p => q)
p q -p -q p=>q -p => -q (p => q)v(-p => q)
T T F F T T T
T F F T F T T
F T T F T F T
F F T T T T T
The argument is valid, since the last column has truth all through.
Related Questions
How do you graph Y=5 on a graph. This is a linear equation. I know how to do it when they give an x too. But I don’t know what to do with just a y=5?
Answers
The equation y=5 represents something we know as a constant function. In a constant function, y, always, no matter what, takes the same value and is the value of the constant. In this case, the constant is 5, it means that for all values of x, y will always be 5.
In a graph, a constant function is an horizontal line, parallel to the x axis, that cuts the y axis at y=c, c is the constant. It means that the graph of y=5 will be an horizontal line that has a y intercept of 5.
estimate 8426 divided by 36 so that it only has one non zero digit.
Answers
Given:
[tex]\frac{8426}{36}[/tex]Required:
To estimate 8426 divided by 36.
Explanation:
[tex]\begin{gathered} \text{ 234.05} \\ 36)8426 \\ \text{ 72} \\ ----- \\ \text{ 1226} \\ \text{ 108} \\ ------- \\ \text{ 146} \\ \text{ 144} \\ ------ \\ \text{ 200} \\ \text{ 180} \\ -------- \\ \text{ 20} \end{gathered}[/tex]Therefore,
[tex]\frac{8426}{36}=234.05555[/tex]Final Answer:
[tex]234.05[/tex]10. You and your date go to a restaurant where there are 5 meats, 6 vegetables, 4 types of bread, and 3 desserts to choose from. In how many ways could you select 2 meats, 3 vegetables, 1 bread, and 2 dessertsformula : nCr= n! / (nr) r!
Answers
You have to select 2 meats from 5 possible meats, that is, 5C2 =
[tex]5C2=\frac{5!}{(5-2)!\cdot2!}=\frac{120}{6\cdot2}=\frac{120}{12}=10[/tex]You have to select 3 vegetables from 6 possible vegetables, that is, 6C3 =
[tex]6C3=\frac{6!}{(6-3)!\cdot3!}=\frac{720}{6\cdot6}=\frac{720}{36}=20[/tex]You have to select 1 bread from 4 possible types of bread, that is, 4C1 =
[tex]4C1=\frac{4!}{(4-1)!\cdot1!}=\frac{24}{6\cdot1}=4[/tex]You have to select 2 desserts from 3 possible desserts, that is, 3C2 =
[tex]3C2=\frac{3!}{(3-2)!\cdot2!}=\frac{6}{1\cdot2}=3[/tex]The total possibilities are:
5C2*6C3*4C1*3C2 = 10*20*4*3 = 2400
Social Security numbers are of the formXYZ - MN - ABCD.The first three digits XYZ are referred toas the area number. The number isassociated with where you registered foryour social security card. X is a number 1- 7. Y and Z can be any number 0 – 9.Also the area code 666 has never beenused. The middle two digits MN arereferred to as the group number. Thegroup number can be any number from01 to 99 (it cannot be 00). The last 4 digitsABCD are the serial number. The serialnumber can be any from 0001 to 9999 (itcannot be 0000). Additionally, thenumber social security number 123-45-6789 is only used in advertisements. Howmany social security numbers arepossible?
Answers
Solution
For XYZ
[tex]\begin{gathered} (7\times10\times10)\text{ = 700} \\ 700-1=699\text{ways} \\ \end{gathered}[/tex]For MN
[tex]\begin{gathered} (10\times10)\text{ =100} \\ 100-1=99\text{ways} \end{gathered}[/tex]For ABCD
[tex]\begin{gathered} (10\times10\times10)\text{ =10,000} \\ 10,000-1\text{ =9,999ways} \end{gathered}[/tex]Finally
[tex]\begin{gathered} (699\times99\times9999)-1 \\ =691,940,798\text{ } \end{gathered}[/tex]Social security numbers are
possible 691, 940,798
Find a logarithmic function to model the dataf(x) = 60.73(0.95)xf(x) = 0.93(60.73)xf(x) = 60.04 – 8.25 ln xf(x) = 8.25 – 60.04 ln x
Answers
Evaluate the logarithmic functions provided at different values of x to see which matches better the data from the y column:
1) f(x)= 60.04 - 8.25 * ln(x)
[tex]\begin{gathered} f(1)=60.04-8.25\ln (1) \\ =60.04 \\ \\ f(2)=60.04-8.25\ln (2) \\ =54.32\ldots \\ \\ f(3)=60.04-8.25\ln (3) \\ =50.97\ldots \\ \\ f(4)=60.04-8.25\ln (4) \\ =48.60 \\ \\ f(5)=60.04-8.25\ln (5) \\ =46.76 \\ \\ f(6)=60.04-8.25\ln (6) \\ =45.26\ldots \\ \\ f(7)=60.04-8.25\ln (7) \\ =43.98\ldots \end{gathered}[/tex]2) f(x) = 8.25 - 60.04 * ln(x)
[tex]\begin{gathered} f(1)=8.25-60.04\ln (1) \\ =8.25 \\ \\ f(2)=8.25-60.04\ln (2) \\ =-33.36\ldots \\ \\ f(3)=8.25-60.04\ln (3) \\ =-57.71\ldots \\ \\ f(4)=8.25-60.04\ln (4) \\ =-74.98\ldots \\ \\ f(5)=8.25-60.04\ln (5) \\ =-88.38\ldots \\ \\ f(6)=8.25-60.04\ln (6) \\ =-99.32\ldots \\ \\ f(7)=8.25-60.04\ln (7) \\ =-108.58\ldots \end{gathered}[/tex]The rest of the given functions are not logarithmic.
We can see from the computed values for the given logarithmic functions, that the one which best fits the data, is: f(x)=60.04-8.25*ln(x).
Therefore, the answer is:
[tex]f(x)=60.04-8.25\ln (x)[/tex]Richard and Teo have a combined age of 32. Richard is 5 years older than twice Teo's age. How old are Richard and Teo?
Answers
The age of Teo is 9 years and the Age of Richard is 23 years.
What is problem-solving?
Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.
Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.
Calculation:-
Richard and Teo have a combined age = of 32
Richard is 7 years older than twice Teo's age
Let the age of Teo = X
Age of Richard = 2X + 7
2X + 5+ X = 31
X = 31 - 5 /3
X = 27/3
= 9 years
Therefore the age of Teo is 8 years
Age of Richard = 19 years
Learn more about Problem-solving here:-brainly.com/question/23945932
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Which one of the following graphs is the graph of:if x > 0If(x) = -1 if x = 0 ?-3if x < 0OA.GB.Ax
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Explain the given piecewise function
We look for where x is greater than zero and f(x) will be x
Where x equals 0 and the f(x) will be -1
Where x is less than 0 and f(x) will be -3
Hence, the correct graph will be:
OPTION D
Dawn's suitcase weighed 25 kilograms. Convert this weight to pounds. (Round youranswer to the nearest tenth.)
Answers
Given: Dawn's suitcase weighed 25 kilograms.
Required: To convert the given weight to pounds.
Explanation: Since 1 kilogram is equivalent to 2.20462 pounds. Hence to convert 25 kg to pounds, we need to multiply by 2.20462.
Thus we have
[tex]\begin{gathered} 25\text{ kg}=25\times2.20462\text{ pounds} \\ =55.1156\text{ pounds} \\ \approx55.1\text{ pounds} \end{gathered}[/tex]Final Answer: Dawn's suitcase weighed 55.1 pounds.
Find the x- and y- intercept of each linear equation.1/2x + 1/4y = 3/2
Answers
hello
the equation given is
[tex]\frac{1}{2}x+\frac{1}{4}y=\frac{3}{2}[/tex]let's rewrite the equation
[tex]\begin{gathered} \frac{1}{2}x+\frac{1}{4}y=\frac{3}{2} \\ \frac{1}{4}y=\frac{3}{2}-\frac{1}{2}x \\ \text{ multiply through by 4} \\ \frac{4}{4}y=4\times\frac{3}{2}-(4\times\frac{1}{2}x) \\ y=\frac{12}{2}-2x \\ y=6-2x \end{gathered}[/tex]now let's find the x and y intercept now
to do this, put x = 0 and solve and then put y = 0 and then solve
[tex]\begin{gathered} y=6-2x \\ \text{put x = 0} \\ y=6-2(0) \\ y=6-0 \\ y=6 \end{gathered}[/tex]now let's put y = 0
[tex]\begin{gathered} y=6-2x \\ 0=6-2x \\ 2x=6 \\ \text{divide both sides by 2} \\ \frac{2x}{2}=\frac{6}{2} \\ x=3 \end{gathered}[/tex]now the coordinates for the equation is (3, 6)
True or False?Dependent is all events which are not included in the specified event.
Answers
Two events are independent, statistically independent if the occurrence of one does not affect the probability of occurrence of the other. So the answer is false.
what is 30% off 10? How u get answer
Answers
We are asked to find out what is 30% off 10?
30% off 10 means that there is a discount of 30% and you are supposed to pay only the remaining 70%
100% - 30% = 70%
So you can simply find the 70% of 10
[tex]70\%\: of\: 10=\frac{70}{100}\times10=7[/tex]Therefore, 30% off 10 is equal to 7
There is another way to find out 30% off 10
First, you find 30% of 10 and then subtract the result from the original amount
[tex]\begin{gathered} 30\%\: of\: 10=\frac{30}{100}\times10=3 \\ 10-3=7 \end{gathered}[/tex]Therefore, 30% off 10 is equal to 7
Find the area to the left of x=73 under a normal distribution curve with mean=71 and standard deviation =2 .Round your answer to four decimal places.
Answers
To find the area to the left of x=73 under a normal distribution curve:
1. Find the corresponding z, use the next formula:
[tex]z=\frac{(x-\operatorname{mean})}{\text{standard deviation}}[/tex][tex]\begin{gathered} z=\frac{73-71}{2} \\ \\ z=\frac{2}{2} \\ \\ \\ z=1 \end{gathered}[/tex]2. Find the z-score corrsponding to z=1, use a z score table:
The area to the left of z is equal to the corresponding z-score.
Then, the area to the left of x=73 is 0.8413please help me ASAP!!!!
Answers
The phrase can be written as:
[tex]\lvert x+5\rvert=3[/tex]therefore the correct choice is the third one.
The function graphed is of the form y=a sin bx or y=a cox bx, where b>0. Determine the equation of the graph.
Answers
The equation is of the form y=asinbx
The amplitude of the graph is a=3 unit
The period is
[tex]\frac{\pi}{2}[/tex]Thus,
[tex]\frac{2\pi}{b}=\frac{\pi}{2}\Rightarrow b=4[/tex]Thus the equation becomes,
y=3sin(4x)
6n+36=0solve the following equation if n=10
Answers
According to the given data we have the following equation:
6n+36=0
So, if the value of n=10 we would solve the equation as follows:
We would substitue the variable of n with 10, so:
6n+36=0
6(10)+36=0
60+36=96
Therefore, the value of the equation 6n+36 when n=10 would be 96
is the number 6.35 a natural number
Answers
The number is 6.35.
The Natural numbers are all numbers 1, 2, 3, 4… They are the numbers you usually count and they will continue on into infinity.
6.35 is a natural number.
Points D, C, B, and A are collinear.What is the slope of DC in simplest form?5BСSlope of DC = [?]D
Answers
Given points D, C, B and A are colinear (they lie on the same line), you can determine that the slope of AB and the slope of DC are the same.
By definition:
[tex]Slope=\frac{Rise}{Run}[/tex]In this case, you can identify that:
[tex]\begin{gathered} Rise=5 \\ Run=1 \end{gathered}[/tex]Therefore, you can determine that:
[tex]\begin{gathered} Slope\text{ }of\text{ }DC=\frac{5}{1} \\ \\ Slope\text{ }of\text{ }DC=5 \end{gathered}[/tex]Hence, the answer is:
[tex]Slope\text{ }of\text{ }DC=5[/tex]convert 7π\12 from radians to degrees
Answers
ANSWER:
[tex]\frac{7}{12}\pi=105\text{\degree}[/tex]STEP-BY-STEP EXPLANATION:
To convert degrees to radians or radians to degrees, we must bear in mind that pi equals 180°, therefore:
[tex]\frac{7}{12}\pi\cdot\frac{180\text{\degree}}{\pi}=105\text{\degree}[/tex]2) The debate team with 18 members is to choose four officers: captain, co-captain, treasurer, and secretary. How many ways can those officers be selected?
Answers
We have 18 members that can be positioned in 4 positions.
As the positions are different from each other, the order matters.
Then, this is a permutation of 18 elements in 4 places with no repetition.
The number of permutations can be calculated as:
[tex]\begin{gathered} P(n,r)=\frac{n!}{(n-r)!} \\ P(18,4)=\frac{18!}{(18-4)!}=\frac{18!}{14!}=18\cdot17\cdot16\cdot15=73440 \end{gathered}[/tex]We could have derived this by doing this analysis:
We have 18 to choose for captain.
Then, we have 17 left to choose for co-captain.
Finally 16 can be chosen for treasurer and 15 are left for secretary.
Then, the posible teams are 18*17*16*15=73440.
Answer: we can select them in 73,440 ways.
Solve the equation (the answer might be no solution or all real numbers)-30= -10(q-1)6+(c+8)=136-(c+8)=13-(c-4)=13-36= -3(2-5m)4-10(n+4)=-56
Answers
We have to find the solution for this equations.
a) -30 = -10(q-1)
[tex]\begin{gathered} -30=-10(q-1) \\ q-1=\frac{-30}{-10} \\ q-1=3 \\ q=3+1 \\ q=4 \end{gathered}[/tex]b) 6+(c+8) = 13
[tex]\begin{gathered} 6+(c+8)=13 \\ c=13-6-8 \\ c=-1 \end{gathered}[/tex]c) 6-(c+8)=13
[tex]\begin{gathered} 6-(c+8)=13 \\ 6-13=c+8 \\ -7=c+8 \\ -7-8=c \\ c=-15 \end{gathered}[/tex]d) -(c-4)=13
[tex]\begin{gathered} -(c-4)=13 \\ c-4=-13 \\ c=-13+4 \\ c=-9 \end{gathered}[/tex]f) -36= -3(2-5m)
[tex]\begin{gathered} -36=-3(2-5m) \\ \frac{-36}{-3}=2-5m \\ 12=2-5m \\ 5m=2-12 \\ 5m=-10 \\ m=\frac{-10}{5} \\ m=-2 \end{gathered}[/tex]g) 4-10(n+4)=-56
[tex]\begin{gathered} 4-10\mleft(n+4\mright)=-56 \\ 4+56=10(n+4) \\ 60=10(n+4) \\ \frac{60}{10}=n+4 \\ 6=n+4 \\ n=6-4 \\ n=2 \end{gathered}[/tex]According to the manual, a battery in a cellular phone loses 2% of its charge eachday. Assume the battery is 100% charged. Write an equation to represent thepercent charge, P, as a function of the number of days, d, since the battery wascharged and use it to determine the number of days until the battery in only 50%charged.
Answers
a.) According to the manual, a battery in a cellular phone loses 2% of its charge each
day.
b.) Assume the battery is 100% charged.
Let,
P = the percent charge
d = the number of days since the battery was charged
The equation will be:
P = 100 - 2d
Let's determine the number of days until the battery in only 50% charged.
P = 100 - 2d
50 = 100 - 2d
2d = 100 - 50
2d = 50
2d/2 = 50/2
d = 25
Therefore, the battey will be only 50% charged in 25 days.
In the figure below, AC || DE, BD measures 8 m, AD measures 12 m, and BE measures 6 m. Find the length of BC.
Answers
Answer:
BC = 15 units===============
Parallel lines divide the transversal into proportional segments.
Set ratios and find the missing lengthBD/AD = BE/ED8/12 = 6/ED2/3 = 6 / EDED = 6*3/2ED = 9Find BCBC = BE + EDBC = 6 + 9BC = 15insert parentheses to make the expression true, 382/292-101+8=10
Answers
Answer:
(382/(292-101))+8=10
(382/191)+8=10
(2)+8=10
10=10
A department store is holding a drawing to give away free shopping sprees. There are 9 customers who have entered the drawing: 3 live in the town of Gaston, 2 live in Pike, and 4 live in Wells. Two winners will be selected at random. What is the probability that both winners live in Pike? Write your answer as a fraction in simplest form.
Answers
We need to find the probability that the two winners line in Pike.
We know that 2 out of the 9 customers who entered the drawing live in Pike.
Thus, the probability of the first winner line in Pike is:
[tex]\frac{2}{9}[/tex]Then, considering the first winner live in Pike, there are left 8 customers, and 1 of them live in Pike. Thus, the probability that the second winner lives in Pike is:
[tex]\frac{1}{8}[/tex]Now, the probability that the first one lives in Pike and the second one also lives in Pike is the product of the two probabilities we found:
[tex]\frac{2}{9}\times\frac{1}{8}=\frac{2}{9\times8}=\frac{1}{9\times4}=\frac{1}{36}[/tex]Therefore, the probability that both winners live in Pike is:
[tex]\frac{1}{36}[/tex]Convert 0.111... to a repeating fraction. simplify if you can
Answers
Explanation:
To convert from a repeating decimal number to a fraction we have to do the following steps:
1. Let 'x' be the repeating decimal:
[tex]x=0.111\ldots[/tex]2. Let 'n' be the number of decimals that repeat. In this case n = 1
3. Multiply both sides of point 1 by 10^n:
[tex]10x=1.111\ldots[/tex]4. Substract (1) from (3) to eliminate the repeating part:
[tex]\begin{gathered} 10x-x=1.111\ldots-0.111\ldots \\ 9x=1 \end{gathered}[/tex]5. Solve for x:
[tex]\begin{gathered} 9x=1 \\ x=\frac{1}{9} \end{gathered}[/tex]6. Simplify: in this case, it is the simplest form for this fraction
Answer:
0.111... as a fraction is 1/9
Katy has $40 in a savings account. The interest rate is 5%, compounded annually.To the nearest cent, how much interest will she earn in 3 years?What’s the answer
Answers
Given:
Katy has $40 in a savings account.
So, the principal = P = 40
The interest rate = r = 5% = 0.05
compounded annually, n = 1
Time = t = 3 years
So, Amount of money after 3 years = A
[tex]\begin{gathered} A=P\cdot(1+\frac{r}{n})^{nt} \\ A=40\cdot(1+\frac{0.05}{1})^3=46.305 \end{gathered}[/tex]So, the interest = A - P =
[tex]46.305-40=6.305[/tex]Rounding to the nearest cent
So, the answer will be:
interest she will earn in 3 years = $6.3
The question is in the image. Answer the question 4.
Answers
Step 1
Given;
[tex]coordinate\text{ points\lparen5,-12\rparen}[/tex]Required; To find the value of θ
Step 2
We use the trigonometric function Toa to find the required angle.
[tex]\begin{gathered} tan\theta=\frac{opposite}{Adjacent} \\ opposite=-12 \\ adjacent=5 \\ tan\theta=\frac{-12}{5} \\ \end{gathered}[/tex][tex]\begin{gathered} Using\text{ pythagoras} \\ (-12)^2+(5)^2=hypotenuse^2 \\ hypotenuse=\sqrt{144+25}=13 \\ Sin\theta=\frac{opposite}{Hypotenuse}=\frac{-12}{13} \end{gathered}[/tex][tex]\begin{gathered} cos\theta=\frac{adjacent}{hypotenuse}=\frac{5}{13} \\ csc\theta=\frac{1}{sin\theta}=\frac{1}{\frac{-12}{13}}=\frac{13}{-12} \end{gathered}[/tex][tex]\begin{gathered} sec\theta=\frac{1}{cos\theta}=\frac{1}{\frac{5}{13}}=\frac{13}{5} \\ cot\theta=\frac{1}{tan\theta}=\frac{1}{\frac{-12}{5}}=\frac{5}{-12} \end{gathered}[/tex]What is the measure of ZXYZ shown in the diagram below?S36°TХ114"ZO A. 78O B. 39OC. 36ОD. 75
Answers
In order to calculate the measure of angle XYZ, we can use the following property of secant lines to a circle:
[tex]\begin{gathered} XYZ=\frac{1}{2}(XZ-ST) \\ \text{XYZ}=\frac{1}{2}(114-36) \\ \text{XYZ}=\frac{1}{2}\cdot78 \\ \text{XYZ}=39\degree \end{gathered}[/tex]So the correct option is B.
What Postulate or theorem proves that these triangles are similar?
Answers
Solution
The Side-Angle-Side (SAS) Theorem states if two sides of one triangle are proportional to two corresponding sides of another triangle, and their corresponding included angles are congruent, the two triangles are similar.
Next
AC is corresponding to EC
BC is corresponding to DC
[tex]\begin{gathered} \frac{AC}{EC}\text{ = }\frac{6}{12}\text{ = }\frac{1}{2} \\ \frac{BC}{DC}\text{ = }\frac{5}{10}\text{ = }\frac{1}{2} \end{gathered}[/tex]The ratio of their corresponding sides is proportional.
Final answer
The Side-Angle-Side (SAS) Theorem
determine the slope of a vertical line, and the slope of a horizontal line.
Answers
The slope of a vertical line is undefine
The slope of a horizontal line is zero