Answer:
C. 120,000 people
Step-by-step explanation:
First thing I did was divide 90 by 45 which gave me 2 as my answer. So now I know that the population 90 years from now will be doubled twice (x4). So I did...
[tex]30,000 \times 4 = 120,000[/tex]
Answer:
80,000 people
Step-by-step explanation:
First, find out how many times the population will double. Divide the number of years by how long it takes for the population to double.
68÷34=2
The population will double 2 times.
Now figure out what the population will be after it doubles 2 times. Multiply the population by 2 a total of 2 times.
20,00022=80,000
That calculation could also be written with exponents:
20,00022=80,000
After 68 years, the population will be 80,000 people.
First-order linear differential equations
1. dy/dt + ycost = 0 (Find the general solution)
2. dy/dt -2ty = t (Find the solution of the following IVP)
Answer:
(a) [tex]\frac{dy}{(2y+1)}=tdt[/tex] (b) [tex]y=\frac{e^{t^2}+e^{2c}-1}{2}[/tex]
Step-by-step explanation:
(1) We have given [tex]\frac{dy}{dt}+ycost=0[/tex]
[tex]\frac{dy}{dt}=-ycost[/tex]
[tex]\frac{dy}{y}=-costdt[/tex]
Integrating both side
[tex]lny=-sint+c[/tex]
[tex]y=e^{-sint}+e^{-c}[/tex]
(2) [tex]\frac{dy}{dt}-2ty=t[/tex]
[tex]\frac{dy}{dt}=2ty+t[/tex]
[tex]\frac{dy}{dt}=t(2y+1)[/tex]
[tex]\frac{dy}{(2y+1)}=tdt[/tex]
On integrating both side
[tex]\frac{ln(2y+1)}{2}=\frac{t^2}{2}+c[/tex]
[tex]ln(2y+1)={t^2}+2c[/tex]
[tex]2y+1=e^{t^2}+e^{2c}[/tex]
[tex]y=\frac{e^{t^2}+e^{2c}-1}{2}[/tex]
If A and B are events with P(A) = 0.5, P(A OR B) = 0.65, P(A AND B) = 0.15, find P(B).
Answer:
P(B) = 0.30
Step-by-step explanation:
This is a probability problem that can be modeled by a diagram of Venn.
We have the following probabilities:
[tex]P(A) = P_{A} + P(A \cap B) = 0.50[/tex]
In which [tex]P_{A}[/tex] is the probability that only A happens.
[tex]P(B) = P_{B} + P(A \cap B) = P_{B} + 0.15[/tex]
To find P(B), first we have to find [tex]P_{B}[/tex], that is the probability that only B happens.
Finding [tex]P_{B}[/tex]:
The problem states that P(A OR B) = 0.65. This is the probability that at least one of this events happening. Mathematically, it means that:
[tex]1) P_{A} + P(A \cap B) + P_{B} = 0.65[/tex]
The problem states that P(A) = 0.5 and [tex]P(A \cap B) = 0.15[/tex]. So we can find [tex]P_{A}[/tex].
[tex]P(A) = P_{A} + P(A \cap B)[/tex]
[tex]0.5 = P_{A} + 0.15[/tex]
[tex]P_{A} = 0.35[/tex]
Replacing it in equation 1)
[tex]P_{A} + P(A \cap B) + P_{B} = 0.65[/tex]
[tex]0.35 + 0.15 + P_{B} = 0.65[/tex]
[tex]P_{B} = 0.65 - 0.35 - 0.15[/tex]
[tex]P_{B} = 0.15[/tex]
Since
[tex]P(B) = P_{B} + P(A \cap B)[/tex]
[tex]P(B) = 0.15 + 0.15[/tex]
[tex]P(B) = 0.30[/tex]
The probability is 1% that an electrical connector that is kept dry fails during the warranty period. If the connector is ever wet, the probability of a failure during the warranty period is 5%. If 90% of the connectors are kept dry and 10% are wet, what proportion of connectors fail during the warranty period?
Answer:
A 1.4% of the total connectors are expected to fail during the warranty period.
Step-by-step explanation:
Let's assume a population of 1000 connectors (to make the math easiest) and let's analize the dry connectors.
Of the 1000 connectors, 900 are kept dry. and of that number, 9 are the ones that fails during the warranty period. (90% of 1000 is 900. 1% of 900 is 9)
Of the 1000 connectors, 100 are wet. And of that number, 5 are connectors that will fail during the warranty period. (10% of 1000 is 100, and 5% of 100 is 5)
So overall we have 14 connectors that will fail from 1000 connectors.
That is a 1.4% of the total samples.
An elementary school class polled 198 people at a shopping center to determine how many read the Daily News and how many read the Sun Gazette. They found the following information: 171 read the Daily News, 40 read both, and 18 read neither. How many read the Sun Gazette?
Answer: 49 people
Step-by-step explanation:
First you need to separate the people that read both from the people that read the daily news. Do this by subtracting 171 - 40 = 131.
Now you can subtract the total amount of people that only read the Daily Mews from the total amount of people polled (198-131=67)
From here you need to subtract the amount of people that read neither from the remaining total. (67-18=49)
this is where you get the 49 people out of 198 that read the Sun Gazette
The number of people who read the Sun Gazette is calculated by subtracting the number of people who only read the Daily News and those who read neither from the total polled. The result is 49 Sun Gazette readers.
Explanation:This problem involves the mathematics concept of set theory, specifically union and intersection of sets. Here, the total number of people polled are considered as the 'Universal Set'. The 'Daily News readers' and the 'Sun Gazette readers' are the two subsets of this Universal set.
The data given can be interpreted as follows:
Total number of people surveyed (universal set) = 198 Number of people who read the Daily News = 171 Number of people who read both newspapers = 40 Number of people who read neither = 18
Since 40 people read both, they are being counted twice in the 171 (Daily News readers) figure. Hence, we subtract 40 from 171.
The number of people who only read the Daily News = 171 - 40 = 131
We subtract this number and those who read neither from the total polled to find the number of Sun Gazette readers.
The number of Sun Gazette readers = 198 - 131 (only Daily News readers) - 18 (neither) = 49 Sun Gazette readers
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let f(x) be a func. satisfying f(-x)=f(x) for all real x.if f"(x) exist, find its value.
Answer:
[tex]f''(x)=f''(-x)[/tex]
Step-by-step explanation:
A function satisfying the equation [tex]f(x)=f(-x)[/tex] is said to be an even function. This denomination comes from the fact that the same relation is satisfied for functions of the form [tex]x^{n}[/tex] with [tex]n[/tex] even. Observe that if [tex]f[/tex] is twice differentiable we can derivate using the chaing rule as follows:
[tex]f(x)=f(-x)[/tex] implies [tex]f'(x)=f'(-x)\cdot (-1)=-f'(-x)[/tex]
Applying the chain rule again we have:
[tex]f'(x)=-f'(-x)[/tex] implies [tex]f''(x)=-f''(-x)\cdot (-1)=f''(-x)[/tex]
So we have that function [tex]f''(x)[/tex] is also an even function.
Determine all values of h and k for which the system S 1 -3x - 3y = h -4x + ky = 10 has no solution. k= ht
Answer:
The system will have no solution when [tex]k = -4[/tex] and [tex]h \neq 7.5[/tex].
Step-by-step explanation:
We can find these values by the Gauss-Jordan Elimination method.
The Gauss-Jordan elimination method is done by transforming the system's augmented matrix into reduced row-echelon form by means of row operations.
We have the following system:
[tex]-3x - 3y = h[/tex]
[tex]-4x + ky = 10[/tex]
This system has the following augmented matrix:
[tex]\left[\begin{array}{ccc}-3&-3&h\\-4&k&10\end{array}\right][/tex]
The first thing i am going to do is, to help the row reducing:
[tex]L_{1} = -\frac{L_{1}}{3}[/tex]
Now we have
[tex]\left[\begin{array}{ccc}1&1&-\frac{h}{3}\\-4&k&10\end{array}\right][/tex]
Now I want to reduce the first row, so I do:
[tex]L_{2} = L_{2} + 4L_{1}[/tex]
So:
[tex]\left[\begin{array}{ccc}1&1&-\frac{h}{3}\\0&k+4&10 - \frac{4h}{3}\end{array}\right][/tex]
From the second line, we have
[tex](k+4)y = 10- \frac{4h}{3}[/tex]
The system will have no solution when there is a value dividing 0, so, there are two conditions:
[tex]k+4 = 0[/tex] and [tex]10 - \frac{4h}{3} \neq 0[/tex]
[tex]k+4 = 0[/tex]
[tex]k = -4[/tex]
...
[tex]10 - \frac{4h}{3} \neq 0[/tex]
[tex]\frac{4h}{3} \neq 10[/tex]
[tex]4h \neq 30[/tex]
[tex]h \neq \frac{30}{4}[/tex]
[tex]h \neq 7.5[/tex]
The system will have no solution when [tex]k = -4[/tex] and [tex]h \neq 7.5[/tex].
Counting 5-card hands from a deck of standard playing cards. A 5-card hand is drawn from a deck of standard playing cards. How many 5-card hands have at least one club? (b) Hown -card hands have at least two cards with the same rank?
Answer:
5-card hands with at least one club: [tex] {52 \choose 5}-{39 ]choose 5}[/tex]
5-card hands with at least two cards of the same rank: [tex]{52 \choose 5}-{13 \choose 5}4^5[/tex]
Step-by-step explanation:
To determine how many 5-card hands have at least one club, we can count how many do NOT have at least one club, and then subtract that from the total amount of 5-card hands that there are.
A 5-card hand that doesn't have at least one club, is one whose 5 cards are from spades,hearts or diamonds. Since a standard deck of cards has 13 clubs, 39 of the cards are spades, hearts of diamonds. Getting a 5-card hand out of those cards, is choosing 5 cards out of those 39 cards. So there are [tex] {39 \choose 5}[/tex] 5-card hands without any clubs.
The total amount of 5-card hands is [tex]{52 \choose 5}[/tex], since a 5-card hand is simply a group of 5 cards out of the full deck, which has 52 cards.
Therefore the number of 5-card hands that have at least one club is [tex] {52 \choose 5}-{39 \choose 5}[/tex].
To determine how many 5-card hands have at least two cards with the same rank we can follow the same approach. We determine how many 5-card hands have NO cards with the same rank, and the subtract that out of the total amount of 5-card hands.
A 5-card hand that doesn't have cards of the same rank, is a group of 5 cards all from different ranks. Such hand can be made then by choosing first which 5 different ranks are going to be present in the hand, out of the 13 available ranks. So there are [tex] {13 \choose 5}[/tex] possible combinations of ranks. Then, choosing which card from each of the chosen ranks is the one that is going to be in the hand, is choosing which of 4 cards from EACH rank is going to be in the hand. So for each rank there are 4 availble choices, and so there are [tex]4^5[/tex] possible ways to choose the specific cards from each rank that will be in the hand. So the amount of 5-card hands with all ranks different is [tex] {13 \choose 5}\cdot{4^5}[/tex]
Therefore the amount of 5-card hands with at least two cards with the same rank is [tex]{52 \choose 5}-{13 \choose 5}\cdot4^5[/tex]
Answer:
b
Step-by-step explanation:
Mark the statement either true (in all cases) or false (for at least one example). If false, construct a specific example to show that the statement is not always true. Such an example is called a counterexample to the statement. If the statement is true, give a justification. If v1,…,v4 are in R4 and {v1,v2,v3} is linearly dependent then {v1,v2,v3,v4} is also linearly dependent.
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
(A) True. Because v3 = 2v1 + v2, v4 must be the zero vector. Thus, the set of vectors is linearly dependent.
(B) True. The vector v3 is a linear combination of v1 and v2, so at least one of the vectors in the set is a linear combination of the others and set is linearly dependent.
(C) True. If c1 =2, c2 = 1, c3 = 1, and c4 = 0, then c1v1 + ........... + c4v4 =0. The set of vectors is linearly dependent.
(D) False. If v1 = __, v2 =___, v3 =___, and v4 = [1 2 1 2], then v3 = 2v1 + v2 and {v1, v2, v3, v4} is linearly independent.
Answer with Step-by-step explanation:
We are given that [tex]v_1,v_2,..,v_4[/tex] are in [tex]R^4[/tex] and [tex]v_1,v_2,v_3[/tex] is linearly dependent then {v_1,v_2,v_3,v_4}[/tex] is also linearly dependent.
We have to find that given statement is true or false.
Dependent vectors:Dependent vectors are those vectors in which atleast one vector is a linear combination of other given vectors.
Or If we have vectors [tex]x_1,x_2,....x_n[/tex]
Then their linear combination
[tex]a_1x_1+a_2x_2+.....+a_nx_n=0[/tex]
There exist at least one scalar which is not zero.
If [tex]v_1,v_2,v_3[/tex] are dependent vectors then
[tex]a_1v_1+a_2v_2+a_3v_3=0[/tex] for scalars [tex]a_1,a_2,a_3[/tex]
Then , by definition of dependent vectors
There exist a vector which is not equal to zero
If vector [tex]v_3[/tex] is a linear combination of [tex]v_1\;and \;v_2[/tex], So at least one of vectors in the set is a linear combination of others and the set is linearly dependent.
Hence, by definition of dependent vectors
{[tex]v_1,v_2,v_3,v_4[/tex]} is linearly dependent.
Option B is true.
need help with algebra 1 make an equation with variables on both sides number 21
Answer:
engineering vs business: 3 yearsengineering vs biology: 8 yearsStep-by-step explanation:
Write expressions for the number of students in each major. Then write the equation needed to relate them the way the problem statement says they are related.
For year y, the number of students in each major is ...
engineering: 120 +22ybusiness: 105 -4ybiology: 98 +6y1) Engineering is twice Business:
120 +22y = 2(105 -4y) . . . . . Engineering is double Business in year y
120 +22y = 210 -8y . . . . . . . eliminate parentheses
120 +30y = 210 . . . . . . . . . . add 8y
4 + y = 7 . . . . . . . . . . . . . . . . divide by 30
y = 3 . . . . . . . . subtract 4
In 3 years there will be 2 times as many students majoring in Engineering than in Business.
__
2) Engineering is twice Biology:
120 +22y = 2(98 +6y) . . . . Engineering is double Biology in year y
120 +22y = 196 +12y . . . . . eliminate parentheses
120 +10y = 196 . . . . . . . . . . subtract 12y
10y = 76 . . . . . . . . . . . . . . . .subtract 120
y = 7.6 . . . . . . divide by 10
In 8 years there will be 2 times as many students majoring in Engineering than in Biology.
Let f and g be decreasingfunctions for all real numbers. Prove
that f o g isincreasing.
Answer with Step-by-step explanation:
We are given that two functions f and g are decreasing function for all real numbers .
We have to prove that fog is increasing.
Increasing Function: If [tex]x_1 \leq x_2[/tex]
Then, [tex]f(x_1)\leq f(x_2)[/tex]
Decreasing function: if [tex]x_1\leq x_2[/tex]
Then, [tex]f(x_1)\geq f(x_2)[/tex]
Suppose [tex]f(x)=-x[/tex]
[tex]g(x)=-2x[/tex]
fog(x)=f(g(x))=f(-2x)=-(-2x)=2x
Therefore, f and g are decreasing function for all real numbers then fog is increasing.
Hence, proved
What are the odds of choosing a red marble from a bag that contains two blue marbles, one green marble and four red marbles?
4:3
4:7
3:4
7:4
Answer:
4:3
Step-by-step explanation:
You count up all the red marbles which equals 4 and put them on one side, then you add up all the rest of the marbles same color or not which equals 3 and put it on the other side of the 4
the age of Jane is 80% of the age of Alice. If we add both ages the result is 45. Find the age of Jane and Alice
Answer:
Age of Alice=25 years
Age of Jane=20 years
Step-by-step explanation:
We are given that the age of Jane is 80 % of the age Alice.
We have to find the age of Jane and Alice.
Let x be the age of Alice
According to question
Age of Jane=80% of Alice=80% of x=[tex]\frac{80}{100}\times x=\frac{4x}{5}[/tex]
[tex]x+\frac{4x}{5}=45[/tex]
[tex]\frac{5x+4x}{5}=45[/tex]
[tex]\frac{9x}{5}=45[/tex]
[tex]x=\frac{45\times 5}{9}=25[/tex]
Age of Alice=25 years
Age of Jane=[tex]\frac{4}{5}\times 25=20 years[/tex]
Age of Jane=20 years
Suppose A is a 3 x 3 matrix such that det (A) = 9. Prove det (3 (A-!') is equal to 3
Answer: The proof is done below.
Step-by-step explanation: Given that A is a 3 x 3 matrix such that det (A) = 9.
We are to prove the following :
[tex]det(3A^{-1})=3.[/tex]
For a non-singular matrix B of order n, we have two two properties of its determinant :
[tex](i)~det(B^{-1})=\dfrac{1}{det(B)},\\\\\\(ii)~det(kB)=k^ndet(B),~\textup{k is a scalar.}[/tex]
Therefore, we get
[tex]det(A^{-1})=\dfrac{1}{det(A)}=\dfrac{1}{9},[/tex]
and so,
[tex]det(3A^{-1})~~~~~~~[\textup{since A is of order 3}]\\\\=3^3det(A^{-1})\\\\=27\times\dfrac{1}{9}\\\\=3.[/tex]
Hence proved.
The vector y = ai + bj is perpendicular to the line ax + by = c. Use this fact to find an equation of the line through P perpendicular to v. Then draw a sketch of the line including v as a vector starting at the origin. P(-1,-9)v = -4i + j The equation of the line is _____.
Answer:
[tex]-4x+y=-5[/tex]
Step-by-step explanation:
It is given that he vector y = ai + bj is perpendicular to the line ax + by = c.
Given given point is P(-1,-9) and given vector is v = -4i + j.
Here, a = -4 and b= 1.
We need to find the equation of the line through P perpendicular to v.
Using the above fact, the vector v = -4i + j is perpendicular to the line
[tex](-4)x+(1)y=c[/tex]
[tex]-4x+y=c[/tex] ... (1)
The line passes through the point (-1,-9).
Substitute x=-1 and y=-9 in the above equation to find the value of c.
[tex]-4(-1)+(-9)=c[/tex]
[tex]4-9=c[/tex]
[tex]-5=c[/tex]
The value of c is -5.
Substitute c=-5 in equation (1).
[tex]-4x+y=-5[/tex]
Therefore the equation of line which passes through P and perpendicular to v is -4x+y=-5.
Triphasil-28 birth control tablets are taken sequentially, 1 tablet per day for 28 days, with the tablets containing the following: Phase 1: 6 tablets, each containing 0.050 mg of levonorgestrel and 0.030 mg ethinyl estradiol Phase 2: 5 tablets, each containing 0.075 mg of levonorgestrel and 0.040 mg ethinyl estradiol Phase 3: 10 tablets, each containing 0.125 mg of levonorgestrel and 0.030 mg ethinyl estradiol Then 7 inert tablets (no drug). How many total milligrams each of levonorgestrel and ethinyl estradiol are taken during the 28-day period?
Over the 28-day cycle of taking Triphasil-28 birth control tablets, a total of 1.925 mg of levonorgestrel and 0.680 mg of ethinyl estradiol are consumed.
Explanation:The Triphasil-28 birth control tablets are taken in a sequence of 21 active pills containing hormones and 7 inactive pills (placebos). To calculate the total amount of levonorgestrel and ethinyl estradiol consumed over the 28-day period, each phase needs to be taken into account.
In phase 1, there are 6 tablets each with 0.050 mg of levonorgestrel and 0.030 mg ethinyl estradiol. So, 6 tablets * 0.050 mg = 0.300 mg of levonorgestrel and 6 tablets * 0.030 mg = 0.180 mg of ethinyl estradiol.
In phase 2, there are 5 tablets each with 0.075 mg of levonorgestrel and 0.040 mg ethinyl estradiol. So, 5 tablets * 0.075 mg = 0.375 mg of levonorgestrel and 5 tablets * 0.040 mg = 0.200 mg of ethinyl estradiol.
In phase 3, there are 10 tablets each with 0.125 mg of levonorgestrel and 0.030 mg ethinyl estradiol. So, 10 tablets * 0.125 mg = 1.250 mg of levonorgestrel and 10 tablets * 0.030 mg = 0.300 mg of ethinyl estradiol.
Adding up all the quantities, we have a total of 0.300 mg + 0.375 mg + 1.250 mg = 1.925 mg of levonorgestrel and 0.180 mg + 0.200 mg + 0.300 mg = 0.680 mg of ethinyl estradiol consumed over the 21 active days of the 28-day cycle.
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A survey of 255 adults found that during the last year, 40 traveled by plane but not by train, 75 traveled by train but not by plane, 50 traveled by bus but not by plane or by train, 55 traveled by bus and plane, 35 traveled by all three, and 170 traveled by plane or train. How many did not travel by any of these modes of transportation?
Answer:
35 people did no travel by any of those modes of transportation.
Step-by-step explanation:
Reviewing the groups described, we can see there are 170 that traveled by either plane or train and 50 traveled by bus, but not plane or train.
This means that the 50 people that traveled by bus are not included in the group of 170 that used either plane or train.
Since those two groups include people that used bus (50 people) and people that used either plane or train (170 people), the union of these two sets include all the people that used at least one of the tree modes of transportation mentioned (bus, plane or train).
The result of the union between these two sets is 50+170=220 people which travel by at least one of those modes of transportation.
Since the total number of surveyed adults is 255, the number of people that did not travel by any of these modes of transportations is 255-220=35 people.
In what type quadrilateral are the diagonals NOT
alwayscongruent to each other?
Answer:
Parallelogram.Rhombus.Trapezoid.Kite.Step-by-step explanation:
There are six basic types of quadrilaterals:
Rectangle. Square. Parallelogram. Rhombus. Trapezoid and isosceles trapezoid. Kite.Then we have:
Quadrilaterals with NOT ALWAYS congruent diagonals:
Parallelogram.Rhombus.Trapezoid.Kite.Quadrilaterals with ALWAYS congruent diagonals:
Rectangle.Square.Isosceles trapezoid.Show your work:
Express 160 pounds (lbs) in kilograms (kg). Round to the nearest hundredths.
Step-by-step explanation:
.454 kilograms= 1 pound.
Multiply .454 by 160
4.54
160
--------
000
2724 0<--Place marker
45400<--Double Place Marker
- - - - - - - -
72640 <-- Add
To find decimal point, count decimal place (Number of digits after the decimal on both numbers you multiply together) In this case, it's 2 ( 5 and 4 in 4.54) So, you count two spaces from right to left in your answer and tah dah!
72.640 (Zero isn't needed- just a placemarker)
Hope I was helpful :)
A physician prescribes 2.5 million units of penicillin G potassium daily for 1 week. If 1 unit of penicilin G potassium equals 0.6 mcg, how many tablets, each containing 250 mg, will provide the prescribed dosage regimen un
If a physician prescribes 2.5 million units of penicillin G potassium daily for 1 week. To provide the prescribed dosage regimen of 2.5 million units of penicillin G potassium daily for 1 week we would need 42 tablets, each containing 250 mg.
What is the Number of tablets needed ?
Total amount of penicillin G potassium required
Since there are 7 days in a week the total amount required is:
Total amount required =2.5 million units/day * 7 days
Total amount required = 17.5 million units
Convert the units of penicillin G potassium to micrograms (mcg)
Total amount required in micrograms:
Total amount required = 17.5 million units * 0.6 mcg/unit
Total amount required = 10.5 million mcg
Convert micrograms to milligrams (mg)
Convert the total amount required to milligrams:
10.5 million mcg / 1000
= 10,500 mg
The number of tablets needed:
Number of tablets needed:
Number of tablets needed = 10,500 mg / 250 mg/tablet
Number of tablets needed = 42 tablets
Therefore to provide the prescribed dosage regimen of 2.5 million units of penicillin G potassium daily for 1 week we would need 42 tablets, each containing 250 mg.
The patient needs to take 42 tablets of penicillin G potassium over one week. This is determined by converting the prescribed units to milligrams and dividing by the tablet dosage.
Calculating Dosage of Penicillin G Potassium
To determine how many tablets of penicillin G potassium are needed, we need to go through several steps of unit conversion.
Convert units to micrograms (mcg):Therefore, the patient needs to take 42 tablets over the course of one week.
Let p, q, and r represent the following statements"
p : Sam has pizza last night.
q : Chris finished her homework
. r : Pat watched the news this morning.
Give a formula (using appropriate symbols) for each of these statements:
a) Sam had pizza last night if and only if Chris finished her homework.
b) Pat watched the news this morning iff Sam did not have pizza last night.
c) Pat watched the news this morning if and only if Chris finished her homework and Sam did not have pizza last night.
d) In order for Pat to watch the news this morning, it is necessary and sufficient that Sam had pizza last night and Chris finished her homework. Express in words the statements represented by the following fomulas.
e) q ⇔ r
f) p ⇔ (q ∧ r)
g) (¬p) ⇔ (q ∨ r)
h) r ⇔ (p ∨ q)
In logic, own symbols are used in order to be able to represent the relations between propositions in a general and independent way to the proposition, in order to be able to find the relationship process that operates in the communicated message, the propositional logic.
For this purpose there are, among others, the following logical operators: conjunction (and) ∧, disjunction (or) ∨, denial (not) ¬, conditional (if - then) ⇒ and double conditional (if and only if, iff) ⇔.
So for this case we have:
Answer
a) Sam had pizza last night if and only if Chris finished her homework.
p⇔q
b) Pat watched the news this morning iff Sam did not have pizza last night.
r⇔¬p
c) Pat watched the news this morning if and only if Chris finished her homework and Sam did not have pizza last night.
r⇔(q∧¬p)
d) In order for Pat to watch the news this morning, it is necessary and sufficient that Sam had pizza last night and Chris finished her homework.
r⇔(p∧q)
e) q ⇔ r
Chris finished his homework if and only if Pat watched the news this morning
f) p ⇔ (q ∧ r)
Sam had pizza last night if and only if Chris finished his homework and Pat watched the news this morning
g) (¬p) ⇔ (q ∨ r)
Sam didn't have pizza last night if and only if Chris finished his homework or Pat watched the news this morning
h) r ⇔ (p ∨ q)
Pat watched the news this morning if Sam had pizza last night or Chris finished his homework
Simplify this expression. -12 - 3 • (-8 +(-4)^2 - 6) + 2
Answer
-16
Step By Step explanation
Answer:
[tex] - 12 - 3 \times ( - 8 + ( { - 4)}^{2} - 6) + 2[/tex]
[tex] - 12 - 3 \times ( - 8 + 16 - 6) + 2[/tex]
[tex] - 12 - 3 \times (8 - 6) + 2[/tex]
[tex] - 12 - 3 \times 2 + 2[/tex]
[tex] - 12 - 6 + 2[/tex]
[tex] - 12 - 4[/tex]
[tex] - 16[/tex]
Evaluate the problem below. Please show all your work for full credit. Highlight or -4 1/2+5 2/3
Answer:
[tex]\frac{7}{6}[/tex]
Step-by-step explanation:
[tex]-4\frac{1}{2} + 5\frac{2}{3} =[/tex]
For the first term you have to multiply 2x(-4) and add 1, for the second term you have to multiply 3x5 and add 2.
[tex]\frac{2(-4)+1}{2} + \frac{3(5)+2}{3} =[/tex]
[tex]-\frac{9}{2} +\frac{17}{3} =[/tex]
Now you need to find the lowest common multiple between the denominators, just cross multiply as it is shown:
[tex]-\frac{9}{2} (\frac{3}{3} )+\frac{17}{3} (\frac{2}{2} )=[/tex]
[tex]-\frac{27}{6} +\frac{34}{6} = \frac{7}{6}[/tex]
finally you get the result by doing a substraction = 7/6, or 1[tex]\frac{1}{6}[/tex]
Five-year-old students at an elementary school were given a 30-yard head start in a race. The graph shows how far the average student ran in 30 seconds.
Age of Runner
Which statement best describes the domain of the function represented in the graph?
55X 560, orx is from 5 to 60
55x5 30. or x is from 5 to 30
30 SXS 60, or x is from 30 to 60
0 SXS 30 or x is from 0 to 30
The domain of the function represented in the graph is 30 SXS 60 or 30 to 60. Hence option C is correct.
Given that,
Five-year-old students at an elementary school were involved.
They were given a 30-yard head start in a race.
The graph represents the distance run by the average student in 30 seconds.
The graph is related to the age of the runner.
Since we can see that,
The graph starts from 30 yards and ends at 60 yards
Therefore,
The domain of the function represented in the graph is 30 SXS 60 or 30 to 60, which is option C.
To learn more about graph of function visit:
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(a) Find an example of sets A and B such that An B = {1,2} and AUB = {1,2,3,4,5).
(b) Find an example of sets A and B such that A Ç B and A e B.
Answer:
(a) Set A = {1,2,3}
Set B = {1,2,4,5}
(b) Set A Ç B = {1,2}
Set A e B = {1,2}
Step-by-step explanation:
As per the question,
Given data :
A ∪ B = read as A union B = {1,2,3,4,5}
A ∩ B = read as A intersection B = {1,2}
(a) An example of sets A and B such that A ∩ B = {1,2} and A U B = {1,2,3,4,5).
So, first draw the Venn-diagram, From below Venn diagram, One of the possibility for set A and set B is:
Set A = {1,2,3}
Set B = {1,2,4,5}
(b) An example of sets A and B such that A Ç B and A e B,
Set A Ç B read as common elements of set A in Set B.
Therefore,
Set A Ç B = {1,2}
Set A e B implies that which element/elements of A is/are present in set B.
Therefore,
Set A e B = {1,2}
Machine A can produce 435 widget in 3 hours. At this rate how many widget can machine A produce in 7 hours?
Answer:
1015 widgets
Step-by-step explanation:
First investigate how many widgets can machine A produce in 1 hour:
If it produces 435 in 3 hours, then it will produce one third of that in one hour:
In ONE (1) hour [tex]\frac{435}{3} = 145[/tex] widgets
Therefore in seven (7) hours it will produce seven times the amount it does in one hour, that is:
[tex]145 * 7 = 1015[/tex] widgets
Answer:
answer is 1015.
Step-by-step explanation:
Use the graph below to determine the number of solutions the system has.
Answer:
one
Step-by-step explanation:
I think, there were 4 lines and the two lines are reaching each other
Find all solutions of the equation algebraically. Use a graphing utility to verify the solutions graphically. (Enter your answers as a comma-separated list.) 16x^4 - 24x^3 +9x^2 =0
Answer:
The solutions of the equation are 0 and 0.75.
Step-by-step explanation:
Given : Equation [tex]16x^4 - 24x^3 +9x^2 =0[/tex]
To find : All solutions of the equation algebraically. Use a graphing utility to verify the solutions graphically ?
Solution :
Equation [tex]16x^4 - 24x^3 +9x^2 =0[/tex]
[tex]x^2(16x^2-24x+9)=0[/tex]
Either [tex]x^2=0[/tex] or [tex]16x^2-24x+9=0[/tex]
When [tex]x^2=0[/tex]
[tex]x=0[/tex]
When [tex]16x^2-24x+9=0[/tex]
Solve by quadratic formula, [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-(-24)\pm\sqrt{(-24)^2-4(16)(9)}}{2(16)}[/tex]
[tex]x=\frac{24\pm\sqrt{0}}{32}[/tex]
[tex]x=\frac{24}{32}[/tex]
[tex]x=\frac{3}{4}[/tex]
[tex]x=0.75[/tex]
The solutions of the equation are 0 and 0.75.
For verification,
In the graph where the curve cut x-axis is the solution of the equation.
Refer the attached figure below.
Draw the top view of this
figure.
find the area of a rectangle with the given base and height
5ft,6 in
Answer:
360 inch
Step-by-step explanation:
Step 1: Converting
6inch = 6inch
5ft = 60inch
Step 2: Finding the area
Area of a rectangle = L x B
A = 6 x 60
A = 360inch
The final exam of a particular class makes up 40% of the final grade, and Moe is failing the class with an average (arithmetic mean) of 45% just before taking the final exam. What grade does Moe need on his final exam in order to receive the passing grade average of 60% for the class?
Answer:
%82.5
Step-by-step explanation:
The final exam of a particular class makes up 40% of the final gradeMoe is failing the class with an average (arithmetic mean) of 45% just before taking the final exam.From point 1 we know that Moe´s grade just before taking the final exam represents 60% of the final grade. Then, using the information in the point 2 we can compute Moe´s final grade as follows:
[tex]FG=0.40*FE+0.60*0.45[/tex],
where FG is Moe´s Final Grade and FE is Moe´s final exam grade. Then,
[tex]\frac{ FG-0.60*0.45}{0.40}=FE[/tex].
So, in order to receive the passing grade average of 60% for the class Moe needs to obtain in his exam:
[tex]FE=\frac{ 0.60-0.60*0.45}{0.40}=0.825[/tex]
That is, he need al least %82.5 to obtain a passing grade.