Answers
g(-1) = -1
g(3) = Undefined
Related Questions
The additive inverse of x/y is
Answers
Answer
The additive inverse is
-x/-y
That is equal to x/y
hope this may help you
In a survey, 205 people indicated they prefer cats, 160 indicated they prefer dots, and 40 indicated they don’t enjoy either pet. Find the probability that if a person is chosen at random, they prefer cats
Answers
Answer: probability = 0.506
Step-by-step explanation:
The data we have is:
Total people: 205 + 160 + 40 = 405
prefer cats: 205
prefer dogs: 160
neither: 40
The probability that a person chosen at random prefers cats is equal to the number of people that prefer cats divided the total number of people:
p = 205/405 = 0.506
in percent form, this is 50.6%
Given a right triangle with a hypotenuse length of radical 26 and base length of 3. Find the length of the other leg (which is also the height).
Answers
Answer:
√17
Step-by-step explanation:
The Pythagorean theorem can be used for the purpose.
hypotenuse² = base² +height²
(√26)² = 3² +height²
26 -9 = height²
height = √17
The length of the other leg is √17.
Find the length of UC
Answers
Answer: 25 units
Step-by-step explanation:
Simply do 40(UN)-15(CN) to get 25(UC)
Hope it helps <3
Answer:
25Option D is the correct option
Solution,
Here,
UN = 40
CN = 15
Now,
UN = UC + CN
plugging the values,
40 = UC + 15
-UC = 15 - 40
-UC = -25
The difference sign (-) will be cancelled in both sides:
UC = 25
hope this helps...
Good luck on your assignment..
I got the answer but I really don’t know if it’s correct or not, please help this is due today
Answers
Explanation: 180-52 = 128
So we have an equation:
2^3x+1=128 ( cuz they are in the same position)
Now we need to find what number that 2 raise to the power of that number is 128
And the answer is 2^7=128
Let’s go back to our equation:
2^3x+1=128
And we know that 2^7=128
Now we just have to make 3x+1=7:
3x+1=7
x=(7-1)/3
x=2
And there you have it x=2
Evaluate the expression (image provided). A.) 1.5 B.) 6 C.) 6^15 D.) 1.5^6
Answers
Answer:
1.5
Step-by-step explanation:
6 to the log base of 6 will be one (they essentially cancel each other out, log is the opposite of exponents) and we are left with 1.5.
What is the complete factorization of x^2+4x-45?
Answers
Answer:(x-5)(x+9)
Step-by-step explanation:
You want two numbers that can give you -45 in multiplication and two numbers that can add to 4 and that is -5 and 9.
Answer: (x - 5)(x + 9)
If you have to solve, x=5 or x= -9
Step-by-step explanation: You need two numbers that multiply to be 45.
(could be 3 × 15 or 5 × 9) . The difference between the two factors needs to be 4, the coefficient of the middle term.
9 - 5 =4, so use those. -45 has a negative sign, so one of the factors must be + and the other - Since the 4 has the + sign, the larger factor has to be + so the difference will be positive.
So (x -5)(x + 9) are your factors. You can FOIL to be sure
x × x += x² . x × 9 = 9x . -5 × x = -5x . -5 × 9 = -45 .
Combine the x terms: 9x -5x = +4x
Prepare the journal entries on December 31, 2019, for the 40 extended contracts (the first year of the revised 3-year contract).
Answers
This is not the complete question, the complete question is:
P18-1 (LO2,3) (Allocate Transaction Price, Upfront Fees)
Tablet Tailors sells tablet PCs combined with Internet service, which permits the tablet to connect to the Internet anywhere and set up a Wi-Fi hot spot. It offers two bundles with the following terms.
1. Tablet Bundle A sells a tablet with 3 years of Internet service. The price for the tablet and a 3-year Internet connection service contract is $500. The standalone selling price of the tablet is $250 (the cost to Tablet Tailors is $175). Tablet Tailors sells the Internet access service independently for an upfront payment of $300. On January 2, 2017, Tablet Tailors signed 100 contracts, receiving a total of $50,000 in cash.
2. After 2 years of the 3-year contract, Tablet Tailors offers a modified contract and extension incentive. The extended contract services are similar to those provided in the first 2 years of the contract. Signing the extension and paying $90 (which equals the standalone selling of the revised Internet service package) extends access for 2 more years of Internet connection. Forty Tablet Bundle A customers sign up for this offer.
INSTRUCTION
a) Prepare the journal entries when the contract is signed on January 2, 2019, for the 40 extended contracts. Assume the modification does not result in a separate performance obligation.
b) Prepare the journal entries on December 31, 2019, for the 40 extended contracts (the first year of the revised 3-year contract).
Answer:
Step-by-step explanation:
(A)
Date Particulars Debit Credit
2-Jan-19 Cash 3600
Unearned Service Revenue 3600
40 * 90 = 3600
services in the extended period are the same as the services that were provided in the original contract period. As they are not distinct hence the modifications will be considered as part of the original contract.
(B)
Date Particulars Debit Credit
31-Dec-19 Unearned Service Revenue 2413
Service revenue 2413
internet = 300, price = 550, connection service = 500
(300/550) * 500 = 273
so
Original internet service contract = 40 * 273 = 10,920
Revenue recognized in 1st two years = 10,920 * 2/3 = 7280
Remaining service at original rates = 10920 - 7280 = 3640
Extended service = 3600
3640 + 3600 = $7240
7240 / 3 = $2413
A metal alloy is 27% copper. Another metal alloy is 52% copper. How much of each should be used to make 22 g of an alloy that is 36.09% copper?
Answers
Answer:
14.0008 grams of 27% and 7.9992 grams of 52%
Step-by-step explanation:
We know that in the end we want 22 grams of 36.09% copper, meaning in the end we want 36.09% of the 22 grams to be copper. This means we can multiply 36.09% by 22 to see how much copper we want in the end.
To find out how much of each alloy to use, we can multiply the percentage of copper in the alloy be a variable x, which will be how much of that alloy we use. For the other alloy, we can multiply the percentage by (22-x) grams as we know in the end we want 22 grams and if x+y=22, than y would equal 22-x, and in this case this simplifies it to only use a single variable.
Now finally, making the equation we get 27x+52(22-x)=36.09(22). We can solve this and get 27x+1144-52x=793.98, then combine like terms and get -25x+1144=793.98. Next you have to subtract 1144 from both sides to get -25x=-350.02. Dividing both sides by -25 we get x=14.0008. This is how many grams of 27% copper was used. Now we can subtract this from 22 to get how much 52% copper was used, and we get 22-14.0008=7.9992 grams of 52% copper.
Figure B is a scaled copy of Figure A.
What is the scale factor from Figure A to Figure B?
Please answer fast!!!!
Answers
Answer:
4
Step-by-step explanation:
We are told that figure B is a scaled copy of B, which means figure A was enlarged by a certain scale factor to get a similar figure as A, now referred to as figure B.
The scale factor = ratio of any two corresponding sides of both similar figures.
Thus,
Scale factor of the similar figures given = 40/10 = 4.
This means that, figure A was scaled up by 4 times its original size to get figure B. Each side of figure B is 4 × the corresponding side in figure A.
Scale factor = 4
2{ 3[9 + 4(7 -5) - 4]}
Answers
Answer:
2{3[9+4(7-5)-4]}
2{3[9+4(2)-4]}
2{3[13(2)-4]}
2{3[26-4]}
2{3[22]}
2{66}
132
Step-by-step explanation:
I need help urgent plz someone help me solved this problem! Can someone plz help I’m giving you 10 points! I need help plz help me! Will mark you as brainiest!
Answers
Step-by-step explanation:
Log T = 11.8 + 1.5.M (with T is the amount of energy released by the earthquake, Log refers to the logarithm to the base 10)
-->T = [tex]10^{11.8 +1.5*6.5}[/tex] ≈3.458 *[tex]10^{21}[/tex]
Answer: 2.00 x 10¹⁰⁹
Step-by-step explanation:
log T = 11.8 + 1.5M
Given: M = 6.5
log T = 11.8 + 1.5(6.5)
log T = 11.8 + 9.75
log T = 21.55
T = 10²¹⁻⁵⁵
T = 1.995 x 10¹⁰⁹
T = 2.00 x 10¹⁰⁹ rounded to the nearest hundredth
if a varies inversely as the cube root of b and a=1 when b=64, find b
Answers
Answer:
b = 64/a³
Step-by-step explanation:
Using the given information, we can only find a relation between a and b. We cannot find any specific value for b.
Since a varies inversely as the cube root of b, we have ...
a = k/∛b
Multiplying by ∛b lets us find the value of k:
k = a·∛b = 1·∛64 = 4
Taking the cube of this equation gives ...
64 = a³b
b = 64/a³ . . . . . divide by a³
The value of b is ...
b = 64/a³
If 16 student drove to school out of a class of 21, what percentage drove to school
Answers
Your answer would be 76.2% to the nearest tenth.
We can find this by first dividing 16 by 21 to get 0.7619. which is the proportion as a decimal. To convert this into a percentage, we need to multiply it by 100 to get 76.19% = 76.2% to the nearest tenth.
I hope this helps! Let me know if you have any questions :)
Simon swapped of 2/5
his 40 marbles for 9 of
Saqib's. How many has
Simon got now?
Answers
Answer:
33
Step-by-step explanation:
2/5x40=16
40-16=24
24+9=33
33 marbles
2/5 is .4
Multiply .4 by 40 to get 16
Subtract 16 from 40 to get 24
Add 9 to 24 to get 33
Hope it helps <3
(If it does, please mark brainliest, only need 1 more to get rank up :) )
Jeremy makes $57,852 per year at his accounting firm. How much is Jeremy’s monthly salary? (There are 12 months in a year.) How much is Jeremy’s weekly salary? (There are 52 weeks in a year.)
Answers
Answer:
Monthly: $4,821
Weekly: $1112.54
Step-by-step explanation:
Monthly
A monthly salary can be found by dividing the yearly salary by the number of months.
salary / months
His salary is $57,852 and there are 12 months in a year.
$57,852/ 12 months
Divide
$4,821 / month
Jeremy makes $4,821 per month.
Weekly
To find the weekly salary, divide the yearly salary by the number of weeks.
salary / weeks
He makes $57,852 each year and there are 52 weeks in one year.
$57,852 / 52 weeks
Divide
$1112.53846 / week
Round to the nearest cent. The 8 in the thousandth place tells use to round the 3 up to a 4 in the hundredth place.
$1112.54 / week
Jeremy makes $1112.54 per week
A right triangle is shown. The length of the hypotenuse is 4 centimeters and the lengths of the other 2 sides are congruent. The hypotenuse of a 45°-45°-90° triangle measures 4 cm. What is the length of one leg of the triangle? 2 cm 2 StartRoot 2 EndRoot cm 4 cm 4 StartRoot 2 EndRoot cm
Answers
Answer:
The leg measures 2 I believe
Step-by-step explanation:
Since the squares of the legs equal C ([tex]A^{2} +B^{2} = C^{2}[/tex]) the square root of 16 would be 4.
The Pythagorean theorem is a basic relationship between the three sides of a right triangle. The length of one leg of the triangle is 2√2 cm.
What is the Pythagoras theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.
[tex]\rm (Hypotenuse)^2 =(Perpendicular)^2 + (Base)^2[/tex]
Let the length of the perpendicular be x.
Given the length of the hypotenuse is 4 centimeters, while the length of the other two sides is the same, therefore, the length of the other two sides is x. Therefore, using the Pythagorus theorem we can write,
[tex]\rm (Hypotenuse)^2 =(Perpendicular)^2 + (Base)^2[/tex]
[tex]4^2 = x^2+x^2\\\\16=2x^2\\\\8=x^2\\\\x= 2\sqrt2[/tex]
Hence, the length of one leg of the triangle is 2√2 cm.
Learn more about Pythagoras Theorem:
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The lengths of adult males' hands are normally distributed with mean 190 mm and standard deviation is 7.4 mm. Suppose that 45 individuals are randomly chosen. Round all answers to 4 where possible.
What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
For the group of 45, find the probability that the average hand length is less than 189.
Find the third quartile for the average adult male hand length for this sample size.
For part b), is the assumption that the distribution is normal necessary?
Answers
Answer:
a. The distribution of the sample means is normal with mean 190 mm and standard deviation 1.1031 mm.
b. The probability that the average hand length is less than 189 is P(M<189)=0.1823.
c. The third quartile for the average adult male hand length for this sample size is M_75=190.7440.
d. The assumption of normality is not necessary as the sampling distribution will tend to have a bell shaped independently of the population distribution.
Step-by-step explanation:
We have a normal distribution, with mean 190 and standard deviation 7.4.
We take samples of size n=45 from this population.
Then, the sample means will have a distribution with the following parameters:
[tex]\mu_s=\mu=190\\\\ \sigma_s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{7.4}{\sqrt{45}}=\dfrac{7.4}{6.7082}=1.1031[/tex]
The probability that the sample mean is less than 189 can be calculated as:
[tex]z=\dfrac{M-\mu}{\sigma/\sqrt{n}}=\dfrac{189-190}{7.4/\sqrt{45}}=\dfrac{-1}{1.1031}=-0.9065\\\\\\P(M<189)=P(z<-0.9065)=0.1823[/tex]
The third quartile represents the value of the sample where 75% of the data is to the left of this value. It means that:
[tex]P(M<M^*)=0.75[/tex]
The third quartile corresponds to a z-value of z*=0.6745.
[tex]P(z<z^*)=0.75[/tex]
Then, we can calculate the sample mean for the third quartile as:
[tex]M=\mu_s+z^*\sigma_s=190+0.6745\cdot 1.1031=190+0.7440=190.7440[/tex]
The assumption of normality is not necessary as the sampling distribution will tend to have a bell shaped independently of the population distribution.
show that 7 1/2 - 4 2/3 = 2 5/6
Answers
Since the end fraction has a denominator of 6 try and multiply both of the ones on the LHS to get 6 as a denominator.
First though convert the improper fractions into fractions solely.
7 1/2 goes to 15/2
While
4 2/3 goes to 14/3
Now
15/2 multiply both numerator and denominator by 3 gives you 45/6
14/3 multiply both numerator and denominator by 2 gives you 28/6
Subtract 45/6 by 28/6= 17/6
Highest multiple of 6 in 17 is 12
12/6 + 5/6 = 2 5/6
Equation is [tex]7\frac{1}{2} -4\frac{2}{3}=2\frac{5}{6}[/tex] is true.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is [tex]7\frac{1}{2} -4\frac{2}{3}=2\frac{5}{6}[/tex]
We need to check whether the left hand side is equal to right hand side.
These are in the form pf mixed fraction we can convert them to the improper fraction.
[tex]7\frac{1}{2}=15/2[/tex]
[tex]4\frac{2}{3}=\frac{14}{3}[/tex]
So Let us subtract 24/3 from 15/2
15/2-14/3
LCM of 2 and 3 is 6
45-28/6
17/6
This can be written as mixed fraction [tex]2\frac{5}{6}[/tex]
Hence, equation is [tex]7\frac{1}{2} -4\frac{2}{3}=2\frac{5}{6}[/tex] is true.
To learn more on Equation:
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expand the linear expression 4(10x -4)
Answers
Answer:
40x - 16
Step-by-step explanation:
(see attached for reference)
By utilizing the distributive property:
4(10x -4)
= (10x)(4) -4 (4)
= 40x - 16
Answer:
4x10x= 40x -4x4=-16 40xtimes-4<-----------thats your answer
Step-by-step explanation:
The following data represent the miles per gallon for a particular make and model car for six randomly selected vehicles. Compute the mean, median, and mode miles per gallon 24.2. 22.2. 37.8, 22.7. 35 4. 31.61. Compute the mean miles per gallon. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The mean mileage per gallon is _______B. The mean does not exist 2. Compute the median miles per gallon. Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. The median mileage per gallon is __________B. The median does not exist. 3. Compute the mode miles per gallon. Select the correct choice below and, if necessary,fill in the answer box to complete your choice. A. The mode is _________B. The mode does not exist.
Answers
Answer:
A. The mean mileage per gallon is _____ 28.99__
A. The median mileage per gallon is _____27.905_____
B. The mode does not exist.
Step-by-step explanation:
Mean= Sum of values/ No of Values
Mean = 24.2 + 22.2+ 37.8+ 22.7 + 35.4 +31.61/ 6
Mean = 173.91/6= 28.985 ≅ 28.99
The median is the middle value of an ordered data which divides the data into two equal halves. For an even data the median is the average of n/2 and n+1/2 value where n is the number of values.
Rearranging the above data
22.2 , 22.7 , 24.2 , 31.61 , 35.4, 37.8
Third and fourth values are =24.2 + 31.61 = 55.81
Average of third and fourth values is = 55.81/2= 27.905
Mode is the values which is occurs repeatedly.
In this data there is no mode.
4
The equation of a circle is x2 + y2 + x + Dy+ E= 0. If the radius of the circle is decreased without changing the coordinates of the center point, how are the coefficients CD,
and E affected?
O A CD, and E are unchanged.
Answers
Answer:
Step-by-step explanation:
in x²+y²+2gx+2fy+c=0
center=(-g,-f)
radius=√((-g)²+(-f)²-c)
if center is not changed ,then c will change .
Here only coefficients of E will change.
Evaluate the expression.........
Answers
Answer:
9
Step-by-step explanation:
p^2 -4p +4
Let p = -1
(-1)^1 -4(-1) +4
1 +4+4
9
The Marine Corps is ordering hats for all the new recruits for the entire next year. Since they do not know the exact hat sizes they will use statistics to calculate the necessary numbers. This is the data from a sample of the previous recruits: 7.2, 6.8, 6, 6.9, 7.8, 6.2, 6.4, 7.2, 7.4, 6.8, 6.7, 6, 6.4, 7, 7, 7.6, 7.6, 6, 6.8, 6.4 a. Display the data in a line plot and stem-and-leaf plot. (These plots don’t need to be pretty; just make sure I can make sense of your plots.) Describe what the plots tell you about the data. b. Find the mean, median, mode, and range. c. Is it appropriate to use a normal distribution to model this data? d. Suppose that the Marine Corps does know that the heights of new recruits are approximately normally distributed with a mean of 70.5 inches and a standard deviation of 1.5 inches. Use the mean and standard deviation to fit the new recruit heights to a normal distribution and estimate the following percentages. d1. What percent of new recruits would be taller than 72 inches? d2. What percent of new recruits would be shorter than 67.5 inches? d3. What percent of new recruits would be between 69 and 72 inches? d4. Between what two heights would capture 95% of new recruits?? By using statistics are the numbers changed to whole numbers?
Answers
Answer:
60-|||
61-
62-||
62
64-|||
65
66
67-|
68-|||
69-|
70-||
71
72-||
73
74-||
75
76-||
77
78-|
This is a stem and leaf plot.
mean is 138.2/20=6.91
median of 20 is half way between 10th and 11th or an ordered plot. The 10th and the 11th are both 6.8, so that is the median.
6.4 and 6.8 are modes, but they are so minimal I would say there isn't a clear mode.
The range is 1.8, the largest-the smallest
This is not a normal distribution.
z=(x-mean) sd
a.(72-70.5)/1.5=1 so z>1 is the probability or 0.1587.
b.shorter than 67.5 inches is (67.5-70.5)/1.5 or z < = -2, and probability is 0.0228.
c.Between 69 and 72 inches is +/- 1 sd or 0.6826.
95% is 1.96 sd s on either side or +/- 1.96*1.5=+/- 2.94 interval on either side of 70.5
(67.56, 73.44)units in inches
Step-by-step explanation:
The mean monthly car payment for 123 residents of the local apartment complex is $624. What is the best point estimate for the mean monthly car payment for all residents of the local apartment complex?
Answers
Answer:
The best point estimate for the mean monthly car payment for all residents of the local apartment complex is $624.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
In this question:
We apply the inverse Central Limit Theorem.
The mean monthy car payment for 123 residents of the local apartment complex is $624.
So, for all residents of the local apartment complex, the best point estimate for the mean monthly car payment is $624.
Heather is writing a quadratic function that represents a parabola that touches but does not cross the x-axis at x = –6. Which function could Heather be writing? f(x) = x2 + 36x + 12 f(x) = x2 – 36x – 12 f(x) = –x2 + 12x + 36 f(x) = –x2 – 12x – 36
Answers
Answer:
f(x) = –x^2 – 12x – 36
Step-by-step explanation:
The parent function, x^2, touches the x-axis at x=0. Translating it 6 units left replaces x with x-(-6) = x+6, so the function is ...
f(x) = (x+6)^2 = x^2 +12x +36
Reflecting the graph across the x-axis doesn't change the x-intercept, so Heather could be writing ...
f(x) = -x^2 -12x -36
It's D.
I have to have at least 20 characters.
The mean MCAT score 29.5. Suppose that the Kaplan tutoring company obtains a sample of 40 students with a mean MCAT score of 32.2 with a standard deviation of 4.2. Test the claim that the students that took the Kaplan tutoring have a mean score greater than 29.5 at a 0.05 level of significance.
Answers
Answer:
We conclude that the students that took the Kaplan tutoring have a mean score greater than 29.5.
Step-by-step explanation:
We are given that the Kaplan tutoring company obtains a sample of 40 students with a mean MCAT score of 32.2 with a standard deviation of 4.2.
Let [tex]\mu[/tex] = population mean score
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 29.5 {means that the students that took the Kaplan tutoring have a mean score less than or equal to 29.5}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 29.5 {means that the students that took the Kaplan tutoring have a mean score greater than 29.5}
The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean MCAT score = 32.2
s = sample standard deviation = 4.2
n = sample of students = 40
So, the test statistics = [tex]\frac{32.2-29.5}{\frac{4.2}{\sqrt{40} } }[/tex] ~ [tex]t_3_9[/tex]
= 4.066
The value of t-test statistics is 4.066.
Now, at 0.05 level of significance, the t table gives a critical value of 1.685 at 39 degrees of freedom for the right-tailed test.
Since the value of our test statistics is more than the critical value of t as 4.066 > 1.685, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the students that took the Kaplan tutoring have a mean score greater than 29.5.
Given a triangle with: a =
150, A = 75°, and C = 30°
Using the law of sines gives: c = 0
Answers
Answer:
[tex] c = 77.6 [/tex]
Step-by-step explanation:
You may have entered the measure of a side as the measure of an angle.
[tex] \dfrac{\sin A}{a} = \dfrac{\sin C}{c} [/tex]
[tex] \dfrac{\sin 75^\circ}{150} = \dfrac{\sin 30^\circ}{c} [/tex]
[tex] c\sin 75^\circ = 150 \sin 30^\circ [/tex]
[tex] c = \dfrac{150 \sin 30^\circ}{\sin 75^\circ} [/tex]
[tex] c = 77.6 [/tex]
You are correct. Good job!
Approximating square roots
Go to le
Without using a calculator, choose the statement that best describes the value of 215.
Choose 1 answer:
The value of 215 is between 13 and 13.5.
The value of 215 is between 13.5 and 14.
The value of 215 is between 14 and 1.5.
The value of v 215 is between 14.5 and 15.
Answers
Step-by-step explanation:
We know that
14^2=196, and
15^2=225
so we know that sqrt(215) is between 14 and 15.
How do we know if it is between 14.5 and 15?
we need to know the value of 14.5^2, which we can calculate in the head as follows:
The square of all numbers ending in 5 such as 15 can be calculated by breaking up the 5 and the preceding digit(s),
The preceding digit is 1. We multiply 1 by the next integer, 2 to get 2.
Attach 25 to 2 gives us 225 (as we saw above.
Example, 145*145 = 14*15 | 25 = 210 | 25 = 21025
so
14.5^2 = 210.25, which gives the more precise answer that
14.5^2 < 215 < 15^2, or
14.5 < sqrt(215) < 15 (fourth choice)
Since the third choice says sqrt(215) is between 14 and 1.5 (not 15), so the third choice is incorrect.
Note: if we eliminated the third choice, i.e. discard the likelihood of typo in the question, the only one left is the fourth choice.
Use ￢, →, ∧ and ∨ to express the following declarative sentences in propositional logic; in each case state what your respective propositional atoms p, q, etc. a) If interest rates go up, share prices go down. b) If Smith has installed central heating, then he has sold his car or he has not paid his mortgage. c) Today it will rain or shine, but not both. d) If Sam met Jane yesterday, they had a cup of coffee together, or they took a walk in the park. e) My sister wants a black and white cat.
Answers
Answer:
a) If interest rates go up, share prices go down : this will be assigned p→q
b) If Smith has installed central heating, then he has sold his car or he has not paid his mortgage. P → (q∨￢r)
c) Today it will rain or shine, but not both:(p∨q) ∨ ￢(p∧q)
d) If Sam met Jane yesterday, they had a cup of coffee together, or they took a walk in the park. P → (q∨r)
e) My sister wants a black and white cat. p∧q
Step-by-step explanation:
A statement is said to be propositionally logical if the statement that can be assigned either true or false.
∧and
∨or
¬not
→implies
a) If interest rates go up, share prices go down : this will be assigned p→q implies because the occurrence of event (share prices go down) depends on the possibility of the other event happening.
b) If Smith has installed central heating, then he has sold his car or he has not paid his mortgage. P → (q∨￢r) : either of the two of the other events (i.e. he has sold his car or he has not paid his mortgage ) can only occur if the first event occur
c) Today it will rain or shine, but not both:(p∨q) ∨ ￢(p∧q) : either of the events can occur but not both i.e. they are mutually exclusive
d) If Sam met Jane yesterday, they had a cup of coffee together, or they took a walk in the park. P → (q∨r) either of the two of the other events (i.e. they had a cup of coffee together or they took a walk in the park ) can only occur if the first event (Sam met Jane yesterday) occur
e) My sister wants a black and white cat. p∧q : both events can only occur together