Answer:
A is a knave
B is a knight
Step-by-step explanation:
If A is telling the truth, then both are knights and B cannot be lying. However, since B claims that A is a knave, they can't be both knights, and there is no possible way that A is a knight.
If A is knave and thus is lying, they aren't both knights. Since B claims A is a knave, his statement can be true and thus B can be knight and A will be knave.
There different kinds of puzzle. The option that is correct about the puzzle is option A which states that A is a knave and B is a knight.
This is known to be a type of progressively hard puzzle that is titled "knights and knaves" puzzles.It is known as a logic puzzles that took place on an island with two kinds of people. It is a puzzle by American mathematician and musician called Raymond Smullyan in his book written in 1978.
Note that knave often lie and thus A may be lying when He said he was a knight Since B claims A is a knave, his statement can be said to be true and thus B can be regarded as knight.
See full question below
The logician Raymond Smullyan describes an island containing two types of people: knights who always tell the truth and knaves who always lie. You are visiting the island and have the following encounters with natives. (a) Two natives A and B address you as follows. A says: Both of us are knights. B says: A is a knave.
What are A and B?
A. A is a knave and B is a knight.
B. A is a knave and A is a knight.
C. Both A and B are knights.
D. Both A and B are knaves.
Learn more about knight from
https://brainly.com/question/11363810
After 2 hours, there are 1,400 mL of fluids remaining in a patient’s IV. The fluids drip at a rate of 300 mL per hour. Let x be the time passed, in hours, and y be the amount of fluid left in the IV, in mL. Write a linear function that models this scenario.
Answer:
[tex] y(2) = 1400[/tex]
Using this condition we got:
[tex]1400= -300*2 +b[/tex]
And solving for b we got:
[tex] b= 1400+ 600= 2000[/tex]
So then our linear function is given by:
[tex] y = -300x +2000[/tex]
Where y is the amount of fluid left and x the number of hours ellapsing
Step-by-step explanation:
We want to set up a linear function like this one:
[tex]y = mx+b[/tex]
Where y is the amount of fluid left, m the slope and b the initial amount. From the info given we know thatm = -300. And we also have the following condition:
[tex] y(2) = 1400[/tex]
Using this condition we got:
[tex]1400= -300*2 +b[/tex]
And solving for b we got:
[tex] b= 1400+ 600= 2000[/tex]
So then our linear function is given by:
[tex] y = -300x +2000[/tex]
Where y is the amount of fluid left and x the number of hours ellapsing
Which of the functions below could have created this graph?
Answer:
i don't know if this is right or not i did to much work to put it all down but i pretty sure it's C.
The container of a breakfast cereal usually lists the number of calories and the amounts of protein, carbohydrate, and fat contained in one serving of the cereal. The amounts for two common cereals are given below. Suppose a mixture of these two cereals is to be prepared that contains exactly 295 calories, 9 g of protein, 48 g of carbohydrate, and 8 g of fat.
a. Set up a vector equation for this problem. Include a statement of what the variables in your equation represent.
b. Write an equivalent matrix equation, and then determine if the desired mixture of the two cereals can be prepared.
$$\begin{matrix}
\text{Nutrient} & \text{General Mills Cherrios} & \text{Quaker 100% Natura Cereal}\
\text{Calories} & \text{110} & \text{130}\
\text{Protein (g)} & \text{4} & \text{3}\
\text{Carbhydrate (g)} & \text{20} & \text{18}\
\text{Fat (g)} & \text{2} & \text{5}\
\end{matrix}$$
Answer:
(a)
[tex]\left[\begin{array}{ccc}110\\4\\20\\2\end{array}\right] x+\left[\begin{array}{ccc}130\\3\\18\\5\end{array}\right] y=\left[\begin{array}{ccc}295\\9\\48\\8\end{array}\right][/tex]
(b)
[tex]\left[\begin{array}{ccc}110&130&295\\4&3&9\\20&18&48\\2&5&8\end{array}\right][/tex]
1.5 servings of cheerios and 1 serving of Quaker 100% natural cereal will give the desired mixture.
Step-by-step explanation:
Given the mixture of cereals below:
[tex]\left|\begin{array}{c|c|c}&$General Mills &$Quaker \\$Nutrient&$Cherrios &100\% $Natural Cereal\\----&---&---\\$Calories&110&130\\$Protein (g)&4&3\\$Carbhydrate (g)&20&18\\$Fat (g)&2&5\end{array}\right|[/tex]
Suppose a mixture of these two portions of cereals is to be prepared that contain exactly 295 calories, 9 g of protein, 48 g of carbohydrate, and 8 g of fat.
(a)Let x be the number of servings of Cheerios
Let y be the number of servings of Natural Cereal
From the table above, we have
[tex]110x+130y=295\\4x+3y=9\\20x+18y=48\\2x+5y=8[/tex]
Then a vector equation for this problem is:
[tex]\left[\begin{array}{ccc}110\\4\\20\\2\end{array}\right] x+\left[\begin{array}{ccc}130\\3\\18\\5\end{array}\right] y=\left[\begin{array}{ccc}295\\9\\48\\8\end{array}\right][/tex]
(b) Next, we obtain an equivalent matrix equation of the data
[tex]\left[\begin{array}{ccc}110&130\\4&3\\20&18\\2&5\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}295\\9\\48\\8\end{array}\right][/tex]
This is of the form AX=B. To solve for X we, therefore have an equivalence matrix:
[tex]\left[\begin{array}{ccc}110&130&295\\4&3&9\\20&18&48\\2&5&8\end{array}\right][/tex]
Next, we row reduce the matrix using a calculator to obtain the matrix:
[tex]\left[\begin{array}{ccc}1&0&1.5\\0&1&1\\0&0&0\\0&0&0\end{array}\right][/tex]
Therefore:
1x+0=1.5
0x+y=1
x=1.5 and y=1
To get the required mixture, we use 1.5 servings of cheerios and 1 serving of Quaker 100% natural cereal.
Need help ASAP please
Answer:
r = l / π/180× θ
11.6 cm
Step-by-step explanation:
l = π/180 × r × θ
r = l / π/180× θ
r = 12.5 / π/180× 62
r = 11.55156845
Find the equation for the plane through the points Upper P0 (-2 ,2 ,-5),Q0 (1,2,-1), and Upper R0 (-1,-5,4 ).
The equation of plane is:________
Answer:
28x - 23y - 21z = 3
Step-by-step explanation:
First, we need to find two vectors in the plane as:
vector PQ = Q - P = (1, 2, -1) - (-2, 2, -5) = (3, 0, 4)
vector PR = R - P = (-1, -5, 4) - (-2 ,2 ,-5) = (1, -7, 9)
Then, we need to find a normal vector to the plane as:
PQ x RQ = ((0*9)-(4*-7), -(3*(9)-(4*1), (3*-7)-(0*1))
PQ x RQ = (28, -23, -21)
Finally, the equation of a plane is:
A(x-x0) + B(y-y0) + C(z-z0) = 0
Where (A,B,C) is a normal vector to the plane and (x0, y0, z0) is a point in the plane. So, replacing (A,B,C) by (28, -23, -21) and (x0, y0, z0) by P0(-2,2,-5), we can write the equation of the plane as:
28(x+2) - 23(y-2) - 21(z+5) = 0
Solving, we get:
28x + 56 - 23y + 46 - 21z - 105 = 0
28x - 23y - 21z - 3 = 0
28x - 23y - 21z = 3
There are 360 animals on a form 1/5 are cows and 3/8 are sheep then the numbers of cows is
135
72
180
Answer: 72 cows
Step-by-step explanation:
Since the question is asking for cows, we will use the given information to do so. Since 1/5 of the animals are cows, we multiply 1/5 and 360 to find the total amount of cows.
[tex]360*\frac{1}{5} =72[/tex]
which table has the largest area, square tables with a side length of 36 inches, rectangular table 20 inches wide and 73 inches long, round tables with a diameter of 42 inches
Answer:
rectangular table
Step-by-step explanation:
You want to know the largest area of tables that are ...
36 inches square20 inches by 73 inches42 inches in diameterArea FormulasThe formulas for the areas of the various shapes are ...
square: A = s²rectangle: A = LWcircle: A = πr² . . . . . . where r is half the diameterSquareThe area of the square table is ...
A = (36 in)² = 1296 in²
RectangleThe area of the rectangular table is ...
A = (20 in)(73 in) = 1460 in²
CircleThe area of the round table is ...
A = π(21 in)² ≈ 1385 in²
The rectangular table has the largest area.
__
Additional comment
You can eliminate the square table right away by realizing the rectangular table is more than twice as long, and more than half as wide. If the rectangle were 18 in by 72 in, it would have the same area as the square.
If 7 - y = 6, then y=
Answer:
y=1
Step-by-step explanation:
7-y=6
6+1=7
7-1=6
Hope this helps:)
Stay Safe
Answer:
y =1
Step-by-step explanation:
7 - y = 6
Subtract 7 from each side
7 - y-7 = 6 -7
-y = -1
Multiply each side by -1
-y*-1 = -1 *-1
y = 1
find the slope of the line that passes through the points (5,1) and (-4,1)
Answer:
B. 0
Step-by-step explanation:
To find slope, use [tex]m = \frac{y2 - y1}{x2 - x1}[/tex] to find m in y = mx + b. Your m is always your slope.
The product of 5 and the sum of 12 and a certain number is 10. What is the number 4
Answer:
-10
Step-by-step explanation:
5(12 + x) = 10
60 + 5x = 10
5x = -50
x = -10
Sean wants to buy a personal insurance policy that will pay monthly benefits to his son after Sean dies. He pays $500
monthly over the next 10 years to the insurer.
What type of insurance should he buy?
A annuity
B premium
C dividends
D liability
Answer:
B.
Step-by-step explanation:
Premium insurance is an insurance amount paid to the insurer periodically. In this type of insurance, the insurer is required to provide coverage. This insurance policy covers healthcare, life, auto, home, etc. In this insurance, one is required to pay a certain amount of money on monthly, quarterly, or annually basis.
In the given scenario, Sean should buy premium insurance as it covers life and healthcare insurance as well. He can pay $500 on monthly basis to the insurance company. And after Sean's death, his son can claim the amount.
So, the correct answer is option B.
Answer:
A. annuity
Step-by-step explanation:
I know it is a little late for this answer, but I thought I would add it for anyone else who is struggling :) I know it is annuity because I literally just took the test and got it right.
The angles of a triangle are such that one angle is 100 degrees more than the smallest angle, while the third angle is 2 times as large as the smallest angle. Find the measure of all three angles.
Answer:
20, 40, 120
Step-by-step explanation:
Smallest angle = x
Second angle = x + 100
Third angle = 2x
4x + 100 = 180
4x = 80
x = 20
20, 120, 40
V. Money Magazine reported that the average price of gasoline in the United States during the first quarter of 2008 was $3.46. Assume that the price reported by Money is the population mean, and the standard deviation σ is $0.15. a. What is the probability that the mean price for a sample of 30 gas stations is within $0.03 of the population mean?
Answer:
[tex] z=\frac{3.43 -3.46}{\frac{0.15}{\sqrt{30}}} = -1.095[/tex]
[tex] z=\frac{3.49 -3.46}{\frac{0.15}{\sqrt{30}}} = 1.095[/tex]
And we can find this probability using the normal standard table and we got:
[tex] P(-1.095<z<1.095) = P(z<1.095) -P(z<-1.095) =0.863 -0.137= 0.726[/tex]
Step-by-step explanation:
Let X the random variable that represent the price of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(3.46,0.15)[/tex]
Where [tex]\mu=3.46[/tex] and [tex]\sigma=0.15[/tex]
And for this case we want to find the following probability:
[tex] P(3.43 \leq \bar X \leq 3.49)[/tex]
And we can use the z score formula given by:
[tex] z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
If we find the z score for the limits we got:
[tex] z=\frac{3.43 -3.46}{\frac{0.15}{\sqrt{30}}} = -1.095[/tex]
[tex] z=\frac{3.49 -3.46}{\frac{0.15}{\sqrt{30}}} = 1.095[/tex]
And we can find this probability using the normal standard table and we got:
[tex] P(-1.095<z<1.095) = P(z<1.095) -P(z<-1.095) =0.863 -0.137= 0.726[/tex]
(3х^2y^3)^3 =
3x^5y^6
9х^6y^9
27x^5y^6
27x^6y^9
Answer:
27x^6y^9
Step-by-step explanation:
The outside exponent multiplies all of the inside exponents. The applicable rules of exponents are ...
(ab)^c = (a^c)(b^c)
(a^b)^c = a^(bc)
__
(3x^2y^3) = (3^3)(x^(2·3))(y^(3·3)) = 27x^6y^9
Explain why the terms of the polynomial y2 + 7 are said to be realitvley prime
Answer:
The terms of the polynomial are relatively prime because the highest integer that divides them both is 1.
Step-by-step explanation:
Two numbers are said to be relatively prime if their greatest common factor ( GCF ) is 1 .
Now, the expression we are given in the question is a polynomial;
y² + 7.
The terms of the polynomial y² + 7 are y² and 7 and have no common factor and in fact cannot be factorized further. Thus, these terms are said to be relatively prime because the highest integer that divides them both is 1.
True or False - the following scenario depicts an independent relationship between variables (tree growth and air quality): 20% of trees growing in a particular region are not growing to their expected height. In a particular neighborhood in that region, the Air Quality Index is labeled as "Unhealthy for Sensitive Groups" or worse 30% of the time. 10% of the trees in the region grow in this neighborhood. If you randomly measured the growth of a tree in that neighborhood, then the probability that that tree is not growing to its expected height is 33.33%.
I will give brainlisest!!!
Lines x and y are parallel.
Parallel lines x and y are intersected by lines s and t. At the intersection of lines x, t, and s, clockwise from top left, the angles are blank, blank, (6 x + 8) degrees, blank, (7x minus 2) degrees, blank. At the intersection of lines x and y, the angles are 106 degrees, 1, blank, blank. At the intersection of lines y and t, the angles are 2, blank, blank, blank.
Given the diagram, which statement is not true?
m∠1 = (6x + 8)° because they are corresponding angles.
m∠1 = 74° because ∠1 is supplementary to the angle marked 106°.
m∠1 + (6x + 8)° + (7x – 2)° = 180° because they can form a straight line which measures 180°.
(7x – 2)° + m∠2 = 106° because the sum of the remote interior angles equals the exterior angle.
Answer:
the third one since the other ones are correct
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
Suppose that it costs $200 per day to search for chanterelle mushrooms at Pt. Reyes National Seashore. On an average day, the total weight of mushrooms M found at Pt. Reyes is M = 100x-x^2 pounds ,where x is the number of people mushroom hunting on that day. Chanterelles can be sold for $60 per pound. How many more people will go mushroom hunting than is socially optimal?
Answer:
For an overall profit, we need at least 97 people to go mushroom hunting.
Any number of people that is more than the socially optimal number should go mushroom hunting on any given day.
Step-by-step explanation:
The socially optimal number of people that will go mushroom hunting is the number where amount spent to go mushroom hunting equally balances the amount obtained by selling the mushrooms obtained.
If x people go mushroom hunting in a day, the total cost of hunting for that day = 200x
The amount of mushroom obtained is given as
M = (100x - x²) in pounds
The selling price of 1 pound = $60
The cost of M pounds = 60M = 60(100x - x²)
= (6000x - 60x²)
At socially optimal number,
200x = 6000x - 60x²
60x² - 6000x + 200x = 0
60x² - 5800x = 0
x(60x - 5800)
x = 0 or (60x - 5800) = 0
x = 0 or x = (5800/60) = 96.67
Socially optimal number of people = 0 or 96.67
For realistic purposes, we take the socially optimal number of people that went mushroom hunting as 96.67
Any number above this number will result in an overall profit, and any number below it results in an overall loss.
So, for an overall profit, we need at least 97 people to go mushroom hunting.
Hope this Helps!!
Answer:
48 people
Step-by-step explanation:
When allocating resources to a particular task it is important to assign optimal units of resources.
In this scenario if the people hunting mushrooms are too many they will not make profit. But an optimal number will guarantee everyone makes positive profit.
Optimal = (M÷x)Px - 200= 0
Optimal= {(100x -x^2) ÷ x} * 60 = 200
Optimal = 6000 - 60x = 200
x= 96.666~ 97 people
However to maximise profit MTB = MTC
Socially Optimal quantity = 60(100x - x^2) -200
∂(Socially Optimal amount) ÷ ∂ x= 6000 - 120x - 200
x = 48.33~ 48 people
So 48 more people go mushroom hunting than is socially optimal
To examine the effect of high-dose green tea extract on weight loss, researchers conducted a randomized, double-blind trial on a random sample of 115 women with obesity from Taiwan. Some of these women were randomly assigned to the main treatment group taking a high-dose green tea extract ("EGCG") daily for 12 weeks. The published abstract of this 2015 study reports that, "Significant weight loss, from 76.8 ± 11.3 kg to 75.7 ± 11.5 kg (p = 0.025), was observed in the treatment group after 12 weeks of high-dose EGCG treatment."
Which of the following inference procedures would be used to reach the quoted conclusion?
a. Z procedure for a proportion
b. Chi-square for two-way tables
c. Chi-square for goodness of fit
d. Two sample t procedure for two means
e. One sample or matched-pairs t procedure for a mean
f. ANOVA for several means
Answer:
d. Two sample t procedure for two means.
Step-by-step explanation:
The study have a treatment group, which is the group of women that are taking the high dose of green tea extract, and a control group, in order to compare. They are assigned randomly to each group.
Then, the difference fo the two sample means is calculated and a t-test is performed in order to conclude if the two populations means are significantly different.
Apparently they are significantly different, as this is the conclusion with a P-value of 0.025.
What is a perfect cube and how can you check if a given number is a perfect cube? Explain why.
Answer:
Read below.
Step-by-step explanation:
A perfect cube is a number cubed (If that makes sense). Such as 3³ will equal a perfect cube because it's being multiplied by itself 3 times. 3×3×3=9. It will work for any whole number. You can check if a given number is a perfect cube by using the cube root ([tex]\sqrt[3]{x}[/tex]).
Hope it makes sense!
Step-by-step explanation:
A perfect cube is a cube whose cube root can be easily gotten by using methods such as factor method eg 125 is a perfect cube whose cube root is 5. You can know if a number is a perfect cube 1.) if it gives you a perfect cube root
Stephanie spent $110 on 1.7 pounds of coffee. she wants to know how much each pound costs. how would she find out how much each pound costs? write equation and explain how you got that answer.
$64.71 rounded, explanation attached
The height of a stream of water from the nozzle of a fire hose is modeled by h(x) =-0.03x2+ 2x + 38 where h(x) is the height in feet, of the stream of water x feet from the fire truck. 1. What is the maximum height the water from this nozzle can reach? What is the maximum distance from the firetruck a firefighter can stand and still reach the fire?
Answer:
height: 71.33 feetreach: 82.10 feetStep-by-step explanation:
The equation can be rewritten to vertex form:
h(x) = -0.03(x² - 200/3x) +38
h(x) = -0.03(x² -200/3x +(100/3)²) +38 +.03(100/3)²
h(x) = -0.03(x -33 1/3)² +71 1/3
The vertex is (33 1/3, 71 1/3), so the maximum height the water will reach is 71 1/3 feet.
__
When h(x) = 0, the water reaches as far as it possibly can.
0 = -0.03(x -33 1/3)² +71 1/3
(-71 1/3)/(-0.03) = (x -33 1/3)² . . . subtract 71 1/3; divide by -0.03
√(2377.78) = x -33.33 . . . . . . . . positive square root
82.10 ≈ x
The maximum distance the water will reach is 82.10 feet.
-3
n is an integer.
Write down the possible values of n.
I
Answer:
since n is an integer you substitute n with all the integers. But since that is too much you should use infinity.
n=[-∞,+∞] where -∞ is a negative infinity which stands for negative numbers and +∞ is a positive infinity where it stands for positive numbers.
an integer contains negative and positive numbers so above is the answer.
Step-by-step explanation:
how do you find the zero(s) of a polynomial function
Answer:
by using the quadratic formula
Step-by-step explanation:
negative b plus or minus the square root of b squared minus 4ac, then all divided by 2a
(3x^7)^2 i need help look at the pictures
Answer:
9x^14
Step-by-step explanation:
(3x^7)^2= 3^2x^(7*2)= 9x^14
no picture?
Answer:
[tex]9x^{14}[/tex]
Step-by-step explanation:
[tex](3x^7)^2[/tex]
[tex]3^2 \times x^{7 \times 2}[/tex]
[tex]9 \times x^{14}[/tex]
Ronaldo is standing by the edge of a circular lake at point A (shown below). He has to get directly to the other side at point B. Instead of walking around the lake from A to B, he decides that he would rather swim. How far must he swim from A to B if the circumference of the lake is 4.71 miles
Diya spent 2/5 of her money on a dress and 1/2 of the reminder on a doll. She spent $8 more o the dress than the doll. How much money did she have left?
year 6 Mathematics
Answer:
$24
Step-by-step explanation:
2/5 — dress
3/5 — remainder
1/2 of remainder = 1/2 × 3/5 = 3/10 — doll
rewrite fraction spent on dress: 4/10
dress - doll = $8
4/10 - 3/10 = 1/10
1/10 = $8
fraction of money left = 10/10 - 4/10 - 3/10
= 3/10
amount of money left = $8 × 3
$24
The graph shows the estimated value of a piece of land, where x is the number of years since the purchase and y is the estimated value in thousands of dollars. The graph shows the estimated value of a piece of land, where x is the number of years since the purchase and y is the estimated value in thousands of dollars. What was the purchase price of the land? $10,200 $100,000 $102,000 $1,000,000
The correct answer is B. $100,000
Explanation:
The graphic shows how the value of the piece of land changed from the moment it was bought to five years later by relating the value in the y-axis to the years passed in the x-axis. The initial value or purchase price of the land is the value shown in the y-axis at 0 years (x-axis )or the first orange dot because this is the initial value of the land before any time had passed. According to this, the value is $100,000 considering the number in this intersection is 100 but this is the value in thousands of dollars.
Answer:
It's B or $100,000
Step-by-step explanation:
Need Help
Please Assist
I need HELP! is the missing value 25?
Answer: choice3) 25
Step-by-step explanation:
The constant ratio of y/x is 2.5
so if the x value is 10 the y value would be 25(10*2.5).