Answer:
A∩(A∪B)=A
Step-by-step explanation:
Let's find the answer as follows:
Let's consider that 'A' includes all numbers between X1 and X2 (X1≤A≥X2), and let's consider that 'B' includes all numbers between Y1 and Y2 (Y1≤B≥Y2). Now:
A∪B includes all numbers between X1 and X2, as well as the numbers between Y1 and Y2, so:
A∪B= (X1≤A≥X2)∪(Y1≤B≥Y2)
Now, A∩C involves only the numbers that are included in both, A and C. This means that 'x' belongs to A∩C only if 'x' is included in 'A' and also in 'C'.
With this in mind, A∩(A∪B) includes all numbers that belong to 'A' and 'A∪B', which in other words means, all numbers that belong to (X1≤A≥X2) and also (X1≤A≥X2)∪(Y1≤B≥Y2), which are:
A∩(A∪B)=(X1≤A≥X2) which gives:
A∩(A∪B)=A
WHAT IS THE PROBABILITY OF GETTING EITHER JACK OR A THREE WHEN DRAWING A SINGLE CARD FROM A DECK OF 52 CARDS? WHAT IS THE PROBABILITY THAT THE CARD IS EITHER A JACK OR A THREE?
Answer:
2/13
Step-by-step explanation:
there are 4 jacks and 4 threes in a standard poker deck.
4+4 is 8
8/52=2/13
The probability of drawing either a Jack or a three from a standard deck of 52 cards is 2/13, because there are 8 such cards in a deck and the total number of cards in the deck is 52.
The question asks for the probability of drawing either a Jack or a three from a standard deck of 52 cards. To solve this, we need to count how many Jacks and threes there are in a deck. Since each suit (hearts, diamonds, clubs, and spades) includes one Jack and one three, there are 4 Jacks and 4 threes in a standard deck. Therefore, there are 8 cards that satisfy the condition (either a Jack or a three).
Since the total number of cards in the deck is 52, the probability of drawing either a Jack or a three is calculated as the number of favorable outcomes (drawing a Jack or a three) divided by the total number of outcomes (drawing any card from the 52-card deck). Thus, the probability is:
Probability = (Number of Jacks + Number of threes) / Total number of cards = (4 + 4) / 52 = 8 / 52 = 2 / 13
Therefore, the probability of drawing either a Jack or a three from a standard deck of 52 cards is 2/13.
6. Let A and B be nxn matrices . Compute (A + B) (A + B). Explain all steps.
Answer:
(A+B)(A+B)=A.A+B.A+A.B+B.B
Step-by-step explanation:
Given that matrices A and B are nxn matrices
We need to find (A+B)(A+B)
For understanding the multiplication of matrices let'take A is mxn and B is pxq matrices,we can multiple only when n=p,so our Ab matrices will be mxq.
We know that that in matrices AB is not equal to BA.
Now find
(A+B)(A+B)=A.A+B.A+A.B+B.B
So from we can say that (A+B)(A+B) is not equal to A.A+2B.A+B.B because AB is not equal to BA in matrices.
So (A+B)(A+B)=A.A+B.A+A.B+B.B
Find the derivative of the function at P 0 in the direction of A. f(x,y,z) = 3 e^x cos(yz), P0 (0, 0, 0), A = - i + 2 j + 3k
The derivative of [tex]f(x,y,z)[/tex] at a point [tex]p_0=(x_0,y_0,z_0)[/tex] in the direction of a vector [tex]\vec a=a_x\,\vec\imath+a_y\,\vec\jmath+a_z\,\vec k[/tex] is
[tex]\nabla f(x_0,y_0,z_0)\cdot\dfrac{\vec a}{\|\vec a\|}[/tex]
We have
[tex]f(x,y,z)=3e^x\cos(yz)\implies\nabla f(x,y,z)=3e^x\cos(yz)\,\vec\imath-3ze^x\sin(yz)\,\vec\jmath-3ye^x\sin(yz)\,\vec k[/tex]
and
[tex]\vec a=-\vec\imath+2\,\vec\jmath+3\,\vec k\implies\|\vec a\|=\sqrt{(-1)^2+2^2+3^2}=\sqrt{14}[/tex]
Then the derivative at [tex]p_0[/tex] in the direction of [tex]\vec a[/tex] is
[tex]3\,\vec\imath\cdot\dfrac{-\vec\imath+2\,\vec\jmath+3\,\vec k}{\sqrt{14}}=-\dfrac3{\sqrt{14}}[/tex]
5. Let A = (x, y), B = {1,2). Find the Cartesian products of A and B: A x B? (Hint: the result will be a set of pairs (a, b) where a E A and b e B)
Answer: A x B = {(x,1), (x,2), (y,1), (y,2)}
Step-by-step explanation:
The Cartesian product of any two sets M and N is the set of all possible ordered pairs such that the elements of M are first values and the elements of N are the second values.
The Cartesian product of sets M and N is denoted by M × N.
For Example : M = {x,y} and N={a,b}
Then , M × N ={(x,a), (x,b), (y,a), (y,b)}
Given : Let A = {x, y}, B = {1,2}
Then , the Cartesian products of A and B will be :
A x B = {(x,1), (x,2), (y,1), (y,2)}
Hence, the Cartesian products of A and B = A x B = {(x,1), (x,2), (y,1), (y,2)}
Find the range of the function f of x equals the integral from negative 6 to x of the square root of the quantity 36 minus t squared
[tex]f(x)=\displaystyle\int_{-6}^x\sqrt{36-t^2}\,\mathrm dt[/tex]
The integrand is defined for [tex]36-t^2\ge0[/tex], or [tex]-6\le t\le6[/tex], so the domain should be the same, [tex]-6\le x\le6[/tex].
When [tex]x=-6[/tex], the integral is 0.
The integrand is non-negative for all [tex]x[/tex] in the domain, which means the value of [tex]f(x)[/tex] increases monotonically over this domain. When [tex]x=6[/tex], the integral gives the area of the semicircle centered at the origin with radius 6, which is [tex]\dfrac\pi26^2=18\pi[/tex], so the range is [tex]\boxed{0\le f(x)\le 18\pi}[/tex].
The range of the function f(x) is the integral from -6 to x of the square root of the quantity 36 minus t squared is [0, 6*π] because the total area of the semicircle is the maximum value.
Explanation:The function f(x) is the integral from -6 to x of the square root of the quantity 36 minus t squared. This is a known geometrical shape, which is a semicircle with radius 6. To find the range of this function, we need to know the possible outcomes of this function. In general, for a semicircle of radius r, the values of the square root of the quantity r squared minus t squared will vary from 0 to r, both inclusive. So, if you consider the function from -6 to 6, the range would be [0, 6*π] because the total area of the semicircle is the maximum value.
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We are given three coins: one has heads in both faces, the second has tails in both faces, and the third has a head in one face and a tail in the other. We choose a coin at random, toss it, and it comes head. What is the probability that the opposite face is tails?
Answer: 0.33
Step-by-step explanation:
Let,
E1 be the coin which has heads in both facesE2 be the coin which has tails in both facesE3 be the coin which has a head in one face and a tail in the other.In this question we are using the Bayes' theorem,
where,
P(E1) = P(E2) = P(E3) = [tex]\frac{1}{3}[/tex]
As there is an equal probability assign for choosing a coin.
Given that,
it comes up heads
so, let A be the event that heads occurs
then,
P(A/E1) = 1
P(A/E2) = 0
P(A/E3) = [tex]\frac{1}{2}[/tex]
Now, we have to calculate the probability that the opposite side of coin is tails.
that is,
P(E3/A) = ?
∴ P(E3/A) = [tex]\frac{P(E3)P(A/E3)}{P(E1)P(A/E1) + P(E2)P(A/E2) + P(E3)P(A/E3) }[/tex]
= [tex]\frac{(1/3)(1/2)}{(1/3)(1) + 0 + (1/2)(1/3)}[/tex]
= [tex]\frac{1}{6}[/tex] × [tex]\frac{6}{3}[/tex]
= [tex]\frac{1}{3}[/tex]
= 0.3333 ⇒ probability that the opposite face is tails.
Given a double-headed coin, a double-tailed coin, and a regular coin, the probability that the opposite face is tails after tossing a head is 33.33%, assuming we picked one coin randomly and tossed it to see a head.
The student is asking about a problem involving conditional probability, with the specific condition that one of the sides that came up is a head. We are given three coins: a double-headed coin, a double-tailed coin, and a regular coin. The aim is to calculate the probability that the opposite face is tails given that the tossed coin shows heads.
First, we need to consider the total number of heads that can come up when choosing any coin. This yields two heads from the double-headed coin, and one head from the regular coin, resulting in three possible heads. However, only the regular coin has a tail on the opposite side.
Consequently, the probability that the opposite face is tails given that a head has been tossed is 1 out of 3, or 33.33%.
what are the values of x and y such that ABCD=PQRS?
Answer:
T(x, y) = T(0, -8)
Step-by-step explanation:
The first reflection can be represented as ...
(x, y) ⇒ (-x, y)
__
The rotation about the origin is the transformation ...
(x, y) ⇒ (-x, -y)
so the net effect of the first two transforms is ...
(x, y) ⇒ (x, -y)
__
Then the reflection across y=4 alters the y-coordinate:
(x, y) ⇒ (x, 8-y)
so the net effect of the three transforms is ...
(x, y) ⇒ (x, 8+y)
__
In order to bring the figure back to place, we must translate it down 8 units using ...
(x, y) ⇒ (x, y-8) . . . . net effect: (x, y) ⇒ (x, (8+y)-8) = (x, y)
The translation is by 0 units in the x-direction and -8 units in the y-direction.
A student standing on the edge of a cliff throws a rock downward at a speed of 7.5 m/s at an angle 40° below the horizontal. It takes the rock 2.4 seconds to hit the ground. How tall is the cliff?
Answer:
42.05 m
Step-by-step explanation:
(see attached)
A company manufactures bicycles at a cost of $50 each. If the company's fixed costs are $700, express the company's costs as a linear function of x, the number of bicycles produced.
Answer:
[tex]y = 700 + 50x[/tex]
Step-by-step explanation:
Hello, great question. These types are questions are the beginning steps for learning more advanced Algebraic Equations.
If the company has a fixed cost (fixed being a keyword) of $700, then that cost will be a steady value before they even start to manufacture the bicycles. Afterwards they have to spend $50 on each bicycle they produce. Since we do not know the amount of bicycles that have been produced we can use the variable x to represent this.
[tex]y = 700 + 50x[/tex]
The equation above states that the company pays $700 plus $50 for every bike produced which comes out to a total of y.
Graph the equation by plotting three
points. If all three are correct, the line
will appear.
-y = -x + 1
Answer:
(0, -1), (1, 0), (2, 1)
Step-by-step explanation:
I find this easier to do after multiplying the equation by -1:
y = x - 1
Pick any value for x, then subtract 1 from it to find the corresponding value of y.
A person pulls horizontally with a force of 64 N on a 14-kg box. There is a force of friction between the box and the floor of 36 N. Find the acceleration of the box in m/s2 Show your work
The net force is what remains of the pull when we subtract the friction force:
[tex]F = 64-36 = 28N[/tex]
Now, use the law
[tex]F=ma[/tex]
and solve it for the acceleration
[tex]a = \dfrac{F}{m}[/tex]
to get the result:
[tex]a = \dfrac{28}{14}=2[/tex]
Answer:
2 m/s²
Step-by-step explanation:
F = applied force in the horizontal direction = 64 N
f = frictional force acting between the box and the floor = 36 N
m = mass of the box = 14 kg
a = acceleration of the box = ?
Force equation along the horizontal direction is given as
F - f = ma
Inserting the values
64 - 36 = 14 a
28 = 14 a
a = [tex]\frac{28}{14}[/tex]
a = 2 m/s²
Consider the sequence 1, 5, 12, 22, 35, 51, . . . (with a0 = 1). By looking at the differences between terms, express the sequence as a sequence of partial sums. Then find a closed formula for the sequence by computing the nth partial sum.
The given sequence can be expressed as a sequence of partial sums by finding the differences between terms and adding them to the previous term. The closed formula for the nth partial sum is Sn = n/2(3n - 1), where Sn represents the nth partial sum.
Explanation:To express the given sequence as a sequence of partial sums, we can find the differences between consecutive terms:
5 - 1 = 4
12 - 5 = 7
22 - 12 = 10
35 - 22 = 13
51 - 35 = 16
From these differences, we can observe that each term in the sequence is obtained by adding the difference to the previous term. Therefore, the sequence can be written as a sequence of partial sums:
1, 1+4, 1+4+7, 1+4+7+10, 1+4+7+10+13, ...
To find a closed formula for the nth partial sum, we can use the formula for the sum of an arithmetic series:
Sn = n/2(a1 + an), where Sn represents the nth partial sum, a1 is the first term, and an is the nth term.
For the given sequence, a1 = 1 and the difference between consecutive terms is 3, so the nth term can be represented as an = 1 + 3(n-1). Substituting these values into the formula, we get:
Sn = n/2(1 + 1 + 3(n-1)) = n/2(2 + 3(n-1)) = n/2(3n - 1).
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When studying radioactive material, a nuclear engineer found that over 365 days, 1,000,000 radioactive atoms decayed to 973 comma 635 radioactive atoms, so 26 comma 365 atoms decayed during 365 days. a. Find the mean number of radioactive atoms that decayed in a day. b. Find the probability that on a given day, 51 radioactive atoms decayed.
Answer:
A. number of decayed atoms = 73.197
Step-by-step explanation:
In order to find the answer we need to use the radioactive decay equation:
[tex]N(t)=N0*e^{kt}[/tex] where:
N0=initial radioactive atoms
t=time
k=radioactive decay constant
In our case, when t=0 we have 1,000,000 atoms, so:
[tex]1,000,000=N0*e^{k*0}[/tex]
[tex]1,000,000=N0[/tex]
Now we need to find 'k'. Using the provied information that after 365 days we have 973,635 radioactive atoms, we have:
[tex]973,635=1,000,000*e^{k*365}[/tex]
[tex]ln(973,635/1,000,000)/365=k[/tex]
[tex] -0.0000732=k[/tex]
A. atoms decayed in a day:
[tex]N(t)=1,000,000*e^{-0.0000732t}[/tex]
[tex]N(1)=1,000,000*e^{-0.0000732*1}[/tex]
[tex]N(1)= 999,926.803[/tex]
Number of atoms decayed in a day = 1,000,000 - 999,926.803 = 73.197
B. Because 'k' represents the probability of decay, then the probability that on a given day 51 radioactive atoms decayed is k=0.0000732.
The radius of a 10 inch right circular cylinder is measured to be 4 inches, but with a possible error of ±0.1 inch. Use linear approximation or differentials to determine the possible error in the volume of the cylinder. Include units in your answer.
Answer:
502.4 ± 30.14 in^3
Step-by-step explanation:
r = 4 in, h = 10 in
error = ± 0.1 inch
Volume of a cylinder, V = π r² h
Take log on both the sides
log V = log π + 2 log r + log h
Differentiate both sides
dV/V = 0 + 2 dr/r + dh /h
dV/V = 2 (± 0.1) / 4 + (± 0.1) / 10
dV/V = ± 0.05 ± 0.01 = ± 0.06 .... (1)
Now, V = 3.14 x 4 x 4 x 10 = 502.4 in^3
Put in equation (1)
dV = ± 0.06 x 502.4 = ± 30.144
So, V ± dV = 502.4 ± 30.14 in^3
Find an equation of the vertical line through (-6, -9) in the form ax+ byc, where a, b, and c are integers with no factor common to all three, and az0. The equation is (Type an equation.)
Answer:
The equation of the vertical line through (-6, -9) is 1x+0y=-6.
Step-by-step explanation:
The standard form of a line is
[tex]ax+by=c[/tex]
where a, b, and c are integers with no factor common to all three, and a>0.
If a vertical line passes through the point (a,b), then the equation of vertical line is x=a.
It is given that the vertical line passes through the point (-6,-9). Here a=-6 and b=-9, so the equation of the vertical line through (-6, -9) is
[tex]x=-6[/tex]
[tex]1x+0y=-6[/tex]
The standard form of the line is 1x+0y=-6. where the value of a,b c are 1, 0, -6 respectively.
Therefore the equation of the vertical line through (-6, -9) is 1x+0y=-6.
Tyree is determining the distance of a segment whose endpoints are A(–4, –2) and B(–7, –7).
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Therefore, d = 2.
Which best describes the accuracy of Tyree’s solution?
a Tyree’s solution is accurate.
b Tyree’s solution is inaccurate. In step 1, he substituted incorrectly.
c Tyree’s solution is inaccurate. In step 2, he simplified incorrectly.
d Tyree’s solution is inaccurate. In step 3, he added incorrectly.
Answer:
Option b Tyree’s solution is inaccurate. In step 1, he substituted incorrectly.
Step-by-step explanation:
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
[tex]A(-4,-2)\\B(-7,-7)[/tex]
step 1
substitute the values in the formula
[tex]d=\sqrt{(-7-(-2))^{2}+(-7-(-4))^{2}}[/tex]
step 2
Simplify
[tex]d=\sqrt{(-7+2)^{2}+(-7+4)^{2}}[/tex]
step 3
[tex]d=\sqrt{(-5)^{2}+(-3)^{2}}[/tex]
step 4
[tex]d=\sqrt{25+9}[/tex]
step 5
[tex]d=\sqrt{34}[/tex]
therefore
Tyree’s solution is inaccurate. In step 1, he substituted incorrectly.
point) Suppose that the trace of a 2 x 2 matrix A is tr(A)= -9 and the determinant is det(A) 18. Find the eigenvalues of A. The eigenvalues of A are (Enter your answers as a comma separated list.)
Answer with explanation:
Matrix A= (2 × 2) Matrix
Trace A= -9
Also,Determinant A= |A|=18
⇒Characteristics Polynomial is given by
Δ(A)=A² -A ×trace (A)+Determinant (A)
=A²+9 A+18
=(A+6)(A+3)
So, eigenvalues can be obtained by substituting :
Δ(A)=0
(A+6)(A+3)=0
A= -6 ∧ A= -3
Two Eigenvalues are = -6, -3
You can afford monthly deposits of 140 into an account that pays 3.8% compounded monthly. How long will be untl you have $11.300 to buy a boat? Type the number of months: (Round to the next higher month it not exact Question He Check Answer Enter your answer in the answer box and then click Check Answer All parts showing
Answer:
72 months approx.
Step-by-step explanation:
Monthly deposit = m = $140
r = 3.8% or 0.038
Amount needed in the account = A = $11300
The formula will be :
[tex]11300=140(\frac{(1+0.038/12)-1}{0.038/12} )[/tex]
[tex]11300=140(\frac{(1+0.038/12)-1}{0.003166})[/tex]
[tex]11300=44219.83((1.003166)^{m}-1)[/tex]
[tex]0.2555=(1.003166)^{m}-1[/tex]
[tex]1.2555=(1.003166)^{m}[/tex]
m=log1.2555/log1.003166
m =71.98 ≈ 72
Hence, it will take 72 months approx.
if I've gained 35 pounds in 186 days, how many pounds per day?
Answer:
.188 pounds per day
Step-by-step explanation:
Given
35 pounds gained in 186 daysDivide the amount of pounds gained by the total number of days
35/186 = .188
Answer
Approximately .188 pounds per day.
Sarah and Max must decide how to split up 8 cookies. Sarah (we'll call her player 1) makes a proposal to Max (we'll call him player 2), of how many cookies each of them should receive. We assume that each kid is trying to maximize the amount of cookies they receive, and that they must follow the rules below: If Max accepts the proposal, they split the cookies according to that agreement. If Max doesn't accept the proposal, he tells their dad. Their dad will eat 4 of the cookies and then split the rest evenly. Assume that if Max is indifferent between accepting and rejecting, he will always accept the offer. How many cookies will Sarah offer Max
She would offer to split the cookies evenly, so they each get 4.
If she offered Max less than 4, he would not accept and their dad would eat half, so each person would only get 2 cookies each.
If she offered Max more than 4, then she doesn't maximize the amount she would get.
Please help me with this
Answer:
Option 1: triangle HFG is congruent to triangle KIJ
Step-by-step explanation:
F and I are same as they are on 90 degrees.
In figure 1, from I to K is the height of the triangle.
In figure 2, from F to H is the height of the triangle.
Therefore, IK is congruent to FH
In figure 1, I to J is the base of the triangle from 90 degrees.
In figure 2, F to G is the base of the triangle from 90 degrees.
Therefore, IJ is congruent to FG
Therefore, triangle HFG is congruent to triangle KIJ.
The first option is correct.
!!
Tim has one apple.
Jerry has one apple as well.
Jerry gives Tim his one apple.
How many apples does Tim have now? How about Jerry?
Answer:
Tim has 2 apples, Jerry has no apple.
Step-by-step explanation:
Given that Tim has 1 apple.
Jerry has 1 apple as well.
After Jerry gives Tim one apple,
Tim has 1 + 1 = 2 apples, and Jerry has 1 - 1 = 0
Tim has 2 apples, Jerry has no apple.
A Game of Thrones fan predicts there is a 70% chance that her favorite character will survive the next season and a 75% chance that her second favorite character will die. There is also a 16% chance that both characters will die. What’s the probability that the second character will die given that the first character dies? What kind of probability is this called?
Final answer:
The probability that the second character will die given that the first character dies is 53.33%. This is known as conditional probability.
Explanation:
To find the probability that the second character will die given that the first character dies, we use the concept of conditional probability.
The formula for conditional probability is P(B|A) = P(A and B) / P(A), where P(B|A) is the probability of event B occurring given that event A has occurred, P(A and B) will be the probability of both events A and B occurring, and P(A) is the probability of event A occurring.
In this scenario, event A is the first character dying, and event B is the second character dying. The student has already stated there is a 70% chance that the first character will survive, which means there is a 30% (100% - 70%) chance that the first character will die.
They've also stated a 16% chance that both characters will die. Applying the formula gives us P(B|A) = P(A and B) / P(A) = 0.16 / 0.30 = 0.5333, or 53.33%.
Therefore, the probability that the second character will die given that the first character dies is 53.33%. This kind of probability is called conditional probability.
Express as the sum or difference of logarithms. log311y
The function log311y can be expressed as the sum of two logarithms, log3(11) + log3(y), according to the product rule of logarithms.
Explanation:The function log311y represents the logarithm base 3 of the product of the numbers 11 and y. Using the rules of logarithms, we can rewrite this expression as a sum of two logarithms.
According to the product rule of logarithms, the logarithm of a product is the sum of the logarithms of the component numbers. Applying this rule to our expression, log311y becomes:
log3(11) + log3(y)
This is the sum of the logarithm base 3 of 11 and the logarithm base 3 of y. In conclusion, the function log311y can be expressed as the sum of the separate logarithms: log3(11) + log3(y).
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The logarithm log3(11y) can be broken down into two simpler logarithms, log3(11) and log3(y), by using properties of logarithms. This is the sum of the two simpler logarithms.
Explanation:To express the logarithm log3(11y) as the sum or difference of logarithms, we will utilize the properties of logs:
The logarithm of a product is the sum of the logarithms of the numbers (log(xy) = log(x) + log(y)).The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number.The logarithm of a quotient is the difference of the logarithms of the numbers.Applying these properties to the given logarithm, we find:
log3(11y) = log3(11) + log3(y)
Thus, the original logarithm has been expressed as a sum of two simpler logarithms.
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Find the amount of time needed for the sinking fund to reach the given accumulated amount. (Round your answer to two decimal places.) $295 monthly at 5.2% to accumulate $25,000.
Answer:
8.82 years.
Step-by-step explanation:
Since, the monthly payment formula is,
[tex]P=\frac{PV(r)}{1-(1+r)^{-n}}[/tex]
Where, PV is the present value of the loan,
r is the rate per month,
n is number of months,
Here,
PV = $ 25,000,
Annual rate = 5.2 % = 0.052 ⇒ Monthly rate, r = [tex]\frac{0.052}{12}[/tex]
( 1 year = 12 months )
P = $ 295,
By substituting the values,
[tex]295=\frac{25000(\frac{0.052}{12})}{1-(1+\frac{0.052}{12})^{-n}}[/tex]
By the graphing calculator,
We get,
[tex]n = 105.84[/tex]
Hence, the time ( in years ) = [tex]\frac{105.84}{12}=8.82[/tex]
Find the mean for the following group of data items. 4.1, 8.9, 3.2, 1.9, 7.3, 6.3, 6.7, 8.6, 3.2, 2.3, 5.9 (Round to 3 decimal places as needed.) The mean is
Answer:
The mean is 5.309.
Step-by-step explanation:
Given group of data,
4.1, 8.9, 3.2, 1.9, 7.3, 6.3, 6.7, 8.6, 3.2, 2.3, 5.9,
Sum = 4.1+ 8.9 + 3.2 + 1.9 + 7.3 + 6.3 + 6.7 + 8.6 + 3.2 + 2.3 + 5.9 = 58.4,
Also, number of observations in the data = 11,
We know that,
[tex]Mean=\frac{\text{Sum of all observation}}{\text{Total observations}}[/tex]
Hence, the mean of given data = [tex]\frac{58.4}{11}=5.30909\approx 5.309[/tex]
List the different combinations of heads and tails that can occur when 3 ordinary coins are tossed. Use h for heads and t for tails. One combination is hht. List the other combinations, taking order into account (Use a comma to separate answers) More i () a Enter your answer in the answer box ere to search
[tex]HTT,HTH,HHH,TTT,THT,THH,TTH[/tex]
The slope of the _________________ is determined by the relative price of the two goods, which is calculated by taking the price of one good and dividing it by the price of the other good. Opportunity cost productive efficiency budget constraint production possibilities frontier
Answer:
The answer is - budget constraint
Step-by-step explanation:
The slope of the budget constraint is determined by the relative price of the two goods, which is calculated by taking the price of one good and dividing it by the price of the other good.
A budget constraint happens when a consumer demonstrates limited consumption patterns by a certain income.
. Break downs occur on a 20-years-old car with rate λ= 0.5 breakdowns/week. The owner of the car is planning to have a trip on his car for 2 weeks. What is the probability that there will be no breakdown on his car in the trip? [ The rate = ? per two weeks]
Answer: 0.3679
Step-by-step explanation:
The formula for Poisson distribution :-
[tex]P(x)=\dfrac{e^{-\lambda}\lambda^{x}}{x!}[/tex]
Let x be the number of breakdowns.
Given : The rate of breakdown per week : 0.5
Then , for 2 weeks period the number of breakdowns = [tex]\lambda=0.5\times2=1[/tex]
Then , the probability that there will be no breakdown on his car in the trip is given by :-
[tex]P(x)=\dfrac{e^{-1}1^{0}}{0!}=0.367879441171\approx0.3679[/tex]
Hence, the required probability : 0.3679
x + y + w = b
2x + 3y + z + 5w = 6
z + w = 4
2y + 2z + aw = 1
For what values a, b (constants) is the system:
(a) inconsistent?
(b) consistent w/ a unique sol'n?
(c) consistent w/ infinitely-many sol'ns?
Answer:
(a) a=6 and b≠[tex]\frac{11}{4}[/tex]
(b)a≠6
(c) a=6 and b=[tex]\frac{11}{4}[/tex]
Step-by-step explanation:
writing equation in agumented matrix form
[tex]\begin{bmatrix}1 &1 & 0 &1 &b\\ 2 &3 & 1 &5 &6\\ 0& 0 & 1 &1 &4\\ 0& 2 & 2&a &1\end{bmatrix}[/tex]
now [tex]R_{2} =R_{2}-2\times R_{1}[/tex]
[tex]\begin{bmatrix}1 &1& 0 &1 &b\\ 0 &1& 1 &3 &6-2b\\ 0& 0 & 1 &1 &4\\ 0& 2 & 2&a &1\end{bmatrix}[/tex]
now [tex]R_{4} =R_{4}-2\times R_{2}[/tex]
[tex]\begin{bmatrix}1 &1& 0 &1 &b\\ 0 &1& 1 &3 &6-2b\\ 0& 0 & 1 &1 &4\\ 0& 0 & 0 &a-6 &4b-11\end{bmatrix}[/tex]
a) now for inconsistent
rank of augamented matrix ≠ rank of matrix
for that a=6 and b≠[tex]\frac{11}{4}[/tex]
b) for consistent w/ a unique solution
rank of augamented matrix = rank of matrix
a≠6
c) consistent w/ infinitely-many sol'ns
rank of augamented matrix = rank of matrix < no. of variable
for that condition
a=6 and b=[tex]\frac{11}{4}
then rank become 3 which is less than variable which is 4.