Answer: [tex]\dfrac{1}{59049}[/tex]
Step-by-step explanation:
The number of keys on the keypad = 9
The number of digits in the required pin code = 4
If repetition is allowed then , the number of possible codes will be
[tex](9)^5=59049[/tex]
Then , the probability that the choosen pin code is correct is given by :-
[tex]\dfrac{1}{59049}[/tex]
The probability of Geometric distribution formula :
[tex]P(X=x)=(1-p)^{x-1}p[/tex], where p is the probability of success and x is the number of attempt.
Using geometric probability , the probability of a correct guess on the first try is given by :-
[tex]P(X=1)=(1-\dfrac{1}{59049})^{1-1}(\dfrac{1}{59049})=\dfrac{1}{59049}[/tex]
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.
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.
Cars enter a car wash at a mean rate of 2 cars per half an hour. What is the probability that, in any hour, exactly 5 cars will enter the car wash? Round your answer to four decimal places.
Answer: 0.1563
Step-by-step explanation:
The Poisson distribution probability formula is given by :-
[tex]P(X=x)=\dfrac{e^{-\lambda}\lambda^x}{x!}[/tex], where [tex]\lambda[/tex] is the mean of the distribution and x is the number of success
Given : Cars enter a car wash at a mean rate of 2 cars per half an hour.
In an hour, the number of cars enters in car wash = [tex]\lambda=2\times2=4[/tex]
Now, the probability that, in any hour, exactly 5 cars will enter the car wash is given by :-
[tex]P(X=5)=\dfrac{e^{-4}4^5}{5!}=0.156293451851\approx0.1563[/tex]
Therefore, the required probability = 0.1563
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.
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)}
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
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.
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.
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]
Joanne and Ed Greenwood built a new barn with an attached arena. To finance the loan, they paid $1,341 interest on $51,700 at 4%. What was the time using exact interest?
Answer:237 days
Step-by-step explanation:
Interest=[tex]\$ [/tex]1341
Principal[tex]\left ( P\right )=\$ 51,700[/tex]
rate of interest[tex]\left ( t\right )=4%=0.04[/tex]
We know
Simple Interest=[tex]\frac{P\times r\times t}{365}[/tex]
[tex]time\left ( t\right )[/tex]=[tex]\frac{I\times 365}{P\times r}[/tex]
[tex]time\left ( t\right )[/tex]=[tex]\frac{1341\times 365}{51700\times 0.04}[/tex]
[tex]time\left ( t\right )[/tex]=[tex]236.68 days\approx 237 days[/tex]
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
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.
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.
A highly selective boarding school will only admit students who place at least 2.5 standard deviations above the mean on a standardized test that has a mean of 300 and a standard deviation of 24. What is the minimum score that an applicant must make on the test to be accepted?
Answer:
The minimum score that an applicant must make on the test to be accepted is 360.
Step-by-step explanation:
Given : A highly selective boarding school will only admit students who place at least 2.5 standard deviations above the mean on a standardized test that has a mean of 300 and a standard deviation of 24.
To find : What is the minimum score that an applicant must make on the test to be accepted?
Solution :
We apply the z formula,
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Where, z value= 2.5
[tex]\mu=300[/tex] is the mean of the population
[tex]\sigma=24[/tex] is the standard deviation
x is the sample mean.
Substituting the values in the formula,
[tex]2.5=\frac{x-300}{24}[/tex]
[tex]2.5\times24=x-300[/tex]
[tex]60=x-300[/tex]
[tex]x=60+300[/tex]
[tex]x=360[/tex]
Therefore, The minimum score that an applicant must make on the test to be accepted is 360.
The minimum score that an applicant must make on the test to be accepted is 360 and this can be determined by using the z formula.
Given :
A highly selective boarding school will only admit students who place at least 2.5 standard deviations above the mean on a standardized test that has a mean of 300 and a standard deviation of 24.
The formula of z can be used in order to determine the minimum score that an applicant must make on the test to be accepted. The z formula is given by:
[tex]\rm z = \dfrac{x - \mu}{\sigma}[/tex]
Now, substitute the values of the known terms in the above formula.
[tex]2.5=\dfrac{x - 300}{24}[/tex]
Cross multiply in the above equation.
[tex]2.5\times 24 = x - 300[/tex]
60 = x - 300
x = 360
So, the minimum score that an applicant must make on the test to be accepted is 360.
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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.
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)
In a large population of college students, 20% of the students have experienced feelings of math anxiety. If you take a random sample of 10 students from this population, the standard deviation of the number of students in the sample who have experienced math anxiety is:
Hey there!:
The number of students in the sample who have experienced math anxiety is a binomial distribution
Bin (n , p) where n = 10 and p = 0.2
The mean of a binomial distribution is np = 2
The variance is np (1- p) = 1.6 so the standard deviation is √ 1.6 = 1.265
mean=2; standard deviation= 1.265
Hope this helps!
The standard deviation of the of the number of students with anxiety in the sample which is the square root of the variance is 1.265
Probability of those who have experienced anxiety :
P(anxiety) ; P = 20% = 0.2 Number of samples, n = 10The standard deviation can be defined thus :
Standard deviation = √Variance Variance = [np(1 - p)] Variance = [(10 × 0.2 × (1 - 0.2)] = 1.6Standard deviation = √1.6Standard deviation = 1.265Therefore, the standard deviation of the number of sampled students with anxiety is 1.265
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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.
Find the derivative of the function by using the product rule. Do not find the product before finding the derivative. yequalsleft parenthesis 6 x plus 5 right parenthesis left parenthesis 8 x minus 2 right parenthesis StartFraction
Answer:
96x+28
Step-by-step explanation:
Given function,
[tex]y=(6x+5)(8x-2)[/tex]
Differentiating with respect to x,
[tex]\frac{dy}{dx}=\frac{d}{dx}[(6x+5)(8x-2)][/tex]
By the product rule of derivatives,
[tex]\frac{dy}{dx}=\frac{d}{dx}(6x+5).(8x-2)+(6x+5).\frac{d}{dx}(8x-2)[/tex]
[tex]\frac{dy}{dx}=6(8x-2)+(6x+5)8[/tex]
[tex]\frac{dy}{dx}=48x-12+48x+40[/tex]
[tex]\frac{dy}{dx}=96x+28[/tex]
Hence, the derivative of the given function is 96x+28.
Let A = {b, c, d, f, g}, B = {a, b, c}.
a) Find (A u B)
b) Find (A n B)
c) A – B
d) B – A
[tex]A\cup B=\{a,b,c,d,f,g\}\\A\cap B=\{b,c\}\\A\setminus B=\{d,f,g\}\\B\setminus A=\{a\}[/tex]
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]
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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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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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.
A company produces two types of solar panels per year: x thousand of type A and y thousand of type B. The revenue and cost equations, in millions of dollars, for the year are given as follows.
R(x,y) = 6x + 8y
C(x,y) =x^2 − 3xy + 8y^2 + 14x − 50y − 4
Determine how many of each type of solar panel should be produced per year to maximize profit. The company will achieve a maximum profit by selling nothing solar panels of type A and selling nothing solar panels of type B.
Answer:
x=2, y=4.
2 thousand of A panels and 4 of B.
Step-by-step explanation:
First, the profit is determined by the revenue minus the cost, so built a profit equation with that information.
[tex]P(x,y)=R(x,y)-C(x,y)\\ P(x,y)=6x+8y-x^{2}+3xy-8y^{2} -14x+50y+4\\ P(x,y)=-8x+58y-x^{2} -8y^{2} +3xy+4[/tex]
Then, use the partial derivative criteria to determine which is the maximum.
The partial derivative criteria says that in the local maximum or minimum, the partial derivatives are equal to zero, so:
[tex]P_{x}=-8-2x+3y=0\\ P_{y} =58-16y+3x=0[/tex]
So, let's solve the equation system:
First, isolate x:
Eq. 1 [tex]2x=3y-8[/tex]
Eq. 2[tex]3x=16y-58[/tex]
Multiply equation 1 by (-3) and equation 2 by 2:
[tex]-6x=-9y+24\\ 6x=32y-116[/tex]
Sum the equations:
[tex]0=23y-92\\ y=\frac{92}{23}=4[/tex]
Find x with eq. 1 or 2:
[tex]x=\frac{3y-8}{2}= \frac{3*4-8}{2}=2[/tex]
To maximize profit, we need to find the values of x and y that satisfy the equations for R(x,y) and C(x,y), then substitute them into the profit equation. The maximum profit is achieved at x = 8, y = 3.
Explanation:To maximize profit, we need to find the values of x and y that maximize the equation P(x,y) = R(x,y) - C(x,y), where P(x,y) represents the profit.
Substitute the equations for R(x,y) and C(x,y) into the profit equation and simplify. We will get: P(x,y) = -x^2 + 9xy - 6y^2 + 6x + 58y + 4.
To find the maximum value of P(x,y), we need to find the critical points. Use partial derivatives to find the critical points and check which ones give the maximum value for profit. The critical point that gives the maximum profit is x = 8, y = 3.
Learn more about Profit Maximization here:https://brainly.com/question/33809682
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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.
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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%.
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.
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.
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.