True. A rational expression is undefined whenever its denominator is zero. This is because division by zero is not defined.
In mathematics, a rational expression is defined as the quotient of two polynomials, where the denominator represents the divisor. When the denominator of a rational expression becomes zero, it results in division by zero, which is undefined. Division by zero is not a valid operation in mathematics, and it leads to an undefined value. Therefore, to determine if a rational expression is undefined, we need to check if its denominator evaluates to zero. If the denominator is zero, the rational expression is undefined. Also there is division by zero, or related concepts in mathematics.
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If f(x) = (x + 7)2 and g(x) = x2 +9,
which statement is true?
A fo)
B f(-4) > g(-3)
C f(1) = g(1)
D f(2) > g(2)
ANSWER : D
EXPLANATION : 81 > 13 is true
we used the Optional Stopping Theorem to solve the Gambler's Ruin Problem. Specifically, we showed that if Sn So +?=1X; is a biased random walk starting at So = 1, where the steps X; are independent and equal to +1 with probability p1/2 and equal to - 1 with the remaining probability q=1 – p, then the probability of hitting N (jackpot") before 0 ("bust") is (g/p) - 1 PJ So = 1) = (g/p)N-1 Recall that the key to this was the martingale Mn = (g/p)Sn, which is only useful when pq. (a) For any pe [0, 1], argue that P(T<) = 1, where T = inf{n> 1: Sne {0,1}} is the first time that the walk visits 0 or N. Hint: One way is to consider each time that the walk visits 1 before time T, and then compare with a geometric random variable. Note: This is the one condition in the Optional Stopping Theorem that we did not verify during the lecture. (b) Find P(J|So = n) when instead So = n, for some 1
(a) To argue that P(T < ∞) = 1, where T is the first time the walk visits 0 or N, we can consider each time the walk visits 1 before time T.
Suppose the walk visits 1 for the first time at time k < T. At this point, the random walk is in a state where it can either hit 0 before N or hit N before 0.
Let's define a new random variable Y, which represents the number of steps needed for the walk to hit either 0 or N starting from state 1. Y follows a geometric distribution with parameter p since the steps are +1 with probability p and -1 with probability q = 1 - p.
Now, we can compare the random variable T and Y. If T < ∞, it means that the walk has hit either 0 or N before reaching time T. Since T is finite, it implies that the walk has hit 1 before time T. Therefore, we can say that T ≥ Y.
By the properties of the geometric distribution, we know that P(Y = ∞) = 0. This means that there is a non-zero probability of hitting either 0 or N starting from state 1. Therefore, P(T < ∞) = 1, as the walk is guaranteed to eventually hit either 0 or N.
(b) To find P(J|So = n), where So = n, we need to determine the probability of hitting N before hitting 0 starting from state n.
Recall that the probability of hitting N before 0 starting from state 1 is given by (g/p)^(N-1), as shown in the Optional Stopping Theorem formula. In our case, since the walk starts at state n, we need to adjust the formula accordingly.
The probability of hitting N before 0 starting from state n can be calculated as P(J|So = n) = (g/p)^(N-n).
This probability takes into account the number of steps required to reach N starting from state n. It represents the likelihood of hitting the jackpot (N) before going bust (0) when the walk starts at state n.
It's worth noting that this probability depends on the values of p, q, and N.
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Find the value of the variable.
20
12
A. 10
В. 13
C. 16
D.18
Answer:
option c.
by Pythagoras theorem.
hypotenuse²=height ²+base²
20²=x²+12²
400=x²+144
400-144=x²
256=x²
256½=x
16=x
9. Consider the following permutation. 2 3 4 5 (₂2 24 5 1 6 a. Decompose into a product of cycles b. Decompose into the product of transposition. C. Decide if o is even or odd. 6 7 3 3)
a. The decomposition into cycles is (2 5 6 3 4).
b. The decomposition into transpositions is (2 5)(5 6)(6 3)(3 4).
c. The permutation is even.
We have,
To decompose the given permutation into cycles, we start with the first element and follow its path:
Starting with 2, we see that it goes to 5.
5 goes to 6.
6 goes to 3.
3 goes to 4.
Finally, 4 goes back to 2, completing the cycle.
The cycle can be represented as (2 5 6 3 4).
To decompose the permutation into transpositions, we consider each adjacent pair of elements and write them as separate transpositions:
(2 5)(5 6)(6 3)(3 4)
Now, we can observe that the permutation has a total of four transpositions.
To determine if the permutation is even or odd, we need to count the number of transpositions.
In this case, there are four transpositions, which means the permutation is even since the number of transpositions is even.
Therefore,
a. The decomposition into cycles is (2 5 6 3 4).
b. The decomposition into transpositions is (2 5)(5 6)(6 3)(3 4).
c. The permutation is even.
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The number of pizzas consumed per month by university students is normally distributed with a mean of 12 and a standard deviation of 3. A. What proportion of students consume more than 13 pizzas per month? Probability = = B. What is the probability that in a random sample of size 10, a total of more than 110 pizzas are consumed? Probability = Note: You can earn partial credit on this problem.
The probability to consume more than 13 pizzas per month is 0.3707 and more than 110 pizzas in a random sample of size 10 is 0.9646.
The number of pizzas consumed per month by university students is normally distributed with a mean of 12 and a standard deviation of 3.
A. Probability that more than 13 pizzas consumed by students:
For finding the probability, we need to find the Z-score first.
z = (x - μ) / σz = (13 - 12) / 3z = 0.3333
Now, we have to use the z-table to find the probability associated with the z-score 0.3333.
The area under the normal distribution curve to the right of 0.3333 is 0.3707 (rounded off to 4 decimal places).
Thus, the probability that a student consumes more than 13 pizzas per month is 0.3707.
B. Probability that more than 110 pizzas consumed in a random sample of size 10:
Let x be the number of pizzas consumed in the random sample of size 10.
Then, the distribution of x is a normal distribution with the mean = 10 × 12 = 120 and standard deviation = √(10 × 3²) = 5.4772
We have to find the probability that the total number of pizzas consumed is greater than 110. i.e. P(x > 110).
For finding the probability, we need to find the Z-score first.z = (110 - 120) / 5.4772z = -1.8257
The area under the normal distribution curve to the right of -1.8257 is 0.9646 (rounded off to 4 decimal places).
Thus, the probability that more than 110 pizzas are consumed in a random sample of size 10 is 0.9646.
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Question is in picture
Step-by-step explanation:
you're multiple times a day po
b. If each square has a side length of 61 cm, write an expression for the surface area and another for the volume of the figure
Answer:
6*(61^2) and 61^3
Step-by-step explanation:
If the squares have a side length of 61 (assuming this is a cube) our surface area is 6*(61^2) because each side is a square and there are six sides.
As for the volume, we have 61^3.
Hope this was helpful.
~cloud
what is 21x+1 in simple form
Answer:
( 21 x X ) + 1
Step-by-step explanation:
What are the first four marks on the x-axis for the following graph?
Y= 3/4sin3x/2
Answer:
uhh i don't know the answer sorry
Step-by-step explanation:
ummm i Don't know
Bakery makes cupcakes and three different flavors chocolate, vanilla, and strawberry, with two choices of topics, butterscotch or pumpkin in two different sizes small or large how many different outcomes are there?
Answer:
24 or 12
Step-by-step explanation:
Multiplication
help me find the answer please
Answer:
A x<1125
Step-by-step explanation:
Nicole has a bag filed win 8 red marbles 6 blue marbles and 9 green marbles. What is the probability of her choosing a red marble, then a blue marble without replacing them
Answer:
34.78
Step-by-step explanation:
8/23
PLEASE HELPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
x = 5 ; z = 70
Step-by-step explanation:
Vertical angles have the same degree measure
(13x + 45) = 110
13x + 45 = 110
-45 -45
13x = 65
/13 /13
x = 5
Complementary angles add up to 180°
110 + z = 180
-110 -110
z = 70
Answer:
X = 5º
Z = 70º
Step-by-step explanation:
So we know that vertical angles are congruent. So what we do to figure out x is set the equation equal to 110º because we are given that. And then we solve for x.
(13x + 45) = 110
13x + 45 = 110
-45 -45
----------------------
13x = 65
÷13 ÷13
---------------
x = 5
Now, we plug x into the equation. (13x5 + 45) = 110 so we know that x = 5
Now, we also know that a straight line equals 180º so what we do is subtract 110 from 180.
180 - 110= 70º
z = 70º
To go from Seattle, Washington, to Los Angeles, California, using the Interstate Train Company, one must travel through San Francisco, California, or Salt Lake City, Utah. Using the information given in the table, which route is shorter and by how much?
Answer:
The answer is BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
To travel 1400miles from Seattle to Los Angeles it will take the train 35 hours
What is rate?A rate is the ratio between two related quantities in different units. For example , the train travels 80 miles in 2hrs . the two quantities that are related here are distance and time
here, we have,
distance in miles and time in hours
the time to travel for 1 mile
= 2/80 = 1/40 miles
for the train to travel 1400 miles , it will take it
1/40× 1400
= 35 hours
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complete question:
There is a train that travels from Seattle, Washington, to Los Angeles, California. In its first 2 hours the train went about 80 miles including stops. At this rate, how longer will it take to travel the 1400 miles from Seattle to Los Angeles?
I wanted to find you a higher-order differential equation that had a real-life application. Here is what I found: a cylindrical shaft of length L is rotating with angular velocity w. Find a function y(x) that models the deformation of the cylinder. Of course this is a little bit more specialized to the field of dynamics than what we studied this semester, but what I learned was that this can be modeled: dºy dx4 - a4y = 0
The given differential equation d⁴y/dx⁴ - a⁴y = 0 models the deformation of a cylindrical shaft rotating with angular velocity ω. The function y(x) represents the deformation of the cylinder.
To solve the differential equation, we can assume a solution of the form y(x) = A*cos(ax) + B*sin(ax), where A and B are constants to be determined, and 'a' is a parameter related to the properties of the cylinder.
Taking the fourth derivative of y(x) and substituting it into the differential equation, we have:
d⁴y/dx⁴ = -a⁴(A*cos(ax) + B*sin(ax))
Substituting the fourth derivative and y(x) into the differential equation, we get:
-a⁴(A*cos(ax) + B*sin(ax)) - a⁴(A*cos(ax) + B*sin(ax)) = 0
Simplifying the equation, we have:
-2a⁴(A*cos(ax) + B*sin(ax)) = 0
Since the equation must hold for all x, the coefficient of each term (cos(ax) and sin(ax)) must be zero:
-2a⁴A = 0 (coefficient of cos(ax))
-2a⁴B = 0 (coefficient of sin(ax))
From these equations, we find that A = 0 and B = 0, which implies that the only solution is the trivial solution y(x) = 0.
Therefore, the solution to the differential equation d⁴y/dx⁴ - a⁴y = 0 is y(x) = 0.
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A hiker is lost in the forest, but has his cell phone with a weak signal. Cell phones with GPS can give an approximate location through triangulation, which works by giving distances from two known points. Suppose the hiker is within distance of two cell phone towers that are 22.5 miles apart along a straight highway (running east to west, double-dashed line). Based on the signal delay, it can be determined that the signal from the hiker's phone is 14.2 miles from Tower A and 10.9 miles from Tower B. Assume the hiker is traveling a straight path south reach the highway quickly. How far must the hiker travel to reach the highway
Answer:
The distance the hiker must travel is approximately 5.5 miles
Step-by-step explanation:
The distance between the two cell phone towers = 22.5 miles
The distance between the hiker's phone and Tower A = 14.2 miles
The distance between the hiker's phone and Tower B = 10.9 miles
The direction of the highway along which the towers are located = East to west
The direction in which the hiker is travelling to reach the highway quickly = South
By cosine rule, we have;
a² = b² + c² - 2·b·c·cos(A)
Let 'a', 'b', and 'c', represent the sides of the triangle formed by the imaginary line between the two towers, the hiker's phone and Tower A, and the hiker's hone and tower B respectively, we have;
a = 22.5 miles
b = 14.2 miles
c = 10.9 miles
Therefore, we have;
22.5² = 14.2² + 10.9² - 2 × 14.2 × 10.9 × cos(A)
cos(A) = (22.5² - (14.2² + 10.9²))/( - 2 × 14.2 × 10.9) ≈ -0.6
∠A = arccos(-0.6) ≈ 126.9°
By sine rule, we have;
a/(sin(A)) = b/(sin(B)) = c/(sin(C))
∴ sin(B) = b × sin(A)/a
∴ sin(B) = 14.2×(sin(126.9°))/22.5
∠B = arcsine(14.2×(sin(126.9°))/22.5) ≈ 30.31°
∠C = 180° - (126.9° - 30.31°) = 22.79° See No Evil
The distance the hiker must travel, d = c × sin(B)
∴ d = 10.9 × sin(30.31°) ≈ 5.5
Therefore, the distance the hiker must travel, d ≈ 5.5 miles.
The ratio of boys to girls at the play was 4 to 3. If there were 15 girls, how many boys were there?
Answer:
20 boys
Step-by-step explanation:
If there are 4 boys for every 3 girls, multiply both numbers by 5 (3*5 = 15) to find the number of boys.
Answer:
20
Step-by-step explanation:
4/3 = ?/15
multiply both sides by 15
15*4/3 = ?
? = 20
in counseling and psychotherapy groups, member-to-member contact outside of group often results in _____ and _____. group of answer choices
In counseling and psychotherapy groups, member-to-member contact outside of the group often results in subgroups and hidden agendas
According to various research studies on Personal relationships among specialty group members, such as counseling and psychotherapy groups, which was concluded that member-to-member contact outside of the group often results in SUBGROUP and HIDDEN AGENDAS.
However, Most of the time, which can lead to damaging situations.
Therefore it is considered a sensible strategy to prevent the formation of such subgroups.
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Please answer correctly! I will mark you Brainliest!
Answer:
4.1 inches
I would appreciate Brainliest, but no worries.
Answer:
6
Step-by-step explanation:
the formula for the sphere's volume is [tex]\frac{4}{3} *\pi *r^3[/tex]
so when you set that equal to 288[tex]\pi[/tex], you get 6 as the radius
Plot the x-intercepts, the y-intercept, and the vertex of the graph (Must use Desmos!)
Answer:
x-intercept: (-1,0)
y-intercept: (0,3)
Vertex: (-2,-1)
Step-by-step explanation:
Let X1 and X2 be independent random variables with mean μ and variance σ2. Suppose that we have two estimators of μ: Math and 1 = X1+X2/2 and math2=x1 + 3x2/4
(a) Are both estimators unbiased estimators of μ? (b) What is the variance of each estimator? Hint: Law of expected values
(a) Math2 is not an unbiased estimator of μ. (b)Math1 has a variance of
σ[tex]^{2}[/tex] and Math2 has a variance of 5σ[tex]^2[/tex]/8
(a) Neither of the estimators, Math1 or Math2, is an unbiased estimator of μ. An unbiased estimator should have an expected value equal to the parameter being estimated, in this case, μ.
For Math1,
the expected value is
E[Math1] = E[([tex]X_{1}[/tex] + [tex]X_{2}[/tex]) / 2]
= (E[[tex]X_{1}[/tex]] + E[[tex]X_{2}[/tex]]) / 2
= μ/2 + μ/2 = μ,
which means Math1 is an unbiased estimator of μ.
For Math2,
the expected value is
E[Math2] = E[([tex]X_{1}[/tex] + [tex]3X_{2}[/tex]) / 4]
= (E[[tex]X_{1}[/tex]] + 3E[[tex]X_{2}[/tex]]) / 4
= μ/4 + 3μ/4
= (μ + 3μ) / 4
= 4μ/4
= μ/2.
(b) To calculate the variances of the estimators, we'll use the property that the variance of a sum of independent random variables is the sum of their variances.
For Math1,
the variance is Var[Math1]
= Var[([tex]X_{1}[/tex] + [tex]X_{2}[/tex]) / 2]
= (Var[[tex]X_{1}[/tex]] + Var[[tex]X_{2}[/tex]]) / 4
= σ[tex]^2[/tex]/2 + σ[tex]^2[/tex]/2
= σ[tex]^2[/tex]
For Math2,
the variance is Var[Math2]
= Var[([tex]X_{1}[/tex] + [tex]3X_{2}[/tex]) / 4]
= (Var[[tex]X_{1}[/tex]] + 9Var[[tex]X_{1}[/tex]]) / 16
= σ[tex]^2[/tex]/4 + 9σ[tex]^2[/tex]/16
= 5σ[tex]^2[/tex]/8
Math1 has a variance of σ[tex]^2[/tex]
and Math2 has a variance of 5σ[tex]^2[/tex]/8
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In the woods, a hunter is shooting at a hare. The probability of success for his first shot is 12. If he misses his first shot, the probability of success for his second shot is 1/4. If he misses his second shot, the probability of success for his third shot is 1/8. If he misses his third shot, the probability of success for his forth shot is 1/16. (1) The probability that he hits the hare within his first 2 shots is most nearly (a) 0.7 (b) 0.8 (c) 0.9 (d) 1 (2) The probability that he hits the hare within his first 3 shots is most nearly (a) 1 (b) 0.9 (c) 0.8 (d) 0.7 (3) The probability that he hits the hare within his first 4 shots is most nearly (a) 0.9 (b) 0.7 (c)1 (d) 0.8
The probability that he hits the hare within his first 4 shots is 0.8789.
Probability of success for the first shot = P1 = 12 Probability of missing the first shot = 1 – P1 = 1 – 12 = 12 Probability of
success for the second shot, given that the first shot missed = P2 = 14Hence, the probability that he hits the hare within
his first 2 shots is:P1 + (1 – P1)P2= 12+(12)×(14)= 12+16= 38(2) The probability that he hits the hare within his first 3 shots is
most nearly (a) 1 (b) 0.9 (c) 0.8 (d) 0.7We have to find the probability of hitting the hare within his first 3 shots. Probability
of success for the first shot = P1 = 12Probability of missing the first shot = 1 – P1 = 1 – 12 = 12Probability of success for the
second shot, given that the first shot missed = P2 = 14Probability of success for the third shot, given that the first two
shots missed = P3 = 18Hence, the probability that he hits the hare within his first 3 shots is:P1 + (1 – P1)P2 + (1 – P1)(1 –
P2)P3= 12+(12)×(14)+(12)×(34)×(18)= 12+16+18×(12)= 1316= 0.8125(3) The probability that he hits the hare within his first 4
shots is most nearly (a) 0.9 (b) 0.7 (c)1 (d) 0.8We have to find the probability of hitting the hare within his first 4
shots. Probability of success for the first shot = P1 = 12Probability of missing the first shot = 1 – P1 = 1 – 12 = 12Probability
of success for the second shot, given that the first shot missed = P2 = 14Probability of success for the third shot, given
that the first two shots missed = P3 = 18 Probability of success for the fourth shot, given that the first three shots missed
= P4 = 116Hence, the probability that he hits the hare within his first 4 shots is:P1 + (1 – P1)P2 + (1 – P1)(1 – P2)P3 + (1 – P1)
(1 – P2)(1 – P3)P4= 12+(12)×(14)+(12)×(34)×(18)+(12)×(34)×(78)×(116)= 12+16+18×(12)+18×(78)×(116)= 7892= 0.8789
Therefore, the answer is (d) 0.8.
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2/5+3/6 GETS BRAINLIEST
Answer:
27/30
Step-by-step explanation:
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Answer:
9/10 or 0.9
Step-by-step explanation:
When adding fractions, you look at each of them as an equal number, or a whole.
25+36
91
So, now all we have to do is convert it to it's closest form. (In tenths, since we are adding tenths.)
90
And it would be 9/10, or 0.9
Hope this helps!
simplify the expression
Answer:
7m ^1÷2
Step-by-step explanation:
see attached joint
hope it helps
Find three numbers whose sum is 21 and whose sum of squares is a minimum. The three numbers are________ (Use a comma to separate answers as needed.)
the three numbers whose sum is 21 and whose sum of squares is a minimum are 7, 7, and 7.
To find three numbers whose sum is 21 and whose sum of squares is a minimum, we can use a mathematical technique called optimization. Let's denote the three numbers as x, y, and z.
We need to minimize the sum of squares, which can be expressed as the function f(x, y, z) = x² + y² + z²
Given the constraint that the sum of the three numbers is 21, we have the equation x + y + z = 21.
To find the minimum value of f(x, y, z), we can use the method of Lagrange multipliers, which involves solving a system of equations.
First, let's define a Lagrange multiplier, λ, and set up the following equations:
1. ∂f/∂x = 2x + λ = 0
2. ∂f/∂y = 2y + λ = 0
3. ∂f/∂z = 2z + λ = 0
4. Constraint equation: x + y + z = 21
Solving equations 1, 2, and 3 for x, y, and z, respectively, we get:
x = -λ/2
y = -λ/2
z = -λ/2
Substituting these values into the constraint equation, we have:
-λ/2 - λ/2 - λ/2 = 21
-3λ/2 = 21
λ = -14
Substituting λ = -14 back into the expressions for x, y, and z, we get:
x = 7
y = 7
z = 7
Therefore, the three numbers whose sum is 21 and whose sum of squares is a minimum are 7, 7, and 7.
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20 points for this!! thank you
Answer:
not a function becuz 2 repeats its self twice
Step-by-step explanation:
Answer:
You are welcome
Step-by-step explanation:
What is the surface area of a cylinder with height 8 ft and radius 4 ft
The Surface area of the cylinder with a height of 8 ft and a radius of 4 ft is approximately 301.44 square feet.
The surface area of a cylinder, we need to consider the lateral surface area and the area of the two circular bases.
The lateral surface area of a cylinder can be determined by multiplying the height of the cylinder by the circumference of its base. The formula for the lateral surface area (A) of a cylinder is given by A = 2πrh, where r is the radius and h is the height of the cylinder.
In this case, the height of the cylinder is 8 ft and the radius is 4 ft. Therefore, the lateral surface area can be calculated as follows:
A = 2π(4 ft)(8 ft)
A = 64π ft²
The area of each circular base can be calculated using the formula for the area of a circle, which is A = πr². In this case, the radius is 4 ft. Therefore, the area of each circular base is:
A_base = π(4 ft)²
A_base = 16π ft²
Since a cylinder has two circular bases, the total area of the two bases is:
A_bases = 2(16π ft²)
A_bases = 32π ft²
the total surface area, we sum the lateral surface area and the area of the two bases:
Total surface area = Lateral surface area + Area of bases
Total surface area = 64π ft² + 32π ft²
Total surface area = 96π ft²
Now, let's calculate the numerical value of the surface area:
Total surface area ≈ 96(3.14) ft²
Total surface area ≈ 301.44 ft²
Therefore, the surface area of the given cylinder, with a height of 8 ft and a radius of 4 ft, is approximately 301.44 square feet.
In conclusion, the surface area of the cylinder with a height of 8 ft and a radius of 4 ft is approximately 301.44 square feet.
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For f, g € L’[a,b], prove the Cauchy-Schwarz inequality |(f,g)| = ||$||||$||. = Hint: Define a function Q(t) = (f + tg, f + tg) for any real number t. Use the rules of inner product to expand this expression and obtain a quadratic polynomial in t; because Q(t) > 0 (why?), the quadratic polynomial can have at most one real root. Examine the discriminant of the polynomial.
Given that f, g ∈ L’[a, b], we need to prove the Cauchy-Schwarz inequality, |(f, g)| = ||$|| . ||$||.
The Cauchy-Schwarz inequality for inner product in L’[a, b] states that for all f, g ∈ L’[a, b],|(f, g)| ≤ ||$|| . ||$||Proof: Consider a function Q(t) = (f + tg, f + tg) for any real number t. Then, by using the rules of inner product, we can expand this expression and obtain a quadratic polynomial in t.$$Q(t) = (f + tg, f + tg) = (f, f) + t(f, g) + t(g, f) + t^2(g, g)$$$$ = (f, f) + 2t(f, g) + t^2(g, g)$$. Now, Q(t) > 0 because Q(t) is a sum of squares. So, Q(t) is a quadratic polynomial that can have at most one real root since Q(t) > 0 for all t ∈ R.
To find the discriminant of Q(t), we need to solve the equation Q(t) = 0.$$(f, f) + 2t(f, g) + t^2(g, g) = 0$$.
The discriminant of Q(t) is:$$D = (f, g)^2 - (f, f)(g, g)$$
Since Q(t) > 0 for all t ∈ R, the discriminant D ≤ 0.$$D = (f, g)^2 - (f, f)(g, g) ≤ 0$$$$\Right arrow (f, g)^2 ≤ (f, f)(g, g)$$$$\Right arrow |(f, g)| ≤ ||$|| . ||$||$$
Thus, |(f, g)| = ||$|| . ||$||, which proves the Cauchy-Schwarz inequality. Therefore, the given statement is true.
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Please help me with this
Answer:
x = -2
Step-by-step explanation:
y = -4
2x -3y = 8
Substitute the first equation into the second equation
2x - 3(-4) = 8
2x +12 = 8
Subtract 12 from each side
2x+12-12 = 8-12
2x = -4
Divide by 2
2x/2 = -4/2
x = -2
The cost of a banquet at Nick's Catering is $215 plus $27.50 per person. If
the total cost of a banquet was $2827.50, how many people were invited?
Answer:
x = 95
Step-by-step explanation:
Given that,
The cost of a banquet at Nick's Catering is $215 plus $27.50 per person
The total cost of a banquet was $2827.50
We need to find the number of people invited. Let there are x people. So,
215+27.5x = 2827.50
27.5x = 2827.50 -215
27.5x = 2612.5
x = 95
So, there are 95 people that were invited.