Answer:
C) 1/2
Step-by-step explanation:
3 of the 6 numbers on a cube are even. 3/6 = 1/2
Evaluating probability: A particular type of mouse's weights are normally distributed, with a mean of 359 grams and a standard deviation of 33 grams. If you pick one mouse at random, find the following: (round all probabilities to four decimal places) a) What is the probability that the mouse weighs less than 405 grams? b) What is the probability that the mouse weighs more than 461 grams? c) What is the probability that the mouse weighs between 406 and 461 grams? d) Is it unlikely that a randomly chosen mouse would weigh less than 405 grams?
a) Probability that the mouse weighs less than 405 grams: 0.8461
b) Probability that the mouse weighs more than 461 grams: 0.0062
c) Probability that the mouse weighs between 406 and 461 grams: 0.8302
d) It is not unlikely that a randomly chosen mouse would weigh less than 405 grams.
What is the probability that the mouse weighs less than 405 grams?Using normal distribution;
a) Probability that the mouse weighs less than 405 grams:
To find this probability, we need to calculate the area under the normal curve to the left of 405 grams. We can use the z-score formula to standardize the value.
z = (x - μ) / σ
where x is the value, μ is the mean, and σ is the standard deviation.
For 405 grams:
z = (405 - 359) / 33
Using a standard normal distribution table or calculator, we can find the probability associated with the z-score.
The probability that the mouse weighs less than 405 grams is approximately 0.8461.
b) Probability that the mouse weighs more than 461 grams:
Similarly, we need to calculate the area under the normal curve to the right of 461 grams.
For 461 grams:
z = (461 - 359) / 33
Using the standard normal distribution table or calculator, we find the probability associated with the z-score.
The probability that the mouse weighs more than 461 grams is approximately 0.0062.
c) Probability that the mouse weighs between 406 and 461 grams:
To find this probability, we calculate the area under the normal curve between the z-scores for 406 and 461 grams.
For 406 grams:
z₁ = (406 - 359) / 33
For 461 grams:
z₂ = (461 - 359) / 33
We can then find the probability associated with each z-score and subtract them to get the desired probability.
The probability that the mouse weighs between 406 and 461 grams is approximately 0.8302.
d) Is it unlikely that a randomly chosen mouse would weigh less than 405 grams?
To determine if it is unlikely, we compare the probability from part (a) with the significance level or threshold value. Let's assume a significance level of 0.05 (5%).
The probability from part (a) is 0.8461, which is greater than 0.05. Therefore, it is not unlikely that a randomly chosen mouse would weigh less than 405 grams.
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Consider the differential equation, and its boundary conditions x2 dạy d.x2 2.x dy da 4y = re-2 y(0) = y(00) = 0 - Determine the Green's function and use it to get the solution
Answer:
y(x)=0
Step-by-step explanation:
To solve the given differential equation using Green's function, we need to first determine the Green's function associated with the given boundary conditions.
The Green's function, G(x, ξ), satisfies the following equation:
(x^2 d^2G / dx^2) + (2x dG / dx) - 4G = δ(x - ξ)
where δ(x - ξ) is the Dirac delta function. We can solve this equation subject to the boundary conditions:
G(0, ξ) = G(∞, ξ) = 0
To solve this differential equation, we assume a solution of the form:
G(x, ξ) = A(x)B(ξ)
Substituting this form into the differential equation and simplifying, we get:
x^2 d^2A / dx^2 + 2x dA / dx - 4A = 0
This is a homogeneous second-order ordinary differential equation. We can solve it by assuming a power series solution of the form:
A(x) = ∑[n=0 to ∞] (a_n x^n)
Substituting this series into the differential equation and equating coefficients of like powers of x, we get:
a_n [(n + 2)(n + 1) - 4] = 0
Solving this equation for the coefficients, we find:
a_0 = 0
a_1 = 0
a_n = 4 / [(n + 2)(n + 1)] for n ≥ 2
Therefore, the solution for A(x) is:
A(x) = 4 * ∑[n=2 to ∞] (x^n / [(n + 2)(n + 1)])
Now, we can substitute the solution for A(x) into the form of the Green's function:
G(x, ξ) = A(x)B(ξ)
G(x, ξ) = 4 * ∑[n=2 to ∞] (x^n / [(n + 2)(n + 1)]) * B(ξ)
To determine B(ξ), we impose the boundary conditions:
G(0, ξ) = 0 => 4 * ∑[n=2 to ∞] (0 / [(n + 2)(n + 1)]) * B(ξ) = 0
G(∞, ξ) = 0 => 4 * ∑[n=2 to ∞] (ξ^n / [(n + 2)(n + 1)]) * B(ξ) = 0
From these conditions, we can conclude that B(ξ) = 0. Hence, the Green's function is:
G(x, ξ) = 0
Now, to obtain the solution to the differential equation, we can use the Green's function in the following integral form:
y(x) = ∫[0 to ∞] G(x, ξ) f(ξ) dξ
where f(ξ) is the inhomogeneous term in the original differential equation.
Since G(x, ξ) = 0, the integral evaluates to zero as well. Therefore, the solution to the given differential equation is:
y(x) = 0
In conclusion, the solution to the differential equation with the given boundary conditions is y(x) = 0.
***WILL BE MARKED BRAINLIEST***
Answer:
a
Step-by-step explanation:
I need help plz I’ll appreciated
Answer:
y = x -3
Step-by-step explanation:
is known that 47% of new freshmen at State University will graduate within 6 years. Suppose we take a random sample of n=64 new freshmen at State University. Let X = the number of these freshmen who graduate within 6 years. (Do not use a normal approximation for this problem. This is a binomial problem.) a) What is the probability that X < 29? b) What is the probability that 28 SXS 31? c) What is the probability that X = 31? d) What is the expected value of X? e) What is the variance of X?
On the probability, expected value and variance :
a) 0.000013b) 0.00414c) 0.000016d) 30.08e) 11.84How to solve for a ransom sample?a) The probability that X < 29 is given by:
P(X < 29) = P(X = 0) + P(X = 1) + ... + P(X = 28)
The probability of each of these events is given by the binomial distribution:
[tex]P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k}[/tex]
where n = 64, p = 0.47, and k = 0, 1, ..., 28.
Plugging in these values:
[tex]P(X < 29) = \binom{64}{0} (0.47)^0 (1 - 0.47)^{64 - 0} + \binom{64}{1} (0.47)^1 (1 - 0.47)^{64 - 1} + ... + \binom{64}{28} (0.47)^{28} (1 - 0.47)^{64 - 28}[/tex]
≈ 0.000013
b) The probability that 28 SXS 31 is given by:
P(28 SXS 31) = P(X = 28) + P(X = 29) + P(X = 30) + P(X = 31)
Plugging in the values from the binomial distribution:
[tex]P(28 SXS 31) = \binom{64}{28} (0.47)^{28} (1 - 0.47)^{64 - 28} + \binom{64}{29} (0.47)^{29} (1 - 0.47)^{64 - 29} + \binom{64}{30} (0.47)^{30} (1 - 0.47)^{64 - 30} + \binom{64}{31} (0.47)^{31} (1 - 0.47)^{64 - 31}[/tex]
≈ 0.00414
c) The probability that X = 31 is given by:
[tex]P(X = 31) = \binom{64}{31} (0.47)^{31} (1 - 0.47)^{64 - 31}[/tex]
≈ 0.000016
d) The expected value of X is given by:
E(X) = np
where n = 64 and p = 0.47.
E(X) = 64 (0.47) = 30.08
e) The variance of X is given by:
Var(X) = np(1 - p)
Var(X) = 64 (0.47) (1 - 0.47) = 11.84
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part d: using the diameter of each pizza, determine the scale factor relationship between the pizzas. (1 point)
To determine the scale factor relationship between the pizzas based on their diameters, we need to compare the sizes of the pizzas. The scale factor represents the ratio between the corresponding measurements of two similar objects.
In this case, we would compare the diameters of the pizzas. The scale factor can be calculated by dividing the diameter of one pizza by the diameter of another pizza. For example, if Pizza A has a diameter of 12 inches and Pizza B has a diameter of 8 inches, the scale factor between them would be: Scale Factor = Diameter of Pizza A / Diameter of Pizza B = 12 inches / 8 inches = 1.5. Therefore, the scale factor relationship between the pizzas is 1.5. This means that the diameter of Pizza A is 1.5 times larger than the diameter of Pizza B.
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A square underwent a dilation using a scale factor of 1:4. Find the missing side length, x, of the smaller square
Answer:
[tex]x= 3.5[/tex]
Step-by-step explanation:
Given
[tex]k =1:4[/tex] --- scale factor
See attachment for squares
Required
Find x
The corresponding side of length x on the bigger square is 14.
So, we have:
[tex]k = x : 14[/tex]
Equate both values of k
[tex]x : 14 = 1 : 4[/tex]
Express as fractions
[tex]\frac{x }{ 14 }= \frac{1 }{ 4}[/tex]
Solve for x
[tex]x= \frac{1 }{ 4} * 14[/tex]
[tex]x= \frac{14}{4}[/tex]
[tex]x= 3.5[/tex]
Which function is graphed?
Answer: it’s B or C
Step-by-step explanation
The equation below has infinitely many solutions.
-53 + 2 + 2x + 4 = ax + b
True
False
Answer:
definatly not infinitely it should be only one correct answer so false
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
-53 + 2+ 2x + 4 = ax + b
-47 + 2x = ax + b
Since there is 3 variables you need 3 equations which you don't have. After simplifying there is nothing else you can do.
please help
A tennis club has 15 members: eight women and seven men. How many different teams may be formed consisting of one woman and one man on each team?
Answer:
12870ways
Step-by-step explanation:
Combination has to do with selection
Total members in a tennis club = 15
number of men = 8
number of women = 7
Number of team consisting of women will be expressed as 15C7
15C7 = 15!/(15-7)!7!
15C7 = 15!/8!7!
15C7 = 15*14*13*12*11*10*9*8!/8!7!
15C7 = 15*14*13*12*11*10*9/7 * 6 * 5 * 4 * 3 * 2
15C7 = 15*14*13*12*11/56
15C7 = 6,435 ways
Number of team consisting of men will be expressed as 15C8
15C8 = 15!/8!7!
15C8 = 15*14*13*12*11*10*9*8!/8!7!
15C8 = 15*14*13*12*11*10*9/7 * 6 * 5 * 4 * 3 * 2
15C8 = 6,435 ways
Adding both
Total ways = 6,435 ways + 6,435 ways
Total ways = 12870ways
Hence the required number of ways is 12870ways
Evaluate the integral by making an appropriate change of variables. x – 2y dA, where R is the parallelogram 3x +y R = = enclosed by the lines &– 2y=0, x-2y=4, 3x+y=1, and 3x +y=8.
a. The parallelogram R is degenerate, consisting of a single point (4, 0).
b. The integral ∬_R (x - 2y) dA over the degenerate parallelogram R evaluates to 0.
a. To evaluate the integral ∬_R (x - 2y) dA, where R is the parallelogram enclosed by the lines -2y = 0, x - 2y = 4, 3x + y = 1, and 3x + y = 8, we can make an appropriate change of variables to simplify the integral. Here's how to do it step by step:
Identify the vertices of the parallelogram R by finding the intersection points of the given lines. Solving the system of equations:
-2y = 0 (equation 1)
x - 2y = 4 (equation 2)
3x + y = 1 (equation 3)
3x + y = 8 (equation 4)
From equation 1, we have y = 0. Substituting this into equation 2, we get x = 4. Therefore, one vertex of the parallelogram is (4, 0).
Next, solving equations 3 and 4, we find another intersection point by equating the expressions for y:
1 - 3x = 8 - 3x
-3x + 1 = -3x + 8
1 = 8
This is a contradiction, so equations 3 and 4 are parallel lines that do not intersect. Therefore, the parallelogram R is degenerate and only consists of a single point (4, 0).
b. Make an appropriate change of variables to simplify the integral. Since the parallelogram R is degenerate and consists of a single point, we can use a change of variables to transform the integral to a simpler form. Let's introduce new variables u and v, defined as follows:
u = x - 2y
v = 3x + y
The Jacobian determinant of the transformation is calculated as follows:
|Jacobian| = |∂(x, y)/∂(u, v)|
= |∂x/∂u ∂x/∂v|
= |1 -2|
= 2
c. Express the integral in terms of the new variables. We need to find the limits of integration in terms of u and v. Since the parallelogram R is degenerate and consists of a single point, the limits of integration are u = x - 2y = 4 - 2(0) = 4 and v = 3x + y = 3(4) + 0 = 12.
The integral becomes:
∬_R (x - 2y) dA = ∫∫_R (x - 2y) |Jacobian| dudv
= ∫∫_R (x - 2y) (2) dudv
= 2∫∫_R (u) dudv
Evaluate the integral. Since R is degenerate and consists of a single point (4, 0), the integral becomes:
2∫∫_R (u) dudv = 2u ∫∫_R dudv = 2u(Area of R)
The area of a degenerate parallelogram is zero, so the integral evaluates to:
2u(Area of R) = 2(4)(0) = 0.
Therefore, the value of the integral ∬_R (x - 2y) dA over the given degenerate parallelogram R is 0.
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The volume of a sphere is 36 cubic inches. What is the radius of the sphere?
Answer:
ok we know that volume of a sphere is 4/3 pi r cubed so just replace the letters with the entities given
Answer:
2.7 cm
Step-by-step explanation:
what is 8.7+[2.7-(4x0.5)]x9
Event A: You roll a double. Event B: The sum of the two scores is even. Event C: The score on the blue die is greater than the score on the red die. Event D: You get a 6 on the red die. 1. Think about the probability of two of these events both happening in one roll of the two dice. For example, the probability that events A and D both occur—"P(A and D)"—is 1/36, because only a double 6 satisfies the requirements. There are five other possibilities of two events both happening in one roll. What are the probabilities of those five other possibilities? a. P(A and B) b. PIA and C) C. P(B and C) d. P(B andD) e. P(C and D)
The probabilities of the five other possibilities are as follows: a) P(A and B) = 1/18, b) P(A and C) = 1/12, c) P(B and C) = 5/18, d) P(B and D) = 1/18, and e) P(C and D) = 1/6.
a) To calculate P(A and B), we need to find the number of outcomes where both a double and an even sum occur. There are 18 possible outcomes with doubles (6 possibilities) multiplied by the number of outcomes where the sum is even (3 possibilities), resulting in a probability of 1/18.
b) P(A and C) requires both a double and the blue die having a higher score than the red die. Out of the 36 possible outcomes, there are 12 outcomes where a double occurs and the blue die score is greater than the red die score, resulting in a probability of 1/12.
c) To calculate P(B and C), we need to find the number of outcomes where the sum is even and the blue die score is greater than the red die score. There are 18 possible outcomes where the sum is even, and out of these, 5 outcomes also satisfy the condition for the blue die score being greater than the red die score. Therefore, the probability is 5/18.
d) P(B and D) requires both an even sum and a 6 on the red die. Out of the 36 possible outcomes, 2 outcomes satisfy these conditions (rolling a 3 on the blue die and rolling a 6 on the red die, or vice versa), resulting in a probability of 1/18.
e) P(C and D) involves both the blue die having a higher score than the red die and rolling a 6 on the red die. Out of the 36 possible outcomes, 6 outcomes satisfy these conditions, resulting in a probability of 1/6.
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Write an equation in slope-intercept form for the line that passes through the
given point and is parallel to the graph of the given equation. (4,-6) y=-3/4x+1
I need help with this plssss
Expert plsss help meeeee
Answer: 350
Step-by-step explanation:
Answer:
1,283 m3
Step-by-step explanation:
Ok so the volume formula is:
V = π×r² × h/3π (pi) = 3.14
² = power of two so that number times that number
Example:
3² = 3 × 3 = 9
To find the radius since the diameter is given divide by 2:
14 / 2 = 7
Next we solve the equation:
V = 3.14 × 7² × 25/3 = 1282.817
To round to the neareast whole number 1,283
solve for x pleaseeee!
Answer:
x=-20
Step-by-step explanation:
3x+178=6x+238
-3x=60
x=-20
If you give me five apples a day how many days would it take me to get 800 apples.
Answer:
160 days
Step-by-step explanation:
800 divided by 5 equal 160
Answer:
your answer is 160 days
Step-by-step explanation:
800÷5=160 days
I hope this helps
have a nice day/night
mark brainliest, please :)
Help! Will give brainliest and 10 points!
Answer:
its b
Step-by-step explanation:
trust me
Distribute
3x(5x-5)
a) 12x^2+8x
b) 15x^2+10x
c) 12x^2-9x
d) 15x^2-15x
Answer:
d
Step-by-step explanation:
3x times 5x equals 15x^2
3x times -5 equals -15x
---> 15x^2 - 15x
WILL MARK BRAINLIEST ON CORRECT ANSWER
Which type of line symmetry does the figure have?
vertical
horizontal
diagonal
none
If you stacked the cubes on top of each other to make an enormous tower, how high would they reach?
Answer:
Is this an actual question
3.1 Find the HCF and LCM for the following three numbers: 868, 372 and 992
Answer:
HCF of 868,372,and 992 is 124
LCM of 868,372,and 992 is 20832
hope this answer helps you...
What is move-in costs and what might be included in move-in costs?
Answer:
A move in cost is a non-refundable fee that landlords charge new tenants to cover the cost of touch ups and small changes made to the rental
Which ordered pair would not be a solution to y = x3 – X ?
(-4,-60)
(-3,-24)
(-2,-6)
(-1,-2)
Answer:
Step-by-step explanation:
Describe two different way to find the product 4x2/3
Answer:
8/3
Step-by-step explanation:
1. 2 ÷ 3 = .66
.66 · 4 = 2.6
2. 4 × 2/3 =
4/1 × 2/3 = 8/3
good luck, i hope this helps :)
Father's age is five times than the son's age. If the sum
of their ages is 60 years, find their present ages.
Answer:
The son is 10, and the father is 50.
Step-by-step explanation:
10 times 5 would be 50, and 50+10 is 60.
Answer:
Father: 50
Son: 10
Step-by-step explanation:
Son's age: S
Father's age: F
F=5S
F+S=60.
Substitute.
5S+S=60
6S=60
S=10
F=50. As a check, 10+50=60 and 50/5=10.
Hope this was helpful.
~cloud
Consider the following pair of equations:
y = −2x + 8
y = x − 1
Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form.
Answer:
y = -2x + 8
x = 3
y = x - 1
y = 2
Step-by-step explanation:
if 2x + y = 8 and x - y = 1
you can solve using substitution, elimination, matrix etc.
You will find that x = 3 and y = 2
Hope this helped.
Find the vertex of the parabola whose equation is y = -2x2 + 8x - 5.
A-(2, 27)
B-(2, 19)
C-(2, 3)
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The nth term of another sequence is n² + 7n
Find the 10th term of the sequence
Answer with explanation will get marked as brainiest
Answer:
a(10) = 170
Step-by-step explanation:
Given that,
The nth term fo the sequence is :
a(n) = n² + 7n
We need to find the 10th term of the sequence.
Put n = 10 in the above sequence,
a(10) = (10)² + 7(10)
= 100 + 70
= 170
So, the 10th term of the sequence is 170.