Answer:
32
Step-by-step explanation:
The formula needed to solve this question by hand is:
[tex]x^{\frac{m}{n}} =\sqrt[n]{x^{m}}[/tex]
256^(5/8) = 8th root of 256^5
256^(5/8) = 8th root of 1280
256^(5/8) = 32
Simone and Leah are playing a game with dice. What is the probability Simone rolls a 6 and then Leah rolls an odd number?
Answer:
1. 1/6
2. 1/2
Step-by-step explanation:
A dice has 6 sides. So the sample space for this question =
[1,2,3,4,5,6]
1. From the sample space we can see that 6 occurs only once in a dice
So probability of a 6
= 1/6
2. Number of odds = 3 (1,3,5)
Probability Leah rolls an odd number
= Odd/total
= 3/6
= 1/2
Use substitution to solve the following system of equations.
y=3x +8
5x+ 2y = 5
Answer:
5x+2(3x+8)
5x+6x+16
11x+16
11x=-16
X=16/11
Suppose that U follows the Uniform distribution U ~ U[2, 3]. Find the probability density function of Y = exp(U).
The probability density function of Y = exp(U) is given by:
f(y) = { 1/y, 2 ≤ y ≤ e³ ; 0, elsewhere }.
Given that: U follows the Uniform distribution U ~ U[2, 3]. We have to find the probability density function of Y = exp(U).
The formula used: The probability density function of a random variable X, is denoted by f(x), is the derivative of the cumulative distribution function (cdf), denoted by F(x). We have F(x) = P(X ≤ x).
The probability density function of the uniform distribution U(a,b), is given by
f(x)=1/(b-a), where a ≤ x ≤ b.
Here, U[2,3]So, a = 2, b = 3
Let's find the probability density function of Y = exp(U).
So, for finding the probability density function of Y = exp(U), first, we need to find the cumulative distribution function F(y) of Y. Let's do that.
So, F(y) = P(Y ≤ y) = P(exp(U) ≤ y) = P(U ≤ ln y)
We have, Y = exp(U), which is a one-to-one function of U and increasing in U. Hence, we can use the one-to-one transformation formula. Hence, the probability density function of Y, f(y) = f(u) / |dy/du|.f(u) = 1/ (3-2) = 1
Here, dy/du = d/dy [exp(u)] = exp(u) = Y
Therefore, f(y) = 1/Y, for 2 ≤ u ≤ 3.
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Suppose that U follows the Uniform distribution U ~ U[2, 3].
Find the probability density function of Y = exp(U).
Let fU(u) be the pdf of U.Since U has a Uniform distribution over the interval [2, 3], its pdf is given by:
fU(u) = {1 / (3 - 2)} = 1, 2 ≤ u ≤ 3, and 0 elsewhere.
Now we need to find the pdf of Y = exp(U).
Let FY(y) be the cdf of Y.
Then we can write:
FY(y) = P(Y ≤ y) = P(exp(U) ≤ y) = P(U ≤ ln(y)), for y > 0.
Since U is continuous and its pdf is given by fU(u), we have:
[tex]FY(y) = ∫_{2}^{ln(y)} fU(u)du = ∫_{2}^{ln(y)} 1du = ln(y) - 2, 2 ≤ ln(y) ≤ 3, and 0 elsewhere.[/tex]
We can differentiate FY(y) to find the pdf of Y:
fy(y) = d/dy FY(y) = (1 / y) fY(ln(y)) = (1 / y), 2 ≤ y ≤ e3, and 0 elsewhere.
Therefore, the probability density function (pdf) of Y = exp(U) is given by:
fy(y) = (1 / y), 2 ≤ y ≤ e3, and 0 elsewhere.
In general, if U is a continuous random variable with pdf fU(u) and Y = g(U) is a monotonic transformation of U, then the pdf of Y can be found using the formula:
[tex]fy(y) = fU(g^{-1}(y)) / |dg^{-1}(y) / dy|,[/tex]
where g^{-1}(y) is the inverse function of g(y) and |dg^{-1}(y) / dy|
is the absolute value of the derivative of g^{-1}(y) with respect to y.
The probability density function (pdf) of the random variable
Y = exp(U)
where U is distributed uniformly over the interval [2, 3] can be found as follows:
Let f_U(u) be the pdf of U.
Since U has a Uniform distribution over the interval [2, 3], its pdf is given by:
f_U(u) = {1 / (3 - 2)} = 1, 2 ≤ u ≤ 3, and 0 elsewhere.
Now we need to find the pdf of Y = exp(U).
Let F_Y(y) be the cdf of Y.
Then we can write:
[tex]F_Y(y) = P(Y ≤ y) = P(exp(U) ≤ y) = P(U ≤ ln(y)), for y > 0.[/tex]
Since U is continuous and its pdf is given by f_U(u), we have:
[tex]F_Y(y) = ∫_{2}^{ln(y)} f_U(u)du = ∫_{2}^{ln(y)} 1du = ln(y) - 2, 2 ≤ ln(y) ≤ 3, and 0 elsewhere.[/tex]
We can differentiate F_Y(y) to find the pdf of Y:
[tex]fy(y) = d/dy F_Y(y) = (1 / y) f_Y(ln(y)) = (1 / y), 2 ≤ y ≤ e^3, and 0 elsewhere.[/tex]
Therefore, the probability density function (pdf) of Y = exp(U) is given by:
fy(y) = (1 / y), 2 ≤ y ≤ e^3, and 0 elsewhere.
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The midpoint of CD is M=(2, -1). One endpoint is C=(-3,-3). Find the coordinates of the other endpoint, D. D (?, ?) M (2,-1) C (-3,-3) D = (-7, -1) Find an ordered pair (x, y) that is a solution to the equation. -x+5y=2
The ordered pair (x, y) that is a solution to the equation -x + 5y = 2 is (0, 2/5).
To find the coordinates of the other endpoint D given that the midpoint of CD is M(2, -1) and one endpoint is C(-3, -3), we can use the midpoint formula:
Midpoint formula:
The coordinates of the midpoint between two points (x₁, y₁) and (x₂, y₂) are given by ((x₁ + x₂) / 2, (y₁ + y₂) / 2).
Using the given information, we can substitute the known values into the midpoint formula and solve for the coordinates of D:
M(2, -1) = ((-3 + x₂) / 2, (-3 + y₂) / 2)
Simplifying the equation:
2 = (-3 + x₂) / 2
-1 = (-3 + y₂) / 2
To solve for x₂:
4 = -3 + x₂
x₂ = -3 + 4
x₂ = 1
To solve for y₂:
-2 = -3 + y₂
y₂ = -3 - 2
y₂ = -5
Therefore, the coordinates of the other endpoint D are D(1, -5).
To find an ordered pair (x, y) that is a solution to the equation -x + 5y = 2, we can choose any value for either x or y and solve for the other variable. Let's choose x = 0:
-0 + 5y = 2
5y = 2
y = 2/5
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A linear function that represents the number of animals adopted from the shelter is compared to a different linear function that represents the hours volunteers work at the shelter each week. Describe the key features of the functions that are needed to determine if these lines intersect.
WILL MARK BRAINLIEST
Answer:
what is this a different answer orrrr?
Find the area of the shaded region. Use the pin button on the calculator. Round to the nearest whole number. 14 70°
Answer:
The area is approximately [tex]588cm^2[/tex]
Step-by-step explanation:
Given
See attachment for figure
Required
The area of the shaded region
The shaded region is as follows:
A major segmentA triangleFirst, calculate the area of the major segment using:
[tex]Area = \frac{\theta}{360} * \pi r^2[/tex]
Where
[tex]r = 14[/tex]
[tex]\theta = 360 - 70 =290[/tex]
So, we have:
[tex]A_1 = \frac{290}{360} * 3.14 * 14^2[/tex]
[tex]A_1 = 495.7711[/tex]
Next, the area of the triangle using:
[tex]Area = \frac{1}{2}ab \sin C[/tex]
Where
[tex]a=b=r = 14[/tex]
[tex]C = 70^\circ[/tex]
So, we have:
[tex]A_2 = \frac{1}{2} * 14 * 14 * sin(70)[/tex]
[tex]A_2 = 92.0899[/tex]
So, the area of the shaded region is:
[tex]Area = A_1 + A_2[/tex]
[tex]Area = 495.7711 + 92.0899[/tex]
[tex]Area = 587.8610[/tex]
[tex]Area \approx 588[/tex]
What is 980x58? I am giving 10 points I am not sure if it’s fair
Answer: 56840
A bit of long multiplication
Answer:
56840
Step-by-step explanation:
A quality control expert at a pretzel factory took a random sample of 101010 bags from a production run of over 500500500 bags and measured the amount of pretzels in each bag in the sample. The sample data were roughly symmetric with a mean of 450, and a standard deviation of 15
Based on this sample, which of the following is a 90%, percent confidence interval for the mean amount of pretzels per bag (in grams) in this production run?
Answer:
H0:μ=440 g
Ha:μ does not equal 440 g
Step-by-step explanation:
kahn
The 90% confidence interval for the mean amount of pretzels per bag (in grams) in this production run for this case is [441.31, 458.69] approximately.
How to calculate confidence interval for population mean for small sample?If the sample size is given to be n < 30, then for finding the confidence interval for mean of population from this small sample, we use t-statistic.
Let the sample mean given as [tex]\overline{x}[/tex] andThe sample standard deviation s, andThe sample size = n, and The level of significance = [tex]\alpha[/tex]Then, we get the confidence interval in between the limits
[tex]\overline{x} \pm t_{\alpha/2}\times \dfrac{s}{\sqrt{n}}[/tex]
where [tex]t_{\alpha/2}[/tex] is the critical value of 't' that can be found online or from tabulated values of critical value for specific level of significance and degree of freedom n - 1.
For this case, we're provided;
The sample mean given as [tex]\overline{x}[/tex] = 450The sample standard deviation s = 15The sample size = n = 10The level of significance = [tex]\alpha[/tex] = 100 - 90% = 10% = 0.1The critical value of t at level of significance 0.1 iand at degree of freedom 10-1=9 is:
Thus, the confidence interval in between the limits
[tex]450 \pm 1.833 \times \dfrac{15}{\sqrt{10}}[/tex]
or
[tex]450 \pm 8.69[/tex] approximately or 441.31 to 458.69 or we write it as: [441.31, 458.69] approximately.
Thus, the 90% confidence interval for the mean amount of pretzels per bag (in grams) in this production run for this case is [441.31, 458.69] approximately.
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At a pet store, Davina counted 12 parrots out of 20 birds. Which is an equivalent ratio of parrots to birds at the pet store?
Refering to #14, what is the approximate area of the lake where the resort has ownership responsibility? (Round your answer to the nearest hundredths) (Type in answer my F G F ZH = 71°.x=1.3. y = 20.0 . ZH = 71°,x= 3.0, y = 19.8 2H = 71°, x = 18.9, y 6.5 LH = 71°.x 6.5. y 18.9 14 A lakaside resort has ownership responsibility for the lako from each edge of their shoreline to the cantor of the roughly circular lake. The distance hom shore to the center of the lake is 130 meters and the central anglo respresenting the resorts Warship's 50° a What is the approudmate length of shoreline owned by the resort (Round your answer to the nearest hundredma) po in answer m)
The approximate area of the lake where the resort has ownership responsibility is 711.82 meters².
How to calculate the areaArea of sector = (central angle / 360°) * π * radius²
We know that the central angle is 50°, the radius is 130 meters, and π is approximately equal to 3.14.
Plugging these values into the formula, we get:
Area of sector = (50° / 360°) * 3.14 * 130²
Area of sector = 25/72 * 3.14 * 16900
Area of sector = 15750/22
Area of sector = 711.82 meters²
Therefore, the approximate area of the lake where the resort has ownership responsibility is 711.82 meters².
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Trigonometry, please answer ASAP, Convert the radian measure to degrees.
12
Answer:
687.549 deg
Step-by-step explanation:
12 rad = 687.549 deg
which expression is equivalent to (1 cos(x))2tangent (startfraction x over 2 endfraction) )? sin(x) 1 – cos(x) 1 – cos2(x) (1 cos(x))(sin(x))
The expression (1 - cos(x))^2 * tangent(x/2) is equivalent to (1 - cos^2(x))(sin(x)).
We can simplify the expression by using the trigonometric identity: cos^2(x) + sin^2(x) = 1. Rearranging this identity, we have sin^2(x) = 1 - cos^2(x).
Substituting this identity into the expression, we get (1 - cos^2(x))(sin(x)).
Expanding the expression further, we have sin(x) - cos^2(x)sin(x).
Therefore, the expression (1 - cos(x))^2 * tangent(x/2) is equivalent to (1 - cos^2(x))(sin(x)).
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Plot the points D(-9,-6) E(-6,-3) F(0,-9)and dilate usinng a scale factor of 1/3 centered at the origin
Answer:
Step-by-step explanation:
Rule for the dilation of a point about the origin is,
(x, y) → (kx, ky)
Here, k = scale factor
Dilating points D, E and F about the origin by a scale factor 'k' = [tex]\frac{1}{3}[/tex]
D(-9, -6) → D'(-3, -2)
E(-6, -3) → E'(-2, -1)
F(0, -9) → F'(0, -3)
Now we can plot these points on graph.
can someone help me on this question?
Answer:
diameter 33
radius 66
area 360
1/3 of your birthday cake is leftover from your party. If you eat 1/4 of the leftover cake, what fraction of the original birthday cake is left
Answer:
a twelth= 1/12
Step-by-step explanation:
PLEASE HELP ITS DUE TODAY!
5. Find the length of the missing side in the figure below. a =
cm.
5.8
2.4
8.5
оо
5.3
Answer:
a=[tex]\sqrt{28.32}[/tex]≈5.3217 cm
Step-by-step explanation:
Use the Pythagorean Theorem
a^2+4.7^2=7.1^2
a^2+22.09=50.41
a^2=28.32
a=[tex]\sqrt{28.32}[/tex]
≈5.3217
Answer:
5.3
Step-by-step explanation:
Check the attached image for explanation if you are interested, as I did not feel like spending 20 minutes re-formatting the equations to work on Brainly.
Also, I did not do this
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
Answer:
I cannot see the picture
Step-by-step explanation:
find the mean of the day 10.25‚9‚4.75‚8‚2.65‚12‚2.35
Answer:
7!
Step-by-step explanation:
If you add all of those numbers together it would be 49!
Then you divide that number how many numbers there are.
There are 7 numbers and 49/7 =7!
I would just like some solving steps or the answers.
Pls help I’m very confused (will mark brainliest)
Can somebody plz help answer these questions correclty (only if u remmeber how to do these) thanks sm!
WILL MARK BRAINLIEST WHOEVER ANSWEERS FIRST :DDD
Answer:
a= 126 degrees
b= 54 degrees
r= 54 degrees
s= 126 degrees
Step-by-step explanation:
can someone help me and explain this?? thanks so much!
Answer:
Step-by-step explanation:
10^7 = 1 and 7 zeros after it.
=> 10000000
Simplify the following expressions to have fewer terms 5x-3+4(4x-6)+2
Answer:
(21x-25)
Step-by-step explanation:
We need to find an equivalent expression for the following.
5x-3+4(4x-6)+2
We can solve it as follows:
5x-3+4(4x-6)+2 = 5x-3+16x-24+2
= 5x+16x-3-24+2
= 21x-25
So, the equivalent expression is equal to (21x-25).
If Sarah has $6453 Dallors of food and has $135 Dollars on her. How much will she need to pay for her food?
A. 6318
B. 233
C. 4555
D None of the Above
Answer:
It will be A
Step-by-step explanation:
6453
- 135
--------
6318 dollars needed for Sarah's food.
Hope this helps!
8 x5/7 need help asap
Answer:
5.71428571429
5 7/10
Step-by-step explanation:
Hope this helps and have a great day!!!!
Answer:
40/7
Step-by-step explanation:
prove the following statement:
Let n be an odd positive integer then the sum of n consecutive
integers is divisible by n.
The sum of n consecutive integers, where n is an odd positive integer, is divisible by n.
To prove the statement, let's consider a set of n consecutive integers starting from a.
The sum of n consecutive integers can be expressed as:
S = a + (a+1) + (a+2) + ... + (a+n-1)
To find the sum, we can use the formula for the sum of an arithmetic series:
S = (n/2) × (2a + (n-1))
Since n is an odd positive integer, we can represent it as n = 2k + 1, where k is a non-negative integer.
Substituting this value of n into the sum formula, we get:
S = ((2k+1)/2) × (2a + ((2k+1)-1))
Simplifying further:
S = (k+1) × (2a + 2k)
S = 2(k+1)(a + k)
Since k is an integer, (k+1) is also an integer. Therefore, we can rewrite the sum as:
S = 2m(a + k)
Now, we can see that S is divisible by n = 2k + 1, where m = (k+1).
Thus, we have proven that the sum of n consecutive integers, where n is an odd positive integer, is divisible by n.
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Kendall bought a vase that was priced at $450. In addition, he had to pay 9% sales tax. How much did he pay for the vase?
Answer:
$436
Step-by-step explanation:
Find the unit rate. Enter your answer as a mixed number.
A fertilizer covers 2/3 square foot in 1/4 hour.
The unit rate is
square feet per hour.
suppose 60% of the banks in switzerland are private organizations. if a sample of 469 banks is selected, what is the probability that the sample proportion of private banks will be greater than 65% ? round your answer to four decimal places.
The probability that the sample proportion of private banks will be greater than 65% is 0.1548.
Given that 60% of banks in Switzerland are private organizations.
If a sample of 469 banks is selected, we need to find the probability that the sample proportion of private banks will be greater than 65%.
Let p be the proportion of private banks in a sample of 469 banks.
Then
q = 1 - p
= 1 - 0.6
= 0.4 (as the percentage of private banks is given to be 60%)
Sample size, n = 469
We are to find the probability that the sample proportion of private banks will be greater than 65%.
That is, we need to find P(p > 0.65).
We use the normal distribution for finding probabilities associated with proportions.
We can use the formula as follows:
z = (p - P) / √[PQ/n],
where P is the population proportion (given as 0.6),
Q = 1 - P
= 0.4, and
n = 469
Putting all the given values in the above formula, we get;
z = (0.65 - 0.6) / √[0.6 × 0.4 / 469]
z = 1.0182
P(p > 0.65) = P(z > 1.0182)
Using the standard normal table, we get; P(z > 1.0182) = 0.1548
Therefore, the probability that the sample proportion of private banks will be greater than 65% is 0.1548 (rounded to four decimal places).
Hence, the answer is 0.1548.
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Use the given values of n and p to find the minimum usual value and the maximum usual value. Round your answer to the nearest hundredth unless otherwise noted. n=267, p=0.239
a. Minimum usual value: 63.85, Maximum usual value: 90.56
b. Minimum usual value: 54.65, Maximum usual value: 79.92
c. Minimum usual value: 42.56, Maximum usual value: 72.01
d. Minimum usual value: 34.32, Maximum usual value: 68.76
Option (b) is the correct answer. Minimum usual value: 54.65
Maximum usual value: 79.92.
The given values are n = 267 and p = 0.239. The minimum usual value and the maximum usual value are to be calculated. We use the formula of the mean and the standard deviation for this purpose:
Mean = µ = np = 267 × 0.239 = 63.93Standard Deviation = σ = sqrt (npq) = sqrt [(267 × 0.239 × (1 - 0.239)] = 5.01The minimum usual value is obtained when the z-value is -2, and the maximum usual value is obtained when the z-value is +2. We use the z-score formula: z = (x - µ) / σwhere µ = 63.93 and σ = 5.01(a) When the z-value is -2, x = µ - 2σ = 63.93 - 2(5.01) = 53.91(b) When the z-value is +2, x = µ + 2σ = 63.93 + 2(5.01) = 73.95
Therefore, the minimum usual value is 53.91, and the maximum usual value is 73.95 (rounded to the nearest hundredth).
Thus, option (b) is the correct answer. Minimum usual value: 54.65Maximum usual value: 79.92.
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The given values are: n=267, p=0.239
We need to find the minimum usual value and the maximum usual value using these values of n and p.
Let X be a random variable with a binomial distribution with parameters n and p.
The mean of the binomial distribution is:μ = np
The standard deviation of the binomial distribution is:σ = sqrt(npq)where q = 1-p
Let X be a binomial distribution with parameters n = [tex]267 and p = 0.239μ = np = 267 × 0.239 = 63.813σ = sqrt(npq) = sqrt(267 × 0.239 × 0.761) = 6.788[/tex]
The minimum usual value is given by:[tex]μ - 2σ = 63.813 - 2 × 6.788 = 50.236[/tex]
The maximum usual value is given by:[tex]μ + 2σ = 63.813 + 2 × 6.788 = 77.39[/tex]
Thus, the minimum usual value is 50.24 and the maximum usual value is 77.39(rounded to the nearest hundredth).
Therefore, the answer is:Minimum usual value: 50.24, Maximum usual value: 77.39
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