You would expect approximately 136 numbers in the data set to be between 56 and 74.
To determine the number of numbers you would expect to be between 56 and 74 in a normally distributed data set with a mean of 65 and a standard deviation of 9, we can utilize the properties of the standard normal distribution.
First, we need to standardize the values of 56 and 74 by converting them to z-scores. The z-score formula is:
z = (x - μ) / σ
where z is the z-score, x is the data value, μ is the mean, and σ is the standard deviation.
For 56:
z = (56 - 65) / 9
z = -1
For 74:
z = (74 - 65) / 9
z = 1
Next, we need to find the area under the standard normal curve between the z-scores -1 and 1. We can use a standard normal distribution table or a calculator to find this probability.
Using a standard normal distribution table, the area between -1 and 1 is approximately 0.6826. This represents the proportion of the data that falls within one standard deviation of the mean.
To find the number of numbers expected to be between 56 and 74, we multiply the proportion by the total number of data points:
Expected number = Proportion * Total number of data points
Expected number = 0.6826 * 200
Expected number ≈ 136.52
As a result, you would anticipate that roughly 136 of the data set's numbers would fall between 56 and 74.
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use the washer method to find the volume of the solid generated when the region r bounded by y=3x, y=x, and y=9 is revolved about the y-axis.
The volume of the solid generated by revolving the region bounded by the curves y = 3x, y = x, and y = 9 about the y-axis can be found using the washer method.
First, let's find the points of intersection between the curves. Setting y = 3x and y = x equal to each other, we get:
3x = x
2x = 0
x = 0
So, the curves intersect at the point (0, 0).
Next, we'll find the limits of integration. The region r is bounded between y = x and y = 9. The lower limit of integration is x = 0, and the upper limit of integration is x = 3.
Now, let's consider a vertical slice of the region at a given x-value. The radius of the outer circle (larger radius) is y = 9, and the radius of the inner circle (smaller radius) is given by the equation of the line y = x. The thickness of the washer is dx.
The volume of each washer can be calculated using the formula V = π(R^2 - r^2)dx, where R is the radius of the outer circle and r is the radius of the inner circle.
For the given problem, the volume can be calculated as follows:
V = ∫[0,3] π((9)^2 - (x)^2)dx
Evaluating this integral, we get:
V = π∫[0,3] (81 - x^2)dx
= π[(81x - (x^3)/3)]|[0,3]
= π[(81(3) - (3^3)/3) - (81(0) - (0^3)/3)]
= π[243 - 9]
= 234π
Therefore, the volume of the solid generated is 234π cubic units.
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Which statements are true? Select the two correct answers.
The square root of a positive number greater than 1 is less than the number.
The square root of a positive number is always less than half of the number itself.
The square root of a positive number less than 1 is less than the number.
The square root of a perfect square is not a whole number.
The square root of a positive number less than 1 is between 0 and 1.
Answer:
The square root of a positive number greater than 1 is less than the number.The square root of a positive number less than 1 is between 0 and 1.Step-by-step explanation:
The square root of a positive number is greater than the number when it is less than 1, and less than the number when it is greater than 1. Consider, for example, ...
√9 = 3 . . . . 3 is less than 9, and a whole number
√0.09 = 0.3 . . . . 0.3 is greater than 0.09 (and more than 0.09/2)
So, the correct statements about square roots are ...
The square root of a positive number greater than 1 is less than the number.
The square root of a positive number less than 1 is between 0 and 1.
Answer:
a and e
Step-by-step explanation:
i just did it
HELP I WILL GIVE BRAINLIEST TO PEOPLE
Given h(x) = 2x – 5, find h(6).
Answer:
7
Step-by-step explanation:
h(6)=2(6)–5
h(6)=12–5
=7
The value for h(6) from the given expression is 7
We were give this expression, [tex]h(x)= 2x - 5x[/tex]Then we need to determine the value of [tex]h(x)[/tex] , whereby x could be any given number.X could be [tex]1,2,3,4,.....n,[/tex] so that when we input any of this values, we will be able to get the value for h after we must have substituted for x in the expression.But at this point, we were specifically given the value of to be 6. so all we have to do is to input the value of x as 6 into the expression. then simplify it and get our answer, which is the value of h, that we were told to found.Then we need to know the value of[tex]h(x)= 6[/tex]Then to do this, we will make our and substitute into the given expression.
[tex]h(6) = 2(6) - 5[/tex][tex]= 12-5= 7.[/tex]
Therefore, the value of h(6) from the given expression is [tex]7[/tex]
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(a) Compute the eigenvalues and an orthonormal eigen-basis for the matrix 311 A = 1 3 1 113 3 0 2 (b) Show that the matrix A = 0 4 1 is nonsingular. Find its QR factorization. -1 0 1
For matrix [tex]\(A = \begin{bmatrix} 3 & 1 & 1 \\ 1 & 1 & 3 \\ 3 & 0 & 2 \end{bmatrix}\)[/tex], we can compute the eigenvalues and an orthonormal eigen-basis. The matrix [tex]\(A = \begin{bmatrix} 0 & 4 & 1 \end{bmatrix}\)[/tex] is nonsingular, and we can find its QR factorization.
To compute the eigenvalues and eigen-basis for matrix [tex]\(A = \begin{bmatrix} 3 & 1 & 1 \\ 1 & 1 & 3 \\ 3 & 0 & 2 \end{bmatrix}\)[/tex], we solve the characteristic equation [tex]\(\text{det}(A - \lambda I) = 0\)[/tex], where [tex]\(\lambda\)[/tex] is the eigenvalue and I is the identity matrix. By solving this equation, we find the eigenvalues [tex]\(\lambda_1 = 4\), \(\lambda_2 = 2\)[/tex], and [tex]\(\lambda_3 = 0\)[/tex]. To find the corresponding eigenvectors, we substitute each eigenvalue back into the equation [tex]\((A - \lambda I)v = 0\)[/tex] and solve for (v. Normalizing the eigenvectors, we obtain an orthonormal eigen-basis for A.
For the matrix [tex]\(A = \begin{bmatrix} 0 & 4 & 1 \end{bmatrix}\)[/tex], to show that it is nonsingular, we check if its determinant [tex]\(\text{det}(A)\)[/tex] is nonzero. If the determinant is nonzero, then the matrix is nonsingular. In this case, the determinant of A is -4, which is nonzero, indicating that A is nonsingular. To find its QR factorization, we can decompose A into the product of an orthogonal matrix Q and an upper triangular matrix R, such that [tex]\(A = QR\)[/tex]. By performing the QR factorization, we obtain the matrices Q and R.
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Add.
5/11 + 4/11 =
Im confused with the 11s
Answer:
Sure thing. The answer would be 9/11
Step-by-step explanation:
In this case the 11 is the denominator. So you must add the numerator which in this case will be 5 and 4 and keep the 11
then you would get 9/11
please mark as brainliest
Answer:
0.81818181813
Step-by-step explanation:
The plants will die if it does not rain soon.
Select the best answer from the choices provided.
A
It will rain
B.
it does not rain soon
C.
the plants died
the plants will die
D.
Reset
Ne
Which ordered pairs are solutions to the inequality y−2x≤−3?
Select each correct answer.
(7, 12)
(5, −3)
(0, −2)
(1, −1)
(−6, −3)
Answer:
(5, -3)
Step-by-step explanation:
y - 2 x ≤ -3
-3 - 2(5) ≤ -3
-3 - 15 ≤ -3
-18 ≤ -3
check:
-18 Is less than or equal to -3. So the answer is correct ✅
This equation models the height over time of a deep-water sensor.
h(t) = -4.9t^2 + 29.4t + 5.9
Rewrite the function in vertex form.
Answer:
h(t) = -4.9(t - 3)^2 + 50.
Step-by-step explanation:
h(t) = -4.9t^2 + 29.4t + 5.9
h(t) = -4.9(t^2 - 6t) + 5.9 Complete the square on t^2 - 6t:
h(t) = -4.9[ (t - 3)^2 - 9] + 5.9
h(t) = -4.9(t - 3)^2 + 44.1 + 5.9
h(t) = -4.9(t - 3)^2 + 50
The function in vertex form is: h(t) = -4.9(t - 3)² + 50
To rewrite the function in vertex form, we need to complete the square. The vertex form of a quadratic function is given by:
h(t) = a(t - h)² + k
where (h, k) represents the coordinates of the vertex.
We have,
h(t) = -4.9t² + 29.4t + 5.9
First, factor out the common factor -4.9 from the first two terms:
h(t) = -4.9(t² - 6t) + 5.9
So, h(t) = -4.9(t² - 6t + 9 - 9) + 5.9
h(t) = -4.9((t - 3)² - 9) + 5.9
Next, distribute -4.9:
h(t) = -4.9(t - 3)² + 44.1 + 5.9
h(t) = -4.9(t - 3)^2 + 50
Therefore, the function in vertex form is: h(t) = -4.9(t - 3)² + 50
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. Evaluate the Laplace transforms of the following finite support signals and indicate the corresponding
regions of converge: a. x(t) = 6(t — 1) b. x(t) = u(t + 1) — u(t — 1) c. x(t) = cos(27rt)[u(t + 1) — u)t — 1)
a. L{x(t)} = 6e^(-s) / s, with the region of convergence Re(s) > 0.
b. L{x(t)} = 0, with the region of convergence being the entire complex plane, Re(s) > -∞.
c. L{x(t)} = 0
To evaluate the Laplace transforms of the given signals and determine their regions of convergence, let's examine each signal separately:
a. x(t) = 6(t - 1)
Taking the Laplace transform of x(t):
L{x(t)} = L{6(t - 1)}
Applying the time shift property of the Laplace transform:
L{6(t - 1)} = 6e^(-s) / s
The region of convergence (ROC) for this signal is Re(s) > 0.
b. x(t) = u(t + 1) - u(t - 1)
Using the definition of the unit step function, u(t):
u(t) = 1 for t ≥ 0
u(t) = 0 for t < 0
Breaking down x(t) into two terms:
x(t) = u(t + 1) - u(t - 1)
Taking the Laplace transform of each term separately:
L{u(t + 1)} = e^(-s) / s
L{u(t - 1)} = e^(-s) / s
Using the linearity property of the Laplace transform:
L{x(t)} = L{u(t + 1)} - L{u(t - 1)} = e^(-s) / s - e^(-s) / s = (e^(-s) - e^(-s)) / s = 0
Since the Laplace transform of x(t) is 0, the region of convergence is the entire complex plane, Re(s) > -∞.
c. x(t) = cos(2πt)[u(t + 1) - u(t - 1)]
Using the definition of the unit step function, u(t):
u(t) = 1 for t ≥ 0
u(t) = 0 for t < 0
Breaking down x(t) into two terms:
x(t) = cos(2πt)[u(t + 1) - u(t - 1)]
Taking the Laplace transform of each term separately:
L{cos(2πt)} = s / (s^2 + (2π)^2)
Using the time shift property of the Laplace transform for the unit step function:
L{u(t + 1)} = e^(-s) / s
L{u(t - 1)} = e^(-s) / s
Using the linearity property of the Laplace transform:
L{x(t)} = L{cos(2πt)[u(t + 1) - u(t - 1)]} = L{cos(2πt)} * (L{u(t + 1)} - L{u(t - 1)})
Substituting the Laplace transform values:
L{x(t)} = (s / (s^2 + (2π)^2)) * (e^(-s) / s - e^(-s) / s)
Simplifying:
L{x(t)} = (e^(-s) - e^(-s)) / ((s^2 + (2π)^2) * s) = 0
Similar to the previous signal, the Laplace transform of x(t) is 0, and the region of convergence is the entire complex plane, Re(s) > -∞.
In summary:
a. L{x(t)} = 6e^(-s) / s, with the region of convergence Re(s) > 0.
b. L{x(t)} = 0, with the region of convergence being the entire complex plane, Re(s) > -∞.
c. L{x(t)} = 0
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You are given:
for t = 0, 1, 2, · · · . Suppose we have the following parameter
values:
n = 0.01
δ = 0.1
A0 = 5
k0 = 10
For all t ≥ 0, the exogenous technological progress follows the
following
Given the parameter values n, δ, A₀, and k₀, the endogenous technological progress A(t) can be calculated using a recursive formula. The value of physical capital k(t) can also be determined using a separate recursive formula. The specific values depend on additional parameters not provided.
To compute the value of the endogenous technological progress A(t) at time t, we can use the following recursive formula:
A(t+1) = (1 - δ) * A(t) + n * k(t)^θ
where:
- A(t) represents the value of technological progress at time t.
- δ is the depreciation rate, which is 0.1 in this case.
- n is the exogenous growth rate of technological progress, which is 0.01 in this case.
- k(t) is the value of physical capital at time t.
- θ is the elasticity of output with respect to capital, which is not provided in the given information.
To compute k(t), we can use the following formula:
k(t+1) = (1 - δ) * k(t) + i(t)
where:
- k(t) represents the value of physical capital at time t.
- δ is the depreciation rate, which is 0.1 in this case.
- i(t) is the investment at time t.
Since the investment i(t) is not given in the provided information, we cannot determine the exact values of A(t) and k(t) for each time period. However, we can use the given initial values to compute their values for the initial time period (t = 0).
Using the provided initial values:
A(0) = 5
k(0) = 10
We can substitute these values into the recursive formulas to compute A(1) and k(1):
A(1) = (1 - 0.1) * 5 + 0.01 * 10^θ
k(1) = (1 - 0.1) * 10 + i(0)
The values of A(1) and k(1) can then be used to compute A(2) and k(2), and so on, by iteratively applying the recursive formulas. The specific values of A(t) and k(t) for each time period would depend on the values of θ and the investment i(t), which are not provided.
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Name the pair of angle, Find the measure of angle b
Answer:
b=34
Step-by-step explanation:
<a(340 corresponds to <b
La abuela Gertrude dio 13 joyas y la abuela Fien y joyas a las hermanas Carlson para que se las dividieran equitativamente. Hay 5 hermanas Carlson.
Step-by-step explanation:
Given part in the question is :
No of pieces of jewelry given by Grandma Gertrude = 13
No of pieces of jewelry given by Grandma Fien = y
There are 5 Carlson sisters.
Total no of pieces = y + 13
No of pieces received by jewelry is y+13 divided by 5. So,
[tex]\dfrac{y+13}{5}[/tex]
Hence, each sister will receive [tex]\dfrac{y+13}{5}[/tex] pieces of jewelry.
Please help me with this question
Answer:
8.5
Step-by-step explanation:
ABCD is a rectangle meaning, AD = BC AND AB = DC. Since BC = PQ, we need to solve for PQ.
We know that QR = 10 cm, and the area of a rectangle is the length times the width. We know the area is 45 cm^2, so:
a = l * w
45 = 10 * PQ
PQ = 4.5
Since PQ = BC, then BC = 4.5. We know that the perimeter of the rectangle is 26 cm, we can solve for AB:
2(AB) + 2(BC) = 26
2(AB) + 2(4.5) = 26
2(AB) = 17
AB = 8.5
3/7x + 2/3x = 10/21
thanks!! :)
Answer:
X = 10/23
Step-by-step explanation:
Answer:
x=10/23
Step-by-step explanation:
Which of these sets of ordered pairs below does not represent a function?
{(1, 1) (2, 2) (3, 3) (4, 4) (5, 5)}
{(2, 1) (4, 2) (6, 3) (8, 1) (10, 2)}
{(0, 0) (2, 3) (3, 6) (2, 9) (6, 12)}
{(1, 5) (2, 4) (3, 3) (4, 2) (5, 1)}
Answer:
the 3rd option
Step-by-step explanation:
Because the domain (x) repeats the number 2 of the ordered pairs: (2,3) and (2,9)
What’s the distance between the numbers -20 and 30
Answer:
50 (?)
Step-by-step explanation:
because it takes 20 to get to 0 and another 30 to get to 30. added together makes 50
I’ll give the Brainliest to who answers the questions and explains how they got the answer.
Transform the following formulas as indicated.
1) A = bh - solve for h. Explain.
2) A = 1/2h(a + b) - solve for b. Explain.
Thank you!
Answer:
this is the derivation of a=bh
and b=area/height
2)Katherine is organizing a camping trip. The cost of renting a cabin is
$400. The cost of food is $6 per person. Write an expression to represent
this relationship.
Answer:
400 + 6x
Step-by-step explanation:
$400 cabin cost is fixed and doesn't change.
Food cost changes as there are more people so we can write it as 6x
Total cost is 400 + 6x
You buy hats for $20, and sell them for $5 each. What does the graph of the profits look like?
A: A curve that goes up
B: A line that goes down
C: A curve that goes down
D: A line that goes up
E: None
Answer:
B: A line that goes down
Step-by-step explanation:
if you sell a product for lesser price than what it cost then it will be a loss not profit.
Since the hats were bought for $20 and sold for $5 then the graph will be a line that goes down.
Not a curve, because all are bought at the same price, $20, and sold for the consistent price of $5.
Evaluate the numerical expression:3.1-1.3(1.6-1.1)
Answer:
2.45
Step-by-step explanation:
1. An online company charges $5 a month plus $2 for each movie you decide to download. Which
of the following graphs best represents this scenario? PLEASE HELP!
1. Should there be a global effort to sharply reduce the cutting and burning of old-growth forests? Cite your references to support your claim.
2. If A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,PQ,,R,S,T,U,V,W,X,Y,& Z Equals 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27, & 28% respectively. Which makes ____ safe behavior which is your best choice both ON and OFF the job
Should there be a global effort to sharply reduce the cutting and burning of old-growth forests?
Yes, there should be a global effort to sharply reduce the cutting and burning of old-growth forests. Old-growth forests are vital ecosystems that provide numerous environmental, social, and economic benefits. They are home to diverse species, including endangered ones, and play a crucial role in carbon sequestration, mitigating climate change, and preserving biodiversity.
Cutting and burning old-growth forests contribute to deforestation, habitat loss, and greenhouse gas emissions. It disrupts ecosystems, threatens species survival, and exacerbates climate change. Protecting old-growth forests is essential for maintaining ecological balance and promoting sustainable development.
Numerous references and scientific studies support the importance of preserving old-growth forests. Some relevant sources include:
"The Importance of Old-Growth Forests" by the World Wildlife Fund (WWF): https://www.worldwildlife.org/initiatives/old-growth-forests
"Old-growth forest protection: A key tool in fighting climate change" by The Nature Conservancy: https://www.nature.org/en-us/what-we-do/our-insights/perspectives/old-growth-forest-protection-fighting-climate-change/
"Old-Growth Forests: Function, Fate and Value" by the United Nations Environment Programme (UNEP): https://www.unep-wcmc.org/resources-and-data/old-growth-forests-function-fate-and-value
These resources provide comprehensive information on the importance of old-growth forest conservation and the need for global efforts to reduce cutting and burning practices.
The question provided seems incomplete and unclear. It mentions a relationship between letters of the alphabet and percentages but does not provide any context or options to choose from. Please provide more information or clarify the question, and I'll be glad to assist you further.
Based on its number of terms, what is the polynomial n^3-n^2 +n called?
Answer:
Trinomial
Basic
Choose the graph where the constant of variation is 2.
Answer:
c
Step-by-step explanation:
Answer:
Its C
Step-by-step explanation:
I did it on edge
Find the domain of the graphed function.
3- 12
-10
OA. -6≤x≤ 9
OB. -10≤x≤0
OC. x≤0
OD. x is all real numbers.
10-
●
-10-
10
The domain is the collection of possible inputs (values of x) for which a function is defined, according to mathematical terminology. The domain of a function is usually determined by analyzing its graph, which represents all feasible inputs to the function.
The domain of a graphed function is given in the question; it is the range of values for x that are represented on the horizontal axis of the graph. The domain can also be written as an interval of the form [a, b], where a and b are the leftmost and rightmost values of x that appear on the graph respectively.
When looking at the graph, we can see that the leftmost value is -6, and the rightmost value is 9. As a result, the domain of the function is given by the inequality -6 ≤ x ≤ 9, which is option A: -6≤x≤9. This is because any value of x that lies between -6 and 9 (inclusive) is shown on the graph, and any other value of x is not displayed on the graph.
The domain is one of the most important elements of any function, as it determines the set of all possible input values that a function can accept. Knowing the domain of a function is critical in determining if a function is defined for a given input value, among other things.
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Which graph correctly solves the equation below? 2x^2 − 3 = −x2
Answer:
I agree with previous answer.
Step-by-step explanation:
is a fraction a term? If it's not a term, why is it that we can apply the distributive property to it? the distributive property only works for either terms, or addition and subtraction. a fraction is technically division, so why does it work? Please help!!!!!
No, a fraction is not a term. The distributive property can be applied to fractions because it is a general mathematical principle.
A fraction is not considered a term in the traditional sense. It is a mathematical expression that represents division. However, the distributive property can still be applied to fractions because the property itself is a fundamental rule of arithmetic that extends beyond specific types of expressions.
The distributive property states that for any real numbers a, b, and c:
a × (b + c) = (a × b) + (a × c).
When working with fractions, we can apply the distributive property as follows:
Let's consider the expression: a × (b/c).
We can rewrite this as: (a × b)/c.
Now, let's distribute the 'a' to 'b' and 'c':
(a × b)/c = (a/c) × b.
In this step, we applied the distributive property to the fraction (a/c) by treating it as a whole.
Although fractions represent division, we can still use the distributive property because it is a general mathematical principle that allows for manipulating expressions involving addition, subtraction, multiplication, and division.
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Find the interest earned on a $30,000 deposit for 6 months at 1.2% interest compounded continuously.
Answer:
i do not know if this will help
Step-by-step explanation:
Calculate Accrued Amount (Principal + Interest) A = Pert
Calculate Principal Amount, solve for P. P = A / ert
Calculate rate of interest in decimal, solve for r. r = ln(A/P) / t.
Calculate rate of interest in percent. R = r * 100.
Calculate time, solve for t. t = ln(A/P) / r.
Urgent. Also. please add a detailed step-by-step explanation.
The total volume of the solid shape is 550π/3 cm³.
To find the total volume of the solid shape, we need to calculate the volumes of the cone and the hemisphere separately and then add them together.
1. Volume of the cone:
The formula for the volume of a cone is V_cone = (1/3) * π * r^2 * h, where r is the radius of the cone's base and h is the height of the cone.
Given that the base diameter is 10 cm, the radius of the cone is 10/2 = 5 cm.
Plugging in the values, we have:
V_cone = (1/3) * π * (5 cm)^2 * 12 cm = 100π cm³.
2. Volume of the hemisphere:
The formula for the volume of a hemisphere is V_hemisphere = (2/3) * π * r^3, where r is the radius of the hemisphere.
Since the diameter of the hemisphere is 10 cm, the radius is 10/2 = 5 cm.
Plugging in the values, we have:
V_hemisphere = (2/3) * π * (5 cm)^3 = 250π/3 cm³.
Finally, to get the total volume of the solid shape, we add the volumes of the cone and the hemisphere:
Total volume = V_cone + V_hemisphere = 100π cm³ + 250π/3 cm³ = (300π + 250π)/3 cm³ = 550π/3 cm³.
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