hi please help i’m stuck

Answer:

B

Step-by-step explanation:

B is the only answer that will ensure she gets graduate students in the sample without getting too few or too many.

Using the concept of systematic sampling, it is found that the correct option is:

c. randomly selects one of the first 5 students to arrive to class, and every 5th student thereafter to take the survey

In a systematic sample, every kth element is chosen.

In this problem, she wants a sample of 30 students, and in total, there are 150 students.

\(\frac{150}{30} = 5\)

Hence, one of the first 5, and then every 5th student should be chosen, and option c is correct.

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The collections of subsets that are partitions of {1, 2, 3, 4, 5, 6} are options (b) and (c).

Among the given options, collections (b) and (c) are partitions of the set {1, 2, 3, 4, 5, 6}. In option (b), the subsets {1}, {2, 3, 6}, {4}, and {5} form a partition since each element of the set belongs to exactly one subset.

Similarly, in option (c), the subsets {2, 4, 6} and {1, 3, 5} form a partition as each element is assigned to exactly one subset. On the other hand, options (a) and (d) do not satisfy the criteria of being a partition.

A partition of a set is a collection of subsets that satisfies two conditions: The subsets are non-empty. Every element in the original set belongs to exactly one subset in the collection. Let's analyze each option to determine if it is a partition of {1, 2, 3, 4, 5, 6}:

a) {1, 2}, {2, 3, 4}, {4, 5, 6}

This option does not form a partition since the element 2 belongs to both the subsets {1, 2} and {2, 3, 4}. So, option (a) is not a partition.

b) {1}, {2, 3, 6}, {4}, {5}

This option forms a partition. Each element belongs to exactly one subset, and the subsets are non-empty. So, option (b) is a partition.

c) {2, 4, 6}, {1, 3, 5}

This option forms a partition. Each element belongs to exactly one subset, and the subsets are non-empty. So, option (c) is a partition.

d) {1, 4, 5}, {2, 6}

This option does not form a partition since the elements 2 and 6 do not belong to any subset in this collection. So, option (d) is not a partition.

Therefore, the collections of subsets that are partitions of {1, 2, 3, 4, 5, 6} are options (b) and (c).

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True , if a and b are matrices corresponding to orthogonal projections, then the matrix is also the matrix corresponding to some orthogonal projection .

Given :

Orthogonal projections of matrices :

A square matrix P is called an orthogonal projector (or projection matrix) if it is both idempotent and symmetric  that is, P^2 = P and P′ = P .

The matrix must obey or to be the both symmetric and idempotent matrices to be an orthogonal projector .

so the matrix is also the matrix corresponding to some orthogonal projection .

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9514 1404 393

Answer:

  $400

Step-by-step explanation:

The formula for the value of an account with interest rate r compounded continuously for t years is ...

  A = Pe^(rt)

We want to find P when A = 550, r = .023, and t = 15.

  550 = Pe^(0.023·15) ≈ 1.41199P

  P = 550/1.41199 = 389.52 ≈ 400

Jocelyn would need to invest about $400 to reach $550 in 15 years.

The volume of the solid is (3π/5) units^3.  To find the volume of the solid formed by rotating the region in the 1st quadrant enclosed by the curves y=x^1/4 and y=x/64 about the y-axis, we can use the method of cylindrical shells.

First, we need to determine the limits of integration. Since the region is in the 1st quadrant, we can integrate from y=0 to y=1. To find the corresponding x-values for these limits, we can set y=x^1/4 and y=x/64 equal to 1 and solve for x:

x^1/4 = 1 => x = 1

x/64 = 1 => x = 64

So, our limits of integration are x=1 to x=64.

Next, we need to find an expression for the radius of each cylindrical shell. The radius is simply the distance from the y-axis to the curve at a given y-value. So, for a given y, the radius is:

r = x - x^1/4

Finally, we need to find an expression for the height of each cylindrical shell. The height is the infinitesimal change in y, which is simply dy. So, the volume of each cylindrical shell is:

dV = 2πr dy

Putting it all together, we have:

V = ∫(2πr) dy from y=0 to y=1

= ∫2π(x - x^1/4) dy from y=0 to y=1

= 2π ∫(x - x^1/4) dy from y=0 to y=1

= 2π ∫(y^4 - y) dy from y=0 to y=1

= 2π [y^5/5 - y^2/2] from y=0 to y=1

= 2π [(1/5) - (1/2)]

= (3π/5) units^3

Therefore, the volume of the solid is (3π/5) units^3.

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Answer:

The answer is 6 i believe sorry if i am wrong

Part a

y = 10x

For x=-3

substitute the value of x in the equation and evaluate it

y=10(-3)=-30

Part b

y = 6 - 2x

For x=11

y=6-2(11)=-16

Part c

y = 4x + 5

For x=1/2

y=4(1/2)+5=7

Answer:

3⅞ is the answer to the question.

Step-by-step explanation:

The ten lightest tomatoes are in ¼, ⅜, ½, ⅝ and ⅞.

In ¼, there are 3 tomatoes, so that would be “¼×3=¾”.

In ⅜, there are 2 tomatoes, so that would be “⅜×2=¾”.

In ½, there are 3 tomatoes, so it would be “½×3=3/2”.

In ⅝, there is 1 tomato, so it would be “⅝×1=⅝”.

In ⅞, there is 1 tomato, so that would be “⅞×1=⅞”.

Now add all together:

¾ + ¾ + 3/2 + ⅝ + ⅞

= 5+5+7+6+8/8

= 31/8

= 3⅞

The correct order of steps to prove the inequality 3^n < (n+1)! for n = 7 is as follows: 3^k < (k+1) * k!, 3 * 3^k = 3^(k+1), 3^(k+1) < (k+1) * 3^k; For n = 7, 3^7 = 2187: 2187 < 7! + 5040.

To prove the inequality 3^n < (n+1)! for n = 7, we can follow these steps:

Start with the assumption that 3^k < (k+1) * k! is true for some positive integer k.

Multiply both sides of the inequality by 3 to get 3^(k+1) < 3 * (k+1) * k!.

Simplify the right side to obtain 3^(k+1) < (k+1) * (k+1) * k!.

Rewrite (k+1) * (k+1) as (k+1)^2.

By substitution, we have 3^(k+1) < (k+1)^2 * k!.

Now, consider the case where n = 7. We substitute k = 6 in the inequality.

Evaluating both sides of the inequality for n = 7, we find that 3^7 = 2187.

Calculate (7+1)! = 8! = 40320.

Compare the values: 2187 < 40320.

Since 2187 is indeed less than 40320, the inequality holds true for n = 7.

Therefore, we have successfully shown that 3^n < (n+1)! for n = 7.

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The polynomial P(x) can be represented as P(x) = a(x - 4)^2(x + 5), where a is a constant.

Given that P(x) has a degree of 3, a root of multiplicity 2 at x = 4, and a root of multiplicity 1 at x = -5, we can determine the general form of the polynomial. A root of multiplicity 2 at x = 4 indicates that the factor (x - 4) appears twice in the polynomial, and a root of multiplicity 1 at x = -5 indicates that the factor (x + 5) appears once.

Hence, the polynomial can be written as P(x) = a(x - 4)^2(x + 5), where a is a constant that needs to be determined.

To find the value of a, we can use the y-intercept information. The y-intercept is given as (0, -48), which means that when x = 0, P(x) = -48. Substituting these values into the polynomial equation, we have -48 = a(0 - 4)^2(0 + 5).

Simplifying this equation, we get -48 = 100a. Solving for a, we find a = -48/100 = -12/25.

Therefore, the polynomial P(x) is P(x) = (-12/25)(x - 4)^2(x + 5).

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The function G(n) in terms of f(n) is G(n) = 2/π² (f(n) - f²(n)).

To find the function G(n) in terms of f(n) based on the given expression, we substitute f(n) into the formula for G(n):

G(n) = 2/π² (Sin nπ/2 - Sin² nπ/2)

Replacing Sin nπ/2 with f(n), we have:

G(n) = 2/π² (f(n) - Sin² nπ/2)

Since f(n) is defined as f(n) = Sin nπ/2, we can simplify further:

G(n) = 2/π² (Sin nπ/2 - Sin² nπ/2)

Now we can substitute f(n) = Sin nπ/2 into the equation:

G(n) = 2/π² (f(n) - f²(n))

Therefore, the function G(n) in terms of f(n) is G(n) = 2/π² (f(n) - f²(n)).

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Answer:

88.8888888889% or 88% rounded

plz Brainliest?!?!?

Answer:

circumference =2πr

2x22/7x4

44/7x4

=176/7

=25.142857

1) ||a|| = sqrt(30)  3) b - a = <5 - 5, 1 - 1, -2 - (-2)> = <0, 0, 0>  4)a · b = 55 + 11 + (-2)*(-2) = 25 + 1 + 4 = 30 5) a x b = <(1*(-2) - (-2)1), (-25 - 5*(-2)), (51 - 15)> = <0, -20, 0>. lim(T → 6) (cos(e) + sin(30) + 0) = cos(6) + sin(30) + 0

Norm of vector a: The norm (or magnitude) of a vector is found by taking the square root of the sum of the squares of its components. For vector a = <5, 1, -2>, the norm ||a|| is calculated as follows:

||a|| = sqrt(5^2 + 1^2 + (-2)^2) = sqrt(30) = answer1.

Cross product of vectors a and b: The cross product of two vectors is calculated using the determinant of a 3x3 matrix. For vectors a = <5, 1, -2> and b = <5, 1, -2>, the cross product a x b is found as follows:

a x b = <(1*(-2) - (-2)1), (-25 - 5*(-2)), (51 - 15)> = <0, -20, 0> = answer5.

Difference b-a: To find the difference between vectors b and a, we subtract the corresponding components. For vectors a = <5, 1, -2> and b = <5, 1, -2>, we have:

b - a = <5 - 5, 1 - 1, -2 - (-2)> = <0, 0, 0> = answer3.

Dot product of vectors a and b: The dot product of two vectors is found by multiplying the corresponding components and summing the results. For vectors a = <5, 1, -2> and b = <5, 1, -2>, we have:

a · b = 55 + 11 + (-2)*(-2) = 25 + 1 + 4 = 30 = answer4.

Limit evaluation: To find the limit of the given expression, we substitute the given value into the trigonometric functions:

lim(T → 6) (cos(e) + sin(30) + 0) = cos(6) + sin(30) + 0 = answer5.

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Answer:

elimination method

x+2y=4     1

5x-2y=8     2

1+2

6x=12

x=2

plug into x+2y=4

2+2y=4

2y=4-2

2y=2

y=1

(2,1)

so graph 1

The maximum height of the projectile is 56.53 meters.

The height of a projectile at time t is represented by the function h (t)= −4.9 t² +18t + 40, where h(t) is the height in meters and t is the time in seconds.

This is a quadratic function of the form h(t) = at² + bt + c, where a = -4.9, b = 18, and c = 40.

To find the maximum height of the projectile, we need to find the vertex of the parabolic graph of the function h(t).

The vertex of the parabola is at the point (t, h(t)) where t = -b/2a. Substituting the values of a and b, we get t = -18/(2(-4.9)) = 1.8367 seconds.

To find the maximum height, we need to substitute t = 1.8367 seconds into the function h(t). h(1.8367) = -4.9(1.8367)^2 + 18(1.8367) + 40 = 56.53 meters.

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To evaluate the integral ∫[0, 0.78] sin(8x²) dx using the Maclaurin series for sin(8x²), we can substitute the Maclaurin series into the integral. The Maclaurin series for sin(8x²) is given by:

sin(8x²) = 8x² - (8x²)³/3! + (8x²)⁵/5! - (8x²)⁷/7! + ...

Substituting this series into the integral, we have:

∫[0, 0.78] (8x² - (8x²)³/3! + (8x²)⁵/5! - (8x²)⁷/7! + ...) dx

Integrating each term separately, we get:

∫[0, 0.78] 8x² dx - ∫[0, 0.78] (8x²)³/3! dx + ∫[0, 0.78] (8x²)⁵/5! dx - ∫[0, 0.78] (8x²)⁷/7! dx + ...

Evaluating each integral term, we have:

(8/3)x³ - (8/3!)(8/3)²x⁵ + (8/5!)(8/5)²x⁷ - (8/7!)(8/7)²x⁹ + ...

To estimate the value of the integral, we can use the first two terms of the series. Plugging in the values, we have:

(8/3)(0.78)³ - (8/3!)(8/3)²(0.78)⁵ ≈ 1.564

Therefore, using the first two terms of the series, the estimated value of the integral ∫[0, 0.78] sin(8x²) dx is approximately 1.564.

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The book is opened to pages 11 and 12.

How to get the product of the page

x * (x + 1) = 132

Expanding the equation, we get:

x² + x = 132

To solve for x, we need to rewrite the equation as a quadratic equation:

x²+ x - 132 = 0

Now, we can factor the quadratic equation:

(x - 11)(x + 12) = 0

This equation has two solutions for x:

x = 11

x = -12

Since page numbers cannot be negative, we discard the second solution. Thus, the left-hand page number is 11, and the right-hand page number is 11 + 1 = 12.

So, the book is opened to pages 11 and 12.

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Answer:

Step-by-step explanation:

To evaluate the given expression, we need to substitute the given values for x, y, and z. The expression becomes:

yz + x²

Substituting the given values, we get:

(6.1 * 0.2) + (3.2^2)

This simplifies to:

1.22 + 10.24

Therefore, the value of the expression is approximately 11.46.

11.46

gimme brainlyest gang

Official guidelines that govern what the group is supposed to do and how members are supposed to behave are called "bylaws" or "rules and regulations."

Official guidelines, such as bylaws or rules and regulations, serve as a framework that outlines the purpose, structure, and functioning of a group or organization. These guidelines provide clarity on the group's objectives, the roles and responsibilities of its members, decision-making processes, and expected behaviors.

Bylaws typically cover various aspects, including membership requirements, meeting procedures, voting procedures, officer positions and duties, financial management, dispute resolution mechanisms, and any other relevant policies. They serve as a reference point for members to understand their rights, obligations, and the overall functioning of the group.

These guidelines help ensure consistency, fairness, and accountability within the group. They establish a common set of expectations and provide a structure for decision-making and problem-solving. Bylaws also help maintain order and facilitate effective collaboration among group members.

In summary, official guidelines, such as bylaws or rules and regulations, are essential for providing a clear framework and establishing standards for the functioning and behavior of a group or organization. They contribute to the group's cohesion, effectiveness, and the achievement of its objectives.

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Answer:

The equation is;

f(x) = -2·x² + 5·x - 1

Step-by-step explanation:

The general form of a quadratic equation  or function f(x) is, f(x) = y = a·x² + b·x + c

Given that the points representing the quadratic function are;

(-1, -8), (0, -1), (1, 2) which  are of the form (x, y)

When x = -1, f(x) = y = -8

Plugging in the above values into the general form of a quadratic function, we have;

-8 = a·(-1)² + b·(-1) + c = a - b + c

-8  = a - b + c.........................(1)

When x = 0, y = -1, we have;

-1 = a·(0)² + b·(0) + c = c

c = -1.......................................(2)

When x = 1, y = 2, which gives;

2 = a·(1)² + b·(1) + c = a + b + c

2 = a + b + c........................(3)

Adding equation (1) to equation (3), we have;

-8 + 2 = a - b + c + a + b + c

-8 + 2 = 2·a + 2·c

From equation (2) c = -1, we get;

-8 + 2 = -6 = 2·a + 2·c = 2·a + 2 × (-1)

-6 = 2·a - 2

-4 = 2·a

a = -2

From equation (3), we have

2 = a + b + c

Substituting the values of a, and c gives;

2 = -2 + b - 1

b = 2 + 2 + 1 = 5

b = 5

The equation is therefore;

f(x) = -2·x² + 5·x - 1.

Answer:

b

Step-by-step explanation:

Answer: 35

Step-by-step explanation:

The ratio of corresponding sides for the given similar triangles is 2/5.

In the given options, the ratio of corresponding sides is provided for each set of similar triangles. Let's analyze each option to determine the correct ratio:

a. 10

This option only provides a single number and does not specify the ratio of corresponding sides. Therefore, it is not the correct answer.

b. 4/5

This option provides the ratio 4/5 for the corresponding sides of the similar triangles. However, the ratio can be simplified further.

To simplify the ratio, we divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 5 is 1.

Dividing 4 and 5 by 1, we get:

4 ÷ 1 = 4

5 ÷ 1 = 5

Therefore, the simplified ratio is 4/5.

c. 10/85

This option provides the ratio 10/85 for the corresponding sides of the similar triangles. However, this ratio cannot be simplified further, as 10 and 85 do not have a common factor other than 1.

Therefore, the correct ratio of corresponding sides for the given similar triangles is 2/5, as determined in option b.

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Answer:

\(\frac{4k}{3}+5=18\)

Step-by-step explanation:

→ Start of with k being divided by 3

\(\frac{k}{3}\)

→ Multiplied by 4

\(\frac{k}{3}*4=\frac{4k}{3}\)

→ Added to 5

\(\frac{4k}{3}+5\)

→ The answer is 18

\(\frac{4k}{3}+5=18\)

7. y = 5x

8. k/3 × 4 + 5 = 18

9. y = 2x + 120

--------------

if the price of house is y

so y=5x

k/\(3x\(4+\(5=18

y for table

according to the problem

y=2x+120

Answer:hello

Step-by-step explanation:

Answer: 2

Step-by-step explanation: