n
A simple random sample of size n-21 is drawn from a population that is normally distributed. The sample mean is found to be x64 and the sample standard deviation is bound to be 10 Construct a 90% conf

Answer:

I only know is:planes r and t intersect at line y

Answer:

B- The line containing points A and B lies entirely in plane

C-Line z intersects plane S at point C.

E-Planes R and T intersect at line y.

Step-by-step explanation:

Ed2022

The solution of the equations are as follows:

A. x = 11

B. No solution

C. Many solution

D. x = 0

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

The solution of the following variables can be found as follows:

A variable is a number represented with letter in an equation. Hence, let's find the variables of the equations.

x - 4 = 1 / 2 (x + 3)

x - 4 = 1 / 2 x + 3 / 2

x - 1 / 2x = 3 / 2 + 4

1 / 2 x = 11 / 2

cross multiply

2x = 22

x = 22 / 2

x = 11

-4x = 1 / 2 (-8x + 2)

-4x = -4x + 1

-4x + 4x = 1

0 = 1

No solution

3 - 2(-3x + 1) = 6x + 1

3 + 6x - 2 = 6x + 1

1 + 6x = 6x = 1

1 - 1 = 6x - 6x

0 = 0

Many solutions

0.5(x + 3) = -3(x - 0.5)

0.5x + 1.5 = -3x + 1.5

0.5x + 3x = 1.5 - 1.5

3.5x = 0

x = 0

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The root of the equation sinx = 2x-3 is 0.8401 (approx).

Given equation is sinx = 2x-3

We need to solve this equation using false position method.

False position method is also known as the regula falsi method.

It is an iterative method used to solve nonlinear equations.

The method is based on the intermediate value theorem.

False position method is a modified version of the bisection method.

The following steps are followed to solve the given equation using the false position method:

1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.

Here, f(x) = sinx - 2x + 3.

2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))

3. Evaluate the function at point c and find the sign of f(c).

4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.

5. Repeat the steps 2 to 4 until we obtain the required accuracy.

Let's solve the given equation using the false position method.

We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.

So, the root lies between 0 and 1.

The calculation is shown in the attached image below.

Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).

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Answer:

4

Step-by-step explanation:

What you have typed is

\( \frac{ {3}^{12} \times {2}^{10} \times {2}^{ - 8} }{ {3}^{12} }\)

=3^12 cancels out

\( \frac{1 \times {2}^{2} }{1} \)

=4

Step-by-step explanation:

if I understand your text right, we are looking at the line going through the points (0, 2) and (5, 3).

the slope is in a line equation always the factor of x.

anyway, it is expressed as ratio y/x indicating how many units y changes, when x changes a certain amount of units when going from one point on the line to another.

so, we are simply going from (0, 2) to (5, 3).

x changes by +5 (from 0 to 5).

y changes by +1 (from 2 to 3).

so, the slope is y/x = 1/5.

Answer:

B. \(\frac{1}{5}\)

Step-by-step explanation:

The plots are just rough sketches to give you an idea of how the cumulative response record and acquisition curve might look based on the provided data. a) figure 2 , b) figure3.

A cumulative response record is a graphical representation of the total number of responses accumulated over time in an experiment. It shows the cumulative sum of responses at each time point, indicating the overall progress or acquisition of the behavior being measured.

To plot a cumulative response record for the given data, you need to calculate the cumulative sum of responses at each time point. Here's how you can do it:

a. Plotting the cumulative response record:

Time (s) on the x-axis and Cumulative Sum on the y-axis.

Here's the plot: (Attached figure 2)

b. Plotting the acquisition or response curve on a separate graph:

Time (s) on the x-axis and Number of Responses on the y-axis.

Here's the plot: (Attached figure 3)

Therefore, the plots are just rough sketches to give you an idea of how the cumulative response record and acquisition curve might look based on the provided data.a) figure 2 , b) figure3.

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Answer:

e = 128

Step-by-step explanation:

All of the angles equal 180

26 + 26 = 52

180 - 52 = 128

Answer: 168 people have to attend

Step-by-step explanation: 2520÷15= 168...just divide it to get it, if it help pls mark as brainliest ^-^, Thank you!

Part A is correct. Nice work

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Part B is close, but you forgot about some of the '1's that you'll need to add up. Check out the diagram below. I've added blue x's and 1's to show the various side lengths. You should have 6 copies of 1 to add up leading to +6 at the end, not +2. The perimeter is 2x+2y+6

Side note: the terms inside the boxes/rectangles represent the area of each little piece. For instance the upper left rectangle is 1 by x so its area is 1*x = x square units.

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

For part C, refer to the diagram below. The perimeter is y+1+y+1+1+y+1+y = 4y+4

Or you can think of each side having (y+1) and we have four of those sides leading to 4(y+1) = 4y+4 as the perimeter.

The area is y^2+y+y+1 = y^2+2y+1. This can be found by using the FOIL rule on (y+1)^2

There are three types of triangle according to sides and angles each.

The triangle is a type of polygon having three sides, angles and vertices.

Classification of triangles :-

Based on sides :-

1) Scalene triangle :- A triangle with all different measurements of sides and angles are called a Scalene triangle.

2) Isosceles triangle :- A triangle with two of the sides and angles are congruent called an Isosceles triangle.

3) Equilateral triangles :- A triangle with all the same measurements of sides and angles is called an Equilateral triangle.

Based on angles :-

1) Acute angled triangle :- A triangle with all the angles less than 90°, are called acute angled triangle.

2) Obtuse angled triangle :- A triangle with all the angles greater than 90° and less than 180°, are called Obtuse angled triangle.

3) Right angled triangle :- A triangle with one angle equals 90° is called a Right angled triangle.

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Answer:

The potato is a root vegetable native to the Americas, a starchy tuber of the plant Solanum tuberosum, and the plant itself, a perennial in the family Solanaceae. Wild potato species, originating in modern day Peru, can be found throughout the Americas, from the United States to southern Chile.

Step-by-step explanation:

Answer:

160 ounces

Step-by-step explanation:

Answer:

a) From A ∩ A' = ∅, we have;

A ∩ (A' ∪ B) = A ∩ B

b) From A ∩ (A' ∩ B') = (A ∩ A') ∩ B' and A ∩ A' = ∅, we have;

A ∩ (A ∪ B)' = ∅

Step-by-step explanation:

a) By distributive law of sets, we have;

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

From the complementary law of sets, we have;

A ∩ A' = ∅

Therefore, for A ∩ (A' ∪ B) = A ∩ B, we have

A ∩ (A' ∪ B) = (A ∩ A') ∪ (A ∩ B) (distributive law of sets)

A ∩ A' = ∅ (complementary law of sets)

Therefore;

(A ∩ A') ∪ (A ∩ B) = ∅ ∪ (A ∩ B)  = (A ∩ B) (Addition to zero identity property)

∴  A ∩ (A' ∪ B) = A ∩ B

b) By De Morgan's law

(A ∪ B)' = A' ∩ B'

Therefore, A ∩ (A ∪ B)' = A ∩ (A' ∩ B')

By associative law of sets, we have;

A ∩ (A' ∩ B') = (A ∩ A') ∩ B'

A ∩ A' = ∅ (complementary law of sets)

Therefore, (A ∩ A') ∩ B' = ∅  ∩ B' = ∅

Which gives;

A ∩ (A ∪ B)' = ∅.

The minimum length of the third side must be greater than 16 feet.

The minimum length of the third side can be determined using the Triangle inequality theorem. This theorem states that the sum of any two sides of a triangle must be greater than the length of the third side. The Triangle Inequality Theorem can be expressed by the following inequality: a + b > c, where a, b, and c are the lengths of the three sides of the triangle. In this case, we have two sides of 4 feet and 12 feet, so the inequality can be written as 4 + 12 > c, which simplifies to 16 > c. Solving for c yields c > 16, which means that the minimum length of the third side must be greater than 16 feet.

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Answer:

\(\large \boxed{\$148.50}\)

Step-by-step explanation:

Regular pay       = $11/h

Time and-a half = 1½ × regular pay = 1½ × $11/h = $16.50/h

\(\text{Overtime} = \text{9 h} \times \dfrac{\$ 16.50}{\text{1 h }} = \mathbf{\$148.50}\\\\\text{Ariel's overtime earnings will be $\large \boxed{\mathbf{\$148.50}}$}\)

a)The probability of female and no opinion is: 0.375

b) The probability of student approves of the proposed change is: 0.5

c) The probability of student is male, given the student does not approve of the proposed change is: 0.398

d)  The probability of student is male and approves of the proposed change is : 0.2

The formula for probability states that the possibility of an event happening, or P(E), equals the ratio of the number of favorable outcomes to the number of total outcomes. Mathematically, it looks like this:

P(E) = favorable outcomes/total outcomes.

They are  70 mathematics majors were asked whether they approved of the proposed change.

The table are as follows:

                Approved(A)    No opinion(No)      Did not approve(DA)

Female      21                   6                           12

Male          14                    10                           7

a) To find the probability that the student is female, given no opinion:

So, The probability of Female and no opinion :

We have to apply the probability formula:

P(F | No) = P(F∩No)/ P(No) = \(\frac{6}{70}/\frac{16}{70}\) = \(\frac{6}{16}\) = 0.375

b) The probability of student approves of the proposed change:

P(A) = \(\frac{21+14}{70}\)= 35/70 = 1/2 = 0.5

c) The probability of student is male, given the student does not approve of the proposed change:

P(M|DA) = P(M∩DA)/P(DA) = \(\frac{\frac{7}{70} }{\frac{19}{70} }\) = 7/19 = 0.398

d) The probability of student is male and approves of the proposed change.

P(M∩A) = 14/70 = 0.2

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Answer:

D. 29 I just know the awnser sorry

To find the value of f(−2), we substitute −2 for x in the function f(x):

f(−2) = 4(-2)^2 − 3(-2) + 7

= 4(4) − 3(2) + 7

= 16 − 6 + 7

= 11

Therefore, f(−2) = 11.

The budgets of Hong Kong, the United States of America, and Korea differ in contents, formats, advantages, and disadvantages. While each budget has its strengths and weaknesses, they all aim to provide a clear and transparent financial plan for their respective countries.

A budget is a financial plan that estimates expected income and expenditure for a specific period. It may include income, expenses, debts, and savings. Budgets may vary from country to country and can be analyzed by comparing their contents, formats, advantages, and disadvantages. Here are the budgets of Hong Kong, the United States of America, and Korea:

United States Budget:

Korean Budget:

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Answer:

s = 41 cm

Step-by-step explanation:

Since all the sides on a square are equal, we can use this formula for perimeter:  P = 4s

Plugging in 164 gives us 164 = 4s, where solving for s gives us s = 41

Answer:

y = 18 - 6x / 2 OR y = 9 - 3x

Step-by-step explanation:

Make y the subject of formula.

The work done by the force field on the particle moving along the given helix is 60π units of work.

To find the work done by the force field F on the particle that moves along the helix r, we use the formula:

W = ∫ F · dr

where · denotes the dot product, and dr is the differential displacement vector along the path of the particle.

First, we need to calculate dr. Since the particle moves along the helix r, we can write:

dr = dx i + dy j + dz k

where dx, dy, and dz are the differentials of x, y, and z with respect to t, respectively. We have:

dx = -2sin(t) dt

dy = 2cos(t) dt

dz = 5 dt

Therefore, we can write:

dr = (-2sin(t) i + 2cos(t) j + 5k) dt

Next, we need to calculate F · dr. We have:

F · dr = (6x i + 6y j + 2k) · (-2sin(t) i + 2cos(t) j + 5k) dt

= -12sin(t) + 12cos(t) + 10 dt

Finally, we can integrate F · dr over the interval 0 ≤ t ≤ 2π to obtain the work done by the force field F on the particle that moves along the helix r:

W = ∫ F · dr = ∫ (-12sin(t) + 12cos(t) + 10) dt

= [-12cos(t) + 12sin(t) + 10t]0\(^(2π)\)

= (-12cos(2π) + 12sin(2π) + 10(2π)) - (-12cos(0) + 12sin(0) + 10(0))

= 20π

Therefore, the work done by the force field F on the particle that moves along the helix r is 20π.

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1. In Step 2, the equation is multiplied by 4 to create a common factor for the coefficient of x.

2. In Step 5, 3² is added to each side to complete the square.

3. In Steps 5 and 6, a perfect square trinomial is created by adding half the coefficient of the x-term squared to both sides of the equation and the constants on the right-hand side rearranged.

In Mathematics and Geometry, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

Part 1.

By critically observing Step 2, we can logically deduce that the equation was multiplied by 4 in order to create a common factor for the coefficient of x;

(2x)² + 6(2x) = -32

Part 2.

In order to complete the square, you should add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

P² + 6P + (6/2)² = -32 + (6/2)²

P² + 6P + 3² = -32 + 3²

Part 3.

In Steps 5 and 6, we can logically deduce that a perfect square trinomial was created by adding half the coefficient of the x-term squared to both sides of the quadratic equation:

P² + 6P + 3² = -32 + 3²

(P + 3)² = 3² - 32

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Answer:

with what what is the question?

Answer:

What is the question?

Also, can I get brainliest? I need it for a challenge.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The total length of the curve swept out by the point (x, y) as θ ranges from 0 to 2π is 64π units.

We can start by finding the derivative of x and y with respect to θ:

dx/dθ = -16 sin θ

dy/dθ = 16 cos θ

Using the formula for arc length of a curve in polar coordinates, we have:

L = ∫(a to b) √(r² + (dr/dθ)²) dθ

where r is the distance from the origin to the point (x, y).

Substituting x and y into r, we get:

r = √(x² + y²) = √(256 \(cos^{2\theta\) + 256 \(sin^{2\theta\)) = 16

Substituting dx/dθ and dy/dθ into (dr/dθ), we get:

(dr/dθ) = √((-16 sin θ)² + (16 cos θ)²) = 16

Therefore, the total length of the curve swept out by the point (x, y) as θ ranges from 0 to 2π is:

L = \(\int\limits^{2 \pi}_0\) √(r² + (dr/dθ)²) dθ

= \(\int\limits^{2 \pi}_0\) √(256 + 256) dθ

= \(\int\limits^{2 \pi}_0\) 32 dθ

= 32θ |o to (2π)

= 64π

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Using the combination formula, it is found that Julia can take 15 combinations.

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by:

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

For this problem, 4 students are taken from a set of 6, hence the number of combinations is given as follows:

\(C_{6,4} = \frac{6!}{4!2!} = 15\)

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The vertex form of the equation is y = (x - 3)² - 4, which corresponds to option OD.

To convert the given equation from standard form to vertex form, we need to complete the square.

The vertex form of a parabola's equation is y = a(x-h)² + k, where (h, k) represents the vertex of the parabola.

Given equation: y = x² - 6x + 14

Move the constant term to the right side:

y - 14 = x² - 6x

Complete the square by adding and subtracting the square of half the coefficient of x:

y - 14 + 9 = x² - 6x + 9 - 9

Group the terms and factor the quadratic:

(y - 5) = (x² - 6x + 9) - 9

Rewrite the quadratic as a perfect square:

(y - 5) = (x - 3)² - 9

Simplify the equation:

y - 5 = (x - 3)² - 9

Move the constant term to the right side:

y = (x - 3)² - 9 + 5

Combine the constants:

y = (x - 3)² - 4

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Answer:

12 cups

Step-by-step explanation:

B) ∅ (empty set); The composition T ∘ S is an empty set (∅) because there are no ordered pairs that satisfy both the conditions of the relations T and S.

To find the composition T ∘ S, we need to determine the set of ordered pairs that satisfy both relations S and T. Let's analyze the definitions of S and T:

S = {(x, y) ∣ x < y}

T = {(x, y) ∣ x > y}

To find T ∘ S, we need to check if there exists an element z such that (x, z) is in T and (z, y) is in S for any (x, y) in the given relations. However, if we observe the definitions of S and T, we can see that there is no common element that satisfies both relations.

For any (x, y) in S, we have x < y, but in T, the relation is defined as x > y. Therefore, there are no elements that satisfy both conditions simultaneously.

As a result, T ∘ S will be an empty set (∅) because there are no ordered pairs that satisfy the composition of the two relations.

The composition T ∘ S is an empty set (∅) because there are no ordered pairs that satisfy both the conditions of the relations T and S.

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Answer:

Lol i don't know.

Step-by-step explanation: