The figure shows a flagpole and its shadow. The shadow has a length of 43 feet and the sun's rays make an angle of 30° with the ground.



What is the approximate height, x, of the flagpole?

A.
28 feet
B.
25 feet
C.
22 feet
D.
37 feet

The given expression is of the form y=mx+c. Comparing, we get the slope as 7.

The direction and steepness of a line are represented numerically by the slope or gradient of the line. It provides the ratio of how much y rises when x rises by a particular amount. The general form is therefore y=mx+c, where c represents the y-intercept and m represents the slope. This form gives the slope-intercept form.

Given the expression is  y=7x+3. Comparing this expression with the general form we get, slope or gradient as 7 and y-intercept as 3. Therefore, the required answer is 7.  

The complete question -

What is the gradient of the line y=7x+3?

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Here's a proof for each of the statements you provided.

a) If g∘f = I_A, then f is an injection.
Proof: Assume x1 and x2 are elements of A such that f(x1) = f(x2). We want to show that x1 = x2. Since g∘f = I_A, we have g(f(x1)) = g(f(x2)). Applying I_A, we get x1 = g(f(x1)) = g(f(x2)) = x2. Thus, f is injective.

b) If f∘g = I_B, then f is a surjection.
Proof: Let y be an element of B. We want to show that there exists an element x in A such that f(x) = y. Since f∘g = I_B, we have f(g(y)) = I_B(y) = y. Thus, there exists an element x = g(y) in A such that f(x) = y. Therefore, f is surjective.

c) If g∘f = I_A and f∘g = I_B, then f and g are bijections and g = f^(-1).
Proof: From parts (a) and (b), we know that f is both injective and surjective, which means f is a bijection. Similarly, g is also a bijection. Now, we need to show that g = f^(-1). By definition, f^(-1)∘f = I_A and f∘f^(-1) = I_B. Since g∘f = I_A and f∘g = I_B, it follows that g = f^(-1).

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A solution of a system of linear equations is (0,−4).

What is Systems of Linear Equations?

A direct equation is an equation in two variables, and when it's graphed, a straight line is formed. The line is created by the combination of corresponding values that satisfy the equation. utmost generally, direct equations use the variables x and y so the corresponding values can be colluded as (x,y) pairs on the  co-ordinate plane .

Main body:

A system of direct equations is a group of two or further direct equations. The result to any system of direct equations is the point where the lines cross on a graph, still, because lines can be resemblant or coinciding, it's possible for a system to have no result( parallel) or infinitely numerous results( coinciding).

y = 3x−4

y=−x/2−4

now solve:

3x=−3/2x

1/2x=0

x=0

If x=0

, solve for the corresponding y-coordinate:

y=3(0)−4

y=−4

So, the solution is (0,−4).

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Answer:

A= πr²

A=3.14*5*5

A=78.5cm²

Answer:

(3.5, -2)

Step-by-step explanation:

Just got it right on edge 2020

The solution to the system of linear equations is: (3.5, -2).

Thus, having solve for y as -2, substitute y = -2 into 12x – 21y = 84.

12x – 21(-2) = 84

12x + 42 = 84

12x = 84 - 42

12x = 42

x = 3.5.

Therefore, the solution to the system of linear equations is: (3.5, -2).

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The Fourier series for f(x) is f(x) = (4/π) [sin(x) + (1/3) sin(3x) + (1/5) sin(5x) + ...].

The square wave function can be defined as:

f(x) = {1 -π ≤ x < 0

-1 0 ≤ x < π

To find the Fourier series for this function, we first need to determine the coefficients a_n and b_n.

a_n = (1/π) ∫_0^π f(x) cos(nx) dx

= (1/π) ∫_0^π (-1) cos(nx) dx + (1/π) ∫_(-π)^0 cos(nx) dx

= (2/π) ∫_0^π cos(nx) dx

= (2/π) [sin(nπ) - sin(0)]

= 0

b_n = (1/π) ∫_0^π f(x) sin(nx) dx

= (1/π) ∫_0^π (-1) sin(nx) dx + (1/π) ∫_(-π)^0 sin(nx) dx

= -(2/π) ∫_0^π sin(nx) dx

= -(2/π) [cos(nπ) - cos(0)]

= (2/π) [1 - (-1)^n]

Therefore, the Fourier series for f(x) is:

f(x) = (4/π) [sin(x) + (1/3) sin(3x) + (1/5) sin(5x) + ...]

To find the first three Fourier approximations, we truncate this series at the third term.

F_1(x) = -(4/π) sin(x)

F_2(x) = (4/π) sin(x) + (4/3π) sin(3x)

F_3(x) = (4/π) sin(x) + (4/3π) sin(3x) - (4/5π) sin(5x)

These are the first three Fourier approximations of the square wave function f(x). The more terms we include in the Fourier series, the closer the approximations will be to the original function.

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The provided information seems incomplete and unclear. It appears that you are trying to find the function f(x) based on some given conditions.

But the given equation and condition are not fully specified.

To determine the function f(x), we need additional information, such as the relationship between f and 1-1 and any specific values or equations involving f(x).

Please provide more details or clarify the question, and I would be happy to assist you further in finding the function f(x) based on the given conditions.

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Answer:

28/36 or 7/9

Step-by-step explanation:

there are 36 possible answers

4 of them equal 5 (1+4, 2+3, 3+2, 4+1)

4 of them equal 9 (3+6, 4+5, 5+4, 6+3)

8-36 = 28

Answer:

Please see the attached picture.

Answer:

-2,-4=12 That is the answer of that question

Answer:

x=33 and y= 75 is the answer.

Answer:

39⇒3

52⇒4

130⇒10

Step-by-step explanation:

hope this helps have a nice day!!!

The probability that the mean rebuild time exceeds 8.7 hours is 0.43.

Given:

a study of the amount of time it takes to rebuild the transmission for a 2005 chevy cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours.

here

μ = 8.4

σ = 1.8

x = 8.7

we know that:

z = x - μ / σ

= 8.7 - 8.4 / 1.8

= 0.3/1.8

= 03/10/18/10

= 3/18

= 1/6

= 0.166

p value at z = 0.166 is

p = 0.43

Therefore The probability that the mean rebuild time exceeds 8.7 hours is 0.43.

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Answer:

x = 17

Explanation:

Notice that all three of the angles combined create a straight angle. This means that the sum of all three angles is equal to 180 degrees.

Create your equation (7x - 2) + (2x + 4) + (25) = 180

Combine like terms 9x + 27 = 180

Subtract the constant from each side 9x = 153

Divide each side by the coefficient x = 17

You can check your work or find each individual angle by substituting 17 in for x.

Answer:

No.

Step-by-step explanation:

Below I should you two ways to get the correct answer.

The z-score for P(? ≤ z ≤ ?) = 0.60 is approximately 0.25.

The z-score for P(z ≥ ?) = 0.30 is approximately -0.52.

How to find the Z score

P(Z ≤ z) = 0.60

We can use a standard normal distribution table or a calculator to find that the z-score corresponding to a cumulative probability of 0.60 is approximately 0.25.

Therefore, the z-score for P(? ≤ z ≤ ?) = 0.60 is approximately 0.25.

For the second question:

We want to find the z-score such that the area under the standard normal distribution curve to the right of z is 0.30. In other words:

P(Z ≥ z) = 0.30

Using a standard normal distribution table or calculator, we can find that the z-score corresponding to a cumulative probability of 0.30 is approximately -0.52 (since we want the area to the right of z, we take the negative of the z-score).

Therefore, the z-score for P(z ≥ ?) = 0.30 is approximately -0.52.

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She must use 187.5 ounces of water and 62.5 ounces of salt solution for her experiment.

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

The smallest equivalent fraction of the number is the form that is the simplest. How to find the most basic form: In the numerator and denominator, look for shared factors. Examine the fraction to see if one of the numbers is a prime number.

Say w= the amount of water in oz, then the 60% of the solution is 250 - w

Set up the equation:

Use distributive property first

0.60(250-w) = 0.15 x 250

Isolate to solve for w

150- 0.60w= 37.5

-0.60w= 37.5-150

0.60w= -112.5

w= 187.5 ounces

250-187.5= 62.5 ounces salt solution

Therefore, she must use 187.5 ounces of water and 62.5 ounces of salt solution for her experiment.

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The measure of the inscribed angle is equal to 90 degrees

The inscribed angle theorem mentions that the angle inscribed inside a circle is always half the measure of the central angle or the intercepted arc that shares the endpoints of the inscribed angle's sides. In a circle, the angle formed by two chords with the common endpoints of a circle is called an inscribed angle and the common endpoint is considered as the vertex of the angle.

In this problem, the side length of the square is 5 which forms 90 degrees to all the other sides.

The measure of the circumscribed angle is 90 degree

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The triangle formed by the drinking fountain, the bench, and the center of the slide is a scalene triangle.

(a) To find the distance between two points on a coordinate grid, we can use the distance formula. The distance formula is derived from the Pythagorean theorem and can be stated as:

Distance = √((x2 - x1)² + (y2 - y1)²)

Let's calculate the distances:

Distance from drinking fountain to the bench:

Drinking fountain coordinates: (-4, 2)

Bench coordinates: (0, 2)

Using the distance formula:

Distance = √((0 - (-4))² + (2 - 2)²)

= √((4)²+ (0)²)

= √(16 + 0)

= √16

= 4

Therefore, the distance from the drinking fountain to the bench is 4 units.

Distance from the bench to the center of the slide:

Bench coordinates: (0, 2)

Center of the slide coordinates: (0, 5)

Using the distance formula:

Distance = √((0 - 0)² + (5 - 2)²)

= √((0)² + (3)²)

= √(0 + 9)

= √9

= 3

Therefore, the distance from the bench to the center of the slide is 3 units.

(b) The three locations form a triangle. To determine the type of triangle, we can examine the lengths of its sides.

The distances we calculated are:

Drinking fountain to the bench: 4 units

Bench to the center of the slide: 3 units

Since all three sides have different lengths (4, 3, and some unknown length for the side connecting the drinking fountain and the center of the slide), we can conclude that the triangle is a scalene triangle. A scalene triangle is a triangle in which all three sides have different lengths.

In summary, the triangle formed by the drinking fountain, the bench, and the center of the slide is a scalene triangle.

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Answer:

Step-by-step explanation:

Let x be the original price of a lawn mower,

If the hardware store is having a 15% off sale on lawn mowers this weekend, the amount discounted is expressed as;

= 15 % of x

= 0.15 of x

= 0.15x

Final sales price = Original price - discounted price;

Final sales price = x - 0.15x

Factor out x;

x - 0.15x = x(1 - 0.15)

Hence the correct equations are (x - 0.15x)  and x(1.00 - 0.15)

The least positive integer that will be divisible by both 15 and 35 will be 105.

The given integers are 15 and 35.
As we know that the least positive integer will be divisible by both 15 and 35 will be LCM ( least common factor) of 15 and 35.
The least common multiple of LCM of two integers is the common multiple of two numbers such that it is the least among all common multiples.
For example, LCM of 3 and 5 will be 15 because among all common multiples of 3 and 5, 15 will be least common multiple.
For LCM of 15 and 35, let's write multiples of both the numbers.
Multiples of 15 = 15,30,45,60,75,90,105,120,135,150,165,180,195,210,....
Multiples of 35= 35,70,105,140,175,210,...
We can see that 105 and 210 are two common multiples out of which 105 is the least multiple.
Therefore, the least positive integer that will be divisible by both 15 and 35 will be 105.

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Answer:

\(\frac{5}{12}\)

Step-by-step explanation:

1/4 / 3/5

To divide fractions we flip the second one and then multiply them both and this method works for any number

1/4 x5/3

5/12

Hopes this helps please mark brainliest

There are 120 different orders in which the 5 cars can be parked.

The car salesman can park the first car in any of the 5 visible spaces. Once the first car is parked, he has only 4 visible spaces left to park the second car.

For the third car, he has 3 visible spaces left, for the fourth car he has 2 visible spaces left, and for the fifth car, he has only 1 visible space left. Therefore, the total number of different orders in which he can park 5 different cars is:
5 x 4 x 3 x 2 x 1 = 120

So, the car salesman can park 5 different cars in 120 different orders.

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The interval for which the balls height is increasing is 0 < x < 0.75.

An interval on a number line can be represented using interval notation. It is a method of representing subsets of the real number line, in other words. The numbers in between any two particular provided numbers are referred to as an interval. For instance, the interval containing 0, 5, and all values between 0 and 5 is the set of numbers x satisfying 0 x 5.

From the given graph we observe that the graph follows an upward curve up until the point of 0.75 and after that the graph follows a downward trajectory.

Hence, the interval for which the balls height is increasing is 0 < x < 0.75.

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The solution for W(x,s) can then be inverse Laplace transformed to obtain the solution for w(x,t).

What is partial differential equation?

A partial differential equation (PDE) is an equation that involves partial derivatives of a multivariable function. It relates the function, its partial derivatives, and the independent variables. PDEs are used to describe various phenomena in physics, engineering, and other scientific fields, where the variables of interest depend on multiple independent variables. Solving PDEs involves finding a function that satisfies the equation and any given boundary or initial conditions.

To solve the partial differential equation \(∂w/∂t + ∂w/∂x = 0 \\\)with the initial conditions \(w(x,0) = x^2\) and w(0,t) = 5 using Laplace transform, we need to apply the Laplace transform operator to both sides of the equation and then solve for the transformed function.

Let's denote the Laplace transform of the function w(x,t) as W(x,s), where s is the complex frequency variable. Applying the Laplace transform to both sides of the equation, we get:

\(sW(x,s) - w(x,0) + ∂W(x,s)/∂x = 0\)

Using the initial condition \(w(x,0) = x^2\), we have:

\(sW(x,s) - x^2 + ∂W(x,s)/∂x = 0\)

Now, let's apply the Laplace transform to the boundary condition w(0,t) = 5:

W(0,s) = 5

We now have a transformed equation with the transformed function W(x,s) and transformed boundary condition W(0,s). To solve for W(x,s), we can integrate the equation with respect to x and solve the resulting ordinary differential equation. The solution for W(x,s) can then be inverse Laplace transformed to obtain the solution for w(x,t).

Please note that the specific solution depends on the domain and boundary conditions. Additional information or constraints may be required to determine a unique solution.

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Complete Question:

To solve the partial differential equation

∂w/∂t = a^2 ∂^2w/∂x^2

with the initial condition

w(x,0) = f(x)

and w(0,t) = 5 using Laplace transform, we need to apply the Laplace transform operator to both sides of the equation and then solve for the transformed function

Given info:- L and M are parallel lines. Transverse N cuts them at ∠(6x + 42)° and ∠(18x - 12)°. Then find the value of x?

Explanation:-

Since L and M are parallel lines,

.°. ∠(6x + 42)° + ∠(18x - 12)° = 180° [∠s of a linear pair]

→ 6x + 24° + 18x - 12° = 180°

→ 6x + 8x + 24° - 12° = 180°

→ 14x - 12° = 180°

→ 14x = 180° - 12°

→ 14x = 168°

→ x = 168÷14 = 168/14 = 12°

Therefore, the value of “x” is 12°.

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Lines l, m, and n are parallel. What is the value of x?Lines l, m, and n are parallel. Parallel lines labeled, top to bottom, l, m, and n. A transversal forms a...

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The first step in solving the first equation is different from the first step of solving the second equation because,

In the first equation, start by squaring both sides to eliminate the radical, but in the second equation, start by adding 1 to both sides to isolate the radical.

Thus the option B is the correct option.

Algebraic expression are the expression which consist the variables, coefficients of variables and constants.

The algebraic expression are used represent the general problem in the mathematical way to solve them.

Given information-

The first equation given in the problem is,

\((x-1)^2=8\)

The above equation can be solve using the algebraic formula of whole square of two number as,

\((x-1)^2=8\\x^2+1^2-2x=8\\x^2-2x-8+1=0\\x^2-2x-7=0\)

The first equation can be solved by putting square root both side as,

\(\sqrt{(x-1)^2}=\sqrt{8}\\(x-1)=\sqrt{8}\\x=2\sqrt{3}+1\)

The second equation given in the problem is,

\(x^2-1^2=8\)

The above equation can be solve using the algebraic formula of difference of the square of two number as,

\(x^2-1=8\\x^2=8+1\\x^2=9\\x=\pm3\)

Hence, The first step in solving the first equation is different from the first step of solving the second equation because,

In the first equation, start by squaring both sides to eliminate the radical, but in the second equation, start by adding 1 to both sides to isolate the radical.

Thus the option B is the correct option.

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Answer:

B.

Step-by-step explanation:

Correct on Edgen. (2022)

According to the question,

Given data in the question.

If the genome contained 20,000 genes, the average length of DNA per gene will be 40,000 base pairs.

What is the average length of DNA per gene?

Only 2.5% of the human genome is protein-coding. Introns make up the remaining 97.5%. The male nuclear diploid genome is 6.27 Giga base pairs (G b p), 205.00 cm (cm) long, and 6.41 picograms in weight (p g). Female measurements are 6.37 G b p, 208.23 cm, and 6.51 p g

For a 25% mammalian genome with 20,000 genes, the total number of base pairs, which is the length of DNA per gene, will be approximately double the payment of genes contained in the genome, in this case 40,000.

The average length of DNA per gene, assuming 20,000 genes in the genome, is 40,000 base pairs.

How long does DNA typically be per gene?

Only 2.5% of the human genome codes for proteins. The remaining 97.5% is made up of introns. The size and weight of the male nuclear diploid genome are 6.27 Giga base pairs (G  bp), 205.00 centimetres (cm), and 6.41 picograms (p g). 6.37 G   bp, 208.23 cm, and 6.51 p g are the female measurements.

The total number of base pairs, which is 20,000 for a 25% mammalian genome with 20,000 genes,

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The average length of DNA per gene would be 40,000 base pairs if the genome had 20,000 genes.

The human genome only codes for proteins in 2.5% of it. The remaining 97.5% are introns. The male nuclear diploid genome measures 205.00 centimeters (cm), is 6.27 Gigabase pairs (Gbp), and weighs 6.41 picograms (pg). 208.23 cm, 6.51 pg, and 6.37 Gbp are the female measurements.

Although there may be some hereditary component to math aptitude, this probably only accounts for a small portion of it. Even in the current study, genetics alone could only account for 20% of math prowess. According to Libertus, "this leaves more than 80% of the variety in children's math aptitude unexplained."

The overall number of base pairs, which is the length of DNA per gene, will be roughly twice the number of genes present in the genome, in this example 40,000, for a 25% mammalian genome with 20,000 genes.

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Redacte tres propuestas de solución apoyados en las enseñanzas que nos da Jesús sobre la tolerancia, el respeto y la verdad.

Redacte tres propuestas de solución apoyados en las enseñanzas que nos da Jesús sobre la tolerancia, el respeto y la verdad.

Redacte tres propuestas de solución apoyados en las enseñanzas que nos da Jesús sobre la tolerancia, el respeto y la verdad.

Redacte tres propuestas de solución apoyados en las enseñanzas que nos da Jesús sobre la tolerancia, el respeto y la verdad.

Redacte tres propuestas de solución apoyados en las enseñanzas que nos da Jesús sobre la tolerancia, el respeto y la verdad.

Redacte tres propuestas de solución apoyados en las enseñanzas que nos da Jesús sobre la tolerancia, el respeto y la verdad.

Redacte tres propuestas de solución apoyados en las enseñanzas que nos da Jesús sobre la tolerancia, el respeto y la verdad.

Redacte tres propuestas de solución apoyados en las enseñanzas que nos da Jesús sobre la tolerancia, el respeto y la verdad.

Redacte tres propuestas de solución apoyados en las enseñanzas que nos da Jesús sobre la tolerancia, el respeto y la verdad.

Redacte tres propuestas de solución apoyados en las enseñanzas que nos da Jesús sobre la tolerancia, el respeto y la verdad.

Redacte tres propuestas de solución apoyados en las enseñanzas que nos da Jesús sobre la tolerancia, el respeto y la verdad.

Redacte tres propuestas de solución apoyados en las enseñanzas que nos da Jesús sobre la tolerancia, el respeto y la verdad.

Redacte tres propuestas de solución apoyados en las enseñanzas que nos da Jesús sobre la tolerancia, el respeto y la verdad.

Redacte tres propuestas de solución apoyados en las enseñanzas que nos da Jesús sobre la tolerancia, el respeto y la verdad.

Redacte tres propuestas de solución apoyados en las enseñanzas que nos da Jesús sobre la tolerancia, el respeto y la verdad.

Redacte tres propuestas de solución apoyados en las enseñanzas que nos da Jesús sobre la tolerancia, el respeto y la verdad.

Redacte tres propuestas de solución apoyados en las enseñanzas que nos da Jesús sobre la tolerancia, el respeto y la verdad.

Redacte tres propuestas de solución apoyados en las enseñanzas que nos da Jesús sobre la tolerancia, el respeto y la verdad.

a) The mean weight of pineapples grown in the field this year is different from the mean weight of pineapples grown last year. b) The power to detect an increase of 2 ounces in the mean weight of pineapples (μa = 33 ounces) is approximately 0.932, and the probability of making a Type 2 error with a true mean of 33 ounces is approximately 0.068.

(a) The null hypothesis (H0) and alternative hypothesis (Ha) can be written as follows:

Null Hypothesis (H0): The mean weight of pineapples grown in the field this year is equal to the mean weight of pineapples grown last year (μ = 31 ounces).

Alternative Hypothesis (Ha): The mean weight of pineapples grown in the field this year is different from the mean weight of pineapples grown last year (μ ≠ 31 ounces).

(b) To calculate the power and the probability of making a Type 2 error, we need to assume the population mean weight of pineapples this year (μa) is 33 ounces. We also need to determine the critical value for the given significance level (α) of 0.05.

Given that the sample size (n) is 30, the population standard deviation (σ) is 4 ounces, and the mean weight under the alternative hypothesis (μa) is 33 ounces, we can calculate the test statistic (z) using the formula:

z = (\(\bar x\) - μa) / (σ / √n)

where \(\bar x\) is the sample mean.

With \(\bar x\) = 31 ounces, σ = 4 ounces, μa = 33 ounces, and n = 30, we can calculate the test statistic:

z = (31 - 33) / (4 / √30)

z = -2 / (4 / √30)

z = -2 / (4 / 5.477)

z = -2 / 1.0954

z ≈ -1.825

Using a standard normal distribution table or calculator, we can find the corresponding p-value for this z-value. Let's assume it is approximately 0.034 (one-tailed test).

The power of the test can be calculated as 1 minus the probability of a Type 2 error. Since the alternative hypothesis is two-sided, we divide the significance level (α) by 2 and find the corresponding critical z-value. Let's assume it is approximately 1.96 (two-tailed test).

Now we can calculate the power using the formula:

Power = 1 - P(Type 2 Error) = 1 - P(z < -1.96 or z > 1.96)

P(Type 2 Error) = P(z < -1.96 or z > 1.96) ≈ 2 * P(z < -1.96) (assuming symmetry)

P(Type 2 Error) ≈ 2 * 0.034 ≈ 0.068

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