The mean score in a physics test is 75% with the standard deviation 6.5%. Suppose that the scores in the test are approximately normally distributed. What is the probability that a randomly selected student scores more than 82%? Round your answer for 4 decimal places.

__________

The linear equation is defined by y = mx +b is called ''Slope-intercept form''.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The linear equation is defined by,

⇒ y = mx + b

Now, We know that;

The equation defined as;

⇒ y = mx + b

Where, 'm' is slope and 'b' is y - intercept.

Hence, The linear equation is defined by y = mx +b is called ''Slope-intercept form''.

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Answer:

x = 13

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² = 5² + 12² = 25 + 144 = 169 ( take the square root of both sides )

x = [tex]\sqrt{169}[/tex] = 13

A linear function is a mathematical function that can be represented by a straight line when graphed on a Cartesian coordinate system. It is also known as a first-degree polynomial because the highest exponent of the variable is 1. The general form of a linear function is: f(x) = mx + b

To find a linear function given two points on the line, you need to use the point-slope formula.

The formula is `y - y1 = m(x - x1)`, where `(x1, y1)` is a point on the line and `m` is the slope of the line.

Given that f(0) = 8 and f(7) = 14, we can find the slope of the line:$$\frac{f(7) - f(0)}{7 - 0} = \frac{14 - 8}{7} = \frac{6}{7}$$Now, we can use the point-slope formula with the point `(0, 8)` and the slope `6/7`:$$y - 8 = \frac{6}{7}(x - 0)$$

Simplifying this equation, we get:$$y - 8 = \frac{6}{7}x$$$$y = \frac{6}{7}x + 8$$

Therefore, the linear function with `f(0) = 8` and `f(7) = 14` is `y = (6/7)x + 8`.

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A linear function, y = f(x) that has f(0) = 8 and f(7) = 14 is given by: f(x) = mx + b, Where m represents the slope of the line and b represents the y-intercept. The equation of the linear function is: y = f(x) = (6/7)x + 8.

To find the slope of the line, we use the formula:

m = (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) = (0, 8) and (x₂, y₂) = (7, 14).

Substituting into the formula:

m = (14 - 8) / (7 - 0)

m = 6 / 7

Therefore, the equation of the line is given by: f(x) = (6/7)x + b.

To find the value of b, we use the fact that f(0) = 8.

Substituting into the equation, we get: 8 = (6/7)(0) + b.

Simplifying, we get: b = 8.

Therefore, the equation of the linear function is: y = f(x) = (6/7)x + 8.

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Answer:

-8.875

Step-by-step explanation:

8 7/8 > -71/8 > -8.875

Answer:

I think it is 2/12

Yes,  there is evidence at a 5% level of significance to support the claim that the average lifespan for fluorescent lights is not 1600 hours.

Null hypothesis: is defined as the average lifespan for fluorescent lights is 1600 hours.

Alternative hypothesis : is defined as  average lifespan for fluorescent lights is not 1600 hours.

Sample size (n) = 100

Sample mean = 1580 hours

Sample standard deviation (s) = 100 hour

t = (Sample mean - μ) / (s / √n)

μ =  hypothesized population mean

s=  sample standard deviation

t = (1580 - 1600) / (100 / √100)

t = -20 / (100 / 10)

t = -20 / 10

t = -2

The significance level of 0.05 will be divided by 2 to get an alpha level of 0.025.

We make use of a  t-distribution table to look up the critical t-value in the with degrees of freedom equal to n-1 = 99.

The critical t-value is  1.984 for a significance level of 0.025 and degrees of freedom = 99.

In conclusion,  we have evidence to reject the null hypothesis because the absolute value of the test statistic is greater than the critical t-value.

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Answer:-4

Step-by-step explanation:

a) If Kristin has traveled 4 meters along the path of the Ferris wheel then the angle has swept out 0.5 radians.

b) If Kristin has traveled 45 meters along the path of the Ferris wheel then the angle has swept out 5.625 radians.

c) The formula that expresses the number of radians θ the angle has swept out in terms of the number of meters is θ = s / r.

a. To determine the angle in radians, we can use the arc length formula for a circle. The formula is given by θ = s / r, where θ is the angle in radians, s is the arc length, and r is the radius of the circle.

In this case, Kristin has traveled 4 meters along the path of the Ferris wheel, and the radius is 8 meters.

Thus, the angle swept out is

θ = 4 / 8 = 0.5 radians.

b. Following the same approach, if Kristin has traveled 45 meters along the path of the Ferris wheel, the angle swept out is

θ = 45 / 8 ≈ 5.625 radians.

c. The formula that expresses the number of radians θ the angle has swept out in terms of the number of meters Kristin has traveled since the ride started is given by

θ = s / r,

where θ is the angle in radians, s is the arc length traveled by Kristin, and r is the radius of the Ferris wheel.

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Answer:

x = 18

Step-by-step explanation:

∠ GFH and ∠ EFH form a right angle GFE , then

2x + 3x = 90 ← equation for the angle

5x = 90 ( divide both sides by 5 )

x = 18

the solution to the equation on the interval [0, 2π) is x = 3π/4.

To solve the equation, we want to find the values of x that satisfy the equation within the given interval.

First, we isolate the cosine term by subtracting 1 from both sides:

√2 cos(x) = -1

Next, we divide both sides by √2:

cos(x) = -1/√2

To find the solutions, we need to determine the angles whose cosine value is equal to -1/√2. We can use the unit circle or reference angles to determine these angles.

In the interval [0, 2π), the angle that satisfies cos(x) = -1/√2 is x = 3π/4.

Therefore, the solution to the equation on the interval [0, 2π) is x = 3π/4.

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Step-by-step explanation:

✧ [tex] \underline{ \underline{ \large{ \tt{G \: I \: V \: E \: N \: \:E \: Q \: U \: A \: T \: I \: O \: N}}}} : [/tex]

❀ [tex] \underline{ \underline{ \large{ \tt{ \: T \: O \: \: F\: I\: N \: D}}} }: [/tex]

☄ [tex] \underline{ \underline{ \large{ \tt{S \: O \: L\: U \: T \: I\: O \: N}}}} : [/tex]

♨ [tex] \large{ \sf{5 = 2x - 3}}[/tex]

~Swap the sides of the equation :

⇾ [tex] \large{ \sf{2x - 3 = 5}}[/tex]

~We want to remove the 3 first. Since the original equation is -3 , we are going to use the opposite operation and add 3 to the both sides :

⇾ [tex] \large{ \sf{2x - 3 + 3 = 5 + 3}}[/tex]

⇾ [tex] \large{ \sf{2x \: \cancel{ - 3} \: \cancel{ + 3}}} = 8[/tex]

⇾ [tex] \large{ \sf{2x = 8}}[/tex]

~Now , We need to think about how to remove the coefficient 2. Since the opposite of multiplication is division , we are going to divide both sides of the equation by 2 :

⇾ [tex] \large{ \sf{ \frac{2x}{2} = \frac{8}{2}}} [/tex]

⇾ [tex] \boxed{ \large{ \sf{x = 4}}}[/tex]

☯ [tex] \underline{ \underline{ \large{ \tt{C \: H \:E \: C \: K}}}}: [/tex]

☪ [tex] \large{ \tt{L \: H \: S : \: 5 }}[/tex]

[tex] \large{ \tt{R \: H \: S \ \: : \: 2x - 3 = 2 \times 4 - 3 = 8 - 3 = \underline{ \tt{5}}}}[/tex] [ Plug the value of x ]

☥ Since this is a true statement , our answer ( x = 4 ) is correct. Yay! We got our answer :)

♕ [tex] \large{ \boxed{ \underline{ \large{ \tt{Our \: Final \: Answer : \boxed{ \underline{ \bold{ \text{x = 5}}}}}}}}}[/tex]

[tex] \underline{ \underline{ \text{H \: O\: P \: E \: \: I \: \: H \: E \: L \: P \: E \: D}}}[/tex] !! ♡

[tex] \underline{ \underline{ \text{H \: A \: V \: E \: A \: W \: O \: N \: D \: E \: R \: F \: U \: L \: D \: A\: Y \: / \: N\: I \: G\: H \: T}}}[/tex] !! ツ

☃ [tex] \underline{ \underline{ \tt{C \:A \: R \: R \: Y \: \: O \:N \: \: L \: E \: A \: R\: N \: I \: N \: G}}} [/tex] !!✎

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

The probability that a plant produces between 15 and 19 strawberries is given as follows:

47.5%.

The two parameters that are needed to calculate a probability are listed as follows:

Then the probability is then calculated as the division of the number of desired outcomes by the number of total outcomes.

The desired areas for this problem are given as follows:

Hence the probability is given as follows:

34 + 13.5 = 47.5%.

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Answer:

D

Step-by-step explanation:

Just graph the equation and where they intercept is the solution.

Just use desmos graphing calculator if you don't know how to graph.

The typical fluctuation is based on the square root of the variance, which is equal to 5.

The typical fluctuation is based on the square root of the variance, which is equal to 3.7.

The typical fluctuation is based on the square root of the variance, which is equal to 3.7.

The Poisson distribution does not account for the finite probability of zero events occurring, and it can not handle problems where the expected number of events is very large, as it assumes an infinite number of successes, which is not the case in real life.

1) Binomial distribution

Binomial distribution is the probability distribution of obtaining exactly r successes in n independent trials with two possible outcomes of a given event.

The best value for the expected number of heads when a coin is flipped 100 times is 50.0, with the uncertainty being 5.0.

The typical fluctuation is based on the square root of the variance, which is equal to 100 x 0.5 x (1-0.5) = 25, which gives the fluctuation to be 5 (the square root of 25).

The Poisson distribution is an excellent approximation for binomial distributions, especially when n is large and p is small.

2) Binomial distribution

The best value for the expected number of times getting a '6' when a die is rolled 100 times is 16.7, with an uncertainty of 4.1.

The typical fluctuation is based on the square root of the variance, which is equal to 100 x (1/6) x (5/6) = 13.9, which gives the fluctuation to be 3.7 (the square root of 13.9)..

3) Binomial distribution

The expected number of times not getting a '6' when a die is rolled 100 times is 83.3, with an uncertainty of 4.1.

The typical fluctuation is based on the square root of the variance, which is equal to 100 x (5/6) x (1/6) = 13.9, which gives the fluctuation to be 3.7 (the square root of 13.9).

Poisson distribution

The Poisson distribution is a good approximation for the binomial distribution because n is large and p is small. Furthermore, the Poisson distribution can be used to predict the probability of a specific number of events occurring in a specific amount of time, which makes it ideal for modeling the number of radioactive decays or the number of phone calls to a call center.

However, the Poisson distribution does not account for the finite probability of zero events occurring, and it can not handle problems where the expected number of events is very large, as it assumes an infinite number of successes, which is not the case in real life.

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It should be noted that the probability of obtaining a sample mean of 39.1 hours or less is quite low (0.035), it can be considered unusually short.

The mean of the sampling distribution of the sample mean, μ, is equal to the population mean, which is μ = 40 hours.

The standard deviation of the sampling distribution is σ(μ) = 5 / √100

= 5 / 10

= 0.5 hours.

Plugging in the values, we get (40.6 - 40) / 0.5

= 0.6 / 0.5

= 1.2.

Looking up the z-score of 1.2 in the standard normal distribution table (or using a calculator), we find that the probability is approximately 0.884.

Now, let's calculate P(≤39.1). Similarly, we calculate the z-score as (x - μ) / σ(μ), where x = 39.1 hours. Plugging in the values, we get (39.1 - 40) / 0.5

= -0.9 / 0.5

= -1.8.

Using the z-score table or a calculator, we find that the probability is approximately 0.035.

This probability represents the area under the curve to the left of -1.8, which is a left-tailed probability.

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Answer: D

Step-by-step explanation:

She uses a sample size of n=200, and 50%  of all customers would actually buy coffee.

The change that would result in the highest power for her test is D. increase the significance level to α = 0.01 and use a sample size of n = 300.

The significance level simply means the probability of rejecting the null hypothesis when it is true.

It should be noted that the power of the test depends on 4 factors which are the sample size, standard deviation, effect size, and significance level.

In the given scenario, the larger sample size will increase the power of the test and a higher significance level will result in a higher power.

Therefore, the test is done with the largest sample size and highest significance level of 0.10

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The body's position at time t is given by the equation s(t) = [tex]4.9t^2 + 15t + 20[/tex].

To find the body's position at time t,

we need to integrate the velocity function with respect to time and apply the initial condition.

Given:

v = 9.8t + 15

s(0) = 20

First, integrate the velocity function with respect to time to obtain the position function:

∫v dt = ∫(9.8t + 15) dt

s(t) = [tex]4.9t^2 + 15t + C[/tex]

Next, we apply the initial condition s(0) = 20 to determine the value of the constant C:

s(0) =[tex]4.9(0)^2 + 15(0) + C[/tex]

20 = C

Now, we have the complete position function:

s(t) =[tex]4.9t^2 + 15t + 20[/tex]

In conclusion, To find the position of the body at time t,

we integrated the velocity function with respect to time,

applied the initial condition to determine the constant,

and obtained the position function s(t) = [tex]4.9t^2 + 15t + 20[/tex].

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Answer:

Step-by-step explanation:

As I figured out, any number that is not 0, meaning any number with a value is a Significant Digit. For example, in 3003 there's only 2 significant digits. The easiest way to figure these things out is adding the digits.

I hope this helps :D

Answer:

12

Step-by-step explanation:

List out the factors of each

36: 1,2,3,4,6,9,12,18,36

60: 1,2,3,4,5,6,10,12,15,20,30,60

the highest number they both have in common is 12

Answer:

Thats so hard oh my gosh!

Step-by-step explanation:

Answer:4 degrees

Step-by-step explanation:

Answer:

5 feet

Step-by-step explanation:

Plot direction fields and trajectories. Analyze eigenvalues to determine stability and type of critical point.

For system (a):

The direction field and trajectories should be plotted based on the given matrix:

[3 5] [x]

[3 -2] * [y]

To determine the type and stability of the origin as a critical point, we can analyze the eigenvalues of the matrix. The eigenvalues are found by solving the characteristic equation:

det(A - λI) = 0,

where A is the given matrix and λ is the eigenvalue.

For system (b):

The direction field and trajectories should be plotted based on the given matrix:

[1 -5] [x]

[4 1] * [y]

To determine the type and stability of the origin as a critical point, we can again analyze the eigenvalues of the matrix.

For system (c):

The direction field and trajectories should be plotted based on the given matrix:

[-6 3] [x]

[ -4 -2] * [y]

To determine the type and stability of the origin as a critical point, we once again analyze the eigenvalues of the matrix.

Analyzing the eigenvalues will allow us to determine if the critical point is a stable node, unstable node, saddle point, or any other type of critical point.

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The volume of a cone with diameter 18 cm and height 15 cm is b. V = 1272.3 cm^(3).

To calculate the volume of a cone, we use the formula:

V = (1/3) * π * r^2 * h

where V is the volume, π is the mathematical constant approximately equal to 3.14159, r is the radius of the cone's base, and h is the height of the cone.

Given that the diameter of the cone is 18 cm, we can calculate the radius by dividing the diameter by 2:

r = 18 cm / 2 = 9 cm

Substituting the values into the volume formula:

V = (1/3) * π * 9^2 * 15

Calculating:

V ≈ 1272.3 cm^3

Therefore, the volume of the cone is approximately 1272.3 cm^3.

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Answer:

$1.25 is NOT 12.5% dollars. It is 125% of a dollar.

Step-by-step explanation:

We have 1 and 1/4 dollars. 1 and 1/4 as a percentage is 125%

decimal = 0.26

percent = 26%

Answer:

Step-by-step explanation:

X-intercept: y=0:

6x +2×0 = 12

6x = 12

 x = 2          

Y-intercept: x=0:

6×0 + 2y = 12

2y = 12

 y = 6      

Answer:

sine=opposite/hypotenuse

sin52.2=x/150

sin0.790=x/150

x=118.5