A variable is normally distributed with mean 8 and standard deviation 2. a. Find the percentage of all possible values of the variable that lie between 4 and 9. b. Find the percentage of all possible values of the variable that exceed 5.
c. Find the percentage of all possible values of the variable that are less than 6

In general, the tallest and shortest plant heights can vary widely depending on the species of plant being considered.

For example, some species of trees can grow over 300 feet tall, while certain species of mosses may only grow a few millimeters in height. The specific environmental conditions, such as the availability of water, sunlight, and nutrients, can also impact the growth and height of plants. Therefore, without more specific information, it is difficult to provide a more precise answer.

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Check the picture below.

I'm not sure if this is correct but 9560 (rectangle surface area) + 900 (triangle surface area) =10460...

DON'T TRUST ME ON THIS ONE CHECK IT YOURSELF BUT IM PRAYING FOR YOU

Answer: 21120

Step-by-step explanation:

Area for the rectangluar prism

A(Rect)= LA+2B  

where LA,Lateral area = Ph   P,Perimeter of base= 30+120+30+120 = 300

                                               h, height =20

LA=300(20)=6000

B,area of base=(30)(120)=3600

A(rect)=LA+2B=6000+2(3600)

=13200

Area for triangular prism, turn on side so triangle is base(columned)

A(triangle) = LA+2B

LA= Ph         Perimeter of triangle = 17+17+30=64     h=120

LA=(64)(120)=7680

B, the base is  the triangle=1/2 bh   where b =30 h=8

B=1/2 (30)(8)

=120

A(triangle)=7680+2(120) =7920

Add the 2 areas

A(total)=13200+7920=21120

a) To calculate the probability that the sample proportion of defective cups from Supplier A is less than 10%, we need to find the probability that the sample proportion is less than 0.10. Thus, we need to find P(p < 0.10).

We can use the central limit theorem to approximate the distribution of the sample proportion as a normal distribution, with mean μ = 0.08 and standard deviation [tex]σ = \sqrt{0.08 (\frac{1-0.08)}{200} )}= 0.024[/tex]. Then, we can standardize the distribution and use a standard normal table or calculator to find the probability:

[tex]P (p < 0.10)=P(\frac{p-u}{σ} < \frac{0.10-0.08}{0.024} = P(z < 0.83)=0.7977[/tex]

Therefore, the probability that the sample proportion of defective cups from Supplier A is less than 10% is approximately 0.7977.

b) To calculate the probability that the sample proportion of defective cups from Supplier A is at least 5%, we need to find the probability that the sample proportion is greater than or equal to 0.05. Thus, we need to find P(p≥ 0.05).

Using the same approach as in part (a), we can find that                                                             P(p < 0.05)=-0.0207. Therefore, P(p ≥ 0.05) = 1 - P(p< 0.05) =0.9793.

Therefore, the probability that the sample proportion of defective cups from Supplier A is at least 5% is approximately 0.9793.

c) To calculate the probability that the sample proportion of defective cups from Supplier A is between 5% and 10%, we need to find the probability that 0.05 ≤ p < 0.10. We can use the same approach as in part (a) to find that P(p < 0.05) = 0.0207 and P(p < 0.10) = 0.7977. Therefore, P(0.05 ≤ p < 0.10) = P(p < 0.10) - P(p < 0.05) = 0.7770.

Therefore, the probability that the sample proportion of defective cups from Supplier A is between 5% and 10% is approximately 0.7770.

d) To calculate the probability that the sample proportion of defective cups from Supplier A is exactly 8%, we need to find P(p = 0.08). Since the sample proportion is a discrete random variable, we can use the binomial distribution to find the probability:

[tex]P(p=0.08)=(200 choose 16) (0.080)^{16} (1-0.08)^{184} = 0.1567[/tex]

Therefore, the probability that the sample proportion of defective cups from Supplier A is exactly 8% is approximately 0.1567.

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Applying the definition of a linear pair, the value of n is calculated as: n =  41.33.

A linear pair consist of two angles that are on a straight line and also have a sum of 180 degrees.

The missing diagram is in the attachment provided below which shows the angles in question.

Angle 1 and (3n - 6) are two angles on a straight line, therefore, they are a linear pair. This also implies that they will have a sum of 180 degrees.

Therefore, we have:

62 + 3n - 6 = 180

Solve for the value of n:

56 + 3n = 180

3n = 180 - 56

3n = 124

n = 124/3

n = 41.33

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To find a polynomial function of the lowest degree with rational coefficients and given zeros -3i and 5, we first need to remember that complex zeros always come in conjugate pairs. Since -3i is one of the zeros, its conjugate 3i is also a zero.

Now, let's find the polynomial using these zeros: (x - (-3i))(x - 3i)(x - 5). We can rewrite this as:

(x + 3i)(x - 3i)(x - 5)

Now, let's multiply the first two factors:

(x^2 - 3ix + 3ix + 9) (x - 5)

Simplifying this gives us:

(x^2 + 9)(x - 5)

Now, let's multiply this with the remaining factor:

x^3 - 5x^2 + 9x - 45

So, the polynomial function of the lowest degree with rational coefficients that has the given zeros -3i and 5 is:

f(x) = x^3 - 5x^2 + 9x - 45

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The product of the numbers is 2.788 x 10^8.

Scientific notation is a method of expressing very large numbers so that they can be easily understood. The process involves expressing the number in terms of the power of ten. For example; 1230000000000 = 1.23 x 10^12.

In the given question, the product of 8.2 x 10^2 and 3.4 x 10^5 is required.

Thus;

8.2 x 10^2 * 3.4 x 10^5 = 8.2 * 3.4 x 10^5 * x 10^2

                                     = 8.2 * 3.4 x 10^(2+5)

                                     = 27.88 x 10^7

                                     = 2.788 x 10^8

Therefore, the product of the numbers expressed in scientific notation is 2.788 x 10^8.

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please see attached...

ignore 8/52 in the top right hand corner

The equation for a line parallel to f(x) = -3x - 5 and passing through the point (2, -6) is y = -3x.

An equation for a line parallel to f(x) = -3x - 5 and passing through the point (2, -6). Here are the steps:

Step 1: Identify the slope of the given line, f(x) = -3x - 5. Since it's in the form y = mx + b, where m is the slope, we see that the slope of the given line is -3.

Step 2: Since we want a line parallel to the given line, the slope of our new line will be the same, which is -3.

Step 3: Use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through. In this case, m = -3 and the point is (2, -6), so x1 = 2 and y1 = -6.

Step 4: Plug the values into the point-slope form equation: y - (-6) = -3(x - 2)

Step 5: Simplify the equation. First, change y - (-6) to y + 6, then distribute -3: y + 6 = -3x + 6

Step 6: Write the equation in slope-intercept form (y = mx + b) by subtracting 6 from both sides: y = -3x

So, the equation for a line parallel to f(x) = -3x - 5 and passing through the point (2, -6) is y = -3x.

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The combined length of two boards is 93/100 or 0.93 of a meter based on the length of two boards.

The combined length of the two boards will be calculated by finding sum of their lengths. The formula that will form is -

Combined length = length of first board + length of second board

Keep the values in formula

Combined length = 7/10 + 23/100

Solving the sum

Total length = (7×10) + 23/100

Solving the parenthesis

Combined length = (70 + 23)/100

Performing addition

Total length = 93/100

Thus, the combined length of the shelf is 93/100 of a meter.

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The interval of t-values such that c(t) = (cos t, sin t) traces the upper half of the unit circle (in the counter-clockwise direction) is [0, pi].

To see why this is the case, recall that the unit circle is given by the equation x^2 + y^2 = 1, where (x,y) are the coordinates of a point on the circle. The upper half of the unit circle corresponds to the set of points (x,y) where y is positive or zero. We want to find the values of t for which c(t) lies on the upper half of the unit circle.

Using the definition of c(t), we have c(t) = (cos t, sin t). The y-coordinate of c(t) is sin t, so we want, sin t to be positive or zero. Since sin t is positive in the first and second quadrants of the unit circle, and zero at t = 0 and t = pi, we have that c(t) traces the upper half of the unit circle when t is in the interval [0, pi].

To see that c(t) traces the upper half of the unit circle in the counter-clockwise direction, note that as t increases from 0 to pi, c(t) moves counterclockwise around the unit circle, starting at (1,0) and ending at (-1,0). Thus, the interval [0, pi] corresponds to one-half of a full counterclockwise rotation around the unit circle, which is exactly the upper half of the circle.

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Answer: A 4 digit PIN number is selected. What is the probability that there are no repeated digits? ... There are 10 possible values for each digit of the PIN (namely: 0 ..

Step-by-step explanation:

Using the dot plot, it is found that a typical amount of chocolate chips in one of Shawn's cookies is around 4.56.

Dot plot:

The dot plot is a graph shows the number of times each measure appears in the data-set.

Researching this problem on the internet, the dot plot states that:

2 cookies have 2 chips.

2 cookies have 3 chips.

5 cookies have 4 chips.

4 cookies have 5 ships.

3 cookies have 6 ships.

2 cookies have 7 chips.

The mean is given by:

M = (2 x 2 + 2 x 3 + 5 x 4 + 4 x 5 + 3 x 6 + 2 x 7)/(2 + 2 + 5 + 4 + 3 + 2) = 4.56.

Hence, a typical amount of chocolate chips in one of Shawn's cookies is around 4.56.

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Correct Question:

The following dot plot shows the number of chocolate chips in each cookie that Shawn has. Each dot represents a different cookie.

Answer:

47 ÷ 3681 is approximately 0.0128

Answer:

The nswer is 0.0127682694919858

(a) the rejection region is n overline x > kappa.

(b) kappa = 13/20 = 0.65. Since n overline x = 11 > kappa, we reject the null hypothesis and conclude that there is evidence in favor of the alternative hypothesis that theta > 0.45.

What is hypothesis?

A hypothesis is a proposed explanation or tentative answer to a research question or phenomenon. The null hypothesis is the default position that there is no significant difference between two groups or variables, while the alternative hypothesis proposes that there is a significant difference.

(a) According to Neyman-Pearson's lemma, the likelihood ratio is the most powerful test for a simple vs. a composite hypothesis. The likelihood function for the Bernoulli distribution is:

[tex]L(\theta | x) = \theta^k (1 - \theta)^{(n-k)[/tex]

where k is the number of successes in n trials. The likelihood ratio is:

[tex]\Lambda(x) = L(\theta_A | x) / L(\theta_0 | x)[/tex]

[tex]= (\theta_A^k (1 - \theta_A)^{(n-k)}) / (\theta_0^k (1 - \theta_0)^{(n-k)})[/tex]

Taking the logarithm and simplifying, we get:

[tex]log \Lambda(x) = k log(\theta_A / \theta_0) + (n-k) log((1 - \theta_A) / (1 - \theta_0))[/tex]

To define the rejection region, we need to find the value of kappa such that [tex]P(n overline x > kappa | \theta = \theta_0)[/tex] = alpha, where overline x is the sample mean. Since n overline x sim Bin(n, theta_0), we have:

[tex]P(n overline x > kappa | \theta = \theta_0) = 1 - P(n overline x < = kappa | \theta = \theta_0)\\= 1 - F(n overline x < = kappa | \theta = \theta_0)\\= 1 - sum from i=0 to floor(kappa*n) (n choose i) (\theta_0^i) ((1-\theta_0)^(n-i))[/tex]

where F is the cumulative distribution function of the binomial distribution. We can use a numerical method or a table to find kappa such that [tex]P(n overline x > kappa | \theta = \theta_0) = \alpha.[/tex]

Therefore, the rejection region is n overline x > kappa.

(b) Using the given values, we have k = 11, n = 20, [tex]\theta_0 = 0.45[/tex], and [tex]\theta_A = 0.65[/tex]. The sample mean is overline x = k/n = 0.55. To find kappa, we need to solve:

[tex]P(n overline x > kappa | \theta = \theta_0) = alpha\\1 - F(n overline x < = kappa | \theta = \theta_0) = 0.05\\F(n overline x < = kappa | \theta = \theta_0) = 0.95[/tex]

Using a binomial table, we find that the 0.95th percentile of the binomial distribution with n = 20 and theta = 0.45 is 13. Therefore, kappa = 13/20 = 0.65. Since n overline x = 11 > kappa, we reject the null hypothesis and conclude that there is evidence in favor of the alternative hypothesis that theta > 0.45.

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The Mean Value Theorem applies over the interval (-5, 5) and (5, ∞).

To determine the interval(s) where the Mean Value Theorem (MVT) applies for the function y=√(x^2-25), we need to ensure that the function is continuous and differentiable on the given interval.

1. The function is continuous when the expression under the square root is non-negative, which means x^2-25≥0. Solving for x, we get x≥5 or x≤-5. In interval notation, the domain for continuity is (-∞,-5] U [5,∞).

2. To check for differentiability, we need to find the derivative of the function. The derivative of y=√(x^2-25) is:

y' = (1/2)(x^2-25)^(-1/2) * 2x
y' = x/√(x^2-25)

Now, we need to ensure that the derivative is defined on the given interval. Since x=5 or x=-5 makes the denominator zero, we should exclude these points. Hence, the interval for differentiability is (-∞,-5) U (5,∞).

Since the MVT requires both continuity and differentiability, the applicable interval(s) for the Mean Value Theorem are (-∞,-5) U (5,∞).

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Answer:

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

Volume of cylinder formula:

We are given values:

Substitute and calculate the volume:

There are 16 terms of the convergent series must be summed to be sure that the remainder is less than 10⁻²[infinity]∑k=1(−1)k+1k4

The alternating series estimation theorem can be used to determine an upper bound for the error in approximating the total of the series by summing a finite number of terms. As an example of an alternating sequence of the form:

∑(-1)^(n-1) b_n

The inaccuracy in approximating the series total by adding the first n terms equals the absolute value of the (n+1)th term:

|(-1)^n b_n+1|

In this case, we have:

∑k=1^∞ (-1)^(k+1) k^4

So the (n+1)th term is:

(-1)^n+1 (n+1)^4

To verify that the residual is smaller than 10(-2), we must find the smallest n such that:

|(-1)^n+1 (n+1)^4| < 10^(-2)

So let us try n = 1:

|(-1)^2 (2)^4| = 16 > 10^(-2)

So let us try n = 2:

|(-1)^3 (3)^4| = 81 > 10^(-2)

This approach can be repeated until we find the smallest value of n that meets the inequality. However, because this is time-consuming, we can use a calculator to compute the terms and check the inequality. As a result, we discover that n = 6 is the least value that works:

|(-1)^7 (7)^4| = 2401 > 10^(-2)

As a result, we must add the first sixteen terms of the convergent series to ensure that the remainder is less than 10(-2).

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From the two column proof below we have been able to show that:

WZ bisects ∠YWX

A two-column proof uses a table to present a logical argument and assigns each column to do one job, and then the two columns work in lock-step to take a reader from premise to conclusion.

The two column proof here is:

Statement 1: WY ≅ WX, zy ≅ zx

Reason 1: Given

Statement 2: ∠WYX ≅ ∠WXY, ∠3 ≅ ∠4

Reason 2: Base angles of Isosceles triangles are congruent

Statement 3: m∠WYX = m∠WXY

Reason 3: Measures of congruent angles are equal

Statement 4: m∠WYX = m∠6 + m∠3: m∠WXY = m∠5 + m∠4

Reason 4: Angle Addition Postulate

Statement 5: m∠6 + m∠3 = m∠5 + m∠4

Reason 5: Substitution

Statement 6: m∠6 + m∠3 = m∠5 + m∠3

Reason 6: Substitution

Statement 7: m∠6 = m∠5

Reason 7: Subtraction Property of equality

Statement 8: ΔWYZ ≅ ΔWXZ

Reason 8: SAS

Statement 9: ∠YWZ ≅ ∠XWZ

Reason 9: Corresponding parts of congruent triangles are congruent.

Statement 10: WZ bisects ∠YWX

Reason 10: Definition of angle bisector

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The value of the output is independent of the value of the input.

In the graph, the input is the x value (x-axis) and the output is the y value (y-axis).

Looking at the graph, you notice the y values are constant (the same) while the x values changes.

What this means is that whatever the value of the input (x value), the value of the output (y value) will remain the same. That is the value of the output is independent of the value of the input.

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Answer:

56 degrees

Step-by-step explanation:

the total sum of the angles in a triangle is 180

90+34+b=180

b=180-124

=56

Answer:

56°

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180°.

The triangle shown in the image is a right triangle so one of the angle measure is 90°.

Given, the other angle is 34°, we can find the value of missing angle with the following equation:

x + 90° + 34° = 180°

x + 124° = 180°

x = 56°

Answer:

  y = 4 is line parallel to x-axis. In that line, each point's y-co-ordinate is 4.

The required amount will be earn is $3400.

This calculation only takes into account the revenue earned from ticket sales and does not include any additional revenue streams such as merchandise sales or sponsorships.

The total earnings will depend on various factors such as ticket pricing strategy, marketing efforts, and concert attendance.

Here given concert tickets are selling for $34.00 each and it is also given a total number of 100 tickets are sold.

the total earnings will be calculated by multiplying the ticket price by the number of tickets sold.

So,total amount earn = $34×100 = $3400.

This is a problem of Multiplication.

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Correct question is " Concert tickets go on sale for $34. 00 each . Now total number of sold tickets are 100 . Count how many money will earn ."

The form of the following quadratic include the following: D. not a quadratic.

In Mathematics and Geometry, the standard or general form of a quadratic function can be modeled and represented by using the following quadratic equation;

y = ax² + bx + c

Where:

Mathematically, the vertex form of a quadratic equation is given by this formula:

f(x) = a(x - h)² + k

Where:

Additionally, the intercept form of a quadratic equation is given by this formula:

f(x) = a(x - p)(x - q)

In conclusion, we can logically deduce that the given expression is a polynomial function.

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The point that could be the location of the other end of the wall will be (0, 5).

By using one or more elements or coordinates, a reference frame can properly pinpoint location alongside other mathematical components on such space, including Euclidean space.

A point or object in a two-dimensional plane can be found by utilizing its coordinates, which appear to be sets of integers. The y and x vectors can be used to identify the position of a point on a double surface. a group of photos used to identify certain areas.

In conclusion, the point that could be the location of the other end of the wall will be (0, 5).

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A linear or exponential model would not model the relationship between the number of employees and number of customers

From the question, we have the following parameters that can be used in our computation:

number of employees 1 2 3 4 10

number of customers 8 4 13 17 39

Testing a linear model

To do this, we calculate the difference between the y values

So, we have

13 - 4 = 4 - 8

9 = -4 ---- this is false

So, the function is not a linear function

Testing an exponential model

To do this, we calculate the ratio of the y values

So, we have

13/4 = 4/8

3.25 = 1/2 ---- this is false

So, the function is not an exponential function

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The evaluation of the dot plots on the top indicates that the mean is 7.5

The table to create a different dot plot with the same mean as the dot plot on top is therefore;

Value  [tex]{}[/tex]          Frequency

4     [tex]{}[/tex]                2

6 [tex]{}[/tex]                    3

8 [tex]{}[/tex]                    3

10 [tex]{}[/tex]                  4

A dot plot is a data visualization method which consists of datapoints located above a number line, such that the number of dots at a datapoint represents the data value.

The mean of the dot plot can be found as follows;

Mean = (3 + 2 × 5 + 4 × 7 + 3 × 9 + 2 × 11)/(1 + 2 + 4 + 3  + 2) = 7.5

Therefore, the sum of the values = (3 + 2 × 5 + 4 × 7 + 3 × 9 + 2 × 11) = 90

The number of dots = (1 + 2 + 4 + 3  + 2) = 12

The required dot plot should therefore, have 12 dots

A possible combination of 12 dots that have a mean of 12 is therefore;

(2 × 4 + 3 × 6 + 3 × 8 + 4 × 10)/(2 + 3 + 3 + 4)

Therefore, one possible dot plot consists of 2 dots at 4, 3 dots at 6, 3 dots at 8, and 4 dots at 10 can be presented as follows;

[tex]{}[/tex]                                             o

[tex]{}[/tex]                         o        o        o

               o[tex]{}[/tex]       o        o        o

 [tex]{}[/tex][tex]{}[/tex]              o       o        o        o

-|----|--------|--------|--------|--------|--------|-

[tex]{}[/tex] 1    2        4        6        8       10      

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A solution to the given expression is -44 4/9.

In order to evaluate and solve this expression, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the equation to the right. Lastly, the mathematical operations of addition or subtraction would be performed from left to right.

Based on the information provided, we have the following mathematical expression:

-36 4/9 - (-10 2/9) - (18 2/9)

By opening the bracket, we have the following:

-36 4/9 + 10 2/9 - 18 2/9

By converting the mixed fraction into an improper fraction, we have the following:

-328/9 + 92/9 - 164/9

(-328 + 92 - 164)/9 = -44 4/9.

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A 10-segment trapezoidal rule is exact to find integrals of polynomials of order 3 or less. Here's a step-by-step explanation:

1. The trapezoidal rule is a numerical integration method used to approximate the integral of a function.
2. It works by dividing the area under the curve of the function into a series of trapezoids and then summing their areas.
3. The number of segments (trapezoids) determines the accuracy of the approximation. In this case, we have 10 segments.
4. The trapezoidal rule is exact for polynomials of order 1 (linear functions) because the area under the curve of a linear function can be exactly represented by trapezoids.
5. However, the trapezoidal rule can also provide exact results for higher-order polynomials in certain cases. For a 10-segment trapezoidal rule, it turns out to be exact for polynomials of order 3 or less.

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