3. Given a normal distribution of test scores from that same statistics class where the mean is 80 and the standard deviation is 7.5, determine BY HAND what percent of the scores were 78 or less. Also, what percent of scores were 85 or better?

Answer:

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

Step-by-step explanation:

12x² - 5x - 2

Since the first term has a coefficient, you need to multiply -2 with 12 to get -24.

Two factors that add up to -5 and have a product of -24 are -8 and 3.

12x² - 8x + 3x - 2

Rearrange the expression to find the GCF.

12x² + 3x - 8x - 2

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

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

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

In the Vasicek term structure model, the covariance between ra and rt is given by cov(ra, rt) = 10²e-(s+t) (e²s 1). From this, we can deduce that the variance of r is var(r) = 10²(1-e-2¹).

In the Vasicek term structure model, the short interest rate, r₁, follows the stochastic differential equation:

dr₁ = a(b - r₁)dt + σdW

where a and b are constants, σ is the volatility parameter, and dW is a standard Brownian motion.

To find the covariance between rₐ and rₜ, we use the covariance formula for the stochastic differentials equation:

cov(dr₁, drₜ) = cov(a(b - r₁)dt + σdW, a(b - rₜ)dt + σdW)

Since the covariance between the Brownian motion terms is zero, we only need to consider the covariance between the drift terms:

cov(a(b - r₁)dt, a(b - rₜ)dt) = a²(b - r₁)(b - rₜ)dt²

Integrating this expression over the time interval [0, s+t], we obtain:

cov(ra, rt) = a²(b - ra)(b - rt)∫[0,s+t] dt = a²(b - ra)(b - rt)(s + t)

Given cov(ra, rt) = 10²e-(s+t) (e²s - 1), we can equate the expressions and solve for a²(b - ra)(b - rt):

10²e-(s+t) (e²s - 1) = a²(b - ra)(b - rt)(s + t)

Simplifying the equation, we have:

(b - ra)(b - rt) = 10²e-(s+t) (e²s - 1)/(a²(s + t))

From this equation, we can see that the covariance depends on the values of b, ra, rt, s, t, and a.

To deduce the variance of r, we set t = s in the above equation:

(b - ra)(b - ra) = 10²e-2s (e²s - 1)/(a²(2s))

Simplifying further, we obtain:

var(r) = (b - ra)² = 10²(1 - e-2s)/a²

Hence, the variance of r is given by var(r) = 10²(1 - e-2s)/a².

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To calculate the increase in net worth from the savings, we need to find 4.5% of the total income earned.

Total income earned = $65,000

To determine the increase in net worth from savings, we calculate 4.5% of the total income. Multiplying $65,000 by 4.5% gives us $2,925.

Savings = 4.5% of $65,000

[tex]=0.045*$65,000\\=$2,925[/tex]

This represents the amount saved by the investor over the course of one year. Therefore, the investor's net worth would have increased by $2,925. This amount reflects the portion of income saved and not spent, contributing to the overall growth of the investor's financial position.

Therefore, the investor would have increased her net worth by $2,925 in one year.

The correct answer is A. $2,925.

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Answer : The value of the missing term is (1+0.2147)^6≈ 150.

Explanation :

A population grows according to an exponential growth model, with an initial population of 3,120 and a population of 3,790 after 6 years.

The formula where P is the population and n is the number of years is given by the expression:

P = 3120*(1+r)^n  where r is the growth rate and n is the number of years.                                                                                     For the given problem, the initial population, P₀ is given as 3,120 and the population after 6 years is given as 3,790.               So, the population increased by 3,790 - 3,120 = 670 people in 6 years.                                                                                                     Using this data, we can calculate the growth rate, r using the following formula:                                                                                          r = (P - P₀)/P₀n=6P = P₀*(1+r)^n Where P₀ = 3,120 and P = 3,790,r = (P - P₀)/P₀ = (3,790 - 3,120)/3,120 = 670/3,120 ≈ 0.2147 P = 3,120*(1+0.2147)^6 ≈ 150 * 3,120

Therefore, the value of the missing term is (1+0.2147)^6 ≈ 150.

Answer: (1+0.2147)^6.

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Answer:

x = 0, -2

Step-by-step explanation:

Answer:

64 = 0.72 (x)

Step-by-step explanation:

Answer: 64 = 0.72 (x)

Step-by-step explanation:

Answer:

35%

Step-by-step explanation:

1. Multiply 78.75 by 100

78.75* 100 = 7875

2. Divide this by 225

7875/225 = 35

3. Make this number a precent 35%

Answer:

79.7°

Step-by-step explanation:

We resolve the speed of the plane into horizontal and vertical components respectively as 300cos75° and 300sin75° respectively. Since the wind blows due west at a speed of 25 miles per hour, its direction is horizontal and is given by 25cos180° = -25 mph.  We now add both horizontal components to get the resultant horizontal component of the airplane's speed.

So 300cos75° mph + (-25 mph) = 77.646 - 25 = 52.646 mph.

The vertical component of its speed is 300sin75° since that's the only horizontal motion of the airplane. So the resultant vertical component of the airplane's speed is 300sin75° = 289.778 mph

The direction of the plane, Ф = tan⁻¹(vertical component of speed/horizontal component of speed)

Ф = tan⁻¹(289.778 mph/52.646 mph)

Ф = tan⁻¹(5.5043)

Ф = 79.7°

Answer:

area = 8167.14 units ²

Step-by-step explanation:

area = πr²

r = 102/2 = 51

area = (3.14)(51²) = 8167.14 units ²

Answer:

$7.35

Step-by-step explanation:

We have 200 shirts

Cost $2.80 each

plus a 5% charge for shipping.

Selling price

150% markup

Recall when we use percentages, we need to express them as decimals.

Michelle's cost for each shirt was

2.80 (1.05) = 2.94

The markup is

2.94 (1.50) = 4.41

The markup is added to the cost to get the final selling price.

2.94 + 4.41 = $7.35

Michelle will sell each shirt for $7.35

The equation of a vertical asymptote to the graph of y = sec(6x - π) is x = π/6. Hence, option a is correct.

The function y = sec(6x - π) has vertical asymptotes at the values of x where the denominator of sec(6x - π) becomes zero. The reciprocal of sec(θ) is cos(θ). Because the cosine function has the values π/2, 3π/2, 5π/2, we will insert such an input that we get 0 in denominator.

6x - π = π/2

Solving for x,

6x = π/2 + π

6x = 3π/2

x = (3π/2) / 6

x = π/6

Therefore, the equation of a vertical asymptote to the graph of y = sec(6x - π) is x = π/6.

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Answer:

LCM of 45 and 60: 180

Step-by-step explanation:

Answer:

19.545

Step-by-step explanation:

Answer:

c = 33.5

Step-by-step explanation:

[tex]30^{2} + 15^{2} = c^{2}[/tex]

[tex]900 + 225 = c^{2}[/tex]

[tex]1125 = c^{2}[/tex]

(find square root of both sides to get c alone)

[tex]c = 33.541[/tex]

The given code contains multiple errors, including syntax errors and incorrect variable assignments. Consequently, it would not produce the intended output.

The intended code is meant to solve a system of equations. However, it contains errors that hinder its functionality. These errors include syntax mistakes and incorrect variable assignments. Let's break down the code to understand the issues and determine the intended output.

In the first part of the code, the matrix A is incorrectly defined. The commas are placed before the plus sign, resulting in a syntax error. Additionally, the second element in the matrix should be 2x^2, but it is not written correctly. The code also uses the *= operator, which is not a valid mathematical operation.

Moving on to the second equation, the matrix b is defined correctly. However, the code uses colons instead of semicolons to separate the elements.

Next, the line "*1-*3 = -1" suggests some arithmetic operation, but it is not written correctly and lacks clarity.

Finally, the code attempts to solve the system of equations by assigning X to the result of A divided by b using the "//" operator, which is not a valid operation for matrix division in MATLAB.

Due to these errors, the code would generate error messages and fail to produce the intended output.

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Answer: hi

Step-by-step explanation:

look at hers

Answer:

secT=

adjacent

hypotenuse

​

=

12

37

​

Step-by-step explanation:

Answer:

Option D

A right angle

Step-by-step explanation:

in circle geometry, we have several theorems that govern angles formed by chords drawn in circles.

One of the theorems states that the angle subtended on the circumference of a circle by a chord which is drawn across the center of the circle (which is the diameter) equals 90 degrees. This means that it is a right-angle.

Analytically, we can also sketch out the problem and see that we can divide the shape formed by points BAC into an isosceles triangle. (The two radii forming the sides while the diameter forms the base).  We can also run a bisector of the isosceles triangle through point A to meet the diameter. We can see that it forms two 45 by 45 degree right-angled triangles. Thus proving that angle BAC is indeed a right angle.

Answer:

A cube

Step-by-step explanation:

If you fold it, you'll see

Answer:  210 mm²

Step-by-step explanation:

A = 1/2(long base + short base) x height

A = 1/2(18 + 10)(15)

A = 1/2(28)(15)

A = 210 mm²

the compositions are:

f∘f: 4n + 3

g∘g: 9n - 4

f∘g: 6n - 1

g∘f: 6n + 2

To find the compositions f∘f, g∘g, f∘g, and g∘f, we substitute the function expressions into the compositions:

1. f∘f:

(f∘f)(n) = f(f(n))

= f(2n+1)

= 2(2n+1) + 1

= 4n + 2 + 1

= 4n + 3

So, (f∘f)(n) = 4n + 3.

2. g∘g:

(g∘g)(n) = g(g(n))

= g(3n-1)

= 3(3n-1) - 1

= 9n - 3 - 1

= 9n - 4

So, (g∘g)(n) = 9n - 4.

3. f∘g:

(f∘g)(n) = f(g(n))

= f(3n-1)

= 2(3n-1) + 1

= 6n - 2 + 1

= 6n - 1

So, (f∘g)(n) = 6n - 1.

4. g∘f:

(g∘f)(n) = g(f(n))

= g(2n+1)

= 3(2n+1) - 1

= 6n + 3 - 1

= 6n + 2

So, (g∘f)(n) = 6n + 2.

Therefore, the compositions are:

- f∘f: 4n + 3

- g∘g: 9n - 4

- f∘g: 6n - 1

- g∘f: 6n + 2

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The book value per share at the end of the fiscal year will be approximately $15.35.

To calculate the book value per share, we need to divide the equity at the end of the fiscal year by the number of shares outstanding. Let's break down the calculation:

The number of shares outstanding: The company has a constant 306,200 shares during the fiscal year.

Equity at the beginning of the year: The balance sheet shows an equity of $4,699,902 at the beginning of the year.

Net income: The income statement indicates a net income of $399,786.

Dividends paid: The company pays out $297,789 in dividends.

To find the equity at the end of the fiscal year, we need to add the net income and subtract the dividends paid from the equity at the beginning of the year:

Equity at the end of the fiscal year = Equity at the beginning of the year + Net income - Dividends paid

= $4,699,902 + $399,786 - $297,789

= $4,801,899

Finally, to calculate the book value per share, we divide the equity at the end of the fiscal year by the number of shares outstanding:

Book value per share = Equity at the end of the fiscal year / Number of shares outstanding

= $4,801,899 / 306,200

≈ $15.65 (rounded to two decimal places)

Therefore, the book value per share at the end of the fiscal year will be approximately $15.35.

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Answer:

its B

Step-by-step explanation: Cause I have big brain. >:)

The following Python code demonstrates how to perform cubic spline interpolation using the scipy library

import numpy as np

from scipy.interpolate import CubicSpline

# Define the data points

x = np.array([20, 21, ...])  # X coordinates of the data points

y = np.array([y0, 31, ...])  # Y coordinates of the data points

# Create the cubic spline interpolation

cs = CubicSpline(x, y)

# Generate interpolated values

x_interpolated = np.linspace(x[0], x[-1], num=100)  # Adjust 'num' for desired number of interpolated points

y_interpolated = cs(x_interpolated)

# Print interpolated values

for i in range(len(x_interpolated)):

   print(f"({x_interpolated[i]:.2f}, {y_interpolated[i]:.2f})")

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Answer:

ok

Step-by-step explanation:

Answer:

Step-by-step explanation:

Solution

The sample must be selected at random.

The optimum solution for the maximization problem is Z = 0 at the point (0, 0). The graph of the feasible region consists of the line y = x and the shaded region above the line y = x - 1.

To compute the optimum solution and draw the graph for the maximization problem:

Maximize Z = x + y

Subject to the constraints:

x - y ≤ 1

-x + y = 0

x, y ≥ 0

First, let's plot the feasible region by graphing the constraints on a coordinate plane.

For the constraint x - y ≤ 1, we can rewrite it as y ≥ x - 1. This represents a boundary line with a slope of 1 and a y-intercept of -1. Shade the region above this line to satisfy the constraint.

For the constraint -x + y = 0, rewrite it as y = x. This represents a line passing through the origin with a slope of 1. Plot this line.

Next, plot the x and y axes and shade the feasible region that satisfies both constraints.

To compute the optimum solution, we need to evaluate the objective function Z = x + y at the corner points (vertices) of the feasible region.

The corner points can be identified by the intersection of the lines and the feasible region boundaries. In this case, there is only one corner point, which is the intersection of the lines y = x and y = x - 1. Solving these equations simultaneously gives x = 0 and y = 0.

Thus, the optimum solution occurs at the corner point (0, 0), where Z = 0 + 0 = 0.

Therefore, the optimum solution is Z = 0 at the point (0, 0).

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Answer: 1.3

Step-by-step explanation:

The radius of the circle that python forms is 1.3 meters.

Circle is a two dimensional figure which consist of set of all the points which are at equal distance from a point which is fixed called the center of the circle.

Given that,

Length of python = 2.6π meters

The length of the python forms the circumference of the circle after curling.

Circumference of a circle = 2π r, where r is the radius.

2π r = 2.6π

2r = 2.6

r = 2.6 / 2

r = 1.3

Hence 1.3 meters is the radius of the circle.

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Answer:

22500 units

Step-by-step explanation:

Ending inventory =. 3000

Beginning inventory = 2500

Good sold = 22000

Beginning inventory + budgeted purchases - goods sold = ending inventory

2500 + x - 22000 = 3000

2500 + x = 3000 + 22000

2500 + x = 25000

x =25000 - 2500

x = 22500 units

Budgeted purchases of product for the year.

Answer:

X = 9

Step-by-step explanation: