The longer piece of wood has dimensions of 1 inch by 1 inch by 8 inches. The
Short piece of wood has dimensions of 1 inch by 1 inch by 4 inches. How many
square inches of paint would be needed to cover all sides of this object?
Answers
Related Questions
Michelle ordered 200 T-shirts to sell at the school carnival. She paid $2.80 per shirt, plus 5% of the total
order for shipping. When she sells each T-shirt at the carnival, she adds a 150% markup to the total price
she paid for the shirt (including the cost of shipping).
For what price does she sell each T-shirt?
Answers
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
5x + 1 = 6x - 8 x= como puedo resolverla
Answers
Answer:
X = 9
Step-by-step explanation:
PLEASE HELP AND SHOW AN EXPLANATION ITS DUE IN 30 MINUTES!! Donna wants to create a stained glass window composed of one quarter circle, two semicircles, and one parallelogram. Which measurement is closest to the amount of stained glass in square inches Donna will
need to create the window?
Answers
A fcompany has a constant 306200 shares during the fiscal year. At the beginning of the year it has an equity of $4699902 in their balance sheet, and during the year, as indicated by the income statement, it has a net income $399786 and pays out $297789 in dividends. What will be its book value per share at the end of the fiscal year? Answer to two places.
Answers
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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please do it in 30 minutes please urgently... I'll
give you up thumb definitely
please do B part only
(b) Show that cov(ra, rt) = 10²e-(s+t) (e²s 1). Deduce that var(r) = 10²(1-e-2¹).
9. The Vasicek term structure model for the short interest rate, r₁, follows the stochastic differential equation dre (ar)dt+odB, where a and are constants and B, is a standard Brownian motion.
Answers
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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What is the area?
____ Square millimeters
Answers
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
Find the metal solution to the linear system of differential equations 937 (b) (2 points) Give a physical description of what the solution curves to this linear system look like. What happens to the solution curves as to 12?
Answers
The solution to the system of equations is[tex]X(t) = c_1 * e^{6t} * [37 \ \ -3] + c_2 * e^{-3t} * [-37\ \ 12][/tex]. The solution curves exhibit a combination of exponential growth and decay, and as t approaches infinity, they converge towards the eigenvector associated with the negative eigenvalue.
To find the general solution to the linear system of differential equations:
[tex]X' = \left[\begin{array}{ccc}9&37\\-1&-3\end{array}\right] X[/tex]
We need to find the eigenvalues and eigenvectors of the coefficient matrix [[9 37] [-1 -3]].
Let A be the coefficient matrix.
The characteristic equation is given by:
det(A - λI) = 0, where λ is the eigenvalue and I is the identity matrix.
The coefficient matrix A - λI is:
[tex]X' = \left[\begin{array}{ccc}9-\lambda&37\\-1&-3-\lambda\end{array}\right] X[/tex]
Setting the determinant equal to zero:
[tex]det (\left[\begin{array}{ccc}9-\lambda&37\\-1&-3-\lambda\end{array}\right] )[/tex]
Expanding the determinant, we get:
[tex](9-\lambda)(-3-\lambda) - (-1)(37) = 0[/tex]
Simplifying the equation, we have:
[tex](\lambda-6)(\lambda+3) = 0[/tex]
Solving for λ, we find two eigenvalues:
[tex]\lambda_1 = 6\\\lambda_2 = -3[/tex]
Next, we find the eigenvectors corresponding to each eigenvalue.
For [tex]\lambda_1 = 6[/tex]:
[tex](A - \lambda_1I)v_1 = 0[/tex]
Substituting the values, we have:
[tex]\left[\begin{array}{ccc}3&37\\-1&-9\end{array}\right] v_1 = 0[/tex]
Solving the system of equations, we find v1 = [37 -3].
For [tex]\lambda_2 = -3[/tex]:
[tex](A - \lambda_2I)v_2 = 0[/tex]
Substituting the values, we have:
[tex]\left[\begin{array}{ccc}12&37\\-1&0\end{array}\right] v_2 = 0[/tex]
Solving the system of equations, we find [tex]v_2[/tex] = [-37 12].
Therefore, the general solution to the linear system of differential equations is:
[tex]X(t) = c_1 * e^{6t} * [37 \ \ -3] + c_2 * e^{-3t} * [-37\ \ 12][/tex]
where [tex]c_1\ and\ c_2[/tex] are constants.
b) The solution curves to this linear system represent trajectories in the state space. The behavior of the solution curves depends on the eigenvalues.
Since we have [tex]\lambda_1 = 6[/tex] and [tex]\lambda_2 = -3[/tex], the system has one positive eigenvalue and one negative eigenvalue. This indicates that the solution curves will exhibit a combination of exponential growth and decay.
As t approaches infinity, the exponential term with [tex]e^{-3t}[/tex] will dominate, and the solution curves will converge towards the eigenvector associated with the negative eigenvalue, [-37 12].
On the other hand, as t approaches negative infinity, the exponential term with [tex]e^{6t}[/tex] will dominate, and the solution curves will diverge away from the origin in the direction of the eigenvector associated with the positive eigenvalue, [37 -3].
In summary, the solution curves will either converge or diverge depending on the initial conditions, and as t approaches infinity, they will converge towards the eigenvector associated with the negative eigenvalue.
Complete Question:
a) Find the metal solution to the linear system of differential equations
[tex]X' = \left[\begin{array}{ccc}9&37\\-1&-3\end{array}\right] X[/tex]
b) Give a physical description of what the solution curves to this linear system look like. What happens to the solution curves as to 12?
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Factoring Perfect Square Trinomials
a^2- 2ab + 4b
Answers
Step-by-step explanation:
[tex]i \: \: think \: \: it \: \: is \: \\ \\ {a}^{2} - 2ab + {b}^{2} \\ \\ that \: is \: for \: \: {(a - b)}^{2} [/tex]
I hope that is useful for you :)
Write the repeating rational number 0.828282… as a fraction.
Answers
Answer:
Step-by-step explanation:0.828282 = 0.828282/1 = 8.28282/10 = 82.8282/100 = 828.282/1000 = 8282.82/10000 = 82828.2/100000 = 828282/1000000
And finally we have:
0.828282 as a fraction equals 828282/1000000
The following code is intended to solve the system of equations but contains errors. What are the errors and so determine the intended output? 3x, +2x2 - *= 10 >> A - 1 3 2 -1; 1 3.2; 1 -1]; --*+ 3x2 + 2xy = 5 >> b = [ 10; 5; -1]: *1-*3 = -1 >> X = A//b Errors Intended MATLAB Output Question 7. The word 'SMILE' can be coded as a column vector by using the relevant numbers for its place in the alphabet (E = 5). The word can then be encrypted using matrix multiplication on the left by A. 3 3 0 30 -30 --2 0 0 0 1 0 0 -3 0 0 0 33 lo-1 2 0 1 (1) What is the column vector of the encrypted word 'SMILE'? 120 -21 (1) What word was encrypted as -63 ? (Don't do it by hand, life's too short.)
Answers
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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Find the optimum solution and draw the graph
Maximise Z= x + y, subject to x - y S-1, -x + y = 0, x,
Answers
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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GIVING BRAINIEST!!
Which equation represents: "72% of what number is 64"
64 = 0.72 (x)
x = 7.2 (64)
64 = 7.2 (x)
x = .72 (64)
Answers
Answer:
64 = 0.72 (x)
Step-by-step explanation:
Answer: 64 = 0.72 (x)
Step-by-step explanation:
Let f and g be functions from the positive integers to the positive integers defined by the equation
f(n)= 2n+1 g(n)=3n-1
f∘f
g∘g
f∘g
g∘f
Answers
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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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. Complete the formula, where P is the population and n is the number of years: P=3,120*(_)
Answers
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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30^2 + 15^2 = c^2
Use pythagorean theorem
Answers
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]
Find the distance between the points (4,10) and (4, -7)
Answers
Answer:
17
Step-by-step explanation:
Hello There!
Once again we are going to use the distance formula to find the answer
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
This time we need to find the distance between the points (4,10) and (4,-7)
*we plug in the values into the formula)
[tex]d=\sqrt{(4-4)^2+(-7-10)^2} \\4-4=0\\-7-10=17\\d=\sqrt{0^2+(-17)^2} \\0^2=0\\-17^2=289\\\sqrt{289} =17[/tex]
so we can conclude that the distance between the points (4,10) and (4,-7) is 17 units
nicole wants to conduct a survey of the opinions of students at her middle school. which survey sample would give her the most accurate results?
Answers
Answer:
Step-by-step explanation:
Solution
The sample must be selected at random.
Use a unit circle and 30°-60°-90° triangles to find the degree measures of the angle.
angles whose sine is
[tex] \frac{ \sqrt{3} }{2} [/tex]
Options:
30° + n × 360° and 330° + n × 360°
60° + n × 360° and 120° + n × 360°
240° + n × 360° and 300° + n × 360°
150° + n × 360° and 210° + n × 360°
Answers
Answer:
its B
Step-by-step explanation: Cause I have big brain. >:)
Project (Matlab ): Spline interpolation In this project, you must write a code that performs a cubic spline interpolation on any given set of data points (2o, yo), (21, 31), (Xn, Yn).
Answers
The following Python code demonstrates how to perform cubic spline interpolation using the scipy library
How to depict the codeimport 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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List the factor pairs of ac for the trinomial 12x^2-5x-2.
Answers
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)
An airplane is flying in a direction of 75° north of east at a constant flight speed of 300 miles per hour. The wind is blowing due west at a speed of 25 miles per hour. What is the actual direction of the airplane? Round your answer to the nearest tenth. Show your work. PLS PLS PLSPLS HELP URGANT
Answers
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°
A python curls up to touch the tip of its own tail with its nose, forming the shape of a circle. The python is
2.6
π
2.6π2, point, 6, pi meters long.
What is the radius
r
rr of the circle that the python forms?
Answers
Answer: 1.3
Step-by-step explanation:
The radius of the circle that python forms is 1.3 meters.
What is Circle?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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It a math study guide plz help me
Answers
the answer is 12.57
Step-by-step explanation:
The formula to find circumference is 2×pi×r. Two is the radius. So when you plug it into the formula you get 12.57.
hypotheses are always statements about which of the following? question content area bottom part 1 choose the correct answer below. sample statistics sample size estimators population parameters
Answers
Hypotheses are always statements about the d. population parameters
Hypotheses are assertions or claims concerning population characteristics stated in statistics. An attribute or value of a population, such the population mean or percentage, is referred to as a population parameter. Based on sample data, hypothese are developed to draw conclusions or inferences about these population attributes.
The hypothesis can be expressed as comparisons of population metrics or as statements of equality or inequality. They serve as a basis for statistical studies and are used to examine certain assertions or research hypotheses. Finding pertinent solutions to the scientific inquiry is the main goal of the hypothesis. It is supported by a few evidences, and experimental methods are used to test the whole statement of the hypothesis.
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Complete Question:
Hypotheses are always statements about which of the following? choose the correct answer below.
a. sample statistics
b. sample size
c. estimators
d. population parameters
The sales budget for Modesto Corp. shows that 20,000 units of Product A and 22,000 units of Product B are going to be sold for prices of $10 and $12, respectively. The desired ending inventory of Product A is 20% higher than its beginning inventory of 2,000 units. The beginning inventory of Product B is 2,500 units. The desired ending inventory of Product B is 3,000 units. Budgeted purchases of Product B for the year would be:
Multiple Choice
24,500 units.
22,500 units.
16,500 units.
26,500 units.
20,500 units.
Answers
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.
In ΔSTU, the measure of ∠U=90°, UT = 12, SU = 35, and TS = 37. What ratio represents the secant of ∠T?
Answers
Answer: hi
Step-by-step explanation:
look at hers
Answer:
secT=
adjacent
hypotenuse
=
12
37
Step-by-step explanation:
What is the area of a circle whose diameter is 102
Answers
Answer:
area = 8167.14 units ²
Step-by-step explanation:
area = πr²
r = 102/2 = 51
area = (3.14)(51²) = 8167.14 units ²
Solving forA
A=1
4πd2=1
4·π·1022≈8171.28249
Use R for this question. Use the package faraway teengamb data (data(teengamb, package="faraway") ) for this question. a. Make a plot of gamble on income using a different plotting symbol depending on the sex (Hint: refer to page 66 in the textbook for similar code).
Answers
The code creates a scatter plot of the "gamble" variable on the "income" variable, with different plotting symbols based on sex, using the "faraway" package in R.
Here's the code to make a plot of the "gamble" variable on the "income" variable using different plotting symbols based on the sex in R:
# Load the required package and data
library(faraway)
data(teengamb)
# Create a plot of a gamble on income with different symbols for each sex
plot(income ~ gamble, data = teengamb, pch = ifelse(sex == "M", 16, 17),
xlab = "Gamble", ylab = "Income", main = "Gamble on Income by Sex")
legend("topleft", legend = c("Female", "Male"), pch = c(17, 16), bty = "n")
This code will create a scatter plot where the "income" variable is plotted against the "gamble" variable. The plotting symbols used will be different depending on the "sex" variable.
Females will be represented by an open circle (pch = 17), and males will be represented by a closed circle (pch = 16). The legend will indicate the corresponding symbols for each sex.
Make sure to have the "faraway" package installed in R and load it using 'library'(faraway) before running this code.
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PLEASE HELP
A company makes two different size ice cream cones The small accounts are 3.5 inches tall and have a diameter of 3 inches The large cones are5.1 inches tall and have a diameter of 4.5 inches about how much greater to the nearest 10th of Cubic inch is the volume The larger cone than the smaller cone 
Answers
Answer:
19.545
Step-by-step explanation:
in the xy-plane, which of the following is an equation of a vertical asymptote to the graph Of y=sec(6x-pi)? (A) x=pi/6 (B) x=pi/4 (C) x=pi/3 (D)=x=pi/2 (E) x=pi
Answers
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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