Answer:
[tex]y=0.11x+1[/tex]
Step-by-step explanation:
y = 0.11x + 1
(y is the monthly cost for x text messages)
:]
Calculate (8.42 x 109) − (2.35 x 108).
A. 8.185 x 108
B. 8.185 x 109
C. 6.07 x 101
D. 6.07 x 109
Answer:
it could be D but D gives us 661.63 C gives us 613.07 B gives us 892.165 and A gives us 883.98 so your closes answer is D
Step-by-step explanation:
8.42x109=917.78-253.8=663.98
A cliff diver plunges from a height of 100 ft above the water surface. The distance the diver falls in seconds is given by the function d(t)=16t^2.a.) after how many seconds will the diver hit the water?b.) with what velocity does the diver hit the water?
(a) The diver hit the water after 2.5 seconds
(b) The diver hit the water with a velocity of 80 ft/s
How to find the diver's velocity?
Since the cliff diver plunges from a height of 100 ft above the water surface and the distance the diver falls in seconds is given by the function d(t) = 16t². We can say d(t) = 100ft. So we have:
d(t) = 16t² = 100
t² = 100/16
t² = √(100/16)
t = 10/4
t = 2.5 seconds
The derivative of the distance will give us the velocity. That is:
v(t) = d'(t) = 32t
Substitute t =2.5 into v(t):
v(2.5) = 32(2.5)
v(2.5) = 80 ft/s
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A young family is looking to buy a house and decides they need at least a 3/4-acre lot so there’s room for the kids and their dog Moose to play. Their agent plans to show them a house with a 30,000-sq-ft lot. Will she be wasting her time?
Answer: We can calculate the size of the lot in acres and then compare it to the minimum size of 3/4 of an acre that the family is looking for.
1 acre = 43,560 square feet
So, a 30,000 sq-ft lot is equivalent to:
30,000 sq-ft / 43,560 sq-ft/acre = 0.6864 acres
Since 0.6864 acres is less than 3/4 of an acre, the family's agent will be wasting her time by showing them the house with a 30,000 sq-ft lot. The lot is not big enough for the family's needs.
Step-by-step explanation:
Question 5.4° A school with 20 professors forms 10 committees, each containing 6 profes- sors, such that every professor is on exactly 3 committees. Prove that it is possible to select a distinct representative from each committee.
Since there are 20 professors and each professor is on exactly 3 committees, there must be a total of 60 committee positions.
Let's assume that it is not possible to select a distinct representative from each committee. This means that there must be some committee that does not have a distinct representative.
Let's consider the professors on this committee. Since each professor is on exactly 3 committees, each of the professors on this committee must also be on 2 other committees.
Let's consider the 2 other committees for each of the professors on this committee. Since there are 6 professors on the committee, there are a total of 12 other committees to consider.
Each of these 12 committees must have a representative chosen from the remaining 14 professors, since we have assumed that it is not possible to select a distinct representative from the original 10 committees.
However, since there are only 14 professors remaining, and each professor can only be on 3 committees, it is not possible to choose a representative from all 12 of these committees without choosing at least one professor to be on 4 committees. This is a contradiction, since we have assumed that each professor is on exactly 3 committees.
Therefore, our assumption that it is not possible to select a distinct representative from each committee must be false, and it is indeed possible to do so.
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An entry-level civil engineer earns an average bi-weekly net pay of $2,250.65. The engineer has created a monthly budget using the following percentages for expenses: Percent Housing 25% Food/Household 20% Savings 10% Transportation 5% Debt 15% Entertainment 5% Medical/Personal Care 5% Giving 5% Clothing 2% Miscellaneous 8% Which balance sheet correctly represents the engineer's income, expenses, and balance?
The engineer's balance sheet would show a monthly income of $9,002.60 ($4,501.30 x 2), total expenses of $4,001.36, and a balance of $499.94.
What is a balance sheet?Balance sheet is a financial statement that contains details of a company's assets or liabilities at a specific point in time.
First we can use the given information to create the following balance sheet for the civil engineer:
INCOME:
Bi-weekly net pay: $2,250.65 x 2 = $4,501.30 (this assumes two pay periods per month)
EXPENSES:
Housing: 25% of $4,501.30 = $1,125.33Food/Household: 20% of $4,501.30 = $900.26Savings: 10% of $4,501.30 = $450.13Transportation: 5% of $4,501.30 = $225.07Debt: 15% of $4,501.30 = $675.20Entertainment: 5% of $4,501.30 = $225.07Medical/Personal Care: 5% of $4,501.30 = $225.07Giving: 5% of $4,501.30 = $225.07Clothing: 2% of $4,501.30 = $90.03Miscellaneous: 8% of $4,501.30 = $360.10TOTAL EXPENSES: $4,001.36
BALANCE: $4,501.30 - $4,001.36 = $499.94
Therefore, the engineer's balance sheet would show a monthly income of $9,002.60 ($4,501.30 x 2), total expenses of $4,001.36, and a balance of $499.94.
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indicate whether the following statements regarding the variance and standard deviation are true or false. a) the population variance and sd use n in the denominator instead of n-1. false b) the sample variance and sd inherit the strengths and weaknesses of the sample mean. _______
c) if we did not square the distances in the numerator, we would end up with 0. ______
d) the sample variance and sd are robust to outliers and/or extreme points.________
a) the population variance and sd use n in the denominator instead of n-1. - false
b) the sample variance and sd inherit the strengths and weaknesses of the sample mean. - True
c) if we did not square the distances in the numerator, we would end up with 0. -false
d) the sample variance and sd are robust to outliers and/or extreme points.-false
a) False. The population variance and standard deviation use N in the denominator, where N is the size of the population. The sample variance and standard deviation use n-1 in the denominator, where n is the size of the sample.
b) True. The sample variance and standard deviation inherit the strengths and weaknesses of the sample mean, since they are based on the deviations of the sample values from the sample mean.
c) False. If we did not square the distances in the numerator, we would end up with the mean deviation, which is a valid measure of dispersion but not the variance.
d) False. The sample variance and standard deviation are not robust to outliers and/or extreme points, as they are sensitive to the values of the data points and can be significantly influenced by the presence of outliers.
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help please see photo
The solution of the inequality using the coordinate pair is 5.
What is Linear Inequality?Linear inequalities are those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.
Given linear inequality is,
y ≤ -2x + 3
We have a coordinate pair (-1, 5).
So substitute x = -1 and y = 5 in the given inequality.
5 ≤ (-2 × -1) + 3
5 ≤ 2 + 3
5 ≤ 5
Hence the missing numbers are found.
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In each of the following systems, find conditions on a, b, and c for which the system has solutions: (a)3x + 2y - z=a x + y + 2z = b 5x+4y + 32=c (b) -3x + 2y + 4z = a
- x - 2y + 3z = b
-X -6y + 232 = 0 (C)4x - 2y + 3z = a 2x - 3y – 2z = b 4x - 2y + 32=c
The conditions on a, b, and c for which the Linear equations has solutions are det(A) ≠ 0, Rank[A|B] = Rank(A).
(a) 3x + 2y - z = a
x + y + 2z = b
5x + 4y + 32 = c
For this system to have solutions, the augmented matrix [A|B] must have a unique solution. This is equivalent to determinant of the coefficient matrix A is non-zero, and the system is consistent (the row rank of the augmented matrix is equal to the row rank of the coefficient matrix). Therefore, the conditions on a, b, and c for this system to have solutions are:
det(A) ≠ 0
Rank[A|B] = Rank(A)
(b) -3x + 2y + 4z = a
-x - 2y + 3z = b
-x - 6y + 232 = 0
For this system to have solutions, the conditions are the same as in (a):
det(A) ≠ 0
Rank[A|B] = Rank(A)
(c) 4x - 2y + 3z = a
2x - 3y – 2z = b
4x - 2y + 32 = c
For this system to have solutions, the conditions are the same as in (a) and (b):
det(A) ≠ 0
Rank[A|B] = Rank(A)
For each system of linear equations to have solutions, the number of equations must be equal to the number of variables, and the determinant of the coefficient matrix must be non-zero.
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PLEASE HELP WILL GIVE 100 PTS AND BRAINLYEST
A sequence of transformations is applied to a polygon. [ The following statements represent a sequence of transformations where the resulting polygon is similar to the original polygon but have a smaller area than the original polygon is that: a dilation about the origin by a scale factor of 2 3 followed by a rotation of 90° counterclockwise about the origin and a translation 5 units left.
For 3y-2x=-18 determine the value of y when x = 0, and the value of x when y = 0
contracts for two construction jobs are randomly assigned to one or more of three firms, a, b, and c. the joint distribution of y1, the number of contracts awarded to firm a, and y2, the number of contracts awarded to firm b, is given by the entries in the following table. y1 y2 0 1 2 0 1 9 2 9 1 9 1 2 9 2 9 0 2 1 9 0 0 find cov(y1, y2). (round your answer to three decimal places.) cov(y1, y2)
The value of covariance cov(y1, y2) is -0.222
y1
y2 0 1 2 Total
0 1/9 2/9 1/9 4/9
1 2/9 2/9 0 4/9
2 1/9 0 0 1/9
Total 4/9 4/9 1/9 1
marginal distribution of y2:
y2 P(y2) y2P(y2) y2^2P(y2)
0 4/9 0.0000 0.0000
1 4/9 0.4444 0.4444
2 1/9 0.2222 0.4444
total 1 0.66667 0.88889
E(y2) = 0.6667
E(y2^2) = 0.8889
Var(y2) = E(y2^2)-(E(y2))^2=0.4444
marginal distribution of y1
y1 P(y1) y1P(y1) y1^2P(y1)
0 4/9 0.0000 0.0000
1 4/9 0.4444 0.4444
2 1/9 0.2222 0.4444
total 1.00 0.6667 0.8889
E(y1) = 0.6667
E(y1^2) = 0.8889
Var(y1)= σy = E(y1^2)-(E(y1))^2 = 0.4444
E(XY) =∑xyP(x,y)=0.2222
Cov(y1,y2) = -0.222
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Answer question on the picture attached
The average rate of change over the interval (-2,0) is -2.
What is the average rate of change?The average rate of change describes how quickly one quantity changes in comparison to another. It indicates how much the function changed per unit during the specified interval.
Given that the interval is (-2,0). The coordinate of the point from the interval -2,0 is ( -2 , 4 ).
The average rate of change will be calculated as:-
Rate of change = ΔY / ΔX
Rate of change = ( 4 - 0 ) ( -2 - 0 )
Rate of change = -2
Therefore, the average rate of change will be -2.
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If ABCD is a parallelogram,
find the value of x.
7x + 2
9x-28
What is the equation of the line that passes through the point (-8, 6) and has a slope
of -1/4?
Answer:
= 4y + x - 16 = 0.
Step-by-step explanation:
Point are (-8,6)
where
x1 = -8 and y1 = 6
the equation o the line is given by the formula
[tex] = \frac{y - y1}{x - x1} = m[/tex]
where (m) is the gradient
the gradient (m) = -1/4
therefore the equation of the line
[tex] \frac{y - y1}{x - x1} = m \\ = \frac{y - 6}{x - ( - 8)} = \frac{ - 1}{4} \\ = \frac{y - 6}{x + 8} = \frac{ - 1}{4} \\ = 4(y - 6) = - 1(x + 8) \\ = 4y - 24 = - x - 8 \\ = 4y = - x - 8 + 24 \\ = 4y = - x + 16 \\ = 4y + x - 16 = 0.[/tex]
therefore the equation of the line is = 4y + x - 16 = 0.
note// y and x where not given any value.
I need help on confused I don’t get it once so ever
The value of x is given as follows:
x = 34.
The angle measures are given as follows:
<B = 102º. <C = 78º.How to obtain the angle measures?In a parallelogram, consecutive angles are supplementary, meaning that the sum of their measures is of 180º.
Angles A and B are consecutive, hence the value of x is obtained as follows:
2x + 10 + 3x = 180
5x = 170
x = 34.
Then the angle measures are given as follows:
<B = 3(34) = 102º. <C = 78º. (consecutive with B, 180 - 102 = 78).More can be learned about angle measures at https://brainly.com/question/2046046
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1.28 Ф Vector operations and units. (Chapter 2) Circle the vector operations below (scalar multiplication, addition, dot-product, etc.) that are defined for a position vector a (with units of m) and a velocity vector b (with units of P. a+b 1.29 Using vector identities to simplify expressions (refer to Homework 1.13). One reason to treat vectors as basis-independent quantities is to simplify vector expressions with- out resolving the vectors into orthogonal x, y, z or i k components. Simplify the following Vector expression (3u-29) x (u + v) vector expressions using various properties of dot-products and cross-products Simplified vector expression Express your results in terms of dot-products - and cross- products x of the arbitrary vectors υ. v. w (ie.. υ. v, w are not orthogonal). 2 1.30 Vector concepts: Solving a vector equation. (Section 2.10.5) Consider the vector equation to the right and the process that follows that solves for θ (a, is a unit vector and v,, θ, R are scalars). This process is a valid way to solve for θ. True/False Explain: vr ax 0
The vector operations defined for a position vector a and a velocity vector b are vector addition and scalar multiplication.
Simplified Vector expression is (3u - 29) x u + (3u - 29) x v.
False, as the process that follows, solving for θ by dividing by the magnitude of v and taking the inverse sine, is only valid if v x a = 0.
1.28: The vector operations defined for a position vector a and a velocity vector b are vector addition and scalar multiplication.
1.29: Using the properties of the cross-product, the simplified expression is:
3u x u + 3u x v - 29 x u - 29 x v
Using the fact that the cross-product is distributive over vector addition, we can write this as:
3u x u + 3u x v - 29 x u - 29 x v = (3u - 29) x u + (3u - 29) x v
So the simplified vector expression is (3u - 29) x u + (3u - 29) x v.
1.30: False.
The given equation,
v x (a x R) = 0,
can be simplified to a scalar triple product,
(v x a) · R = 0.
Since the scalar triple product is equal to the determinant of a matrix formed by the three vectors,
this equation implies that either v x a = 0 or R = 0.
Therefore, the process that follows, solving for θ by dividing by the magnitude of v and taking the inverse sine, is only valid if v x a = 0.
The vector operations defined for a position vector a and a velocity vector b are vector addition and scalar multiplication.
Simplified Vector expression is (3u - 29) x u + (3u - 29) x v.
False as the process that follows, solving for θ by dividing by the magnitude of v and taking the inverse sine, is only valid if v x a = 0.
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Maximize Z = 7X1 + 5X2
Subject to X1 + 2X2 ≤ 6
4X1 + 3X2 ≤ 12
X1, X2 ≥ 0
The solution is [tex]x_1[/tex] = 3 and [tex]x_2[/tex]= 0.
What is Simplex Method?Simplex method is an approach to solving linear programming models by hand using slack variables, tableaus, and pivot variables as a means to finding the optimal solution of an optimization problem.
Given:
We transfer the row with the resolving element from the previous table into the current table, elementwise dividing its values into the resolving element:
[tex]P_2[/tex] = [tex]P_2[/tex] / [tex]x_{2,1[/tex] = 12 / 4 = 3;
[tex]x_{2,1[/tex] = [tex]x_{2,1[/tex] / [tex]x_{2,1[/tex] = 4 / 4 = 1;
[tex]x_{2,2[/tex] = [tex]x_{2,2[/tex] / [tex]x_{2,1[/tex] = 3 / 4 = 0.75;
[tex]x_{2,3[/tex] = [tex]x_{2,3[/tex] / [tex]x_{2,1[/tex] = 0 / 4 = 0;
[tex]x_{2,4[/tex] = [tex]x_{2,4[/tex] / [tex]x_{2,1[/tex] = 1 / 4 = 0.25;
The remaining empty cells, except for the row of estimates and the column Q, are calculated using the rectangle method, relative to the resolving element:
[tex]P_1[/tex] = ([tex]P_1[/tex] . [tex]x_{2,1[/tex]) - ([tex]x_{1,1[/tex] . [tex]P_2[/tex]) / [tex]x_{2,1[/tex]= ((6 x 4) - (1 x 12)) / 4 = 3
[tex]x_{1,1[/tex]= (([tex]x_{1,1[/tex]. [tex]x_{2,1[/tex]) - ([tex]x_{1,1[/tex] . [tex]x_{2,1[/tex])) / [tex]x_{2,1[/tex]= ((1 x 4) - (1 x 4)) / 4 = 0
[tex]x_{1,3[/tex]= (([tex]x_{1, 3[/tex]. [tex]x_{2,1[/tex]) - ([tex]x_{1,1[/tex] . [tex]x_{2,3[/tex])) / [tex]x_{2,1[/tex]= ((1 x 4) - (1 x 0)) / 4 = 1
[tex]x_{1,4[/tex] = (([tex]x_{1, 4[/tex]. [tex]x_{2,1[/tex]) - ([tex]x_{1,1[/tex]. [tex]x_{2,4[/tex])) / [tex]x_{2,1[/tex]= ((0 x 4) - (1 x 1)) / 4 = -0.25
Objective function value
We calculate the value of the objective function by elementwise multiplying the column [tex]C_b[/tex] by the column P, adding the results of the products.
Max P = (C[tex]b_1[/tex] x [tex]P_{01[/tex]) + (C[tex]b_{11[/tex] x [tex]P_2[/tex])= (0 x 3) + (7 x 3) = 21;
Evaluated Control Variables
We calculate the estimates for each controlled variable, by element-wise multiplying the value from the variable column, by the value from the Cb column, summing up the results of the products, and subtracting the coefficient of the objective function from their sum, with this variable.
Max [tex]x_1[/tex]= ((C[tex]b_1[/tex] . [tex]x_{1,1[/tex]) + (C[tex]b_2[/tex] . [tex]x_{2,1[/tex]) ) - k[tex]x_1[/tex] = ((0 x 0) + (7 x 1) ) - 7 = 0
Max [tex]x_2[/tex]= ((C[tex]b_1[/tex] . [tex]x_{1,2[/tex]) + (C[tex]b_2[/tex] . [tex]x_{2,2[/tex]) ) - k[tex]x_2[/tex] = ((0 x 1.25) + (7 x 0.75) ) - 5 = 0.25
Max [tex]x_3[/tex]= ((C[tex]b_1[/tex] . [tex]x_{1,3[/tex]) + (C[tex]b_2[/tex] . [tex]x_{2,3[/tex]) ) - k[tex]x_3[/tex] = ((0 x 1) + (7 x 0) ) - 0 = 0
Max [tex]x_4[/tex]= ((C[tex]b_1[/tex] . [tex]x_{1,4[/tex]) + (C[tex]b_2[/tex] . [tex]x_{2,4[/tex]) ) - k[tex]x_4[/tex] = ((0 x -0.25) + (7 x 0.25) ) - 0 = 1.75
Since there are no negative values among the estimates of the controlled variables, the current table has an optimal solution.
The value of the objective function:
F = 21
The variables that are present in the basis are equal to the corresponding cells of the column P, all other variables are equal to zero:
[tex]x_1[/tex] = 3;
[tex]x_2[/tex]= 0;
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Subtract the polynomials (35 + 83) − (72 − 63). Show all work
Answer:
35 + 83) − (72 − 63) = 109
Step-by-step explanation:
To subtract the polynomials (35 + 83) − (72 − 63), we'll simplify each term in the polynomials first and then subtract the corresponding terms:
(35 + 83) = 118
(72 - 63) = 9
Now we can subtract the corresponding terms:
118 - 9 = 109
So the result of (35 + 83) − (72 − 63) is 109.
Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ
Answer:
Okay first do what is in the parenthesis:
35 + 83 = 118
72 - 63 = 9
Now subtract:
118 - 9 = 109
The answer is: 109
Step-by-step explanation:
Hope it helps!
For each situation, determine why the situation cannot be modelled after a binomial distribution. (2 pts each)a. A bowl of candy contains 23 Pluto Bars, 21 Jolly Farmers, 14 Husky's Kisses, 21 Finnish Fishes, and 18 HairHeads. Kristina decides to pull out 77 pieces of candy, without putting any back, and count only the number of Jolly Farmers that she grabs.b. A bowl of candy contains 23 Pluto Bars, 21 Jolly Farmers, 14 Husky's Kisses, 21 Finnish Fishes, and 18 HairHeads. Ian decides to pull out 70 pieces of candy, with replacement, and record each type of candy the he pulls.c. A bowl of candy contains 23 Pluto Bars, 21 Jolly Farmers, 14 Husky's Kisses, 21 Finnish Fishes, and 18 HairHeads. Marissa decides to pull out pieces of candy, with replacement, until a Husky's Kiss is pulled.
The question is geometric distribution. We are concerned with just the first success. That means there is no fixed number of trials
How to solve this
Before a situation can model binomial distribution.
1) There should be a fixed number of trial2) Each trial should have two possible outcomes (success or failure)3) The probability of success is the same for each trial.4) The trials are independent.For question a.
The probability of success is not the same for each trial. Since we are not putting any back. So it cannot be modeled as binomial distribution
For question b.
This has many outcomes not just success and failure.
Lan needs to record Pluto bar, jolly farm, husky kisses, finish fish, and hair heads.
For question c.
The question is geometric distribution. We are concerned with just the first success. That means there is no fixed number of trials
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Hunter is taking a multiple choice test with a total of 100 points available. Each question is worth exactly 5 points. What would be Hunter's test score (out of 100) if he got 5 questions wrong? What would be his score if he got � x questions wrong?
For answering 5 questions wrong Hunter's score is 75 and for for answering x question wrong his score will be f(x)=100-5*x.
What is a function?A function is defined as the relationship between input and output, where each input has exactly one output. The inputs are the elements in the domain and the outputs are elements in the co-domain.
Hunter is taking a multiple choice test with a total of 100 points available.
Each question is worth exactly 5 points,
From that the number of questions in the test is ,[tex]\frac{100}{5}=20[/tex]questions
Hunter's test score (out of 100) if he got 5 questions wrong,
20-5=15 questions correct.
Each question carries 5 marks, then 15*5= 75 marks.
Hunter score will be 75 marks.
And again each question carries 5 marks, If hunter answers x questions wrong his score will be f(x)=100-5*x.
It is a linear equation.
Hence, for answering 5 questions wrong Hunter's score is 75 and for for answering x question wrong his score will be f(x)=100-5*x.
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Steven sprinted 14 1/3 laps and then took a break by jogging 4 laps. How much farther did Steven sprint than jog?
Write the ratio as a fraction: $42 for 81 juice boxes. Simplify your answer.
Answer: The ratio $42/81$ can be simplified by dividing both the numerator and denominator by the greatest common factor of 42 and 81, which is 9.
$42/81 = (42 \div 9) / (81 \div 9) = 4/9$
So, the ratio $42/81$ can be expressed as the simplified fraction $\frac{4}{9}$.
Step-by-step explanation:
The surface of a table to be built will be in the shape shown below. The distance from the center of the shape to the center of each side is 10.4 inches and the length of each side is 12 inches.
A hexagon labeled ABCDEF is shown will all 6 sides equal in length. ED is labeled as 12 inches. A perpendicular is drawn from the center of the hexagon to the side ED. This perpendicular is labeled as 10.4 inches.
Part A: Describe how you can decompose this shape into triangles. (2 points)
Part B: What would be the area of each triangle? Show every step of your work. (5 points)
Part C: Using your answers above, determine the area of the table's surface. Show every step of your work.
A) We can draw a line perpendicular to side ED from the center of the hexagon, which will bisect side ED and create two additional triangles.
B) Area of each triangle = 31.16 square inches (rounded to two decimal places)
C) Total surface area = 375.87 square inches (rounded to two decimal places)
What is Surface Area ?Any geometric shape with three dimensions can have its surface area determined. The area or region that an object's surface occupies is known as its surface area.
Now in the given question,
Part A: To decompose this shape into triangles, we can draw lines connecting the center of the hexagon to each of its vertices, creating six triangles. We can also draw a line perpendicular to side ED from the center of the hexagon, which will bisect side ED and create two additional triangles.
Part B: Each of the six triangles created by connecting the center of the hexagon to its vertices is an equilateral triangle, because all sides of the hexagon are equal in length. The area of an equilateral triangle can be calculated using the formula:
Area = (√3 / 4) x side²
where side is the length of one side of the equilateral triangle. In this case, the length of each side of the equilateral triangle is also 12 inches, so we have:
Area = (√3 / 4) x 12²
Area = (√3 / 4) x 144
Area = 36√3 square inches
Each of the two triangles created by drawing a perpendicular from the center of the hexagon to side ED is a right triangle, because one of its angles is 90 degrees. We can use the Pythagorean theorem to calculate the length of the other two sides of the right triangle. We know that one side has length 10.4 inches and the hypotenuse (which is also a side of the hexagon) has length 12 inches. Let x be the length of the other side of the right triangle. Then we have:
x² + 10.4² = 12²
x²+ 108.16 = 144
x² = 35.84
x = √35.84
x = 5.99 inches (rounded to two decimal places)
The area of each right triangle can be calculated using the formula:
Area = (1/2) x base x height
where the base is 5.99 inches (the length of the side opposite the 90 degree angle) and the height is 10.4 inches (the length of the side adjacent to the 90 degree angle). We have:
Area = (1/2) x 5.99 x 10.4
Area = 31.16 square inches (rounded to two decimal places)
Part C: To determine the area of the table's surface, we need to add up the areas of all eight triangles. There are six equilateral triangles, each with an area of 36sqrt(3) square inches, and two right triangles, each with an area of 31.16 square inches. Therefore, the total area of the table's surface is:
Total area = 6 x 36√3 + 2 x 31.16
Total area = 216√3 + 62.32
Total area = 375.87 square inches (rounded to two decimal places)
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What is the value of X and Y?
The value of x and y is 31° and 101°. Value is the measure of what something is worth, either financially or in terms of importance.
What is meant by value?The value describes the value of each digit in relation to its position in the number. The place value and face value of the digit are multiplied to arrive at the answer. Value equals Location Value minus Face Value.Value is concerned with how much something is worth, whether in monetary terms or in terms of significance. It can mean "identify how much something is worth" like a reward valued at $200 or it can indicate "hold something in high esteem" like "I value our friendship."The things that someone values are known as their values. In other terms, values are what a person or a group of people see as "important." Examples include valor, integrity, freedom, and creativity, among others.[tex]$\angle \mathrm{PRT}+\angle \mathrm{RTP}+\angle \mathrm{TPR}=180^{\circ} \text { (angle sum property of triangle) } \\[/tex]
[tex]& \Rightarrow \mathrm{x}+\left(180^{\circ}-\angle \mathrm{RTQ}\right)+60^{\circ}=180^{\circ} \text { (linear pair) } \\[/tex]
[tex]& \Rightarrow \mathrm{x}+\left(180^{\circ}-97^{\circ}\right)+60^{\circ}=180^{\circ} \\[/tex]
We get,
[tex]& \Rightarrow \mathrm{x}=31^{\circ} \\[/tex]
[tex]& \text { Now } \angle \mathrm{PRT}+\angle \mathrm{TRQ}+\angle \mathrm{QRS}=180^{\circ} \text { (angle of straight line) } \\[/tex]
[tex]& \Rightarrow \mathrm{x}+48^{\circ}+\mathrm{y}=180^{\circ} \\[/tex]
Simplifying,
[tex]& \Rightarrow 31^{\circ}+48^{\circ}+\mathrm{y}=180^{\circ} \\[/tex]
Then we get,
[tex]& \Rightarrow \mathrm{y}=101^{\circ}[/tex]
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Assume there are 11 homes in the Quail Creek area and 8 of them have a security system. Three homes are selected at random:
What is the probability all three of the selected homes have a security system? (Round your answer to 4 decimal places.)
What is the probability none of the three selected homes has a security system? (Round your answer to 4 decimal places.)
What is the probability at least one of the selected homes has a security system? (Round your answer to 4 decimal places.)
Are the events dependent or independent?
Dependent
Independent
Joint
The probability of all three of the selected homes having a security system is 0.3277, the probability of none of the three selected homes having a security system is 0.0414, and the probability of at least one of the selected homes having a security system is 0.9709. The events are dependent.
The probability of all three of the selected homes having a security system is 0.3277, which can be calculated using the formula P(A and B and C) = P(A) x P(B) x P(C). In this case, P(A) is the probability of the first home having a security system, which is 8/11 (since 8 out of 11 homes have a security system). P(B) is the probability of the second home having a security system, which is 7/10 (since 7 out of 10 remaining homes have a security system). P(C) is the probability of the third home having a security system, which is 6/9 (since 6 out of 9 remaining homes have a security system). Therefore, P(A and B and C) = (8/11) x (7/10) x (6/9) = 0.3277.
The probability of none of the three selected homes having a security system is 0.0414, which can be calculated using the formula P(A and B and C) = P(A') x P(B') x P(C'). In this case, P(A') is the probability of the first home not having a security system, which is 3/11 (since 3 out of 11 homes do not have a security system). P(B') is the probability of the second home not having a security system, which is 3/10 (since 3 out of 10 remaining homes do not have a security system). P(C') is the probability of the third home not having a security system, which is 3/9 (since 3 out of 9 remaining homes do not have a security system). Therefore, P(A and B and C) = [tex](3/11) x (3/10) x (3/9) = 0.0414[/tex].
The probability of at least one of the selected homes having a security system is 0.9709, which can be calculated using the formula P(A or B or C) = 1 - P(A' and B' and C'). In this case, P(A' and B' and C') is the probability of none of the three selected homes having a security system, which is 0.0414 (as calculated above). Therefore, P(A or B or C) = 1 - 0.0414 = 0.9709.
The events are dependent because each selection is affected by the previous selections. For example, the probability of the second home having a security system is affected by whether or not the first home had a security system. If the first home had a security system, then there are 7 out of 10 remaining homes with a security system; if the first home did not have a security system, then there are 8 out of 10 remaining homes with a security system.
The probability of all three of the selected homes having a security system is 0.3277, the probability of none of the three selected homes having a security system is 0.0414, and the probability of at least one of the selected homes having a security system is 0.9709. The events are dependent.
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I am having a very hard time figuring this out can someone help me with #5 please
I need help with this question 632/572(127+276)
Hi! The answer would be 445.272727273
Glad I can help :)
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Consider a triangle ABC like the one below. Suppose that C-96°, a-33, and b=39. (The figure is not drawn to scale.) Solve the triangle.
Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth.
If there is more than one solution, use the button labeled "or".
DSD
X
16
No
solution
5
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The value of C is 108°
How to solve for thisGiven [tex]a=33,\ \ b=26, \ \ \angle B=31^0 .[/tex]
We have to find [tex]\angle C, \ \angle A \ and\ c[/tex]
We can use the cosine formula to find these:
[tex]cosB=\frac{a^2+c^2-b^2}{2ac}\\cos31^o=\frac{33^2+c^2-26^2}{2(33)(c)}\\0.8572=\frac{413+c^2}{66c}\\56.5752c=413+c^2\\i.e. c^2-56.5752c+413=0\\\Rightarrow c=47.9647, \ 8.6104\\So, \mathbf{c=48 \ or \ c=9}\\Now if c=48:\\cosA=\frac{b^2+c^2-a^2}{2bc}\\=\frac{26^2+48^2-33^2}{2(26)(48)}\\[/tex]
[tex]=\frac{1891}{2496}\\=0.75761\\\therefore A=cos^{-1}(0.75761)=40.746^0\approx 41^0\\i.e. \mathbf{\angle A= 41^0}\\cosC=\frac{a^2+b^2-c^2}{2ab}\\=\frac{33^2+26^2-48^2}{2(33)(26)}\\=\frac{-539}{1716}\\=-0.3141\\\therefore C=cos^{-1}(-0.3141)=108.306^0\approx 108^0[/tex]
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if we want to measure the magnitude of the orbital angular momentum and the projection of the angular momentum in
To measure the magnitude of the orbital angular momentum L and the projection of the angular momentum along a particular axis (say, the z-axis), we need to use the mathematical formalism of quantum mechanics.
In quantum mechanics, the orbital angular momentum L of a particle is an operator that acts on the wave function describing the particle's motion. Similarly, the z-component of the angular momentum Lz is also an operator.
The magnitude of the orbital angular momentum L can be calculated from the components of the angular momentum operator using the expression:
L^2 = L₁^2 + L₂^2 + L₃^2
where L₁, L₂, and L₃ are the x, y, and z components of the angular momentum operator, respectively. To measure the magnitude of the orbital angular momentum, we would need to measure the values of L₁ L₂, and L₃ and use them to calculate L^2.
The projection of the angular momentum along a particular axis (say, the z-axis) is given by the operator L₃. To measure the z-component of the angular momentum, we would need to measure the value of L₃ for a particular state of the system.
In practice, these measurements are often carried out using experiments involving the interaction of particles with magnetic fields. The behavior of the particles in the magnetic field allows us to infer information about the angular momentum of the particles.
The measurement of the magnitude and projection of angular momentum is an important part of many areas of physics, including quantum mechanics and solid-state physics.
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The distance traveled in the time interval 0 ≤ t ≤ 6, given the velocity function v(t) = t^2 - 6t - 16, can be determined by calculating the definite integral of the absolute value of the velocity function over the given time interval. The result is 128 units of distance.
To find the distance traveled in the given time interval, we need to integrate the absolute value of the velocity function v(t) = t^2 - 6t - 16 over the interval 0 ≤ t ≤ 6. The reason for taking the absolute value is that distance is a scalar quantity and does not depend on the direction of motion.
Taking the integral of the absolute value of the velocity function, we have:
∫|v(t)| dt = ∫|t^2 - 6t - 16| dt
To evaluate this integral, we need to split it into intervals where the velocity function is positive and negative. The absolute value function essentially removes the negative sign from the expression inside the absolute value brackets.
Next, we find the points where the velocity function changes sign by setting v(t) = 0:
t^2 - 6t - 16 = 0
Solving this quadratic equation, we find t = -2 and t = 8 as the points where the velocity changes sign.
Now, we evaluate the integral over the intervals [0, 2] and [2, 6] separately, considering the absolute value of the velocity function within each interval.
∫|v(t)| dt = ∫(t^2 - 6t - 16) dt over [0, 2] + ∫(-(t^2 - 6t - 16)) dt over [2, 6]
Evaluating the definite integrals, we obtain:
(128/3) + (128/3) = 256/3
Therefore, the distance traveled in the time interval 0 ≤ t ≤ 6 is 256/3 units of distance, which is approximately 85.33 units of distance.
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Ayden is buying bagels for a family gathering. Each bagel costs $2.00. Answer the
questions below regarding the relationship between the total cost and the number of
bagels purchased.