The innovation that was made possible in part because of the Carterfone decision in 1968 is the public Internet. The correct answer is option C
The Carterfone decision was a landmark ruling by the Federal Communications Commission (FCC) that allowed for the interconnection of third-party devices to the telephone network. Prior to this decision, telephone companies had a monopoly on the equipment that could be used on their networks, and customers were not allowed to attach their own devices.
This decision paved the way for the development of the public Internet by allowing for the interconnection of third-party devices to the telephone network, which enabled the creation of new technologies, such as modems. Without the Carterfone decision, the public Internet as we know it today may not have been possible.
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India bought a bag of grapes that weighed 3 pounds, 5 ouncesShe already had a bag at home that weighed pound, 12 ounces. How many pounds/ ounces of grapes does she have altogether?
Answer:
4Pounds 1ounce
Step-by-step explanation:
First bag is 3pound 5ounces
Second bag 12ounces
Add both
3 Pounds and 17ounces
16ounces make 1Pound so 17ounces becomes 1Pound and 1ounces
Add to the 3Pounds
You have 3 Pounds + 1 Pound 1ounce
Let V be an inner product and let S={v1, v2, ..., vm} be an orthogonal set of nonzero elements of V.
a) Show that if the inner product is positive definite, the set S is linearly independent.
b) Give a counterexample of a non-zero inner product, where a non-zero set of orthogonal vectors is linearly dependent.
A.... Any subset of S must be linearly independent, so the set S is linearly independent.
a) Let V be an inner product space and let S = {v1, v2, ..., vm} be an orthogonal set of nonzero elements of V. If the inner product is positive definite, then for any non-zero vector x in V, the inner product x · x is strictly positive. Therefore, for any subset of S, the inner product of the elements in the subset must be strictly positive.
B....This is a counterexample of a non-zero inner product, where a non-zero set of orthogonal vectors is linearly dependent.
b) Consider the inner product space V with inner product (x, y) = x2y2. Let S = {v1, v2} be an orthogonal set of nonzero elements of V, where v1 = (1, 1) and v2 = (1, -1). Since (v1, v2) = 0, S is an orthogonal set. However, S is linearly dependent since v2 = -v1.
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Michael buys 3 shirts for $25 each. He will also have to pay 7% sales tax.
Find the total amount Michael will pay the cashier.
Answer:$22.84
Step-by-step explanation:
The tax is calculated by 0.075 * 21.25 = 1.59375 or $1.59. So the total bill is the cost of items purchased plus tax, which is $21.25 + $1.59 = $22.84.
Find f(−2)given f(x)=−2x3−x2+7
A. 15
B. 17
C. 19
D. -13
HELP PLEASE
Answer:
[tex]\huge\boxed{\sf f(-2)=19}[/tex]
Step-by-step explanation:
Given function:[tex]f(x)=2x^3-x^2+7[/tex]
Put x = -2
[tex]f(-2)=-2(-2)^3-(-2)^2+7\\\\f(-2)=-2(-8)-4+7\\\\f(-2)=16-4+7\\\\f(-2)= 12+7\\\\f(-2)=19\\\\\rule[225]{225}{2}[/tex]
Problem4(10%)LetA,B∈Rn×n, and suppose that eitherAorBis non-singular. IfABis diagonalizable, show thatBAis also diagonalizable.
BA is also diagonalizable
Let A and B be two n x n matrices such that either A or B is non-singular. If AB is diagonalizable, then there exists an invertible matrix P and a diagonal matrix D such that:
AB = PDP-1.
Since P is invertible, we can also write:
BA = (PDP-1)-1PDP-1 = P-1D-1PDP-1
Since D-1 is also diagonalizable, it follows that BA is also diagonalizable.
Answer:Let A, B ∈ Rn×n and suppose that either A or B is non-singular. If AB is diagonalizable, then BA is also diagonalizable. Let AB be diagonalizable, then AB = CDC−1 where C is a diagonal matrix and D is a matrix with non-zero diagonals.Let B−1 and C be invertible matrices such that BA = B−1(AB)B = B−1(CDC−1)B = (B−1CB)(B−1DB−1)Since B is invertible, the matrix B−1CB is diagonal. The matrix B−1DB−1 is also diagonal because its inverse is a diagonal matrix. Thus, BA is diagonalizable. Therefore, if AB is diagonalizable, then BA is also diagonalizable, as required.To sum up:If A, B ∈ Rn×n and either A or B is non-singular, then AB is diagonalizable, which means that BA is also diagonalizable.
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Help Please!!
A student used factor by grouping to factor the expression below. How can you tell that the student made an error when factoring? Explain the error.
Student's work: 6x² – x – 12
6x² – 9x + 8x – 12
3x(2x – 3) – 4(–2x +3)
.
Step-by-step explanation:
the point and goal is to come up with a series of multiplications of terms that is equivalent to the original sum of terms.
in doing so, we try to find the same common factors in the sub-groups we are building.
so, the error was to use "-" with the last term, as this "destroyed" the common factor.
it should have been
3x(2x - 3) + 4(2x - 3)
which gives us via the common terms
(2x - 3)(3x + 4)
that is the correct factoring.
Solve for w. -(7)/((w+1)(w-7))=4+(3)/(w-7) If there is more than one solution, separate the
The two possible solutions for w are 6 and -3/4.
To solve for w, we need to use algebraic manipulation to isolate w on one side of the equation. Here are the steps:
1. Multiply both sides of the equation by (w+1)(w-7) to clear the fractions: -(7) = 4(w+1)(w-7) + 3(w+1)
2. Distribute the 4 and 3 on the right side of the equation: -(7) = 4w^2 - 24w - 28 + 3w + 3
3. Combine like terms on the right side of the equation: -(7) = 4w^2 - 21w - 25
4. Move all terms to one side of the equation: 4w^2 - 21w - 18 = 0
5. Use the quadratic formula to solve for w: w = (-(-21) ± √((-21)^2 - 4(4)(-18)))/(2(4))
6. Simplify the equation: w = (21 ± √(441 + 288))/(8)
7. Simplify the equation further: w = (21 ± √729)/(8)
8. Solve for the two possible values of w: w = (21 + 27)/(8) or w = (21 - 27)/(8)
9. Simplify the two possible values of w: w = 48/8 or w = -6/8
10. Simplify the two possible values of w further: w = 6 or w = -3/4
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Divide. Check your answer by showing that the product of the divisor and t (16y^(3)+y^(4)+93+61y+49y^(2))/(y+3)
The answer is correct. The division of polynomials is a straight forward process. To divide one polynomial by another, we need to divide each term in the numerator (the top part of the fraction) by the denominator (the bottom part of the fraction). Let's use long division to solve this equation.
Step 1: Divide the leading coefficient (the first number) of the numerator by the leading coefficient of the denominator. [tex]16y3 ÷ (y+3) = 16y2.[/tex]
Step 2: Multiply the result of step 1 by the denominator and subtract it from the numerator. 16y2 (y+3) - 16y3 = -3y2.
Step 3: Bring down the next coefficient from the numerator, y4, and repeat the process.
Step 4: Divide the leading coefficient of the new numerator, -3y2, by the leading coefficient of the denominator, [tex]y+3. -3y2 ÷ (y+3) = -3y.[/tex]
Step 5: Multiply the result of step 4 by the denominator and subtract it from the numerator. -3y (y+3) - (-3y2) = 0.
Step 6: Since the numerator is now 0, the division is complete. The final answer is: [tex]16y2 - 3y + (93 + 61y + 49y2) ÷ (y+3).[/tex]
To check your answer, multiply the divisor (y+3) and the result of the division. If the product is equal to the numerator, then the answer is correct.
Let's check: (y+3)(16y2 - 3y + (93 + 61y + 49y2)) = 16y3 + y4 + 93 + 61y + 49y2, which is the numerator of the original equation.
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i’m literally just trying to know what the answer of this question: “What is the result if you simplify 24/32?” and i can’t find the answer anywhere
Answer:
it is 3/4
Step-by-step explanation:
....................
en number line shows the solutions to which inequality?
x + 7 > 4
x+6=3
x +4≤1
<|||
-10 9 8 7 6 5 4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
x+5>-3
The inequality x > 4 - 7 represents a line open circled at - 3 going towards infinity.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, An inequality of the form x + 7 > 4.
x > 4 - 7.
x > - 3.
This can be represented in a number line as a line open circled at - 3 on the number line going towards infinity.
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Blake collects stamps. He collected a total of 250. If 84% of the stamps he collected were foreign, how many other stamps did he collect?
\( \left[\begin{array}{cc}1 & -1 \\ -2 & 2 \\ 2 & -2\end{array}\right] \)
\( \begin{array}{l}\frac{1}{\sqrt{3}}\left[\begin{array}{cc}1 & -1 \\ 1 & 1\end{array}\right] \\ \frac{1}{\sqrt{2}}\left[\beg
The orthonormal basis for this matrix.
To find the orthonormal basis for the given matrix, you will need to begin by taking the right and left singular vectors of the matrix.
The right singular vector for this matrix is 3(1 -1 1 1).
The left singular vector for this matrix is 2(-2 2 2 -2).
Now, divide each vector by its length to make them unit vectors, and you will get the orthonormal basis for the given matrix.
The orthonormal basis for this matrix is 1/3(1 -1 1 1) 1/2(-2 2 2 -2).
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If the product of (2x^(3)+4x-3) and (4x-1) is written in standard form, what will the first term be?
The first term of the product of (2x^(3)+4x-3) and (4x-1) in standard form will be 8[tex]x^{4}[/tex].
Since 4x is multiplied by 2x³, their product is 8x⁴. Then, distributing 4x to the terms inside the first bracket and -1 to the terms inside the second bracket, we have:
8x⁴ - 2x³ + 16x² - 13x + 3.
To write the above expression in standard form, we just need to arrange the terms of the polynomial in descending order of their degree.
Thus, the first term will be 8[tex]x^{4}[/tex].
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Find the scale factor of a drawing if the scale is 1 inch = 1/8 inch.
Thus, the drawing's scale factor is 8:1, or simply 8. This implies that each function measurement on the design is eight times bigger than its actual-world equivalent.
what is function?Mathematicians research numbers, their variants, equations, forms, and related structures, as well as possible locations for these things. The relationship between a group of inputs, each of which has a corresponding output, is referred to as a function. Every input contributes to a single, distinct output in a connection between inputs and outputs known as a function. A domain, codomain, or scope is assigned to each function. Often, functions are denoted with the letter f. (x). The key is an x. There are four main categories of accessible functions: on functions, one-to-one capabilities, so many capabilities, in capabilities, and on functions.
One inch on the illustration equals one eighth of an inch in reality if the scale is 1 inch = 1/8 inch.
We must divide the length of the drawing by the comparable length in reality to determine the scale factor. The scale factor is: because one inch on the design corresponds to 1/8 inch in reality.
1 / (1/8) = 8
Thus, the drawing's scale factor is 8:1, or simply 8. This implies that each measurement on the design is eight times bigger than its actual-world equivalent.
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Use the pattern of the differences of consecutive y-values to write an expression for y when x=6.
y=?
When x=6, the value of [tex]y=ax^2[/tex] is 11a.
What is expression?
One or more variables or numbers are combined with one additional action to form an expression.
Assuming that the function [tex]y=ax^2[/tex] is defined for all real numbers x, we can use the pattern of the differences of consecutive y-values to write an expression for y when x=6.
The differences of consecutive y-values for the function y=ax^2 are given by:
[tex]a(2^2 - 1^2), a(3^2 - 2^2), a(4^2 - 3^2), ...[/tex]
Simplifying these expressions, we get:
3a, 5a, 7a, ...
We can see that the differences between consecutive values are all the same, namely 2a. Therefore, we can express any y-value of the function
[tex]y=ax^2[/tex] as:
y = y(1) + (x-1)Δy
where y(1) is the value of y when x=1, and Δy is the common difference between consecutive y-values, which in this case is 2a.
Substituting the values x=6, y(1)=a(1^2)=a, and Δy=2a into this expression, we get:
y = a + (6-1)(2a) = a + 10a = 11a
Therefore, when x=6, the value of [tex]y=ax^2[/tex] is 11a.
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Given the following functions, evaluate each of the following: f(x) = x2 + 4x – 5 x x- 9(2) = x - 1 (f+g)(9) = (f -9)(9) = (fog)(9) = (1) (9) = g
The given functions f(x) = x² + 4x – 5 and g(x) = x - 1 are to be evaluated.
(f+g)(9). The addition of two functions is denoted by (f+g)(x) = f(x) + g(x). Now, we need to find the value of (f+g)(9). Substituting the values in the formula, we get:
(f+g)(x) = f(x) + g(x)f(x) = x² + 4x – 5g(x) = x - 1
(f+g)(9) = f(9) + g(9) = (9)² + 4(9) – 5 + (9) - 1= 81 + 36 – 5 + 9 - 1= 120
Therefore, (f+g)(9) = 120.
The subtraction of two functions is denoted by (f-g)(x) = f(x) - g(x). Now, we need to find the value of (f-9)(9). Substituting the values in the formula, we get:(f-g)(x) = f(x) - g(x)f(x) = x² + 4x – 5g(x) = x - 1(f-9)(9) = f(9) - g(9) = (9)² + 4(9) – 5 - (9) + 1= 81 + 36 – 5 - 9 + 1= 104
Therefore, (f-9)(9) = 104.3. (fog)(9)The composition of two functions is denoted by (fog)(x) = f(g(x)). Now, we need to find the value of (fog)(9).
Substituting the values in the formula, we get:
(fog)(x) = f(g(x))
f(x) = x² + 4x – 5
g(x) = x - 1
(fog)(9) = f(g(9)) = f(9 - 1) = f(8)= 8² + 4(8) – 5= 64 + 32 – 5= 91
Therefore, (fog)(9) = 91.4. g(x) = x - 1
Now, we need to evaluate g(9). Substituting x = 9 in the formula, we get:
g(x) = x - 1
g(9) = 9 - 1= 8
Therefore, g(9) = 8.
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There are 1000 marbles in a large box. Johnny took a scoop of marbles from the box. He counted 15 red marbles, 20 green marbles, and 5 blue marbles. If the scoop was a good sample of the marbles in the large box, how many red marbles would you expect to find in the large box.
We would expect to find 375 red marbles in the large box if the sample is a good representation of the marbles in the box.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
If the scoop is a good sample of the marbles in the large box, we can assume that the proportion of each color of marbles in the scoop is representative of the proportion of each color in the entire box.
To find the expected number of red marbles in the large box, we need to determine the proportion of red marbles in the sample.
The total number of marbles in the sample is 15 + 20 + 5 = 40. The proportion of red marbles in the sample is:
15/40 = 0.375
This means that 37.5% of the marbles in the sample are red.
To find the expected number of red marbles in the large box, we can multiply the proportion of red marbles in the sample by the total number of marbles in the box:
0.375 x 1000 = 375
Therefore, we would expect to find 375 red marbles in the large box if the sample is a good representation of the marbles in the box.
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Without graphing, decide whether the system of equations has one solution, no solution, or infinitely many
solutions.
y = 4x + 5
y = - 4x + 5
Answer: y=5 x=0
Step-by-step explanation:
Which is NOT behavior of successful sales people?
A)Let the customer talk more than you do
B)Ask the right questions
C)Wait to offer products and solutions until later in the call
D)Try to sell the product or service by being as persistent as possible
The behavior that is NOT characteristic of successful sales people is trying to sell the product or service by being as persistent as possible.
The correct answer is D) Try to sell the product or service by being as persistent as possible.
Successful sales people typically exhibit behaviors such as letting the customer talk more than they do, asking the right questions, and waiting to offer products and solutions until later in the call. However, being overly persistent in trying to sell a product or service can actually be detrimental to the sales process, as it can make the customer feel pressured or uncomfortable.
Therefore, the behavior that is NOT characteristic of successful sales people is trying to sell the product or service by being as persistent as possible.
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Refer to this diagram for the next five statements (Questions 1–5). Write the correct postulate, theorem, property, or definition that justifies the statement below the diagram.
Given: ∠MRS ≅ ∠MRO
In the given figure the equation m∠MRS + m∠MRO = m∠SRO is the postulate describing the linear pair of angles.
From the given figure, It is given that -
∠MRS ≅ ∠MRO
Now, what that means is that ∠MRS is congruent to ∠MRO.
Thus, to understand this concept of equality or congruence, we can prove it since from the given image, we see that -
m∠MRS = m∠MRO = 90°
Since they are both right angles then we can say that the correct theorem is the definition of a right angle triangle.
It can be seen that m∠SRO = 180°
Also, m∠MRS + m∠MRO = 180°
It is seen that the angles form a linear pair and lie on the same plane.
Therefore, the correct postulate is linear pair.
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I need this by tonight please help
Step-by-step explanation:
Refer to pics .............
The function f(x) will model the roller coaster’s height from the ground in feet over time, measured in seconds since the ride started.
Answer:
50
Step-by-step explanation:
good
Healthy Snack. Consider the problem of purchasing afternoon snacks. Health conscious buyers need at least 6 total ounces of chocolate, 10 ounces of sugar, and 8 ounces of cream cheese. There are 2 choices of snacks: brownies and cheescakes whose ingredients are listed below. Brownies cost 50 cents and mini-cheesecakes cost 80 cents. Chocolate Sugar Cream Cheese Brownie 3 2 2
Cheesecake 0 4 5
a. Formulate the minimum-cost healthy purchase snack problem as a linear optimization problem, assuming a friendly bakery that allows fractional purchases, and solve it using the linprog routine from the scipy.optimize library. b. Write out explicitly the Lagrangian for this problem, as well as the optimality conditions. c. Compute the values of the Lagrange multipliers from the optimality conditions above. What is their physical interpretation in this problem? Comment on their values. d. Convert the problem to canonical form (i.e., equality constraints with zero-lower bound inequality constraints). This is the form used internally in the solution.
a. The minimum-cost healthy purchase snack problem can be formulated as a linear optimization problem with the objective to minimize cost. The decision variables are x_b for the number of brownies purchased and x_c for the number of mini-cheesecakes purchased. The constraints are as follows:
The linear optimization problem can be solved using the linprog routine from the scipy.optimize library.
b. The Lagrangian for this problem can be written as follows:
L = 50x_b + 80x_c + λ_1(3x_b + 0x_c - 6) + λ_2(2x_b + 4x_c - 10) + λ_3(2x_b + 5x_c - 8),
where λ_1, λ_2 and λ_3 are the Lagrange multipliers associated with the constraints.
The optimality conditions for this problem are:
c. The values of the Lagrange multipliers can be computed by solving the system of equations given by the optimality conditions. Their physical interpretation in this problem is that they are proportional to the amount by which the constraints are violated. Positive values of the Lagrange multipliers indicate that the corresponding constraints are active, while negative values indicate that the constraints are inactive. The values of the Lagrange multipliers will depend on the optimal solution.
d. The problem can be converted to canonical form by rewriting the inequality constraints as:
The canonical form of the problem is used internally in the solution.
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How much is 80% of water in an apple converted ounces
The weight of the water within an apple is 6.4 ounces if the apple weighs 8 ounces.
The amounts of water in an apple in ounces, given only that it contains 80% water. Yet, it is well known that an average apple contains 84% to 86% water by weight.
We need to know the apple's weight in ounces to translate the water content to 80%.
Assume for the moment that the apple weighs 8 ounces. 80% is listed as the water content percentage. We may use the following formula to determine how much water is in an apple:
Weight of water = (water content percentage / 100) x weight of the apple
By entering the specified values, we obtain:
Weight of water = (80 / 100) x 8 ounces = 6.4 ounces.
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Put the numbers in order, from biggest to smallest. Twenty-four thousand , thirty-six
Answer:
24,000, 36
Step-by-step explanation:
it is literally x100
Go figure.
4x-25=-125 how do you slove it
Answer: 25
Step-by-step explanation:
4x - 25 = -125
4x = -125 + 25
4x = -100
Divide both sides by 4
x = -25
I am thinking of a number in the hundredths. My number is greater than 0. 8 and less than 0. 9. The greatest digit in the place is in the hundredths place. What number am I thinking of?
The only number that satisfies all the given conditions is 0.88, and this is the number that the person is thinking of.
Based on the given clues, we know that the number is greater than 0.8 and less than 0.9 and that the greatest digit is in the hundredth place. This means that the number must have a digit in the hundredth place that is greater than any digit in the tenth place or the one's place.
To find the number, we can start by considering the largest possible digit in the hundredth place, which is 8. This would give us the number 0.88, which satisfies the condition of being greater than 0.8 and less than 0.9, and also has the greatest digit in the hundredth place.
However, we also need to check if there are any other numbers that satisfy the given conditions. If we consider any digit less than 8 in the hundredth place, we would get a number that is less than 0.88, which is not greater than 0.8. On the other hand, if we consider any digit greater than 8 in the hundredth place, we would get a number that is greater than 0.89, which is not less than 0.9.
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Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle C?
Enter your answer in the box.
The measure of angle C is -
∠C = 302° - 6x.
What is the relation between the angles of a quadrilateral?The relation between the angles of a quadrilateral is as follows -
∠A + ∠B + ∠C + ∠D = 360°
Given is a Quadrilateral ABCD is inscribed in this circle.
We know that the relation between the angles of a quadrilateral is as follows -
∠A + ∠B + ∠C + ∠D = 360°
(x + 20) + 3x + (2x + 38) + ∠C = 360°
6x + 58 + ∠C = 360°
6x + ∠C = 302°
∠C = 302° - 6x
Therefore, the measure of angle C is -
∠C = 302° - 6x.
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find the range of the function f(x)
Answer:
62
Step-by-step explanation:
x2 a 4 - 91
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if three times a number is increased by 4 the result is -8
Answer:
-4
Step-by-step explanation:
3x + 4 = -8
3x = -8 -4
3x = -12 /3
x = -4