How many keyboards where made?

Answer:

77 square units

Step-by-step explanation:

Taking π as 22/7

=>(180/360)×(22/7)×(7)^2

=>1/2×22×7

=>11×7

=>77  

The consumption bundle that will not be the consumer's choice, given the assumptions of choosing the optimal bundle, is option B) 30 snacks and 12 meals. To determine the optimal consumption bundle, we need to consider the consumer's budget constraint and maximize their utility.

Given that the price of snacks is $4 and the price of meals is $10, and the consumer has $240 remaining on their meal card, we can calculate the maximum number of snacks and meals that can be purchased within the budget constraint.

For option A) 5 snacks and 20 meals, the total cost would be $4 × 5 + $10 × 20 = $200. Since the consumer has $240 remaining, this bundle is feasible.

For option B) 30 snacks and 12 meals, the total cost would be $4 × 30 + $10 × 12 = $240. This bundle is on budget constraint, but it may not be the optimal choice since the consumer could potentially consume more meals for the same cost.

For option C) 20 snacks and 16 meals, the total cost would be $4 × 20 + $10 × 16 = $240. This bundle is also on budget constraint.

Since options A, C, and D are all feasible within the budget constraint, the only bundle that will not be the consumer's choice is option B) 30 snacks and 12 meals. The consumer could achieve a higher level of utility by reallocating some snacks to meals while staying within the budget constraint. Therefore, the correct answer is option B.

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Answer:A

Step-by-step explanation:

The sale price of a basketball backboard set that sold for $79 is discounted by 15% is $67.15.

We will use the method of percentage to solve the given question.

We are given:

A basketball backboard set that sold for $79 is discounted by 15%.

We need to find the sale price after the discount is given.

We will subtract the discount from the marked price.

Let us solve this;

Sale price = marked price - discount

Sale price =  $79 - $79 * 15%

Sale price =  $79 - $79 * 15 / 100

Sale price =  $79 - $11.85

Sale price = $67.15

So, the sale price will be $67.15.

Thus, the sale price of a basketball backboard set that sold for $79 is discounted by 15% is $67.15.

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Answer: The CORRECT answer is

a=1, b=8, c=6

Step-by-step explanation:

Took the quiz

The values that can be use for a, b and c in the equation 2x² + 7x − 5 = 0 are a = 1, b = 8, c = 6

The quadratic equation formula is represented as follows:

ax² + bx + c

where

Therefore, lets model the quadratic equation x² + 8x + 6 = 0 to ax² + bx + c

Hence,

a = 1

b = 8

c = 6

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To show that the general term of the quadratic number pattern is given by \(tn = n^2 + 4n - 12\) , we need to find a quadratic expression that fits the given pattern.

Let's examine the given sequence: -7, 0, 9, 20. We notice that each term is increasing by a certain amount.

First, let's find the differences between consecutive terms:
0 - (-7) = 7
9 - 0 = 9
20 - 9 = 11

We observe that the differences between consecutive terms are not constant, so this indicates that the sequence is not linear.

To determine if the sequence follows a quadratic pattern, let's find the second differences:
9 - 7 = 2
11 - 9 = 2

The second differences are constant, which suggests a quadratic pattern.

Now, let's find the quadratic expression. We know that the general term of a quadratic sequence can be written as \(tn = an^2 + bn + c\), where a, b, and c are constants to be determined.

Using the given terms, we can form three equations:

1.\(For n = 1: -7 = a(1)^2 + b(1) + c\)
2. \(For n = 2: 0 = a(2)^2 + b(2) + c\)
3.\(For n = 3: 9 = a(3)^2 + b(3) + c\)

Simplifying these equations, we get:
1. a + b + c = -7
2. 4a + 2b + c = 0
3. 9a + 3b + c = 9

Solving this system of equations, we find a = 1, b = 4, and c = -12.

Therefore, the general term of the quadratic number pattern is given by\(tn = n^2 + 4n - 12\).

The general term of the quadratic number pattern is \(tn = n^2 + 4n - 12\).

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Statements a and b describe vectors, while statements c, d, and e do not. A vector is a quantity that has both magnitude and direction. Statements a and b specify both the magnitude (2.5 miles and 1.5 miles, respectively) and the direction (along the beach and due north, respectively). Statements c, d, and e only specify the magnitude, not the direction.

A vector is a quantity that has both magnitude and direction. The magnitude of a vector is its size, and the direction of a vector is the way it is pointing. For example, the vector pointing from the north pole to the equator has a magnitude of 10,000 kilometers and a direction of due south.

Statements a and b describe vectors because they specify both the magnitude and the direction of the movement. Statement a says that I walked 2.5 miles along the beach, which means that the magnitude of the vector is 2.5 miles and the direction of the vector is along the beach. Statement b says that I walked 1.5 miles due north along the beach, which means that the magnitude of the vector is 1.5 miles and the direction of the vector is due north.

Statements c, d, and e do not describe vectors because they only specify the magnitude of the movement, not the direction. Statement c says that I jumped off a cliff and hit the water traveling at a speed of 12 miles per hour. This tells us the magnitude of the velocity, but it does not tell us the direction of the velocity.

Statement d says that I jumped off a cliff and hit the water traveling straight down at a speed of 12 miles per hour. This tells us the direction of the velocity, but it does not tell us the magnitude of the velocity. Statement e says that my bank account shows a negative balance of $28.37. This does not tell us the magnitude or the direction of any movement, so it does not describe a vector.

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\(y=35+25=\bf60\)

Answer:

60

Step-by-step explanation:

find x first

180 - 35 - 25 = 120

x = 120

so y = 180-120

total angles in a triangle is 180

straight line also 180

Answer:

yay thx for the points, hehe

Answer: 5.24 units, 10.48 units , 15.72  units

Step-by-step explanation:

Volume of a rectangular solid is given by :-

V = lwh, where l = length , w= width and h = height

Given: A rectangular solid has edges whose lengths are in the ratio 1:2:3.

Let lengths of the rectangular solid x , 2 x, 3x.

volume of the solid is 864 cubic units

Then, Volume of rectangle = \(x (2x)(3x) =864\ \text{cubic units}\)

\(\Rightarrow\ 6x^3 = 864\\\\\Rightarrow\ x^3 =144\\\\\Rightarrow\ x=(144)^{\frac{-1}{3}}\approx5.24\)

Lengths of rectangular solid 5.24 units, 2 (5.24) units , 3(5.24) units

= 5.24 units, 10.48 units , 15.72  units

Answer:

A

Step-by-step explanation:

Hello There!

First thing we notice is that the y intercept is at (3,0) meaning that they have some sort of fee that has a charge of 3 dollars (represented by the 3)

Because the fee is 3 dollars we can immediately eliminate answers B and C

Now we want to find the charge for each bag of Potpourri (this can be represented by the slope)

Once again we want to choose two points on the line and plug it in into the slope formula

the points are optional but i have chosen the points (1,4.5) and (2,6)

*plug it into the slope formula*

\(slope=\frac{6-4.5}{2-1} \\6-4.5=1.5\\2-1=1\\slope =\frac{1.5}{1} or1.5\)

so we can conclude that the charge per bag of potpourri is $1.50 leading us to answer choice A  

\(\text{If the number is x,}\\\\~~~~~\dfrac 47 \cdot x =36\\\\\implies 4x = 36 \times 7\\\\\implies x =\dfrac{36 \times 7}4\\ \\\implies x = 9 \times 7\\\\\implies x = 63\\\\\text{Hence, the number is 63.}\)

Answer:

\(\huge\boxed{\bf\:x = 63}\)

Step-by-step explanation:

Given,

Let's take the unknown number as 'x'.

Now,

4/7 × x = 36

Take the reciprocal of 4/7 to the other side of the equation .

x = 36 × 7/4

Cancel 36 by 4.

x = 9 × 7

Multiply the 2 numbers

x = 63

\(\rule{150pt}{2pt}\)

A researcher conducted a hypothesis test using a sample from an unknown population, with a t-statistic degrees of freedom (df) of 30, a mean (M) of 46, and a variance of 10.

The number of individuals in the sample can be calculated as 31.

The formula for calculating the degrees of freedom (df) for a t-statistic is given by df = n - 1, where n represents the sample size. In this case, we have df = 30, so n - 1 = 30. Solving for n, we find n = 31.

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Some molecules which cannot be synthesized by cell but must be obtained from environment, then these types of molecules include vitamins and amino acids and are known as growth factors.

The "Growth-factors" are essential for various biological processes, including cell growth, development, and repair. They act as signaling molecules that bind to specific receptors on cells, initiating intracellular signaling pathways and triggering specific cellular responses.

By providing these molecules, the environment supports the cell's ability to function properly and carry out vital processes necessary for growth, development, and overall survival.

Obtaining growth factors from the environment becomes crucial in maintaining the necessary balance of these molecules for the cell's optimal functioning.

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3 x 5 x 7 = 105, which is the smallest result that can be obtained by the process. To reach this result, the three chosen numbers must be 3, 5, and 7. The first step is to add two of the three numbers, which in this case is 3 + 5 = 8. Then, the sum of the two numbers is multiplied by the third number, which in this case is 7.

The product of 8 x 7 is 56, which is the smallest result that can be obtained by this process.  In general, the chosen numbers must be the smallest possible numbers in order to obtain the smallest result. The process involves adding two of the three chosen numbers and then multiplying the sum by the third number.

Thus, the three chosen numbers must be the numbers with the lowest sum when added together, and the third number must be the smallest number of the three. By following this process, the smallest result that can be obtained is the product of the three chosen numbers multiplied together.

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The formula for the area K of the triangle is K = 2ab sin(C). Option C is the answer

A triangle can be defined as a polygon that has three sides. The three sides can be equal or unequal giving rise to different type of triangle.

The appropriate formula for the area K of a triangle with angles A, B, C and opposite sides a, b, and c respectively, is

K = (1/2) a b sin(C)

= (1/2) b c sin(A)

= (1/2) c a sin(B)

By rewriting the the formula in terms of just two sides

K = (1/2) a b sin(C)

By rearranging the expression

We have;

K = (1/2) c a sin(B)

= (1/2) ab sin(C)/sin(B)

= 2ab sin(C)/(2sin(B))

= 2ab sin(C)/2b

= a sin(C)

Hence, option C  which is is the correct formula

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The thing to tell Irene to convince her that these cards don’t match is that the addition of the variables will not give 4x + 2.

An expression can be used to illustrate the relationship between the variables that are given in the data.

The addition of the variables will be illustrated thus:

x + 2 + x + 2 + x + 2 + x + 2 = 28

4x + 8 = 28

In the question, it was written as 4x + 2 = 28. This shows that it won't match.

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Answer:

it rise over run so put 2y on graph count down 4 and move right 1

Step-by-step explanation:

The measure of each interior angle of a regular n-gon is\(\(\frac{180(n-2)}{n}\).\) is a False statement.

The measure of each interior angle of a regular n-gon is\(\(\frac{180(n-2)}{n}\).\)

In a regular n-gon, the sum of all interior angles is equal to \(\((n-2) \cdot 180\) degrees.

Since a regular n-gon has n congruent angles, the measure of each interior angle is \(\(\frac{(n-2) \cdot 180}{n}\)\) degrees.

The term "radial angle" is not applicable to regular polygons. It is used in the context of angles formed by rays extending from a central point, such as in a circle. In regular polygons, the focus is on the interior angles formed by the sides of the polygon.

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Answer:

Step-by-step explanation:

Answer:4/3

Answer:

The tangent of the larger acute angle in a right triangle with side lengths 10, 24, and 26 is 12/5.

Step-by-step explanation:

In a right triangle, the hypotenuse (the side opposite the right angle) is the longest side.

Therefore, in a right triangle with side lengths 10, 24, and 26, the hypotenuse measures 26 units and the legs measure 10 and 24 units.

In a right triangle:

Therefore, the largest acute angle is between the hypotenuse and the shortest leg, which means the side opposite the angle is the longest leg.

The tangent ratio is the ratio of the side opposite the angle to the side adjacent the angle.

Therefore the tangent of the largest acute angle is:

\(\implies \sf \dfrac{O}{A}=\dfrac{24}{10}=\dfrac{12}{5}\)

The amount of storage required to represent a simple graph with n vertices and m edges can vary depending on the chosen representation. Here's the storage requirement for each representation:

a) Adjacency lists:

In an adjacency list representation, we typically use an array of size n to store the vertices, and for each vertex, we maintain a linked list or an array to store its adjacent vertices. The space complexity of this representation is O(n + m), where n is the number of vertices and m is the number of edges.

Each vertex requires constant space, and each edge is represented by a link or entry in the adjacency list.

b) Adjacency matrix:

In an adjacency matrix representation, we use a 2D matrix of size n x n to represent the graph. Each entry (i, j) in the matrix represents whether there is an edge between vertices i and j. The space complexity of this representation is O(n^2), as we need to store n^2 entries for the complete matrix. However, if the graph is sparse (few edges compared to vertices), the space complexity can be reduced to O(n + m) by only storing the entries corresponding to the existing edges.

c) Incidence matrix:

In an incidence matrix representation, we use a 2D matrix of size n x m, where n is the number of vertices and m is the number of edges. Each entry (i, j) in the matrix represents whether vertex i is incident to edge j. The space complexity of this representation is O(n * m), as we need to store n * m entries for the matrix.

Similar to the adjacency matrix, if the graph is sparse, the space complexity can be reduced to O(n + m) by storing only the entries corresponding to the existing edges.

In summary:

a) Adjacency lists: O(n + m)

b) Adjacency matrix: O(n^2) or O(n + m) for sparse graphs

c) Incidence matrix: O(n * m) or O(n + m) for sparse graphs

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Answer:

x=31

Step-by-step explanation:

The length of A + B is approximately 20.35 units and its direction is approximately 76.53 degrees.

Given vectors: Vector A has a length of 10 units and is at a direction of 30 degrees.

Vector B has a length of 15 units and is at a direction of 100 degrees.

We are required to calculate the sum of vectors A and B, i.e., A + B.

Using the component method, we can write the vector A as:

A = 10 cos 30 i + 10 sin 30 j

= 5√3 i + 5 j

And, the vector B as:

B = 15 cos 100 i + 15 sin 100 j

= -5.34 i + 14.52 j

Now, adding the two vectors, we get:

A + B = (5√3 - 5.34) i + (5 + 14.52) j

= (5√3 - 5.34) i + 19.52 j

We can use the Pythagorean theorem to calculate the magnitude of the vector A + B:

Magnitude = √[(5√3 - 5.34)² + 19.52²]

≈ 20.35 units

To determine the direction of the vector, we use the inverse tangent function (tan⁻¹):

Angle = tan⁻¹ [(19.52)/(5√3 - 5.34)]

≈ 76.53°

Therefore, the length of A + B is approximately 20.35 units and its direction is approximately 76.53 degrees.

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2)  (3, -4)

3) y + 3 + 3/5 (x - 6)

Answer:

B

Step-by-step explanation:

- 6x + 3 ≥ 21 ( subtract 3 from both sides )

- 6x ≥ 18

divide both sides by - 6, reversing the symbol as a result of dividing by a negative quantity.

x ≤ - 3

Answer:

The integral diverges.

Step-by-step explanation:

∫₀ᵉ 1/x dx

(ln|x| + C) |₀ᵉ

ln|x| is undefined as x approaches 0, so the integral diverges.

Answer:

The answer is 4.5

The value of mean, variance and covariance matrix is illustrated in following solution as

\(V(\frac{X}{X'} )=\left[\begin{array}{ccc}\frac{1}{12} &\frac{1}{12} \\\frac{1}{12} &\frac{4}{45} \\\end{array}\right]\)

The mean vector consists of the means of each variable and the variance-covariance matrix consists of the variances of the variables along the main diagonal and the covariances between each pair of variables in the other matrix positions. with \bar{x} and \bar{y} denoting the means of X and Y, respectively.

Mean and variance is a measure of central dispersion. Mean is the average of given set of numbers. The average of the squared difference from the mean is the variance. Central dispersion tells us how the data that we are taking for observation are scattered and distributed.

To find the mean, variance and covariance matrix of a random vector

\(\left[\begin{array}{ccc}X\\X'\\\end{array}\right]\) X~ U(0,1)

\(E(X')=\int\limits^1_0 {r} \, dr = \frac{1}{r+1}\)

where, r = 1 , 2, 3...

Now,

\(E(X) = \frac{1}{2}\\ \\E(X^2) = \frac{1}{3}\\ \\E(X^3) =\frac{1}{4}\\\)

\(E(X^4)=\frac{1}{5}\)

So, cov(X , X') =

\(E(X^3)-E(X).E(X')\\\\=\frac{1}{4} -\frac{1}{2}.\frac{1}{3}\\ \\ =\frac{1}{12}\)

\(Var(X) = E(X^4) -E'(X')\\\\\frac{1}{5}-\frac{1}{9}\\ \\ \frac{4}{45}\)

Hence,

\(V(\frac{X}{X'} )=\left[\begin{array}{ccc}\frac{1}{12} &\frac{1}{12} \\\frac{1}{12} &\frac{4}{45} \\\end{array}\right]\)

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The given question is incomplete, complete question is:

suppose y follows a γ(α, β) distribution. find the mean and variance covariance matrix of the random vector x x2 , where x

(a) To guarantee that at least 2 people have a birthday on the same day of the week, at least 8 people must be selected.

(b) To guarantee that at least 6 people have a birthday on the same day of the week, at least 43 people must be selected.

(a) To find the minimum number of people needed to guarantee that at least 2 of them have a birthday on the same day of the week, we can apply the Pigeonhole Principle.

There are 7 days of the week, so each person can have their birthday on one of these 7 days. If we select 8 people, then there are 8 pigeons (people) and 7 pigeonholes (days of the week). Since we have more pigeons than pigeonholes, by the Pigeonhole Principle, at least 2 people must have their birthday on the same day of the week.

(b) Similarly, to find the minimum number of people needed to guarantee that at least 6 of them have a birthday on the same day of the week, we apply the Pigeonhole Principle. Again, there are 7 days of the week, and each person can have their birthday on one of these 7 days.

If we select 43 people, then we have 43 pigeons (people) and 7 pigeonholes (days of the week). Since we have more pigeons than pigeonholes, by the Pigeonhole Principle, at least 6 people must have their birthday on the same day of the week.

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Answer:

D

Step-by-step explanation