consider a collection of envelopes consisting of 2 red envelopes, 1 blue envelope, 1 green envelope, and 3 yellow envelopes. if three envelopes are selected at random, without replacement, determine the probability that they are all yellow envelopes. (type an integer or a simplified fraction.)

Statement Problem: The sum of two numbers is 7. Five times the larger number plus four times the smaller number is 48. Find the numbers.

Solution:

Let x be the larger number and y be the smaller number such that;

From equation 1, we have;

Substitute equation3 in equation2, we have;

Then, substitute the value of y in equation3;

Thus, the larger number is 20 and the smaller number is -13

The value of angle S is 53°

Exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of two remote interior angles.

With this theorem we can say that

7x+2 = 4x+13+19

collecting like terms

7x -4x = 13+19-2

3x = 30

divide both sides by 3

x = 30/3

x = 10

Since x = 10

angle S = 4x+13

angle S = 4(10) +13

= 40+13

= 53°

Therefore the measure of angle S is 53°

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Answer:

-0.8

Step-by-step explanation:

if you grab 2 whole points, such as (-3,1) and (2,-3), you have to get the rise/run which in this case is -4/5. -4/5= -0.8

Answer:

-4/5

Step-by-step explanation:

So you probablly heard of y=mx+b. if you haven't, m is the slope.

You have to use rise over run to find slope so let's first find a point of the line.

(-3,1) is a point!

Since this is a negative line, the slope is going to be negative.

You have to go down 4 times and to the right 5 times for your next point. (2,-3)

So the slope is -4/5

And for slope intercept form it's in y= -4/5x + b (b = y-intercept)

Hope this helps! Leave a comment if it does or doesn't! :)

Answer:

B

Step-by-step explanation:

For a function to be considered a function, every input can have only one output. In this case, the input would be x and the out put would be y. The answer would be B because it is the only answer that doesn't have a repeating x with a different y example. For example, D would not be a function because it has two points that contain 6 with a different y value. (6,-10) (6,6).

When the above is simplified using Boolean Algebra, we have F = x' + y' + w'xy.

We can simplify  the Boolean function F = xy'z' + xy'z+ w'xy +   w'x'y' + w'xy using the following Boolean Algebra rules.

Absorption - x + xy = x

Commutativity -  xy = yx

Associativity - x(yz) = (xy)z

Distributivity - x(y + z) = xy + xz

Using the above , we   have

F = xy'z' + xy'z+ w'xy + w'x'y' +   w'xy

= xy'(z + z') + w'xy(x + x')

= xy' +  w'xy

= (x' + y)(x' + y')  + w'xy

= x' + y' + w'xy

This means that the simplified expression is F = x' + y' + w'xy.

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The resultant of the given sum of the mixed number 1 1/4 + 4 2/3 will be 5 11/12.

The number system is a way to represent or express numbers.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

As per the given sum of the mixed number,

1 1/4 + 4 2/3

⇒ 1 + 1/4 + 4 + 2/3

⇒ 1 + 4 + 1/4 + 2/3

⇒ 5 + 1/4 + 2/3

Take LCM of 1/4 and 2/3 as 12.

⇒ 5 + (3 + 8)/12

⇒ 5 + 11/12 = 5 11/12

Hence "The resultant of the given sum of the mixed number 1 1/4 + 4 2/3 will be 5 11/12".

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Answer:

1. 42 cm²

2. 128 cm²

6. 66 cm²

Step-by-step explanation:

In each case, I am using the front and back faces as bases with length and width. The bottom right dimension is the height.

1.

SA = 2(L + W)H + 2LW

SA = 2(3 cm + 2 cm)(3 cm) + 2(3 cm)(2 cm)

SA = 42 cm²

2.

SA = 2(L + W)H + 2LW

SA = 2(6 cm + 4 cm)(4 cm) + 2(6 cm)(4 cm)

SA = 128 cm²

6.

SA = 2(L + W)H + 2LW

SA = 2(3 cm + 3 cm)(4 cm) + 2(3 cm)(3 cm)

SA = 66 cm²

Answer:

1=40 2=252 3=200 4=36

Step-by-step explanation:

I dint do the top two so start on 3

3#= 1

A function that converts an input of letters and numbers into an encrypted output of a fixed length is called hash. The links in the blockchain that is created using an algorithm.

A hash is a mathematical function that changes an input of any length into an encrypted output of a specific length. Therefore regardless of the quantity of raw data involved or the size of the file, its unique hash is always the same size. Also, a hash cannot be used to "reverse engineer" an input from a hash output, because hash functions are "one-way" (like a meat grinder; you don't can't put ground beef back into a steak). However, if you use such a function on the same data, its hash will be the same, so you can confirm that the data is the same (i.e., unchanged) if you already know its hash.

Hashes are used in various parts of the blockchain system. Each block header contains the hash of the previous block, ensuring nothing has been tampered with as new blocks are added. Cryptocurrency blockchains use hashes to secure information and make the ledger immutable.

It refers to the technique of making an input element of arbitrary length reflect an output element of definite length. For blockchain applications in cryptocurrencies, variable duration transactions are processed by specific hashing algorithms and all produce fixed length outputs. This is true regardless of the duration of the input transaction.

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Complete Question:

Fill in the blanks,

A function that converts an input of letters and numbers into an encrypted output of a fixed length is called ________. The links in the blockchain that is created using an algorithm.

\(\sqrt{1-cos(10x)/2}\)The expression is equivalent to sin(5x)

Given that,

start root start fraction 1 minus cosine (10 x) over 2 end fraction end root which means \(\sqrt{1-cos(10x)/2}\)

To find : The equivalent expression to the equation \(\sqrt{1-cos(10x)/2}\) --> (1)

We know that,

From trigonometry,

Half angle formula

What is the value of 1 cos 2x? The expression 1 - cos2x is written as 1 - cos2x = 2sin2x. This makes it possible to recognize trigonometric identities. These are the phrases that enable you to discover a precise response to your query.

1−cos2x=2sin²x and

Similarly,

1−cosx=2sin²(x/2)

Then

1-cos10x = 2sin²(5x)

Substitute above expression in (1)

Then,

\(\sqrt{1-cos(10x)/2}\) = \(\sqrt{2sin^2(5x)/2}\)

                           = \(\sqrt{sin^2(5x)}\)

                           = sin(5x)

Therefore, \(\sqrt{1-cos(10x)/2}\) is equivalent to sin(5x)

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Hey there!
Linear functions have a continuous change.

Let's check these tables and see if we can tell linear functions from non-linear functions.

The first one is

- we add 1 each time

- we subtract 3 each time

\(\rule{200}{2}\)

Let's try the next one:

- we add 1 each time

- we add 5 each time

\(\rule{200}{2}\)

Let's try the third one:

        - we add 3, then 2, then 1..

So this table doesn't represent a linear function.

Let's check the fourth one:

- we add 1 each time

- we add 1 each time

Thus, Option C is the right option.

Hope everything is clear.

Let me know if you have any questions!

Always remember: Knowledge is power!

Answer: y-3=3(x+6)

Step-by-step explanation:

(-6,3)      m=3

A line in the point-slope form is expressed as:

  \(y-y_1=m(x-x_1)\\\\x_1=-6\ \ \ \ y_1=3\ \ \ \ m=3\)    

Hence,

y-3=3(x-(-6))

y-3=3(x+6)                      

The NPV is positive, it is worth taking the Investment.

Net Present Value (NPV) is an assessment method that determines the attractiveness of an investment. It is a technique that determines whether an investment has a positive or negative present value.

This method involves determining the future cash inflows and outflows and adjusting them to their present value. This helps determine the profitability of the investment, taking into account the time value of money and inflation.The formula for calculating NPV is:

NPV = Σ [CFt / (1 + r)t] – CIWhere CFt = the expected cash flow in period t, r = the discount rate, and CI = the initial investment.

The given problem can be solved by using the following steps:

Calculate the present value (PV) of the expected cash inflows:

Year 1: $28,000 / (1 + 0.08)¹ = $25,925.93Year 2: $28,000 / (1 + 0.08)² = $24,009.11Year 3: $28,000 / (1 + 0.08)³ = $22,173.78Total PV = $72,108.82

Calculate the PV of the initial investment: CI = $7,000 / (1 + 0.08)¹ + $35,000 / (1 + 0.08)²CI = $37,287.43Calculate the NPV by subtracting the initial investment from the total PV: NPV = $72,108.82 – $37,287.43 = $34,821.39

Since the NPV is positive, it is worth taking the investment.

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Answer:

\( x = 3y \)

\(7x+4y= 12 + 4x+7y\)

Step-by-step explanation:

Para resolver la pregunta, basta con definir variables adecuadas y traducir cada relación. Sea x el costo de una caja grande e y el costo de una caja pequeña. Tenemos que el costo de una caja grande es igual a 3 cajas pequeñas. Es decir, x = 3y. Luego, tenemos que

\(7x+4y= 12 + 4x+7y\)

pues al sumarle 12 al costo de 4grande y 7 pequeñas obtenemos el costo de 7 grande y cuatro pequeñas. De aquí, el sistema de ecuaciones que modela el sistema es

\( x = 3y \)

\(7x+4y= 12 + 4x+7y\)

The value of expression will be;

⇒ 7 / 30

⇒ - 14/15

What is Distributive property?

By the rule of distributive property, multiplying the sum of two or more addends by a number gives the same result as when each addend is multiplied individually by the number and the products are added together.

Given that;

The expression is,

⇒ [ 7/5 × - 3/12 ] ± [ 7/5 × 5/12 ]

Now,

Since, The expression is,

⇒ [ 7/5 × - 3/12 ] ± [ 7/5 × 5/12 ]

Solve the expression by using distributive property as;

⇒ [ 7/5 × - 3/12 ] ± [ 7/5 × 5/12 ]

⇒ [ 7/5 ] × [ - 3/12 ±  5/12 ]

It gives two solution as;

⇒ 7/5 × [ - 3/12 + 5/12 }

⇒ 7/5 × 2/12

⇒ 7/5 × 1/6

⇒ 7 / 30

And,  7/5 × [ - 3/12 - 5/12 }

⇒ 7/5 × - 8/12

⇒ 7/5 × - 2/3

⇒ - 14 / 15

Thus, The value of expression will be;

⇒ 7 / 30

⇒ - 14/15

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15/50 = 0.3, or 30%.

Answer:

0.3, or 30%

Step-by-step explanation:

the height of the mast is approximately 51.5 meters.

what is approximately ?

"Approximately" means that the value is an estimate that is very close to the true value but may not be exact. In the context of the answer I provided, "approximately" indicates that the height of the mast is very close to 51.5 meters but may be slightly more or less than that value.

In the given question,

Let's call the height of the mast "h". We can use trigonometry to find the value of "h".

If we draw a diagram, we can see that the angle of elevation of the mast is the same as the angle between the ground and a line from P to the top of the mast. We can call this angle "θ".

We know that tan(θ) = opposite/adjacent = h/150.

We also know that tan(19°) = 0.3431 (rounded to 4 decimal places).

So we can set up an equation:

0.3431 = h/150

To solve for "h", we can multiply both sides by 150:

h = 0.3431 x 150

h = 51.465 (rounded to 3 significant figures)

Therefore, the height of the mast is approximately 51.5 meters.

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If Lisa spends her income on veggie burgers and pints of soy milk and the price of veggie burgers is three times the price of a pint of soy milk, then when Lisa maximizes her utility she will buy both goods until the marginal utility of veggie burgers is three times the marginal utility of soy milk.

Therefore, if Lisa spends her income on veggie burgers and pints of soy milk and the price of veggie burgers is three times the price of a pint of soy milk, then when Lisa maximizes her utility she will buy both goods until the marginal utility of veggie burgers is three times the marginal utility of soy milk.

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The length of the pipe required would be 31.06 meters

The length of the pipe is the hypotenus of the triangle formed :

substituting the values into our equation:

length of pipe = √17² + 26²

length of pipe = √965 = 31.06

Therefore, the length of the pipe needed is 31.06 meters

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Answer:

  0.82

Step-by-step explanation:

You want the probability of A or B given the frequencies shown in the diagram.

The probability of either event is the ratio of the number of times it occurs to the total number of trials. The total number of trials is shown as ...

  num trials = 23 + 18 + 9 = 50

Then the probability of interest is ...

  P(A or B) = P(A) + P(B) . . . . . . . . . . . . . given in the diagram

  P(A or B) = 23/50 +18/50 = 41/50

  P(A or B) = 0.82

Answer:

Te conozco y sé qué

Como Nuevo de fabrica el otro

Volume = base area x height

Base area = Length x width = 10 x 8 = 80 in2

Volume = 80 in2 x 6 in = 480 cubic inches

A(n) scalar cursor is automatically created in procedural SQL when the SQL statement returns only one value.

A scalar cursor is a type of cursor that is used to retrieve a single value from the result set of a query. It is different from a regular cursor, which is used to retrieve multiple rows of data from a result set. When a scalar cursor is created, the result set is stored in a temporary table, and the single value is retrieved from that table. Scalar cursors are often used in stored procedures, functions, and triggers to retrieve a single value from a query and use it in further processing or calculations.

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The statement "If the size of a sample is at least 30, then you can use a z-scores to determine the probability that a sample mean falls in a given interval of the sampling distribution." is true because  when the sample size is at least 30, the Central Limit Theorem applies and the sampling distribution of the sample mean can be approximated by a normal distribution.

If the size of a sample is at least 30, the Central Limit Theorem (CLT) applies, which states that the distribution of sample means is approximately normal, regardless of the underlying distribution of the population, as long as the sample size is sufficiently large.

When the sample size is at least 30, the sampling distribution of the sample mean can be approximated by a normal distribution, and z-scores can be used to calculate probabilities of sample means falling in a given interval.

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The first step is to subtract $500 from $2000 and then you end up with $1500 which you then divide by 5.

Each payment will have to be $300

As h approaches 0, the limit becomes: e(²+0) = e²
The answer is D, e².

The given expression is lim(h→0) (e(2+h) - e²)/h. To find the limit, we can apply L'Hopital's Rule since we have an indeterminate form of the type 0/0. L'Hopital's Rule states that if lim(f(x)/g(x)) as x→a is indeterminate, then it is equal to lim(f'(x)/g'(x)) as x→a, provided the limit exists.

Here, f(h) = e^(²+h) - e^² and g(h) = h. Let's find their derivatives:

f'(h) = d(e(²+h) - e^²)/dh = e^(²+h)
g'(h) = dh/dh = 1

Now, applying L'Hopital's Rule:

lim(h→0) (e(²+h) - e²)/h = lim(h→0) (e²+h))/1

As h approaches 0, the limit becomes:

e(²+0) = e²

So, the answer is D, e².

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Answer:

7/100 × 12800

= 896

896× 8 = 7168

12800+ 7168 = 19968

After 8 years the number of population is going to be 19968

Answer:

10 visits

Step-by-step explanation:

According to the scenario, calculation of the given data are as follows,

Rewards for signing up = 80 points

Reward per visit = 2.5 points

Total points needed = 105

Let, number of visits = x

So, we can calculate number of visits by using following formula,

80 + (2.5 × X) = 105

2.5X = 105 - 80

2.5X = 25

X = 25 ÷ 2.5

X = 10 visits.

Hence, Olivia needs to make 10 visits in order to earn a free movie ticket.

one real eigenvalue. find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace.

What is eigenvalue?

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that, when the linear transformation is applied to it, changes at most by a scalar factor. The factor by which the eigenvector is scaled is known as the associated eigenvalue, frequently denoted by lambda.

a) -4

b) 1

c) 1

Step-by-step explanation:

a) The matrix A is given by:

\(A=\left[\begin{array}{ccc}-3 & 0 & 1 \\2 & -4 & 2 \\-3 & -2 & 1\end{array}\right]\\\)

where lambda are the eigenvalues and I is the identity matrix. By replacing you obtain:

\(A-\lambda I=\left[\begin{array}{ccc}-3-\lambda & 0 & 1 \\2 & -4-\lambda & 2 \\-3 & -2 & 1-\lambda\end{array}\right]\)

and by taking the determinant:\(\begin{aligned}& {[(-3-\lambda)(-4-\lambda)(1-\lambda)+(0)(2)(-3)+(2)(-2)(1)]-[(1)(-4-\lambda)(-3)+(0)(2)(1-} \\& \lambda)+(2)(-2)(-3-\lambda)]=0 \\& -\lambda^3-6 \lambda^2-12 \lambda-16=0\end{aligned}\)

and the roots of this polynomial is:

\(\begin{aligned}& \lambda_1=-4 \\& \lambda_2=-1+i \sqrt{3} \\& \lambda_3=-1-i \sqrt{3}\end{aligned}\)

hence, the real eigenvalue of the matrix A is -4.

b) The multiplicity of the eigenvalue is 1.

c) The dimension of the eigenspace is 1 (because the multiplicity determines the dimension of the eigenspace)

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Complete Quetion

The matrix A= (−3 0 1, 2 −4 2, −3 −2 1) has one real eigenvalue. Find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace. The eigen value = has multiplicity = and the dimension of the corresponding eigenspace is:_______.