. Six years from now, P 5M will be needed to pay for a building renovation. In order to generate this surn, a sinking fund consisting of three beginaineof-year deposits (A) starting today is establishod. No further payments will be made after the said annual deposits. If money is worth 8% per annum, the value of A is closest io a) P1,132,069 c) P 1,457,985 sunk b) 1,222,635 d) P1,666,667

Two samples can have the same mean but different standard deviations if one sample has more variability than the other. For example, one sample may have data points that are tightly clustered around the mean, while the other sample may have data points that are more spread out.

This can result in the same mean value for both samples, but different levels of variability.

Here's an example bar graph to illustrate this concept:

     Sample 1                Sample 2

 ╭────────────────╮   ╭────────────────╮

 │      Mean      │   │      Mean      │

 ├────────────────┤   ├────────────────┤

 │                │   │    ╭─╮         │

 │                │   │    │ │         │

 │                │   │    │ │         │

 │                │   │    ╰─╯         │

 │     o o o      │   │  o o o o o o  │

 │                │   │                │

 │                │   │                │

 │                │   │                │

 ╰────────────────╯   ╰────────────────╯

     Std. Dev.            Std. Dev.

In this example, both Sample 1 and Sample 2 have a mean value of 5. However, Sample 1 has lower variability with a standard deviation of 1, while Sample 2 has higher variability with a standard deviation of 3. The error bars on the graph represent the standard deviation for each sample.

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False. The complement of an event A, denoted by A', is the event consisting of all outcomes in the sample space S that are not in A.

In probability theory, a sample space S represents the set of all possible outcomes of an experiment or random phenomenon. An event A is a subset of the sample space S, representing a specific outcome or a combination of outcomes of interest.

The complement of event A, denoted by A', includes all the outcomes in the sample space S that are not part of event A. In other words, A' consists of all outcomes that do not satisfy the conditions for event A to occur.

For example, let's consider rolling a fair six-sided die. The sample space S consists of the numbers {1, 2, 3, 4, 5, 6}. Now, let event A be the event of rolling an odd number. In this case, A = {1, 3, 5}, and the complement of A, denoted by A', would be A' = {2, 4, 6}. A' includes all the outcomes that are not odd numbers.

It's important to note that the complement of an event A and the event itself together cover the entire sample space S. In other words, A and A' are mutually exclusive and exhaustive, meaning that any outcome must either be in A or in A'.

So, in summary, the complement of an event A is the set of all outcomes in the sample space S that do not belong to A.

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Diamonds are incorporated in solidified magma called kimberlite, which originates deep within the Earth.

Kimberlite is a volcanic rock formed in the Earth's mantle and brought to the surface through volcanic eruptions. The high pressure and temperature conditions in the mantle allow for the formation of diamonds from carbon atoms. When kimberlite eruptions occur, they transport diamonds and other mantle-derived materials to the Earth's surface, where they eventually cool and solidify.

The discovery of diamonds in kimberlite pipes has played a significant role in the development of the diamond mining industry. These pipes serve as primary sources for diamond extraction and are found in various locations around the world, including South Africa, Russia, and Canada. The study of kimberlites also provides valuable information about the Earth's mantle composition and its geodynamic processes. Overall, the relationship between diamonds and kimberlite is an essential aspect of both the gemstone industry and the study of the Earth's interior.

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Answer:

32+n

Step-by-step explanation:

32 more than the number n would be 32+n.

Hope this helps!

Answer:

80

Step-by-step explanation:

you can take the ratio 2:3:4 as

2x + 3x + 4x = 180

9x = 180

x= 20

4(20) = 80

Answer:

D) 20

Step-by-step explanation:

Set up an equation: 2x+3x+4x=180

9x=180

180/9=20

Answer: D) 20degrees

Answer:

it's b

Step-by-step explanation:

it satifies Pythagoras theorem.

29² = 20²+21²

The recurrence relation with the given base case is 3.

To solve this recurrence relation, we can use a technique called "substitution method." The substitution method involves substituting the expression for the () term into the recurrence relation, which will give us an equation in terms of lower-order terms.

Let's start by substituting () into the recurrence relation:

() = ()

() = () + 1

We can simplify this expression by substituting () into it:

() = () + 1

() = ( − 1) ! + 1

We now have an expression for () in terms of lower-order terms, namely (). We can use this expression to find the values of subsequent terms in the sequence.

To find the value of () for = 3, we can substitute = 2 into the expression for ():

() = ( − 1) ! + 1

() = (2 − 1)! + 1

() = 1 + 1

() = 2

Similarly, we can find the value of () for = 4:

() = ( − 1) ! + 1

() = (3 − 1)! + 1

() = 2 + 1

() = 3

We can continue this process to find the values of () for any value of . This is the basic idea behind solving a recurrence relation with a given base case.

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Answer:

i believe the answer is...C

Step-by-step explanation:speed(memory) or s(m)

Step-by-step explanation:

Dependent variable states that  a variable whose value dependent upon the dependent variable.

For example:

x is the independent variable and f(x) is the dependent variable

Given the statement:

The speed of a computer depends on the amount of memory.

Let m represents the amount of memory and s represents the speed of a computer.

m = Independent variable

s(m) = Dependent variable on m

Then

Answer:speed (memory), or s(m)

Step-by-step explanation:

Answer:

\(Rate = -5\)

Step-by-step explanation:

Given

\(f(x) = 2x^2 - x - 4\)

\(-4 \le x \le 2\)

Required

Determine the average slope over the given interval

This is calculated as:

\(Rate= \frac{f(b) - f(a)}{b - a}\)

Where:

\(a = -4\)

\(b =2\)

So:

\(Rate= \frac{f(2) - f(-4)}{2 - (-4)}\)

\(Rate= \frac{f(2) - f(-4)}{2 +4}\)

\(Rate= \frac{f(2) - f(-4)}{6}\)

Solving for f(2) and f(-4), we have:

\(f(x) = 2x^2 - x - 4\)

\(f(2) = 2 *2^2 -2 - 4\)

\(f(2) = 2\)

\(f(-4) = 2*(-4)^2 - (-4) - 4\)

\(f(-4) = 2*16 +4 - 4\)

\(f(-4) = 32\)

So, the equation becomes

\(Rate= \frac{f(2) - f(-4)}{6}\)

\(Rate= \frac{2 - 32}{6}\)

\(Rate= \frac{-30}{6}\)

\(Rate = -5\)

Answer:

x = 128 degrees

Step-by-step explanation:

First figure out the angle inside the triangle

1st step: add 55 and 73 together:

⇒ 55 + 73 = 128

2nd step: subtract the sum from 180:

⇒ 180 - 128 = 52

to find x, take 180 again and then subtract 52 from it:

⇒ 180 - 52 = 128

The given problem states that the ratio of the number of tables to chairs in a restaurant is 4 : 9. After removing 2 tables and 4 chairs, the ratio becomes 7 : 16. After removing 2 tables and 4 chairs, there are 16 tables and 36 chairs left in the restaurant.

Let's assume the number of tables in the restaurant is represented by \($4x$\) and the number of chairs is represented by \($9x$\) (since the ratio is given as 4:9).

According to the given information, if 2 tables and 4 chairs are removed, the new ratio becomes 7:16. This can be represented as

\($\frac{{4x - 2}}{{9x - 4}} = \frac{7}{16}$\).

Cross-multiplying:

\(\[16(4x - 2) = 7(9x - 4)\]\)

Simplifying:

\(\[64x - 32 = 63x - 28\]\)

Subtracting \($63x$\) from both sides and adding 32 to both sides:

\($x = 4$\)

Now, we can find the number of tables and chairs left by substituting \($x = 4$\) them back into the initial representation:

The number of tables: \($4x = 4(4) = 16$\)

The number of chairs: \($9x = 9(4) = 36$\)

Therefore, there are 16 tables and 36 chairs left in the restaurant.

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You can find the slope of the secant line PQ for other values of x by substituting them into the expression for the slope:

For x = 2:

slope = -1 / (3 - 2(2))

slope = -1 / (3 - 4)

slope = -1 / (-1)

slope = 1

To find the slope of the secant line PQ, we need two points on the line: P(x, 4) and Q(3 - x, 3).

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

slope = (y2 - y1) / (x2 - x1)

In this case, the coordinates of P are (x, 4) and the coordinates of Q are (3 - x, 3). Plugging these values into the slope formula, we have:

slope = (3 - 4) / (3 - x - x)

slope = -1 / (3 - 2x)

To find the slope of the secant line for different values of x, we substitute those values into the expression for the slope.

For example, if x = 1, the slope of the secant line PQ is:

slope = -1 / (3 - 2(1))

slope = -1 / (3 - 2)

slope = -1 / 1

slope = -1

Similarly, you can find the slope of the secant line PQ for other values of x by substituting them into the expression for the slope:

For x = 2:

slope = -1 / (3 - 2(2))

slope = -1 / (3 - 4)

slope = -1 / (-1)

slope = 1

And so on, you can calculate the slope of the secant line for different values of x.

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He can invite 7 friends.Because he had $40. He will spent for each person $5.25.

In mathematics, a relationship between two expression that are not equal to each other is called inequality.The word inequality mean not being equal ,especially in status, rights and opportunities.

A statement is a declarative statement that is true or false but both not.A statement is also called proposition.It may contain symbols and  words.

he has total money = $40

 cost of burger        =$4.50

 cost of soda           =$0.75

 Let, he will spend for each person

 4.50+0.75=$5.25

so, he can invite=40/5.25

                          =7.619

he can invite 7 friends.

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We observed Function h(x) is greater than function g(x) for all values of x.

A mathematical expression represents the relationship between independent variables and dependent variables.

when we plot the domain and ranges of a function in the XY coordinate, we get a collection of points. In the next, we join the coordinate to obtain  

line, curves and so on based on the expression of function.

From the graph given in question, we observed that h(x) is greater than g(x) because the domain and ranges of h(x) is greater than g(x).

If we compare for each value of x, we observe that h(x) is always bigger than g(x)

hence, function h(x) is > function g(x) for any values of x

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Answer:

S(A) = 7

Step-by-step explanation:

A ⊆B  means A is a proper subset of B. That means all elements of set A are also elements of set B

S(B\A) means the set of all elements of B that are not in set A. This is given as 28

We are also given S(B)  = 5.S(A)

Since A is a subset of B, S(B) = set of all elements in A and set of all elements in B but not in A

In other words
S(B) = S(A) + S(B\A)

Since S(B) = 5S(A) we get

5S(A) = S(A) + S(B\A)

5S(A) = S(A) + 28

5S(A) - S(A) = 28

4S(A) = 28

S(A) = 7

The answer to fill in the blank is

Mixed Number.

For the reason of:

Each of the numbers 3.25, 26.82 and 125.12 can be written as 3 1/4, 26 41/50 and 125 3/25.

Answer:

See pic below.

Step-by-step explanation:

Draw a triangle in the graph and use the Pythagorean theorem.

So for example we have

1/2 divided by 1/6

What we will do it’s

Leave the first one As it is

Turn the second fraction (the one you want to divide by) upside down

The change the divide to multiply

Multiply the first fraction by that reciprocal

Simplify the fraction (if needed)

So it’s will be like this

1/2 x 6/1 = 6/2

Simplify it

6/2 =3

I hope it’s will help u ✨

Answer:

1/6 chance

Step-by-step explanation:

there are six sides of a dice with only one side being 2. that means there's a one in six chance that a roll of the dice will give the cube landing on a 2

Answer:

x = - \(\frac{3}{2}\), x = 1

Step-by-step explanation:

Given

2x² + x - 1 = 2 ( subtract 2 from both sides )

2x² + x - 3 = 0 ← in standard form

(2x + 3)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = - \(\frac{3}{2}\)

x - 1 = 0 ⇒ x = 1

Answer:

x= -3/2 or 1

Step-by-step explanation:

2x^2 +x-1=2

2x^2 +x-3=0

(2x+3)(x-1)=0

2x+3=0   x-1=0

2x= -3     x=1

x= -3/2    x=1

The value of x in the angles of Quadrilateral is 52 degree.

According to the statement

we have given a four angles and we have to  find the value of x in these give angles.

From given 4 angles it is clear that the these angles are of a quadrilateral.

And we know that the

A quadrilateral is a four-sided polygon, having four edges and four corners.

And the sum of all angles of a quadrilateral is 360 degree.

so,

50° + 3X + X + (X+110) = 360 degree

50° + 4X + (X+110) = 360 degree​

50° + 5X + 110 = 360 degree

160° + 5X  = 360

5X = 360-100

5X = 260

X = 52 degree.

So, The value of x in the angles of Quadrilateral is 52 degree.

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The solution for the given system of linear equations is a ≈ -1.13, b ≈ -4.01, c ≈ 2.75, d ≈ 9.22, and e ≈ -6.09.


1. Write the given equations in matrix form (A * X = B), where A is the matrix of coefficients, X is the matrix of variables (a, b, c, d, e), and B is the matrix of constants (57.1, 27.6, -81.2, -22.2, -12.2).

2. To solve using inverse method, first, find the inverse of matrix A (A_inv). Use any tool or method for matrix inversion, such as Gaussian elimination or Cramer's rule.

3. Multiply A_inv with matrix B (A_inv * B) to obtain the matrix X, which contains the solutions for a, b, c, d, and e.

4. For the left division method, you can use MATLAB or Octave software. Use the command "X = A \ B" to obtain the matrix X, which contains the solutions for a, b, c, d, and e.

After performing the calculations, the approximate solutions are a ≈ -1.13, b ≈ -4.01, c ≈ 2.75, d ≈ 9.22, and e ≈ -6.09.

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Answer:

I am confused on the way you worded you question so I got 41977 which is neither of those responses

Step-by-step explanation:

Given that x = 7.7 m and = 25° the value of  AB is given as 3.254

We have the following data to work with

x = 7.7 m and = 25°,

then we have sin 25 = ∅ = 25 degrees

sin 25 = ab / 7.7

cross multiply from here

AB = sin25 x 7.7

= 0.4226 x 7.7

= 3.254

Hence we would say that in the triangle if x = 7.7 m and = 25°, the value of AB would be solved to be 3.254

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The length of the rectangular painting is equal to 76 cm.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.

The area of a rectangular painting is 4636 cm². The width of the painting is equal to 61 cm.

The length of the painting is calculated as,

Area of rectangle = Length x Width

4636 = Length x 61

Length = 4636 / 61

Length = 76 cm

The length is 76 cm for the rectangle.

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The remainder of the polynomial using the remainder theorem and factor theorem is 6.

Apply the remainder theorem,

When we divide a polynomial

f(x) by (x − c)

f(x) = (x − c)q(x) + r

f(c) = 0 + r

Here,

f(x)=(x−c)q(x)+rf(c)=0+r

and (x−c) is (x−(−2))

Therefore,

f(−2) = \((-2)^{4} - (-2)^3 - 3(-2)^2 + 4(-2) + 2\)

= 16 + 8 − 12 − 8 + 2

= 6

Hence, the remainder of the polynomial using the remainder theorem is 6.

Whereas using the factor theorem and doing synthetic division, we get,  

x = -2 is a zero of f(x), and x+2 is a factor of f(x). To factor f(x), we divide

the coefficients of the polynomial as follows -

         -2   |   1  -1    -3     4      2

                      -2   6    -6      4

        -----------------------------------------

                    1   -3   3    -2     6

Hence, we get that 6 is the remainder when (\(x^4-x^3-3x^2+4x+2\)) ÷ (x+2), using the factor theorem.

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The complete question is -

Find the remainder using the Remainder Theorem and Factor Theorem using the synthetic division of the given polynomial, \(x^4-x^3-3x^2+4x+2\) ÷ (x+2)

The wide is the gym in the drawing is 5

In the given statement is

Cassie measured the middle school and made a scale drawing. The scale of the drawing was 1 inch : 9 feet. the actual width of the gym is 45 feet.

To find how wide is the gym in the drawing

Now, According to the question

and, Based on the given conditions

=45 x1/9

=45/9

=5

Thus, The wide is the gym in the drawing is 5

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Let "x" represent the number of months

Firness Club A charges $28 to join and then $18 each month, you can express the total cost as an equation:

Fitness Club B cherges $35 to join and $11 each month, you can express the total cost as an equation:

You need to know the amount of month needed for both clubs to cost the same:

From the equation determined you can calculate the value of x:

After one month the total cost of each club will be the same.