How many kilograms of chocolate will each person get if 4 people share 1-3 of kilograms of chocolate equally

The present value of the sequence of annual payments of Rs 25000 each, the first being made at the end of the 5th year and the last being paid at the end of the 12th year, if money is worth 6% is Rs. 158620.39.

1: We can use the formula to calculate the present value of the annuity:

P = A x [1 - (1+i)^-n] / i

Where

P = Present Value

A = Annuity

i = Interest Raten = Number of payments

2: Calculate the present value of each payment using the formula:

P1 = 25000 / (1.06)⁵

P2 = 25000 / (1.06)⁶

P3 = 25000 / (1.06)⁷

P4 = 25000 / (1.06)⁸

P5 = 25000 / (1.06)⁹

P6 = 25000 / (1.06)¹⁰

P7 = 25000 / (1.06)¹¹

P8 = 25000 / (1.06)¹²

3: Substitute the values into the formula to find the present value:

P = P1 + P2 + P3 + P4 + P5 + P6 + P7 + P8

P = (25000 / (1.06)⁵) + (25000 / (1.06)⁶) + (25000 / (1.06)⁷) + (25000 / (1.06)⁸) + (25000 / (1.06)⁹) + (25000 / (1.06)¹⁰) + (25000 / (1.06)¹¹) + (25000 / (1.06)¹²)

P = 158620.39

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y < -2x + 2, y ≤ 1/2x + 1, y ≥ 4 which is the first option, represents the solution of the inequality graph

The graph shows three sets of equations

y < -2x + 2

y ≤ 1/2x + 1

y ≥ 4

The first equation

y < -2x + 2

This is represented by a dotted line because it does not have the equality sign. The sign represented is called the less than sign. The feature of being a dotted line helps in knowing the line that solves the equation. Also. the solution of the less than sign is below the line.

The slope also points to y = 2 and x = 1

The second equation

y ≤ 1/2x + 1

This is represented by a solid line since it has the equality sign present. This is read as less than or equal to. It has two signs joined together. The solution of the less than sign is below the line.

The third equation

y ≥ 4

This is represented by a solid line since it has the equality sign present. This is read as greater than or equal to. It has two signs joined together. The solution of the greater than sign is above the line

Tracing the descriptions shows that the shaded portion is correct hence the three equations are the in the first option is the correct answer.

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In linear equation, The mathematical sentence that expresses the information above is s / 2 ≤ 17

What is linear equation?

Therefore,

s = the number of students in Mr. Jones's algebra class

Therefore, the mathematical sentence that expresses the information above is as follows;

= s / 2 ≤ 17

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The complete question is -

Mr. Jones's algebra class has too many students in it. If the class were split exactly in half to form 2 new classes, each class would have no more than 17 students in it. If s = the number of students in Mr. Jones's algebra class, which mathematical sentence expresses the information above?

Answer:

The satisfied table of the given function\(y = log_{b} (x)\)

x                    1/8            1/4             1/2              1             2

y                    -3                 -2            -1               0               1

Step-by-step explanation:

Explanation :-

Given logarithmic function \(y = log_{b} (x)\)   if b >1

Given first table

i)

put x = \(\frac{1}{8}\)     given b > 1 so we can choose b = 2

\(y = log_{2} (\frac{1}{8} )\)

\(y = log_{2} (2^{-3} )\)

we will apply logarithmic formula

log x ⁿ = n log (x)

\(y = log_{2} (2^{-3} ) = -3 log_{2} (2) = -3 (1) = -3\)

y = -3

ii)

put x = \(\frac{1}{4}\)     given b > 1 so we can choose b = 2

\(y = log_{2} (\frac{1}{4} )\)

\(y = log_{2} (2^{-2} )\)

we will apply logarithmic formula

log x ⁿ = n log (x)

\(y = log_{2} (2^{-2} ) = -2 log_{2} (2) = -2 (1) = -2\)

y = -2

iii)

put x = \(\frac{1}{2}\)     given b > 1 so we can choose b = 2

\(y = log_{2} (\frac{1}{2} )\)

\(y = log_{2} (2^{-1} )\)

we will apply logarithmic formula

log x ⁿ = n log (x)

\(y = log_{2} (2^{-1} ) = -1 log_{2} (2) = - (1) = -1\)

y = -1

iv)

put x = 1     given b > 1 so we can choose b = 2

\(y = log_{2} (1 )\) = 0

y = 0

v)

put x = \(2\)     given b > 1 so we can choose b = 2

\(y = log_{2} (2 )\)

y = 1

Final answer:-

The satisfied table of the given function

x                    1/8            1/4             1/2              1             2

y                    -3                 -2            -1               0               1

The first option is correct because that table of values represents the graph of a logarithmic function in the form \(y=\log_b x,b>1\).

Given:

The lograrithmic function form is \(y=\log_b x,b>1\).

To find:

The table of values that represents the graph of a logarithmic function in the form \(y=\log_b x,b>1\).

Explanation:

It is given that \(b>1\). Let \(b=2\), then

\(y=\log_2 x\)          ...(i)

Substitute \(x=\dfrac{1}{8}\) in (i), we get

\(y=\log_2 \dfrac{1}{8}\)

\(y=\log_2 \dfrac{1}{2^3}\)

\(y=\log_2 2^{-3}\)

\(y=-3\)

Substitute \(x=\dfrac{1}{4}\) in (i), we get

\(y=\log_2 \dfrac{1}{4}\)

\(y=\log_2 \dfrac{1}{2^2}\)

\(y=\log_2 2^{-2}\)

\(y=-2\)

Substitute \(x=\dfrac{1}{2}\) in (i), we get

\(y=\log_2 \dfrac{1}{2}\)

\(y=\log_2 2^{-1}\)

\(y=-1\)

Substitute \(x=1\) in (i), we get

\(y=\log_2 1\)

\(y=0\)

Substitute \(x=2\) in (i), we get

\(y=\log_2 2\)

\(y=1\)

The table of values is:

\(x\)     \(y\)

\(\dfrac{1}{8}\)     \(-3\)

\(\dfrac{1}{4}\)     \(-2\)

\(\dfrac{1}{2}\)     \(-1\)

\(1\)     \(0\)

\(2\)     \(1\)

Therefore, the first option is correct.

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Answer:

4x+24

Step-by-step explanation:

4*x+4*6

Answer:

I think it's b

Step-by-step explanation:

its at -25 and the arrow is going the way the > points

Answer:

Step-by-step explanation:

e

The number of pages read by Soua in 10 minutes are 26.7 pages.

It is given in the question that Soua can read 8 pages in 3 minutes.

We have to find the number of pages that she will she read in 10 minutes.

We will use the unitary method for this question.

The method by which we find out the value of one unit and further use it to find the value of multiple units is known as the unitary method.

Pages read by Soua in 1 minute = 8/3 pages

Hence, we can write,

Pages read by Soua in 10 minutes = 10*(8/3) = 80/3 pages = 26 and(2/3) pages = 26.667 pages ≈ 26.7 pages.

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Answer:

Step-by-step explanation:

24trhhh

Using linear function to solve this problem, for every 1 gallon of gas, Francisco travelled 27.9 miles

A linear function is a function that represents a straight line on the coordinate plane. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Since y can be replaced with f(x), this function can be written as f(x) = 3x - 2. A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line. where m is slope of the line and b is the y - intercept

We can use the data given in writing out our equation

390.6 = 14x

If 14 gallons = 390.6 miles

 1 gallon = x miles

x = 390.6 / 14

x = 27.9 miles

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(A) The probability that none of the flights are late today is 0.32768. (B) The probability that exactly one of the flights is late today is  0.4096. (C) The probability that all of the flights are late today is 0.00032.

(A) To find the probability that none of the flights are late today, we use the binomial probability formula, which states that the probability of k successes in n trials is given by P(X = k) = nCk * p^k * q^(n-k), where n is the number of trials, p is the probability of success, q is the probability of failure (1 - p), and nCk represents the binomial coefficient. In this case, we have n = 5 (five flights) and p = 0.20 (probability of a flight being late). Since we want none of the flights to be late (k = 0), the formula becomes P(X = 0) = 5C0 * 0.20^0 * 0.80^5 = 0.32768.

(B) To find the probability that exactly one of the flights is late today, we again use the binomial probability formula. Now, k = 1, so P(X = 1) = 5C1 * 0.20^1 * 0.80^4 = 0.4096.

(C) The probability that all of the flights are late today is the probability that each individual flight is late. Since the flights operate independently, we can simply multiply the probabilities together. Therefore, the probability that all five flights are late today is 0.20^5 = 0.00032.

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Answer:

what work sheet

Step-by-step explanation:

there is nothing there to solve its just white how do we solve the problem if we cant see it

The margin of error with a sample size of 1600 will be smaller than the margin of error with a sample size of 100, assuming the same standard deviation and confidence level, meaning that we can be more confident in the accuracy of the estimate with a larger sample size.

Assuming that both samples have the same standard deviation, the margin of error for a 95% confidence interval for estimating a population mean can be calculated as

Margin of Error = z×(standard deviation/sqrt(sample size))

where z is the z-score corresponding to the desired confidence level (in this case, 1.96 for a 95% confidence level).

For a sample size of 100, the margin of error would be

Margin of Error (n=100) = 1.96×(standard deviation/sqrt(100))

For a sample size of 1600, the margin of error would be

Margin of Error (n=1600) = 1.96*(standard deviation/sqrt(1600))

Since the standard deviation is the same for both samples, the only difference between the two margins of error is the sample size. The margin of error is inversely proportional to the square root of the sample size, so as the sample size increases, the margin of error decreases.

In other words, the margin of error with a sample size of 1600 will be smaller than the margin of error with a sample size of 100, assuming the same standard deviation and confidence level. This means that we can be more confident in the accuracy of the estimate with a larger sample size.

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Based on the characteristics of the line and parabola, the correct answer is:

A. \(\(y = \begin{cases} x^2 + 2, & x \leq 1 \\ -x + 2, & x > 1 \end{cases}\)\)

Based on the given information, let's analyze the characteristics of the line and parabola to determine the correct representation:

1. Line: In the context of graphing, a line appears as a straight line that can extend in any direction across the coordinate plane. It can have a positive or negative slope, or be horizontal or vertical.

- The line passes through the points \((1,1), (2,0), (4,-2), and (8,-6).\)

- It extends along the first and fourth quadrants.

- A closed dot is shown at the point (1,1).

2. Parabola: In the context of graphing, a parabola appears as a curved line. It can open upward or downward and can be concave or convex. The vertex of the parabola represents the lowest or highest point on the curve, and the axis of symmetry is a vertical line that passes through the vertex, dividing the parabola into two symmetric halves.

- The parabola passes through the points \((1,3), (-2,6), and (10,-3).\)

- It extends along the first and second quadrants.

- An open dot is shown at the point (1,3).

- The vertex of the parabola lies at (0,2).

Given these characteristics, we can determine the correct representation:

The correct answer is:

A. \(\(y = \begin{cases} x^2 + 2, & x \leq 1 \\ -x + 2, & x > 1 \end{cases}\)\)

Explanation: The equation \(\(y = x^2 + 2\)\) represents the parabola, and the equation \(\(y = -x + 2\)\) represents the line. The closed dot at (1,1) corresponds to the parabola, and the open dot at (1,3) corresponds to the line.

Therefore, the correct answer is A.

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The probability that a randomly chosen bug will be missed by both QA checkers is 2.88%.

To find the probability that a bug is missed by both QA checkers, we need to calculate the probability of event A (bug missed by proofreader X) and event B (bug missed by proofreader Y) occurring simultaneously.

The probability of event A is given as 16%, which can be written as 0.16, and the probability of event B is given as 18%, or 0.18.

Since the checkers work independently, we can multiply the probabilities to find the probability of both events occurring: P(A and B) = P(A) × P(B) = 0.16 × 0.18 = 0.0288.

To express this probability as a percentage, we multiply by 100: 0.0288 × 100 = 2.88%.

Therefore, the probability that a randomly chosen bug will be missed by both QA checkers is 2.88%.

This probability represents the likelihood that a bug will go unnoticed by both QA checkers during the checking process.

It highlights the importance of having multiple QA checkers to increase the chances of identifying and fixing bugs in the software.

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Answer:

33lbs

Step-by-step explanation:

There are 969 methods for the quality control inspector to randomly check 5 smartphones, of which 2 are defective, from the shipment of 21 smartphones.

We can solve this problem using combinations formula, that is a way of counting the number of ways to select k objects from a fixed of n items without regard to order. The range of combinations of k items from a fixed of n objects is given via:

\(C(n, k) = n! / (k! * (n-k)!)\)

in which:

In this situation, we want to pick out 2 defective smartphones out of 2 defective smartphones and 19 non-defective smartphones, and we need to pick out out three non-defective smartphones out of the ultimate 19 non-defective smartphones.

Consequently, the number of approaches to choose 2 defective smartphones and 3 non-Defective smartphones from the set of 21 smartphones is:

\(C(2, 2) * C(19, 3) = 1 * (19! / (3! * 16!)) = 191817 / (321) = 969\)

Therefore, there are 969 methods for quality control.

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A record's key field is the field whose contents make the record unique among all records in a file.

In computer science and database management, a record's key field, also known as a primary key, is a unique identifier that is used to distinguish one record from another in a database. A key field can be a single field or a combination of fields that uniquely identify a record.

For example, in a database of employee records, the social security number or employee ID number may be used as the key field to identify each employee record. This key field must be unique for each record in the database, and it is typically indexed to allow for faster searching and sorting of records.

The key field plays a crucial role in ensuring data integrity and consistency in a database. It is used to enforce data constraints and relationships between tables, and it is often used as a reference by other tables in a database.

In summary, a record's key field is an important component of a database that uniquely identifies each record and allows for efficient management and organization of data.

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Answer:

a = 35

Step-by-step explanation:

\(a^2+b^2=c^2\\a^2+12^2=37^2\\a^2+144=1369\\a^2=1225\\a=35\)

Therefore , it means if an equation have 2 roots , it means it is a quadratic function .

A number's  root is that factor of the number that, when multiplied by itself, yields the original number. Specifically, squares and square roots are exponents. Think of the number nine. This can be expressed as  or as 3 x 3.

Here,

If an equation have 2 roots , it means it is a quadratic function

If D=0, a quadratic function has two roots that are equal.

D (discriminant) = 0

=>b24ac=0 is required for a polynomial function to have equal roots.

Therefore , it means if an equation have 2 roots , it means it is a quadratic function .

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Answer:

(7÷g)\(^{4}\)

Step-by-step explanation:

The quotient is the answer to a division problem.  So the quotient of 7 and g means to divide 7 and g.  Then raise that to the 4th power.

Answer:

it's 11.

Step-by-step explanation:

15(11)= 165. It's also 4 less than 15, which is the length.

The slope of the line c is - 92.

The points via which the line b passes are:

(-20, 4) and (-21, 96).

The slope of the line is given by:

m = (y₂ - y₁) / (x₂ - x₁)

Slope of the line b passing through these points are:

m = (96 - 4) / (- 21 + 20)

m = (92) / (-1)

m = - 92

Since, line b is parallel to line c,

Slope of line b = slope of line c

So, the slope of line c is also:

m' = - 92

Therefore, we get that, the slope of the line c is - 92.

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Answer:

Step-by-step explanation:

C.) P = 3(a+2)-4

The formula which describes the relation between the height of the apple tree and the height of the pine tree p is P=3(a+2)-4, the correct option is C.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

We are given that;

Growth of apple tree= 2feet

Now,

Let's call the original height of the apple tree "h". According to the problem, if the apple tree grew 2 feet and then tripled its height, it would become 4 feet shorter than the pine tree. So we can write:

3(h+2) - 4 = p

Simplifying, we get:

3h + 2 = p

Now we can see that option (D) P=3a+10 is very similar to our expression, but it has a constant term of 10 instead of 2. This constant term does not match the problem statement, which says that the apple tree would be 4 feet shorter than the pine tree, not taller. Therefore, option (D) is not the correct answer.

Option (A) P-4=3a+2 also does not match the problem statement. If we solve for p, we get:

P = 3a + 6

This means that the apple tree would be 6 feet shorter than the pine tree, not 4 feet shorter as stated in the problem.

Option (B) P=2(a+3)+4 also does not match the problem statement. If we solve for p, we get:

P = 2a + 10

This means that the apple tree would be 10 feet shorter than the pine tree, not 4 feet shorter as stated in the problem.

Option (C) P=3(a+2)-4 matches our expression from earlier. If we solve for p, we get:

P = 3a + 2

Therefore, by equation the answer will be P=3(a+2)-4.

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Answer:

b:  irrational

Step-by-step explanation:

  (√5+2)

--------------  is given.

  (√5 - 2)

If we multiply numerator and denominator by (√5+2), we succeed in removing the square root symbol from the denominator:

(√5+2)(√5+2)

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

(√5+2)(√5- 2)

and the denominator becomes 5 - 2, or 3.  The denominator is now rational, but the numerator still involves the square root symbol, so overall the given number is irrational.

Answer:

c

Step-by-step explanation:

Temperament is to do with the personality of someone.

Thus the dog's temperament would relate to its physical and mental character.

c

Temperament is to do with the personality of someone.

Thus the dog's temperament would relate to its physical and mental character.

Answer:

x = 24

Step-by-step explanation:

if a and b are parallel then

62 and 5x - 2 are same- side interior angles and sum to 180° , that is

5x - 2 + 62 = 180

5x + 60 = 180 ( subtract 60 from both sides )

5x = 120 ( divide both sides by 5 )

x = 24

thus for a to be parallel to b , then x = 24