The sequence is geometric.

1, 6, 30, 60, . . .

The true statements are,

π is irrational because π is a repeating decimal.

7√ is irrational because 7 is not a perfect square.

7.1234… is irrational because it is a nonterminating, nonrepeating decimal.

7√ is rational because 7 is not a perfect square.

Irrational number are real numbers that cannot be expressed as a ratio of two integers.

Now we have,

→π is irrational because π is a repeating decimal.

Since, the value of π is called as infinite decimal-after the decimal point the digits go on forever and repeating.

Hence π is irrational.

⇒This statement is true.

→√7 is irrational because 7 is not a perfect square.

Since, 7 is a prime number this means 7 is without its pair and is not in the power of 2.

Therefore,√7 is irrational

⇒This statement is true.

→7.1234… is irrational because it is a non terminating, non repeating decimal.

Since,the value of decimal in 7.1234… goes on forever and repeating.

Therefore,7.1234… is irrational.

⇒This statement is true.

→√7 is rational because 7 is not a perfect square.

Since, 7 is a prime number this means 7 is without its pair and is not in the power of 2.

Therefore,√7 is irrational

⇒This statement is true.

→π is irrational because π is not a repeating decimal.

π is irrational because  the value of π is called as infinite decimal-after the decimal point the digits go on forever and repeating.

⇒This statement is false.

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Answer:

A. y = 12x + 50

B. x is the monthly price

C. y is the total amount

D. 5 months

Step-by-step explanation:

110 - 50 = 60

60/12 = 5

The number of years the annuity will last if it pays $300 per year is 18 years.

An annuity is an investment that pays the investor a fixed periodic amount for many years in the future.

The annuity payment may be monthly or yearly, as the case may be.

An online finance calculator can compute the annual payment (annuity).

I/Y (Interest per year) = 7%

PV (Present Value) = $3,000

PMT (Periodic Payment) = $-300

FV (Future Value) = $0

Results:

N = 17.795

Sum of all periodic payments = $-5,338.44

Total Interest $2,338.44

Thus, for an annuity with a present value of $3,000, earning 7% per annum and paying $300 per year will last almost 18 years.

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The present value of an annuity is $3,000 and earns 7% per annum.

Find the number of years the annuity will last if it pays $300 per year.

Answer:

First, we need to find the quadratic function that models the given table. We know that a quadratic function has the form: y = ax^2 + bx + c where a, b, and c are constants to be determined. To find these constants, we need to use the values in the table. When x = -5, y = 0, we get: 0 = a(-5)^2 + b(-5) + c 0 = 25a - 5b + c When x = -3, y = 12, we get: 12 = a(-3)^2 + b(-3) + c 12 = 9a - 3b + c When x = -1, y = 12, we get: 12 = a(-1)^2 + b(-1) + c 12 = a - b

The investor should invest Rs 12,000 in bank deposits, Rs 8,000 in a unit trust, and Rs 10,000 in equity shares.

The investor has a total of Rs 30,000 to invest in bank deposits, equity shares, and unit trusts. According to the given conditions, the investment in equity shares should be 20% of the total investment in bank deposits and unit trusts. Also, the ratio between investment in bank deposits and unit trust should be 3:2.

Let x be the investment in bank deposits, y be the investment in a unit trust, and z be the investment in equity shares. Based on the given conditions, we can create the following system of equations:

x + y + z = 30,000 (total investment)
z = 0.2(x + y) (equity shares condition)
x/y = 3/2 (ratio condition)

Using the inverse matrix method, we can rewrite these equations as a matrix equation:

|1 1 1| |x|   |30,000|
|0.2 0.2 -1| |y| = |0      |
|3/2 -1  0 | |z|   |0      |

To solve this matrix equation, we can compute the inverse of the coefficient matrix and multiply it with the constant matrix:

A = |1 1 1|
    |0.2 0.2 -1|
    |3/2 -1  0 |

A_inv = |2/5 -1/5 -1/5|
          |-3/2 1/2 1/2|
          |5/2 1/2 -3/2|

Multiplying A_inv with the constant matrix, we get:

|x|   |12,000|
|y| = |8,000  |
|z|   |10,000|

So, the investor should invest Rs 12,000 in bank deposits, Rs 8,000 in a unit trust, and Rs 10,000 in equity shares.

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Answer:

vertical angles

Step-by-step explanation:

bc they are across from eachother

The correct answer for the required values is 1825.5, 1,812.5, 165.2, 1,690, 1,935, and 245 respectively.

To find the mean, median, standard deviation, first quartile, third quartile, and interquartile range (IQR) of the full-time equivalent number of students (FTES) at Lake Tahoe Community College for the given years, we can solve it using the following formulas for various aspects:

Mean: μ = (Σx)/n

Median: Middle value of the data set

Standard deviation: σ = sqrt[Σ(x-μ)²/n]

First quartile (Q1): Median of the lower half of the data set

Third quartile (Q3): Median of the upper half of the data set

IQR: Q3 - Q1

Year         FTES

2005-06  1,585

2006-07  1,690

2007-08  1,735

2008-09  1,935

2009-10   2,021

2010-11         1,890

1. μ = (Σx)/n = (1,585 + 1,690 + 1,735 + 1,935 + 2,021 + 1,890)/6 = 1,825.2

Therefore the mean is 1,825.2

2. To find the median, arrange the data in ascending order:

1,585, 1,690, 1,735, 1,890, 1,935, 2,021

Since there are an even number of values, the median is the average of the two middle values, which are 1,812.5 and 1,812.5. So, the median is:

Median = (1,812.5 + 1,812.5)/2 = 1,812.5

3. σ = sqrt[Σ(x-μ)²/n]

= sqrt[((1,585-1,825.2)² + (1,690-1,825.2)² + (1,735-1,825.2)² + (1,935-1,825.2)² + (2,021-1,825.2)² + (1,890-1,825.2)²)/6]

= 165.2

4. To find the first quartile (Q1), find the median of the lower half of the data set, which consists of the values 1,585, 1,690, and 1,735.

Since there are an odd number of values, the median is the middle value, which is 1,690. Therefore, Q1 = 1,690.

5. To find the third quartile (Q3), we need to find the median of the upper half of the data set, which consists of the values 1,890, 1,935, and 2,021.

Since there are an odd number of values, the median is the middle value, which is 1,935. Therefore, Q3 = 1,935

6. IQR = Q3 - Q1

Substituting the calculated values in the equation

IQR = 1935 - 1690

= 245

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Answer:

Rounded to the nearest integer, the test had 18 problems in all.

Step-by-step explanation:

Given that a student missed 10 problems on an English test and received a grade of 44%, if all the problems were of equal value, to determine how many problems were on the test the following calculation must be performed:

100 - 44 = 56

56 = 10

100 = X

100 x 10/56 = X

1,000 / 56 = X

17.85 = X

Thus, rounded to the nearest integer, the test had 18 problems in all.

Answer:

1). The rate of change is 30 songs per week — it represents the number of songs Ivy will download every week. This was found by looking at the slope of the graph.

B). The initial value was 150 songs — it represents the maximum number of songs Ivy can download. It was found by looking at the y-intercept of the graph.

C). y = -30x + 150

Answer:

A

Step-by-step explanation:

First notice that the sing does not have a line under it so its an open circle then the line is pointing to right. Your Welcome

Based on simple interest, the solution to the question is that his friend will ultimately owe Darrel $2,875.

A loan or investment's interest can be calculated using simple interest using the principal, interest rate, and duration of the transaction. Because it just considers the original principal and does not account for any compounded interest, it is known as "simple" interest.

Darrel will be indebted to his friend for the following sum if he lends him $2,500 and receives repayment with 15% simple interest after a year:

Interest = Principal x Rate x Time

Interest = $2,500 x 0.15 x 1

Interest = $375

Thus, the total sum his friend will be required to pay Darrel is:

Total amount = Principal + Interest

Total amount = $2,500 + $375

Total amount = $2,875

Thus, the total amount his friend owes Darrel is $2,875.

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Theoretical Probability of rolling a 2= 1/20

Experimental Probability of rolling a 2 =  1/20

Theoretical probability of rolling a 2:

The theoretical probability of an event is the ratio of the number of favourable outcomes to the total number of possible outcomes. Since there are 8 sides to the cube, the total number of possible outcomes is 8. Since the number 2 appeared 200 times out of 4000 rolls, the number of favorable outcomes is 200. Therefore, the theoretical probability of rolling a 2 is:

Theoretical Probability of rolling a 2 = Number of favourable outcomes / Total number of possible outcomes = 200/4000 = 1/20

Experimental probability of rolling a 2:

The experimental probability of an event is the ratio of the number of times the event occurred to the total number of trials. In this case, the  event is rolling a 2, which occurred 200 times out of 4000 rolls.    

Therefore, the experimental probability of rolling a 2 is:

Experimental Probability of rolling a 2 = Number of times the event occurred / Total number of trials = 200/4000 = 1/20

Comparing theoretical and experimental probability:

If the cube is fair, we would expect the theoretical probability and the experimental probability to be similar. In this case, both probabilities are 1/20, which means that the cube appears to be fair. However, we would need to conduct more trials to be more confident in our conclusion.

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18018

Given:

Number of cans = 14

Number of cans of carrots = 5

Number of cans of beets = 1

Number of cans of corn = 8

When there are n  objects to be arranged in order, out of which  r1 objects are of one kind,  r2 objects are of another and so on, then the number of different arrangement is given as:

\(\frac{n!}{r_{1!*rx_{2 }! }.......r_{n} ! }\)

n=14, r1= 5 ,r2=8

therefore 14!/(5!*8!)

            =18,018

Therefore, the distinct orders in which the cans can be arranged is 18018

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The biconditional for the conditional statement is : Two line intersect each other at right angles . The two lines are perpendicular.

A conditional statements are part of mathematical reasoning, a fundamental ability that enables students to evaluate a given hypothesis without reference to a particular context or meaning.

The truth value for the conditional statement is true as we know that when two lines intersect at 90° then they are said to be perpendicular.

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Answer:

Serena had $32 at the end.

Step-by-step explanation:

They both had x in the beginning.

Bryan donated $258, so now he has

x - 258

Serena donated $234, so now she has

x - 234

Serena now has 4 times as much money as Bryan.

x - 234 = 4(x - 258)

x - 234 = 4x - 1032

-3x = -798

x = 266

They both had $266.

$266 - $234 = $32

Answer: Serena had $32 at the end.

Answer:

I'm pretty sure it's 12.55

Step-by-step explanation:

12.55 because

8 makes the 7 a and that 8 makes the 4 a 5

Answer:

0.5

Step-by-step explanation:

7 / 15.02 US dollars = 0.466045273

Round to the nearest tenth: 0.5

We know that she put a principal of $400, the interest rate is 1.5% each year, and the time is 5 years. Using the simple interest formula, we have

Answer: It's kumon?

Step-by-step explanation:

Answer:

The answer is 61

Answer:

61

Step-by-step explanation:

Answer:

Step-by-step explanation:

inorder to solve the area of the shaded area;°/360ñRsquared

arc length you use ;°/360ñD

Answer:

3592

Step-by-step explanation:

interest

Step-by-step explanation:

I dont no because I cannot try 2 counting like that money

The total surface area of the doghouse is 1452 ft²

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The dog house has many surfaces including the roofs . The total surface area is the sum of all the area of the surfaces.

area of the roof part = 2( 13×11) + 2( 12× 10)×1/2

= 286 + 720

= 1006 ft²

surface area of the building

= 2( lb + lh + bh) -bh

= 2( 10× 11 + 10×8 + 11×8) - 10×11

= 2( 110+80+88)-110

= 2( 278) -110

= 556 -110

= 446ft²

The total surface area = 1006 + 446

= 1452 ft²

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Answer

The equation of the line is

y = a

Explanation

The general form of the equation in point-slope form is

y - y₁ = m (x - x₁)

where

y = y-coordinate of a point on the line.

y₁ = This refers to the y-coordinate of a given point on the line

m = slope of the line.

x = x-coordinate of the point on the line whose y-coordinate is y.

x₁ = x-coordinate of the given point on the line

So, we just need to calculate the slope and use one of the points to calculate this equation of the line

For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as

For this question,

(x₁, y₁) and (x₂, y₂) are (4, a) and (-5, a)

Using (4, a) as the point,

Recall,

y - y₁ = m (x - x₁)

m = 0

(x₁, y₁) = (4, a)

x₁ = 4

y₁ = a

y - y₁ = m (x - x₁)

y - a = 0 (x - 4)

y - a = 0

y = 0 + a

y = a

Hope this Helps!!!

Answer:

I am not certain but it's either the last one or second to last my bet is -4<x<4 but you can try I am not certain tho

The solution to the system of equations is x = 4 and y = 0. In summary, the correct substitution step for the system is: -4x - 6(x - 4) = -16 .C answer is correct

To solve the given system of equations:

1) y = x - 4

2) -4x - 6y = -16

We can use the substitution method to eliminate one variable and solve for the other.

Step 1: Solve the first equation (1) for y in terms of x.

  y = x - 4

Step 2: Substitute the expression for y from equation (1) into equation (2).

  -4x - 6(x - 4) = -16

Step 3: Simplify and solve for x.

  -4x - 6x + 24 = -16

  -10x + 24 = -16

  -10x = -16 - 24

  -10x = -40

  x = -40 / -10

  x = 4

Step 4: Substitute the value of x back into equation (1) to solve for y.

  y = 4 - 4

  y = 0

Therefore, the solution to the system of equations is x = 4 and y = 0.

In summary, the correct substitution step for the system is:

-4x - 6(x - 4) = -16

By substituting the expression for y from equation (1) into equation (2) and simplifying, we obtain the equation -4x - 6y = -16, which can be further solved to find the values of x and y. C answer is correct

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Answer:

Option 3: -2

Step-by-step explanation:

The slope of the graph is negative, and the only option with a negative term for the slope is -2.

So the slope of the graph is -2.

Antonio needs to score at least 111 points in his next game to reach his goal of an average of at least 100 points per game.

What are basic arithmetic operations?

Basic arithmetic operations are fundamental mathematical calculations that involve manipulating numerical values using a set of basic operations.

To find out how many points Antonio needs to score in his next game to reach an average of at least 100 points per game, we can use the following formula:

Total points needed = (number of games + 1) × average score goal - total points scored so far

In this case, Antonio has played 5 games, so the number of games he will have played after his next game is 6. His goal is an average of 100 points per game, so his average score goal is 100. The total points he has scored so far is:

105 + 95 + 97 + 82 + 110 = 489

Substituting these values into the formula, we get:

Total points needed = (6) × (100) - 489

Total points needed = 600 - 489

Total points needed = 111

Hence, Antonio needs to score at least 111 points in his next game to reach his goal of an average of at least 100 points per game.

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Answer:

Both B and C should be correct

Step-by-step explanation:

I'm assuming the x in Expression A is a multiplication symbol. If it is not, please tell me and I will change my answer.

Expression B has the value of 8+4 or 12.

Expression A is 3 times (8+4). You could also say that Expression A is 3 times Expression B.

Since both answer B and C say this, they should both be correct.