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The sequence 7, 5, 2, 1, then the

( i ) . The general term d = 2

( ii ) . The next three terms are, [tex]a_{5} =3 ,a_{6} = 5 ,a_{7} = 7[/tex]

( iii ) . The 25th term [tex]a_{25}[/tex] = 55

The sequence is,

⇒ 7, 5, 2, 1

[tex]a_{1} ,a_{n+1} ,a_{n+2} ,a_{n+3} = 7 , 5 , 2 , 1[/tex]

( i ) . The general term,

Let us assume general term = d

We can use this formula,

d = [tex]a_{n+1} -a_{n}[/tex]

where,

[tex]a_{n+1} = 5\\a_{n} = 7[/tex]

d = 7 - 5

d = 2

So,

The general term d = 2

( ii ) . The next three terms, [tex]a_{5} ,a_{6} ,a_{7}[/tex]

We can use this formula,

[tex]a_{n+1} =a_{n} +d[/tex]

[tex]a_{5} =a_{4} +d ;\\a_{6} = a_{5} +d ;\\a_{7} = a_{6} +d[/tex]

[tex]a_{5} = 1+2\\a_{5} = 3[/tex]

[tex]a_{6} = 3+2\\a_{6} = 5[/tex]

[tex]a_{7} = 5+2\\a_{7} = 7[/tex]

So,

The next three terms are, [tex]a_{5} =3 ,a_{6} = 5 ,a_{7} = 7[/tex]

( iii ) .  The 25th term

We can find nth term,

We can use this formula,

[tex]a_{n} =a_{1} +(n-1)d[/tex]

[tex]a_{n} = 7+(n-1)2[/tex]

[tex]a_{n} =7+2n-2\\a_{n} = 2n+5[/tex]

Then, 25th term is,

We can substitute n = 25

[tex]a_{25} = 2(25)+5\\a_{25} =50 + 5\\a_{25} = 55[/tex]

So,

The 25th term [tex]a_{25}[/tex] = 55

Therefore,

( i ) . The general term d = 2

( ii ) . The next three terms are, [tex]a_{5} =3 ,a_{6} = 5 ,a_{7} = 7[/tex]

( iii ) . The 25th term [tex]a_{25}[/tex] = 55

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Using  division we can infer that 50 pages will not be enough.

Division is one of the four basic arithmetic operations, or the process by which two numbers are added together to produce a new number.

Timmy has 810 stamps.

Now each page can hold 16 stamps and he has 50 pages.

Now we will divide 810 by 16 to calculate the number of pages required to put all the stamps.

∴ 810 ÷ 16 = 50 remainder 10.

Therefore after completing the 50 pages there are 10 stamps left.

Hence from division we can infer that 50 pages will not be enough.

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Disclaimer : the complete question is :

Timmy has 810 stamps. He wants to organize them on pages that hold 16 stamps each. He has 50 pages. Does Timmy have enough pages to organize all his​ stamps?

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The sum of 2 numbers is 96, this can be expressed as

The larger number is 9 less than 4 times the smaller, this can be expressed as

Now, we replace the second equation in the first one

We use this number to find x.

Answer:

G.) 4

Step-by-step explanation:

If you get two packs of strawberries for $10, with another $10 you could get another two packs. 2+2=4, and 10+10=20. So you could get 4 packs with with $20.

hypotenuse = 16

perpendicular = 13

base= ?

By using pythogoras theroem :

H² = P² + B²

16² = 13² + B²

256 = 169 + B²

B² = 256 -169

=87

B² = 87

B = √87

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Answer: The correct answer is D - square root of 87

Step-by-step explanation: I took the test and I got it right.

Have a good day/night :)

Answer:

a = 50

50*2=100

Step-by-step explanation:

A cucumber seed needs to be planted 1 inch deep for optimal growth. the plant grows an average of 3 inches every 2 weeks. then the slope in the situation is 2

How do you find the slope of a line?

We need to find the ratio of the difference between the y-coordinates and x-coordinates of the two points, that form the line. The resulted value is the slope of the line. It shows the rise of the line along the y-axis over the run along x-axis.

since seed planted 1 inch deep then y1 = -1 and initial x1 =0

the plant grow an average of 3 inches every 2 weeks then y2 =3 and x2=2

putting in the formula

slope= y2 -y1 /x2 -x1

       = 3-(-1)/2-0

      = 4/2

      =2

thus the slope in this situation is 2

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Answer:

Step-by-step explanation:

4/15

Based on the concept of fraction, 80p is equivalent to 4p/15p as a fraction of £3.

Fraction is a term that is used to describe the portion or part of the whole thing.

Generally, the term fraction represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator.

In this case, to find the fraction of 80p as a fraction of £3, we divide 80p by £3.

Since there are 100 pence in 1 pound the fraction can be expressed as 80p/£3.

To simplify the fraction divide both the numerator and the denominator by 10:

80p/£3 = 8p/30p

Simplifying further both the numerator and the denominator can be divided by 2:

8p/30p = 4p/15p

Therefore, in this case, it is concluded that 80p is equivalent to 4p/15p as a fraction of £3.

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The solution of the given inequality is:

x ≥ 1.

And the graph on the number line can be seen in the image at the end.

The inequality we want to solve and graph is:

-6x + 5 ≤-1

To solve this, we need to start by isolating the variable x in one of the sides, we will get:

-6x + 5 ≤-1

-6x ≤-1 - 5

-6x ≤ -6

Now we can divide both sides by -6 to get:

x ≥ 1.

Then the graph will be like the one below. You need to have a closed dot on x = 1 (because that is a solution to the inequality) and then shade all the region to the right of x = 1, because x also can be larger than 1.

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The value of 7.2 × 10^-4 divided by 3 × 10^-3 when expressed in scientific notation is 2.4 × 10^-7.

It should be noted that scientific notation is simply used to illustrate the numbers that are either too large or too small. It is denoted as a × 10ⁿ.

It should be noted that the exponents will be added. Therefore, 7.2 × 10^-4 divided by 3 × 10^-3 will be:

= 7.2 × 10^-4 / 3 × 10^-3

= 2.4 × 10^-7.

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The inequality that represents the number of minutes of calls made in the United States and in France, can be presented as follows:

An inequality expresses the relationship between two or more values that are not equal.

The value of the calling card = $25

The cost of calls made in the United States = $0.10

Cost of calls made in France = $0.25

The number of minutes that can be used for calls in the U.S. = x

The number of minutes that can be used for making calls in France = y

The duration of calls that can be made in the United states is therefore:

[tex]x_{max} = \dfrac{\$25}{\$0.10} = 250[/tex]

The inequality that represents the number of calls that can be made in the United States is therefore: 0 ≤ x ≤ 250

The duration of calls that can be made in France with the $25 calling card is therefore: [tex]y_{max}=\dfrac{\$25}{\$0.25} = 100[/tex]

The inequality that represents the number of minutes the calling card can be used in making calls in France is: 0 ≤ y ≤ 100

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if I am correct that is the solution.

Based on the number of movies, $12.75 is the constant of proportionality per movie

The given parameters are

Number of the movie tickets = 6

Cost of the movie tickets = 76.50

The constant of proportionality of the movie tickets is calculated as

Constant of proportionality = Cost of the movie tickets/Number of the movie tickets

Substitute the known values in the above equation

So, we have

Constant of proportionality = 76.50/6

Evaluate the quotient

So, we have

Constant of proportionality = 12.75

Hence, the constant of proportionality per movie is $12.75

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Answer:

Step-by-step explanation:

$12.75

Answer:

11 hours

Step-by-step explanation:

let x represent the hours worked

26(x) + 80 = 366

26(x)=366-80

26(x)=286

x=11

.˙. the plumber worked 11 hours

Answe(0.5x²-180x+25,885= 47,925.25

Step-by-step explanation:

x=1

Answer:

circle is 22

Triangle is 34

Step-by-step explanation:

22 + 22 + 22 = 66

22 + 34 + 34 = 90  

Take 90 - 22 = 68

Divide 68 by 2 to get 34

Answer:

7 inches

Step-by-step explanation:

π * 3^2 *7  =  197.920337

The value of 5y in terms of x in the equation is 5y = 15x

The equation is given as y = 3x

Therefore, we are ask to find 5y in terms of x.

This simply means we have to make 5y the subject of the formula in the equation.

In other words, we have to isolate 5y in terms of x in the equation.

Therefore,

y = 3x

multiply both sides by 5

5 ×  y = 3x × 5

5y = 15x

Therefore,

5y = 15x

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The inequality is (3,∞) < x < 4.

A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to. An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. [1] The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:

The symbol a b indicates that an is smaller than b.

When a > b is used, it indicates that an is bigger than b.

Given Data

x is a number less than 4

x<4

Numbers which are less than 4 are 3 to infinity

So,

The inequality is:

(3,∞) < x < 4

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Answer:

A= 5000 e

A= 39,624.12

Step-by-step explanation:

Answer:

no round to the nearest cant and do no

Answer:

Step-by-step explanation:

I believe I need 2 variables to properly work this out but x=12

3=2x-21

24=2x

12=x

The number of runs that Jack must score will be 90.

It should be noted that the mean score from 8 matches is 45. Therefore, the total score will be:

= 8 × 45

= 360

When the coach says that he must increase the mean to 50 in the next match, the total score will be:

= 50 × 9

= 450

Therefore, the number of points that must be scored will be:

= 450 - 360

= 90

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Zander downloaded a total of 19 Songs and 8 Games.

In the given question, it is stated that Zander's downloads had a combination of 30 games and songs in which he downloaded 8 songs more than games. The equation representing the given situation is g + (8 + g) = 30. Here, g represents Games, and (g+8) represents songs.

Now, to find out the number of games and songs, we need to calculate the value of g by the equation.

=> g + (8 + g) = 30

=> 2g + 8 = 30

=> 2g = 22

=> g = 11

We get value of g = 11, So, downloaded games will be 11 and songs will be 19

Hence, the number of Games and Songs will be 11 and 19 respectively.

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Answer:

Step-by-step explanation:

Let L and W be the length and width of a triangle.

Rectangle perimeter (Px) = 2L + 2W, where x is triangle a or b.

Rectangle A: La = 5Wa  [The length of Rectangle A is 5 inches more than its width.]

Perimeter Rectangle A:  Pa = 2La + 2Wa

Substitute L = 5Wa:  

Pa = 2La + 2Wa

Pa = 5Wa + 2Wa

Pa = 7Wa

Perimeter Rectangle B:  Pb = 17   [The perimeter of Rectangle B is 17]

Pb = 17

Difference between Pa and Pb:  Is it  < 9?

See the attached table.  The perimeters of rectangle A are computed for each of the answer options that define the width.  Length (rectangle A) is 5 inches more than the width.  The perimeter is 2*Length + 2*Width, and shown as Pa.

The perimeter of rectangle b is 17, shown as Pb on the table.  The last column of the table is the absolute value of the difference of Pa and Pb.  If it is less than 9, the cell is green (it is a possible integer value for the width of rectangle A),  Red mean it does not meet the "less than 9" requirement,  One cell has the difference as 9.  The problem states "less than 9," so it does not meet the requirement.

An inequality which best models the situation described above is: D. 52 + 3w ≥ 90.

An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments (symbols):

In order to solve this word problem, we would assign a variable to the number of weeks and then translate the word problem into algebraic equation as follows:

Let w represent the number of weeks.

Translating the word problem into an algebraic equation, we have;

Next, we would combine the above parameters to form an algebraic equation as follows:

52 + 3w ≥ 90

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Complete Question:

Antonina needs to have worked at least 90 volunteer hours to graduate. She has already volunteered with a housing organization over the summer for 52 hours. Antonina needs to tutor after school for 3 hours per week to complete the remainder of her volunteer hours. If www is the number of weeks that Antonina needs to tutor in order to complete her volunteer hours, which of the following inequalities best models the situation described above?

answer choices

A. 52w + 30w ≥ 90

B. 52w + 30w ≤ 90

C. 52 + 3w ≤ 90

D. 52 + 3w ≥ 90

The value of her investment at compound interest after 4 years will be £8934.34.

What is compound interest?

Compound interest is the adding of interest to the principle sum of a loan or deposit, or interest on interest plus interest. It is the outcome of making an investment interest, or adding it to the lent assets, rather than repaying it out or requesting return from the borrower, so that interest is received on the principle sum plus previously accrued interest in the next month. In finance and economics, compound interest is the norm. Compound interest differs from simple interest in that previously accrued interest is not added to the main amount of the current month, resulting in no compounding. The simple annual interest rate is calculated by multiplying the interest amount per period by the number of periods per year.

Given,

Principal (P) = £8000

Rate of interest (r) = 2.8% compound interest p.a.

Time (n) = 4 years

Then, according to compound interest compounded annually,

Amount = P(1+r/100)ⁿ

             = 8000(1+2.8/100)⁴

             = 8000(102.8/100)⁴

             = 8934.34

Hence, the value of her investment at compound interest after 4 years will be £8934.34.

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The slope of a line perpendicular to line E is -(5/3).

Given:

Line E passes through the points (-3, 4) and (2, 7).

Slope of line E =  [tex]\frac{y_{2}-x_{1} }{x_{2}-x_{1} }[/tex]

                         =  [tex]\frac{7-4}{2-(-3)}[/tex]

                         =  [tex]\frac{3}{5}[/tex]

So, the slope of a line perpendicular to line E will be the negative reciprocal of the slope of line E i.e. -(5/3).

Therefore, the slope of a line perpendicular to line E is -(5/3).

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Answer:

-2

Step-by-step explanation:

-2y^2=-2y^2

Answer: C

Step-by-step explanation:

- 5/8k -8 + 2 + 1/3k

-5/8 = -15/24

1/3 = 8/24

-15/24k -8 + 2 + 8/24

-7/24k -6

Answer:

22 hats

Step-by-step explanation:

30÷1 1/3=22.5

The question is implying how many completed hats she can make, and since half a hat is not completed, she can only make 22 completed hats.