Vincent and Aidan buy the same number of pens. Vincent buys packs of 6 pens, and Aidan buys boxes of 20 pens. What is the least number of pens each boy can have brought?

More plainly, the sequence is defined recursively by

[tex]a_{n+1} = \begin{cases} 3a_n - 9 & \text{if } a_n \text{ is odd} \\ 2a_n - 7 & \text{if } a_n \text{ is even} \end{cases}[/tex]

and some starting value [tex]a_1[/tex].

We're given that the sequence alternates between two constants, [tex]a[/tex] and [tex]b[/tex], so that [tex]a_1 = a[/tex].

• If [tex]a[/tex] is even, then the second term [tex]b[/tex] must be odd, since

[tex]a_2 = 2a_1 - 7[/tex]

by the given rule, and 2×(even) - (odd) = (odd). So

[tex]a_2 = 2a-7 = b[/tex]

In turn, the third term is even, since we jump back to [tex]a[/tex]. From the given rule,

[tex]a_3 = 3a_2 - 9[/tex]

and so

[tex]3b-9 = 3(2a-7)-9 = a \implies 6a-30=a \implies 5a=30 \implies a=6[/tex]

[tex]3b-9 = 6 \implies 3b = 15 \implies b = 5[/tex]

Then the sum of the two integers is [tex]a+b=\boxed{11}[/tex]

• You end up with the same answer in the case of odd [tex]a[/tex], so I'll omit this part of the solution. (It's almost identical as the even case.)

The value of a₃₃ is 1.

Matrices is a plural form of a matrix, which is a rectangular array or a table where numbers or elements are arranged in rows and columns.

Here,  aₓₙ is the element of matrix in which x represents the number of row and n represents the number of column of element.

So, a₄₃ means element from 4th row and 3rd column.

3rd row  =  [6   7   1   8]

3rd column = [tex]\left[\begin{array}{ccc}8\\6\\1\\3\end{array}\right][/tex]

the common value between them is 1.

Thus, the value of a₃₃ is 1.

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Answer:

6

Step-by-step explanation:

The second rational number equals 2 1/3.

Adding the mixed numbers:

[tex]3 \frac{2}{3} + 2 \frac{1}{3} = 5 \frac{3}{3} = 6 [/tex]

Answer:

shown below

Step-by-step explanation:

a) V = h(pi)r²

let x = height

and c = the constant radius

V1 = 2x(pi)c²

V2 = x(pi)c²

let c = random number, such as 2

let x = 3

2x(pi)4

x(pi)4

pi(4) = 12.57

3 x 12.57 = 37.7

6 x 12.57 = 75.4

We can compare these ans realise that the cylinder with double the height will also have double the volume.

b) SA = h(pi)2c

SA1 = 2x(pi)2c

SA2 = x(pi)2c

let c = 2

let x = 3

2(3)(pi)(2(2))

6(pi)4

24(pi)

3(pi)(2)(2)

3(pi)(4)

12(pi)

I don't need to finish the calulation to see that this is also halved. So the surface area of the one with the double length is twice the surface area of the one with a smaller height.

Comparatively, both the volume and surface area are doubled when the height is doubled.

QED.

Monica win 2 games.

In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)

According to the question,

First we  look from the perspective of one player.

How many games does this person play? 5.

Now, each or the 6 people in the tournament played 5 games,

SO,  

[tex]^{6} C_{2} = \frac{6!}{2! * 4!} = \frac{6*5}{2} = 15[/tex]

Therefore,

We know that there were a total of 15 games played.

This means, there were 15 losses, and more importantly, 15 wins.

Not counting Monica, there were:

4 + 3 + 2 + 2 + 2 = 13 wins.

This leaves,

15 − 13 = 2 wins for Monica.

Hence, 2 games won by monica in a tournament.

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Answer:

n = 7

Explanation:

[tex]\rightarrow \sf 3 + 5(2 + 7n) = 258[/tex]

apply distributive method: a(b + c) = ab + ac

[tex]\rightarrow \sf 3 + 10 + 35n = 258[/tex]

simply add the numbers

[tex]\rightarrow \sf 13 + 35n = 258[/tex]

subtract both sides by 13

[tex]\rightarrow \sf 13-13 + 35n = 258-13[/tex]

simplify the following

[tex]\rightarrow \sf 35n = 245[/tex]

divide both sides by 35

[tex]\rightarrow \sf n = 7[/tex]

Answer:

n = 7

Step-by-step explanation:

1) Subtract 3 from both sides.

5(2 + 7n) = 258 - 3

2) Simplify 258 - 3 to 255.

5(2 + 7n) = 255

3) Divide both sides by 5.

2 + 7n = 255/5

4) Simplify 255/5 to 51.

2 + 7n = 51

5) Subtract 2 from both sides.

7n = 51 - 2

6) Simplify 51 - 2 to 49.

7n = 49

7) Divide both sides by 7.

n = 49/7

8) Simplify 49/7 yo 7.

n = 7

Answer:

The first option.

Explanation:

Since these numbers are given in scientific notation, we must first look at the exponent to determine whether or not it's big or small. Negative exponents are less, so we start with that. Immediately, that eliminates the second and third options as -8 is less than -6 and 3. The last two numbers given in the first and last options, however, both have 3 as the exponent. Now, we look at the number given in front. 2.5 is less than 7, so we know that the first option is in order from least to greatest.

Answer:

something like this

Step-by-step explanation:

you want the line to go as close to as many dots as possible

The conversion of the following units are done below.

Conversion means to convert the same thing into different units.

We know the following unit's conversion.

1 km = 0.62 miles

6 km = 3.72 miles

    1 L = 0.26 gallons

2.5 L = 0.65 gallons

  1 lb = 0.45 kg

90 lb = 40.5 kg

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Answer:

perimeter = 12 z + 3

Explanation:

The perimeter of a shape is the sum of all the sides.

Therefore, we add all the sides' lengths together:

perimeter = (4z - 2)+(3z + 3)+(z + 5)+(4z- 3)

= 12 z + 3

Sue's estimate is best because she throws it more times than Eric. Regarding the probability of Aadi obtaining tails, Statement C is accurate.

The chances of an event occurring are defined by probability. Probability has several uses in games, and in business to create probability-based forecasts.

Ten biased coin throws are made by Eric. He is dealt 3 tails. Sue tosses a coin 50 times. I give her 20 tails.

Aadi will only toss the coin once. Regarding the probability of Aadi obtaining tails.

Sue's estimate is best because she throws it more times than Eric.

Hence option C is correct.

2)

An estimate for the likelihood that Aadi will receive tails using the findings of Eric and Sue. 3/20 will be the fraction of the form a/b.

The probability of the Aadi getting tails;

P(Aadi) = 3 / 360 = 1/120

P(Sue) = 20/50×36 = 1/90

Hence the fraction in the form of a/b willl be 4/3.

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Answer:

vertex: (3,1)

y-intercept = (0,-8)

x-intercept- Smaller=2 Larger=4

Domain= all real numbers, identity, infinite

Range= 1 is greater than or equal to y

axis of symmetry=3

Step-by-step explanation:

Answer:

72

Step-by-step explanation:

yhsvybybyvyyvtvvyyvvt

Answer:

number 9 is the answer for this question

Please, make sure you understand the solution:

We can notice that x + (x - 28) = 90

2x - 28 = 90
2x = 118
x = 59

Now for y:

We can notice that y + 90 + x = 180

y + 90 + 59 = 180
y + 149 = 180
y = 180 - 149

y = 31

Answer:

ttttihbogfpvvovovibjnphgbpvvvohj

Answer:

probability; ( of choosing a yellow marble)

7 yellow marbles + 10 orange marbles = 17 in total

if the no of yellow marbles is 7 therefore = ⁷/10

so that is the probability ⁷/10

Hope this helps

It should be reported as a restricted cash in the long-term section of the company balance sheet.

Note payable  can be defined a the money a company or an organization owes or the money they are expected to payback..

Note payable is classified as long term liabilities. Hence, the cash amount of $100,000 should be reported or recorded in the balance sheet as a restricted cash.

Therefore  the $100,000 is reported as a restricted cash.

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5a. a° = 128°

5b. b° = 1.3°

5c. c° = 341°

5a

a° = 128°

This is because parallel angles are equal and angles a° and 128° are parallel to each other

5b

Angles (4b-10)° and (2b - 2)° are equal.

This is because alternate angles are equal and they are alternate to each other

To find b , equate both angles

4b - 10 = 2b - 2

collect  like terms

4b + 2b = -2 + 10

6b = 8

Make 'b' subject of formula

b = 8/6

b = 1.3°

5c.

c° is at angle at a point.

19° is alternate to the other part of the point

We have, c° + 19° = 360° (angle at a point)

c° + 19° = 360°

Make 'c' subject of formula

c° = 360° - 19°

c° = 341°

Thus, the unknown angles are given as a = 128°, b = 1.3°, c = 341°

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The correct answer is option A which is the value a₃₂ = 7.

A matrix is a specific arrangement of items, particularly numbers. A matrix is a row-and-column mathematical structure. The a_{ij} element in a matrix, such as M, refers to the i-th row and j-th column element.

In the given matrix the value of a₃₂ means that the element of the third row and the second column.

So the value of a₃₂ will be 7. which is present in the third row and the second column.

Therefore the correct answer is option A which is the value a₃₂ = 7.

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Answer:

(-4,-18) and (5,90)

Step-by-step explanation:

I'll assume the first equation is supposed to be y – 10 = 11x + x^2

This is a parabola.  The second equation is a straight line:  

y – 12x = 30

We want to find the points at which these lines intersect.  They will intersect for any (x,y) that

Let's rearrange the second equation to isolate y:

y – 12x = 30

y  = 30 + 12x

Now we can take the this value of y and substitute it into the first equation:

y – 10 = 11x + x^2

(30 + 12x) – 10 = 11x + x^2

20 + 12x = 11x + x^2

0 = x^2 -x -20

We can factor this into (x+4)(x-5)

That means x can be either -4 or 5.

Find the value of y using these values of x in both original equations:

For x = -4

y – 10 = 11x + x^2

y  = 11x + x^2 + 10

y = 11(-4)+(-4)^2 +10

y = -44 + 16 + 10

y = -18    The point both lines meet is at (-4, -18) which was already given in the problem.  

For x = 5

y – 10 = 11x + x^2

y  = 11x + x^2 + 10

y  = 11(5) + (5)^2 + 10

y  = 55 + 25 + 10

y = 90

The second point both lines meet is (5,90).

We should use both solutions in the second equation to verify these values, but I'll graph them, instead.  See the attached graph to prove these points are correct.

Answer:

$15 is the answers

Step-by-step explanation:

please mark me as brainlest

Answer:

$ 35.00   is what you pay     $15.00 off original price

Step-by-step explanation:

30 % discount means you pay 70 %

$ 50 * .70 = $ 35 .00

The true statement is (b) the random variable is x, the possible values are 0 to 3 and the values are numerical

The table is added as an attachment

From the attached image, we have:

Number of girls (x)          P(x)

0                                         0.125

1                                         0.375

2                                         0.375

3                                         0.125

In the above, the random variable is x, while P(x) represents its probabilities.

Also, the possible values are 0 to 3 as shown in the table.

0 to 3 are numerical digits, and the values are numerical

Hence, the true statement is (b)

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Answer:

Linear

Step-by-step explanation:

pretty self explanatory

Answer:

The linear parent function Step-by-step

Step-by-step explanation:

Linear functions are always characterized by a straight line graph with or without an intercept on the vertical or horizontal axis. A linear function usually has an independent variable and a dependent variable.

Hope your having a great day!!

Answer: 3

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

This problem centers on recognizing the relationship between fractions and repeating decimals.

Note the following:

[tex]\frac{1}{3}=0.33333333333333333333333333333333333333333333333...[/tex]  

or more simply [tex]\frac{1}{3}=0.\bar{3}[/tex]

This means that [tex]2\frac{1}{3}=2.\bar{3}[/tex]

Going back to the original expression, [tex]3\frac{2}{3}+2.\bar{3}[/tex]  simplifies to [tex]3\frac{2}{3}+2\frac{1}{3}[/tex]

Next, adding mixed numbers.  For adding mixed numbers, whole number parts and fractional parts can be added separately (this is because of the associative and commutative properties of addition)... because

[tex]3\frac{2}{3}+2\frac{1}{3}[/tex] means the same thing as

[tex](3+\frac{2}{3})+(2+\frac{1}{3})[/tex]

Changing the order, we can write it as

[tex]3+2+\frac{2}{3}+\frac{1}{3}[/tex]

Adding the whole number parts, 3+2 is 5.

Next, adding the fraction parts:

For adding fractions, one must have a common denominator (the bottom part of the fraction must be the same).  Once they are the same, the denominator just sort of "hangs out" until the end without changing, and the numerators (the tops) are added together.

Fortunately, the denominators are already the same.  So, add the numerators, and the denominator will stay as a 3.

[tex]\frac{2}{3}+\frac{1}{3}[/tex]

[tex]\frac{1+2}{3}[/tex]

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

It is important to recognize that any fraction* where the number on the top matches the number on the bottom, the fraction is equivalent to 1.

*(except if the number we're talking about is zero)

So, the fraction parts added together, are equivalent to 1, and the whole number parts added were equal to 5.  Returning to our expression...

[tex]3+2+\frac{2}{3}+\frac{1}{3}[/tex]

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

[tex]5+1[/tex]

[tex]6[/tex]

Answer: The coefficients of binomial expansions are calculated using Pascal's triangle.

The quotient for the given exponential expression (-8a⁸b⁻²)/(10a⁻⁴b⁻¹⁰) is (-4/5)(a¹²b⁸).

Exponents are of the form aˣ, read as "a to the power of x", and signify the product of a multiplied by itself x number of times.

In the question, we are given an exponential expression (-8a⁸b⁻²)/(10a⁻⁴b⁻¹⁰) and are asked to find the quotient of it.

To find the quotient, we will try to simplify the equation using the laws of exponents in the following way:-

(-8a⁸b⁻²)/(10a⁻⁴b⁻¹⁰),

= (-4/5)(a⁽⁸ ⁻ ⁽⁻⁴⁾⁾b⁽⁻² ⁻ ⁽⁻¹⁰⁾⁾) {Using the law of exponent: [tex]\frac{x^{a} }{x^{b} } =x^{(a-b)}[/tex] }

= (-4/5)(a¹²b⁸).

Therefore, the quotient for the given exponential expression (-8a⁸b⁻²)/(10a⁻⁴b⁻¹⁰) is (-4/5)(a¹²b⁸).

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Answer:

This is C

Step-by-step explanation:

The slope is 4, meaning the integers are 4, 8, 12, 16, 20 etc. But then the last point is seen to be 40, meaning the answer is C because it is from 0-40 with a slope of 4.