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Using an arithmetic sequence, it is found that the 35th value of the sequence is given by: [tex]a_{35} = 1[/tex].

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

[tex]a_n = a_1 + (n - 1)d[/tex]

In which [tex]a_1[/tex] is the first term.

Considering that we have the mth term as reference, the nth term is also given as follows:

[tex]a_n = a_m + (n - m)d[/tex]

In this problem, we have that:

[tex]a_{23} = \frac{2}{3}, a_{53} = \frac{3}{2}[/tex].

Hence:

[tex]a_n = a_m + (n - m)d[/tex]

[tex]a_{53} = a_{23} + (53 - 23)d[/tex]

[tex]30d = \frac{3}{2} - \frac{2}{3}[/tex]

[tex]30d = \frac{9 - 4}{6}[/tex]

[tex]30d = \frac{5}{6}[/tex]

[tex]d = \frac{1}{36}[/tex]

Then the 35th term is:

[tex]a_{35} = a_{23} + 12d = \frac{2}{3} + 12\frac{1}{36} = \frac{2}{3} + \frac{1}{3} = 1[/tex]

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If the volume of the popcorn box is 74 cubic inches. Then the length of the popcorn box in inches will be 0.3 inches.

A rectangular prism is a closed solid that has two parallel rectangular bases connected by a rectangle surface.

Gabriel models the volume of a popcorn box as a right rectangular prism and the box can hold 74 cubic inches of popcorn when it is full.

Its width is 3 and 1/2 in and its height is 77 in.

Then the width of the prism will be

[tex]\rm W = 3 + \dfrac{1}{2}\\\\W = \dfrac{7}{2}[/tex]

Then the length of the popcorn box in inches will be

[tex]\rm V \ = LWH\\\\\\74= L \times \dfrac{7}{2} \times 77\\\\\\L\ = 0.2745 \approx 0.3[/tex]

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Answer: the real answer is 3 inches not 0.3.

Step-by-step explanation:

Formula: V=lwh

You are searching for its length, so if width is 3 1/2 then it will convert to 3.5

V=lwh

75=L(3.5)(7)

=3.02040816

L= 3.0

Your welcome :))

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill &\$68000\\ P=\textit{original amount deposited}\\ r=rate\to 3.575\%\to \frac{3.575}{100}\dotfill &0.03575\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &30 \end{cases}[/tex]

[tex]68000=P\left(1+\frac{0.03575}{4}\right)^{4\cdot 30}\implies 68000=P(1.0089375)^{120} \\\\\\ \cfrac{68000}{1.0089375^{120}}=P\implies 23377\approx P[/tex]

Answer: Is (B) 23,377

Step-by-step explanation:

Approximately how much principal would need to be placed into an account earning 3.575% interest compounded quarterly so that it has an accumulated value of $68,000 at the end of 30 years?

a.

$23,706

b.

$23,377

c.

$52,069

d.

$58,944

Please select the best answer from the choices provided

A

( B )

C

D

Answer:

1/6

Step-by-step explanation:

On an unbiased die, the probability of rolling a 3 would be a 1/6 since there are 6 numbers and the chosen outcome is 1/6.

Answer:

3/36 (8.333%)

Step-by-step explanation:

On a two (6 sided) dice roll probability table is

3. 3/36 (8.333%)

4 6/36 (16.667%)

5 10/36 (27.778%)

6 15/36 (41.667%)

Here is the basic salary-to-hourly formula for this method: First, divide the employee’s annual salary by 52 weeks (the number of weeks in a year). Divide the weekly wages by 40 hours.

Regrouping terms in the sum as

x + (-5x + 5x) + (-9x + 9x) + … + (-21x + 21x) - 25x

you can see that all the middle terms cancel and you're left with

x - 25x = -24x

Answer:

B.) 27.5²

Explanation:

This should be the triangle per say:

The Area of a Triangle can be found by using the formula- 1/2 x base x height.

In this case: 1/2 x 11 x 5

This equals 27.5².

Hopefully this may help.

Answer:

i believe its the second

Step-by-step explanation:

so sorry if im wrong

Answer:

A

Step-by-step explanation:

On Monday 4 people signed up plus the 11 who agreed to go the following day

which adds up to 15

For closet

It's a rectangle

Volume

For rolls:-

Cylindrical body

Volume:-

Total rolls:-

Answer:

1372

Step-by-step explanation:

Rectangular closet dimensions:

Modelling the roll of toilet paper as a cylinder with dimensions:

If we sit the rolls of toilet paper in the closet with their circular ends as their bases, then we can calculate the number of rolls that cover the base of the closet by dividing the length (and width) of the closet by the diameter of the toilet roll.

⇒ 36 in ÷ 5 in = 7.2 in

Therefore, we can fit 7 toilet rolls along the length and 7 toilet rolls along the width of the closet, meaning that we can fit 7 × 7 = 49 toilet rolls over the base of the closet.

Now calculate how many toilet rolls we can stack on top of each other.

To do this, divide the height of the closet by the height of the toilet roll:

⇒ 108 in ÷ 3.75 in = 28.8

Therefore, we can stack 28 layers of 49 toilet rolls in the closet.

So the total number of toilet rolls = 28 × 49 = 1372

There are other ways of stacking the toilet rolls in the closet (for example, turning them on their side), however, we cannot calculate the number of rolls the closet fits by simply dividing the volume of the closet space by the volume of a toilet roll, since the toilet rolls are cylinders and so there will always be some space between them.

The difference between a temperate coniferous forest and a taiga forest is a  temperate coniferous forest receive a good amount of rainfall.

Temperate coniferous forest is a terrestrial biome that is found in coastal regions that have warm summers and cool winters. They are also found in montane areas.

A taiga forest is characterised by cold, harsh climate with a low rate of rainfall and snow. They are characterized by coniferous forests.

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[tex]\large \boxed{ \ \sf \dfrac{13}{36} \ }[/tex]

[tex]\rightarrow \sf 10 \dfrac{1}{9} - 9\dfrac{3}{4}[/tex]

[Convert to improper Fractions]

[tex]\rightarrow \sf \dfrac{91}{9} - \dfrac{39}{4}[/tex]

[Make the denominator same]

[tex]\rightarrow \sf \dfrac{4(91)}{36} - \dfrac{9(39)}{36}[/tex]

[Multiply Integers]

[tex]\rightarrow \sf \dfrac{364}{36} - \dfrac{351}{36}[/tex]

[Join both fractions]

[tex]\rightarrow \sf \dfrac{364-351}{36}[/tex]

[Subtract Integers]

[tex]\rightarrow \sf \dfrac{13}{36}[/tex]

Answer:

13/36.

Step-by-step explanation:

First convert to improper fractions:

10 1/9 = (10*9 + 1)/9 = 91/9.

9 3/4 = (9*4 + 3)/4 = 39/4.

Next find the Lowest Common Denominator of 9 and 4.

This is 9*4 = 36.

Now convert both fractions to 36th:

For 91/9 we multiply by 4/4 and for 39/9 we multiply by 9/9

91*4 / 9*4 =  364/36 and 39*9 / 9*4 =  351/36, so we have:

364/36 - 351/36

=  13/36

Answer:

Step-by-this may be done by rearranging the equation. First, we start with the given equation:

0.05*10 = 0.5

In order to form a division equation, we may divide both sides by one of the terms being multiplied on the left-hand side. Let us divide by 10. By doing so, we get:

0.05 * 10 / 10 = 0.5/10

0.05  = 0.5/10ep

explanation:

The cost of pass is $10.5, the cost of burger is $1.75, and the cost of souvenir is $5.25 if the Sharon brought $19.50 to the state fair.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let's suppose the cost of the pass is $x

The souvenir cost 1/2 the cost of the pass, which is x/2

The burger was 1/3 as much as the souvenir, which is (1/3)(x/2) = x/6

x + x/2 + x/6 + 2 = 19.50

x = 21/2

x = $10.5

The cost of pass = $10.5

The cost of burger = $1.75

The cost of souvenir = $5.25

Thus, the cost of pass is $10.5, the cost of burger is $1.75, and the cost of souvenir is $5.25 if the Sharon brought $19.50 to the state fair.

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Using proportions, it is found that your taxable income for this year is given by:

d. $37,735

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, we have that $6,414.95 is 17% of his taxable income, hence it is given by:

T = 6414.95/0.17 = $37,735.

Which means that option D is correct.

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Answer:D

Step-by-step explanation:

bc its D

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

We have to find the probability of not getting odd, whole rolling a 6 sided die ~

Actually dices have 3 odd numbers (1 , 3 , 5) and 3 non - odd numbers (2 , 4 ,6)

When we roll a dice, we may get any of the six numbers, so total possible outcomes are 6

and, The number of Favorable outcomes is 3, i.e non - odd numbers.

[tex] \qquad \sf  \dashrightarrow \: p(not \: odd) = \dfrac{favourable \: outcomes}{total \: \: outcomes} [/tex]

[tex] \qquad \sf  \dashrightarrow \: p(not \: odd) = \dfrac{3}{6} [/tex]

[tex] \qquad \sf  \dashrightarrow \: p(not \: odd) = \dfrac{1}{2} \: \: \: or \: \: \: 0.5[/tex]

Answer:

½

Step-by-step explanation:

Not odd (even) numbers from 1 - 6 = 2, 4, 6

Any of these 3 numbers can come when rolling a cubical 6 - sided dice.

Then,

P (not odd)

= Favourable outcomes / total number of outcomes

= 3/6

= ½

_____

Hope it helps ⚜

The area of a 2D form is the amount of space within its perimeter. The surface area of each polyhedron is 82units², 48units², and 48units², respectively.

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

The surface area of the polyhedrons can be written as,

I Polyhedron

SA = 2[(5×6)+(5×1)+(6×1)] = 2[(30)+(5)+(6)] = 82 units²

II Polyhedron

SA = (4×4)+4(0.5×4×4) = 16+32 = 48 units²

III Polyhedron

SA = (3×3) + 2(0.5×4×3) + (5×3) + (4×3) = 48 units²

Hence, the surface area of each polyhedron is 82units², 48units², and 48units², respectively.

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The total number of workers that earn $75 per day is 48

The average salary is calculated based on reported salaries of respondents. The average salary definition is to add the salaries in the sample together, then divide by the number of respondents.

Given that:

In a group of 60 workers, the average salary is $80 a day per worker.

If some of the workers earn $75 a day and all the rest earn $100 a day.

Let 'x' be the total number of workers that earn $75 per day.

So, the total number of workers that earn $100 per day is (60 - x).

As the average salary of 60 workers is $80.

Then,

[tex]\frac{75x + 100(60-x)}{60} =80[/tex]

or, 75 x + 6000- 100x = 80*68

or, -25x= -1200

       x= 48

So, the total number of workers earn $75 per day is 48.

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Answer:

  66/100 = 0.66

Step-by-step explanation:

You can solve for the question mark value as though it were any other variable, or you can recognize the relationship between the numbers in the proportion.

__

  33/50 = ?/100

  100(33/50) = ? = 66 . . . . . multiply both sides by 100

Then we know ...

  33/50 = 66/100 = 0.66

__

  [tex]\dfrac{33}{50}=\dfrac{\text{?}}{100}\\\\\dfrac{2\cdot33}{2\cdot50}=\dfrac{66}{100}=0.66[/tex]

_____

Additional comment

Both 66/100 and 0.66 are pronounced "sixty-six hundredths".

Answer:

66/100 = 0.66

Step-by-step explanation:

Guy above and my test.

Answer:

-24

Step-by-step explanation:

The common difference (D) is -2. And A1 is -2. so if you just add -2 to the geometric sequence until A12, you would get -24.

The length of the chord RT, PQ, and RS will be 5, 14, and 13. Then the correct option is C.

It is the centre of an equidistant point drawn from the centre. The radius of a circle is the distance between the centre and the circumference.

The graph is given below.

The ratio will remain constant. Then we have

y/10 = 4/8

    y = 5

Then the length of PQ will be

PQ = 4 + 10

PQ = 14

Then the length of RS will be

RS = 5 + 8

RS = 13

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Answer:

[tex]\left( fg\right) \left( x\right) =2x^3\sqrt[3]{x}\\\\\left( \frac{f}{g} \right) \left( x\right) =\frac{2x^{3}}{\sqrt[3]{x} }[/tex]

Step-by-step explanation:

Answer:

See below ~

Step-by-step explanation:

1. The average grade of Brenda :

2. During the second quarter, Brenda scored her lowest grade, which was an 82.