"Negative one times the sum of one and seven times a number,
decreased by 6 times the difference of negative seven and a
number, equals thirty-six."

A) The variable is n, which represents the number of the figure in the pattern.

B) Here is a table for up to 8-figure patterns:

Figure Number of Cheerios

1                      1

2                      3

3                      6

4                     10

5                     15

6                     21

7                    28

8                    36

C) The equation to represent the nth term of the sequence is n(n+1)/2.

D) If the pattern continues, the figure number that will have 20 whole Cheerios in it is 12.

E) It is not reasonable to think this pattern would continue forever. The number of Cheerios in each figure is increasing by 2 each time. This means that the number of Cheerios in the figure will eventually exceed the number of Cheerios in a box.

F) Based on the information provided, the largest figure number we can have using a full box of Cheerios is 107. This is because there are 108 Cheerios in a box, and the number of Cheerios in each figure is increasing by 2 each time.

Here is a more detailed explanation of how to answer each question:

A) Identify and label the variable

The variable is n, which represents the number of the figure in the pattern. For example, the first figure is figure 1, the second figure is figure 2, and so on.

B) Make a table for up to 8-figure patterns

Here is a table for up to 8-figure patterns:

Figure Number of Cheerios

1                        1

2                        3

3                        6

4                        10

5                        15

6                        21

7                        28

8                        36

C) Write an equation to represent the nth term of the sequence

The equation to represent the nth term of the sequence is n(n+1)/2. This equation can be derived by looking at the table of values. For example, the number of Cheerios in the first figure is 1, which is equal to 1(1+1)/2. The number of Cheerios in the second figure is 3, which is equal to 2(2+1)/2. And so on.

D) If the pattern continues, what figure number will have 20 whole Cheerios in it?

If the pattern continues, the figure number that will have 20 whole Cheerios in it is 12. This can be found by solving the equation n(n+1)/2 = 20. The solution is n = 12.

E) Is it reasonable to think this pattern would continue forever? If not, explain.

It is not reasonable to think this pattern would continue forever. The number of Cheerios in each figure is increasing by 2 each time. This means that the number of Cheerios in the figure will eventually exceed the number of Cheerios in a box.

F) Based on the information provided, what is the largest figure number we can have using a full box of Cheerios?

Based on the information provided, the largest figure number we can have using a full box of Cheerios is 107. This is because there are 108 Cheerios in a box, and the number of Cheerios in each figure is increasing by 2 each time.

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Answer:

im not sure if your doing it by 38 dividend by 23 but i got 1.652174.......idk really im doing the same question lol.

Step-by-step explanation:

Using a piece-wise function, the constraints are:

\(65x, x < 7\)

\(375 + 55x, x \geq 7\)

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

A piece-wise function is a function that has multiple definitions, depending on the value of the input.

In this problem:

Less than 7 days the rental price is $65 per day.

Thus, one constraint is:

\(65x, x < 7\)

Once a tenant stays  seven or more days, the price is $375 plus $55 per day past seven.

Thus, the other constraint is:

\(375 + 55x, x \geq 7\)

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Answer: a and d

Step-by-step explanation:

its easy. U can just solve the problem

Answer:

\(281\)

Explanation:

\(-3n+296\)

\(-3(5)+296\)

\(-15+296\)

Answer:

281

Step-by-step explanation:

Answer:

-3/2

Step-by-step explanation:

Take two points from the table and use the slope formula

m= (y2-y1)/(x2-x1)

   = ( 19 - 13)/ ( -4 - 0)

   = 6/-4

   = -3/2

45 people used credit card on that particular day , this could be found out using simplified multiplication.

What is proportion?

A quantitative relation is an ordered try of numbers a and b, written a / b wherever b doesn't equal zero.

A proportion is Associate in Nursing equation within which 2 ratios ar set up to one another.

Main body:

We have been given that during one particular sales day, 75% of the store's customers paid with credit cards. There were 60 customers that day.

To find the number of people, who used credit card, we will find 75% of 60.

The number of people who used credit card = (75 / 100 )* 60

The number of people who used credit card = 0.75 *60

The number of people who used credit card = 45

Therefore, 45 people used credit card on that particular day.

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Answer:

12.5

Step-by-step explanation:

\(400km = 10hr \\ 500km = x \\ \\ 400kmx = 5000kmhr \\ x = 12.5hr\)

Answer: The answer is 12.5

Step-by-step explanation:

I did the math on my paper.

Answer:

Both options (15 and 19) are possible length of the third side.

Explanation:

Given a triangle with one side that measures 1 foot and another side that measures 24 inches.

The measure of the third side must be greater than the difference between the two sides given and less than the sum of the two given sides.

The length of the third side could be any number greater than 12 but less than 36.

From the two given options. Both of the options (15 and 19) falls within the interval.

Therefore, both options (15 and 19) are possible length of the third side.

Answer:

112.5

67.5

Step-by-step explanation:

We know the ratio is:

5:3

So, we can write it as:

5x+3x=180, with 5x being one angle, and 3x being the other

combine like terms

8x=180

divide both sides by 8

x=22.5

5(22.5)=112.5

3(22.5)=67.5

So, one angle is 112.5 and the other is 67.5.

Hope this helps!

Answer:

-3

Step-by-step explanation:

divide top by bottom

-18 / -6 = -3

which makes -18/6 have a whole number of -3

<3 Enjoy,

    Dea

Awnser

-3

Step-by-step explanation:

because if you simplify -18/6 you get 3

Part A: Fraction of all students who does not like Lakers = 3/8.

Part B: Fraction of all student who likes the Clippers = 9/32

Part C: Fraction of all student who does not likes the Clippers =  23/32.

Part D: Fraction of all student who does not likes either the Clippers or Lakers : 35/32

The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection.

Given data:

Students who likes only Los Angeles Lakers = 5/8

Students who does not likes only Los Angeles Lakers: 1 - 5/8 = 3/8

From 3/8, only 3/4 like the Los Angeles Clippers.

= 3/8 * 3/4

= 9/32

Now,

Students who does not like the Los Angeles Clippers: 1 - 9/32 = 23/32.

Part A: Fraction of all students who does not like Lakers = 3/8

Part B: Fraction of all student who likes the Clippers = 9/32

Part C: Fraction of all student who does not likes the Clippers =  23/32.

Part D: Fraction of all student who does not likes either the Clippers or Lakers :

= 3/8 + 23/32

= 35/32

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Answer:

\(x^2 - 6x + 10\) or in general: \(a(x^2 - 6x + 10)\) where "a" is any constant real number except zero.  

Step-by-step explanation:

If we're given a complex root of a polynomial to be: \((a+bi)\text{ or }(a-bi)\), then we know that its conjugate is also a root of the polynomial: \((a-bi)\text{ or }(a+bi)\).

So since we're given the root: \((3+i)\), then we know that its conjugate: \((3-i)\) is also a root. Thus we have two roots so far.

The Fundamental Theorem of Algebra simply states that any polynomial, with degree "n", will have "n" roots, which can consist of both real and imaginary solutions.

So let's say I have a polynomial: \(x^6+3x+2=0\), this has 6 roots, according to the Fundamental Theorem of Algebra, since the degree of the polynomial is 6 (remember the degree is simply the variable with the highest degree)

Since we already have two roots, and a quadratic function has a degree of two, we know that these are all the roots the quadratic has, since the Fundamental Theorem of Algebra states that a quadratic will only have 2 roots.

We can generally express any polynomial in factored form, that is: \(a(x-b)(x-c)(x-d)...=y\)

where "b", "c", and "d", and so on... are zeros of the function. This aligns with the behavior of zeros, since if we plug any of them into the function, then one of the factors will become zero, and since zero times anything is zero, well the entire thing is zero.

For example if I plug in "b", which is zero we get: \(a(b-b)(b-c)(b-d)...=y\implies a(0)(b-c)(b-d)=y\implies 0=y\)

this is since plugging in zero, makes the factor: \(x-b\) equal to zero, making the entire thing zero.

One last thing to mention is the "a" value in front which just generally determines the stretch/compression of the polynomial.

So with this information, we can write a polynomial:

\(a(x-(3+i))(x-(3-i))\)

From here let's distribute the negative sign:

\(a(x-3-i)(x-3+i)\)

Now this may look a bit tough to distribute, but you may notice a pattern here, we have a difference of squares. It may not be obvious, but if we make one substitution, let's say: \(u=x-3\), then we get the equation

\(a(u-i)(u+i)\)

The difference of squares is expressed as: \(a^2 - b^2 = (a-b)(a+b)\), so our expression will expand out into:

\(a(u^2 - i^2)\)

The substitution was just to make things a bit more clear, but let's just substitute x-3 back into the equation.

\(a((x-3)^2 - i^2)\)

From here, we know that i^2 is simply -1, since: \(\sqrt{-1} = i, \text{ so }i^2 = -1\)

We can also easily expand out the polynomial using FOIL

\(a((x^2 - 6x + 9) -(-1))\\a(x^2 - 6x + 9 + 1)\\a(x^2 - 6x + 10)\)

You may notice the "a value, and that's just a constant, which determines the stretch/compression of the polynomial, and can be any real number, except for zero since that will make the entire thing zero regardless of what x is. For the sake of simplicity, let's just write this to be 1.

Answer:

4 1/6 hours

Step-by-step explanation:

2 1/2 + 1 2/3 = 25/6 = 4 1/6

Answer

18 and 54

Step-by-step explanation:

Answer:

c) 13%

Step-by-step explanation:

Given information,

→ The cost of a jacket increased from the price $75.00 to $84.75.

Now we have to,

→ find the % increase of cost of jacket.

Let's solve the problem,

→ ((84.75 - 75)/75) × 100

→ (9.75/75) × 100

→ 0.13 × 100

→ 13%

Hence, the answer is 13%.

Answer:

120 mL of 10% HCL will be used.

Step-by-step explanation:

to solve this, we have to generate an equation for the mixture, to get the volume of 10% HCl needed.

Let the volume needed = x

5% of x + (20% of 60ml) = 10% of ( 60 + x) ml of new mixture

0.05x + (0.2 × 60) = 0.1 × (60 + x)

0.05x + 12 = 6 + 0.1x

12 - 6 = 0.1x - 0.05x

6 = 0.05x

x = 6 ÷ 0.05

x = 120

Therefore, 120 mL of 10% HCL will be used.

\(\begin{array}{r|l}576&2\\288&2\\144&2\\72&2\\36&2\\18&2\\9&3\\3&3\\1\end{array}\)

\(576=2^6\cdot3^2\)

Therefore

\(4\sqrt{576}=4\sqrt{2^6\cdot3^2}\)

Answer:

  5.1% increase

Step-by-step explanation:

You want the percentage change in price per load when the price of detergent went from $16.99 for 52 loads to $16.49 for 48 loads.

The percentage change is given by the formula ...

  ((new price)/(old price) -1) × 100%

The price per load is found by dividing the price of the bottle of detergent by the number of loads it will wash.

  old price per load = $16.99/52 ≈ $0.32673

  new price per load = $16.49/48 ≈ $0.34354

Then the percentage change is ...

  (0.34354/0.32673 -1) × 100% ≈ 0.05145 × 100% ≈ 5.1%

The price per load has increased by about 5.1%.

The distance from Maria's desk to Monique's desk is  \(2\sqrt{13}\)

Given,

In the question:

Maria's desk is located at (2, −1), and Monique's desk is located at (−2, 5).

To find the  distance from Maria's desk to Monique's desk.

Now, According to the question:

We know that :

The formula of Distance:

\(\sqrt{(x_{2} -x_{1} )^2+(y_{2}-y_{1} )^2}\)

Substitute (2, -1) and (-2, 5) into distance formula:

\(\sqrt{(-2-2)^2+(5+1)^2}\)

Calculate:

\(\sqrt{(-4)^2+(6)^2}\)

\(\sqrt{16+36}\\ \\\sqrt{52}\)

= \(2\sqrt{13}\)

Hence, The distance from Maria's desk to Monique's desk is  \(2\sqrt{13}\)

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Answer: square root of 52

Step-by-step explanation:

did the practice test

Answer: 16590

Step-by-step explanation:

Let p be the population proportion of high school students in the area who attend their home basketball games.

As per given,

prior p = 0.5

Margin of error E= 0.01

Criticfor z-value for 99% confidence = 2.576

Sample size will be computed as

\(n=p(1-p)(\frac{z^*}{E})^2\\\\ n= 0.5(1-0.5)(\frac{2.576}{0.01})^2\\\\=0.25(257.6)^2\\\\=0.25 (66357.76)\approx16590\)

Hence, required sample size = 16590

The value of the population mean of the data is 80.875.

Mean is defined as the ratio of the sum of the number of data sets to the total number of data. The mean is calculated same as that of the average.

The average is also calculated by the ratio of the sum of all the data points to the number of data.

Given that the 8 random midterms are 71, 80, 65, 85, 90, 77, 92, 87. The mean will be calculated as,

Mean = (  71 +80 + 65 + 85 + 90 + 77 + 92 + 87 ) / 8

Mean = 647 / 8

Mean = 80.875

The population mean is 80.875.

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5/6 Is the greatest, Hope this helps!

Answer:- 5/6

Explaination:-

As we know that In case of the fraction having different denominators but same numerators, the fraction having least denominator is greatest!

Thus, the answer is 5/6.

Answer:

(-3, -5)

Step-by-step explanation:

point of (-3,5)

the transformation R270 o r y=x means we have to do

-first the reflection over the line y = x and

-then rotate that point 270°

General rule reflection over the line y = x : (x, y)→(y, x)

Point (-3,5) reflected over the line y=x: (-3,5) →(5, -3)

General rule rotation 270° : (x, y) →(y, -x)

Point (5, -3) rotated 270° : (-3, -5)

Answer:

The lateral area is 144 ft^2

The Total surface area is 156ft^2

Step-by-step explanation:

:)

Answer:

6, 12, 144, 156

Step-by-step explanation:

The area of each triangular base is:  A = 1/2(b)(h)  A = 1/2(3)(4)  A =  6  ft2

There are two bases, so total base area is  12  ft2.

The lateral area is:  A = (12)(3)  + 12(5) + 12(4)  A =  144  ft2

The total surface area is 156  ft2.

Answer:

There is a 0.1% chance that a sample mean temperature of at most 58 F will occur by chance if the true mean temperature is 62 F.

Step-by-step explanation:

Took the test :)

To solve for x in the equation 4x3 = -5x - 21, we can follow these steps:

1. Move all the terms containing x to one side of the equation, and move the constant term to the other side. We can do this by adding 5x to both sides and then adding 21 to both sides:

   4x3 + 5x = -21

2. Factor out x from the left-hand side of the equation:

   x(4x2 + 5) = -21

3. Divide both sides by (4x2 + 5):

   x = -21 / (4x2 + 5)

So the solution for x is x = -21 / (4x2 + 5). Note that this is a rational function, which means that the value of x depends on the value of the variable x. This equation has no real solutions because the denominator is always positive, and the numerator is negative.

Answer:

ggg

Step-by-step explanation:

gggg

Given,

The equation of table is

Here,

Hence, the output of the table is F, F, F, and T