Under her cell phone plan, Caroline pays a flat cost of $54.50 per month and $5 per gigabyte. She wants to keep her bill at $74 per month. Write and solve an equation which can be used to determine gg, the number of gigabytes of data Caroline can use while staying within her budget.

My answer to part (a) relates to the explicit formula in an  n  =  n+6  n  a=  n+6  n.

a=  n+6  n

Step-by-step explanation:

n=an−1−5

Step 1: Flip the equation.

an−6=n

Step 2: Add 6 to both sides.

an−6+6=n+6

an=n+6

Step 3: Divide both sides by n.

an  n  =  n+6  n  a=  n+6  n

An arithmetic sequence has the explicit formula a = a + (n - 1)d, and each term of the sequence may be computed without knowing the values of the previous terms. The nth term of an arithmetic, geometric, or harmonic series is usually the explicit formula.

The formal equations for L-functions in mathematics are Riemann's zeta function and links between sums over an L-complex function's number zeroes and sums over prime powers.

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The expanded form of 0.68 is written as 0 x 1 + 6 x 0.1 + 8 x 0.01.

To express decimal numbers in their expanded form simply means writing each number according to its place value. It can be done by multiplying each digit of the decimal by its place value and adding it all together.

Given the decimal 0.68 or sixty eight hundredths in words, first, multiply the digit 0 by its place value, which is 1.

0 x 1

Multiply the digit 6 by its place value, which is 0.1.

6 x 0.1

Multiply the digit 8 by its place value, which is 0.01.

8 x 0.01

Add it all together.

0 x 1 + 6 x 0.1 + 8 x 0.01

Hence, the expanded for of the decimal 0.68 is written as 0 x 1 + 6 x 0.1 + 8 x 0.01.

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The expansion of 6 4 0,409, 210 is given below with the solution.

The division of numbers into groups according to place value, such as ones, tens, hundreds, thousands, ten thousand, and so on, results in the expanded form of the number. The expanded version of the number is the one that is represented by the sum of each digit times its place value.

6 4 0,409, 210 = 6 × 10,00,00,000 + 4 × 100,00,000 + 0 × 10,00,000 + 4 × 100,000 + 0 × 10,000  + 9 × 1000 + 2 × 100 + 1 ×10 + 1 × 0

A number is displayed in expanded form according to the place values of its digits.

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Answer:

x squared

Step-by-step explanation:

x squared and the rest =1

The amount of money after 10 months will be $67.2. The number of months (n) that it takes to have at least $100 will be 2 years or 24 months.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

[tex]\rm A = P \left (1 + r \right ) ^{t}[/tex]

Where A is the amount, P is the initial amount, r is the rate of interest, and t is the number of months.

I keep my savings in a bank account that, at the end of each month, gives me 3% interest on the balance. (If I withdraw my funds before the end of the month, I forfeit the interest I would have accrued.) I opened the account using the $50 I received as a birthday gift.

The amount of money after 10 months will be

A = 50 (1 + 0.03)¹⁰

A = 50(1.03)¹⁰

A = 50 x 1.344

A = $67.2

The number of months (n) that it takes to have at least $100 will be

100 = 50 (1.03)ⁿ

2 = (1.03)ⁿ

n ln 1.03 = ln 2

n = ln 2 / ln 1.03

n = 23.5 ≈ 24 months or 2 years

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Answer:-12

Step-by-step explanation:

6(6-6+ -2)

6(-2)

-12

Answer:

55

Step-by-step explanation:

[tex]\sqrt{3025} =55^2\\\sqrt{55^2}\\\sqrt{55^2}=55\\=55[/tex]

Hope this helps.

The circumference of ®B is 36 units.

A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object.

Now it is given that,

The scale factor from  ®A to ®B = 1/3

⇒Ks = 1/3

∵ Ks = A/B

By comparison we get,

A = 1

and B = 3

Thus, circumference (CA) of ®A = 12

⇒ Since scale factor for A = 1

⇒ 2πr = 12

⇒ r = 6/π

Now, circumference (CB) of ®B = 2πr = 2π* 6/π

⇒ circumference (CB) of ®B = 12

Since scale factor for B = 3

⇒ circumference (CB) of ®B = 3 * 12

⇒ circumference (CB) of ®B = 36 units.

Thus, the circumference of ®B is 36 units.

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Answer:                 x= negative 3

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

-3(-3+3)=0

-3(0)=0

0=0

Answer:

x ≈ 25.73

Step-by-step explanation:

using the tangent ratio in the right triangle

tan25° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{12}{x}[/tex] ( multiply both sides by x )

x × tan25° = 12 ( divide both sides by tan25° )

x = [tex]\frac{12}{tan25}[/tex] ≈ 25.73 ( to 2 dec. places )

The value of the line segment in the right-angle triangle 'x' will be 25.75 units.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The measure of the length 'x' is calculated by the tangent of angle 25°. The tangent of an angle is the ratio of the perpendicular to the base of the right-angle triangle. Then we have

tan 25° = 12 / x

x = 12 / tan 25°

x = 12 / 0.466

x = 25.75 units

The value of the line segment in the right-angle triangle 'x' will be 25.75 units.

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The amounts left after: 1 hour = 642g, 3 hours = 160.6g, 4 hours = 80.3g, as calculated by the formula of radioactive decay.

The formula so used: A = [tex]\frac{-dN}{dt}[/tex]

=> N = A ([tex]e^{-kt}[/tex]), where:

Now,

AS shown in the table (refer to the image attached), for k:

=> 322 = 1284[tex]e^{-2k}[/tex]

=> [tex]\frac{322}{1284}[/tex] = [tex]e^{-2k}[/tex]

=> 0.25 = [tex]e^{-2k}[/tex]

Taking natural logarithm on both sides.

=> ln(0.25) = ln([tex]e^{-2k}[/tex])

=> ln(0.25) = (-2k) ln(e)

As ln (e) = 1,

=> ln (0.25) = -2k

=> -1.386 = -2k

=> k = 0.693

Now, for t = 1 and k = 0.693, in the original formula, we get:

=> N = 1284 ([tex]e^{-0.693(1)}[/tex])

=> N =  1284 (0.5)

=> N = 642

For t = 3 and k = 0.693, in the original formula, we get:

=> N = 1284 ([tex]e^{-0.693(3)}[/tex])

=> N =  1284 (0.125)

=> N = 160.6g

For t = 4 and k = 0.693, in the original formula, we get:

=> N = 1284 ([tex]e^{-0.693(4)}[/tex])

=> N = 1284(0.0625)

=> N  = 80.3g

Thus, The amounts left after: 1 hour = 642g, 3 hours = 160.6g, 4 hours = 80.3g, as calculated by the formula of radioactive decay.

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The 17 th term of each sequence. a₁₈ = -9, d = -11 is [tex]a_{17}[/tex] = -185.

a₁₈ = -9, d = -11 is

[tex]a_{17}[/tex] = -9 + (16)(-11)

[tex]a_{17}[/tex] = -185.

succession: the doing of one thing after another. A list of books is presented in alphabetical order. a succession of sonnets that is continuous or connected. a later event, outcome, or repercussion; something that happens after.

A series of numbers is an ordered list. The three dots signify moving forward in the set pattern. Each digit in the sequence is referred to as a word. The first term in the list is 1, followed by the second by 3, the third by 5, and so on.

Arithmetic sequences, geometric sequences, quadratic sequences, and special sequences are the four primary categories of distinct sequences you need to be familiar with.

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Answer: 0.00390625

Step-by-step explanation:

Answer:

The answer is 1/256 :)

Step-by-step explanation:

This one is actually quite simple! All you need to do is multiply 1/16 by 1/16! 1 x 1 is 1 of course, and 16 x 16 is 256. I've attached an image to help break it down even further. (credit to cymath.com)

Hope this helps!

Answer:

27273763hebvrhejwj27222

The results of the operations between the sets are given as follows:

1. U = {a, d, e, i, l, o, n, p, y}

2. E ∪ I = {d, o, l, e, p, i, n, a, y}.

3. E ∩ I = ∅.

4. J' = {d, a, l, e}

5. I ∪ J = {p, i, n, a, y, o}

6. (J ∩ I) ∪ E = {p,i,n,y,d,o,l,e}

7. E = {p, i, n, a, y}

8. I' ∪ J = {p, i, n, y, d, o, l, e}

9. (E ∪ I) ∩ (I ∪ J) = {p, i, n, a, y, o}

10. (J ∪ I)' = {d, l, e}

The universal set is the set that contains all elements that belong to at least one of the sets E, I and J, hence:

U = {a, d, e, i, l, o, n, p, y}

The union operation between two sets is the set of elements that belong to at least one of the sets.

Hence, in item 2, we have that:

E ∪ I = {d, o, l, e, p, i, n, a, y}

In item 5, we have that:

I ∪ J = {p, i, n, a, y, o}

The negation operation of a set X is the set that contains all elements that belong to the universe U but do not belong to X.

Hence, for item 4, we have that:

J' = {d, a, l, e}

For item 7, we have that:

E = {p, i, n, a, y}

Item 8 involves a negation then a union, hence:

I' = {d,o,l,e}

I' ∪ J = {p, i, n, y, d, o, l, e}

Item 10 involves an union then a negation, just different precedence of 8, hence:

I ∪ J = J ∪ I = {p, i, n, a, y, o}

(J ∪ I)' = {d, l, e}

The union operation between two sets is the set of elements that belong to both of the sets.

Hence, in item 3, we have that:

E ∩ I = ∅ (no element belongs to both sets).

For item 6, we have an intersection then an union, hence:

J ∩ I = {p,i,n,y}

(J ∩ I) ∪ E = {p,i,n,y,d,o,l,e}

For item 9, we have the intersection of two unions, hence:

E ∪ I = {d, o, l, e, p, i, n, a, y}

I ∪ J = {p, i, n, a, y, o}

(E ∪ I) ∩ (I ∪ J) = {p, i, n, a, y, o}

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Answer For Question 2: Associative property. The associative property says that even if you rearrange the parenthesis () the result will still be the same. And that is what is happening in question 2
Answer For Question 3: Commutative property of addition. This is the BEST choice because you will first want to add 3/5 + 2/5. And since the Commutative property says that no matter the order of the addends, you can add what ever you think is the best choice.

Here are some answers. I couldn't really understand Question 1 so i didn't want to give you an incorrect answer. Also are the pictures questions too? Im not too sure but here you go hope this helps you in some way

The equation of the line in point-slope form, which passes through the pair of points located at (7 , 11) and (13 , 17), is y - 11 = (x - 7).

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Getting the slope of the two points: (7 , 11) and (13 , 17).

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

m = (17 - 11)/(13 - 7)

m = 6/6

m = 1

Using the point slope form, plug in the values of the slope and one point to set up the equation.

(y - y1) = m(x - x1)

where m = 1 and (x1 , y1) = (7 , 11)

(y - 11) = 1(x - 7)

y - 11 = (x - 7)

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the reflection of coordinates ( -6, -3 ) on y-axis has coordinates ( 6, -3 ).

The reflection transformation can be with respect to x-axis and y-axis. When a point is reflected about the x-axis, the x-coordinates stay the same and y-coordinates are transformed and written with their opposite signs.

For example, the reflection of the point with coordinates (x, y) across x-axis is (x, -y).

When a point is reflected about the y-axis, the y-coordinates stay the same and the x-coordinates are transformed and written with their opposite signs.

For example, the reflection of the point (x, y) across y-axis is (-x, y).

As we can see that the point with coordinates ( -6, -3 ) lies in the third quadrant and thus the reflection of this point on y-axis lies in fourth quadrant. We know that in fourth quadrant  the x coordinate is positive and y coordinate is negative.  

By changing the signs according to the above rules, we get

from ( -6, -3 ) to  ( 6, -3 ).

Therefore, we can conclude that the reflection of coordinates ( -6, -3 )  on y-axis has coordinates ( 6, -3 ).

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Answer:

Yes

Step-by-step explanation:

We can check using pythagoras theorem, setting a and b equal to the shorter sides.

[tex]51^2+68^2=85^2\\2601+4624=7225\\7225[/tex]

y = -x/2 is the value of y in the equation -10 y=5 x

⇒ -10 y=5 x

⇒ y = -5x/10

⇒ y = -x/2

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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Answer:

x = 2 11/12

Step-by-step explanation:

First of all, on the right you have to combine 15x+3/7x which equals 15 3/7x.

9x + 45 = 15 3/7x

-9x              -9x             Next step is to subtract 9x from both sides.

45 = 15 3/7x

/              /

15 3/7   15 3/7        Third step is to divide 15 3/7 on both sides to leave x          

                              by itself.

35/12 = 2 11/12 = x

x = 2 11/12

The sum of the given finite series is 125

The given finite series is:

           [tex]\sum\limits^{10}_{n=1} {(3n-4)}[/tex]

Use the properties of sum operator:

         [tex]\sum\limits^{10}_{n=1} {(3n-4)}=\sum\limits^{10}_{n=1} {3n}-\sum\limits^{10}_{n=1} {4}[/tex]

Calculate each term on the right side:

[tex]\sum\limits^{10}_{n=1} {4}=4+4+...+4=10\times4=40[/tex]

[tex]\sum\limits^{10}_{n=1} {3n}=3\sum\limits^{10}_{n=1} {n}[/tex]

= 3.(1 + 2 + 3 + ... + 10)

The series in the brackets is an arithmetic series with :

the first term: a(1) = 1

the last term: a(10) = 10

the common difference: d = 2 - 1 = 1

Use the sum formula for arithmetic series:

S(n) = n/2 [a(1) + a(n)]

S(10) = 10/2 [1 + 10]

         =5 . 11 = 55

Therefore,

[tex]\sum\limits^{10}_{n=1} {3n}=3\times{55}=165[/tex]

Combine the sum:

[tex]\sum\limits^{10}_{n=1} {3n}-\sum\limits^{10}_{n=1} {4}=165-40[/tex]

= 125

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I don't know lol ididjdjdj

A normal polyhedron shape is defined as a polyhedron having a symmetry group that acts transitively on the flags. Regular polyhedral are highly symmetrical because they are all edge-transitive, corner-transitive, and face-transitive. Many different equivalent definitions are used in classical contexts. There are many definitions in mathematics defining a regular polyhedron, and is that the faces of a polyhedron are nothing but congruent regular polygons that are constructed in the same way around each vertex of the polyhedron. So the polyhedron having faces/sides that are congruent with regular polygons and the exact number of faces that meet at each vertex is called a regular polyhedron.

Euler's polyhedron formula describes the relationship between the number of vertices, edges, and faces of a three-dimensional polyhedral shape.

V-E+F=2 gives Euler's polyhedron formula.

Where V-corner, E-edge, F-face.

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A sequence is a geometric sequence if all the numbers of a list are found by multiplying the preceding term by the common ratio r of that sequence. Sigma notation can represent the sum of a finite number of terms (although higher mathematics will tell you how it works for infinite numbers as well).

Now the given problem is,

calculate ∑ n=1, 4, 2n

∑n=1 , 4 , 2n

Since the bounds are finite, the number of terms is finite as well, and we just calculate the sum by summing up the terms.

(∑n=1 4 ,2n) = (2+4+8+16) (∑n=1 4, 2n) = (2+4+8+16)

(∑n=1 4 ,2n) = (30) (∑n=1 4, 2n) = (30)

Hence,

∑n=1 4, 2n=30 ∑n=1 4, 2n=30

Answer:

∑n=1 4, 2n=30

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The downloads of the standard version are 1127.25.

So, let the download of the standard version be 'x'.

Then, automatically the download of the high-quality version becomes '3x'.

Now,

Therefore, the downloads of the standard version are 1127.25.

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Samir walked 2 times as many hours as Rex walked.​

A ratio can be defined as the comparison of two or more numbers on the basis of  their sizes in relation to each other.

It also indicates how many times one number contains another.

Given that;

To determine the ratio, we have to divide Samir's walking hours by Rex's working hours

= 10/ 3 ÷ 5/ 3

Take the inverse of the divisor and multiply

= 10/ 3 × 3/ 5

= 2 hours

Thus, Samir walked 2 times as many hours as Rex walked.​

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Answer: 28 miles per hour

Step-by-step explanation:

224 miles / 8 hours=

224/8= 28 miles per hour

The profit of the concession is $350.

So, c - e:

Substitute the values in the expression:

Therefore, the profit of the concession is $350.

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