Rebecca has a monthly plan that charges her $45.50 each month for unlimited talk and text. For each gigabyte of data that she uses, she has to pay an additional $5.25. If the cost of her bill is represented by variable C and the number of gigabytes is represented by the variable g, write an equation that represents this situation.

The items are classified as M1, M2, or neither based on their liquidity and spendability. A line of credit and traveler's checks are neither M1 nor M2 as they are not actual money. Physical currency and money in a checking account are classified as M1, while money in a money market account is classified as M2.

M1 refers to the narrowest definition of the money supply, which includes only the most liquid forms of money that can be easily spent. M2 is a broader measure of the money supply and includes M1 as well as other less liquid forms of money. Neither refers to items that do not fit into either M1 or M2.

a. Your $5,000 line of credit on your Bank of America card is neither in M1 nor M2 as it is not actual money but a credit limit.

b. $50 dollars' worth of traveler's checks you have not used yet is neither in M1 nor M2 as they need to be exchanged for cash before they can be spent.

c. $1 in quarters in your pocket is in M1 as it is physical currency that can be spent.

d. $1200 in your checking account is in M1 as it is a liquid form of money that can be spent.

e. $2000 you have in a money market account is in M2 as it is a less liquid form of money that can be accessed but may have restrictions or penalties for withdrawal.

Answer:

13 pencils.

Step-by-step explanation:

Let x be the pens and y be the pencils

Given:

Brian purchased pens for 75 cents each and pencils for 40 cents each he bought total of 22 writing utensils for $11.95.

Total pens and pencils is 22

So, [tex]x+y=22[/tex]----------------(1)

And he bought all utensils for $11.95. and each pen for 75 cents and pencils for 40 cents.

[tex]0.75x+0.40y=11.95[/tex]------------(2)

solve equation 1 and equation 2 for x and y.

From equation 1.

[tex]x+y=22[/tex]

[tex]y=22-x[/tex]----------------(3)

put y value in equation 2.

[tex]0.75x+0.4(22-x)=11.95[/tex]

[tex]0.75x+0.4\times 22-0.4x=11.95[/tex]

[tex]0.75x+8.8-0.4x=11.95[/tex]

[tex]0.75x-0.4x=11.95-8.8[/tex]

[tex]0.35x=3.15[/tex]

[tex]x=\frac{3.15}{0.35}[/tex]

[tex]x=9[/tex]

Now substitute x value in equation 3.

[tex]y=22-9[/tex]

[tex]y=13[/tex]

So, he buy 13 pencils.

x=-3

9x+2(3x+7)= -31

multiply the "3x" and the "7" by two (distributive property)

[="6x" and "7"]

add the "9x" and the "6x" [="15x"]

subtract "14" from"-31" [= "-45"]

divide "15x" from "-45"

="-3"

put the "-3" in for "x"

multiply 9(-3) [=-27]

multiply 3(-3) [=-9]

distribute the 2 to the "-9" and the "7" [="-18" and "14"]

add the "-18" and "14" [=-4]

add the "-27" and the "-4"

=-31 ✓

9x+2(3x)+2(7)= -31

9x+6x+14= -31

15x+14= -31

-14 -14

15x= -45

/15= /15

x= -3

9x+2(3x+7)= -31

9(-3)+2(3(-3)+7= -31

-27+2(-9+7)= -31

-27+(2(-9)+2(7))= -31

-27+(-18+14)= -31

-27+ (-4)= -31

-31= -31✓

Answer:

G

Step-by-step explanation:

G = -2

-2 is greater than -4, yet, less than 0

Answer:

Step-by-step explanation:

(2/7)^3=8/343

Answer:

(2/7)^3

8/343

Step-by-step explanation:

(2/7)^3=2^3/7^3

=8/343

Answer:

y=3/4x-5

Step-by-step explanation:

3x-4y=20

4y=3x-20

y=3/4x-20/4

y=3/4x-5

Answer:10

Step-by-step explanation:

Adds 7 each time

31 - 3 = 28

Going from first term to fifth term is 4 increases.

28 ÷ 4 = 7

This means we have a common difference of 7.

Sequence is 3, 10, 17, 24, 31

Rahul gets 12 paper clips.

Step-by-step explanation:

Given,

Paper clips Tian have = 56

He gives 3/4 of them to joe.

Joe gets = [tex]\frac{3}{4}*56=\frac{168}{4}[/tex]

Joe gets = 42 paper clips

He given 2/7 of received to Rahul.

Rahul gets = [tex]\frac{2}{7}*42=\frac{84}{7}[/tex]

Rahul gets = 12 paper clips

Rahul gets 12 paper clips.

Keywords: fraction, division

Learn more about fractions at:

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Answer:

1. f(2) = 6

2. Slope, m = [tex]$ \frac{7}{2} $[/tex]

Step-by-step explanation:

Problem 1:

Given f(x) = |3x|

To find f(2), substitute x = 2.

⇒ f(2) = |3(2)|

= |6|

= 6

Problem 2:

The given equation is: 2y = 7x + 8

The general equation of the line is: y = mx + c, where m is the slope of the line.

Therefore, we reduce the given equation to the general form of the line.

Dividing the given equation by 2, we get:

y = [tex]$ \frac{7}{2}x + \frac{8}{2} $[/tex]

[tex]$ \implies y = \frac{7}{2}x + 4 $[/tex]

Thus, slope, m = [tex]$ \frac{7}{2} $[/tex] which is the answer.

Problem 3:

Given with 14 gallons of gas, we can drive 392 miles.

The capacity of the tank if 14 gallons.

If 14 gallons can take us 392 miles, then 1 gallon of gas should take us: [tex]$ \frac{392}{14} $[/tex] miles.

= 28 miles/gallon of gas

Therefore, with 3.7 gallons of gas, we can travel 3.7 X 28 miles

= 103. 6 miles

Answer:

1) The slope of the line is [tex]m=\frac{5}{2}[/tex]  or  [tex]m=2.5[/tex]

2) The equation of the line is [tex]y=2.5x-4[/tex]

Step-by-step explanation:

step 1

Find the slope

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

take any two points from the values in the table

(2,1) and (4,6)

substitute the values in the formula

[tex]m=\frac{6-1}{4-2}[/tex]

[tex]m=\frac{5}{2}[/tex]

[tex]m=2.5[/tex]

step 2

Find the equation of the line in point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=2.5[/tex]

[tex]point\ (2,1)[/tex]

substitute

[tex]y-1=2.5(x-2)[/tex]

Convert to slope intercept form

isolate the variable y

[tex]y-1=2.5x-5[/tex]

[tex]y=2.5x-5+1[/tex]

[tex]y=2.5x-4[/tex]

Answer:

125

Step-by-step explanation:

Answer:

[tex]y=\frac{11}{5}[/tex]

Step-by-step explanation:

Given expression

[tex]\frac{1}{3}(y-2)-\frac{5}{6}(y+1)=\frac{3}{4}(y-3)-2[/tex]

To solve for [tex]y[/tex] for the given expression.

Solution:

We multiply each term with the least common multiple of the denominators of the fraction in order to remove fractions.

The multiples of the denominators are:

3 = 3,6,9,12,15

6 = 6,12

4 = 4,8,12

The least common multiple = 12.

Multiplying each term with 12.

[tex]12.\frac{1}{3}(y-2)-12.\frac{5}{6}(y+1)=12.\frac{3}{4}(y-3)-2(12)[/tex]

[tex]4(y-2)-10(y+1)=9(y-3)-24[/tex]

Using distribution.

[tex]4y-8-10y-10=9y-27-24[/tex]

Simplifying.

[tex]-6y-18=9y-51[/tex]

Adding [tex]6y[/tex] both sides.

[tex]-6y+6y-18=9y+6y-51[/tex]

[tex]-18=15y-51[/tex]

Adding 51 both sides.

[tex]-18+51=15y-51+51[/tex]

[tex]33=15y[/tex]

Dividing both sides by 15.

[tex]\frac{33}{15}=\frac{15y}{15}[/tex]

[tex]\frac{33}{15}=y[/tex]

Simplifying fractions.

[tex]\frac{11}{5}=y[/tex]

∴ [tex]y=\frac{11}{5}[/tex]  (Answer)

The value of n is [tex]1\frac{4}{5}[/tex].

Step-by-step explanation:

Given,

[tex](2\frac{2}{3}-n)/-2\frac{1}{5}=\frac{-13}{33}[/tex]

Writing the fractions in simplified form;

[tex](\frac{8}{3}-n)/\frac{-11}{5}=\frac{-13}{33}[/tex]

Taking LCM on left hand side;

[tex](\frac{8-3n}{3})/\frac{-11}{5}=\frac{-13}{33}\\[/tex]

[tex]\frac{8-3n}{3}*\frac{-5}{11}=\frac{-13}{33}\\\\\frac{-40+15n}{33}=\frac{-13}{33}\\\\[/tex]

Multiplying both sides by 33

[tex]33*(\frac{-40+15n}{33})=\frac{-13}{33}*33\\-40+15n=-13\\15n=-13+40\\15n=27[/tex]

Dividing both sides by 15

[tex]\frac{15n}{15}=\frac{27}{15}\\n=\frac{9}{5}\\n=1\frac{4}{5}[/tex]

The value of n is [tex]1\frac{4}{5}[/tex].

Keywords: fraction, division

Learn more about fractions at:

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Answer:

Therefore the value of 'x' is 7.

Step-by-step explanation:

Given:

[] ABCD is a Parallelogram

AB = 4x+ 7

BC = 8x - 12

CD = 7x - 14

To Find:

x = ?

Solution:

[] ABCD is a Parallelogram ..............Given:

Opposite sides of a Parallelogram are Equal

side AB and CD are the opposite sides of the parallelogram.

∴ AB = CD

On substituting the values we get

[tex]4x+7=7x-14\\\\7x-4x=7+14\\\\3x=21\\\\x=\dfrac{21}{3} =7\\\\\therefore x =7[/tex]

Therefore the value of 'x' is 7.

There are 13 triangles will be in the 7th term.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The sequence is,

Δ, ΔΔΔ, ΔΔΔΔΔ..

Now,

Number of triangles in sequence are;

⇒ 1 , 3 , 5, ...

Clearly, The sequence is in arithmetic sequence, with common difference = 3 - 1 = 2 and first term is 1.

Hence, The 7th term is find as;

⇒ T ₇ = a + (n - 1) d

⇒ T ₇ = 1 + (7 - 1) (2)

⇒ T ₇ = 1 + 6 x 2

⇒ T ₇ = 1 + 12

⇒ T ₇ = 13

Thus,  There are 13 triangles will be in the 7th term.

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Option C

The explicit formula for the arithmetic sequence is [tex]a_n = 9 - 6n[/tex]

Solution:

Given that the arithmetic sequence is:

3, -3, -9, -15, -21, ...

To find: Explicit formula for the arithmetic sequence

The nth term of an arithmetic sequence is given by:

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

Where [tex]a_n[/tex] is nth term of sequence

n is the term's location

[tex]a_1[/tex] is the first term of sequence

d is the common difference between terms

In an arithmetic sequence, the difference between successive terms is constant. This means that we can move from any term to the next one by adding a constant value.

In the given sequence:

3, -3, -9, -15, -21, ...

[tex]a_1 = \text{ first term } = 3[/tex]

d = difference between any two terms in sequence

[tex]d = a_2 - a_1[/tex]

d = -3 - (3) = -6

Substituting the values in above formula,

[tex]a_n = 3 + (n - 1)(-6)\\\\a_n = 3 -6n + 6\\\\a_n = 9 - 6n[/tex]

Thus the explicit formula to find any term in sequence is found

Answer:

The numbers between -5 and 5

Step-by-step explanation:

Intersection of Intervals

Given the intervals A,B,C,etc. The intersection of them all is the set of all values that are common to all the intervals.

We must find

[tex]\{x | x > -5\} \bigcap \ \{x | x < 5\}[/tex]

which is the intersection between the intervals x > -5 and x < 5. The intersection represents all the numbers greater than -5 and less than 5. It can also be said The numbers between -5 and 5 (non inclusive), third option

Answer: The answer is D all real numbers

Answer:

50m

Step-by-step explanation:

Information from the question:

The length is 15m

The width is 10m

Length is represented by "l"

Width is represented by "w"

The perimeter is the total of its side lengths. A rectangle has four sides that are two lengths and two widths.

Use the formula for perimeter:

P = 2(l + w)            Put in the length and width measurements

P = 2(15m + 10m)    Add inside the brackets

P = 2(25m)        Multiply

P = 50m           Answer

Therefore the perimeter of the rectangular swimming pool is 50 meters.

To find the product for 2(2n + 3), use the distributive property to multiply 2 with each term inside the parentheses, resulting in 4n + 6.

The question asks to find the product for 2(2n + 3). To solve this, we need to use the distributive property of multiplication over addition, which states that a(b + c) = ab + ac. Applying this rule to the given expression, we multiply 2 with each term inside the parentheses.

First, multiply 2 by 2n to get 4n. Next, multiply 2 by 3 to get 6. Therefore, the expression simplifies to 4n + 6.

We have successfully used the distributive property to find that the product of 2(2n + 3) is 4n + 6.

Rhonda must collect at least 240 stamps in order to reach her goal.

Step-by-step explanation:

Given,

Stamps Rhonda wants to collect = 575

Stamps already in collection = 335

Let,

d represents the number of stamps Rhonda needs to collect to achieve her goal.

Stamps to collect + Stamps already in collection ≥ 575

[tex]d+335\geq 575\\d\geq 575-335\\d\geq 240[/tex]

Rhonda must collect at least 240 stamps in order to reach her goal.

Keywords: inequality, addition

Learn more about inequalities at:

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Answer:

The maximum value of function is 81 .

Step-by-step explanation:

Given function as :

y = 4 (x + 7) (2 - x)

Now, The function can be written as

y = 4 (2 x - x² + 14 - 7 x)

y = 4 ( - x² - 5 x + 14)

y = - 4 x² - 20 x + 56

Now, For maximum value of function , differentiation of y with respect to x

[tex]\frac{\partial y}{\partial x}[/tex] = 0

Or, [tex]\frac{\partial ( - 4x^{2} - 20 x +56)}{\partial x}[/tex] = 0

Or, - 8 x - 20 = 0

Or, - 8 x = 20

∴  x = [tex]\dfrac{-20}{8}[/tex]

i.e  x = [tex]\dfrac{-5}{2}[/tex]

Now, Putting the value of x in the given equation

y = - 4 ( [tex]\dfrac{-5}{2}[/tex])² - 20 ( [tex]\dfrac{-5}{2}[/tex]) + 56

Or, y = - 4 ([tex]\dfrac{25}{4}[/tex]) + 50 + 56

Or, y = - 25 + 50 + 56

∴    y = 81

So, The maximum value of function is 81

Hence,The maximum value of function is 81 . Answer

Answer:

E

Step-by-step explanation:

There are 48 cards numbered from 1 to 48.

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48

Multiples of 8: 8, 16, 24, 32, 40, 48

Multiples of 6 and 8: 24, 48.

Hence,

Total number of cards = 48,

Number of cards which are multiples of 6 and 8 = 2

The probability that the number card is a multiple of both 6 and 8 is

[tex]P=\dfrac{2}{48}=\dfrac{1}{24}[/tex]

Answer:

File is given in attachements .

Step-by-step explanation:

[tex]y = \sqrt[3]{x}  + 2[/tex] will pass through (0,2) and (-8,0) . Its shape will be as shown in the graph.

Answer:

Graph C

Step-by-step explanation:

Answer:

ok??? whats the question?

Step-by-step explanation:

Answer:

question???

Step-by-step explanation:

Answer:

n=6

Step-by-step explanation:

4(n+2)=2(n+10)

4n+8=2n+20

4n-2n+8=20

2n+8=20

2n=20-8

2n=12

n=12/2

n=6

Answer: 4 pancakes

Step-by-step explanation: because 30min÷6pancakes=5

So, 20min÷5=4

Answer:

3:5

Step-by-step explanation:

Please see attached picture for full solution. ( Unit method)

Answer: Im assuming this is a true or false question anyways the answer would be false if it is

Step-by-step explanation:

Answer: 7c ≤ 63

Ivan will buy at most 9 pounds of candy, which means that multiplying 9 by 7, the cost of the candy, will get your answer: 63. Plug these values into an inequality with a less than or equal to sign (≤) facing away from 63 and you're done!

The possible amounts Ivan will spend on candy can be represented as c ≤ 7.

Let's denote the amount Ivan will spend on candy as c. The cost of candy is $7 per pound, and Ivan will buy at most 9 pounds of candy. Therefore, the maximum amount he could spend on candy is 9 pounds multiplied by $7 per pound, which is 9c ≤ 63.

Since we are looking for possible amounts, we can rewrite this inequality as c ≤ 63/9, which simplifies to c ≤ 7.

So, the possible amounts Ivan will spend on candy are values less than or equal to $7.

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Answer:

The graph is plotted below.

One ordered pair as solution is (0, 0).

Step-by-step explanation:

Given:

The inequality is given as:

[tex]y\geq x-5[/tex]

In order to plot it, we first replace '≥' by '=' sign. This gives,

[tex]y = x-5[/tex]

Now, we plot the above line. For that, we need the x and y intercepts.

At x-intercept, y = 0. So,

[tex]0=x-5\\x=5[/tex]

The point is (5, 0)

At y-intercept, x = 0. So,

[tex]y=0-5\\y=-5[/tex]

The point is (0, -5)

Now, plot these two points and draw a line passing through these two points. The graph is shown below.

Now, replace '=' by '≥' sign. Since, 'y' is greater than equal to 'x - 5'. So, the solution region is above the given including the values on the line.

Therefore, any ordered pair in the solution region is a solution of the given inequality. From the graph, one such ordered pair is (0, 0).

This can be verified from the inequality also.

[tex]0\geq 0-5\\0\geq -5(True)[/tex]

So, one ordered pair is (0, 0).