PLEASE HELP! Marta is buying soft drinks for the class party. The table below shows the prices of 4 different packages of cola, the number of bottles in each package, and the ounces of cola per bottle.

The tables that shows a proportional relationship include the following:

x 1 2 3 4 5

y 4 5 6 7 8

p 1 3 5 7 9

q 3 7 11 15 19

A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two ratios. This ultimately implies that, proportions can be used to establish that two ratios are equivalent and solve for all unknown quantities.

In Mathematics, the graph of any proportional relationship is characterized by a straight line because as the values on the x-axis (x-coordinate) increases or decreases, the values on the y-axis (y-coordinate) increases or decreases simultaneously as shown in tables B and C.

In conclusion, tables B and C comprises data values that shows proportional relationship in a graph.

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The correct responses for the arithmetic and exponential sequence and function are;

1. First part; 32 pennies

Second part; Approximately 50 days

2. 24.6 gallons

3,738.5 minutes

3. $67.2

Approximately 24 months

4. 1106.14 gallons

66.56 minutes

The difference is 1 is an arithmetic sequence while 3 is an exponential function

An arithmetic sequence is a group of numbers in which the difference between subsequent terms is a constant

1. The given parameters are;

The initial amount Savannah placed in the piggy bank = 5 pennies

The amount given to Savannah each day = 3 pennies

Required;

First part;

The amount Savannah will have after 10 days

Solution;

The mathematical model for the situation is an arithmetic sequence or progression

The equation for an arithmetic progression is;

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

Where;

[tex]a_n[/tex] = The amount after n days

[tex]a_1 [/tex] = The first amount Savannah placed in the piggy bank = 5 pennies

n = The number of days

d = The common difference between the amount present in consecutive days = 3 pennies

The amount after 10 days is therefore;

[tex]a_{10} = 5 + (10 - 1) \times 3=32[/tex]

The money after 10 days is 32 pennies

Second part;

The number of days it would take for there to be $1.50 in the piggy bank.

Solution;

100 pennies = $1.00

Therefore;

$1.50 = 150 pennies

Which gives;

150 = 5 + (n - 1) × 3

(n - 1) × 3 = 150 - 5 = 145

(n - 1) × 3 = 145

n - 1 = 145 ÷ 3

n = 145 ÷ 3 + 1 ≈ 49.3 ≈ 50

It will take approximately 50 days for the amount in the piggy bank to be $1.50

2. The volume of the pool = 1,500 gallons

The initial amount of water in the pool = 5 gallons

The rate at which water enters the pool = 2 gallons in 5 minutes

Required;

First part

The volume of water in the pool after 50 minutes

Solution;

2 gallons in 5 minutes = (2/5) gallons/minute = 0.4 gallons/minute

Therefore;

[tex]a_{50} = 5 + (50 - 1) \times 0.4 =24.6[/tex]

After 50 minutes, 24.6 gallons will be in the pool

Second part;

The time it will take to fill the pool is given by the equation;

[tex]1500 = 5 + (n - 1) \times 0.4[/tex]

number

Which gives;

n = 3738.5

It will take 3,738.5 minutes to fill the pool

3. The formula for finding the amount in the account is the compound interest formula;

[tex]\displaystyle{A = P\cdot (1 + r)^n }[/tex]

Where;

A = The amount in the account after n months

P = The initial amount in the account = $50.0

r = The interest rate = 3.0%

n = The number of periods (months)

After 10 months, we have;

[tex]\displaystyle{A = 50 \times (1 + 0.03)^{10} \approx 67.2 }[/tex]

The amount in the account after 10 months is therefore, approximately $67.2

Second part;

Double the initial amount is 2×$50 = $100

Which gives;

[tex]100 = \displaystyle{50 \times (1 + 0.03)^{n} \approx 67.2 } [/tex]

Which gives;

n ≈ 23.45

Therefore it will take approximately 23.45 months or approximately 24 months for the amount to double

4. Using the exponential function formula, we have;

Number of 5 minutes in 50 minutes = 10

[tex] \displaystyle{1500 \times (1 - 0.03)^{10} \approx 1106.14} [/tex]

The water remaining after 50 minutes is approximately 1106.14 gallons

The time it takes for there to be less than 1,000 gallons in the pool is given as follows;

[tex] \displaystyle{ 1000= 1500 \times (1 - 0.03)^{n}} [/tex]

Which gives;

n = 13.3

Therefore;

The water in the pool will be less than 1000 gallons after 13.3, 5 minute periods or 13.3 × 5 minutes≈ 66.56 minutes

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Answer:

Substitute x = 4 into f(x).

f(4) = -7(4+2)

= -28-14

= -42

Answer:

If p(x) = ax²

-3x+10

p(-2) =

f(g(-2))

Part (a)

We can add the total number of males and the total number of students who take biology, and then subtract the intersection.

[tex]42+34-14=62[/tex]

Part (b)

There are 90 people in all, so the probability is [tex]\frac{62}{90}=\frac{31}{45}[/tex]

Assuming they work until their cost become the same, obviously.

The difference between the first charge of painter A and painter B = 376 - 280 = 96.

The hourly cost difference between painter B and painter A = 15 - 12 = 3.

So, painter A in the first hour has 96 more dollars than painter B, and as every hour pass, the difference goes down by 3 (as painter B gets 3 more dollars every hour)

Therefore, it would take 96 : 3 = 32 hours for the cost to be the same

Recheck : After 32 hours, painter A has 376 + 32 x 12 = 760 (dollars)
painter B has : 280 + 15 x 32 = 760 (dollars)

Answer: 1/2

Step-by-step explanation:

its greater than 4/7

1/7 would be greater

Answer:

x(-5.3,0)

y(0,4)

slope 0.75

Step-by-step explanation:

Possible values for the actual distance that the toy cart rolled before stopping with 30% error in the calculation conducted earlier is equal to 10.92centimeters.

As given in the question,

Distance covered by toy cart before stopping =15.6

Percentage of error found in calculation= 30%

30% of 15.6

= (30/100) × 15.6

= 4.68cm

Possible value for the actual distance that toy cart rolled before stopping

= Calculated distance - error distance

= 15.6 -4.68

=10.92centimeters

Therefore, possible values for the actual distance that the toy cart rolled before stopping with 30% error in the calculation conducted earlier is equal to 10.92centimeters.

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The slope of the given line is m =25.

The two points of the given line is (3,75) and (4,100).

The slope of the given line can be found using the formula point-slope equation.

y₂-y₁ = m(x₂-x₁)

We need to find the slope, so let us rearrange the equation,

m =  y₂-y₁ / x₂-x₁

where (x,₁y₁) and (x₂,y₂) is (3,75) and (4,100) respectively

So let us substitute these values in the above equation, we get

m = 100 - 75 / 4 -3

m = 25/1

m = 25

Therefore, the slope of the line passing through the point (3,75) and (4,100) is 25

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Answer:

[tex]a_5 = \frac{17}{20}[/tex]

Step-by-step explanation:

Use the general progression formula where

[tex]d=\frac{3}{20}\\a_n=\frac{1}{4}+\frac{3n-3}{20}[/tex]

Solving this for the 5th term returns the answer

[tex]a_5=\frac{17}{20}[/tex]

Based on the number of equal parts that Lester divided the cake into such that each family member got 1/6 of the whole pie, the proportion of the part of the leftover pie that Lester brought home was 2 / 3

Lester brought back part of some pie from the Sweet Slice pie shop, and then divided it into 4 equal parts for his family. This led to the family getting 1/6 of the pie each.

To find out how much of the total pie that Lester brought back from Sweet Slice pie shop, you need to add the proportions received by his family:

= 1 / 6 + 1 / 6 + 1/ 6  + 1/6

=  4 / 6

At the simplest form this is:

= 4 / 6

= 2 / 3

Rest of the question is:

How much of the pie had Lester brought back from the pie shop?

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Answer:

it

should be something along the lines of math

The transformation is:

g(x) = -f(x) - 4

So is a reflection across the x-axis followed by a translation of 4 units downwards.

Here we have the two functions:

f(x) = 3x + 1

g(x) = -3x - 5

So we start at f(x), first we apply a reflection across the x-axis so we change the sign to get:

g(x) = -f(x) = -3x - 1

Now we can apply a translation of 4 units downwards so we get:

g(x) = -f(x) - 4 = -3x - 1 - 4 = -3x - 5

And in this way we transformed f(x) into g(x).

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We calculate the ratio (in percentage) of 5.2cm to 4cm

5.2 : 4 = 1.3

Because 4cm is 1.3x less than 5.2, its percentage must also be 1.3x less than 96%

-> 4cm = 96% : 130% = approx. 73.85% (2 d.p)

Answer:

896

Step-by-step explanation:

28x32 gives u 896 so that will b your product

value of a2+a4+a6+……+a98 IS EQUAL TO 93.

Given, the common difference (d) =1

Let a1=a Given, a1+a2+……+a98=137

⇒(98/2)(2a+97)=137    [Sn=n/2[2a+(n−1)d]

⇒2a+97=137/49…eq.(1)

a2+a4+…+a98    (n=49 terms)

a2+a4+…+a98=49/2(a2+a98)

a2+a4+…+a98=49/2[(a+1)+a+97]

a2+a4+…+a98=49/2[2a+97+1]

a2+a4+…+a98=49/2[(137/49)+1] [using eq. 1]

a2+a4+…+a98=137/2+49/2

a2+a4+…+a98=186/2 =93

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The number of times larger that the diameter of cell C is more than the diameter of cell D is 9.2 × 10^-6

It should be noted that standard notation simply means writing in standard form. This is illustrated as a × 10ⁿ.

In this case, the cells are measured using this method: Cell C is 7.76 × 10^ {-2} and Cell D is 8.4×10^ −4 centimeters

It should be noted that in order to know the number of times that the cell is larger will be gotten by dividing. This will be;

= (7.76 × 10^-2) / (8.4 × 10^-4)

= 9.2 × 10^-6

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The ways that you can maximize a tax-sheltered retirement program include:

1. when the contributions made by the employer are not taxable

2. when the employee has started making contributions early in life,

A tax-sheltered is a retirement savings plan that enables self-employed individuals and workers of tax-exempt organizations to invest pretax money to create retirement income. A dependable source of income in retirement, tax-sheltered annuities are made to pay out consistently throughout time.

The fact that employer contributions are tax-free is one of the best features of retirement programs. Only when an employee takes money out of their retirement accounts do taxes need to be paid. If the employee starts making contributions early in life, the plans also allow the employee the chance to maximize returns, which is another benefit that the employee can get from them.

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the kangaroo real height is 3 feet and shadow height is 5 feet

if the height of the tree is 7 feet so the real height of the tree is 5 feet

52x - 100y + 490 = 0 , is the required linear function.

What does the term "linear function" mean?

A mathematical function where the variables only occur in the first degree, where the constants are multiplied, and where the only possible combinations are addition and subtraction.

Given, the monthaly cost = y

   the number of minute used = x

Hence,  

           the monthly cost of the phone = (4.90 + 0.52 × the number of minute used)

Given the monthly cost = y

          the number of minute used = x

Hence      y = 4.90 + 0.52 * x

    or    y = [tex]\frac{490}{100} + \frac{52}{100 } * x[/tex]

     or 100y = 455 + 52x

       or 52x - 100y + 490 = 0 , is the required linear function.

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Answer:

A

Step-by-step explanation:

C means the number of miles into the city, while H means the miles on the highway. If (c,h) becomes (138,200), this means that c=138 and h=200. So, 138 miles can be traveled into the city while 200 can be traveled on the highway. hope this helps!

The graph will be a shaded region above and including the straight line y = (3/2)x-1.

We are asked to graph the inequality y ≥ (3/2)x-1. Describing the graph of an inequality, it will be a region on one side of a straight line.

So first we need to sketch the straight line, y = (3/2)x-1.

So find two points (x, y) satisfying this equation of line because a line need at least two points.

x       y  

0       -1

2/3     0

So first sketch a line joining the points (0, -1) and (2/3,0). This line will lie below the origin. That is, origin lies on the region above this line.

So the line y = (3/2)x-1 divided the plane into two regions, one of which represents the inequality y ≥ (3/2)x-1. So to find this required region we will check if origin lies in the region for inequality.

Substituting (0, 0) into y ≥ (3/2)x-1,

0 ≥ -1, which is true.

Thus in the graph, the region for inequality is the region where the origin lies. Hence shade the region above the line y = (3/2)x-1. This is the graph of the inequality y ≥ (3/2)x-1.

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Answer:

A. Opens up with a vertex at (-3, -4)

Step-by-step explanation:

y = (x + 3)² - 4

Vertex: (-3, -4)

Min: y = -4

min = up

I hope this helps!

The given equation represents the equation of a parabola and it represents the curve open up with vertex (-3, -4).

Hence, option A is correct.

A parabola is a U-shaped plane curve in which any point is an equal distance from both a fixed point (known as the focus) and a fixed straight line (known as the directrix).

The given equation is:

y = (x +3)² - 4

Since we know that,

An equation of the parabola is

y = a(x - h)² + k

Where (h, k) is the vertex.

Comparing these equations we get

a = 1

h = -3

k =  -4

So, its vertex is (h, k) = (-3, -4)

Hence,

The graph opens up with vertex (3, -4).

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Answer:

-6(y+3)

Step-by-step explanation:

The number of fiction and non fiction books are 10 and 2 respectively.

There are 5 times as many fiction books in the class library as there are nonfiction books.

Therefore,

let

x = number of non fiction book.

number of fiction book = 5x

The number of information books is 7 more than the sum of the number of fiction and nonfiction books.

Therefore,

number of information book = 7 + x + 5x

number of information book = 7 + 6x

There are 19 information books in the library.

Hence,

19 = 7 + 6x

19 - 7 = 6x

6x = 12

x = 12 / 6

x = 2

Therefore,

The number of non fiction book = 2

The number of non fiction book = 5(2)  = 10

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The difference between the expressions (2n -9) - (2.4n +4) is -0.4n-13

An algebraic expression can be defined as an arithmetic expression made up of variables, coefficients, terms, factors and constants.

They are also known to be composed of mathematical operations which may include;

Given the expressions;

Let's determine their difference

(2n -9) - (2.4n +4)

expand the bracket

2n - 9 - 2.4n - 4

collect like term

2n - 2.4n -4 -9

Subtract like terms

-0.4n - 13

Hence, the difference is -0.4n - 13

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