E Homework: 2.3 Linear Inequalities
Question 14, 2.3.101
Part 1 of 2
Assume that in 2005 consumers used credit and debit cards to pay for 43% of all purchases. This percentage is projected to be 58% in 2011.
(a) Find a linear function that models the data, where x is the year and P(x) is the percentage.
(b) Estimate when this percentage was between 48% and 53%.
(a) P(x) =
(Simplify your answer. Use integers or decimals for any numbers in the expression.)

Answer:

Option A

Step-by-step explanation:

Given the following question:
Mrs. Hernandez earns $35.60 an hour
One week she earned $854.40

To find the answer we divide 8,544 by 356

[tex]8544\div356=24[/tex]
[tex]854.40\div35.60=24[/tex]

Mrs. Hernandez worked "24 hours last week" by using the first options equation, we can find that answer.

Hope this helps.

Solution:

Let's reread the part of the question carefully.

{one more} {than one third the number of dolls than Sally has}

       ↥                                                 ↥                          

       1                                                s/3

This means that Anne has s/3 + 1 dolls, which is 9 dolls.

Hence, the equation that represents the word problem is S/3 + 1 = A.

The number of comedy DVDs will be equal to 604.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that the total number of DVDs are 1830 and the percentage of comedy DVDs is 33%.

The number of comedy DVDs will be calculated as,

N = ( 1830 x 33%)

N = (1830 x 33 ) / 100

N = 604

Therefore, the number of comedy DVDs will be equal to 604.

To know more about percentages follow

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Answer: The new number is 1.44% smaller than the original.

=========================================================

Explanation:

To increase by 12%, we involve the multiplier 1.12

Think of 1.12 as 100% + 12% = 1 + 0.12 = 1.12

We go from x to 1.12x

To decrease by 12%, we will use the multiplier 0.88 because 1 - 0.12 = 0.88

Think of it like a discount. If you save 12%, then you pay the remaining 88%

So 0.88*1.12x = 0.9856x

The value 0.9856 is smaller than 1, meaning that overall we have a net discount going on.

The discount rate is 1 - 0.9856 = 0.0144 = 1.44%

In other words, x ultimately goes down by exactly 1.44%

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

If you want to use an actual number to see an example, let's go for x = 100

Increasing 100 by 12% means we increase by 0.12*100 = 12

We go from 100 to 112

Then decreasing by 12% means the value goes down by 0.12*112 = 13.44 and drops to 112-13.44 = 98.56

The original value 100 becomes the final value 98.56

This is a percent decrease of (100-98.56)/100 = 0.0144 = 1.44%

The marginal cost that can be deduced from the information given about the company is 40e^-t.

Marginal cost simply means the change in production cost due to an additional unit produced.

From the complete question, the cost function is given as 60 - 40e^-t. Therefore, the marginal cost will be:

C'(t) = d/dt (60 - 40e^-t)

= d/dt (60) - 40 d/dt (etc)

= 0 - 40(-1)e^-t

= 40 e^-t.

Learn more about marginal cost on:

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Answer:

1 5/8

Step-by-step explanation:

Answer:

[tex]2x+3y-45=0[/tex]

Step-by-step explanation:

The slope of the line that goes through (18, 3) and (21, 1) is

[tex]\frac{1-3}{{21-18}}=\frac{-2}{3}\\[/tex]

The slope of the line that goes through (18, 3) and (x, y) is

[tex]\frac{y-3}{{x-18}}[/tex]

So

[tex]\frac{y-3}{{x-18}} = \frac{-2}{3}\\-2(x-18)=3(y-3)\\-2x+36=3y-9\\2x+3y-45=0[/tex]

Answer:

A=6 should be the answer.

Answer:A

Step-by-step explanation: Count the edges, which is 6

Answer:

None of them are correct as the correct one is 0.345 (maybe you made a typo when typing the options)

Step-by-step explanation:

We can make:

[tex]\frac{345}{1000}[/tex] which equals 0.345 km

Answer:

[tex]B = A + C \\ \\ C = B - A[/tex]

ANSWER-

Answer:

 7/10

Step-by-step explanation:

1 yard = 3 feet

Then the given ratio is ..

21 feet : 10 yards = 7 yards : 10 yards = 7 : 10

As a fraction, the ratio is 7/10.

Answer:

  a)  21, 34.5, 54.75, 85.125

Step-by-step explanation:

All of the answer choices differ in the first term, so that is the only one you need to figure here. However, we will do them all, so you can see it done.

We note that x > 0 for all of the values of x that we need to use. That means the recursive relation is the one we're using for computation.

f(1) = 3/2·f(0) +3 = (3/2)(12) + 3 = 18 +3 = 21 . . . . . . matches choice (a)

f(2) = 3/2·f(1) +3 = (3/2)(21) +3 = 63/2 +3 = 69/2 = 34.5

f(3) = 3/2·f(2) +3 = (3/2)(34.5) +3 = 51.75 +3 = 54.75

f(4) = 3/2·f(3) +3 = (3/2)(54.75) +3 = 82.125 +3 = 85.125

__

When you're computing for sequential input values, each depends on the previous value you computed.

_____

Additional comment

Using an exponential regression calculator (or spreadsheet), the explicit function can be found to be ...

  f(x) = 18·1.5^x -6

Answer:

The surface area of a rectangular box is the sum of the areas of the flat rectangular faces of the box. The height is the vertical side of the box.  So the other sides are the length and width.  Try to picture a box in your head, or you can draw it on paper.

Let x = length

Let y = width

Let h = height

Using these variables, we can write an equation that represents the surface formula.

A = 2(area of bottom face) + 2(area of front face) + 2(area of side face)

A = 2xy + 2xh + 2yh

This is general equation for surface area.  All we need to do is plug in the known values into it and solve for h.

496 = 2(18)(8) + 2(18)h + 2(8)h

496 = 288 + 36h + 16h

Now it comes down to simple algebra.  Isolate the h terms and solve for h from there.

208 = 52h

Divide both sides of the equation by 52 to get your height.  I let you finish up here.

Step-by-step explanation:

Answer:

0.025

Step-by-step explanation:

The solution is in the attached file

[tex] \tt \dfrac{1}{10} \times 315[/tex]

31.5 <---- Ans

Answer:

31.5

Step-by-step explanation

If you divide something by 10 you move the decimal over one place to the left.

315.0 / 10 = 31.5

Answer:

2(w - 6) > -15

Step-by-step explanation:

2(w - 6) > -15

⇒ 2w - 12 > -15

⇒ 2w > -3

⇒ w > -3/2

Answer:

(5n + 4p)(5n + 4p)

Step-by-step explanation:

25n^2 + 40np + 16p^2

(5n)^2 + 2(5n)(2^2 * p) + (2^2 * p)^2

(5n + 2^2 * p)^2

(5n + 4p)^2 > (5n + 4p)(5n + 4p)

Answer:

32

Step-by-step explanation:

let both sides of equation be squared

((x+4)^½)² = 6²

x+4 = 36

x = 36-4

x = 32

Answer:

Step-by-step explanation:

Both are essentially same questions, considering 30 = 25 + 5.

Solving c)

Solution:

Part-C)

Part-D)

Hoped this helped!

Answer:

2

y = (3 x 1) - 1

         ^

      x = 1

y = 3 - 1 = 2

y = 2

Answer:

1. B
2. A
3. D
4. C

Answer:

12.22 would be her total cost after including 8% of tax.

Step-by-step explanation:

$2.29x3=$6.87

$6.87+1.89x2=$10.65

$10.65+$1.49=$12.14

$12.14+¢.08= $12.22

This is what I think is the answer from my work.

Answer

125,000 tons of garbage per landfill

Step-by-step explanation:

250 million total tons of garbage was sent to 2,000 landfills. Since it is assumed each landfill gets an equal amount of garbage, we can easily divide.

250,000,000 / 2,000 = 125,000 tons of garbage per landfill

henceforth, each landfill received 125,000 tons of garbage

Answer:

Step-by-step explanation:

→ y² -16y +64

→ y²-8y-8y+64

→ y(y-8) -8(y-8)

→ (y-8) (y-8)

The cost per friend is $6.84.

The first step is to determine the total cost of the vegetables the two friends bought.

Total cost of the vegetables = ( 1 x $2.82) + 4.19 X 2 + (1.24 x 2) = $13.60

In order to determine the cost per friend, divide the total cost of the vegetables by the number of friends that purchased the items.

$13.6 / 2 = $6.84

To learn more about division, please check: https://brainly.com/question/194007

Answer:

1. FH, 2. GH,  3.IH  4. GI,  5. FG

Step-by-step explanation:

According to a certain geometric theorem, the smallest angle is always opposite to the smallest side of a triangle. Likewise, the largest angle is always opposite to the largest side. Using this theorem we can properly order the angles and sides.

Additionally, the interior degrees of a triangle will always be 180, and the interior of this quadrilateral is 360 degrees. Using this we can determine the missing angles.

180 - 75 - 55 = 50 (first missing angle)

180 - 59 - 63 = 58 (second missing angle)

The smallest angle would be 50 degrees and the largest 75.

The second smallest is 55 degrees, the third smallest is 58 degrees, the fourth smallest is 59 degrees, and the fifth is 63 degrees.

Now, one thing that seems a bit confusing is the fact that GH is opposite to 2 different angles, so how do we know WHICH angle to use to find its length. From what I understand, we should be able to find the average of the two angles across from this side to see what its place would be in terms of length.

63 + 50 = 56.5

This would make side  GH larger than FH but less than HI

This is how I would solve the problem, and I think this is the correct order. Please let me know whether it turns out right.

Mark the formula/theorem below

Here

So the order is