How can you use quarters to estimate 180+ 320

The table below shows the cost of downloading songs from a website. Number of Songs Total Cost 14 $8.96 16 $10.24 18 $11.52 If c

shepuryov [24]

Given:

c = total cost.

s = number of songs.

To solve this question, follow the steps below.

Step 01: Find 2 points (s, c).

You can choose 2 points from the table.

Let's choose (14, 8.96) and (16, 10.24).

Step 02: Substitute one point in the general equation.

Given the general equation:

$c=ms+b$

Substituting the first point.

$\begin{gathered} 8.96=14m+b \\ 8.96-14m=b \\ b=8.96-14m \end{gathered}$

Isolating b by subtracting 8.96 m from both sides:

$\begin{gathered} 14-8.96m=8.96m+b-8.96m \\ 14-8.96m=b \\ b=14-8.96m \end{gathered}$

Step 03: Substitute b in the general equation.

$\begin{gathered} c=ms+b \\ c=ms+8.96-14m \end{gathered}$

Step 04: Substitute the second point in the equation above.

$\begin{gathered} c=ms+8.96-14m \\ 10.24=16m+8.96-14m \\ 10.24=2m+8.96 \end{gathered}$

Step 05: Solve the equation above for m.

To do it, first, subtract 8.96 from both sides.

$\begin{gathered} 10.24-8.96=2m+8.96-8.96 \\ 1.28=2m \end{gathered}$

Now, divide both sides by 2.

$\begin{gathered} \frac{1.28}{2}=\frac{2}{2}m \\ m=0.64 \end{gathered}$

Step 06: Substitute m in the equation from step 02 to find b.

$\begin{gathered} b=8.96-14m \\ b=8.96-14\cdot0.64 \\ b=8.96-8.96 \\ b=0 \end{gathered}$

Step 07: Write the equation.

$\begin{gathered} c=0.64s+0 \\ c=0.64s \end{gathered}$

Answer:

c = 0.64s

7 0

2 years ago

If l=25, n=8, d=3, and l=a+(n-1)d, find the value of a (I got a=2 am I right if not whats the answer?)

kykrilka [37]

Answer:

A=4 I think

Step-by-step explanation:

I=a+(n-1)d

25=a+(8-1)3

25=a+21

25-21=a+21-21

4=a

8 0

3 years ago

What is the slope of the line below?

Strike441 [17]

Answer:

Positive

Step-by-step explanation:

6 0

3 years ago

A model used for the yield Y of an agricultural crop as a function of the nitrogen level N in the soil ) (measured in appropriat

il63 [147K]

Answer:

A nitrogen level of 1 gives the best yield.

Step-by-step explanation:

We are given the following:

Yield Y of an agricultural crop as a function of the nitrogen level N in the soil

$Y(N) = \displaystyle\frac{kN}{1+N^2}$

First, we differentiate Y(N) with respect to N, to get,

$\displaystyle\frac{d(Y(N))}{dN} = \displaystyle\frac{d}{dN}\Bigg(\displaystyle\frac{kN}{1+N^2}\Bigg)\\\\= \frac{(1+N^2)k-kN(2N)}{(1+N^2)^2}\\\\=\frac{k-kN^2}{(1+N^2)^2}$

Equating the first derivative to zero, we get,

$\displaystyle\frac{d(Y(N))}{dN} = 0\\\\\Rightarrow \frac{k-kN^2}{(1+N^2)^2} = 0$

Solving, we get,

$\displaystyle\frac{k-kN^2}{(1+N^2)^2} = 0\\\\k-kN^2 = 0\\k(1-N^2) = 0\\k \neq 0\\1-N^2 = 0\\N = \pm 1\\N \neq -1\\N = 1$

Again differentiation Y(N), with respect to N, we get,

$\displaystyle\frac{d^2(Y(N))}{dN^2} = \displaystyle\frac{2kN(N^2-3)}{(1+N^2)^3}$

At N = 1

$\frac{d^2(Y(N))}{dN^2} < 0$

Thus, by double derivative test, the maximum value of Y(N) occurs at N = 1.

Thus, largest yield of crop is given by:

Y(1) =

$Y(N) = \displaystyle\frac{k(1)}{1+(1)^2} = \frac{k}{2}$

6 0

4 years ago

Three pizzas are shared equally among 12 people.what fraction of pizza will each person get

8_murik_8 [283]

Answer:

1/4

Step-by-step explanation:

3/12 =0.25

0.25 = 1/4

8 0

3 years ago

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