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3 years ago

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Mathematics

2 answers:

Marat540 [252]3 years ago

8 0

<h3>Answer: D) 12.5%</h3>

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Work Shown:

A = old amount = 48

B = new amount = 54

C = percent change

C = [(B-A)/A]*100%

C = [(54-48)/48]*100%

C = [6/48]*100%

C = 0.125*100%

C = 12.5%

The value of C is positive to indicate a percent increase.

So we have a 12.5% increase.

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Note how 12.5% of 48 is 0.125*48 = 6

A 12.5% increase of 48 means we have an increase of 6

So, 48+6 = 54, which matches with what the instructions say. This confirms the answer.

As a shortcut, we could check it by saying 1.125*48 = 54

dalvyx [7]3 years ago

5 0

Answer:

12.5%

Step-by-step explanation:

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Lesson: 1.08Given this function: f(x) = 4 cos(TTX) + 1Find the following and be sure to show work for period, maximum, and minim

Ber [7]

The given function is

$f(x)=4\cos \text{(}\pi x)+1$

The general form of the cosine function is

$y=a\cos (bx+c)+d$

a is the amplitude

2pi/b is the period

c is the phase shift

d is the vertical shift

By comparing the two functions

a = 4

b = pi

c = 0

d = 1

Then its period is

$\begin{gathered} \text{Period}=\frac{2\pi}{\pi} \\ \text{Period}=2 \end{gathered}$

The equation of the midline is

$y_{ml}=\frac{y_{\max }+y_{\min }}{2}$

Since the maximum is at the greatest value of cos, which is 1, then

$\begin{gathered} y_{\max }=4(1)+1 \\ y_{\max }=5 \end{gathered}$

Since the minimum is at the smallest value of cos, which is -1, then

$\begin{gathered} y_{\min }=4(-1)+1 \\ y_{\min }=-4+1 \\ y_{\min }=-3 \end{gathered}$

Then substitute them in the equation of the midline

$\begin{gathered} y_{ml}=\frac{5+(-3)}{2} \\ y_{ml}=\frac{2}{2} \\ y_{ml}=1 \end{gathered}$

The answers are:

Period = 2

Equation of the midline is y = 1

Maximum = 5

Minimum = -3

3 0

1 year ago

The initial cost of an office fax machine is $100. After 1 year, its value becomes $80. Which is the correct linear depreciation

Elis [28]

Answer:

$y=100-20x$

Step-by-step explanation:

Let the x-axis be the time (in years) and the y-axis the value of the fax machine (in dollars).

We know that the initial value of the fax machine is $100; in other words, when the time is zero years, the value is $100, or as an ordered pair (0, 100). We also know that after 1 year the value decreases to $80, so (1, 80).

Now we can find the slope of the line passing through those two points using the slope formula

$m=\frac{y_2-y_1}{x_2-x_1}$

where

$m$ is the slope

$(x_1,y_1)$ are the coordinates of the first point

$(x_2,y_2)$ are the coordinates of the second point

Replacing values:

$m=\frac{80-100}{1-0}$

$m=-20$

Now, to complete our model we are using the point slope formula

$y-y_1=m(x-x_1)$

where

$m$ is the slope

$(x_1,y_1)$ are the coordinates of the first point

Replacing values:

$y-100=-20(x-0)$

$y-100=-20x$

$y=-20x+100$

$y=100-20x$

We can conclude that the correct linear depreciation model is $y=100-20x$

7 0

3 years ago

For the function f(x)=3xsquared- 2x+5 find f(1) f(-2) and f(a)

Oksanka [162]

$f(x)=3x^2-2x+5\\\\
f(1):\ \ Substitude\ 1 \ as\ x\ into\ function:\\
f(1)=3*1^2-2*1+5=3-2+5=\textbf{6}\\\\
f(-2)\ \ Substitude\ x=-2\\
f(-2)=3*(-2)^2-2*(-2)+5=3*4+4+5=12+4+5=\textbf{21}\\\\
f(a)\ \ substitude\ x=a\\
f(a)=\underline{3a^2-2a+5}$

4 0

4 years ago

14% of 163<br> What is 14% of 163 estimated

Elina [12.6K]

Answer:

22.82

Step-by-step explanation:

it is about 22.82 when taken 14% away

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3 years ago

Area

Nimfa-mama [501]

Answer:

perimeter=2(l+w).

2(10+6)

2(16)

32cm.

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2(14)

c)2(11+10)

2(21)

42.

d)2(20+15)

2(35)

70.

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3 years ago