All categories

3 years ago

A new car is purchased for $47, 000 and over time its value depreciates by one half

Mathematics

2 answers:

andrey2020 [161]3 years ago

5 0

Answer:

$1500

Step-by-step explanation:

you can figure it out by going in increments of 4.5 years because that is the info you have from the problem so

47000 4.5 years later is 23500

9 years = 11750

13.5y = 5875

18y = 2937.5

22.5 years later is 1468.75

22.5 years is about 23 years and to the nearest hundred dollars that is $1500 so that is the answer

Hope this helps! :)

svlad2 [7]3 years ago

3 0

we know the car depreciates every 4.5 years, and we also know its by one half or namely the depreciation rate is 50% of its value.

$\textit{Periodic/Cyclical Exponential Decay} \\\\ A=P(1 - r)^{\frac{t}{c}}\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &47000\\ r=rate\to 50\%\to \frac{50}{100}\dotfill &0.5\\ t=years\dotfill &23\\ c=period\dotfill &4.5 \end{cases} \\\\\\ A=47000(1 - 0.5)^{\frac{23}{4.5}}\implies A=47000(0.5)^{\frac{46}{9}}\implies A\approx 1400$

You might be interested in

A rectangle with an area of 120 in 2 has a length 8 inches longer than two times its width. What is the width of the rectangle?

nlexa [21]

width = x

length = 2x+8

area = l x w

x(2x+8)=120

2x^2+8x−120=0

x^2+4−60=0

(x+10)(x−6)=0

x=−10 and x=6

width has to be a positive number

Width = 6 inches.

5 0

3 years ago

Nuance said she drew a square pyramid and that all of the faces are triangles.Is this possible?

sergeinik [125]

No because a square pyramid must hav a square for its base and a square is not a triangle

answer is not possible

3 0

3 years ago

Read 2 more answers

Need help filling in the blanks.. also not sure if the answers i filled in are correct or not.

tino4ka555 [31]

Answer:

See below.

Step-by-step explanation:

For item 2:

The Net Price Rate = 276 / 460 = 0.60 = 60 % (answer).

Item 3: Net Price Rate = 3247 * 100 / 3820 = 85% (answer).

Item 4 Net Price Rate = 675.11 / * 100 / 987 = 68.4%. (answer).

Item 5 Item's Net Price = 987 * 0.675 = $666.23 (answer).

Item 7 Net price Rate = 2945* 100 / 4750 = 62%. (answer).

Item 8: First find the list place $x:

0.90* 0.80 * 0.70x = 252 ( the 0.90 , 0.80 and 0.70 come from 100 - 10% = 1 - 0.10 = 0.90 and so on)

0.504 x = 252

x = $500

Answer is List Price = $500 and Net Price Rate = 50.4%.

Item 10 List price = 2890.65 / 0.35 = $8259. (answer)

5 0

3 years ago

(High points) please solve with explanation

AysviL [449]

Answer:

The area and the perimeter of the picture are:

Area = 160 cm^2
Perimeter = 67.31 cm

Step-by-step explanation:

To find the area of that figure, you can find the area how if it was a rectangle and next subtract the area of the triangle in the upper part. The area of a rectangle could be found by the next formula:

Area of a rectangle = base * height

As you can see in the picture, the base is 16 cm and the height is 12 cm, then we replace in the formula:

Area of a rectangle = 16 cm * 12 cm
Area of a rectangle = 192 cm^2

Now, we calculate the area of the triangle to subtract to the area we found and obtain the real area, the formula to obtain the area of a triangle is:

Area of a triangle = (base * height) / 2

The height of the triangle is 8 cm, and the base is 8 cm too, because you subtract to the base of the rectangle (16 cm) the measurements in the upper part (16 - 4 - 4 = 8), Now, we replace in the formula:

Area of a triangle = (8 cm * 8 cm) / 2
Area of a triangle = (64 cm^2) / 2
Area of a triangle = 32 cm^2

We subtract to the found area:

Area of the picture = 192 cm^2 - 32 cm^2
Area of the picture = 160 cm^2

To find the perimeter, you must add all the sides of the picture, but, as you can see, there is a side that doesn't have the measurent, this is the hypotenuse of the triangle used before, but how we know the other sides, we can use Pythagorean theorem:

$a^{2}+b^{2}=c^{2}$

Where:

a = Opposite leg (8 cm)
b = Adjacent leg (8 cm)

So, we replace in the theorem:

$a^{2}+b^{2}=c^{2}$

$(8 cm)^{2}+(8cm)^{2}=c^{2}$ (and we clear c)
$\sqrt{(8 cm)^{2}+(8cm)^{2}} =c$
$\sqrt{64 cm^{2}+64cm^{2}} =c$
$\sqrt{128cm^{2}} =c$
c = 11.3137085 cm
c ≅ 11.31 cm

At last, we add all the sides of the picture begining by the base and going by the left side:

Perimeter of the picture = 16 cm + 12 cm + 4 cm + 11.31 cm + 8 cm + 4 cm + 12 cm
Perimeter of the picture = 67.31 cm approximately.

7 0

3 years ago

12, 9, 15, 19, 20, 15 Mean Median Mode

Ede4ka [16]

Answer:

Mean: 15

Median: 15

Mode: 15

Step-by-step explanation:

<h2>Definitions:</h2>

Mean: It represents the average value of a given data set. The formula for finding the mean of a given set of numbers by taking the quotient of all numbers and the number of values. In other words:

$\displaystyle\mathsf{Mean\:=\:\frac{Sum\:of \:all\: values}{Number\:of\:values \:in\: a \:given \:data\:set}}$

Median: It represents the middle value in a given set of numbers. In order to determine the median, it is essential to arrange the given data either in ascending or descending order (although it is customary to arrange the numbers into ascending order).

If there is an odd number of values in a given set, then the middle number is the median of that set.

If a given list comprises of an even number of items, then we must take the average of the two middle numbers.

Mode: It represents the number that occurs most often on a list of items or data.

<h2>Solution:</h2><h3>Find the Mean:</h3>

Using the formula provided in the previous section for finding the mean:

$\displaystyle\mathsf{Mean\:=\:\frac{Sum\:of \:all\: values}{Number\:of\:values \:in\: a \:given \:data\:set}}$

$\displaystyle\mathsf{Mean\:=\:\frac{12+9+15+19+20+15}{6}\:=\:\frac{90}{6}\:=\:15}$

<h3>Find the Median:</h3>

Arrange the given data set in ascending order:

12, 9, 15, 19, 20, 15 ⇒ 9, 12, 15, 15, 19, 20

Next, since there is an even number of items on our given data set, we must take the average of the two middle numbers (which are 15 and 15):

$\displaystyle\mathsf{Median\:=\:\frac{15+15}{2}\:=\:\frac{30}{2}\:=\:15}$

Therefore, the median is 15.

As described in the previous section of this post, the mode is the number that occurs most often on our given data. The only repeating number on our list is 15, hence it is the mode.

Therefore, the mean, median, and mode of the given data set is 15.

6 0

3 years ago