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ArbitrLikvidat [17]

4 years ago

12

Devon purchased a new car valued at $16,000 that depreciated continuously at a rate of 35%. Its current value is $2,000. The equ

ation 2000=16000(1-r)^2 represents the situation, where t is the age of the car in years and r is the rate of depreciation. About how old is Devon’s car? Use a calculator and round your answer to the nearest whole number.
1 year
2 year
5 year
8 year

1 answer:

irga5000 [103]4 years ago

7 0

I hope the equation will be 2000=16000(1-r)^t because t is missing in the equation which we need to find.

Given rate: r= 35%= 0.35.

So, first step is to plug in 0.35 for r in the given formula to get the value of t.

Hence, the equation will be:

2000=16000(1-0.35)^t

2000=16000(0.65)^t (By subtraction)

2000/16000= 16000(0.65)^t /16000 (Dividing each sides by 16000)

0.125 = 0.65^t (By simplifying).

log 0.125 = log 0.65^t (Taking log each sides to isolate t).

log 0.125 = t log 0.65 (By applying the log property).

$\frac{log 0.125}{log 0.65} =t$ (Dividing each sides by log 0.65)

-0.903/-0.187 =t

t= 4.83

t= 5 ( Rounded to nearest integers)

So, Devon's car is 5 years old.

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The graph of an inverse trigonometric function passes through the point (1, pi/2). Which of the following could be the equation

rodikova [14]

Answer: C) $y=sin^-1 x$

Step-by-step explanation:

Since, the graph of an inverse trigonometric function will pass through the point $(1,\frac{\pi}{2})$ ,

If this point satisfies the function,

For the function $y=cos^{-1} x$

If x = 1

$y=cos^{-1}1=0$

Thus, $(1,\frac{\pi}{2})$ is not satisfying function $y=cos^{-1} x$ ,

⇒ The graph of $y=cos^{-1} x$ is not passing through the point $(1,\frac{\pi}{2})$

For the function $y=cot^{-1}x$

If x = 1

$y=cot^{-1}1=\frac{\pi}{4}$

Thus, $(1,\frac{\pi}{2})$ is not satisfying function $y=cot^{-1}x$ ,

⇒ The graph of $y=cot^{-1}x$ is not passing through the point $(1,\frac{\pi}{2})$

For the function $y=sin^{-1} x$

If x = 1

$y=sin^{-1}1=\frac{\pi}{2}$

Thus, $(1,\frac{\pi}{2})$ is satisfying function $y=sin^{-1} x$ ,

⇒ The graph of $y=sin^{-1} x$ is passing through the point $(1,\frac{\pi}{2})$ .

For the function $y=tan^{-1}x$

If x = 1

$y=tan^{-1}1=\frac{\pi}{4}$

Thus, $(1,\frac{\pi}{2})$ is not satisfying function $y=cos^{-1} x$ ,

⇒ The graph of $y=tan^{-1} x$ is not passing through the point $(1,\frac{\pi}{2})$ .

Hence, Option C is correct.

3 0

3 years ago

Find the area of the shape. Either enter an exact answer in terms of pi or use 3.14 for pi and enter your answer as decimal.

SVETLANKA909090 [29]

Answer:

27π units^2

Step-by-step explanation:

This shape is exactly 3/4 of a full circle. Thus, if we find the area of a full circle with radius 6 units, we multiply the result by 3/4 to obtain the area of the figure shown.

A of full circle = πr²

In this particular case,

A of full circle = π(6 units)² = 36π units^2

Then the area of the given figure is

(3/4)(36π) units^2, or 27π units^2.

3 0

4 years ago

I just need help in this last question plsssss

finlep [7]

Answer:

B) 0.8

Step-by-step explanation:

If events are said to be independent, then just multiply the probability of the first event by the second if they are supposed to be happening together.

P (A) * P (B) = 0.8 x 1 = 0.8

8 0

3 years ago

<img src="https://tex.z-dn.net/?f=3%20%20%5Cfrac%7B1%7D%7B2%7D%20%20%2B%202%20%5Cfrac%7B1%7D%7B4%7D%20%20-%201%20%5Cfrac%7B1%7D%

Svetach [21]

Answer:

Step-by-step explanation:

Step 1: Convert into improper fractions

Step 2: Find least common denominator and find equivalent fractions

Step 3 : Do the required operation

$3\frac{1}{2}+2\frac{1}{4}-1\frac{1}{2}=\frac{7}{2}+\frac{9}{4}-\frac{3}{2}\\$

Least common denominator of 2 , 4 = 4

$=\frac{7*2}{2*2}+\frac{9}{4}-\frac{3*2}{2*2}\\\\=\frac{14}{4}+\frac{9}{4}-\frac{6}{4}\\\\=\frac{14+9-6}{4}\\\\=\frac{17}{4}\\\\=4\frac{1}{4}$

5 0

3 years ago

Callie's Gym is a complete fitness center. Owner Callie Ducain employs various fitness trainers who are expected to staff the fr

OLga [1]

Answer:

a)Total Labor Cost = $600x + $30y.

b) Total variable cost = $3000.

c) Total labor cost last month = $6000.

d) Unit cost of labor per class = $60.

e) Total variable labor cost = $30 * 150 = $4500, Total Labor Cost = $3000 + $4500 = $7500, and Unit cost of labor per class = $7500/150 = $50.

Step-by-step explanation:

a) It is given that the labor cost includes two components: cost of trainers, which is actually their salaries, and cost of a fitness class taught. Fitness trainer costs $600 and one fitness class costs $30. Assuming there are x number of trainers and y number of classes, therefore the model can be expressed as:

Total Labor Cost = Fitness Trainer Cost * number of trainers + Fitness Class Cost * number of classes.

Total Labor Cost = $600x + $30y.

b) The total variable labor cost will be the cost spent on the number of classes. Since number of classes are 100 and the cost of one class is $30, therefore:

Total variable cost = cost of one class * number of classes.

Total variable cost = $30 * 100.

Total variable cost = $3000.

c) Furthermore, last month, x = 5 and y = 100. Plug these values in the total labor cost equation:

Total labor cost last month = $600(5) + $30(100).

Total labor cost last month = $3000 + $3000.

Total labor cost last month = $6000.

d) The total labor cost is $600. Number of classes are 100. Therefore:

Unit cost of labor per class = Total Labor Cost/Number of classes.

Unit cost of labor per class = $6000/100.

Unit cost of labor per class = $60.

e) If the number of classes are increases by 50%, this means that the number of classes will be 150 instead of 100. Therefore:

Total variable labor cost = $30 * 150 = $4500.

Total Labor Cost = $3000 + $4500 = $7500.

Unit cost of labor per class = $7500/150 = $50!!!

7 0

3 years ago