Gary bought a car for $40,000. If V = 40,000(.85)t represents the value of the car after t years, how long will it take the car to be worth less than one-fourth of its purchase price? A) 4 years B) 6 years C) 8 years D) 9 years

Answers

Answer 1

Answer:

Answer:

D) 9 years.

Step-by-step explanation:

We have been given that Gary bought a car for $40,000 and equation $V=40,000(0.85)^t$ represents the value of the car after t years.

First of all we will find the one-fourth of 40,000.

$\text{One-forth of car's purchase price}=(\$40,000)/(4)$

$\text{One-forth of car's purchase price}=\$10,000$

To find the time it will take the car to be worth less than one-fourth of its purchase price, we will substitute V=10,000 in our given equation.

$10,000=40,000(0.85)^t$

Let us divide both sides of our equation by 40,000.

$(10,000)/(40,000)=(40,000(0.85)^t)/(40,000)$

$0.25=0.85^t$

Let us take natural log of both sides of our equation.

$ln(0.25)=ln(0.85^t)$

Using natural log property $ln(a^b)=b*ln(a)$ we will get,

$ln(0.25)=t*ln(0.85)$

$(ln(0.25))/(ln(0.85))=(t*ln(0.85))/(ln(0.85))$

$(-1.3862943611198906)/(-0.1625189294977749)=t$

$8.530048563597=t$

Upon rounding our answer to the nearest year we will get,

$t\approx 9$

Therefore, it will take 9 years the car to be worth less than one-fourth of its purchase price and option D is the correct choice.

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Factors of -36 that add to 13

Answers

To solve this problem follow the steps below.

Step 1:List out all of the factors for -36

-36: 1,2,3,4,6,9,12,18,36
-1,-2,-3,-4,-6,-9,-12,-18,-36

Step 2: Start going through a process of guessing and checking (basically take any two factors and add them together to see if they equal 13)

1 plus 12=13
9 plus 4=13

Step 3:Check your calculations and make sure you didn't make any errors

13-12=1 and 13-1=12
13-9=4 and 13-4=9

Answer: 1 and 12
4 and 9

I hope this helps and if any false information was given I apologize in advance.

According to the Rational Roots Theorem, which statement about f(x) = 25x^7 – x^6 – 5x^4 + x – 49 is true?Any rational root of f(x) is a multiple of –49 divided by a multiple of 25.

Any rational root of f(x) is a multiple of 25 divided by a multiple of –49.

Any rational root of f(x) is a factor of –49 divided by a factor of 25.

Any rational root of f(x) is a factor of 25 divided by a factor of –49.

Answers

Answer:

Any rational root of f(x) is a factor of -49 divided by a factor of 25.

Step-by-step explanation:

The Rational Root Theorems states that :

If the polynomial $P(x)= a _nx^n +{a_(n-1)x}^(n-1)+............{a_(2)x}^(2)+{a_(1)x}^(1)+a_0$ has any rational roots, then they must be in the form of

$\pm (factors of a_0)/(factors of a_n)$

Consider the polynomial

$f(x)=25x^7-x^6-5x^4+x-49$

in this case, we have $a_0=-49$ and $a_n=25$

Any Rational root of f(x) is a factor of $a_0=-49$ divided by a factor of $a_n=25$

According to the Rational Roots Theorem, the statement about f(x) = 25x^7 – x^6 – 5x^4 + x – 49 which is true is:

Any rational root of f(x) is a factor of –49 divided by a factor of 25.

The key points are "factors", and "ratio between the constant term and the coefficient of the highest order (exponent) term"

Suppose the radius of a circle is 7. What is its area?

Answers

Answer=153.9 (when you round to the nearest tenth)

Area=π r²
Area=π 7²
Area=π*49
Area=153.938040026
round to the nearest tenth...
Area=153.9

The GDP is $123.7 billion. The population is 4 million. Find the per capita GDP.

Answers

Answer:

The per capita GDP is 30.925.

Step-by-step explanation:

Since,

$\text{Per capita GDP}=\frac{\text{Real GDP}}{\text{Population}}$

Here,

The real G.D.P. = $123.7 billion = $ 123700 million

( 1 Billion = 1000 Million ),

Also, Population = 4 million,

By Substituting the values in the above formula,

$\text{Per capita GDP}=(123700)/(4)=30925= 30.925$

(123.7*10^9)/(4*10^6)=$30,925

i think thats correct

Dylan started with 10,000 baseball cards to sell. In each subsequent week, Dylan started with approximately 85% of the previous week's starting number of cards. What is the explicit rule for the number of cards Dylan starts with in week n and approximately how many cards will he start with in the 6th week? Round to the nearest card. Drag and drop the answers into the boxes to match the situation. Explicit rule Amount of cards after the 6th week.

Answers

Answer:

Number of cards at week n = 10,000(0.85)^(n-1).

At week 6 Dylan has 4437 cards.

Step-by-step explanation:

At the start of week 1 he had 10,000 = 10,000(0.85)^0 cards.

So at the start of week 2 he had 10,000(0.85)^(2-1) cards.

Number of cards for week n = 10,000(0.85)^(n-1).

Number of he will have at the start of the 6th week

= 10,000(0.85)^(6-1)

= 4437 cards (answer).

one of the requirements of becoming a court reporter is the ability to type 225 words per minute. Donald can currently type 180 words per minute, and believes that with practice he can increase his typing speed by 5 words per minute each month. Which of the following represents the number of words per minute that don't believe he'll be able to type M months from now?<br /> A) 5+180m<br /> B) 225+5m<br /> C) 180+5m<br /> D) 180-5m

Answers

D because it is always subtract 5 words every month

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