Ask question

Ask question

All categories

2 years ago

14

Juan purchased an antique that had a value of $200, at the time of purchase. Each year, the value of the antique is estimated to

increase %10, percent over its value the previous year. The estimated value of the antique, in dollars, 2 years after purchase can be represented by the expression 200a, where a is a constant. What is the value of a ?

1 answer:

algol132 years ago

3 0

Answer: a= 1.21

Step-by-step explanation:

Note: This is a compound interest problem

Step 1

The value of the antique after one year is:

100% + 10% of the purchase price

= 110% of 200

=110/100 of 200

=1.10 × 200

Step 2

The value after two years is:

110% of the value after one year

=110% of (1.10 × 200)

=110/100 of (1.10× 200)

=1.10×(1.10×200)

=1.21×200

Step 3

Expressing the above solutionin the form 200a:

= 200× a = 200 × 1.21

|a=1.21

Thanks

You might be interested in

Malika charges $7.20 per hour for babysitting. She babysits 4 hours each week. She spends $10 per week and puts the rest of her

Juliette [100K]

$7.20 $28.8 $18.8 $225.6 $225.6
      4     $10     12          .25    $56.4
X___     -_____    X____ X_____ +_____
$28.8    $18.8 225.6 $56.4 $282

You multiply $7.20 by the 4 hours she's working and you'll get $28.80. Then you would subtract the $10 from your answer and get $18.80. Then you'd multiply $18.80 by 12 for the mouths she's working and get $225.60. Next you multiply $225.60 by .25 from the grandparents and get $56.40. Finally you add $225.60 to $56.40 and get $282 in her savings account.

5 0

1 year ago

Amy has a box containing 6 white, 4 red, and 8 black marbles. She picks a marble randomly. It is red. The second time, she picks

Alika [10]

8/15 or 11/15 would b the probabiltity of those

6 0

1 year ago

Market-share-analysis company Net Applications monitors and reports on Internet browser usage. According to Net Applications, in

ASHA 777 [7]

Answer:

a) There is a 2.43% probability that exactly 8 of the 20 Internet browser users use Chrome as their Internet browser.

b) There is an 80.50% probability that at least 3 of the 20 Internet browsers users use Chrome as their Internet browser.

c) The expected number of Chrome users is 4.074.

d) The variance for the number of Chrome users is 3.2441.

The standard deviation for the number of Chrome users is 1.8011.

Step-by-step explanation:

For each Internet browser user, there are only two possible outcomes. Either they use Chrome, or they do not. This means that we can solve this problem using concepts of the binomial probability distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

Google Chrome has a 20.37% share of the browser market. This means that $p = 0.2037$

20 Internet users are sampled, so $n = 20$ .

a.Compute the probability that exactly 8 of the 20 Internet browser users use Chrome as their Internet browser.

This is P(X = 8).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 8) = C_{20,8}.(0.2037)^{8}.(0.7963)^{12} = 0.0243$

There is a 2.43% probability that exactly 8 of the 20 Internet browser users use Chrome as their Internet browser.

b.Compute the probability that at least 3 of the 20 Internet browsers users use Chrome as their Internet browser.

Either there are less than 3 Chrome users, or there are three or more. The sum of the probabilities of these events is decimal 1. So:

$P(X < 3) + P(X \geq 3) = 1$

$P(X \geq 3) = 1 - P(X < 3)$

In which

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{20,0}.(0.2037)^{0}.(0.7963)^{20} = 0.0105$

$P(X = 1) = C_{20,1}.(0.2037)^{1}.(0.7963)^{19} = 0.0538$

$P(X = 2) = C_{20,2}.(0.2037)^{2}.(0.7963)^{18} = 0.1307$

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0105 + 0.0538 + 0.1307 = 0.1950$

$P(X \geq 3) = 1 - P(X < 3) = 1 - 0.1950 = 0.8050$

There is an 80.50% probability that at least 3 of the 20 Internet browsers users use Chrome as their Internet browser.

c.For the sample of 20 Internet browser users, compute the expected number of Chrome users

We have that, for a binomial experiment:

$E(X) = np$

So

$E(X) = 20*0.2037 = 4.074$

The expected number of Chrome users is 4.074.

d.For the sample of 20 Internet browser users, compute the variance and standard deviation for the number of Chrome users.

We have that, for a binomial experiment, the variance is

$Var(X) = np(1-p)$

So

$Var(X) = 20*0.2037*(0.7963) = 3.2441$

The variance for the number of Chrome users is 3.2441.

The standard deviation is the square root of the variance. So

$\sqrt{Var(X)} = \sqrt{3.2441} = 1.8011$

The standard deviation for the number of Chrome users is 1.8011.

6 0

2 years ago

Which statement describes a process to solve sqrt b+20 - sqrt b=5?

babunello [35]

Answer:

Step-by-step explanation:

The equation is:

√b+20 - √b = 5

The first step is we will add √b to both sides:

√b+20 -√b +√b = 5 +√b

√b+20 = 5+√b

Now take square at both sides:

(√b+20)^2 = (5+√b)^2

b+20 = 25+10√b+b

Now combine the like terms:

b+20-25-b=10√b

-5 = 10√b

Divide both the terms by 10

-5/10 = 10√b/10

-1/2=√b

Take square at both sides:

(-1/2)^2 = (√b)^2

1/4 = b

So in this type of question we add radical terms to both sides and square both sides twice....

7 0

1 year ago

HELP PLEASE!! Based on the table, which best predicts the end behavior of the graph of f(x)?

adelina 88 [10]

Solution: The correct option is option D.

Explanation:

The end behavior is the behavior of function as the input of the function approaches to very large value and very small value.

If a function is f(x), then at $x\rightarrow \infty$ and $x\rightarrow -\infty$ the value of f(x) approaches to either infinity or negative infinity which defines the end behavior.

From the given table it is noticed that the as x decreases and approaches to large negative values then the values of the function is also approaches to the large negative values. According to the table as $x\rightarrow -\infty$ , $f(x)\rightarrow -\infty$ .

From the given table it is noticed that the as x increases and approaches to large positive values then the values of the function is approaches to the large negative values. According to the table as $x\rightarrow \infty$ , $f(x)\rightarrow -\infty$ .

Since only option D satisfy the both conditions, therefore the correct option is option D.

4 0

2 years ago

Read 2 more answers