Evaluate.

Suppose $2000 is invested at 9% interest compounded continuously. How long will it take for the investment to grow to $10,000? U

Lady bird [3.3K]

Answer:

7

Step-by-step explanation:

sing the equation > A = Pe^rt

20000 = 10000e^0.1t > 10% = 0.1

2 = e^0.1t

log 2 = log e^0.1t > log to the base e

log 2 = 0.1t * 1 log e to the base e =1

0.6931 = 0.1t

t = 6.931

= 7 years

Hope this helps <3

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4 0

3 years ago

Explain in words how to find the product of -4 (-1.5) using a number line.where do you end up

Ierofanga [76]

Answer:

To multiply two minus numbers they will result as a positive number.

the product of any numbers when there is a negtive will always have 2 negtives invlved form three numbers including the answer.

-4 x -1.5 is the same as 4 x 1.5

the answer is 6

Three numbers like -1 x 4 will also be 2 numbers of negative.

= -4

We change this to -4 x 1.5 and shows the answer as -6

But the question had 2 negative numbers already and the answer is just positive 6.

8 0

3 years ago

Read 2 more answers

If 2k, 5k-1 and 6k+2 are the first 3 terms of an arithmetic sequence, find k and the 8th term

Klio2033 [76]

Answer:

see explanation

Step-by-step explanation:

The common difference d of an arithmetic sequence is

d = $a_{2}$ - $a_{1}$ = $a_{3}$ - $a_{2}$

Substitute in values and solve for k, that is

5k - 1 - 2k = 6k + 2 - (5k - 1)

3k - 1 = 6k + 2 - 5k + 1

3k - 1 = k + 3 ( subtract k from both sides )

2k - 1 = 3 ( add 1 to both sides )

2k = 4 ⇒ k = 2

--------------------------------------------------------

The n th term of an arithmetic sequence is

$a_{n}$ = $a_{1}$ + (n - 1)d

$a_{1}$ = 2k = 2 × 2 = 4 and

d = 5k - 1 - 2k = 3k - 1 = (3 × 2) - 1 = 5

Hence

$a_{8}$ = 4 + (7 × 5) = 4 + 35 = 39

4 0

3 years ago

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 lb and

egoroff_w [7]

Answer:

a) $P(140$

$P(0.036$

b) $P(140< \bar X$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

$X \sim N(139,28.1)$

Where $\mu=139$ and $\sigma=28.1$

We are interested on this probability

$P(140$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(140$

And we can find this probability like this:

$P(0.036$

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

$P(0.036$

Part b

For this case we select a sample size of n =32. Since the distribution for X is normal then the distribution for the sample mean $\bar X$ is given by: