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Umnica [9.8K]
3 years ago
12

Mr. Valdez puts $10,000 in a retirement account and does not make any deposits or withdrawals. The table below shows the amount

of money in the account after x years.
A 2-column table with 5 rows. The first column is labeled years with entries 0, 10, 20, 30, 40. The second column is labeled amount (dollar sign) with entries 10,000; 16,000; 27,000; 43,000; 70,000.
What values, rounded to the nearest hundredth, complete the exponential regression equation that models the data?



f(x) =
(
)x
Mathematics
2 answers:
Maurinko [17]3 years ago
7 0

Answer:

f(x)= 9,974.73  (1.05)x

Lunna [17]3 years ago
3 0

Answer:

f(x)= 9,974.73  (1.05)x

Step-by-step explanation:

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Root 3 cosec140° - sec140°=4<br>prove that<br><br>​
Lorico [155]

Answer:

Step-by-step explanation:

We are to show that \sqrt{3} cosec140^{0} - sec140^{0} = 4\\

<u>Proof:</u>

From trigonometry identity;

cosec \theta = \frac{1}{sin\theta} \\sec\theta = \frac{1}{cos\theta}

\sqrt{3} cosec140^{0} - sec140^{0} \\= \frac{\sqrt{3} }{sin140} - \frac{1}{cos140} \\= \frac{\sqrt{3}cos140-sin140 }{sin140cos140} \\

From trigonometry, 2sinAcosA = Sin2A

= \frac{\sqrt{3}cos140-sin140 }{sin140cos140} \\\\=  \frac{\sqrt{3}cos140-sin140 }{sin280/2}\\=  \frac{4(\sqrt{3}/2cos140-1/2sin140) }{2sin280}\\\\= \frac{4(\sqrt{3}/2cos140-1/2sin140) }{sin280}\\since sin420 = \sqrt{3}/2 \ and \ cos420 = 1/2  \\ then\\\frac{4(sin420cos140-cos420sin140) }{sin280}

Also note that sin(B-C) = sinBcosC - cosBsinC

sin420cos140 - cos420sin140 = sin(420-140)

The resulting equation becomes;

\frac{4(sin(420-140)) }{sin280}

= \frac{4sin280}{sin280}\\ = 4 \ Proved!

3 0
3 years ago
Anna invests $7,000 in an account that compounds interest continuously and earns 7.5%. How long will it take for her
NeX [460]

Answer:

It will take 36.1 years for her money to reach $105,000.

Step-by-step explanation:

The amount of money earned after t years in continuous interest is given by:

P(t) = P(0)e^{rt}

In which P(0) is the initial investment and r is the interest rate, as a decimal.

Anna invests $7,000 in an account that compounds interest continuously and earns 7.5%.

This means that P(0) = 7000, r = 0.075

How long will it take for her money to reach $105,000?

This is t for which P(t) = 105000.

P(t) = P(0)e^{rt}

105000 = 7000e^{0.075t}

e^{0.075t} = \frac{105000}{7000}

e^{0.075t} = 15

\ln{e^{0.075t}} = \ln{15}

0.075t = \ln{15}

t = \frac{\ln{15}}{0.075}

t = 36.1

It will take 36.1 years for her money to reach $105,000.

6 0
3 years ago
how much does a bag of wood chips weighs 12.4 pounds how much does a bad that contains .42 as many wood chips weigh
Law Incorporation [45]

Answer:

5.208 lbs

Step-by-step explanation:

12.4 lbs times 0.42 is 5.208 lbs

it is simple

3 0
3 years ago
Read 2 more answers
Kennedy buys cell phone cases for $4.50 and sells them to her friends for $18.00. What is the percent mark-up?
lidiya [134]
300% markup is the answer
7 0
3 years ago
Jessica skated 4 laps in 82 seconds.how long does it take her to skate 16 laps
valentina_108 [34]
It would take 328 seconds or 5 minutes and 47 seconds
8 0
3 years ago
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