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2 years ago

How many pennies are on the nth square? 2n 2n â€"" 1 2n 1 2n â€"" 1 2n 1.

Mathematics

1 answer:

Olenka [21]2 years ago

4 0

The number of pennies is an illustration of pattern and sequence.

The number of pennies in the nth square is $2^{n-1$

From the complete question, we have the following parameters

$f(1) =1$

$f(2) =2$

$f(3) =4$

$f(4) =8$

Rewrite the functions as follows:

$f(1) = 2^0$

$f(2) = 2^1$

$f(3) = 2^2$

$f(4) = 2^3$

Express 3 as 4 - 1

$f(4) = 2^{4-1$

Replace 4 with n

$f(n) = 2^{n-1$

Hence, the number of pennies in the nth square is $2^{n-1$

Read more about pattern and sequence at:

brainly.com/question/24655254

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Find the distance between the points (9,3) and (–5,3).

Nutka1998 [239]

Answer:

The answer to the question provided is 14.

Step-by-step explanation:

》The Distance Formula:

$d = \sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2} }$

》Plug in.

$d = \sqrt{( - 5 - 9)^{2} + (3 - 3) ^{2} } \\ d = \sqrt{( - 14)^{2} + (0) ^{2} } \\ d = \sqrt{196 + 0} \\ d = \sqrt{196} \\ d = 14$

6 0

3 years ago

You deposit 2000 in account A, which pays 2.25% annual interest compounded monthly. You deposit another 2000 in account b, which

stellarik [79]

To model this situation, we are going to use the compound interest formula: $A=P(1+ \frac{r}{n} )^{nt}$
where
$A$ is the final amount after $t$ years
$P$ is the initial deposit
$r$ is the interest rate in decimal form
$n$ is the number of times the interest is compounded per year
$t$ is the time in years

For account A:
We know for our problem that $P=2000$ and $r= \frac{2.25}{100} =0.0225$ . Since the interest is compounded monthly, it is compounded 12 times per year; therefore, $n=12$ . Lets replace those values in our formula:
$A=2000(1+ \frac{0.0225}{12} )^{12t}$

For account B:
$P=2000$ , $r= \frac{3}{100} =0.03$ , $n=12$ . Lest replace those values in our formula:
$A=2000(1+ \frac{0.03}{12} )^{12t}$

Since we want to find the time, $t$ , <span>when the sum of the balance in both accounts is at least 5000, we need to add both accounts and set that sum equal to 5000:
</span> $2000(1+ \frac{0.0225}{12} )^{12t}+2000(1+ \frac{0.03}{12} )^{12t}=5000$

Now that we have our equation, we just need to solve for $t$ :
$2000[(1+ \frac{0.0225}{12} )^{12t}+(1+ \frac{0.03}{12} )^{12t}]=5000$
$(1+ \frac{0.0225}{12} )^{12t}+(1+ \frac{0.03}{12} )^{12t}= \frac{5000} {2000}$
$(1.001875)^{12t}+(1.0025 )^{12t}= \frac{5}
{2}$
$ln(1.001875)^{12t}+ln(1.0025 )^{12t}=ln( \frac{5} {2})$
$12tln(1.001875)+12tln(1.0025 )=ln( \frac{5} {2})$
$t[12ln(1.001875)+12ln(1.0025 )]=ln( \frac{5} {2})$
$t= \frac{ln( \frac{5}{2} )}{12ln(1.001875)+12ln(1.0025 )}$
$17.47$

We can conclude that after 17.47 years <span>the sum of the balance in both accounts will be at least 5000.</span>

5 0

3 years ago

dolores and four friends went to a buffet dinner.The total cost was at most $130 including the $20 dollar tip they left.How much

Levart [38]

So the actual meal was at most 130 dollars they paid minus the 20 dolars tip: 130-20=110 dollars.

it was 5 people: Dolores+5 friends, who presumably all paid the same (buffet).

then we have to divide the 110 among the 5 people: it's 110/5=22

so each of them paid at most 22 dollars:

x (the amount they paid)≤22

5 0

3 years ago

16 POINTS HELP ASAP plzzzzzzzzz

schepotkina [342]

Answer:

$\large\boxed{\large\boxed{\sqrt{3}$