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Snowcat [4.5K]
2 years ago
7

Given matrices A and B shown below, find (3)A+(8)B.

Mathematics
1 answer:
Tasya [4]2 years ago
5 0

Answer:

\left[\begin{array}{ccc}32&-55\\3&39\end{array}\right]

Step-by-step explanation:

\left[\begin{array}{ccc}0&-15\\3&15\end{array}\right] +\left[\begin{array}{ccc}32&-40\\0&24\end{array}\right] =\left[\begin{array}{ccc}0+32&-15+(-40)\\3+0&15+24\end{array}\right] = \left[\begin{array}{ccc}32&-55\\3&39\end{array}\right]

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Use the "rule of 72" to estimate the doubling time (in years) for the interest rate, and then calculate it exactly. (Round your
bonufazy [111]

Answer:

Using the rule of 72, the doubling time is 9.35 years.

The exact answer is that the doubling time is 8.89 years.

Step-by-step explanation:

By the rule of 72, we have that the doubling time D is given by:

D = \frac{72}{Interest Rate}

The interest rate is in %.

In our exercise, the interest rate is 7.7%. So, by the rule of 72:

D = \frac{72}{7.7} = 9.35.

Exact answer:

The exact answer is going to be found using the compound interest formula(since the rule of 72 is a simplification of this formula).

The compound interest formula is given by:

A = P(1 + \frac{r}{n})^{nt}

Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.

So, for this exercise, we have:

We want to find the doubling time, that is, the time in which the amount is double the initial amount, double the principal.

A = 2P

r = 0.077

There are 52 weeks in a year, so n = 52

A = P(1 + \frac{r}{n})^{nt}

2P = P(1 + \frac{0.077}{52})^{52t}

2 = (1.0015)^{52t}

Now, we apply the following log propriety:

\log_{a} a^{n} = n

So:

\log_{1.0015}(1.0015)^{52t} = \log_{1.0015} 2

52t = 462.44

t = \frac{462.44}{52}

t = 8.89

The exact answer is that the doubling time is 8.89 years.

6 0
3 years ago
What is 15.062 in word form
Ostrovityanka [42]
Fifteen and sixty two thousanths
6 0
3 years ago
Which sequence or sequences are correct and why?
inessss [21]

Answer:

didn't get the question did u forget to put the sequence ???????

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4 0
3 years ago
Show work. How do you solve for x degree if the hyp= 7 and the opp= 4? (round to the nearest degree)
Stolb23 [73]
So we have the opp and hyp, use sine.

sinx=O/H
sinx=4/7
inverse sine to isolate x.
x=sin⁻¹(4/7)
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3 0
3 years ago
The distance from the center of a circulartrashcan to the edge of the trashcan is 15 inches.What is the area of the top of the t
Black_prince [1.1K]

Answer:

706.95in²

Step-by-step explanation:

This problem bothers on the mensuration of solid shapes, a cylinder

Step one

The trash can has a cylindrical shape

The distance from the center to the edge is the radius r= 15in

Step two

Area of top (circular ) = πr²

A= 3.142*15²

A= 3.142*225

A= 706.95in²

5 0
3 years ago
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