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4 years ago

Explain how to apply the laws of exponents when multiplying and dividing numbers written in scientific notation.

1 answer:

5 0

It is more effective if I explain using examples. So, for multiplication, you just have to multiply the magnitude, then add the exponents of the base 10. For example, when you multiply 5.2×10³ and 1.6×10², the solution would be:

(5.2)(1.6)(10³⁺²) = 8.32×10⁵

Now, for division, you will have to divide the magnitudes, and subtract the exponents by numerator minus denominator. The solution is as follows:

(5.2/1.6)(10³⁻²) = 3.25×10¹

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Marilyn knows that she needs $45,000 for a down payment on a house. She found an investment that earns 3.15% interest compoundin

laila [671]

She should save $38,450.39.

The formula for the amount of money in an interest-bearing account that is compounded is

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

where A is the total amount in the account, p is the amount of principal invested, r is the interest rate as a decimal number, n is the number of times per year interest is compounded, and t is the number of years. Using our information we have:

$45000=p(1+\frac{0.0315}{12})^{12\times5}
\\
\\45000=p(1.002625)^{60}$

Divide both sides:
$\frac{45000}{1.002625^{60}}=\frac{p(1.002625)^{60}}{1.002625^{60}}
\\
\\38450.39=p$

5 0

3 years ago

A square has a length of 2(m+3). What is the perimeter of the square?

katen-ka-za [31]

Answer:

8(m+3)

or 8m+24

Step-by-step explanation:

If one side x has a length of 2(m+3), then using the formula for the perimeter of a square P=4x

You get:

8(m+3)

or 8m+24

6 0

3 years ago

Read 2 more answers

Find the residual values, and use the graphing calculator tool to make a residual plot. A 4-column table with 5 rows. The first

Svetlanka [38]

The best answer from the options that proves that the residual plot shows that the line of best fit is appropriate for the data is: ( Statement 1 ) Yes, because the points have no clear pattern

X Given Predicted Residual value

1 3.5 4.06 -0.56

2 2.3 2.09 0.21

3 1.1 0.12 0.98

4 2.2 -1.85 4.05

5 -4.1 -3.82 -0.28

The residual value is calculated as follows using this formula: ( Given - predicted )

1) ( 3.5 - 4.06 ) = -0.56

2) ( 2.3 - 2.09 ) = 0.21

3) ( 1.1 - 0.12 ) = 0.98

4) (2.2 - (-1.85) = 4.05

5) ( -4.1 - (-3.82) = -0.28

Residual values are the difference between the given values and the predicted values in a given data set and the residual plot is used to represent these values .

attached below is the residual plot of the data set

hence we can conclude from the residual plot attached below that the line of best fit is appropriate for the data because the points have no clear pattern ( i.e. scattered )

learn more about residual plots : brainly.com/question/16821224

5 0

2 years ago

Which of the following is an example of independent events?

Mashcka [7]

Answer:

A. Getting tails from a coin toss and drawing a king from a standard

deck of cards.

Step-by-step explanation:

In probability, independent events are two events that do not affect the outcome of the other. In the first option, whether or not tails is flipped in no way changes the likelihood of a king being drawn. So it is independent because each event can be performed independently of the other.

However, all of the other options are "without replacement". This is a common term used to describe dependent events because since the item is not being replaced, the sample size is changed. This changes the probability of the next outcome. They are called dependent events because the second event depends on the first.

5 0

3 years ago

Pure mathematicsssss

stepan [7]

Answer:

(i) a = 2

b = -1

c = -1

(ii) x= 1

Step-by-step explanation:

Step 1: Factorise

$f(x) = 2(x^{2} -2x+\frac{1}{2})$