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3 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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The radius of Earth is about 6.38 x 10³ kilometers. Write this distance in standard notation.

Nina [5.8K]

Answer:

6380

Step-by-step explanation:

You can use your calculator or knowing that 10^3 is 1000 so 6.38 x 1000= 6380.

7 0

2 years ago

The table shows the average annual cost of tuition at 4-year institutions from 2003 to 2010.

nata0808 [166]

Answer: 1) The best estimate for the average cost of tuition at a 4-year institution starting in 2020 =$ 31524.31

2) The slope of regression line b=937.97 represents the rate of change of average annual cost of tuition at 4-year institutions (y) from 2003 to 2010(x). Here,average annual cost of tuition at 4-year institutions is dependent on school years .

Step-by-step explanation:

1) For the given situation we need to find linear regression equation Y=a+bX for the given situation.

Let x be the number of years starting with 2003 to 2010.

i.e. n=8

and y be the average annual cost of tuition at 4-year institutions from 2003 to 2010.

With reference to table we get

$\sum x=36\\\sum y=150894\\\sum x^2=204\\\sum xy=718418$

By using above values find a and b for Y=a+bX, where b is the slope of regression line.

$a=\frac{(\sum y)(\sum x^2)-(\sum x)(\sum xy)}{n(\sum x^2)-(\sum x)^2}=\frac{150894(204)-(36)718418}{8(204)-(36)^2}=\frac{30782376-25863048}{1632-1296}=\frac{4919328}{336}\\\\=14640.85$

and

$b=\frac{n(\sum xy)-(\sum x)(\sum y)}{n(\sum x^2)-(\sum x)^2}=\frac{8(718418)-(36)150894}{8(204)-(36)^2}=\frac{5747344-5432184}{1632-1296}=\frac{315160}{336}\\\\=937.97$

∴ To find average cost of tuition at a 4-year institution starting in 2020.(as n becomes 18 for year 2020 if starts from 2003 ⇒X=18)

So, Y= 14640.85 + 937.97×18 = 31524.31

∴The best estimate for the average cost of tuition at a 4-year institution starting in 2020 = $31524.31

4 0

3 years ago

You have 6L feet of fence to make a rectangular vegetable garden alongside the wall of your house, where L is a positive constan

nika2105 [10]

Answer:

A(max) = (9/2)*L² ft²

Dimensions:

x = 3*L feet

y = (3/2)*L ft

Step-by-step explanation:

Let call "x" and " y " sides of the rectangle. The side x is parallel to the wall of the house then

Area of the rectangle is

A(r) = x*y

And total length of fence available is 6*L f , and we will use the wall as one x side then, perimeter of the rectangle which is 2x + 2y becomes x + 2*y

Then

6*L = x + 2* y ⇒ y = ( 6*L - x ) /2

And the area as function of x is

A(x) = x* ( 6*L - x )/2

A(x) = ( 6*L*x - x² ) /2

Taking derivatives on both sides of the equation we get:

A´(x) = 1/2 ( 6*L - 2*x )

A´(x) = 0 ⇒ 1/2( 6*L - 2*x ) = 0

6*L - 2*x = 0

-2*x = - 6*L

x = 3*L feet

And

y = ( 6*L - x ) /2 ⇒ y = ( 6*L - 3*L )/ 2

y = ( 3/2)*L feet

And area maximum is:

A(max) = 3*L * 3/2*L

A(max) = (9/2)*L² f²

4 0

2 years ago

Read 2 more answers

The following scores represent students' test grades in Ms. Orr's science class. Test Scores 78 81 78 81 78 81 78 81 78 87 91 87

Alex17521 [72]

Answer:

Its definitely B 84.5

I took the test

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

3 is less then is equal to 7 +g

Helga [31]

G >\ -4 ( g is greater than or equal to negative 4 )

8 0

2 years ago