A set of four stars form the shape of a rectangle in space. The length of the rectangle is approximately 3,080,000 miles, while the width of the rectangle is approximately 6,220,000,000 miles. What is the approximate area of the rectangle?

To find the area of the rectangle, we can use the formula for the area \( A \) of a rectangle:

\[ A = \text{length} \times \text{width} \]

Given:

• Length = 3,080,000 miles
• Width = 6,220,000,000 miles

Let's convert these numbers into scientific notation for easier calculation:

• Length: \( 3,080,000 = 3.08 \times 10^6 \)
• Width: \( 6,220,000,000 = 6.22 \times 10^9 \)

Next, we can calculate the area:

\[ A = (3.08 \times 10^6) \times (6.22 \times 10^9) \]

Using the properties of exponents, we can multiply the coefficients and add the exponents:

\[ A = (3.08 \times 6.22) \times 10^{6 + 9} \]

Calculating the coefficient:

\[ 3.08 \times 6.22 \approx 19.1576 \]

And adding the exponents:

\[ 10^{6 + 9} = 10^{15} \]

Thus, we have:

\[ A \approx 19.1576 \times 10^{15} \text{ square miles} \]

To match this with the provided answer options, we have:

\[ 19.1576 \times 10^{15} = 1.91576 \times 10^{16} \text{ square miles} \]

Therefore, the approximate area of the rectangle is:

D. \( 1.91576 \times 10^{16} \) square miles.

Which shows the expression below in simplified form?

(2.9 × 1012) + (3.5 × 109)
A.
2.90035 × 109
B.
6.4 × 1012
C.
2.9035 × 1012
D.
2.935 × 109

To simplify the expression \((2.9 \times 10^{12}) + (3.5 \times 10^{9})\), we will first express both terms in the same power of ten. It's easier to convert \(3.5 \times 10^{9}\) to \(10^{12}\):

1. Convert \(3.5 \times 10^{9}\) to \(10^{12}\): \[ 3.5 \times 10^{9} = 0.0035 \times 10^{12} \]

2. Now substitute this into the original expression: \[ (2.9 \times 10^{12}) + (0.0035 \times 10^{12}) \]

3. Since both terms now have the same power of ten, we can add the coefficients: \[ (2.9 + 0.0035) \times 10^{12} = 2.9035 \times 10^{12} \]

Thus, the simplified expression is:

C. \( 2.9035 \times 10^{12} \).

The number of managed honey bee colonies in the United States in 1946 was about 5.8 × 106 colonies. In 2008, the number of managed honey bee colonies was about 2,270,000 colonies. What is the difference in the number of colonies in the United States from 1946 to 2008?
A.
1.69 × 107 colonies
B.
3.53 × 106 colonies
C.
1.69 × 106 colonies
D.
3.53 × 107 colonies

To find the difference in the number of managed honey bee colonies in the United States from 1946 to 2008, we can first convert both values into scientific notation:

1. 1946: The number is given as \(5.8 \times 10^6\) colonies.
2. 2008: The number is \(2,270,000\) colonies. In scientific notation, this can be expressed as: \[ 2,270,000 = 2.27 \times 10^6 \]

Now, we can find the difference between the two values:

\[ \text{Difference} = (5.8 \times 10^6) - (2.27 \times 10^6) \]

Since both numbers are expressed in terms of \(10^6\), we can simply subtract their coefficients:

\[ = (5.8 - 2.27) \times 10^6 \]

Calculating the coefficient:

\[ 5.8 - 2.27 = 3.53 \]

Putting it all together, we have:

\[ \text{Difference} = 3.53 \times 10^6 \]

Matching this with the provided answer options, the difference in the number of colonies from 1946 to 2008 is:

B. \(3.53 \times 10^6\) colonies.

Marissa is reading over her blood work results from her doctor. According to the report, there are about 3.7 × 105 platelets and about 9,300 white blood cells in a microliter of blood.

What is the total number of platelets and white blood cells in a microliter of blood?
A.
3.8 × 105
B.
4.63 × 104
C.
3.8 × 104
D.
4.63 × 105

To find the total number of platelets and white blood cells in a microliter of blood, we need to add the two quantities together.

1. Platelets: Given as \(3.7 \times 10^5\).
2. White Blood Cells: Given as \(9,300\).

We can convert \(9,300\) into scientific notation: \[ 9,300 = 9.3 \times 10^3 \]

Now we need to add these two numbers. However, since they are in different powers of ten, we should express \(9.3 \times 10^3\) in terms of \(10^5\):

\[ 9.3 \times 10^3 = 0.093 \times 10^5 \]

Now we can add these two numbers: \[ \text{Total} = (3.7 \times 10^5) + (0.093 \times 10^5) \]

Now we can combine the coefficients: \[ = (3.7 + 0.093) \times 10^5 \] \[ = 3.793 \times 10^5 \]

However, 3.793 is not among the given answer options. The value \(3.793\) can be approximated as \(3.8\).

Thus, rounding to 2 significant figures, we find: \[ \text{Total} \approx 3.8 \times 10^5 \]

So, the total number of platelets and white blood cells in a microliter of blood is:

A. \(3.8 \times 10^5\).