How do I solve this and write it in scientific notation?

Answer:

2n - 1, where "n" is the number of days.

Step-by-step explanation:

By looking at the bar graph.

We list the following information.

Day           The number of followers

1                            1

2                          3

3                          5

4                          7

So, the number of followers increase by 2 each day passes.

This is an arithmetic sequence.

The sequence is 1, 3, 5, 7.....

So the rule [tex]a_n = a_1 + (n -1)d[/tex]

This is the n-term of the arithmetic sequence.

Here [tex]a_ 1 = 1 and d = 2[/tex] and n is the number of days.

Plug in these values in the above sequence, we get

The general rule = 1 + (n -1)2

= 1 + 2n-2

= 2n - 1

So the general rule = 2n - 1

Answer:

1) Twenty-one halves of one-thirds are in seven halves.

2) Fourteen-thirds of three-fourths are in five halves.

Step-by-step explanation:

1) To find : How many one-thirds are in seven halves?

Solution :

Let the required number be 'x',

According to question,

[tex]\frac{1}{3}\times x=\frac{7}{2}[/tex]

Solving the equation,

[tex]x=\frac{7\times 3}{2}[/tex]

[tex]x=\frac{21}{2}[/tex]

Therefore, Twenty-one halves of one-thirds are in seven halves.

2) To find : How many three-fourths are in five halves?

Solution :

Let the required number be 'x',

According to question,

[tex]\frac{3}{4}\times x=\frac{5}{2}[/tex]

Solving the equation,

[tex]x=\frac{7\times 4}{2\times 3}[/tex]

[tex]x=\frac{14}{3}[/tex]

Therefore, Fourteen-thirds of three-fourths are in five halves.

Option: b is the correct answer.

                   b)    7.8 miles.

Let us suppose that the city center is located at C(0,0) on the coordinate grid.

Now, The mall is 2 miles east and 2 miles north of the city's center.

This means that the coordinate of  the mall is located at M(2,2)

and Truth Park is 3 miles west and 4 miles south of the city's center.

This means that the coordinate of the Truth park is located at P(-3,-4)

Hence, the distance between the mall and Truth park is equal to the sum of the distance between the Center city and mall and center city and Truth park.

i.e.   PM=CM+PC

From the figure we may observe that:

 [tex]CM=\sqrt{(2-0)^2+(2-0)^2}\\\\CM=\sqrt{4+4}\\\\CM=\sqrt{8}=2\sqrt{2}[/tex]

Hence, [tex]CM=2.828\ miles[/tex]

Similarly,

[tex]PC=\sqrt{(0-(-3))^2+(0-(-4))^2}\\\\\\PC=\sqrt{3^2+4^2}\\\\\\PC=\sqrt{9+16}\\\\\\PC=\sqrt{25}\\\\\\PC=5\ miles[/tex]

Hence, PM=2.828+5=7.828 miles

       The distance between mall and Truth park to the nearest tenth is:

                          7.8 miles

To solve this problem, establish an algebraic equation that equates the sum of the lengths of the three pieces to the total length of the board. Solving this equation reveals that the first piece of wood is 5 inches, the second piece 20 inches and the third piece 25 inches.

This question represents a simple algebraic equation. Since the second piece is 4 times the length of the first piece and the third piece is 5 times the length of the first piece, the sum of these lengths should equal the total length of the board, which is 50 inches. Given that 'x' represents the length of the first piece, we can establish the following equation:

x + 4x + 5x = 50

This is because '4x' is the length of the second piece and '5x' is the length of the third piece. When you combine like terms, the equation simplifies to:

10x = 50

Upon solving this simplified equation, we find that 'x' or the length of the first piece of wood equals 5 inches. Therefore, based on the information provided, the length of the second piece would be 20 inches (4 times 'x') and the third piece would be 25 inches (5 times 'x').

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Step-by-step explanation:    

Apply Exponent Rule

[tex]a^{-b}=\frac{1}{a^b}[/tex]

[tex]=\frac{1}{8^{\frac{5}{8^{-3}}}}[/tex]

Simplify

[tex]=\frac{1}{8^{8^3\cdot \:5}}[/tex]

[tex]=\frac{1}{8^{2560}}[/tex]

Explanation in words (Short Form)

- The first step to simplify this equation (8^-5 / 8^-3) is to first apply the exponent rule then solve this equation as shown above and in the picture. Regarding back to the equation, we will then simplify it and the answer will result as 0. Without simplify the answer is as [tex]=\frac{1}{8^{2560}}[/tex].

Answer: 0: Simplified form

Answer:  

[tex]=\frac{1}{8^{2560}}[/tex]

OR

= 0

Hope this helps.

Answer:

(4.55×10^13- 1.78×10^12)kg

=4.372×10^13kg

the iceberg is 4.372×10^13kg heavier than the rock.

or the iceberg is approximately 2.4 times heavier than the rock

Step-by-step explanation:

To divide 45.35 by 10,000, you need to move the decimal point 4 places to the left because there are 4 zeros in 10,000. This will give you the answer, 0.004535.

To divide 45.35 by 10,000, you essentially move the decimal point 4 places to the left because there are 4 zeros in 10,000. Here is how you do it in steps:

So, 45.35 divided by 10,000 is indeed 0.004535.

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Answer:

The answer is 360

Here's How

-4 x -6=24

24 x -3=72

72 x -5=360

Step-by-step explanation:

Answer:

360

Step-by-step explanation:

The answer is x=-1.

Add 5x on both sides.

10x=-10

Divide both sides by 10.

x=-1.

scientific notation is the standard form of writing numbers in a particular format

scientific notation is writing a number between 0 and 10 times a power of 10

the number to be written is 427 000

so we need to get the decimal point after the first digit from the right

decimal point should come to the right of digit 4

for the decimal to come next to 4 it has to move 5 places to the left. Then its 4.27 multiplied by 10⁵

scientific notation is - 4.27 x 10⁵

Based on the information given 427 thousand as scientific notation is:4.27 x 10⁵.

Scientific notation is the way of writing or expressing number in simplest form.

4.27 x 10⁵=4.27×10×10×10×10×10

4.27 x 10⁵=427,000

Scientific expression=4.27 x 10⁵

Inconclusion  427 thousand as scientific notation is:4.27 x 10⁵.

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Answer:

Step-by-step explanation:

Penelope has a birdhouse that is 4.9 feet above the roof of her garage.

She has a second birdhouse that is 5.36 feet below the roof of her garage.

The distance of first birdhouse from the roof = 4.9 feet

The distance of the second birdhouse from the roof = 5.36 feet

The distance between the birdhouses = 4.9 + 5.36

                                                                = 10.26 feet

Total distance between the birdhouses are 10.26 feet.

Final answer:

The y-intercept is the value of y when x is zero, represented by the constant b in the linear equation y = mx + b. In the example y = 55x + 75, the y-intercept is 75, indicating where the line intersects the y-axis and signaling the initial value of y before any changes in x.

Explanation:

An example of a y-intercept can be found in the linear equation y = mx + b, where b represents the y-intercept. This value is where the line crosses the y-axis on a graph. If we consider the equation y = 55x + 75, for instance, the y-intercept is 75. This means that when x (the independent variable) is zero, the y value, possibly indicating the starting point of a scenario such as labor charges before work begins, is 75.

A real-world example can be seen in a car repair scenario where the total labor charges (y) depend on the number of hours worked (x). Given the equation y = 55x + 75, when no hours are worked (x=0), the total charges start at $75, which is the y-intercept. The slope of the line is 55, indicating that for each additional hour worked, the labor charges increase by $55.

The two numbers that have a difference of 2 and a rounded difference of 100 are: 149 and 151.

When rounded to the nearest hundred, 149 rounds down to 100, and 151 rounds up to 200.

The difference between 100 and 200 is 100, which is the rounded difference between the two numbers.

149 and 151:

Difference: 151 - 149 = 2

Rounded difference: 100 - 0 = 100 (151 rounds to 100 and 149 rounds to 0)

Therefore, the two numbers that have a difference of 2 and a rounded difference of 100 are 149 and 151.

Complete question:

The difference between two numbers is 2. When each number is rounded to the nearest hundred, the difference between them is 100.

Write what the two numbers could be. (1 Point)

197 and 195

125 and 123

149 and 151

97 and 98

Final answer:

An even number is divisible by 2, while an odd number is not. Examples of even numbers are 8 and 10, while examples of odd numbers are 17 and 21.

Explanation:

An even number is a number that is divisible by 2, while an odd number is not divisible by 2.

For example, 2, 4, and 6 are even numbers because they can be divided by 2 without leaving a remainder. On the other hand, 3, 5, and 7 are odd numbers because they cannot be divided by 2 without leaving a remainder.

So, two examples of even numbers could be 8 and 10, while two examples of odd numbers could be 17 and 21.

Answer:

She scored 25 points in the second game more than in the first one.

Step-by-step explanation:

Daniel has [tex]16[/tex] pets.

Since six of his pets are birds(canaries and parrots and he has two parrots, therefore, he has (6 - 2) = 4 canaries.

Since he has one less canary than goldfish, therefore the number of goldfish is (6 + 1) = 7 goldfish

Since he has four more goldfish than he has turtles, the number of turtles are: = ( 7 - 4) = 3

Therefore, the total number of animals will be:

= Parrot + Canary + Goldfish + Turtle

= [tex]2 + 4 + 7 + 3[/tex]

= [tex]16[/tex]

Therefore, he has [tex]16[/tex] pets.

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Final answer:

To find the value of x in the equation x+3.75=11 1/3, convert the mixed number to an improper fraction, subtract and find a common denominator, and solve for x. The solution to the equation is x is approximately 7.5833 or rounded to 7.58.

Explanation:

To solve for x in the equation x+3.75=11 1/3, we first need to convert the mixed number 11 1/3 to an improper fraction. To do this, multiply the whole number by the denominator of the fraction and add the numerator. In this case, (11×3)+1 equals 34, so 11 1/3 is the same as 34/3.

Next, subtract 3.75 from both sides to isolate x on one side of the equation:

x + 3.75 = 34/3

x + 3.75 - 3.75 = 34/3 - 3.75

x = 34/3 - 3.75

To subtract, first convert 3.75 (which is the same as 3 3/4 or 15/4) to an improper fraction, so we get:

x = 34/3 - 15/4

We need a common denominator to subtract these two fractions. The common denominator of 3 and 4 is 12. Multiply the numerator and denominator of the first fraction by 4 and the numerator and denominator of the second fraction by 3 to get:

x = (34×4)/(3×4) - (15×3)/(4×3)

x = 136/12 - 45/12

x = (136 - 45)/12

x = 91/12

x = 7.5833...

Finally, x is approximately 7.5833, which can be rounded to 7.58 if necessary.

The expression "0.09x" represents the amount of tax that is paid on the bicycle.

Expressions are mathematical statements with a minimum of two terms containing variables or numbers.

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

We have been given that the expression 0.09x + (x - 30) models the final price of a bicycle with an instant rebate in a state that charges a sales tax.

⇒ 0.09x + (x - 30)

Here the tax is on the original price.

Here the tax paid on the bicycle is denoted by the term "0.09x".

Thus, the expression "0.09x" represents the amount of tax that is paid on the bicycle.

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The number of wrenches is 10 for which he paid $1.50, and $2.50. the number of wrenches is 5 for which he paid $4, and the number of wrenches is 6 for which he paid $3.

It is defined as the relation between two variables if we plot the graph of the linear equation we will get a straight line.

If in the linear equation one variable is present then the equation is known as the linear equation in one variable.

We have:

Mr. Abernathy bought a selection of wrenches for his shop and paid $78.

Let's suppose:

The number of $1.50 wrenches is x

The number of $2.50 wrenches is also x

The number of $4 wrenches is x/2

The number of $3 wrenches is 1+x/2

Then linear equation becomes:

[tex]\rm 1.50x+2.50x+\frac{4x}{2} +3(1+\frac{x}{2} ) = 78[/tex]

[tex]\rm 3x+5x+4x +3(2+x ) = 156[/tex]

15x = 150

x = 10

The value of x = 10

=x/2 ⇒ 10/ 2 ⇒ 5

= 1+x/2 ⇒ 1+5 ⇒ 6

Thus, the number of wrenches is 10 for which he paid $1.50, and $2.50. the number of wrenches is 5 for which he paid $4, and the number of wrenches is 6 for which he paid $3.

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By dividing the total change in speed (30 miles per hour) by the total time span (10 seconds), it can be determined that Mr. Diaz decreased his car's speed by an average of 3 miles per hour each second.

In this problem, Mr. Diaz decreased his car's speed by 30 miles per hour over a span of 10 seconds. To find the average change in speed each second, we divide the total change in speed by the total time period.

So, we can calculate the average change as follows:

30 miles per hour ÷ 10 seconds = 3 miles per hour per second

Therefore, the average change in Mr. Diaz's car speed each second is 3 miles per hour.

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