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2 years ago

What is the 185th digit in the following pattern 12345678910111213141516...?

1 answer:

4 0

1-9 = 9 digits
10-99 = 180 digits
So if we continue the pattern to 99, there are 189 digits, and the last 5 digits would be 79899. Counting backwards: 189th = 9, 188th = 9, 187th = 8, 186th = 9, 185th = 7.

The 185th digit is 7.

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Gabi is working on another backyard project. She is building a fence to keep deer out of her garden. One side of her garden is a

nydimaria [60]

Answer:

length: 14 feet , width: 43 feet, or

length: 86 feet, width: 7 feet

Both solutions are valid.

Explanation:

1. First assumption is that the shape of the fence is rectangular.

2. Second, assum the length parallel to the wall measure y feet, so the other two lengths, y, together with x will add up 100 feet

2x + y = 100

3. The, the area of the fence will be:

length × width = xy = 600

4. Now you have two equation with two variables which you can solveL

Solve for y in the first equation: y = 100 - 2x

Substitute the value of y into the second equation: x (100 - 2x) = 600

5. Solve the last equation by completing squares:

Distributive property: 100x - 2x² = 600
Divide both sides by - 1: 2x² - 100x = - 600
Divide both sides by 2: x² - 50x = -300
Add the sequare of the half of 50 to both sides: x² - 50x + 625 = 325
Factor the left side: (x - 25)² = 325
Square root both sides: x - 25 = ± 18.028

Clear x: x = 25 ± 18.028
x = 43.028 ≈ 43 or x = 6.972 ≈ 7

Both values are valid,

If x = 43 , then y = 600/43 = 14

If x = 7, then y = 600/7 = 86

Thus, the lenght and width of the fence may be:

43 feet (width) and 14 feet (length), or

7 feet (width) and 86 feet (length).

3 0

2 years ago

The equation d = can be used to calculate the density, d, of an object with mass, m, and volume, V. Which is an equivalent equat

Kamila [148]

Since:
Density=Mass/Volume
Mass=Volume*Density
Therefore, Volume=Mass/Density

4 0

2 years ago

Read 2 more answers

Craig ran the first part of a race with an average speed of 8 miles per hour and biked the second part of a race with an average

lutik1710 [3]

Let the distance of the first part of the race be x, and that of the second part, 15 - x, then
x/8 + (15 - x)/20 = 1.125
5x + 2(15 - x) = 40 x 1.125
5x + 30 - 2x = 45
3x = 45 - 30 = 15
x = 15/3 = 5

Therefore, the distance of the first part of the race is 5 miles and the time is 5/8 = 0.625 hours or 37.5 minutes
The distance of the second part of the race is 15 - 5 = 10 miles and the time is 1.125 - 0.625 = 0.5 hours or 30 minutes.

4 0

2 years ago

Read 2 more answers

If the probability of winning a carnival game was 2/5 and Max played it five times, write an expression that would calculate the

Dvinal [7]

Prob(winning carnival game) = 2/5
Prob(losing carnival game) = 3/5 

Prob (Max wins first 3 games, but loses last 2 games) 

= Prob(Max wins game 1) * Prob(Max wins game 2) * Prob(Max wins game 3) * Prob(Max loses game 4) * Prob(Max loses game 5)

8 0

2 years ago

Consider the statement: The cube of any rational number is a rational number. a. Write the statement formally using a quantifier

3241004551 [841]

Answer:

(a)∀ r∈ℝ, r∈ℚ, r³∈ℚ

(b)True

Step-by-step explanation:

Definition

1. A real number is said to be rational if and only if there exists two integers a and b such that $\frac{a}{b}=r$ where b≠0.

2. If the product of three numbers is zero, then at least one of the numbers must be zero.

Given Statement

The cube of any rational number is a rational number.

This can be rewritten as:

For all real numbers, if the number is rational then its cube is rational.

If we introduce our variable r,

For all real number r, if r is rational, then r³ is rational.

∀ r∈ℝ, r∈ℚ, r³∈ℚ

(b)The Statement is True.

To prove: The cube of any rational number is rational.

Proof:

We assume that r is a rational number and prove that its cube is a rational number.

By definition, there exists integers a and b such that:

$r=\frac{a}{b}$ where b≠0.

$r^3=(\frac{a}{b})^3$

$r^3=\frac{a^3}{b^3}$

Since the cube of an integer is also an integer, a³ and b³ are also integers.

Since b is non-zero, then the zero product property tells us that its cube is also non-zero.

Conclusion:

$r^3=\frac{a^3}{b^3}$ is rational since a³ and b³ are integers and b is non-zero.

6 0

2 years ago