All categories

3 years ago

Place values and whole number

Mathematics

1 answer:

LenKa [72]3 years ago

7 0

9. ( 1×10,000)+(5×1,000)+(4×100)+(9×1) ; fifteen thousand , four hundred - nine

You might be interested in

Prove A-(BnC) = (A-B)U(A-C), explain with an example

NikAS [45]

Answer:

Prove set equality by showing that for any element $x$ , $x \in (A \backslash (B \cap C))$ if and only if $x \in ((A \backslash B) \cup (A \backslash C))$ .

Example:

$A = \lbrace 0,\, 1,\, 2,\, 3 \rbrace$ .

$B = \lbrace0,\, 1 \rbrace$ .

$C = \lbrace0,\, 2 \rbrace$ .

$\begin{aligned} & A \backslash (B \cap C) \\ =\; & \lbrace 0,\, 1,\, 2,\, 3 \rbrace \backslash \lbrace 0 \rbrace \\ =\; & \lbrace 1,\, 2,\, 3 \rbrace \end{aligned}$ .

$\begin{aligned}& (A \backslash B) \cup (A \backslash C) \\ =\; & \lbrace 2,\, 3\rbrace \cup \lbrace 1,\, 3 \rbrace \\ =\; & \lbrace 1,\, 2,\, 3 \rbrace\end{aligned}$ .

Step-by-step explanation:

Proof for $[x \in (A \backslash (B \cap C))] \implies [x \in ((A \backslash B) \cup (A \backslash C))]$ for any element $x$ :

Assume that $x \in (A \backslash (B \cap C))$ . Thus, $x \in A$ and $x \not \in (B \cap C)$ .

Since $x \not \in (B \cap C)$ , either $x \not \in B$ or $x \not \in C$ (or both.)

If $x \not \in B$ , then combined with $x \in A$ , $x \in (A \backslash B)$ .
Similarly, if $x \not \in C$ , then combined with $x \in A$ , $x \in (A \backslash C)$ .

Thus, either $x \in (A \backslash B)$ or $x \in (A \backslash C)$ (or both.)

Therefore, $x \in ((A \backslash B) \cup (A \backslash C))$ as required.

Proof for $[x \in ((A \backslash B) \cup (A \backslash C))] \implies [x \in (A \backslash (B \cap C))]$ :

Assume that $x \in ((A \backslash B) \cup (A \backslash C))$ . Thus, either $x \in (A \backslash B)$ or $x \in (A \backslash C)$ (or both.)

If $x \in (A \backslash B)$ , then $x \in A$ and $x \not \in B$ . Notice that $(x \not \in B) \implies (x \not \in (B \cap C))$ since the contrapositive of that statement, $(x \in (B \cap C)) \implies (x \in B)$ , is true. Therefore, $x \not \in (B \cap C)$ and thus $x \in A \backslash (B \cap C)$ .
Otherwise, if $x \in A \backslash C$ , then $x \in A$ and $x \not \in C$ . Similarly, $x \not \in C \!$ implies $x \not \in (B \cap C)$ . Therefore, $x \in A \backslash (B \cap C)$ .

Either way, $x \in A \backslash (B \cap C)$ .

Therefore, $x \in ((A \backslash B) \cup (A \backslash C))$ implies $x \in A \backslash (B \cap C)$ , as required.

8 0

2 years ago

What is the standard deviation of the following data set rounded to the nearest tenth?

Georgia [21]

<span>Note that the mean (78 +90 +456 +676 + 111+ 381+ 21)/7 = 259
The differences (in absolute value - we're going to square later so it doesn't matter) between each piece of data and the mean are
181, 169, 197, 417, 148, 122, 238
Square each of these and add the results together to obtain 367452
Now your question depends on whether you want the sample standard deviation or population standard deviation - which you have not specified. In the first case divide by 6. In the second case divide by 7. We get roughly 61242 or 52493. The square root of each yields 247.47 or 229.11 depending on whether you want the sample sd or pop sd. The 4 choices imply you are looking for the latter, so the answer is A.i think</span>

5 0

2 years ago

Read 2 more answers

The perimeter of a rectangular house is 122fr the width is 5ft less than the length find the length and width

Step2247 [10]

Hello,

Let's w the width , l the length, p the perimeter.

w=l-5
p=2(l+w)=2(l+l-5)=4l-10

4l-10=122
==>4l=122+10
==>4l=132
==>l=132/4
==>l=33
So w=33-5=28

Proof:
2*(33+28)=2*61=122

3 0

2 years ago

Read 2 more answers

What is the answer to number 6 and 6 is not apart of the problem

Marina86 [1]

Answer:

perhaps 20??? hope its right!

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

What is a constant of proportionality in the equation 3y equals 2x?

Serga [27]

Answer:

y=2/3x (y equals two-thirds x)

Step-by-step explanation:

3y=2x

(divide by 3 on both sides to get just the y value)

3/3y=2/3x

y=2/3x

6 0

3 years ago