The answer: 7 * 1,829 = " 12,803 " .
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<span>The following is the explanation—"in expanded form" — (as per the specfic instructions— within this very question—as to how to get the answer:
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Given: 7 * 1,829 = ? ; Find the solution; using "expanded form" :
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(7 * 9 = 63 ) ; +
(7 *20 = 140) ; +
(7 * 800 = 5,600) ; +
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(7 * 1,000 = 7,000) ;
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Now, add the the values together to solve the problem:
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→ 7 * 1,829 = 63 + 140 + 5,600 + 7,000 ;
{ = 203 + 5,600 + 7,000 } ;
{ = 5,803 + 7,000 } ;
= 12,803 ; which is the answer.
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Alternately, write out the steps as follows—using "expanded form":
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→ 7 * 1,829 = ?
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→ 7 * 1,829 = (7*9) + (7*20) + (7*800) + (1,000) ;
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→ 7 * 1,829 = 63 + 140 + 5,600 + 1,000 ;
{ = 203 + 5,600 + 7,000 } ;
{ = 5,803 + 7,000 } ;
= 12,803 ; which is the answer.
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→ {Now, is our obtained answer: "12,803" ; the "correct answer"—to the problem: " 7 * 1,829 " ;} ??
→ Let us check: {Note: " 7 * 1,829 " ; is the same as: ↔ " 1,829 * 7 " .}.
→ Using a calculator, does: "7 * 1829 = ? 12,803" ?? ; Yes! ;
→ &, for that matter; does: " 1829 * 7 =? 12,803" ?? ; Yes! .
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Furthermore, let us check, using the "traditional format" ;
→ Does: "1,829 * 7 =? 12,803 ?? " ;
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{NB: We are multiplying 2 (TWO) numbers together; & 1 (ONE) of these 2 [TWO] numbers is a "1-digit" ["single-digit"] number; & the "OTHER" multiplicand is a "multiple-digit" [specifically, a"4-digit"] number.}.
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NB: Yes; using a calculator is sufficient. Below, I simply provide an alternate method to confirm whether our "obtained value" is correct.
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→ Does: "7 * 1,289 = ? 12,803" ?? ;
→ Using the "traditional method"; let us check; as follows:
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₅ ₂ ₆
→ 1, 829
<span> <u> * 7 </u> </span>
12 8 03 ;
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So; does: "12,803 =? 12,803" ?? ; YES!
→ This "traditional method" shows that: "7 * 1,829" ; does, in fact, equal: "12,803".
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{NB: Explanation of the steps used in solving the aforementioned problem using the "traditional method"—just for clarification and confirmation} :
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→Start with: "7*9= 63" ; Write down the "3" & 'carry over' the "6" ; {Note the small-sized digit, "6"; written on top of the "2"; {commonly done—to keep track);
→Then; "7*2 = 14" ; then add the "small digit 6"; to the "14" ; →"14+6 =20" ;
Write down the "0" ; & 'carry over' the "2" ; {Note the "small-sized digit, "2"; written over the "8"; (commonly done—to keep track);
→ Then; "7*8 = 56" ; then add the "small digit 2"; to the "56"; → "56+2 = 58" ; Write down the "8" ; & 'carry over' the "5" ; {Note the "small-sized digit", "5" ; written over the "1" ; (commonly done—to keep track);
→Then; "7*1 = 7" ; then add the "small digit 5"; to the "7" ; → "7+5 = 12" ; Write down the "12" ; in its entirety—since are no digits left [in the multiplicand, "1,829"] ; to "carry over".
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We get: "12,803" ; which =? "12,803" ?? ;→Yes!
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I hope my explanation of how to solve "7 * 1,829" ; using the "expanded form" is helpful. Also, i hope my explanation—albeit lengthy— of confirming that [<em>our</em>] "correctly obtained value"—which is: "12,803"— is of some help.
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The correct answer is: [A]: " 384 in² " .
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Explanation:
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The formula for the surface area of a cube is:
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→ A = 6a² ;
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A = surface area of the cube— for which we shall solve ;
(in "square units" ; or, " in² " ; in our case) ;
a = side length = " 8 in " (given);
→ Note: A cube has all equal side lengths.
→ The "6" in the formula accounts for "6 sides" of a cube.
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→ To solve for the surface area of the cube; plug in our known value(s);
& solve; as follows:
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→ A = 6 a² ;
= 6 * (8 in)² ;
= 6 * 8² * in² ;
= 6 * 8 * 8 * in² ;
= 48 * 8 * in² ;
= 384 in² ;
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The answer is: " 384 in² " ;
→ which is: Answer choice: [A]: " 384 in² " .
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The exponential to describe $100 at 2% interest, compounded annually, for x years is 
<h3><u>Solution:</u></h3>
Given that $ 100 at 2 % interest , compounded annually for "x" years
<em><u>The formula for compound interest, including principal sum, is:</u></em>
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per unit t
t = the time the money is invested or borrowed for
Here in this sum,
P = $ 100
number of years = x
Here given that compounded annually , so n = 1
Let "y" be the amount after "x" years
Substituting the values in formula we get,
Thus the exponential to describe is
