Alright, so you have the basic formula- good.
You have the A value (400), the interest rate r (7.5% -> .075 in decimal), and the final P value (8500). So, we only need to solve for t.
8500 = (400)(1+.075)^t
/400 /400
21.25 = 1.075^t
logarithms are the inverse of exponents, basically, if you have an example like
y = b^x, then a logarithm inverts it, logy(baseb)=x
Makes sense if you consider a power of ten.
1000 = 10^3
if you put logbase10(1000), you'll get 3.
Anyways, though, to solve the problem make a log with a base of 1.075 in your calculator
log21.25(base 1.075) = t
also, because of rules of change of base (might want to look this up to clarify), you can write this as log(21.25)/log(1.075) = t
Thus, t is 42.26118551.
Rounded to hundredths, t=42.26
Answer:
The angle that the ramp makes with the ground is 11.54°
Step-by-step explanation:
From the image attached, we can see that the length of 17 1/2 ft corresponds to the hypotenuse in a right triangle, the length of 3 1/2 ft corresponds to the opposite side.
We can use the fact that the sin(θ) = 
to find the angle that the ramp makes with the ground.
The angle is equal to
Answer:
261.98 is the value of the given expression.
Step-by-step explanation:
We have to find the value of the following expression:
Using the associative property, we can write and solve the given expression as:
Rounding off the answer, we get,
Thus, 261.98 is the value of the given expression.
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:
</span>____________________
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":
________________________________________________
→ 7 * 1,829 = ?
________________________________________________
→ 7 * 1,829 = (7*9) + (7*20) + (7*800) + (1,000) ;
________________________________________________
→ 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! .
_______
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.
_____
→ 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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