Answer:
Pierre invested:
- $9,000 in money market account
- $135,050 in stocks
- $125,050 in the mutual fund
Step-by-step explanation:
A = money market account
B = stocks
C = mutual fund
A + B + C = 269,100
0.031A + 0.04B - 0.02C = 3,180
B = 10,000 + C (we will first replace B)
A + 10,000 + C + C = 269,100
A + 2C = 259,100
0.031A + 0.04(10,000 + C) - 0.02C = 3,180
0.031A + 400 + 0.04C - 0.02C = 3,180
0.031A + 0.02C = 2,780
A + 2C = 259,100
-100(0.031A + 0.02C) = -100 · 2,780
A + 2C = 259,100
-3.1A - 2C = -278,000
-2.1A = -18,900
A = -18,900 / -2.1 = $9,000
C = (259,100 - 9,000) / 2 = $125,050
B = $125,050 + $10,000 = $135,050
The correct answer is: [C]: " m∠H = 91 ° " .
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Explanation:
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Note:
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m∠F + m∠G = 90 ;
{since 2 complementary angles, by definition, add up to 90°.}.
m∠G + m∠H = 180 ;
{since 2 supplementary angles, by definition, add up to 180°.}
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We are asked to find the smallest value of the " m∠H "
(among the given answer choices):
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Note:
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m∠G = 180 − m∠H ;
m∠H = 180 − m∠G ;
m∠F = 90 − m∠G ;
m∠G = 90 − m∠F ;
m∠G = 180 − m∠H ;
m∠H = 180 − m∠G .
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The question is:
"What is the smallest value of " m∠H "; in whole number, among the answer choices given?" ;
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Note: Consider each of the answer choices given:
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Choice: [A]: " m∠H = 1 " ;
{Note, This value is SMALLEST value among ALL the answer choices.}.
If " m∠H = 1" ; then " m∠G = 179 ", since: " m∠G + m∠H = 180".
Then, could "m∠F + m∠G = 90" ?? NO! Because, if "m∠G = 179" ;
then m∠F would have to equal a "negative number" to get:
" m∠F + m∠G = 90 " ;
So, "Choice [A]: " m∠H = 1 " ; is incorrect.
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Choice [B]: " m∠H = 89 " ;
If "m∠H = 89" ; then "m∠G = 91", since: "m∠G + m∠H = 180".
{Note: "180 − m∠H = m∠G " ; → "180 − 89 = m∠G ;
→ "m∠G = 91" .}.
Then, could "m∠F + m∠G = 90" ?? NO! Because, if "m∠G = 91" ; then "m∠F " would have to equal a "negative number" to get: "m∠F + m∠G = 90" ;
So; "Choice: [B]: "m∠H = 89" ; is incorrect.
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Choice [C]: " m∠H = 91 " ;
If "m∠H = 91" ; then "m∠G = 89", since: "m∠G + m∠H = 180".
{Note: "180 − m∠H = m∠G " ; → "180 − 91 = m∠G ; → "m∠G = 89" .}.
Then, could "m∠F + m∠G = 90" ?? YES! Because, if "m∠G = 89" ; then
"m∠F" COULD equal "1" ; and in such a case; "m∠F + m∠G = 1 + 89 = 90."
So; Choice: [C]: " m∠H = 91 " ; is a possible correct answer.
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Let us try the last answer choice:
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Choice [D]: " m∠H = 179 " ;
If "m∠H = 179" ; then "m∠G = 1", since: "m∠G + m∠H = 180".
{Note: "180 − m∠H = m∠G " ; → "180 − 179 = m∠G ; → "m∠G = 1" .}.
Then, would "m∠F + m∠G = 90" ?? Yes! Because, if "m∠G = 1" ; then "m∠F" would equal "89";
{Note: "m∠F + m∠G = 89 + 1 = 90 " .
{Note: "90 − m∠G = m∠F " ; → "90 − 1 = m∠F " ;
→ m∠F = 89° . }.
→ So; "Choice: [D]: " m∠H = 179 " ; is a possible correct answer.
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Note: The question asks:
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"What is the smallest possible measure of "angle H" {" m∠H "} ?
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The 2 (TWO) possible correct answers are:
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Choice [C]: " m∠H "= 91 " ;
and Choice [D]: " m∠H = 179 " .
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The smallest possible " m∠H" is:
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Answer choice: [C]: " m∠H = 91° " .
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Answer:
b
Step-by-step explanation:
-44÷2=-22
34+3.5*-22= -43
$150.00 because if you add all of them up you’ll get 150
Answer: 1/15
Step-by-step explanation: A. If 1/3 cup makes 5 rolls, you need to know how many cups make one. (1/3)/5 = 1/15 Take the number of cups for one roll and multiply it by 3. 1/15 x 3 Final Answer = 3/15
B. Take the number of cups you have divided by 1/3 (since you know how many roles this makes) (5 2/3) / (1/3) Final Answer = 17
C. Well, we already solved for this one in A, didn't we? Final Answer = 1/15