Math Homework Answers - Recent questions and answers
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Powered by Question2AnswerAnswered: In 1995, a certain city had a population of 45,000. If the population continues to increase by 3.5% each year, what is the estimate of the population in the year 2020?
https://www.mathhomeworkanswers.org/250250/population-population-continues-increase-estimate-population?show=250254#a250254
each year the population of the city increases for 45000 * 0.035 people and becomes 45000+45000(0.035)<br />
<br />
or 45000(1+0.035) people in total for the 25 years (2020 - 1995 = 25) the total population of the city will be;<br />
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45000(1 + 0.035) or 45000(1.035)^25 = 45000(2.363) = 106335 people approxAlgebra 1 Answershttps://www.mathhomeworkanswers.org/250250/population-population-continues-increase-estimate-population?show=250254#a250254Sun, 21 Jan 2018 13:58:44 +0000Answered: A population of 1570000 decreases 2.3% each year. what is the population after 17 years
https://www.mathhomeworkanswers.org/250249/population-1570000-decreases-what-population-after-years?show=250253#a250253
<p><em>A population of 1570000 decreases 2.3% each year. what is the population after 17 years</em></p>
<p>The population can be modeled by the equation</p>
<p>Pn = P(1 + a)^n, where</p>
<p>P is the starting population, and P = 1570000</p>
<p>Pn is the population after n years</p>
<p>a is the annual rate of increase of population, and a = -0.023 (a is negative becaise popln is decreasing)</p>
<p>After 17 years,</p>
<p>P17 = 1570000*(1 - 0.023)^17</p>
<p>P17 = 1570000*(0.977)^17</p>
<p>P17 = 1570000*0.673298</p>
<p><span style="text-decoration: underline;"><strong>P17 = 1,057,078</strong></span></p>Algebra 1 Answershttps://www.mathhomeworkanswers.org/250249/population-1570000-decreases-what-population-after-years?show=250253#a250253Sun, 21 Jan 2018 08:50:56 +0000Answered: How many biscuits did Jake bake?
https://www.mathhomeworkanswers.org/250246/how-many-biscuits-did-jake-bake?show=250252#a250252
<p><em>Jack baked some biscuits, He kept 3/7 of the biscuits in container A, 5/8 of the remainder in container B. There are 21 more biscuits in container A than in container C, How many biscuits did Jake bake?</em></p>
<p>Let T be the total number of biscuits</p>
<p>A = (3/7)*T (He kept 3/7 of the biscuits in container A)</p>
<p>B = (5/8)*(T - A) (5/8 of the remainder in container B)</p>
<p>A = C + 21 (There are 21 more biscuits in container A than in container C)</p>
<p>T = A + B + C (The three tins, A, B, and C hold all of the biscuits)</p>
<p>Substituting for A = (3/7)*T,</p>
<p>B = (5/8)*(T - (3/7)*T)</p>
<p>(3/7)*T = C + 21</p>
<p>T = (3/7)*T + B + C</p>
<p>Simplifying the above 3 eqns by muultiplying out</p>
<p>56B = 20T</p>
<p>3T = 7C + 147</p>
<p>4T = 7B + 7C (or, 32T = 56B + 56C)</p>
<p>Substituting for 56B = 20T,</p>
<p>3T = 7C + 147</p>
<p>32T = 20T + 56C</p>
<p>Simplifying,</p>
<p>3T = 7C + 147</p>
<p>12T = 56C (or, 3T = 14C)</p>
<p>Substituting for 3T = 14C,</p>
<p>14C = 7C + 147</p>
<p>7C = 147</p>
<p><span style="text-decoration: underline;"><strong>C = 21</strong></span></p>
<p>Hence <span style="text-decoration: underline;"><strong>T = 98</strong></span></p>
<p>Hence, <span style="text-decoration: underline;"><strong>B = 35</strong></span></p>
<p>Hence, <span style="text-decoration: underline;"><strong>A = 42</strong></span></p>Word Problem Answershttps://www.mathhomeworkanswers.org/250246/how-many-biscuits-did-jake-bake?show=250252#a250252Sun, 21 Jan 2018 08:22:12 +0000Answered: If given 3 vertices of parallelogram, how do I find coordinates of 4th vertex?
https://www.mathhomeworkanswers.org/110305/given-vertices-parallelogram-find-coordinates-4th-vertex?show=250248#a250248
First, construct the diagonals of the parallelogram, then find the coordinates of the point where they bisect. In this case it is (1, 5/2). Then use this point to find the point S. In this case, S(-4, 5).Geometry Answershttps://www.mathhomeworkanswers.org/110305/given-vertices-parallelogram-find-coordinates-4th-vertex?show=250248#a250248Sun, 21 Jan 2018 02:33:27 +0000The product of the page numbers on two facing pages of a book is 156156. Find the page numbers.
https://www.mathhomeworkanswers.org/250247/product-numbers-facing-pages-book-156156-find-page-numbers
For my intermediate algebra classWord Problem Answershttps://www.mathhomeworkanswers.org/250247/product-numbers-facing-pages-book-156156-find-page-numbersSun, 21 Jan 2018 02:14:26 +0000Answered: The hypotenuse of a right triangle is 15cm. The other two sides have a total length of 21cm. Find the lengths of the two unknown sides.
https://www.mathhomeworkanswers.org/250238/hypotenuse-triangle-other-sides-length-lengths-unknown-sides?show=250245#a250245
Let one of the unknown sides be x then the other is 21-x, so:<br />
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x²+(21-x)²=225, 2x²+441-42x=225, 2x²-42x+216=0, x²-21x+108=0=(x-9)(x-12),<br />
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so x=9 or 12, which are the lengths of the other two sides.Algebra 2 Answershttps://www.mathhomeworkanswers.org/250238/hypotenuse-triangle-other-sides-length-lengths-unknown-sides?show=250245#a250245Sun, 21 Jan 2018 01:05:03 +0000Answered: find 3.96/0.7 to the nearest tenth
https://www.mathhomeworkanswers.org/120/find-3-96-0-7-to-the-nearest-tenth?show=250244#a250244
5.657142857 rounded to the nearest tenth is 5.7Algebra 1 Answershttps://www.mathhomeworkanswers.org/120/find-3-96-0-7-to-the-nearest-tenth?show=250244#a250244Sun, 21 Jan 2018 00:58:16 +0000Answered: 28/9x - 49 = 99/97
https://www.mathhomeworkanswers.org/250241/28-9x-49-99-97?show=250243#a250243
<p style="text-align: justify;">The question is ambiguous.
<br>
<br>
(28/(9x))-49=99/97, 28/(9x)=49+99/97=4852/97, 1/x=(9/28)(4852/97)=10917/679 and x=0.0622 approx.
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<br>
(28/9)x-49=99/97, x=10917/679=16.0781 approx.
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<br>
28/(9x-49)=99/97, 9x-49=28(97/99)=2716/99, 9x=49+2716/99=7567/99, x=7567/891=8.4927 approx.</p>Algebra 1 Answershttps://www.mathhomeworkanswers.org/250241/28-9x-49-99-97?show=250243#a250243Sun, 21 Jan 2018 00:55:09 +0000Answered: In an A.P.(arithmatic progression) if Sn = 3n^ 2 + 5n and ak = 164, then find the value of k
https://www.mathhomeworkanswers.org/250235/an-arithmatic-progression-3n-5n-and-ak-164-then-find-the-value?show=250242#a250242
<p style="text-align: justify;">The sign is minus because -(3(n-1)²+5(n-1))=-3(n-1)²-5(n-1) applying the distributive property to the minus sign. The distributive property crops up in the following lines, too, so the logic is correct.</p>Other Math Topicshttps://www.mathhomeworkanswers.org/250235/an-arithmatic-progression-3n-5n-and-ak-164-then-find-the-value?show=250242#a250242Sun, 21 Jan 2018 00:39:56 +0000Answered: The sides of a rectangle are 24 cm and 15 cm. Calculate the length of its diagonal.
https://www.mathhomeworkanswers.org/250236/the-sides-rectangle-are-and-calculate-the-length-its-diagonal?show=250237#a250237
By Pythagoras, the diagonal=√24²+15²=√576+225=√801=28.30cm approx.Word Problem Answershttps://www.mathhomeworkanswers.org/250236/the-sides-rectangle-are-and-calculate-the-length-its-diagonal?show=250237#a250237Sat, 20 Jan 2018 16:19:43 +0000Answered: Suppose that x has the binomial distribution with probability mass function
https://www.mathhomeworkanswers.org/250224/suppose-that-binomial-distribution-probability-function?show=250231#a250231
<p style="text-align:justify">
<br>
I interpret the binomial distribution as
<br>
<br>
∑⁵C ͓(¼)ˣ(¾)⁵⁻ˣ) where 0≤x≤5 as the expansion of (¼+¾)⁵. I have used ⁵C ͓ In place of (5 x).</p>
<p style="text-align:justify">The Binomial Theorem states that (a+b)ⁿ=∑ⁿCᵣaʳbⁿ⁻ʳ for r in {0,n}.
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<br>
The mean is 5×¼=5/4 and the variance is 5×¼×¾=15/16 where mean=np and n=5 and p=¼, and variance=np(1-p).
<br>
<br>
Calculating the mean and variance through M ͓(t) should give these results.</p>
<ol>
<li style="text-align:justify">M ͓(t)=E(eᵗˣ)=∑eᵗˣ(⁵C ͓)(¼)ˣ(¾)⁵⁻ˣ= ∑(⁵C ͓)(¼eᵗ)ˣ(¾)⁵⁻ˣ = (¼eᵗ+¾)⁵ by the Binomial Theorem. So the MGF is M ͓(t)=(¼eᵗ+¾)⁵.</li>
<li style="text-align:justify">To find the mean and variance we need to find dM/dt=5(¼eᵗ+¾)⁴・¼eᵗ. Now we need to evaluate the first moment, M'(0)=5・1⁴・¼=5/4. This is the mean. Now we need d²M/dt²=M''(t), the second moment. M''(t)=vu'+uv' where u(t)=5(¼eᵗ+¾)⁴ and v(t)=¼eᵗ. So u'=5(¼eᵗ+¾)³eᵗ and v'=¼eᵗ. So M''(t)=5e²ᵗ(¼eᵗ+¾)³/4+5eᵗ(¼eᵗ+¾)⁴/4, M''(0)=5/4+5/4=5/2. Variance = M''(0)-(M'(0))² = 5/2-(5/4)² = 5/2-25/16 = <a rel="nofollow" href="denied:tel:40/16-25/16">40/16-25/16</a> = 15/16.</li>
</ol>Other Math Topicshttps://www.mathhomeworkanswers.org/250224/suppose-that-binomial-distribution-probability-function?show=250231#a250231Fri, 19 Jan 2018 18:30:39 +0000Answered: Act it out and use reasoning
https://www.mathhomeworkanswers.org/4798/act-it-out-and-use-reasoning?show=250230#a250230
<p style="text-align: justify;">Sine there are 8 dogs the remaining 8 must be cats and birds. Since there are 3 times as many cats as birds we divide 4 into 8 to get 2 to give us 2 birds and 6 cats.</p>Pre-Algebra Answershttps://www.mathhomeworkanswers.org/4798/act-it-out-and-use-reasoning?show=250230#a250230Fri, 19 Jan 2018 17:52:09 +0000Answered: For a party you can spend no more than $20 on cakes. Egg cake costs $4 and cream cake costs $2. Write the linear inequality that models this situation
https://www.mathhomeworkanswers.org/250215/cakes-cream-costs-write-linear-inequality-models-situation?show=250223#a250223
<p style="text-align: justify;">You have answered your own question: 4e+2c≤20 says the total cost of egg cake is 4e dollars and the total cost of cream cake is 2c dollars, and the sum must not exceed $20, must be less than or equal to $20.</p>
<p style="text-align: justify;">The equation can be divided by 2: 2e+c≤10 or c≤10-2e. This shows clearly the relation between c and e. If, for example, e=3 then c≤4.</p>Algebra 1 Answershttps://www.mathhomeworkanswers.org/250215/cakes-cream-costs-write-linear-inequality-models-situation?show=250223#a250223Fri, 19 Jan 2018 10:41:45 +0000Answered: I need help
https://www.mathhomeworkanswers.org/250221/i-need-help?show=250222#a250222
<table border="1" cellpadding="1" cellspacing="1" style="width:500px">
<tbody>
<tr>
<td style="text-align:justify">y⬇︎x➡︎</td>
<td>1</td>
<td>2</td>
<td>3</td>
</tr>
<tr>
<td>1</td>
<td>k</td>
<td>2k</td>
<td>3k</td>
</tr>
<tr>
<td>2</td>
<td>2k</td>
<td>4K</td>
<td>6k</td>
</tr>
<tr>
<td>3</td>
<td>3k</td>
<td>6k</td>
<td>9k</td>
</tr>
</tbody>
</table>
<p style="text-align:justify">Add up the sum of the products: 36k. This sum must add up to 1 because all outcomes sum to certainty.</p>
<p>Therefore 36k=1 and k=1/36 so f(x,y)=xy/36.</p>Other Math Topicshttps://www.mathhomeworkanswers.org/250221/i-need-help?show=250222#a250222Fri, 19 Jan 2018 10:34:41 +0000Answered: Adult tickets for the school musical were sold for 3.50 and student tickets were sold for 2.50. 138 tickets were sold for 427 how many of each tickets were sold
https://www.mathhomeworkanswers.org/250218/adult-tickets-school-musical-student-tickets-tickets-tickets?show=250219#a250219
let A number of adults and S the number for students, then we will have<br />
<br />
<br />
<br />
3.5A + 2.5S = 427 we will have also A + S = 138<br />
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these are the two equations solving them we have ; S=56 A=82Algebra 1 Answershttps://www.mathhomeworkanswers.org/250218/adult-tickets-school-musical-student-tickets-tickets-tickets?show=250219#a250219Fri, 19 Jan 2018 06:46:33 +0000Answered: Jatonia sold n cups of lemonade at her stand for $0.75 each. She made a total of $18.00. Write an equation to express how many cups of lemonade she sold
https://www.mathhomeworkanswers.org/250213/jatonia-lemonade-stand-total-write-equation-express-lemonade?show=250217#a250217
from the equation Y = 0.75n ( Y is the money received, n is the number of cups sold) we have n = Y/0.75<br />
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for our case we have n=18/0.75 = 24 cupsWord Problem Answershttps://www.mathhomeworkanswers.org/250213/jatonia-lemonade-stand-total-write-equation-express-lemonade?show=250217#a250217Fri, 19 Jan 2018 05:54:45 +0000Answered: How many pages are in the entire book? (% word problem)
https://www.mathhomeworkanswers.org/250214/how-many-pages-are-in-the-entire-book-%25-word-problem?show=250216#a250216
since the 8 pages of the book is the 4% of it, the 8/4 = 2 pages is the 1% of the book<br />
<br />
since the 1% is 2 pages the 100% of the book is 2 x 100 = 200 pagesWord Problem Answershttps://www.mathhomeworkanswers.org/250214/how-many-pages-are-in-the-entire-book-%25-word-problem?show=250216#a250216Fri, 19 Jan 2018 05:41:23 +0000Answered: If 6 counters are 1/2 of a set, how big is the set
https://www.mathhomeworkanswers.org/65661/if-6-counters-are-1-2-of-a-set-how-big-is-the-set?show=250211#a250211
a whole set is 12Word Problem Answershttps://www.mathhomeworkanswers.org/65661/if-6-counters-are-1-2-of-a-set-how-big-is-the-set?show=250211#a250211Fri, 19 Jan 2018 02:41:04 +0000Answered: All of the following are equivalent except _____.
https://www.mathhomeworkanswers.org/50152/all-of-the-following-are-equivalent-except-_____?show=250210#a250210
The answer is the 1st option.Pre-Algebra Answershttps://www.mathhomeworkanswers.org/50152/all-of-the-following-are-equivalent-except-_____?show=250210#a250210Fri, 19 Jan 2018 02:26:31 +0000Answered: How do you solve 5/8 m = 6 3/4
https://www.mathhomeworkanswers.org/250193/how-do-you-solve-5-8-m-6-3-4?show=250208#a250208
6¾=27/4.<br />
<br />
⅝m=27/4, m=27/4×8/5=27×2/5=54/5=10.8 or 10⅘.Other Math Topicshttps://www.mathhomeworkanswers.org/250193/how-do-you-solve-5-8-m-6-3-4?show=250208#a250208Thu, 18 Jan 2018 14:41:02 +0000Answered: The centers of a 10 kg lead ball and a 100 g lead ball are separated by 10 cm.
https://www.mathhomeworkanswers.org/250195/the-centers-of-lead-ball-and-100-lead-ball-are-separated-by-cm?show=250207#a250207
<ol>
<li>Force=m₁m₂G/r²=10×0.1G/(0.1²)=100G N.</li>
<li>100G/0.1g=1000G/g is the ratio.</li>
</ol>
<p>g=acceleration of gravity and G=gravitational constant.</p>
<p>g=9.81m/s² and G=6.674×10⁻¹¹ kms units</p>
<p>In numbers:</p>
<ol>
<li>6.674×10⁻⁸ N</li>
<li>6.80×10⁻⁹ N</li>
</ol>Word Problem Answershttps://www.mathhomeworkanswers.org/250195/the-centers-of-lead-ball-and-100-lead-ball-are-separated-by-cm?show=250207#a250207Thu, 18 Jan 2018 14:33:46 +0000Answered: In a process with continuous paper, the paper passes across three rollers of radii 3 inches, 4 inches, and 6 inches.
https://www.mathhomeworkanswers.org/250196/process-continuous-passes-across-rollers-inches-inches-inches?show=250206#a250206
<p><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=6059537982897716472" style="height:305px; width:400px"></p>
<p>a) d²=(3+4)²+(4+6)²-2(3+4)(4+6)cosθ=49+100-140cosθ=149-140cosθ.</p>
<p>b) θ=arccos((149-d²)/140)</p>
<p>c) arc/circumference=angle/360; s/8π=(360-θ)/360 so s=(360-θ)π/45.</p>
<p><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=9928875240961692332" style="height:109px; width:400px"></p>
<table border="1" cellpadding="1" cellspacing="1" style="width:500px">
<tbody>
<tr>
<td style="text-align: center;">d (inches)</td>
<td style="text-align: center;">θ (degrees)</td>
<td style="text-align: center;">s (inches)</td>
</tr>
<tr>
<td style="text-align: center;">9</td>
<td style="text-align: center;">60.94</td>
<td style="text-align: center;">20.88</td>
</tr>
<tr>
<td style="text-align: center;">10</td>
<td style="text-align: center;">69.51</td>
<td style="text-align: center;">20.28</td>
</tr>
<tr>
<td style="text-align: center;">12</td>
<td style="text-align: center;">87.95</td>
<td style="text-align: center;">18.99</td>
</tr>
<tr>
<td style="text-align: center;">13</td>
<td style="text-align: center;">98.21</td>
<td style="text-align: center;">18.28</td>
</tr>
<tr>
<td style="text-align: center;">14</td>
<td style="text-align: center;">109.62</td>
<td style="text-align: center;">17.48</td>
</tr>
<tr>
<td style="text-align: center;">15</td>
<td style="text-align: center;">122.88</td>
<td style="text-align: center;">16.55</td>
</tr>
<tr>
<td style="text-align: center;">16</td>
<td style="text-align: center;">139.84</td>
<td style="text-align: center;">15.37</td>
</tr>
</tbody>
</table>
<p> </p>Word Problem Answershttps://www.mathhomeworkanswers.org/250196/process-continuous-passes-across-rollers-inches-inches-inches?show=250206#a250206Thu, 18 Jan 2018 13:14:14 +0000Answered: Determine the x and y intercepts from an equation and write each as an ordered pair . 8y+9x=72
https://www.mathhomeworkanswers.org/250197/determine-intercepts-from-equation-write-each-ordered-pair?show=250205#a250205
x-int: (y=0) 9x=72, x=8 (8,0)<br />
<br />
y-int: (x=0) 8y=72, y=9 (0,9)Algebra 1 Answershttps://www.mathhomeworkanswers.org/250197/determine-intercepts-from-equation-write-each-ordered-pair?show=250205#a250205Thu, 18 Jan 2018 13:10:21 +0000Answered: A bowling alley charges $4.00 to rent shoes and $5.00 per game. Which graph shows the cost of bowling 'x' number of games if you also rented shoes?
https://www.mathhomeworkanswers.org/250198/bowling-charges-graph-shows-bowling-number-games-rented-shoes?show=250204#a250204
<p style="text-align: justify;">The graphs are difficult to read. The answer is y=4+5x as an equation. But the answer is to look for the graph that has a y intercept of 4 (which they all appear to do) and the line passes through the following points:
<br>
<br>
(1,9), (2,14), (3,19), (4,24), (5,29), (6,34), (7,39), (8,44),...
<br>
<br>
I think B does this. Look at (4,24) and see if it’s on the line.</p>Algebra 1 Answershttps://www.mathhomeworkanswers.org/250198/bowling-charges-graph-shows-bowling-number-games-rented-shoes?show=250204#a250204Thu, 18 Jan 2018 13:07:19 +0000Answered: which expression is equivalent to 1/3(4 1\2 -1 1\2)+ 5 (6 1\5)
https://www.mathhomeworkanswers.org/247428/which-expression-is-equivalent-to-1-3-4-1-2-1-1-2-5-6-1-5?show=250203#a250203
⅓(4½-1½)+5(6⅕)=⅓(3)+5(6+⅕)=1+30+1=32Word Problem Answershttps://www.mathhomeworkanswers.org/247428/which-expression-is-equivalent-to-1-3-4-1-2-1-1-2-5-6-1-5?show=250203#a250203Thu, 18 Jan 2018 12:58:26 +0000Answered: Planet X has free-fall acceleration 8 m/s2 at the surface.
https://www.mathhomeworkanswers.org/250188/planet-x-has-free-fall-acceleration-8-m-s2-at-the-surface?show=250194#a250194
<p><em><span style="background-color:transparent; color:rgb(0, 0, 0); font-family:arial; font-size:11pt">Planet X has free-fall acceleration 8 m/s</span><span style="background-color:transparent; color:rgb(0, 0, 0); font-family:arial; font-size:6.6pt">2</span><span style="background-color:transparent; color:rgb(0, 0, 0); font-family:arial; font-size:11pt"> at the surface. Planet Y has twice the mass and twice the radius of planet X. On Planet Y what is the free-fall acceleration?</span></em></p>
<p><span style="background-color:transparent; color:rgb(0, 0, 0); font-family:arial; font-size:11pt">The variants are: g, M, r</span></p>
<p><span style="background-color:transparent; color:rgb(0, 0, 0); font-family:arial; font-size:11pt">Using the graviational equation.</span></p>
<p><span style="background-color:transparent; color:rgb(0, 0, 0); font-family:arial; font-size:11pt">F = mg = G.(m.M)/r^2</span></p>
<p><span style="background-color:transparent; color:rgb(0, 0, 0); font-family:arial; font-size:11pt">Cancelling the m on both sides, then rearranging to give g, M and r on the same side, we get</span></p>
<p><span style="background-color:transparent; color:rgb(0, 0, 0); font-family:arial; font-size:11pt">gx.rx^2/Mx = G = gy.ry^2/My</span></p>
<p><span style="background-color:transparent; color:rgb(0, 0, 0); font-family:arial; font-size:11pt">or,</span></p>
<p><span style="background-color:transparent; color:rgb(0, 0, 0); font-family:arial; font-size:11pt">gx/gy = (Mx/My)*(ry/rx)^2</span></p>
<p>where, gx = 8 m/s^2, Mx/My = 1/2, ry/rx = 2/1</p>
<p>Substituting,</p>
<p>gx/gy = (1/2)*(2/1)^2 = (1/2)*4 = 2</p>
<p>gy = gx/2 = 8/2 = <span style="text-decoration: underline;">4 m/s^2</span></p>
<p><span style="text-decoration: underline;"><strong>On Planet Y, the free-fall acceleration is gy = 4 m/s^2</strong></span></p>Word Problem Answershttps://www.mathhomeworkanswers.org/250188/planet-x-has-free-fall-acceleration-8-m-s2-at-the-surface?show=250194#a250194Thu, 18 Jan 2018 01:09:42 +0000Answered: make a conjecture about the diagonals
https://www.mathhomeworkanswers.org/248969/make-a-conjecture-about-the-diagonals?show=250192#a250192
<p>. <img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=10691421525298912708" style="height:393px; width:400px"></p>
<p>SQUARE construction from isosceles right triangle.</p>
<p><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=5344448713104095975" style="height:408px; width:450px"></p>
<p style="text-align:justify">RECTANGLE, RHOMBUS, PARALLELOGRAM and TRAPEZOID construction.</p>
<p style="text-align:justify">The pictures show the constructions that prove the conjectures we’re about to show.</p>
<p style="text-align:justify">The top figure shows the right triangle AOB in bold blue outline. By placing three copies of this triangle together (dotted line triangles) with the original, square ABCD is formed. The conjectures are:</p>
<p style="text-align:justify">The diagonals have equal length.</p>
<p style="text-align:justify">They bisect one another at right angles.</p>
<p style="text-align:justify">The proof can be seen in the way the square has been constructed from four congruent triangles.</p>
<p style="text-align:justify">Now we come to the lower figure. We start with the red right triangle AOB where AO has length a and OB=b. The dotted magenta triangle has been placed so as to form the rectangle OAA'B. Four isosceles triangles are formed within the rectangle with X as their common vertex. From this construction we can prove the conjectures:</p>
<p style="text-align:justify">The diagonals are the same length and they bisect one another.</p>
<p style="text-align:justify">X is the midpoint of each diagonal.</p>
<p style="text-align:justify">Triangle AOB is copied and used to make the rhombus ABCD (dotted green triangles) to prove the conjecture that the diagonals bisect one another at right angles. The side length of the rhombus is √a²+b².</p>
<p style="text-align:justify">ODAA' is a parallelogram with diagonals OA and DA'. Triangles AYD and OYA are congruent. This proves the conjecture that the diagonals bisect one another at Y.</p>
<p style="text-align:justify">DAA'E is a trapezoid and we can work out the lengths of the diagonals and they are not equal.</p>Word Problem Answershttps://www.mathhomeworkanswers.org/248969/make-a-conjecture-about-the-diagonals?show=250192#a250192Wed, 17 Jan 2018 22:53:30 +0000Answered: The gravitational force between two giant lead spheres is 0.010 N when the centers of the spheres are 20 m apart.
https://www.mathhomeworkanswers.org/250186/gravitational-force-between-spheres-centers-spheres-apart?show=250191#a250191
let m1 is the mass of the first sphere and m2 is the mass of the second sphere<br />
<br />
the gravitational force between them will be f = m1m2/d^2 ( d is the distance between the centers of the<br />
<br />
spheres)<br />
<br />
so it will be 0.010=m1m2/400 and 400(0.010)=m1m2 (1) and 0.160(d)^2=m1m2 (2) from the (1) and (2)<br />
<br />
we have; 400(0.010)=0.160(d)^2 --->>> d^2 = (400(0.010))/0.160 --->>> d^2 = 4/0.160 = 25<br />
<br />
so d=sqrt25 = 5 m<br />
<br />
so when the grav force is 0.160 N the distance will be 5 m<br />
<br />
<br />
<br />
a second way solving this is as follows;<br />
<br />
it is. (20/d)^2 = 0.160/0.010 --->>> (20/d)^2 = 16 -->>> taking sqrt we get. 20/d = 4 so d=5 mWord Problem Answershttps://www.mathhomeworkanswers.org/250186/gravitational-force-between-spheres-centers-spheres-apart?show=250191#a250191Wed, 17 Jan 2018 22:21:18 +0000Answered: Tickets to a movie cost $7.25 for adults and $5.50 for students. A group of friends purchased 8 tickets for $52.75.
https://www.mathhomeworkanswers.org/250184/tickets-movie-adults-students-group-friends-purchased-tickets?show=250187#a250187
<p><em>Tickets to a movie cost $7.25 for adults and $5.50 for students. A group of friends purchased 8 tickets for $52.75. </em></p>
<p>Ticket for an adults = $7.25</p>
<p>Ticket for a student = $5.50</p>
<p>Let number of adults be A</p>
<p>Let number of students be S</p>
<p>Then, A + S = 8 (number of people in group)</p>
<p>And, A*7.25 + S*5.50 = 52.75 (sum of individual costs = total cost)</p>
<p>Substituting for A = 8 - S, from 1st eqn, into 2nd eqn gives us,</p>
<p>(8 - S)*7.25 + S*5.5 = 52.75</p>
<p>58 - 7.25S + 5.5S = 52.75</p>
<p>58 - 1.75S = 52.75</p>
<p>58 - 52.75 = 1.75S</p>
<p><span style="text-decoration: underline;">S = 5.25/1.75 = 3</span></p>
<p><span style="text-decoration: underline;">A = 8 - S = 5</span></p>
<p><span style="text-decoration: underline;"><strong>There are 5 adults and 3 students</strong></span></p>Algebra 1 Answershttps://www.mathhomeworkanswers.org/250184/tickets-movie-adults-students-group-friends-purchased-tickets?show=250187#a250187Wed, 17 Jan 2018 21:58:58 +0000Answered: probability of getting four of same sex in family with 4 children.
https://www.mathhomeworkanswers.org/63921/probability-of-getting-four-of-same-sex-family-with-children?show=250185#a250185
Multiply the probabilites together:<br />
<br />
1/2 x 1/2 x 1/2 x 1/2 =<br />
<br />
1/4 x 1/2 x 1/2 =<br />
<br />
1/8 x 1/2 =<br />
<br />
1/16Algebra 2 Answershttps://www.mathhomeworkanswers.org/63921/probability-of-getting-four-of-same-sex-family-with-children?show=250185#a250185Wed, 17 Jan 2018 21:32:00 +0000Answered: What is the probability of getting something with a 0.55% a chance
https://www.mathhomeworkanswers.org/248973/what-is-the-probability-of-getting-something-with-55%25-chance?show=250183#a250183
55/10000Word Problem Answershttps://www.mathhomeworkanswers.org/248973/what-is-the-probability-of-getting-something-with-55%25-chance?show=250183#a250183Wed, 17 Jan 2018 21:29:11 +0000Answered: area problems
https://www.mathhomeworkanswers.org/250176/area-problems?show=250182#a250182
<p style="text-align: justify;">(x-3)(x+8)=42
<br>
<br>
x²+5x-24-42=0
<br>
<br>
x²+5x-66=0=(x+11)(x-6) so x=6 (the other root is negative)
<br>
<br>
(Therefore the sides of the rectangle are 3 and 14 inches, giving an area of 42 sq in)</p>Algebra 1 Answershttps://www.mathhomeworkanswers.org/250176/area-problems?show=250182#a250182Wed, 17 Jan 2018 14:58:37 +0000Answered: It takes 21 yards of fabric to make 7 quilts. How many yards to make 21 quilts
https://www.mathhomeworkanswers.org/250180/takes-21-yards-fabric-make-quilts-how-many-yards-make-quilts?show=250181#a250181
7 quilts need 21 yards, so 1 quilt needs 21/7=3 yds.<br />
<br />
12 quilts need 12×3 yds = 36 yards of material.Word Problem Answershttps://www.mathhomeworkanswers.org/250180/takes-21-yards-fabric-make-quilts-how-many-yards-make-quilts?show=250181#a250181Wed, 17 Jan 2018 14:54:21 +0000Answered: 13 less than twice a number is at least -4
https://www.mathhomeworkanswers.org/250170/13-less-than-twice-a-number-is-at-least-4?show=250179#a250179
<p>If the number is x, then 2x-13≥-4.</p>
<p style="text-align: justify;">2x≥9 adding 13 to each side, x≥9/2</p>
<p><img alt="" src="https://www.mathhomeworkanswers.org/?qa=blob&qa_blobid=9193838975393560978" style="height:294px; width:400px"></p>
<p style="text-align:justify">The orange hatched area is the region covered by the inequality, extending outside the boundary of the picture. In other words the whole area to the right of the slanted line y=2x-13 and above the horizontal line y=-4.</p>
<p> </p>Word Problem Answershttps://www.mathhomeworkanswers.org/250170/13-less-than-twice-a-number-is-at-least-4?show=250179#a250179Wed, 17 Jan 2018 14:43:18 +0000Answered: A satellite orbiting the moon very near the surface has a period of 110 min.
https://www.mathhomeworkanswers.org/250172/satellite-orbiting-moon-very-near-the-surface-period-110-min?show=250178#a250178
<p><em>A satellite orbiting the moon very near the surface has a period of 110 min.</em></p>
<ol>
<li><em>Using this information, together with the radius of the moon being 1.74 x 106 m, to calculate the free fall acceleration on the moon’s surface. (i.e. don’t use the moon’s mass in your calculation).</em></li>
<li><em>Now, based on your answer, estimate the mass of the moon.</em></li>
</ol>
<p>Period of rotation = 110 min = 6600 s</p>
<p>Angular velocity, ω = (2π/6600) rad/sec</p>
<p>Centripetal force = Fc</p>
<p>Fc = m_s.v^2/r = m_s.ω^2.r (m_s = mass of satellite)</p>
<p>Gravitaional force = m_s.g_m (g_m = gravitational accln on moon)</p>
<p>Garvitational force = Centripetal force</p>
<p>m_s.g_m = m_s. ω^2.r</p>
<p>g_m = ω^2.r</p>
<p>g_m = (2π/6600)^2.(1.74*10^6)</p>
<p><strong><span style="text-decoration: underline;">g_m = 1.577 m^2/s</span></strong></p>
<p>We can estimate the mass using the equation</p>
<p>Fg = G.(M1.M2).r^2, where</p>
<p>Fg = gravitational force of attraction between the two bodies, M1 and M2.</p>
<p>G = Gravitational constant = 6.67*10^(-11) N(m/kg)^2</p>
<p>M1 = mass of satellite = m_s</p>
<p>M2 = mass of moon = m_m</p>
<p>r = distance between the centres of mass of the two bodies = radius of moon = r_m</p>
<p>Using Fg = Fc = m_s*g_m,</p>
<p>m_s*g_m = G*(m_s*m_m)/(r_m)^2</p>
<p>g_m = G*(m_m)/(r_m)^2</p>
<p>m_m = g_m*(r_m)^2/G</p>
<p>m_m = 1.577*(1.74*10^6)^2/(6.67*10^(-11))</p>
<p>m_m = 1.577*(1.74)^2/(6.67)*10^(23)</p>
<p><strong><span style="text-decoration: underline;">m_m = 7.158*10^22 kg</span></strong></p>
<p> </p>Word Problem Answershttps://www.mathhomeworkanswers.org/250172/satellite-orbiting-moon-very-near-the-surface-period-110-min?show=250178#a250178Wed, 17 Jan 2018 10:46:23 +0000Answered: projectile motion
https://www.mathhomeworkanswers.org/250175/projectile-motion?show=250177#a250177
<p><em>Natalie found a tennis ball outside a tennis court. She picked up the ball and threw it over the fence into the court. The path of the ball can represented by h= -16t (squared) + 18t +5
<br>
<br>
a. Find the maximum height of the tennis ball.</em></p>
<p><em>b. How long will it take to reach the ground?</em></p>
<p>The equation of motion is,</p>
<p><span style="text-decoration: underline;">h = -16t^2 +18t + 5</span></p>
<p>When the ball starts off, at t = 0, the height of the ball is h = -0 + 0 + 5 = 5</p>
<p><span style="text-decoration: underline;">h = 5</span>, at <span style="text-decoration: underline;">t = 0</span></p>
<p>The ball will reach a maximum height, and then fall back down to a height of h = 5, in a time taken, of t = 2T, where T is the time to reach its maximum height, after being projected from an inital height of h = 5.</p>
<p>So, in the equation of motion. h = -16t^2 + 18t + 5, we set h = 5 and solve for t, to fond the time it takes to reach max heright and fall back to its initial height of 5 again.</p>
<p>5 = -16t^2 + 18t + 5</p>
<p>16t^2 - 18t = 0</p>
<p>8t^2 - 9t = 0</p>
<p>t(8t - 9) = 0</p>
<p><span style="text-decoration: underline;">t = 0</span> or <span style="text-decoration: underline;">t = 9/8</span></p>
<p>But t = 2T</p>
<p>Hence, <span style="text-decoration: underline;">T = 9/16 s</span></p>
<p>(a) Max height is given by substituting t = 9/16 in the equation of motion.</p>
<p>h = -16(9/16)^2 + 18(9/16) + 5</p>
<p><span style="text-decoration: underline;"><strong>h_max = 10.0625</strong></span></p>
<p>(b) To reach the ground, set h = 0 in the equation of motion</p>
<p>0 = -16t^2 + 18t + 5</p>
<p>16t^2 - 18t - 5 = 0</p>
<p>We now simply solve the quadratic equation for t.</p>
<p>t = {18 +/- sqrt[18^2 - 4*16*(-5)]} / (2*16)</p>
<p>t = {18 +/- sqrt[324 + 320]} / (32)</p>
<p>t = {18 +/- 25.377} / (32)</p>
<p><span style="text-decoration: underline;"><strong>t = 1.355 s </strong></span> (we ignore the negative solution)</p>Algebra 1 Answershttps://www.mathhomeworkanswers.org/250175/projectile-motion?show=250177#a250177Wed, 17 Jan 2018 09:27:05 +0000Answered: $350 is what percent of $1500
https://www.mathhomeworkanswers.org/250152/%24350-is-what-percent-of-%241500?show=250154#a250154
(350/1500)100 = (0.233333)100 =23.333%<br />
<br />
so the 350 is the 23.3333% of 1500Word Problem Answershttps://www.mathhomeworkanswers.org/250152/%24350-is-what-percent-of-%241500?show=250154#a250154Mon, 15 Jan 2018 20:42:09 +0000Answered: Calculus word problems
https://www.mathhomeworkanswers.org/250149/calculus-word-problems?show=250153#a250153
price 15 = 2.60 - price 14 = 3.60 = $ -1<br />
<br />
so (-1/3.60)100 = (-0.27777)100 = -27.777%Calculus Answershttps://www.mathhomeworkanswers.org/250149/calculus-word-problems?show=250153#a250153Mon, 15 Jan 2018 20:37:39 +0000Answered: 21 hours paid $486, how much made hourly
https://www.mathhomeworkanswers.org/250150/21-hours-paid-%24486-how-much-made-hourly?show=250151#a250151
486/21 = 23.14 approx. per hourWord Problem Answershttps://www.mathhomeworkanswers.org/250150/21-hours-paid-%24486-how-much-made-hourly?show=250151#a250151Mon, 15 Jan 2018 20:24:58 +0000Answered: Out of 60 problems assigned last week for RSM homework, Steve solved correctly 54 problems. What is his score for this homework?
https://www.mathhomeworkanswers.org/250147/problems-assigned-homework-solved-correctly-problems-homework?show=250148#a250148
it is (54/60)100 = (0.9)100 = 90%Word Problem Answershttps://www.mathhomeworkanswers.org/250147/problems-assigned-homework-solved-correctly-problems-homework?show=250148#a250148Mon, 15 Jan 2018 19:19:12 +0000Answered: What is 6 divided by 2220
https://www.mathhomeworkanswers.org/250065/what-is-6-divided-by-2220?show=250146#a250146
6 / 2220 or 1/370 = 0.00270 approxWord Problem Answershttps://www.mathhomeworkanswers.org/250065/what-is-6-divided-by-2220?show=250146#a250146Mon, 15 Jan 2018 17:59:35 +0000Answered: What is 999,999,999,999,999,999 in word form?
https://www.mathhomeworkanswers.org/80634/what-is-999-999-999-999-999-999-in-word-form?show=250144#a250144
<p><span style="font-size:14px">nine hundred ninety ninety quadrillion, nine hundred ninety ninety trillion, nine hundred ninety ninety billion, nine hundred ninety ninety million, nine hundred ninety ninety thousand, nine hundred ninety ninety. </span></p>Word Problem Answershttps://www.mathhomeworkanswers.org/80634/what-is-999-999-999-999-999-999-in-word-form?show=250144#a250144Mon, 15 Jan 2018 05:48:15 +0000Answered: what’s the range of acceptable tissues in a box?
https://www.mathhomeworkanswers.org/250142/whats-the-range-of-acceptable-tissues-in-a-box?show=250143#a250143
The range is 150-4 to 150+4, so 146 to 154 or {146,154}.Algebra 1 Answershttps://www.mathhomeworkanswers.org/250142/whats-the-range-of-acceptable-tissues-in-a-box?show=250143#a250143Sun, 14 Jan 2018 22:46:23 +0000Answered: How many of each bill are there
https://www.mathhomeworkanswers.org/250132/how-many-of-each-bill-are-there?show=250141#a250141
<p style="text-align: justify;">Let x=number of $1 bills and y=number of $5 bills.
<br>
<br>
y=x+8, so x=y-8.
<br>
<br>
Total value is x+5y=124, so y-8+5y=124, 6y=132, y=22 and x=22-8=14.
<br>
<br>
Check: $14+$110=$124. OK.</p>Algebra 1 Answershttps://www.mathhomeworkanswers.org/250132/how-many-of-each-bill-are-there?show=250141#a250141Sun, 14 Jan 2018 16:36:32 +0000Answered: The ratio of Bart’s marbles to Homer’s marbles is 7:5, before Bart gave away 6 and Homer gave away 30 they had the same amount, how many marbles do they currently have?
https://www.mathhomeworkanswers.org/250131/barts-marbles-homers-marbles-before-amount-marbles-currently?show=250140#a250140
<p style="text-align: justify;">Before they gave marbles away H=B where H and B are the numbers of marbles each has.
<br>
<br>
The situation now is Homer has H+30 and Bart has B+6.
<br>
<br>
The ratio is (B+6)/(H+30)=7/5. But we know B=H, so:
<br>
<br>
(H+6)/(H+30)=7/5. Cross-multiply: 5H+30=7H+210.
<br>
<br>
But: 2H=-180 so H=B=-90! This is clearly nonsense.
<br>
<br>
Let’s reverse the giveaways:
<br>
<br>
(B+30)/(H+6)=(H+30)/(H+6)=7/5, 5H+150=7H+42, 108=2H so H=B=54 and they currently have H=60 and B=84.
<br>
<br>
This is a sensible answer and may be the intended answer: Bart gave away 30 marbles and Homer gave away 6.</p>Other Math Topicshttps://www.mathhomeworkanswers.org/250131/barts-marbles-homers-marbles-before-amount-marbles-currently?show=250140#a250140Sun, 14 Jan 2018 16:29:34 +0000Answered: One nineth divided by two
https://www.mathhomeworkanswers.org/250097/one-nineth-divided-by-two?show=250139#a250139
1/9 divided by 2 is 1/(9×2)=1/18.Other Math Topicshttps://www.mathhomeworkanswers.org/250097/one-nineth-divided-by-two?show=250139#a250139Sun, 14 Jan 2018 15:57:21 +0000Answered: Paul earn $25 for grooming a dog plus $18.50 per day for boarding the same dog.
https://www.mathhomeworkanswers.org/250096/paul-earn-%2425-grooming-plus-%2418-day-for-boarding-the-same-dog?show=250138#a250138
m=25+18.50d is the equation.Algebra 1 Answershttps://www.mathhomeworkanswers.org/250096/paul-earn-%2425-grooming-plus-%2418-day-for-boarding-the-same-dog?show=250138#a250138Sun, 14 Jan 2018 15:55:41 +0000Answered: Marvin has 4 books to read for homework this week. If he reads ⅔ of a book each night, how many night will it take him to read all of the books?
https://www.mathhomeworkanswers.org/250098/marvin-books-homework-reads-book-each-night-night-take-books?show=250137#a250137
<p style="text-align: justify;">4 books can be split into thirds of a book:
<br>
<br>
Call the books A, B, C, D.
<br>
<br>
The three thirds of any book can be represented by the book letter followed by 1, 2 or 3.
<br>
<br>
Now write down the thirds of the books in a line:
<br>
<br>
A1 A2 A3 B1 B2 B3 C1 C2 C3 D1 D2 D3
<br>
<br>
From this picture, where the reading material is split into pairs representing 2/3 of a book or the final 1/3 of a book and the first third of the next, it’s easy to see how many nights it will take him to read all of the books. It will take 6 nights. The same result is obtained by dividing 4 by ⅔=4×3/2=6.</p>Word Problem Answershttps://www.mathhomeworkanswers.org/250098/marvin-books-homework-reads-book-each-night-night-take-books?show=250137#a250137Sun, 14 Jan 2018 15:52:08 +0000Answered: 6x(4x6)4+6x2x3
https://www.mathhomeworkanswers.org/250133/6x-4x6-4-6x2x3?show=250136#a250136
<p style="text-align: justify;">I read this as 6×(4×6)4+6×2×3. The brackets don’t serve any special purpose because only multiplication is involved: 6×4×6×4+6×2×3. This gives us 576+36=612.</p>Other Math Topicshttps://www.mathhomeworkanswers.org/250133/6x-4x6-4-6x2x3?show=250136#a250136Sun, 14 Jan 2018 15:40:59 +0000Answered: Write down an expression, in terms of x, for the number of pages printed by printer a in 1 minute
https://www.mathhomeworkanswers.org/250134/write-expression-terms-number-pages-printed-printer-minute?show=250135#a250135
If y is the number of pages per minute y=60/x.Other Math Topicshttps://www.mathhomeworkanswers.org/250134/write-expression-terms-number-pages-printed-printer-minute?show=250135#a250135Sun, 14 Jan 2018 15:35:18 +0000