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3 years ago

The ratio of boy to girls in a class is 3 : 2. There are 15 boys in the class. How many total boys and girls are in the class?

Mathematics

2 answers:

Ivenika [448]3 years ago

8 0

There should be 15 boys and 10 girls in the class, so there is 25 students in the class total.

densk [106]3 years ago

3 0

If there are 15 boys then there are 10 girls so there are 25 boys and girls in the class

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Show work explain with formulas.

Sedaia [141]

Answer:

$\large\boxed{1.\ a_{44}=481,\ \sum\limits_{n=1}^\infty(11n-3),\ \text{the sum not exist}}$

$\large\boxed{3.\ \sum\limits_{n=1}^{47}(9n+16)=10,904}$

$\large\boxed{4.\ \sum\limits_{n=1}^\infty\bigg(6(2^n)\bigg),\ \text{the sum not exist}}$

Step-by-step explanation:

$1.\\8+19+30+41+...\\\\19-8=11\\30-19=11\\41-30=11\\\\\text{It's an arithmetic series.}\ a_1=8,\ d=11.\\\\\text{The formula for the n-th term of an arithmetic sequence:}\\\\a_n=a_1+(n-1)d\\\\\text{Substitute:}\\\\a_n=8+(n-1)(11)\qquad\text{use the distributive property}\ a(b-c)=ab-ac\\a_n=8+11n-11\\\boxed{a_n=11n-3}\\\\\text{Calculate the 44th term. Put n = 44 to the formula:}\\\\a_{44}=(11)(44)-3=484-3=481$

$\text{The summation notation:}\\\\\sum\limits_{n=1}^\infty(11n-3)\\\\\text{The sum not exist, because}\ d>1,\ \text{therefore}\ 11n-3\rightarrow\infty.$

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$3.\\25+34+43+52+...+436\\\\34-25=9\\43-34=9\\52-43=9\\\\\text{It's an arithmetic series.}\ a_1=25,\ d=9.\\\\\text{The formula for the n-th term of an arithmetic sequence:}\\\\a_n=a_1+(n-1)d\\\\\text{Substitute:}\\\\a_n=25+(n-1)(9)\\a_n=25+9n-9\\a_n=9n+16\\\\\text{Calculate which the term of arithmetic series is the number 439.}\\\text{Put}\ a_n=439:\\\\9n+16=439\qquad\text{subtract 16 from both sides}\\9n=423\qquad\text{divide both sides by 9}\\n=47$

$\text{Therefore we have the series in summation notation:}\\\\\sum\limits_{n=1}^{47}(9n+16)\\\\\text{For calculation of the sum we use the formula of a sum of terms}\\\text{of an arithmetic sequence:}\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\\text{Substitute}\ n=47,\ a_1=25,\ a_{47}=439:\\\\S_{47}=\dfrac{25+439}{2}\cdot47=\dfrac{464}{2}\cdot47=232\cdot47=10904\\\\\sum\limits_{n=1}^{47}(9n+16)=10,904$

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$4.\\12+24+48+...\\\\24:12=2\\48:24=2\\\\\text{It's\ a\ geometric series}\ a_1=12,\ r=2.\\\\\text{The formula for the n-th term of a geometic sequence:}\\\\a_n=a_1r^{n-1}\\\\\text{Substitute:}\\\\a_n=(12)(2^{n-1})\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\a_n=(12)\left(\dfrac{2^n}{2^1}\right)\\\\a_n=(6)(2^n)\\\\\text{The summation notation:}\\\\\sum\limits_{n=1}^\infty\bigg(6(2^n)\bigg)\\\\\text{The sum not exist, because}\ r>1,\ \text{therefore}\ 6(2^n)\to\infty$

6 0

3 years ago

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PLZZ HELPPPPPP I NEED TO FINISH THIS IN 8 MINS

Margaret [11]

Answer:

$29.69

Step-by-step explanation:

23.52 * 1.1 = $25.872 so this is the marked up price. ----- (1.1 = 110%)

25.872 * 0.1475 = $3.81612 is the sales tax.

Total is 25.872 + 3.81612 ~ $29.69

6 0

3 years ago

What is the approximate value of x in the diagram below

Anon25 [30]

Answer:

x = 8 cm

Step-by-step explanation:

The first step in solving this problem is to determine which trig function applies. The diagram shows that this triangle is a right triangle, that side x is opposite the 25-degree angle, and that the hypotenuse has a length of 18 cm.

The sine function of an angle Ф is defined as the ratio of the opposite side to the hypotenuse. In this case, sin Ф (or sin 25 degrees) equals x/(18 cm).

We need to determine the value of x. Adapt the above equation to this particular situation: sin 25 degrees = x/(18 cm).

To solve for x, multiply both sides of the most recent equation, above, by (18 cm). The following results: (18 cm)(sin 25 degrees) = x.

Next, use a calculator to find the value of sin 25 degrees: It is 0.4226.

Then the desired value of x is (18 cm)(0.4226), or x = 7.61 cm. This should be rounded off to x = 8 cm to reflect the level of accuracy of the given 18 cm.

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3 years ago

8,128 in expanded form no spaces

Taya2010 [7]

Haii

Step-by-step explanation:

8000+100+20+8 = 8,128

How to make expanded form:

<em>Its easy! all that must be done is that you break down the number like if you had a number 5091 this is how you break it down 5000 + 90 + 1. Breaking numbers down makes it easier to solve and you will be amazingg at math in no time!</em>

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2 years ago

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Which is the graph of y = log (negative x)?

Yanka [14]

Answer:

Step-by-step explanation:

8 0

3 years ago

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