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3 years ago

(3) (2) --------- -10

Mathematics

1 answer:

Elan Coil [88]3 years ago

7 0

Answer:

-4

Step-by-step explanation:

I hope this helps! if it does please please mark as brainliest!

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Ann needs 3/4 of a book in 2 days. At this rate how many books can she read in 4 1/3 days.

sukhopar [10]

$\bf \begin{array}{ccll} book&days\\ \cline{1-2}\\ \frac{3}{4}&2\\\\ x&4\frac{1}{3} \end{array}\implies \cfrac{~~\frac{3}{4}~~}{x}=\cfrac{~~2~~}{4\frac{1}{3}}\implies \cfrac{~~\frac{3}{4}~~}{x}=\cfrac{~~2~~}{\frac{13}{3}} \implies \cfrac{~~\frac{3}{4}~~}{\frac{x}{1}}=\cfrac{~~\frac{2}{1}~~}{\frac{13}{3}}$

$\bf \cfrac{3}{4}\cdot \cfrac{1}{x}=\cfrac{2}{1}\cdot \cfrac{3}{13}\implies \cfrac{3}{4x}=\cfrac{6}{13}\implies 39=24x\implies \cfrac{39}{24}=x\implies \cfrac{13}{8}=x \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill 1\frac{5}{8}=x~\hfill$

5 0

3 years ago

The sum to infinity of a geometric series is 32.The sum of the first four terms is 30 and

gayaneshka [121]

The terms in the series are

$\displaystyle \sum_{n=1}^\infty ar^{n-1} = a + ar + ar^2 + ar^3 + \cdots$

The series converges, so we $|r|$ . All the terms in this particular series are known to be positive, so $0Consider the [tex]N$ -th partial sum of the series,

$S_N = \displaystyle \sum_{n=1}^N ar^{n-1} = a + ar + ar^2 + \cdots + ar^{N-1}$

Multiply both sides by $r$ :

$r S_N = ar + ar^2 + ar^3 + \cdots + ar^N$

Subtracting this from $S_N$ eliminates all the $r^n$ terms between $n=1$ and $n=N-1$ , leaving us with

$(1 - r) S_N = a - ar^N \implies S_N = \dfrac{a(1-r^N)}{1-r}$

As $N\to\infty$ , the $r^N$ term will converge to zero, and the value of the infinite series is

$\displaystyle \sum_{n=1}^\infty ar^{n-1} = \lim_{n\to\infty} S_N = S = \frac a{1-r}$

Now, we're given

$S = \dfrac a{1-r} = 32 ~~~~ \text{ and } ~~~~ S_4 = \dfrac{a(1-r^4)}{1-r} = 30$

By substitution, we have

$S_4 = 32(1-r^4) = 30 \implies 1-r^4 = \dfrac{15}{16} \implies r^4 = \dfrac1{16} \implies r = \dfrac12$

so that

$S = \dfrac a{1 - \frac12} = 32 \implies a = 16$

Then the sum of the first 8 terms is

$S_8 = \dfrac{a(1-r^8)}{1-r} = \dfrac{16\left(1 - \frac1{2^8}\right)}{1-\frac12} = \dfrac{255}8$

and the difference between this and the infinite sum is

$S - S_8 = 32 - \dfrac{255}8 = \dfrac{256-255}8 = \boxed{\dfrac18}$

3 0

2 years ago

LMN is a right a right angle triangle angle NLM is 90 degrees PQ is parallel to LM. Area of triangle PNQ is 8cm and area of tria

Fiesta28 [93]

Answer: 48cm^2

Step-by-step explanation:

LMN is a right a right angle triangle angle NLM is 90 degrees PQ is parallel to LM. Area of triangle PNQ is 8cm and area of triangle LPQ is 16 cm work out area of LQM

Kindly see attached picture for detailed explanation

6 0

3 years ago

There a 5 seniors on student council. Two of them will be chosen to go to an all-district meeting. How many ways are there to ch

Sladkaya [172]

Answer:

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

5(×+y+4) is equivalent to what

Novosadov [1.4K]

Answer: 5x+5y+20

Step-by-step explanation:

In this equation the variables with no coefficient represent one so x = 1x. Next multiply all numbers in parentheses by 5 to get your final expression.

7 0

3 years ago