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3 years ago

What is the answer to the question -2y-10+2x=0

Mathematics

2 answers:

alekssr [168]3 years ago

8 0

Answer:

if your solving for x: x = y + 5

If your solving for y: y = − 5 + x

Step-by-step explanation:

Pavlova-9 [17]3 years ago

3 0

Answer:

X-y=5

Step-by-step explanation:

-2y-10+2x=0

-2y+2x=10

-y+x=5

x-y=5

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What is the length of an arc with a central angle of 23π radians and a radius of 24 cm?

dalvyx [7]

We can solve for the arc length using the formula shown below:
Arc Lenght = 2pi*r(central angle/360)

We need to convert the central angle such as:
Central angle = 23pi rad * (180°/pi rad) = 23*180
Radius = 24cm

Solving for arc length:
Arc length = 2*3.14 *24*(23*180/360)
Arc length = 1733.28 cm

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3 years ago

A can of paint will cover 400 square feet. What is the length of the edge of the largest square that can be painted with this ca

Masteriza [31]

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3 years ago

2,17,82,257,626,1297 next one please ?

In-s [12.5K]

The easy thing to do is notice that 1^4 = 1, 2^4 = 16, 3^4 = 81, and so on, so the sequence follows the rule $n^4+1$ . The next number would then be fourth power of 7 plus 1, or 2402.

And the harder way: Denote the n-th term in this sequence by $a_n$ , and denote the given sequence by $\{a_n\}_{n\ge1}$ .

Let $b_n$ denote the n-th term in the sequence of forward differences of $\{a_n\}$ , defined by

$b_n=a_{n+1}-a_n$

for n ≥ 1. That is, $\{b_n\}$ is the sequence with

$b_1=a_2-a_1=17-2=15$

$b_2=a_3-a_2=82-17=65$

$b_3=a_4-a_3=175$

$b_4=a_5-a_4=369$

$b_5=a_6-a_5=671$

and so on.

Next, let $c_n$ denote the n-th term of the differences of $\{b_n\}$ , i.e. for n ≥ 1,

$c_n=b_{n+1}-b_n$

so that

$c_1=b_2-b_1=65-15=50$

$c_2=110$

$c_3=194$

$c_4=302$

etc.

Again: let $d_n$ denote the n-th difference of $\{c_n\}$ :

$d_n=c_{n+1}-c_n$

$d_1=c_2-c_1=60$

$d_2=84$

$d_3=108$

etc.

One more time: let $e_n$ denote the n-th difference of $\{d_n\}$ :

$e_n=d_{n+1}-d_n$

$e_1=d_2-d_1=24$

$e_2=24$

etc.

The fact that these last differences are constant is a good sign that $e_n=24$ for all n ≥ 1. Assuming this, we would see that $\{d_n\}$ is an arithmetic sequence given recursively by

$\begin{cases}d_1=60\\d_{n+1}=d_n+24&\text{for }n>1\end{cases}$

and we can easily find the explicit rule:

$d_2=d_1+24$

$d_3=d_2+24=d_1+24\cdot2$

$d_4=d_3+24=d_1+24\cdot3$

and so on, up to

$d_n=d_1+24(n-1)$

$d_n=24n+36$

Use the same strategy to find a closed form for $\{c_n\}$ , then for $\{b_n\}$ , and finally $\{a_n\}$ .

$\begin{cases}c_1=50\\c_{n+1}=c_n+24n+36&\text{for }n>1\end{cases}$

$c_2=c_1+24\cdot1+36$

$c_3=c_2+24\cdot2+36=c_1+24(1+2)+36\cdot2$

$c_4=c_3+24\cdot3+36=c_1+24(1+2+3)+36\cdot3$

and so on, up to

$c_n=c_1+24(1+2+3+\cdots+(n-1))+36(n-1)$

Recall the formula for the sum of consecutive integers:

$1+2+3+\cdots+n=\displaystyle\sum_{k=1}^nk=\frac{n(n+1)}2$

$\implies c_n=c_1+\dfrac{24(n-1)n}2+36(n-1)$

$\implies c_n=12n^2+24n+14$

$\begin{cases}b_1=15\\b_{n+1}=b_n+12n^2+24n+14&\text{for }n>1\end{cases}$

$b_2=b_1+12\cdot1^2+24\cdot1+14$

$b_3=b_2+12\cdot2^2+24\cdot2+14=b_1+12(1^2+2^2)+24(1+2)+14\cdot2$

$b_4=b_3+12\cdot3^2+24\cdot3+14=b_1+12(1^2+2^2+3^2)+24(1+2+3)+14\cdot3$

and so on, up to

$b_n=b_1+12(1^2+2^2+3^2+\cdots+(n-1)^2)+24(1+2+3+\cdots+(n-1))+14(n-1)$

Recall the formula for the sum of squares of consecutive integers:

$1^2+2^2+3^2+\cdots+n^2=\displaystyle\sum_{k=1}^nk^2=\frac{n(n+1)(2n+1)}6$

$\implies b_n=15+\dfrac{12(n-1)n(2(n-1)+1)}6+\dfrac{24(n-1)n}2+14(n-1)$

$\implies b_n=4n^3+6n^2+4n+1$

$\begin{cases}a_1=2\\a_{n+1}=a_n+4n^3+6n^2+4n+1&\text{for }n>1\end{cases}$

$a_2=a_1+4\cdot1^3+6\cdot1^2+4\cdot1+1$

$a_3=a_2+4(1^3+2^3)+6(1^2+2^2)+4(1+2)+1\cdot2$

$a_4=a_3+4(1^3+2^3+3^3)+6(1^2+2^2+3^2)+4(1+2+3)+1\cdot3$

$\implies a_n=a_1+4\displaystyle\sum_{k=1}^3k^3+6\sum_{k=1}^3k^2+4\sum_{k=1}^3k+\sum_{k=1}^{n-1}1$

$\displaystyle\sum_{k=1}^nk^3=\frac{n^2(n+1)^2}4$

$\implies a_n=2+\dfrac{4(n-1)^2n^2}4+\dfrac{6(n-1)n(2n)}6+\dfrac{4(n-1)n}2+(n-1)$

$\implies a_n=n^4+1$

4 0

3 years ago

Historical data indicates that only 20% of cable customers are willing to switch companies. If a binomial process is assumed, th

Natasha_Volkova [10]

Answer:

a. The probability is 0.735

b. The probability is 0.6296

c. The probability is 0

Step-by-step explanation:

If we assume a binomial process, the probability that x customer are willing to switch companies is:

$P(x)=nCx*p^{x}*(1-p)^{n-x}$

nCx is calculated as:

$nCx=\frac{n!}{x!(n-x)!}$

Where n are the 20 cable customers and p is the probability 0.2 that the cable customer are willing to switch companies.

Then, P(x) is:

$P(x)=20Cx*0.2^{x}*(1-0.2)^{20-x}$

The probability that between 2 and 5 (inclusive) customers are willing to switch companies is:

P(2≤x≤5) = P(2) + P(3) + P(4) + P(5)

Where P(2), P(3), P(4) and P(5) are equal to:

$P(2)=20C2*0.2^{2}*(1-0.2)^{20-2}=0.1369$

$P(3)=20C3*0.2^{3}*(1-0.2)^{20-3}=0.2054$

$P(4)=20C4*0.2^{4}*(1-0.2)^{20-4}=0.2182$

$P(5)=20C5*0.2^{5}*(1-0.2)^{20-5}=0.1745$

So, P(2≤x≤5) is:

P(2≤x≤5) = 0.1369 + 0.2054 + 0.2182 + 0.1745 = 0.735

At the same way, the probability that less than 5 customers are willing to switch is:

P(x<5)=P(0)+P(1)+P(2)+P(3)+P(4)

P(x<5)=0.6296

Finally, the probability that more than 16 customers are willing to switch is:

P(x>16)=P(17)+P(18)+P(19)+P(20)

P(x>16)=0

7 0

4 years ago

The sum of three numbers is 131. The second of three numbers is seven more than twice the first. The third number is 12 less tha

Norma-Jean [14]

First number is (x).
Second number is (2x+7).
Third number is (x-12).
Their sum is (x+2x+7+x-12).
x+2x+7+x-12 =131

You can simplify this equation
4x-5=131,

4x=136
x=136/4=34 (first number),
(2x+7)=34*2+7=75 (second number)
34-x=34-12 =22(third number)

Check: 34+75+22=131

6 0

3 years ago