find three consecutive integers whose sum is 1266

Answer:

[tex] \dfrac{3(a + 8)}{(a - 7)(a - 2)(a + 8)} [/tex]

[tex] \dfrac{8a(a - 2)}{(a - 7)(a - 2)(a + 8)} [/tex]

Step-by-step explanation:

[tex] \dfrac{3}{a^2 - 9a + 14} = [/tex]

[tex] = \dfrac{3}{(a - 7)(a - 2)} [/tex]

[tex] = \dfrac{3(a + 8)}{(a - 7)(a - 2)(a + 8)} [/tex]

[tex] \dfrac{8a}{a^2 + a - 56} = [/tex]

[tex] = \dfrac{8a}{(a + 8)(a - 7)} [/tex]

[tex] = \dfrac{8a(a - 2)}{(a - 7)(a - 2)(a + 8)} [/tex]

Answer:

[tex]y(x)=-2x-\frac{11}{6}e^{-x}+\frac{3}{2}e^x+\frac{1}{3}e^{-4x}[/tex]

Step-by-step explanation:

[tex]y''-y=5e^{-4x}+2x,\: y(0)=y'(0)=0\\\\\mathcal{L}\{y''\}-\mathcal{L}\{y\}=\mathcal{L}\{5e^{-4x}\}+\mathcal{L}\{2x\}\\\\s^2Y(s)-sy(0)-y'(0)-Y(s)=\frac{5}{s+4}+\frac{2}{s^2}\\ \\s^2Y(s)-Y(s)=\frac{5}{s+4}+\frac{2}{s^2}\\ \\(s^2-1)Y(s)=\frac{5}{s+4}+\frac{2}{s^2}\\ \\Y(s)=\frac{5}{(s+4)(s^2-1)}+\frac{2}{s^2(s^2-1)}\\ \\Y(s)=\frac{5s^2+2(s+4)}{s^2(s+4)(s^2-1)}\\ \\Y(s)=\frac{5s^2+2s+8}{s^2(s-1)(s+1)(s+4)}[/tex]

Perform the partial fraction decomposition

[tex]\frac{5 s^{2} + 2 s + 8}{s^{2} \left(s - 1\right) \left(s + 1\right) \left(s + 4\right)}=\frac{A}{s}+\frac{B}{s^{2}}+\frac{C}{s + 1}+\frac{D}{s - 1}+\frac{E}{s + 4}\\\\5 s^{2} + 2 s + 8=s^{2} \left(s - 1\right) \left(s + 1\right) E + s^{2} \left(s - 1\right) \left(s + 4\right) C + s^{2} \left(s + 1\right) \left(s + 4\right) D + s \left(s - 1\right) \left(s + 1\right) \left(s + 4\right) A + \left(s - 1\right) \left(s + 1\right) \left(s + 4\right) B[/tex]

[tex]5 s^{2} + 2 s + 8=s^{4} A + s^{4} C + s^{4} D + s^{4} E + 4 s^{3} A + s^{3} B + 3 s^{3} C + 5 s^{3} D - s^{2} A + 4 s^{2} B - 4 s^{2} C + 4 s^{2} D - s^{2} E - 4 s A - s B - 4 B\\\\5 s^{2} + 2 s + 8=s^{4} \left(A + C + D + E\right) + s^{3} \left(4 A + B + 3 C + 5 D\right) + s^{2} \left(- A + 4 B - 4 C + 4 D - E\right) + s \left(- 4 A - B\right) - 4 B[/tex]

Solve for each constant

[tex]\begin{cases} A + C + D + E = 0\\4 A + B + 3 C + 5 D = 0\\- A + 4 B - 4 C + 4 D - E = 5\\- 4 A - B = 2\\- 4 B = 8 \end{cases}[/tex]

[tex]-4B=8\\B=-2[/tex]

[tex]-4A-B=2\\-4A-(-2)=2\\-4A+2=2\\-4A=0\\A=0[/tex]

[tex]A+C+D+E=0\\C+D+E=0\\E=-C-D[/tex]

[tex]-A+4B-4C+4D-E=5\\4(-2)-4C+4D-(-C-D)=5\\-8-4C+4D+C+D=5\\-3C+5D=13\\5D=13+3C[/tex]

[tex]4A+B+3C+5D=0\\4(0)+(-2)+3C+13+3C=0\\-2+6C+13=0\\11+6C=0\\6C=-11\\C=-\frac{11}{6}[/tex]

[tex]5D=13+3C\\5D=13+3(-\frac{11}{6})\\5D=13-\frac{33}{6}\\5D=\frac{15}{2}\\D=\frac{15}{10}\\D=\frac{3}{2}[/tex]

[tex]E=-C-D\\E=-(-\frac{11}{6})-(\frac{3}{2})\\E=\frac{11}{6}-\frac{3}{2}\\E=\frac{2}{6}\\E=\frac{1}{3}[/tex]

Take the inverse transform and solve for the IVP

[tex]Y(s)=\frac{0}{s}+\frac{-2}{s^2}+\frac{-\frac{11}{6}}{s+1}+\frac{\frac{3}{2}}{s-1}+\frac{\frac{1}{3}}{s+4}\\ \\y(x)=-2x-\frac{11}{6}e^{-x}+\frac{3}{2}e^x+\frac{1}{3}e^{-4x}[/tex]

Answer:

  7 - (-3)

Step-by-step explanation:

You want the sum 7 + 3 expressed as a difference.

The difference of A and B is written A - B. The subtraction operation is involved.

Subtraction is the same as addition of the opposite. Or, addition is the same as subtracting the opposite:

  7 + 3 = 7 - (-3)

__

Additional comment

We can also write the difference as ...

  3 - (-7)

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Answer:

[tex]x=27[/tex]

[tex]y=-6[/tex]

Step-by-step explanation:

substitute in values

[tex]x=21-y[/tex]

[tex](21-y)+3y=9[/tex]

[tex]21+2y=9[/tex]

[tex]2y=-12[/tex]

[tex]y=-6[/tex]

[tex]x+(-6)=21[/tex]

[tex]x=27[/tex]

Considering the situation described in the exercise, it is found that the correct null and alternative hypothesis for this test are given by, respectively:

[tex]H_0: \mu = 350[/tex]

[tex]H_1: \mu \neq 350[/tex]

At the null hypothesis, it is tested if the mean is of 350 degrees, that is:

[tex]H_0: \mu = 350[/tex]

At the alternative hypothesis, it is tested if the mean is different of 350 degrees, hence:

[tex]H_1: \mu \neq 350[/tex]

More can be learned about the test of an hypothesis at https://brainly.com/question/26454209

396 cm²

Volume of rectangular prism - -

Formula's :

Here base area:

Length * Width

4 * 9

36 cm²

Volume:

Base area * Height

36 * 11

396 cm²

Answer:

K = [tex]\frac{P}{TV}[/tex]

Step-by-step explanation:

P = KTV

Divide both sides by TV

(P/TV) = K

Answer:

x = 23

Step-by-step explanation:

Add 4x to the left and add 86 to the right.

5x = 115

Now, divide 5 on both sides to get x.

x = 23.

The result is 23.

Answer:

x= – 115/3

Step-by-step explanation:

I don’t know what exact form you want so I’ll give you mixed number form.

Answer:

4

Step-by-step explanation:

4*2=8

and 4/8 also equals four anyway you simplify the question it will equal 4

Answer:

-90x^3y^3

Step-by-step explanation:

This value is slightly over 1.2 million

========================================================

How I got that answer:

We have 45*44*43*42*41 = 146,611,080 different permutations. I started with 45 and counted down by 1 until I had 5 values multiplied out.

If order mattered, then we would stop here. But order doesn't matter. All that matters is the group overall rather than any particular individual or how they rank in the group.

There are 5! = 5*4*3*2*1 = 120 different ways to arrange a five item set, so the very large result we got earlier is overcounting by a factor of 120.

To fix this, we divide by 120 to get

(146,611,080)/120 = 1,221,759

This represents the number of combinations in which we're selecting 5 members from a pool of 45 total.

You could use the nCr formula

[tex]_nC_r = \frac{n!}{r!*(n-r)!}[/tex]

with n = 45 and r = 5 to get the same answer in bold above.

Using the principle of Combination, the number of different random samples of size five which can be obtained form a population of 45 is 1221759

Using the principle of combination, which is defined as :

Hence,

45C5 = 45! ÷ (45 - 5)!5!

45C5 = 45! ÷ 40!5!

45C5 = (45 × 44 × 43 × 42 × 41) / (5 × 4 × 3 × 2 × 1)

45C5 = 1221759

Therefore, there are 1221759 ways of making a selection of 5 samples from a population of size 45.

Learn more :https://brainly.com/question/10699405?referrer=searchResults

Answer:

10,000 is the answer

Step-by-step explanation:

14 465

round up the 4 which is 0 then your answer would be 10000

Answer:

-1/6

Step-by-step explanation:

the equation to do this is y2-y1/x2-x1

therefore you set it up as 4-3/-1-5

then when you simplify it it would be 1/-6

therefore the slope is -1/6

Answer:

14 answers  

Step-by-step explanation:

since there is 1/4 of a chance to get a question right by guessing you need to see what 1/4 of 56 is, which is 14

Answer:

Step-by-step explanation:

Complementary angles sum to 90°.

We have the measure of one angle, find the missing one as below.

Complementary angles have sum 90°

[tex]\\ \sf\longmapsto x+21=90[/tex]

[tex]\\ \sf\longmapsto x=90-21[/tex]

[tex]\\ \sf\longmapsto x=69[/tex]

Answer:

0,180

Step-by-step explanation:

[tex]8 \tan(x) = 0[/tex]

[tex] \tan(x) = 0[/tex]

[tex]x = 0 + 180n[/tex]

This means 0, 180 are the solutions.

Answer:

It should be -4/7

Step-by-step explanation:

I hope i helped. And If you can, can you help me by subing to my YT. It’s called Not Claz and it is the same profile pick I have on Brainly.

Answer:

Each of them would play 2 games to get the same cost amount

Step-by-step explanation:

for example

#1) $5 + $3 = $8 x 2 = $16

#2) $6 + $2 = $8 x 2 = $16

Answer:

y=3x

Step-by-step explanation:

Answer:

c=102°

b=(360-204)/2 = 78°

Answers:

b = 78

c = 102

=================================

Explanation:

Let's find angle b. This angle adds to the 102 to get 180 since the two angles form a straight angle.

102+b = 180

b = 180-102

b = 78

Then we can apply the same idea to find angle c

b+c = 180

78+c = 180

c = 180-78

c = 102

A shortcut to find angle c is to recall that vertical angles are congruent. The proof of the vertical angle theorem is effectively the steps shown above.

Answer:

The input is a contradiction: it has no solutions

Answer:

1.1025rad

Step-by-step explanation:

1°=0.0175rad

63°=0.0175rad*63=1.1025rad

Answer:

$3.43

Step-by-step explanation:

Multiply 7 by 0.49

Answer:

(a) 8.35

(b) 5.98

(c) 3.86

Step-by-step explanation:

The complete question is:

In a recent study on world​ happiness, participants were asked to evaluate their current lives on a scale from 0 to​ 10, where 0 represents the worst possible life and 10 represents the best possible life. The mean response was 5.4 with a standard deviation of 2.3. ​(a) What response represents the 90th ​percentile? ​(b) What response represents the ​60th percentile? ​(c) What response represents the ​first quartile? ​

Solution:

Assume that the world​ happiness ratings follows a Normal distribution with parameters μ = 5.4 and σ = 2.3.

(a)

Compute the response representing the 90th ​percentile as follows:

P (X < x) = 0.90

⇒ P (Z < z) = 0.90

The value of z for the above probability is, z = 1.282.

Compute the value of x as follows:

[tex]x=\mu+z\sigma[/tex]

   [tex]=5.4+(1.282\times 2.3)\\\\=5.4+2.9486\\\\=8.3486\\\\\approx 8.35[/tex]

Thus, the response representing the 90th ​percentile is 8.35.

(b)

Compute the response representing the 60th ​percentile as follows:

P (X < x) = 0.60

⇒ P (Z < z) = 0.60

The value of z for the above probability is, z = 0.25.

Compute the value of x as follows:

[tex]x=\mu+z\sigma[/tex]

   [tex]=5.4+(0.25\times 2.3)\\\\=5.4+0.575\\\\=5.975\\\\\approx 5.98[/tex]

Thus, the response representing the 60th ​percentile is 5.98.

(c)

Compute the response representing the first quartile of the 25th percentile as follows:

P (X < x) = 0.25

⇒ P (Z < z) = 0.25

The value of z for the above probability is, z = -0.67.

Compute the value of x as follows:

[tex]x=\mu+z\sigma[/tex]

   [tex]=5.4+(-0.67\times 2.3)\\\\=5.4-1.541\\\\=3.859\\\\\approx 3.86[/tex]

Thus, the response representing the first quartile is 3.86.