Solve the following linear equation for x 5x

Find the indefinite integral. (use c for the constant of integration.) sin3 5θ cos 5θ dθ

Elina [12.6K]

I'm guessing you mean

$\displaystyle\int\sin^35\theta\cos5\theta\,\mathrm d\theta$

Let $t=5\sin\theta$ . Then $\mathrm dt=5\cos5\theta\,\mathrm d\theta$ . So we have

$\displaystyle\int\sin^35\theta\cos5\theta\,\mathrm d\theta=\frac15\int\sin^35\theta(5\cos5\theta)\,\mathrm d\theta$

$=\displaystyle\frac15\int t^3\,\mathrm dt$

$=\dfrac{t^4}{20}+C$

$=\dfrac{\sin^4\5\theta}{20}+C$

7 0

3 years ago

Lola measures three buttons for a shirt she’s making. One button is 1/8, 3/8 and 1/4 inch. The button hole is 2/6 of an inch. Wh

mel-nik [20]

Answer:

3/8

Step-by-step explanation:

That's the only one bigger than 2/6, any smaller will fall out as it's a button. You'd twist it sort of in half to get it in the hole, therefore, 3/8 is the only button that will fit.

I'm not sure if this is correct but this is how I'd go about it :)

7 0

3 years ago

The Wall Street Journal Corporate Perceptions Study 2011 surveyed readers and asked how each rated the Quality of Management and

kykrilka [37]

Answer:

The calculated χ² = 17.0281 falls in the critical region χ² ≥ 9.49 so we reject the null hypothesis that the quality of management and the reputation of the company are independent and conclude quality of management and the reputation of the company are dependent

The p-value is 0 .001909. The result is significant at p < 0.05

Part b:

40 > 8.5

35> 7.5

25> 4

Step-by-step explanation:

1) Let the null and alternative hypothesis as

H0: the quality of management and the reputation of the company are independent

against the claim

Ha: the quality of management and the reputation of the company are dependent

2) The significance level alpha is set at 0.05

3) The test statistic under H0 is

χ²= ∑ (o - e)²/ e where O is the observed and e is the expected frequency

which has an approximate chi square distribution with ( 3-1) (3-1)= 4 d.f

4) Computations:

Under H0 ,

Observed Expected E χ²= ∑(O-e)²/e

40 35.00 0.71

25 24.50 0.01

5 10.50 2.88

35 40.00 0.62

35 28.0 1.75

10 12.00 0.33

25 25.00 0.00

10 17.50 3.21

15 7.50 7.50

∑ 17.0281

Column Totals 100 70 30 200 (Grand Total)

5) The critical region is χ² ≥ χ² (0.05)2 = 9.49

6) Conclusion:

The calculated χ² = 17.0281 falls in the critical region χ² ≥ 9.49 so we reject the null hypothesis that the quality of management and the reputation of the company are independent and conclude quality of management and the reputation of the company are dependent.

7) The p-value is 0 .001909. The result is significant at p < 0.05

The p- values tells that the variables are dependent.

Part b:

If we take the excellent row total = 70 and compare it with the excellent column total= 100

If we take the good row total = 70 and compare it with the good column total= 80

If we take the fair row total = 50 and compare it with the fair column total= 30

The two attributes are said to be associated if

Thus we see that ( where (A)(B) are row and columns totals and AB are the cell contents)

AB> (A)(B)/N

40 > 1700/200

40 > 8.5

35> 1500/200

35> 7.5

25> 800/200

25> 4

and so on.

Hence they are positively associated

8 0

3 years ago

How do you solve?3(t+4)-2(2t+3)=-4

shepuryov [24]

3t+12-4t-6=-4
-t=-4+6-12
-t=-10
t=10
That's your answer.

8 0

3 years ago

Read 2 more answers

Carl. put $1.10 in his piggy bank every day in the month of July. His total savings was $55 at the end of June. hat is the best

Crank

Carl would have around $90 at the end of July

8 0

3 years ago

Read 2 more answers

Solve the following linear equation for x 5x - 2 + x = 9 + 3x + 10