Find the value of X.

Sketch the curve y=x(x-2)^3 showing any stationary points and points of inflection

ycow [4]

Answer:

hshsnwjsbsbskakdbdbsn

6 0

3 years ago

Read 2 more answers

If nCr : (n+1)Cr : (n+2)Cr = 1:3:7, find the values of n and r.

Troyanec [42]

The solution is n = 5 and r = 4

Step-by-step explanation:

Given,

nCr : (n+1)Cr : (n+2)Cr = 1:3:7

To find the value of n and r.

Formula

nCr = $\frac{n!}{r!(n-r)!}$ [ n! means = n.(n-1).(n-2)....3.2.1]

Now,

nCr : (n+1)Cr = 1:3 and (n+1)Cr : (n+2)Cr = 3:7

or, $\frac{n!}{r!(n-r)!}$ : $\frac{(n+1)!}{r!(n+1-r)!}$ = 1:3 or, $\frac{(n+1)!}{r!(n+1-r)!}$ : $\frac{(n+2)!}{r!(n+2-r)!}$ = $\frac{3}{7}$

or, $\frac{n!}{r!(n-r)!}$ × $\frac{r!(n+1-r)!}{(n+1)!}$ = $\frac{1}{3}$ or, $\frac{(n+1)!}{r!(n+1-r)!}$ × $\frac{r!(n+2-r)!}{(n+2)!}$ = $\frac{3}{7}$

or, $\frac{n+1-r}{n+1}$ = $\frac{1}{3}$ or, $\frac{n+2-r}{n+2}$ = $\frac{3}{7}$

or, 3(n+1-r) = n+1 or, 7(n+2-r) = 3(n+2)

or, 3n+3-3r = n+1 or, 7n+14-7r = 3n+6

or, 2n-3r = -2 or, 4n-7r = -8

Now, by solving

2n-3r = -2 -----(1)

4n-7r = -8 -----(2) we will get n and r

Multiplying (1) by and then subtract with (2) we get,

2(2n-3r) - (4n-7r) = -4-(-8)

or, 4n-6r-4n+7r = 4

or, r = 4

From (1) we get,

2n = -2+3(4)

or, 2n = 10

or, n = 5

Hence,

n = 5 and r = 4

8 0

4 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

if your not going to really help me please leave im spending all my points to get this answer so please dont spam me i really ne

Ipatiy [6.2K]

A)she is not right.because if the remaining peice is the hypotenuse of the triangle, the answer will be around 27.8 if the hypotenuse is 22 then the missing angle is 13.96

b)yes it will work
if you double the measurements of the two sides of a right triangle the other one will be double, too(you can get help from Pythagoras theorem )

c)yes it is possible. if we can double the sides of a right triangle it means that we add measurements to the triangle.
for example:a triangle with sides of 3,4,5
if we add 6,8,10
it will be 9,12,15
hope I could help

7 0

3 years ago

Bytecoin is a new cryptocurrency that is currently valued at $243 per coin. You want to make an investment and purchase 1 Byteco

Digiron [165]

Answer:

Step-by-step explanation:

The growth rate of the coin is exponential. We would apply the formula for exponential growth which is expressed as

y = ab^x

y = b(1 + r)^ t

Where

y represents the value of the coin after x months.

x represents the number of months.

a represents the initial value of the coin.

b represents rate of growth.

From the information given,

a = 243

b = 1 + 15/100 = 1 + 0.15 = 1.15

Therefore, the exponential expression to determine the number of months, x it will take for the coin to attain a certain value, y is expressed as

y = 243(1.15)^x

If y = 1000, it means that

1000 = 243(1.15)^x

1000/243 = 1.15^x

4.115 = 1.15^x

Taking log of both sides, it becomes

log 4.115 = xlog1.15

0.614 = 0.061x

x = 0.614/0.061

x = 10 months

It will take 10 months

7 0

4 years ago