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With these

"no terms independent of x" basically means there is no constant term, or the coefficient of x ⁰ is zero.

Recall the binomial theorem:

[tex]\displaystyle (a+b)^n=\sum_{k=0}^n\binom nk a^{n-k}b^k[/tex]

So we have

[tex]\displaystyle \left(1+ax^2\right)\left(\frac2x-3x\right)^6 = \left(1+ax^2\right) \sum_{k=0}^6 \binom 6k \left(\frac2x\right)^{6-k}(-3x)^k[/tex]

[tex]\displaystyle \left(1+ax^2\right)\left(\frac2x-3x\right)^6 = \left(1+ax^2\right) \sum_{k=0}^6 2^{6-k}(-3)^k\binom 6k x^{2k-6}[/tex]

[tex]\displaystyle \left(1+ax^2\right)\left(\frac2x-3x\right)^6 = \sum_{k=0}^6 2^{6-k}(-3)^k\binom 6k x^{2k-6}+a\sum_{k=0}^6 2^{6-k}(-3)^k\binom 6k x^{2k-4}[/tex]

The first sum contributes a x ⁰ term for 2k - 6 = 0, or k = 3, while the second sum contributes a x ⁰ term for 2k - 4 = 0, or k = 2. The coefficient of the sum of these terms must be zero:

[tex]2^{6-3}(-3)^3\dbinom 63 + a\times2^{6-2}(-3)^2\dbinom 62 = 0[/tex]

which reduces to

2160a - 4320 = 0

2160a = 4320

a = 2

Answer:

(0.123 ; 0.277)

Step-by-step explanation:

Given :

Sample size, n = 180

x = 36

Proportion, p = x / n = 36/180 = 0.2

Confidence interval for sample proportion :

Confidence interval :

p ± Zcritical * √p(1 - p) / n

Zcritical at 99% = 2.576

0.2 ± 2.576 * √0.2(1 - 0.2) / 180

0.2 ± 2.576 * 0.0298142

0.2 ± 0.0768013792

(0.123 ; 0.277)

Answer:

8 inches

48 inches

total 56 inches

Step-by-step explanation:

x+6x = 56

7x = 56

Divide by 7

7x/7 = 56/7

x = 8

The smaller piece is x inches or 8 inches

The larger piece is 6x inches or 6*8 =48 inches

8+48 = 56 inches

The total length is 56 inches

Answer:

8 inches, and 48 inches

Step-by-step explanation:

x+6x=56

Solve the equation.

7x=56

x=8

Interpret the results and write the answer in words.

The smaller piece is x = 8 in.

The longer piece is 6x = 6 (8) = 48 in.

The lengths of the two pieces are 8 in

and 48 in.

Answer: width = 4 and length = 10

Step-by-step explanation:

Width = w and length = w + 6

2(w) + 2 (w + 6) = 28

2w + 2w + 12 = 28

4w = 28 - 12

W = 16/4

W = 4 (width)

Length = w + 6

4 + 6 = 10

Answer:

Fail to reject the null hypothesis.

Step-by-step explanation:

People who live in Florida and also have annual pass to Disney world is 221, sample size selected for group 1 is 350.

People who do not live in Florida and have annual pass to Disney world is 365, sample size selected for Group 2 is 650.

Group 1 sample proportion is : 221 / 350 = 0.6314

Group 2 sample proportion is 365 / 650 = 0.5615

Test statistics is 0.8317

Since test stats value is greater than the sample proportion significance level, we fail to reject the null hypothesis.

Answer:

$150

Step-by-step explanation:

discount=60%

let the price=x

(100-60)% of x=$60

40% of x=60

x=60×(100/40)=150

Answer:

She could wear 7 different outfits

Step-by-step explanation:

pandemic times: Potential ... - CAF

have shown evidence that the effect of corruption on real GDP per capita is more pronounced in countries with low levels of8

Answer:

x≤16

Step-by-step explanation:

1/2x - 3 ≤5

Add 3 to each side

1/2x -3+3 ≤5+3

1/2x≤8

Multiply each side by 2

1/2x*2 ≤8*2

x≤16

Answer:

Graph the same exact curve, but move every y value up 6.

Step-by-step explanation:

A transformation to the y-values is outside of the argument of the function. i.e., outside of the parentheses.

Answer:

D. 9n = 27

Step-by-step explanation:

If we need one adult for every 9 students, we can represent that as 9n:

if n is the number of adults.

Because we have 27 students, the equation 9n = 27 works.

A better way of formatting the equation is:

n = 27/9

Because it directly shows what the number of adults is, but with some reformatting, it is clearly the same equation.

Answer:

4/7 > 2/10

Step-by-step explanation:

4/7 is close to 1/2

2/10 is close to 0

4/7 > 2/10

Answer:

(8.608, 9.392)

Step-by-step explanation:

We have the following information

Population standard deviation = 1.8

Sample mean = 9 hours

Sample n = 81

C I = 95%

So level of significance

Alpha = 1-0.95

= 0.05

Z critical at 0.05/2

Z(0.025) = 1.96

The 95% c.i =

9+-(1.96)(1.8/√81)

9+-(1.96)(0.2)

(9-0.392)(9+0.392)

(8.608, 9.392)

This is the confidence interval at 95%.

I hope you find my solution useful. Good luck!!!

Answer:

7

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Starting from right to left...

9 is in the ones place

8 is in the tenths place

4 is in the hundreds place

7 is in the thousands place.

I hope this helps!

The first or second one because a function can't have the x value repeating

Answer: No, The goal when testing a hypothesis is to to guess a large significant level to possibly have the answer correct based upon evidence. False. It needs to be a large significant level

Step-by-step explanation:

Answer:

Harry collected 180 stamps

Harry's sister collected 60 stamps

Step-by-step explanation:

Let X be the number of stamps that Harry's sister colleted.

The number of stamps Harry colleted is 3 time as many as his sister's

⇒ 3*X + X = 240

⇒ X = 60

⇒ 240 - 60= 180

Answer:

180 for harry and 60 for his sister

Step-by-step explanation:

Answer:

100$or 20.4 that is the answer

Answer:

[tex] \frac{1}{1 + \cos(x) } [/tex]

Step-by-step explanation:

[tex]y = \frac{ \sin(x) }{1 + \cos(x) } [/tex]

differentiating numerator wrt x :-

(sinx)' = cos x

differentiating denominator wrt x :-

(1 + cos x)' = (cosx)' = - sinx

[tex] (\frac{u}{v} )' = \frac{v. \: (u)' - u.(v)' }{ {v}^{2} } [/tex]

here,

[tex] = \frac{((1 + \cos \: x) \cos \: x )- (\sin \: x. ( - \sin \: x) ) }{( {1 + \cos(x)) }^{2} } [/tex]

[tex] = \frac{ \cos(x) + \cos {}^{2} (x) + \sin {}^{2} (x) }{(1 + \cos \: x) {}^{2} } [/tex]

since cos²x + sin²x = 1

[tex] = \frac{ \cos \: x + 1}{(1 + \cos \: x) {}^{2} } [/tex]

diving numerator and denominator by 1 + cos x

[tex] = \frac{1}{1 + \cos(x) } [/tex]

Answer:

- What is the probability at least one of the two televisions does not work?

The probability at least one of the two televisions does not​ work is 0.8163

- The probability that both televisions work is?

The probability that both televisions work is 0.1837

Step-by-step explanation:

Total televisions are 7

Faulty televisions are 4

Number of televisions selected is 2

Answer:

third option

Step-by-step explanation:

Brainliest please~

Answer:

0.84

Step-by-step explanation:

4x2+13a+10=7

13a=7-10-8

13a=-11

a=-11:13

a=0.84

Answer:

9876

Step-by-step explanation:

7:5

x:4115

To find x mulitply 7 by 823 (because this is what we multiplied 5 by in order to get 4115)

7*823= 5761

Take the sum to find the total number of votes

4115+5761= 9876

Answer:

width = 17 m ; length = 31 m

Step-by-step explanation:

w = width

l = length

perimeter of a rectangle = (length + width) * 2

l = 14 + w

(14 + w + w) * 2 = 96

(14 + 2w) * 2 = 96

28 + 4w = 96

4w = 68

w = 17 m

l = 14 + 17 = 31 m

Answer:

yefeihuerijohiftv3ugrhoerfujfy

Step-by-step explanation:

y=-4x²-8x+1

а<0 so we will be looking for maximum

х=-b/2a=8/-8=-1

у=4+8+1=13

Maximum point (-1;13)

7

15

because there are a total of 15 grid and the question asked to pick the grid that doesn't shaded

Answer:

7/15

Step-by-step explanation:

We can count the grids to see that there are 15. This is the total, and will become our denominator. From there, we can count the non blue squares to get to 7, our numerator. We put our numerator, 7, over pur denominator, 15. This gives us 7/15.

Answer: [tex]6.12\ \text{years}[/tex]

Step-by-step explanation:

Given

Rate of interest is [tex]r=3\%[/tex] compounded quarterly

So, annually it is [tex]r=12\%[/tex]

Suppose [tex]P[/tex] is the Principal and A is the amount after certain time period.

Amount in Compound interest is given by

[tex]\Rightarrow A=P[1+r\%]^t[/tex]

for given conditions

[tex]\Rightarrow 2P=P[1+0.12]^t\\\Rightarrow 2=(1.12)^t\\\\\Rightarrow t=\dfrac{\ln (2)}{\ln (1.12)}\\\\\Rightarrow t=6.116\approx 6.12\ \text{years}[/tex]

It take [tex]6.12\ \text{years}[/tex] to double the invested amount.