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Veronika [31]
3 years ago
9

Expand the function. 4 f(x) = (2x + 3)4

Mathematics
2 answers:
Arturiano [62]3 years ago
4 0

Answer:

16 x ^4  −  96 x^ 3  +  216 x ^2  −  216 x  +  81

Step-by-step explanation:

Use the binomial expansion theorem to find each term. ∑

∑The binomial theorem states ( a + b ) n = n ∑ k = 0 n C k ⋅ ( a n − k b k ) . 4 ∑ k = 0 4 ! ( 4 − k ) ! k ! ⋅ ( 2 x ) 4 − k ⋅ ( − 3 ) k

Expand the summation. 4 ! ( 4 − 0 ) ! 0 ! ⋅ ( 2 x ) 4 − 0 ⋅ ( − 3 ) 0 + 4 ! ( 4 − 1 ) ! 1 ! ⋅ ( 2 x ) 4 − 1 ⋅ ( − 3 ) + 4 ! ( 4 − 2 ) ! 2 ! ⋅ ( 2 x ) 4 − 2 ⋅ ( − 3 ) 2 + 4 ! ( 4 − 3 ) ! 3 ! ⋅ ( 2 x ) 4 − 3 ⋅ ( − 3 ) 3 + 4 ! ( 4 − 4 ) ! 4 ! ⋅ ( 2 x ) 4 − 4 ⋅ ( − 3 ) 4

Simplify the exponents for each term of the expansion. 1 ⋅ ( 2 x ) 4 ⋅ ( − 3 ) 0 + 4 ⋅ ( 2 x ) 3 ⋅ ( − 3 ) + 6 ⋅ ( 2 x ) 2 ⋅ ( − 3 ) 2 + 4 ⋅ ( 2 x ) ⋅ ( − 3 ) 3 + 1 ⋅ ( 2 x ) 0 ⋅ ( − 3 ) 4

Simplify each term.

= 16 x ^4  −  96 x^ 3  +  216 x ^2  −  216 x  +  81

VARVARA [1.3K]3 years ago
3 0
Just divide both sides and write it in parametric from and you get

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Given the system of equations, what is the solution?
Phantasy [73]
We can do the elimination method to find the solution for this problem. The elimination method involves adding the two equations together to get rid of a like term.

x + 2y = 7
+ x - 2y = -1
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2x = 6

Now that we eliminated 2y because they cancel out, we are left with 2x = 6. Divide both sides by 2 in order to get x.

The answer is: x = 3.

Now that we know the numerical value of x, all we have to do is plug x into either system of equation in order to find the numerical value of y.

x + 2y = 7

3 + 2y = 7

2y = 4

y = 2

The solution to the problem is (3, 2).

4 0
3 years ago
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4 0
3 years ago
Please help! see attached
nikdorinn [45]

Answer:

  1. The lowest value of the confidence interval is 0.5262 or 52.62%
  2. The highest value of the confidence interval is 0.5538 or 55.38%

Step-by-step explanation:

Here you estimate the proportion of people in the population that said did not have children under 18 living at home.It can also be given as a percentage.

The general expression to apply here is;

C.I=p+-z*\sqrt{\frac{p(1-p)}{n} }

where ;

p=sample proportion

n=sample size

z*=value of z* from the standard normal distribution for 95% confidence level

Given;

n=5000

<u>Find p</u>

From the question 54% of people chosen said they did not have children under 18 living at home

\frac{54}{100} *5000 = 2700\\\\p=\frac{2700}{5000} =0.54

<u>To calculate the 95% confidence interval, follow the steps below;</u>

  • Find the value of z* from the z*-value table

The value of z* from the table is 1.96

  • calculate the sample proportion p

The value of p=0.54 as calculated above

  • Find p(1-p)

0.54(1-0.54)=0.2484

  • Find p(1-p)/n

Divide the value of p(1-p) with the sample size, n

\frac{0.2448}{5000} =0.00004968

  • Find the square-root of p(1-p)/n

=\sqrt{0.00004968} =0.007048

  • Find the margin of error

Here multiply the square-root of p(1-p)/n by the z*

=0.007048*1.96=0.0138

The 95% confidence interval for the lower end value is p-margin of error

=0.54-0.0138=0.5262

The 95% confidence interval for the upper end value is p+margin of error

0.54+0.0138=0.5538

7 0
3 years ago
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IRISSAK [1]
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6 0
4 years ago
Convert the angle to radians. Leave As a multiple of π. -90
alexdok [17]

Answer:

-90° = 3π/2 radians

Step-by-step explanation:

Keep in mind that -90° represents a 90° clockwise rotation from the positive x-axis. This is the same as a 360°-90°=270° counter-clockwise rotation from the positive x-axis.

To convert from degrees to radians, we simply multiply the degrees by π/180 radians. So, the answer is (270)(π/180)=(270π/180)=3π/2 radians

7 0
3 years ago
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