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3 years ago

I REALLY NEED HELP PLS Use the Binomial Theorem to find the binomial expansion of the expression. (x-3)^5

1 answer:

8 0

$(x - 3)^{5}$
$(x - 3)(x - 3)(x - 3)(x - 3)(x - 3)$
$(x^{2} - 6x + 9)(x^{2} - 6x + 9)(x^{2} - 6x + 9)(x - 3) \\(x^{4} - 12x^{3} + 54x^{2} - 108x + 81)(x - 3) \\x^{5} - 15x^{4} + 90x^{3} - 270x^{2} + 189x - 324$

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Kenneth loaned $1,200 to his niece to buy a computer. Two years later, she paid him back the $1,200 along with an interest of $9

insens350 [35]

Answer:

The annual interest rate was 4%

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Loan to Kenneth's niece to buy a computer = US$ 1,200

Duration of the loan = 2 years

Niece paid back to Kenneth = US$ 1,296

Annual interest rate = x%

2. Let's find the annual interest rate after 2 years, using the following formula:

FV = PV * (1 + x)

PV = Loan to Kenneth's niece to buy a computer = US$ 1,200

FV = Niece paid back to Kenneth = US$ 1,296

rate (r) = x

Replacing with the real values:

1,296 = 1,200 * (1 + x)

1.296/1.200 = (1 + x) (Dividing by 1,200 at both sides)

1.08 = 1 + x

1.08 - 1 = x (Subtracting 1 at both sides)

0.08 = x

This is the interest rate for two years, for finding the annual interest rate we divide it by 2, this way:

0.08 / 2 = 0.04 * 100 = 4%

7 0

3 years ago

The radius of a solid hemisphere is 2r. Find its total surface area

Musya8 [376]

Answer:

Radius= 2r

Step-by-step explanation:

Surface area of hemisphere

=2 x 22/7 x (2r)^2

=44/7 x 4 r^2

=174/7 r^2

=25.14 r^2

5 0

3 years ago

Use the sample data and confidence level to construct the confidence interval estimate of the population proportion p. n equals

Alekssandra [29.7K]

Answer:

(0.767,0.833)

Step-by-step explanation:

The 95% confidence interval for population proportion p can be computed as

$p-z_{\frac{\alpha }{2} } \sqrt{\frac{pq}{n} }$

The z-value associated with 95% confidence level is 1.96.

whereas p=x/n

We are given that x=440 and n=550.

p=440/550=0.8

$0.8-1.96\sqrt{\frac{0.8(0.2)}{550} }$

$0.8-1.96\sqrt{\frac{0.16}{550} }$

$0.8-1.96\sqrt{0.00029 }$

$0.8-1.96(0.01706)$

$0.8-0.03343$

$0.76657$

Thus, the required confidence interval is

0.767<P<0.833 (rounded to 3 decimal places)

Hence, we are 95% confident that our true population proportion will lie in the interval (0.767,0.833)

3 0

2 years ago

Help! how do i answer this

navik [9.2K]

Idk but ima try to figure it out ok

7 0

2 years ago

Solve for the missing length and the other two angles in the triangle below

Klio2033 [76]

Answer:

AC = 3.72 units

Angles:

A = 132.6°

C = 27.4°

Step-by-step explanation:

AC² = 5² + 8² - 2(5)(8)cos(20)

AC² = 13.82459034

AC = 3.718143399

3.718143399/sin20 = 8/sinA

sinA = 0.7358944647

A = 180 - 47.38285134

A = 132.6171487

3.718143399/sin20 = 5/sinC

sinC = 0.4599340405

C = 27.38285134

5 0

3 years ago