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3 years ago

Select the correct location in the expression.

Mathematics

1 answer:

kogti [31]3 years ago

4 0

Answer:

Correct term:60

Step-by-step explanation:

We are given that

$\frac{4x^4-6x^3+6x+3}{x-3}$

The quotient of this expression is given by

$4x^3+6x^2+18x+78+\frac{183}{x-3}$

We have to find the term in this expression which contains an error.

$\frac{4x^4-6x^3+6x+3}{x-3}$

The quotient of this expression is given by

$=4x^3+6x^2+18x+60$

$Dividend=Divisor\times quotient+ remainder$

Using the formula

$4x^4-6x^3+6x+3=(x-3)(4x^3+6x^2+18x+60)+\frac{183}{x-3}$

We can see that in the given expression there is 60 in place of 78.

The error in the expression of quotient is 78.

Correct term is 60.

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podryga [215]

Given : Fix amount charges = $200.

Each month additional charge = $50.

Let us assume number of months are taken by x.

So, we can setup a function as

Total charge = Fix charge + each month charge * number of months.

f(x) = 200 + 50*x

Or f(x) = 200 +5x.

Where function f is the total charge of x number of months.

The values of x's represents domain and function value represents range.

According to problem, it is said " first three months".

So, we need to take number of months as x=0,1,2,3.

And we need to find values of function for those x values.

On plugging x=0,1,2 and 3 we would get

f(0) = 200 +5(0) = 200 +0 = 200.

f(1) = 200 +5(1) = 200 +50 = 250.

f(2) = 200 +5(2) = 200 +100 = 300.

f(3) = 200 +5(3) = 200 +150 = 350.

We got function values 200,250,300 and 350.

Therefore, with respect to the given situation, the domain of the funtion is

{0,1,2,3} and Range { 200,250,300, 350}.

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3 years ago

An urn contains 8 red chips, 10 green chips, and 2 white chips. A chip is drawn and replaced, and then a second chip is drawn.

Harlamova29_29 [7]

Answer:

(A) 0.04

(B) 0.25

Step-by-step explanation:

Let R = drawing a red chips, G = drawing green chips and W = drawing white chips.

Given:

R = 8, G = 10 and W = 2.

Total number of chips = 8 + 10 + 2 = 20

$P(R) = \frac{8}{20}=\frac{2}{5}\\P(G)= \frac{10}{20}=\frac{1}{2}\\P(W)= \frac{2}{20}=\frac{1}{10}$

As the chips are replaced after drawing the probability of selecting the second chip is independent of the probability of selecting the first chip.

(A)

Compute the probability of selecting a white chip on the first and a red on the second as follows:

$P(1^{st}\ white\ chip, 2^{nd}\ red\ chip)=P(W)\times P(R)\\=\frac{1}{10}\times \frac{2}{5}\\ =\frac{1}{25} \\=0.04$

Thus, the probability of selecting a white chip on the first and a red on the second is 0.04.

(B)

Compute the probability of selecting 2 green chips:

$P(2\ Green\ chips)=P(G)\times P(G)\\=\frac{1}{2} \times\frac{1}{2}\\ =\frac{1}{4}\\ =0.25$

Thus, the probability of selecting 2 green chips is 0.25.

(C)

Compute the conditional probability of selecting a red chip given the first chip drawn was white as follows:

$P(2^{nd}\ red\ chip|1^{st}\ white\ chip)=\frac{P(2^{nd}\ red\ chip\ \cap 1^{st}\ white\ chip)}{P (1^{st}\ white\ chip)} \\=\frac{P(2^{nd}\ red\ chip)P(1^{st}\ white\ chip)}{P (1^{st}\ white\ chip)} \\= P(R)\\=\frac{2}{5}\\=0.40$

Thus, the probability of selecting a red chip given the first chip drawn was white is 0.40.

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3 years ago

For the geometric sequence 3, 12, 48, 192 find the indicated term

makvit [3.9K]

768

3x4= 12
12x4= 48
48x4= 192
192x4=768

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3 years ago