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3 years ago

Explain why the product of a nonzero rational number and an irrational number is irrational

Mathematics

1 answer:

spayn [35]3 years ago

3 0

Answer:

If you multiply any irrational number by the rational number zero, the result will be zero, which is rational. Any other situation, however, of a rational times an irrational will be irrational.

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All the fourth-graders in a certain elementary school took a standardized test. A total of 81% of the students were found to be

Dvinal [7]

Answer:

The probability that a student is proficient in mathematics, but not in reading is, 0.10.

The probability that a student is proficient in reading, but not in mathematics is, 0.17

Step-by-step explanation:

Let's define the events:

L: The student is proficient in reading

M: The student is proficient in math

The probabilities are given by:

$P (L) = 0.81\\P (M) = 0.74\\P (L\bigcap M) = 0.64$

$P (M\bigcap L^c) = P (M) - P (M\bigcap L) = 0.74 - 0.64 = 0.1\\P (M^c\bigcap L) = P (L) - P (M\bigcap L) = 0.81 - 0.64 = 0.17$

The probability that a student is proficient in mathematics, but not in reading is, 0.10.

The probability that a student is proficient in reading, but not in mathematics is, 0.17

5 0

3 years ago

Eric invested 5000 dollars in the stock market. The value of his stock increased by 13%. a) what is the amount earned from this

blagie [28]

Answer:

$Earnings = 650$

$New\ Value = 5650$

Step-by-step explanation:

Given

$Amount = 5000$

$Rate = 13\%$

Solving (a): The earnings.

This is calculated as:

$Earnings = Amount * Rate$

$Earnings = 5000 * 13\%$

$Earnings = 650$

Solving (b): New Value

This is calculated as:

So, we have:

$New\ Value = Amount + Earnings$

$New\ Value = 5000 + 650$

$New\ Value = 5650$

4 0

2 years ago

Suppose that, for a particular social networking company, the annual revenue from rich media advertisements, in millions of doll

Juli2301 [7.4K]

Answer:

a. Revenue of the company at the beginning of 2010 is 75 million dollar (loss)

b. Rate at which the revenue changing in the year 2010 is 76 million dollar per year ( decreasing)

Step-by-step explanation:

For part a,

Given that x is the number of years at the beginning of 2007.

Therefore, $x=0$ for year 2007.

Hence at the year 2010 value of x will be $x=3$ .

Substitute the value of x=3 in R(x),

$R\left(x\right)=-x^{4}+8x^{3}-38x^{2}+44x$

$R\left(x\right)=-\left(81\right)+8\left(27\right)-38\left(9\right)+132$

$R\left(x\right)=-81+216-342+132$

$R\left(x\right)=-75$

Negative sign indicates that there is loss of revenue at the start of the year 2010

Therefore, there is loss of revenue at the beginning of 2010 which is 75 million dollar.

For part b,

To calculate rate, differentiate the given function with respect to x.

$\dfrac{d}{dx}R\left(x\right)=\dfrac{d}{dx}\left (-\left(x\right)^{4}+8\left(x\right)^{3}-38\left(x\right)^{2}+44\left(x\right)\right)$

Applying sum and difference rule of derivative,

$\dfrac{d}{dx}R\left(x\right)=-\dfrac{d}{dx}\left(x^4\right)+\dfrac{d}{dx}\left(8x^3\right)-\dfrac{d}{dx}\left(38x^2\right)+\dfrac{d}{dx}\left(44x\right)$

Applying constant multiple rule of derivative,

$\dfrac{d}{dx}R\left(x\right)=-\dfrac{d}{dx}\left(x^4\right)+8\dfrac{d}{dx}\left(x^3\right)-38\dfrac{d}{dx}\left(x^2\right)+44\dfrac{d}{dx}\left(x\right)$

Applying power rule of derivative,

$\dfrac{d}{dx}R\left(x\right)=-\left(4x^{4-1}\right)+8\left(3x^{3-1}\right)-38\left(2x^{2-1}\right)+44\left(1x^{1-1}\right)$

$\dfrac{d}{dx}R\left(x\right)=-4\left(x^{3}\right)+8\left(3x^{2}\right)-38\left(2x^{1}\right)+44$

$\dfrac{d}{dx}R\left(x\right)=-4x^3+24x^2-76x+44$

Substituting the value x=3,

$\dfrac{d}{dx}R\left(x\right)=-4\left(3\right)^3+24\left(3\right)^2-76\left(3\right)+44$

$\dfrac{d}{dx}R\left(x\right)=-4\left(27\right)+24\left(9\right)-76\left(3\right)+44$

$\dfrac{d}{dx}R\left(x\right)=-108+216-228+44$

$\dfrac{d}{dx}R\left(x\right)=-76$

Negative sign indicates that rate is decreasing.

Rate at which the revenue is changing in the year 2010 is 76 million dollar per year.

8 0

2 years ago

Y = 2(x - 8)(x+2)

ss7ja [257]

Answer:

Step-by-step explanation:

y=2(x-8)(x+2)

The x intercepts occur when y=0, so when x=8 and -2

The vertex is where the equation is at a minimum/maximum in this case (x,y)=(3,-50)

The axis of symmetry occurs between the two roots, 8 and -2 which x=3

The y intercept is the value of y when x=0, in this case (0, -32)

5 0

2 years ago

The transport layer handles the transmission error by requesting the damaged segments to be retransmitted. if the probability of

Sliva [168]

The geometric distribution applies to experiments employing Bernoulli trials (success or failure) to determine the number of trials to obtain the first success.
This distribution may be applied to the given situation, where the probability of success is p.
Let n=number of transmissions required (n ≥ 1)Then
P(n)=(1-p)^(n-1)*p (probability that n transmissions are required)
and the mean number of transmissions required
μ = 1/p

3 0

2 years ago