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4 years ago

Rewrite the rational exponent as a radical by extending the properties of integer exponents.

Mathematics

1 answer:

Snezhnost [94]4 years ago

7 0

$\cfrac{2^{ \frac{3}{4} }}{2^{ \frac{1}{2} }}=2^{ \frac{3}{4} - \frac{1}{2} } =2^{ \frac{3}{4}- \frac{2}{4} }=2^{ \frac{1}{4} }= \sqrt[4]{2}$

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A parabola can be drawn given a focus of

Volgvan

Answer:

$y=-\frac{1}{4}(x-2)^{2}+9$

Step-by-step explanation:

Any point on a given parabola is equidistant from focus and directrix.

Given:

Focus of the parabola is at $(2,8)$ .

Directrix of the parabola is $y=10$ .

Let $(x,y)$ be any point on the parabola. Then, from the definition of a parabola,

Distance of $(x,y)$ from focus = Distance of $(x,y)$ from directrix.

Therefore,

$\sqrt{(x-2)^{2}+(y-8)^{2}}=|y-10|$

Squaring both sides, we get

$(x-2)^{2}+(y-8)^{2}=(y-10)^{2}\\(x-2)^{2}=(y-10)^{2}-(y-8)^{2}\\(x-2)^{2}=(y-10+y-8)(y-10-(y-8))...............[\because a^{2}-b^{2}=(a+b)(a-b)]\\(x-2)^{2}=(2y-18)(y-10-y+8)\\(x-2)^{2}=2(y-9)(-2)\\(x-2)^{2}=-4(y-9)\\y-9=-\frac{1}{4}(x-2)^{2}\\y=-\frac{1}{4}(x-2)^{2}+9$

Hence, the equation of the parabola is $y=-\frac{1}{4}(x-2)^{2}+9$ .

4 0

3 years ago

the brand name of a certain chain of coffee shops has a 53% recognition rate in the town of coffleton. An executive from the com

Degger [83]

This problem can be solve using the Binomial Distribution, it is a recurrence conveyance of the conceivable number of effective results in a given number of trials in each of which there is a similar likelihood of accomplishment.

Let be X: coffleton residents recognize the brand name

n = 10

p = 0.53

q = 0.47

P(X = 4) =

(10)

(4)*(0.53^4)*(0.47^6) = <span>0.00340</span>

7 0

3 years ago

For the following reports about statistical studies, identify the following items (if possible). If you can't tell, then say so-

Ira Lisetskai [31]

Answer:

Population: Soil around a former waste dump
Parameter: Concentrations of toxic chemicals
Sample frame: Accessible soil around dump
Sample: 16 soil samples
Method: Unclear
Bias: Uncertain if soil samples were randomly chosen

Step-by-step explanation:

The above answer explanation can be more clear by understanding that the population is the soil around the former waste dump and the samples are 16 which were taken from EPA.In report, the method is unclear too.

5 0

3 years ago

Muffins are sold in packages of 18 and cost $27 per package. Each of 6 friends gets an equal share of muffins from p packages of

Rina8888 [55]

Answer:

27/18= 1.5

18/6 = 3

3•1.5= 4.5

Step-by-step explanation:

$27 divided by 18 muffins equals $1.50, 18 muffins divided by 6 people equals 3, 3 muffins times $1.50 equals $4.50. So $4.50 is how much each person would have to pay.

5 0

3 years ago

HELP PLEASE 10 POINTS!!!!!! A country's population in 1993 was 171 million. In 1999 it was 176 million. Estimate the population

Lilit [14]

Let 1993 = time 0 = 0.

Let 1999 = time 6 = 6

Let 2012 = time 19 = 19

So, a = 171 (million). First solve for k.

176 = 171 e^k6

176/171 = e^(k*6)

ln (176/171) = 6k

k = 1/6 ln (176/171)

So, in 2012 we have: P(19) = 171 e^(19k), where k = 1/6 ln (176/171)

Hope this helped!

3 0

3 years ago