Escribir un 1% como decimal

Type the correct answer in each blank. Use numerals instead of words. If necessary, use / for the fraction bar(s). John hosts an

Law Incorporation [45]

We know that John is hosting an art workshop on the weekends. He has an average of 14 students in each session and charges a fee of $12 per session. . He estimates that for every $2 increases in the fee, the average number of students reduces by 1.

Therefore, we can conclude that his revenue is $14 * 12$ or $168$ bucks.

The session price goes up in a pattern of 2.

For example, from 12 the session price goes to 14, 16, 18 and so on.

As each jumps goes by 2, the amount of students drop by 1.

(i.e from 14 students the number decreases to 13, to 12 and so on.)

As we can see the revenue begins at 168 and continues upward until it reaches 200 dollars and then starts to descend.

This indicates that the U-turn or vertex of the revenue function is approximately 4200, where h represents 4, and k is 200.

To solve we can use Parabola.

⇒ Parabola: any point is at an equivalent separation from:

a settled point (the concentration ), and

a settled straight line (the directrix )

____________________________________________________

$f (x) = a(x - h)^2 + k$ , where (h, k) is the vertex of the parabola.

⇒ $\left \{ {{y=192} \atop {x=2}} \right.$

⇒ $192 = a(2-4)^2+200$

⇒ $-8=a(-2)^2$

⇒ $-8=a*2^2$

⇒ $-8=a*4$

⇒ $-8=4a$

⇒ $-\frac{8}{4} = \alpha$

⇒ $\alpha = -2$

Now lets do the final step: Simplifying

$y-2(x-4)^2+200$ 

$y=-2(x^2-8x+16)+200$

$y=-2x^2+16x-32+200$

$c(x) = -2x^2+16x+168$

3 0

4 years ago

A truck going 50 miles per hour

larisa86 [58]

Answer:

133.33 mph

Step-by-step explanation:

The small trick is to notice the time. Is it 8:00 AM the same day. We don't know, but we will assume it is.

So the truck was on the road for 2 hours.

The car was on the road for 2 - 1/2 = 1 1/2 = 1.5 hours.

The distance travelled was 200 miles

Solution

d = r * t

200 = r * 1.5

200/1.5 = r

r = 133.33 miles / hour

The noise you hear is a siren trying to catch up to the car.

7 0

3 years ago

The Half-life of a certain substance is 20 mins. You start with 45 mg of the substance

DochEvi [55]

a. Remaining amount after t minutes = 45 * $(1/2)^{\frac{t}{20 }$

b. 0.010986 mg

c. 109.84 minutes

Step-by-step explanation:

Step 1:

The decay of the substance is exponential. It is given that half life is 20 minutes and initially we start with 45 mg. So in 20 minutes we will have remaining amount 45/2, in 40 minutes remaining amount will be 45/4 etc.

This can be modeled by the equation:

Remaining amount after t minutes = Original amount * $(1/2)^{\frac{t}{t_{1/2} }$

where $t_{\frac{1}{2}}$ represents the half life.

The half life for this substance is 20 minutes.

Hence the Remaining amount after t minutes = 45 * $(1/2)^{\frac{t}{20 }$

Step 2:

We need to calculate the amount remaining after 4 hours (240 minutes).

Substituting t = 240 in above equation we get

Amount remaining after 4 hours = 45 * $(1/2)^{\frac{240}{20 }$ = 0.010986 mg

Step 3:

We need to calculate the time taken when 1 milligram is left. Substituting in the equation we get

1 = 45 * $(1/2)^{\frac{t}{20 }$

Taking log on both sides we get

t = $\frac{20 ln (1/45)}{ln 1/2}$ = 109.84 minutes

Time taken for 1 mg of the substance to be left = 109.84 minutes

Step 4 :

Answer :

a. Remaining amount after t minutes = 45 * $(1/2)^{\frac{t}{20 }$

b. 0.010986 mg

c. 109.84 minutes

7 0

4 years ago

During a storm, why do you see the flash of lightning before you hear the roar of thunder? What would it mean if you saw the fla

Lubov Fominskaja [6]

The speed of light is faster than the speed of sound. So that's why you see a flash of lightning before the roar of thunder. If you heard it at the same time as you saw it, well I will be praying for you. It would literally be exactly where you are. If you hear the thunder a long time after the flash, it means the lightning is far away.

T/5=miles away when T is time from the strike of lightning to hearing thunder

3 0

4 years ago

What is the answer to this problem?

AURORKA [14]

The answer to the problem is x - 1

5 0

3 years ago

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