Suppose you travel at 70 mph for 520 miles. How many hours will take you to reach your destination

An object is launched directly in the air at a speed of 48 feet per second from a platform located 12 feet above the ground. The

anastassius [24]

9514 1404 393

Answer:

48 ft

Step-by-step explanation:

For the quadratic ax^2 +bx +c, the axis of symmetry is x = -b/(2a). For the given quadratic, which defines a parabola opening downward, the axis of symmetry defines the time at which the maximum height is reached.

t = -48/(2(-16)) = 1.5

Then the maximum height is ...

f(1.5) = (-16·1.5 +48)1.5 +12 = (24·1.5) +12

f(1.5) = 48

The maximum height the object will reach is 48 feet.

6 0

2 years ago

You want a snack. One small pear has 100 calories. A small plum has 45 calories. What is the ratio of the calories in a plum to

Anvisha [2.4K]

The ratio would be
45/100
45 to 100
45:100

Hope this helps!

7 0

2 years ago

Read 2 more answers

And one US city the taxi cost is five dollars plus $.60 per mile if you are traveling from the airport there is an additional ch

GenaCL600 [577]

Let the number of miles be x.

Then, x miles cost 0.6x.

The initial fixed fee is $5, and the toll is $5.

cost = initial fixed fee + cost per mile + toll

46 = 5 + 0.6x + 5

0.6x + 10 = 46

0.6x = 36

x = 36/0.6

x = 60

You can travel 60 miles.

4 0

3 years ago

Read 2 more answers

7) PG & E have 12 linemen working Tuesdays in Placer County. They work in groups of 8. How many

BabaBlast [244]

Part A

Since order matters, we use the nPr permutation formula

We use n = 12 and r = 8

$_{n}P_{r} = \frac{n!}{(n-r)!}\\\\_{12}P_{8} = \frac{12!}{(12-8)!}\\\\_{12}P_{8} = \frac{12!}{4!}\\\\_{12}P_{8} = \frac{12*11*10*9*8*7*6*5*4*3*2*1}{4*3*2*1}\\\\_{12}P_{8} = \frac{479,001,600}{24}\\\\_{12}P_{8} = 19,958,400\\\\$

There are a little under 20 million different permutations.

<h3>Answer: 19,958,400</h3>

Side note: your teacher may not want you to type in the commas

============================================================

Part B

In this case, order doesn't matter. We could use the nCr combination formula like so.

$_{n}C_{r} = \frac{n!}{r!(n-r)!}\\\\_{12}C_{8} = \frac{12!}{8!(12-8)!}\\\\_{12}C_{8} = \frac{12!}{4!}\\\\_{12}C_{8} = \frac{12*11*10*9*8!}{8!*4!}\\\\_{12}C_{8} = \frac{12*11*10*9}{4!} \ \text{ ... pair of 8! terms cancel}\\\\_{12}C_{8} = \frac{12*11*10*9}{4*3*2*1}\\\\_{12}C_{8} = \frac{11880}{24}\\\\_{12}C_{8} = 495\\\\$

We have a much smaller number compared to last time because order isn't important. Consider a group of 3 people {A,B,C} and this group is identical to {C,B,A}. This idea applies to groups of any number.

-----------------

Another way we can compute the answer is to use the result from part A.

Recall that:

nCr = (nPr)/(r!)

If we know the permutation value, we simply divide by r! to get the combination value. In this case, we divide by r! = 8! = 8*7*6*5*4*3*2*1 = 40,320

So,

$_{n}C_{r} = \frac{_{n}P_{r}}{r!}\\\\_{12}C_{8} = \frac{_{12}P_{8}}{8!}\\\\_{12}C_{8} = \frac{19,958,400}{40,320}\\\\_{12}C_{8} = 495\\\\$

Not only is this shortcut fairly handy, but it's also interesting to see how the concepts of combinations and permutations connect to one another.

-----------------

<h3>Answer: 495</h3>

5 0

2 years ago

The area of a rectangle is 44 m²<br> The width is 3 2/3m<br> Work out the missing length?

Alika [10]

Answer:

12 meter

Step-by-step explanation:

We know that ,

Area of rectangle = length × breadth

so,44m square = l × 3 2/3 m

or, 44m2 = length × 11/3

or ,( 44m2)/3 2/3m = length

finally, length = 12 meters

3 0

2 years ago