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Bingel [31]
3 years ago
9

The Smiths are moving across the country. Mr. Smith leaves 4 hours before Mrs. Smith. If he averages 60mph and she averages 80mp

h, how many hours will it take Mrs. Smith to catch up to Mr. Smith?
Mathematics
1 answer:
Ronch [10]3 years ago
4 0

60 miles per hour x 4 hours = 240 miles

Mr smith was 240 miles ahead of Mrs/ smith

The difference in speeds was 80 - 60 = 20 miles per hour

240 miles / 20 miles per hour = 12 hours.

It takes 12 hours to catch up.

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Three boys and six girls are being seated in a row of nine chairs on a stage which are numbered from left to right. How many sea
OLga [1]

Answer:

A. 362,880

B. 4,320

C. 14,400

D. 21,600

Step-by-step explanation:

A.

If there are no restrictions as to how they are seated, then we have permutations of 9 elements and there are 9! (factorial of 9) = 362,880 different seating arrangements.

B.  

If the boys sit in the middle three seats, they can sit in 3!=6 different ways, the girls can sit then in 6!=720 different ways. By the fundamental rule of counting, there are 6*720 = 4,320 different seating arrangements.

C.

We now have arrangements of the type

g, g, x, x, x, x, x, x, g  

The three girls at the ends can be chosen in C(6;3) (combinations of 6 taken 3 at a time) =  

\large \frac{6!}{3!(6-3)!}=\frac{6!}{3!3!}=20

different ways. The 6 in the middle can be sit in 6!=720 different ways.

By the fundamental rule of counting, there are 20*720 = 14,400 different seating arrangements.

D.

Now we have arrangements

g,b,g,b,x,x,x,x,x

For the 1st position we have 6 possibilities, for the 2nd we have 3 possibilities, for the 3rd we have 5 possibilities and for the 4th we have 2 possibilities. For the last 5 we have 5!=120 possibilities.

By the fundamental rule of counting, there are 6*3*5*2*120 = 21,600 different seating arrangements.

3 0
3 years ago
If you bought a stock last year for a price of $77, and it has risen 17.9% since then, how much is the stock worth now
sladkih [1.3K]

Answer:

$90.783

Step-by-step explanation:

4 0
2 years ago
A regular pentagon has an apothem of 3.2 and an area of 37.2 m. What
soldier1979 [14.2K]
The area of any regular polygon can be expressed as:

(ns^2)/(4tan(180/n)) where n is number of sides and s is a side length (no apothem needed :D)

37.2=5s^2/(4tan36)

s^2=(148.8tan36)/5

s≈4.65m
8 0
3 years ago
En una clase, 1/3 de los estudiantes eligieron estudiar español como segundo lenguaje vivo. 1/9 eligió italiano, el resto eligió
max2010maxim [7]

Answer:

5/9

12

Step-by-step explanation:

La clase entera es 1.

1/3 estudian español.

1/9 estudian italiano.

1 - 1/3 - 1/9 estudian alemán.

1 - 1/3 - 1/9 = 9/9 - 3/9 - 1/9 = 5/9

<em>5/9 de los estudiantes estudian alemán.</em>

n = numero total de estudiantes en la clase.

5/9 n = 15

9/5 * 5/9 * n = 15 * 9/5

n = 27

Hay 27 estudiantes en la clase.

27 - 15 = 12

<em>12 estudiantes no estudian alemán.</em>

4 0
2 years ago
A cylinder shaped container has a radius of 30 cm and a height of 100 cm. A glass sphere with a redius of 12 cm is placed inside
Artemon [7]
Vcylinder-Vsphere=water


Vcylinder=hpir^2
Vsphere=(4/3)pir^3


given

cylinderradius=30 and h=100
Vcylinder=100pi30^2=100pi900=90000pi
let's leave it in terms of pi for more exactness

sphereradius=12
Vsphere=(4/3)pi12^3=2304pi


cylinder-sphere=90000pi-2304pi=87696pi
using pi=3.14
water=275365.44 cubic cm

last option is corrrect
4 0
3 years ago
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