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Veseljchak [2.6K]
3 years ago
6

a motorboat traveled for 2 hours with an 8km/h current. the return trip against the same current took 3 hours. find the speed of

the motorboat in still water.
Mathematics
1 answer:
Neporo4naja [7]3 years ago
6 0

Let x be the unknown speed, y the unknown distance.

distance equals speed times time.

"With" an 8kph current means our speed is x+8. 2 hours with an 8 kph current gets is a distance y:

y = 2(x + 8)

Against the current, speed x-8, took 3 hours to go y:

y = 3(x-8)

Equating,

2(x+8)=3(x-8)

2x + 16 =3x - 24

40 = x

Answer: 40 km/h

Check: 2(40+8)=96 km. 3(40-8)=3(32)=96 km. Equal, good.

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What is the coeffieent of (x^4)(y^4) in the expansion of (x+y)^8
kap26 [50]
ANSWER

The coefficient is 70.

EXPLANATION

The given binomial expression is

(x+y)^8

The specific term of a binomial expansion can be determined using the formula,

T_{r+1}= nC_ra^{n-r}b^r
where

n=8,r=4,a=x,b=y

We substitute these values into the formula to get,

T_{4+1}= 8C_4x^{8-4}y^4

We simplify to get,

T_{5}= 70x^{4}y^4

Hence the coefficient is 70.
4 0
3 years ago
William has 24 cans of fruit and 60 cans of vegetables that he will be putting into bags for a food drive. He wants each bag to
nataly862011 [7]

Answer:

See explanation

Step-by-step explanation:

William has 24 cans of fruit and 60 cans of vegetables that he will be putting into bags for a food drive.

Factor number 24 and 60:

24=2\cdot 12=2\cdot 2\cdot 6=2\cdot 2\cdot 2\cdot 3=2^3\cdot 3\\ \\60=2\cdot 30=2\cdot 2\cdot 15=2\cdot 2\cdot 3\cdot 5=2^2\cdot 3\cdot 5

Find the greatest common factor

GCF(24,60)=2^2\cdot 3=12

Hence, the greatest number of bags William can make is 12.

Each of these bags will have 24\div 12=2 cans of fruit and 60\div 12=5 cans of vegetables.

If he made fewer bags, 6 bags, each of these bags will have 24\div 6=4 cans of fruit and 60\div 6=10 cans of vegetables.

If he made fewer bags, 4 bags, each of these bags will have 24\div 4=6 cans of fruit and 60\div 4=15 cans of vegetables.

If he made fewer bags, 3 bags, each of these bags will have 24\div 3=8 cans of fruit and 60\div 3=20 cans of vegetables.

If he made fewer bags, 2 bags, each of these bags will have 24\div 2=12 cans of fruit and 60\div 2=30 cans of vegetables.

7 0
3 years ago
A particular restaurant can legally have only 150 people in it at one time. The tables in the restaurant can seat 4 people at a
Alchen [17]

Answer:

a. 37

Step-by-step explanation:

Do 150 divided by 4 so you know how many tables there can be.

150/4

37.5       You can only have 37.5 tables so the awnser is A.37

3 0
3 years ago
What is the measure of angle A?
Zina [86]

Answer:

It b

Step-by-step explanation:

6 0
3 years ago
A 3
Andrew [12]

Answer:

There are (63) combinations. The notation means "six choose three". Out of six items (flavors) choose three.

(nk)=n!k!(n−k)!.

(63)=6!3!3!.

Think of it this way. There are 6 ways to choose a flavor. Once you choose, there are 5 ways to choose the next. After that, there are 4 flavors left. which is 6!/3!=6⋅5⋅4⋅3⋅2⋅13⋅2⋅1=6⋅5⋅4=120.

But, you could have chosen {chocolate,vanilla,strawberry} and you get the same combination as {vanilla, strawberry, chocolate} so we have to divide by 3!=3⋅2⋅1=6 to account for the order of choosing.

So the number of combinations of flavors is (63)=1206=20.

<h3>Mark me a brainlist</h3>

7 0
3 years ago
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