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mestny [16]
1 year ago
5

A family of five recently replaced its 5-gallon-per minute showerheads with water-saving 2-gallon per minute showerheads. Each m

ember of the family averages 8 minutes in the shower per day. In a 30-day period, how many few gallons of water will the family use with the new showerheads?
1. 60
2. 800
3. 2400
4. 3600
5. 7200
Mathematics
1 answer:
lilavasa [31]1 year ago
3 0

Answer:

2400 gallons of water

Step-by-step explanation:

The new shower head releases 2 gallons per minute as compared to the old type.

each person spends an average of 8 minutes in shower per day. This means each person will use 8*2 number of gallons per day.

the number of persons in the family is 5.

if 1 person uses 8*2 gallons per day, 5 people will require 8*2*5

In a 30 days period the number of gallons used by the family will be

=8*2*5*30

=2400 gallons.

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Elaine is in London for one day only. She only has time to see two shows of the three shows she likes. The shows are Hamilton, A
denis-greek [22]

Answer:

\frac 13

Step-by-step explanation:

All three shows she likes are Hamilton, Aladdin, and Thriller.

But she can watch only two shows among the three shown.

The possible combination of the shows she can watch are

(Hamilton and Aladdin), (Aladdin and Thriller) and (Hamilton and Thriller).

So, the total number of possible events (available options)= 3.

As we have to determine the probability of watching Aladdin and Thriller, so here Aladdin and Thriller is the favorable event.

So, the number of favorable event=1

Now,

\text{Probability}=\frac{\text{Total number of possible events}}{\text{Total number of favorable events}}

=\frac{1}{3}

Hence, the probability that she sees Aladdin and Thriller is \frac 1 3.

5 0
1 year ago
For the binomial expansion of (x + y)^10, the value of k in the term 210x 6y k is a) 6 b) 4 c) 5 d) 7
Sloan [31]

Answer:

a) 6

Step-by-step explanation:

Expanding the polynomial using the formula:

$(x+y)^n=\sum_{k=0}^n \binom{n}{k} x^{n-k} y^k $

Also

$\binom{n}{k}=\frac{n!}{(n-k)!k!}$

I think you mean 210x^6y^4

We can deduce that this term will be located somewhere in the middle. So I will calculate k= 5; k=6 \text{ and } k =7.

For k=5

$\binom{10}{5} (y)^{10-5} (x)^{5}=\frac{10!}{(10-5)! 5!}(y)^{5} (x)^{5}= \frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5! }{5! \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 } \\ =\frac{30240}{120} =252 x^{5} y^{5}$

Note that we actually don't need to do all this process. There's no necessity to calculate the binomial, just x^{n-k} y^k

For k=6

$\binom{10}{6} \left(y\right)^{10-6} \left(x\right)^{6}=\frac{10!}{(10-6)! 6!}\left(y\right)^{4} \left(x\right)^{6}=210 x^{6} y^{4}$

5 0
2 years ago
The endpoints of line AB are A(2, 2) and B(3, 8). Line AB is dilated by a scale factor of 3.5 with the origin as the center of d
Musya8 [376]
A` ( 7, 7 )
B ` ( 10.5, 28 )
The slope: m = (28-7) / ( 10.5 - 7 ) = 21 / 3.5 = 6
d ( A` B `) = √ ( 10.5 - 7 )² + ( 28 - 7 )² = √ 3.5² + 21² = 
= √ 12.25 + 441 = √ 12.25 ( 1 + 36 ) = 3.5 √37 ( or 3.5 * (37) ^(1/2))
Answer: 
C ) m = 6, A`B` = 3.5√37
7 0
1 year ago
Read 2 more answers
At noon (12:00), Annette rented a bicycle to travel around Stanley Park. She returned the bicycle at 4:00 pm (16:00) the same da
Doss [256]

Answer:

a. average speed is 12km/hr

b. $5.50 dollars per hour

c. $0.46 per km

Step-by-step explanation:

a. 48km/4hrs = 12km/hr

b. $22/4hrs = $5.50/hr

c. $22/48km = $0.45833/km rounded to $0.46/km

6 0
2 years ago
Drag the cards to create a two-digit number that matches these rules. Note: Not all cards will be used 6 is one of the digits 20
Greeley [361]

Answer:

As i understand this:

We have cards with the values:

0, 1, 2 and 6.

We want to create a two digit number such that:

Not all the cards are used.

6 is one digit of our number.

When we round to the nearest ten, we get 20.

Now, first remember how rounding works.

If we have a number like ab, where a and b are single digits (a is in the tens place and b is in the units place), then:

if b is 5 or more, we round up

if b is less than 5, we round down.

Now in this case we want to have a digit equal 6, if we use this in the units place, then when rounding, we will round up.

Then the other digit can be 1, such that we use the cards:

1 and 6.

then our number is 16:

When rounding, 6 > 5, then we round up to 20.

So this number meets all the conditions.

3 0
1 year ago
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