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8_murik_8 [283]
3 years ago
11

The manager of a softball team needs to prepare a batting lineup using her 9 starting players. How many different lineups can sh

e make?
Mathematics
1 answer:
skad [1K]3 years ago
4 0
Okay so what I know is that when a softball manager does the batting line up he/she will use division. By getting the numbers of the players and the number of bases and the number of the outings which are (First base, second, third, short stop, out fields) And then she will divide all the numbers.
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A paint company mixes it's paint with water to create more paint per gallon. They currently have ten gallon jugs which contain 1
Karo-lina-s [1.5K]
<h3>Answer:  1.25 gallons</h3>

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

Explanation:

They currently have ten gallon jugs that contain 10% water, so this means 0.10*10 = 1 gallon of the jug is water and the other 10-1 = 9 gallons is paint. This is assuming the cans are just paint and water.

The ratio of paint to water is 90:10 which reduces to 9:1

Often it helps to reduce as much as possible, but it's actually more handy in this case to keep it at 90:10 so you can see the two parts add back up to 100%

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

Let x be the amount of water we add. This amount is in gallons.

We start off with 1 gallon of water and it bumps up to 1+x gallons of water.

The overall amount of 10 gallons also bumps up to 10+x gallons.

We want a ratio of 80:20 this time, so we want 20 parts water and 80 parts paint. In other words, we want 20/(20+80) = 20/100 = 20% water

Divide (1+x) over (10+x) to get (1+x)/(10+x). This represents the fraction of water. We want this fraction to be equal to 0.20, which is the 20% water amount. It is also equal to 20/100.

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

(1+x)/(10+x) = 20/100

100(1+x) = 20(10+x) ... cross multiply

100+100x = 200+20x ... distribute

100x-20x = 200-100

80x = 100

x = 100/80 ... divide both sides by 80

x = 1.25

You need to add 1.25 gallons of water

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

If you add 1.25 gallons of water, then,

amount of water = 1+x = 1+1.25 = 2.25

amount of paint&water = 10+x = 10+1.25 = 11.25

So you'll have 2.25 gallons of water out of 11.25 gallons of water&paint mix

2.25/11.25 = 0.2 = 20% water

This confirms our answer.

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

Extra info:

1.25 gallons = 1 gallon + 1/4 gallon

1.25 gallons = 1 gallon + 1 quart

This is because 1 gallon = 4 quarts, so 1 quart = 1/4 gallon.

5 0
3 years ago
Write out the first few terms of the series Summation from n equals 0 to infinity (StartFraction 2 Over 3 Superscript n EndFract
anyanavicka [17]

Answer:

\sum\limits_{n=0}^{\infty} \frac{2}{3^n}\frac{(-1)^n}{5^n} = 15/8

Step-by-step explanation:

The sum you are trying to understand is this.

\sum\limits_{n=0}^{\infty} \frac{2}{3^n}\frac{(-1)^n}{5^n}

Remember that in general when you have a geometric series  

\sum\limits_{n = 0}^{\infty} a*r^n you have that

\sum\limits_{n = 0}^{\infty} a*r^n = \frac{a}{1-r}      and that equality is true as long as     |r| < 1.

Therefore here we have

\sum\limits_{n=0}^{\infty} \frac{2}{3^n}\frac{(-1)^n}{5^n} = \sum\limits_{n=0}^{\infty} 2* \big(\frac{-1}{3*5} \big)^n = \sum\limits_{n=0}^{\infty} 2* \big(\frac{-1}{15} \big)^n        and   \big|\frac{-1}{15} \big| = \frac{1}{15} < 1

Therefore we can use the formula and

\sum\limits_{n=0}^{\infty} 2* \big(\frac{-1}{15} \big)^n =  \frac{2}{1-(-1/15)} = \frac{2}{1+1/15} = 30/16  = 15/8

5 0
2 years ago
Find C to form completing Square<br> <img src="https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B5x%20%2B%20C" id="TexFormula1" title="x^
postnew [5]

Answer:

\frac{25}{4}  (or 6.25)

Step-by-step explanation:

Let's do a simple square problem to see the relationship between the elements of the resulting equation...

(x+3)(x+3) = x(x+3) + 3(x+3) = x^{2} +3x + 3x + 9 = x^{2} + 6x + 9

As you see, the number of 'x' (6) is the double of the numeric part of the binomial expression (3), while the numeric-only part (9) is the square of the numeric part of the binomial expression (3).

So, if we look at the formula from the problem, we see the the number of 'x' is 5. To obtain the C value, we need to divide the 5 by 2... then get the square value of the result.

\frac{5}{2} * \frac{5}{2} = \frac{25}{4}  (or 6.25)

3 0
3 years ago
Anna would like to purchase a new bike that costs $205. She already has $31 saved. If she saves a maximum of $12 a week, the fol
Dmitrij [34]

Answer:

It will take at least 15 weeks

Step-by-step explanation:

12w+31 ≥ 205

Subtract 31 from each side

12w+31-31 ≥ 205-31

12w ≥ 174

Divide each side by 12

12w/12 ≥ 174/12

w ≥ 14.5

Rounding up to the nearest integer

w ≥ 15

It will take at least 15 weeks

5 0
3 years ago
Read 2 more answers
3. Jane wants to plant grass Seed in her yard. If it costs $0.55 per Square foot to plant grass Seed, how much will Jane Spend?
DIA [1.3K]

Answer:

Step-by-step explanation:

area off reg 1

10 x 25 = 250

area of reg 2

45 x 13 = 585

total surface area

585 + 250 = 835ft^2

835ft^2 x $0.55 = $459.25

7 0
2 years ago
Read 2 more answers
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