How many different types of cross sections of a cone are possible? A.3

Mary wants to make 20 gallons of a 52% acid solution by mixing together a 84% acid solution and a 4% acid solution. How much of

Setler [38]

Answer:

12 gallons 84%
8 gallons 4%

Step-by-step explanation:

I like to use an "X-diagram" to solve mixture problems. On the left side are the constituents of the mix; in the middle is the result of the mix; and on the right side are the differences between the numbers on each diagonal. These differences are the ratio numbers for the mix.

Here, that means the ratio of 84% solution to 4% solution is ...

48 : 32 = 12 : 8

Note that the last two "ratio numbers" were chosen so their sum is 20, hence they represent the number of gallons of the corresponding constituent in the mix. (The sum of the first two ratio numbers is 48+32=80, so to get a sum of 20, we divide each by 4.)

Mary must use ...

12 gallons of 84% acid solution
8 gallons of 4% acid solution

You may note that this solution takes much longer to explain than to do. The math here can all be done without a calculator.

_____

Check

12 × 84% + 8 × 4% = 10.40 = 20 × 52%

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Usual Solution

A more conventional approach would be to assign x to the amount of 84% solution needed. Then the number of gallons of acid in the mix is ...

0.84x + 0.04(20 -x) = 0.52(20)

0.80x + 0.8 = 10.4 . . . . simplify

0.80x = 9.6 . . . . . . . . . . subtract 0.8; next, divide by 0.8

x = 9.6/0.8 = 12 . . . . gallons of 84% acid

20-x = 8 . . . . . . . . . . gallons of 4% acid

3 0

3 years ago

What is the median for the following set of data? 2, 3, 6, 8, 9, 10, 11

Inessa05 [86]

Answer:

The median value will be 8.

Step-by-step explanation:

The simplest way to think of a median is as a sort of "middle" value. We want to arrange our numbers from lowest to highest, then select the one in the middle. Here is another example:

3, 5, 2, 7, 3, 9, 1, 4, 7

The first step is to order these numbers from lowest to highest, like so:

1, 2, 3, 3, 4, 5, 7, 7, 9

The number in the middle of this set is 4.

The problem you have presented, as well as the above example, both deal with an odd amount of numbers. Your problem has seven numbers, and the example I gave has nine. For any odd amount of numbers, the median is the value in the middle. But what about an even amount of numbers?

Consider:

9, 4, 3, 7

Let's rearrange this:

3, 4, 7, 9

Now, there will be two "middle" values: 4 and 7. The median value will be the average of these two values:

$\text{median} = \frac{4 + 7}{2} = \frac{11}{2} = 5.5$

I hope that helps!

7 0

3 years ago

Kaylin bought a soda and two bags of popcorn for $3.00 . HER brother bought three sodas and a bag of popcorn for $6.50

Veseljchak [2.6K]

Answer: price of soda (a) = $2 and price of popcorn (b) = $0.5

Step-by-step explanation:

Let's denote soda = a and popcorn = b

Kaylin bought a soda and two popcorn, writing out an equation for this would be

a + 2b = $3...........equation (i)

And her brother bought 3 sodas and 1 popcorn.

3a + b = $6.50..........equation (ii)

From equation (i),

a + 2b = 3

Making a the subject of formula,

a = 3 - 2b......equation (iii)

Using substitution reaction, put equation (iii) into equation (ii)

3(3 - 2b) + b = $6.50

9 - 6b + b = 6.50

9 - 5b = 6.50

Collecting like terms,

5b = 9 - 6.50

Divide both sides by 5,

b = 5.

Put b = 5 into equation (i)

a + 2(0.5) = 3

a + 1 = 3

a = 2

Therefore, the price of soda is $2 per one and $0.5 for each popcorn.

4 0

3 years ago

How could you change the expression (-8)(-5)(-3) so that the product is positive?

LenKa [72]

Answer:

You make one number positive.

Step-by-step explanation:

A negative number multiplied by a negative number is positive, so that means that if you choose two of the numbers in this expression you will get a positive number. However, there is still one negative number left and you will get a negative product if you multiply, because a positive number multiplied by a negative number is a negative number. If you make this last number positive you will get a positive product.

Hope this helps!

5 0

3 years ago

Whoever answers this correctly first gets brainlest if the answer is correct!!

Gre4nikov [31]

Answer:

the awnser is 80

Step-by-step explanation:

add all the angles together equal to 180 solve for x put into 8x +8 get 80

8 0

3 years ago