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sergiy2304 [10]
3 years ago
14

You have 10 cups of a cleaning solution that is 10% white vinegar and 90% water. You want the mixture to be 20% white vinegar an

d 80% water. How many cups of white vinegar do you need to add to the mixture
Mathematics
1 answer:
telo118 [61]3 years ago
4 0

Answer:

1.25 cups

Step-by-step explanation:

The inicial concentration of the 10 cups of mixture is 10% of white vinegar and 90% water. We can then calculate the number of cups of white vinegar in the mixture:

Amount of white vinegar = 10% of 10 cups = 1 cup of white vinegar

Concentration of white vinegar = 1/10 (cups of white vinegar over cups of mixture

So, if we want to add white vinegar (x cups) until the mixture will be 20% white vinegar and 80% water, we have that:

Amount of white vinegar = (1+x) cups of white vinegar

Total number of cups in the mixture = 10+x

Concentration of white vinegar = 20% = (1+x)/(10+x)

(1+x)/(10+x) = 0.2

1 + x = 2 + 0.2x

0.8x = 1

x = 1.25 cups

You need to add 1.25 cups of white vinegar.

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From previous polls, it is believed that 66% of likely voters prefer the incumbent. A new poll of 500 likely voters will be cond
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Answer:

The mean and standard deviation of the number preferring the incumbent is mean = 330, standard deviation = 10.59.

Step-by-step explanation:

We are given that From previous polls, it is believed that 66% of likely voters prefer the incumbent.

A new poll of 500 likely voters will be conducted. In the new poll the proportion favoring the incumbent has not changed.

Let p = probability of voters preferring the incumbent = 66%

n = number of voters polled = 500

<u>So, the mean of the number preferring the incumbent is given by;</u>

         Mean = n \times p = 500 \times 0.66

                                = 330 voters

<u>And, standard deviation of the number preferring the incumbent is given by;</u>

          Variance =  n \times p\times (1-p)  

                          =  500 \times 0.66 \times (1-0.66)

                          =  112.2

So, Standard deviation =  \sqrt{Variance}

                                       = \sqrt{112.2}  = 10.59

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Step-by-step explanation:

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ASSIGNMENT: Show that the correct solution to the following system of equations is (-2, 0). Upload a photo of your work or neatl
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Which ordered pair is a reflection of (3, 7) across the y-axis?
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If its a reflection across the y axis the x value is reflected and the y value stays the same, so (-3,7)
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3 years ago
In a unit circle, ø = 270º. Identify the terminal point and sin ø.
larisa [96]

Answer:

Terminal point (0, -1); sin Ø = -1 ⇒ A

Step-by-step explanation:

In the unit circle, Ф is the angle between the terminal side and the positive part of the x-xis

  • The terminal point on the positive part of the x-axis is (1, 0),which means Ф = 0° or 360° and cosФ = 1, sinФ = 0
  • The terminal point on the positive part of the y-axis is (0, 1),which means Ф = 90° and cosФ = 0, sinФ = 1
  • The terminal point on the negative part of the x-axis is (-1, 0),which means Ф = 180° and cosФ = -1, sinФ = 0
  • The terminal point on the negative part of the y-axis is (0, -1),which means Ф = 270° and cosФ = 0, sinФ = -1

In a unit circle

∵ Ф = 270°

→ By using the 4th rule above

∴ The terminal point is (0, -1)

∴ sinФ = -1

∴ Terminal point (0, -1); sin Ø = -1

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2 years ago
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