How many gallons of a 50​% antifreeze solution must be mixed with 80 gallons of 30​% antifreeze to get a mixture that is 40​% ​antifreeze? Use the​ six-step method.

You need ___ gallons.

Answer:

[tex]log_{100}20 = 0.6505[/tex]

Step-by-step explanation:

log20 = 1.301 (when you see only "log" with no base, it is taken as a base 10)

This basically means:

[tex]10^{1.301} = 20[/tex]  (This is the log in exponential form)

Since we don't know what  [tex]log_{100}20[/tex]  is equal to, we will say  [tex]log_{100}20[/tex] = x

So to solve for [tex]log_{100}20[/tex] = x, you do the same thing. (convert to exponential form)

[tex]100^{x} =20[/tex]

Now you will notice that both of these equations are equal to 20.

Since 20 = 20,

we can say [tex]100^{x}[/tex] = [tex]10^{1.301}[/tex]

Another way of saying 100, is [tex]10^{2}[/tex] (make the bases the same)

Now we get [tex]10^{2x} = 10^{1.301}[/tex]      

(we get 2x because an exponent to the power of an exponent ([tex]2^{x}[/tex]) is the same as 2 * x)

Because you have the same base, you can just ignore the 10s and focus on the exponents. So you get:

2x = 1.301

x = 0.6505

Answer:

Step-by-step explanation:

In order to establish that the sample is truly random you need to obtain two main factors. First, is making sure that the random sample of both groups chosen (men and women) are equal in proportion to the overall population. Meaning both groups must be the same percentage of the overall population of the same gender. The second factor that you need to make sure of is that all chosen individual's had the exact same probability of being chosen from the population and no external factor influenced the probability of them being chosen for the study.

Answer:

You have to specify the question more. There's not enough information. Like how many numbers does the spinner have? I'll help if you could specify it more

Step-by-step explanation:

Answer:

Multiply 1/2 by 1/5 and you get 1/10

Step-by-step explanation:

Answer:

15 cm

Step-by-step explanation:

The perimeter of a rectangle is 2(L + W), where L is length of the rectangle and W is the width.

If we plug in 10 for W, we get this:

2L + 2(10) = 50 <-- the perimeter

2L + 20 = 50

2L = 30

L = 15

Answer:

The mean and standard deviation of the number of questions that each student gets correct are 4 and 1.789 respectively (

Answer: mean: 4

standard deviation: 1.79

Step-by-step explanation:

Answer:

-13=4y+3 -3

-16=4y ÷4

-4=y

Step-by-step explanation:

hope it helps ^^

Answer:

y = -4

explenation in picture

Answer:

2.5ft

Step-by-step explanation:

d=2r

r=1/2d

r=1/2*5ft=2.5 ft

Answer: 20

Step-by-step explanation:

A quotient is th value that is gotten when two numbers are divided. Based on the information given in the question, let the number be represented by x.

Therefore, x/4 = 5

x = 4 × 5

x = 20

The number is 20

Answer:

im allergic to cookies

Step-by-step explanation:

Answer:

4 divided by 8464 equals 0.00047258979

8464 divided by 4 equals 2,226

Step-by-step explanation:

                May I have brainiest I'm trying to level up!

                                  </3 PureBeauty

Answer:

544

Step-by-step explanation:

102 divided by 3 to find how many miles per gallon which is 34 then multiply by 16

Answer:

544

Step-by-step explanation:

102 divided by 3 to find how many miles per gallon which is 34 then multiply by 16 which is 544.

Answer:

26 /33

Step-by-step explanation:

Given that :

Number of days taken filming first movie = 45 1/2

Number of weeks spent filming second movie = 8 1/4

Concerning days to weeks ;

45 1/2 days = 91/2 days = 91/2 ÷ 7 ;

91 / 2* 1/7 = 91/14 = 6. 5 weeks

Hence,

Ratio of first week fuming to second week filming ;

6.5 weeks : 8 1/4 weeks

6 1/2 : 8 1/4

13 / 2 : 33 /4

13 / 2 * 4 /33

52 / 66

26 / 33

Answer:

this isnt spanish

Step-by-step explanation:

Answer:

0.111111

Step-by-step explanation:

Answer:

Step-by-step explanation:

Solution

=2×3/3×3-5×1/9×1

=6/9-5/9

=6-5/9

=1/9

Please mark me brainliest.Ok

Answer:

24a no>?

Step-by-step explanation:

Answer: wheres the attachment..

Step-by-step explanation:

Solution :

Days :              0           1        2         3         4          5        6         7

Probability : 0.68     0.05   0.07   0.08   0.05    0.04   0.01    0.02

This is a valid probability distribution.

In the question it is given that call for a response of Y for short of a sample of people aged between 19 years to 25 years.

Also the event that describes the value of call for response greater than 3 i.e. (Y < 3) is a randomly chosen people between the age 19 to 25 years old who has gone to fitness center or did exercise fewer than 3 days.

Valid probability models add up to 1

The probability is a valid probability model

The probability model is given as:

Days :              0           1        2         3         4          5        6         7

Probability : 0.68     0.05   0.07   0.08   0.05    0.04   0.01    0.02

To determine if the model is a valid probability model, or not

We make use of:

[tex]\mathbf{\sum P(x) = 1}[/tex]

So, we have:

[tex]\mathbf{0.68 + 0.05 + 0.07 + 0.08 + 0.05 + 0.04 + 0.01 + 0.02 = 1}[/tex]

Add the probabilities

[tex]\mathbf{ 1= 1}[/tex]

The above equations shows that:[tex]\mathbf{\sum P(x) = 1}[/tex]

Hence, the probability is a valid probability model

Read more about probability models at:

https://brainly.com/question/9965602

Answer:

12 11/20

Step-by-step explanation:

the answer to the question is 12 11/20

Step-by-step explanation:

x/4=9/x

x.x=4.9

x^2=36

√x=√6

x=6

Answer: 21 +4c

Step-by-step explanation:

Answer:

what is in between 36 and 2c?

Answer:

b² + ( -c + a ) ²

Step-by-step explanation:

Answer:

Side 1=21 ft, Side 2=7, Side 3=24

Step-by-step explanation:

52 = (3x) + (x) + (x+17) -> 52 = 5x + 17 -> 5x = 35 -> x = 7

Plus 7 into the equation whenever you see an x.

Answer:

He invested in stocks Say,  = x $

 He invested in bonds = (x/2)+6000

 So,

 x+ x/2 +6000=30000

 2x+x+12000=60000

 3x= 48000

x=16000

 Investment in stocks= 16000  $

Step-by-step explanation:

!!

Answer:

      $ 3 0 , 0 0 0  in Stocks

       $ 2 7 , 0 00  in Bonds

Step-by-step explanation:

        $ 3 0 , 0 0 0

      - $ 3 , 0 0 0

  _  _ _ _ _ _ _ _ _ _

         $ 2 7 , 0 0 0

Answer:

Option A. y = 4x

Step-by-step explanation:

From the question given above, the following data were obtained:

X >> Y

3 >> 12

4 >> 16

5 >> 20

6 >> 24

7 >> 28

Next, we shall use each of the options to obtain the first two value of y to which will correspond to the table above. This is illustrated below:

For Option A:

1. y = 4x

x = 3

y = 4 × 3

y = 12

2. y = 4x

x = 4

y = 4 × 4

y = 16

For Option B:

1. y = 4x + 12

x = 3

y = 4(3) + 12

y = 12 + 12

y = 24

2. y = 4x + 12

x = 4

y = 4(4) + 12

y = 16 + 12

y = 28

For Option C:

1. y = ¼ x

x = 3

y = ¼ × 3

y = ¾

2. y = ¼ x

x = 4

y = ¼ × 4

y = 1

For Option D:

1. y = ¼x + 12

x = 3

y = ¼(3) + 12

y = ¾ + 12

y = 51/4

2. y = ¼x + 12

x = 4

y = ¼(4) + 12

y = 1 + 12

y = 13

From the calculations made above, only option A ie. y = 4x correspond to the data given in the table above.

Answer:

elevator travel 4.5 feet per second

Answer: A

Step-by-step explanation:

the answer is A

Answer:

d. We are 95% confident that the true proportion of county residents who want the law changed is between 29% and 37%.

Step-by-step explanation:

Meaning of a confidence interval:

A x% confidence interval being between a and b means that we are x% sure that the true population proportion is between a and b.

In this question:

Sample of 600, proportion who wanted to change the law was 33% with a margin of error of +/- 4% (with 95% confidence). This implies:

From the concept of confidence interval above, the correct answer is:

d. We are 95% confident that the true proportion of county residents who want the law changed is between 29% and 37%.