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lisov135 [29]
3 years ago
14

Bruce has a bottle that contains 60% lemon juice and the rest water. The bottle has 1 liter of water. Part A: Write an equation

using one variable that can be used to find the total number of liters of lemon juice and water in the bottle. Define the variable used in the equation. Hint: 0.6x represents the number of liters of lemon juice in the bottle. (5 points) Part B: How many liters of lemon juice are present in the bottle? Show your work. (5 points)
Mathematics
1 answer:
ser-zykov [4K]3 years ago
4 0

Answer:

<em><u>Part A: </u></em>(40/100)*x = 1 where x is the total contents of the bottle.

<em><u>Part B</u></em>: 1.5 Liters = the Lemon Juice

Step-by-step explanation:

Part A

Let the full contents of the bottle = x

<em><u>Equation</u></em>

Since 60% of it is lemon juice, then 100% - 60% = 40% must be water.

(60/100) * x = ??  Equation for Lemon Juice. You have to solve the water first.

(40/100) * x = 1    Equation for water

Part B

(40/100) * x = 1     change the 40% to a decimal

0.4x = 1                 Divide by 0.4

x = 1/0.4 = 2.5 L

Now to find out the amount of lemon juice

0.6 * 2.5 = Lemon Juice

1.5 L = the amount of Lemon Juice.

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Need help on this<br><br> Z+4&gt;2z
snow_lady [41]

Answer: z < 4

z+4 > 2z

z+4-z > 2z-z ..... Subtract z from both sides

4 > z

z < 4

So the solution set for z is any number that is less than 4, which could be something like z = 2 or z = 3.

7 0
2 years ago
Consider a t distribution with 7 degrees of freedom. Compute P(-1.29 &lt; t &lt; 1.29). Round your answer to at least three deci
ss7ja [257]

Answer:

a) 0.76197086

b) -1.73406361

Step-by-step explanation:

a)

Consider a t distribution with 7 degrees of freedom. Compute P(-1.29 < t < 1.29)

P(-1.29 < t < 1.29) would be the area under the t distribution curve with 7 degrees of freedom between -1.29 and 1.29, that is in the interval (-1.29, 1.29).

This can be done the old style by looking up in a table or by using the technology with a spreadsheet.

In Excel, the function TDIST(x,n,2) with x>0 gives the area outside the interval (-x, x) of the t distribution with n degrees of freedom.

So TDIST(1.29,7,2) gives the area outside (-1.29, 1.29).

If we subtract this value from 1 we get the desired result

Hence  

P(-1.29 < t < 1.29) = 1 - TDIST(1.29,7,2) = 1 - 0.23802914 = 0.76197086

In OpenOffice Calc, the function is the same replacing “,” with “;”  

That is

P(-1.29 < t < 1.29) = 1 - TDIST(1.29;7;2) = 0.76197086

b)

Consider a t distribution with 18 degrees of freedom. Find the value of c such that P(t≤ c) = 0.05

We are looking for a point c such that the area of the t distribution with 18 degrees of freedom to the left of c is 0.05

In Excel, the inverse function of TDIST is TINV.  

TINV(p*2,n) with p>0 gives the point c such that the area of the t distribution with n degrees of freedom to the right of c is p.  

Since <em>the t distribution is symmetric with respect to 0</em>, -c would be a point such that the area to the left of -c is p.

So we want to compute  in Excel

-TINV(0.05*2,18) = -1.73406361

In OpenOffice Calc  

-TINV(0.05*2;18) = -1.73406361

3 0
2 years ago
Can you help me plss ??
Agata [3.3K]
4

I hope you have an awesome day
3 0
2 years ago
A fast typist can type 120 words in 100 seconds. At that rate, how many seconds would it take to type 258 words?
Alexeev081 [22]

Answer: 215 seconds

Step-by-step explanation:

This is a ratio problem so you can set up the ratio like this:

120 words : 100 second.

If you divide both sides of the ratio by 120 you get:

1 word: 0.8333 seconds

Multiply both sides of the ratio by 258 and you get:

258 words: 215 seconds.

Therefore typing 258 will take them 215 seconds.

5 0
2 years ago
X+2y-z = 9<br> -2x+y+z= 1<br> 2x-y+2z= -5
hodyreva [135]

Answer:

I don't understand the first one

7 0
2 years ago
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