How many liters of 70% alcohol solution and 30% alcohol solution must be mixed to obtain 8 liters of 60% alcohol solution?

a. Complete the table below with the expressions needed to solve this problem. Then solve it in part b.

70% solution 30% solution Final solution
Number of Liters x y
Liters of Alcohol


b. You need
liters of 70% solution and
liters of 30% solution.

The composition of two translations could describe the taxicab’s final position are (1, -2 + 16) and (1, -2 - 16)

The initial position is given as:

Cab = (1, -2)

Assume the cab travel in one direction, the possible translations are:

(x, y + 16)

(x, y - 16)

(x  + 16, y)

(x  - 16, y)

Using the first two translations, the final positions are:

(1, -2 + 16) = (1, 14)

(1, -2 - 16) = (1, -18)

Hence, the composition of two translations could describe the taxicab’s final position are (1, -2 + 16) and (1, -2 - 16)

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Answer:

-10.7

Step-by-step explanation:

tThe answer is -10.7. What you do is 3/5+7/10 then, you subtract 12 which gives your the answer

Answer:

20 cubic feet

Step-by-step explanation:

First divide the figure into 3 rectangular prisms like in the screen shot provided below.

Volume of the prism on the left:

l×w×h=v

1×2×3=6 cubic feet

Since the volume of the right prism and the left prism are the same, we can multiply the volume (6cubic feet) by 2. Therefore, the volume of both the prisms outlined in purple is 12 cubic feet.

Volume of the rectangular prism in the middle:

2×1×(7-3)

2×1×4=8 cubic feet

Now we add all the volumes together:

8+12=20 cubic feet.

Hope this helps! :)

Answer:

666  2/3

Step-by-step explanation:

45 %  *  x  = 300

.45 x = 300

x = 300 / .45 = 666  2/3

Answer:

68

Step-by-step explanation:

180-112=68

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Answer:

3 + 2/3 = 9/3 + 2/3 = 11/3
11/3 * 2/3 = [tex]\frac{11}{3} * \frac{2}{3}[/tex] = [tex]\frac{22}{9}[/tex] = [tex]2\frac{2}{9}[/tex]

Self note:

Friday says 3 2/5 and Saturday is blank
Sorry I took so long

Answer:

3b-10=20

Step-by-step explanation:

3b-10=20

3b-10+10=20+10

3b=30

3b/3=30/3

b=10

Step-by-step explanation:

Given:

The three points given below are collinear,

[tex](x_1,y_1) = (a,0)\\(x_2,y_2) = (0,b)\\(x_3,y_3) = (1,1)[/tex]

To prove:

[tex] \frac{1}{a} + \frac{1}{b} = 1[/tex]

Proof:

Collinear: given set of points lies on a straight line.

Now we are told that the given set of points are collinear hence they will not be able to form a triangle or the area enclosed by all the points will be equal to zero.

The formula of area of traingle in determinant form is

[tex]Area = \frac{1}{2} \begin{vmatrix} x_{1}& y_{1} & 1 \\ x_{2} & y_{2} & 1 \\ x_{3} & y_{3} & 1 \end{vmatrix}[/tex]

that can also be written as

[tex] \sf \small Area = \frac{1}{2}  [x_1 (y_2 - y_3) + x_3 (y_1 - y_2) + x_2 (y_3 - y_1)][/tex]

Since the points are collinear L.H.S will be zero,

[tex]\sf \small 0 = \frac{1}{2}  [x_1 (y_2 - y_3) + x_3 (y_1 - y_2) + x_2 (y_3 - y_1)][/tex]

Substituting all the given cordinates in above equation.

[tex]\sf \small 0 = \frac{1}{2}  [a (b - 1) + 1 (0 - b) + 0 (1 - 0)] [/tex]

[tex]\sf \small 0 \times 2 = ab - a - b \\ \sf \small 0 = ab - a - b \\ \sf \small a + b = ab \\ \sf \small \: dividing \: both \: sides \: by \: ab \\ \sf \frac{a}{ab} + \frac{b}{ab} = \frac{ab}{ab} \\ \sf \frac{\cancel a}{\cancel ab} + \frac{\cancel b}{a \cancel b} = \cancel \frac{ab}{ab} \\ \sf \frac{1}{a} + \frac{1}{b} = \frac{1}{1} [/tex]

[tex] \sf Hence \: proved,[/tex]

[tex] \Large {\frac{1}{a} + \frac{1}{b} = 1}[/tex]

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Use area of triangle formed by using those points is equal to zero

[tex] \tt Area\: of \:triangle =\frac{1}{2}[a(b-1)+0+1(0-b)][/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex] \tt0=ab-a-b[/tex]

[tex]\: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex] \tt a+b=ab[/tex]

Divide both sides by ab

[tex] \tt \frac{a}{ab} + \frac{b}{ab} = 1[/tex]

[tex]\: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex] \tt\frac{1}{b} + \frac{1}{a} = 1[/tex]

Hence proved~

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

[tex]\large \sf \underline{Problem:}[/tex]

Solve the system of equations by substitution

====================================.

[tex]\large \sf \underline{Answer:}[/tex]

x = - 5y + 4

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

[tex]\large \sf \underline{Explanation:}[/tex]

x + 5y = 42x + 10y = 8

2(- 5y + 4) + 10y = 8

substituted in the equation for x - 10y - 8 + 10y = 8

distributed

8 = 8

combined like terms 0 = 0(- 10y + 10y)

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

Answer:

620. 0.25 x 620 = 155

Step-by-step explanation:

You’ll need a clean, microwave-safe container (a quart-sized bowl works great) to mix the agar with water and then boil it. These proportions make enough nutrient agar to prepare two Petri dishes. Stir these together well:

• ½-teaspoon agar (about 1.2 grams)

• ¼ cup (60 mL) of hot water

Bring this mixture to a boil for three minutes to completely dissolve the agar. CAUTION: Adult supervision is required to boil water. If you are using a microwave oven to boil the mixture, be careful not to let it boil over. The mixture should be clear with no particles floating in it after boiling.

Remove the mixture from the microwave and allow it to cool for 3 to 5 minutes before moving on to the next step.

Take the lid off of the Petri dish (the lid is larger than the dish) and carefully cover the bottom-half of the Petri dish with warm  nutrient agar mixture.

Loosely cover the bottom portion (set the lid ajar so excess moisture can escape) and allow the mixture to cool and harden for at least an hour.

It’s time to collect some bacteria on the end of a cotton swab! The classic test is to roll a clean cotton swab in your mouth and then to lightly draw a squiggle with it on the gelled agar. However, many people like to test something even more gross like the keys on a computer, a cell phone case, the pump handle of a soap dispenser, or the TV remote control. Unless someone recently cleaned the buttons on the remote, you may be seeing some real goobers in a short time. Dampen a cotton swab and roll it in your fingers as you pull it across the surface of your choice.

Lift the lid off the Petri dish and LIGHTLY draw a squiggly line in the agar with the end of the cotton swab. Roll the swab in your fingers as you draw the line. Replace the lid and label the dish with the date and the name of the item you tested.

Use a sanitizing wipe to thoroughly clean one of the surfaces you tested in Step 6, e.g. Cellphone

With a clean swab, redo the squiggle test in the other half of the Petri dish from Step 6 to confirm your cleaning efforts.

Before growing anything, some people place each Petri dish into a separate zipper-lock bag. Place the upside down dishes into a warm – about 98°F (37°C) is fine – and totally dark place to grow. In a closed box on a cable box is a great place. In a short time, you’ll be greeted by an amazing variety of bacteria, molds, and fungi. You likely see more and larger colonies over the next few days. You shouldn’t see too much growth where the disinfectants (hand sanitizers) were used. You might even see a “halo” around each location. This halo is called the “kill zone.” Measure and compare the size of the kill zone to determine the effectiveness of different antibacterial agents.

Remember: Do NOT open the dishes once things begin to grow. You could be culturing some serious goobers and not even know it. The comfort is that they were around you all the time anyway and now you can see them. Just be careful!

Goobers like you’re growing will often stink and make their presence known after a short time. These are not toys or curiosities you’re growing. Proper disposal is essential for both safety and sanitation. Seal all the Petri dishes into larger zipper-lock plastic bags. You can add a generous shot of chlorine bleach to the bag before sealing it to add another level of destruction. Remember: do NOT open the zipper-lock bags… ever! When you’re finished analyzing the cultures, dispose of the entire sealed bag in the trash.

Golly, Mom is right! It IS important to wash your hands with soap and warm water whenever you can!

Answer:

0.7 is the decimal equivalent to 70/100.

Step-by-step explanation:

You can just do the numerator (70) divided by the denominator (100): 70÷100 = 0.7

Answer: The sample might not be a representative of the population because it only included lunch customers.

Step-by-step explanation:

Answer:

The sample might not be representative of the population because it only included lunch customers.

Step-by-step explanation:

Since she is only picking lunch customers and not breakfast and dinner it doesn't show all the people only the people who order lunch

Answer:

B. acute, isosceles

Step-by-step explanation:

The two small lines intersecting the two sides stand for congruency.

Two sides are congruent, so this is an isosceles triangle.

None of the angles here are greater or equal to 90 degrees, so it is an acute triangle.

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Answer:

B. Acute, isosceles

Step-by-step explanation:

Angles can be classified by both their sides and angles. There are 3 classification for each measurement, making 6 total classifications. This includes acute, right, and obtuse for angles and isosceles, scalene, and equilateral for sides.

Sides

The tic marks on 2 sides on the side show that they are congruent. Any triangle that has 2 congruent sides is classified as isosceles.

An additional fact is that the angles opposite of the congruent sides are also congruent. This information is not pertinent to this question, but might be useful in the future.

Angles

A triangle's classification for its angles is always based on the largest angle in the triangle. In this case, the largest angle is an acute angle. Remember that an acute angle is less than 90 degrees. This means that the triangle is acute.

Answer:

$2 shared among 4 is 50 cents each or $0.50 each.

Step-by-step explanation:

2/4 = 50

The value of y will be,y=√(x²-12²).Concept of trigonometry is used in given problem.

The field of mathematics is concerned with the relationships between triangles' sides and angles, as well as the related functions of any angle

Apply phythogorous theorm in the triangle ABC;

AC²=AB²+BC²

16²=z²+x²

Apply Pythagoras theorm in triangle ABD

AB²=BD²+AD²

x²=y²+12²

y²=x²-12²

y=√(x²-12²)

Hence,the value of y will be,y=√(x²-12²).

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Answer:

a. to accuse a public official, before an appropriate tribunal. of misconduct in office

Answer:

[tex]slope=-\frac{1}{4}[/tex]

Step-by-step explanation:

To find the slope of the two points (-9,-3) and (7, -7) w have to use the slope formula

[tex]slope=\frac{y_{2}- y_{1} }{x_{2} -x_{1} }[/tex]             [tex]slope=\frac{(-7)- (-3)}{7 -(-9) }[/tex]      

[tex]slope=\frac{-4 }{16}=-\frac{1}{4}[/tex]  can also be written as a decimal  [tex]slope=-0.25[/tex]

we get - 1/4 because -4 divided by -4 is 1 and -4 divided by 16 is -4

Answer:

  a)  f'(x) = 12x

  b)  -120

  c)  36

  d)  y = 36x -55

Step-by-step explanation:

The derivative is the limit of the average slope on an interval as the interval size approaches zero. The equation for a tangent line is conveniently written in point-slope form when the tangent point and the derivative there are known.

__

The derivative is ...

  [tex]\displaystyle f'(x)=\lim_{h\to 0}{\dfrac{f(x+h)-f(x)}{h}}=\lim_{h\to 0}\dfrac{(6(x+h)^2-1)-(6x^2-1)}{h}\\\\=\lim_{h\to 0}\dfrac{(6x^2+12xh+6h^2-1)-(6x^2-1)}{h}=\lim_{h\to 0}\dfrac{12xh+6h^2}{h}=\lim_{h\to 0}(12x+6h)\\\\\boxed{f'(x)=12x}[/tex]

__

  f'(-10) = 12(-10) = -120

__

  f'(3) = 12(3) = 36

__

The point of tangency is ...

  (3, f(3)) = (3, 6·3² -1) = (3, 53)

The slope there was found in part (c) to be 36. So, the point-slope equation for the tangent line can be written ...

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

  y -53 = 36(x -3) . . . . equation of the tangent line at (3, 53)

This equation can be rearranged to slope-intercept form:

  y = 36x -55 . . . . . add 53 and simplify

The expression that represents the constant of variation, k, in this scenario is StartFraction z Over x y EndFraction.

When a quantity varies directly with one variable and inversely with another, it means that the quantity is directly proportional to one variable and inversely proportional to the other. In this case, x varies directly with y and inversely with z.

To represent the constant of variation, k, we need to find the expression that combines the variables x, y, and z in the correct way.

If x varies directly with y, we can represent this relationship as x = ky, where k is the constant of variation.

If x varies inversely with z, we can represent this relationship as x = k/z.

Combining these two expressions, we can write x = ky = k/z.

Simplifying this equation, we get xz = ky.

To isolate k, we divide both sides of the equation by xy, resulting in StartFraction x z Over y EndFraction = k.

Therefore, the expression StartFraction z Over x y EndFraction represents the constant of variation, k.

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Answer:I think It may be B 4.2%

Step-by-step explanation:

Answer: There are no solutions.

Step-by-step explanation:

1/4(8x - 4) = 2x + 1

2x - 1 = 2x + 1

-1 = 1

Answer: 77

Step-by-step explanation:

[tex]$$Find the range of the list:$$(41,43,52,25,96,19,72)$$The range of a list is given by:(largest element) - (smallest element) \\$(41,43,52,25,\bold{96},19,72)$ We see that the largest element is $96:$ $-(($ smallest element $))+96$\\$(41,43,52,25,96,\bold{19},72)$ We see that the smallest element is $19:$ $96-19$\\$$96-19=77$$Therefore, the range of the set is 77[/tex]

Answer:

b

Step-by-step explanation:

bc solutions are the zeros or the x intercepts of the graph which would be (-3,0) and (3,0)

Answer:

[tex]-\frac{11}{12}[/tex]

Step-by-step explanation:

please can i have brainliest

hope its right