in a chemistry class, 8 liters of a 4% acid solution must be mixed with a 10% acid solution to get a 6% acid solution. how many liters of the 10% acid solution are needed?

The length of the hypotenuse AB is approximately 6.53 units.

In a right angled triangle the side opposite the right angle or the largest side is called the hypotenuse of the triangle.

The length of the hypotenuse is calculated using trigonometric ratios. If in a right-angled triangle, the base angle is θ then:

In the given figure we see in ΔABC

AB is the hypotenuse. ∠BAC = 40 ° AC is the base and BC is the perpendicular.

(The side that contains the given angle is the base and the side opposite the given angle is taken as perpendicular)

Now cos ∠BAC = BC ÷ AB

or, cos 40° = 5 ÷ AB

or, AB = 6.527...

or, AB ≈ 6.53

Hence the value of AB is approximately 6.53 units.

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The largest positive integer d for which d +10 is a divisor of d³ + 2011 is equal to 1001.

As given,

Divisor= d +10

Dividend= d³ + 2011

(d³ + 2011 ) ÷ ( d+ 10) = [(d² -10d +100) (d +10) +1011] ÷ ( d+ 10)

                                 =(d² -10d +100) + [ 1011 / (d+10)]

Largest positive integer d for which d +10 is a divisor of  d³ + 2011

d + 10 =1011

⇒d=1001

Therefore, the largest positive integer d for which d +10 is a divisor of d³ + 2011 is equal to 1001.

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The length of the unknown side of the right triangle is 13

A right triangle (American English), sometimes known as a right-angled triangle (British), is a triangle with one angle that is a right angle (i.e., a 90-degree angle), or two sides that are perpendicular. The link between is the basis of trigonometry.

between the right triangle's angles and sides.

The side across from the right angle is the hypotenuse (side c in the figure). Legs are the sides closest to the ideal angle (or catheti, singular: cathetus). The side a that is next to angle B and across from angle A is referred to as side b, and the side a that is next to angle A and across from angle B is referred to as side a.

Right triangles are referred to as Pythagorean triangles and their side lengths as Pythagorean if all three of their sides are integer lengths.

[tex]\sqrt{(12)^2+(5)^2}=13[/tex]

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The square root of 255 is approximately 15.969.

Given,

Root 255, [tex]\sqrt{255}[/tex]

We have to find the square root of the number:

Square root of a number:

A number multiplied by itself is the square root of that number. Or we may say that after adding a number to itself, we must calculate its square root in order to go back to the original number. The square root of p, if it is a positive integer, is represented by p, so that p = q.

Now,

√255 = 15.9687194227

Which is approximately equals to 15.969

That is,

The square root of 255 is approximately 15.969

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the cost of 4 dozens of buttons will be $ 6 and the organizers can buy 216 buttons for $ 27.

We are given that:

Cost of 48 buttons = $ 6

48 buttons = $ 6

Divide both sides by 48:

1 button = $ 6 / 48 = $ 1 / 8

Now, the cost of 4 dozen buttons will be:

4 dozen buttons = 12 × 4 = 48

So, the cost will be 4 6 only.

For $ 27, the organizers can buy:

Number of buttons = 27 ÷ 1 / 8

Number of buttons = 27 × 8

Number of buttons = 216 buttons.

Therefore, the cost of 4 dozens of buttons will be $ 6 and the organizers can buy 216 buttons for $ 27.

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answer:
Green t-shirt=profit of $1

White t-shirt=profit of $3

Black t-shirt=profit of $1.

To find the answer, selling price minus total money spent (shirt, printing) If the number is negative, it’s loss, and if it’s positive, it’s profit

Answer:

Bread

Step-by-step explanation:

Her commission for the week was $234.

It is given the total earning in past week = $3,925  and jean earns 4% for the first $2000

So, the commission = $2000 x 4/100  = $80

To find additional sales, the formula to refer is

Add –on sales = total sales – base sales

                          = 3,925 – 2000

                          = 1,925

For the $1,925 sales, Jeans earns 8% commission, Her commission

                                                     = 1,925*0.08    = $154

So, the total commission = $80 + $154  = $234

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Answer:

[tex]6.45*10^{-9}[/tex]

Step-by-step explanation:

According to the solving the dimensions of the triangles are as follow:

a . 29

b. 58

c. 57

A mathematical space's dimension is defined informally as the smallest number of coordinates required to specify any point within it. Thus, a line has a dimension of one since only one coordinate is required to identify a point on it - for example, the point at 5 on a number line.

2-D shapes really had no thickness and they can only be measured on two sides. Two-dimensional objects include the square, circle, rectangle, and triangle.

x=length of the shortest side

2x=length of another side

x+28=length of the third side

144=x+2x+x+28

144=4x+28

144-28=4x

116=4x

x=116/4

x=29 feet (one side)

Putting the value of x to find second side

2x=58 feet (second side)

x+28= 57 feet (third side)

the perimeter of the triangle = sum of all the sides

                                                = 29+58+57

                                                =144

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Answer:

Can you only pick one answer?

Answers:

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

Explanation:

After 1 stage, the depth is -340+60*1 = -280 meters. In other words, it's 280 meters below the surface.

After 2 stages, the depth is now -340+60*2 = -220 meters

After 4 stages, the depth is -340+60*4 = -100 meters

After n stages, the depth is -340+60n. Set this equal to zero and solve for n.

-340+60n = 0

60n = 340

n = 340/60

n = 5.667 approximately

This rounds to n = 6

After n = 5 stages, the depth is -340+60n = -340+60*5 = -40 meters

After n = 6 stages, the depth is -340+60n = -340+60*6 = 20 meters, so the submarine is now at the surface. Of course the sub cannot fly to a height of 20 meters above the ocean's surface, so the highest it can go is 0 meters at the surface itself. This means the 6th stage is a movement of 40 meters (instead of 60 meters).

It might help to draw out a vertical number line to visually keep track of everything.

Answer:

the standing line is the "Y line"

the line laying down is the "X line"

wherever the line touches on the y and x line is where it intercepts

for the x it intercepts at 25 since it touches the x line between 20 and 30

for the y line it intercepts at - 55 since it touches the y line in between - 50 and - 60

The equation which represents the net profit of the charity organization is y = 45x-810.

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Using sampling concepts, the population being studied is all visitors that are flying to the state of Hawaii.

The problem is incomplete, but researching it on a search engine, it asks for us to identify who is the population of this study.

In this problem, a set of visitors traveling to Hawaii were sampled, hence the population being studied is all visitors that are flying to the state of Hawaii.

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Answer:

84

Step-by-step explanation:

7x5x4x3= 84

If we shift the origin without changing the direction and point P(x, y) is changed to P(X, Y) then the new coordinates will be x = X + h and y = Y + k.

Shifting of origin is the phenomenon of changing the coordinates of the origin which is generally (0, 0) to another point which has coordinated (h, k). This phenomenon is usually carried out graphically. This is done when there is difficulty to solve the problems in coordinate geometry when we take the origin at (0, 0).

If we shift the origin which is at P(x, y) to another point (h, k) then the coordinates of new point P(X, Y) will be

x = X + h and y = Y + k

If h is positive, then coordinates will be x = X + h and if h is negative then coordinates will be x = X - h. If k is positive, then coordinates will be y = Y + k and if k is negative then coordinates will be y = Y - k.

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Answer:as a fraction it would be 11 3/5

Step-by-step explanation:

Answer:

x = 1/2 or 0.5

Step-by-step explanation:

4 • ((2x • (2x - 1)) -  (2x - 1))  = 0

The rule says: To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is  (2x-1)  and the exponents are :

         1, as  (2x-1), is the same number as  (2x-1)1

and   1, as  (2x-1)  is the same number as  (2x-1)1

The product is therefore,  (2x-1)(1+1) = (2x-1)2

 4 • (2x - 1)2  = 0

4.2      Solve  :    (2x-1)2 = 0

 (2x-1) 2 represents, in effect, a product of 2 terms which is equal to zero

For the product to be zero, at least one of these terms must be zero. Since all these terms are equal to each other, it actually means:   2x-1  = 0

Add  1  to both sides of the equation :

                     2x = 1

Divide both sides of the equation by 2:

                    x = 1/2 = 0.500

Answer:

x = 1/2.

Step-by-step explanation:

4 (2x (2x - 1) - 1 (2x - 1)) = 0

(2x (2x - 1) - 1 (2x - 1)) = 0

(2x - 1) is common to both parts.

(2x - 1)(2x - 1) = 0

2x - 1 = 0

x = 1/2.

Using the law of sines, it is found that the distance from the farthest soccer player to the goalie is 14.723 yards.

Given,

The distance between the two players = 10yards

The angle from each player to the goalie is 64° and 75°, respectively

We have to find,

the distance from the farthest soccer player to the goalie.

In this problem, considering that the sum of the internal angles of a triangle is of 180º, the angle that the goalie makes with the players is given by:

∠A = 180-(∠B+∠C)

∠A = 41°

Using Sine rule

AC/Sin B = BC / Sin A

AC = 10yrd*Sin75°/Sin41°

AC = 14.723 yards

The farthest distance is of 14.723 yards.

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Step-by-step explanation:

Answer:

I have completed it also

Step-by-step explanation:

what the person ontop of me said it correct

Answer: A.  D.

Step-by-step explanation:

A.

x-b-3<0

x-b-3+3<0+3

x-b<3   (yes)

B.

0>b-x+3

0+x>b-x+3+x

x>b+3

x-b>b+3-b

x-b>3   (no)

C.

x<3-b

x+b<3-b+b

x+b<3   (no)

D.

-3<b-x

-3+3<b-x+3

0<b-x+3

0+x<b-x+3+x

x<b+3

x-b<b+3-b

x-b<3    (yes)

Answer:

A and D

Step-by-step explanation:

Option A

[tex]\begin{aligned}& \textsf{Given inequality}: & x-b-3 & < 0\\& \textsf{Add 3 to both side}: \quad & x-b-3+3 & < 0+3\\& \textsf{Simplify}: & x-b & < 3\end{aligned}[/tex]

Option B

[tex]\begin{aligned}& \textsf{Given inequality}: & 0 & > b-x+3\\& \textsf{Add $x$ to both sides}: & 0+x & > b-x+3+x\\& \textsf{Simplify}: & x & > b+3\\& \textsf{Subtract $b$ from both sides}: \quad& x-b & > b+3-b\\& \textsf{Simplify}: & x-b & > 3\end{aligned}[/tex]

Option C

[tex]\begin{aligned}& \textsf{Given inequality}: & x & < 3-b\\& \textsf{Add b to both sides}: \quad & x+b & < 3-b+b\\& \textsf{Simplify}: & x+b & < 3\end{aligned}[/tex]

Option D

[tex]\begin{aligned}& \textsf{Given inequality}: & -3 & < b - x\\& \textsf{Divide both sides by -1}: \quad & \dfrac{-3}{-1} & > \dfrac{b}{-1}-\dfrac{x}{-1}\\& \textsf{Simplify}: & 3 & > -b+x\\& \textsf{Simplify}: & x-b & < 3\end{aligned}[/tex]

Note: When multiplying or dividing by a negative number in an inequality, remember to flip the inequality sign.

Expressions in component form for the position vectors having the  polar coordinates are:

a) -12 cos(40)i + 12sin(40) j = -9.19i + 7.71j

b) 3cos(40) i + 3 sin(40) j = 2.29i + 1.92j

c) -24cos(48)i - 24sin(48) j = -16.059i - 17.83j

Use one or more of the following equations: cos=xr, sin=yr, tan=yx, and r=x2+y2 to convert rectangular coordinates to polar coordinates.

The polar coordinate system is indeed a two-dimensional coordinate system in which the distance from a reference point and the angle from a reference direction are used to determine each point's location on a plane. The polar axis is the ray emanating from the pole inside the reference direction. The pole is the point of reference.

Let the +x and +y represent, respectively, the unit vectors represented by I and j.

(a) 12.6 m, 130° counterclockwise from the +x axis [tex]\overrightarrow{\mathrm{R}}[/tex]= m.

    -12 cos(40)i + 12sin(40) j

     = -9.19i + 7.71j

(b) 3.60 cm, 70.0° counterclockwise from the +x axis [tex]\overrightarrow{\mathrm{R}}[/tex]= cm.

     3cos(40) i + 3 sin(40) j

      = 2.29i + 1.92j

(c) 24.0 in., 206° counterclockwise from the +x axis [tex]\overrightarrow{\mathrm{R}}[/tex]= in.

    -24cos(48)i - 24sin(48) j

    = -16.059i - 17.83j

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I understand that the question you are looking for is:

Obtain expressions in component form for the position vectors having the following polar coordinates.

(a) 12.6 m, 130° counterclockwise from the +x axis

[tex]\overrightarrow{\mathrm{R}}[/tex]= m

(b) 3.60 cm, 70.0° counterclockwise from the +x axis

[tex]\overrightarrow{\mathrm{R}}[/tex]= cm

(c) 24.0 in., 206° counterclockwise from the +x axis

[tex]\overrightarrow{\mathrm{R}}[/tex]= in.

Answer:

-6.34

Step-by-step explanation:

If you used a number line, it'll help! Start at 2.56, and go back (to the left) 8.9, and you will arrive at -6.34

A circle with a circumference of 615.44 units has a radius of 98 units.

A circle is a round closed figure where all its boundary points are equidistant from a fixed point called the center.

The circumference of a circle is the perimeter of the circle. It is the total length of the boundary of the circle. The circumference of a circle is the product of the constant [tex]\pi[/tex] and the diameter of the circle.

C = [tex]\pi[/tex]D

The diameter (D) is the distance across the circle through the center, it is a line that meets the circumference at both ends and it needs to pass through the center. On the other hand, the radius (r) of a circle is the distance from the center of a circle to any point on the circumference of the circle. Radius is half of the diameter.

If r = 1/2 D, then

D = 2r

Evaluating the value of Din the formula of the circumference,

C = [tex]\pi[/tex](2r)

C = 2[tex]\pi[/tex]r

Using the value of [tex]\pi[/tex] as 3.14 and the circumference as 615.44 units,

evaluate the equation.

C = 2[tex]\pi[/tex]r

615.44 = 2(3.14)r

r = 615.44/ (2*3.14)

r = 98 units

Therefore, the radius of the circle is 98 units.

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Answer:

150 degrees

Step-by-step explanation:

Vertical angles

Answer: q(r(5))= 3

Step-by-step explanation: sub in 5 for x in r(x). Once you do that, you'll get -3 for r(5). Now sub in the value of r(5), -3, for x in q(x). Then you'll end up with -9 once the equation has been evaluated.

The percentage of bags that Kia still has to make for the contest is 36 %.

We are given that:

Kia has to make 14 bags out of 25 bags.

Now, she has already made 5 gift bags.

The number of bags she still has to make = 14 - 5 = 9

Now ,we need to find the percentage of 9 from the total of 25 so to get the percentage of bags that Kia still has to make.

So, we get that:

Percentage = 9 / 25 × 100 %

Percentage = 9 × 4 %

Percentage = 36 %

Therefore, we get that, the percentage of bags that Kia still has to make for the contest is 36 %.

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