A fish tank initially contains 15 liters of pure water. Brine of constant, but unknown, concentration of salt is flowing in at 4 liters per minute. The solution is mixed well and drained at 4 liters per minute. Let xx be the amount of salt, in grams, in the fish tank after tt minutes have elapsed. Find a formula for the rate of change in the amount of salt, dx/dtdx/dt, in terms of the amount of salt in the solution xx and the unknown concentration of incoming brine cc. dxdt

Answer:

Hence the correct option is Option (a).

Step-by-step explanation:  

Option (a) is correct.  

The probability does not change from trial to trial.  

p = Probability of sucess.

Answer:

sin(330)=-0.5

cos(330)=0.86

tan(330)=-0.57

Step-by-step explanation:

63+81

gcf = 9

63÷9=7, 81÷9=9

so, 63+81 = (9×7)+(9×9)

= 9×(7+9)

63+81 = 144

9x(7+9) = 9×16 = 144

Answer:

hshdjdjdjffhdiosekskskdkcjfiririrotr8tti5tittttit4i5i6i6832wy

9514 1404 393

Answer:

  x^2/1024 -y^2/7744 = 1

Step-by-step explanation:

The parent hyperbola relation is ...

  x^2 -y^2 = 1

This has asymptotes of y = ±x and x-intercepts of ±1.

For the given hyperbola, we want to scale x by a factor of 32, and y by a factor that is 2.75 times that, or 88. Then the equation could be written as ...

  (x/32)^2 -(y/88)^2 = 1

More conventionally, the denominator is shown at full value:

  x^2/1024 -y^2/7744 = 1

Answer:

first one : inscribed angles create arc twice their degree

so, 115° created a 230 ° arc

360 - 230 = 130°

that means ∠EDG = 1/2 (130) or 65°

second : ∠ABD = 180 - 112 = 68

The arc created APD is 2 times ∠ABD or 136°, therefore ∠x = 136°.

Central Angles and arcs are equal

360° - 136° = 224°

224° is the arc created by ∠APD. Take 1/2 of 224° and you get 112°

Third: ∠ACB and ∠ AOB create the same arc.

since ∠ACB is 48°, the arc is 96° (twice the angle)

if the arc is 98° then the central angle ∠AOB = 98°

360°-98° = 262°

You need this because ∠APB is 1/2(262-98) or 82°

Fourth : Both inscribed angles create the same arc

so the angles are equal

∠DEG = 38°

Answer:

15° created a 230 ° arc

360 - 230 = 130°

that means ∠EDG = 1/2 (130) or 65°

second : ∠ABD = 180 - 112 = 68

The arc created APD is 2 times ∠ABD or 136°, therefore ∠x = 136°.

Central Angles and arcs are equal

360° - 136° = 224°

224° is the arc created by ∠APD. Take 1/2 of 224° and you get 112°

Third: ∠ACB and ∠ AOB create the same arc.

since ∠ACB is 48°, the arc is 96° (twice the angle)

if the arc is 98° then the central angle ∠AOB = 98°

360°-98° = 262°

You need this because ∠APB is 1/2(262-98) or 82°

Fourth : Both inscribed angles create the same arc

so the angles are equal

∠DEG = 38°

Step-by-step explanation:

Answer:

For eleven, it had the same two numbers. For twelve, it continues up by even numbers. For thirteen, it's the same as twelve but by odd numbers. For fourteen, it's a little difficult but they have a pattern for every five multiples of fourteen. For fifteen, the numbers add by five but also counting up.

Step-by-step explanation:

Examples for the table of eleven would be: 11 × 3 = 33 or 11 × 6 = 66.

Table twelve would be (as examples): 12 × 2 = 24 and 12 × 3 = 36.

Table thirteen have numbers/answers like: 13 × 7 = 91 and 13 × 8 = 104.

Table fourteen as examples: 14 × 3 = 42 or 14 × 4 = 56.

Table fifteen would be like: 15 × 6 = 90 and 15 × 7 = 105.

Answer:

may be 11.460

sorry to say this but I'm not sure bout my answer

(ー_ー✿)

Answer:

x=-12  (BUT IS EXTRENUS)

Step-by-step explanation:

If u dont know what extraneous is, dont worry about it...

Answer:

According to Indices

(a⁴)²... The exponents will multiply each other to give (a⁶)

Using this here

The two Index would Multiply to give

½ x ⅔ = ⅓

= (27)⅓

Any Number to the Index of ½ simply means its Square root

so also...

Any Number to the index of ⅓ means its cube root...

Cube root of 27 = 3.

So

Option B is your answer.

Answer:

See explanation

Step-by-step explanation:

Given

Represent the balls with the first letters

[tex]W =1[/tex]

[tex]R =1[/tex]

Solving (a): P(F) --- White balls twice

The event of F is:

[tex]F = \{(W,W)\}[/tex]

So:

[tex]P(F) = P(W) * P(W)[/tex]

[tex]P(F) = \frac{n(W)}{n} * \frac{n(W)}{n}[/tex]

[tex]P(F) = \frac{1}{2} * \frac{1}{2}[/tex]

[tex]P(F) = \frac{1}{4}[/tex]

Solving (b): P(G) --- two different colors

The event of G is:

[tex]G = \{(W,R),(R,W)\}[/tex]

So:

[tex]P(G) = P(W) * P(R) + P(R) * P(W)[/tex]

[tex]P(G) = \frac{n(W)}{n} * \frac{n(R)}{n} + \frac{n(R)}{n} * \frac{n(W)}{n}[/tex]

[tex]P(G) = \frac{1}{2} * \frac{1}{2} + \frac{1}{2} * \frac{1}{2}[/tex]

[tex]P(G) = \frac{1}{4} + \frac{1}{4}[/tex]

[tex]P(G) = \frac{1}{2}[/tex]

Solving (c): P(H) --- White picked first

The event of H is:

[tex]H = \{(W,R),(W,W)\}[/tex]

So:

[tex]P(H) = P(W) * P(R) + P(W) * P(W)[/tex]

[tex]P(H) = \frac{n(W)}{n} * \frac{n(R)}{n} + \frac{n(W)}{n} * \frac{n(W)}{n}[/tex]

[tex]P(H) = \frac{1}{2} * \frac{1}{2} + \frac{1}{2} * \frac{1}{2}[/tex]

[tex]P(H) = \frac{1}{4} + \frac{1}{4}[/tex]

[tex]P(H) = \frac{1}{2}[/tex]

Solving (d): F and G, mutually exclusive?

We have:

[tex]F = \{(W,W)\}[/tex]

[tex]G = \{(W,R),(R,W)\}[/tex]

Check for common elements

[tex]n(F\ n\ G) = 0[/tex]

Hence, F and G are mutually exclusive

Solving (e): G and G, mutually exclusive?

We have:

[tex]G = \{(W,R),(R,W)\}[/tex]

[tex]H = \{(W,R),(W,W)\}[/tex]

Check for common elements

[tex]n(G\ n\ H) = 1[/tex]

Hence, F and G are not mutually exclusive

Answer:

[tex] \frac{4}{9} [/tex]

Step-by-step explanation:

[tex]p = \frac{favorable \: outcomes}{total \: outcomes} = \frac{4}{9} [/tex]

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

Explanation:

The probability you get a black marble on the first selection is 2/3 since we have 2 black marbles out of 2+1 = 3 total.

We put the marble back and then we have 2/3 as the probability of selecting another black marble on the second try. Nothing has changed because we put the marble back. That means the events are independent.

So we get (2/3)*(2/3) = 4/9 as the probability of selecting 2 black marbles in a row (with replacement).

Answer:

10

Step-by-step explanation:

Every time you multiply by 10 you move the decimal point one digit to the right. So if you multiply 1.62 by 10 you move the decimal point one digit to the right so it becomes 16.2.

So the answer is 10

Answer:

The answer is 10

Step-by-step explanation:

Every time you multiply by a power of 10 that does not have a negative exponent, the decimal point moves to the right.

How many times, you might wonder. It all just depends on how many zeroes there are. If there's one 0, (10) then the decimal point just moves one over, if were multiplying by 100 then 2 places over, 1000 three places over, and so on.

1.62 * 10 = 16.2, since the decimal point moved one to the right.

10 is therefore the answer, but if you wanted to you could check the other answers as well.

1.62 * 100 = 162

1.62 * 1000 = 1620

Therefore, the answer is 10. Please mark brainliest if possible. Have a nice day.

Answer:

-x^2 +4x +6

Step-by-step explanation:

f(x)=4x+1

g(x)=x^2-5

(f-g)(x) = 4x+1 - (x^2-5)

Distribute the minus sign

           = 4x+1 - x^2 +5

           = -x^2 +4x +6

Answer:

y=-1/2x+4

Step-by-step explanation:

The line is going down, which means it's negative. You then do rise over run, go up by 1 and go to the left by 2. To find the y intercept, it's 4 since the coordinate is (0,4).

Answer:

rs.1680.67

Step-by-step explanation:

His salary = x

remaining % = 100 - 65 = 35%

= 100 - 15 = 85%

x × 35/100 × 85/100 = 500

x = 1680.67

Answer:

C

Step-by-step explanation:

Mae, Elsa, Rodley, Cristina, Christian

Answer:

17.18400

Step-by-step explanation:

When rounded to the nearest whole number, it's 17.

Hope this helped :)

Answer:

the answer is 97.2

Step-by-step explanation:

Just add 94.2+3

Answer:

y = 0.48(x - 0.5)² - 3

y = 0.48(x² - x - 6)

Step-by-step explanation:

From the graph the zeros are

x = {-2, 3}

The x coordinate of the vertex is the midpoint of the roots

x = (-2 + 3) / 2

x = 0.5

The y coordinate of the vertex is

y = -3

vertex = (0.5, -3)

--------------------------------------

Merhod I - vertex

Vertex form is

y = a(x - h)² + k

plug in the vertex

y = a(x - 0.5)² - 3

to find a plug in either root

using x = 3

0 = a(3 - 0.5)² - 3

0 = a(2.5)² - 3

0 = 6.25a - 3

3 = 6.25a

a = 3/6.25

a = 0.48

y = 0.48(x - 0.5)² - 3

-----------------------------

Method II - roots

y = a(x + 2)(x - 3)

-3 = a(0.5 + 2)(0.5 - 3)

-3 = a(2.5)(-2.5)

-3 = -6.25a

3/6.25 = a

0.48 = a

y = 0.48(x + 2)(x - 3)

Expand

y = 0.48(x² - x - 6)

Answer:

if it cost 410 dollars to make 6 chairs we can divide 410 by 6 which is 68.3333333333 or 68 1/3

now for the other set of chairs we can divide 570 by 22 which is

25.9090909091 or 25.9

and for the rest it doesn't make any sense to me sorry

Answer:

f(x) = 3/4x^2 + 2x -5

quadratic function formula is ax^2+b^2+c

Answer:

Step-by-step explanation:

1). Figure (1) comprises two cuboids, one small cuboid placed on the big cuboid at the bottom.

Volume of the figure = Volume of the cuboid on the top + Volume of the cuboid at the bottom

Volume of the cuboid on the top = Length × Width × Height

                                                   = 4 × 6 × 5

                                                   = 120 mm³

Volume of the cuboid at the bottom = Length × Width × Height

                                                        = 9 × 6 × 4

                                                        = 216 mm³

Volume of the figure = 120 + 216

                                   = 336 mm³

2). Figure shown in the picture has two parts,

Cone placed on the top of a cylinder.

Volume of the given figure = Volume of cone + Volume of cylinder

                                          = [tex]\frac{1}{3}\pi r^{2}h+\pi r^{2}h'[/tex]

                                          = [tex]\frac{1}{3}\pi (\frac{3}{2})^{2}(3)+\pi (\frac{3}{2})^{2}(8.1)[/tex]

                                          = [tex]\frac{9}{4}\pi +18.225\pi[/tex]

                                          = [tex](2.25+18.225)\pi[/tex]

                                          = [tex]20.475\pi[/tex]

                                          = 64.3 ft³

Therefore, volume of the given figure = 64.3 ft³.

Answer:

12

Step-by-step explanation:

A midpoint of a line means that each segment connecting from the midpoint to an end is equal. For this problem, this means that AB = BC, as B is the midpoint, and A and B are the ends. Therefore, we can say that:

AB = BC

2x + 6 = 5x - 3

add 3 to both sides

2x + 9 = 5x

subtract 2x from both sides

9 = 3x

divide both sides by 3

3 = x

Plugging 3=x into AB, this means that 2(3) + 6 = AB = 12

This question is incomplete, the complete question;

At 11:30 a.m. the angle of elevation of the sun for one city is 55.7°. If the height of a monument is approximately 555 ft, what is the length of the shadow it will cast at that time? Round to the nearest foot.

Answer:

the length of the shadow will be 379 ft

Step-by-step explanation:

Given the data in the question and as represented in the diagram below;

height of monument = 555 ft

angle of elevation = 55.7°

From the image below, this makes a right angled triangle

we know that the some of the interior angles of a triangle is 180

so

∠ABC + ∠BCA + ∠CAB = 180°

90° + 55.7° + ∠CAB  = 180°

∠CAB = 180° - 145.7°

∠CAB = 34.3°

Now, using sine rule;

BC / sinA = AB / sinC

so we substitute

BC / sin( 34.3°) = 555 / sin( 55.7° )

BC / 0.563526 = 555 / 0.826098

we cross multiply

BC × 0.826098 = 0.563526 × 555

BC × 0.826098 = 312.75693

BC = 312.75693 / 0.826098

BC = 378.595 ≈ 379 ft

Therefore, the length of the shadow will be 379 ft

Answer:

He is wrong.  

In my answer I found the complete volume of the pool and then what the volume would be 10 cm empty.  You probably only need to find the 10 cm emptied  to answer, just a heads up.  if you have any questions though let me know.

Step-by-step explanation:

To most easily figure out the volume of the empty pool I think it is easiest to break it up into four parts..

First break off that skinny end bit so it will have 1 m in height, 4 m in length and 5m in width.  Width is never going to shange because of how we are breaking this up, and the width is the distance from you into the paper, if that makes sense.  Basically not up and down or left and right.

Next another rectangular prism  from the right side with 2 height, 2m length and again 5m width.

Now you have a trapezoidal prism with one base of length 1m, another of base 2m and a height of length 4m.

To fond the volume of prisms you want to find the area of their bases then multiply it by their heights.  In this instance height is going to be the width again, and the bases are th parts facing us on the picture.

For a rectangular prism area of the base is easy, just multiply length by height.  a trapezoid is taking the two bases (b1 and b2) ading them together and dividing that sum by 2, THEN taking this new number and multiplying it by what would be the height of the trapezoid.  the trapezoid has its bases as two heights, and its height then would be the horizontal length of the pool.  Sorry if that is confusing.  Here are the three volumes though.

Rectangular 1: 4*1*5 = 20 m^3

Rectangular 2" 2*2*5 = 20m^3

Trapezoidal: = ([1+2]/2)*4*5 = 30 m^3

So total it is 70 m^3

The question then says each cubic meter can contain 1,000 liters of water.  70 m^3 then is 70,000 liters

The question also says there are three barrels of 20,000 liters each, so combined that's 60,000 liters.

Finally it wants to know if Sam is right saying if you dump all of the 60,000 liters into the pool the surface of the water will not reach the top of the pool by 10 cm.  60,000 is less than 70,000, but we don't know how much lower it is in cm.  

The trick here is to know that we are lowering a specific dimension of each prism to a certain amount to be lower by 10cm

In the 4x1x5 rectangular prism the 1m side is lowering.

In the 2x2x5 rectangular prism  the 2m side representing the vertical length is getting some amount taken away.

int he trapezoidal prism both of the "bases" are getting an amount taken.

So the trick here is to set up the math again, except this time with 10 cm less being subtracted from each part, then solving t and see if it gets us the 60,000 liters or 60 m^3.  Since we are measurng in meters, 10 cm less is the same a subtracting .1, or if you prefer subtracting a decimeter.

4*1*5 becomes 4(.9)5 = 18

2*2*5 becomes 2(1.9)5 = 19

Trapezoidal: = ([1+2]/2)*4*5 becomes ([(.9)+(1.9)]/2)*4*5 = 28

Adding this all together gets us 65 or 65,000 liters.  This means that if the pool is filled 10 cm from the top the volume would be 65,000 liters, still more than if the three tankers are emptied completely into it.  

You could have probably just done the second part, where we sbtracted 10 cm from each of the dimensions, but I am going to leave it all since I wrote it.

9514 1404 393

Answer:

  Sam is not correct.

Step-by-step explanation:

As shown in the attachment, the "base" (front face) of this prism can be divided into a rectangle and a trapezoid. The relevant area formulas are ...

  A = LW . . . . area of a rectangle of length L and width W

  A = 1/2(b1 +b2)h . . . . area with parallel bases b1 and b2 and height h

__

The rectangle portion of the "base" of the pool has area ...

  A = (10 m)(1 m) = 10 m²

The trapezoid portion of the "base" of the pool has area ...

  A = 1/2(6 m +2 m)(1 m) = 4 m²

Then the "base" area is ...

  B = 10 m² +4 m² = 14 m²

__

The volume of the prism is given by ...

  V = Bh . . . . where B is the base area and h is the distance between bases

  V = (14 m²)(5 m) = 70 m³

We are told that 1 m³ = 1000 L and that 3 tankers of 20,000 L each are emptied into the pool. That leaves an unfilled volume of ...

  70 m³ -3×(20 m³) = 10 m³ . . . . unfilled volume

__

The surface area of the pool is ...

  A = LW = (10 m)(5 m) = 50 m²

So the unfilled volume has a height of ...

  V = Bh

  10 m³ = (50 m²)h

  h = (10/50) m = 20/100 m = 20 cm . . . . . the height of the unfilled space

The water in the pool will be 20 cm below the top, not 10 cm. Sam is not correct.

Answer:

b

Step-by-step explanation:

you have to have psi to have p-e-n-i-s sand you get a jack hammer