The number of goldfish in a tank is 12, and the volume of the tank is 45 cubic feet. What is the density of the tank?

0.27 goldfish per cubic foot
3.75 goldfish per cubic foot
33 goldfish per cubic foot
57 goldfish per cubic foot

Answer:

242/48

Step-by-step explanation:

9514 1404 393

Answer:

  y = 9x^2 -8x +9

Step-by-step explanation:

The given equation has derivative ...

  y' = 2ax +b

The requirements on slope give rise to two equations:

  2a(1) +b = 10

  2a(-1) +b = -26

Adding these equations together gives ...

  2b = -16   ⇒   b = -8

Then we have ...

  2a -8 = 10

  a = (10 +8)/2 = 9

__

The given point lets us find the constant term c.

  y = 9x^2 -8x +c

  c = y -(9x -8)x = 29 -(9(2) -8)(2) = 29 -20 = 9

The equation of the parabola is ...

  y = 9x^2 -8x +9

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

x² - 5xy + 6y² = x² - 3xy - 2xy + 6y²

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

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

x² - 4xy + 3y² = x² -xy - 3xy + 3y²

                      = x(x - y) - 3y(x - y)

                      = (x - y)(x - 3y)

x² - 3xy + 2y² = x² - xy - 2xy + 2y²

                      = x(x - y) - 2y(x - y)

                     = (x - y)(x - 2y)

Least common denominator = (x-y)(x - 2y)(x - 3y)

[tex]RHS = \frac{1*(x-y)}{(x-3y)(x-2y)*(x-y)}+\frac{a*(x-2y)}{(x-y)(x-3y)*(x-2y)}+\frac{1*(x-3y)}{(x-y)(x-2y)*(z-3y)}\\\\= \frac{x- y + ax - 2ay +x -3y}{(x-y)(x-2y)(x-3y)}\\\\= \frac{2x -4y +ax - 2ay}{ x^{3}-5x^{2}y+8xy^{2}-4y^{3}}[/tex]

Answer:

smallest share = $400

second smallest share = $800

largest share = $1200

Step-by-step explanation:

Let the smallest share = x

amount one friend gets = 2x

second friend gets = 3x

2400 = x + 2x + 3x

2400 = 6x

x = 400

2 x 400 = 800

3 x 400 = 1200

Answer:

[tex]slope = \frac{2 - ( - 1)}{0 - ( - 1)} \\ = 3 \\ y = mx + c \\ 2 = (0 \times 3) + c \\ c = 2 \\ { \boxed{y = 3x + 2}}[/tex]

Answer:

The measure of angle R is 112 degrees

Step-by-step explanation:

Using the given markings, we can see that we have an isosceles triangle

so RT is also 3x-2

Mathematically, the sum of the interior angles of a triangle is 180:

Thus;

9x + 4 + (3x-2) + (3x-2) = 180

9x + 3x +3x + 4-2-2 = 180

15x = 180

x = 180/15

x = 12

Recall; Angle R is 9x + 4

= 9(12) + 4 = 108 + 4 = 112

Answer: The clubs goal is to raise  $436.

Step-by-step explanation:

175%  * x  = 763     where x is the goal  

1.75 *x  = 763

1.75x = 763

x= 436

Answer:

I figured out that the probability that both marbles are red is 20/56 and the probability that both are green is 6/56. Then I added them together to get 26/56.

Hope this answer is right !

We can't see what you are talking about. send another one.

Answer:

The answer is 129

Step-by-step explanation:

5(exponent 4)/5 = 125 +4 equals 129

I think

Answer:

129

Step-by-step explanation:

5^4 / 5   + 4

We know that a^b / a^c = a^(b-c)

5^(4-1) +5

5^3 +4

125 +4

129

Answer:

10 and 42

Step-by-step explanation:

The difficulty with word problems is translating them into math.

Let's do that

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

The sum of a number and two times a smaller number is 62.

let's call the bigger number b, and the smaller number s

b + 2s = 62

Three times the bigger number exceeds the smaller number by 116

3b = s + 116

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

Now manipulate one of the equations to isolate the variable

3b = s + 116

Subtract 116 from both sides

3b - 116 = s

substitute for s = 3b - 116 in

b + 2s = 62

b + 2(3b - 116) = 62

Distribute

b + 6b - 232 = 62

combine like terms

7b = 294

Divide both sides by 7

b = 42

to find s plug in b = 42 into

b + 2s = 62

42 + 2s = 62

subtract 42 from both side

2s = 20

divide both sides by 2

s = 10

Answer:

A. y^3 + 27

Step-by-step explanation:

Ed22

Answer: A. y3+27

Step-by-step explanation:

Answer:

$127.75

Step-by-step explanation:

Multiply the cost by the area to find the total cost

Answer: its B.

Step-by-step explanation:

have a good day hope this help

Answer:

B.3

Step-by-step explanation:

just divide 6 by 2

Answer:

4x²+21x-2

  (OR)

2x²-x-6

Step-by-step explanation:

According to the Question,

Given, The difference Between two trinomials is x²-10x+2 & If one of the trinomials is 3x²-11x-4.

Let, Two Trinomials are P(x) = A  &  Q(x) = 3x²-11x-4

Then, P(x) - Q(x) = x²-10x+2

Put Value, We get

A - (3x²-11x-4) = x²-10x+2

A = x²-10x+2 + (3x²-11x-4)

A = x²-10x+2 + 3x²-11x-4

A = 4x²+21x-2

(OR)

If we Let, Two Trinomials are Q(x) = A  &  P(x) = 3x²-11x-4

Then, P(x) - Q(x) = x²-10x+2

Put Value, We get

(3x²-11x-4) - A = x²-10x+2

A = 3x²-11x-4 - (x²-10x+2)

A = 3x²-11x-4 - x²+10x-2

A = 2x²-x-6

Answer:

Step-by-step explanation:

According to the theorem, the angle measuring 110 is one-half the measure of the arc it intercepts. That means that the major arc (this arc of which I'm speaking) measures 110 * 2 = 220.

Since the outside of a circle, regardless of how big or small the circle is, has a degree measure of 360, then x = 360 - 220 so

x = 140°

Answer:

12x+12

Step-by-step explanation:

Multiply 3 to everything in the parenthesis

so it becomes

18+12x-15

=12x+12

Answer:

average revenue

gross profit

total revenue

net profit

marginal revenue

Step-by-step explanation:

Answer:

[tex]\bar x = 260.1615[/tex]

[tex]\sigma = 70.69[/tex]

The confidence interval of standard deviation is: [tex]53.76[/tex] to [tex]103.25[/tex]

Step-by-step explanation:

Given

[tex]n =20[/tex]

See attachment for the formatted data

Solving (a): The mean

This is calculated as:

[tex]\bar x = \frac{\sum x}{n}[/tex]

So, we have:

[tex]\bar x = \frac{242.87 +212.00 +260.93 +284.08 +194.19 +139.16 +260.76 +436.72 +355.36 +.....+250.61}{20}[/tex]

[tex]\bar x = \frac{5203.23}{20}[/tex]

[tex]\bar x = 260.1615[/tex]

[tex]\bar x = 260.16[/tex]

Solving (b): The standard deviation

This is calculated as:

[tex]\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}[/tex]

[tex]\sigma = \sqrt{\frac{(242.87 - 260.1615)^2 +(212.00- 260.1615)^2+(260.93- 260.1615)^2+(284.08- 260.1615)^2+.....+(250.61- 260.1615)^2}{20 - 1}}[/tex][tex]\sigma = \sqrt{\frac{94938.80}{19}}[/tex]

[tex]\sigma = \sqrt{4996.78}[/tex]

[tex]\sigma = 70.69[/tex] --- approximated

Solving (c): 95% confidence interval of standard deviation

We have:

[tex]c =0.95[/tex]

So:

[tex]\alpha = 1 -c[/tex]

[tex]\alpha = 1 -0.95[/tex]

[tex]\alpha = 0.05[/tex]

Calculate the degree of freedom (df)

[tex]df = n -1[/tex]

[tex]df = 20 -1[/tex]

[tex]df = 19[/tex]

Determine the critical value at row [tex]df = 19[/tex] and columns [tex]\frac{\alpha}{2}[/tex] and [tex]1 -\frac{\alpha}{2}[/tex]

So, we have:

[tex]X^2_{0.025} = 32.852[/tex] ---- at [tex]\frac{\alpha}{2}[/tex]

[tex]X^2_{0.975} = 8.907[/tex] --- at [tex]1 -\frac{\alpha}{2}[/tex]

So, the confidence interval of the standard deviation is:

[tex]\sigma * \sqrt{\frac{n - 1}{X^2_{\alpha/2} }[/tex] to [tex]\sigma * \sqrt{\frac{n - 1}{X^2_{1 -\alpha/2} }[/tex]

[tex]70.69 * \sqrt{\frac{20 - 1}{32.852}[/tex] to [tex]70.69 * \sqrt{\frac{20 - 1}{8.907}[/tex]

[tex]70.69 * \sqrt{\frac{19}{32.852}[/tex] to [tex]70.69 * \sqrt{\frac{19}{8.907}[/tex]

[tex]53.76[/tex] to [tex]103.25[/tex]

Given:

z be inversely proportional to the cube root of y.

When y =0.064, then z =3.

To find:

a) The constant of proportionality k.

b) The value of z when y = 0.125.​

Solution:

a) It is given that, z be inversely proportional to the cube root of y.

[tex]z\propto \dfrac{1}{\sqrt[3]{y}}[/tex]

[tex]z=k\dfrac{1}{\sqrt[3]{y}}[/tex]              ...(i)

Where, k is the constant of proportionality.

We have, z=3 when y=0.064. Putting these values in (i), we get

[tex]3=k\dfrac{1}{\sqrt[3]{0.064}}[/tex]

[tex]3=k\dfrac{1}{0.4}[/tex]

[tex]3\times 0.4=k[/tex]

[tex]1.2=k[/tex]

Therefore, the constant of proportionality is [tex]k=1.2[/tex].

b) From part (a), we have [tex]k=1.2[/tex].

Substituting [tex]k=1.2[/tex] in (i), we get

[tex]z=1.2\dfrac{1}{\sqrt[3]{y}}[/tex]

We need to find the value of z when y = 0.125.​ Putting y=0.125, we get

[tex]z=1.2\dfrac{1}{\sqrt[3]{0.125}}[/tex]

[tex]z=\dfrac{1.2}{0.5}[/tex]

[tex]z=2.4[/tex]

Therefore, the value of z when y = 0.125 is 2.4.

Proportional quantities are either inversely or directly proportional. For the given relation between y and z, we have:

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

[tex]p = kq[/tex]

where k is some constant number called constant of proportionality.

This directly proportional relationship between p and q is written as

[tex]p \propto q[/tex]  where that middle sign is the sign of proportionality.

In a directly proportional relationship, increasing one variable will increase another.

Now let m and n are two variables.

Then m and n are said to be inversely proportional to each other if

[tex]m = \dfrac{c}{n}[/tex]

or

[tex]n = \dfrac{c}{m}[/tex]

(both are equal)

where c is a constant number called constant of proportionality.

This inversely proportional relationship is denoted by

[tex]m \propto \dfrac{1}{n}\\\\or\\\\n \propto \dfrac{1}{m}[/tex]

As visible, increasing one variable will decrease the other variable if both are inversely proportional.

For the given case, it is given that:

[tex]z \propto \dfrac{1}{^3\sqrt{y}}[/tex]

Let the constant of proportionality be k, then we have:

[tex]z = \dfrac{k}{^3\sqrt{y}}[/tex]

It is given that when y = 0.064, z = 3, thus, putting these value in equation obtained above, we get:

[tex]k = \: \: ^3\sqrt{y} \times z = (0.064)^{1/3} \times (3) = 0.4 \times 3 = 1.2[/tex]

Thus,  the constant of proportionality k is 1.2. And the relation between z and y is:

[tex]z = \dfrac{1.2}{^3\sqrt{y}}[/tex]

Putting value y = 0.0125, we get:

[tex]z = \dfrac{1.2}{^3\sqrt{y}}\\\\z = \dfrac{1.2}{(0.125)^{1/3} } = \dfrac{1.2}{0.5} = 2.4[/tex]

Thus, for the given relation between y and z, we have:

Learn more about proportionality here:

https://brainly.com/question/13082482

Answer:

$180

Step-by-step explanation:

9% = 0.09

2000 * 0.09 = 180

Answer:

Peter needs to get 36 problems correct to get 12 stars

Step-by-step explanation:

for every 3 correct answers, Peter gets 1 star

1/3

if he wants 12 stars he will have to get 'x' amount of questions correctly

considering this is constant, 1/3 will have to equal 12/x

[tex]\frac{1}{3} = \frac{12}{x} \\\\1x = 36\\[/tex]

1x = x, so you don't need to do anything to 36

therefore the answer is that you need to get 36 problems correct to get 12 stars

Answer:

m = [tex]\frac{y+4}{x+5}[/tex]

Step-by-step explanation:

y-(-4) = m(x-(-5))

Simplify, distribute the negative sign outside of the parenthesis, remember negative times negative equals positive

y + 4 = m (x + 5)

Inverse operations, divide the equation by the value inside of the parenthesis

[tex]\frac{y+4}{x+5}[/tex] = m

Answer:

m=y+4x/x+5 your welcome !!

Answer:

I think $3620.51

Step-by-step explanation:

If i did it right, the equation should be something like this?

13,000(.88)^10

Answer:

[tex]P(X \geq 8)=22*10^{-4}[/tex]

Step-by-step explanation:

From The Question we are told that

Prob that population is colourblind [tex]P(C)=0.10[/tex]

Sample size [tex]N=25[/tex]

Generally the equation for Number of color blinds is mathematically given by

  [tex]P(X \geq 8)=\sum^{25}_{x=8}(25..x)(0.10)^x(0.90)^25-x[/tex]

  [tex]P(X \geq 8)=22*10^{-4}[/tex]

Answer:

1

Step-by-step explanation:

4^0

Any number raised to the 0 power is 1.

Answer:

1

Step-by-step explanation:

Anything raised to  0  is  1.

Answer:

D.

[tex]y = - 4x - 5[/tex]

Step-by-step explanation:

This is because the slopes are the same

Answer:

aef true and bcd false

hope u get well in your exams

Step-by-step explanation: