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:

Answer:

Since i m not sure of the equation i have dont both possible ways :)

Step-by-step explanation:

b)

(5/9) ÷ 5

    [tex]= \frac{5}{9} \div 5\\\\=\frac{\frac{5}{9}}{5}\\\\=\frac{5}{9 \times 5}\\\\=\frac{1}{9}[/tex]

5/(9÷5)

   [tex]=\frac{5}{9 \div5}\\\\= \frac{5}{\frac{9}{5}}\\\\=\frac{5 \times 5}{9}\\\\=\frac{25}{9}[/tex]

Answer:

x = 28

Step-by-step explanation:

HFG = EFI

6x - 4 = 164

6x = 164 + 4

6x = 168

x = 168/6

x = 28

Answer:

[tex]{ \tt{simple \: interest = p \times r \times t}} \\ = 10000 \times 15\% \times 5 \\ = £7500[/tex]

Answer:

PE/SE = 5.02×10¹

Step-by-step explanation:

Sun-Earth (SE) = 93×10⁶ miles

Pluto-Earth (PE) = 4.67×10⁹ miles

so, PE/SE = (4.67×10⁹) / (93×10⁶) = (4.67×10³)/93 =

= 50.215053763440860215... =

= 5.02×10¹ / 1 or simply 5.02×10¹

in other words, Pluto is a little bit more than 50 times farther away from Earth, than Earth is from the Sun.

Step-by-step explanation:

hope it is helpful to you

stay safe happy and healthy

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\mathsf{\dfrac{x}{3}-2=6}[/tex]

[tex]\mathsf{= \dfrac{1}{3}x - 2 = 6}[/tex]

[tex]\textsf{ADD 2 BOTH SIDES}[/tex]

[tex]\mathsf{\dfrac{1}{3}x - 2 + 2 = 6 + 2}[/tex]

[tex]\textsf{CANCEL out: -2 + 2 because that gives you 1}[/tex]

[tex]\textsf{KEEP: 6 + 2 because that helps solve for x}[/tex]

[tex]\mathsf{6 + 2 = \boxed{\bf 8}}[/tex]

[tex]\mathsf{NEW \ EQUATION: \dfrac{1}{3}x = 8}[/tex]

[tex]\textsf{MULTIPLY 8 to BOTH SIDES}[/tex]

[tex]\mathsf{3\times\dfrac{1}{3}x=3\times8}[/tex]

[tex]\mathsf{CANCEL\ out: \ 3 \times \dfrac{1}{3} \ because \ that \ gives \ you \ 1}[/tex]

[tex]\mathsf{KEEP: \ 3 \times 8 \ because \ that\ gives \ you \ the \ value \ of \ x}[/tex]

[tex]\mathsf{\boxed{\bf x}= 3\times8}[/tex]

[tex]\mathsf{3\times8 = \boxed{\bf x}}[/tex]

[tex]\boxed{\boxed{\large\textsf{Answer: \huge \bf x = 24}}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

17

Step-by-step explanation:

Properties used:-

All sides of rhombus are equal therefore in the triangles

EQUAL SIDE OPPOSITE TO ANGLES, ANGLES BECOME EQUAL

then we use alternate interior angles

Then we get,

3x-11=x+23

2x=34

x=17

Answer:

bad gvkvkgcnhvvjzadhljang

v

gjddkfzutwdjtabkf

Answer:

m(∠y) = 64°

Step-by-step explanation:

From the figure attached,

m(∠e) = 90°

m(∠b) + 67° = 180° [Linear pair of angles]

m(∠b) = 180 - 67

          = 113°

m(∠c) + 75° = 180°  [Linear pair of angles]

m(∠c) = 105°

m(∠a) = m(∠d)

By the property of a polygon,

Sum of the interior angles of a polygon is given by,

Sum of interior angles = (n - 2) × 180°

Here, n = number of sides of the polygon

For n = 5,

Sum of interior angles = (5 - 2)×180°

                                     = 540°

m(∠a) + m(∠b) + m(∠c) + m(∠d) + m(e) = 540°

2m(∠d) + 113° + 105° + 90° = 540°

2m(∠d) + 308 = 540°

2m(∠d) = 540 - 308

m(∠d) = 116°

m(∠d) + m(∠y) = 180°

m(∠y) + 116° = 180° [Linear pair of angles]

m(∠y) = 64°

Answer:

Step-by-step explanation:

To calculate the mode, we simply count the number of times that each value appears in the data set and then find the value that appears most often.

A data set can have more than one mode if there is more than one value with the highest count. For example, both 2 and 3 are modes in the data set {1; 2; 2; 3; 3}.

Example of a set of data having more than one node is {1; 2; 2; 3; 3}.

What is Node?

An example S of the data type node. set is a subset of the nodes of a graph G. S is said to be valid for the nodes of G.

Given,

To calculate the mode, we simply count the number of times that each value appears in the data set and then find the value that appears most often.

Now,

A data set can have more than one mode if there is more than one value with the highest count.

For example, both 2 and 3 are modes in the data set {1; 2; 2; 3; 3}.

Learn more about node,

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Given:

The frequency distribution table is:

Values of variable X        Frequency

              32                                2    

              37                                5

              46                                3

              48                                9

To find:

The mode of the given data set.            

Solution:

We know that mode is the most frequent value of the data set.

In the given data set highest frequency is 9 that is corresponding to the value 48.

Therefore, the mode of the given data set is 48. Hence, the correct option is (b).

Answer:

7x + 3y.

Step-by-step explanation:

7 pencils cost 7x cents and 3 erasures cost 3y cents.

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:

Yes, the result does not have statistical significance

Yes, the result has practical significance

Step-by-step explanation:

An experiment or claim may be said to be statistically significant if it's occurence is likely not due to chance for a certain level of stated significance. From the scenario described, it is stated that if vegetarian diet has no effect on blood, then the result obtained wipukd likely occur in less Than 1 of 100 ; this is < 0.01. This means that the effect of vegetarian diet on blood could not have occurred by chance. Hence, result is statistically significant.

The result does have practical significance too, since there is a distinctive difference in blood pressure of non - vegetarians(138mmHg) and Vegetarians (124mmHg).

Answer:

4 in

Step-by-step explanation:

area right : Ar = 5x

area left : Al = 11x

area top : At = 5x

area bottom : Ab = 13x

area front : Afr = rectangle 13×11 minus area triangle

triangle (right-angled) : (11-5)×(13-5)/2 = 24 in²

Afr = 13×11 - 24 = 119 in²

area back = area front = 119 in²

sloped area : As = 10x

all individual shapes in the surface of the object are rectangles except the 2 areas in the front and in the back, where we had to calculate the complete rectangle and then subtract the cut off triangle area.

so, in total we have

414 = 5x+11x+5x+13x+119+119+10x = 44x + 238

176 = 44x

x = 4 in

Answer:

Answer:

express the following equation as two statement each using the word varies and proportional i) v(rl=4/3

Answer:

46

Step-by-step explanation:

Just multiply 6 by 7 2/3 to get 46.

Answer:

The answer is 46 bags

Step-by-step explanation:

Have a good summer!!!

Answer:

add a picture so i can see .

Step-by-step explanation:

Answer:

82

Step-by-step explanation:

Answer:

y = 1/3x -1

Step-by-step explanation:

The slope is  y2 - y1 / x2 - x1

y2 is 1

y1 is -1

x2 is 6

x1 is 0

So it is 1 - (-1) / 6 - 0, or 2/6, or 1/3

The slope is 1/3.

The y-intercept is the place where x is 0. It shows the y-intercept here as

(0, -1),  The y-intercept is  -1

Slope form is y = mx + b. m is the slope, 1/3, and b is the y-intercept, -1

So the equation is: y = 1/3x -1

Answer:

32.25

Step-by-step explanation:

1 quart = 32 fluid ounces

12 months = 1 year

86 quarts/1 month = 1032 quarts/12 months

1032/32 = 32.25 fluid ounces

Answer:

[tex]xy^\frac{2}{9} = x*\sqrt[9]{y^2}[/tex]

Step-by-step explanation:

Given

[tex]xy^\frac{2}{9}[/tex]

Required

The equivalent expression (see attachment)

We have:

[tex]xy^\frac{2}{9}[/tex]

Split

[tex]xy^\frac{2}{9} = x*y^\frac{2}{9}[/tex]

Apply the following laws of indices

[tex]y^\frac{m}{n} = \sqrt[n]{y^m}[/tex]

So, we have:

[tex]xy^\frac{2}{9} = x*\sqrt[9]{y^2}[/tex]

Hence (d) is correct

Answer:

Its D.

Step-by-step explanation:

Just took the quiz on EDGE2022

To find:

(a) Equation for the sphere of radius 5 centered at the origin in cylindrical coordinates

(b) Equation for a cylinder of radius 1 centered at the origin and running parallel to the z-axis in spherical coordinates

Solution:

(a) The equation of a sphere with center at (a, b, c) & having a radius 'p' is given in cartesian coordinates as:

[tex](x-a)^{2}+(y-b)^{2}+(z-c)^{2}=p^{2}[/tex]

Here, it is given that the center of the sphere is at origin, i.e., at (0,0,0) & radius of the sphere is 5. That is, here we have,

[tex]a=b=c=0,p=5[/tex]

That is, the equation of the sphere in cartesian coordinates is,

[tex](x-0)^{2}+(y-0)^{2}+(z-0)^{2}=5^{2}[/tex]

[tex]\Rightarrow x^{2}+y^{2}+z^{2}=25[/tex]

Now, the cylindrical coordinate system is represented by [tex](r, \theta,z)[/tex]

The relation between cartesian and cylindrical coordinates is given by,

[tex]x=rcos\theta,y=rsin\theta,z=z[/tex]

[tex]r^{2}=x^{2}+y^{2},tan\theta=\frac{y}{x},z=z[/tex]

Thus, the obtained equation of the sphere in cartesian coordinates can be rewritten in cylindrical coordinates as,

[tex]r^{2}+z^{2}=25[/tex]

This is the required equation of the given sphere in cylindrical coordinates.

(b) A cylinder is defined by the circle that gives the top and bottom faces or alternatively, the cross section, & it's axis. A cylinder running parallel to the z-axis has an axis that is parallel to the z-axis. The equation of such a cylinder is given by the equation of the circle of cross-section with the assumption that a point in 3 dimension lying on the cylinder has 'x' & 'y' values satisfying the equation of the circle & that 'z' can be any value.

That is, in cartesian coordinates, the equation of a cylinder running parallel to the z-axis having radius 'p' with center at (a, b) is given by,

[tex](x-a)^{2}+(y-b)^{2}=p^{2}[/tex]

Here, it is given that the center is at origin & radius is 1. That is, here, we have, [tex]a=b=0,p=1[/tex]. Then the equation of the cylinder in cartesian coordinates is,

[tex]x^{2}+y^{2}=1[/tex]

Now, the spherical coordinate system is represented by [tex](\rho,\theta,\phi)[/tex]

The relation between cartesian and spherical coordinates is given by,

[tex]x=\rho sin\phi cos\theta,y=\rho sin\phi sin\theta, z= \rho cos\phi[/tex]

Thus, the equation of the cylinder can be rewritten in spherical coordinates as,

[tex](\rho sin\phi cos\theta)^{2}+(\rho sin\phi sin\theta)^{2}=1[/tex]

[tex]\Rightarrow \rho^{2} sin^{2}\phi cos^{2}\theta+\rho^{2} sin^{2}\phi sin^{2}\theta=1[/tex]

[tex]\Rightarrow \rho^{2} sin^{2}\phi (cos^{2}\theta+sin^{2}\theta)=1[/tex]

[tex]\Rightarrow \rho^{2} sin^{2}\phi=1[/tex] (As [tex]sin^{2}\theta+cos^{2}\theta=1[/tex])

Note that [tex]\rho[/tex] represents the distance of a point from the origin, which is always positive. [tex]\phi[/tex] represents the angle made by the line segment joining the point with z-axis. The range of [tex]\phi[/tex] is given as [tex]0\leq \phi\leq \pi[/tex]. We know that in this range the sine function is positive. Thus, we can say that [tex]sin\phi[/tex] is always positive.

Thus, we can square root both sides and only consider the positive root as,

[tex]\Rightarrow \rho sin\phi=1[/tex]

This is the required equation of the cylinder in spherical coordinates.

Final answer:

(a) The equation of the given sphere in cylindrical coordinates is [tex]r^{2}+z^{2}=25[/tex]

(b) The equation of the given cylinder in spherical coordinates is [tex]\rho sin\phi=1[/tex]

Answer:

83.5%

Step-by-step explanation:

90% × 20% + 85% × 30% + 80%× 50%

Answer:

A. using a bar graph where one has a length of 86 units and one bar has a length of 81 units

Step-by-step explanation:

Took the quiz. The usual.

The optimal method to represent this data is with a "bar graph", with one bar 86 units long and the other 81 units long. which is the correct answer that would be an option (A).

A graph can be defined as a pictorial representation or a diagram that represents data or values.

The best way to represent this data is using a "bar graph" where one bar has a length of 86 units and one bar has a length of 81 units.

This is because a bar graph is used to compare the sizes of different data points, and the length of each bar represents the value of the data point.

In this case, the average quiz score is 86% and the average test score is 81%, so the length of the bar representing the quiz score would be longer than the length of the bar representing the test score.

Thus, Option A correctly describes the use of a bar graph to represent the data, so it is the correct answer.

Learn more about the graphs here:

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Answer:

82.31

Step-by-step explanation:

I believe this is correct, if it isn't feel free to let me know and I will fix it. I'm sorry in advance if this is incorrect.