what did the teenage yardstick say to its parents

Answer:

The answer is below

Step-by-step explanation:

Let s(t) represent the amount of salt in the tank at time t. Therefore:

ds / dt = (rate of salt flowing into the tank) - (rate of salt going out of the tank)

[tex]\frac{ds}{dt}=[(0.08\ kg/L*6\ L/min)+(0.09\ kg/L*5\ L/min)]-(\frac{s\ kg}{1000\ L}*11\ L/min ) \\\\\frac{ds}{dt}=(0.48\ kg/min+0.45\ kg/min)-(\frac{11s}{1000}\ kg/min )\\\\\frac{ds}{dt}=0.93\ kg/min-\frac{11s}{1000}\ kg/min \\\\\frac{ds}{dt}=\frac{930-11s}{1000}\ kg/min \\\\\frac{ds}{930-11s}=\frac{1}{1000}dt\\\\Integrating:\\\\\int\limits { \frac{ds}{930-11s}} \, ds=\int\limits {\frac{1}{1000}} \, dt\\\\-\frac{1}{11}ln(930-11s)=\frac{t}{1000}+C\\\\multiply\ through\ by\ -11:[/tex]

[tex]ln(930-11s)= - \frac{11t}{1000}+A\\\\Take \ exponential:\\\\930-11s=e^{ - \frac{11t}{1000}+A}\\\\930-11s=C_1e^{ - \frac{11t}{1000}}\\\\11s=930-C_1e^{ - \frac{11t}{1000}}\\\\s=\frac{930-C_1e^{ - \frac{11t}{1000}}}{11} \\\\To \ find\ C_1,s(0)=0.Hence:\\\\0=\frac{930-C_1e^{ - \frac{11(0)}{1000}}}{11} \\\\0=930-C_1\\\\C_1=930\\\\s(t)=\frac{930-930e^{ - \frac{11t}{1000}}}{11} \\\\s(t)=930(\frac{1-e^{ - \frac{11t}{1000}}}{11})[/tex]

A) So, the required value is [tex]1.01-\frac{11S}{1000}[/tex].

B) The required value is [tex]\frac{1010}{11} (1-e^{-11/1000t} )[/tex]

A differential equation is an equation that contains one or more terms and the derivatives of one variable (i.e., dependent variable) with respect to the other variable (i.e., independent variable).

                                                    [tex]\frac{dy}{dx} =f(x)[/tex]

(A) Let [tex]S(t)[/tex] denotes the number of kg of the salt in the tank at the time [tex]t[/tex] minutes.

Then,

[tex]\frac{ds}{dt}=[/tex](rate of salt in to tank)-(rate of salt of tank)

[tex]\frac{ds}{dt}=\left ( 0.08\times 0.09\times 5 \right )-\left ( \frac{s\left (t\right )}{1000}\times 11 \right ) \\ \therefore \frac{ds}{dt}=1.01-\frac{11S}{1000}[/tex]

(B)

[tex]\frac{ds}{dt}=\frac{101}{100}-\frac{11S}{1000} \\ \Rightarrow \frac{ds}{dt}=\frac{1010-11S}{1000} \\ \Rightarrow \frac{ds}{1010-11S}=\frac{dt}{1000}[/tex]

Integrating we get,

[tex]-\frac{1}{11}I_n|1010-11S|=\frac{t}{1000}+In \ C_1 \\ \Rightarrow 1010-11S=C_1e^{-11/1000t} \\ S(t)=\frac{1010-C_1e^{-11/1000t}}{11}[/tex]

Initially, [tex]S(0)=0\\\Rightarrow C_1=1010[/tex]

Then the required solution is,

[tex]\therefore S(t)=\frac{1010}{11} (1-e^{-11/1000t} )[/tex]

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Answer:

x =(-8+√-32)/6=(-4+2i√ 2 )/3= -1.3333+0.9428i

Step-by-step explanation:

D. A dashed line is used when the inequality is strict ​( < or > ​)

A linear inequality in two variables is obtained by taking a linear equation in two variables, and replacing the equality sign with any one of the four inequality signs: <,>,=<,>=.

The graphed region of points satisfying the inequality is always half of the plane bounded by the corresponding line.

When the inequality is [tex]\leq[/tex] or [tex]\geq[/tex], the line is included. Otherwise, the line is excluded.

So, A dashed line is used when the inequality is strict ​( < or > ​) is not true about the boundary line in the graph of a linear inequality in two​ variables

Therefore, the correct option is D.

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Answer:

There is no picture... But here is a representation of the inequality on a graph

The graph 2x - 5y < 3 cut the x-axis at the point (3,0) and the y-axis at the point (0,-0.6).

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.

Given inequality is 2x - 5y <3. A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

When the inequality 2x - 5y < 3 is plotted on the graph it covers the region which is less than the line 2x - 5y < 3. The graph cut the x-axis at the point (3,0) and the y-axis at the point (0,-0.6).

The graph of the given inequality is attached with the answer below.

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Answer:

8 1/8

Step-by-step explanation:

I used a calculator....

(hope this helps :P)

Answer:

1. 55%

2. 190%

Step-by-step explanation:

1a. set up an expression.

33/60 = x/100

33 out of 60 is the 33 pounds out of the 60 weight limit. The x is what you're solving for, and the 100 is the given percent, because the percent is always going to be out of 100%.

1b. do cross multiplication; so do 33*100, which equals 3300

1c. divide; 3300 divided by 60, which equals 55.

For the second problem, do the same thing. your expression should be 114/60 = x/100

Answer:

-4/10+(-7/10)= -1 1/10(the bottom left one)

Step-by-step explanation:

starts from 0 and subtract 4/10.  From there you subtract 7/10 more.

Answer:

Step-by-step explanation:

Given

The two sides and the included angle - SAS

Correct option is

Answer:

5 thirds

Step-by-step explanation:

Make 1 2/3 into a improper fraction. Now you have 5/3. 5/3-(1/3*5)=0

Therefore, 5x1/3=5/3=1 2/3

Answer:

This guy is wrong. 1 2/3 is equal to 5/3. But that is not the answer(like that dummy above said)

The Question is asking "How many 1/3's are in 1 2/3" (5/3)

The answer is 5, not 5/3's.

Answer:

18,700

Step-by-step explanation:

Answer:

18,700

Step-by-step explanation:

i hope this helps

Answer:

the price Mr. Quick paid is=$1343

I think I can help you with this

you can easily solve this by using a rule of three

Step one

find the discount value  if

$1580⇒  100%

$x? ⇒ 15%

do the relation

the discount is $237

the price Mr. Quick paid is

the price Mr. Quick paid is=regular price - discount

the price Mr Quick paid is=$1580-$237

the price Mr Quick paid is=$1343

I hope it helps, Have a great day!!! :)

Step-by-step explanation:

Answer:

No.

Because,24/4=5.25

Answer:

Yes

Step-by-step explanation:

All rational numbers have endings. Since 25/4=6.25 it is rational

Answer:

B is the correct answer

Step-by-step explanation:

just did this problem

Answer:

212272.71

Step-by-step explanation:

we have the following equation (for interesting that compound yearly)

PV(1+i)^n

200000(1+.015)^4

212272.71

The total amount of interest Katy will get at the end of 4 years is £12,272.71

The steps are as follow:

p = £200 000

r = 1.5%

n = 4 years

A = p(1+r/100)ⁿ

A = 200000(1+1.5/100)⁴

A = 212,272.71 £

C.I. = A - p

C.I. = 212,272.71 - 200,000

C.I. = £12,272.71

So the  total amount of interest Katy will get at the end of 4 years is £12,272.71

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Answer:

m = 18

k = 4

g = 50

s = 18

y = 9

f = 19

Step-by-step explanation:

Answer:

21.96 ; 24.72

Step-by-step explanation:

Given that :

Give the equation:

A(t) = 700(1.03)^t

A.)

Average rate of change over the first 4 years ;

(t=0 to t=4)

At t = 0

A(0) = 700(1.03)^0 = 700

A(1) = 700(1.03)^1 = 721

A(2) = 700(1.03)^2 = 742.63

A(3) = 700(1.03)^3 = 764. 9089

A(4) = 700(1.03)^4 = 787.856167

[(721 - 700) + (742.63 - 721) + (764.9089 - 742.63) + (787.856167 - 764.9089)] / 4

= 87.856167 / 4

= 21.96404175

= 21.96

Over the 2nd 4 years :

A(4) = 700(1.03)^4 = 787.856167

A(5) = 700(1.03)^5 = 811.49185201

A(6) = 700(1.03)^6 = 835.8366075703

A(7) = 700(1.03)^7 = 860.911705797409

A(8) = 700(1.03)^8 = 886.73905697133127

[(811.49185201 - 787.856167) + (835.8366075703 - 811.49185201) + (860.911705797409 - 835.8366075703) + (886.73905697133127 - 860.911705797409)] / 4

= 98.88288997133127 / 4

= 24.72

Answer:

excuss me where the picture

Step-by-step explanation:

Answer:

Step-by-step explanation:

Reflect over the Y axis, then translate (x+[-2], y+[-3])

The composition of transformations that map ABCD to EHGF will be [(x + 6), (y + 1)].

Change is referred to as transformation. As a result, a geometric transformation entails making modifications to any geometric shape.

Vertices of the quadrilateral ABCD having coordinate A,B,C,D are  (-5, 2),(-3, 4), (-2, 4),(-1, 2) respectively.

The image quadrilateral A'B'C'D' is formed by reflecting the supplied quadrilateral ABCD across the x-axis.

The rule for a point's reflection across the x-axis is:

(x, y) → (x , -y)

The picture point A' coordinates will be,

A(-5, 2) → A'(-5, -2)

Point E is produced by translating point A', as shown in the diagram. The rule for translating a point by h units right and k units up is as follows:

A'(x+h, y+k) → E(x', y')

By comparing coordinates of A' and E,

-5 + h = 1

h = 6

-2 + k = -1

k = 1

That is to say, the translation rule will be:

[(x + 6), (y + 1)]

Hence, the composition of transformations that map ABCD to EHGF will be [(x + 6), (y + 1)].

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2/45 in simplest form

Answer:

b

Step-by-step explanation:

Answer:

true.

false

true.

false.

Step-by-step explanation:

1. The domain (x-value) of a function is (-∞, +∞) unless there is some reason for it not to be. No matter what we make x, we do not wind up with something forbidden in the real-number coordinate plane, like a zero denominator or a square root of a negative number, so the domain for x is all real numbers. True.

2. The statement says the range (the y-value) of the function must always be more than zero. There is no particular reason to belive that. If x = -10, then x³ + 6 = -1000 + 6 = -994, which is less that zero. False.

3. We get the y-intercept by making x equal zero. In tha case y = 0³ + 6 = 6. The y-intercept always has an x-coordinate of zero, so the point is (x, y) = (0, 6). True.

4. If a function has symmetry about the origin point, then replacing y with -y and x with -x will get you an equation equivalent to the original. let's try it.

-y = 3(-x)³ + 6    now lets see what happens it we let x = 2

For the original equation:   y = 3(2)³ + 6 = 3(8) + 6 = 24 + 6 = 30

Now we try the test equation:  -y = 3(-2)³ + 6 = 3(-8) + 6 = -24 + 6 = -18

                                               So   -y = -18

                                                So    y = 18

The first equation and the test equation are not equivalent, as they do not yield the same results for the same value of x.

Thus, the origin is not a point of symmetry. False.

I am attaching a picture of this function's graph so you can see the actual point of symmetry is (0, 6), which is also the y-intercept. I made it on Desmos dot com, which is free for everyone.

The Domain  = (-∞, ∞) and Range = (-∞, ∞), y-intercept occurs at (0, 6) and the origin is not a point of symmetry.

Given the function [tex]f(x)=3x^3 + 6[/tex]

Domain and range are the value of input and output that the function exists.

For the given function, the domain and range exist on all real numbers.

Domain  = (-∞, ∞) and Range = (-∞, ∞)

The y-intercept occur at (x) = 0

g(0)= 3(0)^3 + 6

g(0) = 6

Hence the Domain  = (-∞, ∞) and Range = (-∞, ∞), y-intercept occurs at (0, 6) and the origin is not a point of symmetry. False.

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Answer:

160

Step-by-step explanation:

Answer:

15 nickels and 13 dimes

Step-by-step explanation:

5n + 10d = 205 cents

n + d = 28

n = 28-d

5(28-d) +10d = 205

140 -5d + 10d = 205

5d = 65

d = 13

n = 28-d = 28-13 = 15

5n = 5(15) = 75

10d = 10(13) = 130

75+130=205

[tex] \frac{132 }{2?} = 66[/tex]

Answer:

41

Step-by-step explanation:

Ok so you would divide 1,066 by 26 which would equal 41. Have a great day!

Answer:

105

Step-by-step explanation:

A straight line is 180 degrees so 180-75=105

Answer:

x= 105 degrees

Step-by-step explanation:

We know that the sum of x and 75 degrees is equal to 180 degrees.

So that means that x= 180-75 or x=105 degrees