Don’t mind the check mark

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]

Learn more about the topic of Differential Equation: https://brainly.com/question/24546081

Answer:

5 1/2- 1 2/7

11/2-9/7

(11×7-9×2)/14

59/14

4 3/14

Answer:[tex]4x^{3}[/tex][tex]\sqrt[3]{25x^{2} }[/tex]

Step-by-step explanation:

[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the Financials.

Hence,according to the statement given above, the correct answer is

option 1.)

===> Manipulating interest rates and acting as a lender to the banks.

Answer:

24.23 ; 13.47 ; 0.782 ; p value < 0.00001 ;7.45

Step-by-step explanation:

Given that :

ΣX = 3,416, ΣY = 1,899, SDX = 8.84, SDY = 4.70, ΣZXZY = 109.416

Sample size, N = 141

Mean of X:

£X / N = 3416 / 141 = 24.23

Mean of Y:

£Y / N = 1899 / 141 = 13.47

B.) Correlation between the 2 variables :

£ZXZY / N - 1

= 109.416 / 140

= 0.782

C.)

Level of significance and p value :

T = [Rsqrt(n-2)] ÷ sqrt(1 - R²)

T = [0.782 * sqrt(139)] ÷ sqrt(1-0.782^2)

T = 14.79

P value from Tscore calculator

Df = 141 - 2 = 139 ; α = 0.05

Pvalue = 0.00001

Pvalue < α ; Hence, a significant positive relationship exists.

To obtain regression model :

Slope = £ZXZY / SDX²

m = 109.416 / 8.84^2 = 1. 4

yintercept = meanY - slope*x

yintercept = 13.47 - 1.4*24.3

yintercept = - 20.55

Equation in slope intercept form:

y = mx + c

y = 1.4x - 20.55

For x = 20

y = 1.4(20) - 20.55

y = 7.45

Answer:

The zero means nothing, it's just being used as a placeholder, like .7 and 0.7 mean the same thing.

good luck, i hope this helps :)

4.730 and 4.73 are equivalent because 0 has no value therefore if 0 has no value and you take away the 0 than you get 4.73 and 4.73.

Answer:

27

Step-by-step explanation:

The formula for the volume of a cube is given as [tex]V=s^{3}[/tex]. if s=3in, then V=27inches cubed.

Answer:

94

Step-by-step explanation:

Answer:

x = 12

Step-by-step explanation:

Based on the altitude theorem of a right triangle, since x is the altitude/height, therefore,

x = √(4*36)

x = √144

x = 12

788% gdkgdkgdkgdkgdkgdkgdk

Answer:

Step-by-step explanation:

I am pretty sure it’s 4/9 * 6/5 = x

( I think it’s this )

(espero que esto ayude) La respuesta es D que es [tex]\frac{2}{3}[/tex]

Answer:

okkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk

Step-by-step explanation:

answer mujha nahi pata aaaaaaaaaàaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

Answer:

x = 14

Step-by-step explanation:

These angles are vertical each other, another way of saying they are opposite each other in an X. Since these angles are vertical, they are equal!

60 = 5x - 10 | Given, from here on is basic algebra

70 = 5x | Add 10 to both sides

14 = x | Divide both sides by 5

Answer:

14√2

Step-by-step explanation:

This is a 45-45-90 triangle

Because both of the angles are the same all sides, but the hypotonouse are the same

this means that the other length is 14 too

we can use a²+b²=c² to solve

14²+14²=c²

=

392=c²

√392=c

√392=14√2

Answer:

im not sure sorry try asking an addalt

Step-by-step explanation:

nu4

Answer:

C≈18.85 ft

this is the answer I think

Answer:

The answer is 18.85ft

Step-by-step explanation:

To explain is the radius is 3ft and the circumference is 2nr

To show how to solve will be like this and look down here C=2πr=2·π·3≈18.84956ft

18.84956ft round to the nearest is 18.85ft

Answer:

250

Step-by-step explanation:

52%-> 130

100%-> 250

Answer: 2

Step-by-step explanation:

as H=20 and W=10

So H=constant.(W)

H=2(10)

H=20

So constant is 2

Answer:

the answer is 5

Step-by-step explanation:

15/3=5

2/2=1

5×1=5

Answer:

5

Step-by-step explanation:

First multiply the numerators and denominators.

15 x 2 = 30

3 x 2 = 6

Then divide

30/6 = 5

Answer:

s

Step-by-step explanation:

s

Answer:

y≥-1/3+2

y≥2/3-2

Step-by-step explanation:

Answer:

130

Step-by-step explanation:

585/4.5=130

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

Learn more about Compound interest here:

https://brainly.com/question/24924853

#SPJ2

Answer:

[tex]x=10[/tex]

Step-by-step explanation:

We can use the Pythagorean Theorem:

[tex]a^2+b^2=c^2[/tex]

The two legs are x and (x + 14) and the hypotenuse is (x + 16). Therefore:

[tex](x)^2+(x+14)^2=(x+16)^2[/tex]

Expand:

[tex]\displaystyle x^2+(x^2+28x+196)=x^2+32x+256[/tex]

Combine like terms:

[tex]2x^2+28x+196=x^2+32x+256[/tex]

Subtract the right from the left:

[tex](2x^2+28x+196)-(x^2+32x+256)=0[/tex]

Subtract:

[tex]x^2-4x-60=0[/tex]

Factor:

[tex](x-10)(x+4)=0[/tex]

Zero Product Property:

[tex]x-10=0\text{ or } x+4=0[/tex]

Solve:

[tex]\displaystyle x = 10 \text{ or } x = -4[/tex]

The x cannot be negative since a side cannot measure -4. So, our only answer is:

[tex]x=10[/tex]

So, the legs are 10 and 24 with the hypotenuse being 26.

Answer:

0,55

Step-by-step explanation:

1 pound= 16 ounces

8.82 ounces= 8.82/ 16= 0.55 pound

[tex]2c^2-14c+20=0 \\ c^2-7c+10=0 \\ (c-2)(c-5)=0 \\ c_1=2,c_2=5[/tex].

Answer:

the slope of the function is 40 which represents the monthly fee to remain a mrmber.

Step-by-step explanation:

THE SLOPE IS THE COEFFICIENT OF THE INDEPENDENT VARIABLE

C= 40t + 125