a tank with a capacity of 400 l is full of a mixture of water and sugar with the concentration 0.05 g/l. in order to reduce the concentration of sugar, fresh water is pumped into the tank at a rate of 4 l/s. the mixture is kept stirred and is pumped out at a rate of 10 l/s. find the amount of sugar in the tank as a function of time.

The equation of the line is 3y = -4x + 18 and the Graph can draw as given in the picture.

The slope-intercept form a line is given by  

where m is the slope of a line and c is the y-intercept.

Here we use the Slope intercept form to find the line of the equation by using the equation we will draw the graph of the line

Here we have

Slope of line = -4/3

The point of the line

As we know y = mx + c is the line Here m is the slope of the line

From the given data, m = -4/3

=> y = (-4/3)x + c

=> 3y = -4x + 3c

Given that the point on the line is (-6, 2)

=> 3(2) = -4(-6) + 3c

=> 6 = 24 + 3c

=>  3c = 18

=> c = 6

Therefore,

The equation of the line is 3y = -4x + 18 and the Graph can draw as given in the picture.

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The fractions reduced to standard form are -2/5, 1/5, 1/2 and 5/11 for 1), 2), 3), and 4) respectively

To reduce a fraction to standard form, you need to divide both the numerator (the top number) and the denominator (the bottom number) by their greatest common divisor (GCD). The GCD is the largest number that can be evenly divided into both the numerator and the denominator.

Given:

1) -18/45

The GCD of 18 and 45 is 9. Thus:

-18/45 = -2/5

2) -3/-15

The GCD of 3 and 15 is 3. Thus:

-3/-15 = 1/5

3) 28/56

The GCD of 28 and 56 is 28. Thus:

28/56 = 1/2

4) 45/99

The GCD of 45 and 99 is 9. Thus:

45/99 = 5/11

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1)-6/15

2)1/5

3)1/2

4)5/11

1) -18/45

⇒-6/15

2)-3/-15

⇒-1/-5

⇒1/5

3)28/56

⇒4/8

⇒1/2

4)45/99

⇒15/33

⇒5/11

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The time since dinosaurs became extinct is roughly equal to 10⁶ average human lifespans

From the question, we have the following parameters that can be used in our computation:

Rewrite the exponents properly

So, we have the following representation

This means that

Number of times = Time since dinosaurs became extinct/Average human lifespan

Substitute the known values in the above equation, so, we have the following representation

Number of times = 2.4 x 10¹⁰/2.4 x 10⁴

Evaluate the quotient

Number of times = 10⁶

Hence, the number of times is 10⁶

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Answer:

Step-by-step explanation:

Writing this out would be 9+7x=16. minus 9 from 16 which would equal 7 so x=1 because 7+9=16

Sample size  123  is needed to estimate the mean weight to within 135 lbs with a 99% confidence level

What is confidence interval?

In statistics, the probability that a population parameter will fall between a set of values for a predetermined percentage of the time is referred to as the confidence interval. Analysts frequently employ confidence ranges that include 95% or 99% of anticipated observations.

Z(α/2) at 99% confidence level = 2.576

λ = 579

margin of error = ( Z(α/2) * λ ) / √n = 135

                        (2.576 * 579) / √n = 135

On simplifying, n ≈ 123

So, sample size  123  is needed to estimate the mean weight to within 135 lbs with a 99% confidence level

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Answer:

YX = 5.1

if the answer is rounded to the nearest 10th then:

YX = 5.2

Step-by-step explanation:

⭐What is the circumcenter of a triangle?

⭐What are the properties of a circumcenter?

Let's use the properties of a circumcenter to solve for YX.

Because the circumcenter is the intersection of the perpendicular bisectors :

If Y is the circumcenter, then XU = SX.

If Y is the circumcenter, then ∠UXY = 90°.

If ∠UXY = 90°, then ∠SXY = 90°.

If SX = 13, then XU = 13 .

If YT = 14, then YU = 13.

If YU = 13, then YS = 13.

ΔUXY and ΔSXY. YX is the height of both triangles.

Therefore, we can use the Pythagorean Theorem ([tex]c^2 = a^2 + b^2[/tex]) to solve for YX.

Set up the equation. Let c = the hypotenuse and let a and b = the legs:

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

[tex]14^2 = 13^2 + YX^2[/tex]

[tex]196 = 169 + XY^2[/tex]

[tex]27 = XY^2[/tex]

[tex]\sqrt{27} = \sqrt{XY^2}[/tex]

∴ 5.1/5.2 = XY

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Answer:

The cake cost $6.00

Step-by-step explanation:

Let c = the cost of the cake

Let t =  the cost of the tea

c = 2t

c + 5t = 21  Substitute 2t for c

2t + 5t = 21  Combine like terms

7t = 21  Divide both sides by 7

[tex]\frac{7t}{7}[/tex] = [tex]\frac{21}{7}[/tex]

t = 3  

A cup of tea costs $3.00

c = 2t  Substitute 3 for t

c = 2(3)

c = 6

A cake costs $6.00

Answer:

Cake: £6

Step-by-step explanation:

1c = 2t             Eq. 1

1c + 5t = 21      Eq. 2

c = cost of a cake

t = cost of a cup of tea

Replacing Eq. 1 in Eq 2:

2t + 5t = 21

7t = 21

t = 21/7

t = 3

From Eq. 1:

c = 2t

c = 2*3

c = 6

Check:

From Eq. 2:

c + 5t = 21

6 + 5*3 = 21

6 + 15 = 21

Answer:

A and D

Step-by-step explanation:

so sorry im in school

x+y=4

 -y.  -y

x=4-y

4-y-y=2

4-2y=2

-4      -4

-2y= -2

/-2.   /-2

y=1

x+1=4

  -1 -1

x=3

so A and D is correct

The angle 2 is 149° , angle 3 is 31° , angle 4 is 149°

What is the name for two opposing angles?

Angles where two lines cross that are directly opposite one another are known as opposing angles. The vertex, where the lines come together to produce the angle, is the location of the junction. Vertical angles are another name for opposite angles.

Given that :
Angle 1 is = 31°

Angle 2 is = 180 - 31 = 149° (As in a line total angle is 180°)

Angle 3 is = 31° (As equal opposite angle with angle 1)

Angle 4 is = 149°  (As equal opposite angle with angle 2)

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The solution is

a) The compound interest for the second period is $ 2.01 and the amount after the second period is $ 404.01

b) The compound interest for the first period is $ 114.125 and the amount is $ 18,374.125

The compound interest for the second period is $ 114.83828125 and the amount after second period is $ 18,488.96

What is Compound Interest?

Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.

The formula for calculating Compound Interest is

A = P ( 1 + r/n )ⁿᵇ

where A = Final Amount

P = Principal

r = rate of interest

n = number of times interest is applied

b = number of time periods elapsed

Given data ,

a)

Let the principal be P = amount after first period =  $ 402

Now , the rate of interest r = 6 %

The compound interest is calculated by compounding monthly

Now , the interest for the second period = ( PRT / 100 x 12 )

Substituting the values in the equation , we get

The interest for the second period = ( 402 x 6 x 1 ) / 1200

The interest for the second period = $ 2.01

The amount after the second period = amount after first period +  interest for the second period

The amount after the second period = 402 + 2.01

The amount after the second period = $ 404.01

b)

Let the principal be P = $ 18260

The rate of interest r = 2.5 %

The compound interest is calculated by compounding quarterly

Now , the interest for the first period = ( PRT / 4 x 100 )

Substituting the values in the equation , we get

The interest for the first period = ( 18260 x 2.5 ) / 400

The interest for the first period = 45650 / 400

The interest for the first period = $ 114.125

The amount for the first period = 18260 + 114.125

The amount for the first period = $ 18,374.125

Now , the principal for the second period = interest + amount of first period

The principal for the second period = $ 18,374.125

The rate of interest = 2.5 %

The interest for the second period = ( PRT / 4 x 100 )

Substituting the values in the equation , we get

The interest for the second period = ( 18374.125 x 2.5 ) / 400

The interest for the second period = 45935.3125 / 400

The interest for the second period = $ 114.83828125

The amount for the second period = 18,374.125+ 114.84

The amount for the second period = $ 18,488.96

Hence , the amount and interest is calculated

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By using arithmetic progression, it can be calculated that

i) Distance she ran on 21 days = 37 km

ii) Total distance she ran in 21 days = 525 km

What is arithmetic progression?

Arithmetic progression consist of a sequence of numbers in which the difference between the consequent terms of the sequence are same.

This problem is based on arithmetic progression

Distance an athlete ran on first day = 13 km

She increases the distance she runs each day by 1.2km

So this is an arithmetic progression with first term 13 km and common difference 1.2 km

i) Distance she ran on 21 days = 13 + (21 - 1) [tex]\times[/tex] 1.2

                                               =  37 km

ii) Total distance she ran in 21 days = [tex]\frac{21}{2}(13 + 37)[/tex] = 525 km

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Answer:

1/64

Step-by-step explanation:

1/8 x 1/8 = 1/64

Answer:

[tex]51.4^{\circ}[/tex]

Step-by-step explanation:

Since this is a right triangle, the cosine formula says

[tex]\cos(x) = \dfrac{5.3}{8.5}[/tex]

[tex]\longrightarrow cos(x) = 0.6235[/tex]

[tex]So\\\\x = \cos^{-1}(0.6235) = 51.4256^{\circ}[/tex]

Rounded to the nearest tenth this would be
[tex]51.4^{\circ}[/tex]

Answer:

(sqrt3)/2

Step-by-step explanation:

Sin(x)=opposite/hypotenuse

30, 60, 90 right triangle.

ratio of sides are 1, sqrt3, and 2.

Locate the 60 degree angle on the triangle

The opposite side is sqrt3

The hypotenuse is 2

so its (sqrt3)/2

Answer:

√3/2 or 0.866

Step-by-step explanation:

Answer:

y = 1/4x - 4

Step-by-step explanation:

4x + y = 3

y = -4x + 3

Perpendicular slope = 1/4

y = 1/4x + b

-3 = 1/4(4) + b

-3 = 1 + b

b = -4

y = 1/4x - 4

Answer:

B

Step-by-step explanation:

970 + 2436 = 3406

Answer:

[tex]b = 6\sqrt{2}[/tex]

Step-by-step explanation:

Don't say giving brainiest for work, I will still help you.

Use the Pythagorean Theorem to solve:

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

A and B refers to the legs, or the shorter sides. C refers to the hypotenuse, or the longest side.

Plug in what you know:

[tex](7)^2+b^2=(11)^2[/tex]

[tex]49 + b^2 = 121[/tex]

Subtract 49 on both sides.

[tex]49 - 49 + b^2 = 121-49[/tex]

[tex]b^2=72[/tex]

Find the square root of both sides.

[tex]\sqrt{b^2} = \sqrt{72}[/tex]

b = [tex]6\sqrt{2}[/tex]

Answer:

2.  43 degrees

3.  35 degrees

Step-by-step explanation:

Srr the attached worksheet.

Answer:

Step-by-step explanation:

A linear equation has only more than one additional, that may be expressed as , and the further discussion can be defined as follows:

In this, No factor has been raised the power which is greater than one or utilized as the denominator of a fraction.  

When we discover pairs of values that satisfy a linear model and plot them on a coordinate grid, all the points fall on the same line.

Please find the attached file of the graph.

Answer:

A. 36/5

Step-by-step explanation:

cross multiply

6/5 = x/6

5x = 36

x = 36/5

Answer:

A) [tex]\frac{36}{5}[/tex]

Step-by-step explanation:

[tex]\frac{6}{5}[/tex] = [tex]\frac{x}{6}[/tex]  Cross multiply and solve for x

36 = 5x  Divide both sides by 5

[tex]\frac{36}5}[/tex] = [tex]\frac{5x}{5}[/tex]

[tex]\frac{36}{5}[/tex] = x

Answer:

55

Step-by-step explanation:

Using the Pythagorean theorm:

a^2+b^2=c^2

48^2+b^2=73^2

b^2=73^2-48^2

b^2=3025

b=55

A graph is a collection of points and the connections between some subset of those points that may or may not be empty in mathematical terms.

The given function is f (x ) = [tex]3e^{2x}[/tex]

1. Domain :

2.Range :

3.Continuity:

4.Behaviour that is either increasing or decreasing:

5.Symmetry:

6.Boundedness:

7.Extrema:

8.Asymptotes:

9.End behaviour :

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Observing the provided figure and using the transformation rule of geometry, The required transformation to map figure H onto figure I is reflection along y=x axis.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

In a mirror line, reflection is a type of transformation that reverses the shape so that each point is at the same distance from the mirror line as its reflected point.

Figure H

Mapped onto figure I

The required transformation:

reflection along y=x.

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Answer: y=1/2(x)-6=0.5x-6

Step-by-step explanation: y=mx+c is the general equation of a straight line.

We are told that the line passes through the point (2, -5) this means at x=2 and y=-5

We need to substitute these into the general equation.  This gives us the following:

y=mx+c

-5=m*2+c

To solve for c where the graph cuts the y -axis we need to -2m from both sides

-5-2m=2m-2m+c

-5-2m=c

Places this back into the general equation of a straight line gives us the following

y=mx-5-2m

this is the same as

y=m(x-2)-5........we take out a common factor of m

Now we want the above line to be parallel to x-2y=16

To see this we must put the above equation into the form y=mx+c

x-2y=16

We need to make y the subject that is solve for y or have y on its own

To get y term on its own we need to subtract x from both sides

x-x-2y=16-x

-2y=16-x

To finally get y on its own we need to divide both sides by -2

-2y/-2=16/-2 -x/-2

y=-8+x/2

y=x/2-8

this is the same as

y=1/2(x)-8

Therefore m=1/2

we now substitute this back into the previous original equation to get the following

y=1/2(x-2)-5

y=1/2(x)-1-5

y=1/2(x)-6

Answer:

B=28

Step-by-step explanation:

Answer:3-4 times  but im not sure but here my logic

use it to your needs

Step-by-step explanation:

she has 5 shirts and 3 jackets right
so take the first shirt the third jacket then the fourth shirt the 2nd jacket
that 2 outfits then take the second shirt and the last remaining jacket then on the weekend wear one of the non-used shirts no jacket or the first jacket
-ElectricWolfieOnYT

Answer:

find my dad

Step-by-step explanation:

Answer: 40

Step-by-step explanation:

all you have to to is subtract

9 from 49 = 40

Answer:40

Step-by-step explanation:49-9=40

If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle. Explanation is given.

Lines that cross the angle under investigation are known as angle bisectors. To "bisect" is to split into two sections of equal size. Therefore, the bisected halves divide the considered angle in half.

According to the angle bisector theorem;

An angle bisector divides the opposing side of a triangle into two portions that are proportionate to the other two sides, according to the angle bisector theorem.

a point is equally far from both sides of an angle if it is on the angle's bisector.

According to the inverse of the angle bisector theorem, a point is on the angle's bisector if it is both in the interior of the angle and equally far from its sides.

The explanation with diagram is given in the image.

Therefore, If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.

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Answer:

Below

Step-by-step explanation:

m = slope = rise / run

m = 5 for this equation

rise /run = 5

15 / run = 5

run = 3