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The relationship between the depth(d), the base area (b) and volume (V) is d = 2400/b

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

Let d represent the depth of the tank, b represent the area of the base and V represent the volume.

The depth of water is inversely proportional to the area of its base at constant volume. Hence

d = V/b

When b = 200 ft² and d = 12:

12 = V/200

V = 2400

d = 2400/b

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The left side of the two-column proof should be filled as follows:

Statements                                             Reasons_______________

32 = 2x + 4y; x = 2          ⇒                       Given

32 = 2(2) + 4y                ⇒                     Substitution Property

32 - 4 = 4 + 4y - 4        ⇒                   Subtraction Property of Equality

28/4 = 4y/4                  ⇒                  Division Property of Equality

7 = y, y = 7                    ⇒                  Symmetric Property of Equality

The division property of equality states that when both sides (left and right) of an algebraic expression or equation are divided by the same (common) real number that isn't equal to zero (0), the quotients would always remain equal.

The subtraction property of equality states that the two (2) sides of an algebraic expression or equation would still remain equal even when the same number has been subtracted from both sides of an equality.

In conclusion, it has been proven that y is equal to 7 by using the two-column proof.

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1) Let's call Temperature by T

Since the temperature is not more than 82 F, then we exclude any value above 82º F, and we include 82.

T≤82

Answer:

13

Step-by-step explanation:

3X4=12

Answer:

6(3+7)

Step-by-step explanation:

The factors of 18 are 1, 2, 3, 6, 9, 18.

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42.

The greatest common factor is six.

To put it in distributive form, divide both by 6:

6(3+7)

Stocks and bonds both have costs, risks, and returns associated with them. Bonds offer an interest payment through a maturity date while stocks may offer dividends that will grow until it is sold.

Over the long term, stocks have the highest potential for growth for investors. Investors who have chosen to hold onto stocks for an extended length of time have typically been rewarded with robust, profitable returns. However, stock prices fluctuate both up and down.

An IOU-like debt security called a bond. Bonds are issued by borrowers to attract capital from investors ready to extend a loan to them for a specific period of time. When you purchase a bond, you are making a loan to the issuer, which could be a corporate, government, or municipality.

A dividend is a payment made by a corporation to its shareholders that is decided by the board of directors. Dividend payments are frequently made quarterly and might take the form of cash payments or stock reinvestments.

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The probability that that my dog tears up the trash and it rains tomorrow is 0.03.

From the information, the dog has a 30% chance of tearing up the trash on a given day and there's a 10% chance of rain tomorrow.

Therefore, the that my dog tears up the trash and it rains will be:

= Probability of tearing up × Probability of rain

= 30% × 10%

= 0.3 × 0.1

= 0.03

The probability is 0.03.

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An exponential equation that passes through the points (2,1.8) and (5,14.4) is y = (0.6708)2ˣ

Exponential equation:

If you have two points, (x1, y1) and (x2, y2), you can define the exponential function that passes through these points by substituting them in the equation

y = abˣ

and solving for a and b.

In general, you have to solve this pair of equations:

y1 = abˣ¹ and y2 = abˣ²

Given,

The points (2,1.8) and (5,14.4).

Here we need to find the exponential equation that passes through the points.

This yields the following pair of equations:

1.8 = ab²

14.4 = ab⁵

If you divide the second equation by the first, you get

b³ = 14.4/1.8

b³ = 8

b = ∛8

b = 2

so b = 2. It's possible for b to also be equal to -2, but in this case, assume it's positive.

Now, we can substitute this value for b in either equation to get a. It's easier to use the first equation, so:

1.8 = a² x (2)²

1.8 = a²  x 4

a²  = 1.8/4

a²  = 0.45

a = √0.45

a = 0.6708

Therefore, the exponential form of the equation is,

y = (0.6708)2ˣ

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Using transformations, the vector that describes the translation that J underwent is:

(x,y) -> (x - 1, y + 2).

The vertices of the transformed figure K are given as follows:

(4,0), (6,0), (6,-1), (5,-1), (5,-2), (4,-2).

The rule for a reflection about the line y = x is given by:

(x,y) -> (y,x).

Hence, taking the vertices of figure K, the vertices of the translated figure were given by:

(0,4), (0,6), (-1,6), (-1,5), (-2,5), (-2,4).

The vertices of the original figure J are given as follows:

(1,2), (1,4), (0,4), (0,3), (-1,3), (-1,3).

Hence the vector rule from J to the translated figure is given as follows:

(x,y) -> (x - 1, y + 2).

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Answer:

p(2) = 2

f(3) = 7

Step-by-step explanation:

Given p(x) = -3(x - 4)² + 14 find p(2)

Simply substitute x with the value 4 in the above expression

p(2) = -3(2-4)² + 14

= -3(-2)² + 14

= -3(4) -+ 14

= -12 + 14

= 2

f(3) can directly read from the table

for x = 3, f(x) = 7

so f(3) = 7

The labelled points on the intersected planes shown in the attachment are;

1) Lines AB and m are both coplanar on plane S and are perpendicular to each other intersecting at point B

2) Plane R and plane S intersect on line p

3) Line AB and line p are perpendicular to each other and both intersect with line n at point A

We want to label the points, lines, and planes showing the following;

Line AB and line m perpendicular to each other in plane S at point B.

Plane S intersecting plane R in line p.

Line AB both perpendicular to line p and intersecting line n at point A.

Therefore, the given parameters are;

1) Lines AB and m are both coplanar on plane S and are perpendicular to each other intersecting at point B

2) Plane R and plane S intersect on line p

3) Line AB and line p are perpendicular to each other and both intersect with line n at point A

The diagram showing the labelled points is as attached.

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The measure of angle:-

angle 1 = 78 degree

angle 2 = 40 degree

angle 3 =  140 degree  

A triangle is a type of polygon which have only three vertices and no parallel sides.

 In this question we use property of triangle that :-

1:- Sum of interior angle is 180 degree

2:-Exterior angle of a triangle is equal to the sum of angle of opposite sides

A.T.Q:-

  lets vertices of triangle be A,B, and C    

  so,

       angle A + angle B +angle C = 180

       62 +78+ angle C = 180

      140 + angle C = 180

      angle C =40 degree

we know that , angle C and angle 3 makes 180 degree

                        angle C + angle3 =180     , 40+ angle 3= 180

angle 3 = 140 degree                                                                                     And ,  angle 2 = angle C

                :- angle 2=40                                                                               finally;

               angle 1 =  angle B

               angle 1 = 78 degree

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Answer:

[tex]g( - 16) = - 3[/tex]

Step-by-step explanation:

substitute

[tex]x = - 16 \: by \: g(x) = \frac{1}{4} x + 1 \\ g( - 16) = \frac{1}{4} x( - 16) + 1 \\ g( - 16) = - \frac{1}{4} x16 + 1 \\ g( - 16) = - 4 +1 \\ g( - 16) = - 3[/tex]

The total amount to be paid on a 9 year, $60,500 loan at 7.3% p.a. is $100248.50.

It should be noted that simple interest is calculated as:

Interest = Principal × Rate × Time / 100

Interest = 60500 × 7.3 × 9 / 100

Interest = $39748.50

It should be noted that the amount will be the addition of the principal and the interest. This will. be:

= Principal + Interest

= $60500 + $39748.50

= $100248.50

The amount is $100248.50.

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nswer:

cvents A and B are independent because P(A|B) = P(A)

pxplanation:

f aA and B are independent, then:

In this case,

P(A) = 0.4, P(B) = 0.2

If we multiply:

Which verify what the problem tell us.

Next, the definition of two independent events is P(A|B) = P(A)

Answer:

Step-by-step explanation:

d=3n

0.10d+0.05n=1.40

0.10(3n)+0.05=1.40

0.3n+0.05n=1.40

0.35n=1.40

n=4

d=3(4)

d=12

12(0.10)+.05(4)=1.40

1.40=1.40

Answer:

$14540

Step-by-step explanation:

you are earning 4 dollars per 400 dollars per month. there are 12 months in a year. 400 * 12*30 = 144000. 144000 divided by 400 is 360.

360 times 4 is 1440.

15,0

Step-by-step explanation:

As a result of the sequences, the numbers for the first equation are 31,37,43, 64,128,256, and 37,42,47 for the second and third equations, respectively.

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. An arithmetic progression is another name for an arithmetic sequence.

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

so for the first equation:

we see the common difference is constant :

second term/third term - first term/second term =7-1 or 13-7

                        =6

the next three terms in this series would be calculated by adding the common difference to consecutive last terms  =31,37,43

for the third equation

the common difference is a constant:

second term-first term=5

the next three terms in this series would be calculated by adding the common difference to consecutive last terms  =37,42,47

for the second equation we don't see a constant value as a common difference ,then we conclude that it is a Geometric progression

difference in series = second term/first term

                              =4/2

                              =2

so for the three consecutive terms we will multiply the last consecutive terms by 2=64,128,256

Therefore the numbers for First equation are 31,37,43 for the second equation are 64,128,256 and third equation are 37,42,47

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Answer:

252558855555335555422358236

Answer:

[tex]y=\frac{-1}{4}x+2[/tex]

Step-by-step explanation:

The function can be written in point-slope form following this equation:

[tex]y=m(x-x_{0} )+y_{0}[/tex]

where y and x are variables, and [tex]x_{0}[/tex] and [tex]y_{0}[/tex] are x and y values of any chosen point on the curve (line)

m (slope) can be calculated by the equation [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex] where you need to find 2 chosen points on the line where [tex]x_{1}[/tex] and [tex]y_{1}[/tex] are the x and y values of the first set, and [tex]x_{2}[/tex] and [tex]y_{2}[/tex] are the x and y values of the second set.

solve for m and we get [tex]-\frac{1}{4}[/tex]

Plug it into the equation with any set of x and y values on the line into the point-slope form equation, then you get the answer

The length and width of the rectangular box are 13 ft and 6 ft respectively.

The length of the batter's box on a softball field is 1 ft more than twice the width.

The area of the batter's box is 78 ft².

The length and width of the rectangular batter's box can be found as follows:

Therefore,

area of a rectangle = lw

where

Therefore,

area of the rectangular box = 78 ft²

l = 1 + 2w

Hence,

78 = (1 + 2w)w

78 = w + 2w²

2w² + w - 78 = 0

Hence,

w = 6  and w =  -13  /2

we can only use positive values.

Therefore,

width = 6 ft

length  = 2(6) + 1 = 13 ft

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If a car consumes 110 liters of fuel with in a distance of 250 km, then the rate of fuel consumption is 2.5 km/liter

The distance travelled by the car with 110 liters of fuel = 250km

To find the rate of fuel consumption we have to apply the unitary method

The distance travelled by the car with 1 liters of fuel = The distance travelled by the car with 110 liters of fuel /110

Substitute the values in the equation

The distance travelled by the car with 1 liters of fuel = 250/110

= 2.5 km

So a car consumes 1 liters of fuel to cover 2.5 km

The rate of fuel consumption = 2.5 km/liter

Hence, if a car consumes 110 liters of fuel with in a distance of 250 km, then the rate of fuel consumption is 2.5 km/liter

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The value of the ratio of skateboards wheel in its simplest form is 1:4.

The ratio refers to the numerical relationship between two variables.

Ratios show the quantity of one variable contained in another.

Ratios are expressed in fractions, decimals, or percentages.  They can also be written using the ratio symbol (:).

The total number of skateboards = 12

The total number of wheels = 48

The ratio value of skateboards wheels = 48:12

= 4:1 or 1:4

Thus, we can conclude that for every skateboard, there must be 4 wheels, given their ratio values.

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To know if a number is a perfect sqare of a perfect cube you:

perfect sqare

determine if its sqaure root is an integer. If is not an interger, then the number is not a perfect sqare

perfect cube

determine if its Cube root is an interger. If is not an interger then the number is not a perfect cube

Then so, 121 is a perfect cube, because is the result of (11*11)

121 is not a perfect cube

The inverse of the conditional statement w > ~v is ~v < w

An inverse statement is seen as a type of conditional sentence having an immediate change that is made from original statement.

It is known to carry the negation of both the hypothesis and conclusion from the given original statement.

It is known to carry the opposite of the original statement that is given.

An inverse statement is formed by negating the hypothesis and conclusion of a statement.

It is expressed as;

Original statement:  If a, then b

Inverse statement: If not b, not a

Given the expression;

w > ~v

The inverse is represented as;

~v < w

Hence, the inverse is ~v < w

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Answer: 6931

Step-by-step explanation:

79% of all students are taking math this semesters.  So there is an additional 21% of students not taking math.

5476/x = 79/100

cross multiply and divide to get the total number of students.

5476 x 100 = 547600

547600 divided by 79 = 6931  

check 5476 divided by 6931 = 79%  

Further proof of correct answer:

21% of 6931 = 1455

1455 + 5476 equals 6931, so the answer calculated is correct.    

Answer:

[tex]{ \sf{ \frac{dy}{dx} = y( {x}^{2} + 1)}} \\ \\ { \sf{ \frac{dy}{y} = ( {x}^{2} + 1)dx}} \\ \\ { \sf{ \int \frac{1}{y} dy = \int ( {x}^{2} + 1) \: dx}} \\ \\ { \sf{ ln(y) = \frac{ {x}^{3} }{3} + x + c }}[/tex]

Answer:

[tex]\large\text{$y& = e^{\frac{1}{3}x^3+x+\text{C}}$}[/tex]

Step-by-step explanation:

Given differential equation:

[tex]\dfrac{\text{d}x}{\text{d}y}=\dfrac{1}{y(x^2+1)}[/tex]

Rearrange the equation so that all the terms containing y are on the left side, and all the terms containing x are on the right side:

[tex]\begin{aligned}\implies \dfrac{\text{d}x}{\text{d}y}&=\dfrac{1}{y(x^2+1)}\\\\(x^2+1)\;\dfrac{\text{d}x}{\text{d}y}&=\dfrac{1}{y}\\\\(x^2+1)\;\text{d}x}&=\dfrac{1}{y}\;\text{d}y\\\\\dfrac{1}{y}\;\text{d}y&=(x^2+1)\;\text{d}x}\end{aligned}[/tex]

Integrate both sides:

[tex]\begin{aligned}\implies \displaystyle \int \dfrac{1}{y}\;\text{d}y &= \int (x^2+1)\;\text{d}x}\\\\\int \dfrac{1}{y}\;\text{d}y &= \int x^2\;\text{d}x}+\int 1\;\text{d}x}\\\\\ln y & = \dfrac{1}{3}x^3+x+\text{C}\\\\e^{\ln y} & = e^{\frac{1}{3}x^3+x+\text{C}}\\\\y& = e^{\frac{1}{3}x^3+x+\text{C}}\\\\\end{aligned}[/tex]

Therefore, the solution to the given differential equation is:

[tex]\large\text{$y& = e^{\frac{1}{3}x^3+x+\text{C}}$}[/tex]

Integration rules used:

[tex]\boxed{\begin{minipage}{3.5 cm}\underline{Integrating $\frac{1}{x}$}\\\\$\displaystyle \int \dfrac{1}{x}\:\text{d}x=\ln |x|+\text{C}$\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{3.5 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{5 cm}\underline{Integrating a constant}\\\\$\displaystyle \int n\:\text{d}x=nx+\text{C}$\\(where $n$ is any constant value)\end{minipage}}[/tex]