there are two formulas that can be used to find the volume of a rectangle prism. Find the volume using both formulas

Answer:

Step-by-step explanation:

To solve the system of equations 2y + 5x = 13 and 2y-3x = 5 using the substitution method, you can follow these steps:

Begin by solving one of the equations for one of the variables. For example, you could solve the first equation for y:

2y + 5x = 13

2y = 13 - 5x

y = (13 - 5x) / 2

Substitute the expression for y into the second equation and solve for x:

2((13 - 5x) / 2) - 3x = 5

13 - 5x - 3x = 5

-8x = -8

x = 1

Substitute the value of x into the expression for y to find the value of y:

y = (13 - 5(1)) / 2

y = (13 - 5) / 2

y = 8 / 2

y = 4

The solution to the system of equations is (1,4).

Therefore, the correct ordered pair is (1,4).

Josue has 8 pennies and 5 Nickels and N+P=13 and 0.01P + 0.05N ≥ 0.33 are system of equations that could be used to determine the number of pennies and the number of nickels that Josue has

Two or more expressions with an Equal sign is called as Equation.

Given,

Josue has $0.33 worth of pennies and nickels.

total of 13 pennies and nickels altogether.

Let N be number of Nickels and P be number of Pennies

P + N =13..(1)

Therefore

0.01P + 0.05N ≥ 0.33..(2)

From 1,

P=13-N

0.01(13-N)+0.05N ≥ 0.33

0.13-0.01N+0.05N ≥ 0.33

0.13+0.04N ≥ 0.33

0.04N≥ 0.33-0.13

0.04N≥ 0.33-0.13

0.04N≥ 0.2

Divide both sides by 0.04

N=5

From 1, N+P=13

5+P=13

Subtract 5 from both sides

P=13-5

P=8

Hence, Josue has 8 pennies and 5 Nickels and N+P=13 and 0.01P + 0.05N ≥ 0.33 are system of equations that could be used to determine the number of pennies and the number of nickels that Josue has

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The solutions of the equation are given as,
1. 7,  2. 5,  3. 5, 4. 5, 5. 7, 6. -4, 7. 8,  8. 3.

Given that,
A number of equations are given we have to determine the solution of the equaiton,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here
1) 3x + 4 = 25
simplify,
3x + 4 = 25
3x = 25 - 4
x = 21 / 3
x = 7
Similarly, the Solution of the other equation is given as,
2. 5,  3. 5, 4. 5, 5. 7, 6. -4, 7. 8,  8. 3.

Thus, the solutions of the equation are given as,
1. 7,  2. 5,  3. 5, 4. 5, 5. 7, 6. -4, 7. 8,  8. 3.

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The value of the inequality equations are

a) 5040 < 8820

b) 15 > 2

c) -20 < -18

d) -1 < 1

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be A

a)

4<7 Multiply both sides by 7 , then by 6, then by 3, then by 10

The inequality equation is A

The value of A is 4 < 7

Multiplying both sides by 7 , we get

28 < 49

Multiplying both sides by 6 , we get

168 < 294

Multiplying both sides by 3 , we get

504 < 882

Multiplying both sides by 10 , we get

5040 < 8820

Therefore , the inequality equation remains the same.

b)

11>-2 Add 5 to both sides, then add 3, then add (-4)

The inequality equation is A

The value of A is 11 > -2

Adding 5 on both sides , we get

16 > 3

Adding 3 on both sides , we get

19 > 6

Adding -4 on both sides , we get

15 > 2

Therefore , the inequality equation remains the same.

c)

-4<-2 Subtract 6 from both sides, then 8, and then 2

The inequality equation is A

The value of A is -4 < -2

Subtracting 6 on both sides , we get

-10 < -8

Subtracting 8 on both sides , we get

-18 < -16

Subtracting 2 on both sides , we get

-20 < -18

Therefore , the inequality equation remains the same.

d)

-8<8 Divide both sides by -4, then by -2

The inequality equation is A

The value of A is -8 < 8

Dividing both sides by -4 , we get

2 > -2

The sign of the inequality relation changes when multiplying or dividing by a negative number

Now , dividing by -2 on both sides , we get

-1 < 1

So , The sign of the inequality relation changes when multiplying or dividing by a negative number

Therefore , the inequality equation first changes and reverts back to the original relation

Hence , the value of the inequality relations are

a) 5040 < 8820

b) 15 > 2

c) -20 < -18

d) -1 < 1

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Answer: Because the standard form is y=mx+b, and you are already in that form

Step-by-step explanation: y=mx + b is the standard form!

y=2/5x+1 is already in standard form if you compare 2 equations!

Answer:

YEEAH bro its called a graph you should try it

Step-by-step explanation:

The algebraic expression of the phrase Two-tenths of a number is 2x/10. The simplest form of the expression is x/5.

What is a phrase?

A mathematical expression is an expression that contains numbers, variables, and/or operations on those numbers and variables. A mathematical phrase is a verbal phrase that contains words and/or figures that can be turned into a mathematical expression.

Given phrase is Two-tenths of a number.

The value of two tenths is 2/10.

Assume that x be the number.

Two-tenths of x is 2/10 × x = 2x/10

Divide the denominator and numerator by 2:

= x/5

The expression is x/5.

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Step-by-step explanation:

52×7 = 50×7 + 2×7

why?

because 52 = 50 + 2

so,

52×7 = (50 + 2)×7 = 50×7 + 2×7

Answer

The third option 52 x 7 = 50 x 7 + 2 x 7

Step-by-step explanation:

First of 52 x 7 = 364, so whichever other equation is equal to 364 is the correct option

50 x 7 + 2 x 7

350 + 2 x 7

350 + 14

= 364

Jas is incorrect, and that may be because she graphed incorrectly one of the functions.

The correct solution for the system is: (1.75, 2.25)

To solve a system of equations graphically, we need to graph the two equations on the same coordinate axis and find the points where the two graphs intercept.

Here the system of equations is:

y = 3x -3

2x + 2y = 8

The graph is below. There we can see that the intercept is at (1.75, 2.25)

So Jas got an incorrect answer, and that may be because she graphed incorrectly one or both of the equations.

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the weight percentage of VOC content in the paint would be 4.05 pounds / 9 pounds x 100 = 45%.

A percent of a whole is referred to as a percentage. By dividing the portion by the entire and multiplying the result by 100, it is computed and denoted by the sign "%". For instance, if a book contains 100 pages and you have read 50 of them, you have read 50% of the book. In several disciplines, including finance, statistics, and mathematics, percentage is often utilized. To figure out interest rates, taxes, and discounts in finance, we employ percentages. In statistics, percentages are used to represent data that takes the form of proportions or ratios. In mathematics, questions involving proportions and ratios are solved using percentage.

How to solve?

the total weight of VOC in the paint would be 0.45 pounds x 9 pounds per gallon = 4.05 pounds.

the weight percentage of VOC in the paint would be 4.05 pounds / 9 pounds x 100 = 45%.

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The ratio of volumes of Cylinder A to Cylinder B is 1 : 2

What is a Cylinder?

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is

Volume of Cylinder = πr²h

where r is the radius of the cylinder

h is the height of the cylinder

Given data ,

Let the volume of the first cylinder be = A

Let the volume of the second cylinder be = B

Now,

The diameter of first cylinder = 7 cm

Radius of the first cylinder r = 7/2 = 3.5 cm

Height of the first cylinder h = 14 cm

And ,

The diameter of second cylinder = 14 cm

Radius of the second cylinder R = 14/2 = 7 cm

Height of the second cylinder H = 7 cm

To find the ratio between the volumes of both cylinders

Volume of Cylinder A = πr²h

Substituting the values in the equation , we get

Volume of Cylinder A = π x ( 3.5 ) x ( 3.5 ) x ( 14 )

Volume of Cylinder B = πR²H

Substituting the values in the equation , we get

Volume of Cylinder B = π x ( 7 ) x ( 7 ) x ( 7 )

The ratio between volumes of A and B is given by = Volume of Cylinder A / Volume of Cylinder B

So , the ratio is

Volume of Cylinder A / Volume of Cylinder B = π x ( 3.5 ) x ( 3.5 ) x ( 14 ) /  π x ( 7 ) x ( 7 ) x ( 7 )

On simplifying the equation , we get

Volume of Cylinder A / Volume of Cylinder B = 2/4

Therefore , the ratio is

Volume of Cylinder A / Volume of Cylinder B = 1 : 2

Hence , The ratio of volumes of Cylinder A to Cylinder B is 1 : 2

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The unite rate of the kendra's bike ride is found as 3 blocks / min.

The given question is-

Unit rate = number of blocks/ total time

Unit rate = 30 / 10

Unit rate = 3 blocks / min

Thus, the unit rate of the kendra's bike ride is found as 3 blocks / min.

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Let "c" represent the amount of cashews they each bought.

Let "p" represent the amount of peanuts they each bought.

Mike: 2c + 1.5p = 26

Jim: 2.5c + 1 p = 29

That's the system you need to solve.  We can do this with substitution.

Start with Jim:

    2.5c + p = 29

               p = 29 - 2.5c

Substitute that into Mike and solve for c:

                  2c + 1.5p = 26    

   2c + 1.5(29 - 2.5c) = 26    

    2c + 43.5 - 3.75c = 26

           -1.75c + 43.5 = 26

                      -1.75c  = - 17.5

                             c  = 10

Now substitute that back into Jim's last equation:

               p = 29 - 2.5c

               p = 29 - 2.5(10)

               p = 29 - 25

               p = 4

So they each bought 10 pounds of cashews and 4 pounds of peanuts.

The correct name for the set of numbers {-1, √11, 21.6555..., 16} include the following;

A. Real numbers

B. Integers

C. Irrational numbers

E. rational numbers

In Mathematics, there are six (6) common types of numbers and these include the following:

In Mathematics, an irrational number can be defined a type of number which comprises non-terminating or non-repeating decimals such as the square root of 11 or √11.

In conclusion, when the square root of 11 or √11 is taken, the output is neither a terminating decimal nor a repeating decimal. Therefore, it would be classified as an irrational number.

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Complete Question:

Choose the correct name for the set of numbers. {-√11, 21.6555..., √16, 1/9}.

real numbers

integers

irrational numbers

natural numbers

rational numbers

whole numbers

Answer:

  4x -10

Step-by-step explanation:

You want the side length of a square whose perimeter is (16x -40) feet.

The four sides of a square are all the same length. The perimeter is the sum of those lengths, so is 4 times the side length. Conversely, the side length is 1/4 of the perimeter.

  s = P/4 = (16x -40)/4

  s = 4x -10

The side length of the square table is 4x -10 feet.

The concentration of H+ ions at a pH = 2 is 10⁻² mol/L

Theconcentration of H+ ions at a pH = 6 is 10⁻⁶ mol/L

And there are 10,000 times more H⁺ ions in a solution of pH = 2 than that of pH = 6

In this question we have been given the pH of the solution.

We need to find the concentration of H+ ions in the given solution.

The H⁺ ion concentration can be calculated from pH values using the equation: pH = - log [H⁺]

at a pH = 2,

Using the above equation, 2 = - log [H⁺]

[H⁺] = 10⁻² mol/L

at a pH = 6,

Using the above equation, 6 = - log [H⁺]

[H⁺] = 10⁻⁶ mol/L

We need to find how many more h ions are there in a solution at a ph = 2 than in a solution at a ph = 6

Consider the ratio of [H⁺] for pH = 2 and pH = 6, we have

10⁻²/10⁻⁶ = 10⁴

Therefore,  there are 10,000 times more H⁺ ions in a solution of pH = 2 than that of pH = 6

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The estimated probability that there will be more than 100 black bear cubs born in any given year is 41%. Option D. is the answer

Probability is the likelihood of a desired event happening.

Experimental probability is a probability that relies mainly on a series of experiments or past events

Given: from the table, the sum of the frequency for more than 100 cubs (i.e. 101-125, 126-150 and 151-175) is:

Sum of frequency of more than 100 = 24 + 10 + 7 = 41

Total frequency (for everything) = 100

Probability of more than 100 = 41/100 = 41%

Thus, the probability of more than 100 black bear cubs is 41%

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Answer:

Step-by-step explanation:

the graph of g(x) is shifted 7 units to the right and 3 units below the graph of f(x).

The graph of g(x) is shifted 7 units to the left and 3 units below the graph of f(x).

The graph of g(x) is shifted

7 units to the right and 3 units above the graph of f(x).

The graph of g(x) is shifted 7 units to the left and 3 units above the graph of f(x)

Answer:

(-8(-4) + 3) - 7 = 32

Step-by-step explanation:

-8 * -4 = 8 * 4 = 36

36 + 3 = 39

39 - 7 = 32

The length of side AB is 8 units. Option B is the correct option.

What is right angle triangle?

A triangle is a area that bounded by three sides. The length of the sides may not be equal. A right triangle is a triangle with 90 degree angle. The rest two angles are acute angle.

Given that △ABC is a right triangle with right angle at B.

The length of side AC is 10 units. The length of side CB is 6 units.

Pythagoras theorem: The square of hypotenuse is equal to the sum of square of legs.

The legs of △ABC is AB and BC. The hypotenuse of triangle ABC is AC.

Therefore,

AB² + BC² = AC²

AB² + 6² = 10²

AB² + 36 = 100

Subtract 36 from both sides:

AB² = 100 - 36

AB² = 64

Take square root on both sides:

AB = √64

AB = 8

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The final equation for the temperature of the coffee as a function of time is [tex]T = 80 + 100*e^{(-4t)[/tex]. There are no unknown constants in this equation.

The temperature of a substance will naturally cool down over time due to heat transfer to the surrounding environment. The rate at which the substance cools down is described by Newton's law of cooling, which states that the rate of change of the temperature of a substance is proportional to the difference in temperature between the substance and the surroundings. Mathematically, this can be expressed as:

dT/dt = k(T - Ts)

Where T is the temperature of the substance, Ts is the temperature of the surroundings, t is time, and k is the cooling coefficient, which is a constant that depends on the properties of the substance and the surroundings.

Since we know that the initial temperature of the coffee is 180 and the temperature of the surroundings is 80, and the temperature of the coffee after 10 minutes is 130, we can write the following equation:

(180 - 130)/10 = k(180 - 80)

Solving for k, we get:

k = -4

Substituting this value back into the equation for the rate of change of temperature, we get:

dT/dt = -4(T - 80)

This is the equation for the temperature of the coffee as a function of time. To find the temperature of the coffee at any time t, we can integrate this equation with respect to time. The resulting equation will be:

[tex]T = 80 + C*e^{(-4t)[/tex]

Where C is an unknown constant of integration. Since we are given that the initial temperature of the coffee is 180, we can solve for C by substituting t = 0 and T = 180 into the equation:

[tex]180 = 80 + C*e^0[/tex]

Solving for C, we get:

C = 100

Substituting this value back into the equation for T, we get the final equation for the temperature of the coffee as a function of time:

[tex]T = 80 + 100*e^{(-4t)[/tex]

This is the final, simplified equation for the temperature of the coffee as a function of time. There are no unknown constants in this equation.

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The evaluation of P10–Focus 1 indicates that we get by using the equation for the volume of a cuboid and by calculus;

(a) [tex]L = 4\times x + 4\times 2\cdot x + 4\times \frac{81}{2\cdot x} =12\cdot x + \frac{162}{x^2}[/tex]

(b) [tex]L_{min}[/tex] = 54 cm

(c) L'' at x = 3, (where [tex]L_{min}[/tex] = 54 cm) is positive, therefore, x = 3 is a minimum point

P10-Focus2

The area = [tex]2\times x \times y+\frac{\pi\cdot x^2}{4} =4[/tex], therefore, [tex]y = \frac{16- \pi \cdot x^2}{8 \cdot x}[/tex]

The minimum point, which is an extremum point is a point where the derivative of the function is 0.

(a) The length of the cuboid = 2·x

The width of the cuboid = x

The volume of the cuboid = 81 cubic centimeters

The thickness of the cuboid is therefore;

Thickness = 81/(2·x × x) = 81/(2·x²)

The sum of the length of the twelve edges, L, is therefore;

[tex]L=x + x + x + x + x + 2\cdot x + 2 \cdot x + 2 \cdot x + 2\cdot x + \frac{81}{2 \cdot x^2} + \frac{81}{2 \cdot x^2} + \frac{81}{2 \cdot x^2} + \frac{81}{2 \cdot x^2}[/tex]

Therefore;

[tex]L=4\times x + 4\times 2\cdot x + 4\times \frac{81}{2 \cdot x^2} =12\cdot x + \frac{162}{x^2}[/tex]

The sum of the lengths of the twelve edges, L, is [tex]L = 12\cdot x + \frac{162}{x^2}[/tex]

(b) The minimum value of L can be found using calculus by finding the point at which dL/dx = 0 as follows;

[tex]\frac{dL}{dx} = 12 - \frac{324}{x^3} =0[/tex]

Therefore;

[tex]12-\frac{324}{x^3}=0[/tex]

[tex]12 = \frac{324}{x^3}[/tex]

x³ = 324 ÷ 12 = 27

x = ∛(27) = 3

x = 3

The minimum value of L can be obtained when x = 3 as follows;

[tex]L = 12\cdot x + \frac{162}{x^2}[/tex]

[tex]L_{min} = 12\times 3 + \frac{162}{3^2} = 54[/tex]

The [tex]L_{min}[/tex] = 54

The minimum value of L is 54 centimeters

(c) The value of the minimum value of L can be confirmed by further differentiation using the second derivative, L'' as follows;

At the x-value of a minimum point of a function, the value of the further derivative is larger than zero

The further derivative of the specified function is found as follows;

[tex]L'' = \frac{dL'}{dx} =\frac{972}{x^4}[/tex]

At the critical number, x = 3, from the first derivative, we get;

[tex]L'' = \frac{972}{3^4} = 12 > 0[/tex]

The value of the further derivative of the function at the point x = 3, is L'' = 12 > 0, therefore the point x = 3 is a relative minimum.

(b) The radius of the quarter circle = x

The area of the figure = 4 m²

The sum of the area of the composite figures are;

[tex]A = 2 \times x \times y + \frac{\pi \cdot x^2}{4} = 4[/tex]

Therefore;

[tex]y =\frac{\left(4 - \pi \cdot \frac{x^2}{4}\right)}{2\cdot x} = 16 - \frac{\pi \cdot x^2}{8\cdot x}[/tex]

Rearranging the right hand side expression as a fraction, we get;

[tex]y = \frac{16-\pi \cdot x^2}{8\cdot x}[/tex]

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Answer:

h x m=hm

Step-by-step explanation:

on my test

The maximum number of spheres that can be made through ice will be 135.

To convert any unit into another is called a unit conversion.

In order to convert units, we need to care about their dimensions their dimension should not be changed.

As per the given,

Number of ice portions = 40

Weight of one ice portion = 3 ounce

Since, 1 lb = 16 ounce

3 ounce = 3/16 lb

Weight of 40 portion = 120/16 lb

The weight of one sphere of ice = 18 lb

Number of possible spheres = (120/16)/18

⇒ 120/16 x 18

⇒ 135 sphere

Hence "135 spheres are the most that can be produced by ice".

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The correct response is option 3 i.e n = 6.

What is a Sequence?

A sequence is a list of items arranged in a stepwise order, with members coming either before or after.

We know that,

aₙ = a₁ + (n-1)×d     .............................(Arithmetic sequence formulae)

here,

aₙ = -13

a₁ = 7

d = -4

Substituting the values we get,

-13 = 7 + (n-1)×(-4)

∵ (-4)×(n-1) = -20

=> n-1 = 5

=> n = 6

Thus, the final value of n is 6.

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Inequality (A) "y > x-2 represents the given graph when the line passes to 2 and -2 from the x-axis and y;-axis respectively.

In discrete mathematics, more specifically in graph theory, a graph is a structure that resembles a collection of objects where some object pairs are conceptually "connected."

Each pair of connected vertices is referred to as an edge, and the objects are represented by mathematical abstractions known as vertices.

To calculate the slope m and the y-intercept, write the equation y = MX + b.

The slope and y-intercept can then be used to graph the equation (0, b).

So, to find which inequality represents the given graph, simply plot the inequalities on the graph.

After plotting, we can conclude that inequality "y > x-2" represents the graph shown in the question.

(Refer to the image attached below)

Therefore, inequality (A) "y > x-2 represents the given graph when the line passes to 2 and -2 from the x-axis and y'-axis respectively.

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Complete question:
Which inequality does the graph represent?

a. y > x-2

b. y > -X-2

c. y <-x-2

d. y <x-2

Answer:

he drove 30 miles

Step-by-step explanation:

The probability she makes at least 65 is 0.0139.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

[tex]\begin{aligned}P(x \geq 65) & =1-P(x < 65) \\& =1-P\left(\frac{x-\mu}{n} < \frac{65-56}{4.0988}\right) \\& =1-P(z < 2.1958) \\& =1-0.9861 \\& =0.0139\end{aligned}[/tex]

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