What is the volume, in cubic in, of a rectangular prism with a height of 3in, a width of 10in, and a length of 2in

The table representing ratio of peaches in a box should be completed as follows;

Boxes    Peaches

2                 6

3                 9

5                15

6                18

The table representing ratio of strawberries in a box should be completed as follows;

Boxes    Strawberries

2                 6

4                12

5                15

8                24

In order to have a proportional relationship and equivalent ratios that is constant, the variables x for boxes and y for peaches must have the same constant of proportionality. Next, we would determine the constant of proportionality (k) based on the given parameters:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 6/2 = 18/6

Constant of proportionality (k) = 3.

When y = 9 peaches, the value of x is given by;

x = y/k

x = 9/3

x = 3 boxes.

When x = 5 boxes, the value of y is given by;

y = kx

y = 3(5)

y = 15 peaches.

Also, we would determine the constant of proportionality (k) based on the given parameters:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 12/4 = 15/5

Constant of proportionality (k) = 3.

When x = 2 boxes, the value of y is given by;

y = kx

y = 3(2)

y = 6 strawberries.

When x = 8 boxes, the value of y is given by;

y = kx

y = 3(8)

y = 24 strawberries.

Read more on proportionality here: brainly.com/question/12866878

#SPJ1

The area of the window that lets in the most light will be the one that causes the window to transmit the most light overall.

To find the proportions of the window that will admit the lightest, we need to maximize the total area of the window while keeping the perimeter fixed. The total area of the window is the sum of the area of the rectangle and the area of the semicircle. The area of the rectangle is the product of its length and width, and the area of the semicircle is half the product of its radius and the area of a full circle with the same radius.

Since the perimeter is fixed, the length and width of the rectangle are also fixed. The radius of the semicircle can be found using the perimeter and the length and width of the rectangle.

Once we have the radius of the semicircle, we can find the area of the rectangle, the area of the semicircle, and the total area of the window. Since the semicircle is of tinted glass that transmits only half as much light per unit area as clear glass does, we will have to multiply the area of the semicircle by 0.5 to find the total amount of light transmitted by it.

Finally, we will have to compare the total amount of light transmitted by the window for different values of the length and width of the rectangle. The proportion of the window that admits the most light will be the one that results in the maximum total amount of light transmitted by the window.

To learn more about surface area, refer to the link:brainly.com/question/29298005

#SPJ4

On solving the provided question, we can say that - the data from graphs represents a curvilinear and straight graph.

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph

Here,

in graphs,

as per data we can say that there two types

one is curvilinear and other is straight graph.

To know more about graphs visit:

https://brainly.com/question/11950136

#SPJ1

Answer:

3x + 4

Step-by-step explanation:

Using the distributive property simply means that when there is a number in front of a pair of parentheses, every value inside the parentheses is multiplied by the co-efficient to expand the parentheses.

Here, the coefficient is -2, therefore we multiply both terms inside the parentheses (x and -2) by -2 to expand them:

-2(x - 2) + 5x

= (-2)(x) + (-2)(-2) + 5x

Now we simply evaluate and combine like terms to simplify:

= -2x +4 +5x

= 3x + 4

(a) The concentration of our solution in the tank initially is 0.060 kg/L. (b) the amount of salt in the tank after 2. 5 hours is 44.45 kg. (c) The concentration of salt in the solution in the tank as time approaches infinity is 0.030 kg/L.

Divide the solute's gram weight by the total weight of the solution, then multiply the result by 100 to get the mass/mass percent of the solution. The amount of solute (measured in grams) per milliliter of solution is known as the mass/volume percent.

(A) Tank contains 60 kg of salt and 1000 L of water. So the concentration of solution in the tank initially = 60/1000 kg/l

The concentration of solution in the tank initially = 0.060 kg/L

(B) Let y(t) denote the amount of salt in the tank at any time t.

Rate In

A solution of concentration 0.03 kg of salt per liter enters a tank at the rate 9 L/min.

[tex]R_{i}[/tex]  =(concentration of salt in inflow)(input rate of solution)

= (0.03kg/L)*(9L/min)

= 0.27kg/min

Rate Out

The solution is mixed and drains from the tank at the same rate.

Concentration, C(t) = Amount/Volume = y(t)/1000

[tex]R_{out}[/tex] =(concentration of salt in outflow)(output rate of solution)

= {y(t)/1000}kg/L*9L/min

= 0.009y(t) kg/min

Therefore, the differential equation for the amount of Salt in the Tank  at any time t:

dy/dt = 0.27 - 0.009y(t)

So the amount of salt in the tank after 2. 5 hours (2.5*60 min = 150 min) is  44.45 kg.

(c) The concentration of salt in the solution in the tank as time approaches infinity

As t -> -∞, e^-∞ = 0

so, the concentration of salt in the solution in the tank as time approaches infinity is 0.030 kg/L.

To learn more about  concentration of a salt solution visit:

brainly.com/question/11740694

#SPJ4

Function: This means that 2.7 x 10^3 is about 201.593 times smaller than 5.481 x 10^5. This can also be expressed as 0.049 or 4.9%.

A function is a mathematical relation between two sets of values, usually between an input and an output. It can be thought of as a machine that takes a certain input and produces a certain output.

2.7 x 10^3 is about 0.049 times smaller than 5.481 x 10^5.
To determine this, we can divide the two numbers. 5.481 x 10^5 divided by 2.7 x 10^3 equals about 201.593.
This means that 2.7 x 10^3 is about 201.593 times smaller than 5.481 x 10^5. This can also be expressed as 0.049 or 4.9%.

To learn more about function
https://brainly.com/question/10439235
#SPJ1

The linear functions for each situation are given as follows:

Makayla is closer than Addision when:

x < 5.

The linear functions in slope-intercept format for this problem are given as follows:

y = mx + b.

In which:

Hence the functions are defined as follows:

Makayla is closer when:

290 - 40x < 345 - 51x

11x < 55

x < 5.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

Answer:

$821.2

Step-by-step explanation:

cause 2.65 percentage of 800 dollars is 800/100=8*2.65=21.2dollars.+800 =$821.2

By solving, we see that the product of the polynomials 4 - a and a3 + 7a - 18 is a3 + 3a2 + 46a + 72.

The location on the y-axis where the slope of the line passes is known as the intersection point in mathematics. a point on a line or curve where the y-axis crosses. The equation for the straight line is given as Y = mx+c, where m denotes the slope and c the y-intercept. In the intercept form of the equation, the line's slope (m) and y-intercept (b) are highlighted. The slope and y-intercept of an equation with the intercept form (y=mx+b) are m and b, respectively. There are several equations that can be rewritten to look like slope intercepts. The slope and y-intercept are both modified to 1 if y=x is rewritten as y=1x+0, for example.

given

(4 - a) * ( a3 + 7a - 18 )

= 4a3 + 28a - 72 - a4 + 7a2 + 18 a

= a3 + 3a2 + 46a + 72

By solving, we see that the product of the polynomials 4 - a and a3 + 7a - 18 is a3 + 3a2 + 46a + 72.

To know more about polynomial visit :-

https://brainly.com/question/11536910

#SPJ1

Answer:

1. The answer is 40 degrees

2. Adjacent angles are sometimes congruent.

3. UPR is vertical to TPQ

4. The answer is 132 Degrees

Answer:

2x + 2

Step-by-step explanation:

Combine all the like terms:

-5x + 7x -12 + 14 = 2x + 2

Answer:

2x + 2

Step-by-step explanation:

(- 5x - 12) + (14 + 7x) ← remove parenthesis

= - 5x - 12 + 14 + 7x ← collect like terms

= (- 5x + 7x) + (- 12 + 14)

= 2x + 2

The height of the Building is 110.01 feet.

The square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides, according to Pythagoras' Theorem.

Given, Finn leaned a 100-foot ladder against the side of a building. The base of the ladder is 14 feet from the base of the building. The top of the ladder is 11 feet from the top of the building.

For the triangle made by ladder

hypotenuse = 100

base = 14

thus, from the Pythagorean theorem

hypotenuse² = base² + height²

100² = 14² + height²

height² = 10000 - 196

height = √9804

height = 99.01

total height of the wall = height of triangle + remaining height of the wall

Thus the total height of the wall  = 99.01 + 11

the total height of the wall  = 110.01

therefore, the building is 110.01 feet tall.

Learn more about the Pythagorean theorem here:

https://brainly.com/question/14930619

#SPJ1

One mole consists of 6.02214076×10²³ units which is Avogadro's number. Thus one mole is known as Avogadro's number.

What is one mole?

A mole is 6.02214076×10²³ of any chemical unit, including atoms, molecules, ions, and others. Due to the large number of atoms, molecules, or other components that make up any substance, the mole is a useful measure to utilize. The mole was initially defined as the quantity of atoms contained in 12 grammes of carbon-12, but the General Conference on Weights and Measures declared in 2018 that the mole will only contain 6.02214076×10²³ of some chemical unit as of May 20, 2019.

In chemistry, a mole, sometimes spelled mol, is a common scientific measurement unit for significant amounts of very small objects like atoms, molecules, or other predetermined particles.

To learn more about Avogadro's number, click on the below link:

https://brainly.com/question/24175158

#SPJ4

Answer:

81/100 is the answer I believe if I'm wrong my bad

Answer:

81/100

Step-by-step explanation:

brainliest pls

Hence option (B) is a correct choice and rest all other options are incorrect

1/b^2 ∑ (-1)^k(t^2/b^2)^k                                        
                             

Step-by-step explanation:

 Remember that the sum of infinite GP is given by the formula blow:
First term=a
Common ratio=r

S=a/1 - r                                          

Wherever the common ratio r falls within the interval (-1,1)

When the given series is compared to the infinite sum:

First term=a
Common ratio=r
S=  a/1-r = 1/b^2+t^2
Now given: |t| < |b|=0<t^2/b^2<1
S=1/B^2.1/1-(-T^2/B^2)
=A=1
R=-T^2/B^2
Writing the general form:

Hence option (B) is a correct choice.

What are real numbers simple definition?

Real numbers can be defined as the union of both rational and irrational numbers. They can be both positive or negative and are denoted by the symbol “R”. All the natural numbers, decimals and fractions come under this category.

INCOMPLETE QUESTION: if b and t are real numbers such that 0<|t|<|b|, which of the following infinite series has sum 1b2 t2
A) 1/b^2 ∑(t^2/b^2)^k.
B) 1/b^2 ∑(-1)^K(t^2/b^2)^k.
C)B^2∑(T^2/B^2)^K
D)b^2∑(-1)(t^2/b^2)^k

To learn more about real numbers:
https://brainly.com/question/551408
#SPJ4




   

Aisha has 2 chocolates left. You can represent the problem as an equation as follows:

Where x is the total number of chocolates, b is the number of boxes filled and 2 is the remaining chocolates left.

Since we know that Aisha has 50 chocolates, we can substitute this value for x in the equation:

50 = 3b + 2

Solving for b, we find that b = 16. So, Aisha filled 16 boxes and had 2 chocolates left over. The equation is true, and Aisha has 2 chocolates left.

It's worth noting that this is a simple algebraic equation, we can use the same equation to find the number of chocolates given the number of boxes and remaining chocolates, or to find the number of boxes given the number of chocolates and remaining chocolates or to find the remaining chocolates given the number of boxes and the number of chocolates.

Learn more about Algebra here:

https://brainly.com/question/6143254

#SPJ4

Answer:

cash

Step-by-step explanation:

debit - account payable

credit - cash



Answer:16,777,216

Step-by-step explanation:

Thus, 0 itself is the sole position at which [0,∞] and (0,∞] are separated. Since it is in [0,∞] the set is closed. Given that it is not in (0,∞), the set is open interval.

A (real) interval in mathematics is a collection of real numbers that includes all real numbers that fall within any two of the collection's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 x 1. The collection of numbers such that 0 x 1 and the collection of all real numbers are other examples of intervals.

the empty set, any singleton, the set of positive real numbers, the set of nonnegative real numbers, and (set of one element).

Because they are the most basic sets whose "length" (or "measure" or "size") is straightforward to define, real intervals are crucial in the theory of integration. The Borel measure and finally the Lebesgue measure result from extending the notion of measure to more intricate sets of real numbers.

Interval arithmetic is a broad numerical computing technique that automatically generates assured enclosures for arbitrary formulas, even in the presence of uncertainties, mathematical approximations, and arithmetic roundoff. Intervals are at the centre of this technique.

Therefore, 0 itself is the sole place at which [0,∞] and (0,∞] have a boundary. Due to its location in [0,∞] the set is closed. Since it is not in (0,∞), the set is unclosed.

To learn more about intervals:

https://brainly.com/question/13708942

#SPJ4

The answers for Center of the circle is (-4,3) and radius is 2√10 units.

(x - h)2 + (y - k)2 = r2 is the equation of the center of the circle. The radius (r) is specified as 5 units, while the center's (h, k) coordinates are (0, 0). (x - 0)2 + (y - 0)2 = 52 is the result of substituting the values of h, k, and r in the equation.

Finding the simplified term of the given expression is the goal of simplifying the algebraic statement. We must first understand how to join like terms, factor a number, and the order of operations before we can factorize or simplify the statement. When like words are combined, the constant terms are divided for the purpose of simplicity and the variables with the same degree are grouped together.

Examples of  Algebraic Expressions

2x2+3xy+4x+7

Given,

[tex]x^2+y^2+8x-6y-15=0[/tex]

⇒ x².+8x+16–16+y²-6x+.9–9–15=.0

(x+4)²+(y-3)²-16–9–15=0

I.e. (x+4)²+(y-3)²=40

(x+4)²+(y-3)²={2√10}²

Hence center is (-4,3) and radius is 2√10 units.

To know more about Algebraic Expressions visit:

brainly.com/question/9729268

#SPJ1

Answer:

A

Step-by-step explanation:

Se them equal to each other

3x = [tex]x^{2}[/tex] - 4

[tex]x^{2}[/tex] -3x -4 = 0

(x + 1) ( x -4)

x + 1 = 0

x = -1

y = 3x

y = 3(-1)

y = -3

(-1,-3)

x - 4 = 0

x = 4

y = 3x

y = 3(4)

y = 12

(4, 12)

The length of the sides RS, ST and TR are √72, √41 and √37 in the scalene triangle RST.

The distance between any two points A(a,b) and B(c,d) in the plane is given by,

AB = √((c-a)²+(d-b)²)

Here, it is given that the points of the triangle are R(-4,4) S(-2,-2) T(2, 3).

The triangle is scalene so length of every side is different.

Now, Using the above formula,

RS = √((2+4)²+(-2-4)²)

RS = √(36+36)

RS = √72

ST = √((2+2)²+(3+2)²)

ST = √(16+25)

ST = √41

TR = √((2+4)²+(3-4)²)

TR = √(36+1)

TR = √37

So, Brian is correct, the triangle is a scalene triangle.

To know more about triangle, visit,

https://brainly.com/question/17335144

#SPJ4

It will take the toaster about 175 seconds to make 20 slices.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

Given that The toaster takes 35 seconds to make 4 slices of toast.

It takes 70 seconds to make 8 slices of toast, It also takes 105 seconds to make 12 slices.

We are required to calculate how long it may probably take the toaster to make 20 slices.

To calculate the time it takes the toaster to make 1 slice:

4 slices ---------- 35 seconds

1 slice ----------- ? seconds

1/4 × 35 = 35/4 seconds

Now, if 1 slice will be made in 35/4 seconds,

20 slices will be made in:

1 slice --------- 35/4 seconds

20 slices ------ ? seconds

(20/1) × 35/4 = 175 seconds

Hence It will take the toaster about 175 seconds to make 20 slices.

Learn more about the unitary method, please visit the link given below;

https://brainly.com/question/23423168

#SPJ1

An equivalent  is the amount of a substance that reacts with  an arbitrary amount of another substance in a given chemical reaction.

Arbitrary

It is a relative unit of measurement to show the ratio of amount of substance, intensity, or other quantities, to a predetermined reference measurement.

chemical reaction

chemical reaction is a process in which one or more substances, the reactants, are converted to one or more different substances, the products. Substances are either chemical elements or compounds.

Examples of chemical changes include baking soda and vinegar creating carbon dioxide, iron rusting, and wood burning.

There are five types of general chemical reactions: Combination or synthesis, decomposition, single displacement, double displacement, and combustion.

Learn more about equivalents here :-

https://brainly.com/question/14672772

#SPJ4

Answer:

Since A, O and B are collinear,

i.e.,

∠

A

O

B

=

180

∘

or,

∠

A

O

D

+

∠

D

O

C

+

∠

B

O

C

=

180

∘

(

x

−

10

)

∘

+

(

4

x

−

25

)

∘

+

(

x

+

5

)

∘

=

180

∘

Or,

x

+

4

x

+

x

−

10

∘

−

25

∘

+

5

∘

=

180

∘

Or,

6

x

−

30

∘

=

180

∘

Or,

6

x

=

180

∘

+

30

∘

=

210

∘

Or,

x

=

210

∘

6

=

35

∘

∠

B

O

C

=

x

+

5

∘

=

35

∘

+

5

∘

=

40

∘

The ratio of the size of the dollhouse item to the doll house is 14 : 9.

What are ratios?

When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio.

                        A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as 1: 3 (for every one boy, there are three girls), which means that 14 of the population is made up of boys and 34 of the population is made up of girls.

                             The ratio is a mathematical expression that can be used to represent one item as a percentage of another.

First convert feet to inches

1 feet = 12 inches

12 x 6 = 72 inches

dollhouse item : doll house

112 : 72

14 : 9

Learn more about ratios

brainly.com/question/13419413

#SPJ4

Using Pythagoras theorem to solve the right angle triangle, the height of the building is 14.87 feet

Pythagoras Theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as an equation:

x² = y² + z²

where x is the hypothenuse and y, z are the legs of the right angle triangle.

To determine the height of the building in which the ladder will reach, we have to use Pythagoras theorem for that.

x² = y² + z²

15² = 2² + z²

z² = 15² - 2²

z² = 221

z = √221

z = 14.87 feet

The height is 14.87 feet

Learn more on Pythagoras theorem here;

https://brainly.com/question/343682

#SPJ1