any number that can be expressed as a ratio of two integers

The Evaluate the expression (12)2•(3•5−3)+13 is [tex]{7\frac{1}{2}[/tex]

Multiply the numerator by the reciprocal of the denominator:

[tex]5(\frac{3}{2} )[/tex]

Multiply [tex]5(\frac{3}{2} )[/tex]:

Combine [tex]5[/tex] and [tex]\frac{3}{2}[/tex]:

[tex]\frac{5⋅3}{2}[/tex]

Multiply [tex]5[/tex] by [tex]3[/tex]:

[tex]\frac{15}{2}[/tex]

The result can be shown in multiple forms.

Exact Form:

[tex]\frac{15}{2}[/tex]

Decimal Form:

[tex]7.5[/tex]

Mixed Number Form:

[tex]{7\frac{1}{2}[/tex]

Hence, The Evaluate the expression (12)2•(3•5−3)+13 is [tex]{7\frac{1}{2}[/tex]

#SPJ3

Answer:

Step-by-step explanation:

66666

Distance for the anchor drop every 5 seconds is,

⇒ E = 63 meters

Multiplication means to add number to itself a particular number of times. Multiply will be viewed as a process of repeated addition.

Given that;

A big ship drops its anchor.

Here, E represents the anchor's elevation relative to the water's surface (in meters) as a function of time t (in seconds).

E = - 2.4t + 75

Now, Distance for the anchor drop every 5 seconds is,

Put t = 5;

E = - 2.4t + 75

E = - 2.4 × 5 + 75

E = - 12 + 75

E = 63 meters

Learn more about the multiplication visit:

brainly.com/question/10873737

#SPJ1

The value of 729 cube root is 9.

The cube root function is important in various mathematical applications, including calculus, geometry, and physics.

The cube root of 729 is the number that when multiplied by itself three times, results in 729. This number is often represented as the symbol ³√729.

In other words, if we cube the cube root of 729, we get back the original number 729. The cube root of 729 is 9, since 9 x 9 x 9 = 729.

In mathematical terms, the cube root of 729 can be expressed as: ³√729 = 9.

To know more about Cube root:

https://brainly.com/question/1636144

#SPJ4

The shape with 7 sides is called a heptagon.

There a several shapes which has more number of sides than the usual shapes like square, circle or triangle.

As the number of the sides in the shape increases the propertied of the shape also changes. If the shape has 7 sides it is called a heptagon and if it has 6 sides than it is called a hexagon, it it has a 5 sides it is called a pentagon.

If all the 7 sides of the pentagon are equal in magnitude then the heptagon is said to be a regular heptagon but is not equal then they are called heptagon with different features.

To know more about Heptagon, visit,

https://brainly.com/question/27325239

#SPJ4

Answer: It is undefined

Step-by-step explanation:

Hope this helps-just had a test on this!

Answer: Jessica's average clothing budget for the first six months of 2001 was $102.

Explanation: To calculate the average amount of money that Jessica's budget allowed for clothing in the first six months of 2001, we first need to find her monthly budget.

We can do this by dividing her annual salary by 12 (the number of months in a year):

$48,960 / 12 = $4,080 per month

Next, we need to find her clothing budget for one month. We're told that her clothing budget is 5% of her monthly budget, so we can calculate this as follows:

5% of $4,080 = (5/100) x $4,080 = $204

Therefore, Jessica's clothing budget for one month is $204.To find her average clothing budget for the first six months of 2001, we simply need to multiply her monthly clothing budget by the number of months (i.e., 6):

$204 x 6 = $1,224

Finally, we divide this total by the number of months to find the average: $1,224 / 6 = $102

The  1 c sugar is 200 grams.

Gram (originally grams; [1] SI unit symbol g) is a mass unit in the International System of Units (SI), equal to one thousandth of a kilogram.

Originally defined from 1795 as "the absolute mass of a volume of pure water equal to one hundredth of a cubic meter [1 cm3] and at the melting point of ice", [2] the defining temperature (~ 0 °C) ) was later changed to

°C, which is the maximum density of water to temperature.

At the end of the 19th century, however, an attempt was made to make the basic unit the kilogram and a unit derived from the gram. In 1960, the new International System of Units defined the gram as one thousandth of a kilogram (ie, a gram is 1 × 10–3 kg). As of 2019, the International Bureau of Weights and Measures defines the kilogram as a fixed numerical value of Planck's constant (h) of 6.62607015×10−3

kg⋅m2⋅s−1.[3][

] ]

know more about gram click here;

https://brainly.com/question/19170286

#SPJ4

The value of b is given as follows:

b = 18.

Similar triangles are triangles that share these two features presented as follows:

The bisection, represented by the altitude segment in this triangle, divides the triangle into two similar triangles, hence the equivalent side lengths are given as follows:

Then the proportional relationship for these side lengths is given as follows:

b/(28 - b) = 27/15

Applying cross multiplication, the value of b is obtained as follows:

15b = 27(28 - b)

42b = 27 x 28

b = 27 x 28/42

b = 18.

More can be learned about similar triangles at brainly.com/question/14285697

#SPJ1

The solutions to the equation f(x) = g(x) to the nearest hundredth are:  x = -8.85, -5.1 and x = 0.6

To find the solutions to the equation f(x) = g(x), we need to solve for x such that:

0.15x³ + 2x² + 7x - 3.3 = 1.5x - 7.3

We can simplify this equation by bringing all the terms to one side:

0.15x³ + 2x² + 5.5x - 4 = 0

To find the solutions to the nearest hundredth, we can use a graphing calculator or software to graph the functions f(x) and g(x) and find their points of intersection.

Using a graphing calculator , we can plot the two functions and find that they intersect at two points;

approximately x = -8.85, -5.1 and x = 0.6

Learn more about polynomial function here: https://brainly.com/question/2833285

#SPJ1

Answer: 31.5

Step-by-step explanation:  
6*4=24 (Shaded Rectangle)

3*5=15  15/2=7.5 (Shaded Triangle)
7.5 + 24 = 31.5

44 kg is approximately equal to 97.0034 pounds ( rounded to four decimal places )

The conversion factor to convert kg to lbs is 2.20462

1 kg = 2.20462 pounds

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

The mass in lbs = The mass in kg × conversion factor

Substitute the values in the equation

1 kg = 2.20462 pounds

44 kg = 44 × 2.20462

Multiply the numbers

= 97.0034 pounds  ( rounded to four decimal places )

Therefore, 44 kg is 97.0034 pounds

Learn more about conversion factor here

brainly.com/question/5056146

#SPJ4

The simplification of the given expression would be = 6

60 minutes = 1 hour

But 0.1 of 60 minutes simply means the quantity of 60 minutes that is 0.1.

This can be calculated through the multiplication of 0.1 by 60 minutes.

That is;

= 0.1 ×60 = 6.

Therefore, the the quantity of 60 minutes that is 0.1 = 6.

Learn more about multiplication here:

https://brainly.com/question/28768606

#SPJ1

A solution set calculator online is a tool used to find the set of values that satisfy an equation or system of equations.

It is useful in a variety of mathematical fields such as algebra, calculus, and linear algebra. The calculator takes in the equation(s) and returns the solution set, which is the set of values that satisfy the equation(s). These calculators can be used for both linear and nonlinear equations, and can help in finding the solutions to problems that are difficult or time-consuming to solve by hand.

Learn more about Solution Set:

https://brainly.com/question/799909

#SPJ4

Answer:

196 m²

Step-by-step explanation:

area = side × side

area = 14 m × 14 m

area = 196 m²

Answer:

To convert GB to MB multiply the value of a GB by 1000 to get mb.

1gb x 1000 equals 1000 mb

Answer: Correct option is B

Step-by-step explanation:  3/6 + 2/6 = 5/6

15/100

1/10+5/100

step1: di LCM si nye denominator si nye 100..emegbe zã denominator la nàtsɔ ama LCM la ..le ema megbe la, èdzinɛ ɖe edzi kple numerator

10+5/100

afɔɖeɖe 2: ƒo xexlẽdzesifianu la nu ƒu

15/100

ale,1/10+4/100 ƒe ƒuƒoƒo nye 15/100

The college running back ran for a total of 1732 yards in the regular season.

We can use the table provided to find out how many yards he gained after select games.

127 + 252 + 372 + 495 + 612 + 732 + 853 + 974 + 1089 + 1212 + 1335 + 1458 + 1581 + 1704 = 1732

From the table, we can see that the running back gained 127 yards in the first game, 252 yards in the second game, 372 yards in the third game, and so on. By adding up the yards gained in each game, we can find the total number of yards gained in the regular season.

Therefore, the college running back ran for a total of 1732 yards in the regular season.

Learn more about total number of yards here: https://brainly.com/question/11152547

#SPJ11

the volume of the sugar cone is closest to 14.14 cubic inches.

How to determine?

The volume of a cone can be calculated using the formula V = (1/3)πr²2h, where r is the radius of the base, h is the height of the cone, and π is approximately 3.14.

In this case, the diameter of the cone is 3 inches, which means the radius, r, is half of that or 1.5 inches. The height of the cone is given as 6 inches.

Plugging these values into the formula, we get:

V = (1/3)π(1.5²2)(6)

V ≈ 14.14 cubic inches

Therefore, the volume of the sugar cone is closest to 14.14 cubic inches.

To know more about cone visit:

https://brainly.com/question/16394302

#SPJ1

A- The average rate of change of g(x) over the interval [-2, 2] is 4, B- the instantaneous rates of change at the endpoints are different from the average rate of change over the interval.

A) To find the average rate of change of the function g(x) over the interval [-2, 2], we need to compute the difference quotient:

average rate of change = [g(2) - g(-2)] / [2 - (-2)]

First, we find the values of the function at the endpoints of the interval:

g(-2) = [tex]-2^{3}[/tex] - 6 = -14

g(2) = [tex]2^{3}[/tex] - 6 = 2

Substituting these values into the

average rate of change = (2 - (-14)) / (2 - (-2)) = 16 / 4 = 4

Therefore, the average rate of change of g(x) over the interval [-2, 2] is 4.

B) To compare this rate with the instantaneous rates of change at the endpoints of the interval, we need to find the derivatives of the function at x=-2 and x=2 using the power rule of differentiation:

g'(x) = 3[tex]x^{2}[/tex]

g'(-2) = 3[tex]-2^{2}[/tex] = 12

g'(2)  = 12

The instantaneous rate of change at x=-2 is 12, and the instantaneous rate of change at x=2 is also 12. These values are equal to the average rate of change over the interval [-2, 2], which is 4.

This means that the function g(x) is not a linear function over the interval [-2, 2], and the instantaneous rates of change at the endpoints are different from the average rate of change over the interval.

Learn more about  instantaneous rate of change here:

https://brainly.com/question/30782681

#SPJ4

Moore's law is an observation made by Gordon Moore, co-founder of Intel Corporation, in 1965. It states that the number of transistors on a microchip doubles approximately every two years, while the cost of the chip is halved. Essentially, this means that computing power increases exponentially over time.

Moore's law is associated with exponential functions because it describes a situation in which a quantity (the number of transistors) grows at a rate proportional to its size, resulting in exponential growth. Exponential functions are often used to model phenomena in science, engineering, and other fields that exhibit this kind of behavior. In the case of Moore's law, the rate of growth is approximately 41% per year, or a doubling every 1.5 to 2 years. The formula for exponential growth is:

Where:

Moore's law can be expressed using this formula as:

Where:

For example, if a microchip had 1,000 transistors in 2000, according to Moore's law it would have 2,000 in 2002, 4,000 in 2004, 8,000 in 2006, and so on. The exponential function describes the growth of the number of transistors over time, and the formula allows us to predict future values based on past observations.

~ Zeph

The side of the small square is equal to the length of the rectangles, which is 16cm.

Area is a quantity that measures the size of a two-dimensional surface or shape. It is expressed in square units such as square centimetres (cm2), square metres (m2) or square kilometres (km2). Area is used to describe the size of a garden, a house, a room, a city and much more. It can also be used to calculate the amount of material required for a project, such as paint, carpet or tiles. Knowing the area of a shape can help to calculate costs, and to make sure that enough materials are ordered.


We can calculate the area of the small square by using the formula A = side² where A is the area and side is the length of the side of the square. Thus, A = 16² = 256 cm².

Now, the area of the large square is equal to the area of the small square plus the area of the four rectangles. The area of each rectangle is equal to 16 x 4 = 64 cm² Thus, the total area of the large square is 256 + 4(64) = 512 cm²

To know more about area click-
https://brainly.com/question/28012687
#SPJ1

Refer to the attached image.

Answer:

[tex]31.7^\circ[/tex]

Step-by-step explanation:

We use the property that the sin of the angle of a right triangle is the ratio of the side opposite that angle divided by the hypotenus

Therefore
[tex]\begin{aligned}\sin x & = \dfrac{2.1}{4}\\& = 0.525\\\end{aligned}\\\begin{aligned}x &= sin^{-1}(0.525)\\& = 31.7^\circ \end{aligned}[/tex]

The answer is (i) The statement is False, (ii) The statement is false, (iii) The statement is true, (iv) The statement is true.

(i) Let A = {2, 3, 4, 5} and B = {3, 6}

    Now A∩B

    = {2, 3, 4, 5} ∩ {3, 6} = {3}

    Hence, A and B are not disjoint. So the statement is false.

(ii) Let A = {a, e, i, o, u} and B = {a, b, c, d}

    Now A∩B

    = {a, e, i, o, u} ∩ {a, b, c, d}= {a}

    Hence, A and B are not disjoint. So the statement is false.

(iii) Let A = {2, 6, 10, 14} and B = {3, 7, 11, 15}

     Now, A∩B

     = {2, 6, 10, 14} ∩ {3, 7, 11, 15} = Φ

     Hence, A and B are disjoint sets. So the statement is true.

(iv) Let A = {2, 6, 10} and B = {3, 7, 11}

     Now A∩B  

     = {2, 6, 10} ∩ {3, 7, 11} = Φ

     Hence, A and B are disjoint sets. So the statement is true.

To know more about  disjoint sets:

brainly.com/question/29190252

#SPJ4

Answer:

0.5735764

Step-by-step explanation:

sin(55°) = √(1-cos²(55°))

Answer:

The answer is 0.5735764

Step-by-step explanation:

sin(55°) = √(1-cos²(55°)

Hope this helped! Have a GOOD DAY!

The length of missing side of the given right triangle by using pythagoras theorem is x = 12.369 .

The hypotenuse side of a right-angled triangle's square is equal to the sum of the squares of the other two sides, according to Pythagoras' Theorem. The Perpendicular, Base, and Hypotenuse of this triangle are its three sides. Because to its position opposite the 90° angle, the hypotenuse in this case is the longest side. A right triangle's positive integer sides (let's say sides a, b, and c) are squared to obtain a Pythagorean triple equation.

Consider about the triangle given above:

the perpendicular to "a,"

B stands for base,

The letter "c" stands in for the hypotenuse.

The definition provides the following as the Pythagoras Theorem formula:

[tex]Hypotenuse^2 = Base^2 + Perpendicular^2\\\\c^2 = a^2 + b^2[/tex]

The right triangle's sides are as follows:

Perpendicular ( p ) = x

Base ( b ) = 4

Hypotenuse ( h ) = 13

Finding the length of missing side

Using Pythagoras theorem

[tex]p^2 +b^2=h^2[/tex]

plug the values

[tex]x^2+4^2=(13)^2[/tex]

Evaluate the power

[tex]x^2+16=169\\\\x^2=169-16\\\\x^2=153\\\\x=\sqrt{153}\\\\x= 12.369[/tex]

The length of missing side x = 12.369

Learn more about Pythagoras Theorem , visit:

https://brainly.com/question/343682

#SPJ1

The complete question is ,

Find the missing side of the given right triangle whose sides are given as base = 4 units , hypotenuse = 13 units .

The measure of the angles required are,

Angle A = 58.3deg

Angle B = 121.7deg

If two angles sum up to 180 degrees, they are referred to as supplementary angles. When paired, supplementary angles result in a straight angle (180 degrees). In other words, if angle 1 plus angle 2 equals 180 degrees, angle 1 and angle 2 are supplementary. In this case, Angles 1 and 2 are referred to as "supplements" of one another.

Supplementary angles, by definition, add to to a sum of 180deg.

So what we know is:

Angle B + Angle A = 180deg

Angle B - 63.4deg = Angle A

By substitution:

Angle B + (Angle B - 63.4deg) = 180deg

Using the commutative property of addition, we can re-write the equation as:

(Angle B + Angle B) - 63.4deg = 180deg

We can add 63.4deg to both sides of the equation:

(Angle B + Angle B) - 63.4deg + 63.4deg = 180deg + 63.4deg

By simplifying, that gives us:

2(Angle B) = 243.4deg

Dividing both sides of the equation by 2, we can determine the measure of Angle B:

Angle B = 243.4deg/2 = 121.7deg

Now we have the measure of one of the angles, which we can plug back into our first equation:

Angle B + Angle A = 180deg

121.7deg + Angle A = 180deg

Subtracting 121.7deg from both sides, we get:

Angle A = 180deg - 121.7deg = 58.3deg

There’s your answer:

Angle A = 58.3deg

Angle B = 121.7deg

Learn more about supplementary angles, visit:

https://brainly.com/question/13045673

#SPJ1

Answer:

3

Step-by-step explanation:

Set the equations. Let the variable x denote the amount of months that are needed.

Silver Gym:

In Silver Gym, the membership is a flat fee (constant) of $45, and training sessions are $25 for each session (25x, x denoting the amount of sessions).

Therefore, total cost is:

Total Cost (c) = Training session x Training cost per session + Flat Fee

or

c = 25x + 45

Fit Factor:

In Fit Factor, the membership is a flat fee (constant) of $75, and training sessions are $15 for each session (15x, x denoting the amount of sessions).

Therefore, the total cost is:

Total Cost (c) = Training session x Training cost per session + Flat Fee

or

c = 15x + 75

~

You are trying to solve for the amount of training sessions that have to be bought in which both prices will be the same. Note that both equations are equal to c. Based on the transitive property of equality, if a = b and b = c, then a = c. Therefore:

c = 25x + 45

c = 15x + 75

15x + 75 = c = 25x + 45

15x + 75 = 25x + 45

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract 25x and 75 from both sides of the equation:

15x (-25x) + 75 (-75) = 25x (-25x) + 45 (-75)

15x - 25x = 45 - 75

-10x = -30

Next, divide -10 from both sides of the equation:

(-10x)/-10 = (-30)/-10

x = -30/-10 = 3

3 personal training sessions is your answer.

~

Learn more about the transitive property of equality, here:

https://brainly.com/question/14610263?referrer=searchResults

The steps to calculate the equilibrium concentration have been explained below.

Equilibrium concentration is a state in a chemical reaction, at which the rate of forward reaction becomes the same as the rate of backward reaction.

Calculating equilibrium concentration requires several steps depending on the type of equilibrium you are dealing with which are,

1)Write the balanced chemical equation for the reaction.

2)Write the equilibrium expression that describes the relationship between the concentrations of the reactants and products at equilibrium.

3)Determine the initial concentrations of the reactants and/or products

4)Determine the direction of the reaction by comparing the initial concentrations of the reactants and products with the equilibrium constant (Keq).

5)Calculate the change in concentration between the equilibrium concentration and the initial concentration.

6)Calculate the equilibrium concentration by adding the change in concentration to the initial concentration.

Learn more about the equilibrium concentration on

https://brainly.com/question/16645766?referrer=searchResults

#SPJ4