why mathematics is indispensible

The compensation equation for the employee may be stated as follows:

A equation is a mathematical statement that claims the equivalence of two expressions. Equations are used in mathematics, science, engineering, and many other professions to express connections between variables and to solve problems.

If s denotes income, x denotes years of experience, and d denotes years of education.

The employee's remuneration is computed as the basic wage of $35,000 + $2,000 for each year of experience plus $3,000 for each year of study. In deciding an employee's wage, this equation considers both their experience and education.

Therefore, \(\text{S}=35000+2000\text{x}+3000\text{D}\) is the compensation equation for the employee.

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Answer:

  46

Step-by-step explanation:

You want to evaluate the expression t²u+s for t=-2, u=9, s=10.

Put the numbers in the places of the corresponding variables, and do the arithmetic.

  (-2)²·9 +10 = 4·9 +10 = 36 +10 = 46

The value of the expression is 46.

Answer :

a) It is given that

Everyday a machine makes 500000 staples and puts them into the boxes.

The machine need 170 staples to fill a box

One box contans = 170 staples.

Total number of staples = 500000

Number of box required to fill 500000 staples = Total number of staples/No. of staples 1 box contains.

\( \: :\implies \) 500000 /170

\( :\implies \: \) 2941 (approx)

Therefore, 2941 boxes are required to fill with 500000 staples.

b) It is given that,

Each staple is made of 0.21 g of metal .

Total weight of metal = 1 kg = 1000 g

1 staple = 0.21 g

Number of staples = weight of metal/ Weight of 1 staple.

\( \: :\implies \) 1000/0.21

\( \: :\implies \) 4761 (approximately)

Therefore, 4761 staples can be made from 1 kg of the metal.

The measure of angle x on the straight line is 130 degrees.

The sum of interior angles in a triangle equals 180 degrees.

To determine the value of x, we first determine its suplemetary angle x .

Hence:

40 + 90 + ( suplemetary angle of x ) = 180

Solve for the suplementary angle:

130 + ( suplemetary angle of x ) = 180

Suplementary angle of x = 180 - 130

Suplemetary angle of x = 50 degree

Now, we can find the measure of  angle x.

Note that, sum of angles on a straight line equals 180 degree.

Hence:

x + ( suplemetary angle of x )  = 180

x + 50 = 180

Solve for x

x = 180 - 50

x = 130 degrees.

Therefore, the value of x is 130 degrees.

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Answer:

(-0.5, -1)

Step-by-step explanation:

A turning point is a point of the graph where the graph changes from increasing to decreasing (rising to falling) or decreasing to increasing (falling to rising)

Answer:

um i think 8 not really but its maybe 8 or 17 not really sure

Proving  X is computable by the theorem "Let W⊆ω. Then W is computable if both W and ω∖W are c.e".

Given :

If I can prove that X is c.e. and ω∖X is c.e. then I can prove that X is computable by the theorem "Let W⊆ω. Then W is computable if both W and ω∖W are c.e". But I'm not able to proceed on how should I do this.

Take a computable surjection :

f : ω → W.

Defined  G = { f ( x ) ∣ x ∈ ω and ∀y < x ( f ( y ) < f ( x ) ) }.

here clearly, G ⊆ W .

And G is infinite. For if f ( x ) ∈ G, take the smallest y such that f ( y ) > f ( x ); then f ( y ) ∈ V.

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The exact value of the specified trigonometric identity found using the the trigonometric identity for tan(A - B) and tan(arccos(x)) and tanarcsin(x)) is presented as follows;

\(tan\left(sin^{-1}\left(\dfrac{3}{4} \right) - cos^{-1}\left(\dfrac{1}{5}\right) \right) =\dfrac{32\cdot \sqrt{6}- 75\cdot \sqrt{7} }{209}\)

A trigonometric identity is an equality that involves trigonometric functions that is valid for all values of the arguments of the equation

The required trigonometric identities are;

\(tan (A - B) = \dfrac{tan(A) -tan(B)}{1-tan(A)\cdot tan(B)}\)

\(tan(sin^{-1}(x)) = \dfrac{x}{\sqrt{1-x^2} }\)

\(tan(cos^{-1}(x)) = \dfrac{\sqrt{1-x^2}}{x }\)

Therefore;

\(tan\left(sin^{-1}\left(\dfrac{3}{4} \right) - cos^{-1}\left(\dfrac{1}{5}\right) \right) = \dfrac{tan\left(sin^{-1}\left(\dfrac{3}{4} \right)\right)-tan\left(cos^{-1}\left(\dfrac{1}{5} \right)\right)}{1-tan\left(sin^{-1}\left(\dfrac{3}{4} \right)\right)\times tan\left(cos^{-1}\left(\dfrac{1}{5} \right)\right)}\)

Which gives;

\(\dfrac{\dfrac{\frac{3}{4} }{\sqrt{1-\left(\frac{3}{4} \right)^2} } -\dfrac{\sqrt{1-\left(\frac{1}{5} \right)^2}}{\frac{1}{5} } }{1+\dfrac{\frac{3}{4} }{\sqrt{1-\left(\frac{3}{4} \right)^2} } \times \dfrac{\sqrt{1-\left(\frac{1}{5} \right)^2}}{\frac{1}{5} }}=\dfrac{\dfrac{3\cdot \sqrt{7}-14\cdot \sqrt{6} }{7} }{\dfrac{7+6\cdot \sqrt{42} }{7} }\)

\(\dfrac{\dfrac{3\cdot \sqrt{7}-14\cdot \sqrt{6} }{7} }{\dfrac{7+6\cdot \sqrt{42} }{7} }=\dfrac{32\cdot \sqrt{6}- 75\cdot \sqrt{7} }{209}\)

Which indicates that we have;

\(tan\left(sin^{-1}\left(\dfrac{3}{4} \right) - cos^{-1}\left(\dfrac{1}{5}\right) \right) =\dfrac{32\cdot \sqrt{6}- 75\cdot \sqrt{7} }{209}\)

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The number for which the theoretical probability matches the experimental probability is 2.

Experimental probability and theoretical probability are two different ways to determine the likelihood of an event occurring.

Experimental probability is determined by performing an experiment or conducting observations and collecting data to see how often an event occurs. This method involves counting the number of times an event occurs and dividing that number by the total number of trials or observations.

Theoretical probability, on the other hand, is determined by using mathematical principles and calculations to determine the likelihood of an event occurring. It is based on the assumption that all outcomes are equally likely.

In the given table;

For theoretical, P(2) = 1/4

For experimental, P(7) = 7/28 = 1/4

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The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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To determine the type of discontinuity that exists at f(20):

According to the graph,

There is no discontinuity that exists at f(20).

Hence, the correct option is the first one.

Based on the given conditions, the lock solution is 205.

To solve the lock, to calculate the total score based on the given conditions:

Crocus: + 20

Daffodil: + 25

Snowflake: - 50

Tulip: + 30

Bird-Red: + 25, else + 10

Calculating the scores for each input:

TULIP: +30

CROCUS: +20

DAFFODIL: +25

TULIP: +30

DAFFODIL: +25

TULIP: +30

DAFFODIL: +25

CROCUS: +20

Total score = 30 + 20 + 25 + 30 + 25 + 30 + 25 + 20 = 205

Therefore, the solution for the lock is 205.

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Image transcribed:

SPRING NOW LOADING.

<IF CROCUS, THEN +20>

<IF DAFFODIL, THEN +25>

<IF SNOWFLAKE, THEN -50>

<IF TULIP, THEN +30>

<IF BIRD-RED, THEN +25, ELSE + 10>

TULIP

CROCUS

DAFFODIL

TULIP

DAFFODIL

TULIP

DAFFODIL

CROCUS

Solve Lock

Answer:

32\(a^{35}\)

Step-by-step explanation:

using the rules of exponents

\(a^{m}\) × \(a^{n}\) = \(a^{(m+n)}\)

\((a^m)^{n}\) = \(a^{mn}\)

\((2a^3a^4)^{5}\)

= (2\(a^{(3+4)}\) )^5

= \((2a^7)^{5}\)

raise each term inside the parenthesis to power 5

= \(2^{5}\) × \(a^{7(5)}\)

= 32\(a^{35}\)

Answer:

32\(a^{35}\)

Step-by-step explanation:

using the rules of exponents

\(a^{m}\) × \(a^{n}\) = \(a^{(m+n)}\)

\((a^m)^{n}\) = \(a^{mn}\)

\((2a^3a^4)^{5}\)

= (2\(a^{(3+4)}\) )^5

= \((2a^7)^{5}\)

raise each term inside the parenthesis to power 5

= \(2^{5}\) × \(a^{7(5)}\)

= 32\(a^{35}\)

Answer:

Simplifying

14.62 + (-11.302) = 0

14.62 + (-11.302) = 0

Combine like terms: 14.62 + (-11.302) = 3.318

3.318 = 0

Solving

3.318 = 0

Couldn't find a variable to solve for.

This equation is invalid, the left and right sides are not equal, therefore there is no solution.

Step-by-step explanation:

________________________________________________________________

\((1,000,000) + (3,00,000) + (60,000)+(2,000) + (700)+( 40)+8 \\ = 1300000 + 62000 + 740 + 8 \\= 1362000 + 748 \\= 1362748\)

________________________________________________________________

hope it helped you:)

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.

The total number of periods is given as follows:

5 + 6 + 4 = 15.

The frequency of each class is given as follows:

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Answer:

0 theres no solution

Step-by-step explanation:

Part a: Roy sweeps out 2.15/0.7 radians.

Part b: When Roy stops skiing, he is cos(3.071)(0.7) km to the center of the ski trial

Part c: When Roy stops skiing he is sin(3.071)(0.7) km above the centre of the ski trail

The radius of the ski trail= 0.7 km

Roy starts 3 o'clock position and travels 2.15 km in the counter-clockwise direction.

Let O be the centre of ski trial, A be the starting point(3-o'clock position) and consider he is now at point B.

Now, using the formula for arc length.

Arc length=(Radius)(angle at center)

2.15=(0.7)θ

θ=2.15/0.7

Roy sweep out 2.15/0.7 radians.

Part b:

When Roy stops skiing how many km is Roy to the right of the ski trial

In part, a figure draws the vertical line from point B on the horizontal line. Get the right-angle triangle

Here to find the length OP. In right angle triangle cos θ=Adjacent side/hypotenuse,

As in part, a central angle is 2.15/0.7=3.071.

Therefore,

cos(3.071)=OP/0.7

OP=cos(3.071)(0.7)  

cos(3.071)(0.7) km.  

Part c:

When Roy stops skiing how many km is Roy above the centre of the ski trial

From figure part of part b, we have to calculate side BP.

In right angle triangle sin(θ)=Opposite side/hypotenuse

Therefore,

sin(3.071)=BP/0.7

BP=sin(3.071)/(0.7)

sin(3.071)(0.7) km.

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Answer:

Step-by-step explanation:

You want the area and volume ratios when two figures have a similarity ratio of 2 : 7.

The ratio of areas is the square of the similarity ratio:

  2² : 7² = 4 : 49

The ratio of volumes is the cube of the similarity ratio:

  2³ : 7³ = 8 : 343

__

Additional comment

It can help to think about the units of area and volume. For linear dimensions in inches, area dimensions are in square inches, and volume dimensions are cubic inches. Any ratio of inches will be squared when those inch dimensions are used for area, and will be cubed when volume is computed.

  side length of a square or cube: smaller: 2", larger: 7"

  area of the square: smaller: 2² in², larger: 7² in² or 4 in² and 49 in²

  volume of the cube: smaller: 2³ in³, larger: 7³ in³ or 8 in³ and 343 in³

<95141404393>

Answer:

10/12

Step-by-step explanation:

Answer:

Imagine you have half of a cookie. You break it into three pieces to share with friends. You keep one piece, so you have 1/6 of the entire cookie. You can use multiplication to check your work. 1/6x3 =3/6 of 1/2  :D

Step-by-step explanation:

Answer:

\(28km\)

Step-by-step explanation:

\(5miles = 8km\)

\(17.8miles = x\)

\( \frac{17.8}{5} \times 8km\)

\(x = 28km\)

It have get \(24\) customer of them to sign up for the new service feature.

Given:

  Sign up percentage is \(25\) %.

    \(96\) customer.

To find the solution by,

Multiply customer and sign up

   \(=96*25\)%

   \(=96*\frac{25}{100} \\\\=2400/100\\\\=24\)

Thus, it have get \(24\) customer of them to sign up for the new service feature.

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Answer:

V = 1/3 * π * r^2 * h OR V = π * r^2 * h/3

Step-by-step explanation:

hope it will help you dear

you told only formula if you need derevation then say :)

Answer:

Step-by-step explanation:

For \(3^5^m\):

Just like \(9^{0.5m}\) · \(9^{2m}\), \(3^5^m\) equates to \(243^m\).

For \(81^m\):

\(81^m\) does not equate to \(9^{0.5m}\) · \(9^{2m}\).

For \(9^{2.5m}\):

After applying the exponent rule to the equation, it came out to \(9^{2.5m}\).

Why the length of the third (3) side of a triangle cannot be less than the total of any two (2) of its sides is shown in the diagram: B. by demonstrating that two sides with lengths of 4 and 3 cannot ever come together to form a vertex.

The definition of a triangle is a two-dimensional geometric figure with exactly three (3) sides, three (3) vertices, and three (3) angles. According to the length of their sides, triangles fall into one of the following three (3) categories:

By applying the Triangle Inequality Theorem to this diagram (see attachment), we have:

4 + 12 > 3 (True).

3 + 12 > 4 (True).

4 + 3 > 12 (False).

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The equation for the proportion, p, of consumers who shop with coupons is: p = C/N where C is the number of consumers who use coupons and N is the total number of consumers asked.

An equation is a mathematical statement that indicates the equality of two expressions. It consists of two expressions separated by an equal sign (=). The expression on the left side of the equal sign is equivalent to the expression on the right side. Equations can have one or more variables, which are usually represented by letters such as x, y, or z. The goal in solving an equation is to determine the value(s) of the variable(s) that make the equation true. This involves manipulating the expressions on both sides of the equal sign using algebraic operations such as addition, subtraction, multiplication, and division, to isolate the variable on one side of the equation. Equations are used in many areas of mathematics and science to represent relationships between variables and to solve problems. They are also used in various fields such as engineering, physics, and economics to model real-world situations and make predictions based on mathematical analysis.

Here,

This equation represents the ratio of the number of consumers who use coupons to the total number of consumers. It is commonly used in statistics and market research to measure the prevalence of a certain behavior or preference among a population. By calculating the proportion of consumers who use coupons, businesses can make informed decisions about their pricing strategies, promotions, and advertising campaigns.

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Answer:

a) the probability that at least one of 10 successive points indicates a problem when in fact the process is operating correctly is 0.4013

b) the probability that at least one of 40 successive points indicates a problem when in fact the process is operating correctly is 0.8715

Step-by-step explanation:

following how the independence multiplication rule works,

i.e finding p(A)' which is 1 - p(No problem) because what we need is an intersection not a union so;

a) 10 successive points

probability (problem) = 0.05

probability (No problem) = 0.95

required probability = 1 - [probability (No problem)]^10

= 1 - (0.95)^10

= 1 - 0.5987

= 0.4013

the probability that at least one of 10 successive points indicates a problem when in fact the process is operating correctly is 0.4013

b) 40 successive points

probability (problem) = 0.05

probability (No problem) = 0.95

required probability = 1 - [probability (No problem)]^40

= 1 - (0.95)^40

= 1 - 0.1285

= 0.8715

the probability that at least one of 40 successive points indicates a problem when in fact the process is operating correctly is 0.8715

9514 1404 393

Answer:

  a = {1, 2, 3}, b = (2, 4, 7}, c = (-3/14, -3/7, 5/14}

Step-by-step explanation:

For the above vectors, ...

  a × b = a × c = (2, -1, 0)

__

Here, c is found to be a scaled version of (a×(a×b)).

The horns are frequently used as a signal to indicate the end of a segment or a specific task. Hence, a horn blows is the noise that sounds at the end of a segment.

The noise that sounds at the end of a segment is A horn blows.

In geometry, a segment is a part of a line that connects two points.

For example, line segment AB, which is denoted by AB, connects point A and point B and can be visualized as a portion of a line.

In general, line segments are denoted by their endpoints.

A horn is a cone-shaped instrument that is often used as a warning signal or a musical instrument.

However, it is important to note that noise can occur at the end of a segment in certain contexts and situations.

For example, in the context of audio or video editing, you can apply fade-out effects or specific sound effects to signal the end of a segment.

However, these sounds are not universally applicable and depend on the specific creative choices and technical aspects of the project.

In the transportation sector, horns are commonly used to alert pedestrians and other drivers of an oncoming vehicle's presence.

The sound of a horn is usually a sharp and loud noise that is difficult to ignore.

As a result, horns are frequently used as a signal to indicate the end of a segment or a specific task. Hence, a horn blows is the noise that sounds at the end of a segment.

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