explain and answer please

Half life of the radioactive substance is 3.6  days

The half life of the element is calculated from the formula

N(t) = N'(1/2)^(t/t')

N(t) = quantity of the substance remaining

N' = initial quantity of the substance

t = time elapsed

t' = half life of the substance

0.4 = 4.8 (0.5)^13/t'

0.4 / 4.8 =  (0.5)^13/t'

take natural logarithm of both sides

㏑(0.4/4.8) = 13/t' ㏑(0.5)

divide through by natural log of 0.5

-2.4849 / ㏑(0.5) = 13/t'

13/t' = 3.58496

t' = 13 / 3.58496

t' = 3.626 days

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The average value of the function f(t) is [tex]4.433*10^{10}[/tex] .

Given,

[tex]f(t)=te^{3t^2}[/tex] over interval [1,3]

To find average value of the function use formula,

[tex]f(x)_{avg} =\frac{1}{b-a}\int\limits^a_b {f(x)} \, dx[/tex] over the interval {a,b}

[tex]f(x)_{avg} =\frac{1}{3-1}\int\limits^3_1 {te^{3t^2}} \, dt\\\\\\f(x)_{avg} =\frac{1}{2}\int\limits^3_1 {te^{3t^2}} \, dt\\[/tex]

let

[tex]u=3t^2\\\\du=6tdt \\\\tdt=\frac{du}{6}[/tex]

replacing u and du ,

[tex]f(x)_{avg} =\frac{1}{2*6}\int\limits^3_1 {e^{u}} \, du\\\\f(x)_{avg} =\frac{1}{12}\ e^u\|\limits^3_1\\ \\f(x)_{avg} =\frac{1}{12}\ e^{3x^2}\|\limits^3_1\\\\f(x)_{avg} =\frac{1}{12}\ [e^{3(3)^2}-e^{3(1)^2}]\\\\f(x)_{avg} =\frac{1}{12}\ [e^{27}-e^{3}]\\\\f(x)_{avg}=4.433*10^{10}[/tex]

Thus, the average value of the function f(t) is [tex]4.433*10^{10}[/tex] .

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The length of the major arc is (203/18)π.

What is a length of an arc?

The distance along the curved line that makes up the arc is measured using the arc length formula (a segment of a circle). The arc length is, to put it simply, the distance that passes through the curved line of the circle that forms the arc.

Here, we have

The circle with center K has an arc with a radius of 7 inches and an angle subtended at the center which measures 70 degrees.

The major arc LNM would have its central angle measured as:

Angle ∅ = 360 - 70 (Sum of angles on a point equals 360)

Angle ∅ = 290

The calculation for the length of an arc is given as;

Length of arc = (∅/360) x 2πr

Where ∅ = 290, and r = 7, the length of the major arc becomes;

Length of arc = (290/360) x 2 x π x 7

Length of arc = (29/36) x 14π

Length of arc = (29 x π x 14)/36

Length of arc = 203π/18

Hence, the length of the major arc is (203/18)π.

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The value of x in the similar triangles is 11.4.

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other.

Therefore,

ΔACB ~ ΔEFD

Hence,

AC / EF = CB / FD = AB / ED

Therefore, let's find x

x = AB

ED = 3.8

BC = 15

FD = 5

x / 3.8 = 15 / 5

cross multiply

5x = 15 × 3.8

5x = 57

divide both sides of the equation by 5

x = 57 / 5

x = 11.4

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To simplify complex fractions with LCD multiply each term in the numerator and denominator by the LCD

Given,

LCD;- Least Common Denominator

When two or more fractions are supplied, the least common denominator is the smallest number among all the common multiples of the denominators.

We have to find the method of simplification of complex fractions with LCD;

Here,

Multiply each term in the numerator and denominator by the LCD to simplify this complicated fraction. It doesn't matter how complicated these fractions are; all you need to do is discover the LCD to convert the complicated fraction into a simpler one. The technique is done more frequently the more fractions there are in an issue

That is,

To simplify complex fractions with LCD multiply each term in the numerator and denominator by the LCD

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Answer:

The double of 8 is 16. Answer is 16.

The rate of change of the area of the right triangle at that instant is -1.5 sq km/h.

Let ABC be a right triangle, right-angled at B.

the side decreasing be, BC = x

and the increasing side be, AB = y

then, AC = z = √(x² + y²) (using Pythagoras theorem)

It is given that, dx/dt = - 5km/h and dy/dt = 14 km/h

x = 3, y= 9 at certain instant

now, the area of the triangle = 1/2 xy

A = 1/2 xy

dA/dt = 1/2 (y).dx/dt + x/2.dy/dt

at x = 3, y = 9, substituting the values,

(dA/dt) = 1/2 (9)(-5) + 3/2 (14)

= -1.5

therefore, the rate of change of the area of the right triangle at the instant when x=3 and y= 9 is -1.5 sq km/h.

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The probability the couple will have at least two boys is 0.26.

This type of probability is independent probability. Independent probability can only occur if the events are independent or not dependent on previous event and also this event doesn't affect the next event.

For probability the couple will have at least two boys is equal to probability they have two boys plus probability they have three boys. Mathematically is,

P(x≥2) = P(x=2) + P(x=3)

P(x≥2) = 0.127 + 0.133

P(x≥2) = 0.26 or 26%

Thus, the couple will have at least two boys has a probability of 0.26 or 26%

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Mr. Arnett will have to pay $15.75 for the trail mix if it cost $4.50 per pound.

According to the question,

We have the following information:

Amount of trail mix: 15 oz, 14 oz, 10 oz and 17 oz

Cost of 1 pound of trail mix = $4.50

Total amount of trail mix in oz:

15+14+10+17

56 oz

We know that 1 ounce = 0.0625 pounds

So, we have the following expression:

56 oz = 56*0.0625 pounds

56 oz = 3.5 pounds

Now, the cost of trail mix:

3.5*4.50

$15.75

Hence, Mr. Arnett will have to pay $15.75 for the trail mix if it cost $4.50 per pound.

The complete question is here:

At the grocery store, Mr. Arnett allowed each of his children to fill their own bag with trail mix for their hike. The table shows the amount of trail mix for each child.

Child-amount of trail mix in oz

Ava-15

Grayson-14

Mason-10

Tyler-17

The trail mix costs $4.50 per pound. How much will Mr. Arnett pay for all the trail mix?

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The teacher has offered his students a(n): algorithm

What is algorithm?

A method which solve a puzzle or carry out a calculation is known as an algorithm. Algorithms are precise lists of instructions that, in either software or hardware-based routines, carry out predetermined operations step by step. In many facets of IT, algorithms are commonly utilized. An algorithm is typically a short process that resolves a recurring issue in mathematics and computer science. Automated systems heavily rely on algorithms, which are also utilised as guidelines for carrying out data processing. Pseudocode, flowcharts, control tables, and plain languages are all ways to express algorithms. Since they are more ambiguous, natural language expressions are uncommon. Algorithms that a computer executes are typically expressed in programming languages.

A high school physics teacher reassures his class that no matter how confusing this week's word problems appear,

And they all may be solved quite handily through the use of the formula F = MA.

Hence this is the prime example of the algorithm.

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Answer: If it is one of your choices it should be angle angle side(aas)

By using t test, it can be concluded that

The value of t at level of significance = 0.10 with 5 degree of freedom is greater than the value of t at level of significance = 0.10 with 10 degree of freedom

What is t test?

If the observations are from a normal population and the population standard deviation is not known, the distance between the sample mean and the population mean can be calculated by using t test

By using t- table

The value of t at level of significance = 0.10 with 5 degree of freedom = 2.015

The value of t at level of significance = 0.10 with 10 degree of freedom = 1.812

Since 2.015 > 1.812,

The value of t at level of significance = 0.10 with 5 degree of freedom is greater than the value of t at level of significance = 0.10 with 10 degree of freedom

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The point estimate of the population standard deviation is   2.82

Since the  given  simple random sample is   6 8 10 8 10 6. considering  the data of the sample be denoted by X.  the mean of the sample  is

X'=1/n ∑X, where n is the number of data points

 =6+ 8 +10+ 8+ 10+ 6/ 6   =  6

Since  the  formula for The point estimate of the population standard deviation is:

s= [tex]\sqrt{}[/tex](1/(n-1)* ∑(X−X')^2,  where  X' is the sample  mean and n is the

s=[tex]\sqrt{}[/tex]( 1/(6-1)*{(6-6)^2+(8-6)^2+(10-6)^2+(8-6)^2+(10-6)^2)

= [tex]\sqrt{}[/tex](1/5 *(4+16+4+16)

= [tex]\sqrt{}[/tex](1/5 *(40))

=[tex]\sqrt{}[/tex](8)

=1.41*2

=2.82

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Answer:

y=2x-5

Step-by-step explanation:

1 u must calculate the slop then the amount of b

by -3=1×2-b

-5=b

so after we find the number if y we will make an equation y=2x-5

The  common ratio is 4.

The next 3 terms are 192,768, 3072

What is common ratio?

In a geometric sequence, ratio of each term to its immediately preceding term is always constant and is known as common ratio.

Here, 48/12 = 12/3 = 4  ( it is a constant ratio )

Hence it is a geometric sequence and common ratio is 4.

Next 3 terms can be found by multiplying the common ratio with the previous term.

48*4=192

192*4=768

768*4=3072

So, the next 3 terms are 192,768, 3072

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Number of ways to form four letters strings formed using a, b, c, d, e with the given conditions is equal to 150ways.

As given in the question,

Given letters are a, b, c, d, e has

Number of vowel = 2

Number of consonant= 3

Number of letter strings to be formed = 4

Condition:

First letter must be vowel

Last letter must be consonant

First place filled in 2 ways

Second and Third place filled in 5ways

Last place filled in 3 ways

Total number of ways to form four letters strings

= 2 × 5 × 5 × 3

= 150

Therefore, number of ways to form four letter string is 150 ways.

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The algebric expression represents the cost of a four-line ad that runs for a year will be $(192/5)f.

An expression is a combination of some mathematical symbol such that an arithmetic operator and variable such that all are constrained and create an equation.

Expression is very useful to determine the end or root value of constraint.

The constraint of expression is represented as = or <, >.

As per the given,

A local Pennysaver paper charges f dollars weekly for a five-line classified ad.

Cost of five-line ad = $ f / week

Cost of one line ad = $ f/5 / week

Cost of four line ad = $ (4/5) f / week

It is known that,

1 year = 12 x 4 = 48 weeks

Cost of four line ad for one year = $ (4/5)48 f

⇒ $(192/5)f

Hence "The algebric expression represents the cost of a four-line ad that runs for a year will be $(192/5)f".

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Answer: experiment

Step-by-step explanation:

A course of perception that has an unsure result is alluded to as an experiment.

The study of mathematical objects by computing in order to discover their properties and patterns is known as experimental mathematics. It has been described as "that mathematical theory that concerns itself ultimately with both the convention and transmission of insights within the mathematical neighborhood through the use of experimental investigation of conjectures and also more irregular beliefs and just a careful analysis of the information acquired in this endeavor (in either the Galilean, Baconian, Aristotelian or Kantian sense).

The nineteenth century saw the reemergence of experimental mathematical concepts as a distinct field of study as the range of calculations that could be performed was greatly expanded by the development of the electronic computer, which could perform calculations at speeds and with levels of precision that were unimaginable to earlier generations of mathematicians.

A course of perception that has an unsure result is alluded to as an experiment.

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Volume of the cone as a polynomial function., Radius of cone = x + 4 units.

According to our question-

Radius of cone = x + 4 units,

Height of cone = 5 units less than radius,

Volume formula.

Solution

We are given the volume formula:

V = (1/3)πr²h

Find the height:

h = r - 5

h = x + 4 - 5 = x - 1

Substitute all into formula:

V(x) = (1/3)π(x + 4)²(x - 1)

You may keep it as is or simplify:

V(x) =

(1/3)π(x² + 8x + 16)(x - 1) =

(1/3)π(x³ + 8x² + 16x - x² - 8x - 16) =

(1/3)π(x³ + 7x² + 8x - 16)

Hence, Volume of the cone as a polynomial function., Radius of cone = x + 4 units.

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The domain of the given function is {0, 1, 2 3.... 10}.

The range of the function is: {0, 2.69, 3.17, 3.65, 4.13, 4.61, 5.09, 5.57, 6.03, 6.49, 6.95}

A function has a set of input values (x-values) that are corresponding to a set of output values (y-values).

The set of these input values (x-values) is what is referred to as the range of a function, while the set of the corresponding output values (y-values) is the domain of the function.

Given the graph above, all the set of weight are input values which make up the domain of the function, while the set of corresponding prices is the range of the function.

The domain is therefore: {0, 1, 2 3.... 10}.

The range is therefore: {0, 2.69, 3.17, 3.65, 4.13, 4.61, 5.09, 5.57, 6.03, 6.49, 6.95}

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The total VA( volt-ampere ) that must be used in a service calculation for 50' show window is 125000VA.

A volt-ampere (SI symbol: VA or V A, abbreviated as VA) is the unit of perceived power in an electrical circuit. The apparent power is equal to the product of the root mean square voltage (in volts) and the root mean square current (in amperes). Volt-amperes are commonly used to analyze alternating current (AC) circuits. In direct current (DC) circuits, this product equals the real power in watts. The volt-ampere is dimensionally identical to the watt: 1 VA = 1 W in SI units).

The total VA that must be used in a service calculation for 50' show window is, Therefore, by using VA linear foot method,

200 VA per linear foot×50'=10000VA10000VA×1.25

=125000VA

Hence, the total VA that must be used in a service calculation for 50' shadow is 125000VA.

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The rate at which the water level is rising when the water level is 5 cm is; dh/dt = 1.6 cm/s

We are told that;

length of square side; s = 4 cm

height of pyramid; h = 11 cm

volumetric rate; dV/dt = 35 cm³/s

Since the base is square shaped and we know that area of a square = s², then we can say that;

Volume of pyramid = ¹/₃s²h

The pyramid has a height of 11 cm and length of its' square base side is 11 cm.

Now, regardless of the water height, the surface of the water will always be square shaped. This implies that the ratio of the height to the top side of square will always be the same. Thus, we can say that; s = 4/8 h = h/2

Thus, Volume is;

V = ¹/₃ × (h/2)² × h

V = ¹/₃ × h³/4

V = h³/12

dV/dt = (3h²/4) dh/dt

Plugging in the relevant values gives;

30  = (3 × 5²/4) dh/dt

120 = 75 dh/dt

dh/dt = 120/75

dh/dt = 1.6 cm/s

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{4, 5, 6, 7} total 4 values which diagonal can take constraint is it must be an integer.

It is the shape enclosed by 4 line segments. So, it has 4 vertices as well as four angles with the total of 2 diagonals.

It is the shape enclosed by the 3 lines and have 3 vertices with 3 angles and constitute no diagonals.

The triangle inequality applies.

In order for ACD to be a possible triangle, the length of the AC must lie between CD-DA=0 and CD+DA=8.

In order for ABD to be a possible triangle, the length of AC must in range between BC-AB=3 and BC+AB=9.

The values common to both these restrictions are numbers between 3 and 8. Assuming that we don't want the diagonal to be coincident with any of the  sides, its integer length will be one of the ...

{4, 5, 6, 7}

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The rate of change of capital in terms of units of labor is -2.0 As more labor is used, available capital decreases As more capital is used, available labor decreases.

[tex]100x^{0.75} y^{0.25} = 135540[/tex]

x = 1500 units and y = 1000 units

A) [tex]\frac{d}{dx}(100x^{0.75}y^{0.25} = \frac{d}{dx}(135540)[/tex]

[tex]100[{\frac{d}{dx}(x^{0.75})y^{0.25} + x^{0.75}\frac{d}{dx}(y^{0.25})] = 0[/tex]

[tex]0.75 x^{-0.25} y^{0.25} + x^{0.75} (0.25y^{-0.75\frac{dy}{dx} }) = 0[/tex]   ______(1)

X & Y values in equation 1

[tex]0.75(1500^{-0.25}(1000)^{0.25}+(1500)^{0.75}(0.25)(1000)^{-0.75}\frac{dy}{dx} = 0[/tex]

(0.75) (0.16) (5.62) + (0.41) (0.25) (0.0056) [tex]\frac{dy}{dx}[/tex] = 0

0.6744 + 0.3374 [tex]\frac{dy}{dx}[/tex] = 0

0.3374 [tex]\frac{dy}{dx}[/tex] = -0.6744

[tex]\frac{dy}{dx}[/tex] = -1.9988

[tex]\frac{dy}{dx}[/tex] ≈ -2.0

B) If the labor x is increased then the capital invested in manufacturing process decreased

C) As more capital is used then the available labor is reduced

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The average time a customer spend on department store is 1.33 hours.

Average:

In math, mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set is referred as average.

Given,

If there are on average 80 customers at any particular time and 60 customers go through the checkouts every hour

Here we need to find the average time spend by a customer.

Let us consider x be the time spend by the customer on department store.

While we looking into the given question we know that,

Number of customer = 80

Check out per hour = 60.

So, the average time is 1.33 hours.

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Answer:

1.70507 x 10^5

Step-by-step explanation:

First, we multiply 1.67 x 1021:

1.67 x 1021 = 1705.07.

So, 1705.07 is for one drop of water. We need to find 100 drops of water. To do this, we can set up this equation:

1705.07 x 100 = 170,507

Now, we have to convert this number into scientific notation. How do we do this? The proper format for scientific notation is a x 10^b where a is a number or decimal number such that the absolute value of a is greater than or equal to one and less than ten or, 1 ≤ |a| < 10. b is the power of 10 required so that the scientific notation is mathematically equivalent to the original number:

1.70507 x 10^5 is our answer.

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The width of the rectangle is 60 meters

The area A, in square meters, of a rectangle is given by the equation

A = 70w - w²

where w is the width of the rectangle in meters.

70w - w² = 600

70w - w²- 600 = 0

w²-70w+600 = 0

w²-60w-10w+600 = 0

(w-60)(w-10) = 0

w =60

w =10

the width of the rectangle is 60 meters

Subtraction:

The act of removing elements from a collection is represented by subtraction. Subtraction is symbolized by the negative symbol. The stack will now include five oranges rather than nine if, for instance, four of the nine oranges that are stacked together (as in the figure above) are then moved to a basket. As a result, 5 is the difference between 9 and 4, which is the same as 9 less 4. Subtraction can be applied to other types of numbers in addition to natural numbers. Subtraction is represented by the letter "-". The three numerical elements that make up the subtraction operation are the minuend, the subtrahend, and the difference.

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Answer:

Well, since your answer is 4.8n-5, It could be 2+2.4+4n.3+2

Step-by-step explanation:

it's probably wrong but I'm only doing this for points so get rekt

Step-by-step explanation:

just for points

The two expressions can be -5 + 4.8 n and 4.8n + (-5).

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

4.8n-5.

We can write the expression as

-5 + 4.8 n

or, using the integers

4.8n + (-5)

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The four types of agile are:
Scrum, Kanban,
Extreme Programming (XP),
Lean Development, and Cryst.

What is the Agile cycle?

The systematic succession of phases that a product goes through as it develops from start to finish is known as the agile software development life cycle. Concept, conception, iteration, release, maintenance, and retirement are its six phases.

The systematic succession of phases that a product goes through as it develops from start to finish is known as the agile software development life cycle. Concept, conception, iteration, release, maintenance, and retirement are its six phases.

The project management approach a team decides on will have a small impact on the Agile life cycle. For instance, Scrum teams work in sprints, which are brief timeframes akin to iterations. They also have responsibilities that are precisely defined, like Scrum master. Kanban teams, on the other hand, operate more continuously and don't have set roles. Another illustration is Extreme Programming, where teams frequently work in shorter iterations and give engineering practices more attention.

Hence,

The four types of agile are:

Scrum, Kanban,

Extreme Programming (XP),

Lean Development, and Cryst.

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