Prove that the number A= [tex]20^{8^{2014} } }+113 is composite

Answer:

t = 6162 years

Step-by-step explanation:

This equation takes the form of

We are given everything but the amount of C-14 at time t = 0.  But we can figure it out from the info we ARE given.  We are told that when the spear head is found it contains 54% of its original amount of C-14.  Notice we are dealing in percents.  If 54% remains when it is found, it started out with 100% of its amount.  That's our N value.  Filling in:

Our goal is to get that t down from the exponential position that it is currently in.  To do that we will need to eventually take the natural log of both sides, because ln's and e's "undo" each other, much like squaring "undoes" a square, or dividing "undoes" multiplication.  So we take the natural log of both sides.  On the right side, notice that when we take the natural log, the e disappears; it's "undone", gone.  Before that, though, we will simplify by dividing both sides by 54.  100/54 = 1.851851852.  So, altogether...

Simplifying by plugging the log of that number into our calculator, we get

.6161861395 = .0001t  and

t = 6161.8613

Rounding to the nearest year, t = 6162 years

The probability that it will rain both days is [tex]\frac{1}{4}[/tex].

According to the question

Mr. and mrs. smith plan to roof the cabin on 2 consecutive days.

Assuming that the chance of rain is independent of the day

Probability is the chance that some event will happen.

It is the ratio of the number of ways a certain event can occur to the number of possible outcomes.

Probability = Number of ways it can occur/Total number of outcomes

Probability of rain on first day = 1/2

Probability of rain on second day = 1/2

Then

Probability of rain on both days = [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{2}[/tex] = 1/4

Hence,

The probability that it will rain both days is [tex]\frac{1}{4}[/tex].

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Ileana  have to invest for 8 years :

Simple interest is a simple and straightforward formula for figuring out how much interest will be charged on a loan. Simple interest is calculated by dividing the daily interest rate by the principle and the number of days between payments.

The principal amount must be multiplied by the time, interest rate, and time period in order to calculate simple interest. Simple Interest = Principal x Interest Rate x Time is the written formula.

Principal amount = $15,500

interest = $5,084

Time = ?

Rate = 4.1% simple interest

to find the simple interest :

                                         I = [tex]\frac{(p*t*r)}{100}[/tex]

       Then:

         Time = [tex]\frac{I*100}{P*R}[/tex]

                  = [tex]\frac{(5084*100)}{(15500*4.1)}[/tex]

                  = [tex]\frac{508400}{63,550}[/tex]

                  = 8 years

Ileana  have to invest for 8 years

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Answer:

Each number is increasing by [tex]\frac{1}{4}[/tex].  The next number would be 1 [tex]\frac{1}{4}[/tex] or [tex]\frac{5}{4}[/tex]

Step-by-step explanation:

I am not sure what the question is.  I am wondering if they are asking how is the list growing or what would be the next number.

Each number is increasing by 1/4

[tex]\frac{1}{4}[/tex] + [tex]\frac{1}{4}[/tex] = [tex]\frac{2}{4}[/tex] or [tex]\frac{1}{2}[/tex]

[tex]\frac{1}{2}[/tex] + [tex]\frac{1}{4}[/tex] is the same as [tex]\frac{2}{4}[/tex] + [tex]\frac{1}{4}[/tex] = [tex]\frac{3}{4}[/tex] To change [tex]\frac{1}{2}[/tex] to [tex]\frac{2}{4}[/tex]  you multiple the top and the bottom of [tex]\frac{1}{2}[/tex] by2 to get [tex]\frac{2}{4}[/tex]

[tex]\frac{3}{4}[/tex] + [tex]\frac{1}{4}[/tex] = [tex]\frac{4}{4}[/tex] or 1

The lifetime of meson according to laboratory clocks would be 14 μs.

In this question,

Meson decay, Δt = 2μs

Velocity, y = 0.99C, where C is the speed of the light

Time measurement depends on the reference frame of clock.

Time dilation, Δt' = y Δt

⇒  [tex]\frac{\Delta t }{\sqrt{1-\frac{v^{2} }{c^{2} } } }[/tex]

⇒ [tex]\frac{2(10^{-6} ) }{\sqrt{1-\frac{(0.99c)^{2} }{c^{2} } } }[/tex]

⇒ [tex]\frac{2(10^{-6} ) }{\sqrt{1-0.99^{2} } } }[/tex]

⇒ [tex]\frac{2(10^{-6} ) }{\sqrt{1-0.9801 } } }[/tex]

⇒ [tex]\frac{2(10^{-6} ) }{\sqrt{0.0199} } }[/tex]

⇒ [tex]\frac{2(10^{-6} ) }{0.1410} } }[/tex]

⇒ 14.18 × 10⁻⁶ ≈ 14 μs

Hence we can conclude that the lifetime of meson according to laboratory clocks would be 14 μs.

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The simplest form of the given expression ( x⁴ )⁸ exists x³².

Expression in Math exists described as the collection of numbers variables and functions by utilizing characters like addition, subtraction, multiplication, and division.

The given expression will be simplified as:-

( x⁴ )⁸ = x ⁴ ⁽⁸⁾

( x⁴ )⁸ = x ³²

Therefore the simplest form of the given expression exists as x³².

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The roots of the equation f(x) = x^2 - 93987 are x = √93987 and x = -√93987

Quadratic equations are equations that have a second degree and have the standard form of ax^2 + bx + c = 0, where a, b and c are constants and the variable a does not equal 0

The equation of the function is given as:

f(x) = x^2 - 93987

The above equation is a quadratic equation

Express the equation as a difference of two squares

f(x) = (x - √93987)(x + √93987)

Set the equation of the function to 0

(x - √93987)(x + √93987) = 0

Split the factors of the above function equation as follows

x - √93987 = 0 and x + √93987 = 0

Solve for x in the above equations

x = √93987 and x = -√93987

Hence, the roots of the equation f(x) = x^2 - 93987 are x = √93987 and x = -√93987

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Answer:

The approximate radian measure of the angle. So we have 15 nine 0.6 degrees convert degrees to radiance. You have to multiply by pi over 1 80. So if we did that, that'd be 59.6 pi over 1 80. So if we want to know the approximate value, we're going to use the pi button on our calculator to figure out what 59.6 times pi is. That's approximately 187.2389, Divided by 1 80. So now I would divide that number by 180 and that gives me 1.04 radiance, 1.04 radiance is the answer.

Answer:

Step-by-step explanation:

x = time

y = elevation

At x = 0  ,  y  = 0

It takes the submarine 2 hours to make descent of 2100 ft

=> x = 2 , y  = - 2100

Slope = ( -2100 - 0)/(2 - 0)  =  -1050

y - 0 = -1050 ( x -0)

=> y = -1050x

1050x  + y = 0

represent the relationship between the submarine's elevation and time.

Answer:

1. Given

2. Definition of Congruent Angles

3. Triangle Interior Angle Sum Theorem

4. Transitive Property of Equality

5. Substitution Property of Equality

6. Definition of Congruent Angles

The solution for the system of linear equations 2x- y = 3 and y - x = 1 are x = 4 and y = 5

Linear equations are equations that have constant average rates of change, slope or gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

2x- y = 3

y - x = 1

Make y the subject in the second equation, by adding x to both sides of the equation

y - x + x = x + 1

This gives

y = x + 1

Substitute y = x + 1 in 2x- y = 3

2x- x - 1 = 3

Evaluate the like terms

x = 4

Substitute x = 4 in y = x + 1

y = 4 + 1

Evaluate

y = 5

Hence, the solution for the system of linear equations 2x- y = 3 and y - x = 1 are x = 4 and y = 5

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Answer:

Graph B

Step-by-step explanation:

Transform the given equation into the slope intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.

3x - 2y = -12

2y = 3x + 12

y = 3/2x + 6

Graph B represents y = 3/2x + 6 because it has a y-intercept at (0,6) and a slope of 3/2.

480 Ways can the letters be arranged.

What is the meaning of probability ?

First letter can't be n or l

=   4! × [tex]5P_{3}[/tex]

=    24 × 5! /3!

=     24 × 5 × 4

=         480

Therefore, 480 ways can the letters be arranged.

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Answer: 480 ways

Step-by-step explanation:

Answer: line ZX is congruent to line VX (option 4)

Step-by-step explanation:

We already know <X is congruent to <X, we also know that line YX is congruent to line XW. Now all we need is one more line adjacent to X which is going to be ZX ad VX

Answer:

okay it's name is Muhammad Deco alfansia ( ◜‿◝ )

Answer:

Slope, sometimes referred to as gradient in mathematics, is a number that measures the steepness and direction of a line, or a section of a line connecting.

Step-by-step explanation: Hope this helps you!

Using the law of cosines, the ship turned 72 degrees northwest when it changed direction.

The law of cosines states that we can find the side c of a triangle as follows:

c² = a² + b² - 2abcos(C)

In which:

For this problem, the parameters are given as follows:

a = 94, b = 119, c = 173.

Hence the internal angle C is found as follows:

c² = a² + b² - 2abcos(C)

173² = 94² + 119² - 2 x 94 x 119cos(C)

22327cos(C) = -6932

cos(C) = -6932/22327

C = arccos(-6932/22327)

C = 108º.

The turning angle is the outside angle, which is supplementary with C, hence:

T = 180 - C = 180 - 108 = 72º.

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Answer:

Hey there!

Step-by-step explanation:

This is ur answer...

Hope it helps!

Brainliest pls!

Have a good day!^^

Answer + Step-by-step explanation:

(a)

[tex]\overrightarrow{PQ} =a+\frac{3}{5} b[/tex]

(b)

we are given:

[tex]\left\vert \overrightarrow{RQ} \right\vert =\frac{3}{5} \left\vert \overrightarrow{OP} \right\vert[/tex]

Then

[tex]\left\vert \overrightarrow{WR} \right\vert =\frac{3}{5} \left\vert \overrightarrow{WO} \right\vert[/tex]

and we know that :

[tex]\overrightarrow{OW} = \overrightarrow{OR} + \overrightarrow{RW}[/tex]

Then

[tex]\overrightarrow{OW} = a +\frac{3}{5} \overrightarrow{OW}[/tex]

Then

[tex]\frac{2}{5} \overrightarrow{OW} = a[/tex]

Then

[tex]\overrightarrow{OW} = \frac{5}{2} a[/tex]

The power series representation for the function, so the interval of convergence is (-9,9).

The definition of convergence refers to 2 or more matters coming together, joining collectively, or evolving into one. An example of convergence is when a crowd of people all move collectively into a unified organization.

Convergence is when two or extra matters come collectively to shape a brand new whole, like the convergence of plum and apricot genes within the plucot. Convergence comes from the prefix con-, meaning collectively, and the verb verge, because of this to show closer to.

The simple concept of convergence permits multiple responsibilities to be accomplished on a single device, which efficiently conserves space and power. for example, as opposed to wearing separate devices – like a cell cellphone, digital camera, and virtual organizer – each era converges on a single tool or telephone.

We have given f(x)=1/(9+x)

f(x)=(1/9)*(1/(1-(-x/9))

f(x)=summation of (n=0 to infinity) [1/9*(-x/9)n]

=summation of (n=0 to infinity) [(-1)n*(xn/9n+1)]

f(x)=summation of (n=0 to infinity) [(-1)n*(xn/9n+1)]

Let an=(-1)n*(xn/9n+1)

using the Ratio Test

L=lim n-->infinity|an+1/anL=lim n-->infinity|[(-1)n+1*(xn+1/9n+2)]/[(-1)n*(xn/9n+1)]|

=lim n-->infinity|[(-1)n+1*(xn+1/9n+2)]*[9n+1/(-1)n*(xn)]|

=lim n-->infinity|(-1)*(x)/9)|

=|-x/9|<1

x/9<1 and x>9>-1

x<9  and x>-9

x is -9<x<9

for x=9 the series ,summation of (n=0 to infinity) [(-1)n*(9n/9n+1)] =summation of (n=0 to infinity) [(-1)n*(/9)]

=1/9*summation of (n=0 to infinity) [(-1)n]

By the geometric series this summation of (n=0 to infinity) [(-1)n] diverges

=1/9*diverges

the series diverges for x=9

for x=-9 the series ,summation of (n=0 to infinity) [(-1)n*(-9)n/9n+1)] =summation of (n=0 to infinity) [(-1)2n*(/9)]

=1/9*summation of (n=0 to infinity) [(-1)2n]

which is diverges

so the interval of convergence is (-9,9)

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Answer:

f(x) = 5x - 5

Step-by-step explanation:

f(x) = 5x - 5 is a linear equation as it has no power.

Based on the information, there were initially 1200 ferns; the monthly percent rate of change is 68% and this situation is modeled by an exponential growth function

The given parameters from the question are:

P(n) = 1200(1.68)^n

Where

n represent the number of months

An exponential growth function is represented as:

P(n) = a * (1 + r)^n

Where

a represents the initial value

r represents the rate

By comparison, we have

a = 1200

1 + r = 1.68

This gives

r = 0.68 = 68%

Hence, there were initially 1200 ferns; the monthly percent rate of change is 68% and this situation is modeled by an exponential growth function

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1,200

68

growth

Got it right on Edmentum

Step-by-step explanation:

Circumference = πd

= π × 12

= 37.6991

=38

Answer:38

Step-by-step explanation:

Yoshi should buy 3 flats.

To find how many flats Yoshi should buy:

Therefore, Yoshi should buy 3 flats.

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Answer:

Step-by-step explanation:

Add the numbers and divide by 2 and you will find the average

(8.1 + 8.24) : 2 =

8.17

8.17 is exactly half way between them.

The unit rate of Mikayla and brie is 0.16 miles per minutes and 0.25 miles per minutes respectively.

Brie runs faster.

Mikayla

2 miles in 12 1/2 minutes

Unit rate = miles / minutes

= 2 ÷ 12 1/2

= 2 ÷ 25/2

= 2 × 2/25

= 4/25

= 0.16 miles per minutes

Brie

5 miles in 22 1/4 minutes

Unit rate = miles / minutes

= 5 ÷ 22 1/4

= 5 ÷ 89/4

= 5 × 4/89

= 20/89

= 0.25 miles per minutes

Lucy

4 4/5 pounds for $18.50

Unit rate = pounds / price

= 4 4/5 ÷ 18.50

= 24/5 ÷ 18.50

= 24/5 × 1/18.50

= 24/92.50

= $0.26 per pound

Sophie

3 1/2 pounds for $14.75

Unit rate = pounds / price

= 3 1/2 ÷ 14.75

= 7/2 ÷ 14.75

= 7/2 × 1/14.75

= 7/29.5

= $0.24 per pound

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The probability that the jackpot prize will be won in each of four consecutive draws is (1/60)⁴.

The number of consecutive draws needed will be, n = 233

Probability is the likelihood or chance of an event happening or not.

From the given question, the probability of the jackpot being won in any draw is 1/60.

The probability that the jackpot prize will be won in each of four consecutive draws will be:

1/60 * 1/60 * 1/60 * 1/60 = (1/60)⁴

b. The number of consecutive draws that needs to be made for there to be a greater than 98% chance that at least one jackpot prize will have been won is calculated as follows:

There is a 100% - 98% chance that that none has been won = 2% that none has been won.

Also, the probability of the jackpot not being won in a draw is = 1 1/60 = 59/60

The number of consecutive draws needed will be (59/60)ⁿ ≤ 0.02

Solving for n by taking logarithms of both sides:

n = 233

In conclusion, probability measures chances of an event occurring or not.

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Answer:

4/5 of the students would have protractors.

Step-by-step explanation:

Answer:

47/100

Step-by-step explanation:

First you have to make the denominators equal.

4/10 * 10/10 = 40/100

40/100 + 7/100 = 47/100

[tex]\begin{array}{cccccccccccc} &&&&&&&&&\downarrow &&\downarrow \\ value&\stackrel{1^3+1}{2}&&\stackrel{2^3+1}{9}&&\stackrel{3^3+1}{28}&&\stackrel{4^3 + 1}{65}&&\stackrel{5^3 + 1}{126}&&\stackrel{6^3 + 1}{217} \\\cline{1-12} term&1&&2&&3&&4&&5&&6 \end{array}[/tex]

Answer: D

Step-by-step explanation: a^2+b^2=c^2

so use y value for b2 and 6 square root 3 as a and check with it.