The half-life of a radioactive isotope is the time it takes for a quantity of the Isotope to be reduced to half its initial mass. Starting with 210 grams of a
radioactive isotope, how much will be left after 6 half-lives?
Round your answer to the nearest gram

Answer:

Step-by-step explanation:

Given the expression for time

[tex]t =2n-3[/tex]

say a customer buys 5 coffees, hence n=5

substituting n=5 into the function time it takes to prepare a coffee we have the time it will take to prepare 5 coffees

[tex]t= 2(5)-3\\t=10-3\\t=7[/tex]

Hence it will take 7 minutes to prepare 5 coffees

Answer:

The answer is B.

Step-by-step explanation:

You have to substitute x = 2, into the equation of y :

[tex]y = 6 {x}^{3} - 5 {x}^{2} + 4x - 3[/tex]

[tex]let \: x = 2[/tex]

[tex]y = 6 {( 2)}^{3} - 5 {(2)}^{2} + 4(2) - 3[/tex]

[tex]y = 48 - 20 + 8 - 3[/tex]

[tex]y = 33[/tex]

Answer:

25%

Step-by-step explanation:

First you have the fraction of 3/12 and need to turn it into a decimal. So to do that you divide 3 by 12 = 0.25. So your percent is 25%

Answer:

$22

Step-by-step explanation:

Let Vincent = v, Francis= f

Equations to reflect given:

and  

Replacing f with v+8:

Now finding f:

Francis gets $22

Answer:

-2,-1,0,1,2,3

You just have to choose the numbers in between -3 to 3

Hope it helped ;)

Answer:

Interval notation is

[tex]\left(-\infty, -5\right)\cup \left(0,1)[/tex]

Solutions:

[tex]\left(-\infty, -5\right)[/tex]

[tex]\left(0,1)[/tex]

Step-by-step explanation:

[tex]x^3 + 4x^2 - 5x < 0[/tex]

In this inequality, luckly we can easily factor it.

[tex]x^3 + 4x^2 - 5x[/tex]

[tex]x(x^2+4x-5)[/tex]

[tex]x(x-1)(x+5)[/tex]

So we have

[tex]x(x-1)(x+5)<0[/tex]

In exercises of this kind I usually do in my mind, but just to make it clear, let's do a table to organize. This table represents the x-intercepts in order to evaluate the inequality.

Consider [tex]x(x-1)(x+5)=0[/tex]. Here, those are the possible values for [tex]x[/tex] for each factor to be 0:

The first step to complete the table is the x value where the factor will be equal to zero.

       [tex]x<-5[/tex]       [tex]x=5[/tex]         [tex]-5<x<0[/tex]        [tex]x=0[/tex]      [tex]0<x<1[/tex]      [tex]x=1[/tex]      [tex]x>1[/tex]                                                                  

[tex]x[/tex]                                                                        0

[tex]x-1[/tex]                                                                                                    0        

[tex]x+5[/tex]                      0

Then, just consider the signal:

  [tex]x<-5[/tex]       [tex]x=5[/tex]         [tex]-5<x<0[/tex]        [tex]x=0[/tex]      [tex]0<x<1[/tex]      [tex]x=1[/tex]      [tex]x>1[/tex]                                                                  

[tex]x[/tex]    -                -                       -                   0               +                 +             +

[tex]x-1[/tex]  -             -                      -                   -               -                  0             +

[tex]x+5[/tex]  -             0                     +                   +                +               +              +

[tex]x(x-1)(x+5)[/tex]    -     0       +     0      -      0     +

When [tex]x(x-1)(x+5)<0[/tex] ?

It happens when [tex]x<-5[/tex]     and when [tex]0<x<1[/tex]

The solution is

[tex]\{x \in \mathbb{R} | x<-5 \text{ or } 0<x<1 \}[/tex]

[tex]\left(-\infty, -5\right)\cup \left(0,1)[/tex]

Answer:

125975100 the population in 7 years

Step-by-step explanation:

the population in 7 more years : 127,484450(1-0.0017)^7=125975100.1919 close to 125975100

Answer: 125,976,376 IN 7 YEARS

Step-by-step explanation:

A=127,484,450

R=-0.0017/YEAR

T=7/YEARS

Answer:

Option A a right tailed hypothesis test

Step-by-step explanation:

A claim given symbolically is most of the time derived from the alternative hypothesis usually tested against the null hypothesis.

A symbolic claim with the option of a less than indicates a left tailed test, while one with the option of greatest than indicate a right tail test and one with the option of both (not equal to; either less or greater) indicates a two tailed test.

In this case study, the sample proportion for the claim was greater than 0.50 thus, the test is a right tailed hypothesis test

Answer:

One solution, z=-5

Step-by-step explanation:

First, We simplify the right side.

Distribute -5, -5z-5=-2z+10

Now add +2z to both sides, −3z−5=10

Add 5 to both sides, now the equation stands as -3z=15

We can simplify this by dividing -3 to both sides, z=-5.

Now we know there is only one solution to this equation!

Answer:

Step-by-step explanation:

∆ BCD ~ ∆ DCA

[tex] \frac{bc}{dc} = \frac{dc}{ac} [/tex]

Plug the values:

[tex] \frac{5}{y} = \frac{y}{6 + 5} [/tex]

[tex] \frac{5}{y} = \frac{ y}{11} [/tex]

Apply cross product property

[tex]y \times y = 11 \times 5[/tex]

Calculate the product

[tex] {y}^{2} = 55[/tex]

[tex]y = \sqrt{55} [/tex]

Hope this helps...

Good luck on your assignment..

Answer:

.006

:)

Step-by-step explanation:

8 servings can David make with the current amount of spice.

Ratio is defined as a relationship between two quantities, it is expressed one divided by the other.

The rice-to-spice ratio = 15:1

The 75 grams of rice in one serving will require

⇒75/15

⇒5 gram of spice.

David's inventory of 40 gram of spice is enough for

40 g/(5 g/serving) = 8 servings

Hence, 8 servings can David make with the current amount of spice.

Learn more about Ratio

brainly.com/question/1504221

#SPJ2

Answer:

1. x>20   2. x≤1     3.x<4     4.x>9      5.x≥-13

Answer:

-k+8k=7k is the solution

Answer:

x = 96

Step-by-step explanation:

Inscribed Angle = 1/2 Intercepted Arc

48 = 1/2 ( x)

Multiply by 2

96 = x

Answer:

[tex]\boxed{x=96}[/tex]

Step-by-step explanation:

Apply the inscribed angle theorem, where the measure of an inscribed angle is half the measure of the intercepted arc.

[tex]48=\frac{1}{2}x[/tex]

Multiply both sides by 2.

[tex]48(2)=\frac{1}{2}x(2)[/tex]

[tex]96=x[/tex]

Hey there! I'm happy to help!

Let's represent everybody with variables. Raina is R, Justin is J, and Cho is C. Let's write down this information as a system of equations.

R+J+C=79            (they all have 79 total dollars in their wallets combined)

R=J-5                    (Raina has five less than Justin.)

C= 2J                        (Cho has twice that of Justin)

Since we know what R and C equal, we can plug in their values in terms of J into the first equation to solve for J.

J-5+J+2J=79

We combine like terms.

4J-5=79

We add 5 to both sides.

4J=84

We divide both sides by 4.

J=21

This means that Justin has $21. If Raina has 5 less, she has $16 and since Cho has twice that of Justin he has $42. These added up equal 79.

I hope that this helps! Have a wonderful day!

Answer:

Step-by-step explanation:

1. The Hamilton method has you compute the number represented by each board member (total population/# members). Using this factor, the number of board members for each district are computed. This raw value is rounded down.

Because this total does not allocate all board members, the remaining members of the board are allocated to the districts based on the size of the fraction that was truncated when rounding down. Allocations start with the largest fraction and work down until all board members have been allocated.

The attached spreadsheet implements this algorithm using a "threshold" that is adjusted to a value between 0 and 1, signifying the cutoff point between a fraction value that gets an additional member and one that doesn't. (Often, that threshold can be set at 0.5, equivalent to rounding the raw board member value to the nearest integer.)

The resulting allocations are ...

  Town A: 2

  Town B: 2

  Town C: 6

  Town D: 12

__

2. The second attachment shows the result after the population move. The allocations of board members are identical.

__

3. The "factor" (persons per board member) is about 4500, so we don't expect a move of 900 people to make any difference in the allocation. These results make complete sense.

__

4. Of course each town will consider its own interest at the expense of everyone else, so they may or may not consider the results fair. The towns have population ratio of about 9 : 9 : 25 : 56, so the ratios 2 : 2 : 6 : 12 are quite in line. Even in the second year, when the ratios are closer to 9 : 10 : 26 : 56, the changes are small enough that the allocation of board members still makes sense. The results are fair.

_____

Comment on "fair"

The reason there are different methods of allocation is that each seeks to rectify some perceived flaw in one or more of the others. The reason there is not a general agreement on the method to be used is that some benefit more from one method than from another. "Fair" is in the eye of the beholder. I believe in this case it would be very difficult to justify any other allocations than the ones computed here.

Step-by-step explanation:

3500 × 10/100

rs. 350 is the discount

and to find the amnt the customer should pay subtract 350 from 3500

which is,

3150 Rupees

Answer:

[tex]\dfrac{21}{10}\text{ km}[/tex].

Step-by-step explanation:

It is given that,

Area of rectangular plot [tex]=\dfrac{7}{10}\text{ km}^2[/tex]

Width of rectangular plot [tex]=\dfrac{1}{3}\text{ km}[/tex]

We need to find the length of the parking lot.

We know that,

[tex]\text{Area of rectangle}=length\times width[/tex]

[tex]\dfrac{7}{10}=length\times \dfrac{1}{3}[/tex]

[tex]\dfrac{7\times 3}{10}=length[/tex]

[tex]length=\dfrac{21}{10}[/tex]

Therefore, length of the parking lot is [tex]\dfrac{21}{10}\text{ km}[/tex].

Answer:

y=10000 at rate 0.12 or 12%

x=8500 at rate 0.14 0r 14 %

Step-by-step explanation:

x+y=18500   ⇒ x=18500-y

0.14x+0.12y=2390 ( solve by substitution)

0.14(18500-y)+0.12y=2390

2590-0.14y+0.12y=2390

-0.02y=2390-2590

-0.02y=-200

y=-200/0.02

y=10000 at rate 0.12

x=18500-y

x=18500-10000=8500

x=8500 at rate 0.14

check : 0.14(8500)+0.12(10000)=2390 ( correct)

Answer:

Amount invested at 14% = 8500

Amount invested at 12% =  10000

Step-by-step explanation:

Assume money was invested for one year.

18500 at 14% = 18500*0.14 = 2590

18500 at 12% = 18500*0.12 = 2220

actual interest earned = 2390

Let

x = ratio of money invested at 14%

1-x = ratio of money invested at 12%

Then

18500*x * 0.14 + 18500 * (1-x)*0.12 = 2390

0.14x - 0.12x = 2390/18500-0.12

0.02x = 0.1291892-0.12 = 0.0091892

x = 0.0091892/0.02 = 0.4594595

Amount invested in 14% = 18500 * x = 8500

Amount invested in 12% = 18500 * (1-x) = 10000

Answer:

The answer is option A

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

Equation of the line using point (1 , - 2) and slope 1/3 is

y + 2 = 1/3( x - 1)

Multiply through by 3

That's

3y + 6 = x - 1

Simplify

x - 3y - 1 - 6 = 0

We have the final answer as

Hope this helps you

Answer:

Gender and Residence of Students

a) What is the probability that a student is female and lives in a dorm?  

= 58.33%

b) What is the probability that a student is female given that she lives in a dorm?

= 21%

Step-by-step explanation:

a) Data and Calculations:

Gender and Residence of Students  

                                           Males   Females Total

Apartment off campus         50        90        140

Dorm room                          150       210       360

With Parent(s)                      100        50        150

Sorority/ Fraternity House 200      150        350

Total                                    500     500      1,000

a) Probability that a student is female and lives in a dorm:

= number of females who live in a dorm divided by total number of students who live in a dorm * 100

= 210/360 * 100

= 58.33%

b) Probability that a student is female given that she lives in a dorm

= number of female students who live in a dorm divided by the total number of students * 100

= 210/1,000 * 100

= 21%

Answer:

The answer is below

Step-by-step explanation:

A sugar refinery has three processing plants, all receiving raw sugar in bulk. The amount of raw sugar (in tons) that one plant can process in one day can be modelled using an exponential distribution with mean of 4 tons for each of three plants. If each plant operates independently,a.Find the probability that any given plant processes more than 5 tons of raw sugar on a given day.b.Find the probability that exactly two of the three plants process more than 5 tons of raw sugar on a given day.c.How much raw sugar should be stocked for the plant each day so that the chance of running out of the raw sugar is only 0.05?

Answer: The mean (μ) of the plants is 4 tons. The probability density function of an exponential distribution is given by:

[tex]f(x)=\lambda e^{-\lambda x}\\But\ \lambda= 1/\mu=1/4 = 0.25\\Therefore:\\f(x)=0.25e^{-0.25x}\\[/tex]

a) P(x > 5) = [tex]\int\limits^\infty_5 {f(x)} \, dx =\int\limits^\infty_5 {0.25e^{-0.25x}} \, dx =-e^{-0.25x}|^\infty_5=e^{-1.25}=0.2865[/tex]

b) Probability that exactly two of the three plants process more than 5 tons of raw sugar on a given day can be solved when considered as a binomial.

That is P(2 of the three plant use more than five tons) = C(3,2) × [P(x > 5)]² × (1-P(x > 5)) = 3(0.2865²)(1-0.2865) = 0.1757

c) Let b be the amount of raw sugar should be stocked for the plant each day.

P(x > a) = [tex]\int\limits^\infty_a {f(x)} \, dx =\int\limits^\infty_a {0.25e^{-0.25x}} \, dx =-e^{-0.25x}|^\infty_a=e^{-0.25a}[/tex]

But P(x > a) = 0.05

Therefore:

[tex]e^{-0.25a}=0.05\\ln[e^{-0.25a}]=ln(0.05)\\-0.25a=-2.9957\\a=11.98[/tex]

a  ≅ 12

Answer:

6/3x= 2x

12/3=4

-2x

14

2x +4 -2x +14= 18

Answer:

No solution for x

Step-by-step explanation:

it  is Impossible so x= ∅, no solution for x

Answer:

Step-by-step explanation:

Corresponding measurements on a pain scale before and after hypnosis form matched pairs.

The data for the test are the differences between the measurements on a pain scale before and after hypnosis.

μd = the​ measurements on a pain scale before hypnosis minus the​ measurements on a pain scale after hypnosis

Before after diff

6.3 6.5 - 0.2

4 2.5 1.5

9.2 7.7 1.5

9.3 8.4 0.9

11.3 8.6 2.7

Sample mean, xd

= (- 0.2 + 1.5 + 1.5 + 0.9 + 2.7)/5 = 1.28

xd = 1.28

Standard deviation = √(summation(x - mean)²/n

n = 5

Summation(x - mean)² = (- 0.2 - 1.28)^2 + (1.5 - 1.28)^2 + (1.5 - 1.28)^2 + (0.9 - 1.28)^2 + (2.7 - 1.28)^2 = 4.448

Standard deviation = √(4.448/5

sd = 0.94

For the null hypothesis

H0: μd ≥ 0

For the alternative hypothesis

H1: μd < 0

The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 5 - 1 = 4

The formula for determining the test statistic is

t = (xd - μd)/(sd/√n)

t = (1.28 - 0)/(0.94/√5)

t = 3.04

The test statistic for the hypothesis test is 3.04

Answer:

100r^4 + 400r^3 + 600r^2 + 400r + 100

Step-by-step explanation:

Expanding ( r + 1 )^4 gives :-

r^4 + 4r^3 + 6r^2 + 4r + 1

So multiplying 100 with r^4 + 4r^3 + 6r^2 + 4r + 1 gives :-

100r^4 + 400r^3 + 600r^2 + 400r + 100

You probably want the unsigned area, which means you don't compute the integral

[tex]\displaystyle\int_0^{2\pi}\sin x\,\mathrm dx[/tex]

but rather, the integral of the absolute value,

[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx[/tex]

[tex]\sin x[/tex] is positive when [tex]0<x<\pi[/tex] and negative when [tex]\pi<x<2\pi[/tex], so

[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx=\int_0^\pi\sin x\,\mathrm dx-\int_\pi^{2\pi}\sin x\,\mathrm dx[/tex]

[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx=(-\cos x)\bigg|_0^\pi-(-\cos x)\bigg|_\pi^{2\pi}[/tex]

[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx=\boxed{4}[/tex]

Answer:

Rewrite the function as an equation. y= 3/7 Use the slope-intercept form to find the slope and y-intercept. Slope: 0 Y-intercept: 3/7 Hope this can help

Step-by-step explanation:

Answer:

5x 10 ^-5

Step-by-step explanation:

UHM that would be

NaN × [tex]10^{0}[/tex]

I hope this helps!

so my reasoning...  Any number that can be written in the decimal form between 1.0 to 10.0 multiplied by the power of 10.