A tumor is injected with 0.3 grams of Iodine-125, which has a decay rate of 1.15% per day. To the nearest day, how long will it take for half of the Iodine-125 to decay?

Answer:

[tex]{ \bf{formular : \: { \tt{volume = \frac{4}{3} \pi {r}^{3} }}}} \\ { \tt{volume = \frac{4}{3} \times 3.14 \times {( \frac{5}{2}) }^{3} }} \\ { \tt{volume = 65.4 \: cubic \: inches}}[/tex]

Answer:

65

Step-by-step explanation:

formula =   4/3 * 3.14* r^3

               = 4/3 * 3.14 * 2.5^3 (radius is half of the diameter)

                    = 65.44985

                     rounded to 65

Answer:

Matthew travels 0.0161 meters per second.

Step-by-step explanation:

Given that Matthew travels 42/50 meters In 26/30 minutes, to find the speed of Mathew in meters per second the following calculation must be performed:

42/50 = 0.84

26/30 = 0.86

0.86 x 60 = 52

0.84 meters in 52 seconds

0.84 / 52 = 0.01615

Therefore, Matthew travels 0.0161 meters per second.

Given:

In a triangle, length of one side is 8 inches and length of another side is 12 inches, and an angle is a right angle.

To find:

The length of the missing side.

Solution:

In a right angle triangle,

[tex]Hypotenuse^2=Perpendicular^2+Base^2[/tex]

Suppose the measures of sides adjacent to the right angle are 8 inches and 12 inches.  

Substituting Perpendicular = 8 inches and Base = 12 inches, we get

[tex]Hypotenuse^2=8^2+12^2[/tex]

[tex]Hypotenuse^2=64+144[/tex]

[tex]Hypotenuse^2=208[/tex]

Taking square root on both sides, we get

[tex]Hypotenuse=\sqrt{208}[/tex]

[tex]Hypotenuse=14.422205[/tex]

[tex]Hypotenuse\approx 14.4[/tex]

The length of the missing side is 14.4 inches. Therefore, the correct option is D.

Answer:

Moving upwards with an acceleration.

Step-by-step explanation:

weight of the person  = 195 pounds

Apparent weight = 205 pounds

As the weight increases so the scale is moving upwards with some acceleration.

The scale is in elevator which is moving upwards.

Answer:

i think its 2 1

Step-by-step explanation:

Answer:

y =2/3x-1

Step-by-step explanation:

First find the slope

m = ( y2-y1)/(x2-x1)

   = ( 3-1)/ (6-3)

   = 2/3

The slope intercept form of a line is

y = mx+b  where m is the slope and b is the y intercept

y = 2/3x +b

Using a point

3 = 2/3(6)+b

3 = 4+b

3-4 =b

-1=b

y =2/3x-1

Answer:

One

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

Solving systems of equations

Step-by-step explanation:

Step 1: Define

Identify systems

y = 3x + 5

y = 4x

Step 2: Solve

If we compare the 2 lines, we can see that they both have a different slope. If they had the same slope but different y-intercepts, then they would be parallel and have no solution. We can also see that the 2 lines aren't the same. If they were, then they would have infinite solutions.

∴ the systems should have only one solution.

Answer:

B

Step-by-step explanation:

Answer:

a) Their average weight is of 187 pounds.

b) 0.4562 = 45.62% probability that the maximum safe weight will be exceeded.

c) 0.002 = 0.2% probability that the maximum safe weight will be exceeded

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

a. If 44 people are on the elevator, and their total weight is 8228 pounds, what is their average weight?

8228/44 = 187

Their average weight is of 187 pounds.

b. If a random sample of 44 adult men ride the elevator, what is the probability that the maximum safe weight will be exceeded?

For men, we have that [tex]\mu = 186, \sigma = 60[/tex]

Sample of 44 means that [tex]n = 44, s = \frac{60}{\sqrt{44}}[/tex]

This probability is 1 subtracted by the p-value of Z when X = 187. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{187 - 186}{\frac{60}{\sqrt{44}}}[/tex]

[tex]Z = 0.11[/tex]

[tex]Z = 0.11[/tex] has a p-value of 0.5438.

1 - 0.5438 = 0.4562

0.4562 = 45.62% probability that the maximum safe weight will be exceeded.

c. If a random sample of 44 adult women ride the elevator, what is the probability that the maximum safe weight will be exceeded?

For women, we have that [tex]\mu = 157, \sigma = 69[/tex]

Sample of 44 means that [tex]n = 44, s = \frac{69}{\sqrt{44}}[/tex]

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{187 - 157}{\frac{69}{\sqrt{44}}}[/tex]

[tex]Z = 2.88[/tex]

[tex]Z = 2.88[/tex] has a p-value of 0.998.

1 - 0.998 = 0.002.

0.002 = 0.2% probability that the maximum safe weight will be exceeded

Answer:

A. Total=520 loaves

B. Estimate= 180 rolls

Step-by-step explanation:

Step-by-step explanation:

here is the ans

the perimeter= 130m

hope so this might help you

Answer:

7x - 63y

Step-by-step explanation:

Given

7(x - 9y) ← multiply each term in the parenthesis by 7

= 7x - 63y

C. Dilation.

Dilation can resize the image.

Translation will shift the imagine's position but won't change its actual size.

Rotation will mangle with image's orientation but also won't change its size.

Reflection is just a type of rotation which as established, also won't change its size.

Hope this helps.

Answer:

Answer:

Hope this will help.

Answer:

A the answer is A if you look at it .

Answer:

The first one is B) point D

The second one is D) (0,0)

Hope this helps!

btw, coordinates are in (x,y) form, so the other answer above me is wrong.

Answer:

Step-by-step explanation:

2x-3y+6=0 has an x intercept of 2 and a y intercept of -3.

That means the 2 sides of the right triangle are 2 and -3

Area of triangle= 1/2×base×height

                         = 1/2×-3×2

                         =-3

∴ Area of the triangle=-3

The area of the asked triangle is 3 sq units.

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given that, a triangle is formed by the line 2x – 3y +6=0 and the coordinate axis.

When we plot the graph of the line, we get, y-intercept = 2 and x-intercept = -3

Hence, the height and base of the triangle will be 2 and 3 respectively.

Area of a triangle = 1/2 (base) (height)

Area = 1/2 (2)(3)

Area = 3

Hence, the area of the asked triangle is 3 sq units.

Learn more about areas, click;

https://brainly.com/question/27683633

#SPJ2

Answer:

The correct answer will be "-1.66".

Step-by-step explanation:

Let z₀ be,

[tex]P(z<z_0)=4.8 \ percent[/tex]

                [tex]=0.048[/tex]

⇒ [tex]\Phi (z_0)=0.048[/tex]

Now,

⇒ [tex]\Phi (-1.6646)=0.048[/tex]

   [tex]z_0=-1.6646[/tex]

       [tex]\simeq -1.66[/tex]

Thus the above is the right answer.

Look at one side of the triangle. It forms a right triangle with 45 degree angles.

A 45 degree triangle the base and height are the same, so the height would also be 26.

The hypotenuse(x) of a 45 degree right triangle is the side length time the sqrt(2)

The answer is: 26 sqrt(2)

Answer:

v nnv vb n

Step-by-step explanation:

b ng chfxhc.jx.gc,fhxfgfdkhgvn gghcjfuoctykfd mmyegfiuegfypgerukf khergfuoegrfyurgfirge jgreuyofrgiregvoifgr riygfepiygfreu;k frugfyrfbhrevf rrgfbreuobghfre rgeuherhbgerui freurehuregh ruogysfhurgiugwhlerghre rgiuyrge97grukbgr ker ruipuhrgeugregariyarga ;rskfglfsglgsfuifgryrgljs kjger;ugiergs hope this was helpful good luck!

Answer:

$11.22

Step-by-step explanation:

100% = 187

1% = 187/100 = $1.87

6% = 1%×6 = 1.87×6 = $11.22

Answer:

In this case, you need to calculate the 6% of the price, which is 187 $.

We only need to multiply the price (187) by the percentage (6%):

187 * 0.06 = 11.22

So the tax would be $11.22

Answer:

5x^2(2-3x)

(n+4)(x+y)

Step-by-step explanation:

Answer:

The appropriate solution is "259".

Step-by-step explanation:

According to the question,

[tex]\sigma = 300[/tex]

[tex]M.E=25[/tex]

At 82% CI,

[tex]\alpha = 0.18[/tex]

Critical value,

[tex]Z_c=1.341[/tex]

Now,

The sample size will be:

⇒ [tex]n=(Z_c\times \frac{\sigma}{E} )^2[/tex]

By substituting the values, we get

      [tex]=(1.341\times \frac{300}{25} )^2[/tex]

      [tex]=(1.341\times 12)^2[/tex]

      [tex]=259[/tex]

ANSWERS:

a) 16 students

b) 25 students

c) 2 students

STEP BY STEP:

There are 42 students in total. This question can be solved by "Principal of Inclusion and Exclusion"

Question a)

The students that studied on Sunday in total with overlaps is 30. To figure out the students that ONLY studied on Sunday you need to first minus the overlaps in the combos:

the combos:

3, 10, 6, 2

Since the last combo included all of the other dates, we need to minus it:

1, 8, 4, 2

Now we can use the total of Sunday and minus the combos that includes Sunday:

30 - (4 + 2 + 8)  = 16 students

Question b)

To figure out all the students that only studied on ONE day, not 2 not 3, just one day. We need to figure out the students that studied for Saturday and Friday using the same method before for figuring out Sunday:

Friday: 9 - 4 - 1 -2 = 2 students

Saturday: 18 - 1 - 2- 8 = 7 students

and now add them all together: 2 + 7 + 16 = 25 students

That is the total number of students that studied on one day.

Question c)

Now for the numbers of students that didn't study... We can just use the total to minus everything else!

42 - (25 + 1 + 4 + 8 + 2) = 2 students!!!

And thats all done!  If you still don't get it, please ask!

Answer:

0.055 = 5.5% probability that exactly 5 employees were over 50.

Step-by-step explanation:

The employees are removed from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

7 + 18 = 25 employees, which means that [tex]N = 25[/tex]

7 over 50, which means that [tex]k = 7[/tex]

10 dismissed, which means that [tex]n = 10[/tex]

What is the probability that exactly 5 employees were over 50?

This is P(X = 5). So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 5) = h(5,25,10,7) = \frac{C_{7,5}*C_{18,5}}{C_{25,10}} = 0.055[/tex]

0.055 = 5.5% probability that exactly 5 employees were over 50.

Answer:

option B

Step-by-step explanation:

option B

gdyfudjfjghfhguftduc

Answer:

(11.847 ; 15.813)

Step-by-step explanation:

We are given 12 samples which are :

8, 20, 20, 11, 18, 12, 6, 5, 7, 22, 12, 25

We use a T-distribution to find the confidence interval since the sample size. is small, n < 30

Using a calculator :

The sample mean, xbar = 13.83

Sample standard deviation, s = 6.87

The confidence interval, C.I

C.I = xbar ± Tcritical * s/√n)

Tcritical at 95%, df = n - 1, 12 - 1 = 11

Tcritical(0.05, 11) = 2.20

Hence,

C.I = 13.83 ± 2.20(6.87/√12)

C.I = 13.83 ± 1.9831981

C. I = (13.83 - 1.983 ; 13.83 + 1.983)

C. I = (11.847 ; 15.813)

Answer:

= c^4 d^8 a^2

Step-by-step explanation:

Apply exponent rule: aa= a^2

= c^3 da^2 cd^7

= c^4 da^2 d^7

= c^4 d^8 a^2

Answer:

4 cm by 5 cm (4 x 5)

Step-by-step explanation:

The area of a rectangle with length [tex]l[/tex] and width [tex]w[/tex] is given by [tex]A=lw[/tex]. Since the length of the rectangle is 7 less than 3 times its width, we can write the length as [tex]3w-7[/tex]. Therefore, substitute [tex]l=3w-7[/tex] into [tex]A=lw[/tex]:

[tex]A=lw,\\20=(3w-7)w[/tex]

Distribute:

[tex]20=3w^2-7w[/tex]

Subtract 20 from both sides:

[tex]3w^2-7w-20=0[/tex]

Factor:

[tex](w-4)(3w+5)=0,\\\begin{cases}w-4=0, w=\boxed{4},\\3w+5=0, 3w=-5, w=\boxed{-\frac{5}{3}}\end{cases}[/tex]

Since [tex]w=-\frac{5}{3}[/tex] is extraneous (our dimensions cannot be negative), our answer is [tex]w=4[/tex]. Thus, the length must be [tex]20=4l, l=\frac{20}{4}=\boxed{5}[/tex] and the dimension of the rectangle are 4 cm by 5 cm (4 x 5).