A doctor prescribes 250 milligrams of a therapeutic drug that decays by about 10% each hour. Write an exponential model representing the amount A in milligrams of the drug remaining in the
patient's system after t hours.
A(t)=
Use the formula to find the amount of the drug that would remain in the patient's system after 3 hours. Round to the nearest milligram.
mg

A population has a mean of 180 and a standard deviation of 36. A sample of 84 observations will be taken. The probability that the sample mean will be between 181 and 185 is

Given n(sample size) = 84

Population mean(μ) = 180

Standard Deviation(σ) = 36

Standard error of the mean = σx-bar = σ/√n = 36/√84 = 36/9.165 = 3.927

Standardizing the sample mean we have

Z = (x-bar - μ)/σx-bar = (x-bar - μ)/σ/√n

x-bar = 180

Z(x-bar=185 at point C) = (185 - 180)/3.927 = 5/3.927 = 1.273

Z(x-bar=181 at point D) = (181 - 180)/3.927 = 1/3.927 = 0.254

The area ABCD is the probability that the sample mean will lie between 181 and 185.

The shaded Area ABCD = (Area corresponding to Z = 2 or x-bar = 185) - (Area corresponding to Z = 1 or x-bar = 181)

Area corresponding to Z = 1.273 = 0.898

Area corresponding to Z = 0.254 = 0.598

The shaded Area ABCD = 0.898-0.598 = 0.300

Therefore the probability that the sample mean will lie between 181 and 185 is 0.300.

To learn more about Probability, click here https://brainly.com/question/25870256

#SPJ4

Answer:

66%

Hope this helps! :)

The function f(x)=[tex]x^2[/tex]-2x+3 after putting x=1 then f(1)=2.

What is function?

An association between each element of a non-empty set A and at least one element of a different non-empty set B is called a function. In mathematics, a function is defined as a relation f between a set A (the function's domain) and a set B (its co-domain). f = (a,b)| for all values of a A and b B. Every element of set A must have exactly one image in set B for a relation to be considered a function. A relation from a non-empty set B is called a function if it has the property that no two separate ordered pairs in f have the same first element.  

Here the given function is ,

=> f(x)=[tex]x^2[/tex]-2x+3

Now put x= 1 then

=> f(1) = [tex]1^2[/tex]-2(1)+3

=>f(1) = 1-2+3

=> f(1) = 2

Hence the value of f(1)=2.

To learn more about function refer the below link

https://brainly.com/question/11624077

#SPJ9

Answer:

$19.43

Step-by-step explanation:

when 5.5 pounds cost $14.74 then 1 pound costs $2.68
because 14.74 divided by 5.5 equals 2.68
To calculate the price of 7.25 you multiply the price for 1 pund by 7.25
7.25 * 2.68 = 19.43

Answer:

16 : 3

Step-by-step explanation:

(a+3b)/5=(a-b)/2 or 2 (a+3b) = 5 (a-2b) or 2a + 6b = 5a-10b or 3a. or a/b = 16/3 so a.b = 16:3

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

Step 1: Simplify

[tex]\frac{12}{12} =1[/tex]

Step 2: Multiply by [tex]\frac{1}{3}[/tex]

[tex]1*\frac{1}{3}=\frac{1}{3}[/tex]

Hope this helps! :)

Answer:

534.1875

Step-by-step explanation:

7500 ⋅ (1+3.5%)²-7500

534.1875

Answer:

x = 0; y = -5

x = 9; y = 13

Step-by-step explanation:

y = x² - 7x - 5

y = 2x - 5

Use substitution to set the two right sides equal.

x² - 7x - 5 = 2x - 5

x² - 9x = 0

x(x - 9) = 0

x = 0  or  x - 9 = 0

x = 0  or x = 9

Now for each x value, we find a corresponding y vlaue.

x = 0

y = 2x - 5 = 2(0) - 5 = -5

x = 9

y = 2x - 5 = 2(9) - 5 = 13

Answer:

x = 0; y = -5

x = 9; y = 13

Answer:

(0,-5) and (9,13)

Step-by-step explanation:

Step 1: Set up

Step 2: Solve

 Substitution:

 Elimination:

If Minstrel Manufacturing incurred total overhead costs of $167,800 during the month, the underapplied overhead was $2,800.

Underapplied overhead arises when the applied overhead is less than the actual overhead incurred.

On the other hand, overapplied overhead suggests that the applied overhead is more than the actual overhead incurred.

Overhead application is the allocation of overhead costs to units of products or jobs using a predetermined application rate.

Predetermined overhead application rate = 150% of direct labor cost

Direct labor cost = $110,000 ($150,000 - $40,000)

Applied overhead = $165,000 ($110,000 x 150%)

Actual overhead = $167,800

Underapplied overhead = $2,800 ($165,000 - $167,800)

Thus, during the month, the company underapplied overhead by $2,800.

Learn more about overhead applications at https://brainly.com/question/26511051

#SPJ1

Answer:

b = -3.16

Step-by-step explanation:

3b² + 5 = -25

3b² = -30

b² = -10

b = -3.1623 (5 significant figures)

= -3. 16

If AB and CD are straight lines. Then x is 45 degrees.

Angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Given,

AB and CD are straight lines

The angle at O is 360 degrees which makes complete circle.

Few of the angles are given.

x+x+4x+90=360

6x+90=360

Subtract 90 from both sides

6x=270

x=45 degrees.

Hence the value of x is 45 degrees.

To learn more on Angles click:

https://brainly.com/question/28451077

#SPJ1

The expression 5 × 5 × 5 is expressed using the exponent [tex]5^3[/tex]

The given expression is

5 × 5 × 5

The expression is the mathematical statement that consist of different variables, numbers and mathematical operator.

The power of a number that consider of base number and the exponent.

Therefore the power of a number is the a base number raised to the exponent.

The exponent of the number is defined as the number of times a number is multiplied by itself.

Here the given expression is

5 × 5 × 5 = [tex]5^3[/tex]

Where 5 is the base number and 3 is the exponent

Hence, the expression 5 × 5 × 5 is expressed using the exponent [tex]5^3[/tex]

Learn more about exponent here

brainly.com/question/15993626

#SPJ1

you have a fair die, with six faces containing the numbers 1,2,3,4,5,6. are the two events a and b then A and B are exhaustive.

Given

A= { 1,2,4}

B= { 2,3,4,5,6}

C= { 3,4}

D= { 2,4,5}

Solving (a): The mutually exclusive events

These are events that have no common or mutual elements

Events A to D are not mutually exclusive because each of the events have at least 1 common element with one another.

Solving (b): Exhaustive events.

Two events X and Y are said to be exhaustive if:

S= P(X n Y)

i.e. if the sample space equals the intersection of X and Y

For events A to D, we have:

AnB= { 1,2,3,4,5,6}

and the sample space is:

S= {1,2,3,4,5,6}

By comparison;

A n B= S

Hence, A and B are exhaustive.

learn more about of dice here

https://brainly.com/question/24129793

#SPJ4

The solution of linear equation x/6-3 = 2 is given by x=30.

Given the linear equation is,

x/6 - 3 = 2

Solving the linear equation we get,

x/6-3 = 2

x/6-3+3 = 2+3, adding 3 to both sides

x/6 = 5

x = 5*6, multiplying 5 to both sides

x = 30

Hence the solution for the given linear equation is x=30.

To know more about Linear Equation refer to:

https://brainly.com/question/2030026

#SPJ1

Answer:

  (d)  x equals the quantity negative 5 times y plus 9 end quantity over 4

Step-by-step explanation:

You want to solve for x: 4x +5y = 9.

This can be treated like any other 2-step equation. First isolate the variable term of interest. Then divide by its coefficient.

  4x = -5y +9 . . . . . . subtract 5y

  x = (-5y +9)/4 . . . . . divide by 4

Answer:

y = [tex]\frac{3}{2}[/tex] x - 11

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (16, 13 ) and (x₂, y₂ ) = (4, - 5 )

m = [tex]\frac{-5-13}{4-16}[/tex] = [tex]\frac{-18}{-12}[/tex] = [tex]\frac{3}{2}[/tex] , then

y = [tex]\frac{3}{2}[/tex] x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (12, 13 ) , then

13 = 24 + c ⇒ c = 13 - 24 = - 11

y = [tex]\frac{3}{2}[/tex] x - 11 ← equation of line

Answer:  |-2|  is greater

Step-by-step explanation:

I hope it's right(Which i'm like 99.9 percent sure it is)

Answer:

|-2| < -4

Step-by-step explanation:

Take the absolute value of -2.

Which is 2.

2 is larger than -4.

Answer:

B

Step-by-step explanation:

D is the father of J, who is the brother to R and A happens to be his sister.

Therefore, D is the father of J,R and A

Answer:

The sum of 6 times a number and 7 turned into an equation would be:

6n + 7

Step-by-step explanation:

I found this out because the term "sum" means addition, and if you are multiplying 6 by a number, you are supposed to simplify the "number" into n. So, that's what I did:

6n + 7

May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

A)  number of ways in which president is not next to the VP =3628800-725760 =2903040

B) Number of ways =9*9!=3265920

C) number of ways VP is in one end  =2*9!=725760

Permutations and combinations are  ways of representing groups of objects by selecting them  and sub-setting them into sets. It defines different ways of arranging a particular data group. When we choose data or objects from a particular group, it is called a permutation and the order in which they are presented is called a combination. Both concepts are very important in mathematics.

a)

number of ways to line up 10 members =10! =3628800

number of ways so that VP and president are next to each other =N(consider president and VP as 1 member which can interchange in 2 ways , and now we need to arrange 9 members) =2*9!=725760

therefore number of ways in whcih president is not next to the VP =3628800-725760 =2903040

b)

Number of ways =N(9 choices for left most posiition except VP and arrange rest of 9 persons)

=9*9!=3265920

c)

number of ways VP is in one end =N(choose 1 place out of 2 end for VP and then arrange rest of 9 )

=2*9!=725760

therefore number of ways VP is not at one end =3628800-725760 =2903040

learn more about permutations and combinations here :

brainly.com/question/28720645

#SPJ4

The equation of the function that inputs the number of weeks since the beginning of the semester and outputs the money in his bank account is

Money = 5340 - 356X(weeks)

The table will be as follows:

        Weeks                                 Money

             0                                      5340

             3                                      4272

             7                                      2848

             11                                      1424

             15                                       0

Define an account.

An account in banking is an arrangement whereby a company, typically a financial institution like a bank or credit union, accepts a customer's financial assets and holds them on the customer's behalf at the discretion of the customer.

A financial account, specifically one that covers financial asset claims or liabilities to nonresidents, is a part of a country's balance of payments in macroeconomics. Direct investment, portfolio investment, and reserve assets are broken down by sector and are all parts of the financial account.

To learn more about an account, use the link given
https://brainly.com/question/26690519
#SPJ1

Answer:

Step-by-step explanation:

3 is 10% of 30. Therefore, the other 27 is the resulting 90% of the whole number of 30.

Answer:

37.8 litres

Step-by-step explanation:

V=a*b*c

a=1.5m=150cm

b=1.8m=180cm

c=1.4cm

1l=1000cm³

V=150cm*180cm*1.4cm=37800cm³

(37800cm³:1000cm³)*l=37,8l

The store's profit on the video game is $35.

According to the question,

We have the following information:

Elsie bought a video game for $85.00. And the store charges 170% of its cost for the game.

Now, let's take the original price of the video game to be $x.

So, we have the following expression:

170% of x = 85

170x/100 = 85

Using the cross multiplication method:

170x = 85*100

x = 8500/170

x = 50

So, we have the cost of the video game.

Now, we know that the formula to find the profit is as follows:

Profit = Selling price - cost of the product

Profit = $(85-50)

Profit = $35

Hence, the store's profit on the video game is $35.

To know more about profit here

https://brainly.com/question/28886059

#SPJ1

48 students can fit in one bus.

Given, a group of 234 students are going to see a thanksgiving parade, traveling in 4 busses and 3 vans.

Each bus holds 6 more than 3 times a number a van can hold.

Let the van holds 'x' students

then, bus holds 6 + 3x students

Now, according to the question

4(6 + 3x) + 3x = 234

24 + 12x + 3x = 234

24 + 15x = 234

15x = 234 - 24

15x = 210

x = 210/15

x = 14

So, bus holds 6 + 3x students

= 6 + 3(14)

= 6 + 42

= 48

Hence, 48 students can fit in one bus.

Learn more about Linear Equations here https://brainly.com/question/25858757

#SPJ1

Answer:

y = 4x - 9

Step-by-step explanation:

y = mx + b

m = (y_2 - y_1)/(x_2 - x_1) = (-17 - (-5))/(-2 - 1) = -12/(-3) = 4

y = 4x + b

-5 = 4(1) + b

-9 = b

y = 4x - 9

Answer:

It will take Ernie 6 hours to do the job by himself

Step-by-step explanation:

Rate x time = job

Burt's rate x time + Ernie's rate x time = 1 job getting completed.

[tex]\frac{1}{3}[/tex](2) + x(2) = 1  To clear the fraction multiply everything by 3

2 + 6x = 3  Subtract 2 from both sides

6x = 1  Divide both sides by 6

x = [tex]\frac{1}6}[/tex]  This is Ernie's rate

The rate is the number of jobs 1 over the number of hours 6, so it will take Ernie 6 hours to do this job by himself

Breakdown of clearing the fraction:

([tex]\frac{1}{3}[/tex])(2) + x2 = 1  Multiply everything by 3 to clear the fraction.

([tex]\frac{3}{1}[/tex])([tex]\frac{1}{3}[/tex](([tex]\frac{2}{1}[/tex]) + (3)(x2) =  (3) (1)

[tex]\frac{6}{3}[/tex] + 6x = 6

2 + 6x = 6

Answer:

Thus, one of the numbers is 85

Step-by-step explanation:

Answer:

Step-by-step explanation:

Volume of the frustum of right circular cone =  271.22 [tex]units^{3}[/tex]

Volume of frustum of right circular cone:

Formula for the Volume of Frustum of Cone (V)= 1/3 πH ([tex]R^{2}[/tex]+Rr+[tex]r^{2}[/tex] )

where,

          H = Height of frustum

          R = Radius of lower base

          r = Radius of top base

According to given question,

       Height of frustum(H) = 25 units

        Radius of lower base(R) = 13 units

         Radius of top base (r) =  5 units

Substituting all the given values in the formula of volume of frustum of cone we will get,

     Volume of frustum of right circular cone(V) =  1/3 πH ([tex]R^{2}[/tex] + Rr + [tex]r^{2}[/tex] )

                                                = 1/3 π ( 13x13 + 13x5 + 5x5)

                                                = 1/3 π ( 169 + 65 +25)

                                                = 1/3 π (259)

                                                = 86.33 π

                                                = 271.22 [tex]units^{3}[/tex]

Volume of the frustum of right circular cone =  271.22 [tex]units^{3}[/tex]

To learn more about Frustum of Cone visit: https://brainly.com/question/15437523

#SPJ4