Answer:
116.31468544 mg ibuprofen left
Step-by-step explanation:
Since there are 800 mg at the beginning and the system decreases by about 32% of the ibuprofen
After 1 hour
→ 800 - (800x32/100) = 800 - 256 = 544 mg ibuprofen left
After 2 hours
→ 544 - (544x32/100) = 544 - 174.08 = 369.92 mg ibuprofen left
After 3 hours
→ 369.92 - (369.92x32/100) = 369.92 - 118.3744 = 251.5456 mg ibuprofen left
After 4 hours
→ 251.5456 - (251.5456x32/100) = 251.5456 - 80.494592 = 171.051008 mg ibuprofen left
After 5 hours
→ 171.051008 - (171.051008x32/100) = 171.051008 - 54.73632256 = 116.31468544 mg ibuprofen left
To find the amount of ibuprofen left after 5 hours, the initial 800 mg is multiplied by 0.68 raised to the 5th power, resulting in approximately 115.28 mg remaining.
To calculate the amount of ibuprofen left after 5 hours, we can use the exponential decay formula. Since the amount decreases by 32% each hour, we can represent this as a decay rate of 68% (100% - 32%) remaining each hour. Therefore, the amount of ibuprofen after one hour is 68% of the initial amount, and we can represent this as a multiplication by 0.68 for each passing hour.
The formula to find the amount of ibuprofen left after 5 hours is:
Final amount = initial amount × (0.68)⁵
Using the initial amount of 800 mg and raising 0.68 to the 5th power:
Final amount = 800 mg × 0.68⁵
Final amount = 800 mg × 0.1441
Final amount ≈ 115.28 mg
So, approximately 115.28 mg of ibuprofen is left in the adult's system after 5 hours.
Suppose a car tire has a diameter of 32 inches. How many complete rotations will the tire make if it travels one mile
Answer: about 630.57 rotations per mile.
Step-by-step explanation: There are 1760 yards in one mile. 36 inches per yard. Convert miles to inches: 1760×36=63360
Figure the circumference of the tire: C=π×32 3.14×32=100.48=C
Divide the length of the mile by the circumference of the tire:. 63360/100.48 = 630.57 approximately.
You open a business selling school supplies and tutoring sessions. In your first week, you had $9,000 in sales. You ran a promotion on tutoring sessions totaling $900 in discounts. Your returns equaled $150. Calculate total net sales.
Answer: total net sales = $7950
Step-by-step explanation:
The formula for determining total net sales is expressed as
total net sales = Gross sales - (sales returns + allowances + discount)
Gross sales means total sales.
From the information given,
Gross sales = $9000
Discounts = $900
Returns = $150
Allowances = 0(this is because it was not given)
Therefore,
total net sales = 9000 - (900 + 150)
= 9000 - 1050
total net sales = $7950
Answer:
7950
Step-by-step explanation:
In a lab experiment, 590 bacteria are placed in a petri dish. The conditions are such
that the number of bacteria is able to double every 24 hours. How many bacteria
would there be after 13 hours, to the nearest whole number?
Answer:
There would be 859 bacteria after 13 hours.
Step-by-step explanation:
The population of bacteria after t hours is given by the following equation:
[tex]P(t) = P(0)e^{rt}[/tex]
In which P(0) is the initial population and r is the growth rate.
The number of bacteria is able to double every 24 hours.
This means that [tex]P(24) = 2P(0)[/tex]. So
[tex]P(t) = P(0)e^{rt}[/tex]
[tex]2P(0) = P(0)e^{24r}[/tex]
[tex]e^{24r} = 2[/tex]
[tex]\ln{e^{24r}} = \ln{2}[/tex]
[tex]24r = \ln{2}[/tex]
[tex]r = \frac{\ln{2}}{24}[/tex]
[tex]r = 0.0289[/tex]
590 bacteria are placed in a petri dish.
This means that P(0) = 590. So
[tex]P(t) = P(0)e^{rt}[/tex]
[tex]P(t) = 590e^{0.0289t}[/tex]
How many bacteria would there be after 13 hours, to the nearest whole number?
This is P(13).
[tex]P(t) = 590e^{0.0289t}[/tex]
[tex]P(13) = 590e^{0.0289*13} = 859[/tex]
There would be 859 bacteria after 13 hours.
Which shape is always a parallelogram?
A. A rectangle because it has 2 pairs of parallel sides.
B. A quadrilateral because it has 4 sides.
C. A trapezoid because it has 1 pair of parallel sides.
D. A hexagon because it has 3 pairs of parallel sides.
Answer:
the answer is A because it has 2 sides of parallel line
Step-by-step explanation:
The correct shape which is always a parallelogram is,
⇒ A rectangle because it has 2 pairs of parallel sides.
We have to given that,
To find shape which is always a parallelogram
Since, A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Hence, We can say that;
Rectangle shape is always a parallelogram.
Thus, The correct shape which is always a parallelogram is,
⇒ A rectangle because it has 2 pairs of parallel sides.
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Which expressions are equivalent to -2(5x-3/4)? Check all that apply.
A. -2(5x)+(-2)(-3/4)
B. -10x-3/4
C. -10x+ 6/2
D. -10x+3/2
E. -10x-6/2
I WILL CHOOSE YOU FOR BRAINLIESS
Answer:
A
Step-by-step explanation:
-2(5x)+(-2)(-3/4) = -10x +6/4
-2(5x-3/4) = the same
I got D is this correct?
Answer:no
Step-by-step explanation:
Answer:
C. x [tex]\geq[/tex] 0
Step-by-step explanation:
The answer is C, x is greater than or equal to zero, because that is the only answer that makes sense.
A) x can also be equal to 0, so this answer is wrong
B) x can't be -2, and it definitely can't be less than -2, so that's wrong.
D) Again, x can't be -2, or -1. It can't be any negative number because 4 * (a negative number) would put a negative sign under the square root. You can't take square roots of negative numbers.
Hope this is correct and that it helps you!
please help me with this fast
Answer:
5
Step-by-step explanation:
A negative plus a negative equals a positive so the equation would be 4 1/3 + 2/3 and the sum is 5.
Hopes this helps :)
Fiona is trying to prove that a pair of expressions are equivalent by using substitution. Which pair of expressions has the same value if she substitutes y = 3? 3 (4 minus y) minus 7; 5 + 3 y 9 + y + 4 y minus 2 minus 3 y; Negative 2 y + 7 5 + y minus 2 minus 6 y + y; 8 y + 3 2 y + 7 + y minus 2 + y; 4 y + 5
Answer:
D
Step-by-step explanation:
i used calculator and i all did tast and i got it right
Answer:
The answer is D
Step-by-step explanation:
I did get it correct on edg 2021
I hope it helps
Have great day!
Caleb went to Kroger and spent $83.47 on groceries. He had a coupon for $1.99 off bottled water and $0.89 off organic strawberries. How much did Caleb spend at Kroger?
Answer:
$86.35
Step-by-step explanation:
Total amount he spent at Kroger
= $83.47 on groceries. +coupon for $1.99 off bottled water + $0.89 off organic strawberries
= 83.47+0.89+1.99
= $86.35
Final answer:
After applying coupons for bottled water and organic strawberries, Caleb spent a total of $80.59 at Kroger. The discounts of $1.99 and $0.89 were subtracted from the initial spend of $83.47.
Explanation:
Caleb went to Kroger and initially spent $83.47 on groceries. He had two coupons: one for $1.99 off bottled water and another for $0.89 off organic strawberries. To calculate how much Caleb spent after using his coupons, we need to subtract the value of the coupons from the initial amount.
First, we calculate the total discount by adding the two coupon values:
$1.99 for bottled water
$0.89 for organic strawberries
Total discount = $1.99 + $0.89 = $2.88.
Then, we subtract this total discount from the initial spend:
$83.47 - $2.88 = $80.59
Therefore, Caleb spent $80.59 at Kroger after applying his coupons.
Pat earns 4% in his bank account each
year. He has $2,400 in his account. How
much will he have in 5 years if he does not
make any more deposits?
A. $12,480.00
B. $12,907.78
C. $2,919.97
D. $2,457.60
Which formula is the correct formula to use when finding volume of a
cylinder?
Answer:
The last option.
Step-by-step explanation:
A total of 13.2 inches of snow fell during a snowstorm that lasted 5.5 hours. The same amount of snow fell each hour of the storm. How many inches of snow fell each hour? Enter your answer as a decimal in the box.
Answer:
2.4 inches per hour
Step-by-step explanation:
A total of 13.2 inches of snow fell during a snowstorm that lasted 5.5 hours and the same amount of snow fell each hour of the storm.
This means that there was a constant rate of snow fall.
To find how many inches of snow fell each hour, we divide the amount of snow fall by the amount of time that the snowstorm lasted.
That is:
[tex]R = \frac{13.2}{5.5}[/tex]
R = 2.4 inches per hour
This means that 2.4 inches of snow fell each hour during the snowstorm.
Answer:
2.4 inches
I did the quiz
which of these expressions equal 15 when x = 1/2 and y = 3. Choose all that apply
Answer:
WHERES THE PIC??
Step-by-step explanation:
Answer:
Btw I got this for home work.
Step-by-step explanation:
Mrs. Allard asked her students to identify which of the polynomials below are in standard form and explain why.
1. 15x4 - 6x + 3x2 - 1
II. 12x3 + 8x + 4
III. 285 + 8x2 + 10%
Which student's response is correct?
Answer:
Only II. is written in standard form
Step-by-step explanation:
The three polynomials given are:
I. [tex]15x^4 - 6x + 3x^2 - 1[/tex]
II. [tex]12x^3 + 8x + 4[/tex]
III. [tex]285 + 8x^2 + 10%[/tex]
A polynomial is said to be in standard form when the variables are written in terms of descending powers i.e. the term with the highest power first, followed by the next and so on.
Examining the three polynomials I, II and III, there is only one which follows this rule and that is:
II. [tex]12x^3 + 8x + 4[/tex]
The term with the highest power (3) came first, followed by the term with the next degree of power (1) and the last term with degree of power as 0.
Hence, only II. is written in standard form.
Only the second polynomial, 12x3 + 8x + 4, is in standard form because its terms are arranged in descending order of degrees. The first polynomial is not in standard form due to the incorrect order of terms by degree. The third expression contains a percentage sign (%) and wasn't written in order of descending degree, hence it doesn't qualify as a polynomial in standard form.
Explanation:In mathematics, a polynomial is said to be in standard form when its terms are written in descending order by degree. The degree of a term is the exponent used in the term. Let's evaluate each option:
15x4 - 6x + 3x2 - 1: This polynomial is not in standard form because the terms are not arranged in descending order of degrees. Properly ordered, it would read 15x4 + 3x2 - 6x - 1.12x3 + 8x + 4: This is in standard form because the terms are arranged in descending order of degrees from 3 to 0.285 + 8x2 + 10%: This is not a polynomial in the standard sense of the word due to the presence of the percentage sign (%). Also, it was not written in descending order of degrees.Learn more about Polynomials in Standard Form here:https://brainly.com/question/32213698
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144 students enter a spelling bee, but only 1/6 of the group will make into the semi-final round, and only 2 /3 that group will make into the final round. How many students will enter the final round of the spelling bee?
Answer:
16 students
Step-by-step explanation:
144 students enter a spelling bee contest.
Step 1
For the semi final round we are told that only 1/6 of the group will make it into that round.
This is calculated as
1/6 × 144/students = 24 students.
This means that only 24 students would make it into the semi final rounds.
Step 2
We are also told in the question that only 2/3 of THAT group would make it into the final round.
" THAT" group been referred to in the question means the number students that made it to the semi final round
This is calculated as
2/3 of that group( the group that made it to the semi finals)
= 2/3 × 24 students
= 16 students.
Therefore, the number of students that will enter the final round of the spelling bee is 16 students.
To calculate the number of students who will make it to the final round of the spelling bee, we first determine the semi-finalists by multiplying the total students by 1/6, and then the number of finalists by multiplying the semi-finalists by 2/3, resulting in 16 students.
Explanation:To solve this problem, we first need to determine the number of students who will make it into the semi-final round. Since only 1/6 of the total students will make it to the semi-final round, we can calculate that by multiplying the total students (144) by 1/6, which results in 24 students.
Next, we need to calculate the number of students that will make it into the final round from the semi-final round. This means we need to multiply the semi-finalists (24) by 2/3, which results in 16.
Therefore, 16 students will make it into the final round of the spelling bee.
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In the given figure, measure HK= 50° and measure GKL is 50° which statement is true?
Answer: A
Step-by-step explanation:
The answer is a because the measure of angle KGH is 25 degrees since it is an inscribed angle. Angle GKJ is 130 degrees because angle GKL is 50 degrees. Therefore angle J is equal to 25 degrees which makes the triangle an isosceles triangle since angle J and angle KGH are equal to one another.
Answer:
A
Step-by-step explanation:
Felipe takes a commuter train to get to work. He pays a one-time fee to store his bike at the train station. He pays a
monthly fee for train passes. The total cost c for Felipe to travel to work for m months is given by the equation
80m + 50. What do the numbers 80 and 50 represent?
Answer:
80 represents the monthly fees and 50 represents the fixed one-time fee to store the bike at the train station.
The number 80 represents the monthly train pass cost, while 50 represents the one-time bike storage fee. Multiply the monthly fee by the number of months and add the bike storage fee to get total cost c for m months.
The number 50 is the initial, one-time cost to store Felipe's bike at the train station. To calculate the total commuting cost c for Felipe for m months, you multiply the number of months m by the monthly train pass cost, and then add the one-time bike storage fee.
rry YUVIVU W
ulluDIUTUMIT
Question 3 of 10
2 Points
What would be the most logical first step for solving this quadratic equation?
x2 + 2x-11 = 4
Answer:
Subtract 4 from both sides
Step-by-step explanation:
Ap ex
how much will you have to invest to have $6,000 in 4 years 3 months at 4 1\5% annual interest, compounded monthly.
$7,185.50
$5,020.71
$1,016.90
$4,957.33
Answer:
You have to invest $5,020.71 to have $6,000 in 4 years 3 months at 4 1\5% annual interest, compounded monthly.
Step-by-step explanation:
Let the principal be x
Amount = $6000
Time = 4 years 3 months = [tex]4 years +\frac{3}{12} years = 4.25 years[/tex]
Rate of interest = [tex]4 \frac{1}{5}\% = \frac{21}{5}\%[/tex]
No. of compounds per year = 12
Formula:[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
[tex]6000=P(1+\frac{21}{500 \times 12})^{12 \times 4.25}[/tex]
[tex]\frac{6000}{(1+\frac{21}{500 \times 12})^{12 \times 4.25}}[/tex]=P
P=$5,020.71
Hence You have to invest $5,020.71 to have $6,000 in 4 years 3 months at 4 1\5% annual interest, compounded monthly.
There are 91 eighth-grade students signing up for electives.
Of these 91 students, 68 sign up for the art, 31 sign up for
band, and 18 signed up for both. 10 Students are not signing
up for either art or band.
Let S = {all eighth students}
Let A = {students in Art}
Let B = (students in band)
PLS HELP!! I’LL GIVE U 5 stars
Answer:
A). 81 students
B). 18 students
C). 10 students
Step-by-step explanation:
Let S = {All students of 8th grade} = 91
A = {Students in Art} = 68
B = {Students in band} = 31
Part A : A∪B = A + B - A∩B
A∪B = 68 + 31 - 18
A∪B = 81
A∪B represents the total number of students enrolled in art and band.
Part B : A∩B = 18
A∩B represents the number of common students enrolled in art and band.
Part C: ~(A∪B) = S - A∪B
~(A∪B) = 91 - 81
~(A∪B) = 10
~(A∪B) represents the number of students enrolled neither in art nor in band.
Find m∠7 if m∠8 = 119°
m∠7 = ???
Answer:
119
Step-by-step explanation:
it will be the same as 8 because they are adjacent..
A packet of 8 pens costs £1.84 how much does each pen cost
Answer:
23p
Step-by-step explanation:
Pens : Cost
8 : £1.84
divide each by 8
1 pen = £0.23 = 23p
Carmen simplified the expression (4y+8x+6)+25+(4x-6y+7) The coefficient of the variable y In her simplified answer is
Answer:
Step-by-step explanation:
(4y + 8x + 6) + 25 + (4x - 6y + 7) =4y + 8x + 6 + 25 + 4x - 6y + 7
= 4y -6y + 8x + 4x + 6 + 25 + 7
= -2y + 12x + 38
Coefficient of y = -2
Help out please!!!!!!
Answer:
6.4
Step-by-step explanation:
A^2+B^2=C^2
(5*5)+(4*4)=C^2
25+16=[tex]C^{2}[/tex]
41=[tex]C^{2}[/tex]
[tex]\sqrt{41}[/tex]=[tex]\sqrt{C^{2} }[/tex]
c= 6.4
3x^2-8x+4 pls factor step by step
What is mode to a data set
Answer:
The number that occurs the most frequently
Step-by-step explanation:
For example, in the number set below
1, 1, 2, 3, 3, 3, 3, 4, 5, 6, 6, 85, 95
The number that shows up the most is 3, so 3 is the mode
What value of x will make parallelogram ABCD a rhombus?
x = ?
Answer:
x=34
Step-by-step explanation:
3x-12=90
3x-12+12=90+12
3x=102
3x/3 = 102/
x=34
Answer:
x = 34Step-by-step explanation:
From the picture we have
AD = CD = BC = AB
it's enough to say that this quadrangle is a rhombus.
The diagonals in each rhombus are perpendicular and divide to half.
Therefore we have the equation:
3x - 12 = 90 add 12 to both sides
3x - 12 + 12 = 90 + 12
3x = 102 divide both sides by 3
3x : 3 = 102 : 3
x = 34
In how many ways can the first 4 guests arrive at a party if 15 guests have been invited.
Answer:
The first 4 guests can arrive in 32,760 ways.
Step-by-step explanation:
The order in which the guests arrive is important. For example, A,B,C,D is a different outcome to B,A,C,D. So we use the permutations formula to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this question:
4 guests from a set of 15. So
[tex]P_{(15,4)} = \frac{15!}{(15-4)!} = 32760[/tex]
The first 4 guests can arrive in 32,760 ways.
Answer:
the first 4 guests can arrive in 32,760 ways.
Step-by-step explanation:
how many ways can the first 4 guests arrive at a party if 15 guests have been invited.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
4 guests from a set of 15
P(15,4) = 15 * 14 * 13 * 12
= 32760
Therefore, the first 4 guests can arrive in 32,760 ways.
The length of a rectangle is 5 inches more than the width. The area is 33 square inches. Find the length and width . Round to the nearest tenth if necessary.
Answer:
the length and width . Round to the nearest tenth are 8.8 inches and 3.8 inches respectively.
Step-by-step explanation:
The area A of a rectangle is the product of the length L and width W. This may be expressed mathematically as
A = L * W
As such, given that the length is 5 inches more than the width,
L = W + 5
33 = W(W + 5)
W² + 5W - 33 = 0
Using the formula method which states that
s = -b±√(b²-4ac)/2a
W = -5 ± √5² - 4(1)(-33)/2
= -5 ± 12.53/2
= 7.53/2 (since length cannot be negative)
= 3.755 inches
L = 3.755 + 5
= 8.755 inches
Mei-ling invested $2,000 in a simple interest account for 3 years. At the end of 3 years, she had earned $150 in interest. What was the simple interest rate of the account?
Answer:
2.5%
Step-by-step explanation:
Simple Interest formula : V = P + P*r*t
I = Prt
$150 = $2000*r * 3
r = $150 / ($2000*3) = 5/200 = 0.025 = 2.5%