The equation to model Exponential Decay is:
y = a[1 – r)
y= total amount
a= starting amount
r= the growth rate as a decimal
t= number of growth periods
Question 1 (1 point)
Sarah takes 550 mg of an antibiotic. Every hour,
her body breaks down 25% of the remaining drug.
How much will be left after 12 hours?
Guys help me please I really don’t understand this
Answers
I will give some hints. We know most values, we have to solve for y as that is the remaining amount.
y = We have to find.
a = 550 mg (She takes this much)
r = 0.25 (This is 25% as a decimal, don't forget to subtract 1)
t = 12 (This is because over the 12 hours, each hour it breaks down so (12 hours total * 1 hour periods) gives us 12 periods.
I hope this helps!
Related Questions
What is the least common multiple? 27, 21
Answers
Answer:
189 is the LCM of 27 and 21
Jasmine is trying to replace the flooring in her rectangular bedroom. When she measured the width and length of the floor, she found that the length is 5 ft. longer than the width. If the perimeter of the room is 50 ft., how much flooring will she need to replace the existing flooring in her room?
Answers
Answer:
150ft^2
Step-by-step explanation:
FINDING THE LENGTHS
50 = x + 5 + x + x + 5 + x
50 = 4x + 10
50 - 10 = 4x
40 = 4x
40/4 = x
10ft = x
AMOUNT OF FLOORING
area = l x b
= (10 + 5) x 10
= 15 x 10
= 150ft^2
Simplify −4(x+1)+6x . Write your answer in factored form.
Answers
Answer:
2(x - 2)
Step-by-step explanation:
- 4(x + 1) + 6x ← distribute parenthesis by - 4
= - 4x - 4 + 6x ← collect like terms
= 2x - 4 ← factor out 2 from each term
= 2(x - 2)
=================================================
Let's simplify this expression.
The first step is to use the distributive property, which states:-
[tex]\bigstar{\boxed{a(b+c)}[/tex]
Simplify:-
[tex]\bigstar{\boxed{-4(x+1)}[/tex]
[tex]\longmapsto\sf{-4x-4}[/tex]
Add 6x:-
[tex]\longmapsto\sf{-4x+6x-4}[/tex]
Combine Like Terms:-
[tex]\longmapsto\sf{2x-4}[/tex]
Now, we should write our answer in factored form, so we factor 2 out:-
[tex]\longmapsto\sf{2(x-2)}[/tex]
=============================================
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)
A map is placed on a coordinate grid. On the map, city 1 is located at the
point (35, 78), and city 2 is located at the point (47, 122). What are the
coordinates of a city located halfway between city 1 and city 2?
Answers
Answer:
its b trust me i had that one (12,44)
Step-by-step explanation:
The area of a rectangle is 175 cm. And the width of the rectangle is 5 cm. What's the perimeter of the rectangle?
Answers
Answer:
80cm
Step-by-step explanation:
The area of the rectangle is given by Area = L*W (length, L and width, W).
175 cm^2 = 5*L
L = 35 cm
Perimeter is 2L + 2W
2(35cm)+2(5cm)
70cm + 10cm
Perimeter = 80cm
Which choices are equivalent to the expression below? Check all that apply.
x + 2x + 9x
O A. 12x
O B. 12y3
O C. 12
D. (1 + 2+ 9)x
SUBMIT
Answers
Will give BRAINLIEST!! Write a polynomial and show all the steps you would take to factor this polynomial completely. Please explain each step thoroughly.
I am not accepting links. Thank you:)
Answers
Step-by-step explanation:
Consider this polynomial,
[tex]8 {x}^{2} + 2x - 3[/tex]
First, I do the AC memethod. To find my two numbers,
That is to find two numbers that multiplied will equal my leading coeffeicent, A times my constant, C
And that will also add to 2, my middle term.
So using that
[tex]8 \times - 3 = - 24[/tex]
So let find factors of-24:
Factors can be positve or negative
The factors of 24 are : 1,2,3,4,6 8,12,24.
So which one of these add up to 2.
[tex]6 + ( - 4) = 2[/tex]
and
[tex]6 \times - 4 = - 24[/tex]
So six and negative four is our numbers.
Now, let set up our binomials
Step 1: Rewrite the orginal equation by using 6x and -4x instead of 2x.
Disclaimer: The placement of these numbers doesn't matter.
So we have
[tex]8 {x}^{2} + 6x - 4x - 3[/tex]
Step 2: Group the first two terms and last two terms
[tex](8 {x}^{2} + 6x) + ( - 4x - 3)[/tex]
Factors the first group by finding the GCF.
x is the greatest common variable, and 2 is the gcf so we have
[tex]2x(4x + 3) + ( - 4x - 3)[/tex]
Next, factor the next group by -1.
[tex]2x(4x + 3) - 1(4x + 3)[/tex]
Combine the outside factors.
[tex](2x - 1)(4x + 3)[/tex]
So those are the factors.
Let T be the set of things found in a toy store, and V be the set of things that cost more than $50.
Select the words from the drop-down menus to correctly complete the sentences.
The set T∪V is the set of things that
Choose...
.found in a toys store and cost more then 50$
found in a toys store or cost more then 50$
The set T∩V is the set of things that
Choose...
.found in a toys store and cost more then 50$
found in a toys store or cost more then 50$
The set T′ is the set of things that
Choose...
cost under 50$
not found in toy store
not found in toy store and cose more then 50
Answers
Answer:
found in a toys store and cost more than 50$
Step-by-step explanation:
it makes the most sense don't you think?
help please, can you figure it out?
Answers
Answer:
4,333$
Step-by-step explanation:
There are 12 months in a year so we divide 52,000 by 12 and it equals 4,333 if you rounded it.
A ratio of boys to girls in the classroom is 4 to 5 if there are 20 girls how many boys would there be
Answers
Answer:
16 to 20
Step-by-step explanation:
Let's do our math.
4 to 5
8 to 10
12 to 15
16 to 20
In order to get to 20, you'd have to multiply 5 by 4. So in order to get an equal ratio, you multiply 4 by 4 and get 16.
I hope this helps!
-No one
Can someone please help me with this question?
Answers
Answer:
x< -6 or x > 0 (C is correct for question 1.) x ≤ 2 (C is correct for question 2)
Step-by-step explanation:
You have given me 2 questions:
| x + 3 | + 7 > 10
3x + 6 ≤ 12
Let's solve the first one:
| x + 3 | + 7 > 10
Before we start, the greater-than sign means that the point on the number line has to not be filled in.
| x + 3 | + 7 > 10
**Along with this equation you need to do a negative one meaning you need to flip the sign to a less than one and make 10 and 7 negative.
| x + 3 | - 7 < -10
| x + 3 | + 7 > 10
**Notice that this one is the original one.
Subtract 7 both sides
| x + 3 | > 10 -7
Now do 10-7
| x + 3 | > 3
Now subtract 3 both sides
x > 0
The negative case:
| x + 3 | - 7 < -10
Add 7 both sides
| x + 3 | < -10 + 7
Do -10 + 7
| x + 3 | < -3
Subtract 3 both sides
x < -3-3
Solve -3-3
x < -6
Your inequalities:
x< -6 or x > 0
The or statement is for greater than and the "and" is for less than.
Answer Choice C is correct.
Next Question:
3x + 6 ≤ 12
**Before we do anything, we have a less than or equal sign**
The point will be filled on the number line.
This is a typical inequality two-step:
3x + 6 ≤ 12
Subtract 6 from both sides
3x ≤ 12-6
Do 12-6
3x ≤ 6
Now divide 6 by 3
x ≤ 2
Answer Choice C is correct.
What is the length of PR?
Answers
Answer:
c 6
Step-by-step explanation:
since angles are equal then the sides can be equal
(AB÷PQ)=(AC÷PR)
(20÷5)=(24÷X)
4=24÷X
X=6
I want to know how to find EF and what the answer is.
Answers
[tex]\huge\underline\mathtt\colorbox{cyan}{37✅✅✅}[/tex]
Step-by-step explanation:
5x+12=6x+7 (opposite sides of a parallelogram are equal) 12=x+7 (subtract 5x from both sides) x=5 (subtract 7 from both sides) Now put x in any of the equations-- 5(5)+12=37 or 6(5) +7=37A rectangular-shaped badminton court has an area of 880 square feet. The width of the court is 20 feet. What is the length of the badminton court?
Answers
Answer:
length = 44 ft.
Step-by-step explanation:
A = lw
[tex]880 = 20l\\[/tex]
Solving for l gives us l = 44 ft.
The rate at which people learn about a secret is directly proportional to the number of people who know the secret. If two people know the secret on day 0, and 20 people know it on day 2, how long will it take for the whole school (4000 people) to know?
Answers
Answer:
between 222 and 223 days
Step-by-step explanation:
This relation includes the point (0, 2).
A proportional relation must include the point (0, 0).
This is not proportional, but it may be linear.
Points: (0, 2), (2, 20)
y = mx + b
20 = (20 - 2)/(2 - 0) × 2 + b
20 = 18/2 × 2 + b
b = 2
y = 18x + 2
When 4000 people know, y = 4000.
y = 18x + 2
4000 = 18x + 2
3998 = 18x
x = 3998/18
x = 222.111...
Answer: between 222 and 223 days
You are starting a savings account for college. You put $1,000 in as your starting balance. You earn simple interest at 10% every year. You also must pay 30% income tax on the interest earned annually. Calculate the balance for the account after 5 years
Answers
Answer:
$1,350
Step-by-step explanation:
Simple interest formula
I = Prt
where:
I = interestP = principalr = interest rate (in decimal form)t = time (in years)Given:
P = $1,000r = 10% = 0.1t = 5 years⇒ Total interest earned = 1000 × 0.1 × 5 = $500
If you have to pay 30% income tax on the interest earned annually, then you will keep 70% of your earned interest.
⇒ 70% of $500 = 0.7 × $500 = $350
Account balance = principal + interest earned after tax
= $1,000 + $350
= $1,350
What is the area of this figure?
Answers
Answer:
234 mm^2
Step-by-step explanation:
These questions are tricky but to make them easier, try to break down the shape into smaller regular shapes and work them out.
I would divide this shape into 2 rectangles and one triangle
Area of small bottom rectangle: 4 x 11 = 44mm^2
Area of rectangle in the middle: 14 x 8 = 112mm^2
Area of triangle: 12 x 13/2 = 78mm^2
Add all the areas together = 44+112+78 = 234mm^2
enrollment is a business seminar increased from 50 people to 62 people. what was the percent increase?
Answers
well, it went up from 50 to 62, so it really went up by 12 folks.
if we take 50 to be the 100%, what is 12 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 50 & 100\\ 12& x \end{array} \implies \cfrac{50}{12}=\cfrac{100}{x}\implies \cfrac{25}{6}=\cfrac{100}{x} \\\\\\ 25x=600\implies x=\cfrac{600}{25}\implies x=24[/tex]
The two-way table shows the number of sport utility vehicles with certain features for sale at the car lot. a 4-column table has 3 rows. the first column has entries third-row seats, no third-row seats, total. the second column is labeled 4-wheel drive with entries 18, 7, 25. the third column is labeled no 4-wheel drive with entries 12, 28, 40. the fourth column is labeled total with entries 30, 35, 65. what is the probability that a randomly selected car with no 4-wheel drive has third-row seats? 0.3 0.4 0.7 0.8
Answers
The probability that a randomly selected car with no 4-wheel drive has third-row seats is given by: Option B: 0.4
How to calculate the probability of an event?Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.
Then, suppose we want to find the probability of an event E.
Then, its probability is given as
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]
where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.
What is chain rule in probability?For two events A and B, by chain rule, we have:
[tex]P(A \cap B) = P(B)P(A|B) = P(A)P(B|A)[/tex]
where P(A|B) is probability of occurrence of A given that B already occurred.
For this case, the table given is:
Entries 4-wheel drive No 4-wheel drive Total
Third Row Seats 18 12 30
No Third Row Seats 7 28 35
Total 25 40 65
Let we take
A = event that a randomly selected car has no-4 wheel drive
B = event that a randomly selected car has third row seats
The total ways a car can be selected = 65 = n(S)
Total ways A can happen = n(A) = 40 (from the table).
Similarly, n(B) = 30
P(A) = n(A)/n(S) = 40/65
P(B) = n(B)/n(S) = 30/65
P(A∩B) = n(A∩B)/n(S) = 12/65
As by chain rule, we have:
P(A∩B) = P(A)P(B|A) = P(B)P(A|B)
We need P( A randomly selected car has three seats given that the selected car is with no 4-wheel drive)
which is symbolically P( B | A)
Thus, we use: P(A∩B) = P(A)P(B|A)
or
[tex]12/65 = (30/65)(P(B|A))\\\dfrac{12/65}{30/65} = P(B|A)\\\\P(B|A) = \dfrac{12}{30} = \dfrac{2}{5} = 0.4[/tex]
Thus, the probability that a randomly selected car with no 4-wheel drive has third-row seats is given by: Option B: 0.4
Learn more about probability here:
brainly.com/question/1210781
Answer:
b. 0.4
Step-by-step explanation:
took the test
Mr. Jones and Mr. Griebel each bought new shoes, Mr. Jones used a 20% off coupon and paid $82. Mr. Griebel used a $20 off coupon. How much Mr Griebel pay for his shoes?
Please help meee
Answers
Answer:
Assuming they bought the same shoes, $82.5
Step-by-step explanation:
80% of Original Shoe price = $82
Divide by 0.8 to find the original price.
82 / 0.8 = 102.5
102.5-20=82.5
Does anyone know the answer to these?
Answers
Rowan has 3 pieces of yarn, as described below. *a red piece of yarn that is 3/4 foot long *a yellow piece of yarn that is 6/8 foot long * a blue piece of yarn that is 4/12 foot long Wich number sentence correctly compares the lengths of 2 of these pieces of yarn. A 3/4 < 3/6 B 4/12 < 3/4 C 3/4 > 6/8 D 4/12 > 6/8
Answers
Answer:
b
Step-by-step explanation:
because all the orher ones are wrong and not correct.
These triangles are similar. Solve for the scale factor.
Answers
Answer:
Scale factor = 3
Step-by-step explanation:
A - B = 1-3
3 - 1 = 2
A' - B' = 3-9
9 - 3 = 6
6 / 2 = 3
this question is too hard
Answers
Answer:
There are 33 nuts in the bag, to 21 dried fruits.
Total number of dried fruits is 21, while the total number of nuts is 33.
Step-by-step explanation:
3. Use multiplication to find 5% of 180. 5/100 of 180 =…. 180. = ?/100 = ? %5 of 180 is ….
Answers
Answer:
9
Step-by-step explanation:
5% of 180 = 5/100 x 180
=> 5/10 x 18
=> 90/10
=> 9
Answer:
9
Step-by-step explanation:
5% of 180 = 5/100 of 180
10% = 18 -----> 5% = 9
180 = ?/1000 -------> 180 = 18000 / 100 = 180
5% of 180 = 9
8. A 140-pound female has three mixed drinks one right after the other.
a. What is her BAC after consuming the three drinks?
BAC =
b. What is her BAC three hours after finishing the last drink?
Answers
The BAC of the female is an illustration of proportion
The BAC after consuming the three drinks is 0.029wThe BAC three hours after consuming the drinks is 0.087 wHow to calculate the BAC?BAC is calculated using:
BAC = Alcohol consumed/(Body Weight * R)
The weight is given as:
Body weight = 140 lb
Convert to kg
Body weight = 63.5 kg
For female
R = 0.55
So, we have:
BAC = Alcohol/(63.5 * 0.55)
BAC = Alcohol/34.925
BAC = 0.029Alcohol
The weight or volume of the alcohol consumed is given.
So, we represent it with w.
BAC = 0.029w
Hence, the BAC after consuming the three drinks is 0.029w
How to calculate the BAC after 3 hours?We have:
BAC1 = 0.029w
Time (t) = 3 hours
The BAC after 3 hours is
BAC = BAC1 * (t - 0.015)
So, we have:
BAC = 0.029w * (3 - 0.015)
Evaluate the product
BAC = 0.087w
Hence, the BAC three hours after consuming the drinks is 0.087 w
Read more about BAC at:
https://brainly.com/question/1781657
Form and solve an equation to find x
Perimeter = 42 cm
2x
- 3
Х
Х
2x – 3
-
Answers
+6 +6
6x=48 divide both sides by 6
Answer:x=8
What is the value of In e^4
a 0
b 1
c 2
d 4
Answers
Answer:
[tex]4[/tex]
Step-by-step explanation:
[tex]\ln e^4= 4\ln e = 4 \log_e e = 4 \times 1 = 4[/tex]
What is the correct answer for this?
Answers
Volume:-
side³a³5³125cm³what numbers between the number 7-15 make 33
Answers
33/3
33/11
when you subtract or add any numbers together it wouldn’t be between 33
Check:
33/3=11