Using exponential functions, it is found that:
a) Since the amount of caffeine will be less than 50 mg, the patient will be ready for the blood test by 6 a.m.
b) The patient could have ingest 231 milligrams of caffeine.
A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.In this problem:
Caffeine metabolize at a rate of 13% per hour, hence [tex]r = 0.13[/tex].Then:
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]A(t) = A(0)(1 - 0.13)^t[/tex]
[tex]A(t) = A(0)(0.87)^t[/tex]
Item a:
The coffee cup contains 150 milligrams of caffeine, hence [tex]A(0) = 150[/tex].
At 6 a.m., it is 8 hours after drinking the coffee, hence we have to find A(8).
[tex]A(t) = A(0)(0.87)^t[/tex]
[tex]A(8) = 150(0.87)^8[/tex]
[tex]A(8) = 49.2[/tex]
Since the amount of caffeine will be less than 50 mg, the patient will be ready for the blood test by 6 a.m.
Item b:
This A(0), considering A(11) = 50, hence:
[tex]50 = A(0)(0.87)^{11}[/tex]
[tex]A(0) = \frac{50}{(0.87)^{11}}[/tex]
[tex]A(0) = 231[/tex]
The patient could have ingest 231 milligrams of caffeine.
A similar problem is given at https://brainly.com/question/25537936
Complete the given ordered pairs for the equation.
y = 2x + 1
(5, )
(0, )
(-2, )
Answer:
(5,11)
(0,1)
(-2,-3)
Step-by-step explanation:
y=2(5)+1
y=10+1
y=11
so... (5,11)
y=2(0)+1
y=0+1
y=1
so... (0,1)
y=2(-2)+1
y=-4+1
y=-3
so... (-2,-3)
anish spend 1/5 of 4000 and Anil spend 1/3 of 4500.who spend more and by how much
Answer:
Anil
Step-by-step explanation:
This is because 1/3 is greater then 1/5
PLEASE HELP ME WILL GIVE BRAINLIEST FOR RIGHT ANSWER
Answer:
Step-by-step explanation:
I dont really know how to find out the variables but what i assume to do is this:
Find the square root of n and add it to m. The sum of both you divide by p. then when you figure that out, you distribute the x value into the parenthesis. This might be obvious but i looked at this question for 10 minutes and couldnt find the value sorry :(
To prepare for a bake-off, Kim used 580 grams of flour each day for 2 weeks. How many kilograms did Kim use in those 2 weeks?
1 g = 0.001 kg
Answer:
below
Step-by-step explanation:
1 day = 580g
2weeks(14days)= 580×14g
= 8,120g
1g= 0.001kg
8,120g= 8,120 × 0.001(kg)
=8.12kg
NEED HELP ASAP PLS
Rearrange the equation, make the graph table, graph
y -3x=0
if clare goes to the bank every 7 days and clare go's to the bank every 5 days what day will they bolth go to the bank
Help help help help math
Answer:
A = 192
Step-by-step explanation:
r = 16/2 = 8
A = 3x(8)^2
8^2 = 64
A = 3 x 64 = 192
Radius is half the diameter.
The diameter is shown as 16, so the radius would be 16/2 = 8 in.
Area = 3 x 8^2
Area = 3 x 64
Area = 192 square inches
The average number of students in ten 5th grade classes is 27. Which of the following can be extrapolated from this information? *
A the average teacher to student ratio
B the average grade of a 5th grader
C the average number of students in all grades
D the average number of students in all 5th grade classes
Answer:
D
Step-by-step explanation:
Answer:
D would be the answer:) hope this helps
Sara is saving up to purchase a small T.V.
She has saved $80, which is 64% of the total
cost of the television. How much does the
television cost?
Answer:
You got this just keep trying
Step-by-step explanation:
Answer:
It might be 80
Step-by-step explanation:
first you put 64% and $80 as a fraction. 64%/$80. Then next to the fraction, you put x/100. Then you cross multiply. 64 times 100 is 6400. 6400 divided by 80 is 80. Therefore, the answer is 80. Hope this helps!
The function f(x) is shown in this graph.
5
(0,2)
The function g(x) = -3x - 6. Compare the slopes,
Help plz
Answer:
The slopes are equal
Step-by-step explanation:
Calculate the slope m of f(x) using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 5) and (x₂, y₂ ) = (0, 2) ← 2 points on the line
m = [tex]\frac{2-5}{0-(-1)}[/tex] = [tex]\frac{-3}{0+1}[/tex] = [tex]\frac{-3}{1}[/tex] = - 3
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
g(x) = - 3x - 6 ← is in slope- intercept form
with slope m = - 3
Then the slopes of f(x) and g(x) are equal, meaning the lines are parallel
Which has a greater rate of change?
pick one
A right triangle has leg lengths that are 5 meters and 6 meters, respectively. Which of the following lengths, in meters, is closest to that of the hypotenuse of the right triangle? answer
Answer:
7.8 or 8
Step-by-step explanation: To get the hypotenuse of a right triangle we must square each part.
5^2 is 25 and 6^2 is 36
Now you add the two squared parts, which equals 61. 61 squared isn't a perfectly squared. This means the answer is 7.8 or rounded to the nearest tenth the answer will be 8.
evaluate 2x+y for x=1/3 and y=2/3
a.1/3
b.2/3
c.4/3
d.5/3
Answer:
C. 4/3
Step-by-step explanation:
2 × ⅓ + ⅔
⅔ + ⅔ = 4/3
Use X as ⅓, and use Y as ⅔.
Gravitational energy_____.
A. is a type of potential energy
B. Is the energy of an object position
C. Is stored energy
D. All of the above
SOLVE QUICKLY PLEASE!!
Answer:
A. is the type of potential energy
Step-by-step explanation:
examples of gravitational potential energy : a raised in weight , a yoyo,water in a dam,a car parked on a hill
Please help, im stuck
Solve 6[9 - (9x - 8)] + 3x = 0.
A. 2
B. -5/4
C. -32/47
D. 2/15
E. None of the above
Answer: 2
Step-by-step explanation:
distribute: 6 [ 9 − 9 + 8 ] + 3 = 0
add the numbers: 6 [ 1 7 − 9 ] + 3 = 0
rearrange terms: 6 [ − 9 + 1 7 ] + 3 = 0
distribute again: − 5 4 + 1 0 2 + 3 = 0
combine like terms: − 5 4 + 1 0 2 + 3 = 0
Subtract 102 from both sides of the equation: − 5 1 + 1 0 2 − 1 0 2 = 0 − 1 0 2
simplify:− 5 1 = − 1 0 2
Divide both sides of the equation by the same term: -51x/-51 = -102/-51
simplify: 2
i hope this helps! ^^
um. ill give brainliest help please !!!
No, Poppy did not answer the problem correctly.
The mistake I see is that she did not include the exponent on the first 3. She also forgot to keep the -8.
The correct answer would be -7. (see attachment)
Have a nice day :)
[tex]\sqrt{\frac{15}{6} }[/tex]
Simplify, and show work please :D
Hello! :p
Simply 15/6 to 5/2 = [tex]\sqrt{5/2}[/tex]
2. Simply again [tex]\sqrt{5} \\\sqrt{2}[/tex]
3. rationalize the denominator so 5/2 times 2/2 [tex]\sqrt{5} \sqrt{2} \\ ---\\2[/tex]
4. Simply [tex]\sqrt{5} \sqrt{2}[/tex] to [tex]\sqrt{10}[/tex]
answer: [tex]\sqrt{\frac{10}{2} }[/tex]
Hope this helps! Have a wonderful day1 :)
Sorry, I had a hard time finding all the symbols, so I had to get creative!
A 3-quart carton costs $2.79, while a 4-quart carton costs $3.88. Which is the better buy and why?
Answer: the 4 quart is a better buy
Step-by-step explanation:
The Sea Lions are facing off against The Otters in fantasy football. The Sea Lions scored -12 points this
week The Otters scored -17 points this week
Which one of the following inequalities correctly compares the scores?
Choose 1 answer:
-17> -12
8
B
-12 > -17
Which one of the following descriptions is correct?
Choose 1 answer:
Answer:
the answer is b -12 is closer to being a positive number making it worth more than -17. so you're answer would be -12>-17
Can someone please explain the steps?
Answer:
There all 67 degrees
Step-by-step explanation:
Answer:
y= 119
Step-by-step explanation:
From the diagram we know that opposite angles are the same so we can assume that y and its opposite angle will be the same too
All inner angles of a parallelogram add up to 360
61+61=122
360-122=238
238/2=119
Solve the following equation for b. Be sure to take into account whether a letter is capitalized or not.
gb-m=9
Answer:
g=10
b=1
m=1
Step-by-step explanation:
Choose the linear equations.
Answer:
y = [tex]\frac{3}{3}[/tex]x - 5
y = 2x + 5
Step-by-step explanation:
In linear equations, both variables x and y must have the exponent of 1 (i.e. they cannot have a small number at the top-right). And they cannot be in the exponents (i.e. cannot be the small number at the top-right).
The line plot shows the costs of 5 books. A teacher buys all 5 books. She pays
with a $100 bill. How much change should she get?
Answer:
$36 in change
Step-by-step explanation:
book cost total: 64
100-64=36
If you aren't sure how to read the chart, each "X" represents one book and the numbers below represent the price.
PLEASE HELP WORTH 50 POINTS!
Answer:
the question was not correctly solved
Step-by-step explanation:
A=½bh
23=½*b*h
²/1×23= bh
²/1×23=6h
46=6h
h=7.666666667 / h=23/3
I hope this is helpful
Match the vocabulary word with the correct definition,
1. coefficient
a number, a variable, or the product
of a number and variable(s)
a letter used to represent an
unknown number
The number in front of a variable in
2. constant
3. term
a term
a single term, multiple terms
connected by an addition or subtraction
sign
a number, a term containing no
4. variable
5. expression
variables
TURNITIN
NEXT QUESTION
READ NEXT SECTION
ASK FOR HELP
Answer:
Definitions matched below with vocabulary wordsStep-by-step explanation:
A number, a variable, or the product of a number and variable(s)
→ 3. termA letter used to represent an unknown number
→ 4. variableThe number in front of a variable in a term
→ 1. coefficientA single term, multiple terms connected by an addition or subtraction sign
→ 5. expressionA number, a term containing no variables
→ 2. constantplesae urgent hurryy for brainlist !!!!!!!!!!!
i really really hope can see this
Answer:
did u ever figure it out?
Step-by-step explanation:
Rewrite the fraction 2/7 as a division expression with the same numbers.
Answer:
EZ. Btw you kinda already did it. 2/7 is a division problem. Another way is 2 divided by 7
Step-by-step explanation:
Your softball team is ordering equipment from a catalog. Each bat costs $42. The cost of shipping is $12 no matter how much you order. The total cost is $348. How many bats did your team order?
During a sale at a furniture store, sofas were marked down 30%. You have a coupon for an additional 15% off. What is the final price of a sofa that originally cost $550?
Answer:
327.25
Step-by-step explanation:
550*0.7=385
385*0.85=327.25
!!! MUST REMEMBER!!!
dont add 30% and 15% together, 15% is another discount on the price that has been marked down.
The final price of a sofa will be $302.5.
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
The original price of a sofa = $550
During sale at a furniture store, sofas marked down = 30%
Coupon for an additional 15% off.
Now,
Total percent for profit on a sofa = 30% + 15%
= 45%
Hence, The cost of a sofa after discount will be calculate as;
The cost of discount at a sofa = 45% of 550
= 45/100 x 550
= 24,750 / 100
= 247.5
So, The final cost of a sofa = $550 - $247.5
= $302.5
Therefore, The final price of a sofa will be $302.5.
Learn more about the percentage visit:
https://brainly.com/question/843074
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