Evan's body metabolizes caffeine at a rate of 12.3% per hour (so the amount of caffeine in Evan's body decreases by 12.3% each hour). a. If Evan consumes a cup of coffee with 98 mg of caffeine in it, how long will it take for Evan's body to metabolize half of the 98 mg of caffeine?
b. If Evan consumes an energy drink with 198 mg of caffeine in it, how long will it take for Evan's body to metabolize half of the 198 mg of caffeine?
c. If Evan consumes a cup of coffee with c mg of caffeine in it, how long will it take for Evan's body to metabolize half of the cmg of caffeine? (Hint: your answer will be a numerical value)
Answers
a. It will take 5.62 hours for Evan's body to metabolize caffeine half of the 98 mg. b. It will also take 5.62 hours for Evan's body to metabolize half of the 198 mg.c. It will take 5.04(c/98) hours for Evan's body to metabolize half of the c mg.
a. The half-existence of caffeine in Evan's not entirely set in stone by the situation: 0.5 =\((0.877)^t\) where t is the time in hours. Addressing for t, we get t ≈ 5.63 hours. Subsequently, it will require around 5.63 hours for Evan's body to utilize half of the 98 mg of caffeine.
b. Involving a similar condition as in the past, 0.5 =\((0.877)^t\) and settling for t, we get t ≈ 7.29 hours. Accordingly, it will require roughly 7.29 hours for Evan's body to process half of the 198 mg of caffeine.
c. Involving a similar condition as in the past, 0.5 =\((0.877)^t\) and settling for t, we get t ≈ (ln 0.5)/(ln 0.877) ≈ 5.04 hours. In this manner, it will require roughly 5.04 hours for Evan's body to process half of the c mg of caffeine.
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Related Questions
The sun produces 3.9 x 10(33) ergs of radiant energy per second. How many ergs of radiant energy does the Sun produce in 2.45 x 10(5) seconds? Please help!
Answers
Answer:
3.9
Step-by-step explanation:
Answer:
157657.5 ergs of radiant energy
brainliest plz
6 feet
4.5 feet
3 feet
The rectangles are similar. What is the length in feet of the smaller
rectangle?
A 4
B. 4.2
C. 5
D. 5.5
Answers
Answer:
140
Step-by-step explanation:
(7/4) (80) =140 this is the answer for you.
3x+2 < 2x-5 for x=8
How do I do this
Answers
Answer:
3x+2 is not less than 2x-5
Step-by-step explanation:
3(8)+2<2(8)-5; 24+2 < 16-5; 26 < 9
A cylinder has a base diameter of 16cm and a height of 20cm. What is its volume in cubic cm, to the nearest tenths place?
Answers
Answer:
4021.76
Step-by-step explanation:
v= πr^2h
3.142x8×8×20
1. You want to plant a flower garden in your yard so that you can make a beautiful bouquet to put on the alter at church for Easter Sunday services. There are two types of flowers that you are going to be planting. You will be planting some tulips and daffodils. At the store tulips come in packs of 6 and daffodils come in packs of 9.
a.What is the least amount of packs of daffodils and tulips you would need to buy to have the same amount of each?
b.How many should you have of each kind of flower?
2.Each pack of tulips costs $4.75 and each pack of daffodils cost $3.50. From the previous problem, you know how many packs of each you will need. The sales tax is 7.5%.
a.How much tax will you be paying for all the flowers, to the nearest cent?
b.How much total will you be paying for all flowers, to the nearest cent?
3.You remember that you have a discount coupon for $2.75 off your total purchase before tax.
a. How much did the flowers cost with the discount including tax (Round to the nearest penny)?
b.How much money did you save with the coupon including tax?
4.When you get home to plant the flowers, you have 3 different flowerbeds in which you plan on planting flowers. You have two flowerbeds where you want the same ratio for tulips to daffodils. In one of these flowerbeds you have 4 tulips and 6 daffodils. The other flowerbed you have 3 daffodils.
a. How many tulips should there be in the second flowerbed to have the same ratio of tulips and daffodils as the first flowerbed?
b.How many total daffodils are used in these two flowerbeds?
c.How many total tulips are to be used in these two flowerbeds?
d.How many of each do we have left to use in the remaining flowerbed?
5.The flowers are supposed to get 1.5 cups of water per plant. You have a 3-quart water pail.
How many flowers can you water before having to go back to fill up your pail?
6.After a few days 1/3 of all your tulips and 1/2 of all your daffodils died.
How many tulips and how many daffodils do you need to purchase of each kind of plant to replace the flowers that died?
7.Next year you want to have 7 more than double the amount of plants you had this year.
How many total plants should you have for next year?
Answers
The solution to each total amount is as follows
1a. 3 packs of tulips and 2 packs of daffodils. 1b. 18 tulips and 18 daffodils.
2a. The tax $1.60 2b. The total cost $22.85.
3. total cost with discount and tax is $19.89. 3b. Amount saved is $2.95.
4. 2 tulips. 4b. 9 daffodils 4c. 6 tulips. 4d. 12 tulips and 9 daffodils.
5. 8 flowers before having to refill the pail.
6. you need to purchase 6 tulips and 9 daffodils.
7. you should aim to have 79 plants next year.
How did we solve for each amount of tulips and daffodils?1. least common multiple of 6 and 9 is 3. 6/3 = 2 and 9/3 = 3.
Cross multiply ⇒ 9 x 2 = 18 and 6 x 3 = 18
2. The cost of tulip and daffodil packs are
3×$4.75 = $14.25
2×$3.50 = $7.
The total cost before tax⇒ $14.25 + $7 = $21.25.
The tax⇒ $21.25 × 7.5/100 = $1.60 (rounded to the nearest cent).
The total cost including tax is $21.25 + $1.59 = $22.85.
3. Before tax ⇒ $21.25.
After applying a $2.75 discount, ⇒ $21.25 - $2.75 = $18.50.
The tax on this discounted amount is $18.50 × 7.5/100 = $1.39
Total cost with discount and tax is $18.50 + $1.39 = $19.89. (rounded to the nearest penny).
The total amount saved $22.85 - $19.89 = $2.95
4. ratio of tulips to daffodils is 4:6. simplify ⇒ 2:3. for every 3 daffodils, 2 tulips
The total number of daffodils 6 + 3 = 9
The total number of tulips 4 + 2 = 6
18 - 6 = 12 tulips and 18 - 9 = 9 daffodils are left for the remaining flowerbed
5. A 3-quart⇒ 12 cups ⇒ 1 quart = 4 cups.
∴ 12/1.5 = 8 flowers before refill.
6. 1/3 of the tulips died, ⇒ 1/3 ×18 = 6 tulips.
1/2 of the daffodils died, ⇒1/2 × 18 = 9 daffodils.
7. 18 tulips and 18 daffodils for a total of 36 plants.
36×2 = 72 + 7 = 79
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I need help pleasee!! Asap!
Answers
The midpoints of a rectangle always form parallelogram.
22. Look at the given triangles.
4x + 2
7x+7
C.
x+3
2x-5
X+7
5x-4
a Write an expression in simplest form for the perimeter of each triangle.
b. Write another expression in simplest form that shows the difference between the perimeter
of the larger triangle and the perimeter of the smaller triangle.
Find the perimeter for each triangle when x = 3
U
Answers
a. The perimeter of the first triangle is and the perimeter of the second triangle is
b. The difference between the perimeters is
c The perimeter of the triangles when x is 3 are
What is perimeter of triangle?Perimeter is a math concept that measures the total length around the outside of a shape.
The perimeter of a triangle = a+b+c
1. 4x+2 + 7x+7 + x+3
= 4x+7x+ x +2+7+3
= 12x +12
Perimeter of the second triangle
= 2x-5+x+7+5x-4
= 2x+5x+x-5+7-4
= 8x-2
2. The difference of the perimeters
= 12x+12 -( 8x-2)
= 12x-8x +12+2
= 4x +14
3. when x is 3
The perimeter of the first triangle
= 12(3) +12
= 36+12
= 48 units
The perimeter of the second triangle
= 8(3)- 2
= 22 units
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Two families visited an amusement park. the first family bought 2 hot dogs and 3 bottles of waters, which totaled $18. the second family bought 4 hot dogs and 2 bottles of waters, which totaled $28. how much did one hot dog cost? a. $2 b. $4c. $5 d. $6
Answers
Answer:
d. $6
Step-by-step explanation:
List three additional combos of length width and height that have a volume of 24 and please include the surface area too
Answers
The solution is then:
l = 6cm
w = 2cm
h = 2cm
What is the total surface area of cuboid?The surface area of a cuboid is the total area of all of the faces of a cuboid. If, the length (l), width (w), and height (h) of the cuboid
then, use the formula: surface area (SA)=2lw+2lh+2hw.
here, we have,
We know that the formula for the volume of a box is:
V = l*w*h
Where:
l = length
w = width
h = height
The formula of the surface area of a box is:
SA = 2(lw+lh+wh)
Based on the given we know the following:
24 = l*w*h
and
56 = 2(lw+lh+wh)
If we factor out the given volume, you can come up with 3 numbers that will satisfy the surface area formula:
24 = 6*2*2
Let:
l = 6cm
w =2cm
h =2cm
Now let's try this on the surface area formula:
56 = 2(6*2+6*2+2*2)
so, 56 = 56
The answer is then:
l = 6cm
w = 2cm
h = 2cm
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Alan washed 60 plates in 30 minutes. It took him 3 minutes to wash 6 plates. Is the number of plates washed in 3 minutes proportional to the total number of plates he washed in 30 minutes?
Answers
Answer:
Yes
Step-by-step explanation:
The numbers both multiplied by 10
3 -6
30-60
What do the following two equations represent?
Answers
(B) Distinct parallel lines
Answer:
B. Distinct parallel lines
Step-by-step explanation:
These two equations have the same slope 4/3 which means they are parallel.
y = mx + b
m is slope
b is y-intercept
\(y = \frac{4}{3} x + \frac{5}{3}\)
\(y - 8 = \frac{4}{3} (x + 6)\)
\(y = \frac{4}{3} x + 16\)
Point K is located at (7, 4) in the coordinate plane. Its image is created by the following rule: K' = Ro270°(K).
Which transformation of point K would produce the same result for K as seen in the previous question?
P.S. Pervious question
Point K is located at (7,4) in the coordinate plane. Its image is created by the following rule:
K'=Ro 270°^(k)
What are the coordinates of k'?
A. (4,-7)
B. (4, 7) This is the correct answer.
C. (7, -4)
D. (-7, 4)
Answers
After the transformation of 270° clockwise rotation we get K(7, 4)→K'(-4, 7). Therefore, option B is the correct answer.
The given coordinate point is (7, 4).
What is the transformation?A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure. The original shape of the object is called the Pre-Image and the final shape and position of the object is the Image under the transformation.
Rotation of object 270° clockwise direction
The rule of rotating a figure 270 degrees clockwise is (x, y)→(-y, x)
So, K(7, 4) rotated by 270° clockwise we get K'(-4, 7).
After the transformation of 270° clockwise rotation we get K(7, 4)→K'(-4, 7). Therefore, option B is the correct answer.
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Ada makes sparkling juice by mixing 2 cups of sparkling water with every 4 cups of apple juice. Let s represent the number of cups of sparkling water and j represent the number of cups of apple juice. Write an equation that shows how and are related.
Answers
Answer:
s = 2j
Step-by-step explanation:
Given - Ada makes sparkling juice by mixing 2 cups of sparkling water
with every 4 cups of apple juice. Let s represent the number of
cups of sparkling water and j represent the number of cups of
apple juice.
To find - Write an equation that shows how s and j are related.
Proof -
Let total number of cups of sparkling water make = s
Total number of cups of apple juice make = j
Now,
Given that, Ada makes sparkling juice by mixing 2 cups of sparkling water with every 4 cups of apple juice.
⇒2s = 4j
⇒s = 2j
∴ we get
Ada can makes sparking water by mixing 2j cups of sparking water with every j cups of apple juice.
Finding Missing Angles and Sides and Round to the nearest tenth.
(FOR ALL PLEASE)
Answers
The right triangle, like the other triangles, has three sides, three vertices, and three angles. The difference between the other triangles and the right triangle is that the right triangle has a 90 angle.
To find missing angles and sides and round to the nearest tenth, you can use different methods depending on the given information and the type of triangle or shape involved.
Some common methods include:
Trigonometric ratios (sine, cosine, tangent) for right triangles.
Angle sum property or exterior angle property for triangles.
Pythagorean theorem for right triangles.
Law of cosines and law of sines for non-right triangles.
To help find the missing angles and sides of a triangle, you need certain information about the triangle, such as known angle and side measurements, or information about the properties of the triangle.
Without this information, no concrete calculations can be made.
Provide the necessary information or describe the problem in more detail and we will help you find the missing corners and sides of the triangle and round it to tenths.
Remember to always check if any additional information is given, such as side lengths or angles ' 7 and to apply the appropriate formula or property to find the missing value.
Round your answer to the nearest tenth as specified.
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The graph of a function is shown below. What is its range?
O (1, 2, 4)
O (1, 2, 3, 5)
O All real numbers.
O (1, 2, 3, 4)
Answers
(1,2,4)
Step-by-step explanation:Range describes the y-values of a graph.
Range
Range is the y-values that a graph covers. Remember that the y-values are found on the vertical axis. If the graph is not continuous, then the values between the points are not included in the range. Similar to the range, the domain of a graph is the x-values that a graph covers. If there is a coordinate point with a y-value, then that y-value should be included in the range.
Finding Range
In order to find the range, we need to find all the unique y-values of the graph. Additionally, the range is given in numerical order. This means starting from the least value and going up to the greatest. The lowest y-value is 1, then 2, and finally 4. Even though there are two points where y = 2, we are only looking for unique values. This means that the range is (1,2,4).
Order the numbers from least to greatest.
53.77
54
53.61
53.6
Answers
Answer:
53.6, 53.61, 53.77, 54
Step-by-step explanation:
That's the right order
Find the formula for the exponential function that passes
through the two points given.
(x,y) = (0,4) and (x, y) = (3, 108)
f(x)=
Answers
f(x) = 4 * 3^x
To find the formula for the exponential function that passes through the points (0, 4) and (3, 108), we need to follow these steps:
Step 1: Write the general exponential function
The general exponential function is of the form f(x) = ab^x, where a and b are constants.
Step 2: Plug in the first point (0, 4)
Using the point (0, 4), substitute x=0 and y=4 into the equation and solve for a:
4 = a * b^0
Since any number raised to the power of 0 is 1, we have:
4 = a * 1
So, a = 4.
Step 3: Plug in the second point (3, 108) and solve for b
Now we have the function f(x) = 4 * b^x. Using the point (3, 108), substitute x=3 and y=108 into the equation and solve for b:
108 = 4 * b^3
Divide by 4:
27 = b^3
Now take the cube root of both sides:
b = 3
Step 4: Write the final formula
Now that we have found a and b, we can write the final formula for the exponential function that passes through the two points (0, 4) and (3, 108):
Therefore, f(x) = 4 * 3^x
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Find the equation of the line with a slope of − 1/2 through (4, 5)
Answers
Answer: Hello:
Slope - intercept form is y = mx + b.
Since -1/2 is your slope and 5 is your y - intercept, all you need to do is substitute those values into the equation:
y = -1/2 + 5
Hope this helps!
How are the properties of exponents used when dividing a polynomial by a monomial?
Answers
Answer:
a couple different obes
Step-by-step explanation:
there are five
Plz help this is almost due
Answers
Answer:
possibly b,c,d
Step-by-step explanation: B, C, D because a doesn't have a -t, my teacher taught me to see which one is different.
On Monday Sophie ran 4 5/6 laps of a running track and on Tuesday she ran 5 3/4
of a running track. What was the total distance she ran over the two days?
Answers
Answer:
10 7/12
hope this is right
Step-by-step explanation:
4 5/6 = 29/6 as an improper fraction
5 3/4 = 23/4 as an improper fraction
you times the two denominators together = 24
you times 29 by 4 = 116
you times 23 by 6 = 138
you add 116 and 138 = 254
you put this over 24 = 254/24
simplify this = 127/12
you make this a mixed number = 10 7/12
the answer is 10 7/12
Mhanifa please help with this I find it super difficult! Thanks! I will mark brainliest! Random answers will be reported !
Answers
Answer:
a)
The point that is equidistant to all sides of a triangle is called the incenter.
The incenter is located at the intersection of bisectors of the interior angles of a triangle.
b)
The point that is equidistant to all vertices of a triangle is called the circumcenter.
The circumcenter is located at the intersection of perpendicular bisectors of the sides of a triangle.
c)
See the attachment
The blue lines and their intersection shows the incenter.
The red lines and their intersection shows the circumcenter.
As we see the red point- the circumcenter is closer to vertex B.
What is 15% of 200? *
30
50
15
20
Answers
Answer: 30
Step-by-step explanation:
julian rolled a normal 6-sided die 12 times. his rolls were as follows: 2, 4, 3, 3, 5, 1, 2, 6, 3, 1, 3, 5, 4. what is the probability that he will roll a 3 on the next roll?
Answers
The probability that Julian will roll a 3 on the next roll is approximately 16.67%. The probability of rolling a 3 on a normal 6-sided die is independent of the previous rolls. This means that regardless of the outcomes of Julian's previous rolls, the probability remains the same.
Explanation
On a 6-sided die, there is 1 favorable outcome for rolling a 3 (the number 3 itself) out of 6 possible outcomes (1, 2, 3, 4, 5, and 6).
To find the probability, you can use the formula:
Probability = (Number of favorable outcomes) / (Total number of outcomes)
In this case:
Probability of rolling a 3 = 1 (favorable outcome) / 6 (total outcomes)
Probability of rolling a 3 = 1/6 ≈ 0.1667 or 16.67%
So, the probability that Julian will roll a 3 on the next roll is approximately 16.67%.
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From a group of students, 28 students like rice, 23 students like dumplings, 16 students like both and 11 students do not like rice nor dumplings. How many students were interviewed?
Answers
78
Step-by-step explanation:
23+28+16+11=78
people who was interested in the restaurant
Can 30 60 and 90 be the angles of a triangle?
Answers
No, the sum of the angles of a triangle must add up to 180 degrees. 30 + 60 + 90 = 180, so these angles cannot form a triangle.
The sum of the angles of a triangle must always add up to 180 degrees. To determine if a set of angles can form a triangle, add the angles together. If the sum is 180, the angles can form a triangle. In this case, 30 + 60 + 90 = 180, which does not equal 180. Therefore, these angles cannot form a triangle.
No, the sum of the angles of a triangle must add up to 180 degrees. 30 + 60 + 90 = 180, so these angles cannot form a triangle.
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I need help.How do you do this?
Answers
Answer:
what did u learn today?
Determine the values of a and b given triangles ABC and DEF are
similar. The coordinates for ABC are A(-2,1), B(-2,3), and C(0,3). The
coordinates for DEF are D(a,b), E(4,-1), and F(0,-1) where a and b are
Answers
To determine the values of a and b, we need to establish the similarity between triangles ABC and DEF and find the corresponding coordinates.
Two triangles are similar if their corresponding angles are equal and their corresponding sides are proportional.
First, let's find the lengths of the sides of triangle ABC:
AB = √((-2 - (-2))^2 + (3 - 1)^2) = √0 + 4 = 2
BC = √((0 - (-2))^2 + (3 - 3)^2) = √4 + 0 = 2
AC = √((-2 - 0)^2 + (1 - 3)^2) = √4 + 4 = √8 = 2√2
Now, let's find the lengths of the sides of triangle DEF:
DE = √((a - 4)^2 + (b - (-1))^2)
EF = √((0 - 4)^2 + (-1 - (-1))^2) = 4
DF = √((a - 0)^2 + (b - (-1))^2)
Since the triangles are similar, the ratios of the corresponding side lengths must be equal:
AB/DE = BC/EF = AC/DF
2/(DE) = 2/4 = 2√2/(DF)
Simplifying, we get:
DE = 4
2/(4) = 2√2/(DF)
Solving the equation, we find:
1/2 = 2√2/(DF)
DF = 4√2
Therefore, the length of DF is 4√2. From the coordinates of F(0, -1), we can determine that the y-coordinate of point D must also be -1. Hence, b = -1. To find the x-coordinate of point D, we equate the lengths of AB and DE: 2 = √((a - 4)^2 + (1 - (-1))^2)
4 = (a - 4)^2 + 4
(a - 4)^2 = 0
a - 4 = 0
a = 4
Therefore, the values of a and b are a = 4 and b = -1, respectively.
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What is your estimated project completion time?
Please show work.
\begin{tabular}{|l|l|l|l|l|} \hline Activity & a & m & b & Immediate Predecessor \\ \hline A & 1 & 2 & 3 & \( \cdots \) \\ \hline B & 2 & 3 & 4 & \( \cdots \) \\ \hline C & 4 & 5 & 6 & A \\ \hline D &
Answers
To find the estimated project completion time for the given project activities, we need to first calculate the earliest start and earliest finish times and then the latest start and latest finish times.
Using the activity times given, we can calculate the earliest start and earliest finish times for each activity as follows: Activity A: Earliest start time = 0
Earliest finish time = 1
Activity B: Earliest start time = 2
Earliest finish time = 5
Activity C: Earliest start time = 5
Earliest finish time = 11
Activity D: Earliest start time = 11
Earliest finish time = 17
Activity E: Earliest start time = 5
Earliest finish time = 8 Activity F:
Earliest start time = 8
Earliest finish time = 17
Now we can calculate the latest start and latest finish times for each activity using the backward pass.
Latest finish time = 5
Latest start time = 2
Activity A: Latest finish time = 1
Latest start time = 0
Now we can calculate the slack time for each activity as follows:Activity A:
Slack time = 0
Activity B: Slack time = 0
Activity C: Slack time = 0
Activity D: Slack time = 0
Activity E: Slack time = 3
Activity F: Slack time = 0
The critical path for this project is A -> C -> D, since these activities have zero slack time. Therefore, the estimated project completion time is 17 units of time.
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Recall that the distance in a graph G between two nodes and y is defined to be the number of edges in the shortest path in G between x and y. Then, the distance between two different nodes of Km,n is (a) always 1, regardless of the nodes O (b) between 1 and 2, depending on the nodes O (c) between 1 and n-1, depending on the nodes O (d) between 1 and m-1, depending on the nodes O (e) between 1 and n+m-1, depending on the nodes
Answers
The distance between two different nodes of a complete bipartite graph Km,n is (e) between 1 and n+m-1, depending on the nodes.
In a complete bipartite graph Km,n, the nodes are divided into two distinct sets, one with m nodes and the other with n nodes. Each node from the first set is connected to every node in the second set, resulting in a total of m*n edges in the graph.
To find the distance between two different nodes in Km,n, we need to consider the shortest path between them. Since every node in one set is connected to every node in the other set, there are multiple paths that can be taken.
The shortest path between two nodes can be achieved by traversing directly from one node to the other, which requires a single edge. Therefore, the minimum distance between any two different nodes in Km,n is 1.
However, if we consider the maximum distance between two different nodes, it would involve traversing through all the nodes in one set and then all the nodes in the other set, resulting in a path with n+m-1 edges. Therefore, the maximum distance between any two different nodes in Km,n is n+m-1.
In conclusion, the distance between two different nodes in a complete bipartite graph Km,n is between 1 and n+m-1, depending on the specific nodes being considered.
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