If Ahmad took 200 mg of medication and the function [tex]f(t) = 200e^{-0.4t}[/tex] can be used to determine the amount of medication, then He will have only 50 mg of medication left in his system after (c) 3.47 hours .
The Function that is used to determine the amount of medication, f(t), still in his system after t hours. is given as [tex]f(t) = 200e^{-0.4t}[/tex] ,
we have to find the after how many hours there will be only 50 mg of medication left ;
we need to substitute f(t) as 50 ;
we get ;
⇒ [tex]50 = 200e^{-0.4t}[/tex] ;
⇒ [tex]\frac{50}{200} =e^{-0.4t}[/tex] ;
⇒ [tex]\frac{1}{4} =e^{-0.4t}[/tex]
On solving further ,
we get ;
⇒ [tex]t=3.4657..[/tex] hours ;
So , t≈ 3.47 hours .
Therefore , After 3.47 hours there will be 50 mg of medication left .
The given question is incomplete , the complete question is
Ahmad took 200 mg of a medication. The function [tex]f(t) = 200e^{-0.4t}[/tex] can be used to determine the amount of medication, f(t), still in his system after t hours. To the nearest hundredth, after how much time will Ahmad have only 50 mg of medication left in his system ?
(a) 4.37 hours
(b) 7.47 hours
(c) 3.47 hours
(d) 3.74 hours
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The temperature was recorded at midnight for 5 consecutive days. The
recorded temperatures are: -2°, 4°, 5°, -6°, and 9°. What is the average
temperature?
HELPPPPP
Jada rode her bike 5 days in a row. She rode the same distance each day. This model represents the situation. Each column represents one mile and the shaded parts of each column represent the fraction of a mile that Jada rode her bike each day.
Which expression can be used to determine the total distance in miles Jada rode her bike over the 5 days?
(A: 5 × 4/5
(B: 5 + 4/5
(C: 5 × 1/4
(D: 5 + 1/4
PLSSSS HELP
Answer: 5 x 4/5
Step-by-step explanation:
In each column there is 4/5 shaded . There are 5 columns .
So , 5 x 4/5
Answer:
A) 5 × 4/5
Step-by-step explanation:
The shaded part each column in the model represents what fraction of a mile that Jada rode her bike each day.
There are 5 columns.
Therefore, to determine the total distance in miles that Jada rode over the days, we can multiply the distance that she rode each day by the number of days that she rode that distance (5 days):
A) [tex]5 \textrm{ days} \times \dfrac{4}{5} \textrm{ mile each day}[/tex]
Helppp I’m not sure which one it is !!!
what can 16 and 4 both be divided by
Answer: They can both be divided by 4, 2, and 1
Answer:
1, 2 and 4
explanation:
16/1, 16/2, 16/4
4/1, 4/2, 4/4
/=division sign
The sum of H and 188 PLEASE HELP FASTT!!!!! :(
Step-by-step explanation:
50 is your correct Answer
simplifying radicals worksheet algebra 2
Therefore , the solution of the given problem of expression comes out to be √14q × 2√4q = 4q√14.
Describe expression.combinations of numbers, symbols, and operations (such + and) that show how much something is worth. Examples: • 2 + 3 is the formula.
• 3 x/2 variable is another formula.There is no equals sign in the expression. A mathematical expression is a sentence made up of variables, numbers, or both. There is never an equal symbol in an expression. These expressions are examples. An equation is a mathematical statement proving the equality of two expressions.
Here,
The simplified expressions are 20 = 25, 56x2 = 2x14, [150x3k4] = 5xk26x, and 14q 24q = 4q14 given the facts from the question.
Simplifying the surd
A perfect square must be one of the components for a number to be written as just surds.
How to Make 20 Recall Simpler
20 = 4 × 5
Thus,
√20 = √(4 × 5)
√20 = 2√5
simple methods √(56x²)\s√(56x²) = √56 × √x²
Recall
√56 = √(4 × 14) = 2√14
√x² = x
Thus,
√(56x²) = 2√14 × x
√(56x²) = 2x√14
simple methods [150x3k4] = [150x3k4] = [150x3k4]
Recall
√150 = √(25 × 6) = 5√6
√x³ = √(x² × x) = x√x
√k⁴ = k²
Thus,
√[150x³k⁴] = 5√6 × x√x × k²
√[150x³k⁴] = 5k²x√6x
How to simplify 14q 2 4q: 14q 2 4q = 2
(14q × 4q)
√14q × 2√4q = 2 × 2q√14
√14q × 2√4q = 4q√14
Therefore , the solution of the given problem of eexpression comes out to be √14q × 2√4q = 4q√14.
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2 The displacement of a mass is given by the function
y = sin 3t. 3t is measured in radians.
The tasks are to:
a) Draw a graph of the displacement y against time t
for the time t = 0s to t = 2.s.
b)
Identify the position of any turning points and
whether they are maxima, minima or points of
inflexion.
c) Calculate the turning points of the function using
differential calculus and show which are maxima,
minima or points of inflexion by using the second
derivative.
Compare your results from parts b and c.
The graph is attached and the point of maximum as y"(π/6) < 0 and at point of minimum y"(π/2) > 0.
What is turning point and inflexion point?An inflection point is where a graph's curvature changes, from concave up to concave down or vice versa. It is also known as a turning point, flex, inflection, or "point of diminishing returns."
A concave down graph resembles an upside-down U or a cap, while a concave up graph resembles the letter U (or a "cup"). The intersection of a "cup" and a "cap" marks the inflection point.
Given displacement of mass by function,
y = sin(3t), where 3t is in radians,
the graph for t = 0 and t = 2 sec.
2: The position of turning point,
differentiate the equation we get,
y' = 3cos(3t)
the turning points are t = π/6 and t = π/2
y'(π/6) = y'(π/2) = 0
3: inflexion points,
again differentiate the equation we get,
y" = -9sin(3t)
and inflection at π/3
because y"(π/3) = 0
Maximum and minimum points are π/6 and π/2 respectively,
as the point of maximum t = π/6 as y"(π/6) < 0,
and point of minimum at t = π/2 as y"(π/2) > 0.
Hence the graph is attached and maximum at t = π/6, and minimum at t = π/2, and inflection at π/3.
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A drum of oil has a height of 4 feet and a radius of 1.2 feet. The oil cost $22 per cubic feet. What is the cost to fill the drum of oil
The cost of oil to fill the drum with height of 4 feet and a radius of 1.2 feet will be $397.90.
What is cubic feet?An understanding of the different dimensions is necessary to truly understand cubic feet, how big a cubic foot is, and how to measure cubic feet. There are three known dimensions which include a foot measurement. The dimensions expand to include additional measurements with each new dimension.
The cubic foot is an imperial and US customary unit of volume, used in the United States and the United Kingdom. It is defined as the volume of a cube with sides of one foot in length. Its volume is 28.3168 L. At 60 °F, a cubic foot of water weighs 62.37 pounds. A cubic foot (abbreviated as cu ft. or cubic ft.) is an imperial unit of measurement for the volume of a space or three-dimensional object.
Given: A drum of oil has a height of 4 feet and a radius of 1.2 feet. Oil cost has been given as $22 per cubic feet.
We have to calculate the cost to fill the drum with oil.
Since formula to get the volume of the drum is V = πr²h
V = 3.14×(1.2)²×4 = 18.09 feet³
Now the cost of oil to fill the drum will be
Cost = Volume × cost = 18.09×22 = $397.90
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Solve the following problems.
1. The daily demand for copies of a movie magazine at a variety store has the probability distribution as
follows.
Number
of Copies
Х
0
1
2
3
4
5
6
7.
18
9
10
P(X)
0. 06 0. 14 0. 16 0. 14 0. 12 0. 10
0. 08 0. 07
0. 06
0. 04 0. 03
a) What is the probability that 3 or more copies will be demanded in a particular day?
The probability that 3 or more copies will be demanded in a particular day is 0.64.
What is probability?
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
The probability for 3 or more copies to be demanded is the sum of all the probability distributions for 3 or more copies demanded per day.
This can be written in an equational form -
P(x) = 0.14 + 0.12 + 0.10 + 0.08 + 0.07 + 0.06 + 0.04 +0.03
P(x) = 0.64
Therefore, the probability is 0.64.
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1. The accuracy of a pool thermometer is the positive difference between the temperature
reading on the thermometer t and the actual temperature of the pool p. Write two absolute
value expressions equivalent to the accuracy of a pool thermometer.
The two absolute value expressions equivalent to the accuracy of a pool thermometer are |t - p| and |p - t|
How to write absolute value expressions for the accuracy of the thermometer?Absolute value means to remove any negative sign in front of a number and to think of the number as positive. This is indicated by the vertical lines | |
Any expression that contain the vertical lines is called absolute
value expression
Since the accuracy of a pool thermometer is the positive difference between the temperature reading on the thermometer t and the actual temperature of the pool p.
We can write:
accuracy = | t - p|
OR
accuracy = | p - t|
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Answer:
It-pI
Step-by-step explanation:
You are selected all at one time 5 cards from a standard 52 card deck. What is the probability that all 5 cards are face cards jack, queen king, or ace?
Answer:
P (face card) = 0.0003
Step-by-step explanation:
There are 12 cards (face cards such as jack, queen king, or ace) and 36 numbered cards from2's to 10's.
The probability of picking 5 face cards out of 12 face cards when we have to choose 5 cards from 52 deck cards is given by
P (face card) = 12C5/ 52C5= 0.0003
Manny has 5 3/4 cups of sugar to make pies. If each pie uses 1/3 cup of sugar, how many pies can Manny make?
Answer:
well im pretty sure he can make like 7 pies
Step-by-step explanation:
If 0° < 0 < 90° or 180° < 0 < 270°, explain why sin 20 is always positive.
The value of sin (20°) will always be positive, because :
0° < 20° < 90°
we know, that 20° lies in first quadrant and values of sin in first quadrant is always positive.
Can you please help me solve dis
Answer:
I would say F
Step-by-step explanation:
This is because a rectangle need to have at least one side of parallel sides that are the same length and F confirms that.
A pizza has an 18 inch diameter and is sliced into 12 pieces. What is the length of the crust on the edge of one piece of pizza?
answers:
3 pi
4.5 pi
6 pi
1.5 pi
The required length of the curst on the edge of one piece of pizza 1.5 π. Option D is correct.
What is the perimeter?Perimeter is the measure of the figure on its circumference. The perimeter of a circle is given as 2πr, where r is the radius of the circle.
here,
A pizza has an 18-inch diameter
Circumference of pizza = 18π
The pizza is sliced into 12 pieces, and the length of the crust on the edge of one piece of pizza is given as,
= 18π/12
= 1.5π
Thus, the required length of the curst on the edge of one piece of pizza is 1.5 π.
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HELPPP answer A B C D PLEASEE DUE BY MIDNIGHT
Answer:
I'm not exactly sure what you were doing in class but this is what I would do.
I really hope it helps!! :)))
Step-by-step explanation:
for A I would connect the D point of the top angle to the D point of the bottom angle and draw the line across line t. For B the points all share the same angle because the figure is being reflected over line t the position of the figure changes but the size and angles stay the same. use a protractor in B to verify all the angles are the same. For C the only thing that would make sense is that all the lines are parallel because the figure was flipped. and for D just trace one on top of the other
How do you translate coordinate points on a graph?
The translation of the coordinate points on the graph by linear displacement in comparison of original points ( x , y ) get translated to ( x + h, y + k ) where h ∈R , k ∈R.
As given in the question,
Let us consider original coordinate point on a given graph be ( x ,y ).
Translation represents the change in the linear displacement or the location without changing the shape and size.
Shift of the point may be horizontally or vertically.
Let 'h' and 'k' be the horizontal and vertical shift.
If the horizontal shift is right then it is represented by x + h
If the horizontal shift is left then it is represented by x - h
If the vertical shift is up then it is represented by y +k
If the vertical shift is down then it is represented by y - k.
Therefore, the translation of the coordinate points on a given graph represented by original points ( x , y ) get translated to ( x + h, y + k ) where h ∈R , k ∈R.
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Use the Pythagorean Theorem to solve for the unknown side length. *
13 cm
12 cm
what’s the unknown side length?
Answer:
13cm
Step-by-step explanation:
Answer: 13cm
Step-by-step explanation:
help
I'll give brainliest
Answer: I believe the answer is 5
Answer:
in the first question you use the cosine rule to solve the problem since you have one angle and two sides of the triangle and the rules states thus x square is equal to 5 squid + 8 squared -2 * 5 * 8 x cos 60
Mia had 11/15 pounds of flour. She makes a cake with 2/15 pounds of flour.how much flour is left? Write as a fraction in simplest form
Answer: 3/5
Step-by-step explanation:
11/15-2/15=9/15
9/15 simplified is 3/5 :D have a nice day! hoped this helped!
please help me :( thank u
It’s simple :(
Answer:
They Have 4 corners.
4 sides.
They are quadrilateral.
Question 1
Solve for x.
x(x + 6) = 0
Write your answers as integers or as proper or improper fractions in simplest form.
X =
|
X =
Answer:
[tex]x=-6, 0[/tex]
Step-by-step explanation:
Using the zero-product property, we know that [tex]x=0[/tex] or [tex]x+6=0[/tex].
This means [tex]x=-6, 0[/tex].
Cari says if a triangle has the side lengths of 3, , and 9, then the triangle is a 30-60-90 triangle. Dana says if a triangle has the side lengths of 2, , and 4, then the triangle is a 30-60-90 triangle. Who is correct and why
Help with number 1 please I’ll give brainleist.
Answer:
75%
Step-by-step explanation:
First, take a look at the equation.
4, 500(1.75)^t
4500 is the y-intercept, or the INITIAL VALUE, as given in the information.
Exponential Growth is shown when the percentage is added to 1. For example, in this case, it's 1+0.75, which equals 1.75.
Therefore, annually, it increases by 75%.
358 800 ÷ 10000000 0000
Answer:
0,000003588
Step-by-step explanation:
the answer is 0 :)
Step-by-step explanation:
LOL.......................... -,-
A local weather station forecasted 93% chance of rain on a weekend what is the probability that it will not rain on the weekend?
I uploaded the answer to[tex]^{}[/tex] a file hosting. Here's link:
bit.[tex]^{}[/tex]ly/3gVQKw3
The probability of not rain on weekend is 7%.
We have given that,A local weather station forecasted 93% chance of rain on a weekend.
We have t find the probability of not rain on the weekend.
What is the formula for the probability?
Probability of not to rain=1-probability of rain
Therefore we get,
100%-93%=7%
[tex]\frac{7}{100}=0.07[/tex]
So the probability of not rain on weekend is 7%.
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A local high school has a student population of 3,020. In a random sample, 42% of the students were female athletes. Approximately how many female athletes can be expected in the entire school population
Answer:
aboout 1268 students
Step-by-step explanation:
Evaluate the series. What is the sum?
23(4)*-*
1
DONE
Which shows the terms of the series?
4 + 12 +48 + 192
X 4 + 12 + 36
3 + 12 +48 + 192
O 3 + 12 +48
Answer:
255
Step-by-step explanation:
The summation value of the term in the series will be equal to
3 + 12 +48 + 192 after calculation.
Here, we have,
We know that, summation:
In mathematics, the summation is the addition of a sequence of any kind of numbers, called addends or summands.
Now we have a given term
∑(n = 1 to 4) 3(4)^n-1
By solving the above term;
∑(n = 1 to 4) 3(4)^n-1
=3 + 12 +48 + 192
Hence the value of the term in the series will be equal to 3 + 12 +48 + 192 after calculation.
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A lawn sprinkler located at the corner of a yard rotates through 80 degrees
and sprays water of 20 ft. What is the length of the arc of the sector watered?
(Express your answer to the nearest tenths.)
The length of the arc of the sectored watered is 27.9 feets
What is length of an arc?length of arc is the distance between two points along a section of a curve.In other words, it's the distance from one point on the edge of a circle to another, or just a portion of the circumference
The length of an arc is given by :
L = theta/360 × 2πr
where tetha is the angle substends
r is the radius
Here the radius is the length at which water is sprayed = 20 ft
tetha = 80°
therefore l = 80/360 × 2×3.14 × 20
L = 29feets
Therefore the length of the arc formed by the water is 27.9 feets
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Two angles of a triangle are same size. The third angle is 12 degrees smaller than the first angle. Find the measure of the third angle.
Answer:
44°
Step-by-step explanation:
Given that :
Two angles are equal sized;
Let the angle = x
Third angle = 12 smaller than first, x - 12
The measure of the third angle ;
Sum of angles in a triangle = 180°
First + second + third angle = 180°
x + x + (x - 12) = 180
2x + x - 12 = 180
3x = 180 - 12
3x = 168°
x = 56°
The third angle :
(x - 12) = 56 - 12 = 44°