the concentration of a drug in a patient's bloodstream t hours after the drug was administrated presented by the equation c(t) = 5t-t²+1 (in mg/mL). construct a table of values for c(t) for t=1,2,5,10. Round off answer to tree decimal places. use use the table to sketch a graph and interpret the result by giving the (a) domain, (b) range, (c) vertical asymptote, and (d) horizontal asymptote.
Answers
The graph of the function has no asymptotes.
The table of values of c(t)The function is given as:
c(t) = 5t - t² + 1
When t = 1, 2, 5, 10;
We have:
c(1) = 5(1) - 1² + 1 = 5
c(2) = 5(2) - 2² + 1 = 7
c(5) = 5(5) - 5² + 1 = 1
c(10) = 5(10) - 10² + 1 = -49
So, the table of values is
t c(t)
1 5
2 7
5 1
10 -49
See attachment for the graph of the function
The domain
From the question, we understand that t represents time.
Time cannot be negative i.e. t ≥ 0 The time does not exceed 5.2 i.e. t ≤ 5.2So, the domain is 0 ≤ t ≤ 5.2
The range
From the graph, the maximum of the graph is 7.25
So, the range is 0 ≤ f(t) ≤ 7.25
Asymptotes
From the graph, we can see that the graph has no asymptotes.
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Related Questions
Complete the steps in order to write the inverse of f(x)=x+5
=x45
1.
Writing the Inverse of a Function
2.
3,
1-x-5
Answers
The equation of the inverse function of the function f(x) = x + 5 is f'1(x) = x - 5
What are inverse functions?Inverse functions are the opposite of an original equation. This means that for a function f(x), the inverse of the function f(x) is f-(x); it also represents the opposite function
How to determine the inverse functions?The function f(x) is given as
f(x) = x + 5
As a general rule, we start by writing f(x) as a variable (say f(x) = y).
So, the equation of the function becomes
y = x + 5
The next step is to switch/swap the positions of x and y in the above equation y = x + 5
The equation becomes
x = y + 5
The next step is to make y the subject of the formula in the above equation x = y + 5
The equation becomes
y = x - 5
This is done by subtracting 5 from both sides of the equation.
So, we have:
y = x - 5
Express as an inverse function
f'1(x) = x - 5
Hence, the inverse function of the function f(x) = x + 5 is f'1(x) = x - 5
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A company estimates that its cost and revenue can be modeled by the functions C)-0.75x+20,000
and R(x)-1.50x where x is the number of units produced. The company's profit, P, is modeled by
P(z) R(x)-C(z). Find the profit function P(x).
Answers
Let C(x) = -0.75x + 20,000 and R(x)= -1.50x then the profit function exists noted as P(x) = R(x) - C(x)
P(x) = -1.50x - (-0.75)x + 20,000
P(x) = -0.75x + 20000
Therefore, the profit function exists -0.75x + 20000.
How to find profit function?
The profit function can be estimated by subtracting the cost function from the revenue function. Let profit be expressed as P(x), the revenue as R(x), the cost as C(x), and x as the number of items traded. Then the profit function exists noted as P(x) = R(x) - C(x).
Given:
C(x) = -0.75x+20,000 and R(x)= -1.50x
P(x) = R(x) - C(x)
= -1.50x - (-0.75)x + 20,000
= -1.50x + 0.75x + 20,000
Apply rule -(-a) = a
= -1.5x + 0.75x + 20000
Add similar elements:
-1.5 x + 0.75x = -0.75x
P(x) = -0.75x + 20000
Therefore, the profit function exists -0.75x + 20000.
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1. Convert the numeral to a numeral in base ten.
3205 six
43
125
4325
725
Answers
Expanding the digits, we have
[tex]3205_6 \equiv 3\cdot6^3 + 2\cdot6^2 + 0\cdot6^1 + 5\cdot6^0 = \boxed{725}[/tex]
can you please help me with the question the link is down below
Answers
Answer:
output = 9
Step-by-step explanation:
add 5 to the input to obtain output
output = 4 + 5 = 9
Find the value of x
(4x+10)
108° 67° 3x
Answers
Angles in quadrilateral add to 360
108 +67 +10 =185
4x + 3x = 7x
185 + 7x = 360
- 185
7x. = 175
÷ 7
x = 25
Check:
4x25 = 100
100 + 67 + 108 = 275
275 + (3x25) = 350 + extra 10 is 360
Hope this helps!
Which number best represents the slope of the graphed line?
A graph is a line that extends from second quadrant to fourth quadrant through left parenthesis 0, 2 right parenthesis, and left parenthesis 0.5, 0 right parenthesis.
Answers
The number that best represents the slope of the graphed line that is given is: -4.
What is the Slope of a Line?The slope of a line is the ratio of the vertical distance to the horizontal distance across the line. It is calculated using the formula:
Slope (m) = rise/run = change in y / change in x = (y2 - y1)/(x2 - x1)
Given the two points on a coordinate plane as shown in the mage below, let:
(x1, y1) represent (0, 2)
(x2, y2) represent (0.5, 0)
Plug in the values
Slope (m) = change in y / change in x = (0 - 2) / (0.5 - 0)
Slope (m) = -2/0.5
Slope (m) = -4
Therefore, we can state that, the number that best represents the slope of the graphed line that is given is: -4.
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The actual answer is C.1/2
chust mee am a doktor
Csn u please help me o have no idea
Answers
Answer:
D.= √29
Step-by-step explanation:
Greetings!The distance between the two complex numbers,
Z₁=a+bi and Z₂=c+di in the complex plane is
[tex]d = \sqrt{(c - a) {}^{2} + (d - b) {}^{2} } [/tex]
In the Cartesian plane, the distance between, one point and other is (x₁,y₁) and (x₂,y₂) is the distance formula is
[tex]d = \sqrt{(X₂-X₁)² + (Y₂-Y₁)²} [/tex]
To find the distance between the two complex numbers using the formula
[tex]d = \sqrt{(c - a) {}^{2} + (d - b) {}^{2} } [/tex]
where,
a=4b=3c=6d=-2[tex]d = \sqrt{(a - b) {}^{2} + (d - b) {}^{2} } \\ d = \sqrt{(6 - 4) {}^{2} + ( - 2 - 3) {}^{2} } \\ d = \sqrt{(2) {}^{2} + ( - 5) {}^{2} } \\ d = \sqrt{4 + 25} = \sqrt{29 \\ } [/tex]
Some randomly selected high school students were asked to name their favorite sport to watch. The table displays the distribution of results. A 2-column table with 5 rows. Column 1 is labeled sport with entries football, basketball, baseball, soccer, none. Column 2 is labeled probability with entries 0.23, 0.18, 0.26, 0.17, 0.16. What is the probability that a student chose football given that they like watching sports? 0.16 0.23 0.27 0.77
Answers
The probability that a student chose football given that they like watching sports is: c. 0.27.
Conditional ProbabilityUsing this formula
P[Like (Football)/Like (Sport)]
Where:
P=Probability
Like (Football)=0.23
Like (Sport)=0.23+0.18+0.26+0.17=0.84
Let plug in the formula
P[Like (Football)/Like (Sport)]=0.23/0.84
P[Like (Football)/Like (Sport)]=0.27
Therefore the probability that a student chose football given that they like watching sports is: c. 0.27.
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Answer:
C.
Step-by-step explanation:
Which of the following is a function?
A. {(2,9), (2,8), (-3,7), (-3,6))
B. ((-4,3), (1,0), (1,2), (2,3)}
C. {(2,1), (4,2), (6,3), (8,4))
D. {(1,2), (-2,3), (1,3), (-2,2))
Answers
Answer: C
Step-by-step explanation:
A function only exists if each x-value has only one possible y-value.
C is the only function because each x-value has only one y-value.
The other answer choices have x-values that have multiple y-values. In answer choice A, it has (2,9) and (2,8). In answer choice B, the set has (1, 0) and (1,2). And in answer D, it has (1,3) and (1,2)
Answer + Step-by-step explanation:
let f be the relation that we are studying.
f is a function if it associates a unique output (number) to each input (number) .
A. {(2,9), (2,8), (-3,7), (-3,6))
Since f(-3) = 7 and f(-3) = 6
Then
f associates -3 to two different outputs 7 and 6.
Then
f cannot be a function.
B. ((-4,3), (1,0), (1,2), (2,3)}
Since f(1) = 0 and f(1) = 2
Then
f cannot be a function.
C. {(2,1), (4,2), (6,3), (8,4))
f is a function.
D. {(1,2), (-2,3), (1,3), (-2,2)
Since f(-2) = 3 and f(-2) = 2
Then
f cannot be a function.
Suppose your parents decide to give you $10,000 to be put in a college trust fund that will be paid in equally quarterly installments over a 5 year period. If you deposit the money into an account paying 1.5% per quarter, how much are the quarterly payments (Assume the account will have a zero balance at the end of period.)
Answers
The quarterly annuity payment is $582.46.
What is an ordinary annuity?
An ordinary annuity in case of investment is the one that pays its end-of-the period cash flows rather than at the beginning as it is case of annuity due.
The applicable formula in this case is the present value formula of an ordinary annuity as shown below:
PV=quarterly payment*(1-(1+r)^-N/r
PV=initial investment=$10,000
quarterly payment=unknown(assume it is X)
r=quarterly interest rate=1.5%
N=number of quarterly payments in 5 years=5*4=20(there are 4 quarterly payments in a year)
$10,000=X*(1-(1+1.5%)^-20/1.5%
$10,000=X*(1-(1.015)^-20/0.015
$10,000=X*(1-0.742470418223773)/0.015
$10,000=X*0.257529581776227/0.015
X=$10,000/(0.257529581776227/0.015)
X=quarterly payment=$582.46
Note that the unknown in this case is the annuity payment, the present value can also be the unknown as well.
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25) Every month the cafeteria orders 120 gallons of milk and 220 gallons of chocolate milk. What is the ratio of milk to chocolate milk as a fraction in simplest form?
Answers
Answer:
Step-by-step explanation:
120:220
2 will go into 120 60 times and go into 220 110 times. So your answer comes down to;
60:110
10 will go into 60 6 times and go into 110 11 times So your answer comes down to;
6:11
That is your final answer 6:11
Assume that adults have iq scores that are normally distributed with a mean of μ=100 and a standard deviation σ=15. find the probability that a randomly selected adult has an iq less than 130
Answers
The probability that a randomly selected adult has an IQ less than 130 is 0.9332
For given question,
We have been given adults IQ scores that are normally distributed with a mean of μ = 100 and a standard deviation σ = 15.
We need to find the probability that a randomly selected adult has an IQ less than 130
Sketch the curve.
The probability that X < 130 is equal to the area under the curve which is less than X = 130
Since μ = 100 and σ = 15 we have:
⇒ P ( X < 130 ) = P ( X- μ < 130 - 100 )
⇒ P ( X < 130 ) = P((X− μ)/ σ < 130 - 100/20 )
Since (X-μ)/σ = Z and (130 - 100)/20 = 1.5 we have:
P (X < 130) = P (Z < 1.5)
Now, we use the standard normal table to conclude that:
P (Z < 1.5) = 0.9332
Therefore, the probability that a randomly selected adult has an IQ less than 130 is 0.9332
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If the first two angles of a triangle measure 37° and 104°, what is the measurement of the third?
Answers
Answer:
67
Step-by-step explanation:
All triangles have three angles. The sum of the three angles should equal up to 180 degrees.
108-104-37= 67
Eduro solved -4x > 120 by adding 4 to each side lf the inequality what mistake did he make?
Answers
Eduro's mistake of solving the inequality -4x > 120 is adding 4 to both sides instead of dividing both sides by -4
Inequalityminus four x greater than 120
-4x > 120
divide both sides by -4x < 120/-4
There is a change in the inequality sign from greater than to less than because the inequality is been divided by -4
x < -30
Check:
-4x > 120
-4(-30) > 120
120 > 120
Therefore, Eduro's mistake of solving the inequality -4x > 120 is adding 4 to both sides instead of dividing both sides by -4
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use substitution to solve the system 3x+8y = -56 2x-y = 7
Answers
Answer: x = 0 ; y = -7
Step-by-step explanation:
Given equation:
1) 3x + 8y = -56
2) 2x - y = 7
Subtract 2x on both sides of 2) equation to isolate y-value
2x - y - 2x = 7 -2x
-y = 7 - 2x
Divide -1 on both sides of 2) equation
-y / -1 = (7 - 2x) / -1
y = 2x - 7
Current system
1) 3x + 8y = -56
2) y = 2x - 7
Substitute 2) equation into the y-value of 1) equation
3x + 8 (2x - 7) = -56
Simplify by distributive property
3x + 8 × 2x - 8 × 7 = -56
3x + 16x - 56 = -56
Combine like terms
19x - 56 = -56
Add 56 on both sides
19x - 56 + 56 = -56 + 56
19x = 0
Divide 19 on both sides
19x / 19 = 0 / 19
[tex]\Large\boxed{x=0}[/tex]
Substitute the x-value into one of the equations to find the y-value
2x - y = 7
2 (0) - y = 7
0 - y = 7
-y = 7
[tex]\Large\boxed{y=-7}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
jean loads a ream of paper 500 sheets into the tray of her photocopier she has 23 sheets and need 20 copies each sheet how many sheets of paper remain unused
Answers
The answer is 40
you just times 23 by the number of photocopies you need with is 20
so 23x20 which is 460
500-460 is 40
The number of sheets of papers remain unused are 40.
Given that, Jean loads a ream of paper 500 sheets into the tray of her photocopier she has 23 sheets and need 20 copies each sheet.
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Number of sheets used = 23×20
= 460
Remaining sheets = 500-460
= 40
Therefore, the number of sheets of papers remain unused are 40.
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What is the following simplified product? Assume x 20.
(√6x² +4√8x³)(√9x-x√5x^5)
O 3x√√6x+x²√30x+24x²2x+8x³10x
O 3x√6x+x√30x+24x²√2+8x5/10
O 3x√√6x-x+√30x+24x² √2-8x² 10
O3x6x-x30x+24x²2x-8x510x
Answers
The simplified product of (√6x² +4√8x³)(√9x-x√5x^5) is 3x√6x + 24x^2√2 - x^4√30x - 8x^5√10
How to determine the simplified product?The product expression is given as:
(√6x² +4√8x³)(√9x-x√5x^5)
Evaluate the exponents
(√6x² +4√8x³)(√9x-x√5x^5) = (x√6 +8x√2x)(3√x - x^3√5x)
Expand the brackets
(√6x² +4√8x³)(√9x-x√5x^5) = x√6 * 3√x + 8x√2x * 3√x - x√6 * x^3√5x - 8x√2x * x^3√5x
This gives
(√6x² +4√8x³)(√9x-x√5x^5) = 3x√6x + 24x^2√2 - x^4√30x - 8x^5√10
Hence, the simplified product of (√6x² +4√8x³)(√9x-x√5x^5) is 3x√6x + 24x^2√2 - x^4√30x - 8x^5√10
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Circle T is shown. Line segment Q S is a diameters. Point R is opposite of point T. Lines are drawn from points Q and S to point R to form a right triangle. Angle Q R S is a right angle.
The measure of arc QS is (4x – 18)°.
What is the value of x?
40.5
49.5
94.5
180
Answers
The value of angle x of the given cyclic segment is; 49.5°
How to find the angle of an arc?We are given the measure of the angle of arc QS as (4x – 18)°
Now, to find the measure of arc QS, this angle is to be equal to 180° and as such;
Thus;
(4x – 18)° = 180°
4x - 18 = 180
4x = 180 + 18
4x = 198
x = 198/4
x = 49.5°
The angle subtended by the arc at the center of a circle with center C is the angle of the arc. It is denoted by. m AB, where A and B are the endpoints of the arc. With the help of the arc length formula, we can find the measure of arc angle.
The formula to measure the length of the arc is;
Arc Length Formula (if angle θ is in degrees); s = 2πr (θ/360°)
Arc Length Formula (if θ is in radians) s = ϴ × r.
Thus, the value of x of the given cyclic segment is; 49.5°
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I need help here’s a picture can somone explain what I need to do??
Answers
Answer:
176 square feet
Step-by-step explanation:
add the areas of the rectangle and triangle
rectangle area is
16 times 8 which is
128
rectangle area is
1/2 times 12 times 8 which is
48
then add them
128 plus 48 is
176 square feet
Given the function h(x) = x² − 10x + 21, determine the average rate of change of the function over the interval -1 ≤ x ≤ 10.
Answers
Answer: the average rate of change of the function is 23.
Step-by-step explanation:
[tex]h(x)=x^2-10x+21\ \ \ \ \ -1\leq x\leq 10 \ \ \ \ A(x)=?\\\displaystyle\\A(x)=\frac{\Delta y}{\Delta x}=\frac{h(x-g)-h(x)}{g} \\g=x_{max}-x_{min}\\g=10-(-1)\\g=10+1\\g=11.\ \ \ \ \ \Rightarrow\\A(x)=\frac{(x-11)^2-10*(x-11)+21-(x^2-10x+21)}{11} \\A(x)=\frac{x^2-22x+121-10x+110+21-x^2+10x-21}{11} \\A(x)=\frac{231-22x}{11}\\ A(x)=\frac{11*(21-2x)}{11}\\ A(x)=21-2x.\\x=x_{min}\ \ \ \ \ \Rightarrow\\A(x)=21-2*(-1)\\A(x)=21+2\\A(x)=23.[/tex]
Jessica is a Custodian at an oracle Arena. She waxes 20m^2 of the floor in 3/5 of an hour. Jessica waxes the floor at a constant rate. How many square metres can she wax per hour?
Answers
Answer:
Step-by-step explanation:
Just multiply how much she waxes in 3/5 hour by 5/3. Answer is 100/3 or 33.33 sq. meters per hour
A private grassland has an area of 2/5km squared. The owner of the garden buys an extra of 1/3km squared of land from the neighbour to make his grassland bigger. What is the new size of the grassland?
Answers
Answer:
11/15 km
Step-by-step explanation:
Simply sum the areas:
2/5 + 1/3 = (6 + 5)/15 = 11/15
a basketball player signs a cantract that pays him $16 million over 4 year. What is his average pay per year?
Answers
the average pay per year is $4 million
Answer:
The average is 4millon
Step-by-step explanation:
because 16 millon divide by 4 =4
ez
Someone please help me with Graph!!
(My answers keep coming wrong)
Topic= Solving systems of equations by Graphing
Answers
See below for the solution to the systems of equations
How to solve the systems of equations?System of equations 1
Here, we have
y = -5x/3 + 3
y = x/3 -3
We start by plotting the graph of both equations
Next, we write out the point of intersection of the equations
See attachment for the equation of the system
From the attached graph, the point of intersection of the equations is (3, -2)
Hence, the solution to the system is (3, -2)
System of equations 2
Here, we have
y = 4x + 3
y = -x -2
We start by plotting the graph of both equations
Next, we write out the point of intersection of the equations
See attachment for the equation of the system
From the attached graph, the point of intersection of the equations is (-1, -1)
Hence, the solution to the system is (-1, -1)
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Given the following information, calculate the perimeter of triangle RST. Assume triangle RZX is similar to triangle RST.
RZ = 21, RY = 24, RX = 42, ZY = 9, and SW = 15.
Answers
Check the picture below.
From the top of a 6m house, the angle of elvation to the top of a flappole is across the street is 9 degrees. the angle of depression is 22 degrees to the base of the flapole. Redraw the diagram below and label all the angles. How tall is the flagpole? Round naswer to one decimal place.
Answers
The height of the flag pole which is described as in the task content is; 8.2m.
What is the height of the flagpole as described from the top of the 6m house?The horizontal distance between the 6m house and the flagpole in discuss can be evaluated by means of the angle of depression and trigonometric identity, tan as follows;
tan 22° = 6/x
x = 6/tan 22 = 14.9m.
Consequently, the horizontal distance from the top of the house to the top of the flagpole is therefore;
tan 9° = y/14.9
y = 14.9 tan 9° = 2.2m
Ultimately, the height of the flagpole is; 6+2.2 = 8.2m.
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if b=7, what is the value of the expression2(10-b)?
Answers
Answer: 6
Step-by-step explanation: Since we substitute the b with 7, 10-7= 3. Since the 2 is next to the parentheses, we multiply 3 by 2, getting 6.
Hey there!
2(10 - b)
= 2(10 - 7)
= 2(10) + 2(-7)
= 20 - 14
= 6
OR
2(10 - b)
= 2(10 - 7)
= 2(3)
= 6
Therefore, your answer should be: 6
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
If f (x) = startroot 4 x 9 endroot 2, which inequality can be used to find the domain of f(x)? startroot 4 x endroot greater-than-or-equal-to 0 4 x 9 greater-than-or-equal-to 0 4 x greater-than-or-equal-to 0 startroot 4 x 9 endroot 2 greater-than-or-equal-to 0
Answers
Inequality can be used to find the domain of f(x) is (B) 4x+9 greater-than-or-equal-to 0.
What is inequality?The term inequality refers to a mathematical expression in which the sides are not equal. An inequality compares any two values and reveals that one is smaller, greater, or equal to the value on the opposite side of the equation.To find the domain:
“f(x) = StartRoot 4 x + 9 EndRoot + 2” should be written as, note that√(4x + 9) is a variation of the basic function y = √x, whose domain is [0, ∞ ). The domain of f(x) = √(4x + 9) + 2 is found by taking the “argument” 4x + 9 of √(4x + 9) and setting it equal to zero: 4x + 9 ≥ 0, or 4x ≥ -9, or x ≥ -9/4 This is the domain of the given function f(x) = √(4x + 9) + 2. So long as x is ≥ -9/4, the function f(x) will be defined.Therefore, inequality can be used to find the domain of f(x) is (B) 4x+9 greater-than-or-equal-to 0.
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The correct question is given below:
If f (x) = start root 4 x 9 enroot 2, which inequality can be used to find the domain of f(x)?
(A) startroot 4 x endroot greater-than-or-equal-to 0
(B) 4x+9 greater-than-or-equal-to 0
(C) 4 x greater-than-or-equal-to 0
(D) startroot 4 x 9 endroot 2 greater-than-or-equal-to 0
Answer:
(B)- 4X+9 greater than or equal to 0
Step-by-step explanation:
can someone help me please?
Answers
Answer:
the answer to the question is answer C
Answer:
Step-by-step explanation:
B is your answer
Given any two events, e1 and e2, what does the probability p(e1 ∪ e2) represent?
Answers
The equation of P(e₁ ∪ e₂) describes the condition that the mutually exclusive event stands one of the events occurs, or both occur.
What are Mutually Exclusive events?Mutually Exclusive events are described as in probability the particular addition rule exists practical when two occurrences exist incompatible with one another. It claims that the probability of either event exists equivalent to the probability of each possibility separately.
If e₁ and e₂ stand said to be mutually exclusive events then the probability of an event e₁ happening or the probability of event e₂ occurring exists given as P(e₁) + P(e₂) :
P(e₁ ∪ e₂) = P(e₁) + P(e₂)
Therefore, the equation of P(e₁ ∪ e₂) describes the condition that the mutually exclusive event stands for one of the events that happens, or both happen.
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