Answers
Given the function:
[tex]A(t)=40(0.83)^t[/tex]Where A(t) shows the amount of drug in a body after t hours.
Let's solve for the following:
• (a). Initial dosage:
Apply the exponential functions:
[tex]f(x)=a(b)^x[/tex]Where:
a is the initial value
b is the change factor.
Thus, we have the following:
a = 40
b = 0.83
Therefore, the initial dose is 40 mg.
• (b). What percent leaves the body each hour?
Apply the function:
[tex]f(x)=a(1-r)^x[/tex]Where:
r is the decay rate.
Thus, we have:
b = 1 - r
r = 1 - b
r = 1 - 0.83
r = 0.17
The percent that leaves the body each hour will be:
0.17 x 100 = 17%
Therefore, 17 percent of the drug leaves the body each hour.
• (c). What amount of drug is left after 12 hours?
Substitute 12 for t and solve for A(12):
[tex]\begin{gathered} A(12)=40(0.83)^{12} \\ \\ A(12)=40(0.1068900077) \\ \\ A(12)=4.28 \end{gathered}[/tex]The amount left after 12 hours is 4.28 mg.
• (d). The first whole number of hours at which there is less than 6 mg left.
Plug in 5.9 for A(t) and solve for t.
[tex]5.9=40(0.83)^t[/tex]Divide both sides by 40:
[tex]\begin{gathered} \frac{5.9}{40}=\frac{40(0.83)^t}{40} \\ \\ 0.1475=(0.83)^t \end{gathered}[/tex]Take the natural logarithm of both sides:
[tex]\begin{gathered} ln(0.1475)=tln(0.83) \\ \\ t=\frac{ln(0.1475)}{ln(0.83)} \\ \\ t=10.2 \end{gathered}[/tex]Therefore, the first whole number of hours where there is less than 6 mg left is 10 hours.
ANSWER:
• (a) 40 mg
,• (b) 17%
,• (c). 4.28 mg
,• (d). 10 hours
Related Questions
-2x + y = 3 5x - y = -3
Answers
we have
-2x + y = 3 -----> equation A
5x - y = -3 -----> equation B
Solve the system of equations
Solve by elimination
Adds equation A and equation B
-2x + y = 3
5x - y = -3
-----------------
-2x+5x=3-3
3x=0
x=0
Find the value of y
substitute the value of x in equation A or equation B
-2(0)+y=3
y=3
therefore
the solution is the point (0,3)Samuel is 10 years old. He moaned the neighbors lawn on Saturday and I and $40. It took him 2 hours come on the lawn in 2 hours to clean his room. How much money did Samuel earn an hour? A) $4.00B) $6.67C) $10.00D) 20.00
Answers
If he earned $40 in total and it took 4 hours to finish everything, he earns in an hour:
[tex]\frac{40}{4}=10[/tex]Answer: Samuel earns $10.00. Letter C.
Answer:
He got paid 10$ an hour. It does not say he gets paid for cleaning his room. Step-by-step explanation:10 x 4 = 40$
Step-by-step explanation:
Which two ratios are equivalent to 11/12?A. 4/5 and 12/13B. 22/24 and 33/36C. 22/33 and 33/34D. 23/24 and 35/36
Answers
Two ratios are equivalent if the division between them is equal to one. We need to look at the options to check for which these are true.
For A:
[tex]\frac{\frac{11}{12}}{\frac{4}{5}}=\frac{11}{12}\cdot\frac{5}{4}=\frac{55}{48}[/tex]Since the answer is different than one, this is not the correct option.
For B:
[tex]\frac{\frac{11}{12}}{\frac{22}{24}}=\frac{11}{12}\cdot\frac{24}{22}=\frac{264}{264}=1[/tex][tex]\frac{\frac{11}{12}}{\frac{33}{36}}=\frac{11}{12}\cdot\frac{36}{33}=\frac{396}{396}=1[/tex]Since the result of the division is one for both ratios, the correct option is "B".
1. Solve -4x < -3(6x - 2) and sketch the solution set on a number line.
Answers
We need to solve the inequality:
[tex]-4x<-3\mleft(6x-2\mright)[/tex]Let's multiply right side out and take variables to one side and numbers to another. The process is shown below:
[tex]\begin{gathered} -4x<-3\mleft(6x-2\mright) \\ -4x<-18x+6 \\ -4x+18x<6 \\ 14x<6 \\ x<\frac{6}{14} \\ x<\frac{3}{7} \end{gathered}[/tex]The solution set is:
[tex]\begin{gathered} x<\frac{3}{7} \\ or \\ x<0.4286 \end{gathered}[/tex]This means that x is less than 3/7, or
x is less than 0.4286
On the number line it looks:
can you please help me with this question. it's geometry
Answers
To find the angle A we need to find first the value of x. To do this we need to use the fact the the addition of the interior angles of any triangle is 180°.
The right side angle is equatl to 4x+4 since its vertically opposite to the one shown in the picture. The upper angle is 100° since it has to be supplementary to the angle of 80° shown in the picture.
With this in mind we have the equation:
[tex](4x+4)+(4x+4)+100=180[/tex]Solving for x we have:
[tex]\begin{gathered} (4x+4)+(4x+4)+100=180 \\ 8x+108=180 \\ 8x=180-108 \\ 8x=72 \\ x=\frac{72}{8} \\ x=9 \end{gathered}[/tex]Once we know the value of x we plug it in the expression for the angle A:
[tex]4(9)+4=40[/tex]Therefore the angle A is 40°.
Translate this sentence into an equation 43 is the difference of Chrissy’s age and 14 Use the variable c to represent Chrissy’s age
Answers
When translating into mathematical equations, "is" uses the equal sign and "difference" means that the operation to be used is subtraction.
So, "43 is the difference of Chrissy's age and 14" is written as:
43 = C - 14
Which of the following transformations shows a rotation 270 degrees counterclockwise? *
Answers
Explanation:
A rotation 270 degrees counterclockwise happens when the y and x axis value are interchanged and the interchanged y value becomes negative.
When we look at the options given, we look for the image whose rotation is in the positive x axis and negative y axis.
Also the movement will be thrice while moving anticlockwise.
From the options, the one which fits into the description above is B.
There is a movement of counterclockwise
Solve the system of two linear inequalities graphically,2y <&- 1618v 2 - 7x+56Step 1 of 3: Graph the solution set of the festlinear InequallyAnswerThe line will be drawn once all required data is provided and will update whenever a value is updated. The regions will be added once the line is drawEnable ZoonpanChoose the type of boundary linesSolid (-) Dashed)Enter two points on the boundarytine:10Select the region you wish to be shaded:
Answers
Given
[tex]\begin{gathered} 2y<8x-16 \\ 8y\ge7x+56 \end{gathered}[/tex]The graph
Two boundary points
(0,7) (2,0)
Find the next three terms in this sequence: 5120, 1280, 320, 80...-160, -400, -64020, 5, 1.2540, 20, 1076, 72, 68
Answers
Given the first four terms of this sequence:
[tex](5120,1280,320,80,\ldots)[/tex]We can see a pattern. To analize this pattern, let's first check the difference between those terms.
[tex]\begin{gathered} 5120-1280=3840 \\ 1280-320=960 \\ 320-80=240 \end{gathered}[/tex]From those differences, we can verify the following equations:
[tex]\begin{gathered} 3840=4(960) \\ 960=4(240) \end{gathered}[/tex]From this, we can write the general rule for this sequence:
[tex]a_n=\frac{5120}{4^{n-1}}[/tex]This sequence gives us:
[tex]\begin{gathered} a_1=5120 \\ a_2=1280 \\ a_3=320 \\ a_4=80 \\ a_5=20 \\ a_6=5 \\ a_7=1.25 \end{gathered}[/tex]Then, we have the following 3 terms. (20, 5, 1.25)
Please Help! An eight foot ladder leans against a building. if the ladder makes an angle of 60 degrees with the ground, haw far from the building is the base of the ladder. Round you answer to the nearest tenth.
Answers
The base of the ladder is 4 ft away from the buliding
Here, we want to calculate the distance from the building to the base of the ladder
To properly answer this, an image of the question is needed
We have this as follows;
From the diagram, what we want to calculate is the distance d
To calculate this, we need the appropriate trigonometric identity
Firstly, we need to identify the parts of the triangle present
As we can see, we have the hypotenuse which is the side that faces the right angle and also is the longest side
The side we want to get is the adjacent
Mathematically, the trigonometric ratio that connects the adjacent to the hypotenuse is the cosine
Thus, we have it that;
[tex]\begin{gathered} \cos \text{ 60 = }\frac{d}{8} \\ \\ d\text{ = 8 cos 60} \\ d\text{ = }4.0\text{ ft} \end{gathered}[/tex]To solve the inequality -7x<24, the inequality sign must be reversed.A. TrueB. False
Answers
ANSWER
True
EXPLANATION
To solve the inequality given:
-7x < 24
we have to divide both sides of the inequality by -7.
Dividing both sides of an inequality causes the sign to change direction (or be reversed) and so we will have:
x > -24 / 7
Therefore, it is true that the sign will be reversed.
Calculate the mean for each set of data round to the nearest tenths
Answers
The mean is the average of the numbers.
It is easy to calculate: add up all the numbers, then divide by how many numbers there are
[tex]\bar{x=\frac{\sum ^{\square}_{\text{ of numbers}}}{Number\text{ of items}}\text{ }}[/tex]the numbers given in the question are
[tex]2,11,5,6,13,4,9[/tex]there are 7 numbers in total.
Therefore, the mean will be
[tex]\begin{gathered} \operatorname{mean}=\frac{2+11+5+6+13+4+9}{7} \\ \operatorname{mean}=\frac{50}{7} \\ \operatorname{mean}=7.143 \\ to\text{ the nearest tenths, the mean is} \\ \operatorname{mean}=7.1 \end{gathered}[/tex]Hence,
the mean of the above set of values to the nearest tenth is = 7.1
Helpppppppp I can’t answer because I am bad at math
Answers
The magnitude of a number is the absoulute value of the number. Recall, the absolute value of a number is always positive. The absolute value of a is written as IaI
Hence,
magnitude of - 7.5 is 7.5
The correct option is D
8. If the slope of the equation y = -3/5x + 4 is changed to 3/5 and the y-intercept is changed to -4, which statement best describes this situation? You can use a calculator to graph or create your own graph.*A The new line is perpendicular to the original line. B The new line is parallel to the original line. C The new line and the original line have the same y-intercept. D The new line and the original line have the same x-intercept.
Answers
Answer:
Explanation:
Given that the line
[tex]y=-\frac{3}{5}x+4[/tex]is changed to
[tex]y=\frac{3}{5}x-4[/tex]solution of the system of equations.2. (3, 0) 2x+y=-63x + 2y = 94. (-2,3) y =2x+75x+y=-76. (0,-7) 2x -2y = 14X-Y=-7
Answers
We can solve these systems of equations as follows:
First CaseWe have:
[tex]\begin{cases}2x+y=-6 \\ 3x+2y=9\end{cases}[/tex]And we can solve this system by substitution as follows:
[tex]\begin{gathered} 2x+y=-6 \\ 2x-2x+y=-6-2x \\ y=-6-2x \end{gathered}[/tex]Now, we can substitute the corresponding value of y into the second equation as follows:
[tex]\begin{gathered} y=-6-2x \\ 3x+2y=9 \\ 3x+2(-6-2x)=9 \\ 3x+(2)(-6)+(2)(-2x)=9 \\ 3x-12-4x=9 \\ 3x-4x-12=9 \\ -x-12=9 \\ -x-12+12=9+12 \\ -x=21\Rightarrow x=-21 \end{gathered}[/tex]Now, we can substitute the value x = -21 into either of the original equations to find the value of y. We will use the first equation:
[tex]\begin{gathered} 2x+y=-6 \\ 2(-21)+y=-6 \\ -42+y=-6 \\ -42+42+y=-6+42 \\ y=36 \end{gathered}[/tex]Therefore, the solution to this first system is (-21, 36).
We can check this result if we substitute both values into the original equations:
[tex]\begin{gathered} \begin{cases}2x+y=-6 \\ 3x+2y=9\end{cases} \\ x=-21,y=36 \\ \begin{cases}2(-21)+36=-6 \\ 3(-21)+2(36)=9\end{cases} \\ \begin{cases}-42+36=-6 \\ -63+72=9\end{cases} \\ \begin{cases}-6=-6\Rightarrow This\text{ is true.} \\ 9=9\Rightarrow This\text{ is true.}\end{cases} \end{gathered}[/tex]Therefore, the solution to the first system of equations is (-21, 36).
Second Case
[tex]\begin{cases}y=2x+7 \\ 5x+y=-7\end{cases}[/tex]We can rewrite the system as follows:
[tex]\begin{cases}-2x+y=7 \\ 5x+y=-7\end{cases}[/tex]And we can solve this system by the elimination method: We have to multiply one of the equations by -1 and then add them algebraically as follows:
[tex]\begin{gathered} \begin{cases}-2x+y=7 \\ -1(5x+y=-7)\end{cases} \\ \begin{cases}-2x+y=7 \\ (-1)(5x)+(-1)(y)=(-1)(-7)\end{cases} \\ \begin{cases}-2x+y=7 \\ -5x-y=7\end{cases} \end{gathered}[/tex]If we add both equations, then we have:
[tex]\begin{gathered} \frac{\begin{cases}-2x+y=7 \\ -5x-y=7\end{cases}}{-7x=14} \\ -\frac{7x}{-7}=\frac{14}{-7} \\ x=-2 \end{gathered}[/tex]And now we can substitute this value in either equation to find y:
[tex]\begin{gathered} y=2x+7 \\ y=2(-2)+7 \\ y=-4+7 \\ y=3 \end{gathered}[/tex]And we got y = 3.
Therefore, the solution to this system is equal to (-2, 3), and we can also check the solutions using the original equations:
[tex]\begin{gathered} \begin{cases}y=2x+7 \\ 5x+y=-7\end{cases} \\ \begin{cases}3=2(-2)+7 \\ 5(-2)+3=-7\end{cases} \\ \begin{cases}3=-4+7 \\ -10+3=-7\end{cases} \\ \begin{cases}3=3\Rightarrow This\text{ is true.} \\ -7=-7\Rightarrow This\text{ is true.}\end{cases} \end{gathered}[/tex]In summary, we have that:
The solution to the first system ---> (-21, 36).
The solution to the second system ---> (-2, 3).
#1) Write the ratio of 60 km in 28 minutes in simplest form.#2) Is this ratio a rate? Explain your answer using words. [C
Answers
1. Expressing 60km per 28 minutes in its simplest form requires us to get it per 1 minute. This, we can easily obtain by:
[tex]\frac{60\operatorname{km}}{28\min}=\frac{15\operatorname{km}}{7\min}=2\frac{1}{7}\frac{km}{\min }[/tex]2.143 km per minute
2. The ratio is a rate. A rate is a measure of a quantity with respect to another, especially with respect to time.
As can be seen, this ratio is speed. Speed is a measure of distance covered per time.
Working with special triangles. Find y. I have attached the picture.
Answers
In this case, we'll have to carry out several steps to find the solution.
Step :
Data:
diagram:
right triangle
Step 02:
special right triangles:
we must analyze the triangle to find the solution.
special right triangle example:
right triangle:
side y:
[tex]\begin{gathered} 88\text{ = }\sqrt{2}y\text{ } \\ \\ \frac{88}{\sqrt{2}}\text{ = y} \end{gathered}[/tex]That is the full solution.
A new bank customer with $2,500 wants to open a money market account. The bank is offering a simple interest rate of 1.8%.
a. How much interest will the customer earn in 30 years?
b. What will the account balance be after 30 years?
a. The customer will earn $_ in interest.
Answers
Using the simple interest formula, the interest will the customer earn in 30 years is $1350, the account balance be after 30 years is $3850 and the customer earn $1350 interest.
In the given given that;
A new bank customer with $2,500 wants to open a money market account.
The bank is offering a simple interest rate of 1.8%.
So the Principal Amout(P)=$2500
Interest Rate(R)=1.8%
(a) So we have to find the interest will the customer earn in 30 years.
So the time (T)=30 years
So the formula of Simple Interest;
I=PRT/100
I=2500*1.8*30/100
I=1350
So the interest will the customer earn in 30 years is $1350.
(b) Now we have to find the account balance be after 30 years.
The account balance = Principal Amount+Interest Amount
The account balance = 2500+1350
The account balance = $3850
(c) Now we have to find the customer will earn $_ in interest.
The customer earn $1350 interest.
To learn more about Simple Interest link is here
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CAN SOMEONE HELP WITH THIS QUESTION?✨
Answers
The coterminal angle is 943° .
What is a coterminal angle?Coterminal angles are angles with the starting side on the positive x-axis and a shared terminal side. They are in standard position. Examples include the coterminal nature of the angles 30, -330, and 390. The phrase "coterminal angle" refers to angles with the same starting side and terminal side. If the specified angle is given in radians or degrees, finding coterminal angles is as easy as adding or subtracting 360° or 2 to each angle. It is possible to find all possible coterminal angles. The coterminal angle is described in mathematics as the angle formed by two angles drawn side by side in the same plane. Furthermore, both of them share the same location for their terminal sides. As an illustration, 405 and -315 are the coterminal angles of 45.
1294° = 360° + 934°
So the coterminal angle for 1294° is 934° .
To know more about coterminal angle ,visit:
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Multiply. Write the result in standard form.(2 + 1)(3^4 + 7 + 2)
Answers
To multiply polynomials, we use the distributive law
[tex]\begin{gathered} (2x+1)(3x^4+7x+2)=(2x+1)(3x^4)+(2x+1)(7x)+(2x+1)(2) \\ =2x(3x^4)+1(3x^4)+2x(7x)+1(7x)+2x(2)+1(2)_{} \\ =6x^5+3x^4+14x^2+7x+4x+2 \end{gathered}[/tex]The last part follows by the laws of exponentials, finally we combine like terms
[tex]\begin{gathered} 6x^5+3x^4+14x^2+7x+4x+2=6x^5+3x^4+14x^2+(7+4)x+2 \\ =6x^5+3x^4+14x^2+11x+2 \end{gathered}[/tex]A triangle has angle measures of 27 degrees , 50 degrees, and x degrees, use the triangle sum theorem to find the value of x.
Answers
ANSWER:
Angle x is 103 degrees
EXPLANATION
The sum of all the angles in a triangle is 180 degrees
Hence, Let angle A = 27 degrees
Angle B = 50 degrees
Angle C = x degrees
Triangle sum theorem state that
50 + 27 + x = 180
77 + x = 180
x = 180 - 77
x = 103 degrees
I inserted a picture of the question answer choices E. 15 F.x
Answers
Recall that two terms are called like terms if they have the same variables with the same exponents, in simpler words, two terms are like terms if when adding them the result is a simplification of the sum.
Answer: 8 and 12, 1, and 15 are like terms.
Which of the following options could you do before subtracting the equations so that one variable will be eliminated when you subtract them?
Answers
We need to do something to both equations so we can eliminate one variable
We can multiply the first equation by 3 and the second equation by 4
3( 4x-2y = 7) yields 12x -6y = 21
4( 3x-3y = 15) yields 12x -12y = 60
Now when we subtract
12x -6y = 21
-(12x -12y = 60)
---------------------------
12x -6y = 21
-12x +12y = -60
------------------------
6y = 39
The x terms are eliminated
Choice D multiply the top equation by 3 and the bottom equation by 4
If f (x) = -3x - 2, find each value
Answers
Given:
The function is given as
[tex]f(x)=-3x-2[/tex]Required:
We want to find the value of
[tex]f(-7)[/tex]Explanation:
[tex]f(-7)=-3(-7)-2=21-2=19[/tex]Final answer:
19
A bag of numbered lottery balls contains the numbers 1 through 50. What is the probability that a randomly selected ball will be a number that is not a multiple of 8? Give your answer as a simplified fraction.
Answers
A bag of numbered lottery balls contains he numbers 1 through 50.
One ball is selected at random.
From 50 balls, one ball can be selected in 50 different ways.
So, the total number of points in sample space is 50.
Let us consider the event that the number is a multiple of 8 be A.
There are six numbers between 1 o 50 which are multiple of 8.
Therefore, one ball can be selected from 6 balls in 6 different ways.
So, the number of points in sample space in favour of the event A is 6.
Therefore, by the classical definition of probability,
[tex]\begin{gathered} P(A)=\frac{6}{50} \\ =\frac{3}{25} \end{gathered}[/tex]Then, the probability that the selected number is not a multiple of 8 is
[tex]\begin{gathered} P(A^C)=1-P(A) \\ =1-\frac{3}{25} \\ =\frac{22}{25} \end{gathered}[/tex]So, the required probability is 22/25.
it's under the saying you add an extender different you subtract which a person does this explain
Answers
Operations
add → symbol "+"
subtract → symbol "-"
Multiply/divide → symbol "*/÷"
The braking distance of a car is proportional to the square of its speed.17. According to Graham's law, the rate of diffusion of two gases is inverselydproportional to density and is given bywhere ', and r2 are12rates of diffusion of two gases and d, and d2 are their respectivedensities. Which equation represents d, in terms of the other variables?
Answers
Ok in this problem you have to take Graham's law which is given to you and manage to write the density d1 as a function of the others. We have:
[tex]\frac{r_1}{r_2}=\sqrt[]{\frac{d_2}{d_1}}[/tex]Since we want to have d1 alone in one side of the equation the first thing we have to do is pass the square root to the other side. Square roots pass as square powers:
[tex](\frac{r_1}{r_2})^2=\frac{d_2}{d_1}[/tex]Then we have to pass d1 multiplying on the other side:
[tex]d_1\frac{r^2_1}{r^2_2}^{}=d_2[/tex]Now we only need to pass both r1 and r2:
[tex]d_1=d_2\frac{r^2_2}{r^2_1}[/tex]This is the same expresion that the one in item B so that is the correct answer
5) Given the following matrices, find the products of LN and MN
Answers
Answer:
The products MN and LN are not possible.
Explanation:
Matrix multiplication is only possible when the column number of the first matrix equals the row number of the second matrix.
Now, matrix L is a 2 x 2 matrix and N is a 5 x 2 matrix. Now L has 2 columns and N has 5 rows. Meaning, that columns of L are not equal to the rows of N. Therefore, matrix multiplication is not possible.
Matrix M is 2 x 4 and matrix N is 2 x 2. Since columns of matrix M equal the rows of matrix N, matrix multiplication is possible.
Therefore,
[tex][/tex]If a bow requires 3/4 yards of lace how many bows can u make with 12 yards of lace
Answers
3/4 yards of a lace for each bow
for 12 yards of lace:?
Simply divide the 12 yards of lace by the lace required by each bow (3/4)
12 / (3/4) = 16 bows
I need help on 4 please it says find the value of x round each answer to the nearest tenth
Answers
The pythagorean theorem is :
[tex]c^2=a^2+b^2[/tex]where c is the hypotenuse
a and b are the legs of the triangle.
From the problem, a = x, b = 19.1 and c = 30.5
Using the formula :
[tex]\begin{gathered} 30.5^2=x^2+19.1^2 \\ 930.25=x^2+364.81 \\ x^2=930.25-364.81 \\ x^2=565.44 \\ x=\sqrt[]{565.44} \\ x=23.779 \end{gathered}[/tex]The answer rounded to the nearest tenth is x = 23.8