1) To find the inverse function of this f(x) function, we need to presume this is a bijective function, and then follow these steps all the way through it:
2)
[tex]\begin{gathered} f(x)=5x+18 \\ \\ y=5x+18\:\:\:\:Swap\:the\:variables \\ \\ x=5y+8\:\:Isolate\:the\:y-term\:on\:the\:left\:side \\ \\ 5y+18-18=x-18\:\:\:Subtract\:18\:from\:both\;sides \\ \\ 5y=x-18\:\:\:Divide\:both\:sides\:by\:5 \\ \\ \frac{5y}{5}=\frac{x}{5}-\frac{18}{5}\:\:\:Simplify: \\ \\ y=\frac{x-18}{5}\:\:\:Write\:the\:proper\:notation \\ \\ f^{-1}(x)=\frac{x-18}{5} \end{gathered}[/tex]Thus, this is the answer.
Solve for h.-18 + h = 28h =
We have to solve for h:
[tex]\begin{gathered} -18+h=28 \\ -18+h+18=28+18 \\ h=46 \end{gathered}[/tex]Answer: h = 46
This diagram is a straightedge and compass construction.1.Select all true statements.luA. Line EF is the bisector of angle BAC.B. Line EF is the perpendicular bisector of segment BA.C. Line EF is the perpendicular bisector of segment Ac.D. Line EF is the perpendicular bisector of segment BD.E. Line EF is parallel to line CD.А
Only option A is correct
A. Line EF is the bisector of angle BAC.
A bisector is a line that splits an angle into two equal angles
find the mean graphically 4,4,1,7what is the sum of the numbers
Given data:
The given data are 4, 4, 1, 7.
The mean of data is,
[tex]\begin{gathered} x=\frac{4+4+1+7}{4} \\ =\frac{16}{4} \\ =4 \end{gathered}[/tex]The sum of the numbers is,
[tex]\begin{gathered} a=4+4+1+7 \\ =16 \end{gathered}[/tex]If you are selling your house with a local realtor who requires a 4% commission fee, what can youexpect to pay the realtor if your house sells for $161,000?Answer: $ _____________
SOLUTION:
Step 1:
In this question, we are given the following:
If you are selling your house with a local realtor who requires a 4% commission fee, what can you expect to pay the realtor if your house sells for $161,000?
Answer: $ _____________
Step 2:
The details of the solution are as follows:
We need to get
[tex]\begin{gathered} 4\text{ \% of \$ 161,000} \\ =\text{ }\frac{4}{100}\text{ x \$ 161,000} \\ =\text{ }\frac{644,000}{100} \\ =\text{ \$ 6,440} \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]6,440\text{ dollars}[/tex]Which of the following equations could be a line perpendicular to the x-axis?x = 8x = yy = –2y = –xI DON'T NEED AN EXPLANATION JUST THE ANSWER QUICK
Solution:
Concept:
The equation of the line perpendicular to the x-axis is` x=k`.
It is given that x=k has intercept -2 on the x-axis. This means that the line x=k passes through `(-2,0).
Step 1:
The graph of
[tex]x=8[/tex]is given below as
The graph of
[tex]x=y[/tex]is given below as
The graph of
[tex]=-2[/tex]Is given below as
The graph of
[tex]y=-x[/tex]Is given below as
Hence,
The final answer is OPTION A
6. Which table shows a geometric sequence? 1 4 3 Term 2 5 3 Term 1 2 4 ur A © Value 15 30 45 60 60 75 Value 9 | 18 | 27 36 45 Term 1 3 4 2 5 Term 4 1 Ол 2 3 B D Value 2 16 128 1024 | 8192 Value 220 260 300 340 380
For the geometric sequence, there is a common ratio between the terms
that mean the quotient of two consecutive terms = constant
So, lets check the options:
Table A: 30/15 = 2 and 45/30 = 1.5
So, Table A is not a geometric sequence
Table B : 16/2 = 8 and 128/16 = 8
So, table B is geometric sequence
Table C : 18/9 = 2 and 27/18 = 1.5
So, table C is not a geometric sequence
Table D : 260/220 = 1.18 and 300/260 = 1.15
So, table D is not a geometric sequence
So, the answer is B
what is the solution of each system ? use elimination 5x-6y=-32-3x-3y=9
Answer:
x = -50/11
y = 17/11
Explanation:
We have the following system of equations:
5x - 6y = -32
-3x - 3y = 9
To solve by elimination, we will multiply both sides of the second equation by -2, so:
[tex]\begin{gathered} -2(-3x-3y)=-2(9) \\ -2(-3x)-2(-3y)=-18 \\ 6x+6y=-18 \end{gathered}[/tex]Now, we can add this equation with the first equation, so:
5x - 6x = -32
6x + 6x = -18
11x + 0 = -50
So, solving for x, we get:
11x = - 50
11x/11 = -50/11
x = -50/11
Then, we can replace the value of x by -50/11 on the first equation:
[tex]\begin{gathered} 5x-6y=-32 \\ 5(-\frac{50}{11})-6y=-32 \end{gathered}[/tex]So, solving for y, we get:
[tex]\begin{gathered} -\frac{250}{11}-6y=-32 \\ -\frac{250}{11}-6y+\frac{250}{11}=-32+\frac{250}{11} \\ -6y=-\frac{102}{11} \\ \frac{-6y}{-6}=\frac{-102}{11}\cdot\frac{1}{-6} \\ y=\frac{17}{11} \end{gathered}[/tex]Therefore, the solution of the system is:
x = -50/11
y = 17/11
2. For Exercises 3 and 4, find the volume of each figure. Round to the nearest tenth if necessary. 3. A. 28.9 in C. 57.8 in B. 43.3 in D. 86.7 in 4 in A 3 in. 3. 4. F. 824.8 ft3 H. 412.4 ft I. 28.3 ft G. 530.8 ft 10.7 ft 9.4 ft 8.2 ft 4
EXPLANATION
The first figure is a triangular prism, so the equation that applies to find the volume is
[tex]Volume=\frac{1}{2}\text{bhl}[/tex]In this case, b=3 inches L= 6 2/3 inches = 20/3 inches h= 4 1/3 inches = 13/3 inches.
Replacing terms:
[tex]\text{Volume}=\frac{1}{2}\cdot3\cdot\frac{13}{3}\cdot\frac{20}{3}[/tex]Multiplying the fractions:
[tex]\text{Volume}=\frac{130}{3}=43.3in^3[/tex]The answer is the OPTION B: 43.3 inches^3
Can you please walk me they how to answer this
For this problem we are presented with an isosceles triangle, for which we have the length of the height and one of the sides. We can determine the length of the base by using pythagora's theorem on the triangle formed between the side, height and half of the base. This is shown on the drawing below:
Applying Pythagora's theorem, we have:
[tex]\begin{gathered} 17^2=15^2+(\frac{base}{2})^2 \\ 289=225+\frac{base^2}{4} \\ \frac{base^2}{4}=289-225 \\ \frac{base^2}{4}=64 \\ \text{base}^2=256 \\ \text{base}=\sqrt[]{256} \\ \text{base}=16 \end{gathered}[/tex]Now we can determine the perimeter of the triangle, by adding the measurements for all the sides:
[tex]P=16+17+17=50[/tex]For the area, we need to use the following expression:
[tex]\begin{gathered} A=\frac{b\cdot h}{2} \\ A=\frac{16\cdot17}{2} \\ A=136 \end{gathered}[/tex]The perimeter is equal to 50 ft.
The area is equal to 136 square ft.
how would I simplify the rational expression x^2_2x-24÷ x^2+7x+12?
we have the expression
[tex]\frac{x^2-2x-24}{x^2+7x+12}[/tex]step 1
Simplify the numerator
[tex]x^2-2x-24[/tex]Solve the quadratic equation, using the formula
a=1
b=-2
c=-24
substitute
[tex]x=\frac{-(-2)\pm\sqrt[]{(-2)^2-4(1)(-24)}}{2(1)}[/tex][tex]\begin{gathered} x=\frac{2\pm\sqrt[]{100}}{2} \\ \\ x=\frac{2\pm10}{2} \end{gathered}[/tex]the values of x are
x=6 and x=-4
therefore
[tex]x^2-2x-24=(x+4)(x-6)[/tex]step 2
Simplify the denominator
[tex]x^2+7x+12[/tex]Solve the quadratic equation, using the formula
a=1
b=7
c=12
substitute
[tex]x=\frac{-7\pm\sqrt[]{7^2-4(1)(12)}}{2(1)}[/tex][tex]x=\frac{-7\pm1}{2}[/tex]the values of x are
x=-3 and x=-4
therefore
[tex]x^2+7x+12=(x+3)(x+4)[/tex]step 3
substitute the given values in the original expression
[tex]\frac{(x+4)(x-6)}{(x+3)(x+4)}[/tex]simplify
[tex]\frac{x-6}{x+3}[/tex]Question Lincoln bought 3 bottles of an energy drink for $4.50. Write an equation relating the total cost y to the number of energy drinks bought x.
y=1.5x
Explanation
Step 1
you can easily solve this by using a rule of three.
Let
Lincoln bought 3 bottles of an energy drink for $4.50
[tex]\begin{gathered} 3\text{ bottles }\rightarrow4.5 \\ 3\rightarrow4.5 \\ \text{the proportion between the number of bottles and the price is} \\ \frac{3\text{ bottles}}{4.5\text{ usd}}=0.666 \end{gathered}[/tex]x= the number of energy drinks bought
y=the total cost
Step 2
make the equations
the proportions must be the same, then
[tex]\begin{gathered} \frac{x}{y}=\frac{3}{4.5} \\ \text{isolate y} \\ 4.5x=3y \\ 3y=4.5x \\ y=\frac{4.5x}{3} \\ y=1.5x \end{gathered}[/tex]I hope this helps you
What is the volume of the right cylinder below, in terms of ?
For this problem we use the formula for the volume of a cylinder:
[tex]V=h\cdot\pi\cdot r^2^{}[/tex]For this problem, h = 10 in, r= 12 in
[tex]V=\text{ 10 in }\cdot\text{ }\pi\cdot(12in)^2\text{ = 1440}\pi in^3[/tex]You flip a coin 80 times how many times should you expect to get tails
Closer to 40 times.
1) Since the Theoretical Probability tells us that the chances of getting tails in one flip are 50%
2) If we flip it 80 times we'll have it closer to 50% of those 80 times, i.e. closer to 40 times to get tails.
Not exactly 40 but closer to 40. Because the more we flip it the more we get it closer to the Theoretical Probability
Find the focus and directrix of the parabola y = 1∕2(x +1)^2 + 4.Question 2 options:A) Focus: (–1,41∕2); Directrix: y = 31∕2B) Focus: (1,31∕2); Directrix: y = 41∕2C) Focus: (1,41∕2); Directrix: y = 31∕2D) Focus: (–1,31∕2); Directrix: y = 41∕2
Given the equation:
[tex]y=\frac{1}{2}\mleft(x+1\mright)^2+4[/tex]• You can identify that it has this form:
[tex]y=a\mleft(x-h\mright)^2+k[/tex]Where its Vertex is:
[tex](h,k)[/tex]And the Focus is:
[tex](h,k+\frac{1}{4a})[/tex]In this case, you can identify that:
[tex]\begin{gathered} h=-1 \\ k=4 \\ \\ a=\frac{1}{2} \end{gathered}[/tex]Therefore, you can determine that the Focus is:
[tex](-1,4+\frac{1}{4\cdot\frac{1}{2}})=(-1,\frac{9}{2})[/tex]In order to write the y-coordinate of the Focus as a Mixed Numbers, you need to:
- Divide the numerator by the denominator.
- The Quotient will be the whole number part:
[tex]4[/tex]- The new numerator will be the Remainder:
[tex]1[/tex]- The denominator does not change.
Then:
[tex]\frac{9}{2}=4\frac{1}{2}[/tex]• In order to find the Directrix, you need to remember that, by definition, the Directrix has the same distance from the vertex that the Focus of the parabola is. Therefore:
[tex]y=k-a[/tex][tex]y=4-\frac{1}{2}[/tex][tex]y=\frac{7}{2}[/tex]Apply the same procedure shown before, in order to convert the Improper Fraction to a Mixed Number. Hence, you get:
[tex]y=3\frac{1}{2}[/tex]Therefore, the answer is: Option A.
Perform the following division and write the quotient in trigonometric form. Write the magnitude in exact form. Write the argument in radians and round it to twodecimal places if necessary.-3 - 6i6 + 4i
To perform the division of complex numbers, we have to multiply by the unitary conjugate of the denominator. In this case we would have the following:
[tex]\begin{gathered} \frac{-3-6i}{6+4i}*\frac{6-4i}{6+4i}=\frac{(-3-6i)(6-4i)}{(6)²-(4i)²}=\frac{-18+12i-36i+24i²}{36-16i²} \\ =\frac{-42-24i}{52} \end{gathered}[/tex]therefore, the result of the division is -42/52 -24/52i
one tenth of a number decreased by 12?
One tenth = 1/10
A number = x
Decreased by 12 = -12
The final expression:
1/10x-12
3.54.03.64.02.62.46.84.94.55.43.72.93.74.73.4Find the mean and sample standard deviation of these data. Round to the nearest hundredth.mean_____sample standard deviation________
The number of terms is 15.
The means is defined as the ratio of sum of terms by number of terms.
Mean:
Determine the mean of the data.
[tex]\begin{gathered} \mu=\frac{3.5+4.0+3.6+4.0+2.6+2.4+6.8+4.9+4.5+5.4+3.7+2.9+3.7+4.7+3.4}{15} \\ =\frac{60.1}{15} \\ =4.0066 \\ \approx4.01 \end{gathered}[/tex]Standard deviation:
Determine the sum of square of difference between each observation and mean of the data.
[tex]\begin{gathered} \sum ^n_{i\mathop=1}(x_i-\mu)^2=(3.5-4.01)^2+(4.0-4.01)^2+(3.6-4.01)^2+(4.0-4.01)^2+(2.6-4.01)^2 \\ +(2.4-4.01)^2+(6.8-4.01)^2+(4.9-4.01)^2+(4.5-4.01)^2+(5.4-4.01)^2 \\ +(3.7-4.01)^2+(2.9-4.01)^2+(3.7-4.01)^2+(4.7-4.01)^2+(3.4-4.01)^2 \end{gathered}[/tex][tex]\begin{gathered} =0.2601+0.0001+0.1681+0.0001+1.9881+2.5921+7.7841+0.7921+0.2401 \\ +1.9321+0.0961+1.2321+0.0961+0.4761+0.3721 \end{gathered}[/tex][tex]=18.0295[/tex]The formula for the statndard deviation is,
[tex]\sigma=\sqrt[]{\frac{\sum ^n_{i\mathop=1}(x_i-\mu)^2}{n-1}}[/tex]Substitute the values in the formula to determine the standard deviation of the data.
[tex]\begin{gathered} \sigma=\sqrt[]{\frac{18.0295}{15-1}} \\ =\sqrt[]{\frac{18.0295}{14}} \\ =1.1348 \\ \approx1.13 \end{gathered}[/tex]Answer:
Mean: 4.01
Standard deviation: 1.13
Questioncd - 6c +2Evaluatewhen c = 2 and d = -2. Enter an integer or a fraction in simplest form.-5c-9d3 + 9 + 10Provide your answer below:cd - 60+25c + 90-9d-10e BasicI need help I’m not sure if my answer is correct.
You have to replace the variables with the given vlaues c=2 and d=-2
[tex]\frac{(2\cdot(-2))-6\cdot2+2}{-5\cdot2-9(-2)^3+9(-2)+10}=\frac{-14}{54}=\frac{-7}{27}=\text{ -0.259}[/tex]Hello, I need some assistance with this homework question, please? This is for my precalculus homework. Q5
Answer:
[tex]T\text{he domain of H\lparen x\rparen is }\lbrace x\lvert x-3,1\rbrace[/tex]Step-by-step explanation:
The domain of a function is all the set of possible x-values that the function can take. Then, for the given function:
[tex]H\left(x\right)=\frac{-7x^2}{\left(x-1\right)\left(x+3\right)}[/tex]The function is undefined when the denominator is equal to 0, then equalize each factor of the denominator to 0:
[tex]\begin{gathered} x-1=0 \\ x=1 \\ \\ x+3=0 \\ x=-3 \\ \\ \text{ Then, the domain of H\lparen x\rparen is }\lbrace x\lvert x\ne-3,1\rbrace \end{gathered}[/tex]For the exponential function f, find f^-1 analytically and graph both f and f^-1.f(x)=5^x-1
Given the function :
[tex]f(x)=5^x-1[/tex]We will find the inverse of the function analytically as following :
[tex]y=5^x-1[/tex]Solve for x
[tex]\begin{gathered} y+1=5^x \\ x=\log _5(y+1) \end{gathered}[/tex]make y in the place of x. so,
[tex]\begin{gathered} y=\log _5(x+1) \\ \\ f^{-1}(x)=\log _5(x+1) \end{gathered}[/tex]The graph of both function will be as shown in the following picture .
The given function f(x) = 5^x - 1 is the graph of the blue color
And the inverse with the red color
each function is written closer to its graph
Josh and his teammates are running the 1600-meter relay. How many feet will the team run?
We need to convert from meters to feet to determine the number of feet the team will run:
[tex]\begin{gathered} 1\text{ foot = 0.3048 }meter \\ \text{let the number of f}eet\text{ for 1600 m = y} \end{gathered}[/tex][tex]\begin{gathered} 0.3048\text{ meter = 1 foot} \\ 1600\text{ meter = y} \\ \text{cross multiply:} \\ y(0.3048\text{ m) = 1 ft(1600 m)} \\ \end{gathered}[/tex][tex]\begin{gathered} 0.3048y\text{ = 1600} \\ y\text{ = }\frac{1600}{0.3048} \end{gathered}[/tex][tex]\begin{gathered} y\text{ = 5249.34} \\ \text{Hence, the team will run 5249.34 f}et \end{gathered}[/tex]A minor league baseball team plays 80 games in a season. If the team won 17 more than twice as many games as they lost, how many wins and losses did the team have?How many games did the team lose?
We know that
• There are 80 games in total.
,• The team won 17 more than twice as they lost.
Each statement can be expressed as an equation.
[tex]w+l=80[/tex]Because there are 80 games in total.
[tex]w=17+2l[/tex]Now, we replace the second equation in the first one.
[tex]17+2l+l=80[/tex]We solve for l
[tex]\begin{gathered} 17+3l=80 \\ 3l=80-17 \\ l=\frac{63}{3}=21 \end{gathered}[/tex]Therefore, the team lost 21 games.
We use this value to find the games they won.
[tex]w=17+2(21)=17+42=59[/tex]Therefore, the team won 59 games.In the diagram below, line segment AB has endpoints at A(-2,-6) and B( 3,-1) .Draw A'B' the image of AB after a counterclockwise rotation of 90° about the origin. Give the coordinates of its endpoints below. Is A'B' congruent to AB? Explain.
By definition, you know that when a point is rotated 90 degrees counterclockwise about the origin, point A (x, y) becomes A'(- y, x).
Then, if you rotate 90 degrees counterclockwise about the origin the points A and B you get:
[tex]\begin{gathered} A(-2,6)\rightarrow A^{\prime}(-6,-2) \\ B(3,-1)\rightarrow B^{\prime}(-(-1),3)=B^{\prime}(1,3) \end{gathered}[/tex]Now graphing points A and B and their respective rotations you have
Now, to know if the segments AB and A'B 'are congruent, you can find a measure of each one of them using the distance formula, which is
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]So, for the measure of segments AB you have
[tex]\begin{gathered} (x_1,y_1)=(-2,-6) \\ (x_2,y_2)=(3,-1) \\ d_{AB}=\sqrt[]{(3-(-2))^2+(-1-(-6))^2} \\ d_{AB}=\sqrt[]{(3+2)^2+(-1+6)^2} \\ d_{AB}=\sqrt[]{(5)^2+(5)^2} \\ d_{AB}=\sqrt[]{25+25} \\ d_{AB}=\sqrt[]{50} \\ d_{AB}=7.07 \end{gathered}[/tex]For the measure of segments A'B' you have
[tex]\begin{gathered} (x_1,y_1)=(-6,-2) \\ (x_2,y_2)=(1,3) \\ d_{A^{\prime}B^{\prime}}=\sqrt[]{(1-(-6))^2+(3-(-2))^2} \\ d_{A^{\prime}B^{\prime}}=\sqrt[]{(1+6)^2+(3+2)^2} \\ d_{A^{\prime}B^{\prime}}=\sqrt[]{(7)^2+(5)^2} \\ d_{A^{\prime}B^{\prime}}=\sqrt[]{49+25} \\ d_{A^{\prime}B^{\prime}}=\sqrt[]{74} \\ d_{A^{\prime}B^{\prime}}=8.6 \end{gathered}[/tex]Then, as you can see, the segments AB and A'B'do not have the same measure and therefore are not congruent.
Find the measure of
We can see that the angles of 39° and 90° in the figure are adjacent, that is, they have one side in common.
We can also see that the angle x includes both smaller angles. The angles x and 39° have one side in common, and the angles x and 90 have one side in common.
Then, we can conclude that the angle x is the sum of those 2 smaller angles in the figure.
So we have that:
[tex]\begin{gathered} x=39\degree+90\degree \\ x=129\degree \end{gathered}[/tex]So the measure of x is 129°.
At Cityville High School, 33% of the students participate in sports, 37% of the students participate in academic clubs, and 19% of the students participate in both sports and academic clubs. Find the proportion of students who participate in either sports or academic clubs.
Let's begin by listing out the information given to us:
Sports = 33% = 33/100 = 0.33
Academic clubs = 37% = 37/100 = 0.37
Sports and Academic clubs = 19% = 19/100 = 0.19
Remainder (Neither Sports nor Academic clubs) = 100 - (33 + 37 + 19)
= 100 - 99 = 1% = 1/100 = 0.01
We will find the proportion of students who participate in either sports or academic clubs by summing together the percentage of students that participate in Sports alone & those that participate in Academic clubs alone as shown below:
[tex]\begin{gathered} n=0.33+0.37=0.70 \\ n=0.7 \end{gathered}[/tex]Therefore, the proportion of students who participate in either sports or academic clubs is 70% or 0.7
Help! I’ll mark u brainly and helps me now please
Start by typing the numbers: 4 (for the box that reads "Min" since the list of values (which they gave you already ordered from least to largets) is showing that the minimum value of your set is 4.
You can do the same with the number 16, placing it as the maximum "Max".
AT the same time, it seems that you can move the different parts of the box diagram, so please, grab the left end of the whisker of the box diagram, and move it to align with the number "4" in the horizontal axis.
Do also an adjustment of the right end of the whisker and take it to align with the number 16 in the horizontal axis.
The Median in this case (of even number of values in the set) is given by the average of the two numbers around the middle of the list. So you do : (6+9)/2 = 15/2 = 7.5
7.5 is the median.
The first quartile is for value 6, and the third quartile for the value 10.
So, please move the ends of the box to align with the numbers 6 and 10 on the horizontal axis, and the center of the box
The manager of a movie theater found that Saturday's sales were $335. He knew that a total of 65 tickets were sold. Adult tickets, a, cost $7, and childtickets, c, cost $4.The system of equations shown can be used to represent the situation.a+c=657a +4c335How many child tickets were sold? Enter your answer in the box provided. (Numbers Only)child tickets
Create 2 new equivalent fractions by multiplying the numberator and denominator of the given fractions by a non-zero number.
Part a
we have
5/7
Multiply the numerator and denominator by a number
Example (3/3) to obtain an equivalent fraction
(5/7)*(3/3)=1521
15/21 is an equivalent fraction
Part b
we have
4/11
Multiply the numerator and denominator by a number
Example (7/7) to obtain an equivalent fraction
(4/11)*(7/7)=28/77
28/77 is an equivalent fraction
If you multiply the numerator and denominator of a fraction by the same number, the fraction is the same, you obtain an equivalent fraction
Example
you have
4/5
if you multiply 4/5 by 1, the result is the same fraction 4/5
if you have 4/4 this is the same that 1
so
if you multiply the fraction 4/5 by 4/4 or 7/7, is the same that you multiply the fraction by 1
the result is an equivalent fraction
so
4/5*(4/4)=16/20
4/5*(7/7)=28/35
16/20 and 28/35 and 4/5 are equivalent
because
16/20=0.8
28/35=0.8
4/5=0.8
is the same result
the fractions are equivalent
This is actually a 5 part question, here's the first part.
Since the time of the half-life is 3 hours, then we have to divide the number of hours given by 3
The form of the exponential function is
[tex]D(t)=a(b)^{\frac{t}{n}}[/tex]a is the initial amount
b is the factor of increasing or decreasing
In our situation:
Half-life means b = 1/2
Since the initial amount given is 20 mg, then
a = 20
Since the time of half-life is 3 hours, then
t must be the time divided by 3
The function which represents the situation is
[tex]D(t)=20(\frac{1}{2})^{\frac{t}{3}}[/tex]Since t = 3, then
[tex]\begin{gathered} f(3)=20(\frac{1}{2})^{\frac{3}{3}} \\ f(3)=20(\frac{1}{2})^1 \\ f(3)=10\text{ mg} \end{gathered}[/tex]a.
At t = 6
[tex]\begin{gathered} f(\frac{6}{3})=20(\frac{1}{2})^{\frac{6}{3}} \\ f(2)=20(\frac{1}{2})^2 \\ f(2)=20(\frac{1}{4}) \\ f(2)=5\text{ mg} \end{gathered}[/tex]At t = 9
[tex]\begin{gathered} f(9)=20(\frac{1}{2})^{\frac{9}{3}} \\ f(9)=20(\frac{1}{2})^3 \\ f(9)=20(\frac{1}{8}) \\ f(9)=2.5\text{ mg} \end{gathered}[/tex]b.
To find the amount at t = 10 hours, substitute t by 10
[tex]\begin{gathered} f(10)=20(\frac{1}{2})^{\frac{10}{3}} \\ f(10)=1.98425\text{ mg} \end{gathered}[/tex]We know that by using the exponential function above
2.
The function form is
[tex]D(t)=A(\frac{1}{2})^{\frac{t}{n}}[/tex]Where A = 20 -------- initial amount
n = 3 ------- the period of half-life
The formula is
[tex]D(t)=20(\frac{1}{2})^{\frac{t}{3}}[/tex]3.
The drug remains after 1 hour means substitute t by 1 first, then divide the answer by the initial amount, and change it to percent
[tex]\begin{gathered} D(1)=20(\frac{1}{2})^{\frac{1}{3}} \\ D(1)=15.87401052 \end{gathered}[/tex]We will find the percent
[tex]\begin{gathered} \text{ \%D=}\frac{15.87401052}{20}\times100\text{ \%} \\ \text{ \%D=79.37\%} \end{gathered}[/tex]To find the percent of the amount eliminated subtract 79.37% from 100%
[tex]\text{ \%E=100\%-79.37=20.63\%}[/tex]4.
The direction for adults is
Do not exceed 4 doses per 24 hours
5.
Since the table has a period of 2 hours, then we will use t = 2, 4, 6, 8, 10, 12 in the formula above to find the amount of Dex.
[tex]\begin{gathered} D(2)=20(\frac{1}{2})^{\frac{2}{3}}=12.599\text{ mg} \\ D(4)=20(\frac{1}{2})^{\frac{4}{3}}=7.937\text{ mg} \end{gathered}[/tex][tex]\begin{gathered} D(6)=20(\frac{1}{2})^{\frac{6}{3}}=5\text{ mg} \\ D(8)=20(\frac{1}{2})^{\frac{8}{3}}=3.150\text{ mg} \end{gathered}[/tex][tex]\begin{gathered} D(10)=20(\frac{1}{2})^{\frac{10}{3}}=1.984\text{ mg} \\ D(12)=20(\frac{1}{2})^{\frac{12}{3}}=1.25\text{ mg} \end{gathered}[/tex]florence took a total of 12 quizzes over the course of 2 weeks. how many weeks of school will florence have to attend this quarter before she will habe taken a total of 36 quizze?
EXPLANATION
Number of quizzes = 12
Time = 2 weeks
The number of weeks of school that florence will have to attend this quarter before 36 quizzes is:
12x3= 36 quizzes
Hence, Florence will need 2x3= 6 weeks
Let's call x to the number of weeks.
The relationship is:
[tex]\text{Number of w}eeks\text{ =x = }\frac{2}{12}\cdot36=\frac{72}{12}=6\text{ w}eeks[/tex]