Answer:
A) The initial size o the culture is 640
B) The doubling period is 47 minutes
C) The population after 60 minutes is 1563
D) The population will reach 13000 after 3 hours 22 minutes
Explanation:
The form of an exponential grow model is:
[tex]S=Pb^t[/tex]Where:
S is the population after t hours
P is the initial population
b is the base of the exponent
t is the time, in hours
We know that after 15 minutes, the population was 800. 15 minutes is a quarter of an hour. Thus, t = 1/4, S = 800:
[tex]800=Pb^{\frac{1}{4}}[/tex]Also, we know that after 30 minutes, the population was 1000. Thus, t = 1/2, S = 1000
[tex]1000=Pb^{\frac{1}{2}}[/tex]Then, we have a system of equations:
[tex]\begin{cases}800=Pb^{\frac{1}{4}}{} \\ 1000=Pb^{\frac{1}{2}}{}\end{cases}[/tex]We can solve the first equation for P:
[tex]\begin{gathered} 800=Pb^{\frac{1}{4}} \\ P=\frac{800}{b^{\frac{1}{4}}} \end{gathered}[/tex]And substitute in the other equation:
[tex]1000=\frac{800}{b^{\frac{1}{4}}}b^{\frac{1}{2}}[/tex]And solve:
[tex]\frac{1000}{800}=\frac{b^{\frac{1}{2}}}{b^{\frac{1}{4}}}[/tex][tex]\begin{gathered} \frac{5}{4}=b^{\frac{1}{2}-\frac{1}{4}} \\ . \\ \frac{5}{4}=b^{\frac{1}{4}} \end{gathered}[/tex][tex]\begin{gathered} b=(\frac{5}{4})^4 \\ . \\ b=\frac{625}{256} \end{gathered}[/tex]Now, we can find the initial population P:
[tex]P=\frac{800}{(\frac{625}{256})^4}=\frac{800}{\frac{5}{4}}=\frac{800\cdot4}{5}=640[/tex]The initial population is 640
To find the doubling period, we want that the population equal to twice the initial population:
[tex]S=2P[/tex]Then, since we know the equation, we can write:
[tex]2P=P(\frac{625}{256})^t[/tex]Then:
[tex]\begin{gathered} \frac{2P}{P}=(\frac{625}{256})^t \\ . \\ 2=(\frac{625}{256})^t \\ \ln(2)=t\ln(\frac{625}{256}) \\ . \\ \frac{\ln(2)}{\ln(\frac{625}{256})}=t \\ . \\ t\approx0.7765 \end{gathered}[/tex]If an hour is 60 minutes:
[tex]60\cdot0.7765=46.59\approx47\text{ }minutes[/tex]To find the population after 60 minutes, we use t = 1 hour and we want to find S:
[tex]\begin{gathered} S=640(\frac{625}{256})^1 \\ . \\ S=640\cdot\frac{625}{256}=1562.5 \end{gathered}[/tex]To find when the population is 13000, then we use S = 13000 and solve for t:
[tex]\begin{gathered} 13000=640(\frac{625}{256})^t \\ . \\ \frac{13000}{640}=(\frac{625}{256})^t \\ . \\ \frac{325}{16}=(\frac{625}{256})^t \\ . \\ \ln(\frac{325}{16})=t\ln(\frac{625}{256})^ \\ . \\ t=\frac{\ln(\frac{325}{16})}{\ln(\frac{625}{256})}\approx3.373 \\ \\ \end{gathered}[/tex]We have 3 full hours and 0.373. Since one hour is 60 minutes:
[tex]60\cdot0.373\approx22[/tex]The population reach 13000 after 3 hours 22 minutes
write the expanded form of the expression : 7(2x + y)
ANSWER
14x + 7y
EXPLANATION
We want to write the expanded form of the expression given:
7(2x + y)
To do this, we have to use the distribution property by using the number outside the bracket to multiply each of the terms in the bracket.
So, we have that:
7(2x + y) = (7 * 2x) + (7 * y)
= 14x + 7y
That is the answer.
what is the answer to -8+3v-5-4v
We solve as follows:
[tex]-8+3v-5-4v=-13-v[/tex]Can you explain to me why I got this wrong? And what are the correct answers
To get the true statements, we will be testing the options one by one in order.
First option
[tex]\begin{gathered} \cos (25)=0.9063 \\ \cos (65)=0.4226 \\ \therefore\cos (25)\ne\cos (65) \end{gathered}[/tex]Second option
[tex]\begin{gathered} \cos (25)=0.9063 \\ \sin (65)=0.9063 \\ \therefore\cos (25)=\sin (65) \end{gathered}[/tex]Third option
[tex]\begin{gathered} \sin (25)=0.4226 \\ \cos (65)=0.4226 \\ \therefore\sin (25)=\cos (65) \end{gathered}[/tex]Fourth option
[tex]\begin{gathered} \tan (45)=1 \\ \tan (45)=1 \\ \therefore\tan (45)=\tan (45) \end{gathered}[/tex]Fifth option
[tex]\begin{gathered} \tan (65)=2.1445 \\ \tan (25)=0.4663 \\ \therefore\tan (65)=\tan (25) \end{gathered}[/tex]Hence, the correct options are Options 2, 3, 4.
Three math classes at Sunview High School collected the most box tops for a school fundraiser, and so they won a $600 prize to share among them. Mr. Aceves’ class collected 3,760 box tops, Mrs. Baca’s class collected 2,301, and Mr. Canyon’s class collected 1,855. How should they divide the money so that each class gets the same fraction of the prize money as the fraction of the box tops that they collected?
The total amount fundraised is given as follows:
[tex]3760+2301+1855=7916\text{ box tops}[/tex]The proportion of Mr. Aceves' class collected is given as follows:
[tex]\frac{3760}{7916}\text{ box tops}[/tex]The proportion of Mr. Baca's class collected is given as follows:
[tex]\frac{2301}{7916}\text{ box tops}[/tex]The proportion of Mr. Canyon's class is given as follows:
[tex]\frac{1855}{7916}\text{ box tops}[/tex]Now compute the amount for Mr. Aceves' class is given as follows:
[tex]\frac{3760}{7916}\times600\approx284.99[/tex]Again, compute the amount for Mr. Baca's class is given as follows:
[tex]\frac{2301}{7916}\times600\approx174.41[/tex]Again, compute the amount for Mr. Canyon's class is given as follows:
[tex]\frac{1855}{7916}\times600\approx140.60[/tex]As a result, $284.99 will go to Mr. Aceve's class, $174.41 will go to Mr. Baca's class, and $140.60 will go to Mr. Canyon's class.
which of the following is equivalent to the logarithmic equation below? log4 64=3
help me with this question
Answer:
Step-by-step explanation:
just 3,2
fine the value of x in(2x+5)(8x+5)
We are given the value of two angles as functions of "x"
[tex]\begin{gathered} \text{angle 1 = 2x+5;} \\ \text{angle 2 = 8x+5} \end{gathered}[/tex]These are supplentary angles, that is, their sum is 180 degrees
[tex]\text{angle 1 + angle 2 =180}^{\circ}[/tex]Replacing the values for the angles
[tex](2x+5)+(8x+5)=180[/tex]Now we solve the equation, first by adding similar terms
[tex]10x+10=180[/tex]Now we substract 10 on both sides
[tex]10x=170[/tex]Now we divide by 10 on both sides
[tex]x=\frac{170}{10}=17[/tex]The value of x is 17
Determine if the following equations are parallel, perpendicular, or neither. 5(x + 3) = 3y + 12 and 5x + 3y = 15
Solution
We have the following equation:
5(x+3)= 3y+12 (1)
Solving for y we got:
3y= -12+ 5(x+3)
3y = -12 + 5x+15
3y= 5x +3
y= 5/3 x +1
The slope for the first case is: m1= 5/3
5x + 3y = 15 (2)
Solving for y we got:
3y= 15-5x
y= 5 -5/3x
The slope is given by : m2= -5/3
Then m1*m2 is not equal to -1 (NOT perpendicular)
m1 is different from m2 (NOT parallel)
Then are not perpendicular or parallel
I need help on in the answer to this question
Using the 2 tangents line formula:
[tex]m\angle Q=\frac{1}{2}((360-mPR)-mPR)[/tex][tex]\begin{gathered} 81x-1=\frac{1}{2}(360-2(100x)) \\ 81x-1=\frac{1}{2}(360-200x) \\ 81x-1=180-100x \\ \end{gathered}[/tex]Solve for x:
[tex]\begin{gathered} 81x+100x=1+180 \\ 181x=181 \\ x=\frac{181}{181} \\ x=1 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} mPR=100(1)_{} \\ mPR=100 \end{gathered}[/tex]Answer:
A. 100
In simple layman’s English please explain the difference between uniform probability models and non-uniform probability models.
In a uniform probability model, all events have the same chance of occurring. For a non-uniform probability model, all events do not have the same chance of occurring
Please find entire surface are of a stereo receiver (question 17)
We could approach the stereo receiver to a rectangular prism, that has the formula of surface area (A):
[tex]A=2ab+2bc+2ac[/tex]As the dimensions are given: a = 18", b = 16", c = 9"; then we just have to replace these values in the formula:
[tex]A=2(18)(16)+2(16)(9)+2(18)(9)[/tex]Simplifying:
[tex]A=576+288+324[/tex][tex]A=1188[/tex]Answer: 1188 in²
Lisa receives a net pay of $619.06 biweekly. She has $143withheld from her pay each pay period. What is her annual gross salary?a. $ 762.06b. $18,289.44c. $19,813.56d. $39,627.12
Answer:
c. $19,813.56
Explanation:
Given:
• Lisa receives a net pay of $619.06 biweekly.
,• $143 is withheld from her pay each pay period.
We are required to find her annual gross salary.
First, determine her gross salary for each pay period.
[tex]\begin{gathered} \text{Gross Salary}=\text{Net Pay+Deduction} \\ =619.06+143 \\ =\$762.06 \end{gathered}[/tex]Next, determine the number of payment periods.
[tex]\begin{gathered} \text{Lisa is paid biwe}ekly,\text{ that is every 2 weeks.} \\ The\text{ number of weeks in a year}=52 \\ \text{Therefore:} \\ \text{The number of payment periods}=\frac{52}{2}=26 \end{gathered}[/tex]Finally, multiply her gross salary per period by the number of periods to get her annual gross salary.
[tex]\begin{gathered} \text{Gross annual salary}=26\times762.06 \\ =\$$19,813.56$ \end{gathered}[/tex]Lisa's annual gross salary is $19,813.56.
Option C is correct.
Which expression is -7 +6 X 5 - 2? O A) 13 X 5 - 2 O B) 7+11 – 2 OC) 13 X 3OD) 37 - 2
Which expression is equal to 7 + 6 x 5 - 2?
The first step is to use the PEMDAS, and this rule ensures that certain rules are followed in number operations. It simply means some mathematical signs would be given preference over the others. The acronym PEMDAS ensures that Exponents comes first, followed by Multiplication, Addition an then Subtraction. In this question, the Multiplication sign would be considered first and so we now have;
7 + [6 x 5] - 2
7 + 30 - 2
Then the addition sign would take prefernce now, and you have
[7 + 30] - 2
And that results in option D
D) 37 - 2
A bag contains 6 green balls and 4 yellow balls. What is the probability that two balls picked randomly are both of the same color?
Given:
The number of green balls is G = 6.
The numer of yellow balls is Y = 4.
Explanation:
Determine the total number of balls.
[tex]\begin{gathered} T=6+4 \\ =10 \end{gathered}[/tex]Determine the probability for both selected balls to be green.
[tex]\begin{gathered} P(G)=\frac{6}{10}\cdot\frac{5}{9} \\ =\frac{15}{45} \end{gathered}[/tex]Determine the probability for selected balls to be yellow.
[tex]\begin{gathered} P(Y)=\frac{4}{10}\cdot\frac{3}{9} \\ =\frac{6}{45} \end{gathered}[/tex]Determine the probability for both selected balls to be of same colour.
[tex]\begin{gathered} P=P(G)+P(Y) \\ =\frac{15}{45}+\frac{6}{45} \\ =\frac{21}{45} \\ =\frac{7}{15} \end{gathered}[/tex]Lionfish are considered an invasive species, with an annual growth rate of 69%. A scientist estimates there are 9,000 lionfish in a certain bay after the first year.
Given:
Lionfish are considered an invasive species, with an annual growth rate of 69%. A scientist estimates there are 9,000 lionfish in a certain bay after the first year.
The general equation of the growth is:
[tex]P(t)=P_0\cdot(1+r)^t[/tex]Given rate = r = 69% = 0.69
After 1 year, P = 9000
Substitute to find the initial number of Lionfish
So,
[tex]\begin{gathered} 9000=P_0\cdot(1+0.69)^1 \\ 9000=P_0\cdot1.69 \\ P_0=\frac{9000}{1.69}\approx5325 \end{gathered}[/tex]Part (A), we will write an explicit formula f(n) that represents the number of lionfish after n years
so, the formula will be:
[tex]f(n)=5325\cdot1.69^n[/tex]Part (B): we will find the number of lionfish after 6 years
so, substitute with n = 6 into the equation of part (a)
[tex]f(6)=5325\cdot1.69^6=124,073[/tex]So, after 6 years, the number of lionfish = 124,073
Part (C): The scientists remove 1400 fish per year after the first year
So, we the number of lionfish:
[tex]9000-1400=7600[/tex]Then after 2 years, the number of lionfish
[tex]7600\cdot1.69-1400[/tex]After 3 years:
[tex]\begin{gathered} (7600\cdot1.69-1400)\cdot1.69-1400 \\ =7600\cdot1.69^2-1400\cdot1.69-1400 \\ =7600\cdot1.69^2-1400\cdot(1+1.69) \end{gathered}[/tex]So, after (n) years:
[tex]7600\cdot1.69^{n-1}-1400\cdot(1+1.69)^{n-2}^{}[/tex]y=4x+6slope: 4y-int: (0,6)why after graphing y-int, is the second point on the line given a slope of 4/1? shouldn't it be 4,0?
The given line is,
[tex]y=4x+6[/tex]Here, the slope is, 4 and y intecept is 6.
For x = 4, we have,
[tex]y=4\times4+6=16+6=22[/tex]Therefore, the two points on the graph is, (0, 6) and (4, 22).
Now, for y = 1, we have,
[tex]\begin{gathered} 1=4x+6 \\ 4x=-5 \\ x=-\frac{5}{4} \end{gathered}[/tex]A graph shows three linear relationships but different y y-intercepts the following slopes line1: 1 / 5 line 2: 3/5 line 3: 6 / 5 write an equation for each line type your answers in the boxes below
Explanation
Step 1
we have 3 lines, the slopes and the Y-intercept( or a point of the line)
use :
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{where} \\ P1(x_1,y_1) \\ \text{and m is the slope} \end{gathered}[/tex]Step 2
Let
[tex]\begin{gathered} \text{slope}=\frac{1}{5} \\ P(0,5)\text{ gr}een \\ \text{replacing} \\ y-5=\frac{1}{5}(x-0) \\ y=\frac{1}{5}x+5\text{ Equation(1) ( gre}en) \end{gathered}[/tex]Step 3
[tex]\begin{gathered} \text{slope}=\frac{3}{5} \\ P(0,7) \\ \text{replacing} \\ y-y_1=m(x-x_1) \\ y-7=\frac{3}{5}(x-0) \\ y=\frac{3}{5}x+7\text{ function (2) Blue} \end{gathered}[/tex]Step 4
[tex]\begin{gathered} \text{slope}=\frac{6}{5} \\ P(0,3)\text{red} \\ \text{replacing} \\ y-y_1=m(x-x_1) \\ y-3=\frac{6}{5}(x-0) \\ y=\frac{6}{5}x+3\text{ Function (3) red} \end{gathered}[/tex]I hope this helps you
Combine like terms to simplify the expression: 1.17 -0.07a + (-3.92a) 1.17 - 3.850 Stuck? Watch a video or use a hint.
The given expression is
[tex]1.17-0.07a+(-3.92a)[/tex]Observe that -0.07a and -3.92a are like terms, let's add them.
[tex]\text{1}.17-3.99a[/tex]Hence, the final expression is 1.17 - 3.99a.What is the value of x? 830 R 620 5х-130 6x – 360
Question:
Solution:
The entire circumference is equivalent to traveling 360 degrees. Therefore, we have the following equation:
[tex]83+62+(5x-13)+(6x-36)\text{ = 360}[/tex]this is equivalent to:
[tex]83+62-13-36+(5x+6x)\text{ = 360}[/tex]this is equivalent to:
[tex]96\text{ +11x = 360}[/tex]this is equivalent to:
[tex]11x\text{ = 360-96 = 297}[/tex]and solving for x, we obtain:
[tex]x\text{ = }\frac{264}{11}=\text{ 2}4[/tex]then, the correct answer is:
[tex]x\text{ = 2}4[/tex]Without dividing how can you decide whether the quotient of 7.16 ÷ 4 will be less than or greater than 2
Answer:
Hope this helps : )
Step-by-step explanation:
We know that the quotient of 7.16 ÷ 4 can be multipled with 4 to get 7.16. So if we multiply 4 × 2, then the product is 8. Now we know that the quotient of 7.16 ÷ 4 is less than 2.
Check:
7.16 ÷ 4 = 1.79
1.79 < 2 ✓
Is the ordered our (-2,8) a solution to: y-9=3x
It is not a solution
1) To get to know that, we need to plug it in the equation and check whether it is true or false.
2) Picking point (-2,8) and plugging -2 into x and 8 into y, we get:
[tex]\begin{gathered} y-9=3x \\ (8)-9=3(-2) \\ -1=-6\:False \end{gathered}[/tex]2) Hence, we can tell that (-2,8) is not a solution to that equation
Find the sum of the first three terms of the geometric series represented by the formula an = (825)(52)(n - 1).
ANSWER:
2nd option: 78/25
STEP-BY-STEP EXPLANATION:
We have the following geometric series:
[tex]a_n=\left(\frac{8}{25}\right)\cdot\left(\frac{5}{2}\right)^{\left(n-1\right)}[/tex]We calculate the sum, replace n by 1,2,3, just like this:
[tex]\begin{gathered} s_n=\left(\frac{8}{25}\right)\cdot\left(\frac{5}{2}\right)^{\left(1-1\right)}+\left(\frac{8}{25}\right)\cdot\left(\frac{5}{2}\right)^{\left(2-1\right)}+\left(\frac{8}{25}\right)\cdot\left(\frac{5}{2}\right)^{\left(3-1\right)} \\ s_n=\left(\frac{8}{25}\right)\cdot\left(\frac{5}{2}\right)^0+\left(\frac{8}{25}\right)\cdot\left(\frac{5}{2}\right)^1+\left(\frac{8}{25}\right)\cdot\left(\frac{5}{2}\right)^2 \\ s_n=\frac{8}{25}+\frac{4}{5}+\frac{8}{4} \\ s_n=\frac{32+80+200}{100} \\ s_n=\frac{312}{100} \\ s_n=\frac{78}{25} \end{gathered}[/tex]The sum of the first 3 terms is 78/25
(c) When the local time in Athens is 09 00, the local time in Berlin is 08 00.
A plane leaves Athens at 13.15
It arrives in Berlin at 1505 local time.
(i) Find the flight time from Athens to Berlin.??
Answer:
l _ to the cinema at least a week
The flight time from Athens to Berlin is 50 minutes as per the given data.
What is local time?Local time refers to the time in a specific location or time zone. It is the time that is used and observed by people in a particular region or city.
To find the flight time from Athens to Berlin, we need to calculate the time difference between the two cities and subtract it from the elapsed time between the departure and arrival times.
Athens is one hour ahead of Berlin when it is 9:00 AM in Athens, it is 8:00 AM in Berlin. This means that when the plane leaves Athens at 13:15 local time, it is 12:15 in Berlin.
The elapsed time between the departure time (13:15) and the arrival time (15:05) is 1 hour and 50 minutes.
However, we need to account for the time difference between the two cities. Since Berlin is one hour behind Athens, we need to subtract one hour from the elapsed time:
1 hour and 50 minutes - 1 hour = 50 minutes
Therefore, the flight time from Athens to Berlin is 50 minutes.
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The box-and-whisker plot below represents some data set. What percentage of the data values are greater than 80?
Answer:
25%
Explanation:
In the given box-and-whisker plot, the third quartile, Q3 = 80.
The percentage of data values that are greater than the third quartile is 25%.
Therefore, the percentage of the data values greater than 80 is 25%.
Persent to a decinal 7%.
To express a percentage as decimal numbers you have to make the following convertion:
Consider that 100% is equal to 1, use cross multiplication to convert 7%:
100%____1
7%____x
[tex]x=\frac{7\cdot1}{100}=\frac{7}{100}=0.07[/tex]So, remember, to transform any percentage in decimal numbers, just divide it by 100.
The average price of a new home in a neighborhood in thousands of dollars (f(x)) is related to the number of years since the neighborhood was built (x) in the function: Use the graph of the function to describe its domain.A. The domain is the average price of homes in a new neighborhood, which is represented by all real numbers from 0 to 100B. The domain is the average price of homes in a new neighborhood, which is represented by all real numbers from 0 to infinity C. The domain is the number of years since the neighborhood was built, which is represented by all real numbers from zero to infinityD. The domain is the number of years since the neighborhood was built, which is represented by all real numbers from 0 to 100l
As given by the question
There are given that the graph of the function.
Now,
According to the domain concept, the domain is defined for the input valuewhich is given in the x-axis.
That means, all x-axis input value range is called domain.
Then,
From the given graph:
The domain is the number of years since the neighborhood was built, that represent the range of x-axis 0 ti infinity.
Hence, the correct option is C.
Which of the following pairs of points define a line segment parallel to the x-axis?A. (4,3)(-4,3)B. (4,3)(4,-3)C. (-4,-3)(4,-3)D. (3,4)(-3,-4)
EXPLANATION:
1.We must first locate the pairs of points.
-Points A:
You deposit $75 in an account that earns simple interest at an annual rate of 5% . How much money is in the account after 3 years?
The account balance in the account $86.25 after 3 years by using simple interest.
What is the simple interest?
Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
The formula of the simple interest is I = PRt.
P = Principal
R = Rate of interest per year
t = time
In the given question Principal = $75, R = 5% = 0.05, t = 3 years.
I = 75 × 0.05 × 3 = 11.25
The account balance after 3 years will be sum of principal and interest.
The account balance after 3 years is = $(75 + 11.25) = $ 86.25.
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A starship is orbiting lax, a large moon of the planet sylow II. The ships sensor array detects that the temperature on the surface of the moon is -12.3 f. What is the temperature in degrees Celsius
The temperature in degrees celsius of the surface of the moon is -24.6111.
Fahrenheit and Celsius are directly proportionate to one another due to their relationship. When the temperature rises on the Celsius scale, it likewise rises on the Fahrenheit scale. Similar to how the Celsius scale, the Fahrenheit scale similarly drops in temperature when the Celsius scale does.
The ships sensor array detects that the temperature on the surface of the on is -12.3 F.
To convert the Fahrenheit to Celsius we will use the given formula.
[tex]C=\frac{5}{9}(F-32)[/tex]
Given F=-12.3
Substituting F in the equation, we get
[tex]C=\frac{5}{9}(-12.3-32)[/tex]
[tex]C=\frac{5}{9}(-44.3)[/tex]
[tex]C=\frac{-221.5}{9}[/tex]
[tex]C=-24.6111[/tex]
Therefore, the temperature -12.3 f to Celsius is -24.6111 C on the surface of the moon.
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(−2,1) is a solution to the following system of linear equations6−3=−152+=−3
We have the following system of linear equations:
[tex]\begin{gathered} 6x-3y=-15 \\ 2x+y=-3 \end{gathered}[/tex]We want to know if the pair (x,y) = (-2,1) is a solution of the system above.
To see if this pair is a solution, we simply replace the values of x and y in the equations above and we verify if the equality holds.
1) Replacing in the first equation we see that:
6x - 3y = 6*(-2) - 3*(1) = -12 -3 = -15 ✓
The equality holds.
2) Replacing in the second equation we see that:
2x + y = 2*(-2) + 1 = -4 + 1 = -3 ✓
The equality holds.
We conclude that (-2,1) is a solution to the system of linear equations.
Answer: True