Answer:
The best interpretation of one of the values of the function is that the rate increases by 12% each day.
Step-by-step explanation:
Given:
F(x)=245(1.12)^x
To Find:
statement is the best interpretation of one of the values of the function
Solution:
Depending upon the values given the statement can be developed
As the function is itself the exponential growth structure ,
In this the statement ,Growth can be significantly depends on all factor
Such as time period initial value and rate.
But here the formula is simplified as ,
[tex]P=A(1+r)^t[/tex]
Here A= initial value r=rate and t =time period
Here A=245 and 1+r=1.12
i.e r=0.12 i.e 12%
Hence the rate give the best interpretation and more information about the function and scenario.
The function f(x)=245(1.12)^x models the exponential growth of bacteria in a sample over x days, with the base 245 being the initial number and 1.12 representing the daily growth rate.
Explanation:The function f(x)=245(1.12)^x describes the exponential growth of bacteria, where the base number (245) represents the initial amount of bacteria and 1.12 indicates the growth rate per day.
For example, if we want to determine the number of bacteria at the end of the first day (x=1), we substitute 1 into the function to get f(1)=245(1.12)^1, which would give us the total number of bacteria at the end of day one.
The exponent x stands for the number of days and shows how the population grows at an increasing rate over time, which is a signature characteristic of an exponential function in a context like bacterial growth.
A can of cat food has a diameter of 8 cm. Which measurement is the best estimate for the circumference of the cat food inside the can?
Answer:
ok The circumference of a circle is 2πr or πD if diameter is given.
The answer is 25.13 cm
Step-by-step explanation:
Now method 1:
C=2πr
So finding for radius in this equation=diameter/2
8/2=4 cm
So now 2 × 22/7 × 4
176/7=25.13 cm
OR
C=πD
22/7 × 8
176/7=25.13 cm
of 100 students, 32 are taking Calculus, 29 are taking French, and 13 are taking both Calculus and French, if a student is picked at random
what is the probability that the student is taking Calculus or French?
(Reduce fraction to lowest form)
Step-by-step explanation:
The total number of students = 100
Let A represents calculus and B represents French
The no of students taking calculus = 32
The no of students taking French = 29
The no of students taking calculus and french = 13
the probability that the student is taking Calculus or French = ?
P (AUB) = P(A) + P(B) - P(A∩B)
= [tex]\frac{32}{100}[/tex] + [tex]\frac{29}{100}[/tex] - [tex]\frac{13}{100}[/tex]
= [tex]\frac{48}{100}[/tex]
Reducing to lowest fraction, it becomes [tex]\frac{12}{25}[/tex]
The probability that the student is taking Calculus or French = [tex]\frac{12}{25}[/tex]
The probability that a randomly selected student is taking Calculus or French is 12/25.
To find the probability that a randomly picked student is taking either Calculus or French, we use the principles of set theory, specifically the formula for the union of two sets:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Here,
A = Students taking Calculus = 32
B = Students taking French = 29
A ∩ B = Students taking both Calculus and French = 13
Total students = 100
The formulas for the probabilities are:
P(A) = 32/100
P(B) = 29/100
P(A ∩ B) = 13/100
Now substitute these values into the union formula:
P(Calculus or French) = 32/100 + 29/100 - 13/100 = 48/100 = 12/25
Therefore, the probability that a randomly picked student is taking either Calculus or French is 12/25.
As a centerpiece for her design, Hevesh build a tower 72 inches tall made of dominoes that are 2 2/5 inches tall. How many rows of dominoes stacked on top of each other tower have
Answer:
72 divided by 2 2/5 (or 2.4) = 30 in a row
Answer:
the answer is 30 in a row
Step-by-step explanation:
divide 72 by 2 2/5 and you get 30 in a row of the domino's
The cost of a jacket increased from $70.00 to $82.60. What is the percentage increase of the cost of the jacket?
Answer:
18%
Step-by-step explanation:
Say that the percent increase was x%. So, we can write this problem as:
70 + x% * 70 = 82.60
Remember that % means "out of 100", so x% is actually the same as x/100. We can then replace x% with x/100:
70 + (x/100) * 70 = 82.60
Both terms on the left side have 70, so we can factor that common number out:
70 * (1 + (x/100)) = 82.60
Divide both sides by 70:
1 + x/100 = 82.60/70 = 1.18
Subtract 1 from both sides:
x/100 = 0.18
Multiply by 100:
x = 18
Thus, the percent increase is 18%.
Hope this helps!
Answer:
18%
Step-by-step explanation:
Increase: 12.6
12.60/70 = 0.18
Your answer: 15.26%
A 13 ft ladder leaning against a building touches the building exactly 12 feet above the ground. How far is the building is the base of the ladder round to the nearest hundredth foot
............................
8=8a-4(a + 8) what is the answer
Answer:
Step-by-step explanation:
8=8a-4(a+8) => 8=8a-4a-32 =>4a=40 => a=10.
If you meant 8=(8a-4)(a+8), then it is 8a^2+60a-32=8 => 8a^2+60a-40=0.
Use the quadratic formula, to get your answer.
after graphing 4x-2y=5 and y=x, in how many points do they intersect
Answer:
1 at (2.5, 2.5)
Step-by-step explanation:
you can try graphing it on desmo
Solve the system by the substitution method.
7x + 8y = -22
3x - y = 26
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The solution set is { } (Type an ordered pair.)
O B. There are infinitely many solutions.
O C. There is no solution.
Answer:
A) The solution set is (6,-8).
Step-by-step explanation:
3x - y = 26
-3x - 3x Subtract 3x from both sides
-y = -3x + 26 Divide both sides by -1
y = 3x - 26
Now plug this into 7x + 8y = -22 to solve for x
7x + 8(3x - 26) = -22 Distribute
7x + 24x - 208 = -22 Combine like terms
31x - 208 = -22
+ 208 + 208 Add 208 to both sides
31x = 186 Divide both sides by 31
x = 6
Plug this into y = 3x - 26 to solve for y
y = 3(6) - 26 Multiply
y = 18 - 26 Subtract
y = -8
If this answer is correct, please make me Brainliest!
Final answer:
The system of equations is solved using the substitution method, resulting in x = 6 and y = -8. Hence, the correct choice is the ordered pair (6, -8).
Explanation:
To solve the system of equations by the substitution method, let's start by solving the second equation for y:
3x - y = 26
=> y = 3x - 26.
Now, substitute this expression for y into the first equation:
7x + 8(3x - 26) = -22
=> 7x + 24x - 208 = -22
=> 31x = 186
=> x = 6.
Now, substitute x back into the expression we found for y:
y = 3(6) - 26
=> y = 18 - 26
=> y = -8.
The solution to the system is the ordered pair (6, -8), which means the correct choice is:
O A. The solution set is { (6, -8) } (Type an ordered pair.)
Which statement is true of a rectangle that has an area of 4x^2 +39x-10 square units and a width of (x+10) units
Answer: ( C ) The perimeter of the rectangle is (10x+18) Units
Step-by-step explanation: This is the right answer because I just checked and I did the math
Answer:
it is c i had the same problem
Step-by-step explanation:
4. Use a proportion to find the length of the missing side in the following similar figures. (1 point)
10 cm
22 cm
x= 28 cm
x= 30.8 cm
x= 6.4 cm
X = 19 cm
Answer:
x = 19cm
Step-by-step explanation:
use pythagorean theorem:
a² - c² = b²
10² - 22² = b²
100 - 484 = b²
384 = b²
√384 = b
19cm = b or x
Answer:
30.8cm
Step-by-step explanation:
i am from connexus 8th grd pre algrabra
unit 5 lesson 3
1. 1:2
2. C. yes they are similar they have porportional side lengths and = ange measures
3. x = 4.5m
4. x = 30.8cm
5. x = 6 m
i hope this helps! = ) <3
You have a drawer with five pairs of white socks, three pairs of black socks, and one pair of red socks. You choose one pair of socks at random each morning, starting on Monday. You do not put the socks you choose back in the drawer. Find the probability of each event. 3. You select black socks on Monday and white socks on Tuesday.
Answer:
20.8%
Step-by-step explanation:
To find the final probability, two separate events must be done and the final propagation is the multiplication of these, like this:
First event:
Probability of black socks on Monday:
Total pair of socks: 1 + 3 + 5 = 9
Number of black socks on Monday: 3
Thus:
3/9 = 1/3
Second event:
Probability of white socks on Tuesday:
Total pair of socks: 8
Number of white socks on Tuesday: 5
Thus:
5/8
Final probability:
1/3 * 5/8 = 5/24
P = 0.208
So the probability would be 20.8%
The probability of black socks on Monday = 1/3
The probability of white socks on Tuesday = 5/8
The calculation for probability:To find the final probability, two separate events must be done and the final propagation is the multiplication of these, like this:
First event:
Probability of black socks on Monday:
Total pair of socks: 1 + 3 + 5 = 9
Number of black socks on Monday: 3
Thus:
Probability will be: 3/9 = 1/3
Second event:
Probability of white socks on Tuesday:
Total pair of socks: 8
Number of white socks on Tuesday: 5
Thus:
Probability will be: 5/8
Final probability:
1/3 * 5/8 = 5/24
P = 0.208
So, the probability would be 20.8%.
Find more information about Probability here:
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castel invests $7178 in a savings account with monthly compounding. after 7 years, the balance reaches $12,543.00. What is the interest rate of the account?
Answer:
r = 129.1 %
Step-by-step explanation:
Using the compounding formula:
A = P (1 + r/t)^nt
$12, 543 = $7178 (1 + r/12)^12(7)
-7178
$5365 = (1 + r/12)^84
[tex]\sqrt[84]{5365}[/tex] = [tex]\sqrt[84]{(1 +\frac{r}{12})^{84}}[/tex]
1.107642572 = 1 + r/12
(0.108 = r/12) (12)
r = 1.2917 = 129.1 %
Can someone please help
Answer:
x= 52°Step-by-step explanation:
x+90°+33°+165°+20°=360° (complete angle)
x+ 308°=360°
x= 360°-308°
x= 52°
Answer:
x=52
Step-by-step explanation:
So what you would want to do is add up all of the angle measurements given. This give you 308. Now you take this number (308) and subtract it from 360, to give you the answer of 52.
A researcher wishes to estimate the proportion of adults who have high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.04 with 99% confidence if
(a) she uses a previous estimate of 0.52?
(b) she does not use any prior estimates?
Answer:
Step-by-step explanation:
Solution:-
- The sample size = n
- The Error of estimation, E = 0.04
- The confidence level, CI = 99%
a)
What size sample should be obtained when she uses previous estimate of p = 0.52?
- We are given the sample proportion p = 0.52, the required sample size is a function of confidence value and error of estimation (E):
[tex]n = p*( 1 - p ) * (\frac{Z-critical}{E})^2[/tex]
Where,
- The critical value of the confidence level = 99% would be:
significance level ( α ) = 1 - CI = 1 - 0.99 = 0.01
Z-critical = Z_α/2 = Z_0.005 = 2.575
- The required sample size (n) can be calculated:
[tex]n = 0.52*( 1 - 0.52 ) * (\frac{2.575}{0.04})^2\\\\n = 0.2304*(51.5)^2 = 611.0784[/tex]
- Hence, the minimum required sample size (n) should be = 612 adults.
b)
- If the preliminary estimate of proportion is missing or not given, we are to assume the proportion p = 0.5.
- Similarly, repeat the calculations for sample size (n) when p = 0.5
[tex]n = 0.5*( 1 - 0.5 ) * (\frac{2.575}{0.04})^2\\\\n = 0.25*(51.5)^2 = 663.0625[/tex]
- Hence, the minimum required sample size (n) should be = 664 adults.
A cyclinder has a volume of 703 cm3 and a height of 18.5 cm. What can be concluded about the cyclinder? Check all that apply.
The formula for the volume of a cyclinder can be applied to find the area of the base.
To find the area of the base, multiply volume and height.
The radius of the cyclinder is half the height.
The area of the base is 38 cm2.
To verify the solution is correct, substitute the given measures and the solution into the equation and verify the result is a true statement.
Step-by-step explanation:
Cylinder volume = 703 [tex]cm^{3}[/tex], height = 18.5 cm
(i) Volume or area of the cylinder = [tex]\pi r^{2} h[/tex]
The formula for the volume of a cyclinder can be applied to find the area of the base.
Option (i) is correct
(ii) Volume or area of the cylinder = [tex]\pi r^{2} h[/tex]
The volume should be divivded by height to get the area
Option (ii) is wrong
(iv) Area of the base = [tex]\frac{703\pi }{18}[/tex] = 38[tex]\pi cm^{2}[/tex]
Option (iv) is correct
(iii) The radius of the cyclinder is half the height.
[tex]\frac{38}{2}[/tex] = 19 cm not 18.5 cm
Option (iii) is wrong
(v)Area of the base = [tex]\frac{703\pi }{18}[/tex] = 38[tex]\pi cm^{2}[/tex]
Option (v) is correct
Answer:
1 , 4 , & 5 ... which is also a , d, & e
Step-by-step explanation:
Explain how you could use 25% of a number to find the number
Answer:
you know 25% is one fourth of 100%, aka the whole number, so just multiply the 25% of the number times 4 to get the whole number
Which statement is true about the graphs of the two lines y =-4/5x+
2 and y=-5/4x-1/2?
The slopes are the only thing we care about when it comes to determining if the lines are parallel or perpendicular. The y intercepts do not affect the answer, so we can ignore them entirely.
The slopes of the two given equations are -4/5 and -5/4. Note how they are both negative. This means that we do not have perpendicular lines. One slope must be positive and the other negative, for perpendicular lines to form.
Another way to see it: the two slopes must multiply to -1 to have perpendicular lines form. We see that (-4/5)*(-5/4) = 1 instead.
Yet another way to see it: The term "opposite reciprocals" means we flip the fraction and we flip the sign (from positive to negative). The reciprocal part happens, but the sign change does not happen.
The lines are not parallel because the slopes would have to be equal for that to happen.
How does the mean absolute deviation (MAD) of the data in set 1 compare to the mean absolute deviation of the data in set 2?
Set 1: 82, 80, 90
Set 2: 82, 80, 60, 90
1 The MAD of set 1 is 6 less than the MAD of set 2.
2 The MAD of set 1 is 5 less than the MAD of set 2.
3 The MAD of set 1 is 5 more than the MAD of set 2.
4 The MAD of set 1 is 6 more than the MAD of set 2.
Answer:
The MAD of set 1 is 5 less than the MAD of set 2.
Step-by-step explanation:
A Broadway theater has 400 seats, divided into orchestra main, and balcony seating. Orchestra seats sell for $70, main seats for $45, and balcony seats for $35. If all the seats are sold, the gross revenue to the theatre is $18,800. If all the main and balcony seats are sold , but only half the orchestra seats are sold, the gross revenue is $16,000. How many are there of each kind of seat.
Answer:
-80 orchestra seats
-200 main seats
- 120 balcony seats
Step-by-step explanation:
Let x b number of orchestra seats
Let y be number of main seats
Let z be number of balcony seats.
Thus, we have the following equations;
For all seats sold;
70x + 45y + 35y = 18,800 - - - - eq1
For half of orchestra sold;
70•½•x + 45y + 35y = 16,000 - - eq2
For total seats;
x + y + z = 400 - - - - eq3
Solving eq1, eq2 and eq3 simultaneously, we have;
x = 80
y = 200
z = 120
Thus, we have;
-80 orchestra seats
-200 main seats
- 120 balcony seats
(20 points)
Which number can be multiplied with a rational number to illustrate that the product of
two rational numbers is rational
Answer:
The answer would be B) -2 1/8
Step-by-step explanation: i just took the test and i got that right
Answer:
B) -2⅛
Step-by-step explanation:
All other options are irrational
The distance from a ship to two lighthouses on the shore are 4 miles and 7 miles respectively. If the angle between the two lines of sight is 45, find the distance between the lighthouses
Answer:
5 miles
Step-by-step explanation:
In the diagram, the distance between the lighthouse is |AB|=c.
Using Cosine Rule,
c²=a²+b²-2abCos C
=7²+4²-2(4)(7)Cos 45°
=49+16-56cos45°
=25.40
c=√25.40=5.04 miles
The distance between the lighthouses is approximately 5 miles.
Answer:
The distance between the two lighthouse is 5miles
Step-by-step explanation:
Since the shape of the sketch is a right angled triangle we use SOHCAHTOA to solve. An image showing the step by step working is attached.
How would you do this question?
2/3 a = 8
Tom's stockbroker offers an investment that is compounded continuously at an annual interest rate of 3.7%. If Tom wants a return of $25,000, how long will Tom's investment need to be if he puts $8000 initially? Give the exact solution in symbolic form and then estimate the answer to the tenth of a year.
Answer:
It'll take 38.3 years to obtain the desired return of $25,000.
Step-by-step explanation:
In order to solve a continuosly coumponded interest question we need to apply the correct formula that is given bellow:
M = C*e^(r*t)
Where M is the final value, C is the initial value, r is the interest rate and t is the time at which the money was applied. Since he wants an return of $25,000 his final value must be the sum of the initial value with the desired return. So we have:
(25000 + 8000) = 8000*e^(0.037*t)
33000 = 8000*e^(0.037*t)
e^(0.037*t) = 33000/8000
e^(0.037*t) = 4.125
ln[e^(0.037*t)] = ln(4.125)
t = ln(4.125)/(0.037)
t = 1.4171/0.037 = 38.2991
t = 38.3 years
if 3a-2b=8 and a+3b=7 what is the value of 4a+b
Answer:
Step-by-step explanation:
If a + 3b = 7, subtract 3b from both sides of the equation
-3b = -3b then you get
a = 7-3b now plug this into the other equation: 3a-2b=8
3(7-3b) - 2b = 8
21 - 9b - 2b = 8
21 - 11b = 8 add 11 b to both sides
+ 11b +11b
21 = 8 + 11b subtract 8 from both sides
-8 -8
13 = 11b
What is 4a+b?
4(7-3b) + b =
(28 - 12b) + b =
28-11b (from above 13=11b)
28 - 13 = 15
A sample of salary offers (in thousands of dollars) given to management majors is: 48, 51, 46, 52, 47, 48, 47, 50, 51, and 59. Using this data to obtain a 95 percent confidence interval resulted in an interval from 47.19 to 52.61. True or False: The confidence interval obtained is valid only if the distribution of the population of salary offers is normal.
Answer:
Step-by-step explanation:
number of samples, n = 10
Mean = (48 + 51 + 46 + 52 + 47 + 48 + 47 + 50 + 51 + 59)/10 = 49.9
Standard deviation = √(summation(x - mean)/n
Summation(x - mean) = (48 - 49.9)^2 + (51 - 49.9)^2 + (46 - 49.9)^2+ (52 - 49.9)^2 + (47 - 49.9)^2 + (48 - 49.9)^2 + (47 - 49.9)^2 + (50 - 49.9)^2 + (51 - 49.9)^2 + (59- 49.9)^2 = 128.9
Standard deviation = √128.9/10 = 3.59
Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
The sample mean, x is the point estimate for the population mean.
Margin of error = z × s/√n
Where
s = sample standard deviation
From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score
In order to use the t distribution, we would determine the degree of freedom, df for the sample.
df = n - 1 = 10 - 1 = 9
Since confidence level = 95% = 0.95, α = 1 - CL = 1 – 0.95 = 0.05
α/2 = 0.05/2 = 0.025
the area to the right of z0.025 is 0.025 and the area to the left of z0.025 is 1 - 0.025 = 0.975
Looking at the t distribution table,
z = 2.262
Margin of error = 2.262 × 3.59/√10
= 2.57
the lower limit of this confidence interval is
49.9 - 2.57 = 47.33
the lower limit of this confidence interval is
49.9 + 2.57 = 52.47
So it is false
Water drains very slowly from the nearly level ground in the Gulf Prairies and Marshes ecoregion of Texas. How does the slow movement of water impact the ecoregion?
A. Sediment carried in the water causes significant physical weathering.
B. The water increases the amount of sediment eroded by wind.
C. Sediment carried in the slowly moving water is deposited.
D. The slowly moving water erodes sediment.
Answer:
The correct option is;
C. Sediment carried in the slowly moving water is deposited.
Step-by-step explanation:
Here we note that the drainage rate of the water is slow and the plane of the drainage is given as level ground.
Therefore, there would less mass transport of sedimentary materials from the region and the level planes with slow drainage would favor the deposition of sediments along the level plane
From the above, the correct option is C.
Answer:
C
Step-by-step explanation:
Round 2,253 to hundred
Answer:
2300
Step-by-step explanation:
Answer:
2,300
Step-by-step explanation:
When we round to the hundreds place, we make sure the numbers behind the hundreds place are zero. Then we round. Here's the general rule for rounding: If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up. In this case we round the 2 in the hundreds place up to three because it is followed by a five.
An initial population of 7 chipmunks in Mary's yard increases by 6% each year. If the function f(x) = abx models this situation, what is the population of the chipmunks in 5 years? (to the nearest whole number)
Answer: there would be 9 chipmunks after 5 years.
Step-by-step explanation:
An initial population of 7 chipmunks in Mary's yard increases by 6% each year. It means that the population is increasing in an exponential rate.
The function that models the situation is expressed as
f(x) = ab^x
Where
a represents the initial population of chipmunks
b represent the rate of growth
x represent the number of years
From the information given,
a = 7
b = 1 + 6% = 1 + 6/100 = 1.06
x = 5 years
After 5 years,
f(5) = 7 × 1.06^5
f(5) = 9
Which mathematical terms originated from the Arabic mathematician, al-Khwarizmi
Answer:
algorithm
Step-by-step explanation:
It sounds like algorithm.
The mathematical terms that originated from the Arabic mathematician, al-Khwarizmi, are ""algorithm"" and ""algebra.""
Al-Khwarizmi was a Persian mathematician and astronomer who lived in the 8th and 9th centuries. His works were instrumental in the development of algebra and the use of Hindu-Arabic numerals. The term ""algorithm"" is derived from a Latinization of his name, Algoritmi, and originally referred to the numerical methods he described in his treatise on arithmetic.
The word ""algebra"" comes from the Arabic word ""al-jabr,"" which appears in the title of his book ""Kitab al-Jabr wa-l-Muqabala"" (The Compendious Book on Calculation by Completion and Balancing). This book laid the foundations for algebra as a branch of mathematics, and the terms he introduced are still in use today to describe mathematical procedures and the study of equations and algebraic structures.
Which of the following shows the extraneous solution to the logarithmic equation below? log Subscript 3 Baseline (18 x cubed) minus log Subscript 3 Baseline (2 x) = log Subscript 3 Baseline 144
The extraneous solution of the logarithmic problem log₃( 18x³) -log(2x) = log₃144 is -4.
What is Logarithm?A log function is a way to find how much a number must be raised in order to get the desired number.
[tex]a^c = b[/tex] can be written as,
log[tex]_a[/tex]b = c
where a is the base to which the power is to be raised,
b is the desired number that we want when power is to be raised,
c is the power that must be raised to a to get b.
Solving the function using the basic logarithmic value, we get,
log₃( 18x³) -log(2x) = log₃144
log₃ (18x³/2x) = log₃144
log(9x²) = log₃144
Take antilog.
9x² = 144
x = ±4
If we solve further we will get that the value of x can be either -4 or 4, if take the value of x as -4, in the beginning then you will get log₃(18(-4)³) as the log of negative value which is impossible.
Hence, x=-4 is an extraneous solution for the given expression log₃( 18x³) -log(2x) = log₃144.
Learn more about Logarithms:
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