Answers
The function y = 0.4(1.06)^t represents exponential growth function and rate of change is 6%.
What is exponential growth function?A function called exponential growth depicts population growth that happens consistently over time. You can assume that data increases exponentially when populations double or triple in size.
Exponential decay, which occurs when data contracts rather than expands, is the opposite of exponential growth.
A function of the form [tex]y=a(1 - r)^t[/tex], where a > 0and 0 < r < 1, is an exponential decay function.
A function of the form [tex]y=a(1 +r)^t[/tex], where a > 0 and r > 0, is an exponential growth function.
As 1.06 > 1,
y = 0.4(1.06)^t is an exponential growth function and the
growth factor = 1 + r
= 1 + 0.06
Percent rate of change = 0.06
= 6/100 × 100%
= 6%
Thus, the function y = 0.4(1.06)^t represents exponential growth function and rate of change is 6%.
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Related Questions
Use the Law of Sines to solve (if possible) the triangle for the value of c. Round answers to the nearest tenths. A = 27.5°, a = 15.0 cm, b = 36.4 cm
Answers
The law of sines cannot be used to calculate the side c.
How to solve for side c?The given parameters are:
A = 27.5°, a = 15.0 cm, b = 36.4 cm
Based on the above values,
The law of sines cannot be used to calculate the side c.
This is so because the angle C is not given
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The fatal crash rate of teenage drivers 16 years of age is nearly twice as high at night. Select one: True False
Answers
TRUE
The fatal accident rate for young drivers aged 16 to 19 is about four times higher than at night. Two or more passengers of the same age triple the risk of a fatal accident driving a teenager.
An accident in which someone dies. Synonyms: Accident. Type: Collateral damage.
Of the collisions between cars, angled collisions are the most deadly (about 8,000 in 2020). The interactive chart also shows the estimated number of fatalities, injuries, casualties, and all accidents in different types of car accidents.
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Let’s apply this understanding to situations when we’re given the context and function.
A new species of fish is released into a lake, and the fish multiply quickly. The growth of their population is modeled by the exponential function ()=5 where is the time in weeks after the release and is a positive unknown base. According to the model, how many fish of the new species were released initially?
Answers
The function [tex]P(t)=5(b)^t[/tex], The initial number of fish species released was 5.
The function [tex]S(t)=152(1.045)^t[/tex], The growth rate is 4.5%
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
An exponential function is in the form:
y = abˣ
Where a is the initial value and b is the multiplication factor.
Given the function [tex]P(t)=5(b)^t[/tex], The initial number of fish species released was 5.
The function [tex]S(t)=152(1.045)^t[/tex], The growth rate is 4.5%
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Which letter has point symmetry?
Answers
Answer:
Letters A, M, and T
Step-by-step explanation:
All of these letters have a point of symmetry.
Answer: m
Step-by-step explanation:
12 / (2+1) + 6 * 2 please help me and include steps i am not sure where to go or this
Answers
Answer:
12 / (2+1) + 6 * 2 = 16 (The answer is 16)
Step-by-step explanation:
Step 1: Calculate within parentheses ( 2 + 1 ) : 3
= 12/3 + 6 * 2
Step 2: Multiply and divide (left to right) 12/3 : 4
= 4 + 6 * 2
Step 3: Multiply and divide (left to right) 6 * 2 : 12
= 4 + 12
Step 4: Add and subtract (left to right) 4 + 12 : 16
= 16
Hope this helps out!
Find the surface area of the prism. Round to the nearest tenth if necessary.
Answers
The surface area of the prism is 544 mm²
How to determine the surface area
The formula is given thus;
SA=2B+ph
Where
B = area of the base
p = perimeter of the base
h = height
B = 1/2 h(b1+b2)
B = [tex]\frac{1}{2} * 8 * (17 + 9)[/tex]
B = 108 mm²
Perimeter = sum of length of sides
Perimeter = 17 + 9 + 15
Perimeter = 41 mm
Surface area = 2 ( 108 ) + 41 ( 8)
Surface area = 216 + 328
Surface area = 544 mm²
Thus, the surface area of the prism is 544 mm²
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24. A dealer paid 72 cents for a fountain pen listed at 90 cents. What was the rate of discount allowed him? (A) 5% (B) 2% (C) 8% (D) 20%
Answers
Answer:
20%
Step-by-step explanation:
To find the percentage of change find the difference between the two numbers, divide by the original number, then multiply by 100.
Find difference
90-72=18
Divide difference by original
18/90=0.2
Multiply by 100
0.2*100=20
A family arrives home at 01:10 after a journey that took 7 1/2 hours . At what time of the pervious day did bay start their journey ?
Answers
Answer:
they started their journey at 5:40
Solve for m.
[tex] \frac{5}{4 - m} = \frac{ - 3}{m + 2}[/tex]
A. [tex] - \frac{11}{3} [/tex]
B. [tex] - 11[/tex]
C. [tex] - \frac{7}{3} [/tex]
D. [tex] - 3[/tex]
Answers
Hello,
[tex] \frac{5}{4 - m} = \frac{ - 3}{2 + m} [/tex]
[tex]5(2 + m) = - 3(4 - m)[/tex]
[tex]10 + 5m = - 12 + 3m[/tex]
[tex]5m - 3m = - 12 - 10[/tex]
[tex]2m = - 22[/tex]
[tex]m = \frac{ - 22}{2} [/tex]
[tex]m = - 11[/tex]
→ Answer B
Variable m cannot be equal to any of the values −2,4 as division by zero is undefined. Multiply both sides of the equation by (m − 4)(m + 2), the lowest common denominator of 4−m,m + 2.
−(2 + m) ×5 = (m −4 )( −3 )To find the opposite of 2+m, find the opposite of each term.
(−2 −m) ×5 = ( m−4 )( −3 )Use the distributive property to multiply −2−m by 5.
−10 −5m = ( m−4 )( −3 )Use the distributive property to multiply m−4 by −3.
−10 −5m =−3m + 12Add 3m to both sides.
−10 − 5m + 3m =12Combine −5m and 3m to get −2m.
−10 −2m = 12Add 10 to both sides.
−2m = 12 + 10Add 12 and 10 to get 2.
−2m = 22Divide both sides by −2.
m = 22 / -2Divide 22 by −2 to get −11.
m = −11Therefore, the correct option is "B".
Suppose the daily customer volume at a call center has a normal distribution with mean 4,900 and standard deviation 700. What is the probability that the call center will get fewer than 4,400 calls in a day
Answers
The probability that the call center will get fewer calls than 440 is 0.26115.
Given mean of 4900 and standard deviation of 700.
We have to calculate the probability that the call center will get fewer than 4400 calls.
Probability lies between 0 and 1.
μ=4900
σ=700
We can apply z as well as t statistics because the sample size is not given.
We are applying z statistics.
P(X<4400)=0.5-P(4400<X<4900)
z=X-μ/σ
where μ= mean
σ=standard deviation
z=4400-4900/700
=-500/700
=-0.71
p value of -0.71 is 0.23885.
So the p value of calls less than 4400 is 0.5-0.23885=0.26115.
Hence the probability that the call center will get calls less than 440 is 0.26115.
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PLEASE HELP
If two lines are perpendicular, then the lines intersect to form four right angles that are 180° each.
False O True
Answers
Answer:
False
Step-by-step explanation:
[If two lines are perpendicular, then the lines intersect to form four right angles] It's true up till here, but a right angle is 90 degrees, not 180 degrees
Please help me ASAP!! I really appreciate it
Answers
Answer:
a = -1
Step-by-step explanation:
1. Subtract [tex]\frac{2}{3}[/tex] from both sides.
[tex]6a=-\frac{16}{3} - \frac{2}{3}[/tex]
2. Solve the side after the equal sign.
[tex]6a=-6[/tex]
3. Divide 6 from both sides.
[tex]a=-1[/tex]
4. Hope this helped!
[tex]:)[/tex]
The probability that a professor in the business department is full time is 30%. If we randomly select 9 professors; What is the probability that 3 or fewer of them are FULL TIME
Answers
The probability that a professor in the business department is full time is [tex]30[/tex]%. If we randomly select [tex]9[/tex] professors; the probability that [tex]3[/tex] or fewer of them are FULL TIME is [tex]10[/tex]%
How can find the probability of full time ?
Probability of selecting [tex]3[/tex] from [tex]9[/tex]people = [tex]3/9[/tex]
Probability of selecting [tex]2[/tex] people= [tex]2/9[/tex]
Probability of selecting [tex]1[/tex] people=[tex]1/9[/tex].
Probability of selecting up to to 3 people is [tex]1/9+2/9+3/9 = 6/9[/tex].
Every person who got selected is full time person has probability [tex]0.3[/tex]
=> For selection of people up to [tex]3[/tex] is
[tex]=\frac{3}{9} *0.3\\=0.1\\[/tex]
[tex]=10[/tex]%
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WILL GIVE BRAINLEST!!!!
Find the measure for the unknown angle.
Answers
The measure for the unknown angle is 65 degrees.
What is the measure for the unknown angle?
The two perpendicular lines form a right angle. A right angle would always have a value of 90 degrees.
In order to determine the unknown angle, subtract 25 degrees from 90 degrees.
90 - 25 = 65 degrees
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Can someone help mw please :)
Answers
The following graph shows the tons of sugar Bel sugar mill fabricated from its opening day in 2008 to 2013
Answers
A journalist's statement about this piece of information after analyzing the data could be (a) the owner made a mistake because the rate is constant
How to determine the Journalist statement about this piece of information after analyzing the data?From the question, we have the following highlights:
Year = 2008 to 2013 (this represents the domain)Owner's claim: Production increased at an exponential rateFrom the graph attached to the question, we can see that the graph that shows the tons of sugar Bel sugar mill fabricated from its opening day in 2008 to 2013 is a linear graph
This is so because the points on the graph are connected by a straight line.
Linear graphs have constant rate
Hence, a journalist's statement about this piece of information after analyzing the data could be (a) the owner made a mistake because the rate is constant
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Complete question
The following graph shows the tons of sugar Bel sugar mill fabricated from its opening day in 2008 to 2013. The owner of the sugar mill said in an interview that the production increased at an exponential rate since the inauguration. What would a journalist say about this piece of information after analyzing the data?
The graph below represents which type of power function of the form y = kx'?
Direct Variation with an odd r-value & a positive k-value
O Direct Variation with an even r-value & a positive k-value
Inverse Variation with an odd r-value & a negative k-value
O Inverse Variation with an even r-value & a positive k-value
Answers
The graph represents the type of power function of the form y = kx in the form of D. Inverse Variation with an even r-value & a positive k-value.
How to illustrate the graph?It should be noted that a graph simply means a diagrammatic representation of a particular thing.
Here, the function of the for y = kx is illustrated in the graph.
This is an inverse variation with an even r-value and a positive k-value.
In conclusion, the correct option is D.
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JJ decided to leave a tip that is 15% of the original price for his meal. How much should he leave as tip for the $5.50 cheeseburger and $2.50 milkshake? Express you answer to the hundreaths place.
Answers
If JJ decided to leave a tip that is 15% of the original price for his meal, he should leave $1.2 as tip for the $5.50 cheeseburger and $2.50 milkshake.
How to calculate discount?According to this question, JJ bought a $5.50 cheeseburger and a $2.50 milkshake.
This means that in total, JJ purchased $5.50 + $2.50 = $8 worth of meal.
If he decided to leave a tip that is 15% of the original price of his meal, hence,
15/100 × $8 = $1.2
Therefore, if JJ decided to leave a tip that is 15% of the original price for his meal, he should leave $1.2 as tip for the $5.50 cheeseburger and $2.50 milkshake.
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Suppose there is a triangle with sides a, b, and c and angles A, B, and C. Using the known given information below and the law of cosines, what is the measure of angle C? Round your answer to the nearest whole number, if necessary.
A=29
C=24
B=101
Answers
The measure of angle C is obtained as 35 degrees
What is the angle C?Give that;
b^2 = a^2 + c^2 - 2ac Cos B
a = 29
c = 24
B = 101 degrees
b^2 = (29)^2 + (24)^2 - [2 * 29 * 24 cos 101]
b^2 = 841 + 576 + 266
b = 41 cm
Now;
b/sinB = c/sinC
bsinC = csinB
sinC = csinB/b
sinC = 24 * sin 101/41
C = sin-1(24 * sin 101/41)
C = 35 degrees
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40 points please help
Answers
Answer:
five number summary is a specially useful in the scriptive analysing what during the premier league investigation of a large data set a summary consists of 5 values of the most extreme values in data set the maximum and minimum values of the lower and upper quality and the meridian
v(t)=37,036(0.84)¹ What is the initial cost of the car, and what will the car be worth after 4 years? Round to the nearest whole number.
Answers
The initial value is 37,036 dollars and in 4 years, the value will be 18,439.16 dollars.
How to work with the exponential decay equation?Here we have an exponential decay that models the value of a car as time passes, the exponential decay is:
[tex]v(t) = 37,036*(0.84)^t[/tex]
The initial value is what we get when we evaluate in t = 0.
[tex]v(0) = 37,036*(0.84)^0 = 37,036[/tex]
The initial value is 37,036 dollars.
The value in 4 years is what we get when we evaluate in t = 4:
[tex]v(4) = 37,036*(0.84)^4 = 18,439.16[/tex]
In 4 years, the value will be 18,439.16 dollars.
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PLEASE I NEED HELP ON THIS QUESTION
Answers
Answer:
Option c is the correct answer
Step-by-step explanation:
distance of satrun - distance of jupiter
Where is the horizontal center of mass of the entire upper extremity?
Answers
Answer:
can you tell me please
Step-by-step explanation:
nicest
Determine the measure of the indicated angle in the following triangle:
Answers
Answer:
Θ ≈ 58°
Step-by-step explanation:
using the Cosine Rule in the triangle
cosΘ = [tex]\frac{80^2+60^2-70^2}{2(80)(60)}[/tex] = [tex]\frac{64000+3600-4900}{9600}[/tex] = [tex]\frac{5100}{9600}[/tex] = [tex]\frac{51}{96}[/tex] , then
Θ = [tex]cos^{-1}[/tex] ( [tex]\frac{51}{96}[/tex] ) ≈ 58° ( to the nearest degree )
The line l cuts the y-axis at (0, 5). l also passes through the point (2, 1). find the equation of the line which is parallel to l and which passes through the point (3, 0).
Answers
Answer: [tex]y=-2x+6[/tex]
Step-by-step explanation:
The slope of line l is
[tex]\frac{5-1}{0-2}=-2[/tex]
Since parallel lines have the same slope, the slope of the line we need to find is -2.
Substituting into point-slope form,
[tex]y=-2(x-3)\\\\y=-2x+6[/tex]
By using a number line, arrange each of the each of the following in descending order (a) 4 29upon 33, -2.365,5.5,-3 upon 4 (b) 5 upon 8,-8, 10 1 upon 2 , 5.855, - 2π
Answers
The arrangement of the numbers in descending order (largest to smallest) are as follows;
a). 5.5, 4, 29/33, -3/4, -2.365b). 10, 5.855, 5/8, 1/2 -2π, -8What is the arrangement of the numbers in descending order in each case?It follows from convention that the positive numbers are larger than negative numbers and hence, should appear before negative numbers when the arrangement is in descending order.
Consequently, the numbers can be evaluated and arranged as in the answer above with positive numbers increasing rightwards and negative numbers decreasing leftward of 0 on the number line.
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- What is the value of x in the figure
(5x)
140
Answers
Answer:
Step-by-step explanation:
5x = 140
= x = 140/5
= x = 28
Sarah has just opened her own nail salon. Based on experience, she knows that her daily profit, P, can be modelled by = −122 + 168 − 510, where x is the number of clients per day. How many clients should she book each day to maximize her profit?
Answers
Answer:
Step-by-step explanation:
p=-12x^2 + 168 - 510
isolate the varible by diveding each side by factors that dont conatin the varible
x= square root of -p+342/3/2
x= - square root of -p+ 342/3/2
I hope this has helped if you need any clarfcation just ask
Luiza wants to go on a popular talent TV show. In order to be accepted, her audition must get at least 60%
positive votes from the people in the crowd. She was afraid she will not get enough votes, so she made a
video of her act and showed it to 60 random people from the crowd before the show. 50% of the people
said they would vote for her.
Let's test the hypothesis that the actual percentage of positive votes among the crowd is 60% versus the
alternative that the actual percentage is lower than that.
The table below sums up the results of 1000 simulations, each simulating a sample of 60 votes, assuming
there are 60% positive votes.
According to the simulations, what is the probability of getting a sample with 50% positive votes or less?
Let's agree that if the observed outcome has a probability less than 1% under the tested hypothesis, we
will reject the hypothesis.
What should we conclude regarding the hypothesis?
Choose 1 answer:
We cannot reject the hypothesis.
We should reject the hypothesis.
Answers
We cannot reject the null hypothesis as the p value is less than 0.01.
How to illustrate the hypothesis?From the information given, Luiza wants to go on a popular talent TV show and in order to be accepted, her audition must get at least 60% positive votes from the people in the crowd.
The observed outcome also has a probability less than 1% under the tested hypothesis. Based on the information, the test statistic will be - 1.58.
After this, this will be checked under the standard normal distribution table where the p value will be 0.0571.
Based on this information, we cannot reject the null hypothesis as the p value is less than 0.01.
In conclusion, the correct option is that we cannot reject the hypothesis.
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Solve for x: -8 < 3x +1 < 13
Answers
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{-8 < 3x+1 < 13 }} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{-8+-1 < 3x+1+-1 < 13+-1 \ (Add \ -1 \ to \ all \ parts) }} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{-9}{3} < \frac{3x}{3} < \frac{12}{3} \ (Divide \ all \ parts \ by \ 3) }} \end{gathered}$}[/tex]
[tex]\red{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{-3 < x < 4 }} \end{gathered}$} }}[/tex]