The annual growth rate is 4.73 %
The continuous growth rate is 4.62 %
What is exponential growth function ?
A process called exponential growth sees a rise in quantity over time. When a quantity's derivative, or instantaneous rate of change with respect to time, is proportionate to the quantity itself, this phenomenon takes place.
Let us assume:
The initial amount of 1, so results are 2.
Let x be the percent in decimal form
Growth rate per year:
[tex]1(1+x)^{15} = 2[/tex]
Take ln on both the sides
[tex]ln((1+x)^{15}) = ln(2)[/tex]
15*ln(1+x) =0 .693
ln(x+1) = 0.693/15
ln(x+1) = 0.04621
Take anti ln on both the sides
x+1 = 1.0473
x = 1.0473 - 1
x = .0473
x =4.73 % annual growth rate
Continuous growth rate:
[tex]1*e^{15x} = 2[/tex]
[tex]ln(e^{15x}) = ln(2)[/tex]
15x*ln(e) = ln(2)
ln(e) = 1
15x =0.693
x =0 .693/15
x = .0462
x = 4.62 %
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A certain statistic dˆ is being used to estimate a population parameter d. The expected value of dˆ is not equal to d. What property does dˆ exhibit?.
The statistic's bias is a quality that the statistic does not display, according to the Central Limit Theorem for proportions.
Central limit theorem:
According to the central limit theorem in statistics, samples will be normally distributed and their means will be roughly equal to those of the entire population when the big sample size has a finite variance.
Given,
A certain statistic The population parameter d is being estimated using the function d. D's predicted value is not the same as D.
Find the property that does d display in this case.
According to the Central Limit Theorem, the following is true for a proportion p in an n-person sample:
Value anticipated, μ = p
Standard deviation: s = √p(1 - p) /n
Therefore,
The statistic is biased because the expected value in this case differs from the expected.
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The edges of three squares are joined together to form a right triangle with legs of lengths r and s and a hypotenuse of length t . what must be true
For the triangle to be true, the square of the hypothenuse is equal to sum of the square of the leg and the sum of the angles is equal to 180 degrees
Pythagoras TheoremThe Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides. Observe the following triangle ABC, in which we have BC² = AB² + AC2². Here, AB is the base, AC is the altitude (height), and BC is the hypotenuse. It is to be noted that the hypotenuse is the longest side of a right-angled triangle.
In this case, for the triangle to be true,
1. The sum of square of two sides (s) and (r) must be equal to the square of t
t² = s² + r²
2. The sum of angles in the right angle triangle must be equal to 180 degrees
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5. A retail store selling soaps, lotions, and candles must ship products to each of their locations. Each shipping box must contain 40 items and weigh exactly 25 pounds (400 ounces) Each body spray weighs 8 ounces and each shower gel weighs 12 ounces. The graph shows a system of equations for this scenario where z is the number of body sprays and is the number of shower gels in one shipping package In parts a-d determine which point(s) best match each description
The solution of the system of equations is given as follows:
x = 20 -> 20 body sprays.y = 20 -> 20 shower gels.How to obtain the amounts with the system of equations?
The variables of the system of equations are given as follows:
Each shipping box must contain 40 items, hence:
x + y = 40.
The box weighs 400 ounces, hence, considering the weight of each item, we have that:
8x + 12y = 400.
From the first equation, we have that:
x = 40 - y.
Then the number of shower gels is obtained as follows:
8(40 - y) + 12y = 400
4y = 80
y = 80/4
y = 20.
The number of body sprays is of:
x = 40 - 20 = 20.
Missing InformationThe problem is incomplete, hence we build and solve the equations, which will help you obtain the other information.
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Amira is solving the equation x2 - 6x - 1. Which value must be added to both sides of the equation to make the left side a perfect-square trinomial?
Use the slope formula to determine the slope of a line that passes through the points (-5,-3) and (9,-10)
Answer:
-1/2
Step-by-step explanation:
y2-y1/x2-x1
-10-(-3)/9-(-5)=-7/14=-1/2
A final exam in Math 160 has a mean of 73 with standard deviation 7.8. If 24 students are randomly selected, find the probability that the mean of their test scores is greater than 78. A) 0.0103 B) 0.0008 C) 0.8962 D) 0.0036
The correct answer is b that is the probability that the mean of their test scores is greater than 78 is 0.0008.
What is Probability?The field of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number that lies between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The probability is calculated on dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas where odds are calculated by dividing the likelihood of an event by the likelihood that it won't.
mean, μ = 73
standard deviation σ =7.8
η = 24
P (X*=78)
P( Z>3.1403)
Hence, the probability that the mean of their test scores is greater than 78 is 0.0008.
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He brightness of some stars can fluctuate over time. Suppose that the brightness of a certain star can be modeled by the following: B(t) = 7. 8 + 10. 8sin((2pi/63)t) In this equation, B(t) represents the magnitude of brightness, and t is the time (in days). Suppose we start at t = 0 days. During the first 63 days, when will the star's magnitude of brightness be 13? Do not round any intermediate computations, and round your answer(s) to the nearest day. Please especially explain the portion when calculating arcsin - thanks!
The days needed are 5 days
What is the rate of decay?The reduction in radioactive nuclei per unit of time is the rate of decay, or activity, of a sample of a radioactive substance.
How is the decay rate calculated?The rate of change is determined by the equation dN/dt = N, where is the decay constant, assuming N is the size of a population of radioactive atoms at a given time t and dN is the amount by which the population decreases in time dt.
What is the decay factor?Exponential decay is the opposite of exponential growth; it has a constant multiplier that is less than 1 when a quantity decreases by the same amount over equal intervals of time. This quantity also referred to as the decay factor, can be written as (1-r).
From the above question
B= 7.8+10.8sin((2pi/63)t)
B=13=7.8+10.8 sin((2pi/63)t)
sin((2pi/63)t)=13/27
(2pi/63)t=sin(13/27)=0.502344 radians
t=5 days
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Last year, Pinwheel Industries introduced a new toy. It cost $2500 to develop the toy and S25 to manufacture each toy. Fill in the blanks below as appropriate.
A.) Give a linear equation in the form Cmn + b that gives the total cost, C, to produce n of these toys Preview
B.) The total cost to produce n 3000 toys is S
C.) With $32500, a total of toys can be produced.
Equation is C=25n + 2500 And The total cost to produce 3000 toys is $77,500 And With $32500, a total of 1200 toys can be produced
A linear equation is what, exactly?
An algebraic equation with only a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
A) Lets have linear equation y=mx+b,
C (total cost) = y and n (number of toys) =x.
The original development cost plus the production cost of each toy would equal the overall cost of creating n toys.
Because m is multiplied by n, the number of toys, the cost to produce a toy will equal m.
Due to the fact that b is a constant and its value is unaffected by the quantity of toys, it will always equal the development cost.
Therefore, C=25n + 2500
B) by above, equation put n=1750
C= 25(3000) + 2500
C= $77,500
C) Now, again by same equation, but C instead of n.
=> 32500= 25n +2500
=> 30000=25n
=> n = 1200
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in 2006, 68.1 million people subscribed to cable television. in 2013, that number had decreased to 57.1 million. find the percent decrease in the number of cable tv subscribers from 2006 to 2013.
The percent decrease in the number of cable TV subscribers from 2006 to 2013 is 17.92%.
In the given question, in 2006, 68.1 million people subscribed to cable television. in 2013, that number had decreased to 57.1 million.
We have to find the percent decrease in the number of cable TV subscribers from 2006 to 2013.
The number of subscriber in 2006 is 68.1 million.
The number of subscriber in 2013 is 57.1 million.
Then the percent decrease in the number of cable tv subscribers from 2006 to 2013 is
Percent decrease in the number of cable TV subscribers = (subscriber in 2006 - subscriber in 2006)/subscriber in 2006 *100
Percent decrease in the number of cable TV subscribers = (61.4-50.4)/61.4 *100
Percent decrease in the number of cable TV subscribers = 11/61.4 *100
Percent decrease in the number of cable TV subscribers = 0.1792*100
Percent decrease in the number of cable TV subscribers = 17.92%
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The angles of a triangle add up to 180 degrees. The second angle is 6 degrees larger than the smallest angle. The third angle is 4 times as big as the smallest angle. Find the measure of the smallest angle (in degrees) degrees
Please help ! Need to know what the answer is solve while using the Pythagorean theorem !
Answer:
y ≈ 16.12452
Step-by-step explanation:
Pythagorean theorem = a² + b² = c²
In this example, 14 = a, 8 = b, and y = c
14² = 196, 8² = 64
196 + 64 = 260 = y²
y² = [tex]\sqrt{260}[/tex] ≈ 16.12452
Please help me with this. It will be really appreciated <3!
Find the value of y
7 x 7 x 7 x 7 x 7 x 7 =7y
Thank you a lot if you do! This is no rush <3
Answer: y = 16807
Step-by-step explanation:
7 * 7 * 7 * 7 * 7 * 7 = 117649
7^16807 = 117649
t would be appropriate to use a distribution to simulate customer arrival times at a bank or restaurant. a. exponential b. normal c. poisson d. weibull e. uniform
t-distribution in the bank or restaurant to get the customer arrival time is a b) normal distribution.
The t-distribution is defined by degrees of freedom. These are related to sample size. The t distribution is most useful when the sample size is small, the population standard deviation is unknown, or both. As the sample size increases, the t-distribution will become more normal.
The t distribution is the continuous probability distribution of z scores when the estimated standard deviation is used in the denominator instead of the true standard deviation. The purpose of the t-test is to compare a specific characteristic that describes the groups, and the means will be representative of the populations that are normally distributed.
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Response time is an important statistic for measuring the effectiveness of a fire department, and is measured as the difference between the time a fire house receives a call and the time the first piece of fire equipment leaves the station. The response times for fire departments in a large city are found to have an approximately Normal distribution, with a mean of 4.5 minutes and a standard deviation of 1.2 minutes. What percentage of fire station response times are between 4 and 6 minutes?
37.7%
44.3%
55.7%
62.3%
Step-by-step explanation:
55.7% of fire station response times are between 4 and 6 minutes. This can be calculated using the z-score formula, which is (x-μ)/σ, where x is the value of interest (in this case, 4 and 6 minutes), μ is the mean (4.5 minutes), and σ is the standard deviation (1.2 minutes). The z-score for 4 minutes is -0.42 and the z-score for 6 minutes is 0.42. Using a standard
A computer chess game and a human chess champion are evenly matched. They play fourteen games. Find probabilities for the following events.
(Round all answers to four decimal places.)
(a) They each win seven games. P =
(b) The human chess champion wins eleven games. P =
(c) The computer wins at least eleven games. P =
The probability that they each win six games is 0.225.
Given : A computer chess game and a human chess champion are evenly matched. They play twelve games.
To find : The probability that they each win six games?
Applying binomial distribution,
Here n=12 and p=0.5
(a) They each win seven games. P =
[tex]P(X=k)=\frac{n !}{k !(n-k) !} \times p^k \times(1-p)^{n-k}[/tex]
The probability that they each win six games is k=6.
(b) The human chess champion wins eleven games. P =
[tex]\begin{aligned}& P(X=6)=\frac{12 !}{6 !(12-6) !} \times 0.5^6 \times(1-0.5)^{12-6} \\& P(X=6)=\frac{12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 !}{6 \times 5 \times 4 \times 3 \times 2 \times 6 !} \times 0.015625 \times 0.015625 \\& P(X=6)=11 \times 2 \times 3 \times 2 \times 7 \times 0.015625 \times 0.015625 \\& P(X=6)=0.225\end{aligned}[/tex]
(c) The computer wins at least eleven games. P =
Therefore, The probability that they each win six games is 0.225.
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In cell I5, insert the AVERAGEIFS function to calculate the average SAT score that meets two conditions: Scores in the range I11:I67 are greater than or equal to 3500 and Final Decisions in the range J11:J67 are Early Admissions (cell E3). Use mixed references appropriately.
The term in cell I5 will be for the AVERAGEIFS function:
AVERAGEIF( I11:I67 ,"<3500",J11:J67 ,"E3")
For the given question the termed AVERAGEIFS is the function formula in excel which returns the average of all the cells available in the sheet in a range that meets a given condition.the syntax for the term is AVERAGEIF(range, criteria, [average_range]), where the range is Required like One or more cells to get the average. Criteria os the basically the form of an expression, number, or cell reference, and at last the average range is optional it is just the set of cells to average.
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please solve this quadratic inequality:
x^2+10x+16>-5
Answer: x<-7 or x>-3
Step-by-step explanation: Tell me if its wrong ill fix it
answer:
x>-7, x>-3
step-by-step explanation:
- the first step would to be to add five to both sides: x^2+10x+21>0
- then you can solve be grouping which results in: (x+7)(x+3)>0
- the final answer will be: x>-7, x>-3
hope that helps!
Who were the Greek oligarchs?
Answer:
"Broadly speaking, an oligarchy is a form of government characterized by the rule of a few persons or families. More specifically, the term was used by Greek philosopher Aristotle in contrast to aristocracy, which was another term to describe rule by a privileged few."
Step-by-step explanation: I hope this helps with something
a car is purchased for . each year it loses of its value. after how many years will the car be worth or less? (use the calculator provided if necessary.)
Answer: I calculated the value after 5 years to be 5,734.40 or 5,734
Step-by-step explanation:
describe the center and spread of the data using either the mean and standard deviation or median and iqr. describe how you determined which one to use.
For symmetric distributions without outliers, the mean should be used to get the measure of center.
What are the Center and Spread of the data?
The spread in the data measures how far the numbers in the data set are away from the mean and the center in the data measures the standard deviation.
To determine the measure of center for symmetric distributions without outliers, one should use the mean. They should use the median to determine the measure of center in all other situations. The range is a suitable metric for determining the spread of a distribution.
However, the interquartile range should be used when using the median as the measure of center, and the standard deviation should be used when using the mean as the measure of center.
Hence, For symmetric distributions without outliers, the mean should be used to get the measure of center.
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A machine is used to fill several bags each of 20-ounces of spicey
chips. After each bag is filled, another machine weighs them. If the
bag weighs .25 less or more than the desired weight, the bag is
rejected. Write an equation to represent the maximum weight for a
bag of chips that the machine will approve.
Answer: 19.75oz < x > 20.25oz
Step-by-step explanation: let x represent the weight of the bag of chips.
This equation states that the. weight must not exceed 20.25 but it must not be below 19.75oz.
Answer: 19.75oz < x > 20.25oz
Step-by-step explanation:
is it possible for two quantities to (a) have the same units but different dimensions or (b) have the same dimensions but different units? explain.
If two quantities have same units, they will be comprised of the same basic physical quantities and hence their dimensions will be same. Same dimensions do not represent the same physical quantity. For example, The kinetic energy and the potential energy are measured in the same units but they possess different physical quantities.
What is dimensions?The minimal set of coordinates required to specify any point within a mathematical space is known as the dimension of the space in physics and mathematics. As a result, a line has a dimension of one because a point on it can be specified by a single coordinate, such as the point at 5 on a number line.
Two quantities with the same units will be made up of the same fundamental physical quantities, resulting in identical dimensions. The same physical quantity does not have the same dimensions. For instance, although having different physical properties, kinetic energy and potential energy are measured in the same units.
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A school is arranging a field trip to the zoo. The school spends 778.72 dollars on passes for 29 students and 2 teachers. The school also spends 259.26 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?
Answer:
Step-by-step explanation:
first, you have to divide the total cost of the passes by the number of teachers and students combined. Then you must multiply the individual cost of the pass by the number of students. Finally, you have to take the total cost for student passes and add it to the cost of the lunches, then you answer.
Which of these relations is a function?
By using the vertical line test we will see that the relation that is a function is the one in the top left graph.
Which of these relations is a function?Here we ave the graphs of some relations, and we want to see which one of these represents a function.
To check that, we need to do the vertical line test.
The test says that if we draw a vertical line on the coordinate axis, and that line intercepts the graph of the relation more than one time, then the relation is not a function.
With that test we can see that the only relation that is a function is the one in the top left graph, is the only one that passes the vertical line test.
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What’s y=-3(x-1)2 squared +3 in factored form
Answer: y=−16.309691adqrsux+16.309691adqrsu+3
Let's solve for y.
y=((((((((−3(x−1))(2))(s))(q))(u))(a))(r))(2.718282))(d)+3
This is the best I could come up with
What is the equation in slope-intercept form of the line that passes through the point (8, - 7) and is parallel to the line represented by y = 6x + 2
A. Y=1/6x+55
B. Y=1/6x-55
C. Y=6x+55
D. Y=6x-55
Answer:
:Equation of line is[tex]y=1.2x+3.8[/tex]To find:The equation of line that passes through the point (5, 0) and parallel to the given line.
Step-by-step explanation:
Which of the following is equal to √√√√5? (4 points)
O
O
O
O
53
1
56
2
53
3
N/W
52
Answer:
b
Step-by-step explanation:
help me i actually cant figure this out :(
To complete the square of the quadratic function x² + 10x + 4 we need to add 21
Completing The SquareCompleting the square is a method in algebra that is used to write a quadratic expression in a way such that it contains the perfect square. In simple words, we can say that completing the square is a process where consider a quadratic equation of the ax² + bx + c = 0 and change it to write it in the form a(x + p)² + q = 0. This method is generally used to find the roots of a quadratic equation.
Completing the square formula is a technique or method to convert a quadratic polynomial or equation into a perfect square with some additional constant. A quadratic expression in variable x: ax² + bx + c, where a, b and c are any real numbers but a ≠ 0, can be converted into a perfect square with some additional constant by using completing the square formula or technique
The equation given is
x² + 10x + 4 = 0
Take 4 to right side
x² + 10x = -4
rewrite in (x + a)² = b form
(x + 5)² = 21
x + 5 = ±√21
x = √21 - 5
x = -√21 - 5
To complete the square, we need to add 21
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find the value of m n (4x-33) (3x+30)
Answer: 4(x + y) = 4x + 4y 2(3x + 4) = 2(3x) + 2(4) = 6x + 8
Step-by-step explanation:
How do you write as a percentage?
39
100
The percentage of 39/100 can be written as 39% as given in the question.
What is meant by percentage?A percentage is a figure or ratio stated as a fraction of 100. The abbreviations "pct.", "pct," and "pct" are also used. A% is a dimensionless (pure) number with no unit of measurement.
The word "percent" comes from the Latin per centum, which means "hundred" or "by the hundredth." The symbol for "percent" emerged gradually from the Italian expression per cento. The "cento" symbol was developed from two circles divided by a horizontal line.
As money denominations expanded in the Middle Ages, computations with a denominator of 100 were increasingly prevalent, to the point where it became normal for mathematics texts to incorporate such computations from the late 15th to the early 16th centuries
We write 39/100 in the percentage as 39%
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