Maria has the highest standardized score of 2.13, making her the one who made the best score.
Janna's standardized score is 0.80, and Maria's is 2.13.
Janna scored 77 on her history test, while the class average was 72.7 with a standard deviation of 6.1. To find the standardized score, the formula is (score - average) / standard deviation. Therefore, the standardized score for Janna is [tex](77-72.7)/6.1[/tex]= 0.80.
Maria scored 89 on her biology test, while the class average was 82.6 with a standard deviation of 5.6. To find the standardized score, the formula is (score - average) / standard deviation. Therefore, the standardized score for Maria is [tex](89-82.6)/5.6[/tex]= 2.13.
Maria has the highest standardized score of 2.13, making her the one who made the best score.
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[amc10b.2011.7] the sum of two angles of a triangle is $\frac{6}{5}$ of a right angle, and one of these two angles is $30^{\circ}$ larger than the other. what is the degree measure of the largest angle in the triangle?
The degree measure of the largest angle is 72° in the triangle.
We have, The sum of two angles of a triangle is 6/5 of a right angle.
One of these two angles is 30° larger than the other.
Let A and B be the two angles of the triangle such that A = B + 30°.
We know that the sum of three angles in a triangle is 180°.
⇒ A + B + C = 180°
⇒ B + 30° + B + C = 180°
⇒ 2B + C = 150°
We also know that the sum of two angles of a triangle is 6/5 of a right angle.
⇒ A + B = 6/5 × 90°
⇒ B + 30° + B = 108°
⇒ 2B = 78°
⇒ B = 39°
C = 150° - 2B ⇒ 72°
A = B + 30° ⇒ 39° + 30° ⇒ 69°
Therefore, the degree measure of the largest angle in the triangle is 72°.
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Draw a diagram to help you set up an equation(s). Then solve the equation(s). Round all lengths to the neatest tenth and all angles to the nearest degree. (number 2)
The angle of elevation of the sun is approximately 22.6 degrees.
What is trigonometry?The partnerships between the sides and angles of triangles are the subject of the mathematical discipline of trigonometry. It is used exhaustively in fields such as physics, engineering, and assessing.
In a right triangle, the side opposite the right angle is called the hypotenuse, while the other two sides are called the legs.
Given that, 7.6 m flagpole casts an 18.2 m shadow.
Using trigonometric ratio we have:
tan(θ) = h / s
Substituting the values:
tan(θ) = 7.6 / 18.2
tan(θ) ≈ 0.417
θ ≈ 22.6°
Hence, the angle of elevation of the sun is approximately 22.6 degrees.
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On January 1,1999 , the average price of gasoline was $1.19 per gallon. If the price of gasoline increased by 0.3% per month, which equation models the future cost of gasoline? y=1.19(1.003)^(x) y=1.19(x)^(1.03) y=1.19(1.03)^(x)
Answer:
first one
Step-by-step explanation:
The equation that models the future cost of gasoline is y=1.19(1.003)^(x), where "y" represents the future cost of gasoline per gallon and "x" represents the number of months since January 1, 1999.
In this equation, the initial cost of gasoline is $1.19 per gallon, and the cost increases by 0.3% per month, which is represented by the factor of (1.003)^(x).
Using this equation, you can calculate the future cost of gasoline for any number of months after January 1, 1999. For example, if you want to calculate the cost of gasoline 24 months after January 1, 1999, you can plug in x=24 and calculate y as follows:
y = 1.19(1.003)^(24)
y = 1.19(1.08357)
y = 1.288 per gallon
Therefore, the predicted cost of gasoline 24 months after January 1, 1999 is $1.288 per gallon.
-17.R Using Percents, Homework
Sarted: Mar 10 at 8:30pm
Question 1 of 9
The Quick Slide Skate Shop sells the Ultra 2002 skateboard for a price of $60.20. However, the Quick Slide
Skate Shop is offering a one-day discount rate of 45% on all merchandise. About how much will the Ultra 2002
skateboard cost after the discount?
$33.00
$87.00
$46.20
$27.00
The price after discount is $33 and option 1 is the correct answer.
What is a discount?A discount is a drop in a product's or service's price. Discounts can be provided for a variety of purposes, such as to entice consumers to make larger purchases, to get rid of excess inventory, or to draw in new clients. Discounts can be represented as a set monetary amount or as a %, as in the example above. For instance, a shop may give customers $10 off any purchase of more than $50.
Given that, one-day discount rate of 45% is applied.
Thus,
Discount = 60.20 * 0.45 = 27.09
Price after discount = 60.20 - 27.09 = 33.11
Hence, the price after discount is $33 and option 1 is the correct answer.
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Solve the following: 2x + y = 15 y = 4x + 3
The ratio of distance runners to sprinters on a track is 5:3 how many distance runners and sprinters could be on the track team
Runners and sprinters could be on the track team is 25 distance.
Distance:
Distance is a qualitative measurement of the distance between objects or points. In physics or common usage, distance can refer to a physical length or an estimate based on other criteria (such as "more than two counties"). The term Distance is also often used metaphorically to refer to a measure of the amount of difference between two similar objects.
According too the Question:
Based on the based Information:
15× 5÷3
canceling all the common factor, we get:
5 × 5 = 25
Now, the Product or Quotient is 25.
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polygon ABCD is similar to polygon ZYXW list the relationships between angles and sides
The corresponding sides and angles of two polygons ABCD and ZYXW must be proportionate if they are identical.
What does a polygon shape mean?With straight sides around its perimeter, a polygon is really a circular, two-dimensional, flat of planar structure. Its sides are straight with no bends. Another term for a polygon's sides is its edges. The points at which two sides of a polygon converge are known as its vertices (or corners). These are numerous examples of polygonal geometry.
Has a polygon always had four sides?A closed polygon is a form with more than three sides. A quadrilateral is a 4-sided polygonal shape. A quadrilateral is any closed 4-sided form, however there are six particular quadrilaterals with distinctive characteristics that give them their own names.
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The product of two consecutive positive even integers is 120. Find the value of the
lesser integer.
Answer:
10. Other number is 12.
Explanation:
The prime factors of 120 are 2*2*2*3*5
To end up with even numbers, the odd numbers must be multiplied by even numbers. The only even numbers are 2s, while there are two odd numbers, 3 and 5.
So we MUST be talking about 2*3 and 2*5 with a 2 left over. That’s 6 and 10, which are by no stretch of the imagination consecutive. But we can either double the 10 (giving us 6 and 20, even less “consecutive”) or the 6.
Double 6 and we have 12. 10 and 12 are consecutive even numbers, because you can add two to get the next one.
Use the graph of f(x)=−8x-2x^2 to answer the question.
Is f(x) increasing, decreasing, or constant for -2
At x = -2, which is the vertex of the quadratic function, the function f(x) is constant.
How to classify a function as increasing, decreasing or constant?To classify the graph of a function as increasing, decreasing, or constant, you need to examine the direction in which the graph is moving.
A function is considered increasing if its graph moves up and to the right as you follow it from left to right. In other words, if the y-values of the function increase as the x-values increase, then the function is increasing.A function is considered decreasing if its graph moves down and to the right as you follow it from left to right. In other words, if the y-values of the function decrease as the x-values increase, then the function is decreasing.A function is considered constant if its graph remains at the same level and does not move up or down as you follow it from left to right. In other words, if the y-values of the function do not change as the x-values increase, then the function is constant.x = -2 is the vertex of the quadratic function, which is the turning point of the function, where it changes from increasing to decreasing, hence the function is considered to be constant at x = -2, as it has a derivative of zero at x = -2.
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In 2008 , the population of a district was 39,700 . With a continuous annual growth rate of approximately 3%, what will the population be in 2033 according to the exponential growth function?
The population will be approximately 84,161 in 2033 according to the exponential growth function.
The given information in the problem is;Population in 2008 = 39,700
Annual growth rate = 3%
We need to find out the population in 2033.
The formula for continuous exponential growth is;P(t) = P₀e^(rt)
where;P₀ is the initial populationr is the annual growth rate (in decimal form)t is the time elapsed (in years)
We are given P₀ = 39,700r = 0.03t = 2033 - 2008 = 25 years
Put these values in the formula of continuous exponential growth;
P(25) = 39,700e^(0.03 x 25)P(25)
= 39,700e^(0.75)P(25)
= 39,700 x 2.1170000493605122P(25)
= 84,161.13
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Jenny works at Sammy's Restaurant and is paid according to the rates in the following
table.
Jenny's weekly wage agreement
Basic wage $600.00
PLUS
$0.90 for each customer served.
In a week when Jenny serves n customers, her weekly wage, W, in dollars, is given by
the formula
W = 600+ 0.90n.
(i) Determine Jenny's weekly wage if she served 230 customers.
(ii) In a good week, Jenny's wage is $1 000.00 or more. What is the LEAST number
of customers that Jenny must serve in order to have a good week?
(iii) At the same restaurant, Shawna is paid a weekly wage of $270.00 plus $1.50 for
each customer she serves.
If W, is Shawna's weekly wage, in dollars, write a formula for calculating Shawna's
weekly wage when she serves m customers.
(iv) In a certain week, Jenny and Shawna received the same wage for serving the same
number of customers.
How many customers did they EACH serve?
Jenny works at Sammy's Restaurant and is paid according to the rates in the following
table.
Jenny's weekly wage agreement
Basic wage $600.00
PLUS
$0.90 for each customer served.
In a week when Jenny serves n customers, her weekly wage, W, in dollars, is given by
the formula
W = 600+ 0.90n.
(i) Determine Jenny's weekly wage if she served 230 customers.
(ii) In a good week, Jenny's wage is $1 000.00 or more. What is the LEAST number
of customers that Jenny must serve in order to have a good week?
(iii) At the same restaurant, Shawna is paid a weekly wage of $270.00 plus $1.50 for
each customer she serves.
If W, is Shawna's weekly wage, in dollars, write a formula for calculating Shawna's
weekly wage when she serves m customers.
(iv) In a certain week, Jenny and Shawna received the same wage for serving the same
number of customers.
How many customers did they EACH serve?
3 / 3
(i) If Jenny serves 230 customers, her weekly wage is
W = 600 + 0.90n = 600 + 0.90(230) = $807.00
Therefore, Jenny's weekly wage if she serves 230 customers is $807.00.
(ii) We want to find the least number of customers, n, that Jenny must serve in order to earn $1,000 or more. That is,
600 + 0.90n ≥ 1,000
0.90n ≥ 400
n ≥ 444.44
Since n must be a whole number, Jenny must serve at least 445 customers in order to earn $1,000 or more in a week.
(iii) Shawna's weekly wage, W, in dollars, when she serves m customers is given by the formula:
W = 270 + 1.50m
Therefore, Shawna's weekly wage when she serves m customers is $270.00 plus $1.50 for each customer she serves.
(iv) Let's assume that Jenny and Shawna received the same wage, W, for serving the same number of customers, x. Then we have:
Jenny's wage = 600 + 0.90x
Shawna's wage = 270 + 1.50x
Setting these two expressions equal to each other, we get:
600 + 0.90x = 270 + 1.50x
330 = 0.60x
x = 550
Therefore, Jenny and Shawna each served 550 customers.
Let Y be a binomial random variable with n trials and probability of success given by p. Use the method of moment-generating functions to show that U = n - Y is a binomial random variable with n trials and probability of success given by 1 - p.
U is a binomial random variable with n trials and probability of success given by 1 - p.
As Y is a binomial random variable with n trials and probability of success given by p. Using the moment-generating functions method, it can be shown that U = n - Y is a binomial random variable with n trials and probability of success given by 1 - p. The binomial distribution is described by two parameters: n, which is the number of trials, and p, which is the probability of success in any given trial. If a binomial random variable is denoted by Y, then:[tex]P(Y = k) = \binom{n}{k}p^{k}(1 - p)^{n-k}[/tex]
The method of generating moments can be used to show that U = n - Y is a binomial random variable with n trials and probability of success given by 1 - p. The moment-generating function of a binomial random variable is given by: [tex]M_{y}(t) = [1 - p + pe^{t}]^{n}[/tex]
The moment-generating function for U is: [tex]M_{u}(t) = E(e^{tu}) = E(e^{t(n-y)})[/tex]
Using the definition of moment-generating functions, we can write: [tex]M_{u}(t) = E(e^{t(n-y)})$$$$= \sum_{y=0}^{n} e^{t(n-y)} \binom{n}{y} p^{y} (1-p)^{n-y}[/tex]
Taking the summation of the above expression: [tex]= \sum_{y=0}^{n} e^{tn} e^{-ty} \binom{n}{y} p^{y} (1-p)^{n-y}$$$$= e^{tn} \sum_{y=0}^{n} \binom{n}{y} (pe^{-t})^{y} [(1-p)^{n-y}]^{1}$$$$= e^{tn} (pe^{-t} + 1 - p)^{n}[/tex]
Comparing this expression with the moment-generating function for a binomial random variable, we can say that U is a binomial random variable with n trials and probability of success given by 1 - p.
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twenty percent of americans ages 25 to 74 have high blood pressure. if 16 randomly selected americans ages 25 to 74 are selected, find each probability. a. none will have high blood pressure. b. one-half will have high blood pressure. c. exactly 4 will have high blood pressure.
Then we will get the following odds
a. None will have high blood pressure. Let the probability of having high blood pressure be denoted by P(A) and the probability of not having high blood pressure be denoted by P(A'). Since none will have high blood pressure, it means all the sixteen Americans selected are healthy, and therefore P(A') = 1. Therefore
P(A) = 1 - P(A')= 1 - 1= 0
b. One-half will have high blood pressure. The probability that one-half of the sixteen Americans will have high blood pressure can be found using the binomial distribution formula that is given by the expression
[tex]P(X = r) = (nCr) * p^r * q^{(n-r)}[/tex]
Where
r = 8n = 16 p = 0.2 q = 1 - p = 0.8Therefore
[tex]P(X = 8) = (16C8) * 0.2^8 * 0.8^8= 0.202[/tex]
c. Exactly 4 will have high blood pressure Similarly, the probability that exactly four of the sixteen Americans will have high blood pressure can be found using the binomial distribution formula as follows:
[tex]P(X = r) = (nCr) * p^r * q^{(n-r})[/tex]
Where
r = 4n = 16p = 0.2q = 1 - p = 0.8Therefore
[tex]P(X = 4) = (16C4) * 0.2^4 * 0.8^{12}= 0.236[/tex]
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a researcher wishes to study railroad accidents. he wishes to select 3 railroads from 10 class i railroads, 2 railroads from 6 class ii railroads, and 1 railroad from 5 class iii railroads. how many different possibilities are there for his study?
There are, 6300 different possibilities for the researcher’s study.
How do we calculate the different possibilities?Total number of class I railroads = 10Number of class I railroads selected = 3Total number of class II railroads = 6Number of class II railroads selected = 2Total number of class III railroads = 5Number of class III railroads selected = 1Number of different possibilities for selecting 3 class I railroads from 10 class I railroads = 10C3 = (10 x 9 x 8)/(3 x 2 x 1) = 120
Number of different possibilities for selecting 2 class II railroads from 6 class II railroads = 6C2 = (6 x 5)/(2 x 1) = 15Number of different possibilities for selecting 1 class III railroad from 5 class III railroads = 5C1 = 5Total number of different possibilities for selecting 3 class I railroads from 10 class I railroads, 2 class II railroads from 6 class II railroads, and 1 class III railroad from 5 class III railroads = 10C3 x 6C2 x 5C1= 120 x 15 x 5= 6300Therefore, there are 6300 different possibilities for the researcher’s study.
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which number is greater? Explain. −−√70, 8
Answer:
Ans = 8
Step-by-step explanation:
because -- is + and −−√70 is positive
so square root =8.366600265340757
and 8 is bigger as 8.366600265340757 is a decimal number.
4-77 Is the relationship shown in the 28+
graph at right below proportional? If
241
so, find the unit rate. If not, explain
why not.
The graph is/is not proportional
because
Unit rate:
Cost ($)
20
16-
12+
8
2 3 4 5
Number of Books
Purchased
Answer:
Step-by-step explanation:
A graph is proportional if the relationship between the two variables represented on the axes is constant, meaning that if one variable increases, the other variable also increases by the same factor. In other words, the graph forms a straight line that passes through the origin.
To find the unit rate, you need to look for the constant of proportionality, which is the ratio between the two variables represented on the graph. In this case, the variables are the number of books purchased and the cost in dollars.
If the graph is proportional, then the unit rate is the constant of proportionality, which is the cost per book. You can find the unit rate by dividing the total cost by the number of books purchased. For example, if the total cost for 4 books is $16, then the unit rate would be $4 per book.
If the graph is not proportional, then there is no constant of proportionality, and the unit rate cannot be calculated. The relationship between the two variables may be nonlinear, meaning that the rate of change between the variables is not constant.
Find a basis for the vector space of polynomialsp(t)of degree at most two which satisfy the constraintp(2)=0. How to enter your basis: if your basis is1+2t+3t2,4+5t+6t2then enter[[1,2,3],[4,5,6]]
In the following question, among the conditions given, {q1, q2} is a basis for the vector space of polynomials p(t) of degree at most two that satisfy the constraint p(2) = 0. In this particular case, we must enter our basis as [[1,0,-4],[0,1,-2]], since q1(t) = t^2 - 4 and q2(t) = t - 2.
To find a basis for the vector space of polynomials p(t) of degree at most two which satisfy the constraint p(2)=0, we can take the following steps:
1. Rewrite the polynomials as linear combinations of the form a + bt + ct^2
2. Use the constraint p(2) = 0 to eliminate one of the coefficients a, b, or c
3. Normalize the polynomials so that they are unit vectors
For example, if your basis is 1 + 2t + 3t^2, 4 + 5t + 6t2 then you can enter it as [[1,2,3],[4,5,6]].
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a cyclist rides her bike at a speed of 21 kilometers per hour. what is this speed in kilometers per minute? how many kilometers will the cyclist travel in 2 minutes? (do not round the answer)
Answer:
see the answer and explanation in the attached figure below
Step-by-step explanation:
. A circular fence is being used to surround a dog house. How much fencing is needed to build the fence?
45.53 ,fencing is needed to build the fence.
What is area?A solid object's surface area is a measurement of the total area that the surface of the object takes up.
The definition polyhedra of arc length for one-dimensional curves and the definition of surface area for (i.e., objects with flat polygonal faces), where the surface area is the sum of the areas of its faces, are both much simpler mathematical concepts than the definition of surface area when there are curved surfaces.
A smooth surface's surface area is determined using its representation as a parametric surface, such as a sphere.
This definition of surface area uses partial derivatives and double much simpler mathematical concepts than the definition of surface area integration and is based on techniques used in infinitesimal calculus.sought a general definition of surface area.
Henri Lebesgue and Hermann Minkowski at the turn of the century sought a general definition of surface area.
2*3.14*14.5/2
45.53ft
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Write down two factors of 24 that are primenumber
the prime factors of 24 are 2 and 3, which combine to give the unique prime factorization of 24 as 2^3 × 3.
There are no factors of 24 that are prime numbers. A factor of a number is a whole number that divides that number without leaving a remainder. Prime numbers, on the other hand, are numbers that are divisible only by 1 and themselves, and cannot be expressed as the product of any other numbers.
The prime factors of 24 are 2, 2, and 3. We can factorize 24 as 2 × 2 × 2 × 3 or 2^3 × 3. Here, 2 and 3 are both prime numbers, but they are not factors of 24 in isolation. They are only prime factors of 24 when combined in the manner shown.
This fact highlights an important concept in number theory: the uniqueness of prime factorization. Every composite number can be expressed as a unique product of prime numbers. This fundamental theorem of arithmetic is crucial in many areas of mathematics, including cryptography, where it is used to secure communications and protect sensitive information.
In summary, there are no factors of 24 that are prime numbers. However, the prime factors of 24 are 2 and 3, which combine to give the unique prime factorization of 24 as 2^3 × 3.
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Question
The average of three numbers is 16. If one of the numbers is 18, what is the sum of the other two
numbers?
12
14
20
30
If the average of three numbers is 16 and one of the numbers is 18, then the sum of the other two numbers is option (d) 30
Let's use algebra to solve this problem. Let x and y be the other two numbers we are looking for. We know that the average of the three numbers is 16, so we can write:
(18 + x + y) / 3 = 16
Multiplying both sides by 3, we get,
[(18 + x + y) / 3] × 3 = 16 ×3
18 + x + y = 48
Subtracting 18 from both sides, we get,
18 + x + y - 18 = 48
x + y = 30
Therefore, the correct option is (d) 30
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Select all numbers that are solutions to the inequality w < 1
In the case of the inequality w < 1, we found that the set of solutions is (-∞, 1), which represents all real numbers less than 1.
The inequality w < 1 means that w is less than 1. To identify all the numbers that satisfy this inequality, we need to look for values of w that are less than 1.
We can continue this process and substitute different values of w in the inequality w < 1 to find more solutions. For instance, if we substitute w = -1, we get -1 < 1, which is also true.
Therefore, -1 is a solution to the inequality w < 1. However, if we substitute w = 2, we get 2 < 1, which is false. This means that 2 is not a solution to the inequality w < 1.
Therefore, the set of all numbers that are solutions to the inequality w < 1 is the set of all real numbers that are less than 1. We can represent this set using interval notation as (-∞, 1), where (-∞) represents all numbers less than negative infinity and 1 represents the upper bound of the interval.
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A(-2,6) B(2,3) C(2,-2) D(-2,1) whats the most descriptive name for this quadrilateral? justify your conclusion
Please help!!
Answer:
Parallelogram
Step-by-step explanation:
a quadrilateral (4 sides figure) whose opposite sides are parallel. The opposite sides have the same length and opposite angles are equal.
Helping in the name of Jesus.
suppose a population grows according to a logistic model with initial population 200 and carrying capacity 2,000. if the population grows to 500 after one year, what will the population be after another three years?
Suppose a population grows according to a logistic model with initial population 200 and carrying capacity 2,000. If the population grows to 500 after one year, the population will be 852.78 after another three years.
What is the logistic model?A logistic model, also known as the Verhulst-Pearl model, is a type of function used to describe population growth that is limited. It’s a form of exponential growth that takes into account the carrying capacity of an environment.
Population growth that is limited and slows down as the population approaches its carrying capacity is modeled using the logistic model. It is given by this equation:
[tex]P(t) = K / (1 + Ae^{-rt})[/tex]
where P(t) is the population at time t, K is the carrying capacity, A is the constant of proportionality, and r is the growth rate.
Suppose a population grows according to a logistic model with initial population 200 and carrying capacity 2,000. If the population grows to 500 after one year, substitute this information into the logistic model: [tex]P(1) = 500[/tex], [tex]K = 2000[/tex], and [tex]P(0) = 200[/tex].
[tex]500 = 2000 / (1 + Ae^{-r(1)})[/tex]
Now, solve for A by dividing both sides by 2000 / (1 + A):
[tex]1 + A = 4A = 3[/tex]
Substitute the value of A back into the logistic model equation:
[tex]P(t) = 2000 / (1 + 3e^{-rt})[/tex]
Solve for r by using the data provided in the problem for the first year (t = 1) and second year (t = 4):
[tex]P(1) = 500 = 2000 / (1 + 3e^{-r(1)})[/tex]
[tex]P(4) = ? = 2000 / (1 + 3e^{-r(4)})[/tex]
Solve the first equation for r:
[tex]500 = 2000 / (1 + 3e^{-r})\\1 + 3e^{-r} = 4e^{-r}\\1 + 3e^r = 4e[/tex]
Solve for e using the quadratic formula to get:
e = 0.4274 and e = 1.1713
Let e = 0.4274:
[tex]1 + 3e^{-r} = 4e^{-r}\\1 + 3(0.4274)^{-r} = 4(0.4274)^{r}\\1 + 0.5746^r = 1.7166^r[/tex]
Take the natural logarithm of both sides:
[tex]ln(1 + 0.5746^r) = ln(1.7166^r) - lnr\\ln(1 + 0.5746^r) = rln(1.7166) - lnr[/tex]
Use a graphing calculator to solve for r:
[tex]ln(1 + 0.5746^r) = rln(1.7166) - lnr[/tex]; -0.1568 < r < 0.7534
Solve for r using the second year’s data:
[tex]2000 / (1 + 3e^{-r(4)}) = P(4)\\2000 / (1 + 3(0.4274)^{-r(4)}) = P(4)\\P(4) = 852.78[/tex]
Thus, the population will be 852.78 after another three years.
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A light bulb manufacturer claims its light bulbs will last 500 hours on average. The lifetime of a light bulb is assumed to follow an exponential distribution. (15 points) a. What is the probability that the light bulb will have to be replaced within 500 hours? s. RSS THE b. What is the probability that the light bulb will last more than 1,000 hours? c. What is the probability that the light bulb will last between 200 and 800 hours?
a.There is a 63.21% chance that the light bulb will have to be replaced within 500 hours.
The probability that the light bulb will have to be replaced within 500 hours can be calculated by finding the area under the exponential probability density function (PDF) from 0 to 500. Using the formula for the exponential PDF with a mean of 500, we get:
P(X ≤ 500) = 1 - e^(-500/500) ≈ 0.6321
Therefore, there is a 63.21% chance that the light bulb will have to be replaced within 500 hours.
b. There is a 39.35% chance that the light bulb will last between 200 and 800 hours.
The probability that the light bulb will last more than 1,000 hours can be calculated by finding the area under the exponential PDF from 1000 to infinity. Using the same formula, we get:
P(X > 1000) = e^(-1000/500) ≈ 0.1353
Therefore, there is a 13.53% chance that the light bulb will last more than 1,000 hours.
c. The probability that the light bulb will last between 200 and 800 hours is0.3935.
It can be calculated by finding the area under the exponential PDF from 200 to 800. Again, using the same formula, we get:
P(200 < X < 800) = e^(-200/500) - e^(-800/500) ≈ 0.3935
Therefore, there is a 39.35% chance that the light bulb will last between 200 and 800 hours.
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a normal distribution of exam scores has a standard deviation of 8. a score that is 12 points above the mean would have a z-score of: a score that is 20 points below the mean would have a z-score of:
The standard deviation of a normal distribution of exam scores is 8. A score that is 12 points above the mean would have a z-score of 1.5, and a score that is 20 points below the mean would have a z-score of -2.5.
What is the z-score?The z-score can be calculated by dividing the difference between a data value and the mean of the data set by the standard deviation of the data set.
The z-score of a score that is 12 points above the mean in a normal distribution of exam scores with a standard deviation of 8.
z = (x−μ)/σ = (x−μ)/σ = (12−0)/8 = 1.5
The z-score of a score that is 12 points above the mean in a normal distribution of exam scores with a standard deviation of 8 is 1.5.
The z-score of a score that is 20 points below the mean in a normal distribution of exam scores with a standard deviation of 8.
z = {x-μ}/{σ} = {-20-0}/{8} = −2.5
The z-score of a score that is 20 points below the mean in a normal distribution of exam scores with a standard deviation of 8 is -2.5.
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In right triangle RST, with m∠S = 90°, what is sin T?
The ratio of the length of the side directly opposite the angle to the length of the hypotenuse is known as the sine of an acute angle in a right triangle.
Hence, the sine of angle T in the right triangle RST with a right angle at S is given by:
opposite side / hypotenuse = sin T
We must know the triangle's side lengths in order to calculate the value of sin T. We can use trigonometric ratios to calculate the lengths of the remaining sides.
if we know the length of the hypotenuse and the measurement of one acute angle.
thus, we cannot define the value of triangle RST.
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A grocer has two kinds of candies, one selling for 90 cents a pound and the other for $1.40 per pound. How many pounds of each kind must he use to make 100 pounds worth 85 cents a pound?
? pounds of 40 − cent candies, ? pounds of candies that cost $1.40 per pound
Using equations we know that 45 pounds are included in the $1.40 worth of groceries and 55 pounds worth of groceries are being purchased for 40 cents.
What are equations?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.
As in 3x + 5 = 15, for example.
There are many different types of equations, including linear, quadratic, cubic, and others.
So, we have:
x + y = 100 .........A
40 × x + 140 y = 85 × 100
40 x + 140 y = 8500 ........B
Solving (A) and (B) as follows:
(40 x + 140 y) - 40 × ( x + y ) = 8500 - 40 × 100
(40 x - 40 x) + (140 y - 40 y) = 8500 - 4000
0 + 100 y = 4500
y = 4500/100
Hence, the price per unit of grocery is $1.40 = y = 45 pounds.
Now, put the value of y in equation (A) as follows:
x + y = 100
x = 100 - y
x = 100 - 45
x = 55 pounds
The number of groceries at the 40-cent price is x = 55 pounds.
Therefore, using equations we know that 45 pounds are included in the $1.40 worth of groceries and 55 pounds worth of groceries are being purchased for 40 cents.
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Correct question:
A grocer has two kinds of candies, one selling for 40 cents a pound and the other for $1.40 per pound. How many pounds of each kind must he use to make 100 pounds worth 85 cents a pound?
1. Find the given derivative by finding the first few derivatives and observing the pattern that occurs. (d115/dx115(sin(x)). 2. For what values of x does the graph of f have a horizontal tangent? (Use n as your integer variable. Enter your answers as a comma- separated list.) f(x) = x + 2 sin(x).
The values of x such that the graph of f has a horizontal tangent are;x = 2π/3 + 2πn, 4π/3 + 2πn, where n is an integer.
1. The given derivative can be found by finding the first few derivatives and observing the pattern that occurs as shown below;Differentiating sin x with respect to x gives the derivative cos x. Continuing this process, the pattern that emerges is that sin x changes sign for every odd derivative, and stays the same for every even derivative. Therefore the 115th derivative of sin x can be expressed as follows;(d115/dx115)(sin x) = sin x, for n = 58 (where n is an even number)2. To find the values of x such that the graph of f has a horizontal tangent, we differentiate f with respect to x, and then solve for x such that the derivative equals zero. We have;f(x) = x + 2sin xDifferentiating f(x) with respect to x gives;f'(x) = 1 + 2cos xFor a horizontal tangent, f'(x) = 0, thus;1 + 2cos x = 02cos x = -1cos x = -1/2The solutions of the equation cos x = -1/2 are;x = 2π/3 + 2πn or x = 4π/3 + 2πnwhere n is an integer. Therefore the values of x such that the graph of f has a horizontal tangent are;x = 2π/3 + 2πn, 4π/3 + 2πn, where n is an integer.
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Write the product in standard form.
(x - 7)²
Answer:
x² - 49
Step-by-step explanation:
(x - 7)² =
(x - 7) * (x - 7) =
x * x - 7 * 7 =
x² - 49