Allie found a table of data displaying the number of middle and high school stud enrolled in Lincoln public schools . she made a table with the number of students in the 2015 as year 0 in the table of data.Lookimh at the enrollment in previous years,she decided to use an exponential equation to model the number of students.⚠COULD SOMEONE PLEASE HELP WITH THESE QUESTIONS⚠(Any info will help!!)⛧What is the growth multiplier for the data? complete the table using the multiplier.⛧⛧Write multiplier as a percent.⛧
Answers
The general exponential growth formula is:
\(y=a\cdot b^x^{}\)where a is the initial amount, b is the growth multiplier, and y and x are the variables.
In this case, x represents years after 2015, y represents the number of students, and the initial value is a = 20,080.
Substituting with y = 20,582 when x = 1, we get:
\(\begin{gathered} 20,582=20,080\cdot b^1 \\ \frac{20.582}{20,080}=b \\ 1.025=b \end{gathered}\)Now, we can complete the table as follows:
\(\begin{gathered} x=2 \\ y=20,080\cdot1.025^2=21097 \\ x=3 \\ y=20,080\cdot1.025^3=21624 \\ x=4 \\ y=20,080\cdot1.025^4=22165 \end{gathered}\)Expressing the exponential growth formula with the rate of growth r:
\(y=a(1+r)^x^{}\)where b has been replaced by 1 + r. This means that r = 0.025, which expressed as a percent is 0.025*100 = 2.5% growth
Related Questions
When posted overseas to country A at age r, the employees of
a large company are subject to a force of mortality such that, at exact duration
†years after arrival overseas (1 = 0, 1,2, 3,4),
Answers
The probability that an employee posted to country A at age 30 will survive to age 40 if she remains in that country is 2 x 10⁻⁶³
Probability is a mathematical concept that describes the likelihood of a specific event occurring within a set of possible outcomes
Let's start by defining some terms. The force of mortality, also known as the death rate, is the number of deaths per unit time per unit of population.
The probability of survival is the chance that an individual will live past a certain age. In our case, we want to know the probability of surviving from age 30 to age 40 while living in country A.
To calculate the probability of survival, we will use the formula:
\(P(x) = e^{-qx}\)
Where P(x) is the probability of survival at age x and qx is the force of mortality at age x.
First, we will calculate the force of mortality for the first five years after arrival in country A using the equation given in the question:
90x+1 = (6 - 1)9x+1
For x = 30, we have:
90(30) + 1 = (6 - 1)9(30) + 1
2701 = 5 * 891 + 1
2701 = 4445 + 1
2700 = 4445
So, q30 = 4445/30 = 148.5
Next, we will use this value to calculate the probability of survival for the first five years in country A:
\(P30 = e^{-q3} = e^{-148.5} = 1.2 \times 10^{-64}\)
Since the force of mortality for those who have lived in country A for at least five years is 50% greater than the US Life Tables, 2002, Females, we can calculate the force of mortality for the next 10 years as follows:
qx = 1.5 x qx from US Life Tables
Using the values from Table 3.11, we have:
q31 = 1.5 x 98,424 = 147,636
q32 = 1.5 x 98,362 = 147,543
q33 = 1.5 x 98,296 = 147,444
q34 = 1.5 x 98,225 = 147,338
q35 = 1.5 x 98,148 = 147,222
q40 = 1.5 x 97,500 = 146,250
Finally, we can use these values to calculate the probability of survival from age 31 to age 40:
\(P31 = e^{-q31} = e^{-147,636} = 1.3 \times 10^{-65}\\ \\P32 = e^{-q32} = e^{-147,543} = 1.4 \times 10^{-66}\\\\P33 = e^{-q33} = e^{-147,444} = 1.5 \times 10^{-67}\\\\P34 = e^{-q34} = e^{-147,338} = 1.6 \times 10^{-68}\\\\P35 = e^{-q35} = e^{-147,222} = 1.7 \times 10^{-69}\\\\P40 = e^{-q40} = e^{-146,250} = 2.0 \times 10^{-63)}\\\\\)
Complete Question:
When posted overseas to country A at age x, the employees of a large company are subject to a force of mortality such that, at exact duration t years after arrival overseas (t = 0,1,2,3,4), 90x+1 = (6 - 1)9x+1 where qx+t is on the basis of US Life Tables, 2002, Females. For those who have lived in country A for at least five years the force of mortality at each age is 50% greater than that of US Life Tables, 2002, Females, at the same age. Some lx values for this table are shown in Table 3.11.
An extract from the United States Life Tables, 2002,
Females. Age,
x 30 31 32 33 34 35 40
1x 98,424 98,362 98,296 98,225 98,148 98,064 97,500
Calculate the probability that an employee posted to country A at age 30 will survive to age 40 if she remains in that country.
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The height of a right triangular prism is 1 5/6 inches each side of the triangular base measures 10 inches and the height of the bases eight2 over 3 inches the triangular prism is place to top of cube whose side measures 10 inches so that one of the triangular prisms bases lies completely on one side of the cube what is the surface area of the solid formed
Answers
The surface area of the solid formed is approximately, 598.3 in².
What is the Surface Area of a Right Triangular Prism?Surface area of the solid is the area covered by the solid all round.
The given parameters are:
Height of the prism (L) = 1 5/6 = 1.83 in.Side of base (s1) = 10 in.Side of base (s2) = 10 in.Side of base (s3) = 8 2/3 = 8.67 in.base (b) = 10Height (h) = 8.67 in.a = 10 in.Surface area of the solid formed = 5(10×10) + (0.5×10×8.67) + 3(10×1.83) = 598.3 in²
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Corrine picked 1/4 gallon of blackberries. She poured the berries equally into 4 containers. What fraction of a gallon is in each container?
Answers
Answer:
1/16 of a gallon
Step-by-step explanation:
total = 1/4 gallon
split into 4 containers
1/4 ÷ 4 = 1/4 • 1/4 = 1/16
1/16 of a gallon
help me answer a. b. c. d. e. and f
Answers
Answer:
The correct answer is F hope you have a hood day
Suppose there are 15 jelly beans in a box—2 red, 6 blue, 4 white, and 3 green. A jelly bean is selected at random.
What is the probability that the jelly bean is blue?
Answers
Answer:
6 out of 15
Step-by-step explanation:
i dont know if this is right plz tell me if its wrong
a seagull flies 24 1/2 feet above sea level. it dives and changes its elevation by -47 2/3. what the seagull's elevation relative to sea level? show your work
Answers
David and Ken took part in a cycling race. Both of them did not change their speed throughout the race. David completed the race in 5 hours while Ken took 7 hours. Ken's average speed was 9.8 km/h less than David's average speed.
A) What was David average speed
B)What was the distance of the cycling race?
Answers
Let's assume David's average speed is S km/h.
A) To find David's average speed, we can use the formula: Speed = Distance / Time.
David completed the race in 5 hours, so his speed is S km/h. Therefore, we have:
S = Distance / 5
B) Ken's average speed is 9.8 km/h less than David's average speed, which means Ken's average speed is (S - 9.8) km/h.
Ken took 7 hours to complete the race, so we have:
S - 9.8 = Distance / 7
Now, we can solve the system of equations to find the values of S and Distance.
From equation (1): S = Distance / 5
Substitute this into equation (2):
Distance / 5 - 9.8 = Distance / 7
Multiply both sides of the equation by 35 to eliminate the denominators:
7 * Distance - 35 * 9.8 = 5 * Distance
7 * Distance - 343 = 5 * Distance
Subtract 5 * Distance from both sides:
2 * Distance - 343 = 0
Add 343 to both sides:
2 * Distance = 343
Divide both sides by 2:
Distance = 343 / 2 = 171.5 km
Therefore, the distance of the cycling race is 171.5 kilometers.
To find David's average speed, substitute the distance into equation (1):
S = Distance / 5 = 171.5 / 5 = 34.3 km/h
So, David's average speed was 34.3 km/h.\(\)
Answer:
A) 34.3 km/h
B) 171.5 km
Step-by-step explanation:
Since Ken's average speed is said to be 9.8km/h less than David's average speed, and we know that Ken's average speed is dependent on him traveling for 7 hours, then we have our equation to get the distance of the cycling race:
\(\text{Ken's Avg. Speed}=\text{David's Avg. Speed}\,-\,9.8\\\\\frac{\text{Distance}}{7}=\frac{\text{Distance}}{5}-9.8\\\\\frac{5(\text{Distance})}{7}=\text{Distance}-49\\\\5(\text{Distance})=7(\text{Distance})-343\\\\-2(\text{Distance})=-343\\\\\text{Distance}=171.5\text{ km}\)
This distance for the cycling race can now be used to determine David's average speed:
\(\text{David's Avg. Speed}=\frac{\text{Distance}}{5}=\frac{171.5}{5}=34.3\text{ km/h}\)
Therefore, David's average speed was 34.3 km/h and the distance of the cycling race was 171.5 km.
What is the value of the expression below when y=4y=4? 3y^2 +y+8 3y 2 +y+8
Answers
Answer:
1. 18
2. 13.5
3. 3rd choice
4. 2nd choice
5. 18.6
6.3m + 8
7. 5x2 + y
i hope this work for you
How many different sums of money can be made from 4coins of different denomination
Answers
Answer:
15 different sums----------------------
There are various combinations of coins.
1 coin:4 options2 coins:4C2 = 4!/(2!2!) = 6 options3 coins:4C3 = 4!/(3!1!) = 4 options4 coins: 1 optionIn total there are:
4 + 6 + 4 + 1 = 15 different sums6/10 + 5/100
is it
65/100 or 65/110 or 56/100 or 56/110
Answers
Answer:
65/100 that is the answer to this question
What is a in this question
Answers
The value of the segment a for the similar triangles is equal to 6.
How to calculate for a for the similar trianglesThe triangles MNO and YXO are similar, this implies that the length OX of the smaller triangle is similar to the length ON of the larger triangle
and the length OY of the smaller triangle is similar to the length OM of the larger triangle
so;
a/(a + 18) = 4/(4 + 12)
16a = 4(a + 18) {cross multiplication}
16a = 4a + 72
16a - 4a = 72 {collect like terms}
12a = 72
a = 72/12 {divide through by 12}
a = 6.
Therefore, the value of the segment a for the similar triangles is equal to 6.
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To which subsets of 3/4 belong.
Answers
The given number 3/4 which subsets belong to a rational number. The answer is option (A) rational numbers.
As per the question,
The given number is 3/4.
As we know that a rational number is one that can be written as a ratio of two integers, where the denominator is greater than zero.
The result is rational because 3/4, can be expressed as a ratio of two integers can be 3/4 of two integers, a numerator 3, and a denominator 4 (which is a non-zero).
So, the given number 3/4 which subsets belong to a rational number.
Therefore, the correct answer is option (A) rational numbers.
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The complete question is as follows:
To which subset of real numbers does the number 3/4 belong?
A. rational numbers
B. irrational numbers
C. whole numbers, integers, rational numbers
D. whole numbers, natural numbers, integers
Help help help ASAP
Answers
Find the area of the rectangle if the length is (x-2) inches and the width is (3x+1) inches shown in the picture PLEASE HURRY!!!!!!
Answers
What are the roots of this quadratic equation?-10.x2 + 12x – 9 = 0Ο Α.r=OB.ivo5+3iv24203iv6+10+ܩܙܗ ܕܐܗO C.ODm =2 3iv65ResetNext2021 Edmentum. All rights reserved.
Answers
For the general quadractic equation,
\(ax^2+bx+c=0\)the roots are given by the quadratic formula,
\(x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}\)In our case,
\(\begin{gathered} a=-10 \\ b=12 \\ c=-9 \end{gathered}\)Then, by substituting these values into the formula, we have
\(x=\frac{-12\pm\sqrt[]{12^2-4(-10)(-9)}}{2(-10)}\)which gives
\(\begin{gathered} x=\frac{-12\pm\sqrt[]{144^{}-360}}{-20} \\ x=\frac{-12\pm\sqrt[]{-216}}{-20} \\ x=\frac{6}{10}\pm\frac{6\sqrt[]{6}i}{-20} \end{gathered}\)help again...its for math offering 15 points
Answers
Answer:
\(\tan \dfrac{\theta}2 = \dfrac{1}2\)
Step by step Explanation:
\(\sin \theta = \dfrac{\text{Perpendicular} }{\text{Hypotenuse}} = \dfrac{12}{15}\\\\\\\cos \theta = \dfrac{\text{Base}}{\text{Hypotenuse}}= \dfrac{9}{15}\\\\\text{Now,}\\\\\tan \dfrac{\theta}2 = \dfrac{\sin \tfrac{\theta}2}{\cos \tfrac{\theta}2}\\\\\\~~~~~~~~=\dfrac{2\cos \tfrac{\theta}2 \sin \tfrac{\theta}2 }{2\cos^2 \tfrac{\theta}2}~~~~~~;\left[\text{Multiply by}~ 2\cos\tfrac{\theta}2 \right]\)
\(=\dfrac{\sin \theta}{1+ \cos \theta}~~~~~~~~~~~~;[2 \sin x \cos x = \sin 2x ~ \text{and}~ 2\cos^2 x =1+\cos 2x]\\\\\\=\dfrac{\tfrac{12}{15}}{1+ \tfrac{9}{15}}\\\\\\=\dfrac{\tfrac{12}{15}}{\tfrac{24}{15}}\\\\\\=\dfrac{12}{15}\times \dfrac{15}{24}\\\\\\=\dfrac{12}{24}\\\\\\=\dfrac{1}2\)
Your brother is going away to college, so you no longer have to share a bedroom. You decide to redecorate a wall by
hanging two new posters on the wall. The wall is 14 feet wide and each poster is four feet wide. You want to place the
posters on the wall so that the distance from the edge of each poster to the nearest edge of the wall is the same as the
distance between the posters, as shown in the diagram below. Determine that distance.
14 Feet
4 Feet
4 Feet
Answers
Answer:
2 feet apart each
Step-by-step explanation:
Atlanta's population is two million, eight hundred thirty-three thousand, five hundred
eleven. Write this number in standard form (using numbers).
??
Answers
Answer:
2,833,500
Step-by-step explanation:
Which of these contexts describes a situation that is impossible?
Rolling a number less than 1 on a standard six-sided die, numbered
from 1 to 6,
Spinning a spinner divided into four equal-sized sections colored
red/green/yellow/blue and landing on some color,
Winning a raffle that sold a total of 100 tickets if you bought 50 tickets,
Reaching into a bag full of 15 strawberry chews and 5 cherry chews
without looking and pulling out a strawberry or a cherry chew.
Answers
Rolling a number less than 1 on a standard six-sided die, numbered
from 1 to 6 is an impossible situation.
What is a sure event?Suppose we have a coin with sides heads and tails then the occurrence of a head or a tail is a sure event.
If we observe the given options we can conclude that Rolling a number less than 1 on a standard six-sided die, numbered from 1 to 6 is an impossible situation as we couldn't get a number less than 1 on the die not possible right?
All the other options seem possible in some different ways but the first option is an impossible situation.
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10. Prime numbers from 1 to 100 are running a restaurant - PRIME SPOT, near a tourist point. On a winter holiday, 1 and the composite numbers up to 100 enter the restaurant for dinner after their picnic at the same point. The dining hall has tables with seating capacity 15 for each. If they occupy tables without leaving any chair free, how many tables are required? If each prime number attender has to serve equal number of customers, how many customers should each one get to serve?
Answers
6 tables are required. Each prime number attender should serve 3 customers each.
The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
All the numbers other than prime numbers are composite numbers.
The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.
Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.
Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables
Therefore, 6 tables are required.
Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.
Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.
Thus, each prime number attender should serve 3 customers each.
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Polly would like to buy a crystal vase with an original price of $940. Which coupon should she use? $125 off any vase or 15% off any item
Answers
Solution:
Given that Polly would like to buy a crystal vase with an original price of $940. We want to determine which coupon should she use
Coupon 1: $125 off any vase
Coupon 2: 15% off any item
Let us get the look at the value of
Julie plans to invest her bonus of P100, 000.00 in two banks. The first bank earns an interest of 6% per annum while the other bank earns 8% interest per annum. If she wants her investment to earn a total interest of exactly P7, 200.00 after a year, how much does she need ot invest in each bank?
Answers
The amount of money that is invested in the first and second accounts will be 40,000 and 60,000, respectively.
What is the solution to the equation?The possible value of the variables that satisfy the equation which is known as the solution of the equation.
The interest is given as,
I = PRT / 100
Let 'x' be the amount invested in the first bank. Then the amount of investment in the second bank is (100,000 - x). Then the equation is given as,
x · 0.06 · 1 + (100,000 - x) · 0.08 · 1 = 7,200
0.06x + 8,000 - 0.08x = 7,200
-0.02x = -800
x = 40,000
The amount in the second bank is given as,
⇒ 100,000 - 40,000
⇒ 60,000
The amount of money that is invested in the first and second accounts will be 40,000 and 60,000, respectively.
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Y=2X squared -12 X +20 for quadratic formula
Answers
x = (12 ± √(-16)) / 4,The solutions would be complex numbers.
What is the quadratic formula?To solve quadratic equations of the form ax2 + bx + c = 0, use the quadratic formula. For this situation, your condition is as of now as a quadratic condition, with a = 2, b = - 12, and c = 20.
The quadratic formula is:
x = (-b ± √\((b^2 - 4ac)\)) / 2a
Plugging in the values for a, b, and c, we get:
x = (-(-12) ± √\(((-12)^2 - 4(2)(20)))\) / 2(2)
Simplifying the expression inside the square root:
x = (12 ± √\((144 - 160)\)) / 4
x = (12 ± √(-16)) / 4
Since the square foundation of a negative number is definitely not a genuine number, this condition has no genuine arrangements. Complex numbers would provide the answers.
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Can you answer this? Take ur time I'm not in a hurry.
Thanks!
Answers
i believe the correct graph is the bottom left
Find the Value of Y.
Answers
The value of y in the triangle is 2√10 units.
How to find the side of similar triangle?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
The value of y can be found using the similar triangle ratios as follows:
Hence,
8 / y = y / 5
cross multiply
y² = 8 × 5
y²= 40
square root both sides of the equation
y = √40
Therefore,
y = 2√10 units
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Please awnser asap I am
Stuck
Answers
Answer:
it is too blury to read
Step-by-step explanation:
Find the square root of 1681
Answers
Answer: The square root of 1681 is 41.
Answer:
41
Step-by-step explanation:
It is 41
41 * 41 = 1681
41 ^ 2 = 1681
Mario has save $200 towards the cost of buying a $1000 computer in the weeks to come he passes seven additional $30 per week create an expression that represents the amount of money Mario has saved after W weeks
Answers
Answer:
30w+200=1000
Step-by-step explanation:
Solve the system of equations§ 42 +-215y8y62 +34How many solutions are there? Select an answerVIf there arelup solutions, enter DNE below. If there is one solution, enter it below as an ordered pair.If there are infinitely many solutions, enter any ordered pair which is a solution.> Next Questionji
Answers
Answer
x = 1
y = -5
Hence, the system of equations only has one solution.
Writing this solution as an ordered pair would require us to put it in the form (x, y). So, the ordered pair solution is
(1, -5)
Explanation
We are asked to solve the system of equations and determine how many solutions it has
4x + 5y = -21
6x + 8y = -34
To do this, we try to make the coefficients of x the same; so, we multiply the first equation by 6 and the second equation by 4
(4x + 5y = -21) × 6
(6x + 8y = -34) × 4
24x + 30y = -126
24x + 32y = -136
We can then subtract the first equation from the second equation
24x - 24x + 32y - 30y = -136 - (-126)
0 + 2y = -136 + 126
2y = -10
Divide both sides by 2
(2y/2) = (-10/2)
y = -5
We can then solve for x
4x + 5y = -21
4x + 5(-5) = -21
4x - 25 = -21
4x = -21 + 25
4x = 4
Divide both sides by 4
(4x/4) = (4/4)
x = 1
Hope this Helps!!!
The scale on a road map is 1 cm = 250 miles. If the distance between two cities on the map is 6.5 cm, what is the actual distance between the cities?
Answers
Answer:
1625
Step-by-step explanation:
multiply 6.5x250 since each cm is 250 and you have 6.5 cm