Answer:
The population will be 240,116
Step-by-step explanation:
Exponential growth can be represented by the expression:
[tex]P(t) = P_i\,(1+r)^t[/tex]
where:
[tex]P(t)[/tex] is the population at time (t)
[tex]P_i[/tex] is the initial value of the population
"r" is the annual rate of growth (written in decimal form)
and "t" is the time in years.
Therefore in this situation, P(16) is what we want to find [the population after 16 years]
the initial population [tex]P_i[/tex] is 110,000
the rate of growth is 0.05 [decimal form of 5%]
and t is 16 years.
Replacing all these in the given functional form gives:
[tex]P(t) = P_i\,(1+r)^t\\P(16)=110000\,(1+0.05)^16\\P(16)=240116[/tex]
An exponential function to model a population of 110,000 that grows at 5% per year for 16 years is P(t) = 110,000 ∙ (1.05)^t. After 16 years, using this exponential function, the population would be approximately 242,884.
Explanation:To model the population growth using an exponential function, we can use the formula P(t) = P0 ∙ (1 + r)t, where P(t) is the population after t years, P0 is the initial population, r is the growth rate, and t is the time in years. In this case, the initial population P0 is 110,000, the growth rate r is 5% (or 0.05), and the time t is 16 years.
The exponential growth function would be:
P(16) = 110,000 ∙ (1 + 0.05)16
To find the projected population after 16 years, we'll calculate:
P(16) = 110,000 ∙ (1.05)16
P(16) = 110,000 ∙ 2.20804
P(16) = 242,884.4
After rounding, the population would be approximately 242,884 after 16 years.
Solve for x. Each figure is a trapezoid,
Answer:
x=5
Step-by-step explanation:
Since a Trapizode has 360 Degrees total and since the sides are equal we can say that
180=110+17x-15
70=17x-15
85=17x
x=5
The value of x in the trapezoid is 5
How to calculate the value of xThe sum of the sides on a trapezium is 180 ;
Using the expression :
17x - 15 + 110 = 18017x + 95 = 180
17x = 180 - 95
17x = 85
x = 85/17
x = 5
Therefore, the value of x is 5.
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PLEASE HELP!!!!!
The graph of g(x) is a translation of y = 3 square root of x
Which equation represents g(x)?
g(x) = 3 square root of x-4
g(x) = 3 square root of x+4
g(x) = 3 square root of x+1.5
g(x) = 3 square root of x-1.5
Answer:
Here we do not have the image, but i will try to give a explanation about this type of problem.
When we have the function f(x), the graph of the function h(x) = f(x - x0) means that the graph is displaced by x0 units to the right.
This is because the value of f(x = 0) is equivalent to h( x = x0), but the first one corresponds to the pair (0, f(0)) and the other corresponds to (x0, f(0))
This means that:
g(x) = 3√(x - 4) is displaced 4 units to the right.
g(x) = 3√(x + 4) = g(x) = 3√(x - (-4)) is diplaced 4 units to the left.
g(x) = 3√(x - 1.5) is displaced 1.5 units to the right.
g(x) = 3√(x + 1.5) is displaced 1.5 units to the left.
3. Which of the following are the roots of the quadratic function below?
Select all that apply.
f(x) = x2 - 144
12
2
Answer:
x = ± 12
Step-by-step explanation:
Given
f(x) = x² - 144
To find the roots set f(x) = 0, that is
x² - 144 = 0 ( add 144 to both sides )
x² = 144 ( take the square root of both sides )
x = ± [tex]\sqrt{144}[/tex] = ± 12
Final answer:
The roots of the given quadratic function f(x) = x² - 144 are x = 12 and x = -12.
Explanation:
The roots of a quadratic function can be found by setting the function equal to zero and solving for x. In the case of f(x) = x² - 144, this is equivalent to solving the equation x² - 144 = 0. This equation is a difference of squares and can be factored as (x - 12)(x + 12) = 0. The roots of the equation are the values of x that make the equation true, which in this case are x = 12 and x = -12.
What are the coordinates for point G?
Answer:
G: (-2, 0.5)
Step-by-step explanation:
the "X" is -2 and then the "Y" is 0.5 because it is between 0 and 1, so we could the that Y-axis is being added by 0.5 each time.
can you plz help me out on this one please having a haerd time with it
Answer:
the line should have an open circle on 75.7 and point to the right
solve the equation-27.5-m=21.1
Answer:
m=-48.6
Step-by-step explanation:
-27.5-m=21.1
m=-27.5-21.1
m=-48.6
Answer:
48.6 Is your correct answer :)
Step-by-step explanation:Please mark brainlies :)
what is the answer to 43.26 ÷ 14
Answer:
3.09
Step-by-step explanation:
Answer:
3.09
The drawing will help
Who ever answers will get brainlest and revive 50 points ( and if u can put answers to whole assessment that will be fine to ;)
First add the two fractions inside parenthesis:
5/7 - 6/14
Rewrite 5/7 to have a common denominator:
5/7 = 10/14
Now you have 10/14 - 6/14
10-6 = 4
The answer is 4/14, which can be reduced to 2/7
Answer:
(a)
Step-by-step explanation:
2/7 hope it helps
find the circumference of the circle with 1/4 Pi square centimetre square 2
Answer:
The circumference of the circle is 6 cm (approximately).
Step-by-step explanation:
Given:
Area of the circle = 1/4π²
Now, to get the circumference of the circle we need the radius.
So, finding the radius by putting the formula of area:
Area = [tex] \pi r^{2}[/tex]
[tex]\frac{1}{4} \pi ^{2}[/tex] = [tex] \pi r^{2}[/tex]
dividing π by both sides:
[tex]\frac{1}{4}\pi[/tex][tex]=r^{2}[/tex]
using square root on both the sides:
[tex]\frac{1}{2}\sqrt{\pi } = r[/tex]
So, the radius is [tex]\frac{1}{2}\sqrt{\pi } [/tex]
Now, putting the formula of circumference:
[tex]circumference=2\pi r[/tex]
=[tex]2\pi\frac{1}{2} \sqrt{\pi}[/tex]
=[tex]\pi \sqrt{\pi}[/tex]
putting the value of π =3.14
=[tex]3.14\times\sqrt{3.14}[/tex]
=[tex]3.14\times1.77[/tex]
=[tex]5.56[/tex]
Circumference = 5.56 cm
Therefore, the circumference of the circle is 6 cm (approximately).
The class average on test 1 was 84. The class average on test 2 was 8 points lower. What was the class average on test 2?
The class average on test 2 is 76 points
Solution:Given that, the class average on test 1 was 84.
And the class average on test 2 was 8 points lower.
We have to find what was the class average on test 2?
Now, according to the given information.
Class average on test 2 is 8 points lower than class average on test 1.
So, class average on test 2 = class average on test 1 – 8 points
Class average = 84 – 8
Class average = 76 points.
Hence, the class average on test 2 is 76 points
Fred buys a binder for $4.50 and six reams of paper. Latasha buys an ink cartridge for $17.50 and four reams of paper. Both spend the same amount of money. What is the price of one ream of paper?
Price of one ream of paper is $6.5
Step-by-step explanation:
Let,
x be the total cost.
Cost of one ream of paper = y
Cost of binder = $4.50
Cost of ink cartridge = $17.50
According to given statement;
x = 4.50 + 6y Eqn 1
x = 17.50 + 4y Eqn 2
As both spent the same amount, therefore,
Eqn 1 = Eqn 2
[tex]4.50+6y=17.50+4y\\6y-4y=17.50-4.50\\2y=13\\[/tex]
Dividing both sides by 2
[tex]\frac{2y}{2}=\frac{13}{2}\\y=6.5[/tex]
Price of one ream of paper is $6.5
Keywords: linear equation, division
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8 avocados cost $16.what is the cost of the one avocado
Answer:
one avocado cost 2 dollars
Step-by-step explanation:
16 divided by 8 is 2 so therefor one cost $2
Divide 16 by 8.
16 ÷ 8 = 2.
So, one avocado costs $2.
Use n to represent the position of a term in the sequence where n =1 for the first term 0, 1, 2, 3, ...
Answer:
[tex]a_{n} = a_{1} + (n-1)[/tex]this is the required representation for showing the position of a term in the sequence.
Step-by-step explanation:
Given:
The sequence is as follow:
0, 1, 2, 3, .......
To Find:
The expression while using 'n' to represent the position of a term in the sequence where n = 1 for the first term 0, 1, 2, 3, ....
Solution:
n = to represent the position of the term in the sequence.
[tex]a_{1} = \textrm{represent the first term in the sequence.} = 0[/tex]
d = Common difference.,i.e difference between the consecutive term.
d = second term - first term.
or
d = third term - second term.
Here we have d = 1 - 0 = 1
or d = 2 - 1 = 1
So, the required expression is
[tex]a_{n} = a_{1} + (n-1)\times d[/tex]
[tex]a_{n} = a_{1} + (n-1)[/tex]
If we require first term put n = 1
[tex]a_{1} = a_{1} + (1-1)[/tex]
[tex]a_{1} = 0[/tex]
If we require second term put n = 2
[tex]a_{2} = a_{1} + (2-1)[/tex]
[tex]a_{2} = 0 + 1[/tex]
[tex]a_{2} = 1[/tex]
If we require third term put n = 3
[tex]a_{3} = a_{1} + (3-1)[/tex]
[tex]a_{3} = 0 + 2[/tex]
[tex]a_{3} = 2[/tex]
and so on.......
Solve 38 x 21 using an area
model.
Answer:
798
Step-by-step explanation:
hsushshxhuxvshsjsvs
The area of a rectangle is given as:
Area = Length x width
Length = 38
Width = 21
The value of 38 x 21 as an area model is 798.
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
38 x 21 as an area model.
This can be considered as,
Length = 38
Width = 21
Now,
The area of a rectangle.
= 38 x 21
= 798
Thus,
The value of 38 x 21 as an area model is 798.
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PLEASE HELP THIS IS EASY BUT IM JUST BAD AT MATH
Melissa bought 3 loaves of freshly baked bread at a specialty bread shop. She paid twice as much for the whole grain bread as for the French bread, and $2.50 more for the cinnamon raisin bread than for the whole grain bread. She spent a total of $11.25 for the 3 loaves. If f represents the price of a loaf of French bread, which equations describe this situation? Select two answers. ANSWERS BELOW YES E IS X'ED OUT BUT IM NOT SURE ABOUT IT!
Answer:
Its B
Step-by-step explanation:
Try and read throught it slowly and everytime you hit a variable go down the the answer and find where it is. That helped me a lot
Answer:
b
Step-by-step explanation:
the french bread is f. the whole grain is double the price of f so it would be f(2) OR 2f. the cinnamon rasin is f + 2.50.
What is 3+7? :p
ok thx
Answer:
10
Step-by-step explanation:
3 + 7 = 10
Y= -(x - 6²) +6
How to right this equation in standard form equation of each parabola?
Answer:
-x^2+12x-30
Step-by-step explanation:
Find all values of x such that [tex]\sqrt{4x^2} -\sqrt{x^2}= 6[/tex]
From the given slopes of the lines, identify whether the two lines are parallel, perpendicular, or neither.
Slope 1
2
Slope 2
1/2
Answer:
Neither
Step-by-step explanation:
Parallel lines have equal slopes.
Clearly the lines are not parallel.
The product of the slopes of perpendicular lines equals - 1
2 × [tex]\frac{1}{2}[/tex] = 1 ≠ - 1
Thus the lines are not perpendicular.
Lines with Slope 1 = 2 and Slope 2 = 1/2 are neither parallel nor perpendicular.
To determine whether the two lines represented by Slope 1 = 2 and Slope 2 = 1/2 are parallel, perpendicular, or neither, we must consider the relationship between their slopes. Two lines are parallel if they have the same slope. In contrast, two lines are perpendicular if their slopes are negative reciprocals of each other (the product of their slopes is -1). In this case, since the slopes are different and their product (2 * 1/2) equals 1, not -1, the lines are neither parallel nor perpendicular.
Look at each expression. Is it equivalent to "the quotient of 10 plus x and y minus 3"?
10+X - 3
10+ x
y-3
10+-3
10+x-3
10+X-3
Answer:
b. [tex]\frac{(10+x)}{(y-3)}[/tex]
Step-by-step explanation:
Question:
Look at each expression. Is it equivalent to "the quotient of 10 plus x and y minus 3"?
a. (10+x)/(y)
b. (10+x)/(y-3)
c. 10+(x)/(y)-3
d. (10+x-3)/(y)
Solution:
Given statement:
The quotient of 10 plus [tex]x[/tex] and [tex]y[/tex] minus 3
From the statement we can have the following:
Dividend =[tex]10+x[/tex]
Divisor [tex]=y-3[/tex]
The quotient is given by dividend divided by divisor.
The quotient thus can be expressed as:
[tex]\frac{(10+x)}{(y-3)}[/tex]
Dan is comparing the cost of having printed and prepared by two companies
Company a charges $6 to prepare and $2.50 per copy to print
Company B charges $4 to make and $3 per print
How many copies will the total cost for preparing and printing by each company be the same
For 4 copies, the total cost for preparing and printing will be the same.
Step-by-step explanation:
Let,
p be the number of pages
Company A;
Charges of preparing = $6
Charges of per page print = $2.50
A(p)= 2.50p + 6 Eqn 1
Company B;
Charges of preparing = $4
Charges of per page print = $3
B(p)= 3p + 4 Eqn 2
For equaling the cost;
A(p) = B(p)
[tex]2.50p+6=3p+4\\2.50p-3p=4-6\\-0.50p=-2[/tex]
Dividing both sides by -0.50
[tex]\frac{-0.50p}{-0.50}=\frac{-2}{-0.50}\\p=4[/tex]
For 4 copies, the total cost for preparing and printing will be the same.
Keywords: Addition, division
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A deli receives a large order for sandwiches for a company picnic. The company wants one club sandwich and two regular sandwiches for each person. The company also wants an extra Dagwood sandwich. A club sandwich has $3$ slices of bread. A regular sandwich has $2$ slices. A Dagwood has $5$ slices.
If there are $n$ people going to the company picnic, how many slices of bread does the deli need to make this order? Write your answer as a fully simplified expression. Your answer should have the variable $n$ in it exactly once.
Answer:
7n +5
Step-by-step explanation:
For each person, the bread required is ...
1 club + 2 regular sandwiches = 1(3 slices) + 2(2 slices) = 7 slices
Then for n people, 7n slices of bread are required.
In addition, there is one Dagwood sandwich requiring 5 slices of bread. The total is then ...
7n +5 . . . . slices of bread required to fill the order.
Answer:
15n+5
Step-by-step explanation:
To determine the number of slices of bread needed to fulfill the deli's order for the company picnic, we need to calculate the total number of sandwiches required and then multiply it by the number of slices each type of sandwich contains.
Let's break it down step by step:
1. For each person attending the picnic, the company wants three sandwiches: one club sandwich and two regular sandwiches. So, for $n$ people, we have $3n$ sandwiches in total.
2. A club sandwich has 3 slices of bread, and a regular sandwich has 2 slices. Therefore, the number of bread slices required for $3n$ sandwiches can be calculated as follows:
- For the $3n$ club sandwiches, we need $3 \times 3n$ slices of bread, which is $9n$ slices.
- For the $3n$ regular sandwiches, we need $2 \times 2 \times 3n$ slices of bread, which is $6n$ slices.
3. In addition to the club and regular sandwiches, the company wants just one Dagwood sandwich, which has 5 slices of bread.
4. To find the total number of slices of bread needed, we add up the slices needed for each type of sandwich:
- $9n$ slices for the club sandwiches
- $6n$ slices for the regular sandwiches
- 5 slices for the Dagwood sandwich
Therefore, the total number of slices of bread required is $9n + 6n + 5$, which can be simplified to $15n + 5$.
So, the fully simplified expression for the number of slices of bread needed by the deli to fulfill the order for the company picnic is $15n + 5$.
Simplify the expression (9 + 2i)(9 − 2i).
(9 + 2i)(9 − 2i)=85
What is the square of imaganiry number i?The square of an imaginary number i is always -1. i.e. i²=-1
So according to asked question,
(9+2i)(9-2i)
using the algebric identity (a+b)(a-b)=a²-b²
where a=9 , b=2i
=(9)²-(2i)²
=9²-(4*i²)
=81-4i²
if we want to simplify the following expression
=81-(4(-1)) where i²=-1
=81+4
=85
Therefore (9 + 2i)(9 − 2i)=85
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3. A model rocket is launched from the ground with an initial velocity of 352 ft/sec.
e. How long will it take the rocket to reach its maximum height? Show all work in the space provided.
f. Assume the model rocket’s parachute failed to deploy and the rocket fell back to the ground. How long would it take the rocket to return to Earth from the time it was launched? Show all work in the space provided.
Answer:
e. It will take 11 seconds to reach the maximum height of 1,936 feet.
f. It will take 22 seconds to return to the earth.
Step-by-step explanation:
Given:
Initial velocity [tex]v_0[/tex] = 352 ft/sec
Solving for question e.
To find the time required to reach the maximum height we will use the formula,
[tex]h(t) = -16t^2+v_0t+h_0[/tex],
where [tex]v_0[/tex] is the starting velocity
[tex]h_0[/tex] is the initial height.
Using the velocity and starting height from our problem we have,
[tex]h(t) = -16t^2+352t+0[/tex],
The path of this rocket will be a downward facing parabola, so there will be a maximum.
This maximum will be at the vertex of the graph.
To find the vertex we start out with [tex]x= \frac{-b}{2a}[/tex] which in our case is,
[tex]x=\frac{-352}{2(-16)}=\frac{-352}{-32}= 11[/tex]
So, It will take 11 seconds for the rocket to reach its maximum height.
We will find maximum height using the formula by substituting value of t we get,
[tex]h(11)=-16(11^2)+352(11)+0\\h(11) = -16 \times121+ 352 \times 11 = -1936+3872= 1936 \ ft[/tex]
Hence the maximum height will be [tex] 1936 \ ft[/tex]
Now Solving for question f.
To find the time required for rocket to reach earth.
We will set our formula to 0 to find the time.
[tex]0= -16t^2+352t+0\\-16t(t-22)=0[/tex]
Using the zero product property, we know that either -16t = 0 or t - 22 = 0. When -16t = 0 is at t = 0, when the rocket is launched. t - 22 = 0 gives us an answer of t = 22.
So the rocket reaches the Earth again at 22 seconds.
The population of a town was 230000. For 12 years, the population grew by 4% per year, compounded continuously. What was the population at the end of the 12 year period according to the exponential growth function? Round your answer down to the nearest whole number, and do not include units.
Answer: 371697
Step-by-step explanation:
For continuously compounded values, we use the formula Pe^rt, or Pert. P is our principal/initial value, 230000. e is the constant e, r is our rate, 4% or .04, t is our time, 12. So, 230000*e^(.04*12)=371697.112504, rounding down, 371697.
which three expressions are equavalent to the expression 3x-12-2(x+12)
3(x^2+4x)+4(y^2-2y)=32
Answer:
3x^2 + 12x + 4y^2 - 8y = 32
Step-by-step explanation:
3(x^2+4x)+4(y^2-2y)=32
At first we have to break the parenthesis to get the variables in normal position. To break those, we have to multiply each with the help of algebraic expression:
or, (3*x^2) + (3 × 4x) + (4 × y^2) - (4 × 2y) = 32
or, 3x^2 + 12x + 4y^2 - 8y = 32
Since the equation does not have anything to add or deduct, therefore, it is the answer.
PLEASE HELP Two bells ring every 10 and 25 minutes respectively. They start ringing together at 6 a.m. At what time will they next ring together?
They next ring together will be at 6:50 a.m.
Step-by-step explanation:
The given is:
Two bells ring every 10 and 25 minutes respectivelyThey start ringing together at 6 a.m.We need to know at what time will they next ring together
To solve the problem lets find the lowest common multiple of 10 and 25
∵ The multiples of 10 are 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 , 90 , 100 , .....
∵ The multiples of 25 are 25 , 50 , 75 , 100 , ........
∵ The common multiples of 10 and 25 are 50 , 100 , ......
∴ The lowest common multiple of 10 and 25 is 50
∵ The two bells start ringing together at 6 a.m.
∵ The first bell rings every 10 minutes
∴ The first bell rings at 6:10 a.m. , 6:20 a.m. , 6:30 a.m. , 6:40 a.m. ,
6:50 a.m. , .........
∵ The second bell rings every 25 minutes
∴ The second bell rings at 6:25 a.m. , 6:50 a.m. , ........
∴ They start ringing together at 6:50 a.m.
They next ring together will be at 6:50 a.m.
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Final answer:
To determine when two bells will next ring together, find the Least Common Multiple (LCM) of their ringing intervals. The LCM of 10 and 25 is 50, therefore the bells will next ring together at 6:50 a.m.
Explanation:
The question is about finding the next time two bells, ringing at different intervals, will ring together. To solve this, we need to find the Least Common Multiple (LCM) of the two bell ringing intervals: 10 minutes and 25 minutes. The LCM of 10 and 25 is 50 since 10 × 5 = 50 and 25 × 2 = 50. Since the bells start ringing together at 6 a.m., they will next ring together 50 minutes later.
Adding 50 minutes to 6 a.m., we get 6:50 a.m. Therefore, the two bells will next ring together at 6:50 a.m.
Hep hep help help help
Answer: The answer will be C.
Answer:
the process of retting softens the tissue and helps to separate the fibres
Step-by-step explanation:
the process of retting softens the tissue and helps to separate the fibres
Thanks
Evaluate the expression. Choose the best answer.
4! + 5! . 6!
A. 86,424
B. 120,840
C. 86,394
D. 85,424