Answers
Answer:
a. 18.5 million
b. 2002
Step-by-step explanation:
Given that A = 18.5·e^(0.1708t) models a population t years after 2000, you want to know the population in 2000 and when it will reach 26.6 million.
Population in 2000The year 2000 is 0 years after 2000, so we can find the population using t=0 in the given equation.
A = 18.5·e^(0.1708·0) = 18.5·e^0 = 18.5
The population in 2000 was 18.5 million.
Year of 26.6 millionWe can solve for t to find the year in which the population reached 26.6 million:
26.6 = 18.5·e^(0.1708t)
26.6/18.5 = e^(0.1708t)
ln(266/185) = 0.1708t
t = ln(266/185)/0.1708 ≈ 2.13 . . . . . . 2.13 years after 2000
The population will reach 26.6 million in the year 2002.
__
Additional comment
The population of 26.6 million represents about a 44% increase over the initial population of 18.5 million. The exponential term tells you the rate of growth is 17.08% compounded continuously. Thus we expect the larger population to be reached in a time slightly less than 44/17 ≈ 2.6 years.
(These numbers were found using a calculator. It is sufficient to do the estimating by realizing that 1.50·18 = 27, and 17·3 = 51, so the growth to 26.6 from 18.5 is less than 50% and will take less than 3 years.)
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Related Questions
Suppose that the functions g and h are defined for all real numbers x as follows.
g(x)=x-6
h(x)=4 x+3
Answers
By using the concept of function, it can be calculated that-
(h.g)(x) = 4x - 21
(h + g)(x) = 5x - 3
(h - g)(-1) = 6
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Here,
a) The given functions are
g(x)= x - 6
h(x) = 4x + 3
(h.g)(x) = h(g(x)) = 4(x - 6) + 3 = 4x - 21
(h + g)(x) = h(x) + g(x) = 4x + 3 + x - 6 = 5x - 3
(h - g)(x) = h(x) - g(x) = 4x + 3 - x + 6 = 3x + 9
(h - g)(-1) = 3 [tex]\times[/tex] (-1) + 9 = 6
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Jonah ran 1 Taps on Monday, 21 laps on Tuesday, and 6 laps on Wednesday.
How much farther did he run on Wednesday than on the other two days
combined? Show your work.
Answers
Jonah runs 2 (19/20) laps more than the remaining two days
Adding Fractions:The fractions that have the same denominator are like fractions, to add like fractions directly, But if the denominators are not the same then we need to change their denominators to the same then we can add the fractions.
To make denominators as same we need to take the LCM of denominators of two fractions.
Here we have
Jonah ran 1(3)/(4) laps on Monday
=> 1 3/4 = 7/4 laps
On Tuesday he ran 2(3)/(10) laps
=> 2 3/10 = 23/10 laps
On Wednesday he ran 6(1)/(5) laps
=> 6 1/5 = 31/5 laps
The total number of laps ran combining Monday and Tuesday
= 7/4 laps + 23/10 laps
= (35 + 46)/20 [ take Lcm of 4, 10 i.e 20 ]
= 81/20
From the above calculations,
Jonah ran 81/20 laps on combining Monday and Tuesdays
The difference between Wednesday's counted laps and Monday, and Tuesday's counted laps
= 31/5 - 81/20
= (140 - 81)/20 [ Take Lcm of 5, 20 i.e 20 ]
= 59/20
= 2 (19/20)
Therefore,
Jonah runs 2 (19/20) laps more than the remaining two days
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Complete Question:
Jonah ran 1(3)/(4) laps on Monday, 2(3)/(10) laps on Tuesday, and 6(1)/(5) laps on Wednesday. How much farther did he run on Wednesday than on the other two days combined? Show your work.
Solve the following inequality and graph the solution:
(x-4)(x-5)<0
Choose test values and indicate whether the inequality is true or false in each region.
Enter the test values from smallest to largest.
Draw the solution above.
Write the solution as a compound inequality
4
Answers
The solution to the inequality (x - 4)(x - 5) < 0 is given as follows:
4 < x < 5.
The test values are given as follows:
x < 4 -> x = 3: false.4 < x < 5 -> x = 4.5: true.x > 5 -> x = 6: false.The graph of the inequality is given by the image shown at the end of the answer.
How to solve the inequality?The inequality in this problem is given as follows:
(x - 4)(x - 5) < 0
The inequality is a product, meaning that there is two cases for when it is negative, which are:
x - 4 > 0 and x - 5 < 0.x - 4 < 0 and x - 5 > 0.For the first case, the solution is given as follows:
x > 4 and x < 5 -> 4 < x < 5 (intersection).
For the second case, the solution is given as follows:
x < 4 and x > 5 (impossible).
Hence the compound inequality that gives the solution is of:
4 < x < 5.
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A wire is first bent into the shape of a rectangle with width 5cm and length 16 cm . Then the wire is unbent and reshaped into a triangle. If each side of the triangle has equal length, what is this length?
Answers
Hello,
I hope you and your family are doing well!
To find the length of each side of the triangle, we can use the formula for the perimeter of a rectangle: perimeter = 2 * (width + length). In this case, the perimeter of the rectangle is 2 * (5cm + 16cm) = 42 cm. Since each side of the triangle has the same length, and the perimeter of the triangle is equal to the perimeter of the rectangle, the length of each side of the triangle is 42cm / 3 = 14 cm.
Therefore, the length of each side of the triangle is 14 cm.
---
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Happy Holidays!
Shelby and Aisha baked homemade dog treats to sell. They baked 116 dog treats in all.
Shelby baked 3 times as many treats as Aisha.
4) How many dog treats did Aisha bake?
Answers
Answer:
87
Step-by-step explanation:
If Shelby and Aisha baked a total of 116 dog treats to sell, and Shelby baked 3 times as many dog treats that Aisha, then we need to figure out what 3/4 of 116 dog treats is.
116 ÷ 4 = 29
29 × 3 = 87
Shelby baked 87 dog treats.
Prove that a line parallel to one side of a triangle divides the other two sides proportionally. Be sure to create and name the appropriate geometric figures.
Answers
A line parallel to one side of a triangle divides the other two sides proportionally.
What is triangle?
A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.
Let ΔADE and ΔABC are two triangles.
Given: DE∥BC
To prove: DB/AD = EC/AE
ΔADE and ΔAC share ∠A
∠A ≅∠A reflexive property
DE∥BC is given
∠ADE ≅ ∠B because they are corresponding angles when transversal
AB cuts parallel lines DE and BC
ΔADE ∽ ΔABC a pair of angles in each are congruent.
AB / AD = AC / AE
because corresponding sides of similar triangle's are proportional.
Now subtract 1 from each side
AB / AD - 1 = AC / AE - 1
Combining fractions,
(AB - AD) / AD = (AC - AE) / AE
⇒ DB / AD = EC / AE
Hence, a line parallel to one side of a triangle divides the other two sides proportionally.
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Geometric figure:
If the lengths of two sides of a triangle are represented by 2x + 5 and 3x + 7 (in which x is positive), describe in terms of x the possible lengths of the third side whose
length is represented by y.
Answers
Answer:
x + 2 < y < 5x + 12
Step-by-step explanation:
given 2 sides of a triangle then the third side y is within the limits
difference of 2 sides < y < sum of 2 sides
3x + 7 - (2x + 5) < y < 3x + 7 + 2x + 5
3x + 7 - 2x - 5 < y < 5x + 12
x + 2 < y < 5x + 12
everything at a store is on sale. The store offers a 25% discount. The regular price of a t-shirt is 20%. What is the discount price? Please help me.
Answers
The discount price of the shirt will be $15.
How to calculate the price?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.
From the information, the store offers a 25% discount and the regular price of a t-shirt is $20. Therefore, based on the information illustrated, the main points to note will be:
Discount = 25%
Regular price = $20.
In this case, the discount price will be the difference between the regular price and the discount.
The discount price will be:
= Regular price - Discount
= $20 - ($20 × 25%)
= $20 - $5
= $15
The price is $15.
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Complete question
everything at a store is on sale. The store offers a 25% discount. The regular price of a t-shirt is $20. What is the discount price? Please help me
A rectangular solar panel has a length that is 11 inches shorter than 4 times it’s width. If the perimeter of the panel is 178 inches, what are the dimensions of the panel?
The width of the panel is *blank* inches.
Answers
Answer:
The width of the panel is 20 inches----------------------
Let the width be x, then the length is 4x - 11.
The perimeter of the rectangle is:
2(x + 4x - 11) = 178Solve it for x:
2(5x - 11) = 1785x - 11 = 895x = 100x = 20X
Y
If L=4, Y=30 and Z=14. Solve for X. (round to 2 decimal places)
L
N
Answers
Answer:
Y+Z/Z = X/L
X= (44/14)4 = 12.57(nearest 2 decimal
5 + w - 9 = 8
How do I solve this equation? Please explain step by step
Answers
Answer:
w=12
Step-by-step explanation:
w+5-9=8
w-4=8
w=12
Answer:
w = 12
Step-by-step explanation:
Subtract the numbers.
5 + w - 9 = 8
-4 + w = 8
Rearrange terms
-4 + w = 8
w - 4 = 8
Add 4 to both sides
w - 4 = 8
w - 4 + 4 = 8 + 4
Add
w - 4 + 4 = 8 + 4
w = 8 + 4
Add
w = 8 + 4
w = 12
The number of bacteria in a certain population increases Accor to a continuous growth model,with a growth parameter of 9.6% per hour. How many hours does it take for the size of the sample to double
Answers
The required number of hours does it take for the size of the sample to double is 11 hours.
What is percentage?Percentages are basically divisions where the denominator is 100. To show that a number is a percent, we utilize the percent image (%) close to the number. For instance, in the event that you got 75 inquiries right out of 100 on a test (75/100), you would have scored 75%.
According to question:Let initial population be x.
As question says number of bacteria increases by 9.6% per hours.
9.6% of x takes 1 hours,
So, in 11 hours size of sample become 105.6%, means almost double of initial size.
Thus, 11 hours will be taken to make size double.
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At the school fair, students used a scatter plot to compare the number of T-shirts sold
with the number of jars of jam sold. What can you conclude about the relationship
between the sales of the T-shirts and the jars of jam?
Answers
Answer: The jars of jam sales and the T-shirt sales have a positive correlation, but neither may cause the other.
Step-by-step explanation:
The correlation is a positive slope but selling T-Shirts and Jam shouldn't correlate to each other.
Describe how the values of r, x, and y relate to each of sinø, cosø and tanø
Answers
the values of r, x, and y are related to the sine, cosine, and tangent of angle ø as:
sin ø = y / r
cos ø = x / r
tan ø = y / x
What is trigonometry?
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
In a right triangle, the sides are typically labeled as follows:
The side opposite the angle ø is called the "opposite side" and is labeled "y".
The side adjacent to angle ø is called the "adjacent side" and is labeled "x".
The hypotenuse is the side opposite the right angle and is labeled "r".
The values of r, x, and y can be used to calculate the sine, cosine, and tangent of angle ø. These trigonometric functions are defined as follows:
Sine (sin ø): sin ø = y / r
Cosine (cos ø): cos ø = x / r
Tangent (tan ø): tan ø = y / x
Hence, the values of r, x, and y are related to the sine, cosine, and tangent of angle ø through the above equations.
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Select the correct answer.
What is the y-intercept of f(x) = 3x+2?
Ο Α.
OB.
O C.
OD.
(9, 0)
(0, 9)
(0, -9)
(9,-9)
4
Answers
Answer:
C, (0, 9)
Step-by-step explanation:
The y-intercept is when the x-value is 0. We pug in 0 for x, getting f(0) = 3^2=9. The x-coordinate must be 0, and the y-value is 3^2, or 9. The correct answer is (0, 9)
2. Determine the theoretical probability of rolling a two with one standard die. Write this probability in three equivalent forms: as a fraction, a decimal (rounded to three places), and a percentage (rounded to one decimal place).
Answers
The theoretical probability of rolling a two with one standard die in three equivalent form is 1/6, 0.167 and 16.7%
How to determine the theoretical probability?From the question, we have the following parameters that can be used in our computation:
The rolling of a standard die
In this case, we assume that the standard die is a fair die
i.e. the faces have equal chance of appearing
This means that the sample space of the die is
Sample space = {1. 2. 3. 4. 5. 6}
In this sample space, we have
Number of occurrence of 2 = 1
Number of items in the sample space = 6
The theoretical probability of 2 is then calculated as
Probability = Number of occurrence of 2/Number of items in the sample space
Substitute the known values in the above equation, so, we have the following representation
Probability = 1/6 --- in fraction
Evaluate the quotient
Probability = 0.167 -- in decimal
Express as percentage
Probability = 16.7%
Hence, the probability is 16.7%
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We want to determine if [u, v, w is linearly independent. To do that we write the vectors as columns of a matrix A and row reduce that matrix To check this we add We then add We then add We conclude that times the first row to the second. times the first row to the third. times the new second row to the new third row. OA. The set [u, v, w} is linearly dependent. O B. The set {u, v, w] is linearly independent. C. We cannot tell if the set [u, v, w] is linearly independent or not.
Answers
Option C, If your row reduces the matrix A and obtains a row of all zeros except for a single 1 in the rightmost column, then the set {u, v, w} is linearly dependent.
This is because the row of all zeros except for a 1 in the rightmost column indicates that one of the vectors in the set can be expressed as a linear combination of the other vectors.
On the other hand, if your row reduces the matrix A and does not obtain a row of all zeros except for a single 1 in the rightmost column, then the set {u, v, w} is linearly independent. This is because the absence of such a row indicates that none of the vectors in the set can be expressed as a linear combination of the other vectors.
If you are unable to row reduce the matrix A for any reason, then it is not possible to determine if the set {u, v, w} is linearly independent or not.
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Fill in the chart on paper,
then list the coefficient
of the "x" term.
4x
-10
3x²
-8x
+2
Enter
Answers
Answer:
2
Step-by-step explanation:
add 2 by 6 to get 02
I need help completing the proving Statement
Answers
This looks like a fill-in the blanks question for a two column proof :]
3. CPCTC
The reasoning for this is that because triangle ABC and EDC are congruent, their corresponding parts are also congruent, (CPCTC; Corresponding Parts of Congruent Triangle are Congruent) or AC = EC
4. ACE
Because AC = EC, triangle ACE is isosceles
5. Base Angles Theorem
The base angles of a isosceles triangle are congruent
:]
Fill in the blanks below in order to justify whether or not the mapping shown represents a function.
The mapping diagram above a function since
in where there
Answers
Answer:
This is a function
Step-by-step explanation:
For every input there is only one output.
Anita Jacobs could deposit R600 every 3 months in her credit union which pays 12% interest compounded quarterly. How much more would she have in her account at the END of 4 years if she deposited the R600 at the BEGINNING of each quarter rather than at the END of each quarter?
Answers
Answer: 1890
Step-by-step explanation:
Fully simplify. -15xy(15x^5y^3)
Answers
Answer:
−225x^6y^4
Step-by-step explanation:
Simplify: 3/8(4a-5)-5/12(3a-4)=1/6
Answers
Answer:
Step-by-step explanation:
3/8(4a-5)-5/12(3a-4)=
9/24(4a-5)-10/24(3a-4)=1/6 | x24
9*(4a-5)-10(3a-4)=4
36a-45-30a+40=4
6a=9
a=3/2
Cindy bought 7/8 yard of ribbion at the craft store. Jacob bought 4/5 the length of ribbon as Cindy. How many yards of ribbon did jacob buy?
Answers
A cafeteria serves lemonade that is made from a powdered drink mix. There is a proportional relationship between the number of scoops of powdered drink mix and the amount of water needed to make it. For every 2 scoops of mix, one-half gallon of water is needed, and for every 6 scoops of mix, one and one-half gallons of water are needed. Part A: Find the constant of proportionality. Show every step of your work. (4 points) Part B: Write an equation that represents the relationship. Show every step of your work. (2 points) Part C: Describe how you would graph the relationship. Use complete sentences. (4 points) Part D: How many gallons of water are needed for 10 scoops of drink mix? (2 points)
Answers
a) The constant of proportionality of the given problem is; 4
b) An equation that represents the relationship is; y = 4x
c) The graph is as attached.
d) The gallons of water that are needed for 10 scoops of drink mix is; 2.5 gallons
How to find the proportional relationship?The general equation for the equation of a line in slope intercept form is;
y = mx + c
where;
m is slope of line which tells us the unit rate of change of y with respect to x
c is the y - intercept
Now, it is pertinent to note that y = mx also represents direct proportionality. Making m the subject gives;
m = y/x
Thus, with proportion, we can say;
y₁/x₁ = y₂/x₂
The proportional relationship will be written as;
y = kx
where k is constant of proportionality
From the question, we can say that;
2 scoops require 0.5 gallon of water
6 scoops require 1.5 gallon of water
a) Thus;
k = 2/0.5
k = 2/(1/2)
k = 2 * 2 = 4
b) Equation that represents the relationship can be written as;
y = 4x + c
Since 2 scoops require 0.5 gallon of water, then;
2 = (4 * 1/2) + c
2 = 2 + c
c = 0
The equation will be; y = 4x.
c) Graph of y = 4x is attached at the end.
d) For 10 scoops of water;
10 = 4x
x = 2.5 gallons of water required.
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You are playing a game that involves tossing a single die. If you roll a one, you win $50.
If you roll a 2, you win $25. If you roll anything else, you lose $15. What are you expected winnings?
Answers
Answer:
the answer is: 01111001 01101111 01110101 00100000 01101000 01100001 01110110 01100101 00100000 01101000 01100001 01110110 01100101 00100000 00110011 00110000 00100101 00100000 01100011 01101000 01100001 01101110 01100011 01100101 00100000 01101111 01100110 00100000 01110111 01101001 01101110 01101110 01101001 01101110 01100111 00100000 01100001 01110011 01110011 01110101 01101101 01101001 01101110 01100111 00100000 01110100 01101000 01100101 00100000 01100100 01101001 01100011 01100101 00100000 01101000 01100001 01110011 00100000 00110110 00100000 01110011 01101001 01100100 01100101 01110011 00101110 . do a bit of work decoding it to get the right answer
Step-by-step explanation:
Solve for x Round to the nearest tenth, if necessary.
Answers
Answer:
1.7
Step-by-step explanation:
tan30°=1/XX=1/tan30°X=1/0.57741.73191.7(to the nearest tenth)Consider the piecewise function shown on the graph, which is composed of polynomial, constant, and exponential pieces.
10
-10-8-6-4-2 02 4
O
2
D. (-00, 4)
-2.
-6-
-8
-10-
Over which interval of the domain is the function increasing?
A. (1,4)
OB. (-00, 1)
OC. (-00,-4)
10
4
Answers
"Increasing" means the y-values are increasing as x-values increase. Or visually, if you were walking along the graph, from left-to-right, where would you be walking uphill?
The uphill portion is from (-infty, -4). Once you get to an x-value of -4, then it levels off (so it's "constant") until you get to x = 1, when it goes downhill (the function is decreasing).
The interval of the domain in which the function is increasing is(-∞, -4). so option C is correct.
What is a piecewise function?A function that is composed of several smaller functions, each with a distinct domain, is said to be piecewise. The term "piecewise" refers to the way in which these sub-functions are defined in terms of various intervals or "pieces" of the function's overall domain.
Given that,
The piecewise function which is discontinuous at x =1
In the interval
(-∞, -4) the value of the function is increasing.
[-4, 1) the value of the function is constant.
(1, ∞) the value of the function is decreasing.
Hence, the function is increasing in the domain (-∞, -4)
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2. Find the 72nd term in the arithmetic sequence 2,
-8, -18, -28, ..
Answers
Answer:
The 72nd term is -708
Step-by-step explanation:
Are the triangles congruent, if so which triangles?
S
3 in
AD
Q
4 in
R
X
3 in
4 in
O Yes, A RSQ =A XÚC
O Yes, AUXC = AQRS
O Yes, A XCU A SRQ
O No, these triangles are not congruent
O Yes, AUXCAQSR
Answers
Answer:
Yes, [tex]\triangle UXC \cong \triangle QRS[/tex]
Step-by-step explanation:
The triangles are congruent by SAS.