Answers
We can find the average rate of change of change using the following expression:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]for the period betwen 1999 and 2002, we have the following:
[tex]\begin{gathered} m=\frac{1483-1336}{2002-1999}=\frac{147}{3}=49 \\ \Rightarrow m=49 \end{gathered}[/tex]therefore, the average rate of change of population between 1999 and 2000 is 49.
Next, we do the same for the period between 2001 to 2005:
[tex]\begin{gathered} m=\frac{801-1591}{2005-2001}=-\frac{790}{4}=-197.5 \\ \Rightarrow m=-197.5 \end{gathered}[/tex]thus, the average rate of change of population between 2001 and 2005 is 197.5
Finally, notice that the population increased from 1997 to 2001, while it decreased from 2002, to 2006
Related Questions
how do I find a triangle congruence postulate that can be used to prove that the triangles are congruent if any with the options below?
Answers
First figure
we have that the triangles
ABC is congruent with triangle DCB by HL (hypotenuse leg)
Second figure
The triangles are congruent by Angle-Side- Angle
Third figure
The triangles are congruent by Side-angle -side
juanita makes leather lanyards to sell she charges a base fee and a cost per inch of the finished lanyard.
Answers
Answer
y = ½x + 5
If y is the total amount Juanita makes for x inches of finished lanyard,
Base fee = y-intercept = 5
Cost per inch = Slope = 0.5 = ½
Explanation
To write the expression for this, we need to write the equation for the line representing the whole function
The slope and y-intercept form of the equation of a straight line is given as
y = mx + b
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
b = y-intercept of the line.
From the gaph, we can easily see that
b = y-intercept = point where the line crosses the y-axis = 5
For the slope, for a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]For this question,
(x₁, y₁) and (x₂, y₂) are (2, 6) and (6, 8)
[tex]\text{Slope = }\frac{8-6}{6-2}=\frac{2}{4}=\frac{1}{2}=0.5[/tex]Recall,
y = mx + b
m = slope = 0.5 = ½
b = y-intercept = 5
y = ½x + 5
If y is the total amount Juanita makes for x inches of finished lanyard,
Base fee = y-intercept = 5
Cost per inch = Slope = 0.5 = ½
Hope this Helps!!!
how do i convert .035 into a fraction
Answers
Answer:
35/1000
Step-by-step explanation:
the 5 is in the thousandths place therefore it is over 1000
Answer:
you would make it a 7 for the top and 200 for the bottom
Step-by-step explanation:
Claire has a loyalty card good for a discount at her local grocery store. The item she wants to buy is priced at $27, before discount and tax. After the discount, and before tax, the price is $25.38. Find the percent discount.
Answers
The percent discount of the item in the grocery store if the item is priced at $27, before discount and tax and $25.38 after discount and before tax is 6%.
How to find percent discount?Price of item before discount and tax = $27Price of item after discount before tax = $25.38Percent discount = (Price of item before discount and tax - Price of item after discount before tax ) / Price of item before discount and tax × 100
= (27 - 25.38) / 27 × 100
= 1.62 / 27 × 100
= 0.06 × 100
= 6%
In conclusion, the percent discount of the item is given as 6%
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The cost of making a large circle is an amount in dollars and cents. The cost of making the smaller circle is 3/4 the cost of making the larger circle. Is the cost of making the smaller circle a rational or irrational number? Justify your answer.
Answers
The cost of making the smaller circle a rational number.
What is rational number?A number is rational if it has a terminating or repeating decimal; for example, 1/2 = 0.5. It is irrational if a number has a non-terminating and non-repeating decimal.
A rational number is one that can be written as P/Q, where P and Q are integers and Q = 0. However, an irrational number cannot be written in simple fractions. A rational number is 2/3, whereas an irrational number is ✓2.
It should be noted that in this situation, the cost of making the larger circle can be 4.0. The cost of making the small one will be:
= 3/4 × $4.0
= $3.0
This illustrates a rational number.
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Please help me with this problem it’s 1 question of 3 please help me I will leave good feedback for you(((
Answers
tan T = 8/8 = 1
tan ^-1 T = 45°
angle T = 45°
2) angle J = tan J = 2/4
tan J = 1/2
tan^-1 J = 26.57
rounded J = 26.6
Find the domain of the piecewise function and evaluate it for the given values. Then use the drop down menu to select the correct symbols to indicate your answer in interval notation. If a number is not an integer then round it to the nearest hundredth. To indicate positive infinifty ( \infty ) type the three letters "inf". To indicate negative infinity(-\infty ) type "-inf" with no spaces between characters. f(x) = \left\lbrace \begin{array}{cc} x+1 & x<-2 \\ -2x-3 & x\ge -2 \end{array}\right. The domain is:AnswerAnswer,AnswerAnswerf(-3)=Answerf(-2)=Answerf(-1)=Answerf(0)=Answer
Answers
SOLUTION
Let us make a graph of the function
[tex]\begin{gathered} f(x)=x+1\mleft\{x<-2\mright\} \\ f(x)=-2x-3\mleft\{x\ge-2\mright\} \end{gathered}[/tex]This is shown below
(a) The domain is usually determined from the x-axis. From the graph, the domain is all real numbers, that is, it is infinite for both positive and negative values for x, as you can see that if the graph is extended, there is no limit for x-values that it can contain. So the domain is (-infinity, infinity)
Hence the answer, Domain is
(-inf, inf)
(b)
[tex]f(-3)[/tex]In
[tex]\begin{gathered} f(x)=x+1\{x<-2\} \\ -3\text{ is less than -2, so -3 is valid here, so } \\ f(-3)=-3+1 \\ f(-3)=-2 \end{gathered}[/tex]Hence, the answer is -2
(c)
[tex]f(-2)[/tex]In
[tex]\begin{gathered} f(x)=-2x-3\{x\ge-2\} \\ -2\text{ is equal to -2, so we will put -2 for x here, so } \\ f(-2)=-2(-2)-3 \\ f(-2)=4-3 \\ f(-2)=1 \end{gathered}[/tex]Hence, the answer is 1
(d)
[tex]f(-1)[/tex]In
[tex]\begin{gathered} f(x)=-2x-3\{x\ge-2\} \\ -1\text{ is greater than -2, hence, it is valid, so we will put -1 for x here, so } \\ f(-1)=-2(-1)-3 \\ f(-1)=2-3 \\ f(-1)=-1 \end{gathered}[/tex]Hence, the answer is -1
(e)
[tex]f(0)[/tex]In
[tex]\begin{gathered} f(x)=-2x-3\{x\ge-2\} \\ 0\text{ is greater than -2, so we will put 0 for x here, so } \\ f(0)=-2(0)-3 \\ f(0)=0-3 \\ f(0)=-3 \end{gathered}[/tex]Hence, the answer is -3
It costs $2 to download a song and $12 to download an entire album. Jorge has $50 to spend on downloading music. Create an inequality that represents the number of songs (s ) and albums (a ) that Jorge could download.
Answers
Answer:
312
Step-by-step explanation:
42 43 312
y=-x^2-2x+3 what is the vertex of the graph? Answer an order pair.
Answers
Given:
[tex]y=-x^2-2x+3[/tex]a) To find the vertex:
Here, a=-1, b=-2, and c=3
We know that the formula to find the x- coordinate of the vertex is given by,
[tex]\begin{gathered} -\frac{b}{2a}=-\frac{(-2)}{2(-1)} \\ =-1 \end{gathered}[/tex]Substitute x=-1 in the given equation we get,
[tex]\begin{gathered} y=-(-1)^2-2(-1)+3 \\ =-1+2+3 \\ =4 \end{gathered}[/tex]Hence, the vertex of the graph is (-1, 4).
b) To find the range of the graph:
Let us find the y-intercept.
Put x=0, we get
[tex]\begin{gathered} y=-(0)^2-2(0)+3 \\ =3 \end{gathered}[/tex]From the figure, we observe that
The range of the graph is
[tex]\lbrack0,4\rbrack[/tex]c) To find the domain of the graph:
Let us find the x-intercept.
Put y=0, we get
[tex]\begin{gathered} -x^2-2x+3=0 \\ (x+3)(x-1)=0 \\ x=-3,1 \end{gathered}[/tex]From the figure, we observe that,
The domain of the graph is,
[tex]\lbrack-3,0)[/tex]In the table below, replace a with a value that will make the relation a function: 1 3 5 b(n) 9 8 9 11 a
Answers
Function:
A function is a relation in which each input (x) has only one output (y).
If any one input (x) has more than one output (y) then it is not a function.
As you can see from the given table, the value of (a) must be anything other than (2)
So we can set a value of 4 for (a)
Now if you notice, each input will have exactly one output value so the criteria of a function is satisfied.
So, the answer is 4
four students write algebraic math expressions and equations on their whiteboard. Which of the following students wrote expressions?
Answers
Answer:
Expressions: Student 1 and 4
Equations: Student 2 and 3
Step-by-step explanation:
Equations have an = sign. Expressions do not.
Find the point where the tangent line to Y=x^3 at x=0.6 crosses the x-axis.X-intercept =?
Answers
curve: Y=x^3
The equation of the tangent line is:
y =
what is the range of the function f(x)=3x^2+18x
Answers
Range of the function f(x) = 3x² +18x is [-27,∞).
What is the range of a function?
The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.
Here, we have f(x) = 3x² +18x.
Let f(x) = y
⇒ y = 3x² +18x
⇒ y = 3(x²+6x)
⇒ y/3 = x²+6x
⇒ y/3 = x²+ 6x + 9 - 9
⇒ y/3 = (x+3)² - 9
⇒ y/3 + 9 = (x+3)²
⇒ (y+27)/3 = (x+3)²
Taking square root on both sides, we get
⇒ [tex]\sqrt{(y+27)/3}[/tex] = x+ 3
⇒ [tex]\sqrt{(y+27)/3} - 3[/tex] = x
Now since f(x) = y ⇒ x = f⁻¹(y)
⇒ f⁻¹(y) = [tex]\sqrt{(y+27)/3} - 3[/tex]
⇒ range = [-27,∞).
Therefore, range of the function f(x) = 3x² +18x was found to be [-27,∞).
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The number of distinct right triangles with hypotenuse length 10 and a leg of length 5 is ____
1. Infinite
2. 0
3. 2
4. 1
Answers
According to the Pythagorean theorem we see that there are no distinct right triangles possible with hypotenuse length 10 and a leg of length 5. Thus, option 2 is correct.
It is given to us that -
Hypotenuse length = 10
Leg of length = 5
We have to find out the number of distinct right triangles that have the given hypotenuse length and leg of length.
For a right triangle, the Pythagorean theorem states that -
[tex]a^{2} +b^{2} =h^{2}[/tex] ---- (1)
where, a and b = Legs of the right triangle
and, h = hypotenuse of the right triangle
Substituting the given values of hypotenuse length and one leg of length in equation (1), we have
[tex]a^{2} +b^{2} =h^{2}\\= > 5^{2} +b^{2} =10^{2}\\= > b^{2} = 100-25\\= > b^{2} = 75\\= > b = 8.65[/tex]------ (2)
From equation (2), we see that another leg's length of the right triangle is equal to 8.65 which is not possible it is not a real number.
Therefore, applying the Pythagorean theorem we see that there are no distinct right triangles possible with hypotenuse length 10 and a leg of length 5. Thus, option 2 is correct.
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If sin 6A = cos 9A, then m/A is equal 1) 6 2) 36 3) 45 4) 1 1/2
Answers
Original expresion
[tex]\sin (6A)=\cos (9A)[/tex]Let's use the following relationship to determine the answer
[tex]\sin 6A=\cos (90-6A)[/tex]Now in the original expression
[tex]\begin{gathered} \cos (90-6A)=\cos 9A \\ 90-6A=9A \\ 90=6A+9A \\ 15A=90 \\ A=\frac{90}{15} \\ A=6 \end{gathered}[/tex]The answer would be A = 6
Determine the slope and equation of a line passing through the point (2, –1) and parallel to the x-axis
Answers
Answer:
slope = 0
eq of line: y = -1
Step-by-step explanation:
A line parallel to the x-axis is a horizontal line. The equation of a horizontal line is " y = anumber". Horizontal lines have 0 slope. The point given is (2,-1). In the point (2,-1) the y is -1. The equation of the horizontal line thru (2,-1) is
y = -1
Two numbers differ by 2, and their squares differ by 48. What are these numbers?
Answer needs to be: 11 and 13
Thank sou<3
Answers
Answer:
Below
Step-by-step explanation:
a - b = 2 so a = 2+b
a^2 - b^2 = 48 <===== substitute the value for 'a' underlined above
(2+b)^2 - b^2 = 48 expand L side
b^2 + 4b +4 - b^2 = 48 simplify
4b+4 = 48
4b = 44
b = 11 then a = 2+b = 13
c=(5f-32)/9 solve for F
Answers
⇒They simply want you to make F the subject for the equation, since there are multiple variables in one equation we cannot solve for the exact values
[tex]c=\frac{(5f-32)}{9} \\c(9)=5f-32\\9c=5f-32\\5f-32=9c\\5f=9c+32\\\frac{5f}{5} =\frac{9c+32}{5} \\f=\frac{9c+32}{5}[/tex]
determine the miss term 3:5:7:?:25:
Answers
Calculate the measure of angle T.
A - 100
B - 105
C - 110
D - 115
Answers
Answer:
b
Step-by-step explanation:
4) when Mrs. Oglethorpe sold her house recently, She received $210,000 for it, This was 40% more than she paid for it 10 years ago, What was the original purchase price?
Answers
the original purchase price was:
original purchase= 210,000- 0.4(210,000)=210,000-84,000=126,000
So the final answer will be that she paid $126,000, 10 years ago for her house.
we can check that our answer is correct by adding 126,000+84,000=210,000
Translate and solve. Twice a number plus 6 is -14
Answers
translation 2x + 6 = -14
2x = -14 - 6
2x = -20
x = -20/2
x = -10
Out of 40 students, 14 are taking English composition, 29 are taking Chemistry. If 5 students are in both class how many students are in neither classes.What is the probability that a randomly chosen student from this group is taking only chemistry class.
Answers
The probability that a randomly chosen student from this group is taking only a chemistry class will be 0.60.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
Out of 40 understudies, 14 are taking English organization, and 29 are taking chemistry. Assuming 5 understudies are in both classes the number of understudies that are in neither class.
The number of students in neither class will be given as,
⇒ 40 - (29 + 14 - 5)
⇒ 40 - 38
⇒ 2
The probability that a randomly chosen student from this group is taking only a chemistry class will be
P = (29 - 5) / 40
P = 24 / 40
P = 0.60
The probability that a randomly chosen student from this group is taking only a chemistry class will be 0.60.
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suppose a 5 minute overseas call costs 5.91 and a 10 minute call costs 10.86. the cost of the call and length of the call are related. the cost of each minute is constant. How long can you talk on th phone if you only have 12.00 to spend on the call?
Answers
Please I need you to help me and show the steps please so I can understand it better
I will mark brainliest
Answers
Answer:
LM = √34
Step-by-step explanation:
L is at (-7, 4), and M is at (-2, 1).
LM
[tex] \sqrt{ {( - 7 - ( - 2))}^{2} - {(4 - 1)}^{2} } [/tex]
[tex] \sqrt{ {( - 5)}^{2} + {3}^{2} } = \sqrt{25 + 9} = \sqrt{34} [/tex]
2. A bird flew from a point on the ground directly to the edge of the roof of a building. The height of the building is 40 feet, and the angle of elevation the bird's flight path made with the ground is 26°. Which expression models the total distance, in feet, the bird flew? А 40 cos 26 B 40 sin 26 с cos 26 40 D sin 26 40 I
Answers
We can draw the flight as:
We can use the trigonometric ratio that relates the sine of an angle with the opposite side and the hypotenuse:
[tex]\begin{gathered} \sin (26\degree)=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{h}{D} \\ D=\frac{h}{\sin (26\degree)} \\ D=\frac{40}{\sin (26\degree)} \end{gathered}[/tex]Answer: the distance can be expressed as 40 / sin(26 deg)
Answer:
Step-by-step explanation:
Ethan buys 3.2 pounds of peanuts at a local market. He pays $8.64. The next day, he buys 1.5 pounds of peanuts. The price per pound for peanuts is the same. How much money does Ethan pay.
Answers
Answer:
$4.05
Step-by-step explanation:
8.64÷3.2=2.7
1.5×2.7=4.05
(not very sure)
The graph shows Elizabeth's speed during a 55-minute run. Elizabeth's Run 7 Speed (mph) Time (minutes) During which time interval did Elizabeth's speed increase? Select one o 5 to 10 minutes O 25 to 30 minutes O 15 to 25 minutes O O to 5 minutes
Answers
Elizabeth's speed increased during the 0 to 5 minute interval
This interval shown on the graph is indicated by the rising line on the vertical axis (y-axis).
The x-axis shows the time intervals graded in 5-minute intervals. the other options shows a flat line (no change in speed) and a downward line (reduction in speed).
The 0 to 5 minute period of her run however is a rising line which means incresing speed.
Gianna purchased 5\tfrac{1}{2}5
2
1
pints of ice cream for a party. If each guest will be served exactly \tfrac{1}{3}
3
1
pint of ice cream, what is the maximum number of guests Gianna can serve?
Answers
The maximum number of guests Gianna can serve will be 16.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers
From the information, Gianna purchased 5 1/2 pints of ice cream for a party. If each guest will be served exactly 1/3 pint of ice cream
The maximum number of guests Gianna can serve will be:
= 5 1/2 ÷ 1/3
= 11/2 ÷ 1/3
= 11/2 × 3
= 33/2
= 16.5
The maximum number will be 16.
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Complete question
Gianna purchased 5 1/2 pints of ice cream for a party. If each guest will be served exactly 1/3 pint of ice cream, what is the maximum number of guests Gianna can serve?
Answer the question thx
Answers
The height, h of the airplane to the nearest foot is 536 feet (option D).
What is the height of the airplane?The diagram shown is a right angled triangle. The take off point and the height of the plane form a right angled triangle.
Trigonometry would be used to solve of the height of the airplane. We are to determine the opposite side given the adjacent side and the angle of elevation.
Tan = opposite / adjacent side
Tan 15 = h / 2000
0.2679 = h / 2000
h = 2000 x 0.2679
h = 536 feet
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