The population P of Phoenix, Arizona (in thousands) from 1970 through 2000 can be modeled by the equation P = 590e ^ (0.027t) where r represents the year, with t = 0 corresponding to 1970. According to this model, when will the population reach 1.5 million.
Answers
The population of Phoenix , Arizona will reach 1.5 million in the year 2005 .
In the question ,
it is given that ,
the equation , modelling the the population P of Phoenix, Arizona (in thousands) from 1970 through 2000 is
P = 590[tex]e^{0.027\times t}[/tex]
where t represents the year corresponding to 1970 .
we need to find the time required for the population to reach 1.5 million.
since population is represented in thousands , so ,
1.5 million = 1500000 will be taken as 1500 .
Substituting P = 1500 in the equation ,
we get ,
1500 = 590[tex]e^{0.027\times t}[/tex]
1500/590 = [tex]e^{0.027\times t}[/tex]
2.5423 = [tex]e^{0.027\times t}[/tex]
taking ㏑ both the sides , we get
㏑(2.5423) = (0.027t)×㏑(e)
0.93306 = 0.027×t
t = 0.93306/0.027
t = 34.55 years
t ≈ 35 years
the year will be 1970 + 35 = 2005 .
Therefore , The population of Phoenix , Arizona will reach 1.5 million in the year 2005 .
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Related Questions
Analysts at the Milk Company calculated the average price of a gallon of its milk over 10 years. The
following table shows the years since 2010 and the average price of a gallon of milk at those times.
Years (since 2010) 1 3 6 8 9
Price (in dollars) 3.57 3.49 3.20 2.90 3.04
Which data display would you use to represent this data?
Histogram
Line plot
Scatter plot
Line graph
Answers
The data display method that can be used to represent the data is a scatter plot. The correct option is therefore;
Scatter plot
What is a scatter plot?A scatter plot is a graph formed by plotting the ordered pairs of a set of data on the coordinate axis such that a pattern is formed that reveals the presence of any correlation or pattern between the variables.
The data in the table are presented as follows;
Year (since 2010) [tex]{}[/tex] Price (in Dollars)
1 [tex]{}[/tex] 3.57
3 [tex]{}[/tex] 3.49
6 [tex]{}[/tex] 3.2
8 [tex]{}[/tex] 2.9
9 [tex]{}[/tex] 3.04
The value calculated by the analysts at the Milk Company = The average price of a gallon of the company's milk over 10 years.
The information obtainable from the data includes the variation of the price of milk with the number of years.
The number of data points are 5, while the number of years in 10 years is 10. Therefore, 5 data points are left out and can be estimated using a trend line that matches the data.
The data display method that will suitable represent the data is therefore a scatter plot that can be further analyzed with a trend line.
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Answer:
it the second graph im taking the quiz right noww
Step-by-step explanation:
equation represents the distancetraveled against the wind?ProblemAt full speed, Hal travels 600 miles in 2 hourswith the wind. The same distance againstthe wind takes 3 hours.What's the maximum speed of Hal's airplanein still air? What's the speed of the wind?Click on the correct answer.3(x - y) = 6003(x + y) = 600x-speed of the airplane in still airy speed of the wind2(x - y) = 6002(x + y) = 60080888Ma
Answers
Take into account:
x = speed of the airplane
y = speed of the air
consider that the product in between time and speed is equal to the distance traveled in the time.
Then, if the airplane took 3 hours complete 600 miles, agaist the wind, you have that the distance traveled by the airplane is 3x without wind. The speed of the wind decelerates the airplane. The "distance traveled by the wind is 3y"
Then, when you subtract the previous terms you obtain:
3x - 3y = 600 factorize 3 left side
3(x - y) = 600
Alexa went shopping for a new pair of pants. Sales tax where she lives is 8.75%. What
number should she multiply the price of the pair of pants by to find the total plus tax
in one step?
Answers
To find the total plus tax she must multiply the price of the pair of pants and 108.75% ≈ 1.0875.
Given:
Alexa went shopping for a new pair of pants.
Sales tax where she lives is 8.75%.
Let x be the price of pants.
Total plus tax = prices of pair of pants * 1.0875.
= x * 1.0875
= 1.0875x.
Therefore to find the total plus tax she must multiply the price of the pair of pants and 108.75% ≈ 1.0875.
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Please help fast f(x) = 4x2 - 2x + 4 Find f(-9)
Answers
Answer:
346
Step-by-step explanation:
substitute the -9 for the x and solve. you will get 346 that will be the function of -9 for this equation
Put the following equation of a line into slope-intercept form, simplifying all fractions.
12x-20y=
12x−20y=
\,\,-100
−100
Answers
The slope intercept form of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept. The given equation can be written in terms of slope in y = 0.6x + 5.
What is the equation for a straight line?A straight line can be written in the form of equation as, y = mx + c.
Two straight lines intersect each other only at one point.
When two straight lines are parallel to each other the angle between them is zero.
Given that,
The equation of the line is 12x - 20y = -100
In order to write the given equation in slope-intercept form, write the given equation in terms of y as,
12x - 20y = -100
=> 20y = 12x + 100
=> y = 12 / 20x + 100 / 20
=> y = 0.6x + 5
Where slope is 0.6 and y-intercepts is 5.
Hence, the slope-intercept form of the given equation is y = 0.6x + 5.
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Please help I have a test on this and I’m not sure how to do this
Answers
ANSWER
[tex]y=-\frac{1}{4}x^2+\frac{3}{4}x+1[/tex]EXPLANATION
We want to find the equation for the function graphed.
We see that the function passes through -1 and 4 on the x-axis and 1 is the y-intercept.
These are called the roots of the function. The roots are the x values where the function equals 0.
We can find the function by applying the roots:
[tex]y=a\mleft(x-x_1\mright)\mleft(x-x_2\mright)[/tex]where x1 and x2 are the roots.
a = leading coefficient
Therefore, we have that:
[tex]\begin{gathered} y=a(x-(-1))(x-4) \\ y=a(x+1)(x-4)_{} \end{gathered}[/tex]Expand the brackets:
[tex]\begin{gathered} y=a(x^2-4x+x-4) \\ y=ax^2-4ax+ax-4a \\ y=ax^2-3ax-4a \end{gathered}[/tex]Now, we have to find a.
To do that, we use the y-intercept of the function (0, 1). The y-intercept is the value of the function when x is 0.
Therefore, when x = 0, y = 1:
[tex]\begin{gathered} 1=0-0-4a \\ \Rightarrow-4a=1 \\ a=-\frac{1}{4} \end{gathered}[/tex]Now, substitute the value of a into the function obtained earlier.
[tex]\begin{gathered} y=-\frac{1}{4}x^2-3(-\frac{1}{4})x-4(-\frac{1}{4}) \\ \Rightarrow y=-\frac{1}{4}x^2+\frac{3}{4}x+1 \end{gathered}[/tex]That is the equation of the function graphed.
What would be the property of all ( 7=2x-5) (12=2x) and (6=x), which property would they be, Addition property of equality, Subtraction Property of Equality, Multiplication property of equality, Division Property of Equality, or Substitution Property
Answers
Answer
Step-by-step Explanation
7 = 2x - 5
12 = 2x
6 = x
The movement from the first step to the second step involves adding 5 to both sides.
7 = 2x - 5
7 + 5 = 2x - 5 + 5
12 = 2x
Adding 5 to both sides, is what the addition property of equality means.
Then, the movement from the second step to the third step involves dividing both sides by 2.
The area a of a circle is pi times the radius R squared as an equation
Answers
Answer:
pi r squared
Step-by-step explanation:
A=pir2
pi is 3.14
hope it helps
PLEAS HELP ME TYYYYYYY
Answers
Answer:I would say if there are 15 leaches then there will be 20 toads
Step-by-step explanation: I multiplied the 4 times 5
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
Answers
Step by step
We know slope intercept form is
y =mx + b
m = slope
b = y intercept
We find slope on the graph by creating a slope triangle as shown on the attachment.
We find rise 3 and run 6, slope is rise over run so 3/6 simplified to 1/2
We find the y intercept is at 3 on the y axis
So y = 1/2x + 3 is your answer
Sally picked five buckets of blueberry she put 500 berries in each basket how many blueberries did Sally pick in all
Answers
Since each bucket contained 500 berries and there are 5 buckets we can find the total amount of berries by multiplying the number of berries per bucket by the number of buckets. This is done below:
[tex]\begin{gathered} \text{total}=500\cdot5 \\ \text{total}=2500\text{ berries} \end{gathered}[/tex]Sally picked 2500 blueberries.
find the area of a sector with a central angle of 1/2 pi and a radius of 11.3
Answers
First, let's find the length of an arc:
[tex]L=\text{r}\cdot\theta=11.3\cdot\frac{\pi}{2}=\frac{113\pi}{20}[/tex]Therefore, the area is:
[tex]A=\frac{rL}{2}\approx100.3[/tex]DCF = FB and AE = EBCB = 38 and AB = 22DE = [?]EBFLLEnter
Answers
Given
Also, CF = FB and AE = EB, CB = 38 and AB = 22.
To find the length of DE.
Explanation:
It is given that,
Also, CF = FB and AE = EB, CB = 38 and AB = 22.
That implies,
By using midpoint theorem of triangle, we have,
[tex]DE=\frac{1}{2}BC[/tex]Therefore,
[tex]\begin{gathered} DE=\frac{1}{2}\times38 \\ =19 \end{gathered}[/tex]Solve: -4x + 3 > 27
Please explain and show your work step-by-step.
Answers
The value of x is less than -6.
What is an inequality?A relationship between two expressions or values that are not equal to each other is called inequality.
Given that, -4x + 3 > 27
-4x + 3 > 27
-4x + 3 - 3 > 27 - 3 → (subtracting 3 from both sides)
-4x > 24
-4x/4 > 24/4 → (dividing by 4 both the side)
-x > 6x
x < -6
Hence, x < -6
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Can you help me I can’t understand this question
Answers
Answer:
the graph given has a greater unit rate
Step-by-step explanation:
basically, you have to compare the gradients of both the graphs
one graph's equation is given i.e y=47/2 where 47/2 is the gradient/slope now find the gradient/slope of the given graph:
slope = x2-x1/y2-y1
chose any two coordinates on the graph and input them in the equation
I chose (2,94) and (4,188)
inputting them in the equation:
188-94/4-2
=94/2
now see which one is greater 47/2 or 94/2
94/2 is greater than 47/2 so it has a greater unit rate
What is the slope of the line shown?
A. slope = 3
B.slope = 12
C. slope = 2
D. slope = -3
Answers
The slope of the line shown is 0.5 .
How to find the slope of a given line?
For a line passing through the points (x₁, y₁) and (x₂, y₂), the slope for the same can be defined with the mathematical value of m i.e.,
m = (y₂ - y₁)/(x₂ - x₁)
Given, the line in picture passes through the points (0, -3) and (6, 0).
Following the formula established in the literature above, the given line has slope as m, which is:
m = (y₂ - y₁)/(x₂ - x₁) = (0 - (-3))/(6 - 0) = 3/6 = 0.5
Thus, the slope of the given line in question is 0.5 .
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A ____________________ is a protective barrier that surrounds only plant cells, providing structural support.
Mitochondria
Chloroplast
Cell wall
Nucleus
Answers
A Cell wall is a protective barrier that surrounds only plant cells, providing structural support.
A cell wall, a large central vacuole, and plastids like chloroplasts are all present in plant cells. The cell wall is a thick, stiff layer that surrounds and supports the cell structurally and physically. It is located outside the cell membrane.
What is cell wall?the dense, nonliving covering that protects and sustains the majority of plant, bacterial, fungal, and algal cells. cellular wall.
The cell membrane is a layer of defense that covers the surface of the cell and serves as a partition between the interior of a cell and its surroundings. The cell membrane also regulates the materials that enter and exit the cell.
A cell is protected by its cell membrane, also known as the plasma membrane. Additionally, it maintains a constant environment inside the cell, and that membrane serves a variety of purposes. One is to move compounds out of the cell that are harmful as well as nutrients into the cell.
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Fill in the table and sketch the exponential function on a graph. y = 4^xxy-3-2-1023
Answers
We must plot the following exponential function:
[tex]y=f(x)=4^x.^{}[/tex]Replacing the values of x in the function above, we complete the table:
[tex]\begin{gathered} x=-3\rightarrow y=f(-3)=4^{-3}=\frac{1}{64}=0.015625, \\ x=-2\rightarrow y=f(-2)=4^{-2}=\frac{1}{16}=0.0625, \\ x=-1\rightarrow y=f(-1)=4^{-1}=\frac{1}{4}=0.25, \\ x=0\rightarrow y=f(0)=4^0=1, \\ x=1\rightarrow y=f(1)=4^1=4, \\ x=2\rightarrow y=f(2)=4^2=16, \\ x=3\rightarrow y=f(3)=4^3=64. \end{gathered}[/tex]So we have the following points:
• (-3, 1/64) = (-3, 0.015625),
,• (-2, 1/16) = (-2, 0.0625),
,• (-1, 1/4) = (-1, 0.25),
,• (0, 1),
,• (1, 4),
,• (1, 16),
,• (1, 64).
Now, plotting each point (x, y) and joining them, we get the following graph:
One clarification: the label of the points in the graph have been rounded.
Answer
The points of the table are:
• (-3, 1/64)
,• (-2, 1/16)
,• (-1, 1/4)
,• (0, 1),
,• (1, 4),
,• (1, 16),
,• (1, 64).
The graph of the points and the function is:
One clarification: the label of the points in the graph have been rounded.
Ethanol fuel mixtures have "E" numbers that indicate the percentage of ethanol in the mixture by volume. For example, E10 is a mixture of 10% ethanol and 90% gasoline. How much E7 should be mixed with 4000 gal of E10 to make an E9 mixture?
Answers
We have to blend two mixtures of ethanol (E7 and E10) to make an E9 mixture.
We know that the amount of E10 mixture is 4000 gal.
Let x be the amount of E7 mixture.
As we have x gallons of E7 and 4000 gallons of E10, the volume of the E9 mixture will be (x+4000).
The volume of ethanol in the E7 mixture will be 0.07*x gallons.
The volume of ethanol in the E10 mixture is 0.1*4000 = 400 gallons.
The volume of ethanol in the E9 mixture will be 0.09*(x+4000) gallons.
As the sum of the ethanol volume in the E7 and E10 mixtures has to be equal to the ethanol in the E9 mixture, we can write:
[tex]0.07\cdot x+0.1\cdot4000=0.09\cdot(x+4000)[/tex]We can use this equation to solve for x:
[tex]\begin{gathered} 0.07\cdot x+0.1\cdot4000=0.09\cdot(x+4000) \\ 0.07x+400=0.09x+0.09\cdot4000 \\ 0.07x+400=0.09x+360 \\ 0.07x-0.09x=360-400 \\ -0.02x=-40 \\ x=\frac{40}{0.02} \\ x=2000 \end{gathered}[/tex]Then, the volume of the E7 mixture has to be 2000 gallons.
Answer: 2000 gallons of E7 mixture.
PLEASE I NEED HELP ASAP!!
What are the three forms of quadratic functions?
For each of the three forms, list all features we can use to characterize the equation.
Answers
The three types of quadratic functions are as follows: We can quickly find the y-intercept using the standard form. We can quickly locate the vertex in vertex form, and we can quickly determine the roots/zeros in factored form.
What are the 3 forms of a quadratic function and their features?The three forms of quadratics are the standard form, the vertex form, and factored form. Each of them reveals a specific part of the quadratic.
A quadratic has the following standard form:
A quadratic in standard form can immediately convey only two details: (1) the leading coefficient a and (2) the y-intercept. The leading coefficient a determines whether the parabola curves upwards or downwards. The y-intercept will be given by the constant c.
Vertex Form: The vertex form of a quadratic is:
There are also two details that can be conveyed by a quadratic in vertex form: (1) the vertex, and (2) the leading coefficient. The leading coefficient is given by a. This tells us the orientation of the parabola. The vertex is given by (h, k). Hence, in my opinion, vertex form is the best form of a quadratic since it immediately reveals the vertex, the most important aspect of a quadratic.
Factored Form: The factored form of a quadratic is:
Where p and q are the zeros/roots/solutions of the quadratic. Factored form gives us two details about the quadratic: (1) the leading coefficient, and (2) the zeros. The zeros tell us when the parabola crosses the x-axis, which can assist in graphing.
Therefore,
Each form of a quadratic equation has its own benefits.
The standard form allows us to find the y-intercept.
The vertex form allows us to quickly locate the vertex.
The factored form allows us to quickly determine the roots/zeros.
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10. Two classes work together on a project. One class has 18 students,8 of whom are girls. The other class has 10 girls and 7 boys.What is the ratio of boys to the total number of students working on theproject? Express your answer as a fraction.lo0OOOOOOCOOOOO
Answers
Solution
For this case we have the following info:
Class 1: Total 18 students, 8 girls and 10 boys
Class 2: Total 17 students, 10 girls and 7 boys
The total of students are: 18+17 = 35
Total of boys: 10 + 7 = 17
Then the ratio of boys to the total number of students is given by:
r = 17/35
Which of the following square roots is a rational number
Answers
First, we need to define rational numbers
Rational numbers are numbers that can be express as a quotient or fraction
From the question given, The square root of 16 is 4, this can be express as 4/1
Hence, it is a rational number
Therefore the correct option is A
Which of the following statistics could you find given the information above (see
question #1)? Select all that apply.
mode
range
standard deviation
interquartile range
Answers
The statistics you could find given the information above (see attachment) include the following:
range.standard deviation.interquartile range.What is a box and whisker plot?A boxplot is also referred to as box and whisker plot and it can be defined as a type of chart that can be used to graphically represent the five-number summary of a data set with respect to locality, skewness, and spread.
In Mathematics, the five-number summary of any box and whisker plot include the following:
MinimumFirst quartileMedianThird quartileMaximumFor the range, we have:
Range for women = 150 - 0 = $150
Range for men = 35 - 0 = $35
For the standard deviation, we have:
Standard deviation for women = range/4
Standard deviation for women = 150/4 = 37.5
Standard deviation for men = range/4
Standard deviation for men = 35/4 = 8.75.
For the interquartile range, we have:
Interquartile range = third quartile - first quartile.
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Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Also let A = {1, 3, 5, 7, 9} and B = {2, 4, 5, 6, 7}.
Answers
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
A = {1, 3, 5, 7, 9}
B = {2, 4, 5, 6, 7}.
A = {1, 3, 5, 7, 9}
B' = {1,3,8,9,10}
A U B' = {1,3,5,7,8,9,10}
Answer:
A U B' = {1,3,5,7,8,9,10}
Which statement is true about the function f(x) = 4x^5?
A) The function is even because f(–x) = f(x).
B) The function is odd because f(–x) = f(x).
C) The function is odd because f(–x) = –f(x).
D) The function is even because f(–x) = –f(x).
Answers
The function is odd because f(–x) = –f(x).
What is a function?
A function is a special form of relation where each input has exactly one output. In other words, for each input value, the function returns exactly one value. A relation rather than a function is depicted in the above graph because one is mapped to two different values. However, if one were instead mapped to a single value, the relationship described above would change into a function. Furthermore, output values could match input values exactly.
Odd function means f(-x) = -f(x)
and Even function means f(-x) = f(x)
Here the given function f(x) = 4[tex]x^{5}[/tex]
Put, x = -x
We have f(-x) = 4 ([tex](-x^){5}[/tex])
5 is an odd number so we will get a negative value. So f(-x) = -f(x)
Hence, The function is odd because f(–x) = –f(x).
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You have 80$ to spend on clothes jeans cost 34$ and t shirts cost 9$ without any added tax how many pairs of jeans can I purchase if I buy 1 t shirt
Answers
Answer:
2 pairs of jeans
Step-by-step explanation:
1) Subtract the cost of the t-shirt
As we are given the information that she will only be buying one t-shirt it
means that we can get rid of the price of it...
$80-$9 = $72
2) Find the number of jeans
Knowing that we have $72 left we have figure out how many jeans she
can buy by dividing 72 by 34...
$72 ÷ $34 = 2
Hope this helps, have a great day!
Suppose that the amount in grams of a radioactive substance present at time t (in years) is given by A(t) = 800e -0.86t. Find the rate of change of the quantity present at the time when t = 5. O 9.3 grams per year 0 -72.7 grams per year 0-9.3 grams per year O 72.7 grams per year
Answers
Let's begin by listing out the information given to us:
[tex]\begin{gathered} A\mleft(t\mright)=800e^{-0.86t} \\ \Delta A(t)=-0.86\cdot800e^{-0.86t} \\ \Delta A(5)=-0.86\cdot800e^{-0.86\mleft(5\mright)} \\ A(5)=-9.34 \\ A(5)=-9.3g\text{ / year} \end{gathered}[/tex]Hence, the correct option is the third option -9.3 grams per year
6x2 - 24x + 18 = 0
Answer please
Answers
Answer:
The answer is -1 or -3
Step-by-step explanation:
You woud use the quadritic formula
[tex]x=\frac{ -b+- \sqrt{b^{2} -4ac} \\}{2a}[/tex]
[tex]x=\frac{-24 +- \sqrt{576-432} }{12} \\[/tex]
[tex]x=\frac{-24+- \sqrt{144} }{12}[/tex]
[tex]x=\frac{-24+12}{12}\\\\x=\frac{-12}{12} \\x = -1[/tex]
or
[tex]x=\frac{-24-12}{12} \\\\x= \frac{-36}{12} \\\\x= -3[/tex]
To get the answer of -1 or -3
Can I get some help on this please?Options 1: reflection accross the y-axis, 90 degree counterclockwise rotation about the point a, 90 degree clockwise rotation about the point a, 90 degree counterclockwise rotation about point bOptions 2: clockwise rotation about point b and a translation 20 units down, reflection across the y-axis and 20 units down, reflection across the x-axis and 15 units down, reflection across the y-axis and 25 units down
Answers
Answer:
The sequence of transformation that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral GHIJ is a 90 degrees counterclockwise rotation about point A followed by reflection across the y-axis and a translation of 20 units down.
Explanation:
The sequence of transformations are described in the following figure:
Therefore, the first transformation is a rotation of 90 degrees counterclockwise about point A. After that transformation, we get the figure A'B'C'D'
Then, we reflect the figure across the y axis, so we get A''B''C''D''
Finally, we translate the figure 20 units down to get GHIJ
So, the answers are:
The sequence of transformation that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral GHIJ is a 90 degrees counterclockwise rotation about point A followed by reflection across the y-axis and a translation of 20 units down.
Candace order a $4 sandwich a $2 drink in the $3 smoothie for lunch she has $10 as symbols to the equation to represent this situation and solve it
Answers
Let's start by adding all the values for what Candace order:
Total for the order: $4 + $2 + $3 = $9
since she has a $10 bill,
she will be able to pay for it, and have the following change back:
$10 - $9 = $1
she will get back $1.
The math equations we created are then:
4 + 2 + 3 = 9
10 - 9 = 1