Over the next 10 years, town A is expecting to gain 1000 people each year. During the same time period, the population of town B is expected to increase by 5% each year. Both town A and town B currently have populations of 10,000 people. The table below shows the expected population of each town for the next three years.Which number of years is the best approximation of the time until town A and town B once again have the same population?
Answers
From the given figure we can see
The population in town A is increased by a constant rate because
[tex]\begin{gathered} 11000-10000=1000 \\ 12000-11000=1000 \\ 13000-12000=1000 \end{gathered}[/tex]Since the difference between every 2 consecutive terms is the same, then
The rate of increase of population is constant and = 1000 people per year
The form of the linear equation is
[tex]y=mx+b[/tex]m = the rate of change
b is the initial amount
Then from the information given in the table
m = 1000
b = 10,000
Then the equation of town A is
[tex]y=1000t+10000[/tex]Fro town B
[tex]\begin{gathered} R=\frac{10500}{10000}=1.05 \\ R=\frac{11025}{10500}=1.05 \\ R=\frac{11576}{11025}=1.05 \end{gathered}[/tex]Then the rate of increase of town by is exponentially
The form of the exponential equation is
[tex]y=a(R)^t[/tex]a is the initial amount
R is the factor of growth
t is the time
Since R = 1.05
Since a = 10000, then
The equation of the population of town B is
[tex]y=10000(1.05)^t[/tex]We need to find t which makes the population equal in A and B
Then we will equate the right sides of both equations
[tex]10000+1000t=10000(1.05)^t[/tex]Let us use t = 4, 5, 6, .... until the 2 sides become equal
[tex]\begin{gathered} 10000+1000(4)=14000 \\ 10000(1.05)^4=12155 \end{gathered}[/tex][tex]\begin{gathered} 10000+1000(5)=15000 \\ 10000(1.05)^5=12763 \end{gathered}[/tex][tex]\begin{gathered} 10000+1000(6)=16000 \\ 1000(1.05)^6=13400 \end{gathered}[/tex][tex]\begin{gathered} 10000+1000(30)=40000 \\ 10000(1.05)^{30}=43219 \end{gathered}[/tex]Since 43219 approximated to ten thousand will be 40000, then
A and B will have the same amount of population in the year 30
The answer is year 30
Related Questions
2. (5 points) A very special island is inhabited only by knights and knaves. Knights always tell
the truth, and knaves always lie. You meet two inhabitants: Sue and Marge. Sue says that
Marge is a knave. Marge claims. "Sue and I are not the same." Determine who is a knight and
who is a knave.
Answers
Answer:
Sue is knave and Marge be knightStep-by-step explanation:
Let Sue be knight and Marge be knave.
Sue says: "Marge is a knave". Since Sue is knight, she is right and Marge should lie.
Marge says: "Sue and I are not the same." - this is right answer too, so this is not a correct response and our assumption is wrong.
Now, let Sue be knave and Marge be knight. Then Marge's response is right and Sue's is wrong. This is a match and this assumption is correct.
what is the solution set for the inequality
A. x ≤ -5
B. x ≤ 5
C. x ≤ 1
d. x ≤ -14
Answers
The solution set to the inequality, 4x + 12 ≤ -8, is determined as: A. x ≤ -5.
How to Find the Solution Set of an Inequality?The solution set is the value of x that would make an inequality statement true. To find the value of x, solve as you would solve a normal equation.
Using the key to the given model in the diagram, we can write the inequality as follows:
On the left, we would have, 4x + 12.
On the right, we would have, -8.
The inequality would be expressed as:
4x + 12 ≤ -8
Solve for x
4x + 12 - 12 ≤ -8 - 12 [subtraction property of equality]
4x ≤ -20
4x/4 ≤ -20/4
x ≤ -5
The solution set is: A. x ≤ -5.
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The general form of an ellipse is 15x2+4y2+30x−16y−29=0.
What is the standard form of the ellipse?
Answers
The equation of ellipse in standard form is (x + 1)² / 4 + (y - 2)² / 15 = 1.
How to determine the standard form of the ellipseIn this problem we find the equation of an ellipse in general form, whose standard form can be found by algebra properties. The general form of the equation of an ellipse centered at (h, k) is introduced below:
(x - h)² / a² + (y - k)² / b² = 1
Where:
a, b - Lengths of the semiaxes.(h, k) - Coordinates of the center.The complete procedure is now presented:
15 · x² + 4 · y² + 30 · x - 16 · y - 29 = 0
(15 · x² + 30 · x) + (4 · y² - 16 · y) = 29
15 · (x² + 2 · x) + 4 · (y² - 4 · y) = 29
15 · (x² + 2 · x + 1) + 4 · (y² - 4 · y + 4) = 29 + 15 · 1 + 4 · 4
15 · (x + 1)² + 4 · (y - 2)² = 29 + 15 + 16
15 · (x + 1)² + 4 · (y - 2)² = 60
(x + 1)² / 4 + (y - 2)² / 15 = 1
The equation of ellipse is (x + 1)² / 4 + (y - 2)² / 15 = 1.
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Your brother is buying textbooks for college. He has to buy 3 math textbooks and 2 science textbooks. The total cost of his textbooks is $487. Write a linear equation to represent the cost of his textbooks.
Answers
Let's define the following variables,
x: cost of a math textbook
y: cost of a science textbook
He has to buy 3 math textbooks and 2 science textbooks, that is,
Total cost = 3x + 2y
The total cost of his textbooks is $487, then the linear equation is,
487 = 3x + 2y
Hello, I had a question on how to find the leading coefficient and the degree.
Answers
Given:
given polynomial is
[tex]23v^5-2v+4v^8-18v^4[/tex]Find:
we have to find the leading coefficient and degree of the polynomial.
Explanation:
The lewading coefficient is the coefficient of highest power term of the polynomial.
Highest power of v is 8 and its coefficient is 4.
Therfore, leading coefficient is 4.
and the degree of the polynomial is equal to the highest power of v in the polynomial, which is 8.
Therefore, the leading coefficient of polynomial is 4 and degree is 8.
For the following set of data, find the number of data within 2 population standard deviations of the mean.28, 65, 114, 74, 68, 75, 70, 69, 64
Answers
To determine the data that is within 2 population standard deviations of the mean, let's calculate the mean first.
To determine the mean, let's add all the data and divide the result by the total number of data.
[tex]28+65+114+74+68+75+70+69+64=627[/tex][tex]627\div9=69.66667[/tex]The mean is 69.66667.
Let's now calculate the standard deviation. Here are the steps:
1. Subtract the mean from each data, then square the result.
[tex]\begin{gathered} 28-69.66667=(-41.66667)^2=1,736.1114 \\ 65-69.66667=(-4.66667)^2=21.7778 \end{gathered}[/tex][tex]\begin{gathered} 114-69.66667=(44.33333)^2=1,965.4441 \\ 74-69.66667=(4.33333)^2=18.7777 \end{gathered}[/tex][tex]\begin{gathered} 68-69.66667=(-1.66667)^2=2.7778 \\ 75-69.66667=(5.33333)^2=28.4444 \end{gathered}[/tex][tex]\begin{gathered} 70-69.66667=(0.33333)^2=0.1111 \\ 69-69.66667=(-0.66667)^2=0.4444 \\ 64-69.66667=(-5.66667)^2=32.1111 \end{gathered}[/tex]2. Add the results in step 1.
[tex]1,736.1114+21.7778+1,965.4441+18.7777+2.7778=3,744.8888[/tex][tex]28.4444+0.1111+0.4444+32.1111=61.111[/tex][tex]3,744.8888+61.111=3,805.9998[/tex]The sum is 3, 805.9998.
3. Divide the sum by the total number of data.
[tex]3,805.9998\div9=422.8889[/tex]4. Square root the result in step 3.
[tex]\sqrt{422.8889}\approx20.56[/tex]The standard deviation is approximately 20.56.
So, the data that are within 2 population standard deviations of the mean are between:
[tex]\begin{gathered} 69.67-(2)(20.56)=28.55\approx29 \\ 69.67+(2)(20.56)=110.79\approx111 \end{gathered}[/tex]The data that are within 2 population standard deviations of the mean are between 29 and 111. Based on the given data, the data that are between 29 and 111 are the following: 64, 65, 68, 69, 70, 74, and 75. There are 7 data that are within 2 population standard deviations of the mean.
The standard normal curve is grafted below. Shade the region under the standard normal curve to the left of x=1.00Use the table to find the area under the standard normal curve to the left of x=1.00
Answers
Explanation
Part A
The shaded area under the standard normal curve to the left of z=1.00 can be seen below.
Part B
Using the z table, the area under the standard normal curve to the left of z.=1.00 is
Answer: 0.8413
The order in which you write the ratio is ____ to the meaning.
Answers
The ratio is defined as fraction in which one number is numertor and other number is denominator.
For example the ratio 2/3 has 2 in numerator and 3 in denominator, but if we write the ratio as 3/2 then it is different from previous ratio 2/3. So in ratio order is important in which you write the ratio.
Thus answer is,
The order in which you write the ratio is important to the meaning.
Section 5.2-10. Solve the following system of equations by substitution or elimination. Enter your answer as (x,y).-2x+3y = 15-x-3y = 12
Answers
1)-2x2)
[tex]-2x+3y-(-2x-6y)=15-2\times12\Rightarrow-2x+3y+2x+6y=15-24\Rightarrow9y=-9\Rightarrow y=-1[/tex]y=-1 implies
[tex]-2x+3\times(-1)=15\Rightarrow-2x-3=15\Rightarrow-2x=18\Rightarrow x=-9[/tex]Hence the solution is
[tex](-9,-1)[/tex]a^2 - b^4 Evaluate is a= -5 and b= 2
Answers
21
Explanations:Given the expression
[tex]a^2-b^4[/tex]We are to find the resulting value given that a = -5 and b = 2
[tex]\begin{gathered} =(-5)^2-(2)^2 \\ =25-4 \\ =21 \end{gathered}[/tex]Hence the value of the expression if a = -5 and b = 2 is 21
Use the times and corresponding closing prices of the stock to create coordinate pairs. Let X represent the number of weeks since the first at a point, and Y represent the closing price of each time. So, X equals zero represents the data point from five years ago. There are 52 weeks in a year, and you can write the time for each closing price recorded in terms of weeks that have passed since five years ago, when X equals zero. Fill in the table to represent your data as coordinate pairs
Answers
Combining both tables we get:
247474647447x4747474747
Answers
Answer:
1174879639277360520909 in exact form
or
in decimal form 1.17487963 x 10^21
Step-by-step explanation:
-2(6.× -8 - 8 × 4)^0
Answers
Every number raised to the power of zero is equal to one.
[tex]-2\cdot1=-2[/tex]The final expression is -2
hi, can you help me answer this question please, thank you!
Answers
The correct option is B
Explanation:The given statement shows that there is a 95% chance that the mean of a sample of 29 gadgets will be between 12.8 and 34.9
For an arc length s, area of sector A, and central angle θ of a circle of radius r, find the indicated quantity for the given value. r= 6.45 in, θ= 5 pi\6, s=?
Answers
Calculate the arc length by using the following formula:
[tex]s=r\theta[/tex]Replace the values of r and θ and simplify:
[tex]\begin{gathered} s=(6.45in)(5\frac{\pi}{6})=(6.45)(\frac{5}{6})(3.14) \\ s=16.8775in \end{gathered}[/tex]Hence, the arc length is 16.8775 in
Good evening, I need help on this questions. Thanks :)
Answers
Answer:
A and B ---> decreasing
B and C ---> constant
C and D ---> decreasing
D and E ---> increasing
Explanation:
A function is increasing if we go from left to right and the graph goes up, it is constant when it is a horizontal line and it is decreasing if when we go from left to right the graph goes down.
Therefore, for each part of the function, we get
A and B ---> decreasing
B and C ---> constant
C and D ---> decreasing
D and E ---> increasing
need help asap look at attachmen
Answers
The rectangle has a width of 7 yards and a length of 42 yards.
How to find the length and width?For a rectangle of length L and width W, the perimeter is:
P = 2*(L + W)
Here we know that:
L = 6*W
P = 98yd = 2*(L + W)
Then we have the system of equations:
L = 6*W
98yd = 2*(L + W)
If we substitute the first equation into the second one, we get:
98yd = 2*(6*W + W)
98yd = 14*W
98yd/14 = W = 7yd
So the width is 7 yards, and the length is 6 times that, so:
L = 6*7yd = 42yd
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QUESTION 31 POINTThe area of a triangle is 18. The base is 6 inches. What is the height? Do not include units in your answer.
Answers
ANSWER:
6
STEP-BY-STEP EXPLANATION:
The area of a triangle is given by the following equation:
[tex]A=\frac{b\cdot h}{2}[/tex]We replace and solve for h (height)
[tex]\begin{gathered} 18=\frac{6\cdot h}{2} \\ h=\frac{18\cdot2}{6} \\ h=6 \end{gathered}[/tex]The height of the triangle is 6 inches
The endpoints of diameter in a circle form an angle with point C. What is the measure of angle BCD?
Answers
Answer:
90 degrees
Explanation:
Please note that whenever a triangle is inscribed in a circle and one side of the triangle is a diameter of the circle as in the given figure, then the angle that is opposite the diameter of the circle is a right angle;
[tex]\therefore\angle BCD=90^{\circ}[/tex]4. A teacher can only make 3000 copies in a month. If a teacher-has-made 2700 copies so far this month, what percentage of her copies has she used?
Answers
In order to determine the percentage, let x as the percentage. Then, you can write:
[tex]\frac{x}{100}\cdot3000=2700[/tex]factor x/100 is the percentage in decimal form. The product of this factor and 3000 equals 2700.
Solve for x and simplify:
[tex]x=\frac{2700}{3000}\cdot100=90[/tex]Hence, teacher has used 90% of the copies.
Debra will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $50 and costs anadditional $0.15 per mile driven. The second plan has an initial fee of $59 and costs an additional $0.11 per mile driven.for what amount of driving do the two plans cost the same? i need the answer for miles and cost
Answers
First plan cost is modeled as:
50 + 0.15x
where x are the miles driven
Second plan cost is modeled as:
59 + 0.11x
If the two plans cost the same, then:
50 + 0.15x = 59 + 0.11x
0.15x - 0.11x = 59 - 50
0.04x = 9
x = 9/0.04
x = 225 miles
which corresponds to a cost of:
50 + 0.15*225 = $83.75
How many modes does the following dataset have? 9,29,13,4,2,16,10,14,27
Answers
Given:
[tex]9,29,13,4,2,16,10,14,27[/tex]To find- the mode of the given dataset.
Explanation-
We know that the mode is the most occuring frequency of the dataset. Let us arrange the data in ascending order first, and we get
[tex]2,4,9,10,13,14,16,27,29[/tex]Since there is no repeated frequency, we can say that there is no mode for the given data set.
The answer is 0.
when graphed on a coordinate plane,Bumby Avenue can be represented by the equation y=-4x-7. primrose can be represented by the equation 8x+2y=17. Are these streets parallel ?
Answers
Answer:
The lines are not parallel because their slopes are opposite reciprocals.
Explanation:
The lines:
[tex]\begin{gathered} y=-4x-7 \\ \text{and} \\ 8x+2y=17 \end{gathered}[/tex]are not parallel because their slopes are not the same
Note:
Two straight lines are said to be parallel when their slopes are the same, and have different y-intercepts.
Solve the following/3x=7-3/x
Answers
Value of x is 8.46 for equation 3x=7-3/x
What is Equation?Two or more expressions with an Equal sign is called as Equation
The given equation is 3x=7-3/x
3x+3/x=7
3x²+3=7x
3x²-7x+3=0
Use quadratic equation formula
a=3, b=-7, c=3
x=-b±√b²-4ac/2a
x=7±√49-4(3)(3)/2(3)
x=7±√49-36/6
x=7±√13/6
x=7±√2.16
x=7+1.46
x=8.46
Hence value of x is 8.46 for equation 3x=7-3/x
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this lettuce i have is 25 calories per serving. serving size is 85 grams. i had 27 grams. how many calories would that be??
Answers
Answer:
7.94117647059 Calories
Step-by-step explanation:
25 Calories = 85 Grams
25/85 = 0.294117647059
0.294117647059 = 1 Gram
0.294117647059 times 27 = 7.94117647059
Find the distance between:(4,-9) and(-8,0)Round your answer to the nearest hundredth.
Answers
The distance between 2 points (x1, y1) and (x2, y2) is calculated as:
[tex]\text{distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]So, if we replace (x1, y1) by (4, -9) and (x2, y2) by (-8,0), we get:
[tex]\begin{gathered} \text{distance}=\sqrt{(-8-4)^2+(0-(-9))^2} \\ \text{distance}=\sqrt{(-12)^2+(9)^2} \\ \text{distance}=\sqrt{144+81} \\ \text{distance}=\sqrt{225} \\ \text{distance}=15 \end{gathered}[/tex]Answer: the distance is 15
Suppose you are choosing at random from the numbers 1 through 12 (inclusive). If the event E is "the number is even," find the set representing E. Express your answer as a bracketed set in the form {a,b,c,d}.
Answers
The set numbers from 1 to 12(inclusive) is:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
The set even numbers are:
2, 4, 6, 8, 10, 12
Given that the event E is "the number is even"
Therefore, the set representing the event E as a bracketed set is:
[tex]E=\mleft\lbrace2,4,6,8,10,12\mright\rbrace[/tex]
CASSANDRA WENT FOR A JO9.SHE RAN AT A PACE OF 7.3 MILESPER HOUR. IF SHE RAN FOR 0.75HOURS, HOW FAR DID CASSANDRARUN?
Answers
We can use one simple formula, that is d=vt
d=distance
v=pace
t=time
So,
d=(7.3miles per hour)(0.75 hours)=5.475 miles
Your cousin is building a Sandbox for his daughter how much sand will he need to fill the Box? Explain. How much paint will he need to paint all six surface of the sandbox? Explain. 1ft 4ft 6ft not answer choices
Answers
Since the image is a rectangular prism
The volume of the box can be obtained by using the formula:
Volume = l x b x h
The box has a dimension of 1ft x 4ft x 6ft
The volume of the box = 1 x 4 x 6 = 24 cubic feet
Therefore, the volume of sand needed to fill the box will be = 24 cubic feet of sand
The surface area of the box can be obtained using the formula:
2(lb + lh + bh)
= 2(1x4 + 1x6 + 4x6)
=2(4 + 6 + 24)
=2 (34)
= 68 square feet
Therefore a total surface area of 68 square feet needs to be painted
2.) Part A: complete the following table for the functions
Answers
Complete the following table for the functions:
[tex]\begin{gathered} f(x)=x^2+1 \\ g(x)=f(x-5) \\ h(x)=f(x+3) \end{gathered}[/tex]The below function represents the transformation of the independent variables:
[tex]\begin{gathered} f(x)=x^2+1 \\ g(x)=f(x-5)\ldots\ldots\text{.f(x) will decrease by 5 units} \\ h(x)=f(x+3)\ldots\ldots.f(x)\text{ will increase by 3 units} \end{gathered}[/tex]