Answers
An exponential function has the form:
\(y=A(r)^x\)Where A is the initial value, r is the ratio that is applied for each period of time and x is the time since the initial A in the same unit as the period of r.
The initial value of the population was 15500, so:
\(A=15500\)It decreases 3% per year, so x is the time since the population was 15500 in years and, since it is a 3% decrease, this means that after each year there are just 97% left, so the ratio is 97% or, in the decimal form, 0.97.
\(\begin{gathered} x\Longrightarrow\; \text{time in years since the initial population of 15500} \\ r=0.97 \end{gathered}\)So, the function is:
\(y=15500(0.97\text{)}^x\)To graph the function, we can first plot some points.
Let's plot one point per 10 year until we pass the value of 8000.
For x = 0:
\(y=15500(0.97)^0=15500\cdot1=15500\)For x = 10:
\(y=15500(0.97)^{10}=15500\cdot0.737424\ldots\approx11.430\)For x = 20:
\(y=15500(0.97)^{20}=15500\cdot0.543794\approx8429\)Now that we are close, let's do 2 years:
For x = 22:
\(y=15500(0.97)^{22}=15500\cdot0.511656\ldots\approx7931\)So, ploting the points and graphing, we have:
The dotted line is the y = 8000. We can see that in the 21th year, the population is still above 8000, but at year 22 the population went belowe 8000.
So, the population will drop below 8000 by the 22th year since the initial population of 15500.
Related Questions
Rebekah bought g gallons of paint for $12.85 per gallon and b brushes for $4.79 each. Which expression can be used to determine the total amount Rebekah spent on paint and brushes?
Answers
Answer:
g12. 85 + b4. 79
Step-by-step explanation:
g and b is just the amount she buys
Answer:
Step-by-step explanation:
Cost = 12.85g + 4.79b
That's all you can do to set up the total cost. There is no further reduction or combination that can take place. B and G are different.
If F(x) and f(x) are inverse functions of each other and f(x) = 2x+5, what is f(-1) (8) ?
-1
3/2
41/8
23
Answers
Answer:
3/2
Step-by-step explanation:
Cell towers are used to transmit calls. Each tower transmits to a circular region. On a grid of a city, the coordinates of three towers and the radius of its transmission are provided.
Tower A is at (0, 0) and has a radius of 3 miles.
Tower B is at (5, 3) and has a radius of 2. 5 miles.
Tower C is at (2, 5) and has a radius of 2 miles. 16)
Write the equation of the transmission boundary for all three towers. (eq of the 3 circles)
Answers
The equation of the transmission boundary for all three towers are x^2 + y^2 = 3^2, (x - 5)^2 + (y - 3)^2 = 2.5^2 and (x - 2)^2 + (y - 5)^2 = 2^2 respectively
To write the equations of the transmission boundaries for all three towers, we can use the equation of a circle.
The equation of a circle with center (h, k) and radius r is given by:
(x - h)^2 + (y - k)^2 = r^2
For Tower A:
Center: (0, 0)
Radius: 3 miles
Equation: x^2 + y^2 = 3^2
For Tower B:
Center: (5, 3)
Radius: 2.5 miles
Equation: (x - 5)^2 + (y - 3)^2 = 2.5^2
For Tower C:
Center: (2, 5)
Radius: 2 miles
Equation: (x - 2)^2 + (y - 5)^2 = 2^2
These three equations represent the transmission boundaries of the respective towers.
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PLEASE HELP ASAP!!! I'LL MARK BRAINLIEST TO RIGHT ANSWER!!!
Answers
The solution of the inequality is, x ∈ (- ∞, 5) ∪ (10, ∞)
Where, x represent the number of totts.
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
We have to given that;
My friend Raw has either no more than 5 toots and more than 10 toots.
Now, Let number of toots = x
Hence, We get;
⇒ x < 5
And, x > 10
Thus, The solution of the inequality is,
⇒ x ∈ (- ∞, 5) ∪ (10, ∞)
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Farmer Hank has fewer than 100 pigs on his farm. If he groups five to a pen, there are always three pigs left over. If he groups the pigs seven to a pen, there is always one left over. However, if he groups the pigs three to a pen, there no pigs left. What is the greatest number of pigs that Farmer Hank could have on his farm?
Answers
Answer:
the answer is 99
Step-by-step explanation:
Close ties between the members of the group typically are formed during which stage of group development? a. Storming b. Adjourning c. Norming d. Forming
Answers
Close ties between the members of the group typically are formed during the norming stage of group development.
The norming stage of group development is the third stage, where the group begins to establish a sense of cohesion and unity. During this stage, members start to accept each other's ideas and opinions, develop relationships with one another, and establish patterns of communication and interaction. As a result of these positive developments, close ties between the members of the group often begin to form.
In the norming stage, group members also start to identify common goals and work together to achieve them. This shared sense of purpose can further strengthen the bonds between group members and contribute to the formation of close ties.
Overall, the norming stage is an important period of transition for groups as they move from the early stages of forming and storming to a more cohesive and productive group dynamic. The close ties formed during this stage can help to foster a supportive and collaborative environment that benefits the group as a whole.
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Square root of 120 over the square root of 30. what is the following quotient.
Answers
Answer:
21.90890230 or 21.91 (I'm assuming you're saying 120/ √30)
Step-by-step explanation:
What is the integrated rate law for a 1st order reaction?
Answers
Expiation: the half-life of a first-order reaction is independent of concentration, and this equation has the form y=mx + b so a plot of the natural log of [A] as a function of time yields a straight line
Source: khanacadamey.org
Hope this helps!
8 piglets are evenly sharing 5 liters of milk.
How many liters of milk should each piglet get?
Choose 1 answer:
A. 1 3/8 liters of milk
B. 13/8 liters of milk
C. 5/8 liters of milk
D. 8/5 liters of milk
Answers
Answer:
C.
Step-by-step explanation:
5 liters divided by 8.
5 divided by 8 = 5/8
Answer: 5/8 liter
line 1: y=-2x+4 and line 2: y=-2x the system has exactly on solution or infinite solution or no solutions.
Answers
The system of equation line 1: y=-2x+4 and line 2: y=-2x has no solution.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
We are given the system of equation as;
line 1: y=-2x+4
line 2: y=-2x
Here we can put x = 1
Then;
y= -2(1) + 4
y = -2 + 4
y = 2
-2x=-2x+4
x = 0
Therefore, we can see that the system of equation has no solution.
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0.110 is _____ than 0.450?
A. less
B. greater
C. equal
D. greatest
Answers
Ian invested $20,000 in an account paying an interest rate of 3\tfrac{1}{4}3 4 1 % compounded continuously. Lauren invested $20,000 in an account paying an interest rate of 3\tfrac{7}{8}3 8 7 % compounded monthly. After 20 years, how much more money would Lauren have in her account than Ian, to the nearest dollar?
Answers
Answer:
$5047
Step-by-step explanation:
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Write an equation that represents the line. use exact numbers.
Answers
Equation that represents the line is , x + y =1
General form of straight line:
ax+by+c = 0
here,
a is the coefficient of x,and it is a constant.
b is the coefficient of y,and it is a constant.
c is the constant term.
again,
a and b can never be zero together,one of the value either a or b can be zero,while c can be zero.
If c will be zero,straight line will pass through origin (0,0).
If a=0 then,
by+c =0
by = -c
y = -c/b,Represents a line parallel to X-axis.
If b=0 then,
ax +c = 0
ax =-c
x = -c/a, Represents a line parallel to Y-axis.
Now we have to write an equation that represents the line,
so,
x + y =1
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If the government imposes a minimum wage of $12, how many workers will be unemployed? 4,000 10,000 2,000 0
Answers
If the government was to impose a minimum wage of $12 then the number of unemployed workers would be 4,000.
How many workers would be unemployed?If the government was to impose a minimum wage of $12 then a situation would arise where the demand for workers is 8,000 yet the supply for workers is 12,000.
This would lead to an unemployment rate of:
= 12,000 - 8,000
= 4,000 people
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Bebe paid $8.00 for 20 pounds of oranges. What is the ratio of the price
of oranges to the pound of oranges?
Answers
Answer:
2.50 per pound
Step-by-step explanation:
The ratio of the price of oranges to the pound of oranges will be $0.40 per pound.
What is the rate?The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
Bebe paid $8.00 for 20 pounds of oranges. Then the ratio of the price of oranges to the pound of oranges will be given as,
Rate = $8 / 20
Rate = $0.40 per pound
The ratio of the price of oranges to the pound of oranges will be $0.40 per pound.
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5. (5 points) Use a truth table to show the following equivalence: ~(~pg)^(pVq) =P 6. Dumpulus is dishing out gossip about himself and his friends Abforsoft, Bloronski, and Crafloniae. He tells you that, among this group of four, Dumpulus knows all three of the others, Abforsoft knows exactly 2 of the others, Bloronski knows exactly 2 of the others, and Crafloniae knows exactly 2 of the others. (Assume that if Person in knows Person n, then Person n knows Person m, and we won't count a person knowing themself as something worth mentioning.) Dumpulus is a BIG OL LIAR!!! How do we know that what Dumpulus is saying is not true? (Hint: Think graph theory.) 8. Without using any theorems from the book, prove the following statement: The sum of any two odd numbers is even.
Answers
Dumpulus's claim can be analyzed using graph theory. If we represent Dumpulus and his friends as vertices in a graph and draw an edge between two vertices if one person knows the other, we can examine the degrees of the vertices. Dumpulus claims to know all three of his friends, which would result in a degree of 3 for his vertex.
However, if Abforsoft, Bloronski, and Crafloniae each knew Dumpulus, their vertices would also have a degree of 1. This contradicts the claim that Abforsoft, Bloronski, and Crafloniae each know exactly 2 of the others, as their degrees would be 3, not 2. Therefore, we can conclude that Dumpulus's claim is false.
To prove that the sum of any two odd numbers is even, we can consider the properties of odd and even numbers. An even number can be represented as 2k, where k is an integer, and an odd number can be represented as 2m + 1, where m is an integer. Let's consider two odd numbers, 2m1 + 1 and 2m2 + 1, where m1 and m2 are integers.
The sum of these two odd numbers is:
(2m1 + 1) + (2m2 + 1) = 2m1 + 2m2 + 2 = 2(m1 + m2 + 1).
Since m1 + m2 + 1 is an integer, we can represent it as k, where k is an integer. Therefore, the sum of two odd numbers can be expressed as 2k, which is an even number.
This proof demonstrates that when we add two odd numbers, the result is always an even number. It doesn't rely on any specific theorems but rather uses the fundamental properties of even and odd numbers.
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Find the center and radius of the circle that passes through the points (−1,5),(5,−3) and (6,4).
Answers
A circle can be defined as a geometric shape consisting of all points in a plane that are equidistant from a given point, which is known as the center. The distance between the center of the circle and any point on the circle is referred to as the radius.
In order to find the center and radius of a circle, we need to have three points on the circle's circumference, and then we can use algebraic formulas to solve for the center and radius. Let's look at the given problem to find the center and radius of the circle that passes through the points (-1,5), (5,-3), and (6,4).
Center of the circle can be determined using the formula:
(x,y)=(−x1−x2−x3/3,−y1−y2−y3/3)(x,y)=(−x1−x2−x3/3,−y1−y2−y3/3)
Let's plug in the values of the given points and simplify:
(x,y)=(−(−1)−5−6/3,−5+3+4/3)=(2,2/3)
Next, we need to find the radius of the circle. We can use the distance formula to find the distance between any of the three given points and the center of the circle:
Distance between (-1,5) and (2,2/3) =√(x2−x1)2+(y2−y1)2=(2+1)2+(2/3−5)2=√10.111
Distance between (5,-3) and (2,2/3) =√(x2−x1)2+(y2−y1)2=(5−2)2+(−3−2/3)2=√42.222
Distance between (6,4) and (2,2/3) =√(x2−x1)2+(y2−y1)2=(6−2)2+(4−2/3)2=√33.361
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Find the lengths of PR and QS
Answers
The length of PR and QS will be 20 units. And the area of the rectangle will be 173.21 square units.
What is the area of the right-angle triangle?The area of the right-angle triangle is given as
A = 1/2 x B x H
Where B is the base and H is the height of the right triangle.
The length of PT is 10 and the angle ∠TPS is 60°.
The length of PR is given as,
PR = PT + TR
PR = 10 + 10
PR = 20
And the length of QS is given as,
QS = QT + TS
QS = 10 + 10
QS = 20
The area of the rectangle is given as,
A = Area of triangle ΔPQR + Area of triangle ΔPSR
A = 2 [(1/2) x (20 cos 60°) x (20 sin 60°)
A = 173.21 square units
The length of PR and QS will be 20 units. And the area of the rectangle will be 173.21 square units.
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The table below shows the number of miles Tony ran and the calories he burned per mile.
CALORIES BURNED
PER MILE
Miles
OB 200
OC. 240
Celories
Which number completes the table?
O A 160
D. 180
60
2
Answers
The required number of calories burned at the 4 miles of running is 160 calories. Option A is correct.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
The rate of the calorie burning per mile = 40 calorie/mile,
For the running of the 4 miles,
Calorie burned at 4 mile of running = 40 (4) = 160 calories,
Thus, the required number of calories burned at the 4 miles of running is 160 calories.
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what percentage of the u.s. population practice mindfulness and meditation techniques?14 percent28 percent42 percent56 percent
Answers
Step-by-step explanation:
14.2% of adults practice meditation in the us
what is the inverse of f(x)=4(x+17)
Answers
Answer:
1/4x-7/4
Step-by-step explanation:
If you have 3 means that need to be compared, you should not simply do multiple t-tests because ________.
a. it's too time consuming.
b. the joint alpha level decreases.
c. you inflate the experiment wise alpha.
d. you will be forever shunned by statiscians.
Answers
If you have 3 means that need to be compared, you should not simply do multiple t-tests because you will inflate the experiment-wise alpha. The experiment-wise alpha is the probability of making a Type I error (rejecting a true null hypothesis) in any of the tests in the series. When multiple t-tests are conducted, the overall chance of making a Type I error increases with the number of comparisons. This is called the problem of multiple comparisons or the family-wise error rate problem.
To control for this problem, you need to use multiple comparison procedures that adjust the alpha level for the number of comparisons being made, such as the Bonferroni correction, Tukey's HSD (honestly significant difference) test, or the Scheffe test. These procedures reduce the risk of making a Type I error and increase the chance of detecting true differences among the means.
Is infinity positive or negative?
Answers
A vanilla cake has a diameter of 8 inches. What is the radius?
Answers
Answer:
4
Step-by-step explanation:
d = 8 inches
r = 8/2 = 4 inches
Answer:
4 inches.
Explanation:
If the diameter is a circle, divide the diameter by two and you will have the answer of 4. This gives you the radius.
8 / 2 = 4
Hope this helps. Have a wonderful day.
T is the midpoint of KL¯¯¯¯¯. K has coordinates (2,−6), and T has coordinates (−4,2). Identify the coordinates of L.
Answers
Using the midpoint formula, the coordinates of L is determined as: (-10, 10).
How to Determine the Coordinates of a Midpoint of a Segment?To find the coordinates of the midpoint of a segment, we have to apply the midpoint formula, which is: (x, y) = [(x2 + x1)/2, (y2 + y1)/2].
Given the following:
K(2,−6) = (x1, y1)L(?, ?) = (x2, y2)T(−4,2) = (x, y) [midpoint]Substitute the given values into the midpoint formula:
(-4, 2) = [(x2 + 2)/2, (y2 + (-6))/2]
(-4, 2) = [(x2 + 2)/2, (y2 - 6)/2]
Solve for x2:
-4 = (x2 + 2)/2
2(-4) = x2 + 2
-8 = x2 + 2
-8 - 2 = x2
x2 = -10
Solve for y2:
2 = (y2 - 6)/2
2(2) = y2 - 6
4 = y2 - 6
4 + 6 = y2
10 = y2
y2 = 10
Therefore, L has the coordinates, (-10, 10).
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66.67 mph in 1.5 hours
How long does it take the car to travel 26 miles at this speed?
Answers
Answer:
5
Step-by-step explanation:
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Ndidi rides y km at 10 km/hr, then walks 0.5y km at 3 km/hr. She is away from. home less than 4hours. Find the range of values of y
Answers
Ndidi rides y km at 10 km/hr, then walks 0.5y km at 3 km/hr. She is away from. home less than 4hours.Range of the values of Y is =24/7
Let's call the total time spent riding and walking t hours. We know that t is less than 4 hours, so:
t = time spent riding + time spent walking < 4 hours
The time spent riding is given by y / 10 km/hr and the time spent walking is given by 0.5y / 3 km/hr. So, we can write the inequality as:
t = y / 10 + 0.5y / 3 < 4
Expanding and simplifying the expression on the left side gives:
7/6y < 4 * 6/7
Multiplying both sides by 6/7 gives:
y < 4 * 6/7 * 6/7 = 24/7
So, the range of values of y is 0 < y < 24/7 km. This means that Ndidi rode less than 24/7 km, but more than 0 km.
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a red die and a blue die are rolled. you win or lose money depending on the sum of the values of the two dice.if the sum is 5, 6, or 8, you win $5.if the sum is 4, 9, or 10, you win $2.if the sum is any other value (2, 3, 7, 11, or 12), you lose $4.let x be a random variable that corresponds to your net winnings in dollars. what is the expected value of x?
Answers
The expected value of your net winnings, x, is $1.39.
To find the expected value of x (net winnings), first calculate the probability of each outcome and multiply it by the respective winnings. There are 6 sides on each die, so there are 36 possible outcomes (6 sides on red die * 6 sides on blue die).
1. Winning $5: Sum of 5, 6, or 8 has 4+5+5 = 14 successful outcomes. Probability = 14/36.
2. Winning $2: Sum of 4, 9, or 10 has 3+4+3 = 10 successful outcomes. Probability = 10/36.
3. Losing $4: Sum of 2, 3, 7, 11, or 12 has 1+2+6+2+1 = 12 successful outcomes. Probability = 12/36.
Now, multiply each probability by its respective winnings/loss and sum them to find the expected value of x:
E(x) = ($5 * 14/36) + ($2 * 10/36) + (-$4 * 12/36) = $1.39
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Graph
Y-7=-3/5-(x+2)
Answers
Answer:
See attached
Step-by-step explanation:
A simpler form of the same equation is:
y = -4 +(4+2/5)
There are 6 red marbles, 5 green marbles, and 4 yellow marbles in a bag. If Joe picks 2 marbles one after the other without replacement, then what is the probability that both are red in color? P(R,R)
Pilihan jawaban
2/5
1/21
5/35
1/7
Answers
Answer:
1/7
Step-by-step explanation:
6 + 5 + 4 = 15
There are 15 marbles to start with.
p(event) = (number of desired outcomes)/(total number of outcomes)
First pick (there are 6 desired outcomes out of a total of 15 possible outcomes):
p(r) = 6/15
Now there are 5 red marbles left and a total of 14 marbles left.
Second pick (there are 5 desired outcomes out of a total of 14 possible outcomes):
p(r) = 5/14
These events are independent, so we multiply the two probabilities.
p(r, r) = 6/15 × 5/14
p(r, r) = 3/7 × 1/3
p(r, r) = 1/7