The population of McKinney after 2 years with an average growth rate of 8.4% will be approximately 210,099.76.
To calculate the population of McKinney after 2 years with an average growth rate of 8.4%, we can use the formula for compound interest:
[tex]P = P_0 * (1 + r/100)^t[/tex]
Where P0 is the initial population, r is the growth rate, and t is the number of years. In this case, P0 = 180,000, r = 8.4, and t = 2. Plugging these values into the formula, we get:
[tex]P = 180,000 * (1 + 8.4/100)^2[/tex]
[tex]P = 180,000 * 1.084^2[/tex]
[tex]P = 180,000 * 1.174996[/tex]
[tex]P = 210,099.76[/tex]
So, the population of McKinney after 2 years with an average growth rate of 8.4% will be approximately 210,099.76.
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The complete question is :
The population of McKinney is about 180,000. The population is increasing at an average rate of 8.4% . It's population after 2 years will be.
A phone sells for $230. It is now on sale for 30% off. How much money will April save if she buys the phone on sale?
If the phone is in sale of 30% off, the money April save if she buys the phone on sale is $69.
A sale is a reduction of the basic price of a good or a service. It can occur on any stage in the process of production.
It is given that a phone sells for $230. It is now on sale for 30% off.
Now, Cost price = $230
sale percentage = 30%
so, the sale price = [tex]230 \times 30\%\\[/tex]
or [tex]230 \times \frac{30}{100}[/tex] = $69
therefore, the money April will save if she buys the phone on sale is $69.
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Please help, I’ll give brainliest!!!!!!!!!!!!
The solution to the given system of equation is (-2,7) and (2, -1).
What is system of equation?A system of equations are the set of equations where the solution for these equations are the intersecting point between the equations.
The graph denotes the two equations in which one is line and another one is parabola.
These system equation has two solutions.
That is, the point where the curve and line intersect is the solution for the system.
In this graph, the line and the curve intersects at two points,
i.e., (-2,7) and (2, -1).
Hence, the solution to the given system of equation is (-2,7) and (2, -1).
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A parabola can be drawn given a focus of (0, 4) and a directrix of y =
be said about the parabola?
Answer: A parabola can be defined as the set of all points that are equidistant from a focus and a directrix. Based on the information provided, the focus of the parabola is (0, 4) and the directrix is y =.
The parabola will open upwards or downwards depending on the location of the focus and the directrix. Since the focus is at (0, 4), and the directrix is at y =, the parabola must open upwards. The axis of symmetry of the parabola will pass through the focus and will be perpendicular to the directrix.
Without more information, it is not possible to fully determine the shape and equation of the parabola. The shape of the parabola and its equation can be found by using the focus and directrix and other information, such as the vertex or a point on the parabola.
Step-by-step explanation:
The seats in a theater are arranged in rows with an equal number of seats in each row. The graph shows the relationship between the number of rows and the total number of seats. How many seats are in each row (The variables can only be positive numbers.)
The number of seats in each raw by the given graph is 30.
How do we make graph of a function?Suppose the considered function whose graph is to be made is
f(x)
The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values
f(x)
are plotted on the vertical axis.
They are together plotted on the point
(x,y) = (x, f(x))
This is why we usually write the functions as:
y = f(x)
Let the number of rows in the original arrangement be x. Then, the number of seats in each row in original arrangement = x
Total number of seats = x x x = x²
From the given information,
2x(x-10)= x²+ 300
2x²-20x = x²+300
x²-20x-3000
(x-30) (x+10) = 0
x = 30, -10
Since, by the function number of rows or seats cannot be negative. So, x = 30.
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rectangle abcd is dilated by a scale factor of 1/4 to form a’b’c’d’. point t is the center of dilation and lies on segment ab as shown
The slope of A'B' is 0 and the length of A'B' is 1/4(5) = 1.25 units.
What is transformation?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
The line AB has the following coordinates.
A = (1, 4)
B = (6, 4)
The distance between AB is given as:
AB = √(6 - 1)² + (4 - 4)²
AB = √(5)²
AB = 5
The slope of AB = 0.
For the dilated rectangle the slope remains the same.
The slope of A'B' is 0 and the length of A'B' is 1/4(5) = 5/4 = 1.25 units.
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The correct question is:
10. at a pizza shop there is a deal going on that you can get a pizza for $3.00. you can choose thick or thin crust, red or white sauce, and one topping of either pepperoni, sausage, or vegetarian. create a tree diagram to display the sample space on your worksheet. how many total outcomes are there?
The number of total outcomes is 12.
Here is a tree diagram for the pizza options:
Copy code
/ | \
Thick Thin
/ | \
Red White Red White
/ | \ / | \ / | \
Pep Saus Veg Pep Saus Veg Pep Saus Veg
There are two (2) options for the crust, two (2) options for the sauce, and three (3) options for the topping. Therefore, the total number of outcomes is:
Total Outcomes = 2 (options for crust) x 2 (options for sauce) x 3 (options for topping)
Total Outcomes = 12
Therefore, there are 12 total outcomes.
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The phrases exponential growth and exponential decay appear quite often in media reports these days, referring to environmental, technological, and scientific changes.
In your own words, how would you describe exponential growth and exponential decay to someone unfamiliar with these phrases?
Exponential growth is a pattern of data that shows a rapid increase over time, while exponential decay is a pattern of data that shows a rapid decrease over time.
What is xponential growth and exponential decay?An rise in the resultant quantity for a given quantity is referred to as exponential growth, and a decrease in the resultant quantity for a given quantity is referred to as exponential decay.
The fundamental distinction between the two is that in an exponential decay relationship, the output values rise quickly as the input value rises, whereas in an exponential growth relationship, the output rises noticeably faster as the input value rises.
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At a restaurant, Table A's bill of €72 is split equally
between the people at the table. Table B has two more
people than Table A, and its bill of €108 is also split
equally between the people at the table. Each person at
Table A pays the same amount as each person at Table B.
How many people were at Table A?
There were total 4 people at table A and each of them pay €18.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Table A's bill of €72 is split equally.
and, Table B has two more people than Table A and its bill of €108 is also split equally.
let number of people at table A be x and at table B be (x+2).
So, the number of people
x/ 72 = (x+2)/108
108x = 72x + 144
108x - 72x = 144
36x= 144
x=4
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3.37 examples of correlated variables. give an example of two variables in your field of study that are a. positively correlated b. negatively correlated
The length and width of a rectangle is Positively correlated variables and the base and height of a triangle is negativley correlated variables.
In mathematics, there are many examples of variables that can be positively or negatively correlated. Here are two examples:
a. Positively correlated variables: The length and width of a rectangle. If you increase the length of a rectangle, the width tends to increase as well. So, there is a positive correlation between the length and width of a rectangle.
b. Negatively correlated variables: The base and height of a triangle. If you increase the base of a triangle, you can keep the area the same by decreasing the height, and vice versa. So, there is a negative correlation between the base and height of a triangle.
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Forest rangers at a state park have observed a decline in the rate of trees per
acre over a 5-year period. At the beginning of their observations, there was an
average of 48 trees per acre. At the end of the 5-year period, there was an
average of 42 trees per acre. If this trend continues, how many trees per acre
will there be 4½ years from the end of the 5-year observation period?
helppp
There will be 36.6 trees per acre after 4½ years from the end of the 5-year observation period. The solution has been obtained by using unitary method.
What is the unitary method?
The value of each individual unit is first determined using the unitary method, and only then is the value of the required number of units determined.
We are given that at the beginning of their observations, there was an average of 48 trees per acre. At the end of the 5-year period, there was an average of 42 trees per acre.
So, decline in trees per acre in 5 years is 48 - 42 = 6 trees per acre
So, decline in 1 year = 6/5 = 1.2 trees per acre
Similarly, decline in 4.5 years = 1.2 * 4.5 = 5.4 trees per acre
Thus, trees left per acre = 42 - 5.4 = 36.6 trees
Hence, there will be 36.6 trees per acre after 4½ years.
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how many pattern block triangles would create 2 hexagons
Answer:
Step-by-step explanation:
twelve triangles make 2 hexagons, which means there are 12 groups of in 2
Fill in the missing numbers to complete the linear equation that gives the rule for this table.
x y
3 91
4 89
5 87
6 85
The linear equation for the given coordinate points is y=-2x+97.
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
From the given table, the coordinate points are (3, 91) and (4, 89).
Here, slope (m)= (89-91)/(4-3)
m= -2
Substitute m=-2 and (x, y)=(3, 91) in y=mx+c, we get
91=-2(3)+c
91=-6+c
c=97
So, the equation is y=-2x+97
Therefore, the linear equation is y=-2x+97.
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Suppose that you plan on taking a summer job selling magazine subscriptions. The magazine company will pay you 1.50 for selling the first subscription. For each additional subscription sold, the magazine company will pay you 20 cent more than what was paid for the previous subscription. How much will you earn by selling magazine subscriptions?
As per unitary method, you'll earn $9.50 by selling five magazine subscriptions.
The unitary method is a method of finding a single value of a quantity or unit, given the value of a unit of the same quantity. In this case, we need to find out how much money you'll earn by selling magazine subscriptions.
We know that for selling the first subscription, the magazine company will pay you $1.50. For each additional subscription sold, the magazine company will pay 20 cents more than what was paid for the previous subscription.
Let's use the unitary method to find out how much you'll earn by selling the second subscription.
The magazine company pays 20 cents more than $1.50 for the second subscription. Therefore, the payment for the second subscription is
=> $1.50 + $0.20 = $1.70.
Using the same method, we can calculate the payment for the third subscription, which is
=> $1.70 + $0.20 = $1.90.
Similarly, we can use the unitary method to calculate the payment for the fourth, fifth, and so on, subscriptions.
By adding up the payments for each subscription, we can calculate your total earnings. Let's assume you sold five subscriptions.
The payment for the first subscription is $1.50, for the second subscription, it's $1.70, for the third subscription, it's $1.90, for the fourth subscription, it's $2.10, and for the fifth subscription, it's $2.30.
Total earnings = $1.50 + $1.70 + $1.90 + $2.10 + $2.30 = $9.50.
Therefore, you'll earn $9.50 by selling five magazine subscriptions.
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The 3rd term of an arithmetic sequence is 1407 and the 10th term is 1183. Calculate the number of positive terms in the sequence.
Answer:
Let a be the first term and d be the common difference.
3rd term = 1407
a+2d = 1407 ------- 1
10th term = 1183
a+9d = 1183 ------- 2
By solving 1 and 2, a = 1471 and d = -32
so the general term T(n) = 1471 + (n-1)(-32)
= 1471 - 32n +32
= -32n + 1503
-32n + 1503 [tex]\geq[/tex] 0
-32n [tex]\geq[/tex] -1503
n [tex]\leq[/tex] 46.96875
The number of positive terms = 46
is 27 goldfish to 15 frogs a equivalent ratio
please help with show work. urgent
Answer:
51
Step-by-step explanation:
Use the grouping method to factor the polynomial below completely. 3x³ + 9x² + 5x + 15 O A. (3x²+3)(x + 5) O B. (3x²+5)(x+3) ○ C. (3x² + 3)(x+3) D. (3x² + 5)(x + 5)
The factor of the expression is (3x²+ 5)(x + 3)
How to factor the expressionFrom the question, we have the following parameters that can be used in our computation:
3x³ + 9x² + 5x + 15
Group the terms in two's and factor each term
Using the above as a guide, we have the following:
3x²(x + 3) + 5(x + 3)
Factor out x + 3
So, we have the following representation
(3x²+ 5)(x + 3)
Hence, the solution is (3x²+ 5)(x + 3)
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hello can anyone help me wiith this
Answer: Correct answer is -1
Step-by-step explanation:
It is given that the volume of the cylinder and the cuboid are the same. Find the value of x and give your answer correct to two decimal places. Jawapan / Answer: 7 cm 8 cm [3 markah/ 3 marks] For Examine Use
who can help me pls
Step-by-step explanation:
the radius of the circular base is 7/2=3.5 cm
the surface of the base is πr^2=π*(3.5)^2=38.465
volume of the cylinder is surface of the base*high
38.465*30=1153.95
the cuboid volume=8^2*x=64x
64x=1153.95
x=1153.95/65=18.03 cm=18 cm
Find −23−(−12). Write your answer as a fraction or mixed number in simplest form
The simplest fraction form of an expression, (- 2/3) - (-1/2) is equals to the -1/6.
A fraction is a number that represents a part of whole. It is expressed as quoitent, in which numerator is divided by denominator. For ex : 3/4 is a fraction, where 3 is numerator and 4 is denominator. We have an expression, (- 2/3) - (-1/2). This expression is substraction of two rational number and both are negative rational numbers. Using sign law of multiplication: - × - = + , i.e., multiplation of two negative numbers result positive number.
=> - 2/3 + 1/2
Both fraction has different denominators. Write as least common multiple of 2 and 3, i.e., LCM(2,3)= 6
=> ( -2 × 2 + 3 )/6
Simplify the expression as possible
=> (- 4 + 3 )/6
=> - 1/6
This is the needed simplified fraction. Hence, The solution in simplest fraction is -1/6.
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the density of zinc is 7.13 g/cm3. calculate the probability that a density measurement of the post-1982 pennies made using the caliper method is within 5% of the density of zinc. use the caliper data for the entire lab session to perform your calculation, and assume that the data fits a normal distribution.
As per the density the probability that a density measurement of the post-1982 pennies is 0.3565 g/cm3.
Density is an important physical property that can help identify materials. In this case, we are interested in the density of zinc and how it relates to the post-1982 pennies.
To calculate the probability of a density measurement within 5% of the density of zinc, we need to first determine the range of densities that fall within 5% of the zinc density.
The 5% range of the zinc density is calculated by multiplying the zinc density (7.13 g/cm3) by 5% (0.05), which gives us 0.3565 g/cm3.
The upper and lower limits of this range are then calculated by adding and subtracting this value from the zinc density, respectively.
The upper limit is 7.4865 g/cm3 (7.13 + 0.3565),
while the lower limit is 6.7735 g/cm3 (7.13 - 0.3565).
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The inn has ten rooms. One-half of the rooms are reserved for Friday. The rest are vacant. Of 12 more rooms are reserved for Friday, what will be the total number of occupied rooms on Friday?
Using, the mathematical inequalities, we can conclude that the total number of occupied rooms on Friday is 10.
Number of rooms in the inn = 10
It is given that One-half of the rooms are reserved for Friday which means 5 rooms were initially reserved on Friday.
Now, 12 more rooms are reserved for Friday.
So, the Initial reservation for Friday = 5
Final reservations for Friday = 5 + 12 = 17
Now, Final reservations for Friday(17) > Total number of rooms in the inn(10).
As the reservation exceeds the capacity of the hotel, 7 reservations will be cancelled and all 10 rooms will be occupied on Friday.
Hence, the total number of occupied rooms on Friday is 10.
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Tara has been planting young trees in her garden. The maple tree that is 10 inches taill is
growing 4 inches per month, whereas the oak tree that is 25 inches taill is growing 1 inch per
month. In a few months, the two trees will be the same height. What will that height be?
Write a system of equations, graph them, and type the solution.
The system of the equations are:
y = 10 + 4x
y = 25 + x
The height of tree is 30 inches tall.
The graph is given below.
The solution is (5, 30).
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 8 is an equation
We have,
Maple tree:
The maple tree that is 10 inches tall is
growing 4 inches per month,
This can be written as,
y = 10 + 4x _____(1)
Where y is the height of the tree.
Oak tree:
The oak tree is 25 inches tall and is growing 1 inch per
month.
This can be written as,
y = 25 + x ______(2)
Where y is the height of the tree.
Now,
From (1) and (2),
In a few months, the two trees will be the same height.
So,
10 + 4x = 25 + x
4x - x = 25 - 10
3x = 15
x = 5
Now,
y = 10 + 4x = 10 + 4 x 5 = 10 + 20 = 30
y = 25 + x = 25 + 5 = 30
Thus,
The height of tree is 30 inches tall.
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Assume d varies directly as t and d = 180 when t = 3. Find t when d = 390.
The value of t is 6.5. The value of the constant is 60
What varies directly?
The relationship between two variables in which one is a constant multiple of the other is referred to as direct variation. For instance, two variables are said to be in proportion when one affects the other. b = ka is the equation if b is directly proportional to a. (where k is a constant).
Given that d varies directly as t.
The relation between d and t is
d = kt.
Given that d = 180 when t = 3.
Putting d = 180 and t = 3 in d = kt
180 = 3k
Divide both sides by 3:
k = 180/3
k = 60
Putting k = 60 in d = kt:
d = 60t
Now putting d = 390 in d = 60t:
390 = 60t
60t = 390
Divide both sides by 60
t = 6.5
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In a group of 48 children, 25% have blue eyes. How many children do not
have blue eyes?
Answer:
Step-by-step explanation:
48----------------100%
x------------------75%
x=36
How many 200 mL glasses can be filled using a 2.2 L bottle of cola?
Answer:
11 glasses
Step-by-step explanation:
There are 200 ml glasses and we have 2.21 liter of bottels. So first of all covert liter into ml so we get 2210 ml of coca cola.now divide 2210 by 200 so we get 11 glasses
2/2^(4-3x)= 8
find x
The equation will be solved x = 2.
What is an Equations?Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
The given equation 2/[tex]2^{(4-3x)}[/tex] = 8
[tex]2^{(4-3x)}[/tex] = 2/8
[tex]2^{(4-3x)}[/tex] = 2⁻²
So we can take 4-3x = -2
3x = 4+2
x = 6/3 = 2
Hence, the equation will be solved x = 2.
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The growth of a bacteria population is modeled by the equation p(h)=1,000e(0.4h).
a. How long does it take for the population to double? Round to the nearest quarter of an hour.
a. 1 hour and 45 minutes for the bacteria population to double.
To find out how long it takes for the bacteria population to double, we need to solve the equation:
2p(0) = p(h)
where p(0) is the initial population and h is the time it takes for the population to double.
Since p(h) = [tex]1000e^{(0.4h)}[/tex], we can write:
2p(0) = [tex]1000e^{(0.4h)}[/tex]
Dividing both sides by 1000, we get:
2p(0)/1000 = [tex]e^{(0.4h)}[/tex]
Taking the natural logarithm of both sides, we get:
ln(2p(0)/1000) = 0.4h
Solving for h, we get:
h = ln(2p(0)/1000) / 0.4
We know that p(0) = 1, since the initial population is given as 1,000. Substituting this value, we get:
h = ln(2) / 0.4
h ≈ 1.73
So it takes approximately 1.73 hours for the bacteria population to double.
Rounding to the nearest quarter of an hour.
we get:
h ≈ 1.75 hours
h ≈ 1 hour and 45 minutes
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how to convert 26kg 45g in kg
Step-by-step explanation:
45g = 0.045kg
0.045 + 26 = 26.045
Final answer is 26.045 kg
2. Order the following decimals from least to greatest.
0.439
0.394
0.441
0.531
0.342
Answer: 0.342 -> 0.394 -> 0.439 -> 0.441 -> 0.531
Step-by-step explanation:
0.342 -> 0.394 -> 0.439 -> 0.441 -> 0.531
If you convert the decimals into fractions out of a hundred, then it will be easily to keep going from least to greatest or greatest to least and soon you won't need help. Keep trying! :)
