An exponential function is a mathematical function that models a relationship between a variable (in this case, t) and a constant multiplied by the power of another variable (in this case, y). The general form of an exponential function is y = ab^t, where
a is the initial valueb is the growth factor (also called the base)t is the independent variable (in this case, the number of years since 1997).In this specific scenario, we are told that in 1997, the population of a city was 220,000 people and that each year since then, the population has grown by 6.2%. We can use this information to find the values of a and b in the exponential function.
The initial value, a, is simply the population of the city in 1997, which is given as 220,000.
To find the value of b, we need to determine how much the population increases each year as a proportion of the current population. We are told that the population grows by 6.2% each year. This means that if the population is currently P, the population will be (1 + 0.062)P the next year. We can write this as P(1.062) as the growth factor b.
So, combining the values of a and b, we have:
y = 220,000 * (1.062)^t
This equation tells us that the population of the city, y, is equal to the initial population of 220,000 multiplied by the growth factor of 1.062 raised to the power of t, where t is the number of years since 1997. This equation expresses the relationship between population and time.
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An experienced ice kater pin on the ice, creating a perfect circle with a diameter of 2 yard. What i the circle' radiu?
The radius of the circle created by the ice skater is 1 yard.
What is circle ?
A circle is a two-dimensional geometric shape that is defined by a set of points that are all the same distance from a central point called the center. The distance from the center to any point on the circle is called the radius. The distance across the circle, passing through the center, is called the diameter.
The radius of a circle is half of its diameter, so the radius of a circle with a diameter of 2 yards is 1 yard.
Radius = Diameter/2
Radius = 2/2 = 1 yard
So, the radius of the circle created by the ice skater is 1 yard.
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The radius of a circle is half of its diameter, so the radius of a circle with a diameter of 2 yards is 1 yard.
Radius = Diameter/2
Radius = 2/2 = 1 yard
So, the radius of the circle created by the ice skater is 1 yard.
what are the order pairs to the fallowing solution of the sytems of equations
f(x)=x^2-2x+3: f(x)=-2x+12
The order pairs to the given equations are (-3, 18) and (3, 6)
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given are two equation, f(x) = x²-2x+3 and f(x) = -2x+12
For solving, equate them,
x²-2x+3 = -2x+12
x² = 2x-2x+12-3
x² = 9
x = ±3
Put x = -3 in f(x) = -2x+12
f(-3) = -2(-3)+12
f(-3) = 18
And, Put x = 3 in f(x) = -2x+12
f(3) = -2(3)+12
f(3) = 6
Therefore, the ordered pairs are (-3, 18) and (3, 6)
Hence, the order pairs to the given equations are (-3, 18) and (3, 6)
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Winston planned to spend no more than $150 on a helmet and goggles for skiing. After spending $90.50 on a helmet, he bought a pair of goggles that put him over his budget.
Answer:
the number would be anything over 59.50
Step-by-step explanation:
Tyrone went to a baketball game and bought a jerey that wa on ale at a 30% dicount. He alo bought a hat that cot $37. 89. Tyrone pent a total of $83. 39. Write an equation to find the original cot of the jerey
By applying discounted price concept, the original cost of the jersey can be determined from this equation 83.39 = 37.89 + 0.70x. The original cost of the jersey is $65.
Discounted price is a price obtained after a reduction by a certain percentage from the normal price. Thus, a discounted price is lower than the normal price.
The formula: discounted price = original price × (100% - %discount)
Some information given from the problem:
Jersey discount = 30%
Hat cost = $37.89
Total spent = $83.39
Let's say the cost of the jersey = x
Total spent = hat cost + discounted jersey cost
83.39 = 37.89 + (x * (100% - 30%))
83.39 = 37.89 + (x * (70%))
83.39 = 37.89 + (x * 0.7)
83.39 = 37.89 + 0.7x
Thus this is the equation.
If we want to know the original cost of the jersey, we can continue the calculation:
83.39 = 37.89 + 0.7x
83.39 - 37.89 = 0.7x
45.5 = 0.70x
x = 45.5/0.70
x = 65
Thus, the original cost of the jersey is $65.
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Please help me with this question!
Tysm!
The equations of four lines are given. Identify which lines are parallel.y=1/2x−6 Line 2: x−2y=−1 Line 3: y=4x+6 Line 4: y+3=1/4(x−6)
The lines which are parallel among the given answer choices are; line 1; y = 1/2x - 6 and line 2; x - 2y = -1.
Which among the answer choices are parallel lines?Recall that parallel lines are described by the feature such that; they have equal slopes but different y-intercepts.
Hence, by representing the equations in slope-intercept form; we have;
line 1; y = 1/2x - 6
line 2; x - 2y = -1;. y = 1/2x + 1
line 3; y = 4x + 6
line 4; y + 3 = 1/4 (x-6);. y = 1/4x - 9/2.
By comparison with the slope-intercept form equation; it follows that the lines which have equal slopes but different y-intercepts is the pair; line 1 and 2.
Hence, the parallel lines are; lines 1 and 2.
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[tex]8 \div \sqrt{2x} [/tex]Help me please.
y=-1/x=2 -3
i need help with this crazy warm-up for math class
The transformed equation is y = -1/(x + 2) - 3
How to transform the equationFrom the question, we have the following parameters that can be used in our computation:
y = -1/x
We have the transformation to be
(2, -3)
This implies that we transform the function be (x + 2, y - 3)
using the above as a guide, we have the following:
y = -1/(x + 2) - 3
The above represents the new equation when the previous is transformed
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Can the square root of a negative number be negative?.
The square root of negative number can be negative imaginary number (complex number)
As we know the square root of a number is nothing but the factor/value that we can multiply by itself to get that number.
Finding a square root of number is an inverse method of squaring a number.
A radical symbol '√' used to represent the square root of number.
If m is the square root of n, then it is represented as m = [tex]\sqrt{n}[/tex],
We can write above relation as, m² = n
We know that square of any real number is positive.
For example, 3² = (3 × 3) = 9
(-3)² = (-3) × (-3) = 9
i.e., the square root of 9 is 3 and -3
Thus the square root of a negative number is undefined among the set of Real Numbers.
As we know the set of real numbers is subset of complex numbers.
In complex numbers, the imaginary number 'i' is the square root of negative 1.
When an imaginary number is squared, the result is negative number.
Consider example,
[tex]\sqrt{-16}\\\\ =\sqrt{16} \times \sqrt{-1}\\\\ =(\pm 4)\times i\\\\=\pm4i[/tex]
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What number is 10 more than 89?.
The number is 10 more than 8910+89 = 99
given that
One of the four fundamental operations of mathematics is addition, which is typically denoted by the plus sign (+). The other three are subtraction, multiplication, and division. The entire amount or sum of the two whole numbers is obtained by adding them. Three apples and two apples are combined to make five apples in the example in the adjacent image. This observation is analogous to the formula "3 + 2 = 5" in mathematics (that is, "3 plus 2 is equal to 5").
In addition to counting things, addition can also be defined and performed using abstractions known as numbers, such as integers, real numbers, and complex numbers. A branch of mathematics called arithmetic includes addition. Addition can also be done on abstract objects like vectors, matrices, subspaces, and subgroups in algebra, another branch of mathematics.
10 more than 89
more than means plus or addition or sum
10+89 = 99
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What is the nature of roots of quadratic equation → 4x² 8x+ 9 0?.
A quadratic function has no real roots and does not intersect the x-axis if the discriminant of the function is less than zero.
How do you tell if a quadratic equation doesn't have any true roots?How many roots f(x) has is shown by the discriminant's value: - The quadratic function has two unique real roots if b2 - 4ac > 0 A repeated real root exists in the quadratic function if b2 - 4ac = 0. The quadratic function doesn't have any real roots if b2 - 4ac is less than 0.
Formula for the quadratic 4x2-8x9=0
4x2−8x−9=0
The answers can be found using the quadratic formula.
−b±√b2−4(ac)/2a
Replace the values
a=4
, b=−8
, and
c=−9
Then enter it into the quadratic formula to find
x.8±√(−8)2−4⋅(4⋅−9)/2⋅4
Simplify.
To continue, tap...
x=2±√13/2
There are various ways to display the outcome.
precise form:
x=2±√13/2
Number Form:
x=2.80277563…,−0.80277563…
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Full Question = What is the nature the roots of quadratic equation 4x²-8x+9=0?
How to find mean and standard deviation from frequency table in R?.
This article will demonstrate how to use Data Frame in the R programming language to calculate the mean by group.
Mean by A, B, and C group:
A(mean) = sum/number of terms divided by 20/3 equals 6.67.B(mean) = 14/3, or 4.67 times the sum of the terms.C(mean) = sum x number of terms x 8/3 = 2.67Can a frequency table be used to determine the mean?To determine the mean from a frequency table, follow these steps: Divide the values of the numbers by the frequencies. Determine the sums.
What is the standard deviation of a frequency distribution?Divide the total by n.
Three distinct series can be used to calculate it: viz., Frequency, discrete, and individual series of distributions. "The Standard Deviation is the square root of the arithmetic mean of the squares of all deviations," Spiegel states.
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If There are 1 hamster 4 dogs running at 5mph and 2 chickens running at 3mph.One dog speeds up 5mph and the chickens speeds up 10mph.Then the dogs quit (except 1) and the chickens keep going and speed up at 3 mph.Then who will win.After this if the prize is 100$ 1st place 2nd place is 50$ and 3rd 11$ what three animals won.
Names are sam salk paul arina corina
shills baul pauna
The two chickens and a dog three animals won.
What is Speed?The speed of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time.
Given that There are 1 hamster 4 dogs running at 5mph and 2 chickens running at 3mph.
One dog speeds up 5mph and the chickens speeds up 10mph.
Then the dogs quit and the chickens keep going and speed up at 3 mph.
We have to find the winner.
The chicken win the race.
Hence, the two chickens and a dog three animals won.
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Suppoe p(x) = 2x2 − 5x 10 and p(x) over x-n
ha a remainder of 7. Which one of the following tatement are true?
7. 2n^2 - 5n + 10 = 7, is true.This means that if we substitute the value of n in the given equation we will get 7.
The Remainder Theorem states that if a polynomial is divided by a linear function, then the remainder is equal to the value of the polynomial at the root of the linear function.
In this case, we have the polynomial p(x) = 2x^2 - 5x + 10, which is being divided by x-n, and we are told that the remainder is 7. This means that when we substitute the root of x-n (which is n) into p(x), we get a remainder of 7. 2n^2 - 5n + 10 = 7, so this statement is true.
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Use the information given in the figure to find the length BC.
If applicable, round your answer to the nearest whole number.
The lengths on the figure are not drawn accurately.
A
85
41
B
D
0
Answer:
66
Step-by-step explanation:
First find AD:
AD² + 9² = 41²
AD² = 1681-61=1600
AD = √1600 = 40
Now find BD:
BD² + 40² = 85²
BD² = 7225-1600=5625
BD = √5625 = 75
BC = BD - 9 = 75 - 9 = 66
In a packet of 40 skittles, 35% are not red. How may skittles are not red?
Answer:
14
Step-by-step explanation:
35/100= .35
.35 x 40= 14
Not red skittles: 14
Answer:
14
Step-by-step explanation:
35/100= .35
.35 x 40= 14
Not red skittles: 14
88+32
[tex]90 + 30[/tex]
how are these two equations equivalent to each other
Answer:
These two equations are equivalent to each other because they both represent the same mathematical operation and they both yield the same result.
The first equation, 88 + 32, is adding 88 to 32, which results in the sum of 120.
The second equation, 90 + 30, is adding 90 to 30, which also results in the sum of 120.
In other words, both equations represent the same mathematical operation (addition) of two numbers (88 and 32 or 90 and 30) and both yield the same result (120).
Step-by-step explanation:
a brainliest pls
Simultaneous equations
The evaluation of the simultaneous equation is as follows;
a) The simultaneous equations, indicates by plugging in the value of the variable x in the first equation, that the first equation is; 7·x² + 5·y + 3 = 0
b) The equation has no real solutions
What are simultaneous equations?Simultaneous equations are set two or more equations that have common solution.
The simultaneous equations are;
y² + x·y + 3 = 0...(1)
x = 6·y + 5...(1)
Plugging in x = 6·y + 5, in equation (1) we get;
y² + x·y + 3 = y² + y × (6·y + 5) + 3 = 0
y² + 6·y² + 5·y + 3 = 0
7·y² + 5·y + 3 = 0b) The number of solutions the simultaneous equation has can be obtained by solving the equation, obtained in part (a), 7·y² + 5·y + 3 = 0, as follows;
7·y² + 5·y + 3 = 0
The quadratic formula for finding the solution of the equation; a·x² + b·x + c = 0, is; -b±√(b² - 4·a·c)/(2·a)
Where the discriminant is; b² - 4·a·c
Comparing the equations, we get;
a = 7, b = 5, and c = 3
b² - 4·a·c is therefore; 5² - 4 × 7 × 3 = -59
The discriminant is less than 0, therefore, there are no real solutions to the equation, but there are to imaginary solutions
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How much is a 30 angle?.
A 30-degree angle is a measure of an angle, which is one-sixth of a full rotation or circle.
The measure of an angle is the amount of rotation between the two rays that form the angle, measured in degrees. The full rotation of a circle is 360 degrees, so one-sixth of a full rotation is 360 degrees divided by 6, which equals 60 degrees. However, a 30-degree angle is half of a 60-degree angle, so it is half of one-sixth of a full rotation, which is 30 degrees. It's also a right angle's complement angle, meaning that the sum of the 30 and 60 degrees angles is 90 degrees, a right angle. In geometry, 30-degree angles are often used in various calculations and constructions, such as finding the measure of complementary and supplementary angles, solving trigonometric problems, and drawing geometric figures.
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Jane wrote all the natural numbers from m to k (where k>m) how many numbers did she write?
its due in 2 mins btw
The amount of natural numbers from m to k that Jane wrote is given as follows:
k - m + 1.
What are the natural numbers?The natural numbers are the numbers that represent countable amounts, hence they are non-decimal and non-negative amounts.
The set of natural numbers can be represented as follows:
{0, 1, 2, 3, ...}
The number of natural numbers between 0 and 1 is given as follows:
2, which are 0 and 1.
2 = 1 - 0 + 1.
Hence the number of natural numbers between m and k is given as follows:
k - m + 1.
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Samantha purchased a package of sugar cookies. The nutrition label states that each serving size of cookies contains 160 calories. Samantha creates the graph below showing the number of cookies eaten and the number of calories consumed.
Part A: Write an equation that represents the data graphed by Samantha.
Part B: What is the slope of the line? What does it mean in the context of the problem?
Part C: Provide a verbal description of the graph.
Antionette order T hirt for her volleyball camp. Adult ized T hirt cot $6. 25 each and youth ized T hirt cot $4. 50 each. Antionette ha $550 to purchae both adult ized and youth ized T hirt. If he purchae 45 youth ized T hirt, determine algebraically the maximum number of adult ized T hirt he can purchae
Antionette can purchase a maximum of 56 adult-sized t-shirts.
What is algebraic ?
Algebraic refers to anything that pertains to algebra, which is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. Algebraic concepts include using variables (such as x or y) to represent unknown values, using operations such as addition, subtraction, multiplication and division.
Let x be the number of adult-sized t-shirts that Antionette purchases.
We know that ,
The cost of each adult-sized t-shirt is $6.25
The cost of each youth-sized t-shirt is $4.50
Antionette has $550 to purchase both adult-sized and youth-sized t-shirts
Antionette purchases 45 youth-sized t-shirts
We can set up the equation to represent the total cost of all the t-shirts and the money Antionette has ,
(x6.25) + (454.50) = 550
To solve for x, we can simplify the equation by multiplying the number of adult-sized t-shirts by the cost per t-shirt and the number of youth-sized t-shirts by the cost per t-shirt, and then set it equal to the total money Antionette has ,
x*6.25 + 202.5 = 550
then we can subtract 202.5 from both sides , x*6.25 = 347.5
then divide both sides by 6.25 to get , x = 56
So, Antionette can purchase a maximum of 56 adult-sized t-shirts.
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The cost of each adult-sized t-shirt is $6.25
The cost of each youth-sized t-shirt is $4.50
Antionette has $550 to purchase both adult-sized and youth-sized t-shirts
Antionette purchases 45 youth-sized t-shirts
(x*6.25) + (454.50) = 550
x*6.25 + 202.5 = 550
then we can subtract 202.5 from both sides , x*6.25 = 347.5
then divide both sides by 6.25 to get , x = 56
So, Antionette can purchase a maximum of 56 adult-sized t-shirts.
The ending balance on an investment is $11,139.58. If the principal was
invested at 2.45% compounded weekly for 78 months, what was the
principal?
According to the given statement, If the principal was invested at 2.45% compounded weekly for 78 months, then The principal is 9521.
How much is the principal?When you first take out a home loan, you borrow a certain amount of money, which is known as the principal. Simply deduct your deposit for a house from the final selling price of your home to determine your mortgage principal.The principal amount means the amount you owe at any point in time.
The formula is =
11139.58 = x (1 + 0.0245) ^6.5
11139.58 = x (1.0245) ^ 6.5
11139.58 = 1.17x
x = 11139.58/ 1.17
x = 9521 (approx)
Hence, the principal is 9521.
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What is the function of logarithmic function?.
The logarithmic function is a mathematical function that expresses the exponent of a number to produce a given value, with the property of simplifying multiplication to addition and it is the inverse of the exponential function.
A logarithmic function is a mathematical function that expresses the power to which a number (the base) must be raised in order to produce a given value. The logarithm of a number is the exponent to which the base must be raised to produce that number.
A logarithmic function can be represented in the form of log_b(x) or logb(x), where b is the base of the logarithm and x is the value being evaluated.
For example, the logarithm of 1000 to the base 10 is 3, because 10^3 = 1000. It can be written as log10(1000) = 3.
The logarithm function has the property that log_b(x*y) = log_b(x) + log_b(y), which means that logarithms simplify the multiplication of numbers to the addition of logarithms.
The logarithmic function also has an inverse function, which is the exponential function, that's why logarithms and exponents are inverses of each other.
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If a hockey player takes 78 shots and scores 16 goals, what would be the probability of this player scoring a goal on their next shot?
0. 173
0. 205
0. 013
0. 263
The player's chances of scoring a goal on their next shot are 0.205, or 20.5%.
This is calculated by dividing the number of goals they scored (16) by the number of shots they took (78).
The formula for finding the probability:
P(A) = number of favorable outcomes / total number of possible outcomes
16 / 78 = 0.205
Probability is a mathematical concept that quantifies the likelihood that an event will occur. It is expressed as a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is unavoidable.
A probability of 0.5 (or 50%) means that the event is equally likely to occur or not occur.
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Luke has some nails in his toolbox.
The heads of these nails are all circular and have a diamater of 2.4mm.
Ten of these nails are knocked into a piece of wood, so that just the metal heads are seen.
Using an estimate of pi=3, calculate the total area of metal that can be seen on the surface of the wood.
You must show your working and give the units of your answer.
The total area of metal that can be seen on the surface of the wood is 43.2 square millimeters.
How to calculate the total area of metal that can be seen on the surface of the wood?To find the total area of metal that can be seen on the surface of the wood, we need to find the area of one nail head and then multiply that by the number of nails.
The area of a circle is given by the formula:
A = πr²,
where π is the mathematical constant pi (estimated as 3 in this case) and r is the radius of the circle (half of the diameter).
So, the area of one nail head in square millimeters is:
A = 3 ×(2.4/2)² = 3 × 1.2² = 3 × 1.44 = 4.32 square millimeters
As there are 10 nails, so the total area of metal that can be seen on the surface of the wood in square millimeters is:
Total area = 4.32 square millimeters/nail × 10 nails = 43.2 square millimeters
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Problem and inncorrect solution
-2(8m +8)= -16
Answer:
no its incorrect
Step-by-step explanation:
-2(8m+8)=-16 is worng its m=0
The problem is incorrect.
The correct solution for the given equation is:
-2(8m +8) = -2(8m) -2(8) = -16m -16
You cannot simplify it to -16 as the equation is not a true equation.
Please let me know if there is something more I can assist you with.
What is y=1/3x-2 graphed on a graph
y = (1/3)x - 2 is an equation of a line where the slope of the line is 1/3 and the y-intercept of the line is -2.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
y = (1/3)x - 2
This is in the form of y = m + c
So,
This is an equation of a line.
The slope of the line = 1/3
The y-intercept of the line is -2.
Thus,
y = (1/3)x - 2 is an equation of a line.
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Hello I need help as soon as possible, please someone respond, thank you.
Its value is expressed as f(x). The line has a slope of m.In the coordinate plane, the point where the line crosses the y-axis is where the function's value, or b, is determined when x is equal to zero.The coordinate's value, x, is given. The f(x) is 1.2x.
Find the F(x) ?Its value is expressed as f(x). The line has a slope of m.In the coordinate plane, the point where the line crosses the y-axis is where the function's value, or b, is determined when x is equal to zero.The coordinate's value, x, is given.
Detailed explanation:
Given:
f(x - 5) = 1.2x - 6
Required:Find f (x) In order to solve f(x), we must translate f(x - 5) into terms of f. (x). The procedure is as follows.
f(x - 5) = 1.2x - 6
The expression to the right should be factored.
f(x - 5) = 1.2(x - 5) (x - 5)
Now that we have changed x for x - 5 in the previous formula, we may solve for f(x) (on the right hand side and the left hand side).
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how do you get n=2^2x7
Answer:
n = 28
Step-by-step explanation:
2^2 is equal to 4, so we can plug in 2^2 as 4. Then, 4 * 7 = 28, so n = 28.
