The function that correctly depicts the scenario is f(x) = 18.50 * (1.06)^x
The cost of the buffet in 10 years is $33.13The cost of the buffet 15 years ago is $7.71How to write a function that correctly depicts the scenario.From the question, we have the following parameters that can be used in our computation:
Value of buffet = $18.50
Rate of increment = 6%
The function that correctly depicts the scenario is represented as
f(x) = Value of buffet * (1 + Rate of increment)^x
Substitute the known values in the above equation, so, we have the following representation
f(x) = 18.50 * (1 + 6%)^x
So, we have
f(x) = 18.50 * (1.06)^x
How much will the buffet cost 10 years from nowThis means that
x = 10
Substitute the known values in the above equation, so, we have the following representation
f(10) = 18.50 * (1.06)^10
Evaluate
f(10) = 33.13
How much did the buffet cost 15 years ago?This means that
x = -15
Substitute the known values in the above equation, so, we have the following representation
f(-15) = 18.50 * (1.06)^(-15)
Evaluate
f(-15) = 7.71
Hence, the amount 15 years ago is $7.71
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q19 ANSWER FOR 20 POINTS
Answer
[tex]\sqrt[3]{4^{2} }[/tex]
Step-by-step explanation:
evaluate 1 + (-2/3) - (-m) where m= 9/2
The value is evaluated to 5 1/4
What is a fraction?A fraction can be described as the part of a whole value, variable or element.
The different types of fractions are;
Mixed fractionsProper fractionsSimple fractionsComplex fractionsImproper fractionsFrom the information given, we have that;
1 + (-2/3) - (-m)
If the value of m = 9/2, let's substitute the value, we have;
1 - 2/8 - ( 9/2)
expand the bracket
1 - 2/8 + 9/2
Find the LCM
8 - 2 + 36 /8
42/8
5 1/4
Hence, the value is 5 1/4
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The table represents a continuous exponential function f(x).
X | 2 3 4 5
f(x) | 12 24 48 96
Graph f(x) and identify the y-intercept.
A. 0
B. 3
C. 6
D. 12
A graph of this continuous exponential function f(x) is shown in the image attached blow. Also, the y-intercept is equal to: B. 3.
What is an exponential function?Mathematically, an exponential function can be modeled by using this equation:
f(x) = ab^x
Where:
a represents the initial value or y-intercept.x represents time.b represents the slope or rate of change.Based on the data points (2, 12) and (3, 24) given in the table representing a continuous exponential function f(x), we create a system of equations as follows;
12 = ab² .....equation 1.
24 = ab³ .....equation 2.
Dividing equation 2 by equation 1, we have:
24/12 = ab³/ab²
2 = b
For the value of a, we have;
12 = a(2)²
12 = 4a
a = 12/4
a = 3
Therefore, the y-intercept (a) is 3.
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an extraneous solution is a value that appears to be part of the solution set. but when tested it does not create a true statement x-1=√x+1
The extraneous solution of the equation x - 1 = √x + 1 is x = 0
How to determine the extraneous solutionFrom the question, we have the following parameters that can be used in our computation:
x - 1 = √x + 1
Take the square of both sides
So, we have
x² - 2x + 1 = x + 1
Evaluate the like terms
x² - 3x = 0
So, we have
x(x - 3) = 0
Solving for x, we have
x = 3 and x = 0
Substitute x = 3 and x = 0 in x - 1 = √x + 1
3 - 1 = √3 + 1
2 = 2 ---- true
0 - 1 = √0 + 1
-1 = 1 ---- false
Hence, the extraneous solution is x = 0
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Jocelyn estimates that a piece of wood measures 5.62 cm, what is the percent error of Jocelyn’s estimate
The percent error of Jocelyn’s estimate will be - 2.14%.
How to calculate the percentage?A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100. In this case, the percentage then refers to a component per hundred. The word percentage simply means per 100 and it is represented by %.
Here, Jocelyn estimates that a piece of wood measures 5.5cm when it's actually 5.62 cm. We simply want to calculate the percentage error which will be calculated thus:
The percent error of Jocelyn’s estimate will be:
= (Estimated measurement - Original measurement) / Original measurement × 100
= (5.5 - 5.62) / 5.62 × 100
= -0.12 / 5.62 × 100
= - 2.14%
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Complete question
Jocelyn estimates that a piece of wood measures 5.5cm when it's actually 5.62 cm, what is the percent error of Jocelyn’s estimate
find x in the following equation:
2/3 x-8=24
To solve this equation, we need to get x by itself on one side of the equation. To do this, we can start by adding 8 to both sides of the equation to get:
2/3 x - 8 + 8 = 24 + 8
This simplifies to:
2/3 x = 32
Then, we can divide both sides of the equation by 2/3 to get:
(2/3) / (2/3) * x = 32 / (2/3)
This simplifies to:
x = 48
So the solution to this equation is x = 48.
Given f of x is equal to the quantity 4x minus 7 end quantity divided by the quantity 8x plus 8 end quantity, what is the end behavior of the function?.
The end behavior of the function f(x) describes the behavior of the function as x approaches the +∞ f(x) approaches to 1/2 and the x approaches the -∞ f(x) approaches to 1/2.
What is a function?
It is defined as a special type of relationship and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable is known as a function. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
For the end behavior:
As x → ∞ f(x) → 1/2
And x → -∞ f(x) → 1/2
Thus, the end behavior of the function f(x) describes the behavior of the function as x approaches the +∞ f(x) approaches to 1/2 and the x approaches the -∞ f(x) approaches to 1/2.
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Using either the sine or cosine law, how do i find the angle of p?
Answer:
Use the Cosine Rule to find unknown sides and angles
Step-by-step explanation
Aiden is fundraising for the disney chorus trip. He started the year (4w+12) dollars. He has raised (10w+42) dollars. Write an expression that represents the total amount Aiden has for his disney trip.
Answer:
Step-by-step explanation:
u just add the two equations together.
14w +56
I-Ready
Compare Functions-Quiz-Level H
The equation and the table show the cost, y, for different sports programs as functions of the number
of classes, z.
Complete the statement.
LOOK AT PHOTO
From the given function, When the number of classes is 1 the football is less expensive.
When the number of classes is 1, the basketball is less expensive.
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Four main categories can be used to classify different sorts of functions. dependent upon element Function is a one-to-one relationship, a many-to-one relationship, onto function, one-to-one and into function.
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is -1 greater or less than -3.6
Answer: I don’t know
Step-by-step explanation:
chi-square analysis can help us to decide whether __________.
Answer:
See below
Step-by-step explanation:
The chi-squared analysis aims to check whether observed frequencies in one or more categories match up with expected frequencies. I don't see any answer choices, but hopefully this short explanation will help!
What is the perimeter of the cafe?
The perimeter is the total distance around the outer boundaries of a shape. It is used to measure the size of an area by adding the lengths of all the sides of the shape together.
What is the perimeter?The perimeter of a café refers to the total length of the outer boundaries of the café's floor plan. To find the perimeter, you would add together the lengths of all four sides of the café. It is used to measure the total distance around the café's floor area, which is important for determining the size of the café and the amount of space available for tables, chairs, and other amenities. For example, if a café has a rectangular floor plan with sides measuring 20 feet by 30 feet, the perimeter would be 100 feet (20 feet + 20 feet + 30 feet + 30 feet). The perimeter is also a useful measurement for determining the amount of flooring, paint, or other materials needed for the café. It can also be used to plan the layout of tables and chairs, to ensure that there is enough space for customers to move around comfortably.It is commonly used in geometry, construction, and interior design, to measure and plan the size of a space. The perimeter can be calculated for many shapes such as squares, rectangles, circles, polygons and so on.To learn more about perimeter refer to:
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How many even numbers can be formed from the digits 1,2 3 4 5?
There are six even numbers that can be formed from the digits 1, 2, 3, 4, and 5: 2, 4, 12, 14, 23, and 24.
To calculate the number of even numbers, we can first calculate the total number of combinations of all the digits. This is done by multiplying the total number of digits (5) by the total number of combinations of each digit (4). This gives us 5 x 4 = 20.
To calculate the number of even numbers, we then divide this number in half, as half of the combinations will be even numbers. Therefore, 20 divided by 2 = 10 even numbers. Hence, there are six even numbers that can be formed from the digits 1, 2, 3, 4, and 5: 2, 4, 12, 14, 23, and 24.
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The straight line has equation y=5x+6
Find an equation of the straight line perpendicular to L which passes through (-2,5)
Answer:
y = -0.2x + 4.6
Step-by-step explanation:
We can set up a point-slope form to calculate for the equation:
y - y1 = m (x - x1)
Before we plug the coordinate into the formula, we need m, the slope of L, we know that L is perpendicular to the straight line, and the slope of the straight line is 5:
Perpendicular slope form is: opposite reciprocal of m, which is:
-1/5 or -0.2
Now we plug all the numbers into the previous equation:
y - 5 = -0.2 (x + 2)
y = -0.2 (x + 2) + 5
y = -0.2x + -0.4 + 5
y = -0.2x + 4.6
Now this is a slope-intercept form.
Question 3 Part C: Explain what the solutions to the inequality represent. Choose all that apply. (2 points) A. The outside air temperature must be greater than −40° F. B. The outside air temperature must be greater than 120° F. C. The outside air temperature must be less than 120° F. D. The outside air temperature must be less than or equal to 120° F. E. The outside air temperature must be less than −40° F. F. The outside air temperature must be greater than or equal to −40° F.
The linear inequality that represents the given temperature is; -40 < x < 120
How to solve Linear Inequality Problems?Linear inequalities are defined as inequalities that involve at least one linear algebraic expression.
Linear inequalities are usually written in the form of expressions where any two values are often compared by the inequality symbols such as, ‘<’, ‘>’, ‘≤’ or ‘≥’. Now, these values could be numerical or algebraic or even a combination of both.
The linear inequality from the question expressed as -40 < x < 120 shows us that the outside air must be between the range of -40 degrees to 120 degrees.
This can be explained as the least temperature must be above -40°F and the highest temperature must not exceed 120°F
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The exterior angles of triangle UVW are ∠X, ∠Y, and ∠Z, and they are adjacent to ∠U, ∠V, and ∠W, respectively.
If m∠V is 95°, and m∠Z is 129°, what is m∠U?
A.
129
B.
95°
C.
51°
D.
34°
The value of the angle ∠U using the exterior angle theorem is calculated as; D: 34°
How to find the exterior angles of a triangle?An exterior angle of a triangle is created by extending one side of the triangle. Now, the theorem of exterior angle of a triangle is that If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.
Now, since we are given that m∠V = 95°, and m∠Z = 129°, then it means we can say that;
∠X, ∠Y = ∠Z
Similarly;
∠U + ∠V = ∠W
By congruency and external angles theorem, we can say that;
∠U + ∠V = ∠Z
Thus;
∠U + 95° = 129°
Thus;
∠U = 129 - 95
∠U = 34°
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What is the distance between the points (7, 8) ank(-8, 0) on a coordinate grid?
The distance between the given two points on the coordinate grid is 17 units.
What is coordinate grid?A coordinate grid has two perpendicular lines, or axes labelled just like number lines. The horizontal axis is usually called the x-axis. The vertical axis is usually called the y-axis. The point where the x- and y-axis intersect is called the origin.
Given that, are two points (7, 8) and (-8, 0) on a coordinate grid, we need to find the distance between the points
We know that, the distance between two points on a coordinate grid is given by;
D = √(x₂-x₁)²+(y₂-y₁)²
Here, x₁ = 7, x₂ = -8 and y₂ = 0, y₁ = 8
Therefore,
D = √(-7-8)²+(0-8)²
D = √(-15)²+(-8)²
D = √225+64
D = √289
D = 17
Hence, the required distance is 17 units.
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What kind and how many variables do you need to make a scatter plot?
There are two quantitative variables that are required to measure the scatter plot.
The values of one variable appear on the horizontal axis and the values of the other variable appear on the vertical axis.
A scatterplot is a type of data display that shows the relationship between two numerical variables and a graphical representation of individual scores on two variables.
Each member of the dataset gets plotted as a point whose (x, y) left parenthesis, x, comma, y, and right parenthesis coordinates relate to its values for the two variables.
The values of one variable appear on the horizontal axis and the values of the other variable appear on the vertical axis.
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ms.graves gave her class 15 minutes to read. carrie read
The rate per hour of Carrie's reading is 27.5 pages per hour
How to determine the rate per hourFrom the question, we have the following parameters that can be used in our computation:
A mathematical statement
The mathematical statement is given as:
Ms. Graves gave her class 12 minutes to read. Carrie read 5 ½ pages in that time.This means that the rate of reading is
Rate = 5 ½ pages per 12 minutes
Express as decimal
This gives
Rate = 5.5 pages per 12 minutes
Convert minute to hours
So, we have the following representation
Rate = 5.5 pages per 0.2 hour
Evaluate the quotient
Rate = 27.5 pages per hour
Hence, the rate is 27.5 pages per hour
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Complete question
Ms. Graves gave her class 12 minutes to read. Carrie read 5 ½ pages in that time.
At what rate, in pages per hour, did Carrie read?
Landon hands out 90 flyers in 2 hours. Fernando hands out 29 flyers in 30 minutes which equation can be used to determine f, the numbers of flyers Fernando handed out in two hours
The equation that can be used to determine f, the numbers of flyers Fernando handed out in two hours will be f= (120 / 30) × 29
How to illustrate the rate?It should be noted that a rate demonstrates how many times one number can fit into another number. It simply contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point to another data point.
In this case, Landon hands out 90 flyers in 2 hours. Fernando hands out 29 flyers in 30 minutes.
Note that 2 hours = 120 minutes.
The equation that can be used to determine f, the numbers of flyers Fernando handed out in two hours will be:
f = (120 / 30) × 29
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whats 9 4/5 - 2 3/10
Answer:
7 1/2
Step-by-step explanation:
9 4/5 - 2 3/10 =
(9 + 4/5) - (2 + 3/10) =
(9 + 4/5) - 2 - 3/10 = ==> distribute the minus sign to 2 and 3/10
9 + 8/10 - 2 - 3/10 = ==> change 4/5 to 8/10 to have common denominators
9 - 2 + 8/10 - 3/10 = ==> combine like terms
7 + 5/10 = ==> simplify
7 + 1/2 = 7 1/2
2x-3y=-9 x-5=-29 in the substitution form
Answer:
Step-by-step explanation:
point form:
(-24,-13)
Equation form:
x = -24 y = -13
The value of [tex]x[/tex] and [tex]y[/tex] is [tex]x=-24[/tex] and [tex]y=-13[/tex]
The two given equation are
[tex]2x-3y=-9\\x-5=-29[/tex]
We need to find [tex]x[/tex] and [tex]y[/tex]
that is ,
[tex]x=-29+5\\x=-24[/tex]
We can substitute the value of [tex]x[/tex] in equation [tex]2x-3y=-9[/tex]
that is ,
[tex]2(-24)-3y=-9\\-48-3y=-9\\-3y=-9+48\\-3y=39\\y=-13[/tex]
The value of [tex]x=-24,y=-13[/tex]
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The complete question is , Find the value of [tex]x[/tex] and [tex]y[/tex] if [tex]2x-3y=-9 , x-5=-29[/tex] in the substitution form.
Particles q1 = -66.3 UC, q2 = +108 uC, and
93 = -43.2 uC are in a line. Particles q1 and q2 are
separated by 0.550 m and particles q2 and q3 are
separated by 0.550 m. What is the net force on
particle q2?
The net force on particle q2 is 32203.65N
What is net force?The sum total of all the forces which are acting on an object is known as the net force. A mass that can accelerate due to net force on an object. Whether a body is at rest or in motion, it is a subject to another force. When there are a lot of forces which are acting on a system, the term net force is used to denote it.
Given;
r₁₂ = 0.550m r₂₃ = 0.550m. Then the distance from the first charge to the third one will be;
r₁₃ = r₁₂ + r₂₃ = 0.550 + 0.550 = 1.1m
Now, according to the Coulomb's law, the net force on particle q₂ will be equal to the sum of the forces on particle q₂ from the particle q₁ and q₃.
F₃+ = F₁₃ +F₂₃ = q₁q₂/r²₁₃ + k q₃q₂/r²₂₃
Where, k = 9 × 10⁹ N m²/C²
Substituting numerical values;
F₃ = 9 × 10⁹ (-66.3 × 10⁻⁶)(-43.2 × 9 × 10⁻⁶)/ 1.45² + 9 × 10⁹ × 108 × 10⁻⁶ (-43.2 × 10⁻⁶) / 0.550²
F₃= 231.996x 41.9904/0.3025
F₃= 32203.65
Therefore, the net force will be 32203.65N
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solve this equation with an explaination
Answer:
x < -2 or x > 4
Step-by-step explanation:
This is an absolute value inequality of the form
|X| ≥ b
where X is an expression with a variable, and b is a non-negative number.
An absolute value inequality of this form is solved by changing the form into a compound inequality using the word "or."
To solve
|X| ≥ a,
solve the compound inequality
X < - a or X > a
In other words, when the absolute value of an expression is greater than (or greater than or equal to) a number, rewrite the absolute value inequality as
expression < -number or expression > number
In your problem, you have
|2x - 2| ≥ 6
The expression is 2x - 2.
The number is 6.
You change the absolute value inequality to the following compound inequality:
2x - 2 ≤ -6 or 2x - 2 > 6
Now you solve each inequality always keeping the word "or" in between them.
2x - 2 ≤ -6 or 2x - 2 > 6
2x < - 4 or 2x > 8
x < -2 or x > 4
I hope you understand the solution and explanation. If you have any questions, ask in the comments.
If the simple interest on $3,000 for 7 years is $1,680, then what is the interest rate?
The rate on the interest of $1680 with principle $3000 is 8 %
What is simple interest ?Simple interest is a way to figure out how much interest will be paid on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the following year's principal to compute interest, the principal amount under simple interest remains constant.
Simple interest is a quick and simple approach to figure out how much money has accrued interest. Interest is always applied to the initial principle amount and is calculated at the same rate for each period of time. Any bank where we deposit money will pay us interest on that amount. Simple interest is one of several forms of interest that banks charge. Now, let's first clarify what a loan is before delving further into the idea of simple interest.
Here, Principle amount = $3000
Interest = $1680
Time = 7 years
rate = r %
So,
1680 = (3000*r*7)/100
⇒ 1680 = 30*7*r
⇒ r = 1680/210
⇒ r = 8
So the rate of interest is 8 %
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Eden is working on an experiment for her science fair project. she is planting a total of 10 herbs for an herb garden. she is going to plant basil and mint. the basil plants cost $.50 per plant and the mint plants cost $.25 per plant. eden has a total of $3 to spend on plants because she also has to purchase potting soil and a long planter pot. write a system of equations and solve either using elimination or substitution.
Answer:
Eden planted 2 basil plants and 8 mint plants.
Step-by-step explanation:
Here's one possible way to write a system of equations to represent the information given in the problem:
Let x be the number of basil plants and y be the number of mint plants.
The first equation represents the total number of plants:
x + y = 10 (because Eden is planting a total of 10 herbs)
The second equation represents the total cost of all the plants:
x* $0.50 + y* $0.25 = $3
Elimination Method:
Multiply the first equation by $0.50
x* $0.50 + y* $0.50 = $5
subtracting this equation from the second equation
y* $0.25 = $3-$5 = -$2
y = 8
then substitute the value of y in first equation
x + 8 = 10
x = 2
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A line is perpendicular to y = -x-2
and intersects the point (-5, 10).
What is the equation of this
perpendicular line?
y = x + [?]
Hint: Use the Point-Slope Form: y - y₁ = m(x - X1)
Then write the equation in slope-intercept form.
H
Answer:
To find the equation of a line that is perpendicular to the line y = -x - 2 and intersects the point (-5, 10), we can use the Point-Slope Form of a line: y - y₁ = m(x - X1)
The Point-Slope Form allows us to find the equation of a line when we know the slope of the line (m) and the coordinates of a point on the line (X1, Y1).
In this case, we know that the slope of the line y = -x - 2 is -1, because the coefficient of x is -1. We also know that the line intersects the point (-5, 10), so we can substitute those values into the Point-Slope Form:
[tex]y - 10 = -1(x - (-5))\\[/tex]
Next, we can simplify this equation by distributing the -1:
[tex]y - 10 = -1x + 5[/tex]
Finally, we can write the equation in slope-intercept form by adding 10 to both sides and simplifying:
[tex]y = -1x + 15[/tex]
So, the equation of the line that is perpendicular to y = -x - 2 and intersects the point (-5, 10) is y = 1x+15.
I hope this helps! If you have any questions about this problem or if you need further clarification, just let me know.
Andre wrote the expression −3+7x÷4 to represent the relationship shown in the table. Find two other expressions that also represent the relationship shown in the table.
What is the greatest possible error for a measurement of 0.05 metric tons?
Answer:The greatest possible error of a measurement is considered to be one-half of the measuring unit. If you measure a length to be 4.3 cm. (measuring to the nearest tenth), the greatest possible error is one-half of one tenth, or 0.05. This means that any measurements in the range from 4.25 cm. to 4.35 cm. are perceived as correct.
Step-by-step explanation:
Answer:
The greatest possible error for a measurement of 0.05 metric tons would depend on the accuracy of the measurement device or technique being used. Without more information about the specific measurement method, it is impossible to determine the greatest possible error.
Step-by-step explanation:
