Brandon purchased a new guitar in 2012. The value of his guitar, t years after he bought it, can be modeled by the function A(t)=145(0.95)t.
Answers
The term (0.95)^t represents the decay factor, where t is the number of years elapsed since the purchase. Each year, the value of the guitar decreases by 5% (or 0.95) of its previous value.
The function A(t) = 145(0.95)^t represents the value of Brandon's guitar t years after he purchased it in 2012. In this exponential decay model, the initial value of the guitar is $145, and the value decreases by 5% (0.95) each year.
The function A(t) calculates the current value of the guitar after t years, where A(t) is the value in dollars. Let's break down the equation to understand it further:
A(t) = 145(0.95)^t
The coefficient 145 represents the initial value of the guitar when t = 0, i.e., the value of the guitar at the time of purchase in 2012.
The term (0.95)^t represents the decay factor, where t is the number of years elapsed since the purchase. Each year, the value of the guitar decreases by 5% (or 0.95) of its previous value.
For example, if we want to find the value of the guitar after 5 years, we substitute t = 5 into the equation:
A(5) = 145(0.95)^5
By evaluating this expression, we can determine the current value of the guitar after 5 years.
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Related Questions
Find the length of the curve x = y^3/3 + 1/4y from y = 1 to y = 3. The length of the curve is ______(Type an integer or a simplified fraction.)
Answers
The answer of the given question based on the finding the length of the curve is the length of the curve is approximately 6.1 units.
What is Curve?In mathematics, a curve is a geometric object that is a subset of a two-dimensional space, typically the Euclidean plane. It can be thought of as a path that is continuous, meaning that it has no abrupt changes in direction or "jumps." A curve can be described mathematically by an equation or a parametric equation, which gives the relationship between the coordinates of points on the curve. Curves can take on various shapes, such as straight lines, circles, parabolas, and more complex curves like spirals and ellipses.
To find the length of the curve x = y³/³ + 1/4y from y = 1 to y = 3, we use the arc length formula:
L = ∫[a,b] sqrt[1 + (dx/dy)²] dy
where a = 1, b = 3, and dx/dy is the derivative of x with respect to y.
Taking derivative of x with the respect to y, we will get:
dx/dy = y² + 1/4
Substituting this into the arc length formula, we get:
L = ∫[1,3] sqrt[1 + (y² + 1/4)²] dy
We can simplify this expression by expanding the square and combining like terms:
L = ∫[1,3] sqrt[(16y⁴ + 8y² + 1)/16] dy
L = (1/4) ∫[1,3] sqrt(16y⁴ + 8y² + 1) dy
To evaluate this integral, we make the substitution u = 4y² + 1, which gives us du/dy = 8y and dy = du/8y. Substituting this to integral, we wii get:
L = (1/32) ∫[5,37] sqrt(u) du
L = (1/48) [u⁽³/²⁾]_[5,37]
L = (1/48) [(37⁽³/²⁾ - 5⁽³/²)]
L ≈ 6.1
Therefore, the length of the curve is approximately 6.1 units.
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the probability that a local travel agent will make a sale from a sales call is 0.65. if 10 sales calls are made to potential customers, what is the probability that he will make at least 6 sales (assume a binomial distribution)?
Answers
The probability that the travel agent will make at least 6 sales out of 10 sales calls can be calculated using the binomial distribution. The probability is approximately 0.891.
The binomial distribution is used to model the probability of success in a fixed number of independent Bernoulli trials. In this case, the sales calls are the trials, and the probability of making a sale is 0.65.
To calculate the probability of making at least 6 sales, we need to sum the probabilities of making 6, 7, 8, 9, and 10 sales. Using the binomial probability formula, we can calculate the individual probabilities for each number of sales and then sum them.
The probability of making exactly k sales out of n trials with probability p is given by the formula: P(X = k) = C(n, k) * p^k * (1 - p)^(n - k), where C(n, k) is the binomial coefficient. Using this formula for k = 6, 7, 8, 9, and 10 and summing the probabilities, we get approximately 0.891.
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A youth hockey team has scored 6, 9, and 2 goals in three games in a hockeytournament. How many goals must they score in the fourth game for their average tobe greater than 5 goals per game?Solve the inequality
Answers
The youth hockey team already played 3 matches in which they scored 6, 9 and 2 goals.
Let
the score of the fourth goal = x
\(\begin{gathered} \frac{6+9+2+x}{4}>5 \\ \frac{17+x}{4}>5 \\ \text{multiply both sides by 4} \\ (\frac{17+x}{4})4>5\times4 \\ 17+x>20 \\ \text{subtract 17 from both sides} \\ 17-17+x>20-17 \\ x>3 \end{gathered}\)The number of goals must be greater than 3 for the average score to be greater than 5
Ethan works as a server in a restaurant. He gets a `15\%` tip on the cost of every order. What t
Answers
The amount of tip that Ethan receives on every order, we can use the formula Tip amount = (Tip percentage) x (Cost of order) and plug in the values accordingly.
To calculate the amount of tip that Ethan receives on every order, we can use the formula:
Tip amount = (Tip percentage) x (Cost of order)
In this case, the tip percentage is `15\%` and the cost of order is the variable we need to find.
Let's assume that the cost of an order is $100. Using the formula above, we can calculate the amount of tip that Ethan receives:
Tip amount = (`15\%`) x ($100)
Tip amount = $15
Therefore, Ethan receives a $15 tip on an order that costs $100.
If the cost of an order is different, we can simply plug in the new value into the formula and calculate the tip amount accordingly. For example, if the cost of an order is $50, the tip amount would be:
Tip amount = (`15\%`) x ($50)
Tip amount = $7.50
In conclusion, to calculate the amount of tip that Ethan receives on every order, we can use the formula Tip amount = (Tip percentage) x (Cost of order) and plug in the values accordingly.
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6.
Giselle pays $210 in advance on her account at the athletic club. Each time she uses the club, $15 is deducted from the account. Model the situation with a linear function.
A. b = 195 – 15x
B. b = 210 – 15x
C. b = 195 + 15x
D. b = 210 + 15x
Answers
Answer:
B is correct. Your starting amount is 210$ And you're taking away 15$ each time she uses the club,x.
Step-by-step explanation:
Answer:
The linear function model the situation is b = 210 - 15x .
Option (B) is correct .
Step-by-step explanation:
Let us assume that the number of times giselle uses the club be x .
As given
giselle pays $210 in advance on her account at the athletic club.
Each time she uses the club,$15 is deducted from the account.
Let suppose that the money left after giselle uses the club x times is b .
Than the equation becomes
Money left = Amount pay in advance - Deducted amount × Number of times giselle uses the club .
Put all the values in the above
b = 210 - 15 × x
b = 210 - 15x
Therefore the linear function model the situation is b = 210 - 15x .
Option (B) is correct .
Graph :StartFraction x squared Over 49 EndFraction + StartFraction (y + 1) squared Over 4 EndFraction = 1
Answers
The graph of the equation x^2/49 + (y + 1)^2/4 = 1 is added as an attachment
How to graph the equationThe expression that represents the function in words is given as
StartFraction x squared Over 49 EndFraction + StartFraction (y + 1) squared Over 4 EndFraction = 1
Express the equation properly
So, we have
x^2/49 + (y + 1)^2/4 = 1
The above equation is an ellipse
Next, we plot the graph on a coordinate plane using a graphing tool
See attachment for the graph of the equation
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i need help plssssssssss
Answers
Answer:
answer is provided below
Step-by-step explanation:
5 ----> constant
+ ------> operator
2 ------> coefficient
2x ------> variable term
x --------> variable
Hope the above solution helps
1/2 x + 13 = 9 (x Is Variable)
Answers
Answer:
x= -8
Step-by-step explanation:
1/2x + 13=9
- move 13 to the other side
1/2x= 9-13
-simply 9-13
1/2x= -4
-multiply 2 on both sides
1x=-8
x=-8
Answer:
x = -8
Step-by-step explanation:
1/2 x + 13 = 9
- Combine all like terms by subtracting 13 from both sides.
1/2x = -4
- Divide 1/2 from both sides of the equation to isolate the variable.
x = -8
determinar el decimal correspondiente
A)71% B)172% C)6%
Answers
\(71\% = \frac{70}{100} = \frac{7}{10} = 0.7 \\ 172\% = \frac{172}{100} = 1.72 \\ 6\% = \frac{6}{100} = 0.06\)
Ashly has money automatically deposited in to a saving account each week after 4 weeks she have 20 dollars after 6 weeks she have 30
Answers
Answer:
5 dollars per week
Step-by-step explanation:
20 ÷ 4 = 5
30 ÷ 6 = 5
I believe that is your question.
If humans lost the ability to see all color except one, which color would you want to survive?
Answers
Answer:
The color blue. There’s many shades of blue and plus blue is my favorite color. I’ll be able to tell if I’m drinking water or not.
What 1+1 help i'll give 15 points
Answers
Answer:
11
Step-by-step explanation:
am so smart
HELP ASAP
Find x to the nearest hundredth.
Answers
Answer:
x = 10.28
Step-by-step explanation:
sin = opp/hyp
sin 40 = x / 16
multiply both sides by 16
16 * sin40 = x
x = 10.284601754984629
Rounded
x = 10.28
You are standing at a point, about 4 feet from a circular aquarium. If a tangent from your point to a point on the circle measures 10 feet, determine the length of the tanks’ radius
Answers
Answer:
10.5 feet
Step-by-step explanation:
You want to know the radius of a tank when the tangent from a point 4 ft from the tank is 10 ft long.
Secant relationsTwo secants of a circle drawn from the same point have the same product of their lengths to the near and far intersection points with the circle.
When one of those secants degenerates to a tangent, the near and far points are the same point, and the product is the square of the tangent length.
ApplicationReferencing the attached diagram, we have ...
MA² = MB·MC
10² = 4·MC
100/4 = MC = 25
Solving for radius r, we have ...
MC = 4 +2r
25 -4 = 2r = 21 . . . . . subtract 4
r = 21/2 = 10.5 . . . . . divide by 2
The radius of the tank is 10.5 feet.
__
Additional comment
The radius can also be found using the Pythagorean theorem:
10² +r² = (4+r)² . . . . . . . . . Pythagorean relation
100 +r² = 16 +8r +r² . . . . . expanded
84 = 8r . . . . . . . . . . . subtract 16+r²
10.5 = r . . . . . . . divide by 8
What are the domain and range of f (x) = log (x + 6) minus 4?
domain: x > –6; range: y > 4
domain: x > –6; range: all real numbers
domain: x > 6; range: y > –4
domain: x > 6; range: all real numbers
Mark this and return
Answers
Domain: x > –6; range: all real numbers are the domain and range of f (x).
What is domain and range ?
The range of values that can be plugged into a function is known as its domain. The x values for a function like f make up this set (x).
The collection of numbers that the function assumes is known as its range. After we enter an x value, the function outputs this sequence of values.
we need to remove all the values of x such that:
x + 6 ≤ 0
Solving for x, we get
x ≤ -6
So the only values of x allowed are the ones that make the next inequality true:
x > -6.
Thus we can write the domain as:
D {x | x ∈ R | x > -6}
Where the second part, x ∈ R, is usually ignored, as we assume that x is a real number .
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Answer:
B
Step-by-step explanation:
2. A number cube is labelled 1 to 6
The cube is rolled 60 times.
Predict how many times each outcome will occur.
Explain each answer.
a) 1 is rolled.
b) An even number is rolled
c) A number greater than 3 is rolled.
d) 9 is rolled.
I
Answers
Answer:
a fair cube is expected to come up an equal number of times on each side
6 sides, 60 rolls
... each side is expected 10 times
a) 10 ... expected outcome
b) 30 ... expected outcome
c) 30 ... expected outcome
d) 0 ... only 6 sides
Solve algebraic!!!!!!!!!!
Answers
Answer:
(-1,-1)
Step-by-step explanation:
-3x+8y = -5
6x+2y = -8
Multiply the first equation by 2.
2(-3x+8y = -5)
-6x + 16y = -10
Add this equation to the second equation and eliminate x.
-6x + 16y = -10
6x+2y = -8
-------------------------
18y = -18
Divide by 18.
18y/18 = -18/18
y = -1
Now we can find x.
6x+2y = -8
6x+2(-1) = -8
6x -2 = -8
6x = -6
x = -1
The solution is (-1,-1)
Graph y=x−2
please help
Answers
Answer:
Start at -2 on the graph on the y axis (the line that goes up and down) and then go up one square and to the right one square all the way up and then draw the line
Step-by-step explanation:
Adele made bookmarks and name tags for her friends. The number of bookmarks she made is 4 times as many as the number of name tags she made. If she made 8 name tags, how many bookmarks did she make?
A.
12
B.
32
C.
40
Answers
Answer:
32
Step-by-step explanation:
The number of bookmarks she made is 4 times as many as the number of name tags she made.
4 times = 4*
If she made 8 name tags, how many bookmarks did she make?
Hence, equation is 4*8 which equal 32.
[RevyBreeze]
if f(x) is continuous and positve and g(x) is its antiderivative, then is g(x) increasing?
Answers
Yes, if f(x) is continuous and positive and g(x) is its antiderivative, then g(x) is increasing.
By the Fundamental Theorem of Calculus, if f(x) is continuous on an interval [a, b] and g(x) is an antiderivative of f(x) on that interval, then the definite integral of f(x) from a to b is equal to g(b) - g(a). Since f(x) is positive, the definite integral of f(x) over any subinterval of [a, b] will also be positive. This implies that g(b) - g(a) is positive whenever b > a, which means that g(x) must be increasing. Intuitively, this is because the area under a positive function is always increasing as you move along the x-axis, and g(x) represents the cumulative area under the curve of f(x).
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Use the drawing tool(s) to form the correct answer on the provided graph.
The graph of function fis shown on the coordinate plane. Graph the line representing function g, if gis defined as shown below.
g(x) = -1/(x + 2)
Answers
Answer:
Step-by-step explanation:
The graph for the linear function, g(x) = -x + 1 is shown in the image attached below.
What is a Linear Function?If m represents the slope and b represents the y-intercept of a function, the equation that represents the linear function would be expressed as, y = mx + b
Slope (m) = rise/run = change in y/change in x.
Find the equation of function f:
Slope (m) of function f = rise/run = 2/1
Slope (m) = 2
y-intercept, b, for function f = the point on the y-axis that the line intercepts = -6.
Write the equation for function f by substituting m = 2 and b = -6 into f(x) = mx + b.
f(x) = 2x + (-6)
f(x) = 2x - 6
Given that, g(x) = -½f(x + 2), therefore:
g(x) = -½(2(x + 2) - 6)
g(x) = -½(2x + 4 - 6)
g(x) = -½(2x - 2)
g(x) = -x + 1
Thus, the graph for the linear function, g(x) = -x + 1 is shown in the image attached below.
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Please help it's urgent if you do not help you will become Jeffery Epstein son!
Answers
A community is building a square park with sides that measure 110 meters. To separate the picnic area from the play area, the park is split by a diagonal line from the opposite corners Determine the approximate length of the diagonal line that splits the square.
Answers
Answer:
155.56 m
Step-by-step explanation:
The Pythagoras theorem : a² + b² = c²
where a = length
b = base
c = hypotenuse
√110² + 110²
HELP DUE AT MIDNIGHT TN
Answers
Answer:
102
Step-by-step explanation:
These angles are congruent due to corresponding angles thm
3x + 21 = 6x - 60
3x - 6x = -60 - 21
-3x = -81
x = 27
3x + 21
3(27) + 21
81 + 21
102
The money I have is represented by the equation: y = 10x + 100 where x = number of weeks and y = money remaining. How does my money CHANGE each week? A. decreases by $10 each week B. decreases by $100 each week C. increases by $10 each week D. increases by $100 each week
Answers
Therefore, according to the equation, when the weeks change, the money grows by $10 each week as it is added.
what is equation ?The numeral is said to be in its simplistic form when divided through its smallest analogous fraction. What must be done to find one of most basic form. Examine common factors in the numerator and the numerator. Verify a fractional integer to verify if it passes as a prime number. A statement having two collinear and an equal sign in the intermediate is called an equation in mathematics. The simplified version of any equation contains full degrees of all the variables in lowest to highest. The conventional solution of a linear function is an x + b = 0. The general form of a mathematical expression with two variables is an x + b y + c = 0. (or something similar). Mathematics can be categorized as identities or contingent equations.
given
equation: y = 10x + 100
as x = number of weeks
y = money remaining
Therefore, according to the equation, when the weeks change, the money grows by $10 each week as it is added.
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Malik asked his teacher if there was a way to check his answer after writing equivalent expressions. What should be his teacher’s response? Choose a number to substitute for the variable. Find the value of each expression. If the values are even, the expressions are equivalent. Substitute a number for the variable. If the simplified expressions have the same value, the expressions are equivalent. Multiply each expression by the same number. If the expressions are equal, the expressions are equivalent. Add a number to each expression. If the simplified expressions are equal, the expressions are equivalent.
Answers
Replace the variable with a number, the teacher says in response. The simplified expressions are comparable if they have the same value.
What is an equivalent expression?Expressions that function identically despite having different appearances are called equivalent expressions. If two algebraic expressions are equivalent, then when we enter the same value(s) for the variable, the two expressions have the same value.
It is given that, Malik asked his teacher if there was a way to check his answer after writing equivalent expressions.
Substitute a number for the variable. If the simplified expressions have the same value, the expressions are equivalent.
Thus, replace the variable with a number, the teacher says in response. The simplified expressions are comparable if they have the same value.
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Ethan is watering his plants. He starts with a watering can filled with 32 ounces of water, and he pours 3.5 ounces onto each plant. When Ethan finishes watering his plants, he has 14.5 ounces of water left. How many plants does he have? Write and solve an equation to find the answer.
Answers
The number of plants Ethan has are 5.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let x be the number of plants Ethan has.
Ethan uses 3.5 ounces of water for each plant, so he will use a total of 3.5p ounces of water.
If he starts with 32 ounces of water and ends up with 14.5 ounces
Total of 32 - 14.5 = 17.5 ounces of water.
As given the amount of water used is equal to the amount of water per plant times the number of plants:
3.5x = 17.5
Divide both sides by 3.5
x=5
Hence, , Ethan has 5 plants.
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Can anyone help? Dont quite understand.
Answers
The value of x in the two angles decsribed in the circle as the pizza to be shared by the two friends is 11.2
What is the sum of angles on a straight line?It stated that the sum of angles on a straight is equal to 180°.
For us to know the value of x, we must understand that the two angles
AOB=(5x-5)° and BOD=(10x+17)° lies on the straight line AD in the circle.
Therefore;
(5x-5)°+(10x+17)°= 180°
5x+10x+17°-5°= 180°
15x+12°=180°
15x=180°-12° (subtracting 12° from both sides of the equation)
15x=168° (dividing both sides of the equation by 15)
x=11.2
Thus, we can see with the proper application of law on the sum of angles on a straight line, the value of x derived to be 11.2
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HELP ME QUICK
In Shawn's class, all the students have pets. Of those pets,1/5 are cats. Of those cats, 2/3 are alley cats. What fraction of the pets are alley cats?
Answers
Answer:
2/15
Step-by-step explanation:
You want to know the fraction that is 2/3 of 1/5.
TimesIn this context, "of" means "times."
2/3 of 1/5 = (2/3)×(1/5) = (2·1)/(3·5) = 2/15
2/15 of the pets are alley cats.
Type the correct answer in the box. Use numerals instead of words. If necessary, use/ for the fraction bar.
Given the figure, find the total area of the shaded region.
D
8-
6-
4-
2-
O
-2-
o
S
The area of the shaded region is
B
R
8
с
square units
Answers
The value of the total area of the shaded region are,
⇒ 42 units²
We have to given that;
Sides of rectangle are,
AB = 9
BC = 6
Hence, The area of rectangle is,
⇒ 9 x 6
⇒ 54 units²
And, Area of triangle is,
A = 1/2 × 4 × 6
A = 12 units²
Thus, The value of the total area of the shaded region are,
⇒ 54 - 12
⇒ 42 units²
So, The value of the total area of the shaded region are,
⇒ 42 units²
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