Answer: 480
Step-by-step explanation:
300 In Account
15% of 300 = 45
45x4= 180
300+180= 480
Answer:
If Natalie had simple interest: $180
If Natalie had compound interest: $224.70
Step-by-step explanation:
Simple Interest.
P(1 +rt)
300(1 + 0.15 x 4) = 480
480 - 300 = 180
Compound interest.
P(1 + r/n)^nt
300(1 + 0.15)^4 = 524.70
524.70 - 300 = 224.70
help me please :(.......
Answer:
a) $2125
b) $2000
Step-by-step explanation:
In this problem, we are asked to solve for the manufacturing price of different printers if the printer company sells their printers at a price that makes them 25% profit, assuming there are no extra expenses.
We can solve this type of problem by manipulating ratios, like for example:
manufacturing price : sale price
100 : 125
This ratio represents the the sale price being 25% more than the manufacturing price.
a) We can equate the above ratio to the ratio of the manufacturing price (in this problem, $1700) to the sale price of the printer (represented by x).
100 : 125 = 1700 : x
This can be solved for x when the ratios are represented as fractions.
[tex]\dfrac{100}{125} = \dfrac{1700}{x}[/tex]
↓ simplify the fraction on the left side
[tex]\dfrac{4}{5} = \dfrac{1700}{x}[/tex]
↓ cross multiply
[tex]4x = 1700 \cdot 5[/tex]
↓ divide both sides by 4
[tex]x=\$ \, 2125[/tex]
So, the price that the customer would pay for a printer that the company bought for $1700 is $2125.
b) We can solve in the same way that we did for section a.
However, this time, the variable (y) represents the manufacturing price, NOT the sale price.
100 : 125 = y : 2500
↓ rewrite with fractions
[tex]\dfrac{100}{125} = \dfrac{y}{2500}[/tex]
↓ simplify the fraction on the left side
[tex]\dfrac{4}{5} = \dfrac{y}{2500}[/tex]
↓ cross multiply
[tex]5y = 2500 \cdot 4[/tex]
↓ divide both sides by 5
[tex]y = \$ \, 2000[/tex]
So, the price that the company would pay for a printer that a customer buys for $2500 is $2000.
A party planner organized a dinner party. The party planner recorded the height of the candlesticks over time and graphed the relationship.
graph with the x axis labeled time in hours and the y axis labeled height of candlestick in inches and a line going from the point 0 comma 9 through the point 2 comma 6
Find and interpret the slope and y-intercept in this real-world situation.
The slope is negative two thirds, and the y-intercept is 9. The candle starts at a height of 9 inches and decreases two thirds of an inch every hour.
The slope is negative three halves, and the y-intercept is 9. The candle starts at a height of 9 inches and decreases three halves of an inch every hour.
The slope is 9, and the y-intercept is negative two thirds. The candle starts at a height of two thirds of an inch and decreases 9 inches every hour.
The slope is 9, and the y-intercept is negative three halves. The candle starts at a height of three halves of an inch and decreases 9 inches every hour.
The meaning of the slope and of the intercept of the linear function are given as follows:
The slope is negative -3/2, and the y-intercept is 9. The candle starts at a height of 9 inches and decreases 3/2 of an inch every hour.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change of the output variable relative to the input variable.The intercept b represents the value of y when the graph of the function touches of crosses the y-axis.The two points for the function in this problem are given as follows:
(0,9) and (2,6).
When x = 0, y = 9, hence the intercept b is given as follows:
b = 9.
Meaning that the initial value of the problem is of 9.
The slope is given as the change in y divided by the change in x, hence:
m = (6 - 9)/(2 - 0)
m = -3/2.
Meaning that the rate of change is a decrease of 3/2 units for each unit of the input.
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a team played 7 games. In those games the team won by 7points,lostby10,won by 8, won by 11,lostby2 and won by 10. What was the mean difference in game scores in the six games
The mean difference in game scores over the six games is 12
What is mean difference?The mean difference, or difference in means, measures the absolute difference between the mean value in two different groups.
Given the points by which a basketball team either won or lost 6 games.
- Won by 7 points = +7
- Lost by 10 points = -10
- Won by 8 points = +8
- Won by 11 points = +11
- Lost by 2 points = -2
- Won by 10 points = +10
Thus;
Mean difference of the 6 games is;
= (+7 - 10 + 8 + 11 - 2 + 10)/6
= 24/6
= 12
Hence, the mean difference in game scores over the six games is 12
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determine if the subset of consisting of vectors of the form , where is a subspace.
The subset of consisting of vectors of the form is indeed a subspace.
A subspace is a special type of set within a vector space that has the same properties as the larger vector space.
In order to determine if a subset of a vector space is a subspace, we must check if it satisfies certain conditions.
The first condition is that the subset must contain the zero vector.
The second condition is that the subset must be closed under addition.
The third condition is that the subset must be closed under scalar multiplication.
Now, let's apply these conditions to the subset of consisting of vectors of the form . It is clear that the zero vector satisfies this condition, as.
The subset is also closed under addition, as adding two vectors of the form and will result in a vector of the form.
Finally, the subset is closed under scalar multiplication, as multiplying a vector of the form by a scalar will result in a vector of the form .
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I need the second answer please.
Answer: 40.75
Step-by-step explanation:
Question 1 (2 points)
Kala is financing a house for $123,500. She has to pay $300 plus 1. 05% for a brokerage fee.
How much are the mortgage brokerage fees? (2 points)
a$429. 68
b$1,296. 75
c$1,596. 75
d$2,152. 50
Total mortgage brokerage fees is $1,596.75. Thus, option c is correct.
What is the math formula for mortgage?These factors include the total amount you're borrowing from a bank, the interest rate for the loan, and the amount of time you have to pay back your mortgage in full. For your mortgage calc, you'll use the following equation: M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1].
Calculate H = P*J, this is your current monthly interest.
Calculate C = M - H, this is your monthly payment minus your monthly interest, so it is the amount of principal you pay for the month.
Calculate Q = P - C, this is the new balance of your principal of your loan.
P = the payment.
L = the loan value.
c = the period interest rate, which consits of dividing the APR as a decimal by the frequency of payments. ...
n = the total number of payments in the life of the loan (for monthly loan payments this is the loan term in years times twelve)
With given data:
123,500 x 1.05% =$1,296.75 percentage of the fee.
Total mortgage brokerage fees
$1,296.75 + $300 =$1,596.75
Thus, Total mortgage brokerage fees is $1,596.75. Thus, option c is correct.
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Rectangle PQRS is dilated by a scale factor of 5 to form rectangle '. Side QR measures 5. What is the measure of Q'R'?
The length of Q'R' is 5 * 5 = 25.
Dilating Rectangle MeasurementThe steps to find the measure of Q'R' are:
Start with the length of QR, which is given as 5.Apply the dilation factor of 5 to find the length of Q'R'.The length of Q'R' is obtained by multiplying the length of QR by the scale factor: 5 * 5 = 25.So, the measure of Q'R' is 25.
This method is applicable for finding the length or width of a dilated figure when the original length or width and the scale factor are given. The formula to find the length (or width) of a dilated figure is: length (or width) of dilated figure = scale factor * length (or width) of original figure. The formula for finding the length or width of a dilated figure is a basic concept in geometry and is widely used in solving related problems.
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when u, v are nonzero vectors, then span{u, v} contains the line through u and the origin, as well as the line through v and the origin. true or fal
When u, v are nonzero vectors, then span{u, v} contains the line through u and the origin, as well as the line through v and the origin, this statement is false.
The span of two nonzero vectors, u and v, is the set of all linear combinations of u and v. This can be a line, a plane, or even the entire space, depending on the vectors u and v. In general, the span of two nonzero vectors does not contain the line through each vector and the origin, unless the two vectors are collinear (i.e. they lie on the same line).
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carbon-14 has a half-life of 5,730 years. if a sample contains 80 mg originally, how much is left after 17,190 years?
Answer:
After 17,190 years, the amount of carbon-14 left would be approximately 5 mg.
The half-life of carbon-14 is 5,730 years, which means that every 5,730 years, half of the remaining carbon-14 decays. To calculate the amount of carbon-14 remaining after 17,190 years, we can use the formula:
A = A0 * (1/2)^(t/T)
where:
A0 is the initial amount (80 mg)
t is the time elapsed (17,190 years)
T is the half-life (5,730 years)
A = 80 * (1/2)^(17,190/5,730)
A = 80 * (1/2)^3
A = 80 * (1/8)
A = 10 mg * 1/2
A = 5 mg
a faucet is turned on at 9:00am and water starts to flow into a tank at the rate of r(t)=7t√, where t is time in hours after 9:00am and the rate r(t) is in cubic feet per hour.
7/3 t^(3/2) + C This equation represents the volume of water in the tank as a function of time t.
The equation r(t) = 7t √ represents the rate at which water is flowing into the tank, measured in cubic feet per hour, at time t after 9:00am. The expression 7t √ means that the rate of flow increases over time, starting at 0 cubic feet per hour at t = 0 and increasing as t increases.
To find the volume of water in the tank at a specific time t after 9:00am, we can integrate the rate of flow over the time interval from 9:00am to t. The volume of water in the tank at time t can be expressed as:
V(t) = ∫ r(t) dt from 9:00am to t
= ∫ 7t √ dt from 0 to t
= 7/3 t^(3/2) + C
where C is an arbitrary constant of integration. This equation represents the volume of water in the tank as a function of time t.
Therefore, 7/3 t^(3/2) + C This equation represents the volume of water in the tank as a function of time t.
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While playing a game of chance, Tarik rolled a regular six-sided die 100 times and noticed that it landed on the number 1 exactly 52 times. What could Tarik conclude about the die?
A: We are 90% confident that the true proportion of times the die would land on the number 1 is between 0.422 and 0.618. Since this includes 0.5, the die appears to be fair.
B: We are 90% confident that the true proportion of times the die would land on the number 1 is between 0.422 and 0.618. Since this is much greater than 1 out of 6, the die appears to be unfair.
C: We are 90% confident that the true proportion of times the die would land on the number 1 is between 0.438 and 0.602. Since this includes 0.5, the die appears to be fair.
D: We are 90% confident that the true proportion of times the die would land on the number 1 is between 0.438 and 0.602. Since this is much greater than 1 out of 6, the die appears to be unfair.
We are 90% confident that the true proportion of times the die would land on the number 1 is between 0.438 and 0.602. Since this includes 0.5, the die appears to be fair.
The correct option is C.
What is the probability?The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.
Given:
While playing a game of chance,
Tarik rolled a regular six-sided die 100 times and noticed that it landed on the number 1 exactly 52 times.
The probability P is = 52/100 = 0.52.
The lower limit = P - z√(P(1 - P)/n
The lower limit = 0.52 - 1.645√(0.52 x 0.48)/100
The lower limit ≈ 0.438.
The upper limit = P + z√(P(1 - P)/n
The upper limit = 0.52 + 1.645√(0.52 x 0.48)/100
The upper limit ≈ 0.602.
Therefore, the die would land on the number 1 is between 0.438 and 0.602.
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Given the following table with selected values of the linear functions g(x) and h(x), determine the x-intercept of g(h(x))
The x-intercept of the composition is x = -1/2.
How to find the x-intercept of the composition?Remember that a linear function can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If a liear function passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:
a = (y₂ - y₁)/(x₂ - x₁)
For g(x) we can use (-1, 2) and (1, 6), the slope is:
a = (6 - 2)/(1 + 1) = 2
Then the function is something like:
g(x)= 2x + b
To find the value of b, we use again the point (1, 6)
g(1) = 6 = 2*1 + b
6 - 2 = b
4 = b
So:
g(x) = 2x + 4
Now the same for h(x), we can use the points (-1, -1) and (1, 7), we will get:
a = (7 + 1)/(1 + 1) = 4
h(x) = 4x + b
Using the point (1, 7)
h(1) = 7 = 4*1 + b
7 - 4 = b
3 = b
h(x) = 4x + 3
The composition is:
g( h(x)) = 2*h(x) + 4
= 2*(4x + 3) + 4
= 8x + 10
The x-intercept is the value of x such that:
0 = 8x + 4
-4 = 8x
-4/8 = x
-1/2 = x
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Sandy ha 26 meter of brown wire and 20 meter of red wire. She need to cut both wire into maller piece o that all of the maller piece are the ame length and there i no wire leftover. The length of each piece mut be a whole number of meter. What i the longet he can make each maller piece of wire? Give your anwer in meter
Each malleable piece of wire he can produce has a length of 2 metres.
How to calculate length?When given an area A and a width w, the length w is calculated using the formula h = A/w. Its length can be calculated using h = P/²w if you know its perimeter (P) and width (W). Its length is h = (d²w²) if you have a diagonal d and a width w.The definition of length is the distance or measurement between two points. In other terms, the largest two or highest three dimensions of a geometric shape or item. As an illustration, the length and width of a rectangle are its dimensions.The number of digits in the base-numerical for, as determined by the formula, determines a number's base length. A vector's magnitude (length), which is a scalar and determined by the square root of the sum of the squares of its components, is called a scalar vector. This is an exception to the general rule that the Euclidean distance in n-space between any two places is equal to the square root of the sum of the squares of the elemental differences.Prime factorization
26 = 2 × 13
20 = 2² × 5
HCF = 2
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determine the new limits of integration after the given substitution is made.
[tex]$\int_{-2}^{4} f(x)dx$[/tex] with the substitution [tex]$u = x^2$[/tex] . The new limits of integration are 0 and 8.
The substitution [tex]$u = x^2$[/tex] implies that [tex]$du = 2x dx$[/tex], so when [tex]x = -2$, $u = (-2)^2 = 4$[/tex]. Similarly, when [tex]x = 4$, $u = 4^2 = 16$[/tex]. Thus, the new limits of integration are 0 and 8.
To determine the new limits of integration, we must first find the values of u for the original limits of integration. Since we have [tex]$u = x^2$[/tex], when x = -2, we have [tex]$u = (-2)^2 = 4$[/tex]. Similarly, when x = 4, we have [tex]u = 4^2 = 16$.[/tex]Therefore, the new limits of integration are 0 and 8.
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The circumference of a circular garden is 75.36 feet. What is the diameter of the garden?
Answer:
24.12 feet.
Step-by-step explanation:
The formula to find the diameter of a circle from its circumference is:
diameter = circumference / π
Plugging in the given values:
diameter = 75.36 feet / π
diameter = 75.36 / 3.14
diameter ≈ 24.12 feet
So, the diameter of the circular garden is approximately 24.12 feet.
Write the product using exponents.
(-4) x (-4) x (-4) x Y x Y
Using exponents, the product is _.
The product of the expression (-4) x (-4) x (-4) x y x y is -64y²
What are expressions?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given that, an expression, (-4) x (-4) x (-4) x y x y
We need to find its product,
(-4) x (-4) x (-4) x y x y
= -4³ × y²
= -64 × y²
= -64y²
Hence, the product of the expression (-4) x (-4) x (-4) x y x y is -64y²
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Given the following exponential function,
identify whether the change represents
growth or decay, and determine the
percentage rate of increase or decrease.
y = 25(1.071)^x
Answer:
Step-by-step explanation:
The given exponential function will grow at 6.1%
Given,
y =
To find,
identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
Solution,
We have,
y =
The equation represents exponential growth because the growth factor is greater than 1.
The general form equation is:
y(x)= a(1-r)^x such that r is the growth percent.
==> 1+r = 1.061
==> r = 0.061 = 6.1%
Which graph do you create if you plot the function on a coordinate plane?
Answer:
B
Step-by-step explanation:
B..................
22 miles in 20 minutes A < B > C = 38 miles in 30 minutes
It is found that 22 miles in 20 minutes is LESS
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We have to compare the two rates:
=> 22 miles in 20 minutes
=> 38 miles in 30 minutes
Let's simplify each rate by finding the speed, which is distance divided by time.
That is:
Speed = distance/time
For the first one:
s = 22/20 = 1.1 milesl/min
For the second one:
s = 38/30 = 1.27 milesl/min
Since 1.1 is less than 1.27, so, 22 miles in 20 minutes is less than 38 miles in 30 minutes.
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The complete question is;
Is 22 miles in 20 minutes greater than, equal to or less than 38 miles in 30 minutes?
Determine whether the system of equations
is consistent or inconsistent and if it is
independent or dependent.
3x + 5y = -5
6y +15=-15x
Unresolved problems are referred to be inconsistent systems.
How to find the Equation?Find the solution to the system of equations by attempting to remove one of the variables to see whether there is a single solution, no solution, or never-ending options (If these two equations' lines all fall on the same line, then
By adding -2 to the first equation
-4x - 6y = -22
the second equation after that, adding it.
5x + 6y = 14
getting x = -8
Returning to either equation, plug in the following: the first one,
2(-8) + 3y = 11
-16 +3y = 11
3y = 27
y = 9
These two lines come together at one point since there is only one possible answer. They remain dependable.
The graphs of the equations yield two distinct lines, proving the independence of this system. Should the equations result in
In a same vein, they are interdependent.
They would have produced a constant equation, such as 0 = 0, if they had been the same line and had been solved for one variable.
Thus, (D) is still true because they are reliable and separate.
The Complete Question is :
Determine whether the system is consistent or inconsistent and whether the equations are dependent or independent.
2x + 3y = 11
5x + 6y = 14
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1 x 103 + 3 x 102 + 9 x 101 + 2
Answer:
1320
MDAS Method
Answer:
Your answer is 1320
Step-by-step explanation:
hope this is what you were looking for
for the matrices a = −3 2 1 4 and b = 5 1 0 −2 in m2,2, determine whether the given matrix is a linear combination of a and b. −19 4 3 16
The given matrix is non linear matrix combination of a and b matrix.
a - b = [tex]\left[\begin{array}{ccc}-8&1\\0&4\\\end{array}\right][/tex] ≠ [tex]\left[\begin{array}{ccc}-19&4\\3&16\\\end{array}\right][/tex]
An equation in which the maximum degree of a term is 2 or more than two is called a nonlinear equation.
Matrix, a set of numbers arranged in rows and columns so as to form a rectangular array. The numbers are called the elements, or entries, of the matrix. Matrices have wide applications in engineering, physics, economics, and statistics as well as in various branches of mathematics.
Given that,
a = [tex]\left[\begin{array}{ccc}-3&2\\1&4\\\end{array}\right][/tex]
b = [tex]\left[\begin{array}{ccc}5&1\\0&-2\\\end{array}\right][/tex]
The given matrix is a linear combination of a and b
a - b = [tex]\left[\begin{array}{ccc}-3&2\\1&4\\\end{array}\right] - \left[\begin{array}{ccc}5&1\\0&-2\\\end{array}\right][/tex] ≠ [tex]\left[\begin{array}{ccc}-19&4\\3&16\\\end{array}\right][/tex]
a - b = [tex]\left[\begin{array}{ccc}-3-5&2-1\\1-1&4-0\\\end{array}\right][/tex] ≠ [tex]\left[\begin{array}{ccc}-19&4\\3&16\\\end{array}\right][/tex]
a - b = [tex]\left[\begin{array}{ccc}-8&1\\0&4\\\end{array}\right][/tex] ≠ [tex]\left[\begin{array}{ccc}-19&4\\3&16\\\end{array}\right][/tex]
Therefore,
The given matrix is non linear matrix combination of a and b matrix.
a - b = [tex]\left[\begin{array}{ccc}-8&1\\0&4\\\end{array}\right][/tex] ≠ [tex]\left[\begin{array}{ccc}-19&4\\3&16\\\end{array}\right][/tex]
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It costs $12. 50 to enter an amusement park and $1. 50 to play each game. Solve an inequality to find the number of games, g, Cole can play if he has $35 to spend at the park
The number of games cole can play $12.5 to enter and $1.5 to play each game by subtracting and dividing with $35 is 15 games.
The total money cole have is $35
To enter an amusement parks it costs around $12.5
so, remaining money by subtracting = 35-12.5 = $22.5
so, by dividing the remaining money with $1.5 paid per each game gives how many games does cole can play.The number of games cole can play $12.5 to enter and $1.5 to play each game by subtracting and dividing with $35 is 15 games. By dividing the remaining money with $1.5 paid per each game gives how many games does cole can play. Total number of games does cole can play is 22.5/1.5 = 14 games.
Therefore , the number of games cole can play are 14 games exactly.
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find the value of the integral ∫ (∇ × a® ).® if the vector a® = eˆ eˆ eˆ and is the surface defined by the paraboloid = 1 − 2 − 2 , where ≥ 0.
The integral is equal to zero, since the divergence of a constant vector is always zero.
The integral ∫ (∇ × a® ).® is equal to zero. This is due to the fact that the curl of a constant vector is always zero. The vector a® is given to be eˆ eˆ eˆ, therefore it is a constant vector. Since the divergence of a constant vector is always zero, the integral is equal to zero.
To further illustrate this point, we can expand the integral in terms of its components. ∇ × a® is equal to 0 as it is the curl of a constant vector. Similarly, a® .® is equal to 0 since the inner product of two constant vectors is always zero. Therefore, the integral is equal to 0.
The surface defined by the paraboloid is not used in this calculation, as the surface does not affect the value of the integral. The surface is used to define the range of the integral, but not to calculate the value of the integral itself.
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Use the drop-down menus to compare −2. 25 and −3.
please i need help!!!
-2.25 is larger when it compares to -3, because when you order negative numbers, the larger the number after the negative sign, the smaller the number actually is. This means -2.25 > -3
What is negative numbers?
On a number line, numbers always move from right to left and grow (become "more positive") in that direction. The numbers to the right are bigger than the numbers to the left, while the numbers to the left are smaller. Numbers with a minus sign before them are considered negative numbers. They could be fractions, decimals, or integers. Negative numbers include, for instance, -4, -15, -4/5, and -0.5. A negative number in mathematics represents the reverse. A negative number is one that is less than zero in the real number system. Negative numbers are frequently used to indicate how great a loss or a shortage is.
-2.5>-3 because the bigger a negative number is like -15,-18, etc the smaller it’s value actually gets so -2.5 is greater because it is closer to 0 on a number line.
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Could the lengths 6 8 and 15 represent the sides of the triangle?
The lengths 6, 8 and 15 cannot represent the sides of the triangle. The solution has been obtained by using the triangle inequality theorem.
What is the triangle inequality theorem?
The triangle inequality theorem outlines the relationships between a triangle's three sides. According to this theorem, the lengths of any triangle's two shorter sides add up to be longer than the triangle's third side. In other terms, this theorem states that the shortest path between any two places is always a straight line.
We are given the lengths to be 6, 8 and 15.
Using the triangle inequality theorem,
⇒ 6 + 15 > 8
⇒ 21 > 8
Also,
⇒ 8 + 15 > 6
⇒ 23 > 8
Also,
⇒ 6 + 8 > 15
But,
⇒ 14 < 15
Hence, the lengths 6, 8 and 15 cannot represent the sides of the triangle.
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Stuck on homework please help
please help!
A gumball machine contains 200 gumballs. A random sample of 25 gumballs was collected from the machine. The results from the random sample are shown.
10 gumballs are red
8 gumballs are blue
5 gumballs are green
2 gumballs are white
Based on the random sample results, complete the prediction statements for the entire machine of 200 gumballs.
Move the answers to the correct boxes.
There are
red gumballs in the machine.
There are
more green gumballs than white gumballs in the machine.
There are
gumballs that are either blue or green in the machine.
Based on the random sample results, the prediction statements for the entire machine of 200 gumballs is completed below;
There are 10 red gumballs in the machine.There are 3 more green gumballs than white gumballs in the machine.There are 13 gumballs that are either blue or green in the machine.Complete the prediction statement using the random sample?Total gumballs in the gumball machine= 200 gumballs
Result from the random sample= 25 gumballs
From the random sample selected:
10 gumballs are red
8 gumballs are blue
5 gumballs are green
2 gumballs are white
There are 10 red gumballs in the machine.
There are 3 more green gumballs than white gumballs in the machine.
= Green gumballs - red gumballs
= 5 - 2
= 3 gumballs
There are 13 gumballs that are either blue or green in the machine.
= Blue gumballs + green gumballs
= 8 + 5
= 13 gumballs
Ultimately, the prediction statement is completed using 10, 3 and 13 respectively.
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Explain how to ue a table to write an equation that repreent the relationhip in the table
A table can be used to write an equation that represents the relationship in the table by using the values in the table to determine the coefficients of the equation.
Here's how you can use a table to write an equation:
1. Identify the dependent and independent variables in the table. The dependent variable is the value that depends on the independent variable.
2. Choose one of the variables as the dependent variable and write the equation in terms of the dependent variable.
3. Use the values in the table to find the coefficients of the equation. For example, if the independent variable is x and the dependent variable is y, you can use the values in the first column for x and the values in the second column for y to find the coefficients.
4. Write the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. The slope represents the change in y for a unit change in x, and the y-intercept represents the value of y when x is 0.
5. Substitute the coefficients from step 3 into the equation from step 4.
6. Check your equation by plugging in the values from the table and verifying that they match the corresponding values in the dependent variable column.
By using a table to write an equation, you can easily find the mathematical relationship between the variables and make predictions for new values of the independent variable.
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A table can be used to write an equation that represents the relationship in the table by using the values in the table to determine the coefficients of the equation.
Here's how you can use a table to write an equation:
1. Identify the dependent and independent variables in the table. The dependent variable is the value that depends on the independent variable.
2. Choose one of the variables as the dependent variable and write the equation in terms of the dependent variable.
3. Use the values in the table to find the coefficients of the equation. For example, if the independent variable is x and the dependent variable is y, you can use the values in the first column for x and the values in the second column for y to find the coefficients.
4. Write the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. The slope represents the change in y for a unit change in x, and the y-intercept represents the value of y when x is 0.
5. Substitute the coefficients from step 3 into the equation from step 4.
6. Check your equation by plugging in the values from the table and verifying that they match the corresponding values in the dependent variable column.
By using a table to write an equation, you can easily find the mathematical relationship between the variables and make predictions for new values of the independent variable.
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Enter the correct answer in the box.
Write the inverse of the cube root function used to represent the situation in
Model 2:
"Jack owns a company that manufactures a product that we’ll call product A. After producing and selling x units of product A, the profit his company made is represented by the cube root function [tex]f (x) = \sqrt[3]{(x+4)^{2} }[/tex]"
The inverse of the cube root function used to act for the situation in model is f⁻¹(x) = √x³ - 4
Inverse of the cube root function f(x)
f(x) = ∛ (x + 4) ²
To find the inverse function, let f(x) = y
So, y = ∛ (x + 4) ²
Taking the cube of both sides, we have
y³ = [∛ (x + 4) ²] ³
y³ = (x + 4) ²
Taking square root of both sides, we have
√y³ = √ (x + 4) ²
√y³ = (x + 4)
Subtracting 4 from both sides, we have
√y³ - 4 = x + 4 - 4
√y³ - 4 = x
change y with x, we have
√x³ - 4 = y
Replacing y with f⁻¹(x), we have
f⁻¹(x) = √x³ - 4
So, the inverse of the cube root function used to represent the situation in model is f⁻¹(x) = √x³ - 4
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