The bacteria will reach its maximum size at t = 8.94 weeks.
To find when the bacteria will reach its maximum size, we need to find the maximum value of p(t). The first step is to find the derivative of p(t):
dp(t)/dt = -8000(t^2 - 80)/(80 + t^2)^2
Next, we need to find the critical points of this derivative by setting it equal to 0 and solving for t:
dp(t)/dt = 0
-8000(t^2 - 80)/(80 + t^2)^2 = 0
t^2 - 80 = 0
t = √80
t = 4√5
t ≈ 8.94
Since t = 4√5 is the only critical point, we can see that it is a local maximum. To confirm this, we need to find the second derivative and evaluate it at t = 0:
d^2p(t)/dt^2 = 16000t (t^2 - 240) / (80 + t^2)^3
d^2p(t)/dt^2 = 160000 * -160 / (80 + 80)^3 < 0
Since the second derivative at t = 4√5 is less than 0, it is a local maximum.
--The question is incomplete, answering to the question below--
"The size of a bacteria population grows at a rate of p(t) = 8000t/ (80 + t^2) where t is measured in weeks. Determine when the bacteria will reach its maximum size."
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If DE = 4x + 5 and GJ = 3x + 25, find DE.
If DE = 4x + 5 and GJ = 3x + 25, and the value of both the expressions is same, then value of DE is, 85
What are expressions?An expression is a sentence with at least two numbers or variables having mathematical operation. Maths operations can be addition, subtraction, multiplication, division.
For example, 2x+3
Given that,
Two expressions,
DE = 4x + 5 and GJ = 3x + 25,
If DE = 4x + 5 and GJ = 3x + 25, and they have the same value, then we can set the two expressions equal to each other:
4x + 5 = 3x + 25
Solving for x, we get:
x = 20
So, when x = 10,
DE = 4 x20 + 5
= 85
and GJ = 3 x 20 + 25
= 85
Therefore, the value of DE is 85.
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An outcome table with 36 possible outcomes. The number of desired outcomes is 9. What is the probability of rolling an even number and then an odd number when rolling two number cubes? size of sample spaces = number of desired outcomes = p(first is even and second is odd) =.
The probability of rolling an even number and then an odd number when rolling two number cubes is 1/4 or 0.25.
The sample space is the set of all possible outcomes, which in this case is 36. The number of desired outcomes is 9, as the question specifies.
The probability of rolling an even number and then an odd number when rolling two number cubes is 1/4 or 0.25. You calculate this by taking the number of desired outcomes (9) and dividing it by the total number of possible outcomes (36).
The probability of rolling an even number and then an odd number when rolling two number cubes is 1/4 or 0.25. This is calculated by taking the number of desired outcomes (9) and dividing it by the total number of possible outcomes (36).
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When rolling two number cubes, the likelihood of first getting an even number and then an unusual one is 1/4, or 0.25. You can determine this by dividing the total number of possible outcomes by the number of intended outcomes (9). (36).
When rolling two number cubes, the likelihood of first getting an even number and then an unusual one is 1/4, or 0.25. This is calculated by dividing the total number of possible outcomes (which is 36) by the number of intended outcomes (9). (36).
A triangular land having area 336 q meter and perimeter 84 meter ha length of an edge 26 meter. Calculate the meaurement of remaining two ide
A triangular land has area 336 q meter, perimeter 84 meter and length of an edge 26 meter. The lenght of the remaining two sides are both 29 meters long.
Let's call the length of the remaining two sides x.
Since the perimeter of the triangle is 84, then the sum of all three sides is 84, so:
x + x + 26 = 84
Therefore, the sum of the remaining two sides is:
2x = 84 - 26 = 58
And the length of each remaining side is:
x = 58 / 2 = 29 meters required lenght of the remaining two sides.
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use a maclaurin series in this table to obtain the maclaurin series for the given function. f(x) = arctan(x8) [infinity] n = 0
The Maclaurin series for the function f(x) = arctan(x8) can be obtained as follows: f(x) = arctan(x8) = ∑ (-1)^n x^(8n+1) / (8n + 1), n = 0 to ∞
The Maclaurin series for arctan(x) is an alternating series, meaning that the signs of the terms alternate between positive and negative. The terms of the series also get smaller in magnitude as n increases, so the series converges rapidly for small values of x.
The Maclaurin series for the function f(x) = arctan(x8) can be obtained as follows: f(x) = arctan(x8) = ∑ (-1)^n x^(8n+1) / (8n + 1), n = 0 to ∞
This Maclaurin series representation of arctan(x8) is useful for approximating the value of the function for small values of x. To obtain more accurate results for larger values of x, one can use more terms from the series or use other numerical methods to calculate arctan(x8).
Therefore, The Maclaurin series for the function f(x) = arctan(x8) can be obtained as follows: f(x) = arctan(x8) = ∑ (-1)^n x^(8n+1) / (8n + 1), n = 0 to ∞
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Tell whether the fractions are equivalent. Write equal or not equal. 2/3 and 4/10 5/6 and 10/12 1/4 and 4/8
find the compsoite funciton which expresses the given correspeonecce correctly
The composite function which expresses the given correspondence correctly is f of g of x
Composite functions are when the output of one function is used as the input of another. If we have a function f and another function g, the function f g ( x ) fg(x) fg(x), said as “ f of g of x”, or “ f g fg fg of x”, is the composition of the two functions.
The composite function rule shows us a quicker way. If f(x) = h(g(x)) then f (x) = h (g(x)) × g (x). In words: differentiate the 'outside' function, and then multiply by the derivative of the 'inside' function.
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Write an expression that includes multiplication to show how to find the total amount of the plant growth in inches. then slove your expression.
Answer:
Step-by-step explanation:
Add, Added to, the sum of, more than, increased by, the total of, plus. +. Add x to y x + y y added to 7.
In a car i moving in a traight line with peed 18 km/h. It i topped in 55 by applying brake. Find the peed of car after 2 of applying the brake
The car travel before stopping is 400 meters
The car's initial speed was 80 m/s.
Acceleration/Deferral = 8 m/s2.
The following is the equation of motion for time t and distance s:
v = u + at
s = ut + 1/2 * a * t ^2
v = final velocity = 0 where
Thus, s = 80 * 10 - 1/2 * 8 * 10 *10
= 800 - 400
= 400 meters were covered before stopping, giving us 0 = 80 - 8 * t t
= 80/8
= 10 seconds.
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The full question:
A car moving a straight highway with a speed of 80 m/s is forced to slow down at a rate of 8 m/s^2. How far does a car travel before stopping?
emma uses turquoise beads to make bracelets to sell at an event. the total amount emma earns, y, is proportional to the number of bracelets, x, she sells. emma earns $10 for each sold bracelet. which equation represents the total amount emma earns at the event?
The equation representing the total amount Emma earns at the event is y = $10x.
If the total amount Emma earns, y, is proportional to the number of bracelets, x, she sells and she earns $10 for each sold bracelet, then we can write the equation as follows:
y = kx
where k is the constant of proportionality. To find k, we can use the information that Emma earns $10 for each sold bracelet:
y = $10 * x
Therefore, the equation representing the total amount Emma earns at the event is y = $10x.
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The equation representing the total amount Emma earns at the event is y = $10x.
If the total amount Emma earns, y, is proportional to the number of bracelets, x, she sells and she earns $10 for each sold bracelet, then we can write the equation as follows:
y = kx
where k is the constant of proportionality. To find k, we can use the information that Emma earns $10 for each sold bracelet:
y = $10 * x
Therefore, the equation representing the total amount Emma earns at the event is y = $10x.
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assume that a customer shops at a local grocery store spending an average of $ a week, resulting in a retailer profit of $ each week from this customer. assuming the shopper visits the store all 52 weeks of the year, calculate the customer lifetime value if this shopper remains loyal over a 10-year life span. also assume a percent annual interest rate and no initial cost to acquire the customer.
"The customer yields $780 per year in profits for this retailer."
Customer lifetime value (CLV) is a prediction of the total value a customer will bring to a business over their entire relationship with the company. Retailer profits refer to the financial gain a retailer makes after subtracting all costs, including the cost of goods sold, operating expenses, and taxes, from the revenue generated by their retail sales.
The customer spends $250 a week, so the retailer profits:
= $250 - $235= $15 from each visit.If the shopper visits the store every week for a year, the retailer profits:
= $15 x 52= $780 per yearIf this shopper remains loyal for a 10-year lifespan, the retailer profits:
= $780 x 10= $7,800This is the CLV without considering inflation or any other factors. To consider inflation, we can apply the 8% annual interest rate to calculate the present value of the future profits. The present value of $7,800 over 10 years with an 8% interest rate is approximately $5,100 (the exact value will depend on the method used to calculate the present value).
This question should be provided as:
Assume that a customer shops at a local grocery store spending an average of $250 a week, resulting in a retailer profit of $15 each week from this customer. Assuming the shopper visits the store all 52 weeks of the year, calculate the customer lifetime value if this shopper remains loyal over a 10-year life span. Also assume a 8 percent annual interest rate and no initial cost to acquire the customer.
The customer yields $_____ per year in profits for this retailer.
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Pls hurry !!
Which of the following represents the total area of the figure? 16.425 in² 20.775 in² 24.15 in² 28.5 in²
Answer: A) 16.425 in^2.
Step-by-step explanation: The figure is broken down, so let's find the area of the rectangle first. We are given 4 in and 2.3 in, which can be multiplied to get 9.2 in. Now, we need to find the area of the two triangles, but let's start with the one to the left. The area of a triangle is b x h x 1/2. 2.3 in x 2.5 in is 5.75 in, but we need to multiply that by 1/2 which is 2.875 in. Finally, we can find the area of the bottom triangle by using the same formula. 3 in x 2.9 in is 8.7 in, but we need to multiply it by 1/2, which is 4.35 in. Now, all we need to do is add all the areas we found together to get the total area of the figure. 9.2 in + 2.875 in + 4.35 in is 16.425 in^2, which means that option A is your answer.
Let me know if this is right! :)
Answer:
16.425 in²
Step-by-step explanation:
total area of the figure= area of (left triangle+ rectangle+ down triangle)
=1/2*base*height+length*breath+ 1/2*base*height
=1/2*2.5*2.3+4*2.3+1/2*3*(5.2-2.3)
=16.425 in²
Each year, a physicist measures the remaining radioactivity in a sample. She finds that it reduces by 18% each year. If there was 1.52 g of radioactive material left after 4 years: a. Find the initial quantity of radioactive material.
b. How many more years will it take for the amount of radioactive material to reduce to 0.2 g?
It will take an additional 7.15 years for the amount of radioactive material to reduce to 0.2 g.
Now, According to the question:
"Information available from the question"
A physicist measures the remaining radioactivity in a sample.
She finds that it reduces by 18% each year.
If there was 1.52 g of radioactive material left after 4 years.
In order to find the initial quality of radioactive material, we will use the formula:
Initial Quality = Final Quantity * (1 - Reduction Rate)^Years
We know that -
The final Quantity is 1.52 g, the reduction rate is 18% (or 0.18), and the number of years is 4.
Initial Quantity = 1.52 g × [tex](1-0.18)^4[/tex]
Initial Quantity = 1.52 g × 0.452
Initial Quantity = 0.68 g
Hence, the initial quantity of the radioactive material is 0.68 g.
b. In order to find how many more years it will take for the amount of radioactive material to reduce to 0.2 g, we will use the formula:
Years = log(Final Quality / Initial Quality) / log(1 - Reduction Rate)
We know that -
the final quality is 0.2 g, the initial quality is 0.68 g, and the reduction rate is 18% (or 0.18).
Years = log(0.2 / 0.0.68) / log(1 - 0.18)
Years = 7.15
Therefore, it will take an additional 7.15 years for the amount of radioactive material to reduce to 0.2 g.
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in slope intercept form
y+3/5=-4(x-1/2)
Answer:
y = -4 + 1.4
Step-by-step explanation:
y+3/5 = -4(x-1/2)
y + 3/5 = -4x + 2
y + 0.6 = -4x + 2
y = -4 + 1.4
42= −7( z − 3)
TYSMFYH
Answer:
z = -3
Step-by-step explanation:
-7(z - 3) = 42
Distribute -7 to both numbers inside the parenthesis:
(-7(z) - -7(3)) = 42
-7z + 21 = 42
Subtract 21 from both sides:
-7z = 21
Divide both sides by -7:
[z = -3]
Jenny has ten chickens that lay eggs every day. She wants to give away
her extra eggs to her neighbors, but she wants to give each neighbor an
equal number of eggs. She figures out that she needs to give 7 of her
neighbors eggs for them to get the same amount, otherwise there is one
egg left over. What is the smallest number of eggs she needs for this
situation to be true?
Answer: 14 eggs
Step-by-step explanation: Hello!
You know that there are 10 chickens that lay eggs every day. There are 7 neighbors that she needs to give eggs to so that they each get the same amount otherwise there is one egg left over. We know that each chicken must produce at least one egg per day, meaning that the bare minimum amount of eggs per day is 10. Let's try 10.
10/7 = 1 and 3/7. This means that there would be 3 eggs remaining. This is not possible. Let's try 11.
11/7 = 1 and 4/7. This means there would be 4 eggs remaining. Let's try 14.
14/7 = 2. This is the smallest number of eggs for each neighbor to get the same amount of eggs each per day (2). The smallest number of eggs she needs in total is 14.
Question Decide if the expressions in each pair are equivalent. Select true or false for each.
a) (x + x + x + x) and (4x) are equivalent (Select ] b) (5x) and (x + 5) are equivalent
true or false
(a) The expressions (x + x + x + x) and (4x) are equivalent.
(b) The expressions (5x) and (x + 5) are not equivalent.
Equivalent expressions are expressions that perform the same function notwithstanding their appearance. If two algebraic expressions are equivalent, they have the same value when the variable is set to the same value.
a) True
The expressions (x + x + x + x) and (4x) are equivalent.
Both expressions represent the same mathematical operation, which is adding x four times.
b) False
The expressions (5x) and (x + 5) are not equivalent. They represent different mathematical operations.
The expression (5x) is multiplying x by 5, while the expression (x + 5) is adding x and 5.
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Write the next three terms of the geometric sequence. 81, - 27, 9, - 3, ...
Answer:
1 - 1/3 1/9
Step-by-step explanation:
Common ratio is
81 * r = - 27
r= - 1/3
-3 * - 1/3 = 1
1 x - 1/3 = -1/3
-1/3 * - 1/3 = 1/9
the sum of lukes age and gibsons age is 73 if lukes age is five years less than twice gibsons age how old is luke
Lukes's age is 47
Gibson's age is 26
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Lukes's age = x
Gibson's age = y
Now,
x + y = 73 ______(1)
x = 2y - 5
Substituting in (1)
2y - 5 + y = 73
3y = 78
y = 26
Now,
x = 2 x 26 - 5
x = 52 - 5
x = 47
Thus,
Lukes's age = 47
Gibson's age = 26
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the rate of change of the weight of a laboratory mouse can be modeled by the equation where t is the age of the mouse in weeks and . what does mean?
dW/dt represents rate of change of mouse weight with respect to time, or derivative of weight with respect to time.
What is weight ?
Weight is a measure of the force exerted on an object due to gravity. It is commonly defined as the mass of an object multiplied by the acceleration due to gravity. In physics, weight is often expressed in units of Newtons or pounds.
The expression dW/dt represents the rate of change of the weight of the mouse (W) with respect to its age (t) in weeks. The symbol dW/dt is known as the derivative of the weight with respect to time and represents the rate of growth or decline of the mouse's weight.
dW/dt represents rate of change of mouse weight with respect to time, or derivative of weight with respect to time.
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dW/dt represents rate of change of mouse weight with respect to time, or derivative of weight with respect to time.
Weight is a measure of the force exerted on an object due to gravity. It is commonly defined as the mass of an object multiplied by the acceleration due to gravity. In physics, weight is often expressed in units of Newtons or pounds.
The expression dW/dt represents the rate of change of the weight of the mouse (W) with respect to its age (t) in weeks. The symbol dW/dt is known as the derivative of the weight with respect to time and represents the rate of growth or decline of the mouse's weight.
dW/dt represents rate of change of mouse weight with respect to time, or derivative of weight with respect to time.
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find an angle that is coterminal with a standard position angle measuring -210° that is between -720°and -360°
The coterminal angle with -210° is -570°. This is because subtracting 360° from -210° gives us -570° which is between -720° and -360°.
To find an angle coterminal with -210° that is between -720° and -360°, we need to subtract 360° from -210°. By doing this, we end up with -570° which is the coterminal angle with -210° that lies between -720° and -360°. This is because angles on the circle can 'wrap around' infinitely, and when we subtract 360° from -210°, we end up with an angle that is still equivalent to -210°, but between the two values we are looking for. Therefore, the angle we were looking for is -570°.
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How to solve system of equations using Gauss-Jordan elimination?
Gauss-Jordan Elimination is a technique for solving systems of linear equations and for determining the inverse of any invertible matrix.
What is meant by Gauss-Jordan elimination?Gauss-Jordan Elimination is a method for finding the inverse of any invertible matrix and for solving systems of linear equations. It is based on the three simplest row operations one may do on a matrix: Place two of the rows in opposite positions. A nonzero scalar multiplied by one of the rows
Since a similar version was described by Wilhelm Jordan in 1888 in his book "Handbuch der Vermessungskunde" independently of B. I. Clasen, who published something similar in the same year, the procedure known as Gauss-Jordan elimination for converting a matrix into reduced echelon form also includes the name Jordan.
This method, which is also known as row reduction, has two steps: forward elimination and back substitution. These two Gaussian elimination method steps differ from one another not by the operations that can be performed through them but rather by the outcome that is obtained.
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how ot see how fast membership is incresing initially calculus
The first derivative will give the slope of the function.
The second derivative will give you the point at which the function is increasing or decreasing the most rapidly.
If the 3rd derivative is negative, the rate of increase at the 2nd derivative point will be maximum; if positive, it will be a minimum.
A function's varied rate of change with respect to an independent variable is referred to as a derivative. When there is a variable quantity and the rate of change is irregular, the derivative is most frequently utilized. The derivative is used to assess how sensitive a dependent variable is to an independent variable (independent variable).
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Im doing Financial position throughout the life cycle homework and i would like to know Chuck And Wendy's investment assets and total assets?
Chuck and Wendy's investment assets is to use their gross assets as a base and then add in any net assets.
For example, if Chuck and Wendy have $100,000 in gross assets and $50,000 in net assets, their investment assets would be $120,000.
Chuck and Wendy's fixed assets and total wealth depend on many factors, including the level of risk they are willing to take, expected return, and overall financial stability.
For example, Chuck and Wendy's may have higher risk if they have a higher return on investment but still have $100,000 in total assets if their expected return is 5%.
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RST has vertices R(0,0), S(6,3), and T(,3-3). R'S'T' is the image of RST after a dilation with center (0,0) and scale factor 2/3 . What are the coordinates of point T'?
The coordinates of point T' is (2, -2)
How to determine the image pointA dilation is a transformation that changes the size of a figure but not its shape.
In a dilation with respect to the origin, a point (x, y) is transformed to a point (kx, ky) where k is a scale factor.
In this case, the point T (3, -3) is transformed under a dilation of 2/3 with respect to the origin.
So the image point is (kx, ky) = (3 * 2/3, -3 * 2/3) = (2, -2)
So the image point of T under a dilation of 2/3 with respect to the origin is (2, -2)
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You have been asked to find the value of f(-5) for the function
f(x)=3x2 -2x+5
Which of the following options is NOT a possible way to evaluate that function and find the correct answer?
A. Substitute (-5) wherever there is an x and solve using a calculator
B. Graph the equation and look at the table to find the y-value when x=-5
C. Graph the equation and find the y-value of the ordered pair when x=-5
D. See what x is when y=-5
The option D. See what x is when y = -5 is not a possible way to evaluate the value of f(-5).
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
The given function is f(x) = 3x² - 2x + 5.
f(-5) is actually the value of y or f(x) when x = -5.
By substituting -5 in place of x of the function, we will get f(-5).
Also we can find the value of f(-5) by graphing the function and finding the y value corresponding to the x value of -5.
Hence the way that is not possible is option D.
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Two brothers each purchase a new pair of hiking boots and two canteens. The hiking boots cost 34. 00 each. The total of their purchase wad 98. 0.
Write an equation and solve
The equation formed will be - cost × number of hiking boots + cost × number of canteens and the cost of canteens will be 15.
The equation that will be formed is -
Total cost of purchase = cost of hiking boots × number of hiking boots + cost of canteens × number of canteens
Keep the values in formula to find number of canteens, as it is the only value not provided in the question.
98 = 2×34 + 2× cost of canteens
Performing multiplication on Right Hand Side of the equation
98 = 68 + 2×cost of canteens
Rewriting the formula -
2× cost of canteens = 98 - 68
Performing subtraction on Right Hand Side of the equation
2× cost of canteens = 30
Cost of canteens = 30/2
Performing division on Right Hand Side of the equation
Cost of canteens = 15 each
Thus, the cost of canteens is 15 each.
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geometric mean of 3 and 17
Answer:
To calculate the geometric mean of two numbers, you would multiply the numbers together and take the square root of the answer.
3 * 17 = 51
The square root of 51 is: 7.141
7.141 is the geometric mean of 3 and 17.
Step-by-step explanation:
Hope it helps! =D
What is wrong with the following statement? "The results of the experiment do not agree with the theory, there's something wrong with the experiment"?
The statement "The results of the experiment do not agree with the theory, there's something wrong with the experiment" is wrong as it does not indulge any other reasons for the results of the experiment not agreeing with the theory.
This statement assumes that the experiment is always at fault and neglects the possibility that the theory may be incorrect or incomplete.
The outcome of an experiment can be influenced by various factors, such as measurement errors, incorrect experimental design, or limitations of the equipment used.
Thus, it is always important to consider multiple explanations before concluding that there is a problem with the experiment.
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You have two coupons for your favorite store. One coupon takes $100 off your purchase. The amount you spend after using this coupon can be represented by the function f ( x ) = x - 100 where x represents the initial cost of your purchase. The other coupon takes 30% off your purchase. The amount you spend after using this coupon can be represented by the function g ( x ) = 0 . 7 x where x represents the initial cost of your purchase. You want to use both coupons at once so the store decides to first take $100 off your purchase, then take 30% off your purchase. Write a function h ( x ) , in terms of the initial cost of your purchase, x , which represents the amount you will spend after both coupons are applied.
Work Shown:
x = initial cost before any discounts
x-100 = cost after taking off $100
0.7(x-100) = cost after taking 30% off from the previous value
Therefore, we end up with h(x) = 0.7(x-100)
Optionally you could distribute to get h(x) = 0.7x-70, but I think the first version of this is a bit more descriptive.
12. Mary and Jenny worked in a bookstore during the summer. Because of the experience, Mary's pay is 20% more than Jenny's. Last week, Mary worked for 30 hours and Jenny worked for 25 hours. Together they made $610. What are Mary's and Jenny's hourly rates?
Answer:
Let x be Jenny's hourly rate. Then Mary's hourly rate is x + 0.2x = 1.2x.
The total amount of money they earned for the hours they worked is the same, so we can set up the equation:
30x + 25(1.2x) = 610
Expanding the second term and solving for x:
30x + 30x = 610
60x = 610
x = 10.17
So Jenny's hourly rate is $10.17 and Mary's hourly rate is $12.20.