The model predicts that the number of stores will be at a minimum of approximately 8,123 stores in the year 2009, and will increase from there without bound.
What do you mean by term cubic function ?A cubic function is a type of polynomial function with the highest degree term being 3. In other words, a cubic function is a function of the form[tex]f(x) = ax^3 + bx^2 + cx + d[/tex], where a, b, c, and d are constants. The graph of a cubic function is a curve that can take on various shapes depending on the values of the coefficients.
b) To find the predicted number of stores in 2020, we need to find the value of the function when x = 20 (since 2020 is 20 years after 2000). We can substitute x = 20 into the function and evaluate:
[tex]y = 10.4x^3 - 403x^2 + 5585x - 8695\\y = 10.4(20)^3 - 403(20)^2 + 5585(20) - 8695\\y = 140,385[/tex]
Therefore, the model predicts that the number of stores in 2020 will be 140,385.
c) To determine if the number of stores ever decreases over the period of years ending in 2020 according to the model, we can look at the behavior of the function. The function is a cubic function with a positive leading coefficient, which means it will have a global minimum (i.e., the lowest point on the graph) and then increase without bound as x approaches positive or negative infinity.
To find the global minimum, we can take the derivative of the function and set it equal to zero:
[tex]y' = 31.2x^2 - 806x + 5585\\0 = 31.2x^2 - 806x + 5585[/tex]
x ≈ 8.68 or x ≈ 22.12
The first solution, x ≈ 8.68, is within the range of interest (2000 to 2020), so we can use it to find the global minimum:
[tex]y = 10.4x^3 - 403x^2 + 5585x - 8695[/tex]
y ≈ 8,123
Therefore, the model predicts that the number of stores will be at a minimum of approximately 8,123 stores in the year 2009, and will increase from there without bound. So according to the model, the number of stores never decreases over the period of years ending in 2020.
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The same item is on sale at two stores. Which one is the better price? 60% off $60 or 55% off %50
Answer:
The item when it is costs $50 and there is a 55% item, as the cost would be $22.50
Step-by-step explanation:
Whenever a discount is offered on a certain item, we can find the new price of the item using the formula.
[tex]N(P)=O-(P*O)[/tex], where N(P) is the new price (price when discount is applied), P is the percentage (converted to a decimal to simplify the problem), and O is the old price (price before discount is applied)
First store: Since the item costs $60 (O) at this store and there is a 60% discount (60% becomes 0.60 and is our P value), we can find the new price aka N(P):
[tex]N(0.60)=60-(0.60*60)\\N(0.60)=60-36\\N(0.60)=24[/tex]
Second store: For this store, our O value is $50, and our P value is 0.55 (55% becomes 0.55):
[tex]N(0.55)=50-(0.55*50)\\N(0.55)=50-27.50\\N(0.55)=22.50[/tex]
Thus, the second store has the better price
(6-x):(7-x)::(18-x):(22-x)
Using the property of proportionality for the equation (6-x) : (7-x) :: (18-x) : (22-x), then, x = ⁶/₇.
How did we get the value of x?Solving this problem by using the property of proportionality, which states that the ratio of the first two terms in a proportion is equal to the ratio of the last two terms. In this case:
(6-x) : (7-x) :: (18-x) : (22-x)
Solving for x, cross-multiply the ratios:
(6-x) x (22-x) = (7-x) x (18-x)
Expanding both sides:
132 - 28x + x² = 126 - 25x + x²
Simplifying, we get:
7x = 6
Therefore, x = ⁶/₇.
Thus, the solution to the proportion is:
(6-x) : (7-x) :: (18-x) : (22-x)
or
⁶/₇ : ¹/₇ :: ¹²/₇ : ¹⁶/₇
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Seven undergraduate students tagged A, B, C, D, E, F & G are to be allocated seven bed spaces in a hall in the University’s hostel. Student A doesnot want a bed next to student B because he is aware that student B snores. In how many ways can the bed spaces be allocated to them if the concern of student A is to be honoured?
By permutation and combination we can say there are 25200 ways to allocate the bed
What exactly are permanence and combination?Mathematical concepts like permutation and combination count the number of possible arrangements or choices for an object.
The quantity of possible arrangements of objects in a given order is referred to as a permutation.
Combination refers to the variety of possible selections of objects that are made without respect to their sequence.
The number of ways to distribute the seven students' beds in a way that ensures student A doesn't share a bed with student B is equal to the number of ways to distribute the six students' beds in a way that ensures student A doesn't share a bed with student B multiplied by two. (since there are two possible positions for student B).
The following formula can be used to determine how many options there are to distribute the six available beds among the students so that Student A does not have a bed next to Student B:
In this instance, seven students with the identifiers A, B, C, D, E, F, and G will each receive seven bed places in a dormitory at the university. Because he is aware that student B snores, student A does not want to share a bed with him. As a result, we can group students A and B together and arrange them in six different ways.
Then we can arrange the remaining students C, D, E, F and G in 5! ways. Therefore, the total number of ways to allocate bed spaces to them if the concern of student A is to be honored is 6! * 5! = 17,280 .
the bed spaces to seven students such that student A does not get a bed next to student B
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Someone help I have no idea how to do this, it would help if I could get a step by step
Answer: x=3
Step-by-step explanation:
shaded part is 5/6 of the full circle, so just make an equation.
5/6 pi r^2(formula to find area)=15/2 pi(area given)
cancel out pi and simplify
r^2=9
r=+-3 but cant be negative so r=3
Your parents are purchasing a mobile home for $89,000. The sales tax is 4.2%, they make a $3,000 down payment, and they have an average credit score. How much is the PRINCIPAL BALANCE after applying their first month’s payment of $925.67?
Secured Unsecured
Credit APR (%) APR (%)
Excellent 4.75 5.50
Good 5.00 5.90
Average 5.85 6.75
Fair 6.40 7.25
Poor 7.50 8.40
A. $89,249.80
B. $88,245.05
C. $88,912.03
D. $89,021.98
Two coins are tossed. Assume that each event is equally likely to occur.
a) Use the counting principle to determine the number of sample points in the sample space.
b) Construct a tree diagram and list the sample space.
c) Determine the probability that no tails are tossed.
d) Determine the probability that exactly one tail is tossed.
e) Determine the probability that two tails are tossed.
f) Determine the probability that at least one tail is tossed.
Question content area bottom
Part 1
a) There is/are --------- sample point(s) in the sample space.
a. There are 4 sample points in the sample space.
What are the probability values for the toss?a) There are 4 sample points in the sample space.
b) The tree diagram and sample space are:
HH (two heads)
HT (one head, one tail)
TH (one head, one tail)
TT (two tails)
c) The probability that no tails are tossed (two heads) is 1/4 or 0.25.
d) The probability that exactly one tail is tossed (HT or TH) is 1/2 or 0.5.
e) The probability that two tails are tossed is 1/4 or 0.25.
f) The probability that at least one tail is tossed (HT, TH, or TT) is 3/4 or 0.75.
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Given: mzA+m/B=m/B + mzC
Prove: m₂C=m/A
Write a paragraph proof to prove the statement.
We have proven that m∠C = m∠A.
We have,
We are given that m∠A + m∠B = m∠B + m∠C.
We want to prove that m∠C = m∠A.
Using algebra,
We can subtract m∠B from both sides of the equation, which gives us m∠A = m∠C.
This shows that the measure of angle A is equal to the measure of angle C, and therefore, m∠C = m∠A.
We can also use the transitive property of equality to show that
m∠A = m∠B, since m∠A + m∠B = m∠B + m∠C, which implies that
m∠A = m∠C.
Therefore,
We have proven that m∠C = m∠A.
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You are making scarves for presents. Each scarf needs 5/6 yd of fabric. How many yards of fabric do you need for 6 scarves?
The entire graph of the function g is shown in the figure below.
Write the domain and range of g as intervals or unions of intervals.
domain=
range =
For the given function 'g':
domain = (-4, -2) ∪ (1, 3]
range = (-5, 4]
If the function is defined as f(x) = y, then the values of x for which the value of function exists, the set of that values is said to be the domain of the function f.
If the function is defined as f(x) = y, then the set of all possible values of the function that is the set of all possible values of y is said to be the range of the function f.
Here given the graph of 'g'.
From the graph we can see that for -4 < x < -2 and 1 < x [tex]\le[/tex] 3 the function has graph.
So the domain = (-4, -2) ∪ (1, 3]
And it is clear that the value of y lies between -5 < y [tex]\le[/tex] 4.
So the range = (-5, 4].
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A boy has 30 spellings to learn.
12 words included an 5, 16 a T and 18 an E.
10 words had an E and a T, 6 words had an Sand aT and 5 words had an E and an S.
4 words had all three.
Probability that?
A • the first two spellings in the test both included only one of the three letters?
C• the first two spellings in the test both had an E and at least one other letter
Answer:
A
Step-by-step explanation:
true or false ? is (b^9)^3 = b^27
It is true that the product of the index [tex](b^9)^3 = b^2^7[/tex]
What is indices?Indices track asset performance in finance and specify array elements in math and programming; their use varies by subject. Different methods refer to list, vector, or matrix elements. Power law of indices: larger number or letter must match.
This can be expressed mathematically as am+n.
Additionally, there are several Laws of Indices that provide rules for simplifying calculations or expressions involving powers of the same base.
The given question is true or false is [tex](b^9)^3[/tex]= [tex]b^27(b^9)^3[/tex] = [tex](b^9)^3 = b^2^7[/tex]
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A quality expert can test 18 units in 32 minutes. If there are 400 units to be tested, about how long will it take to test them?
It will take about 711.12 minutes or approximately 11.85 hours to test all 400 units.
To find out how long it will take to test 400 units, we need to use the information given in the problem. We know that the quality expert can test 18 units in 32 minutes. We can use this information to find out how long it will take to test one unit.
First, we need to find out how many units can be tested in one minute:
18 units / 32 minutes = 0.5625 units per minute
This means that the quality expert can test 0.5625 units per minute. To find out how long it will take to test one unit, we can divide 1 by 0.5625:
1 / 0.5625 = 1.7778 minutes per unit
So it takes about 1.7778 minutes to test one unit. To find out how long it will take to test 400 units, we can multiply this value by 400:
1.7778 minutes per unit * 400 units = 711.12 minutes
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What is the domain of g(x)=log(7x−10)?
The domain of g(x) = log (7x - 10) is all real numbers greater than 10/7.
Set-builder notation: x > 10/7. Interval notation: (10/7,∞)
What is the domain of the function?Given the function in the question:
g(x) = log( 7x - 10 )
For the function g(x) = log (7x - 10), the domain consists of all the possible values of x that can be plugged into the function without resulting in an undefined expression.
Here, the logarithm (in this case, (7x - 10) must be greater than zero, since the logarithm of zero or a negative number is undefined in the real numbers.
So we set the argument of the logarithm to be greater than zero, and solve for x:
7x - 10 > 0
Solve for x
7x - 10 + 10 > 0 + 10
7x > 10
Dividing both sides by 7:
7x/7 > 10/7
x > 10/7
Therefore, the domain of g(x) = log (7x - 10) is x > 10/7
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PLEASE SOMEONE HELP ME THIS IS SO HARD. ILL GIVE 60 POINTS TO WHOEVER HELPS ME. PLEASE I GIVE BRAINLIEST
Answer:
B
Step-by-step explanation:
Vertex form is: y=a(x-h)²+k
Vertex would be (h,k)
Based on this, the only equation in vertex form is B
Answer:
Step-by-step explanation:
B is the easiest way to see vertex because that is the vertex form:
y=a(x-h)²+k where (h,k) is the vertex
Vertex (2, 27)
what is the mode of 14, 17, 21, 28, 40
Answer:
24
Step-by-step explanation:
14 + 17 + 21 + 28 +40 / 5
120 / 5
24
e) Write a proof to show AABC ~ ACFD.
f) What is the longest cart that can pass through the second doorway?
Explain.
Some of the factory's products are long fragile rods that are carried through
the door by hand. The first door is 72 inches west of the start of the second
door. Assume the rod has zero width and BA = 13 in.
Answer:
Step-by-step explanation:
no
Which of the following vectors represents u + v?
The vector u+v can be represented as < √85, -41.19° >, which is obtained by adding vector u marked on the y-axis from 0 to 6 and vector v marked on the x-axis from 0 to -7 on a coordinate plane.
To add vectors on the coordinate plane. The vector u is marked on the y-axis from 0 to 6, and the vector v is marked on the x-axis from 0 to -7.
To add them, we start at the tail of u and move horizontally to the left by 7 units (since v has a negative x-component) and then vertically up by 6 units (since u has a positive y-component) to reach the head of the resulting vector. This gives us the vector u+v.
So, the vector u+v can be represented as
Magnitude √(6^2 + 7^2) = √85
Direction atan(6/(-7)) = -41.19 degrees (measured counterclockwise from the positive x-axis)
Notation < √85, -41.19° >
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There are 8 blue marbles, 6 red marbles, 2 green marbles and 4 black marbles in a box. What is the probability that the marble is not green?
A) 92
B) 10
C) 85
D)20
We have 20 marbles in the bag. The probability of a marble that is not green is 20/20.
So the probability of the randomly that the marble is not green is 20/20 or just 20.
The expression 5(2) gives the number of leaves on a plant as a function
of the number of weeks since it was planted.
What does 2 represent in this expression?
Choose 1 answer:
B
The plant was planted 2 weeks ago.
There were initially 2 leaves on the plant.
The number of leaves is multiplied by 2 each week.
C: the number of leaves is multiplied by 2 each week
Step-by-step explanation
The proper expression ought to be 5(2) ^ t =5(2)^{t}
where t speak to the number weeks after it planted.
On the off chance that we put to the time(t) we are going know how numerous clears out at first are. The calculation will be:
5(2)^{t}= 5(2)^{0} =5
This appear that coefficient 5 decide how much the takes off at first are.
Let see how the number going for distinctive esteem of t. On the off chance that its 1 week after plant, the leaf will ended up:
5(2)^{t}= 5(2)^{1} = 10
At that point the number of takes off 2 weeks after planted will be:
5(2)^{t}= 5(2)^{2}= 20
The number keeps twofold each week since coefficient 2 speaks to the proportion of the development of the work and the proportion decides how much takes off duplicated each week.
So, the reply will be C.
A triangle has side lengths of (6.2x - 9.4y) centimeters, (6.2x - 2.5z)
centimeters, and (8.3z + 1.4y) centimeters. Which expression represents the
perimeter, in centimeters, of the triangle?
O-3.2xy +3.7xz +9.7yz
O 12.4x8y + 5.8z
O-10.5yz +20.7xz
O-1.1z + 12.4x - 1.1y
Submit Answer
The perimeter of the given triangle is 12.4x-8.0y+5.8z. Therefore, option C is the correct answer.
Given that, triangle has sides of lengths of (6.2x-9.4y) centimeters, (6.2x-2.5z) centimeters and (8.3z+1.4y) centimeters.
We know that, perimeter of triangle is sum of all the sides.
Now, perimeter = 6.2x-9.4y+6.2x-2.5z+8.3z+1.4y
= (6.2x+6.2x)+(-9.4y+1.4y)+(-2.5z+8.3z)
= 12.4x-8.0y+5.8z
Therefore, option C is the correct answer.
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Mrs Smith uses 5 lemons to make 2/3 gallon lemonade. How many gallons of lemonade can Mrs Smith make with 15 lemons?
Match the following:
1. Counts as Demand
2. Does Not Count as Demand
3. Demand Increases
4. Demand Decreases
What happens to the demand for
goods and services if the population in
town decreases?
Sue buys a new computer.
Adam likes the new cell phone, but
cannot afford it.
What happens to the demand for
jeans if the price of a popular brand of
jeans decreases?
Amanda’s new job has a 50% employer match on the first 4% of her salary contributed to her 401(k). How much was deposited in Amanda’s account if she makes $61,000 a year and she took advantage of the entire contribution match?
Answer:
$2,440 + $1,220 = $3,660
Step-by-step explanation:
If Amanda makes $61,000 a year, and she contributes 4% of her salary to her 401(k), that would be:
$61,000 x 0.04 = $2,440
Since her employer has a 50% match on the first 4% of her salary, they would contribute:
$2,440 x 0.5 = $1,220
The graph y=4f(x-5) is the graph of y=f(x)
Answer:The graph of y = 4f(x-5) is not the same as the graph of y=f(x) because it is a transformation of the function f(x) that involves a horizontal shift to the right and a vertical stretch by a factor of 4.
9. (a) The scale model of the rocket stood 54 inches high. What was the height of the actual rocket?
(b) Find the height of the actual rocket in feet.
10. The volume of the rocket in problem 9 is how many times the volume of the model?
The actual rocket height is 1080 inches and the height of the actual rocket is 90 feet.
How to calculate the valueIf the 1/20 scale model of the rocket stands 54 inches high, we can find the height of the actual rocket by multiplying the height of the model by 20:
Actual rocket height = 54 inches x 20 = 1080 inches
In order to convert inches to feet, we divide by 12:
Actual rocket height = 1080 inches / 12 = 90 feet
Therefore, the height of the actual rocket is 90 feet.
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The 1/20 scale model of the rocket stood 54 inches high What was the height of the actual rocket?
(b) Find the height of the actual rocket in feet.
Find the degree of the polynomial y = -3x^5 + 4x^4 + 2 + x^2
The degree of a polynomial is the highest exponent of the variable in the polynomial.
In this case, the degree of the polynomial y = -3x^5 + 4x^4 + 2 + x^2 is 5, because the highest exponent of x is 5 (in the term -3x^5). Therefore, the answer is 5.
Solve the following system of equations.
The solutions for the system of equations " 3x²-2y²+5=0 and 2x²-y²+2=0" are :
First Solution : x = 1, y = 2
Second Solution : x = 1, y = -2
Third Solution : x = -1, y = 2
Fourth Solution : x = -1 , y = 2.
In order to solve the system of equations 3x²-2y²+5=0 and 2x²-y²+2=0, we use substitution method;
From the second equation, we solve for y² in terms of x²:
The second equation is : 2x² - y² + 2 = 0;
We get, y² = 2x² + 2
Substitute this expression for y² into the first equation:
We get,
3x² - 2(2x² + 2) + 5 = 0
3x² - 4x² - 4 + 5 = 0
-x² + 1 = 0
x² = 1
We get, x = ±1
Substitute these values of x into the equation for y²:
y² = 2x² + 2
For x = 1, y² = 4,
Which means the solution set is (1,2) and (1,-2),
For x = -1, y² = 4
the solution set is (-1,2) and (-1,-2).
Therefore, the solutions to the system of equations are (1, 2), (1,-2), (-1,2) and (-1, 2).
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Someone help i really need help with this
Step-by-step explanation:
step A is incorrect.
-40/5 does not equal to -40/-5.
-40/-5 is equal to 40/5 as we can simplify the negative 1 out.
Answer:
The correct answer is step A
100 Points! Algebra question. Describe the scatter plot and an appropriate scale for the data set below. Photo attached. Thank you!
Note that the scatter plot (attached) for the given data is described below.
What is the description of the attached scatter plot?The scatter plot for the given data set shows a moderately strong negative linear relationship between x and y. The data points appear to form a somewhat linear pattern, indicating that there is a linear association between the variables.
The scatter plot suggests that as the x values increase, the corresponding y values decrease.
An appropriate sale for this data set would be a linear regression, which can provide a mathematical model for predicting y values based on x values.
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5 divided by -3 minus 3 times the square root of 3
The result of the operation that we have done here is -5√3.
How do you convert it to equation?We know that one of the most important things that we have to do in mathematics is that we have to convert word equations into mathematical equations and this is quite critical in how we can be able to work it so as to get the equation that we are looking for.
We now have that;
5/-3 * 3 * √3
5/-1 * √3
-5* √3
-5√3
We can see that after the computation of the word problem that we have here, the result is -5√3
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