The required function that describes the area A in terms of x is:
C.) A(x) = 2x² + 9x + 4
The area of a rectangle is given by the formula:
A = length x width
In this case, the length is x+4 feet and the width is 2x+1 feet. So, we have:
A = (x+4)(2x+1)
Expanding the expression on the right side, we get:
A = 2x² + 9x + 4
Thus, the function that describes the area A in terms of x is:
C.) A(x) = 2x² + 9x + 4
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To test the hypothesis that 55% of those families who plan to purchase a vacation residence in Florida want a condominium, the null hypothesis is π = 0.55 and the alternate is π ≠ .55. A random sample of 400 families who planned to buy a vacation residence revealed that 228 families want a condominium. To perform the hypothesis testing, we need to satisfy two things. The first thing is to have a binomial distribution in the question, which is the number of families who planned to buy condominiums in the sample. What is the other requirement we need to meet?
The answer of the given question based on hypothesis is ,(a) the number of family is the sample size of 400 satisfies this requirement. (b) that the sample size should be sufficiently large.
What is Hypothesis?In mathematics, a hypothesis is statement or proposition that is assumed to be true for sake of argument or investigation, but has not been proven or demonstrated to be true. It is an educated guess or prediction that is based on previous observations or knowledge, and is used to guide further investigation or experimentation.
The other requirement that we need to meet to perform the hypothesis testing is that the sample size should be sufficiently large. A general rule of thumb is that the sample size should be at least 10 times larger than the number of successes and 10 times larger than the number of failures.
In this case, since we have 228 successes (families who want a condominium) and 172 failures (families who do not want a condominium), the sample size of 400 satisfies this requirement.
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18. Yesterday the Rockville Corporation instituted a 2-for-1 stock split. Before the split, the market share price was $63.44 per share and the corporation had 2.3 billion shares outstanding. What was
the pre-split market cap for Rockville?
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Thus, the pre-split market cap for Rockville corporation is found to be - $145,912,000,000.
Explain about the pre-split market cap:Stock splits have no impact on the market capitalization as a whole. Just the share price and total number of outstanding shares are impacted. Overall, we have doubled the number of shares outstanding while halving the share price, having no impact on the market capitalization.
The number of shares of a firm grow when it announces a stock split, but the market capitalization stays the same. Although existing shares were split, the underlying value was not altered. Price per share decreases as the number of shares rises.
Given data:
Number of shares = 2.3 billion = 2,300,000,000
Market price = $63.44
Pre-split market cap = Number of shares x Market price
Pre-split market cap = 2,300,000,000 x $63.44
Pre-split market cap = $145,912,000,000
Thus, the pre-split market cap for Rockville corporation is found to be - $145,912,000,000.
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Complete Question:
Yesterday the Rockville corporation instituted a 2-for-1 split. Before the split, the market share price was $63.44 per share and the corporation had 2.3 billion shares outstanding. ?
What was the pre-split market cap for Rockville?
Find the rate of change on the interval [0, 3] for the function below
A. 7/3
B.3/7
C.2
D.7
The average rate of change of the function on the interval [0,3] is given as follows:
A. 7/3.
How to obtain the average rate of change?The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.
The numeric values for the function are given as follows:
When x = 0, y = 1.When x = 3, y = 8.Hence the average rate of change is given as follows:
r = (8 - 1)/(3 - 0)
r = 7/3.
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13
Use the drawing tools to form the correct answer on the graph.
Graph the composite function (f(x)).
f(x) = -2x- 5
g(x) =x - 1
Drawing Tools
Select
Point
Click on
The graph of the composition of functions is on the image at the end.
How to graph the composite function?Here we want to graph the composition of the functions g(x) and f(x), where:
f(x) = -2x - 5
g(x) = x - 1
The composition:
g(f(x)) will give:
g(f(x)) = f(x) - 1 = -2x - 5 - 1 = -2x - 6
So it is just a linear function, basically it is a translation of 1 unit down of f(X), the graph of this composition is on the image at the end.
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Find the 20th term of A(n) = 4n3-3
The 20th term of the sequence A(n) = [tex]4n^3 - 3[/tex]is 31997.
What are sequence?A sequence is an ordered set of numbers that is often produced using a formula or rule.
Terms refer to the individual numbers in a series. One infinite series of odd integers is the sequence 1, 3, 5, 7, 9,..., where each term is created by adding 2 to the term before it.
To find the 20th term of A(n) = 4n^3 - 3, we can substitute n = 20 into the equation:
[tex]A(20) = 4(20)^3 - 3[/tex]
[tex]= 4(8000) - 3[/tex]
[tex]= 32000 - 3[/tex]
[tex]= 31997[/tex]
Therefore, the 20th term of the sequence A(n) = [tex]4n^3 - 3[/tex]is 31997.
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Write an explicit formula for an, the nth term of the sequence 30, 35, 40
Answer:
The sequence is increasing by 5 at each step. So, we can write:
a1 = 30
a2 = 30 + 5 = 35
a3 = 30 + 25 = 40
a4 = 30 + 35 = 45
a5 = 30 + 4*5 = 50
We notice that the nth term is given by:
an = 30 + (n-1)5
So, the explicit formula for the nth term is:
an = 25n + 5
PLEASE HELPPPP LOOK AT THE PICTURE BELOW
Answer:
a) 29.0%
b) 25.2%
Step-by-step explanation:
denote T: total number of MM; G: green MM; R: red MM
a)
(G)/(T) * (G-1)/(T-1)
(32)/(27+32) * (32-1)/(27+32-1)
=(32/59) *(31/58)
=0.289888953
b)
(R)/(T) * (G)/(T-1)
(27)/(27+32) * (32)/(27+32-1)
=(27/59) * (32/58)
=0.252483927
The weights X of an animal are distributed according to the
probability distribution shown.
What is the probability that the animal's weight will be less than
151 pounds?
O 0.25
O 0.50
O 0.60
O 0.75
The probability that the animal's weight will be less than 151 pounds is 0.50.
The correct option is B.
What is the probability that the animal's weight will be less than 151 pounds?Since the given probability distribution ranges from 148 to 152, and we need to find the probability that the animal's weight will be less than 151 pounds, we can add the probabilities corresponding to the weights less than 151.
From the distribution, we see that the probability of the animal's weight being less than 151 pounds is 0.2 + 0.3 = 0.5.
Therefore, the answer is O 0.50.
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d. tan 0 = 0.7536
Hypotenuse = 29 miles
Opposite side?
Based on the lengths shown in the parabola below, what is the distance from point A to the directrix?
The distance from Point A to the directrix can be found to be 6.
How to find the distance to the directrix ?For any point on a parabola, the distance to the focus is equal to the distance to the directrix. This property is what defines a parabola. This is the relationship between the distance from a point on a parabola to the focus and the distance from that point to the directrix.
So, if the distance between Point A on the parabola and the focus is 6, then the distance from Point A to the directrix is also 6.
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the angle of depression of a point on the ground from the top of a hill 60 if the distance of the point from the foot of the hill is 35m, calculate the height of the hill.
The height of the hill is approximately 60.62 meters.
What is height?Height often refers to the perpendicular distance between the base of a geometric shape (such as a triangle, rectangle, or cylinder) and its highest point.
According to question:To solve this problem, we can use the tangent function, which relates the opposite and adjacent sides of a right triangle to the tangent of an angle.
Let h be the height of the hill, and let d be the horizontal distance from the foot of the hill to the point on the ground. Then, we can draw a right triangle with the height of the hill as the opposite side, the distance d as the adjacent side, and the angle of depression (60 degrees) as the angle between the hypotenuse and the adjacent side.
Using the tangent function, we can write:
tan(60) = h / d
We know that d = 35 meters, so we can substitute that into the equation and simplify:
tan(60) = h / 35
We can solve for h by multiplying both sides by 35 and simplifying:
h = 35 * tan(60)
Using a calculator, we find:
h ≈ 60.62 meters
Therefore, the height of the hill is approximately 60.62 meters.
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Why is this sales projection graph misleading? (is it the 2 dashes in the y-axis?)
A. the vertical axis is an exaggeration of the profit the company made because of the break in the axis(2 dashes)
B. the X axis is the problem. the gap between each year may be missing information
C. a stem and leaf plot would be better for this
D. a circle graph would be better
Choice A correctly describes the problem with the graph and the misleading nature of the break on the vertical axis
What is a vertical axis called?The vertical axis is usually called the y-axis. The point where the x- and y-axis intersect is called the origin.
The most likely reason this sales forecast chart is misleading is a break or gap on the vertical (y) axis.
This type of truncation is known as a broken axis, where the axis is intentionally truncated or broken to exaggerate or emphasize differences in data points. In this case, the break on the y-axis makes the profit values larger than they really are and can cause the data to be misinterpreted.
By breaking the y-axis, small changes in profit values can appear much larger than they actually are, creating a false scale or magnitude. This can be particularly misleading if the reader is not aware of the discontinuity of the axis and assumes that the scale is continuous. Choice A correctly describes the problem with the graph and the misleading nature of the break on the vertical axis. Option B is not directly related to the graph problem, although the absence of data on the x-axis can also lead to a misinterpretation of the data. Choices C and D offer alternative chart types that could be used, but they do not solve the specific problem of the given sales forecast chart.
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Graph the system below and write its solution.
y = 1/3x+1
-2x+y=-4
Note that you can also answer "No solution" or "Infinitely many" solutions.
The solution to the system is the point (-3, 0).
Define Infinitely many solutions ?
Infinitely many solutions is a term used in mathematics to describe a situation where a system of equations or inequalities has an unlimited number of solutions. In other words, there are an infinite number of values for the variables that satisfy all the equations or inequalities in the system. This can occur when the equations or inequalities are redundant or when they represent lines or curves that overlap or are parallel.
Given equation:
y = 1/3x + 1
y = 2x - 4
Setting the two expressions for y equal to each other, we get:
1/3x + 1 = 2x - 4
Simplifying this equation, we get:
5/3x = -5
Multiplying both sides by 3/5, we get:
x = -3
Substituting this value back into either equation, we get:
y = 1/3(-3) + 1 = 0
Therefore, the solution to the system is the point (-3, 0).
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What is the purpose of headings in a table?
A. To help users understand the categories of information found in
each column and row
B. To identify the specific source of the information or data found in
the columns
C. To provide detailed and colorful information that is easy to
understand
OD. To briefly describe what information is included in the table as a
whole
SUBMIT
The purpose of headings in a table is option A. To help users understand the categories of information found in each column and row
Headings in a table.A table is a method of classifying a given set of information into appropriate number of columns with respect to their individual class called headings.
Headings are used in the categorization of a set of information into a presentable form of columns called a table. It thus helps to identify a the source of an information as presented in the table.
Therefore, the purpose of headings in a table is that given in option A. That is; To help users understand the categories of information found in each column and row.
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A Kenkey seller operates in two markets. In market 1, research indicates that the price elasticity of demand is (-) 0.25 while that for market 2 is (-) 2.5. The seller has decided to reduce the price of Kenkey by 10% this month in both markets.
i. Calculate the percentage change in quantity demand for Kenkey in both markets. Explain the result of the Kenkey seller’s action on the total revenue for both markets.
ii. Compute the marginal revenue for both markets if the price charged in market 1 and 2 are GH¢ 2 and GH¢ 1.50 respectively.
iii. As the firm’s adviser, suggest an alternative pricing strategy to the Kenkey seller.
In market 1, the quantity demanded will increase by 2.5% while in market 2, the quantity demanded will increase by 25%.
How to calculate the value% Change in Quantity Demanded (Market 1) = (-) 0.25 * (-10%) = 2.5%
% Change in Quantity Demanded (Market 2) = (-) 2.5 * (-10%) = 25%
The negative sign for price elasticity of demand means that demand is inversely related to price.
For market 1:
Price = GH¢ 2
Quantity demanded = Q1
Change in price = -10% x GH¢ 2 = -GH¢ 0.20
Change in quantity demanded = 2.5% x Q1
Change in revenue = GH¢ 2.00 x 2.5% x Q1 = GH¢ 0.05 Q1
Marginal revenue = Change in revenue / Change in quantity demanded
Marginal revenue = (GH¢ 0.05 Q1) / (2.5% x Q1)
Marginal revenue = GH¢ 2.00
For market 2:
Price = GH¢ 1.50
Quantity demanded = Q2
Change in price = -10% x GH¢ 1.50 = -GH¢ 0.15
Change in quantity demanded = 25% x Q2
Change in revenue = GH¢ 1.50 x 25% x Q2 = GH¢ 0.375 Q2
Marginal revenue = Change in revenue / Change in quantity demanded
Marginal revenue = (GH¢ 0.375 Q2) / (25% x Q2)
Marginal revenue = GH¢ 1.50
iii. An alternative pricing strategy for the Kenkey seller could be to implement a tiered pricing system based on the price elasticity of demand in each market.
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I know that x^2 + y^2 in cartesian coordinates is r^2 in polar coordinates.
However, in my problem, I’m given x^2 + z^2. On a graph, it still forms a circle, except on a different plane than just x^2 + y^2.
Is it okay if I simplify x^2 + z^2 in my work to just r^2, or is that wrong?
Yes, it is okay to simplify x^2 + z^2 to r^2 in your work. This is because in polar coordinates, r represents the distance from the origin to a point, regardless of which plane the point is on.
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[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]
[tex]\textcolor{blue}{\small\textit{If you have any further questions, feel free to ask!}}[/tex]
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Select the postulate of equality or inequality that is illustrated. If 5 = x + 2, then x + 2 = 5, Thank you
If you put all the sunflowers together end to end, what would be the total length of all the sunflowers?
inches
Using multiplication, the total length of all the sunflowers in the garden is 1,260 inches.
What is multiplication?Multiplication is one of the four basic mathematical operations, including addition, subtraction, and division.
Multiplication operation involves the multiplicand, the multiplier, and the product.
The total number of sunflowers in the garden = 210
The length of each sunflower = 6 inches
The total length of all the sunflowers = 1,260 inches (210 x 6)
Thus, based on multiplication operation, the total length of the sunflowers in the garden can be stated to be 1,260 inches.
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Question Completion:Assume that each sunflower measures 6 inches in length and there are 210 sunflowers in the garden.
The Tasty as Pi Bakery has two locations! Each location offers the same flavors. Both locations display one pie of each flavor in a rectangle.
The downtown location has 4 rows in its display. The uptown location has 6 rows in its display. If one of the locations has a square display, how many pies are in each of the other location's rows?
The number of pies in each of the other locations rows are 32 and 18.
Given that, the downtown location has 4 rows in its display. The uptown location has 6 rows in its display.
At the downtown location, there would be 8 pies in each row since the display is a 6×4=32 rectangle.
At the uptown location, there would be 3 pies in each row since the display is a 6×18=18 rectangle.
Therefore, the number of pies in each of the other locations rows are 32 and 18.
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7x - 2y - 4z - (- 2x + 3y - 5z)
Answer: 9x - 5y + z
Step-by-step explanation:
A snack company can pack 16 granola bars in a box. How many boxes are needed for 800 granola bars?
Answer: 50
Step-by-step explanation:
Divide the amount of granola bars by 800
800dividedby16=50
If x
and y
are right angles, then x
and y
are supplementary angles.
saline IV fluid cost 64.20 for 24 for 10000 ml bags from a supplier, another offers 2.00 a bag for 500 ml. hospital uses 10000 a month, which supplier offers best price
The supplier offering 2.00 a bag for 500 ml is offering the best price. This is because the cost per bag is lower than the cost of the 10000 ml bag, and the total cost for the hospital is significantly lower.
What is IV fluid?IV fluid is a sterile solution usually composed of water and electrolytes. It is administered intravenously, meaning it is delivered directly into a vein using a syringe or an IV bag.
To calculate this, divide the cost of the 10000 ml bag by the number of 500 ml bags it contains.
This can be done by dividing 64.20 by 20,i.e.,
64.20/20= 3.21
This means that the cost of one 500 ml bag is 3.21.
This is significantly lower than the 2.00 per bag offered by the other supplier.
To figure out the total cost for the hospital, multiply the number of bags needed by the cost per bag.
For the hospital, 10000 ml of IV fluid is used each month, so the number of bags needed would be 20.
Multiplying 20 by 2.00, 20*2= 40, gives a total cost of 40.00 per month. This is significantly lower than the cost of the 10000 ml bag at 64.20.
Therefore, the supplier offering 2.00 a bag for 500 ml is offering the best price.
This is because the cost per bag is lower than the cost of the 10000 ml bag, and the total cost for the hospital is significantly lower.
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use your own words to interpret the following numbers sentence ñ²+5
The numbers sentence has an interpretation of the square of a number n is added to 5
Interpreting the numbers sentenceFrom the question, we have the following parameters that can be used in our computation:
n² + 5
The above sentence means that
The square of a number n is added to 5
Also, in the numbers sentence;
The variable is n
Hence, the interpretation is the square of a number n is added to 5
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1. Simplify the expression.
Answer:x^2 * 5/y^5
Step-by-step explanation:
Question is below ⬇️.
22 inches is the measure of the unknown side ZW
Properties of a parallelogramGiven a parallelogram WXYZ, since the opposite sides of a parallelogram is equal, hence WX = YZ
Given the following
WX = 8x + 2
YZ = 5x + 11
Substitute
8x + 2 = 5x + 11
8x - 5x = 11 - 2
3x = 9
x = 3
Determine the measure of ZW
ZW = XY = 6x + 4
ZW = 6(3) + 4
ZW = 18 + 4
ZW = 22
Hence the measure of the side ZW is 22 inches
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calculate the area of the triangle: 7m 4m
Answer:
14m^2
Step-by-step explanation:
What is area?Area is the space taken up by a two dimensional object.
The formula is (1/2) base times height for only triangles. Other shapes or objects use different formulas.
7m * 4m = 28m^2
28m^2 * 1/2
28m^2/2
Divide 2 into 28, which is 14. And two variables multiplied by each other become variable squared or to the second power.
14m^2
So, the area of the triangle is 14m^2.
What is an ecosystem
Answer:
An ecosystem is a biological community of interacting organisms (including animals, plants, and microorganisms) and their physical environment (such as air, water, and soil).
Step-by-step explanation:
Solve for x to make A||B
Answer: x = 50
Step-by-step explanation:
In the given image, the alternate interior angles are equal. Therefore, 80 + x = 180 - 50 (since straight angles measure 180 degrees). Simplifying this equation, we get 130 + x = 180, which gives us x = 50 degrees. Thus, A||B when x = 50 degrees.
A company estimates that 0.4% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $150.
If they offer a 2 year extended warranty for $11, what is the company's expected value of each warranty sold?
Answer:
To calculate the company's expected value of each warranty sold, we need to consider the probability of a product failing within 2 years of the purchase, with and without the extended warranty.
Without the extended warranty:
- Probability of product failure = 0.4%
- Replacement cost = $150
Therefore, the expected cost of a product failure without the extended warranty is:
0.4% x $150 = $0.60
With the extended warranty:
- Probability of product failure = 0% (since the warranty covers the 2-year period)
- Cost of the warranty = $11
Therefore, the expected cost of a product failure with the extended warranty is:
0% x $150 = $0
$11 (warranty cost) + $0 = $11
To calculate the overall expected value, we need to weigh these two scenarios by their probabilities:
Expected value = (probability of product failure without warranty) x (expected cost without warranty) + (probability of product failure with warranty) x (expected cost with warranty)
Expected value = (0.4% x $150) + (99.6% x $11)
Expected value = $0.60 + $10.96
Expected value = $11.56
Therefore, the company's expected value of each warranty sold is $11.56.
