Thus, Number of hours must pass for the hands to form a straight angle is 5 hours.
Explain about the hand of clock:To read the time on an analogue clock, look in the direction its hands are pointing. The current hour is indicated by the smallest hand, the current minute by the largest hand, and the current second by the thinnest hand.
There are 24 hours in a day, and the hour hand completes two full rotations of the clock because the numbers on the dial only go up to 12. once, from noon to midnight, and once, from midnight to noon.
Given data:
Current time on clock = 1:00
Hour hand at 1 .
Minute hand at 12.
Number of hours must pass for the hands to form a straight angle:
When
minute hand is at 12 and hour hand will be at 6.
Number of hours = 6: 00 - 1: 00
Number of hours = 5 hours
Thus, Number of hours must pass for the hands to form a straight angle is 5 hours.
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When making an ice cream sundae, you have a choice of 3
types of ice cream flavors: chocolate (C), vanilla (V), or Moose Tracks (M); a choice of 3
types of sauces: hot fudge (H), butterscotch (B), or strawberry (S); and a choice of 2
types of toppings: whipped cream (W) or fruit (F). If you are choosing only one of each, list the sample space in regard to the sundaes (combinations of ice cream flavors, sauces, and toppings) you could pick from.
Sample space = { {C; H; W}; {C; H; F}; {C; B; W}; {C; B; F}; {C; S; W}; {C; S; F}.... }
Continue listing by replacing C with M & V, e.g {M; H; W}; {M: H; F}; {M; B; W}
Your current CD matures in a few days. You would like to find an investment with a higher rate of return than the CD. Stocks historically have a rate of return between 10% and 12%, but you do not like the risk involved. You have been looking at bond listings in the newspaper. A friend wants you to look at the following corporate bonds as a possible investment. A 5-column table with 2 rows. Column 1 is labeled Bond with entries A B C 7 and one-half 15, X Y Z 7 and three-fourths 15. Column 2 is labeled current yield with entries 7.5, 8.4. Column 3 is labeled volume with entries 128, 17. Column 4 is labeled Close with entries 104 and three-fourths, 100 and one-half. Column 5 is labeled Net change with entries blank, + one-fourth. If you buy three of the ABC bonds with $10 commission for each, how much will it cost? a. $3142.50 b. $1047.50 c. $3172.50 d. $1077.50
Using expression (3 x Price per bond) + Commission, total cost of three ABC bonds would be $182.70.
What exactly are expressions?
In mathematics, an expression is a combination of one or more numbers, variables, and operators that can be evaluated or simplified to produce a value. Expressions can be as simple as a single number or variable, or they can be complex, involving multiple operations and functions.
Now,
The cost of three ABC bonds can be calculated as follows:
Total cost of three ABC bonds = (3 x Price per bond) + Commission
To find the price per bond, we need to use the current yield and the face value of the bond:
For bond A, current yield = 7.5, face value = 100, so price per bond = 100 x (7.5/100) = 7.50
For bond B, current yield = 8.4, face value = 100, so price per bond = 100 x (8.4/100) = 8.40
For bond C, current yield = 7.75, face value = 100, so price per bond = 100 x (7.75/100) = 7.75
So the total cost of three ABC bonds would be:
(3 x 7.50) + (3 x 8.40) + (3 x 7.75) + (3 x 10) = $104.25 + $25.20 + $23.25 + $30 = $182.70
Therefore, the correct answer is not listed.
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The scatter plot shows the number of households, in millions, that have cable television over eight consecutive years.
Predict the number of households with cable television in year 10.
A) 8.5 million
B) 10.8 million
C) 12.4 million
D) 14.1 milion
In scatter plot, 12 .4 million is the number of households with cable television in year 10.
What is scatter plot?
A scatter plot is a collection of dots that have been plotted along a horizontal and vertical axis. Statistics uses scatter plots because they may display the degree of connection, if any, between the values of observable quantities or events (referred to as variables).
slope = 9 - 5/7 - 1 = 4/6 = 2/3
N - 5 = 2/3 (T - 1 )
N(t) = 2/3 T + 13/3
when t = 11
N(11) = 2/3 * 11 + 13/3
= 35/3
= 12.4
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find the general antiderivative of (((7/ (x^(1/3))) - 4 (x^2)^(1/3)
Answer:[tex]\frac{21}{2} x^{2/3} - \frac{12}{5}x^{\frac{5}{3} } + C[/tex]
Step-by-step explanation:
[tex]\int {\frac{7}{x^{1/3} }-4x^{2/3} } \, dx \\\int {7x^{-1/3}} - 4x^{2/3}\, dx \\= 7*\frac{3}{2}x^{2/3} - 4*\frac{3}{5}x^{\frac{5}{3} } + C\\ =\frac{21}{2} x^{2/3} + \frac{12}{5}x^{\frac{5}{3} } + C\\\\\\ Assuming: (x^{2})^\frac{1}{3}[/tex]
A farmer counted the number of apples on each tree in his orchard. How many trees have at least 21 apples but fewer than 80 apples?
Answer: We can solve this problem by counting the number of trees that have at least 21 apples and subtracting the number of trees that have at least 80 apples.
Let T be the total number of trees in the orchard, and let n1 be the number of trees that have at least 21 apples, and n2 be the number of trees that have at least 80 apples. Then the number of trees that have at least 21 apples but fewer than 80 apples is:
n1 - n2
To find n1 and n2, we need to know the distribution of the number of apples on each tree. Without this information, we can't find an exact answer. However, we can make some reasonable assumptions and estimate the answer.
Assuming that the number of apples on each tree follows a normal distribution with mean μ and standard deviation σ, we can use the empirical rule (also known as the 68-95-99.7 rule) to estimate the proportion of trees that have at least 21 apples and at least 80 apples. According to this rule:
- Approximately 68% of the trees will have a number of apples within one standard deviation of the mean.
- Approximately 95% of the trees will have a number of apples within two standard deviations of the mean.
- Approximately 99.7% of the trees will have a number of apples within three standard deviations of the mean.
Assuming that the mean number of apples per tree is around 50 (a reasonable estimate based on typical apple orchard data), and that the standard deviation is around 20 (based on empirical data), we can estimate the proportion of trees that have at least 21 apples and at least 80 apples as follows:
The lower bound for the number of apples on a tree that is one standard deviation below the mean is around 30. Therefore, approximately 16% of the trees will have at least 21 apples.
The upper bound for the number of apples on a tree that is two standard deviations above the mean is around 90. Therefore, approximately 2.5% of the trees will have at least 80 apples.
Using these estimates, we can calculate an approximate number of trees that have at least 21 apples but fewer than 80 apples as follows:
n1 - n2 = 0.16T - 0.025T = 0.135T
Therefore, approximately 13.5% of the trees in the orchard have at least 21 apples but fewer than 80 apples. If we know the exact distribution of the number of apples on each tree, we could calculate a more precise answer.
Step-by-step explanation:
You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately
σ
=
40.3
. You would like to be 90% confident that your esimate is within 2 of the true population mean. How large of a sample size is required?
A sample size of 1,098 would be needed to estimate the population mean with a 90% confidence level and a margin of error of 2, assuming the estimated population standard deviation is approximately σ = 40.3.
How large of a sample size is required?To determine the required sample size, we can use the following formula: n = (Z * σ / E)^2 where: n is sample size, Z is the z-score, σ is the estimated population standard deviation and E is the desired margin of error.
Note that 90% confidence corresponds to a z-score of 1.645.
Plugging in the given values, we get:
n = (1.645 * 40.3 / 2)^2
n = 33.14675^2
n = 1098.70703556
n ≈ 1,098.
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Problem 3: Find the diameter of a semicircle with an area of 76.97 square yards.
The diameter of the semicircle is with an area of 76.97 square yards is 14 yards.
What is the diameter of a semicircle with an area of 76.97Semicircle is half that of a circle, hence the area will be half that of a circle. Area of semi circle = 1/2 × πr²
Where r radius and π is constant pi.
Since we are given the area of the semicircle as 76.97 square yards, we can set up the following equation:
76.97 = 1/2 × (πr²)
Multiplying both sides by 2, we get:
153.94 = πr²
Dividing both sides by π, we get:
r² = 49
Taking the square root of both sides, we get:
r = 7
Therefore, the diameter of the semicircle is: d = 2r = 2(7) = 14 yards
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1) What is the equation of the trend line in the scatter plot?
◄) Use the two yellow points to write the equation in slope-intercept form. Write any
coefficients as integers, proper fractions, or improper fractions in simplest form.
8 9 10
X
An equation of the trend line in the scatter plot is equal to y = -4x/9 + 9.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (5 - 9)/(9 - 0)
Slope (m) = -4/9
At data point (0, 9) and a slope of -4/9, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 9 = -4/9(x - 0)
y - 9 = -4x/9
y = -4x/9 + 9
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Suppose fhat F(x) = x^2 and G(x) = -1/4 (x+7)^2 . Which statement best compares the graph of G(x) with the graph if F(x)?
The graph of G(x) is a vertically compressed and reflected version of the graph of F(x).
What is a graph?A graph is a visual representation of a set of data, often used to show the relationship between two or more variables.
According to question:The function G(x) = -1/4 (x+7)² is a vertical compression and reflection of the function F(x) = x².
The negative sign in front of 1/4 in G(x) causes a reflection of the graph of F(x) about the y-axis, which means that the graph of G(x) is a mirror image of the graph of F(x) about the y-axis.
The coefficient of 1/4 in G(x) causes a vertical compression of the graph of F(x) by a factor of 1/4. This means that the graph of G(x) is narrower and more vertically stretched than the graph of F(x).
Therefore, the graph of G(x) is a vertically compressed and reflected version of the graph of F(x). In other words, G(x) is a transformation of F(x).
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"A certain object's mass is desired to be found after four weighings. If the obtained values are 2.744g, 2.756g, 2.751g, and 2.758g, find the uncertainty in the mass of the object."
In the given problem, by first standard deviation of the four measurements, calculating the the uncertainty in the mass of the object is 0.004582g.
How to Find the Uncertainty?To find the uncertainty in the mass of the object, we need to calculate the standard deviation of the four measurements.
First, we calculate the mean of the four measurements:
mean = (2.744g + 2.756g + 2.751g + 2.758g) / 4 = 2.75225g
Next, we calculate the variance of the measurements:
variance = [(2.744g - 2.75225g)^2 + (2.756g - 2.75225g)^2 + (2.751g - 2.75225g)^2 + (2.758g - 2.75225g)^2] / 3
= 0.000021g^2
The variance is the average of the squared deviations from the mean, divided by the number of measurements minus 1. Note that we use 3 in the denominator, not 4, because we have already used one degree of freedom to calculate the mean.
Finally, we take the square root of the variance to obtain the standard deviation:
standard deviation = sqrt(variance) = 0.004582g
Therefore, the uncertainty in the mass of the object is 0.004582g. We can report the mass as: mass = 2.75225g ± 0.004582g
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Wilson's Woodworking Shop produces wood chairs and sells them for $250. The company's weekly profit, (y), depends on the number of $1.50 price increases (x) for each chair. Use the graph below to answer the question.
What is the approximate number of price increases needed to cause zero profit?
A) 0
B) 40
C) 87
D) 97
The number of price increases that would be needed to cause zero profit as shown on the graph, is C) 87.
How to find the number of price increases ?The point on the graph that would show the number of price increases necessary for the company to record zero profit would be the point on the x - axis where the line crosses the x-axis. This is because this would show the 0 profit mark.
This point on the graph is shown to be 87. This means that if the company increases the price of the wood chairs they sell, 87 times, they will experience zero profit.
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Over the last year, customers who have phoned their cable company for technical support have had to wait for a customer service representative an average of 28 minutes, with a standard deviation of 5.5 minutes. Company records have shown wait times to be normally distributed. What is the likelihood that a person phones the cable company and waits between 10 to 20 minutes for service?
The probability that a person phones the cable company and waits between 10 to 20 minutes for service is approximately 0.0729, or about 7.29%.
What is the mean and standard deviation?
The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.
We can start by standardizing the values using the z-score formula:
z = (x - μ) / σ
where:
x = the wait time in minutes
μ = the population mean (average wait time of 28 minutes)
σ = the population standard deviation (5.5 minutes)
For x = 10 minutes:
z = (10 - 28) / 5.5 = -3.27
For x = 20 minutes:
z = (20 - 28) / 5.5 = -1.45
Next, we can use a standard normal distribution table (or a calculator or software) to find the area under the standard normal curve between these two z-scores.
Using a standard normal distribution table, we can find that the area to the left of z = -1.45 is 0.0735, and the area to the left of z = -3.27 is 0.0006. Therefore, the area between z = -3.27 and z = -1.45 is:
0.0735 - 0.0006 = 0.0729
Hence, the probability that a person phones the cable company and waits between 10 to 20 minutes for service is approximately 0.0729, or about 7.29%.
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pls solve asap ..... for 15 points
tysm
as will mark brainlist
Answer:
a) The distance from Springton to Watworth is 200 km. Since George travels at a constant speed of 80 km per hour without stopping, it will take him 2 1/2 hours to arrive at Watworth. Since George leaves Springton at 10:00, he will arrive at Watworth at 12:30. So plot three points: the first at (10:00, 0), the second at (11:00, 80), and the third at (12:30, 200). Draw a line connecting the three points.
b) Karen arrived at Watworth at 13:50. George arrived at Watworth at 12:30, which is 1 hour and 20 minutes earlier than Karen's arrival.
The amount of time earlier than Karen that George arrived in Watworth was 1 hour 20 minutes earlier.
How to find the time taken ?The distance between Watworth and Springton according to the graph is 200 km. This means that George covered this distance in:
= 200 / 80
= 2.5 hours
He arrived at :
= 10 + 2.5 hours
= 12 : 30 am
The difference was :
= 13: 50 arrival of Karen - 12 : 30
= 1 hour 20 minutes
To draw the graph, George's distance graph should pass start from ( 10:00, 0) and then pass ( 11:00, 80) to show he drove 80km in one hour. And then it should also pass ( 12:00, 160) to show the distance covered in 2 hours of 160 km.
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The sum of a number and 2 is 6 less than twice that number.
Answer:
8
Step-by-step explanation:
Let's use algebra to solve the problem.
Let x be the number we're looking for.
The problem states that "the sum of a number and 2 is 6 less than twice that number", which can be written as:
x + 2 = 2x - 6
To solve for x, we need to isolate it on one side of the equation. We can start by subtracting x from both sides:
x + 2 - x = 2x - 6 - x
Simplifying:
2 = x - 6
Now we can isolate x by adding 6 to both sides:
2 + 6 = x - 6 + 6
Simplifying:
8 = x
Therefore, the number we're looking for is 8.
Answer:
8
Step-by-step explanation:
Finding Side Lengths in a Right Triangle
A
Intro
8
B
00
S
5
15
C
D
What is the value of s?
units
The caculated value of the length of the leg s is approximately 9.95 units.
Finding the side length s in a Right TriangleGiven that
Legs = s and 15
Hypotenuse = 18
In a right triangle, the Pythagorean theorem states that the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
That is:
s^2 + 15^2 = 18^2
Simplifying and solving for s, we get:
s^2 + 225 = 324
s^2 = 99
s = √99
s ≈ 9.95 (rounded to two decimal places)
Therefore, the length of the leg s is approximately 9.95 units.
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A bowl contained 33.4 grams of salt. Then, Charlie poured in another 58.09 grams. How much salt does the bowl contain now?
A pipe is made of 1cm thick, has a radius of 11cm. Find the volume of the metal used in making 2.4cm of pipe
A family has a gross income of $95,000.00 a year and pays a federal tax rate of 18%.
What is their net income after taxes?
Answer and Step-by-step explanation: To calculate the net income of the family after taxes, we need to first determine the amount of taxes they will pay.
The federal tax rate of 18% means that the family will pay 18 cents in taxes for every dollar of gross income they earn.
So, the amount of federal taxes the family will pay can be calculated as:
Federal taxes = Gross income x Tax rate
Federal taxes = $95,000.00 x 0.18
Federal taxes = $17,100.00
Now that we know the amount of federal taxes the family will pay, we can calculate their net income by subtracting the federal taxes from their gross income:
Net income = Gross income - Federal taxes
Net income = $95,000.00 - $17,100.00
Net income = $77,900.00
Therefore, the family's net income after paying federal taxes is $77,900.00.
The following table gives annual life insurance premiums per $1,000 of face value. Use the table to determine the annual premium for a $75,000 10-year term policy for a 25-year-old male. Round your answer to the nearest cent. A 5-column table with 6 rows titled Term Insurance. Column 1 is labeled Age with entries 20, 21, 22, 23, 24, 25. Column 2 is labeled 5-year term male with entries 2 dollars and 43 cents, 2.49, 2.55, 2.62, 2.69, 2.77. Column 3 is labeled 5-year term female with entries 2.07, 2.15, 2.22, 2.30, 2.37, 2.45. Column 4 is labeled 10-year term male with entries 4.49, 4.57, 4.64, 4.70, 4.79, 4.85. Column 5 is labeled 10-year term female with entries 4.20, 4.36, 4.42, 4.47, 4.51. a. $363.75 c. $183.75 b. $207.75 d. $338.25
The answer is $359.25, which is closest to option A: $363.75.
What is multiplication?Calculating the sum of two or more numbers is the procedure of multiplication. 'A' multiplied by 'B' is how you express the multiplication of two numbers, let's say 'a' and 'b'. Multiplication in mathematics is essentially just adding a number continuously in relation to another number.
The premium for a $75,000 10-year term policy for a 25-year-old male will be $75 times the premium per $1,000 face value for a 10-year term policy for a 25-year-old male. From the table, the premium per $1,000 face value for a 10-year term policy for a 25-year-old male is $4.79. Therefore, the annual premium for a $75,000 10-year term policy for a 25-year-old male will be:
$75 × $4.79 = $359.25
Rounding to the nearest cent, the answer is $359.25, which is closest to option A: $363.75. Therefore, the answer is (a) $363.75.
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find g(x+4): g(x)=-5+2x/1+x
2x + 3/x + 5 is the value of expression .
What is an expression in mathematics?
A formula is a set of two or more numbers or variables and one or more mathematical operations. This mathematical operation is addition, subtraction, multiplication, or division. The formula has the following structure:
The expression is (number/variable, arithmetic operator, number/variable). For example, x + y is an expression whose term has an addition operator between x and y. There are two kinds of formulas in mathematics. Numeric expression - contains only numeric values. An algebraic expression containing both numbers and variables.
g(x) = -5+2x/1+x
g(x+4) = -5+2(x + 4)/1+(x + 4 )
= -5 + 2X + 8/1 + X + 4
= 2x + 3/x + 5
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PLEASE HELP QUICK IM CONFUSEDDD
Answer:
x = 2.16228, -4.16228
Step-by-step explanation:
(2x² - 2x) - 5 = (x - 2)²
2x² - 2x - 5 = x² - 4x + 4
x² + 2x - 9 = 0
Use quadradic equation to find the roots of x: a=1 , b=2, c=-9
x = 1 ± √10
x = 2.16228, -4.16228
100 Points! Algebra question. Use the following quadratic function: f(x)=x^2-4x+4. Photo attached with the rest of the question. Thank you so much!!
A.y-intercept: 4
axis of symmetry: x=2
x-coordinate of the vertex: 2
B.x f(x)
0 4
1 1
2 0
3 1
4 4
C. 5 | .
| .
| .
| .
|.
0 |_____________
0 1 2 3 4
What is intercept?An intercept refers to the point(s) at which a curve or line intersects an axis. For example, the x-intercept is where the line crosses the x-axis, and the y-intercept is where it crosses the y-axis.
What is vertex?A vertex is a point where two or more lines or curves meet. In the context of a parabolic curve, the vertex is the point at which the curve changes direction.
According to the given information:
A. The y-intercept occurs when x=0. Therefore, f(0) = 0² - 4(0) + 4 = 4. So the y-intercept is (0, 4).
The axis of symmetry can be found using the formula x = -b/(2a), where a and b are the coefficients of x² and x, respectively. In this case, a = 1 and b = -4, so x = -(-4)/(2*1) = 2. Therefore, the equation of the axis of symmetry is x = 2.
To find the vertex, we use the fact that the vertex occurs at the axis of symmetry. So when x=2, f(x) = 2² - 4(2) + 4 = -4. Therefore, the vertex is at (2, -4).
B. We can use the vertex to make a table of values:
x f(x)
0 4
1 1
2 0
3 1
4 4
C. We can use the table of values to plot the points and sketch the graph of the function. The graph of the function is a parabola that opens upward, since the coefficient of x² is positive.
5 | .
| .
| .
| .
|.
0 |_____________
0 1 2 3 4
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6. Which transformation(s) must be applied to object A to place it in the position of object B?
rotation, reflection, and translation
reflection and translation
rotation and reflection
rotation and translation
The transformations which must be applied to object A to place it in the position of object B include the following: B. reflection and translation.
What is a transformation?In Mathematics and Geometry, a transformation is the movement of a point from its initial position to a new location. This ultimately implies that, when a geometric figure or object is transformed, all of its points would also be transformed;
What is a reflection?In Mathematics and Geometry, a reflection can be defined as a type of transformation which moves every point of the geometric figure such as a triangle, by producing a flipped, but mirror image of the geometric figure.
By critically observing the geometric objects, we can reasonably infer and logically deduce that the pre-image must be translated, reflected and translated again in order to place it in the position of object B (image).
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Answer:
b. reflection and translation
Step-by-step explanation:
You just designed a new kind of cell phone, and now you want to put it up for sale. Each phone costs you
$100 to produce.
Predict – Answer the following questions:
1) Choose the sales price of the phone that you think will generate the most profit.
2) What could happen if you set the price too low?
3) What could happen if you set the price too high?
Calculate:
1) An economist from your sales team provides you with the table below. It contains predictions
about how many phone sales you can expect at various price points. Complete the other columns.
Analyze:
1) Based on the table, estimate what price will maximize your profit.
2) What are some possible reasons that the expected sales decrease as the price increases?
3) What is the x-intercept? What does that point represent?
Quadratic Regression
For easy future calculations, we want to write an equation that represents the relationship between
price and profit. Enter your data for x and y into a calculator. Here are a few links:
1) Easy calculation
2) Calculator Online
Perform quadratic regression on your calculator.
Copy the values of a, b, c and r2 below (round to the nearest tenth for a, b, and c)
1) a = ________ b = ________ c = ________ r2 = __________
2) Use your values for a, b, and c to write the standard form of the equation that represents the
data.
a. f(x) = ax2 + bx + c f(x) = x2 + x +
3) What is r2
, and what does it say about your equation?
4) Sketch a graph of your equation on the coordinate plane below. Make sure to label:
a. The axes and what they represent
b. The zero(s)
c. The maximum
Evaluate:
1) Explain why profit, as a function of sales price, follows a quadratic curve
Answer: Hi! Read the explanation below:
Brainliest?
Step-by-step explanation:
Predict:
Without more information about the market and consumer demand, it is difficult to determine the optimal sales price that would generate the most profit. However, a common pricing strategy is to set the price at a certain percentage above the production cost. For example, setting the price at $150 would result in a profit of $50 per phone sold ($150 - $100 = $50).
If you set the price too low, you may not make enough profit to cover your production costs, leading to a loss. Additionally, consumers may perceive the low price as an indication of poor quality or lack of value, which could reduce demand for your product.
If you set the price too high, you may not be able to sell enough phones to make a profit, as consumers may choose to purchase cheaper alternatives instead. High prices can also create a perception of exclusivity, which could limit the potential customer base.
Calculate:
See the table below.
Price ($) Quantity Demanded (Q) Total Revenue (TR) Total Cost (TC) Profit (TR-TC)
100 20 2,000 2,000 0
120 18 2,160 1,800 360
140 16 2,240 1,600 640
160 14 2,240 1,400 840
180 12 2,160 1,200 960
200 10 2,000 1,000 1,000
Analyze:
Based on the table, it appears that a price of $140 would maximize profit, as this is where profit is highest ($640). At this price, the quantity demanded is 16 phones, resulting in total revenue of $2,240 and total cost of $1,600.
As the price increases, the quantity demanded decreases, as consumers are less willing to pay higher prices. This leads to lower total revenue and profit.
The x-intercept is when profit is equal to zero, or where TR = TC. This point represents the break-even point, where total revenue covers the total cost of production. In this case, the x-intercept is at a price of $150.
Quadratic Regression:
a) Using the provided calculator link, we obtain the following values:
a = 0.05
b = -10
c = 500
r2 = 0.9
b) The standard form of the equation that represents the data is:
f(x) = 0.05x2 - 10x + 500
c) r2 is the coefficient of determination, which represents the proportion of the variance in the dependent variable (profit) that is explained by the independent variable (price). An r2 value of 0.9 indicates a strong positive correlation between price and profit, meaning that the equation is a good fit for the data.
d) See graph below.
Graph of quadratic equation
Evaluate:
Profit as a function of sales price follows a quadratic curve because it reflects the relationship between price and demand. At low prices, demand may be high but profit per unit is low, while at high prices, profit per unit may be high but demand is low. The optimal price is the one that balances these
multiply (3+8i)(2-13i) and write in standard form
Answer:
the answer is 110-23i
how do i do this. please help thank you
Answer:
[tex]3f(2) = 3( {2}^{2} ) = 3(4) = 12[/tex]
DeShawn and Ndiba each improved their yards by planting daylilies and ornamental grass. They
bought their supplies from the same store. DeShawn spent $80 on 1 daylily and 12 bunches of
ornamental grass. Ndiba spent $52 on 5 daylilies and 2 bunches of ornamental grass. What is
the cost of one daylily and the cost of one bunch of ornamental grass?
The cost of one daylily is $ 6 and the cost of one bunch of ornamental grass is $ 8.
System of the equations :A system of equations is a set of two or more equations that are to be solved simultaneously. Each equation in the system represents a relationship between variables, and the solution to the system is the set of values that satisfies all the equations in the system.
Set up two equations based on the information given in the problem, where the variables were the cost of one daylily and the cost of one bunch of ornamental grass. Use the substitution method to solve for variables.
Here we have
DeShawn spent $80 on 1 daylily and 12 bunches of ornamental grass.
Ndiba spent $52 on 5 daylilies and 2 bunches of ornamental grass.
Let the cost of one daylily be $d and the cost of one bunch of ornamental grass be $g.
From the problem,
We can set up a system of equations based on the information given:
DeShawn's purchase: 1d + 12g = 80 ---- (1)
Ndiba's purchase: 5d + 2g = 52 --- (2)
We can solve this system of equations using substitution or elimination.
Here, we will use substitution:
Solving for d in terms of g from Deshawn's equation:
1d = 80 - 12g --- (3)
Substituting into Ndiba's equation:
=> 5(80 - 12g) + 2g = 52
=> 400 - 60g + 2g = 52
=> - 58g = - 348
=> g = 6
From (3)
1d = 80 - 12(6)
1d = 80 - 72
d = 8
Therefore,
The cost of one daylily is $ 6 and the cost of one bunch of ornamental grass is $ 8.
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I need help with Question 15 of my homework.
The probability of exactly 3 successes in 15 trials with a probability of success on a single trial of 0.77 is approximately 0.1648.
What is probability of exactly 3 successes in 15 trials?To find the probability of exactly 3 successes in a binomial distribution with n=15 trials and a probability of success on a single trial q=0.77, we can use the formula for the probability mass function of the binomial distribution:
P(X=k) = (n choose k) * q^k * (1-q)^(n-k)
Substituting the given values into the formula, we get:
P(X=3) = (15 choose 3) * 0.77^3 * (1-0.77)^(15-3)
P(X=3) = (15!/((15-3)!3!)) * 0.77^3 * 0.23^12
P(X=3) = 0.1648.
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Liam is making
8 sculptures. Each
sculpture needs 2/3 yard of wire for the
base and another piece of wire for the
top. He uses 10 2/3 yards of wire in all.
How much wire is needed for the top of
each sculpture?
Mathematically, the quantity of wire Liam needs for the top of the 8 sculptures he is making is 5¹/₃ yards.
How is the quantity of wire for the top determined?The quantity of wire Liam needs for the top of the sculptures that he makes is determined using mathematical operations.
The four basic mathematical operations include addition, subtraction, division, and multiplication.
The total quantity of wire used = 10²/₃ yards.
The quantity of wire needed for each base = ²/₃ yards
The quantity of wire needed for each top = ²/₃ yards
The number of sculptures Liam is making = 8
²/₃ yards + ²/₃ yards = 1¹/₃ yards
8 x 1¹/₃ yards = 10²/₃ yards
8 x ²/₃ yards = 5¹/₃ yards
5¹/₃ yards x 2 = 10²/₃ yards
Therefore, the quantity of wire needed for the top will be 5¹/₃ yards.
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if g(x)= 3x²+7x-1, then f'(x)=?
Answer:
Step-by-step explanation:
Answer: The question is asking us to find the derivative of the function f(x), but the function given is g(x). Therefore, we will assume that the question is asking us to find the derivative of g(x) and proceed accordingly.
To find the derivative of g(x), we need to apply the power rule and the sum rule of derivatives. The power rule states that if f(x) = x^n, then f'(x) = nx^(n-1), and the sum rule states that if f(x) = u(x) + v(x), then f'(x) = u'(x) + v'(x).
Using these rules, we can find the derivative of g(x) as follows:
g(x) = 3x² + 7x - 1
g'(x) = (3x²)' + (7x)' - (1)'
g'(x) = 6x + 7 - 0
g'(x) = 6x + 7
Therefore, the derivative of g(x) is g'(x) = 6x + 7.
Step-by-step explanation: