18
If the mean for a data set was 8 and the standard deviation was 1.5, where would most of the data points be located?
A) Above 9.5
B) Between 6.5 and 9.5
Above 12
D) None of these answer choices are correct.
the correct answer is B, between 6.5 and 9.5.The solution of given standard deviations Problem isit is unlikely that most of the data points would be located there.
what is standard deviations?Standard deviation is a statistical measure of the amount of variation or dispersion in a set of data values. It represents the average distance of each data point from the mean of the data set.
According to given informationThe answer to this question can be found using the empirical rule, which states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations of the mean, and 99.7% falls within three standard deviations of the mean.
Given that the mean is 8 and the standard deviation is 1.5, one standard deviation above the mean would be 8 + 1.5 = 9.5, and one standard deviation below the mean would be 8 - 1.5 = 6.5. Therefore, approximately 68% of the data would be expected to fall between 6.5 and 9.5.
Based on this information, we can eliminate answer choices A and D. Answer choice C is more than two standard deviations above the mean, so it is unlikely that most of the data points would be located there. Therefore, the correct answer is B, between 6.5 and 9.5.
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A college student takes the same number of credits each semester. She had 12 credits when she started, and after 3 semesters, she had 54 credits.
The rate at which the college student is earning credits, given the semesters taken, would be E. 14 credits per Semester.
How to find the credits ?The formula to find the number of credits the student takes per semester, would be :
( total credits after 3 semesters - total credits at the start ) / number of semesters = credits per semester
total credits after 3 semesters = 54 credits
total credits at the start = 12 credits
The credits per semester is therefore;
= ( 54 - 12 ) / 3
= 42 / 3
= 14 credits per semester
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The complete question is:
Which of these expresses the rate at which she is earning credits? Select the correct answer below:
3 credits per semester
42 credits per semester
14 semesters per credit
12 credits per semester
14 credits per Semester
7 semesters per credit
Find LM
A. 18
B. 24
C. 28
D. 36
Applying the Two-Tangent Theorem, the length of segment LM in the circle is: A. 18.
What is the Two-Tangent Theorem?
If two tangent segments are drawn to one circle from the same external point, the Two-Tangent Theorem states that both segments are congruent together.
Applying the theorem, we have:
4x - 2 = 3x + 3
Find the value of x:
4x - 3x = 2 + 3
x = 5
Find the length of LM:
LM = 3x + 3
Plug in the value of x:
LM = 3(5) + 3
LM = 18
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9. A counting number is totally odd if all its digits are odd and their sum is odd. How many totally odd counting numbers less than 1000 are there?
We need to first determine how many totally odd counting numbers there are between 1 and 9. The answer is 250.
What is odd counting number?It is an integer that is not divisible by two and therefore has a remainder of 1 when divided by two. It is also referred to as an odd number, an odd integer, or an uneven number.
For this, let us consider all the digits from 1 to 9, and their respective sums.
Digit: 1 Sum: 1 (odd)
Digit: 3 Sum: 3 (odd)
Digit: 5 Sum: 5 (odd)
Digit: 7 Sum: 7 (odd)
Digit: 9 Sum: 9 (odd)
Since all the digits between 1 and 9 and their respective sums are all odd, it means that any counting number less than 10 that is composed of only these digits would be totally odd. This means that there are 5 totally odd counting numbers less than 10, i.e., 1, 3, 5, 7 and 9.
Now, since any counting number less than 1000 can be composed of any combination of these 5 digits, the total number of totally odd counting numbers less than 1000 can be calculated by multiplying the number of digits (5) by the number of combinations of those digits (999). The result of this calculation is 250, which is the answer to the question.
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help! please help me with this math
The only function that represents a range as less than zero only is: Option C: 1/(x - 2)²
How to find the range of the function?The range of a function is defined as all the possible values y could be. The formula to find the range of a function is y = f(x). In a relation, it is only a function if every x value corresponds to only one y value.
Now, we want to find the function for which the range is a set of all real numbers less than zero. This means that the range is made up of only negative numbers.
The only option that denotes the range to be less than zero is option C because no matter the domain value, the range will remain a negative number.
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A boat leaves a pier and travels 15 miles due east, then turns and travels 15 miles in the direction N 20° E. Which diagram represents the boat’s current distance, x, from the pier?
(diagrams attached below)
Answer: 20.64 miles.
Step-by-step explanation: The assignment of nomenclature to the location of the boat's initiation as point A, the termination of the first course of the excursion as point B, and the termination of the second course of the journey as point C is proposed. The present study reveals that the spatial positioning of point A and point B is separated by a distance of precisely 15 miles in an eastward direction. Similarly, point B and point C are separated by a distance of 15 miles, but oriented along the vector of N 20° E.
The application of trigonometry provides a means to determine the spatial separation between point B and point C. Based on computations, the distance from point B to point C has been estimated to be approximately 7.83 miles along the northward direction and approximately 14.16 miles along the eastward direction.
Henceforth, the computation of the distance between point A and point C (i.e., the prevailing separation of the boat from the pier) can be determined by the ensuing method:
The mathematical expression denoting the distance between points A and C, designated as AC, is given by the square root of the sum of the squares of the distances between points A and B, designated as AB, and between points B and C, designated as BC. In formulaic notation, this can be expressed as AC = √((AB)² + (BC)²).
The magnitude of the distance denoted by AC, between two points A and C, can be calculated using the Euclidean distance formula, which involves the square root of the sum of the squares of the differences between the corresponding coordinates of the two points. In this particular case, the calculation results in the expression √(15² + 14.16²).
The distance between points A and C, denoted as AC, can be expressed mathematically as the square root of the sum of the squares of the horizontal and vertical distances between them. Thus, AC = √(225 + 200.89), where 225 and 200.89 represent the square of the horizontal and vertical distance, respectively. This equation can be simplified to yield the measurement of the physical distance between points A and C in the applicable units of length.
The distance between points A and C is determined to be the square root of 425.89 in units of length.
The measurement of the distance between point A and point C is approximately equivalent to 20.64 miles.
Answer: Graph A.
Step-by-step explanation:
Find the indefinite integral.
The indefinite integral, given the integral can be found to be √14x + C.
How to find the indefinite integral ?An indefinite integral is an antiderivative of a function. More specifically, if f(x) is a function, then an antiderivative of f(x) is a function F(x) such that F'(x) = f(x), where F'(x) represents the derivative of F(x) with respect to x.
To find the indefinite integral of a constant (in this case, √14) with respect to x, simply multiply the constant by x and add a constant of integration (C):
∫√14 dx = √14 × ∫dx = √14 × x + C
So, the indefinite integral of √14 with respect to x is:
√14x + C
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A teacher makes a garage showing the way students get to school he needs to have five more students two car how many fewer students get to school by skateboard then by car and bus combined into the answer in the Box
The number of fewer students to get to school by skateboard than by car and bus combined would be 60 fewer students.
How to find the number of students ?To find how many fewer students get to school by skateboard than by car and bus combined, we need to add the number of students who use car and bus and then subtract the number of students who use skateboard.
Car: 30 students
Bus: 40 students
Car + Bus = 30 + 40 = 70 students
Skateboard: 10 students
Difference = (Car + Bus) - Skateboard
Difference = 70 - 10 = 60 students
So, 60 fewer students get to school by skateboard than by car and bus combined.
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Juan buys candy that costs $8 per pound. He will spend at least $48 on candy. What are the possible numbers of pounds he will buy?
Use p for the number of pounds Juan will buy.
Write your answer as an inequality solved for p.
In a case whereby Juan buys candy that costs $8 per pound and will spend at least $48 on candy the possible numbers of pounds he will buy written in inequality is is p>5 (at least 5 pounds).
How can these number be determined?Inequality in math refers to a statement that one quantity is either greater than, less than, or not equal to another quantity. Inequalities are often represented using symbols such as "<" (less than), ">" (greater than), or "≤" (less than or equal to) and "≥" (greater than or equal to). For example, the inequality "x > 3" states that the variable "x" is greater than the value of 3. The inequality "y ≤ 5" means that the variable "y" is less than or equal to 5.
From the question, p = number of pounds Juan will buy.
candy=costs $8 per pound
$20/$4 = 5 pounds
p>5
at least 5 pounds
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Find the surface area for the figure ( on photo )
The surface area of the square pyramid given above would be = 400ft²
How to calculate the surface area of the given shape?The diagram above is a typical example of the square based pyramid which has four triangles connected to a vertex.
To calculate the surface area of the given figure, the formula that should be used would be = b² +2bs
where b = base length= 10ft
s = slant height= 15ft
Surface area = 100+2(10×15)
= 100+300
= 400ft²
Therefore the surface area of the square based pyramid given above would be = 400ft².
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The factorization of x2 – 6x – 72 is:
Step-by-step explanation:
x^2 -6x - 72 = ( x-12)(x+6)
If you can't do this 'in your head' you can always use Quadratic Formula
with a = 1 b= - 6 and c= -72
to find roots x = 12 and -6 then write the equation as above
What is the volume of a rectangular prism that is 120 centimeters by 2 meters by 1.5 meters in cubic centimeters? 3,600,000 cm 3 3,600 cm 3 36,000 cm 3 3.6 cm 3
The volume of the rectangular prism in cubic centimeters is 3,600,000
What is the volume of the rectangular prismFrom the question, we have the following parameters that can be used in our computation:
Dimension = 120 centimeters by 2 meters by 1.5 meters
The volume of the rectangular prism is the product of the dimensions
i.e.
Volume = Length * width * height
Substitute the known values in the above equation, so, we have the following representation
Volume = 120 * 2 * 1.5
Convert to cm
Volume = 120 * 200 * 150
Evaluate
Volume = 3600000
Hence, the volume in cubic centimeters is 3,600,000
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how do I find the IQR for the numbers 7,9,8,9,6
Answer:
There are three steps to find IQR
1. Know how the IQR is used. Essentially, it is a way of understanding the spread or "dispersion" of a set of numbers. The interquartile range is defined as the difference between the upper quartile (the highest 25%) and the lower quartile (the lowest 25%) of a data set.
2. Understand quartiles. To visualize a quartile, chop a list of numbers into four equal parts. Each of these parts is a "quartile."[2] Consider the set: 1, 2, 3, 4, 5, 6, 7, 8.
1 and 2 are the first quartile, or Q1
3 and 4 are the second quartile, or Q2
5 and 6 are the third quartile, or Q3
7 and 8 are the fourth quartile, or Q4
3. Learn the formula. In order to find the difference between the upper and lower quartile, you'll need to subtract the 25th percentile from the 75th percentile.
The formula is written as: Q3 – Q1 = IQR.
Answer:
the answer would be 2.5
Explanation:
The formula for finding the interquartile range takes the third quartile value and subtracts the first quartile value. Equivalently, the interquartile range is the region between the 75th and 25th percentile (75 – 25 = 50% of the data).
. Labor Variances Ellen Chenoweth, the manager of the city of St. Paul road maintenance shop, uses standards to judge performance. Because a clerk mistakenly discarded some labor records, however, Ellen has only partial data for April. She knows that the total direct-labor flexible-budget variance was $1,643 favorable. Moreover, a recent pay raise produced an unfavorable labor price variance for April of $1,157. The actual hours of input were 1,780 and the standard labor price was $20 per hour. 1. Find the actual labor rate per hour 2. Determine the standard hours allowed for the output achieved.
Labor Variances Ellen Chenoweth, the manager of the city of St. Paul road maintenance shop, uses standards to judge performance, the actual labor rate per hour for April was $19.35.
1. Actual Labor Rate per Hour:
The labor price variance formula is:
Labor Price Variance = (Actual Labor Rate - Standard Labor Rate) x Actual Hours
We are given that the labor price variance for April was unfavorable and equal to $1,157. We also know that the standard labor rate was $20 per hour. Using the formula above and plugging in the known values, we can solve for the actual labor rate:
-1,157 = (Actual Labor Rate - 20) x 1,780
-1,157 = 1,780Actual Labor Rate - 35,600
1,780Actual Labor Rate = 34,443
Actual Labor Rate = 19.35
Therefore, the actual labor rate per hour for April was $19.35.
2. Standard Hours Allowed for the Output Achieved:
The flexible-budget variance formula is:
Flexible-Budget Variance = (Actual Hours - Standard Hours) x Standard Labor Rate
We are given that the flexible-budget variance for April was favorable and equal to $1,643. We also know that the standard labor rate was $20 per hour.
Using the formula above and plugging in the known values, we can solve for the standard hours allowed:
1,643 = (1,780 - Standard Hours) x 20
1,643 = 35,600 - 20Standard Hours
20Standard Hours = 33,957
Standard Hours = 1,697.85
Therefore, the standard hours allowed for the output achieved in April was 1,697.85.
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The polynomial function f has exactly one positive zero. Approximate the zero correct to two decimal places.
f(x) = 2x² - 1
-16x³-3x²-8x-2
The positive zero of f is approximately
(Round to two decimal places as needed.)
PLEASE HELP FOR 100 POINTS Polygon KLMN is drawn with vertices at K(0, 0), L(5, 2), M(5, −5), N(0, −3). Determine the image vertices of K′L′M′N′ if the preimage is rotated 270° clockwise.
K′(0, 0), L′(−2, 5), M′(5, 5), N′(3, 0)
K′(0, 0), L′(−2, −5), M′(−5, 5), N′(−3, 0)
K′(0, 0), L′(−5, −2), M′(5, −5), N′(3, 0)
K′(0, 0), L′(−5, −2), M′(−5, −5), N′(0, 3)
Answer: a
Step-by-step explanation:
Suppose that the function h is defined, for all real numbers, as follows.
h(x) =
-2 if x-2
-1 if x=-2
Find h(-5), h (-2), and h (5).
h(-5) =
h (-2) = 0
h (5) = 0
8
X
S
The given function h(x) is h(-5) = -2, h(-2) = -1 and h(5) = -2.
What is the defined function for all real numbers?The set of all possible inputs is the domain of a function. For instance, all real integers other than x=0 are in the domain of f(x)=x2 and g(x)=1/x, respectively. Additionally, custom functions with more restricted domains can be defined.
The definition of the function h(x) is as follows:
h(x) =
-2 if x < 2
-1 if x = -2
Using this definition, we can find the values of h(-5), h(-2), and h(5) as follows:
h(-5): Since -5 < 2, we use the first part of the definition and set h(-5) = -2.
h(-2): Since -2 = -2, we use the second part of the definition and set h(-2) = -1.
h(5): Since 5 > 2, we use the first part of the definition and set h(5) = -2.
Therefore, we have:
h(-5) = -2
h(-2) = -1
h(5) = -2
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answer is a
i think question is about implicit differentiation
The x-coordinates of the points on the curve where the tangent line is horizontal will be option A.
How to explain the coordinate(x² + y²)² = 4(x² – y²)
x⁴ + 2x²y² + y⁴ = 4x² - 4y²
y⁴ + 2x^2y² + 4y² - 4x² = 0
Now we can use implicit differentiation to find the derivative of y with respect to x:
4y³(dy/dx) + 4xy² + 4y(dy/dx)x² + 8y(dy/dx) - 8x = 0
Simplifying this expression, we get:
4y³(dy/dx) + 4xy² + 4xy²(dy/dx) + 8y(dy/dx) - 8x = 0
(dy/dx)(4y³ + 4x²y²) + 8y(dy/dx) = 8x - 4xy²
(dy/dx)(4y³ + 4x^2y² + 8y) = 4x(2-y²)
(dy/dx) = 4x(2-y²)/(4y³ + 4x²y² + 8y)
Based on the information, x-coordinates of the points on the curve where the tangent line is horizontal will be option A.
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Dean ran 2.3 fewer kilometers than Sam. If Dean ran 6.8 km, how far did Sam run? A 2-column table with 4 rows. Column 1 is labeled Situation with entries increasing, difference, finding part of a total, sharing or grouping. Column 2 is labeled Operation with entries +, minus, times, divided by. Select all that apply. You know the difference in the distances the boys ran, so this is a subtraction problem. You are finding the total distance the boys ran, so this is an addition problem. Dean ran part of the distance Sam ran, so this is a multiplication problem. The correct equation is s + 2.3 = 6.8. The correct equation is s – 2.3 = 6.8. The correct equation is 2.3s = 6.8.
The correct equation to use is "s - 2.3 = 6.8", where s represents the distance Sam ran.
What is distance?Distance is a measurement of how far apart two objects or points are from each other. It is usually measured in units such as meters, kilometers, miles, or feet. Distance can refer to physical space between two points, or it can be used to describe the extent of an abstract concept, such as a difference in opinion or a cultural divide.
According to question:The Situation column should have two entries: "finding part of a total" and "difference".
The Operation column should have only one entry: "minus".
The right formula is "s - 2.3 = 6.8", where s stands for the distance Sam ran.
To solve for s, we can add 2.3 to both sides of the equation:
s - 2.3 + 2.3 = 6.8 + 2.3
s = 9.1
Therefore, Sam ran 9.1 kilometers.
So, the Situation entries are: "difference" and "finding part of a total".
The Operation entry is: "minus".
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find the surface area of the figure
Answer:
The answer for Surface area is 332m²
Step-by-step explanation:
S.A=area of 2 triangle +Area of 2 rectangle +Area of rectangle
S.A=2×1/2×4×3 + 2(20×5) + 20×6
S.A=12+2(100)+120
S.A=12+200+120
S.A=212+120
S.A=332m²
find the surface area of the figure
The surface area of the square pyramid is 416.23 ft²
How to find the surface area of a square pyramid?
The surface area of a square pyramid is given by the formula:
A = a² + 2a√(a²/4 + h²)
Where a is the base length of the square pyramid and h is the height of the square pyramid.
From the figure, we have: a = 10 ft and h = 15 ft
A = a² + 2a√(a²/4 + h²)
A = 10² + 2*10√(10²/4 + 15²)
A = 100 + 20√(100/4 + 225)
A= 100 + 20√250
A = 416.23 ft²
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NO LINKS!! URGENT HELP PLEASE!!
Select all that apply
b. Symmetric with respect to the x-axis
The ones that are symmetric with respect to the x-axis is:
y = -7x^2Checking the symmetric for all equationsA function is symmetric with respect to the x-axis if replacing y with -y in the equation does not change the equation. In other words, if the graph of the function is the same when reflected across the x-axis.
y = -7x^2 is symmetric with respect to the x-axis, since replacing y with -y gives -(-y) = y and the equation remains the same.y = 6x² - 9 is not symmetric with respect to the x-axis, since replacing y with -y gives -(-y) = y, but the equation changes to -y = 6x² - 9, which is not the same as the original equation.x=1/4y^2 is not a function, since it does not pass the vertical line test and has multiple values of x for some values of y.y=x^3-1 is not symmetric with respect to the x-axis, since replacing y with -y gives -(-y) = y, but the equation changes to -y = x^3 - 1, which is not the same as the original equation.x=-y^2+9 is not symmetric with respect to the x-axis, since replacing y with -y gives -(-y) = y, but the equation changes to x = -(-y)^2 + 9, which is not the same as the original equation.y=sqrt(x) is not symmetric with respect to the x-axis, since replacing y with -y gives -(-y) = y, but the equation changes to -y = sqrt(x), which is not the same as the original equation.y=sqrt(x)-6 is not symmetric with respect to the x-axis, since replacing y with -y gives -(-y) = y, but the equation changes to -y = sqrt(x) - 6, which is not the same as the original equation.Therefore, only the equation y = -7x^2 is symmetric with respect to the x-axis.
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How many gallons of a 80% alcohol solution and a 20% alcohol solution must be mixed to get 9 gallons of 60% alcohol solution?
In linear equation, x = 6 gallons (of 80% alcohol)
y = 3 gallons (of 20% alcohol)
What is a linear equation in mathematics?
A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.
Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.
Let
x = liters of 80% alcohol
y = liters of 20% alcohol
There are two unknowns, we need two equations
x + y = 9. (1)
0.80x + 0.20y = 0.60(x+y) (2)
From (1)
x + y = 9
y = 9-x
Substitute the value of y into (2) and solve for x:
0.80x + 0.20y = 0.60(x+y)
0.80x + 0.20(9-x) = 0.60(x+9-x)
0.80x + 1.8 - 0.20x = 0.60(9)
0.80x + 1.8 - 0.20x = 5.4
0.6x = 3.6
x = 6 gallons (of 30% alcohol)
Substitute x=6 into (1) and solve for y:
x + y = 9
6 + y = 9
y = 3 gallons (of 60% alcohol)
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Suppose we are given the following....(picture below)
Line 1: slope = 1/4
Line 2: slope = -4
Line 3: slope = -1/12
Line 1 and Line 2: perpendicular
Line 1 and Line 3: neither
Line 2 and Line 3: neither
How to find the slope of the lines?Slope is the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run.
Mathematically, the slope is the change in y divided by the change in x. That is:
Slope = (y₂-y₁) / (x₂-x₁)
Line 1:
(4, -1) and (8, 0)
Slope = (0--(-1)) / (8-4)
= 1/4
Line 2:
(2, -6) and (0, 2)
Slope = (2-(-6)) / (0-2)
= 8/(-2)
= -4
Line 3:
(3, -6) and (6, -7)
Slope = (-7-(-6)) / (6-(-6))
= -1/12
Remember:
1. When the two lines are parallel, they have the same (equal) slope.
2. When the two lines are perpendicular, the product of their slope is -1 i.e.
m₁ * m₂ = -1. Where m₁ and m₂ represent the slope of the lines.
Let's check:
Line 1 and Line 2:
They are not parallel but they are perpendicular (i.e. 1/4 * (-4) = -1).
Line 1 and Line 3:
Neither
Line 2 and Line 3:
Neither
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Please see the attached.
Answer:
min: 56
lower quartile: 70
median: 74
upper quartile: 80
max: 86
Solve for x:-
2^x=32
Answer:
x=5
Step-by-step explanation:
2^x= 32
2^x=2^5
(comparing, common denominator)
therefore x=5.
It took a crew 1 h 30 min to row 5 km upstream and back again. If the rate of flow of the stream was 8 km/h, what was the rowing speed of the crew in still water? km/h
The rowing speed of the crew in still water is:
x = 12 km/h.
What is meant by speed?
Speed is a measure of how fast an object is moving. It is usually expressed in units of distance per unit of time, such as miles per hour or meters per second. Speed can be calculated using the formula speed = distance/time.
According to the given information
We can use the formula:
distance = rate × time
to set up two equations based on the information given.
When the crew rows upstream for 5 km, the time it takes is:
time = distance/rate
time = 5 / (x - 8)
When the crew rows downstream for 5 km, the time it takes is:
time = distance/rate
time = 5 / (x + 8)
The total time for the round trip is 1 hour 30 minutes, or 1.5 hours:
total time = time upstream + time downstream
1.5 = 5/(x-8) + 5/(x+8)
To solve for x, we can start by multiplying both sides of the equation by (x - 8)(x + 8) to clear the denominators:
1.5(x - 8)(x + 8) = 5(x + 8) + 5(x - 8)
Expanding and simplifying, we get:
1.5x^2 - 72 = 10x
Bringing all the terms to one side of the equation, we get:
1.5x^2 - 10x - 72 = 0
We can factor this quadratic equation by first dividing both sides by 1.5:
x^2 - (10/1.5)x - 48 = 0
We can then factor this expression as:
(x - 12)(x + 4) = 0
This gives us two possible values of x: x = 12 and x = -4.
Since we are looking for a rowing speed (which is a positive quantity), we can discard the negative solution and conclude that the rowing speed of the crew in still water is:
x = 12 km/h.
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Sophia has the following data:
131213141313h
If the range is 3, which number could h be?
A. 10
B. 11
Answer:
To determine the possible values of h, we need to first understand what is meant by the range.
The range is the difference between the highest value and the lowest value in a set of numbers. In this case, we don't know what the full set of numbers is, but we know that the range is 3.
The highest number in the set is 4 (since there are no higher numbers in the set than 4), and the lowest number in the set is either 1 or 2. This is because the range is 3, and there are only two possible sequences of three consecutive integers that include the number 4: 2, 3, 4 and 1, 2, 3.
So to find the possible values of h, we need to add 3 to each of the possible lowest numbers in the sequence.
If the lowest number is 1, then the possible highest numbers are 4 and 5 (4 + 3 = 7 but the sequence only goes up to 4 so the highest should be 5). Therefore, the possible values of h are either 10 or 11.
Therefore, the correct answer is B. 11.
Question 10
Find a polynomial of degree 5 with integer coefficients that has zeros -2, √3i, √2i, and y-intercept of 36.
a polynomial of degree 5 with integer coefficients that has zeros -2, √3i, √2i, and y-intercept of 36 is
[tex]f(x) = x^{5} + 5x^{4} + 13x^{3} + 21x^{2} - 6x + 84[/tex]
How to find the 5 degree polynomial?Let us begin by writing the polynomial factors using the supplied zeros:
Because -2 is a zero, the polynomial has a component of (x + 2).
Because [tex]\sqrt{ 3i }[/tex] is a zero, its conjugate -[tex]\sqrt{ 3i }[/tex] is likewise a zero, implying that the polynomial has a component of (x - [tex]\sqrt{3i}[/tex])(x + [tex]\sqrt{3i}[/tex]) = (x2 + 3).
Similarly, because [tex]\sqrt{2i}[/tex] is a zero, its conjugate -[tex]\sqrt{ 2i }[/tex] is also a zero, implying that the polynomial has a component of (x - [tex]\sqrt{ 2i }[/tex])(x + [tex]\sqrt{ 2i }[/tex]) = (x2 + 2).
Finally, we know that the y-intercept is 36, which means that the polynomial's constant term is 36 when x=0.
When we add these components together, we get:
[tex]f(x) = (x + 2)(x^2 + 3)(x^2 + 2) + 36[/tex]
Extending on this, we get:
[tex]f(x) = x^{5} + 5x^{4} + 13x^{3} + 21x^{2} - 6x + 84[/tex]
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Question 7 (3 points)
The graph and table below represent the constant rate for the amount of time it takes for a given
number of gallons of water to flow from a hose.
a. Find the rate of both the graph and table. Be sure to show all work.
b. Which one has the greater rate? Explain how you know.
The rate of water flow is 6 gallons per unit of time.
What is slope?
Slope is a measure of the steepness of a line. It is defined as the change in y-coordinate divided by the change in x-coordinate between any two points on the line.
a. To find the rate, we need to calculate the amount of water that flows per unit of time.
Method 1: Using the Graph
First, we can plot the points (5,30), (7,42), and (10,60) on a graph and connect them with a line.
From the graph, we can see that the line passes through the points (5,30) and (10,60), which means that the change in y-values is 60 - 30 = 30, and the change in x-values is 10 - 5 = 5.
So, the slope of the line is:
slope = change in y-values / change in x-values
= (60 - 30) / (10 - 5)
= 6
Therefore, the rate of water flow is 6 gallons per unit of time.
Method 2: Using the Table
We can also find the rate by calculating the differences in y-values and x-values in the table.
x y Difference in y Difference in x Rate (y/x)
-------------------------------------------------------
5 30 - - -
7 42 12 2 6
10 60 18 3 6
From the table, we can see that the rate of water flow is 6 gallons per unit of time.
b. Both the graph and table have the same rate of 6 gallons per unit of time. We know this because we calculated the rate using both methods, and they gave us the same result.
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