Answer:
The following statements about Josiah's solution are true:
He found the proportion of rock songs to the total number of songs correctly: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction.
He solved the proportion correctly: StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction.
He correctly determined that the number of rock songs on his MP3 player is 300 (x = 300).
Therefore, the statements that are true are:
He found the proportion of rock songs to the total number of songs correctly.
He solved the proportion correctly.
He correctly determined that the number of rock songs on his MP3 player is 300 (x = 300).
(4) 2. Determine the exact answer for each of the calculations in question 2.1 above, by working out the errors caused by rounding, and compensating for them. 2.2.1. 723 + 586 2.2.2. 2850-1155
what justifies the use of the normal distribution for the sampling distribution of the proportion?
The ability of the normal distribution to approximate the binomial distribution under appropriate conditions justifies the use of the normal distribution for the sampling distribution of the proportion.
A sampling distribution is a statistical probability distribution derived from a larger number of samples gathered from a certain population. The sampling distribution of a particular population is the distribution of frequencies of a range of possible outcomes for a population statistic.
A population is the whole pool from which a statistical sample is selected in statistics. A population can be defined as a large group of people, things, events, medical visits, or measures. A population can thus be defined as an aggregate observation of persons linked by a common trait.
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Which of the following represents vector vector t equals vector PQ in trigonometric form, where P (–13, 11) and Q (–18, 2)?
t = 10.296 sin 60.945°i + 10.296 cos 60.945°j
t = 10.296 sin 240.945°i + 10.296 cos 240.945°j
t = 10.296 cos 60.945°i + 10.296 sin 60.945°j
t = 10.296 cos 240.945°i + 10.296 sin 240.945°j
The correct answer is option (C).
What are the fundamental forms of trigonometry?Sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent are the six functions (cot).
The equation t = Q - P, where Q and P are the specified locations, can be used to determine the components of the vector t. Therefore:
t = (–18, 2) – (–13, 11) = (–18 + 13, 2 – 11) = (–5, –9) (–5, –9)
The vector's magnitude is given by:
|t| = √(–5)^2 + (–9)^2 = √106 ≈ 10.296
The formula = tan1 (y/x), where x and y are the vector's components, can be used to determine the direction of the vector t. The direction must be expressed in terms of sine and cosine functions because we are required to represent the vector in trigonometric form.
θ = tan⁻¹ (–9/–5) ≈ 60.945°
In trigonometric form, the vector t is thus represented as follows:
t = [t|cos|i] + [t|sin|j]
We get the following by altering the values of |t| and:
t = 10.296 cos I + 10.296 sin j of angle 60.945
As a result, the following is the proper trigonometric representation of the vector t:
t = 10.296 cos I + 10.296 sin j of angle 60.945
Thus, alternative is the right response (C).
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We revisit a probabilistic model for a fault diagnosis problem from an earlier homework. The class variable C represents the health of a disk drive: C = 0 means it is operating normally; and C = 1 means it is in failed state. When the drive is running it continuously monitors itself using temperature and shock sensor, and records two binary features, X and Y. X =lif the drive has been subject to shock (e.g;, dropped) , and X = 0 otherwise Y =1if the drive temperature has ever been above 70*C, and Y = 0 otherwise. The following table defines the joint probability mass function of these three random variables: pxyc(r,y, c) 0.1 0.2 0.2 0 0 0 0 0 0 0.05 0.25
The probability of the disk drive being in a normal state is 0.5, and the probability of the disk drive being in a failed state is 0.3.
The given table represents the joint probability mass function of the random variables, pxyc (r, y, c). r, y, and c denote the temperature, shock sensor, and health status of the disk drive. The values of r, y, and c are binary.The joint probability mass function of three random variables r, y, and c can be represented as follows:pxyc (r, y, c)= P(r, y, c)Here,P(r=0, y=0, c=0)= 0.1, P(r=0, y=1, c=0)= 0.2, P(r=1, y=0, c=0)= 0.2,P(r=0, y=0, c=1)= 0, P(r=0, y=1, c=1)= 0, P(r=1, y=0, c=1)= 0,P(r=0, y=0, c=0)= 0, P(r=0, y=1, c=0)= 0, P(r=1, y=1, c=0)= 0.05,P(r=0, y=0, c=1)= 0.25, P(r=0, y=1, c=1)= 0, P(r=1, y=0, c=1)= 0.From the given table, the probability of the disk drive being in a normal state, C=0, is P(C=0)=P(r=0, y=0, c=0)+P(r=0, y=1, c=0)+P(r=1, y=0, c=0)=0.1+0.2+0.2=0.5Hence, the probability of the disk drive being in a failed state, C=1, is:P(C=1)=P(r=0, y=0, c=1)+P(r=0, y=1, c=1)+P(r=1, y=0, c=1)+P(r=1, y=1, c=0)=0.25+0+0+0.05=0.3Therefore, the probability of the disk drive being in a normal state is 0.5, and the probability of the disk drive being in a failed state is 0.3.
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If the midpoint of 2 sides of a triangle are connected with a segment then
The Midpoint is the middle- point of the line member. The midpoint connecting two sides of a triangle is resemblant to the third side and half as long.
The midpoint is the middle of the line member. It's equidistant from both endpoints and is the centroid of the member and endpoints. Cut a member in two.
The midpoint theorem states that a line member drawn from the midpoint of two sides of a triangle is resemblant to the third side and half the length of the third side of the triangle.
The mean theorem helps us find the missing values for the sides of triangles. Connects the sides of a triangle with a line member drawn from the midpoints of two sides of the triangle.
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In an introductory psychology class with n = 50 students, there are 9 freshman males, 15 freshman females, 8 sophomore males, 12 sophomore females, and 6 junior females. A random sample of n = 2 students is selected from the class. If the first student in the sample is a male, what is the probability that the second student will also be a male?
a. 8/14
b. 12/20
c. 20/44
d. 20/50
Answer: Total number of males= C
Step-by-step explanation:
If P = 2y² + 4xy + 4
Q = − 3y² + 7 - 3xy
R=- 3xy + 8
Find P+Q=R.
Answer:
P = [tex]2y^{2}[/tex] + 4xy +4
Q = [tex]-3y^{2}[/tex] + 7 -3xy
R = -3xy +8
Step-by-step explanation:
the primary purpose of statistical analysis is to: group of answer choices transform information into data.
The primary purpose of statistical analysis is to transform information into data. Therefore, the correct option is a)transform information into data.
What is statistical analysis?Statistical analysis is the method of using statistical techniques to collect and analyze data, evaluate its reliability and determine its statistical significance. The following are the primary purposes of statistical analysis:Provide summaries and descriptions of data: One of the most important applications of statistical analysis is to present data in a clear and concise manner. Summarizing the data can assist people in making sense of the data and drawing inferences from it.
For example, data can be summarized using graphs, charts, or tables. Identify patterns and relationships: The goal of statistical analysis is to identify any patterns or relationships that exist within the data. For example, statistical analysis can be used to determine if a product's sales are correlated with a specific time of year.
Test hypotheses and draw conclusions: Statistical analysis is used to test hypotheses and draw conclusions about a population or phenomenon. This is accomplished by using statistical techniques to determine whether or not the data supports a particular hypothesis. Statistical analysis can also be used to determine the probability of an event occurring in the future.
The primary purpose of statistical analysis is to transform information into data. Therefore, the correct option is a)transform information into data.
The complete question is as follows:
The primary purpose of statistical analysis is to:
a)transform information into data.
b)select samples and make inferences about populations
c)convert data into useful desicion-making information
d)perform statistical computations
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1) y = |x+2| how do i make a table and graph this solution! someone help!!
Answer:
(-1,1)
(0,2
(1,3)
(2,4)
a bin can hold 28 pounds. each toy car weighs 7 ounces. how many toy cars can the bin hold? (2 points) 64 toy cars 72 toy cars 88 toy cars 92 toy cars
A bin can hold 28 pounds. each toy car weighs 7 ounces., so the bin can hold 64 toy cars.
How to determine the number of toy carsTo determine the number of toy cars the bin can hold, we must first convert the weight limit of the bin and the weight of the toy cars to a uniform unit of measure.
We'll then divide the weight limit of the bin by the weight of one toy car. After that, we'll multiply the resulting value by the number of ounces in one pound (16).
Here's how to solve the problem:
1 pound = 16 ounces
Therefore, a bin that can hold 28 pounds can hold:28 × 16 = 448 Ounces
The weight of one toy car is 7 ounces.
Divide the weight limit of the bin (448 ounces) by the weight of one toy car (7 ounces):
448 ÷ 7 = 64
Therefore, the bin can hold 64 toy cars.
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I cant figure it out
4x - 4/4x² + x is the value of linear equation.
What in mathematics is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
Equations with power 1 variables are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
28x³ - 28x²/28x⁴ + 7x³
= 28x²( x - 1 )/7x³( 4x + 1)
= 4( x - 1)/x( 4x + 1)
= 4x - 4/4x² + x
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If the GM between √2 and 2√2 is a find the value of a.
Answer:
If the GM between √2 and 2√2 is a find the value of a.
Step-by-step explanation:
To find the geometric mean between two numbers, we simply take the square root of their product.
In this case, we want to find the geometric mean between √2 and 2√2.
Their product is:
√2 * 2√2 = 2√4 = 2*2 = 4
So, the geometric mean between √2 and 2√2 is the square root of 4, which is:
√4 = 2
Therefore, the value of a is 2.
Soccer ball specifications require a diameter of 8.65 inches with an allowable margin of error of 0.05 inch.
Use this information to complete these statements.
The equation that can be used to find d, the diameter of a new soccer ball, is
| ____ | = ____
The minimum possible diameter of a soccer ball is ____,
and the maximum possible diameter is ____
The equation that can be used to find d, the diameter of a new soccer ball, is: |d - 8.65| = 0.05
What is diameter ?
Diameter is the distance across a circle passing through its center, and it is defined as the length of a straight line passing through the center of a circle and connecting two points on the circumference of the circle. In the case of a soccer ball, the diameter is the distance between two opposite points on the surface of the ball, passing through its center.
Radius is a term used in geometry to refer to the distance from the center of a circle to any point on its circumference. It is defined as half of the diameter of a circle. In the case of a soccer ball, the radius is the distance from the center of the ball to its surface. The radius is related to the diameter by the formula:
radius = diameter / 2
The minimum possible diameter of a soccer ball is:
d = 8.65 - 0.05 = 8.60 inches
The maximum possible diameter is:
d = 8.65 + 0.05 = 8.70 inches
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for h(x) = 4x-1, find h(0) and h(2)
Answer:
- 1 and 7
Step-by-step explanation:
to find h(0) substitute x = 0 into h(x)
h(0) = 4(0) - 1 = 0 - 1 = - 1
to find h2) substitute x = 2 into h(x)
h(2) = 4(2) - 1 = 8 - 1 = 7
Keenan scored 80 points on an exam that had a mean score of 77 points and a standard deviation of 4. 2 points. Rachel scored 78 points on an exam that had a mean score of 75 points and a standard deviation of 3. 7 points. Find Keenan's z-score, to the nearest hundredth
Keenan's z-score is 0.71, rounded to the nearest hundredth.
The z-score measures how many standard deviations an individual's score is from the mean, and can be calculated using the formula:
z = (x - μ) / σ
where x is the individual's score, μ is the mean score, and σ is the standard deviation.
For Keenan's exam:
z = (80 - 77) / 4.2
z = 0.71
Therefore, Keenan's z-score is 0.71, rounded to the nearest hundredth.
Rounding to the nearest hundredth means the rounding of any decimal number to its nearest hundredth value. In decimal, hundredth means 1/100 or 0.01. For example, the rounding of 2.167 to its nearest hundredth is 2.17.
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Remove brackets of 3(2a+5b)
5. Solve the following problems. Note: In those problems the geometric multiplicity is less than algebraic multiplicity. (a)d/ dx = ( 1 −44 −7) x2−30
Answer:
-130
Step-by-step explanation:
Michelle asked 30 people entering a movie theater how many movies they had seen over the past year. Here are the results of her poll. 0, 5, 3, 2, 6, 8, 10, 12, 11, 16, 0, 3, 4, 7, 2, 0, 1, 9, 6, 4, 4, 8, 14, 16, 17, 18, 5, 3, 6, 8 (a) Create a frequency table for the data with 5 classes. (b) Create a histogram from your frequency table. Label the axes and give the histogram a title. Answer: (c) Number of movies Frequency
Part (a) of this sentence displays the frequency chart, and part (c) displays the histogram (b) .
what is histogram ?A graph that displays the distribution of a collection of continuous data is called a histogram. It is composed of a number of bars, each of which represents a set of values, and whose height denotes the frequency or number of data points that lie within a given range. Histograms are used to depict a distribution's shape, centre, and spread graphically. They are frequently used to find patterns and trends in data in areas like statistics, data analysis, and scientific study.
given
(A) We must first identify the data's range before dividing it into 5 intervals of equal width in order to construct a frequency table with 5 classes. The values are in the range of 0 to 18.
(b) We plot the class intervals on the x-axis and the frequency on the y-axis to generate a histogram from the frequency chart. The counts are used to illustrate how frequently each class interval occurs.
Part (a) of this sentence displays the frequency chart, and part (c) displays the histogram (b).
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I need help I need to show my work please help
Answer: 19
Step-by-step explanation:
This is an isosceles trapezoid. Note that because this is an isosceles trapezoid, QN and MP are equal. Use the lengths given and solve:
3x + 1 + 6 = 6x - 5
3x = 12
x = 4
Plug x = 4 in 3x + 1 + 6, and we get 3(4) + 1 + 6 = 12 + 7 = 19
Hope this helps!
Q4.
The diagram shows a regular hexagon OABCDE.
a
E
OA = a
AB = b
M is the midpoint of OE.
N is the midpoint of AB.
(a) Find MN in terms of a and/or b.
b
B
D
Diagram NOT
accurately drawn
By answering the presented question, we may conclude that So, the Pythagorean theorem length of MN is expressed in terms of a and b.
What is Pythagorean theorem?Its Pythagorean theorem is just a fundamental mathematical principle that explains the connection between the sides of a triangle that is right. It asserts that the sum of the squares of both the widths of the other two sides is a square of both the width of the hypotenuse (the side facing the perfect angle) the side opposite the right angle). The mathematical mathematics is as follows: c2 = a2 + b2 At which "c" indicates the length of the right triangle and "a" and "b" reflect the extents of the additional two sides, started referring to as the legs.
Because M is the midpoint of OE and N is the midpoint of AB, we can draw a line segment connecting M and N that is parallel to OB and AE and perpendicular to AB.
the Pythagorean theorem
[tex]OE² = OX² + XE²OE²[/tex]
[tex](a + b/2)² + (2a - b/√3)²OE² = 7a²/4 + 3ab/2 + b²/4AN²[/tex]
[tex]AE² + EN²AN² = (2a√3)² + (b/2)²AN²[/tex]
[tex]12a² + b²/4MN² = AN² + AM²MN² \\\\ 12a² + b²/4 + (7a²/4 + 3ab/2 + b²/4)MN²\\\\19a²/2 + 3ab/2 + b²/2MN = √(19a²/2 + 3ab/2 + b²/2)[/tex]
So, the length of MN is expressed in terms of a and b.
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Pls help me I will make u brainest
How many different numbers can be obtained from multiplying 2 distinct integer divisors of 10?
3
4
5
6
7
8
9
We can obtain 6 different numbers by multiplying 2 distinct integer divisors of 10.
How many different numbers can be obtained from multiplying 2 distinct integer divisors of 10?The divisors of 10 are 1, 2, 5, and 10.
To determine how many different numbers can be obtained from multiplying 2 distinct integer divisors.
We need to select 2 distinct divisors and find their product.
The possible pairs are:
1 and 2, product = 21 and 5, product = 51 and 10, product = 102 and 5, product = 102 and 10, product = 205 and 10, product = 50Therefoore, we can obtain 6 different numbers.
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consider using a z test to test h0: p 5 .6. determine the p-value in each of the following situations. a. ha:p..6,z51.47 b. ha:p,.6,z522.70 c. ha:p?.6,z522.70 d. ha:p,.6,z5.25
a) P-value = P(z<1.47) = 0.9292.
b) P-value = P(z>2.70) = 0.0036.
c) P-value = 2 × P(z>2.70) = 0.0072.
d) P-value = P(z>2.5) = 0.0062.
Z-test is a statistical test for the null hypothesis, which refers to the population mean, where the population standard deviation is known. P-value represents the probability value for any hypothesis, where a small p-value indicates that the null hypothesis is less accurate.
P-value, for the given values of z-test is calculated as follows: a) For ha: p < .6, z=1.47The p-value for this hypothesis test is calculated as follows: P-value = P(z<1.47) = 0.9292. Therefore, the P-value is 0.9292. b) For ha: p > .6, z=2.70The p-value for this hypothesis test is calculated as follows.
P-value = P(z>2.70) = 0.0036. Therefore, the P-value is 0.0036.c) For ha: p ≠ .6, z=2.70The p-value for this hypothesis test is calculated as follows: P-value = 2 × P(z>2.70) = 0.0072.
Therefore, the P-value is 0.0072.d) For ha: p > .6, z=2.5The p-value for this hypothesis test is calculated as follows: P-value = P(z>2.5) = 0.0062. Therefore, the P-value is 0.0062.
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ABCD is a quadrilateral A) Calculate the value of x. B) When ABCD is drawn to scale, would the lines AD and BC be parallel or not? You must justify your answer without using a scale drawing
A) The value of x = 45 degrees
B) Lines AD and BC are not parallel when ABCD is drawn to scale.
To solve this problem, we can use the fact that the sum of the angles in a quadrilateral is 360 degrees.
A) angle A + angle B + angle C + angle D = 360
2x + 90 + x + 3x = 360
6x + 90 = 360
6x = 270
x = 45
Therefore, x = 45 degrees.
B) To determine if lines AD and BC are parallel, we can look at the opposite angles of the quadrilateral. If they are supplementary (add up to 180 degrees), then the lines are parallel.
angle A + angle C = 2x + x = 3x = 135 degrees
angle B + angle D = 90 + 3x = 90 + 135 = 225 degrees
Since angle A + angle C and angle B + angle D do not add up to 180 degrees, the opposite angles are not supplementary, and therefore, lines AD and BC are not parallel.
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The given question is incomplete, the complete question is:
ABCD is a quadrilateral A) Calculate the value of x. B) When ABCD is drawn to scale, would the lines AD and BC be parallel or not?
3. When x = 6, which number is closest to the value of y on the line of best fit in the graph below?
09
01
07
10
0987
65
432
2
1
➤X
0 1 2 3 4 5 6 7 8 9 10
Answer:
9
Step-by-step explanation:
I really need help on this question!
Answer:
The 2nd table
Step-by-step explanation:
For the first set of x and y values, divide y (9/4) by x(3)
Change 3 to 1/3 due to the keep-change-flip rule and multiply that by 9/4 as 9/4 × 1/3= 9/12 which is equivalent to 3/4
Do the same process with 6 and 9/2 and that should give you 3/4 as well
Therefore the second table of values have a proportional relationship to each other as they have the same quotient.
Hope this helps.
please help i have been trying to get an answer for 5+ hours
How is the quotient of 556 and 16 determined using an area model?
Enter your answers in the boxes to complete the equations. Your final answer should be a mixed number in simplest form.
Answer:
To use an area model to determine the quotient of 556 and 16, we can divide a rectangle of area 556 into 16 equal parts. Each part will have an area of 556/16.
We can start by dividing 556 into 16 groups of 10 (160), and then into 16 groups of 3 (48). That leaves us with a remainder of 4.
So we have:
556 = 16 x 34 + 48 + 4
This shows that 556 can be written as 16 times some whole number (34) plus a remainder of 48 + 4/16.
Simplifying the remainder, we have:
48 + 4/16 = 48 + 1/4 = 48.25
Therefore, the quotient of 556 and 16 is:
556/16 = 34 1/4
The quotient of 556 and 16 using an area model can be determined by producing a rectangle with the total area of 556 and one side of 16. The length of the other side will be the quotient. In this case, the quotient is 34 3/4.
Explanation:When asked to determine the quotient of 556 and 16 using the area model, one way to think of this is making a rectangle. The total area is 556 and one side is 16. The length of the other side will be the quotient.
Start by first estimating how many times 16 could fit into 556. Let's take 30 as an estimate, because 30*16 = 480, which is relatively close to 556. Draw a rectangle with the width of 16 and the length of 30.
Find the difference between the rectangle's area and 556. So, 556 - 480 = 76. Now, 76 is our remaining area to fill. 16 goes into 76 four more times, adding up to 64.
There is still a leftover area, which is 76-64 = 12. This is smaller than our width of 16. So, your final answer is 34 12/16 or 34 3/4 in simplest form.
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Solve this math problem below
the only option that satisfies both conditions is option B:[tex]y = 12 \sqrt{(x)} - 1[/tex]. Its range is all real numbers and its graph is decreasing from left to right.
What is quadratic equation?
A quadratic equation is a type of polynomial equation of degree two, meaning it contains one or more terms that involve x raised to the power of two (i.e., x^2).
To determine which of these functions has a range of all real numbers and a graph that is decreasing from left to right, we can examine the behavior of the functions as x approaches positive or negative infinity.
For option A, we see that the term (x+7) inside the square root will approach infinity as x approaches infinity, and since the term is subtracted from 3 and multiplied by -6, the y-values will approach negative infinity.
For option B, as x approaches infinity, the square root term will also approach infinity, and since it is being multiplied by 12 and subtracted by 1, the y-values will approach positive infinity.
For option C, as x approaches negative infinity, the term (x+1) inside the cube root will approach negative infinity, and since it is being multiplied by 3 and subtracted by 4, the y-values will approach negative infinity.
For option D, as x approaches negative infinity, the cube root term will approach negative infinity, and since it is being multiplied by -5 and added to 15, the y-values will approach positive infinity.
Therefore, the only option that satisfies both conditions is option B: y = [tex]12 \sqrt{(x)} - 1.[/tex] Its range is all real numbers and its graph is decreasing from left to right.
For the first question, we know that the given square root function has an endpoint at (-4, 19). Let's substitute these values into the function to solve for the unknown parameter 'a':
[tex]y = a\sqrt{(x-h)}+k[/tex]
[tex]19 = a \sqrt{(-4-h)}+k[/tex]
We also know that the square root function has a domain of all values of 'x' such that the expression inside the square root is non-negative. Therefore:
(x-h) >= 0
x >= h
Combining the two equations, we get:
[tex]19 = a\sqrt{(-4-h)}+k[/tex]
h <= x
Since we have only one equation with two unknowns ('a' and 'k'), we cannot solve for the exact values of 'h' and 'a'. However, we can eliminate some of the answer choices based on the domain condition:
For the second question, we need to find a function that has a range of all real numbers and a graph that is decreasing from left to right. Let's analyze each option:
Option A: y=-6√x+7+3 has a maximum value of 3 and a decreasing graph from left to right, but its range is limited to y <= 3, so it does not satisfy the range condition.
Option B: y = 12-1 has a constant value of 11, so its range is limited to y = 11, which does not satisfy the range condition.
Option C: y=3x+1-4 has a graph that is increasing from left to right, so it does not satisfy the decreasing graph condition.
Option D: y=-5 +15 has a constant value of 10, so its range is all real numbers, and its graph is decreasing from left to right (a horizontal line).
Therefore, the answer is Option D: y=-5 +15.
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listed are 29 ages for academy award winning best actors in order from smallest to largest. 18; 21; 22; 25; 26; 27; 29; 30; 31; 33; 36; 37; 41; 42; 47; 52; 55; 57; 58; 62; 64; 67; 69; 71; 72; 73; 74; 76; 77 a. (5pts) find the score at the 20th percentile
The score at the 20th percentile is 27.
To find the score at the 20th percentile of the 29 ages for Academy Award winning best actors, follow the steps below:
Arrange the given ages from smallest to largest.
18; 21; 22; 25; 26; 27; 29; 30; 31; 33; 36; 37; 41; 42; 47; 52; 55; 57; 58; 62; 64; 67; 69; 71; 72; 73; 74; 76; 77
Determine the total number of data points
n = 29
Find the rank of the percentile
20th percentile = (20/100) * 29 = 5.8 = 6 (rounded to the nearest whole number).The rank of the percentile is 6.
Use the rank to determine the corresponding data value. The corresponding data value is the value at the 6th position when the data is arranged in ascending order. The score at the 20th percentile is 27.
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A barista mixes 12lb of his secret-formula coffee beans with 15lb of another bean that sells for $18 per lb. The resulting mix costs $20 per lb. How much do the barista's secret-formula beans cost per pound?
Answer: $22.50
Step-by-step explanation:
Let x be the cost per pound of the secret-formula coffee beans.
The total cost of the secret-formula beans is 12x dollars.
The total cost of the other beans is 15 × 18 = 270 dollars.
The total cost of the mix is (12 + 15) × 20 = 540 dollars.
Since the barista mixed 12 pounds of the secret-formula beans with 15 pounds of the other beans, the total weight of the mix is 12 + 15 = 27 pounds.
We can set up an equation based on the total cost of the mix:
12x + 270 = 540
Subtracting 270 from both sides:
12x = 270
Dividing both sides by 12:
x = 22.5
Therefore, the barista's secret-formula coffee beans cost $22.50 per pound.
This is a modification of A7 - Quadratic Approximation. Create a Matlab function called myta which takes four arguments in the form myta(f,n,a,b). Heref is a function handle, n is a nonnegative integer, and a and b are real numbers. The Matlab function should find the nth Taylor Polynomial to f(x) at x = a and plug in x = b, then it should return the absolute value of the difference between this value and f(b). The the nth Taylor Polynomial to f (x) is the function g(x) = f(a) + f'(a)(x – a) += f'(a)(x – a)? + 1 1 f''(a)(x – a)3 + + f(n)(a)(x – a)". 1 3! n! 3 Here are some samples of input and output for you to test your code. When you submit your code the inputs will be different. Here vpa is being used to show lots of digits
As we have defined the Matlab function called myta which takes four arguments in the form myta(f,n,a,b).
The purpose of the function is to find the nth Taylor polynomial of the function f(x) at x = a and evaluate it at x = b. Then, it should return the absolute value of the difference between this value and f(b).
Now that we have the nth Taylor polynomial of f(x) at x = a, we can evaluate it at x = b and calculate the absolute difference between this value and f(b).
function result = myta(f,n,a,b)
syms x; % define x as symbolic variable
g = f(a); % initialize g as f(a)
for i=1:n % iterate from 1 to n
deriv = diff(f,x,i-1); % calculate the ith derivative of f
term = deriv*(x-a)^(i-1)/factorial(i-1); % calculate the ith term of the Taylor series
g = g + term; % add the ith term to g
end
result = abs(g - f(b)); % calculate the absolute difference between g(b) and f(b)
end
This code calculates the absolute difference between g(b) and f(b) using the "abs" function and assigns it to the output variable "result".
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