The given family of functions is y = c1ex + c2e−x which is the general solution of the differential equation y'' − y = 0 on the indicated interval which is (−∞, ∞).
Now, we are required to find a member of the family that is a solution to the initial-value problem which is
y(0) = 0 and y′(0) = 5.
The differential equation is y'' − y = 0
The characteristic equation is r2 − 1 = 0r2 = 1r1 = 1 and r2 = −1
The general solution of the differential equation is y = c1ex + c2e−x
Let us solve for the constants by using the given initial conditions:
At x = 0,y(0) = c1e0 + c2e0 = 0 + 0 = 0y(0) = 0
means c1 + c2 = 0or c1 = -c2At x = 0, y′(0) = c1ex |x=0 + c2e−x |x=0(d/dx)(c1ex + c2e−x) |x=0y′(0) = c1 - c2 = 5c1 - c2 = 5c1 - (-c1) = 5c1 + c1 = 5c1 = 5/2c1 = 5/2
Let's replace c1 = 5/2 in c1 = -c2, c2 = -5/2
The solution of the initial-value problem y = (5/2)ex − (5/2)e−x is a member of the family y = c1ex + c2e−x that is a solution of the initial-value problem y(0) = 0 and y′(0) = 5.
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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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Jason is going to invest $720 and leave it in an account for 6 years. Assuming the interest is compounded continuously, what interest rate, to the nearest hundredth of a percent, would be required in order for Jason to end up with $930
Answer: A = Pe^(rt)
Where A is the amount of money at the end of the investment period, P is the principal amount, e is the mathematical constant e (approximately equal to 2.71828), r is the interest rate, and t is the time period.
In this case, we know that:
P = $720 (the initial investment)
A = $930 (the desired end amount)
t = 6 years (the investment period)
We can solve for r by rearranging the formula:
r = ln(A/P) / t
Where ln is the natural logarithm.
Plugging in the numbers, we get:
r = ln($930/$720) / 6
r = 0.0436 or 4.36%
Therefore, Jason would need an interest rate of approximately 4.36% (to the nearest hundredth of a percent) in order to end up with $930 after 6 years of continuous compound interest.
Answer:4.27%
Step-by-step explanation:
What is the perimeter of parallelogram ABCD, and what is AC? Please help!
The perimeter of the parallelogram is 68 and the length of AC is 15.
Calculating the perimeter of a ParallelogramFrom the question, we are to calculate the perimeter of the parallelogram and the length of AC
First,
Let half the length of AC be x
Then,
From the Pythagorean theorem, we can write that
17² = x² + 8²
289 = x² + 64
x² = 289 - 64
x² = 225
x = √225
x = 15
Recall,
x = 1/2 AC
Therefore,
AC = 2x
AC = 2(15)
AC = 30
To calculate the perimeter, we will determine the length of BC
|BC|² = x² + 8²
|BC|² = 225 + 64
|BC|² = 289
|BC| = √289
|BC| = 17
Perimeter of the parallelogram = 17 + 17 + 17 + 17
Perimeter of the parallelogram = 68
Hence, the perimeter is 68
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The population of Toledo, Ohio, in 2000 was approximately 500,000. Assume the population is increasing at a rate of 5% per year. a. Write the exponential function that relates the total population as a function of t. b. Use a. to determine the rate at which the population is increasing in t years. c. Use b. to determine the rate at which the population is increasing in 10 years.
The population of Toledo, Ohio is increasing at a rate of approximately 32,263 people per year after 10 years.
What is exponential function?An exponential function is a mathematical function of the form f(x) = a^x, where "a" is a positive constant called the base, and "x" is a variable that can take on any real value. The base "a" is typically greater than 1, which means the function grows at an increasing rate as "x" increases.
According to question:a. The exponential function that relates the total population as a function of t is given by:
P(t) = P₀ × (1 + r)ᵗ
where P₀ is the initial population, r is the annual growth rate (as a decimal), and t is the time in years.
Using the given values, we have:
P₀ = 500,000 (given)
r = 0.05 (5% expressed as a decimal)
Thus, the exponential function is:
P(t) = 500,000 × (1 + 0.05)ᵗ
b. The rate at which the population is increasing in t years is given by the derivative of the population function with respect to time:
dP/dt = P₀ × r × (1 + r)ᵗ
Substituting the given values, we get:
dP/dt = 500,000 × 0.05 × (1 + 0.05)ᵗ
c. To determine the rate at which the population is increasing in 10 years, we simply substitute t = 10 into the expression we derived in part b:
dP/dt = 500,000 × 0.05 × (1 + 0.05)¹⁰
Using a calculator, we get:
dP/dt ≈ 32,263
Therefore, the population of Toledo, Ohio is increasing at a rate of approximately 32,263 people per year after 10 years.
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Can someone help me with this please? Thank you!
Answer:
a. f(10)= 20*10+14
f(10)=200+14
f(10)= 214
214
Will give brainly award
Using the other endpoint of the diameter, and the center of the circle write an equation of the circle
Answer:
Step-by-step explanation:
C(1,2), radius=6
Equation using [tex](x-h)^2+(y-k)^2=r^2[/tex]:
[tex](x-1)^2+(y-2)^2=36[/tex]
12. Melanie collects data about the number of text messages students send each day. Number of Text Message: 94 ,105, 87, 76, 110, 80, 87, 76,101, 113, 85 Select all the true statements
a.The data set is numerical data.
b.The data set is categorical data.
c. The data set has an outlier.
d.The data set does not have an outlier.
e.A circle graph is an appropriate data display for this data.
f.A box plot is an appropriate data display for this data.
Answer: a, f. In Melanie's data set, she is collecting numerical data, specifically the number of text messages sent each day.
What is a Numerical data?Numerical data is data that is represented by numbers. It is data that can be measured and compared. Examples include age, weight, height, and number of text messages.
In Melanie's data set, she is collecting numerical data, specifically the number of text messages sent each day. This data is numerical because it can be measured and compared. This data set does not have an outlier because all of the values are within a reasonable range and no single value is significantly higher or lower than the others.
A box plot is an appropriate data display for this data because it allows for an easy comparison of the data. The box plot will show the median, the range of values, and any outliers.
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How do you find height when you are doing volume with cubic units?
Answer:calculate the cube root of a cube's volume.
Step-by-step explanation:
pls answert this within 1 hour or else i will be DOOMED
In the fractions prompts given, the correct output are:
(1 ÷2) ÷ 4 = 1/8(1 ÷5) ÷ 2 = 1/10(1 ÷3) ÷ 5 = 1/15(1 ÷4) ÷ 4 = 1/16The solution to the problem for (1/2) ÷ 3 is given below.What is a fraction?A fraction represents a part of a whole. It consists of a numerator and a denominator, with the numerator indicating the number of parts and the denominator indicating the total number of parts.
The calculations are given as follows;
1 )
= (1/2) x (1/4) [dividing by a number is the same as multiplying by its reciprocal]
= 1/8
2) (1/5) ÷ 2
= (1/5) x (1/2)
= 1/10
3)
(1/3) ÷ 5
= (1/3) x (1/5)
= 1/15
4) (1/4) ÷ 4
= (1/4) x (1/4)
= 1/16
5) One day, Amy baked a cake and wanted to divide it equally among 3 of her friends. She realized she only had half a cake left, so she decided to divide it into equal parts. Each friend received 1/6 of a cake. To check her calculation, she multiplied 1/6 by 3 and got 1/2. Thus, (1/2) ÷ 3 = 1/6, since dividing by 3 is the same as multiplying by 1/3.
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Assume that "a" is the average of p, 2q, and 4; "b" is the average of 2p, 4q, and 8; and "c" and the average of 6p, 3q, and 6. What is the average of "a, b, c" in terms of p and q?
a) p + q + 2
b) p + q + 4
c) 3p + 6q + 6
d) 9p + 6q + 2
The average of "a, b, c" in terms of p and q is a) p + q + 2
How to determine the averageThe question asks us to find out the average of a, b, and c in terms of p and q.
The given data in the question are -a, b, and c are the averages of p, 2q, and 4; 2p, 4q, and 8; and 6p, 3q, and 6, respectively.
We need to find the average of these averages.
Let's solve for a first:a = (p + 2q + 4) / 3
We can solve for b as:
b = (2p + 4q + 8) / 3
And, solving for c,c = (6p + 3q + 6) / 3
Now, let's sum a, b, and c:
a + b + c = [(p + 2q + 4) / 3] + [(2p + 4q + 8) / 3] + [(6p + 3q + 6) / 3]= [p + 2q + 4 + 2p + 4q + 8 + 6p + 3q + 6] / 3= (9p + 9q + 18) / 3= 3(p + q + 2)
Therefore, the answer is option A, p + q + 2.
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A company has hired 12 new employees and must assign eight to the dayshift and four to the night shift and how many ways can the assignment be made ?
There are 495 ways to assign 8 employees to the day shift and 4 employees to the night shift from a group of 12 employees.
How many ways can the company assign eight employees to the dayshift and four employees to the night shift?Given that, we need to find the number of ways to assign 8 employees to the day shift and 4 employees to the night shift from a group of 12 employees.
We can use combinations to solve this problem.
The number of ways to choose 8 employees from 12 for the day shift is:
C(12,8)
= 12! / ( 12 - 8 )! × 8!
= 495
Similarly, the number of ways to choose 4 employees from the remaining 4 for the night shift is:
C(4,4) = 1
= 4! / ( 4 - 4 )! × 4!
= 4!/4!
= 1
Therefore, the total number of ways to make the assignment is:
495 × 1 = 495
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what is the phase angle, , in degrees if the expression is since angles are not unique, they can differ by multiples of 360, select the answer to be in the range of -180 to 180 degrees.
The phase angle, in degrees is -135.
A wave that repeats as a function of time and position is referred to as a periodic wave. Amplitude, frequency, wavelength, speed, and energy describe the properties of the wave. The phase angle is used to describe the characteristics of a periodic wave.
In phasors, a wave exhibits twofold characteristics: Magnitude and Phase. The phase angle refers to the angular component of a periodic wave.
The Phase Angle is one of the crucial characteristics of a periodic wave. It is similar to the phrase in many properties. The angular component periodic wave is known as the Phase Angle. It is a complex quantity measured by angular units like radians or degrees. A representation of any pure periodic wave is as follows.
A∠θ, where A is the magnitude and θ represents the Phase Angle of the wave.
A is the magnitude
θ is the phase angle
The expression is, which can be reduced to. Since angles are not unique, they can differ by multiples of 360, the answer is -135 degrees, which is in the range of -180 to 180 degrees.
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Given A = (-3,2) and B = (7,-10), find the point that partitions segment AB in a 1:4 ratio
The point that partitions segment AB in a 1:4 ratio would be (-3/5, -1/5).
How to find the ratio?To find the point that partitions segment AB in a 1:4 ratio, we can use the section formula.
We can use the formula for finding the coordinates of a point that partitions a line segment in a given ratio. The formula is:
C = ((1 - r) * A + r * B) / 4
where, r is the ratio (in this case, 1:4, so r = 1/5).
Substituting the values for A, B, and r, we get,
C = ((1 - 1/5) * (-3, 2) + (1/5) * (7, -10)) / 4
Simplifying,
C = (4/5 * (-3, 2) + 1/5 * (7, -10)) / 4
C = (-12/5, 8/5 - 2) / 4
C = (-12/20, 8/20 - 10/20)
C = (-3/5, -1/5)
Therefore, the point that partitions segment AB in a 1:4 ratio is (-3/5, -1/5).
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NEED HELP DUE TODAY!!!! GIVE GOOD ANSWER
2. How do the sizes of the circles compare?
3. Are triangles ABC and DEF similar? Explain your reasoning.
4. How can you use the coordinates of A to find the coordinates of D?
The triangles ABC and DEF are similar triangles, but DEF is twice as big as ABC.
What does it signify when two triangles are similar?
Congruent triangles are triangles that share similarity in shape but not necessarily in size. All equilateral triangles and squares of any side length serve as illustrations of related objects.
Or to put it another way, the corresponding angles and sides of two triangles that are similar to one another will be congruent and proportionate, respectively.
How do the sizes of the circles compare?
Given the triangles ABC and DEF
From the figure, we have
AB = 1
DE = 2
This means that the triangle DEF is twice the size of the triangle ABC
Are triangles ABC and DEF similar?
Yes, the triangles ABC and DEF are similar triangles
This is because the corresponding sides of DEF is twice the corresponding sides of triangle ABC
How can you use the coordinates of A to find the coordinates of D?
Multipliying the coordinates of A by 2 gives coordinates of D.
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on her way to visit her parents, jennifer drives 265 miles in 5 hours what is her average rate of speed in miles per hour?
Answer:
53 miles per hour
Step-by-step explanation:
To calculate Jennifer's average rate of speed in miles per hour, we can use the formula:
average speed = total distance / total time
In this case, Jennifer drove a total distance of 265 miles and it took her a total time of 5 hours, so:
average speed = 265 miles / 5 hours
Simplifying the expression, we get:
average speed = 53 miles per hour
Therefore, Jennifer's average rate of speed in miles per hour is 53 miles per hour.
Answer: 53 miles per hour
Step-by-step explanation:
To find Jennifer's average rate of speed in miles per hour, we divide the distance she traveled by the time it took her:
Average speed = distance ÷ time
Average speed = 265 miles ÷ 5 hours
Average speed = 53 miles per hour
Therefore, Jennifer's average rate of speed was 53 miles per hour.
Austin has a dimes and y nickels, having at most 28 coins worth a minimum of $2
combined. At least 18 of the coins are dimes and no more than 6 of the coins are
nickels. Solve this system of inequalities graphically and determine one possible
solution.
The solution of system of inequalities solved graphically is (18,6).
What is system of linear inequalities?A group of two or more linear inequalities are graphed together on a coordinate plane to discover the solution that concurrently satisfies all the inequalities. This is known as a system of linear inequalities. The location where all the half-planes overlap is where the system is solved. Each inequality defines a half-plane on the coordinate plane. Every point in this area, which is referred to as the feasible region, fulfils all of the system's inequalities. To identify the optimum solution for an optimization problem given a set of constraints, systems of linear inequalities are frequently utilised.
Let us suppose the number of dimes = a.
Let us suppose the number of nickels = y.
According to the problem we have the following conditions:
a + y ≤ 28 (at most 28 coins)
0.10a + 0.05y ≥ 2 (worth at least $2)
a ≥ 18 (at least 18 dimes)
y ≤ 6 (no more than 6 nickels)
Using different values of a and y plot the points.
The solution of this system of inequality is any point that lies in the feasible region.
One such point is (18, 6).
Hence, the solution of system of inequalities solved graphically is (18,6).
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Find the distance between each pair of points.
a. M= (0,-11) and P=(0,2)
b. A= (0,0) and B= (-3,-4)
c. C= (8,0) and D=(0,-6)
Answer:
To calculate the distance between each pair of points given, we can use the distance formula which is derived from the Pythagorean theorem. The formula is:
distance = square root of [(x2 - x1)^2 + (y2 - y1)^2]
Using this formula, we can calculate the following distances:
a. Distance between M and P = 13 units
b. Distance between A and B = 5 units
c. Distance between C and D = 10 units
three cards are drawn with replacement from a standard deck of 52 cards. find the the probability that the first card will be a diamond, the second card will be a black card, and the third card will be a face card. express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
The probability of drawing a diamond, then a black card, and then a face card from a standard deck of 52 cards with replacement is 3/104 or 0.028846 .
What is the probability?The probability that the first card will be a diamond, the second card will be a black card, and the third card will be a face card is given by the expression, `(13/52) × (26/52) × (12/52)`.
In a standard deck of 52 cards, there are 13 diamonds, 26 black cards (13 clubs and 13 spades), and 12 face cards (4 Jacks, 4 Queens, and 4 Kings).
To calculate the probability that the first card will be a diamond, the second card will be a black card, and the third card will be a face card, we use the formula of probability:
`P(E) = n(E) / n(S)`
where, P(E) = Probability of an event
n(E) = Number of favorable outcomes
n(S) = Total number of outcomes
Total number of outcomes = 52
First card will be a diamond
Number of diamonds in a deck of 52 cards = 13
Total number of outcomes after drawing the first card = 52
Probability of drawing a diamond in the first attempt = P(diamond)`= 13/52
Probability of drawing a black card in the second attempt, given that the first card is a diamond= `P(black/diamond)`= (26/52) = `(1/2)`
Probability of drawing a face card in the third attempt, given that the first card is a diamond and second card is a black card= `P(face/diamond and black)`= `(12/52)` = `(3/13)`
Therefore, probability that the first card will be a diamond, the second card will be a black card, and the third card will be a face card`= P(diamond) × P(black/diamond) × P(face/diamond and black) = (13/52) × (1/2) × (3/13)= 3/104`
Therefore, the required probability is 3/104 or 0.028846 rounded to the nearest millionth.
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Algebra question help asap
If the value of the Bulls Eye stock has fallen 8% annually since 2010, it will be worth $32.90 in 2015.
What is the mathematical formula for profit?The formula Profit = Selling Price - Cost Price can be used to determine the profit when the selling price and the cost price of a product are known. The formula for calculating profit percentage is then applied, which is profit percentage = (profit/cost price) x 100.
If the value of the Bulls Eye stock has dropped by 8% annually, it has dropped to 92% (100% - 8%) of its value from the prior year.
Since we're moving from 2010 to 2015, we must multiply this loss five times to determine the stock's value in 2015:
Value in 2011 = 92% of $50 = $46
Value in 2012 = 92% of $46 = $42.32
Value in 2013 = 92% of $42.32 = $38.89
Value in 2014 = 92% of $38.89 = $35.77
Value in 2015 = 92% of $35.77 = $32.90
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in a box there are yellow pens and green pens. pens are randomly selected, one at a time, until a yellow one is obtained. assume that each selected pen is replaced before the next one is drawn. what is the probability that you need to pick up a pen at least 3 times?
Suppose that we randomly choose pens from a box that contains yellow and green pens until a yellow pen is obtained. Assume that each selected pen is replaced before the next one is drawn. In order to find the probability of picking up a pen at least three times, we need to use the probability formula.
For this problem, the probability of choosing a yellow pen on the first draw is P(Y) = number of yellow pens / total number of pens = y / (y+g), where y is the number of yellow pens and g is the number of green pens. The probability of not choosing a yellow pen on the first draw is P(NY) = g / (y+g).After selecting a pen, if it is not yellow, we need to select a pen again. The probability of selecting a pen that is not yellow on the second draw is the same as the probability of not selecting a yellow pen on the first draw, that is[tex]P(NY) = g / (y+g).[/tex]
Therefore,
the probability of choosing a yellow pen on the second draw is P(Y and NY) = [tex]P(Y) × P(NY) = y × g / (y+g)²[/tex].The probability of not choosing a yellow pen on the first two draws is P(NYY) = P(NY) × P(NY) = g² / (y+g)².To calculate the probability of choosing a yellow pen on the third draw, we need to consider two cases: the pen selected on the first two draws is green, and the pen selected on the first two draws is not green.
Case 1: The pen selected on the first two draws is green. The probability of selecting a yellow pen on the third draw is P(Y and NY and G) =[tex]P(Y) × P(NY) × P(G) = y × g × (y+g) / (y+g)³.[/tex]
Case 2: The pen selected on the first two draws is not green. The probability of selecting a yellow pen on the third draw is P(Y and NY and NY) = P(Y) × P(NY) × P(NY) = y × g² / (y+g)³.Therefore, the probability of picking up a pen at least three times is P(at least 3) = P(NYY) + P(Y and NY and G) + P(Y and NY and NY) = g² / (y+g)² + y × g × (y+g) / (y+g)³ + y × g² / (y+g)³ = g² / (y+g)² + 2y × g / (y+g)³.
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1. The relationship between the amount of time a car is parked, in hours, and the cost
of parking, in dollars, can be described with a function.
a. Identify the independent variable and the dependent variable in this function.
b. Describe the function with a sentence of the form "
is a function of
a. The independent variable is the amount of time a car is parked, measured in hours. The dependent variable is the cost of parking, measured in dollars.
b. The function describes the relationship between the amount of time a car is parked and the cost of parking. It can be written as Cost of parking = f(Time parked)
a) The independent variable in this function is the amount of time a car is parked, measured in hours. The dependent variable is the cost of parking, measured in dollars.
b) The function describes the cost of parking as a function of the amount of time a car is parked, where the independent variable is the amount of time in hours, and the dependent variable is the cost in dollars. For example, the function could be written as "Cost of parking = f(Time parked)" or "C = f(T)" where C is the cost and T is the time parked. The specific function would depend on the details of the parking fee structure.
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give a binary representation for each number given below in hex. drop the leading zeroes in your binary representation. (a) a3 (b) 1fc (c) 2a0b
The binary representation is (a) a3 in binary is 10100011(b) 1fc in binary is 11111100(c) 2a0b in binary is 1010100000001011
In hexadecimal, each digit represents four bits, which means that two hexadecimal digits can represent eight bits. As a result, converting from hexadecimal to binary is straightforward. The four bits corresponding to each hexadecimal digit can be written down, resulting in an 8-bit binary value.
To convert hexadecimal to binary, simply convert each hexadecimal digit to binary, then combine them to get the final binary representation. For instance, in a, the hexadecimal digit a has a binary representation of 1010, while the digit 3 has a binary representation of 0011.
Combining these results in a binary representation of 10100011. Similarly, the binary representations of 1f and c are 00011111 and 00001100, respectively.
Combining them results in 11111100. Finally, the binary representation of 2a0b is obtained by converting 2, a, 0, and b to binary, resulting in 0010, 1010, 0000, and 1011, respectively. Combining them results in 1010100000001011.
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a market research firm conducts telephone surveys with a historical response rate. what is the probability that in a new sample of telephone numbers, at least individuals will cooperate and respond to the questions? in other words, what is the probability that the sample proportion will be at least ? calculate the probability to decimals. use z-table.
The probability that the sample proportion will be at least k is 0.7580.
Let P be the probability that any one person in the population will cooperate and respond to the questions. We are looking for the probability that at least k people out of n in the sample will cooperate and respond to the questions. Let X be the number of people who cooperate and respond to the questions in the sample. X follows the binomial distribution with parameters n and P.To calculate this, use the following formula:
Z = (X - μ) / σ
Here, X = number of people who cooperate and respond to the questions in the sample
μ = E(X) = np, σ = sqrt(npq)
q = 1 - P
Now, to calculate the probability, first calculate μ = np =
σ = sqrt(npq)
Then, find the z-score using z = (k - μ) / σ.
Now, use the z-table to find the probability corresponding to the z-score obtained in the previous step. The probability obtained from the z-table is the probability that the sample proportion will be at least k.
The probability that the sample proportion will be at least k is 0.7580.
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Two lines are plotted on the same coordinate plane. The first line passes through the points (-5, -5) and (-3, -3). The second line passes through the points (3, 1) and (4, 2). The two lines are best described as:
A. intersecting, not perpendicular
B. intersecting and perpendicular
C. parallel
D. no relationship
The slopes of the two line are equal. Hence, the two lines are parallel.
What is slope of a line?A line's slope is a gauge of the line's steepness. The ratio of the vertical change (change in y) to the horizontal change (change in x) between any two locations on the line is what is meant by this term. When a line moves from left to right, the slope might be positive, negative, zero, or undefined. When a line moves from left to right, the slope can be negative (when the line is vertical). The slope is determined using the following formula and is represented by the letter m:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are any two points on the line.
Given that, the first line passes through the points (-5, -5) and (-3, -3).
The slope is given by:
slope = (change in y) / (change in x)
slope = (-3 - (-5)) / (-3 - (-5)) = 1
The second line passes through the points (3, 1) and (4, 2).
slope = (2 - 1) / (4 - 3) = 1
The slopes of the two line are equal. Hence, the two lines are parallel.
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4) A bus company charges $2 per ticket but wants to raise the price. The daily revenue is modeled by R(x)=-30(x-6)² + 320, where x is the number of $0.15 price increases and R(x) is the revenue in dollars. What should the price of the tickets be for a maximum profit? Hint: don't forget what price where you started.
Answer:
$2.90
Step-by-step explanation:
6 × 0.15 = 0.9
2 + 0.9 = 2.9
R(x) = -30(x - 6)² + 320
This equation for the revenue is a quadratic equation model written in the form of completing the square;
This form appears like so:
f(x) = a(x + b)² + c
It is quite useful, especially for this type of question;
Firstly, if a is positive, the quadratic equation will be a u shaped graph when illustrated, if negative, it will be an n shaped graph;
What this means is if a is positive, the vertex of the graph is the lowest point, i.e. the minimum value of f(x), and if a is negative, the vertex will be the highest point, i.e. the maximum value of f(x);
Secondly, the coordinates of the vertex will be:
(-b, c)
So, with regards to the question:
We have -30 in the position of a, the curve is therefore n shaped and the vertex is the highest point (known as the local maximum);
And in place of b and c, we have -6 and 320, so the coordinates of this local maximum are:
(6, 320)
We interpret this like so:
320 is the highest possible value of R(x), which represents revenue, so $320 is the maximum revenue according to this model, and it is achieved when x = 6, i.e. when the price is increased by $0.90 (= 6 × $0.15);
Finally, to get the new ticket price, we add this to the original price to get $2.90.
Here are two closed containers and four balls just fit in each container. Each ball has a diameter of 54 mm. Which container has the smaller surface are? You must show your working
both containers have the same surface area and neither has a smaller surface area than the other.
Container 1:
Surface area of a single ball = π x (54/2)^2 = 3,092.62 mm^2
Total surface area of 4 balls = 12,370.48 mm^2
Container 2:
Surface area of a single ball = π x (54/2)^2 = 3,092.62 mm^2
Total surface area of 4 balls = 12,370.48 mm^2
Both containers have the same surface area.
To calculate the surface area of the two containers, I first calculated the surface area of one ball by using the formula π x (diameter/2)^2. I then multiplied this by 4 to get the total surface area of 4 balls. I repeated this process for both containers and found that both containers had the same surface area of 12,370.48 mm^2. both containers have the same surface area and neither has a smaller surface area than the other.
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With the information given, can you prove
that this quadrilateral is a parallelogram?
A. Yes
B. No
AB = DC
We cannot prove that the quadrilateral is a parallelogram with only the given information that AB = DC.
What is quadrilateral and parallelogram ?
A quadrilateral is a four-sided polygon, which means it is a closed shape with four straight sides. Some examples of quadrilaterals include rectangles, squares, trapezoids, and rhombuses.
A parallelogram is a special type of quadrilateral where both pairs of opposite sides are parallel. This means that the opposite sides never intersect, and they have the same slope. Additionally, the opposite sides of a parallelogram are congruent (i.e., have the same length), and the opposite angles are also congruent. Some examples of parallelograms include rectangles, squares, and rhombuses.
To prove that a quadrilateral is a parallelogram, we need to show that both pairs of opposite sides are parallel. Knowing that AB = DC only gives us information about the lengths of the sides, but it doesn't tell us anything about their orientation or whether they are parallel.
We would need additional information, such as the measures of angles or the lengths of other sides, to determine whether the quadrilateral is a parallelogram.
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HELP DUE TODAY!!!!!!!!!
. Write the (x, y) coordinates for P in terms of cosine and sin.
6. Using the image above, if cos(Θ) = 0.6, what are the coordinates of P? Explain your reasoning.
Explanation:
Use the pythagorean trig identity to determine sine based on cos(theta) = 0.6
[tex]\sin^2(\theta)+\cos^2(\theta) = 1\\\\\sin^2(\theta)=1-\cos^2(\theta)\\\\\sin(\theta)=\pm\sqrt{1-\cos^2(\theta)}\\\\\sin(\theta)=-\sqrt{1-\cos^2(\theta)} \ \ \text{....sine is negative in quadrant Q4}\\\\\sin(\theta)=-\sqrt{1-(0.6)^2}\\\\\sin(\theta)=-\sqrt{1-0.36}\\\\\sin(\theta)=-\sqrt{0.64}\\\\\sin(\theta)=-0.8\\\\[/tex]
Since [tex]\cos(\theta)=0.6 \text{ and } \sin(\theta)=-0.8[/tex], the location of point P is (0.6, -0.8)
Recall that for any point (x,y) on the unit circle, we have:
[tex]\text{x}=\cos(\theta)\\\\\text{y}=\sin(\theta)[/tex]
meaning cosine is listed first in any (x,y) pairing.
PLS ANWSER ASAP VERY HARD FOR ME
Answer:
x = 6
Step-by-step explanation:
Verticle angles are equal to each other...
m∠A = m∠B
Thus...
4x + 6 = 2x + 18
Now, we isolate x:
4x + 6 = 2x + 18
Subtract 6 from both sides
4x = 2x + 12
Subtract 2x from both sides
2x = 12
Divide both sides by 2
x = 6
Five percent of my students suffer from a terrible malady called Lazybrain(LB). A blood test detects LB accurately 90% of the time. Yusuke is told that his blood test is positive for LB. Yusuke hopes that this is a "flase positive" and he actually doesn't have LB. i. Draw the tree with all the probabilities. Indicate which branches are false positive, false negative, correct positive, and correct negative.
The tree diagram with probabilities that shows all possible outcomes for Yusuke's situation is mentioned below .
What is tree diagram?A tree diagram is a visual tool used to represent hierarchical structures or relationships.
It consists of a branching structure where each branch represents a different category or possibility, allowing for easy visualization of complex systems or decision-making processes.
LB (+) LB (-)
Test (+) 0.045 (true) 0.055 (false positive)
Test (-) 0.005 (false negative) 0.895 (true negative)
The probabilities are as follows:
0.05 (5%) of the students have LB, and therefore the probability of Yusuke having LB is 0.05.
The blood test detects LB accurately 90% of the time, meaning that the probability of a correct positive test result (i.e., Yusuke has LB and the test detects it) is 0.05 * 0.9 = 0.045.
The probability of a false positive test result (i.e., Yusuke does not have LB but the test detects it) is 0.95 * 0.1 = 0.055.
The probability of a true negative test result (i.e., Yusuke does not have LB and the test does not detect it) is 0.95 * 0.9 = 0.855.
The probability of a false negative test result (i.e., Yusuke has LB but the test does not detect it) is 0.05 * 0.1 = 0.005.
Note that the sum of the probabilities for each possible outcome (i.e., correct positive, false positive, true negative, false negative) should add up to 1.
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Yusuke having LB is 0.05. Yusuke has LB, the test detects it is 0.05 * 0.9 = 0.045. Yusuke does not have LB, the test detects it is 0.95*0.1 = 0.055. Yusuke does not have LB , the test does not detect it is 0.95 0.9 =0.855.
What is tree diagram?A tree diagram is a visual tool used to represent hierarchical structures or relationships.
It consists of a branching structure where each branch represents a different category or possibility, allowing for easy visualization of complex systems or decision-making processes.
LB (+) LB (-)
Test (+) 0.045 (true) 0.055 (false positive)
Test (-) 0.005 (false negative) 0.895 (true negative)
The probabilities are as follows:
0.05 (5%) of the students have LB, and therefore the probability of Yusuke having LB is 0.05.
The blood test detects LB accurately 90% of the time, meaning that the probability of a correct positive test result (i.e., Yusuke has LB and the test detects it) is 0.05 * 0.9 = 0.045.
The probability of a false positive test result (i.e., Yusuke does not have LB but the test detects it) is 0.95 * 0.1 = 0.055.
The probability of a true negative test result (i.e., Yusuke does not have LB and the test does not detect it) is 0.95 * 0.9 = 0.855.
The probability of a false negative test result (i.e., Yusuke has LB but the test does not detect it) is 0.05 * 0.1 = 0.005.
Note that the sum of the probabilities for each possible outcome (i.e., correct positive, false positive, true negative, false negative) should add up to 1.
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