The distance between the factories is approximately 1704 meters.
To solve this problem, we can use the Law of Cosines. Let's denote the distance between the man and Factory 1 as x, the distance between the man and Factory 2 as y, and the distance between the factories as z.
Given that the time difference for the man to hear the blasts from Factory 1 and Factory 2 is 4.2 seconds and 5.9 seconds respectively, we can calculate x and y using the speed of sound (344 m/s):
x = 4.2 seconds * 344 m/s = 1444.8 meters
y = 5.9 seconds * 344 m/s = 2030.4 meters
Now, we apply the Law of Cosines using the given angle of 40.8°:
z² = x² + y² - 2xy * cos(40.8°)
z² = 1444.8² + 2030.4² - 2(1444.8)(2030.4) * cos(40.8°)
z² ≈ 2904106.33
Take the square root to find the distance between the factories:
z ≈ √2904106.33 ≈ 1704.14 meters
Rounded to the nearest meter, the distance between the factories is approximately 1704 meters. However, this answer is not included in the given options. There might be an error in the question or the provided options.
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Determine whether the series 2 + cos(n) n 71.1 is convergent or divergent using the Comparison Test. ow
To use the Comparison Test, we need to find a series that we know is either always greater than or always less than our given series
. Since cosine values oscillate between -1 and 1, we know that 2 + cos(n) is always greater than or equal to 1. Therefore, we can compare our given series to the series 1/n, which we know is a p-series with p = 1 and is divergent.
Using the Comparison Test, we can say that since 1/n is divergent and 1/n ≤ 2 + cos(n) for all n ≥ 71.1, then the series 2 + cos(n) n 71.1 must also be divergent. Therefore, the series 2 + cos(n) n 71.1 is divergent.
Hi! To determine whether the series Σ(2 + cos(n)), where n ranges from 1 to infinity, is convergent or divergent using the Comparison Test, we need to compare it with another series whose convergence behavior is known.
Consider the series Σ(2), which is a constant series where every term is 2. This series diverges, as its partial sums keep increasing without bound. Since cos(n) is bounded between -1 and 1, we know that for every n, 1 ≤ (2 + cos(n)) ≤ 3.
Now, using the Comparison Test, we can compare Σ(2 + cos(n)) with Σ(2). Since Σ(2) is divergent and 2 + cos(n) is always greater than or equal to 2, we can conclude that the series Σ(2 + cos(n)) is also divergent.
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When the mortgage is completely paid off for Mark and Lynne’s house, it will be 3 times as old as it is now. If they have 12 years left on the mortgage, how old is the house right now?
The house is currently 6 years old.
It is mentioned that when the mortgage is completely paid off for Mark and Lynne's house, it will be 3 times as old as it is now. They have 12 years left on the mortgage.
Let's denote the current age of the house as x. When the mortgage is paid off, the house will be x + 12 years old (since they have 12 years left on the mortgage). At that point, the house will be 3 times its current age, so we can write the equation:
x + 12 = 3x
Now we can solve for x:
12 = 2x
x = 6
So, the house is currently 6 years old.
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The scatter plot shows the number of miles per gallon (MPG) for trucks with different weights. Select all the associations shown by the scatter plot.
positive association
negative association
linear association
nonlinear association
no association
The associations rhat are shown by the graph are
negative associationlinear associationHow does a graph show negative association linear associationA graph depicting a negative linear association appears as points on the chart are concomitantly placed around a straight line that confidently descends from left to right. In simpler terms, there is a notable inverse correlation between the x and y variables, which can be best comprehended with the help of an illustration.
For instance, if one were to consider a dataset representing the age of an automobile (x) and its fuel efficiency in miles per gallon (y), a graph displaying a rigorous negative linear association implies that with an increase in the age of the car, its energy proficiency has an inclination to decrease.
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Determine the equation of the line that passes through the point ( 3,-1/2) and is perpendicular to the line y =-2x+3
The equation for the line that passes through the point ( 3,-1/2) and is perpendicular to the line y =-2x+3 is:
y = (1/2)*x - 2
How to find the equation of the line?Remember that two linear equations are perpendicular if the product between the slopes is -1, here we want a line perpendicular to:
y =-2x+3
Then if the slope of our line is a, we must have that:
a*-2 = -1
a = 1/2
Then our line is something like:
y = (1/2)x + b
Now we also want our line to pass through (3, -1/2), then:
-1/2 = (1/2)*3 + b
-1/2 = 3/2 + b
-1/2 - 3/2 = b
-2 = b
The linear equation is:
y = (1/2)*x - 2
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In the number 217 361. 05 which digit is in the hundreds place?
Answer:3
Step-by-step explanation: We see that 217361.05 =217000+361.05 so our answer is 3
Define a useful quantity for our expectation about the amount of a time an
in-control process will remain ostensibly in-control, the average run length (ARL), to be the number of samples that will be observed, on average, before a point falls outside control limits. If p is the probability that any given point falls outside the control limits, then:
ARL = 1/p
(Estimating the true ARL may be useful for detecting an out-of-control process, but not
necessarily doing so quickly.) A process is Gaussian with mean 8 and standard deviation 2. The process is monitored by taking samples of size 4 at regular intervals. The process is declared to be out of control if a point plots outside the 3σ control limits on an X-chart. If the process mean shifts to 9, what is the average number of samples that will be drawn before the shift is detected on an X-chart?
Answer:
First, we need to calculate the control limits for the X-chart. Since the sample size is 4, the standard deviation of the sample mean is:
σ/√n = 2/√4 = 1
The 3σ control limits for the X-chart are:
Upper Control Limit (UCL) = 8 + 3(1) = 11
Lower Control Limit (LCL) = 8 - 3(1) = 5
Next, we need to find the probability that a point falls outside the control limits when the process mean shifts to 9. This can be calculated using the Gaussian distribution:
P(X < 5 or X > 11) = P(Z < (5-9)/2) + P(Z > (11-9)/2) = 0.00135 + 0.00135 = 0.0027
where Z is the standard normal distribution.
Therefore, the average run length (ARL) is:
ARL = 1/p = 1/0.0027 = 370.37
So on average, it will take 370.37 samples before the process mean shift is detected on an X-chart.
Chord eg measures 8 inches and the distance from the center of j to the chord is 3 inches
The length of chord segment EG = 6 inches and the length of FG = √23 inches.
Given, chord EG = 8 inches and the distance from the center of J to the chord is 3 inches.
We can draw a diagram as follows:
J
/ \
/ \
/ \
/ \
E-----------G
|
|
|
|
|
F
Here, OJ is perpendicular to chord EG at point F.
As per the theorem, the length of the perpendicular from the center of the circle to a chord is half the length of the diameter intersecting the chord.
So, we can find the length of the diameter intersecting chord EG and then use it to find the radius of the circle.
Length of chord EG = 8 inches
Length of OJ = 3 inches
Using Pythagorean theorem in right triangle OFG, we get:
OG² = OF² + FG²
Let x be the length of FG
We know that OF = OJ = 3 inches
OG = radius of the circle
So, we have:
radius of circle = OG = √(OF² + FG²) = √(3² + x²)
The diameter of the circle = 2(radius) = 2√(3² + x²)
Now, using the theorem mentioned above, we can say:
Length of perpendicular from the center of the circle to chord EG = OF = 3 inches
Length of diameter intersecting chord EG = 2√(3² + x²)
So, we get:
Length of chord segment EG = 2 * length of perpendicular
= 2 * 3 inches
= 6 inches
Now, we know that the chord segment EG divides the diameter intersecting it into two equal parts.
So, we have:
Length of one part of the diameter = (2√(3² + x²))/2 = √(3² + x²)
Using Pythagorean theorem in right triangle OJF, we get:
OJ² + JF² = OF²
3² + JF² = 8²
JF² = 8² - 3² = 55
JF = √55
Using Pythagorean theorem in right triangle JFG, we get:
JG² + FG² = JF²
(√(3² + x²))² + x² = 55
9 + x² + x² = 55
2x² = 46
x² = 23
x = √23
Therefore, the length of chord segment EG = 6 inches and the length of FG = √23 inches.
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The number of coyotes found in certain state counties is decreasing at a rate of 4. 5% per year. A wildlife biologist recently counted 100 coyotes in one tri-county area. The biologist uses a function to model the population over time and then uses this model to predict the coyote population. Which function model did the biologist correctly use to predict when the population would be fewer than 50 in this tri-county area?
The biologist predicts that the population would be fewer than 50 in approximately 30 years from the initial count.
The biologist likely used the exponential decay function to model the coyote population over time. This function takes the form:
P(t) = P0 * (1 - r)^t
Where:
P(t) is the population at time t,
P0 is the initial population (100 coyotes),
r is the rate of decrease (0.045 or 4.5%),
t is the time in years.
To predict when the population would be fewer than 50, the biologist would solve the equation:
50 = 100 * (1 - 0.045)^t
t = 30
This equation can be used to find the value of t, which represents the number of years it takes for the population to decrease to fewer than 50 coyotes in the tri-county area, which is 30 years.
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Richard lends to Martin P154,600. 00 under the condition that simple interest will be charged at 8. 5% per annum and the debt is payable after months. How much will Martin have to pay Richard after 36 months ?
We know that after 36 months, Martin will have to pay Richard P193,969.
Hi! Based on your question, Richard lends P154,600 to Martin at an 8.5% simple interest rate per annum, and the debt is payable after 36 months. To find out how much Martin will have to pay Richard after 36 months, we'll first calculate the interest.
Simple Interest = Principal × Rate × Time
Interest = P154,600 × 8.5% × (36 months / 12 months per year)
Interest = P154,600 × 0.085 × 3
Interest = P39,369
Now, add the interest to the principal to find the total amount Martin needs to pay Richard:
Total Amount = Principal + Interest
Total Amount = P154,600 + P39,369
Total Amount = P193,969
After 36 months, Martin will have to pay Richard P193,969.
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i need to know the full quadratic equation answer
Required Answer :
x(2x + 4)= x²+ 4 (9 - 3x)
2x² + 4x = x² + 36 - 12x
2x² - x² + 4x + 12x - 36=0
x² + 16x - 36=0
Quadratic equation in Standard form,
a = 1, b = 16c = -36Using Quadratic formula,
[tex] \implies \sf x = \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ \implies \sf x = \dfrac{ - 16 \pm \sqrt{ {16}^{2} - 4(1)( - 36)} }{2 \times 1} \\ \\ \implies \sf x = \dfrac{ - 16\pm \sqrt{256 - ( - 144)} }{2} \\ \\ \implies \sf x = \frac{ - 16 \pm \sqrt{256 + 144} }{2} \\ \\ \implies \sf x = \frac{ - 16 \pm \sqrt{400} }{2} \\ \\ \implies \sf x = \dfrac{ - 16 \pm20}{2} \\ \\ \implies \sf x = \dfrac{ - 16 \pm 20}{2} \\ \\ \implies \sf x = \dfrac{4}{2} \: or \: \dfrac{ - 36}{2} \\ \\ \implies \sf x = 2 \: or \: - 18[/tex]
Help on problem 2 and 3!
(I already did 1. Stepby step please ASAP!)
The missing angles ;
22.6°
53.1°
28.1°
Right triangleA right triangle is a type of triangle that has one of its angles measuring 90 degrees (a right angle). The side opposite to the right angle is called the hypotenuse, and the other two sides are called legs or catheti.
We have that;
[tex]Sin \alpha = 5/13\\ \alpha = Sin-1(5/13)\\ \alpha = 22.6[/tex]
[tex]Tan \alpha = 16/12\\\alpha = Tan-1 (16/12)\\= 53.1[/tex]
[tex]Sin \alpha = 8/17\\\alpha = Sin-1(8/17)\\\alpha = 28.1[/tex]
Right triangles have many practical applications, such as in trigonometry, engineering, and architecture.
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X varies jointly as y and z.
Write an equation that express each relationship. Then solve the equation for y.
An equation that express each relationship for the joint variation is X = kyz. Solving for y will give the equation y = X/(kz)
What is joint variationJoint variation is a mathematical concept that describes the relationship between two or more variables.
If X varies jointly as y and z, we can express this relationship mathematically using the formula:
X = k × y × z
X = kyz
where k is a constant of proportionality.
We can solve for y by dividing both sides by kz follows:
X/kz = kyz/kz
X/(kz) = y
Therefore, the equation that express each relationship for the joint variation is X = kyz. And the equation solved for y is y = X/(kz).
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A 4.0kg box slides with an initial speed of 3.0 m/s, end fraction towards a spring on a frictionless horizontal surface. when the box hits the spring, the spring compressed by 0.30m. what is the spring constant.
The spring constant is 180 N/m.
To solve for the spring constant, we can use the equation: k = (m * g) / x
where k is the spring constant, m is the mass of the box, g is the acceleration due to gravity (9.8 m/s^2), and x is the compression distance of the spring.
First, let's get the final velocity of the box when it hits the spring. We can use the equation:
v^2 = u^2 + 2as
where v is the final velocity (0 m/s), u is the initial speed (3.0 m/s), a is the acceleration (which is constant and equal to -k/m since the force from the spring is in the opposite direction of the box's motion), and s is the compression distance of the spring (0.30 m).
Rearranging the equation, we get:
k/m = (u^2 - v^2) / (2s)
k/4.0 = (3.0^2 - 0^2) / (2 * 0.30)
k/4.0 = 45
k = 180 N/m
Therefore, the spring constant is 180 N/m.
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please can someone help i really need help thank you
The equation of the function h(x) from the transformation is h(x) = f(x + 1)
Describing the transformation of f(x) to h(x).From the question, we have the following parameters that can be used in our computation:
The functions f(x), g(x) and h(x)
In the graph, we can see that
The graph of f(x) is the parent functionThe graph of h(x) is a shift of 1 unit leftHorizontal Shift = 1 unit left
This is represented as
h(x) = f(x + 1)
This means that the transformation of f(x) to h(x) is f(x) is shifted left 1 unit to h(x).
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Pythagorean theorem help quickly please
Answer:
In an isosceles right triangle, the length of the diagonal is √2 times the length of a leg.
c = 6√2 in. = 8.5 in.
Dilate the figure by the scale factor. Then enter
the new coordinates.
(-1. 4)
A
K = 3
SB
(3,2)
1962,-2)
A’ ([?], []).
B'(]], [])
C), D
Dilating the figure by a scale factor of 3, the new coordinates are:
A' (-3, 12)
B' (9, 6)
C' (5886, -6)
D (unknown)
To dilate a figure by a scale factor, we need to multiply the coordinates of each point by the scale factor. Given the scale factor K = 3, we can dilate the figure using the formula:
New x-coordinate = K * original x-coordinate
New y-coordinate = K * original y-coordinate
Let's apply this to the given coordinates:
(-1, 4)
New x-coordinate = 3 * (-1) = -3
New y-coordinate = 3 * 4 = 12
A' (-3, 12)
(3, 2)
New x-coordinate = 3 * 3 = 9
New y-coordinate = 3 * 2 = 6
B' (9, 6)
(1962, -2)
New x-coordinate = 3 * 1962 = 5886
New y-coordinate = 3 * (-2) = -6
C' (5886, -6)
Dilating the figure by a scale factor of 3, the new coordinates are:
A' (-3, 12)
B' (9, 6)
C' (5886, -6)
D (unknown)
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Last month, lucy and lara sold candy to raise money for their debate team. lara sold 1/5 as much candy as lucy did. if lucy sold 3/5 of a box of candy, how many boxes of candy did lara sell?
Lara sold 3/5 of a box of candy, which is the same as 0.6 boxes of candy.
How many boxes of candy did Lara sell last month to raise money?If Lucy sold 3/5 of a box of candy, then Lara sold 1/5 of 3/5, which is:
(1/5) * (3/5) = 3/25
Therefore, Lara sold 3/25 of a box of candy.
To find the number of boxes Lara sold, we can divide 3/25 by 1/5:
(3/25) ÷ (1/5) = (3/25) * (5/1) = 15/25 = 3/5
So Lara sold 3/5 of a box of candy, which is the same as 0.6 boxes of candy.
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Gianna keeps track of the number of people inside a music hall to attend a concert by looking at the number of scanned tickets. She plotted the data on the graph below, where x = 0 x=0 represents the time at 6 p.m., then drew a line of best fit. What does the point ( 1 , 92 ) (1,92) represent?
Note that the point ( 1 , 92 ) (1,92) represents the estimated number of people in the hall at 7pm.
How is this so?This is based on the given graph.
Note tha the horizontal axis = x = 0
which corresponds to 6pm
the vertical is the number of scanned tickets.
Also, the pont (1, 92) is the line of best fit so that means that at 7pm which is a n hour after 6pm, there were about 92 persons still in the hall.
Hence we are correct to state that the point ( 1 , 92 ) (1,92) represents the estimated number of people in the hall at 7pm.
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Full Question:
See attached image/graph
Can someone please help me ASAP? It’s due tomorrow.
Answer: m*n
Step-by-step explanation:
Already Know The Vertex but need help on the opens and axis of symmetry
Answer: x = -3
Step-by-step explanation:
Hope this helps.
Find the sum of all the integers between 100 and 400 that are multiples of 6.
Answer:
The sum of all numbers divisible by 6 between 100 and 400 is 12450.
Step-by-step explanation:
I think this is correct.
If it isn't, I'm sorry.
Which unique sequence of rigid motions maps quadrilateral abcd to quadrilateral efgh?
s
а
ib
4
d
ll2_3 4 5 6
e
f
h
g
a a reflection over the x-axis followed by a translation of (,y) → (, y - 4).
b. a reflection over the y-axis followed by a translation of (1,y) → (, y-6).
c a translation of (+,y) → (2, y - 3) followed by a reflection over the y-axis.
a translation of (cv) (1-6, y) followed by a reflection over the x-axis.
d.
The correct answer is option B, a reflection over the y-axis followed by a translation of (1,y) → (1, y-6).
To solve this problem, we need to find the sequence of rigid motions (i.e., transformations that preserve distance and angle) that maps quadrilateral ABCD to quadrilateral EFGH.
First, we need to identify the corresponding vertices of the two quadrilaterals. Let's assume that vertex A maps to vertex E, vertex B maps to vertex F, vertex C maps to vertex G, and vertex D maps to vertex H.
Now, we can apply different transformations to map each vertex of quadrilateral ABCD to the corresponding vertex of quadrilateral EFGH. We can try each option provided and check if it maps all the vertices correctly.
Option A involves a reflection over the x-axis, followed by a translation of (0,y) → (0, y - 4). This transformation does not map vertex A to vertex E correctly.
Option B involves a reflection over the y-axis, followed by a translation of (1,y) → (1, y - 6). This transformation maps vertex A to vertex E, vertex B to vertex F, vertex C to vertex G, and vertex D to vertex H, which is the correct mapping.
Option C involves a translation of (+,y) → (2, y - 3) followed by a reflection over the y-axis. This transformation does not map vertex A to vertex E correctly.
Option D involves a translation of (1-6, y) followed by a reflection over the x-axis. This transformation does not map vertex A to vertex E correctly.
Therefore, the unique sequence of rigid motions that maps quadrilateral ABCD to quadrilateral EFGH is a reflection over the y-axis followed by a translation of (1,y) → (1, y-6), which is option B.
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please help me with this Pythagoras theorum
Step-by-step explanation:
18 m = hypotenuse = c
5 m = b
a² + b² = c²
a² + (5)² = (18)²
a² + 25 = 324
a² = 324 - 25
a² = 299
a = √299
a = 17.29 or 17.3 m
perimeter = a + b + c
= 17.3 + 18 + 5
= 40.3 m
#CMIIW1. Direct or indirect characterization? "Nina was so annoyed at her little brother for bothering her. " Direct Indirect 2. Direct or indirect characterization? "Tim's room was a mountain of dirty clothes and used dishes that had been piled up for weeks. " Direct Indirect 3. An author can show indirect characterization through a character's thoughts, feelings, actions, and the setting of the story. Their effect on others. The rising action. Do all 3
An author can show indirect characterization through a character's thoughts, feelings, actions, and the setting of the story, as well as through their effect on others and their role in the rising action of the plot.
All of these elements can provide insights into a character's personality, motivations, and values, without the author explicitly stating them.
By carefully observing the character's interactions with others, their reactions to events, and the situations in which they find themselves, readers can draw conclusions about who the character is and what drives them.
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Which linear equation represents a relation that is NOT a function? y = 3x +6 y = 9 −4y + 5x = 20 x = 7
Answer:
x = 7 is not a function--it is a vertical line.
< Question 7 Σ Next Use partial fraction decomposition to evaluate the integral: (198r2 + 9r – 50 dr 99r2 - 26r - 8
The value of integral of (198r² + 9r – 50 dr is (16/27)ln|11r + 2| - (2/3)ln|9r - 4| + C
Now, we can write the integrand as a sum of two fractions:
(198r² + 9r - 50) / (11r + 2)(9r - 4) = A/(11r + 2) + B/(9r - 4)
To find A and B, we need to solve for them using the method of equating coefficients:
198r² + 9r - 50 = A(9r - 4) + B(11r + 2)
Setting r = 4/9 and r = -2/11, we get two equations:
198(4/9)² + 9(4/9) - 50 = A(9(4/9) - 4) + B(11(4/9) + 2)
198(-2/11)² + 9(-2/11) - 50 = A(9(-2/11) - 4) + B(11(-2/11) + 2)
Solving these equations gives A = 16/27 and B = -2/3.
So, the integral can be written as:
∫(198r² + 9r - 50) / (11r + 2)(9r - 4) dr = ∫16/27(11r + 2)^-1 dr - ∫2/3(9r - 4)^-1 dr
Integrating each term gives:
(16/27)ln|11r + 2| - (2/3)ln|9r - 4| + C
where C is the constant of integration.
In summary, using partial fraction decomposition, we can express the given integral as a sum of two simpler integrals, which can be evaluated using the natural logarithm function.
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21. if you have the raw scores of two individuals on a norm-referenced test, which of the following is important in terms of making meaning of those scores? a. measures of central tendency (mean, median, mode) b. the relative positions of the scores to the rest of the group c. whether higher scores are better than lower scores d. how an individual feels about his or her score e. all of these are important.\
The term which is important in terms of making meaning of those scores is measures of central tendency (mean, median, mode), option A.
A single number that seeks to characterise a set of data by pinpointing the centre location within that set of data is referred to as a measure of central tendency. As a result, measurements of central location are occasionally used to refer to measures of central tendency.
These also fit within the category of summary statistics. You are probably most familiar with the mean (sometimes known as the average), but there are additional central tendency measures, including the median and the mode.
The mean, median, and mode are all reliable indicators of central tendency, however depending on the situation, certain indicators are more useful than others.
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Ross Times, the student newspaper of Ross College, printed a "What do you think?" column feature asking: "Do you think that the college is doing enough to provide student parking?" Anyone could mail in a response or use the paper's Web site to respond. In all, 126 answers were received.
This is an example of:
(a) a voluntary response sample.
(b) a multistage sample.
(c) a simple random sample.
(d) a convenience sample.
(e) the placebo effect
The answer is (d) a convenience sample.
This is because the sample is not randomly selected from the population of all students at Ross College. Instead, it relies on individuals who are willing and available to respond to the question through the methods provided by the newspaper.
Therefore, the sample is more likely to be composed of individuals who feel strongly about the issue of student parking or who have had particularly positive or negative experiences with it, rather than being representative of the entire population of Ross College students.
In conclusion, the Ross Times student newspaper's feature column asking for opinions on the provision of student parking at Ross College represents a convenience sample of responses, and may not be representative of the entire population of Ross College students.
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V=-x2+14x -24 I need to find the range domain and graph?
A tray of lasagna comes out of the oven at 200°F and is placed on a table
where the surrounding room temperature is 70°F. The temperature T (in °F) of
the lasagna is given by the function (0) -e(486753-1) +70, 0 s t, where tis time
(in hours) after taking the lasagna out of the oven. What is the rate of change
in the temperature of the lasagna exactly 2 hours after taking it out of the
oven?
Rate of change in the temperature of lasagna given by function T(t) = 70 + (200 - 70) × [tex]e^{(-0.0001t)}[/tex] exactly 2 hours after taking it out of oven is -0.013 °F/hour.
Surrounding room temperature is equal to 70°F
Temperature at which lasagna comes out of the oven = 200°F
The temperature T (in °F) of the lasagna at time t (in hours) after taking it out of the oven is equal to,
T(t) = 70 + (200 - 70) × [tex]e^{(-0.0001t)}[/tex]
To find the rate of change in the temperature of the lasagna exactly 2 hours after taking it out of the oven,
Find the derivative of the temperature function with respect to time t.
T'(t) = -0.013[tex]e^{(-0.0001t)}[/tex]
Substituting t = 2 into this expression gives:
T'(2) = -0.013[tex]e^{(-0.0001\times 2)}[/tex]
= -0.013[tex]e^{-0.0002}[/tex]
= -0.013 × 0.99980
= -0.0129974
= -0.013
Therefore, the rate of change in the temperature of the lasagna exactly 2 hours after taking it out of the oven is approximately -0.013 °F/hour.
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The given question is incomplete, I answer the question in general according to my knowledge:
A tray of lasagna comes out of the oven at 200°F and is placed on a table where the surrounding room temperature is 70°F. The temperature T (in °F) of the lasagna is given by the function T(t) = 70 + (200 - 70) × [tex]e^{(-0.0001t)}[/tex] where t is time(in hours) after taking the lasagna out of the oven. What is the rate of change in the temperature of the lasagna exactly 2 hours after taking it out of the oven?
