Answer: c
Step-by-step explanation:
The number of solutions on the graph is zero.
What is graph?In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.
here, we have,
to determine the number of solutions:
The graph shows a linear equation (the straight line) and a non linear equation (the curve)
From the graph, we can see that the straight line and the curve do not intersect
This means that the graph do not have any solution
Hence, the number of solutions on the graph is zero
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1. How long does pia's journey take?
2. How much longer does Sam spend driving then Pia?
a) Pea's journey takes 2.25 hours.
b) Sam spends 0.25 hours longer driving than Pea.
a. To find Pea's journey time, we use the formula:
time = distance / speed
Substituting the values given, we get:
time = 180 km / 80 km/h
time = 2.25 hours
b. To find how much longer Sam spends driving than Pea, we can subtract the journey times.
time taken by Sam = distance / speed = 200 km / 80 km/h = 2.5 hours
Time difference = Sam's journey time - Pea's journey time = 2.5 hours - 2.25 hours = 0.25 hours
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an international company has employees in one country. if this represents of the company's employees, how many employees does it have in total? round your answer to the nearest whole number.
The total number of employees in the company would be 5, rounded to the nearest whole number.
The formula to calculate the total number of employees in a company is:
Total Number of Employees = Number of Employees in One Country x Proportion of Company's Employees.
For example, if a company has 10 employees in one country and that represents 50% of the company's employees, then the total number of employees in the company would be:
Total Number of Employees = 10 x 0.5 = 5
Therefore, if a company has 10 employees in one country and that represents 50% of the company's employees, then the total number of employees in the company would be 5, rounded to the nearest whole number.
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the average athlete is able to begin activity 90 days after having a knee operation. the standard deviation is 15 days. fifty percent of athletes are able to participate within how many days? round to the nearest day.
On average, 50% of athletes are able to begin activity 90 days after a knee operation, with a standard deviation of 15 days.
This means that the median time for 50% of athletes to be able to participate is 75 days, rounded to the nearest day.
The average time for an athlete to begin activity after a knee operation is 90 days, and the standard deviation is 15 days.
Standard deviation is a measure of how spread out the data points are in a data set; a larger standard deviation means that the data points are more spread out.
In this case, 50% of athletes can begin activity within 75 days, which is the median. By rounding to the nearest day, this would be 75 days. Therefore, 50% of athletes are able to participate within 75 days, rounded to the nearest day.
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The manager at Braums recorded the orders of their customers over the last hour and had the following number of ice cream cones 4 vanilla, 5 chocolate, 2 peanut butter cup, 3 strawberry, and 2 coffee. Based on these numbers, what is the probability of the next customer ordering peanut butter cup? Write your answer as a decimal
Answer:
To find the probability of the next customer ordering peanut butter cup, we need to determine the total number of ice cream cones and the number of cones that are peanut butter cup.
The total number of cones is:
4 + 5 + 2 + 3 + 2 = 16
The number of cones that are peanut butter cup is 2.
Therefore, the probability of the next customer ordering peanut butter cup is:
2/16 = 0.125
So, the probability of the next customer ordering peanut butter cup is 0.125 or 12.5%.
I tried and it did not make sense help
Answer: D) -20.99
Step-by-step explanation:
-4.97-2.36+-5.19-8.47 = -20.99
100 points please helq
Answer:
x^2 - 4x + 6 = 0
Step-by-step explanation:
x^2 + 2 - 4x = -4
x^2 - 4x + 2 + 4 = 0
x^2 - 4x + 6 = 0
Determine if the given functions are even, odd or neither f(x)=x^2-7
The function f(x) = x² - 7 is an example of a function that is neither even nor odd, as it does not exhibit either type of symmetry.
To determine whether a function is even, odd, or neither, we need to examine its algebraic form and look for a particular type of symmetry.
Let's apply this concept to the given function, f(x) = x² - 7. To determine whether f(x) is even or odd, we need to evaluate f(-x) and compare it to f(x).
f(-x) = (-x)² - 7 // substitute -x for x
= x² - 7 // simplify
Comparing f(-x) to f(x), we can see that they are not equal:
f(-x) = x² - 7
f(x) = x² - 7
Since f(-x) is not equal to f(x), the function is not even. To determine whether it is odd, we need to evaluate f(-x) + f(x) and see if the result is zero.
f(-x) + f(x) = (x² - 7) + (x² - 7) // substitute -x for x in the second term
= 2x² - 14
Since f(-x) + f(x) is not equal to zero for all values of x, the function is not odd either.
Therefore, we can conclude that the given function, f(x) = x² - 7, is neither even nor odd.
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17 identical tasks are assigned to 7 different people. each task is assigned to exactly one person and there are no restrictions on the number of tasks that can be given to any one person. how many ways are there to assign the tasks?
There are 100,947 ways to assign the tasks to the 7 people.
This problem can be solved using combinations. We need to choose 17 tasks from a total of 17, which can be done in one way, and then assign each of these tasks to one of the 7 people. We can do this by considering all possible combinations of tasks that each person could be assigned.
Let's use the stars and bars method to count the number of ways to distribute the tasks. We can represent the tasks as stars and the people as bars, with each bar representing a separate person. For example, if person 1 is assigned 4 tasks, person 2 is assigned 2 tasks, and person 3 is assigned 1 task,
The number of ways to distribute the tasks is then the number of ways to arrange the 17 stars and 6 bars, which is
(17 + 6) choose 6 = 23 choose 6 = 100947
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the defect levels, as reported by motorola in their six sigma program, were higher than they expected from using a standard normal table for their capability calculations. why was this true? motorola found their processes followed the exponential distribution motorola allowed for failure in one tail only motorola had not allowed for a 1.5 sigma shift in the mean motorola found that six sigma efforts increased process variation
The defect levels reported by Motorola in their Six Sigma program were higher than expected because of the nature of their processes following an exponential distribution.
This means that Motorola only allowed for failure in one tail of the distribution, which increases the likelihood of failure and causes the defect levels to be higher than the standard normal table's capability calculations. Additionally, Motorola had not accounted for a 1.5 sigma shift in the mean, which also contributed to the higher defect levels. Through their Six Sigma efforts, Motorola found that their process variation had increased, which explains why their defect levels were higher than expected.
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Triangle A: All sides have length 12 cm.
Triangle B: Two sides have length 10 cm, and the included angle measures 60°.
Triangle C: Base has length 15 cm, and base angles measure 40°.
Triangle D: All angles measure 60°.
Which triangle is not a unique triangle? (5 points)
a
Triangle A
b
Triangle B
c
Triangle C
d
Triangle D
triangle C
Step-by-step explanation:
If you draw it out, it looks unique
A student has a rectangular bedroom. If listed as ordered pairs, the corners of the bedroom are (21, 18), (21, −7), (−12, 18), and (−12, −7). What is the perimeter in feet?
116 feet
58 feet
33 feet
25 feet
The perimeter of the rectangular bedroom is 116 feet.
How to get the perimeter?We know that the distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:
d = √( (x₂ - x₁)² + (y₂ - y₁)²)
Here the corners of the room are at: (21, 18), (21, −7), (−12, −7) and (−12, 18)
Let's find the distances between these points:
d₁ = √( (21- 21)² + (18 + 7)²) = 25
d₂ = √( (21 + 12)² + (-7 + 7)²) = 33
d₃ = √( (-12 + 12)² + (-7 - 18)²) = 25
d₄ = = √( (-12 - 21)² + (-7 + 7)²) = 33
The perimeter is the sum of these distances so we will get:
d₁ + d₂ + d₃ + d₄ = 25 + 33 + 25 + 33 = 116
The correct option is the first one.
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the graph of f(x) to answer the question.
f(x) 18
16-
(-10, 14)
10-
6
(-6, 1.2)
-14-12-10-8-6-4-2
(-5, -1)
(10, 14)
(8, 6.8)
6 8 10 12 14
(5, -1)
(0, -6)
©2018 StrongMind. Created using GeoGebra.
What is the output off when x = -6?
Enter your answer as the numerical value shown in the graph
The output of the graphed function when x = 6 is given as follows:
y = 1.2.
How to define a quadratic function according to it's vertex?The coordinates of the vertex are (h,k), meaning that:
h is the x-coordinate of the vertex.k is the y-coordinate of the vertex.Considering a leading coefficient a, the quadratic function is given as follows:
y = a(x - h)² + k.
The vertex is the turning point of a quadratic equation, hence it's coordinates for this problem are given as follows:
(0, -6).
Meaning that the function is defined as follows:
y = ax² - 6.
When x = 5, y = -1, hence the leading coefficient a is obtained as follows:
-1 = 25a - 6
a = 0.2.
Hence the function is:
y = 0.2x² - 6.
Hence the output when x = -6 is given as follows:
y = 0.2(-6)² - 6
y = 1.2.
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find two divergent series summation from n equals 1 to infinity of the quantity a sub n and summation from n equals 1 to infinity of the quantity b sub n such that summation from n equals 1 to infinity of the quantity a sub n times b sub n end quantity converges.
To find two divergent series, summation from n equals 1 to infinity of a_n and summation from n equals 1 to infinity of b_n, such that their product converges, we can consider the following series:
1. Summation from n equals 1 to infinity of a_n = ∑(1/n)
2. Summation from n equals 1 to infinity of b_n = ∑n
Solution:
1. The first series, ∑(1/n), is known as the harmonic series. It is a famous example of a divergent series, meaning that its sum approaches infinity as n approaches infinity.
2. The second series, ∑n, is an arithmetic series where the terms increase linearly. This series is also divergent, as the sum increases without bound as n approaches infinity.
Now, we need to verify that the product of these series converges:
3. Summation from n equals 1 to infinity of (a_n * b_n) = ∑((1/n) * n)
4. Simplifying the expression, we get ∑(1), which is a constant series with all terms equal to 1.
5. The sum of the constant series converges, as it approaches a finite value when n approaches infinity.
In conclusion, the two divergent series summation from n equals 1 to infinity of a_n = ∑(1/n) and
summation from n equals 1 to infinity of b_n = ∑n, have a product that converges, as their product ∑((1/n) * n) simplifies to a constant series ∑(1), which has a finite sum.
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Suppose you select a number at random from the sample space {1, 2, 3, 4, 5, 6, 7, 8}. probability.
P(the number is positive)
P(the number is even)
Suppose you select a number at random from the sample space {1, 2, 3, 4, 5, 6, 7, 8}. probability.
P(the number is positive)
P(the number is even)
Answer:
The probability of selecting a number at random from the sample space {1, 2, 3, 4, 5, 6, 7, 8} that is positive is:
There are 8 possible outcomes in the sample space, and 4 of them are positive (1, 2, 3, 4).
Therefore, P(the number is positive) = 4/8 = 1/2 = 0.5
The probability of selecting a number at random from the sample space {1, 2, 3, 4, 5, 6, 7, 8} that is even is:
There are 8 possible outcomes in the sample space, and 4 of them are even (2, 4, 6, 8).
Therefore, P(the number is even) = 4/8 = 1/2 = 0.5
So the probability of selecting a number at random from the sample space {1, 2, 3, 4, 5, 6, 7, 8} that is positive is 0.5 and the probability of selecting a number at random from the same sample space that is even is also 0.5.
lara ran the first leg of a relay race in 14.06 seconds. sheela ran the second leg. the total time it took both girls to run the race was 27.89 seconds. how long did it take sheela to run the second leg of the race?
it takes Sheela to run the second leg of the race: Ascertain the total or contrast: x = 13.83.
In view of the given circumstances, plan:: 14.06+ x = 27.89
Modify variables to the left half of the situation: x = 27.89 - 14.06
Ascertain the total or contrast: x = 13.83
Speed = Distance/Time - This lets us know how slow or quick an article moves. It portrays the distance voyaged partitioned when taken to cover the distance.
Speed is straightforwardly Relative to Distance and Conversely corresponding to Time. Thus,
Distance = Speed X Time, and
Time = Distance/Speed, as the speed builds the time taken will diminish as well as the other way around.
Utilizing these recipes any fundamental issues can be settled. Nonetheless, the right utilization of units is additionally something essential to consider while utilizing equations.
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The triangle shown is rotated about line m.
A triangle with side lengths of 6 centimeters, 8 centimeters, and 10 centimeters is shown. The triangle is rotated about line m at the side with length 8 centimeters.
What is the approximate base area of the resulting three-dimensional figure?
Area of a circle: A = πr2
38 sq. cm
113 sq. cm
201 sq. cm
314 sq. cm
Answer:
Step-by-step explanation:
When the triangle is rotated about the side with a length of 8 cm, it forms a cone with a base radius equal to 4 cm and height equal to 6 cm.
Using the formula for the volume of a cone, V = 1/3 * πr^2h, where r is the radius and h is the height, we can find the volume of the resulting solid:
V = 1/3 * π * 4^2 * 6
V ≈ 100.53 cubic centimeters
To find the approximate base area, we need to calculate the area of the circle with a radius of 4 cm (the base of the cone):
A = πr^2
A ≈ 50.27 sq. cm
Therefore, the approximate base area of the resulting three-dimensional figure is about 50.27 sq. cm.
So, the closest option available in the given choices is 38 sq. cm, but the correct answer based on calculations is approximately 50.27 sq. cm.
Answer:
I just did the quiz. Look below.
Step-by-step explanation:
your chronometer is set for greenwich mean time (gmt or universal time, ut). high noon at your present location is 9 pm ut. what is your longitude?
Your longitude in DMS is 135 degree. So the option D is correct.
This is because there are 12 hours left in the local time ( i.e. 12 hours noontime or mid-day).
As UT (or GMT) time is 9 p.m., there are 9 hours between GMT time and local time.
9 hours = 9 × 60 minutes = 540 minutes
Now, we know that:
Every four minutes, the Earth turns one degree.
Thus, 1-degree longitude difference = 4 minutes
Or, 4 minutes of time difference = 1 degree of longitude
Or, 1 minute of time difference = 1/4 degree of longitude
Or, 540 minutes of time difference = (1/4) × 540 degrees of longitude
540 minutes of time difference = 135 degrees of longitude
Also, we can infer that the current location is in the Western hemisphere because we know that it is 9 hours behind GMT (or UT) time.
Hence, the longitude of the current location = 135⁰
So the option 4 is correct.
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The complete question is:
Your chronometer is set for Greenwich Mean Time (GMT or Universal Tim, UT). High noon at your present location is 9 pm UT. What is your longitude in DMS (not decimal degrees)?
1. 30° 18'W
2. 30° 16'W
3. 30° 17'W
4. none of the above
Rename 1 foot with an equivelint fraction in yards
Renaming 1 foot to equivalent fraction in yards as 1/3 yards
We multiply the number of feet by 1/3 to convert this to yards, and then we need to identify the two elements of this equation that have a functional relationship.
As we are aware,
1 foot equals 3 yards.
As a result, we must multiply the unknown numbers, denoted by the letter x, by 1/3 in order to get the feet.
Let's say that the variables in this situation are x and y, where x stands for feet and y for yards.
To get the unit in yards, multiply the unit in feet by a factor of three-quarters. x = 1/3y
Hence, the renaming of 1 feet as 1/3 yards, where the fraction is 1/3.
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what is the average rate of change of f(x) from x = -3 to x = 6? f(x) = x^2 + 4x − 15 enter your answer in the blank.
The average rate of change of f(x) from x = -3 to x = 6 is 7.
What is meant by average?
The term "average" is used to describe a number that represents the central or typical value in a set of data. There are several different types of averages, including the mean, median, and mode.
To find the average rate of change of a function, we need to compute the difference between the function values at the two given points, and then divide by the difference in the input values.
For the function [tex]f(x) = x^2 + 4x - 15[/tex], the value of the function at [tex]x = -3[/tex] is:
[tex]f(-3) = (-3)^2 + 4(-3) -15 = 9 - 12 - 15 = -18[/tex]
The value of the function at [tex]x = 6[/tex] is:
[tex]f(6) = 6^2 + 4(6) - 15 = 36 + 24 - 15 = 45[/tex]
The difference in the function values is:
[tex]f(6) - f(-3) = 45 - (-18) = 63[/tex]
The difference in the input values is:
6 - (-3) = 9
Therefore, the average rate of change of f(x) from x = -3 to x = 6 is:
average rate of change = [tex](f(6) - f(-3)) / (6 - (-3)) = 63 / 9 = 7[/tex]
So, the average rate of change of f(x) from x = -3 to x = 6 is 7.
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Let S be the sphere of radius 1 centered at (1,2,3).
Find the distance from S to the plane x+y+z=0.
(Hint: Use Lagrange multipliers to find the distance from the plane to the center of the sphere)
The distance from S to the plane x+y+z=0 is sqrt(105)/7.
To find the distance from the sphere S to the plane x+y+z=0, we need to first find the center of the sphere S. We know that the center of the sphere S is (1, 2, 3) and the radius of the sphere is 1. We can use the equation of the plane x+y+z=0 to find the distance from the center of the sphere to the plane.
We can use Lagrange multipliers to find the distance from the center of the sphere to the plane. We need to minimize the function [tex]f(x, y, z) = (x-1)^2 + (y-2)^2 + (z-3)^2[/tex] subject to the constraint x+y+z=0. Using Lagrange multipliers, we get the following system of equations:
2(x-1) = λ
2(y-2) = λ
2(z-3) = λ
x+y+z = 0
Solving these equations, we get x = 1-λ/2, y = 2-λ/2, and z = 3-λ/2. Substituting these values into the equation x+y+z=0, we get λ = 12/7. Substituting this value of λ into x, y, and z, we get the coordinates of the point on the plane closest to the center of the sphere: (5/7, 4/7, -9/7).
To find the distance from the center of the sphere to the plane, we can use the distance formula. The distance from the center of the sphere to the plane is given by the length of the vector connecting the center of the sphere to the point on the plane closest to the center of the sphere. Therefore, the distance from the sphere S to the plane x+y+z=0 is:
d = sqrt[(5/7 - 1)^2 + (4/7 - 2)^2 + (-9/7 - 3)^2] = sqrt[105/49] = sqrt(105)/7.
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please i need help, i’ve wasted like six papers trying to get this one right
Answer:5
Step-by-step explanation:
angle h and k are equal (because alternate exterior angles are equal)
2x+7=5x-8
8+7=5x-2x
15=3x
15/3=x
5=x
h=2x+7=2*5+7=17degrees
in an arithmetic sequence, the sum of the second and eighth terms is $5$, and the product of the fourth and fifth terms is also $5$. what is the sum of the first $20$ terms of this sequence?
The sum of the first $20$ terms of the arithmetic sequence is $420$.
In an arithmetic sequence, the sum of the second and eighth terms is $5$, and the product of the fourth and fifth terms is also $5$. The sum of the first $20$ terms of this sequence can be calculated using the following formula:
Sum of the first $20$ terms = $20$/2($a_1 + a_{20})$, where $a_1$ is the first term of the sequence and $a_{20}$ is the twentieth term of the sequence.
Therefore, we need to find the first term of the sequence and the twentieth term of the sequence. To find the first term, we use the following equation:
$5 = a_2 + a_8$, where $a_2$ is the second term and $a_8$ is the eighth term.
To find the twentieth term, we use the following equation:
$5 = a_4 \times a_5$, where $a_4$ is the fourth term and $a_5$ is the fifth term.
Solving both equations, we get $a_2 = 1$ and $a_{20} = 40$. Then, we can calculate the sum of the first $20$ terms of the sequence:
Sum of the first $20$ terms = $20$/2($1 + 40$) = $420$.
Therefore, the sum of the first $20$ terms of the arithmetic sequence is $420$.
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Sketch the qraphs. 2x+3y=1
Answer:
y = -2/3x + 1/3
Step-by-step explanation:
2x + 3y = 1
3y = -2x + 1
y = -2/3x + 1/3
To sketch:
Pretend x is 3. y would be -1 2/3.
Now that you have this point, draw through the point (0, 1/3).
There ya go
Ethan also wants to buy some shoes that were originally $80. This week they’re on sale for 50% off the original price. Ethan also has a 50% off coupon. Will the shoes be free with coupon? If not, how much will they cost?
Answer:
20$
Step-by-step explanation:
since there is a discount we first find the discount allowed which is 40$. After we also use the coupon which is 50% off. then you get 20$ as your answer
I need the questions 25,28 and 29
Using the given values, the values of the expression and equations are:
25. -0.8
28. S ≈ 137.22
29. V ≈ 50.94
Evaluating an expressionFrom the question, we are to evaluate each of the expressions for the given values
25.
[-b + √(b² -4ac)]/2a
a = 2, b = 8, c = 5
Substituting the values into the expression
[-b + √(b² -4ac)]/2a
= [-8 + √((8)² - 4(2)(5))]/2(2)
= [-8 + √(64 - 40)]/4
= [-8 + √(24)]/4
= [-8 + 2√6]/4
= -2 + 1/2(√6)
= -0.775
≈ -0.8
28.
S = 2πrh + 2πr²
r = 2.3, h = 7.1 (Take π = 3.14)
Thus,
S = 2(3.14)(2.3)(7.2) + 2(3.14)(2.3)²
S = 103.9968 + 33.2212
S = 137.218
S ≈ 137.22
29.
V = 4/3 πr³
r = 2.3(Take π = 3.14)
V = 4/3 × 3.14 × (2.3)³
V = 50.939
V ≈ 50.94
Hence, the value of V is 50.94
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Which of these schedules follow the guidelines for a teenager's daily physical
activity? Select the two correct answers.
• A. 30 minutes practicing gymnastics and 30 minutes cycling
B. 15 minutes washing dishes, 10 minutes shopping at the mall, and
Im minutes dancing
• C. 15 minutes raking leaves and 15 minutes walking
• D. 30 minutes playing soccer, 20 minutes climbing a rock wall, and
10 minutes practicing yoga
describe a dataset where defining a confidence interval would be important for testing validity of data. what do you want to know about the data? which population parameter (and test statistic) would you use? what confidence interval would you choose and why.
Defining a confidence interval is important in analyzing a dataset to test the validity of data. The choice of population parameter, test statistic, and confidence interval depends on the type of data being analyzed and the level of confidence required by the researcher.
When analyzing a dataset, it is important to determine the confidence interval to test the validity of the data. The confidence interval measures the precision of an estimate and indicates the range in which the population parameter is likely to exist.
There are several types of datasets where defining a confidence interval would be important for testing validity of data, some of them include;
1. Medical research: In medical research, researchers gather data to examine how a treatment plan affects a group of people. They can define a confidence interval to determine the range of possible outcomes. They use the test statistic to help them determine how significant the results are.
2. Business Data: When analyzing business data, defining a confidence interval is crucial to determine the success rate of a marketing campaign, sales data, or employee turnover. It allows the business to assess their performance and make data-driven decisions.
3. Political Polling: When conducting political polls, defining a confidence interval is necessary to determine the reliability of the data. It helps the pollsters to estimate the likely outcome of the election and the level of confidence that can be placed in the results.
When analyzing a dataset, it is essential to determine which population parameter and test statistic to use. The population parameter is the numerical value that describes the entire population. It can be the mean, proportion, variance, or standard deviation. The test statistic is used to determine if the population parameter is within the confidence interval, or if it lies outside the interval. The choice of population parameter and test statistic depends on the type of data being analyzed.
The confidence interval to choose depends on the level of confidence required by the researcher. The commonly used confidence intervals are 90%, 95%, and 99%. The level of confidence chosen by the researcher determines the size of the interval. The higher the confidence level, the wider the confidence interval. The researcher should choose a confidence interval that is wide enough to contain the population parameter, but not too wide to reduce the precision of the estimate.
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1. A rain barrel collects water off the roof of a house during three hours of heavy rainfall. The height of the water in the barrel increases at the rate of r(t) = 47-15 feet per hour, where is the time in hours since the rain began. At time t = 1 hour, the height of the water is 0. 75 foot. What is the height of the water in the barrel at time = 2 hours? (A) 1. 361 ft (B) 1. 500 ft (C) 1. 672 (D) 2. 111
As per integration, the height of the water in the barrel at time = 2 hours is 1.672 feet (option C).
The formula is r(t) = 47-15, where t is the time in hours since the rain began. This formula tells us how fast the water level is changing at any given time t.
In this case, we're asked to find the height of the water in the barrel at t = 2 hours, given that the height at t = 1 hour is 0.75 feet. To solve this problem, we'll integrate the rate formula from t = 1 to t = 2, and add the starting height of 0.75 feet.
∫(47-15)dt from t=1 to t=2 = [47t-15t] from t=1 to t=2 = 0.922
So the total increase in height from t=1 to t=2 is 0.922 feet. Adding this to the starting height of 0.75 feet, we get the height of the water at t=2:
0.75 + 0.922 = 1.672 feet
Therefore, the correct option is (C).
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What is 3x+7y=11 equal to
(6,-1)
(1,-2)
(0,4)
The given equation 3x + 7y = 11 is equal to (1,-2).
The given equation is 3x + 7y = 11.
To find the solution of the equation, we need to consider the given options:
(6,-1)(1,-2)(0,4)
Now substitute each value of x and y in the given equation, we get,
If x = 6 and y = -13(3 × 6) + (7 × -1) = 18 - 7 = 11 ≠ 11
If x = 1 and y = -2(3 × 1) + (7 × -2) = 3 - 14 = -11 ≠ 11
If x = 0 and y = 4(3 × 0) + (7 × 4) = 0 + 28 = 28 ≠ 11
Therefore, the given equation 3x + 7y = 11 is equal to (1,-2).
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please I really need help by tmr!!
How many intersections are there between the graphs of f(x) = 0.8x and g(x) = \lfloor x \rfloor?
The answer is one intersection.
What is a function?
A function is a relationship or expression involving one or more variables. It has a set of input and outputs.
The graph of the function f(x) = 0.8x is a straight line with slope 0.8 passing through the origin (0, 0). The graph of the function g(x) = ⌊x⌋ is the collection of all points (x, y) where y is the greatest integer less than or equal to x. This function is not continuous and has a discontinuity at each integer.
To find the intersections between the two graphs, we need to determine where the values of f(x) and g(x) are equal.
we need to find the integer values of x where 0.8x and x are equal.
0.8x = x
0.2x = 0
x = 0
Thus, the two graphs intersect at the point (0, 0). There are no other intersections between the two graphs, since they have different slopes and one is continuous while the other is not. Therefore, the answer is one intersection.
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