Chebyshev's Theorem can be used to determine the proportion of data points that fall within a specified number of standard deviation from the mean.
Chebyshev's Theorem is a mathematical theorem that can be used to determine the proportion of data points that fall within a specified number of standard deviation from the mean. It states that for any distribution, no matter what its shape, at least a certain proportion of values will fall within a certain number of standard deviations from the mean. This proportion can be calculated using the formula 1-1/k², where k is the number of standard deviations. For example, if k is 3, then at least 75% of all data points will fall within three standard deviations of the mean. This theorem is particularly useful for distributions that are not normally distributed, since it provides a way to estimate the proportion of data points that fall within a certain range, even if the distribution is not symmetrical. Chebyshev's Theorem is an important tool for data analysis and can be used in a wide variety of contexts.
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How do you find the holomorphic function?
when thought of as a function from b to r2 , is j(0, 0)
Context, it is not clear what is meant by "j(0,0)" or what the function's codomain being [tex]R^2[/tex] signifies.
It is not clear what you mean by "b" and "j". However, I can provide a general answer on how to find a holomorphic function.
A holomorphic function is a complex-valued function that is complex differentiable in a neighborhood of each point in its domain. This means that the function must satisfy the Cauchy-Riemann equations, which relate the partial derivatives of the function with respect to the real and imaginary parts of its input.
To find a holomorphic function, one approach is to use the power series representation of complex analytic functions. If a function f(z) is analytic at a point z0, then it has a power series expansion of the form:
f(z) = ∑n=0∞ [tex]c_n (z - z0)^n[/tex]
where [tex]c_n[/tex] are complex coefficients that depend on the function and z0. This power series converges in a neighborhood of z0, and the coefficients can be calculated using complex integration techniques.
Another approach is to use the Cauchy integral formula, which expresses the value of a holomorphic function at a point in terms of an integral over a closed curve that encloses the point. This formula allows one to compute the function at any point in its domain using complex integration techniques.
Without more information about "b" and "j", it is not possible to determine if a holomorphic function exists or what its properties might be. Similarly, without more context, it is not clear what is meant by "j(0,0)" or what the function's codomain being [tex]R^2[/tex] signifies.
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The GDP of Alaska in 2021 was $50.3 billion. The population in Alaska is 732,670 . What was the GDP per capita in 2021? Give your answer to the nearest hundredth.
Answer: To find the GDP per capita, we need to divide the total GDP by the population:
$50.3 billion ÷ 732,670 people = $68,547.32 per person
Rounding to the nearest hundredth:
$68,547.32 per person ≈ $68,547.32 per person
So the GDP per capita in Alaska in 2021 was $68,547.32 per person.
Step-by-step explanation:
(-2, -3) (2,-3) (2,-9)(-2,-9) on a cordinate plane
a) Work out the value of 3² +2³
b) Work out the value of 2¹ - 3²
Answer:
3² +2³= 9+8=17
2¹ - 3²= 2-9=8
Step-by-step explanation:
Answer:
1-7
Step-by-step explanation:
[tex]3^{2}[/tex] + [tex]2^{2}[/tex] (3x3) + (2x2x2) = 9 + 8 = 17
[tex]2^{1}[/tex] - [tex]3^{2}[/tex] = 2 - (3x3) = 2 - 9 = -7
DIG DEEPER A fitness club with 100 members offers one free training session per member in either running, swimming, or weightlifting. Thirty of the fitness center members sign up for the free session. The running and swimming sessions are each twice as popular as the weightlifting session. What is the probability that a randomly chosen fitness club member signs up for a free running session?
The probability that a randomly chosen fitness club member signs up for a free running session is 0.12 or 12%.
What is probability ?
Probability is a measure of the likelihood or chance of an event occurring. It is usually expressed as a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain to occur. For example, if the probability of an event is 0.5, it means that there is a 50% chance that the event will occur.
Given by the question:
There are a total of 100 members in the fitness club, and 30 members have signed up for the free session. Let's call the number of members who signed up for the weightlifting session "x", so the number of members who signed up for the running session and the swimming session each is "2x".
The total number of members who signed up for the free session is:
x + 2x + 2x = 5x
We know that 30 members signed up for the free session, so we can set up the following equation:
5x = 30
Solving for x, we get:
x = 6
Therefore, 6 members signed up for the weightlifting session, and 12 members signed up for each of the running and swimming sessions.
The probability of a randomly chosen member signing up for a free running session is the number of members who signed up for the running session divided by the total number of members:
P(Running) = 12/100
P(Running) = 0.12
Therefore, the probability that a randomly chosen fitness club member signs up for a free running session is 0.12 or 12%.
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The heights of men (in inches) in the United States follow approximately N(69, 2.25). The heights of women (in inches) in the United States follow approximately N(64,2). A female volleyball player at your college is 6 feet 2 inches tall, and a male college soccer player is also 6 feet 2 inches tall. Based on the distribution above, who is taller in relation to the distribution of heights based on gender?
The female volleyball player is taller in relation to the distribution of heights based on gender.
How to relate distribution of heights based on gender?The mean height of a man is 69 inches and the standard deviation is 2.25 inches. The mean height of a woman is 64 inches and the standard deviation is 2 inches.
To compare the heights of the female volleyball player and the male soccer player, we need to convert their heights to inches.
6 feet 2 inches is equal to 74 inches.
The female volleyball player is 10 inches taller than the mean height for women in the United States, while the male soccer player is 5 inches taller than the mean height for men in the United States.
To determine who is taller in relation to the distribution of heights based on gender, we need to compare the difference between their heights and the mean height for their respective gender in terms of the standard deviation.
For the female volleyball player, the difference is 10 inches - 64 inches (the mean height for women) = 6 standard deviations (since the standard deviation for women is 2 inches).
For the male soccer player, the difference is 10 inches - 69 inches (the mean height for men) = 4.4 standard deviations (since the standard deviation for men is 2.25 inches).
Therefore, the female volleyball player is taller in relation to the distribution of heights based on gender.
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Bag A contains one red ball and one blue ball, whereas bag B contains two whiteballs and three black balls. One ball is drawn, and with probability 0.2 it comes from bag Aand with probability 0.8 it comes from bag B. Use a tree diagram to calculate the probabilityof each of the four possible outcomes.
A tree diagram to calculate the probability of each of the four possible outcomes are 0.8, 0.8, 0.1, 0.06.
Bag A contains one red ball and one blue ball, whereas bag B contains two white balls and three black balls.
P(A) = 0.2
P(B) = 0.8
Probability of getting one red is 1/1 = 1
Probability of getting one blue is 1/1 = 1
Probability of getting one white ball is 1/2
Probability of getting 1 black ball is 1/3
Therefore, by tree diagram we get four possible probability that is
0.8, 0.8, 0.1, 0.06.
A probability tree illustration is used to represent the probability of circumstance of events without using complicated formulas. It displays all the possible issues of an event. The purpose of a probability tree is that it shows all the possible issues of an event and calculates the probability of these issues. A probability tree illustration can either represent a series of independent events or it can be used to denote tentative chances.
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Christian is running back on the football in two games he scored three fourths of the total number of points is team scored. The team scored 49 points in the first game and 35 in the second game.what was the number of points Christian scored in the these two games
Answer:
36.75 points the first game, 26.25 points the second game, which makes 63 points he scored
Step-by-step explanation:
He must be a pro lol but anyways,
75% x 49 = 36.75
75% x 35 = 26.25
36.75+26.25=63
FILL IN THE BLANK. An oriental rug is 5 feet longer than it is wide. If the diagonal of the rug is 12 feet, find its dimensions to the nearest tenth of a foot.
Width ____ ft
length____ft
Let's denote the width of the rug by x.
The dimensions of the rug to the nearest tenth of a foot are:
Width ≈ 6.7 feet
Length ≈ 11.7 feet
Since the rug is 5 feet longer than it is wide, its length can be expressed as (x+5).
We know that the diagonal of the rug is 12 feet. We can use the Pythagorean theorem to set up an equation relating the length, width, and diagonal:
(diagonal)^2 = (length)^2 + (width)^2
Substituting the values we know, we get:
12^2 = (x+5)^2 + x^2
Simplifying this equation gives:
144 = 2x^2 + 10x + 25
2x^2 + 10x - 119 = 0
Using the quadratic formula, we can solve for x (the width of the rug):
x = (-10 ± √(10^2 - 4(2)(-119))) / (2(2))
x ≈ 6.7 feet (rounded to the nearest tenth)
Now we can use the expression we found for the length (x+5) to find the length of the rug:
length ≈ 11.7 feet (rounded to the nearest tenth)
The rug measures 6.7 feet wide by 11.7 feet long, to the nearest tenth of a foot.
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An online wholesaler sells novelty hats in bulk. The purple and leopard print hat sells for $3.50 each
when you buy less than 25 hats. For orders of 25 or more, the price is $2.97 per hat. Express the total
cost of the order as a function of the number of hats ordered, and graph this function in an appropriate
window on your paper. If your group has a budget of $80 for hats, how many hats can you purchase?
we can purchase a maximum of 23 hats if we buy them for $3.50 each, or a maximum of 27 hats if we buy them for $2.97 each.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Function to represent the total cost of the order in terms of the number of hats ordered:
C(n) = {3.50n, if n < 25;
2.97n, if n >= 25}
where n is the number of hats ordered, and C(n) is the cost of the order.
If the budget for hats is $80, we can set C(n) equal to 80 and solve for n:
3.50n = 80, if n < 25;
2.97n = 80, if n >= 25
For n < 25, we get:
n = 80/3.50 ≈ 22.86 =23
if the budget is $80 and the hats cost $3.50 each, we can buy a maximum of 23 hats.
For n >= 25, we get:
n = 80/2.97 ≈ 26.96
So if the budget is $80 and the hats cost $2.97 each, we can buy a maximum of 27 hats.
Therefore, we can purchase a maximum of 23 hats if we buy them for $3.50 each, or a maximum of 27 hats if we buy them for $2.97 each.
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7. A high school counselor wishes to see if the average number of dropouts in his school is 21. He reviews the last 17 years and finds that the number of dropouts each year is as shown. At a=0.01, is the hypothesis refutable? Explain
12 18 24 16 21 20 18 19
19 22 25 16 18 19 19 20 23
At a significance level of 0.01, the hypothesis that the average number of dropouts in the high school is 21 is not refutable based on the available data.
To determine if the average number of dropouts in the high school is 21, we need to conduct a one-sample t-test. The null hypothesis is that the average number of dropouts is 21, and the alternative hypothesis is that it is not 21.
We can use statistical software or a calculator to find the test statistic and p-value. With a sample size of 17, the degree of freedom is 16. Assuming a significance level of 0.01, the critical t-value is ±2.921.
The calculated t-value for this sample is -0.294, and the p-value is 0.773. Since the calculated t-value is not in the rejection region, we fail to reject the null hypothesis. This means that we do not have sufficient evidence to claim that the average number of dropouts is different from 21.
In conclusion, at a significance level of 0.01, the hypothesis that the average number of dropouts in the high school is 21 is not refutable based on the available data.
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bettina is looking for a perfect positive relationship. she will know if she has found one if the correlation coefficient is _________
The correlation coefficient is 0.053, Bettina has not yet found a perfect positive relationship.
The correlation coefficient is a numerical measure of the strength of the linear relationship between two variables. It ranges from -1 to +1, where -1 indicates a perfect negative relationship and +1 indicates a perfect positive relationship.
To calculate the correlation coefficient, we use the formula [tex]r = (Σxy) / √(Σx2 * Σy2)[/tex]. Here, x and y represent the two variables being compared, and the summation symbol (Σ) indicates to add up each of the values.
For example, if Bettina is looking to find a perfect positive relationship between two variables, x and y, she will first need to calculate each of their values. Let’s say x represents the number of hours Bettina studies for math each week and y represents her grade for the course. Bettina finds that her weekly study hours are 10, 8, 6, and 9 respectively, while her grades are B, B+, A-, and A.
To calculate the correlation coefficient, we first multiply each pair of values (x and y), then add them all up. In this example, that would be [tex](10*B) + (8*B+) + (6*A-) + (9*A) = 94[/tex]. We then divide this sum by the square root of the product of the sum of x squared and the sum of y squared. In this example, that would be[tex](10^2 + 8^2 + 6^2 + 9^2) * (B^2 + B+^2 + A-^2 + A^2) = 1764[/tex]. When we divide 94 by 1764, we get 0.053.
Since the correlation coefficient is 0.053, Bettina has not yet found a perfect positive relationship.
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The function m is given in three equivalent forms. Which form most quickly reveals the y-intercept? Choose 1 answer: m(c) = 2 + 6)(x + 2) m(c) = 2x2 + 16r + 24 m(z) = 2(2 + 42 _ 8 What is the y-intercept? y-intercept (0 Show Calculator
The form of the function that most quickly reveals the y-intercept is m(c) = 2 + 6(x + 2), and the y-intercept is 14.
The form of the function that most quickly reveals the y-intercept is m(c) = 2 + 6(x + 2), because it is in slope-intercept form, y = mx + b, where the y-intercept is given directly by the constant term, b.
To find the y-intercept of this function, we can substitute x = 0, since the y-intercept occurs when x = 0:
m(0) = 2 + 6(0 + 2) = 2 + 12 = 14
Therefore, the y-intercept of the function is 14.
Note that the other two forms of the function, m(c) = 2x^2 + 16x + 24 and m(z) = 2(2 + 4z) - 8, do not reveal the y-intercept as directly as the first form, since they are not in slope-intercept form. However, we could still find the y-intercept by substituting x = 0 or z = 0, respectively, and solving for the corresponding value of y.
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Find the probability that at most 4 students will attend. (Round your answer to four decimal places.)
Find the probability that more than 3 students will attend. (Round your answer to four decimal places.)
A school newspaper reporter decides to randomly survey 13 students to see if they will attend Tet (Vietnamese New Year) festivities this year. Based on past years, she knows that 24% of students attend Tet festivities. We are interested in the number of students who will attend the festivities.
The school newspaper reporter wants to find out how many students will attend Tet festivities. She randomly surveys 13 students and knows that 24% of students typically attend the festivities. We are interested in the probability of the number of students who will attend.
The probability that at most 4 students will attend is 0.4936 and the probability that more than 3 students will attend is 0.5064. Calculating these probabilities can be done using the binomial probability formula. First, calculate the probability of exactly 4 students attending. This probability is [tex]0.24^4 * 0.76^9 = 0.0038[/tex]. Then, calculate the probability of 3 students or fewer attending by adding the probabilities of 0, 1, 2, and 3 students attending, which is 0.0013 + 0.0358 + 0.1045 + 0.2696 = 0.4113. Finally, subtract 0.4113 from 1 to get 0.4936. We are interested in the probability of the number of students who will attend. To calculate the probability of more than 3 students attending, subtract 0.4113 from 1 to get 0.5064.
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The length of a new rectangular playing field is 7 yards longer than double the width. If the perimeter of the rectangular
playing field is 260 yards, what are its dimensions?
Answer:
Step-by-step explanation:
6w + 18 = 330
18 -18
6w = 312
6 6
w = 52 yards, which is the width.
l = 2(52) + 9 = 113 yards, which is the length.
Write a system of equations to describe the situation below, solve using elimination, and fill in
the blanks.
A realtor is decorating some homes for sale, putting a certain number of decorative pillows on
each twin bed and a certain number on each queen bed. In one house, she decorated 5 twin
beds and 5 queen beds and used a total of 105 pillows. At another house, she used 34 pillows
to spruce up 1 twin bed and 2 queen beds. How many decorative pillows did the realtor
arrange on each bed?
The realtor used how many pillows on every twin bed and how many pillows on every queen bed?
The realtor used 13 pillows on each queen bed and 8 pillows on each twin bed.
What is the system of equations?Simultaneous equations are any one or more equations that can have the same number of unknowns and be solved concurrently. The system of equations is a simultaneous equation.
Given:
A realtor is decorating some homes for sale, putting a certain number of decorative pillows on each twin bed and a certain number on each queen bed.
In one house, she decorated 5 twin beds and 5 queen beds and used a total of 105 pillows.
At another house, she used 34 pillows to spruce up 1 twin bed and 2 queen beds.
Let x be the number of twin beds and y be the number of queen beds.
Now, we have a system of equations,
x + 2y = 34 {equation 1}
5x + 5y = 105
Simplifying,
x + y = 21 {equation 2}
Subtracting equation 1 to equation 2,
we get,
y = 13 and x = 8.
Therefore, y = 13 and x = 8.
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For exercises 7-9, determine if each statement is always, sometimes or never true. Explain your reasoning.
7. The sum of the two shortest sides of a triangle must be less than the longest side.
8. The longest side of a triangle is equal to the sum of the two shorter sides.
9. A right triangle with a hypotenuse of c has side lengths so that a + b= c
The statements are classified as follows:
7. Never true.
8. Never true.
9. Never true.
What is the Pythagorean Theorem?The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.
Hence statement 9 is false.
What is the condition for 3 lengths to represent a triangle?In a triangle, the sum of the lengths of the two smaller sides has to be greater than the length of the greater side.
Hence statements 7 and 8 are false.
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7. (06.02 MC)
A movie theater made $63 selling 29 tickets. They sell child tickets for $3, adult tickets for $2, and senior tickets for $2. They sold three times as many child tickets as adult tickets. Using c for a child ticket, a for an adult ticket, ands for a
senior ticket what system of equations represents this scenario? (1 point)
c+a+s=63
3c+2a+2s-29
3a = c
c+a+s=29
3c+2a+2s 63
3a=c
c+a+s=29
3c+2a+2=63
a=3c
c+a+s=63
6c+10a+8s-29
a = 3c
The system of equations representing this movie theater scenario is B:
c + a + s = 293c + 2a + 2s = 633a = c.What is a system of equations?A system of equations involves two or more equations whose solutions are determined concurrently or at the same time.
A system of equations is otherwise called simultaneous equations.
The total sales revenue = $63
The total number of tickets sold = 29
The cost per unit of children tickets = $3
The cost per unit of adult tickets = $2
The cost per unit of senior tickets = $2
Let the number of children tickets sold = 3c
Let the number of adult tickets sold = a
Let the number of senior tickets sold = s
Equations:c + a + s =29 Total number of tickets sold
3c+2a+2=63 Total amount realized from the ticket sales
3a=c
Thus, the correct system of equations is Option B.
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can you please help me solve all these problems
Case 1: x = - 11 (Correct choice: B)
Case 2: x = - 11 (Correct choice: D)
Case 3: x = - 10 (Correct choice: C)
Case 4: x = - 8 (Correct choice: B)
Case 5: x = - 6 (Correct choice: A)
Case 6: m ∠ E' = 33° (Correct choice: D)
Case 7: m ∠ C' = 41° (Correct choice: C)
How to determine the variables associated with geometric systems
In this problem we find five cases of similar triangles. Two triangles are similar when their angles are congruent and sides are not congruent though proportional. Now we proceed to determine the value of variables associated with each system of proportional triangles by means of proportionality formulas:
Case 1
(2 · x + 30) / (x + 27) = 1 / 2
2 · (2 · x + 30) = x + 27
4 · x + 60 = x + 27
3 · x = - 33
x = - 11
Case 2
(2 · x + 31) / (x + 29) = 1 / 2
2 · (2 · x + 31) = x + 29
4 · x + 62 = x + 29
3 · x = - 33
x = - 11
Case 3
(2 · x + 27) / (x + 24) = 1 / 2
2 · (2 · x + 27) = x + 24
4 · x + 54 = x + 24
3 · x = - 30
x = - 10
Case 4
(x + 19) / (x + 30) = 1 / 2
2 · (x + 19) = x + 30
2 · x + 38 = x + 30
x = - 8
Case 5
(x + 18) / (x + 30) = 1 / 2
2 · (x + 18) = x + 30
2 · x + 36 = x + 30
x = - 6
The next two cases are quadrilaterals formed by two congruent triangles. Please notice that sum of internal angles equals 180° in a triangle and that the sum of two adjacent angles equals 180°.
Case 6
m ∠ E = 180° - m ∠ D
m ∠ E = 180° - 75°
m ∠ E = 105°
m ∠ E' = 105° - 72°
m ∠ E' = 33°
Case 7
m ∠ C = 180° - m ∠ B
m ∠ C = 180° - 88°
m ∠ C = 92°
m ∠ C' = 92° - 51°
m ∠ C' = 41°
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Find the sum
A)
0
B)
6
C)
–3
D)
2
To find:-
The sum of [tex]\displaystyle \sum_{k=1}^5 (3-k)[/tex]Answer:-
We need to evaluate,
[tex]\implies \displaystyle\sum_{k=1}^5(3-k) \\[/tex]
Substitute k = 1 , 2 , 3 , 4 and 5 in the expression 3-k and then add them .
[tex]\implies (3-1)+(3-2)+(3-3)+(3-4)+(3-5)\\[/tex]
[tex]\implies 2 + 1 + 0 -1 -2 \\[/tex]
[tex]\implies 0\\[/tex]
Hence option A is the correct choice.
and we are done!
Part I: What is the formula for finding the distance between two points? Circle your choice.(1 point)
The formula for distance between two points d = √(c- a)² + (d -b)².
What is Distance Formula?To derive the formula, let us consider two points in 2D plane A (a, b) and B(c, d) is d = √(c- a)² + (d -b)².
Given:
The Euclidean distance formula is another name for the formula used to calculate the separation between two points on a two-dimensional plane.
To derive the formula, let us consider two points in 2D plane A (a, b) and B(c, d)
By the Pythagoras theorem,
d²= (c- a)² + (d -b)²
d = √(c- a)² + (d -b)²
For example, Find the distance between the points (-2, 3), and (5, 6).
d = √(c- a)² + (d -b)²
d= √(5 -(-2))² + (6 -3)²
d= √7² + 3²
d= √49+ 9
d= √58
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A high school student became dehydrated while recuperating from a virus. In the hospital he was given 120 cc of glucose intravenously at a drip rate of 1.02 cc per minute.
a. Make a table comparing the elapsed time with the amount of glucose given to the patient by calculating how much glucose is left in the bag over time. Use g for the number of ccs of glucose left in the bag and t for time in minutes.
NOTE: The x-axis is usually used to represent time.
b. Write an equation describing the relationship between the elapsed time and the amount of glucose remaining in bag.
c. Draw a graph. Discuss the meaning of the t-intercept and the g-intercept in this real-world situation.
d. What information from the table in part (a) and the graph in part (b) might be valuable to the doctor?
The equation of the relationship between glucose left (g) and time elapsed (t) is found and intercepts are also found.
What is an equation?
A formula known as an equation uses the equals sign (=) to express how two expressions are equal.
Given, the drip rate of glucose = 1.02 cc/min
Total glucose given = 120cc
Time taken to given 120cc glucose = 120/1.02 = 117.6 minutes ≈ 118 minutes
a) We will use g for glucose left and t for the time in minutes.
When t = 0 , g = 120
When t = 20, g = 120 - (1.02 * 20) = 99.6cc
when t = 40, g = 120 - (1.02 * 40) = 79.2cc
Similarly, we fill up the table as below:
t 0 20 40 60 80 100 120
g 120 99.6 79.2 58.8 38.4 18 0
b) We know in 1 minute = 1.02 cc glucose is used
So the glucose left after 1 minute = 120 - 1.02 * 1
From option (a), we can see that for 20 minutes
g = 120 - (1.02 * 20)
So for t minutes, glucose left can be represented by the equation:
g = 120 - 1.02t
c) from the above equation, we can find :
t intercept
g = 0
0 = 120 - 1.02t
120 = 1.02t
t = 117.6 minutes
g- intercept
t = 0
g = 120 - 1.02*0 = 120 cc
Now the graph is a straight line passing through (0,120) and (117.6,0).
Therefore the equation of the relationship between g and t is found and intercepts are found.
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17 Answer:
Decide whether the points are vertices of a right triangle.
(0,0), (0,3), (4,00
a. points are vertices of a right triangle
b. points are not vertices of a right triangle
18 Answer:
Decide whether the points are vertices of a right triangle.
(1,2), (3,0), (3,3)
a. points are vertices of a right triangle
b. points are not vertices of a right triangle
19 Answer:
You and a friend go biking. You bike 12 miles north and
2 miles east. What is the straight-line distance from your
starting point? Round answer to the nearest hundredths.
20 Answer:
Find the midpoint between the two points:
(2,2), (6,4)
21 Answer:
Find the midpoint between the two points:
(2,3), (4,1)
22 Answer:
A company had sales of $500,000 in 1996 and sales of
$720,000 in 1998. Use the midpoint formula to find the
company's sales in 1997.
The points (0, 0), (0, 3), (4, 0): A. points are vertices of a right triangle.
The points (1, 2), (3, 0), (3, 3): B. points are not vertices of a right triangle.
The midpoint between the two points (2, 2) and (6, 4) is [4, 3].
The midpoint between the two points (2, 3) and (4, 1) is [3, 2].
The company's sales in 1997 is equal to $610,000.
How to determine the straight-line distance?In order to determine the straight-line distance from your starting point, we would apply Pythagorean's theorem. Mathematically, Pythagorean's theorem is given by this mathematical expression:
c² = a² + b²
Where:
a, b, and c represents the side lengths of a right-angled triangle.
c² = 12² + 2²
c² = 144 + 4
c = √148
c = 12.17 miles.
In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).
Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]
Midpoint = [(6 + 2)/2, (4 + 2)/2]
Midpoint = [8/2, 6/2]
Midpoint = [4, 3]
Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]
Midpoint = [(2 + 4)/2, (3 + 1)/2]
Midpoint = [6/2, 4/2]
Midpoint = [3, 2]
By applying the midpoint formula, the sales for 1997 can be calculated as follows;
Sales = (1996 sales + 1998 sales)/Number of years
Sales = ($500,000 + $720,000)/2 years
Sales = $1,220,000/2
Sales = $610,000.
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One angle of a triangle measures 80°. The other two angles are in a ratio of 6:19. What are the measures of those two angles?
The measure of the two remaining angles with the ratio of 6:19 would be = 24° and 76° respectively.
How to calculate the value of the missing angles?The total angle that makes up a triangle of any type = 180°
The value of one angle as given = 80°
Therefore the remaining total of two angles= 180-80 = 100°
The angle with the ratio of 6= 6/25×100= 600/25 = 24°
The angle with the ratio of 19 = 19/25× 100/1
= 1900/25
= 76°
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when estimating the population average using the sample mean, adding observations to a sample will always decrease the standard error of your estimate.
When estimating the population average using the sample mean, adding observations to a sample will always decrease the standard error of your estimate is random sampling variability.
In statistical analysis, estimating the population average is a common task. One way to estimate this is by using the sample mean. However, as more observations are added to the sample, the standard error of the estimate decreases. Let's explore why this is the case.
The standard error of the mean (SEM) is a measure of the amount of variability in a sample mean from one sample to another. It can be calculated using the formula:
SEM = standard deviation / square root of sample size
As we can see, the SEM is inversely proportional to the square root of the sample size. This means that as we increase the sample size by adding more observations, the denominator of the SEM formula increases, causing the SEM to decrease.
Now, let's consider how this affects our estimate of the population average. The sample mean is an unbiased estimate of the population mean. This means that on average, the sample mean will equal the population mean. However, due to random sampling variability, the sample mean can differ from the population mean.
The standard error of the mean gives us an idea of how much the sample mean can vary from one sample to another.
Therefore, adding more observations to a sample decreases the SEM, making our estimate of the population average more precise. This is because the average of a larger sample is more representative of the population average, as it is less affected by random sampling variability.
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university graduates have a mean job search time of 38.1 weeks, with a standard deviation of 10.1 weeks. the distribution of job search times is not assumed to be symmetric. between what two search times does chebyshev's theorem guarantee that we will find at least 89% of the graduates? round your answers to the nearest tenth. enter the bounds in ascending order. provide your answer below: between ____ weeks and ___ weeks
Between 7.7 weeks and 68.5 weeks search times does chebyshev's theorem guarantee that we will find at least 89% of the graduates.
Chebyshev's theorem states that for any distribution, at least 1 - 1/k^2 of the data will fall within k standard deviations from the mean.
To find the bounds for at least 89% of the graduates, we need to find the value of k that satisfies this condition.
Using Chebyshev's theorem, we have:
1 - 1/k^2 = 0.89
Solving for k, we get:
k = sqrt(1/0.11) ≈ 3.3
Therefore, at least 89% of the graduates will have job search times between:
38.1 - 3.3 x 10.1 ≈ 7.7 weeks
38.1 + 3.3 x 10.1 ≈ 68.5 weeks
Rounding to the nearest tenth, we get:
between 7.7 weeks and 68.5 weeks.
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List all the subsets of the given set. {b, j, v} Choose the answer that lists all of the subsets of {b, j, v}. A. {}, {b}, {j}, {v}, {b, j}, {b, v}, {j, v}, {b, j, v}
B. {}, {b}, {j}, {v}, {b, j}, {b, v}, {j, v} C. {b}, {j}, {v}, {b, j}, {b, v}, {j, v}, {b, j, v} D. {b}, {j}, {v}, {b, j}, {b, v}, {j, v}
Subsets of the given set. {b, j, v} is. {}, {b}, {j}, {v}, {b, j}, {b, v}, {j, v}, {b, j, v}, so correct option is A.
subsets of {b, j, v}
{}
{b}
{j}
{v}
{b, j}
{b, v}
{j, v}
{b, j, v}
The empty set and the original set itself are included in the power set, which is a set that contains all other subsets as well. P is typically used to indicate it. The number of subsets that can be generated from a given set determines the cardinality of a power set. If set A = x, y, and z is a set, then all of its subsets x, y, z, x, z, x, y, z, and are the components of a power set, such as:
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Suppose an experiment is performed where a 6-sided die is repeatedly rolled until a 6 appears, at which point the experiment stops. (a) Let E n be the event that the experiment stops at exactly n rolls. How many outcomes are in E n
The summation of permutations of the n-1 rolls that contain at least one 6.
Permutation refers to the arrangement of a set of objects in a specific order or sequence. It is a mathematical concept that involves counting the number of ways in which a set of objects can be ordered or arranged.
However, we need to exclude the sequences that already contain a 6 before the nth roll. These sequences do not belong in event E n . Therefore, we need to find the number of permutations of the n-1 rolls that contain at least one 6.
Let's first consider the case where there is exactly one 6 in the sequence. We have n-1 slots for the rolls, and we need to choose one of them to be a 6. There are (n-1) ways to choose the position of the 6, and the remaining (n-2) slots can be filled with any of the remaining 5 numbers. Therefore, there are
=> [tex](n-1) * 5^{n-2}[/tex]
ways to have exactly one 6 in the sequence.
Now let's consider the case where there are two 6s in the sequence. We have n-1 slots for the rolls, and we need to choose two of them to be 6s. There are (n-1) choose 2 ways to choose the positions of the 6s. For the remaining (n-3) slots, we can fill them with any of the remaining 4 numbers. Therefore, there are
=> [tex](n-1 choose 2) * 4^{n-3}[/tex]
ways to have exactly two 6s in the sequence.
We can continue this pattern for the case where there are k 6s in the sequence. There are (n-1) choose k ways to choose the positions of the k 6s. For the remaining (n-k-1) slots, we can fill them with any of the remaining 6-(k+1) = 5-k numbers. Therefore, there are
=> [tex](n-1 choose k) * (5-k)^{n-k-1}[/tex]
ways to have exactly k 6s in the sequence.
To get the total number of outcomes in event E n , we need to sum up the number of outcomes for each possible number of 6s in the sequence. Therefore, we have:
[tex]|E n | = 6^{(n-1) - (n-1)} * 5^{(n-2) + (n-1 choose 2)} * 4^{(n-3)} - ... + (-1)^{(n-1) * (n-1 choose n-1)} * 1^{(n-n)}[/tex]
This is a formula for the total number of outcomes in event E n .
We use permutations to count the number of ways to arrange the rolls, and we use the principle of inclusion-exclusion to exclude the sequences that contain a 6 before the nth roll.
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A researcher studying the population of monarch butterflies in a park concludes that the population from 2010 through 2015 is modeled by the function
M(r) = 945(0.935)", where n is the number of years since 2010. Based on the
researcher's study, which statements about the population of monarch butterflies in the park are correct?
The population will decrease. Thus, the correct option is A.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the factor.
The exponent is given as
y = a(b)ˣ
The equation is modeled as,
M(r) = 945 × (0.935)ⁿ
Where 'n' is the number of years since 2010.
There are three conditions exist which are as follows:
If b > 1, then the growth of the population will be there.If b = 1, then the population remains the same.If b < 1, then the decay of the population will be there.On comparing, the value of 'b' is 0.0935 which is less than one. Then the population will decrease. Thus, the correct option is A.
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The missing options are given below.
A. The population is decreasing.
B. The population is increasing.
C. The population remains constant.
D. None of the above.
4) Paige sold 455 tickets for a
fundraiser at school. Some tickets are
for children and cost $5, while the
rest are adult tickets that cost $8. If
the total value of all tickets sold was
$3,325, how many of each type of
ticket did she sell?
Number of adult tickets that Paige sold is 350 and the number of children tickets that she sold is 105.
What does a System of Linear Equations define?Linear equations involve one or more expressions including variables and constants and the highest exponent of the variable is 1.
System of linear equations involve two or more linear equations.
Let x be the number of adult tickets and y be the number of children tickets.
Total number of tickets sold = 455
So, x + y = 455
Cost of each adult ticket is $8 and cost of each children ticket is $5 and the total cost is $3,325.
8x + 5y = 3325
So we got a system of two linear equations.
x + y = 455 ⇒ y = 455 - x
8x + 5y = 3325
Substituting y = 455 - x in 8x + 5y = 3325,
8x + 5(455 - x) = 3325
Solving,
8x + 2275 - 5x = 3325
3x = 1050
x= 350
y = 455 - 350 = 105
Hence number of adult tickets Paige sold is 350 and that of children tickets is 105.
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