Using a 99% confidence level and the given data, the confidence interval for Denise's average weekly running mileage can be calculated using the sample mean, standard deviation, and z-score for the confidence level.
Explanation:Denise, a professional swimmer, uses her running mileage as part of her training analysis. To estimate the population mean for the number of miles she runs weekly, we will calculate the 99% confidence interval using the sample mean and standard deviation from her 20 weeks of data. The formula for a confidence interval is:
CI = mean ± (z* × (s/sqrt(n)))
Where mean is the sample mean, z* is the z-score corresponding to the desired confidence level, s is the sample standard deviation, and n is the sample size.
The given data for Denise's running mileage is a mean (μ) of 17.5 miles and standard deviation (s) of 3.8 miles with a sample size (n) of 20 weeks. Since the sample size is greater than 30, we can use the z-distribution to approximate the t-distribution.
To find the appropriate z-score for a 99% confidence interval, we can use a graphing calculator or a z-table. The z-score for a 99% confidence level is approximately 2.576. Plugging the values into the confidence interval formula:
CI = 17.5 ± (2.576 × (3.8/sqrt(20)))
Calculating the margins of error and applying them to the sample mean, we will obtain the confidence interval for the average number of miles Denise runs in a week.
(6.04)The line of best fit for a scatter plot is shown:
What is the equation of this line of best fit in slope-intercept form?
y = 1x + one half
y = one halfx + 1
y = 1x − one half
y = negative one halfx + 1
Answer: The correct option is (B) [tex]y=\dfrac{1}{2}x+1.[/tex]
Step-by-step explanation: We are given a line of best fit for a scatter plot in the figure.
We are to find the equation of the line of best fit in slope-intercept form.
We know that the slope-intercept form of a line is given by
[tex]y=mx+c,[/tex]
where m is the slope and c is the y-intercept of the line.
From the figure, we note that
the line passes through the points (0, 1) and (2, 2). So, the slope of the line will be
[tex]m=\dfrac{2-1}{2-0}\\\\\\\Rightarrow m=\dfrac{1}{2}.[/tex]
At x = 0, y = 1, so the y-intercept of the line, c = 1.
Therefore, the equation of the line will be
[tex]y=mx+c\\\\\Rightarrow y=\dfrac{1}{2}x+1.[/tex]
Thus, the equation of the line of best fit in slope-intercept form is
[tex]y=\dfrac{1}{2}x+1.[/tex]
Option (B) is CORRECT.
Glenn needs 20 minutes to clean his room. If his little sister Veronika pulls things out while he is cleaning, it takes 60 minutes for him to clean the room. How many minutes does it take for Veronika to pull everything out?
The rate of Glenn in finishing a job would be equivalent to:
Rate (G) = 1 job / 20 minutes
While the rate of Veronika is:
Rate (V) = 1 job / x ---> x is the unknown
Where 1 job for Glenn means completely cleaning his room while 1 job for Veronika means pulling out everything. Therefore the equation to use would be:
1 / 20 – 1 / x = 1 / 60
The rate of Veronika is subtracted from the rate of Glenn since Veronika is slowing Glenn down. Solving for x:
Multiply both sides by 60 x
(1 / 20 – 1 / x = 1 / 60) * 60 x
3 x – 60 = x
2 x = 60
x = 30
Therefore it takes 30 minutes for Veronika to pull everything out.
I will give you the simple version, if it takes 30 min for the brother to clean and the sister takes 20 minites to mess it up before he cleaned, then the sister messed the room up for 30 min because 30x2= 60.
Write the complex number in the form a + bi. 5/2(cos 150° + i sin 150°)
Answer:
It's actually this
Step-by-step explanation
(told it to convert to rectangular form)
The complex number 5/2(cos 150° + i sin 150°), in the form a + bi, can be written as -(5√3)/4 +i(5/4).
What are complex numbers?Complex numbers are used to define imaginary numbers, that is, the square roots of negative numbers. √-1 is represented as i.
How to solve the question?In the question, we are given a complex number 5/2(cos 150° + i sin 150°), and are asked to represent it in the form a + bi.
We know that complex numbers can be written in two forms, a + bi or r(cos θ + i sin θ).
The relation between these are:
r² = a² + b²,
a = r cos θ, b = r sin θ,
tan θ = b/a.
So, comparing 5/2(cos 150° + i sin 150°), to r(cos θ + i sin θ), we can say that r = 5/2, and θ = 150°.
Therefore, a = r cos θ = (5/2) cos 150° = (5/2) (-cos 30°) = -(5√3)/4
b = r sin θ = (5/2) sin 150° = (5/2) sin 30° = 5/4.
Therefore, the complex number 5/2(cos 150° + i sin 150°), in the form a + bi, can be written as -(5√3)/4 +i(5/4).
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which repeating decimal is equal in value to the fraction below? 8/9
a) 0.7777777
b) 0.8888888
c) 0.5555555
Which of the following is equal to the rational expression when x does not equal 3 or -10? (x+5)(x-3)/(x-3)(x+10)
A x+5/x-3
Bx-3/x+10
Cx+5/x+10
Dx-3/x+5
Answer:
C. x+5/x+10
Step-by-step explanation:
Just had this question on A.P.E.X and C was correct!:) good luck on yall's studies you got this!
Write the inverse of the conditional statement. Determine whether the inverse is true or false. If it is false, find a counterexample.
Independence Day in the United States is July 4.
Select one:
a. July 4 is not Independence Day in the United States. False; it is Independence Day.
b. Non-Independence Day in the United States is not July 4. True
c. Non-Independence Day in the United States is July 4. False; July 4 is Independence Day in the United States.
d. Non-July 4 is not Independence Day in the United States. True
Answer:
The correct answer is option B. Non-Independence Day in the United States is not July 4. True
Step-by-step explanation:
The inverse of the conditional statement is found by negating both the hypothesis and conclusion of that conditional statement.
Here the given statement is :
Independence Day in the United States is July 4.
Its inverse will be :
B. Non-Independence Day in the United States is not July 4. True
And yes this is true.
Quadrilateral jklm is a rhombus. the diagonals intersect at n. if the measure of angle jkl is 104°, find the measure of angle jkn.
Answer:
It is 52 degrees
Step-by-step explanation:
In a rhombus each diagonal bisects a pair of opposite angles.
Angle JKN is half of angle JKL
Angle JKN = 52°
The weights of bags of pet food are distributed normally about the mean, 50 lb. The standard deviation is 0.2 lb. In a group of 20 bags, about how many would you expect to be within one standard deviation from the mean?
Using the empirical rule for normal distributions, approximately 68% of the data falls within one standard deviation of the mean. Therefore, in a group of 20 bags of pet food with a normal distribution, about 14 bags are expected to be within one standard deviation from the mean.
Explanation:The question involves the concept of a normal distribution in statistics, and specifically, how it applies to the weights of bags of pet food. Given that the bags have a mean weight of 50 lb and a standard deviation of 0.2 lb, we can use the empirical rule (68-95-99.7 rule) for normal distributions. This rule states that approximately 68% of the data in a normal distribution falls within one standard deviation of the mean.
In this scenario, we have a group of 20 bags of pet food. To find out how many bags we would expect to fall within one standard deviation from the mean, we would calculate 68% of 20:
Expected number of bags within one standard deviation = 0.68 × 20 = 13.6
Rounding to the nearest whole number, we can expect about 14 bags to fall within one standard deviation from the mean.
formula one race cars reach speeds of approximately 100 meters Per second. what is the speed in meters per minute?
A fair coin is tossed 16 times. what is the probability that exactly 7 tails occur?
To calculate the probability of getting exactly 7 tails in 16 tosses of a fair coin, use the binomial probability formula with p = 0.5, q = 0.5, n = 16, and k = 7. Calculate C(16, 7) and then multiply it by (0.5^7) × (0.5^9) to find the probability.
Explanation:Calculating Probability of Exactly 7 Tails in 16 Coin Tosses
To find out the probability of getting exactly 7 tails when a fair coin is tossed 16 times, you can use the binomial probability formula. The formula for the binomial probability of getting exactly k successes (in our case, tails) in n trials (coin tosses) is given by:
P(X = k) = C(n, k) × (p^k) × (q^(n-k))
Where:
Here, the probability of getting a tail p is 0.5, the probability of not getting a tail q is also 0.5, n is 16, and k is 7. Substituting these values into the formula, we can calculate the probability of getting exactly 7 tails in 16 tosses of a fair coin.
The combination C(16, 7) can be calculated using the binomial coefficient formula or by using a calculator with binomial functions. Once we have the value of C(16, 7), we multiply it by (0.5^7) × (0.5^9) to get the probability. The final answer represents the probability of getting exactly 7 tails when a fair coin is tossed 16 times.
The city is planning to install streetlights and wants five lights along a walkway of 60 yards. if there is a light at the beginning and at the end of the walkway and the lights are evenly spaced, what is the distance between each light
The sum of two numbers is 46 . the larger number is 12 more than the smaller number. what are the numbers?
The required number for the given arithmetic problem is 29 and 12.
Given that,
The sum of the two numbers is 46 . the larger number is 12 more than the smaller number. what the numbers are to be determined.
What is arithmetic?
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
Let the number be x and y
According to the question,
x = y + 12 - - - - - (1)
x + y = 46 - - - - - - (2)
Substitute x in equation 2
y + 12 + y = 46
2y = 46 - 12
2y = 34
y = 17
mow put this y in equation 1
x = 17 + 12
x = 29
Thus, the required number for the given arithmetic problem is 29 and 17.
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The tens digit is two less than the units digit. If the digits are reversed, the sum of the reversed number and the original number is 154. Find the original number.
The value of the original number obtained using a system of linear equations is 68
Let the two digit number = ab
Tens digit = a Unit digit = bWe can create the system of equations as follows :
b - a = 2 - - - - - - - - - - - - (1)
(10b + a) + (10a + b) = 154
10b + a + 10a + b = 154
11b + 11a = 154 - - - - - - - - - (2)
From (1) :
b = 2 + a ----- (3)
Substitute b = 2 + a into (2)
11(2 + a) + 11a = 154
22 + 11a + 11a = 154
22 + 22a = 154
22a = 154 - 22
22a = 132
a = 132 / 22
a = 6
From (3) :
b = 2 + 6
b = 8
Therefore, the original number, ab = 68
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A 33912 cubic feet
B 2260.8 cubic feet
C 54259.20 cubic feet
D 13564.8 cubic feet
volume of cylinder = pi x r^2 x height
using 3.14 for pi
volume = 3.14 x 12^2 x 30 = 13564.8 cubic feet
D is the correct answer
What is h(x) = –3x2 – 6x + 5 written in vertex form?
h(x) = –3(x + 1)2 + 2
h(x) = –3(x + 1)2 + 8
h(x) = –3(x – 3)2 – 4
h(x) = –3(x – 3)2 + 32
Answer:
its b
Step-by-step explanation:
I just did the assignment
Which number produces a rational number when added to 0.6?
A. 0.5050050005...
B. square root of 2
C. pie
D. 5/7 (fraction)
Answer:
Correct option is D.
Step-by-step explanation:
we have to choose the option for which number produces a rational number when added to 0.6
A rational number is an algebraic term expressed as a fraction. The fraction can also be in decimals but only if the decimal places are not repeating or finite(infinite then repeating). If they aren't, then these are called irrational numbers.
Let's try each of the choices:
A. The term 0.5050050005... is irrational number. Now, when 0.6 is added to it, the sum would be irrational.
B. √2 is an irrational number because its exact value is 1.4142135.. Even if you add 0.3 to it, the answer would still be irrational
C. Obviously, π is an irrational number and addition of rational to irrational always results in irrational.
D. The term [tex]\frac{5}{7}[/tex] is a rational number. Now, when 0.6 or [tex]\frac{6}{10}[/tex] is added to it, the sum would be [tex]\frac{92}{70}[/tex] This is a rational number.
Therefore, the answer is D.
Amanda's penny bank is 23 full. After she removes 120 pennies, it is 12 full. How many pennies can Amanda's bank hold?
8. A brick oven has an opening as shown. What is the area of the entire opening?
A. 22.1 ft2
B. 20 ft2
C. 16.8 ft2
D. 13.5 ft2
What are the key aspects of any parabola? What do the key aspects tell you about the graph?
A parabola is an open curve that is formed when a cone is sliced parallel to the side of it. The key aspects of a parabola when it is graphed looks like a curve that opens upward, downward, leftward or rightward. It has a latus rectum which is the length of the ends of a curved line. The directrix is the distance between the vertex of a parabola and the line. The vertex is the point where the curve ends.
One of the key aspects of any parabola is that It looks like a curve that opens upward, downward, leftward or rightwards.
What is a Parabola?This refers to the open curve that is so shaped when there is a sliced parallel to a cone on either side of it.
From the complete question, there is an image shown and some key concepts that can be gotten from it are:
It has a latus rectum which is the length of the ends of a curved line. The directrix is the distance between the vertex of a parabola and the line. The vertex is the point where the curve ends.Read more about parabolas here:
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When n is divided by 7, the remainder is 4. What is the remainder when n+3 is divided by 7
Determine whether the expression is a polynomial. If it is a polynomial, state the degree of the polynomial.
x^3-9
a. yes, 3
b. yes, 1
c. yes, 2
d. no, it is not a polynomial
Final answer:
The expression x^3 - 9 is indeed a polynomial because it consists of a variable raised to a non-negative integer exponent and a constant. The highest power of the variable is 3, which makes the degree of the polynomial also 3.
Explanation:
To determine whether the expression x^3 - 9 is a polynomial and to state its degree, we need to look at the characteristics of polynomials. A polynomial is an expression that consists of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
The expression in question, x^3 - 9, fits this definition because it involves a single variable x raised to a non-negative integer exponent (3), and a constant term (-9).
Next, to identify the degree of the polynomial, we look for the highest power of the variable in the expression. The highest power of x in x^3 - 9 is 3. Therefore, this expression is indeed a polynomial, and its degree is 3.
The correct answer to the question is: a. yes, 3.
What is 8.61×10^−8 in decimal form?
Answer:
0,00000000861
hope this helps all u k12 cheaters. :)
Twice a certain number is tripled. The resulting number is _____.
Please help me!!! I'm super confused
In the middle of the page draw an equilateral triangle with 2 inch sides and the bottom parallel to the bottom of the page. From the center of the right side draw two parallel lines an inch apart and an inch long. Draw a line from the end of one of the parallel lines to the end of the other parallel line. Which direction is the arrow pointing
Solution:
Drawn an equilateral triangle of side 2 inches.
One side is parallel to Bottom of page.
Then from the center of the right side draw two parallel lines an inch apart and an inch long.
Then drawn a line from the end of one of the parallel lines to the end of the other parallel line.
The Arrow is pointing in East of South or South of East and North of West or West of North Direction.
A card is drawn at random from a deck. what is the probability it is a red card, an ace, or both?
52 cards total
26 are red
so you would have a 26/52 reduced to 1/2 probability of picking a red one.
There are 4 aces so you would have a 4/52 reduced to 1/13 probability of picking an ace.
There are 2 red aces so you would have a 2/52 reduced to 1/26 probability of picking a red Ace
The graph below represents the price of the banana at one store. What is the constant of proportionality?
Carlos Martin received a statement from his bank showing a balance of $56.75 as of March 15. His checkbook shows a balance of $87.37 as of March 20. The bank returned all the cancelled checks but two. One check was for $5.00 and the other was for $13.25. How much did Carlos deposit in his account between March 15 and March 20?
Geometry Help Please
The sum of two numbers is twice their difference. the larger number is 2 more than twice the smaller. find the numbers. smaller number 1 larger number 3
The smaller number is 1 and the larger number is 3.
What is a linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
Let the numbers be x and y.
The sum of two numbers is twice their difference.
(x + y) = 2(x -y)
The larger number is 2 more than twice the smaller.
That means,
y = x + 2.
Then,
(x + x + 2) = 2(x + 2 - x)
2x + 2 = 4
x = 1
And y = 3
Therefore, the numbers are 1 and 3.
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