To determine which interval contains the root of f(x) = 2x - x3 + 2, we need to examine the behavior of the function around the x-axis.
First, we can find the critical points by setting f(x) = 0: 0 = 2x - x3 + 2
Rearranging, we get: x3 - 2x + 2 = 0
This is a cubic equation, which can be difficult to solve exactly. However, we can use the Intermediate Value Theorem to determine whether there is a root in a given interval.
One critical point is x ≈ -1.7693. We can test whether there is a root in the interval (-∞, -1.7693) by evaluating f(x) at a point in the interval, such as x = -2:
f(-2) = 2(-2) - (-2)3 + 2 = -12
Since f(-2) is negative and f(x) is a continuous function, there must be at least one root in the interval (-∞, -1.7693).
Another critical point is x ≈ 1.7693. We can test whether there is a root in the interval (1.7693, ∞) by evaluating f(x) at a point in the interval, such as x = 2: f(2) = 2(2) - 23 + 2 = 0.
Since f(2) is zero and f(x) is a continuous function, there must be at least one root in the interval (1.7693, ∞).
Therefore, the intervals that contain the root of f(x) = 2x - x3 + 2 are (-∞, -1.7693) and (1.7693, ∞).
To determine which interval contains the root of the function f(x) = 2x - x^3 + 2, we can follow these steps:
Step 1: Identify the intervals of interest. For this question, the intervals are not specified, so we will assume the intervals are (-∞, 0) and (0, ∞).
Step 2: Check the value of f(x) at the endpoints of each interval. In our case, we will check f(0) for both intervals. f(0) = 2(0) - (0)^3 + 2 = 2.
Since f(0) > 0, we know that there is a root between the intervals (-∞, 0) and (0, ∞) if there's a change of sign between the intervals.
Step 3: Check the sign of f(x) within each interval. Pick a representative point from each interval and evaluate f(x) at that point.
For the interval (-∞, 0), let's pick x = -1:
f(-1) = 2(-1) - (-1)^3 + 2 = -1
For the interval (0, ∞), let's pick x = 1:
f(1) = 2(1) - (1)^3 + 2 = 3
Step 4: Determine which interval contains the root based on the change of sign.
The function f(x) changes its sign from negative to positive as we move from the interval (-∞, 0) to the interval (0, ∞). Therefore, the interval that contains the root of the function f(x) = 2x - x^3 + 2 is (-∞, 0).
To know more about theorem click here
brainly.com/question/30242664
#SPJ11
A project is graded on a scale of 1 to 5. If the random variable, X, is the project grade, what is the mean of th
probability distribution below?
The mean of the probability distribution of the random variable is 3
What is the mean of the probability distribution?From the question, we have the following parameters that can be used in our computation:
The probability distribution
From the probability distribution, we can see that the data are normally distributed
This means that the mean, the median and the mode are equal
From the distribution of the random variable, we have the following readings
mean = 3 median = 3mode = 3Hence. the calculated mean of the random variable is 3
Read more about probability distribution at
https://brainly.com/question/23286309
#SPJ1
PLSS HELP WITH THISSSSS
Answer:
i d k which means i don't know
find two numbers whose difference is 132 and whose product is a minimum. (smaller number) (larger number)
The two numbers whose difference is 132 and whose product is a minimum are 66 and 198.
Let x and y be the two numbers. We are given that their difference is 132, so we can write:
y - x = 132
We want to minimize their product, which is given by:
P = xy
We can solve for one of the variables in terms of the other using the first equation:
y = x + 132
Substituting this expression for y in the equation for P, we get:
P = x(x + 132)
Expanding this expression and simplifying, we get:
P = x^2 + 132x
To find the minimum value of P, we can take the derivative of P with respect to x and set it equal to zero:
dP/dx = 2x + 132 = 0
Solving for x, we get:
x = -66
Since we want the two numbers to be positive, we take the absolute value of x and add 132 to get y:
x = 66
y = x + 132 = 198
Therefore, the two numbers whose difference is 132 and whose product is a minimum are 66 and 198.
To learn more about product visit: https://brainly.com/question/22852400
#SPJ11
Write the standard equation of the circle centered at (2, -3), which passes through (3, 5).
Answer:
Step-by-step explanation:
the standard equation for the circle is:
(x-a)²+(y-b)² = r²
the center is : A(a,b) and ridus r
you have : a= 2 and b= - 3 r²= (3-2)²+(5+3)²= 1+ 64
r² 65
the standard equation for the circle is:
(x-2)²+(y²+3 )=65
Suppose that X and Y are random variables with the same variance. Show that X - Y and X + Y are uncorrelated.
X - Y and X + Y are uncorrelated. To show that X - Y and X + Y are uncorrelated, we need to show that their covariance is zero.
The covariance between X - Y and X + Y is given by:
[tex]Cov(X - Y, X + Y) = E[(X - Y)(X + Y)] - E[X - Y]E[X + Y][/tex]
Expanding the first term:
Cov(X - Y, X + Y) = E[X^2 - Y^2] - E[X - Y]E[X + Y]
Using the fact that X and Y have the same variance, we have:
[tex]E[X^2 - Y^2] = E[(X - Y)(X + Y)] = E[X^2] - E[Y^2][/tex]
And since X and Y have the same variance[tex], E[X^2] = E[Y^2][/tex], so we can simplify:
[tex]E[X^2 - Y^2] = 0[/tex]
Next, we can expand the second term:
E[X - Y]E[X + Y] = (E[X] - E[Y])(E[X] + E[Y])
Since X and Y have the same variance, we have E[X] = E[Y], so:
E[X - Y]E[X + Y] = (E[X] - E[X])(E[X] + E[X]) = 0
Putting it all together:
Cov(X - Y, X + Y) = 0 - 0 = 0
Therefore, X - Y and X + Y are uncorrelated.
Learn more about uncorrelated here:
https://brainly.com/question/30507987
#SPJ11
If a is uniformly distributed over [−12,15], what is the probability that the roots of the equation
x^2 + ax + a + 35 = 0
are both real? ___
To determine the probability that the roots of the given quadratic equation are both real, we need to find the values of a for which the discriminant of the equation is non-negative.
The discriminant of the quadratic equation ax^2 + bx + c = 0 is b^2 - 4ac. In this case, the discriminant of the given equation is:
a^2 - 4(a+35)
For the roots to be real, this discriminant must be non-negative. That is:
a^2 - 4(a+35) ≥ 0
Simplifying this inequality, we get:
a^2 - 4a - 140 ≥ 0
Factorizing the left-hand side, we get:
(a-14)(a+10) ≥ 0
This inequality is satisfied for a ≤ -10 or a ≥ 14, or when a is in the interval [-12, -10) or (14, 15].
Since a is uniformly distributed over the interval [-12, 15], the probability that lies in the interval [-12, -10) or (14, 15] is:
Probability = Length of the interval [-12, -10) + Length of interval (14, 15] / Total length of the interval [-12, 15]
Probability = (2 + 1) / (15 - (-12))
Probability = 3/27
Probability = 1/9
Therefore, the probability that the roots of the given quadratic equation are both real is 1/9.
Learn more about probability here:
https://brainly.com/question/31316555
#SPJ11
Simplify the polynomial expression. (64m^8n^12)^1/2
The simplified value of the polynomial-expression "√(64m⁸n¹²)" is 8m⁴n⁶..
A "Polynomial-Expression" is an expression which consists of variables, coefficients, and exponents having operations of addition, subtraction, multiplication, and non-negative integer exponents.
To simplify the given polynomial expression √(64m⁸n¹²), we can use the property of square-roots which states that √(a×b) = √a × √b;
So, We have
⇒ √(64m⁸n¹²) = √(64) × √(m⁸) × √(n¹²),
Now, we simplify each of square roots separately:
⇒ √(64) = 8, because 8×8 = 64;
⇒ √(m⁸) = m⁴, because m⁴×m⁴ = (m⁴)² = m⁸;
⇒ √(n¹²) = n⁶, because n⁶×n⁶ = (n⁶)² = n¹²,
Substituting the values,
We get,
⇒ √(64m⁸n¹²) = 8m⁴n⁶
Therefore, the simplified polynomial expression is 8m⁴n⁶.
Learn more about Expression here
https://brainly.com/question/8724203
#SPJ1
The given question is incomplete, the complete question is
Simplify the polynomial expression. √(64m⁸n¹²).
a 'scooped' pyramid has a cross-sectional area of x 4 at a distance x from the tip. what is its volume if the distance from tip to base is 5?
The volume of the 'scooped' pyramid is approximately 26.6667 cubic units.
To find the volume of the 'scooped' pyramid, we first need to determine the area of its base. Since the cross-sectional area of the pyramid is x 4 at a distance x from the tip, we can assume that the area at the tip is zero. This means that the area of the base is 4 times the area at a distance of 5 from the tip (since the distance from tip to base is 5).
Therefore, the area of the base is 4x4 = 16 square units. To find the volume, we can use the formula for the volume of a pyramid, which is:
Volume = (1/3) x Base Area x Height
In this case, the height of the pyramid is 5 units. So, we can substitute the values we have:
Volume = (1/3) x 16 x 5
Volume = 26.6667 cubic units
Know more about pyramid here:
https://brainly.com/question/13057463
#SPJ11
if a binomial experiment has seven trials in which the probability of success is p and the probability of failure is q, write an expression that could be used to compute each of the following probabilities: a) p(exactly five successes) b) p(at least five successes) c) p(at most five successes)?
To calculate the probability of getting at most five successes, we can add up the probabilities of getting 0, 1, 2, 3, 4, or 5 successes
Sure, here are the expressions that can be used to compute each of the probabilities:
a) p(exactly five successes) = (7 choose 5) * p^5 * q^2
This expression uses the binomial coefficient (7 choose 5), which represents the number of ways to choose 5 successes out of 7 trials. We then multiply this by the probability of getting 5 successes (p^5) and the probability of getting 2 failures (q^2).
b) p(at least five successes) = p(five successes) + p(six successes) + p(seven successes)
To calculate the probability of getting at least five successes, we can add up the probabilities of getting exactly 5, 6, or 7 successes. We can use the expression from part a to calculate each of these probabilities.
c) p(at most five successes) = p(zero successes) + p(one success) + p(two successes) + p(three successes) + p(four successes) + p(five successes)
. We can again use the expression from part a to calculate each of these probabilities.
Know more about probability here:
https://brainly.com/question/30034780
#SPJ11
A store buys a jackey for 20$ and sells it to there cosutomer 80% more than that, what is the selling price
the height of the tree below is log2n, where n is the number of leaves because that is the height of a binary tree.
Answer: That is correct. In a binary tree, each node has at most two child nodes (hence the name "binary"), and the height of the tree is the length of the longest path from the root node to a leaf node.
If the tree has n leaves, then the number of nodes in the tree is at most 2n-1 (since each node can have at most 2 child nodes and there is only one root node), and the height of the tree is log2(2n) = log2n + 1 (since there are 2n nodes at level log2n, and we need to add 1 for the root node).
However, if the tree is not perfectly balanced, it is possible for the height to be slightly larger than log2n + 1. Nonetheless, log2n is still a tight upper bound on the height of a binary tree with n leaves.
A researcher is interested in exploring the way that nutrition and psychological health can influence fitness as measured by a physical assessment battery. The dataset of physical fitness scores appears as follows: (12 pts) (10, 13, 17, 21, 23, 27, 27, 29, 36, 40) Create a relative frequency table of raw score values using class intervals with a width of 5. Be sure to include columns for raw scores, frequency, cumulative frequency, & cumulative percentage. (4 pts) tl From your frequency table, draw a relative frequency histogram and identify the shape of the distribution. Be sure to label all axes and provide a title. (2 pts) What value corresponds to the percentile rank of 30%? What is the approximate percentile rank of X = 36? (2 pts - Hint: Use the table that you made)
The value corresponding to the percentile rank of 30% is found in the 10-14 class interval, as its cumulative percentage is 30%. The approximate percentile rank of X = 36 is 90%, as the cumulative percentage for the class interval of 35-39 is 90%.
To create a relative frequency table of raw score values, we first need to create class intervals with a width of 5. The class intervals are: 5-9, 10-14, 15-19, 20-24, 25-29, 30-34, and 35-39.
| Raw Scores | Frequency | Cumulative Frequency | Cumulative Percentage |
|------------|-----------|----------------------|-----------------------|
| 5-9 | 0 | 0 | 0% |
| 10-14 | 2 | 2 | 20% |
| 15-19 | 1 | 3 | 30% |
| 20-24 | 1 | 4 | 40% |
| 25-29 | 3 | 7 | 70% |
| 30-34 | 1 | 8 | 80% |
| 35-39 | 1 | 9 | 90% |
To draw a relative frequency histogram, we plot the class intervals on the x-axis and the relative frequencies on the y-axis. The shape of the distribution appears to be positively skewed.
The value corresponding to the percentile rank of 30% can be found by looking at the cumulative percentage column in the frequency table. The cumulative percentage at the end of the 2nd class interval is 20%, so the value corresponding to the 30th percentile is somewhere between 10 and 14. Using linear interpolation, we can estimate that the value corresponding to the 30th percentile is approximately 11.6.
To find the approximate percentile rank of X = 36, we can look at the raw scores column in the frequency table and find the class interval that contains 36, which is 35-39. The cumulative frequency at the end of this interval is 9, and the total number of scores is 10. Therefore, the percentile rank of X = 36 is approximately 90%.
To create a relative frequency table of raw score values using class intervals with a width of 5, we can categorize the data as follows:
Class Intervals (Raw Scores): 10-14, 15-19, 20-24, 25-29, 30-34, 35-39, 40-44
Frequency: 2, 1, 2, 3, 0, 1, 1
Cumulative Frequency: 2, 3, 5, 8, 8, 9, 10
Cumulative Percentage: 20%, 30%, 50%, 80%, 80%, 90%, 100%
Next, draw a relative frequency histogram with the class intervals on the x-axis and the frequency on the y-axis. The shape of the distribution is positively skewed, as most data points are on the lower end of the scale, with a few points in the higher range.
The value corresponding to the percentile rank of 30% is found in the 10-14 class interval, as its cumulative percentage is 30%.
The approximate percentile rank of X = 36 is 90%, as the cumulative percentage for the class interval of 35-39 is 90%.
Learn more about histogram at: brainly.com/question/30664111
#SPJ11
Find the indicated probability using the standard normal distribution.P(z>−2.75)
The probability P(z > -2.75) using the standard normal distribution is approximately 0.9970.
To find the indicated probability using the standard normal distribution, we need to use a z-table.
The standard normal distribution has a mean of 0 and a standard deviation of 1. The z-score represents the number of standard deviations away from the mean.
To find P(z>-2.75), we need to find the area under the standard normal distribution curve to the right of -2.75.
Using a z-table, we can find that the area to the right of -2.75 is 0.9970.
Therefore, P(z>-2.75) = 0.9970 or approximately 0.997.
This means that there is a 99.7% probability that a randomly selected value from the standard normal distribution will be greater than -2.75 standard deviations from the mean.
To find the indicated probability P(z > -2.75) using the standard normal distribution, follow these steps:
1. Identify the z-score: In this case, the z-score is -2.75.
2. Use the standard normal distribution table or a calculator with a built-in z-table function to find the area to the left of the z-score.
3. Since we need to find the probability P(z > -2.75), we'll subtract the area to the left of the z-score from 1 (the total probability).
Step-by-step calculation:
1. z-score = -2.75
2. Look up the area to the left of the z-score in the standard normal distribution table or using a calculator. For z = -2.75, the area to the left is approximately 0.0030.
3. To find the probability P(z > -2.75), subtract the area to the left from 1:
P(z > -2.75) = 1 - 0.0030 = 0.9970
So, the probability P(z > -2.75) using the standard normal distribution is approximately 0.9970.
Learn more about probability at: brainly.com/question/30034780
#SPJ11
A researcher is interested in whether there is a difference in charitable donations based on the Type of Organization and Gender. She does an experiment to assess the average donations for the Salvation Army, Planned Parenthood, and the Humane Society. And she marks each donor's gender when they donate. What statistical test should she use?
This statistical test is appropriate because it allows for the examination of the effects of two independent variables (Type of Organization and Gender) on a continuous dependent variable (average donations).
The researcher should use a two-way ANOVA (analysis of variance) test to assess the difference in charitable donations based on both the type of organization and gender. This will allow the researcher to determine whether To analyze the difference in charitable donations based on the Type of Organization and Gender, the researcher should use a Two-Way ANOVA (Analysis of Variance). This statistical test is appropriate because it allows for the examination of the effects of two independent variables (Type of Organization and Gender) on a continuous dependent variable (average donations).
learn more about two-way ANOVA
https://brainly.com/question/23638404
#SPJ11
A boat traveled 140 miles in 6 hours. It traveled part of the distance at 10 miles/hour and
the other part of the distance at 30 miles/hour.
How long did it travel at 10 miles/hour?
How long did it travel at 30 miles/hour?
Answer:
The boat traveled at 10 miles per hour for 2 hours and at 30 miles per hour for 4 hours.
Step-by-step explanation:
Let x be the time (in hours) that the boat traveled at 10 miles per hour, and let y be the time (in hours) that it traveled at 30 miles per hour.
We know that:
x + y = 6 (the total time the boat traveled)
We also know that the boat traveled a total distance of 140 miles, which can be expressed as:
10x + 30y = 140
We can use the first equation to solve for one of the variables in terms of the other:
y = 6 - x
Substituting this expression for y into the second equation, we get:
10x + 30(6 - x) = 140
Simplifying and solving for x, we get:
10x + 180 - 30x = 140
-20x = -40
x = 2
Therefore, the boat traveled at 10 miles per hour for 2 hours and at 30 miles per hour for 4 hours.
A researcher asked 120 people if they preferred swimming in a pool or swimming at the beach. The data collected show that two out of 10 people preferred swimming at the beach. What was the total number of people who preferred swimming at the beach?
A. 12
B. 60
C. 2
D. 24
PLEASE ANSWER WITH EXPLANATION / WORK
The total number of people who preferred swimming at the beach is: 24
How to find the probability of selection?In survey sampling, the term probability of selection is one that refers to the chance (i.e. the probability from 0 to 1) that a member (element) of a population can be chosen for a given survey.
We are told that two out of 10 people preferred swimming at the beach. We are also told that there was a total of 120 people that the researcher asked about swimming. Thus:
Fraction of people that prefer swimming = 2/10 = 0.2
Thus, number of people that prefer swimming in a sample of 120 people is: 0.2 * 120 = 24 people
Read more about Probability of selection at: https://brainly.com/question/251701
#SPJ1
Solve for a and b so that f(x) is continuous at all points.
[tex]f(x) = \begin{cases}\frac{x^2-4}{x-2} & \text{if } x\ \textless \ 2 \\ax^2-bx+3 & \text{if } 2\le x \ \textless \ 3\\2x-a+b & \text{if } x\ge 3\end{cases}[/tex]
Answer:
[tex]a=\dfrac{1}{2},\;\;b=\dfrac{1}{2}[/tex]
Step-by-step explanation:
A function f is continuous at x = a when:
[tex]\bullet\quad\textsf{$f(a)$\;is\;d\:\!efined.}[/tex]
[tex]\bullet\quad\textsf{$\displaystyle \lim_{x \to a} f(x)$\;exists.}[/tex]
[tex]\bullet\quad\displaystyle \lim_{x \to a} f(x) = f(a)[/tex]
To ensure that f(x) is continuous at x = 2 and x = 3, we need to make sure that the limit of f(x) as x approaches 2 from the left is equal to the limit of f(x) as x approaches 2 from the right, and similarly for x = 3.
First, factor the numerator and simplify the rational function:
[tex]f(x)=\dfrac{x^2-4}{x-2}=\dfrac{(x+2)(x-2)}{x-2}=x+2[/tex]
As x approaches 2 from the left, x < 2. Therefore, to find the limit as x approaches 2 from the left, substitute x = 2 into the first sub-function:
[tex]\displaystyle \lim_{x \to 2^{-}} f(x)=2+2=4[/tex]
As x approaches 2 from the right, x > 2. Therefore, to find the limit as x approaches 2 from the right, substitute x = 2 into the second sub-function:
[tex]\begin{aligned}\displaystyle \lim_{x \to 2^{+}} f(x)&=a(2)^2-b(2)+3\\&=4a-2b+3\end{aligned}[/tex]
To ensure continuity at x = 2, equate the limits:
[tex]4=4a - 2b + 3[/tex]
Solve for b in terms of a:
[tex]\begin{aligned}4&=4a - 2b + 3&\\ 2b+4&=4a+3\\2b&=4a-1\\b&=2a-\dfrac{1}{2}\end{aligned}[/tex]
Now, we need to find a and b so that f(x) is continuous at x = 3.
As x approaches 3 from the left, x < 3. Therefore, to find the limit as x approaches 3 from the left, substitute x = 3 into the second sub-function:
[tex]\begin{aligned}\displaystyle \lim_{x \to 3^{-}} f(x)&=a(3)^2 - b(3) + 3\\&= 9a - 3b + 3\end{aligned}[/tex]
As x approaches 3 from the right, x > 3. Therefore, to find the limit as x approaches 3 from the right, substitute x = 3 into the third sub-function:
[tex]\begin{aligned}\displaystyle \lim_{x \to 3^{+}} f(x)&= 2(3) - a + b\\&= 6 - a + b\end{aligned}[/tex]
To ensure continuity at x = 3, equate the limits:
[tex]9a - 3b + 3 = 6-a+b[/tex]
Solve for b in terms of a:
[tex]\begin{aligned}9a - 3b + 3 &= 6-a+b\\10a-3b+3&=6+b\\10a+3&=6+4b\\10a-3&=4b\\4b&=10a-3\\b&=\dfrac{5}{2}a-\dfrac{3}{4}\end{aligned}[/tex]
Substitute this expression for b into the equation obtained from continuity at x = 2:
[tex]\dfrac{5}{2}a-\dfrac{3}{4}=2a-\dfrac{1}{2}[/tex]
Solve for a:
[tex]\begin{aligned}\dfrac{5}{2}a-\dfrac{3}{4}&=2a-\dfrac{1}{2}\\\\\dfrac{1}{2}a-\dfrac{3}{4}&=-\dfrac{1}{2}\\\\\dfrac{1}{2}a&=\dfrac{1}{4}\\\\a&=\dfrac{1}{2} \end{aligned}[/tex]
Substitute the found value of a into the expression for b and solve for b:
[tex]\begin{aligned}b&=2\left(\dfrac{1}{2}\right)-\dfrac{1}{2}\\b&=1-\dfrac{1}{2}\\b&=\dfrac{1}{2}\end{aligned}[/tex]
Therefore, the values of a and b that make f(x) continuous at all points are:
[tex]a=\dfrac{1}{2},\;\;b=\dfrac{1}{2}[/tex]
So the function f(x) is:
[tex]f(x)=\begin{cases} \dfrac{x^2-4}{x-2}&\text{if}\;\;x < 2\\\\\dfrac{1}{2}x^2-\dfrac{1}{2}x+3\quad&\text{if}\;\;2 \leq x < 3\\\\2x&\text{if}\;\;x \geq 3\end{cases}[/tex]
Determina cuáles de las siguientes expresiones son proposiciones. 1. Sube al 1
1.cuarto piso.
2.el triangulo ABC es equilatero
3. ¿que es un àngulo obtuso?
4. la suma de una medida de dos angulos complenmetanrios es igual a 90
5. un triangulo es isoceles si tiene solamente dos angualos congruentes
Write and solve each inequality. You do not have to check.
5. A fast-food company allows its hourly employees to work a maximum of 38 hours each week. Anita
works 26 hours one week. Determine the number of hours Anita can work for the rest of the week.
Then interpret the solution.
The inequality showing the maximum number of hours left for her to work that week is: x ≤ 12 and this means she can work a maximum of 12 remaining hours for that week
How to solve Inequality word problems?Inequalities could either be in these forms:
Less than
Greater than
Greater than or equal to
Less than or equal to
We are given the parameters:
Maximum number of hours per week = 38 hours
Number of hours she has worked so far this week is 26
If the remaining number of hours she can work is x, then we have the inequality as:
x + 26 ≤ 38
Subtract 26 from both sides to get:
x ≤ 12
Read more about Inequality word problems at: https://brainly.com/question/25275758
#SPJ1
The manager of a jelly bean factory wants to add a new flavor. The manger plans to survey a sample of the customers to find out which type of jelly bean would be popular.
a. Describe one way a manager could select a random sample of the jelly bean customers?
b. Is the most popular jelly bean in the sample guaranteed to be the most popular jelly bean for all customers? Explain.
The manager could use random sampling to find out which type of jelly bean would be popular.
What is random sampling?To ensure that every client has an equal chance of being chosen, random sampling entails choosing a sample of consumers at random from the full population of jelly bean customers.
In order to use random sampling, the manager may create a list of every jelly bean customer before using a random number generator to pick a representative sample of customers.
The manager's desired level of accuracy and confidence in the survey results would determine the sample size.
Learn more about random sampling:https://brainly.com/question/29852583
#SPJ1
Identify which transformation or sequence of transformations identified below will map triangle ABC onto triangle DEF.
A Single transformation maps triangle ABC onto triangle DEF.
Given that Reflection the single transformation maps ABC onto A'B'C' is reflection .
The rigid transformations can map triangle Δ ABC onto triangle Δ DEF is reflection then translation .
The rigid transformations that will map Δ ABC to Δ DEF is rotation then translation .
However pair of triangles can be proven congruent by the HL theorem is rotation then translation .
Thus, rigid transformation S can map Triangle ABC onto Triangle DEF is reflection then rotation .
Learn more about the triangle here:
brainly.com/question/2773823
#SPJ1
How do I figure this out?!
A. Optgion C is correct. y = - 4/5x + 94
b. The distance that Maria would have covered from her house is given as 58 meters
How to solve for the distance abd the slopeThe formula to use here is
y2 - y1 / x2 - x1
= 70 - 94 / 30 - 0
= - 24 / 30
divide through by 6
= - 4 / 5
y = - 4/5x + 94
When x = 45
y = - 4/5x + 94
= -4 / 5 * 45 + 94
y = 180 / 5 + 94
y = -36 + 94
y = 58
Read more on slope here:https://brainly.com/question/12339452
#SPJ1
use the graph to evaluate the compostable (f•g)(0)=
Answer: The answer is 3
Step-by-step explanation: I had the same question.
A normal population has known mean u = 75 and variance o = 5. What is the approximate probability that the sample variance is greater than or equal to 7.442 less than or equal to 2.56? For a random sample of size a. n= 16 b. n=30 c. Compare your answers to parts (a)-(b) for the approximate probability that the sample variance is greater than or equal to 7.44. Explain why this tail probability is increasing or decreasing with increased sample size. d. Compare your answers to parts (a)-(b) for the approximate probability that the sample variance is less than or equal to 2.56. Explain why this tail probability is increasing or decreasing with increased sample size.
Using a chi-square table or calculator, we find that this probability is approximately 0.025.
To answer this question, we need to use the chi-square distribution, which is used to find probabilities for sample variances.
a) For a random sample of size n = 16, we use the formula:
Chi-Square = (n-1) * sample variance / population variance
Chi-Square = 15 * 7.442 / 5
Chi-Square = 22.326
The probability of a sample variance being greater than or equal to 7.442 is the same as the probability of a chi-square value of 22.326 or more. Using a chi-square table or calculator, we find that this probability is approximately 0.05.
The probability of a sample variance being less than or equal to 2.56 is the same as the probability of a chi-square value of 7.692 or less. Using a chi-square table or calculator, we find that this probability is approximately 0.025.
b) For a random sample of size n = 30, we use the formula:
Chi-Square = (n-1) * sample variance / population variance
Chi-Square = 29 * 7.442 / 5
Chi-Square = 41.256
The probability of a sample variance being greater than or equal to 7.442 is the same as the probability of a chi-square value of 41.256 or more. Using a chi-square table or calculator, we find that this probability is approximately 0.005.
The probability of a sample variance being less than or equal to 2.56 is the same as the probability of a chi-square value of 13.767 or less. Using a chi-square table or calculator, we find that this probability is approximately 0.025.
c) Comparing the probabilities in parts (a) and (b) for the sample variance being greater than or equal to 7.442, we see that the probability decreases with increased sample size. This is because as the sample size increases, the sample variance is more likely to be closer to the population variance, resulting in a smaller chi-square value.
d) Comparing the probabilities in parts (a) and (b) for the sample variance being less than or equal to 2.56, we see that the probability remains the same regardless of sample size. This is because a smaller sample variance is always more likely than a larger one, regardless of the sample size.
In a normal population with a known mean (µ) of 75 and variance (σ²) of 5, we want to find the approximate probability that the sample variance is greater than or equal to 7.442 and less than or equal to 2.56 for random samples of size n=16 and n=30.
a) For a random sample of size n=16, the chi-square distribution with degrees of freedom (df) = n-1 = 15 is used to calculate the probability.
b) For a random sample of size n=30, the chi-square distribution with degrees of freedom (df) = n-1 = 29 is used to calculate the probability.
c) Comparing the answers to parts (a) and (b) for the approximate probability that the sample variance is greater than or equal to 7.44, it is observed that the tail probability may either increase or decrease with an increased sample size, depending on the underlying distribution of the population.
d) Comparing the answers to parts (a) and (b) for the approximate probability that the sample variance is less than or equal to 2.56, it is observed that the tail probability may either increase or decrease with an increased sample size, again depending on the underlying distribution of the population.
The actual probabilities will depend on the specific calculations made using the chi-square distribution and the given parameters.
Learn more about chi-square at: brainly.com/question/14082240
#SPJ11
Nth term=5n+6
What is the sequence when the nth term = 5n+6
The sequence for the nth term = 5n+6 is: 11, 16, 21, 26, 31,...
How to find the the sequence when the nth term = 5n+6The sequence for the nth term = 5n+6 is:
n = 1, the nth term is 5(1)+6 = 11
n = 2, the nth term is 5(2)+6 = 16
n = 3, the nth term is 5(3)+6 = 21
n = 4, the nth term is 5(4)+6 = 26
n = 5, the nth term is 5(5)+6 = 31
and so on.
Therefore, the sequence for the nth term = 5n+6 is: 11, 16, 21, 26, 31,...
Learn more about sequence at https://brainly.com/question/30762797
#SPJ1
Ratio of men, women and children is 5:9:10
There are 480 more women than men,
how many:
(a) men,
(b) women,
(c) children are there?
The proportion is solved and the number of men , women and children are 600 men, 1080 women, and 1200 children respectively
Given data ,
Let the proportion be represented as A
Now , the value of A is
Ratio of men : women : children = 5 : 9 : 10
And , Men:Women:Children = 5x : 9x : 10x
It is also given that there are 480 more women than men.
Since the ratio of men to women is 5:9, we can set up the equation:
9x - 5x = 480
Simplifying, we get:
4x = 480
Dividing both sides by 4, we get:
x = 120
Now we can substitute the value of x back into the ratio to find the actual number of men, women, and children.
(a) Men = 5x = 5 x 120 = 600
(b) Women = 9x = 9 x 120 = 1080
(c) Children = 10x = 10 x 120 = 1200
Hence , there are 600 men, 1080 women, and 1200 children
To learn more about proportion click :
https://brainly.com/question/7096655
#SPJ1
pls help i need help with this question
The term that represents the typical average speed is 30/3s
Selecting the term that represents the average speedFrom the question, we have the following parameters that can be used in our computation:
Expression = 20/s + 30/3s
We understand that
She traveled at 20 miles per second for some time and the rest at her typical speed
This means that
Typical speed = 30/3s
Hence, the term of the average speed is 30/3s
Read more about expression at
https://brainly.com/question/15775046
#SPJ1
an agricultural field test compares two varieties of corn, silver queen and country gentlemen. the researches takes 10 plots and divides each of these plots in half. each plot has a similar amount of sun light, shade, quality of soil and irrigation. the variety of corn is randomly chosen for each half of a plot. after the harvest, the yield of corn is measured for each half plot at each location. the yield from silver queen was compared to the yield of country gentlemen. note: differences were taken by taking silver queen - country gentlemen the 95% confidence interval for the mean is (-0.223, 0.988). what can we expect will be the p-value for a two sided test using this data? group of answer choices the p-value should be smaller than 0.95. the p-value should be higher than 0.95. the p-value should be higher than 0.05. the p-value should be smaller than 0.05.
Based on the given information, we can expect the p-value for a two-sided test using this data to be smaller than 0.05. This is because the 95% confidence interval for the mean does not contain 0, which indicates that there is a statistically significant difference between the yield of silver queen and country gentlemen.
A p-value is a measure of the evidence against the null hypothesis (which in this case would be that there is no difference between the two corn varieties). The smaller the p-value, the stronger the evidence against the null hypothesis and the more likely we are to reject it. In general, if the p-value is smaller than the chosen significance level (usually 0.05 or 0.01), we reject the null hypothesis and conclude that there is a significant difference between the two groups being compared.
Therefore, in this case, we can expect the p-value to be smaller than 0.05 and conclude that there is a significant difference in the yield of silver queen and country gentlemen.
Learn more about gentlemen. here:
https://brainly.com/question/13876722
#SPJ11
are you smarter than a second-grader? a random sample of 54 second-graders in a certain school district are given a standardized mathematics skills test. the sample mean score is x
It is difficult to say much more about the sample mean score.
If we know the sample mean score, which is denoted by x in your question, we can use it to make some inferences about the overall population of second-graders in that school district. However, we would need more information about the distribution of scores, such as the standard deviation or the range, to draw any conclusions about the entire population.
For example, if we assume that the distribution of scores is approximately normal, we could use the sample mean and standard deviation to calculate a confidence interval for the population mean score. This interval would give us a range of scores within which we can be reasonably confident the true population mean falls.
Without more information about the sample or the population, it is difficult to say much more about the sample mean score.
Complete question: Are you smarter than a second-grader? A random sample of 45 second-graders in a certain school district are given a standardized mathematics skills test. The sample mean score is x-54. Assume the standard deviation of test scores is o = 15. The nationwide average score on this test is 50. The school superintendent wants to know whether the second-graders in her school district have different math skills from the nationwide average. Use the a=0.05 level of significance and the P-value method with the TI-84 calculator al Part: 0/4 Part 1 of 4 State the appropriate null and alternate hypotheses.
Previous question
To learn more about distribution visit:
https://brainly.com/question/29062095
#SPJ11
true/false. among the 30 largest u.s. cities, the mean one-way commute time to work is 25.8 minutes. the longest one-way travel time is in new york city, where the mean time is 37.5 minutes. assume the distribution of travel times in new york city follows the normal probability distribution and the standard deviation is 6.5 minutes.
The statement is true. The mean one-way commute time for the 30 largest U.S. cities is 25.8 minutes, and New York City has the longest mean travel time at 37.5 minutes, with a normal probability distribution and a standard deviation of 6.5 minutes.
True. The question states that among the 30 largest U.S. cities, the mean one-way commute time to work is 25.8 minutes. This means that on average, the commute time for these 30 cities is 25.8 minutes. However, the question also states that the longest one-way travel time is in New York City, where the mean time is 37.5 minutes. This means that New York City has a longer commute time compared to the other 29 cities.
Assuming the distribution of travel times in New York City follows the normal probability distribution and the standard deviation is 6.5 minutes, it is possible to calculate the probability of having a certain commute time. For example, the probability of having a commute time between 30 and 40 minutes can be calculated using the normal distribution formula.
Overall, it is true that among the 30 largest U.S. cities, the mean one-way commute time to work is 25.8 minutes and the longest one-way travel time is in New York City, where the mean time is 37.5 minutes.
True. Among the 30 largest U.S. cities, the mean one-way commute time to work is 25.8 minutes. New York City, known for its extensive public transportation system and traffic congestion, has the longest one-way travel time with a mean time of 37.5 minutes. Since the distribution of travel times in New York City follows the normal probability distribution, we can use this information to understand the variation in commute times for its residents.
The standard deviation for this distribution is 6.5 minutes, which indicates how spread out the travel times are from the mean. A smaller standard deviation would mean that most commute times are closer to the mean, while a larger standard deviation signifies that the data is more spread out, with some individuals having much shorter or longer commutes than the average.
In conclusion, the statement is true. The mean one-way commute time for the 30 largest U.S. cities is 25.8 minutes, and New York City has the longest mean travel time at 37.5 minutes, with a normal probability distribution and a standard deviation of 6.5 minutes.
To learn more about mean, click here:
brainly.com/question/31101410
#SPJ11