A 90-inch pipe is cut into two pieces. One piece is five times the length of the other. Find the length of the shorter piece.
Answer:
5x+x=90
Step-by-step explanation:
5 times the other = 5x
the other piece is x
Answer: the small pipe is 15 inches long
Step-by-step explanation: since the larger pipe is 5 times larger than the small pipe, the 90 inch pipe would have too be divided by 6 to make sure the 5 times of the large pipe and the 1 small pipe. so, you would do 90/6=15. so the small pipe is 15 inches long. the large pipe is 75 inches long.
The sum of two forces, one having a magnitude of 9 N acting due east and other having a magnitude of 4 N acting due north is _ _ _ _ _.
The sum of two forces, one having a magnitude of 9 N acting due east and other having a magnitude of 4 N acting due north is 9.85 N.
One of the forces is of magnitude 9 N acting due east
The second force is of magnitude 4 N acting due north
Therefore, the sum of the two forces (say F1 and F2) will be the resultant of the two forces,
that is: sqrt ( (F1) ^ 2 + (F2) ^ 2)
= sqrt ( (9) ^ 2 + (4) ^ 2) = sqrt (97) = 9.8488 N ≈ 9.85 N
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What is the equation of this line?
y=4 x+6
y=6 x+4
y=12 x+2
v=4 x-6
Answer:
y = 4x - 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, - 2) and (x₂, y₂ ) = (2, 2) ← 2 points on the line
m = [tex]\frac{2-(-2)}{2-1}[/tex] = [tex]\frac{2+2}{1}[/tex] = [tex]\frac{4}{1}[/tex] = 4
the line crosses the y- axis at (0, - 6 ) ⇒ c = - 6
y = 4x - 6 ← equation of line
A random sample of 115 observations results in 46 successes. Use Table 1.
a. Construct a 90% confidence interval for the population proportion of successes. (Round intermediate calculations to 4 decimal places, "z" value to 2 decimal places, and final answers to 3 decimal places.)
Confidence interval to
b. Construct a 90% confidence interval for the population proportion of failures. (Round intermediate calculations to 4 decimal places, "z" value to 2 decimal places, and final answers to 3 decimal places.)
Confidence interval to
Option a) 90% confidence interval for the population proportion of successes = 0.402
Option b) 90% confidence interval for the population proportion of failures = 0.598
According to the question given,
Critical values of Standard deviations are to be used to construct the proportions for the confidence interval.
The formula of a confidence interval that we will be using for the solution will be,
p = [tex]z_{a} * \sqrt{\frac{p(1-p)}{n} }[/tex]
In the above expression,
p = observed population.
n = sample size
[tex]z_{a}[/tex] = critical value of confidence interval
Now the given observations in question = 115
That result in success = 46
The resultant sample proportion = [tex]\frac{46}{115}[/tex]
⇒ 0.40 and it is for both success and failure
Here we can see that the answer for both parts will be identical.
The critical value of z at 90% confidence = 1.64
a) Lower bound = [tex]0.4 - 1.64 * \sqrt{\frac{0.4(1-0.4)}{90} }[/tex]
⇒ 0.402
b) Upper bound = [tex]0.4 + 1.64 * \sqrt{\frac{0.4(1-0.4)}{90} }[/tex]
⇒ 0.598
Confidence interval = 0.402 to 0.598
Therefore,
Option a) 90% confidence interval for the population proportion of successes = 0.402
Option b) 90% confidence interval for the population proportion of failures = 0.598
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First try was incorrect
Evaluate the following expression when x=2 (round to the nearest tenth, if necessary)
{x}/{19}
The value of the following expression x/19 when x=2 is 0.11.
What is meant by an expression?An expression or mathematical expression is a finite arrangement of symbols that are well-formed in line with context-dependent criteria. To help define the logical grammar and order of operations, mathematical symbols can be used to represent variables, operations, functions, brackets, punctuation, and grouping. A sentence qualifies as a mathematical expression if it comprises one or more mathematical operations, at least two numbers, or variables. Mathematicians are proficient in addition, subtraction, multiplication, and division. An expression has the following components: an expression, a number or variable, and a mathematical operator.
Given expression is x/19
When x=2,
Then the value of the given expression is:
x/19=2/19
=0.105
≈0.11
Therefore, The value of the following expression x/19 when x=2 is 0.11.
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(16,-4); 7x-4y=-5
Find the equation of the line that contains the given point and is parallel to the given line. Write the equation in slope-intercept form, if possible
The equation of the line parallel to the line 7x - 4y = - 5 and passing through (16, - 4) is y = (7/4)x - 32.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
We know lines parallel to each other have the same slope which is
7x - 4y = - 5 ⇒ - 4y = - 7x - 5 ⇒ y = (7/4)x + (5/4) to our required line will also have the same slope passing through the point (16, - 4).
Therefore, - 4 = 16(7/4) + b.
- 4 = 28 + b.
b = - 32.
Therefore, y = (7/4)x - 32 is the required line.
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Awnser if this is a function or not yes or no please.
Answer: NO
Step-by-step explanation:
This is not a function, since there are multiple outputs for ONE input.
Answer:
no
Step-by-step explanation:
to be a function, the x's can only have one partner. Here, 7 has two partners (7 goes to 20 and also to 18) and the 11 has two partners also. This relation is not a function.
gravel is being dumped from a conveyor belt at a rate of 40 cubic feet per minute. it forms a pile in the shape of a right circular cone whose base diameter and height are always equal. how fast is the height of the pile increasing when the pile is 16 feet high? recall that the volume of a right circular cone with height h and radius of the base r is given by v=(1/3)xpix(r^2)xh
The height of the pile increasing when the pile is 16 feet high is 5/32 ft/min.
We are given dV/dt=10 cubic ft/min and we want to find dh/dt. Therefore, first we need to write a formula relating v and h.
V=pi*r^2*h/3 since d=h at any moment, we know that r=h/2 at any moment and if we substitute h/2 for r, we get
V=pi(h/2)^2*h/3 and if we simplify this, we get
V=pi*(h^3)/12
Now we need to take the derivative of both sides with respect to t
dV/dt = pi * ( 3 * h^2 ) */12 * dh/dt
= pi * h^2 / 4 * dh/dt, substitute 40 for dV/dt and 16 for h and solve for dh/dt and we get
40 = pi * 16^2/4*dh/dt
dh/dt = 40 * 4 / ( 256 * pi )
= 40/(256*pi) ft/min,
= 10/64
= 5/32 ft/min
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C d Question 13 (1 point) Spheres A and B are similar. The volume of Sphere A x 27 = the volume of Sphere B How many times greater is the radius of sphere A? b The surface area and the base Od 16 3 4 27
I will give brainliest to anyone who answers.
The radius of the sphere B is 3 times greater than the radius of the sphere A or radius of the sphere A is 1/3 times greater than the radius of the sphere B.
What is Sphere?A sphere is a three dimensional shape formed by the set of all points which are at equidistance from a point called the center of the sphere.
Volume of a sphere = [tex]\frac{4}{3}[/tex] π r³
Let the volume and radius of sphere A is V₁ and r₁ respectively and the volume and radius of sphere B be V₂ and r₂ respectively.
We have,
V₁ × 27 = V₂
[tex]\frac{4}{3}[/tex] π r₁³ × 27 = [tex]\frac{4}{3}[/tex] π r₂³
Common terms [tex]\frac{4}{3}[/tex] π get cancelled.
⇒ 27r₁³ = r₂³
⇒ r₁³ / r₂³ = 1 / 27
Taking cube root on both sides,
⇒ r₁ / r₂ = 1 / 3
⇒ 3r₁ = r₂
⇒ r₁ = [tex]\frac{1}{3}[/tex] r₂
Hence the radius of the sphere A is 1/3 times greater than the radius of the sphere B.
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52% of 70
what is the answer
Answer: 36.4
Step-by-step explanation:
Just convert the percentage to decimal and multiply.
70 x 0.52 = 36.4
Review the graph of f(x).
On a coordinate plane, a curve goes through (negative 4, 1), (0, 0) and then curves up and approaches x = 2 in quadrant 1. Another curves approaches x = 2 in quadrant 4.
Which function g(x) has the same end behavior as f(x)?
g (x) = StartFraction 3 Over x EndFraction
g (x) = StartFraction x Over 3 EndFraction
g (x) = negative StartFraction 3 Over x EndFraction
g (x) = negative StartFraction x Over 3 EndFraction
The function g(x) that has the same end behavior as function f(x) is given as follows:
g(x) = -x/3.
How to obtain the end behavior of a function?The end behavior of a function is given by the limits of the function as x goes to infinity.
On the graph, these limits are found looking at the behavior at the left tail and at the right tail of the graph, as follows:
Left tail: x -> ∞.Right tail: x -> -∞.Then the function with the same end behavior as f(x) graphed is given as follows:
g(x) = -x/3.
At the left tail, we have that:
g(-∞) = -(-∞)/3 = ∞/3 = ∞.
At the right tail, we have that:
g(∞) = -(∞)/3 = -∞/3 = -∞.
Hence the fourth function is the correct option among those given.
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Suppose that in an election voter preference is sharply divided along gender lines. 60% of women will vote for Candidate J, the rest will vote for Candidate K; 30% of men will vote for Candidate J, the rest for Candidate K. Which of the following represents the lowest percentage of voters that must be women on election day, in order that Candidate J wins the election?
* 65%
* 67%
* 69%
* 71%
* 73%
By using proportions, it is discovered that 67% of voters who are female and vote for Candidate J to win.
What exactly is a ratio ?A percentage is a component of a total amount, and the three-step rule is used to relate the measurements.
The percentage of voters who select Candidate J is:
60% of x are voters are female
30% of (1 - x), who vote are male
If the total of these percentages is larger than 50% = 0.5, Candidate J will be elected; therefore:
0.6x + 0.3(1 - x) > 0.5
0.6x + 0.3 - 0.3x > 0.5
0.3x > 0.2
x > 2/3
x > 0.667
x > 67%
By using proportions, it is discovered that 67% of voters who are female and vote for Candidate J to win.
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In a hardware store you must first go to server 1 to get your goods and then go to a server 2 to pay for them. Suppose that the times for the two activities are exponentially distributed with means six and three minutes. Compute the average amount of time it takes Bob to get his goods and pay if when he comes in there is one customer named Al with server 1 and no one at server 2.
The average amount of time it takes Bob to get his goods and pay if when he comes in there is one customer named Al with server 1 and no one at server 2 will be 16 minutes.
Let us assume that, T = the total amount of time Bob spends in the hardware store.
Let us assume that, T1 = the amount of time Bob spends waiting in line for Al to get his goods from server 1
Let us assume that, T2 = the amount of time it takes for Bob to get his goods from server 1
Let us assume that, T3 = the amount of time Bob spends waiting in line for Al to pay server 2 for his goods
Let us assume that, T4 = the amount of time it takes for Bob to pay server 2 for his goods
So, the value of total time T will be
T = T1 + T2 + T3 + T4 and E[T] = E[T1] + E[T2] + E[T3] + E[T4]
Now, E[T1] = 6 min. because of the memoryless property of the exponential distribution
E[T2] = 6 min.
To find E[T3], the condition on the availability of server 2 after Bob is done with server 1
So, the value of E[T3] will be
E[T3] = E[T3 | Server 2 is free] P(Server 2 is free) + E[T3 | Server 2 is not free] P(Server 2 is not free)
= 0 + 3 . P(Bob is done with server 1 before AI is done with server 2)
[tex]$$=3 \cdot \frac{1 / 6}{1 / 6+1 / 3}$$[/tex]= 3(1/3) = 1 min. and E[T4] = 3 min.
So, E[T] = E[T1] + E[T2] + E[T3] + E[T4]
or, E[T] = 6+6+1+3= 16 minutes
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a high school statistics class wants to estimate the average number of chocolate chips in a generic brand of chocolate chip cookies. they collect a random sample of cookies, count the chips in each cookie, and calculate a 95% confidence interval for the average number of chips per cookie (18.6 to 21.3). items 28, 29, 30 and 31 present four different interpretations of these results. indicate if each interpretation is valid or invalid. We are 95% certain that each cookie of this brand has approximately 18.6 to 21.3 chocolate chips. We expect 95% of the cookies to have between 18.6 and 21.3 chocolate chips. We would expect about 95% of all possible sample means from this population to be between 18.6 and 21.3 chocolate chips. We are 95% certain that the confidence interval of 18.6 to 21.3 includes the true average number of chocolate chips per cookie.
1. This is not wrong at all, but there is a problem. In this case, the target parameter is not mentioned. Average in this case is not the most valid conclusion.
2. Not FALSE as in option #1, but the same problem occurs if the statement does not express a conclusion about the parameter of interest (mean) in this case.
3. This is not the case at all, as the statement refers to possible samples and not confidence levels or parameters of interest. So it's not the best option in this case.
4. true average number of chocolate chips per cookie.
This is the best interpretation, because confidence levels are used to construct the intervals. The most complete answer in this case, as the result is related to the parameter of interest.
Confidence Interval:
A confidence interval is "a range of values that is likely to encompass the values of a population with some degree of confidence. Often expressed as a percentage. The error bar is the range of values above and below the sample statistic in the confidence interval
Normal Distribution:
"A probability distribution that is symmetric about the mean and indicates that data close to the mean are more common than data far from the mean."
X : represents sample mean
μ: population mean (variable of interest)
s : represents sample standard deviation
n : represents sample size
2) The mean confidence interval is given by the formula:
X ± [tex]t_{\alpha /2} \frac{s}{\sqrt{n} }[/tex] --------------------------- (1)
The 95% confidence interval obtained in this case is (18.6; 21.3)
Based on this, the statements can be analyzed individually as :
1: We are 95 years old We believe that each cookie from this brand contains approximately 18.6 to 21.3 chocolate chips.
This is not wrong at all, but there is a problem. In this case, the target parameter is not mentioned. Average in this case is not the most valid conclusion.
2: His 95% of cookies are expected to contain 18.6 to 21.3 chocolate his chips.
Not FALSE as in option #1, but the same problem occurs if the statement does not express a conclusion about the parameters of interest in this case.
3: About 95% of all possible sample means from this population are expected to be between 18.6 and 21.3 chocolate chips. This is not the case at all, as you are not referring to some parameter. So it's not the best option in this case.
4: 95% confident that the confidence interval of 18.6 to 21.3 contains the true average number of chocolate chips per cookie.
This is the best interpretation because of the confidence level used to construct the interval. The most complete answer in this case, as the result is related to the parameter of interest.
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Dae and Eric are working together on a paper. Dae typed 333 words in 9 minutes, and Eric typed 252 words in 6 minutes. How many more words per minute did Eric type?
Eric typed 15 words more than Dae per minute.
What is a Linear Equation?Linear equations are equations whose highest power of the variables is 1. The graph of a linear equation is a straight line. A nonlinear equation is an equation whose highest power of the variables is not 1 and the graph is not a straight line.
To find the amount of words typed in 1 minute for both;
Dae = 333/9
Dae = 27 words per minute
Eric = 252/6
Eric = 42 words per minute
Therefore 42 - 27 = 15 words per minute
Eric typed 15 more words per minute.
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help!!
find the measures of each angle
The measures of angles x, y and z are 40°, 50° and 130° and measures of the segments are AY = 16, IY = 9, FG = 30, AP = 24
What is centroid?Centroid is the point in a triangle where all the medians of the triangle intersects.
Given are two triangles, in first we have to find the missing angles and in the second one we need to find the asked segments,
1) We know that, in a right triangle, one angle is 90° and the sum of other two sides is 90°,
Therefore, 40°+y = 90°
y = 50°
x+y = 90°
x = 90°-50°
x = 40°
z = 180°-50° (linear pair)
z = 130°
2) we know that, the centroid divides the medians into 2:1
AY = 2YP
AY = 16
IY = TY/2
IY = 9
FG = GY+YF (segment addition postulate)
GY = YF/2
GY = 10
FG = 10+20 = 30
PA = AY+YP (segment addition postulate)
PA = 8+16
PA = 24
Hence. the measures are x, y and z are 40°, 50° and 130° and AY = 16, IY = 9, FG = 30, AP = 24
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identify the independent variable in the following hypothesis: interstate migration in the united states lowers state poverty levels.
The independent variable in the following hypothesis: interstate migration in the united states lowers state poverty levels is IV ( Interstate migration ) and DV ( State poverty level ) .
Given :
identify the independent variable in the following hypothesis: interstate migration in the united states lowers state poverty levels.
Independent variable :
An independent variable is exactly what it sounds like. It is a variable that stands alone and isn't changed by the other variables you are trying to measure.
Here in the given statement the independent variable is :
IV = Interstate migration
DV = State poverty level
Unit of Analysis = U.S. states
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A student completes ⅘ of a math project in ⅔ hour. If the student continues at the same rate, how long will it take the student to complete the project?
The number of hours it will take the student to complete the project is 5 / 6 hours.
How to find the time the project will be completed?A student completes ⅘ of a math project in ⅔ hour. If the student continues at the same rate, the time it will take the student to complete the project can be calculated as follows:
Therefore,
let
x = time it will take the student to complete the project
Hence
if 4 / 5 x = 2 / 3 hours
x = ? hours
cross multiply
Therefore,
number of hours to complete the whole math project = x × 2 / 3 ÷ 4 / 5 x
number of hours to complete the whole math project = 2 / 3 x × 5 / 4x
number of hours to complete the whole math project = 10x / 12x
number of hours to complete the whole math project = 10 / 12
number of hours to complete the whole math project = 5 / 6 hours
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Suppose that the daily number of miles driven per school bus driver in the United States is normally distributed with a mean of 300 mi and standard deviation equal to 26 mi. A local school bus budget committee believes the daily number of miles driven per bus driver in their community is different from 300 mi, but they are not sure if it is greater than or less than the national average.
To test their hypothesis, the committee chooses a random sample of 40 school bus drivers and records how many miles each of them drives per day during a typical week. On average, the bus drivers from the sample drive 309 mi per day. To test the hypothesis that the average number of miles driven by local bus drivers is different from the national average, the budget committee calculates the z-statistic to be 2.19 standard deviations above the population mean.
Use the standard normal z-distribution table to calculate the P-value that represents the probability of mistakenly rejecting the claim that the daily number of miles driven by local bus drivers is not statistically different from the national average. Give your answer as a decimal rounded to four places.
P-value:
The p-value for the z-distribution table is 0.4854.
What is z-distribution?
A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution, or z-distribution. By transforming the values of any normal distribution into z scores, it is possible to standardise it. Z scores provide the number of standard deviations from the mean that each value falls within.
Given that the z statistic to be 2.19 standard deviation above the population mean.
2.19 can be written as 2.1 + 0.09
Z₂.₁₉ = Z₂.₁₊₀.₀₉ = 0.4854
Therefore p-value is 0.4854.
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Ac is a radius diameter or chord? please help! I dont have that much time.
The line AC in the figure is the diameter of the circle also it is a chord.
What is a chord of a circle?The chord of a circle is a straight path that connects two locations on the circle's circumference. The chord is one of the line segments whose ends are on the perimeter of a circle that can be drawn.
As per the information obtained from the figure,
The line AC in the given diagram is the diameter of the circle, but it is also a chord of the circle because another definition of diameter is as a chord that runs across the center of the circle.
Note the point that every diameter can be said as a chord, but every chord cannot be the diameter of the circle.
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3. Which of the following is the solution to lx + 12| = 3x.
A. x = 3
C. x = 6
b. x = -6
d. x = - 3
please answer this is a final
[tex]a_n = 11n + 91[/tex] is the nth term arithmetic progression for the following term.
What is arithmetic progression?The difference between any two successive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence.
For instance, the sequence 1, 2, 3, 4, 5, 6,... The standard progression in mathematics is a, (a + d), (a + 2d), and (a + 3d).
Given that,
the first five terms given in the table with position.
Denoted as: a₁ = 102, a₂ = 113, a₃ = 124, a₄ = 135, and a₅ = 146
Thus, the nth term for the arithmetic sequence is given as:
[tex]a_n = a_1 + (n-1)d[/tex]
here, d = (113-102) = 11
[tex]a_1 = 102[/tex]
d is the common difference
So, [tex]a_n = 102 + (n-1)11[/tex]
or, [tex]a_n = 102 +11n-11[/tex]
or, [tex]a_n = 11n + 91[/tex]
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Enter the ordered pair for the vertices for Rx-axis(QRST).
The ordered pair after Rx-axis will be equal to Q' (1, -3), R' (3, 3), S' (0, 2), T' (-2, -1).
What is a graph?In math, graph science is the theory of geometric structures called graphs that are used to represent pairwise different objects. Vertices—also known as nodes or points—that are joined by edges make form a network in this sense.
Undirected graphs, where edges connect two vertices equally, and focused therapy, where edges connect two vertices unevenly, are distinguished.
The initial coordinates of given quadrilateral are,
Q = (1, 3)
R = (3, -3).
S = (0, -2).
T = (-2, 1)
The deflection rule along the x-axis is,
(x, y) ⇒ (x, -y)
Now, the coordinates are,
Q' = (1, -3)
R' = (3, 3)
S' = (0, 2)
T' = (-2, -1)
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Data is collected from the US Geologic Survey about the flow rate of the Poudre river. After some study, and unit conversions, a scientist makes a first model of the historical flow rate data as F(t) = 1.5 + 1.2 cos(2 t) in billions of cubic feet per year, while t is measured in fractions of a year since May 1, 2000. Use the Fundamental Theorem of Calculus to find the net amount of water from t = 0) to t = using this flow rate F"(t).First, F(t) = +C The model predicts the net amount of water discharged from the Poudre is F112 -Filo 0.75 What does the model predict the net discharge will be from t = 0 to t = 12 Net discharge = 1.5 Billions of ft 3
The model predicts that the net discharge will be -0.8 + 1.2 cos(24) billions of cubic feet from t = 0 to t = 12.
The net amount of water discharged from the Poudre river from t = 0 to t = 12 can be found using the Fundamental Theorem of Calculus, which states that the net change in a function over an interval is equal to the function evaluated at the endpoints of the interval minus the function evaluated at the beginning of the interval.
In this case, the net discharge from t = 0 to t = 12 can be calculated as follows:
Net discharge = F(12) - F(0)
= (1.5 + 1.2 cos(212)) - (1.5 + 1.2 cos(20))
= 1.5 + 1.2 cos(24) - 1.5 - 1.2
= -0.8 + 1.2 cos(24)
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Select the correct symbol.
9.48 ? 9.480
The 2 3/4 is greater than 1 5/6, hence 1 1/4 × 2 1/5 > 5/6 × 2 1/5
What is meant by Inequality expressions?An algebraic inequality is a mathematical statement that uses the inequality sign to connect an expression to a value, a variable, or another expression.
Relationships between two expressions that aren't equal to one another are known as inequalities. Inequalities are represented by the symbols, >,,, and. has the connotation "7 is greater than" (or "is less than 7," when read left to right).
Given the incomplete expression
1 1/4 × 2 1/5 _ 5/6 × 2 1/5
We are to fill it with the necessary inequality sign
For the expression:
1 1/4 × 2 1/5 = 5/4 * 11/5
1 1/4 × 2 1/5 = 55/20
1 1/4 × 2 1/5 = 2 3/4
For the expression 5/6 × 2 1/5
5/6 × 2 1/5 = 5/6 * 11/5
5/6 × 2 1/5 = 55/30
5/6 × 2 1/5 = 1 25/30
Since 2 3/4 is greater than 1 5/6, hence 1 1/4 × 2 1/5 > 5/6 × 2 1/5
The complete question is : Select the correct symbol to compare the expressions below.
1 1/4 × 2 1/5 _ 5/6 × 2 1/5
Symbols: <, >, =
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Andreas has $18. Bonnie has 1 2/3 times as much as Andreas. Cheryl has 1 3/5 times as much as Bonnie.
How much money do
they have altogether?
When you are testing hypotheses by using proportions, what are the necessary requirements? OA. np 25 and nq 25 ?B.np < 5 and nq < 5 C. The population standard deviation is unknown. D. p
The following conditions must be met in order to test hypotheses using proportions: np ≥ 5 and nq ≥ 5
To test hypotheses using proportions, the following requirements are necessary:
np ≥ 5 and nq ≥ 5: It is necessary to have a sufficient number of samples in each group being compared.
The rule of thumb is to have at least 5 observations in each group, where n is the sample size and p is the proportion in that group.
This ensures that the sampling distribution of the proportion is approximately normal, which is necessary for hypothesis testing.
Hence, the correct answer would be an option (A).
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Forest Fires and Acres Burned Numbers (in thousands) of forest fires over the year and the number (in hundred thousands) of acres burned for 7 recent years are shown. Number of fires x 69 58 47 84 62 57 72 Number of acres burned y 64 53 42 79 57 52 67 The correlation coefficient for the data is r=1 and α=0.05. Should regression analysis be done? The regression analysis should not be done. The regression analysis should be done. Find the equation of the regression line. y′=a+bx a= Find y' when x=50
The equation of the regression line is y = 4 + x and the regression analysis of the given data need not be done.
Straight line equation is y = a + bx.
The normal equations are
∑y = a·n + b ∑x ∑ xy = a ∑x + b∑x² Hence the regression analysis of the data :
The values are calculated using the following table
x y x² x⋅y
58 62 3364 3596
47 51 2209 2397
84 88 7056 7392
62 66 3844 4092
57 61 3249 3477
72 76 5184 5472
69 73 4761 5037
hence :
∑x = 449
∑y = 477
∑x² = 29667
∑x⋅y = 31463
Substituting these values in the normal equations
7a+449b=477
449a+29667b=31463
Solving these two equations using Elimination method,
7a+449b=477
and 449a+29667b=31463
7a+449b=477→(1)
449a+29667b=31463→(2)
equation(1)×449
⇒3143a+201601b=214173
equation(2)×7
⇒3143a+207669b=220241
Substracting
⇒-6068b = -6068
⇒6068b = 6068
⇒b = 1
Putting b = 1 in equation (1), we have
7a+449(1) = 477
⇒7a = 477 - 449
⇒7a = 28 or a = 4.
Now Estimate y for x=50
y = a + bx , we get
y = 4 + 1×50
y = 4 + 50
y = 54
At x equals 50 we get the value of y as 54 .
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Which points have a distance of 6 units between them?
Select all that apply.
A-(-12,2) and B-(-6,2)
B-(-6,2) and C-(-6-4)
C-(-6-4) and D-(6,2)
D-(6.2) and E=(6,4)
E-(64) and F=(-12.4) please help me with this
The points that have a distance of 6 units between them are A(-12, 2) and B(-6, 2); B(-6, 2) and C(-6, -4).
Distance between two points:The distance between two points P(x₁, y₁) and Q(x₂, y₂) is given by
Distance PQ = [tex]\sqrt{(x_{2} -x_{1})^{2} +(y_{2} - y_{1})^{2} }[/tex]Here we have
A (-12, 2) and B(-6, 2)
B (-6, 2) and C(-6, -4)
C (-6, -4) and D(6, 2)
D (6, 2) and E(6, 4)
E (6, 4) and F(-12, 4)
Here we will find the distance between given points to find the point which has 6 units between them.
As we know Distance = [tex]\sqrt{(x_{2} -x_{1})^{2} +(y_{2} - y_{1})^{2} }[/tex]
For Option A
A (-12, 2) and B(-6, 2)
Distance = √(-6 + 12)² + (2 - 2)²
= √[(6)² + (0)²] = √36 = 6
For Option B
For B (-6, 2) and C(-6, -4)
Distance = √(-6 - (-6))² + ( - 4 - 2)²
= √[(0)² + (-6)²] = √36 = 6
For Option C
For C (-6, -4) and D(6, 2)
Distance =√(6 - (-6))² + (2 - (-4))²
= √(12)² + (6)² = √180 = 6√5
For Option D
For D (6, 2) and E(6, 4)
Distance = √(4 - 2)² + ( 6 - 6)²
= √[(2)² + (0)²] = √4 = 2
For Option E
For E (6, 4) and F(-12, 4)
Distance = √(-12 - 6)² + (4 - 4)²
= √[(18)² + (0)²] = √18² = 18
Therefore,
The points that have a distance of 6 units between them are A(-12, 2) and B(-6, 2); B(-6, 2) and C(-6, -4).
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60 POINTS!!! As a special promotion for its 12-ounce cans of cold coffee, a coffee drink company printed a message on the bottom of each can. Some of the bottoms read, "Better luck next time!" whereas others read, "You won!" The company advertised the promotion with the slogan "One in five wins a prize!" Suppose the company is telling the truth and that every 12-ounce can of coffee has a one-in-five chance of being a winner. Six friends each buy one 12-ounce can of coffee at a local convenience store. Let X equal the number of friends who win a prize.
Part A: Explain why X is a binomial random variable.
Part B: Find the mean and standard deviation of X. Interpret each value in context.
Part C: The store clerk is surprised when two of the friends win a prize. Is this group of friends just lucky, or is the company's one-in-five claim inaccurate? Compute P(X ≥ 2) and use the result to justify your answer.
A) Yes, X is a binomial random variable because all of the requirements for a binomial distribution have been established
B) The mean and standard deviation are respectively; 1.2 and 0.6
C) The probability given as P(X ≥ 2) is 0.34464
How to solve binomial probability distribution?The binomial probability is defined as the probability of exactly x successes on n repeated trials, with p probability.
The general formula of binomial probability distribution is;
P(X = x) = nCr * p^(x) * (1 - p)^(n - x)
where;
p = probability of "success"
n = number of trials, or the sample size
x = the number of "successes" in the probability we are trying to calculate.
A) We are told that 6 friends each buy one 12-ounce bottle of the soda at a local convenience store. Let X = the number who win a prize.
Probability of success; p = 1/5
Number of events; n = 6 which is the random variable being binomial random variable:
There are two types of accomplishments: successes and failures.
Candies are unrelated to one another.
There is a set number of buddies available.
In addition, the chance of success is fixed.
Because all of the requirements for a binomial distribution have been established, then it is a binomial probability distribution.
B) The formula for the mean here is;
μ = np
Plugging in the relevant values gives;
μ = 6(1/5) = 1.2
Formula for the standard deviation is;
σ = √(np(1 - p))
Thus;
σ = √(6 * 1/5)(1 - (1/5)))
σ = 0.6
C) The probability P(X ≥ 2) calculated with online binomial probability calculator gives;
P(X ≥ 2) = 0.34464
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