The p-value is 0.01, which means that it is very rare to observe a test statistic that is equal to or more extreme than the one that was actually observed. SO the option a is correct.
In the given question, in a hypothesis test for population proportion, we calculated the p-value is 0.01 for the test statistic, we have to find which statement of the p-value is correct.
The p-value is the probability of obtaining results as extreme as, or more extreme than, the observed results of a statistical hypothesis test, assuming that the null hypothesis is true. A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.
A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.
If the null hypothesis is correct, the p-value is the likelihood that a test statistic will be equal to or more extreme than the one that was actually observed. Given that the null hypothesis is correct in this situation, the p-value of 0.01 indicates that it is extremely unusual to see a test statistic as dramatic as the one that was actually seen. This shows that the alternative hypothesis is more likely to be correct and that the null hypothesis is probably not true.
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An investor invested a total of $2,300 in two mutual funds. One fund earned a 6% profit while the other earned a 4% profit. If the investor's total profit was $102, how much was invested in each mutual fund?
The amounts in each mutual fund are $500 and $1800. By using a system of equations, the required values are evaluated.
What is a system of equations?The system of equations is a set of one or more equations that intersects at locations called solutions of the system.The system of equations is solved for solutions in three different methods. They are the Elimination method, Substitution method, and Graphing method.Calculation:It is given that, an investor invested $2300 in two mutual funds.
Consider the amount invested in two mutual funds as fund1 = x and fund2 = y.
So, we can write the equation for the total investment is
x + y = 2300 ...(1)
The percentage of profit earned from the fund1 = 6% = 0.06
The percentage of profit earned from the fund2 = 4% = 0.04
The total profit for the investor = $102
Then, the equation from this statement is
0.06x + 0.04y = 102 ...(2)
Then the system of equations is
x + y = 2300 ...(1)
0.06x + 0.04y = 102 ...(2)
Applying the substitution method to solve the obtained system of equations.
So, from (1), we can write x = 2300 - y
Then, equation (2) becomes
0.06(2300 - y) + 0.04y = 102
⇒ 6(2300 - y) + 4y = 10200
⇒ 13800 - 6y + 4y = 10200
⇒ 13800 - 2y = 10200
⇒ 2y = 13800 - 10200 = 3600
∴ y = 3600/2 = $1800
So, the value of x is x = 2300 - 1800 = $500
Thus, the amount of investment in two mutual funds is $500 and $1800.
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If there is inverse variation and y = 3 y = 3 when x = 24 x = 24 , find x x when y = 18 y = 18 . x = 1 x = 4 x = − 1 x = − 6
chapter 4 review worksheet You want to get the new Iphone. You have two options when purchasing the phone. You can pay a one-time charge of 200$ and then an additional $15 per month . The second option is not paying any money at this time and having a monthly bill of 40$ a month Set up a system of equations to represent this situation. Remeber to define a variable. Find the time in months when both of these plans would pay off the same amout of money for the new phone
The months when both of these plans would pay off the same amout of money for the new phone is 8 months.
How many months will both of these plans would pay off the same amount?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario
Let the number of months be x
You can pay a one-time charge of 200$ and then an additional $15 per month. This will be 200 + 15x. The second option is not paying any money at this time and having a monthly bill of 40$ a month. This will be 40x.
The equation will be
200 + 15x = 40x
Collect like terms
40x - 15x = 200
25x = 200
Divide
x = 200/25
x = 8
The number of months is 8.
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aspurpinion has 17 teeth and a diametral pitch of 8 teeth/in. it runs at 1120 rpm and drives a gear at 544 rpm. find the number of teeth on the gear and the distance between the centers of the pinion and gear
Theoretical centre-to-centre distance (C)=3.25 which is the distance between the centers of the pinion and gear
Given data:
No. of teeth on the pinion(TP)=17.
Diametral pitch(pd)=8 teeth/in.
The rotational speed of the pinion(NP)=1120 rev/min or 1120 rpm.
The rotational speed of the gear(NG)=544 rev/min or 544 rpm.
To calculate:
No. of teeth on gear(TG) & theoretical centre-to-centre distance(C).
We know that;
Diametral pitch(pd)=No. of teeth in the gear/Diameter of the gear
For pinion,
pd=TP/DP
Pittiong the values in above eq.
8 teeth/in =17/DP =>DP=17/8 in.
or DP=2.125 in.
Gear ratio(G)=(NP/NG)=(TG/TP)=(DG/DP)
(NP/NG)=(TG/TP)
1120/544 =TG/17 =>TG=35
therefore No. of teeth the gear(TG)=35 {Ans}
Also from gear ratio formula,
(NP/NG)=(DG/DP)
1120/544=DG/2.125
DG=4.375 in.
In figure I have drawn a rough diagram of the pinion and gear arrangement which will help you to understand how to calculate the centre-to-centre distance(C)
From fig.,
centre to centre distance,C=rP+rG {Where rP and rG are the radii of pinion and gear respectively}
C=(DP+DG)/2 {\large \because Diameter =2*radius}
C=(2.125+4.375)/2 in. =3.25 in.
therefore Theoretical centre to centre distance (C)=3.25
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the coordinates of a quadrilateral are r(-3, 2), s(-2, -1), t(-4, 0), and v(-1, 1). what classification best describes the quadrilateral? a square b rhombus c rectangle d parallelogram
Option D. parallelogram is the correct option of the given statement.
The parallelogram is a quadrilateral with two sets of opposing sides that are equally and parallel. The opposing angles are also equal in magnitude.
In mathematics, what is a quadrilateral?Four sides, four vertices, and four angles make up a quadrilateral, which is a two-dimensional shape. Concave and convex are the two most common forms. Additionally, there are numerous subgroups of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombus, and squares.
The significance of quadrilateralsThe significance of quadrilaterals Creating floor plans for new buildings, as well as engineering and designing buildings and spaces, all rely on the properties and mathematical rules regulating the geometric shape known as a quadrilateral.
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Gravitational potential energy depends on which two of the following
Gravitational potential energy depends on which two of the following weight and height.
What is Gravitational potential energy ?The energy that an object can possess or acquire when its position changes as a result of a gravitational field is known as gravitational potential energy. The energy connected to gravity or gravity is what is known as gravitational potential energy.
What exactly does GCSE Gravitational Potential Energy mean?The motion, position, and deformation of an object can all contribute to its energy storage. Gravity affects you constantly on Earth. There is a latent (stored) energy present in everyone on Earth's surface. the gravitational potential energy of this.
Answer is - The gravitational potential energy of an object depends upon its weight and height.
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The correct question is -
What two things does gravitational potential energy depend on?
Please help! More points!
Answer:
LOL
Step-by-step explanation:
Jack borrowed $600
from his dad and
paid him back $475.
How much does he
still owe his dad?
Answer:
$125
Step-by-step explanation:
600 - 475 = 125
Answer:
600-475
275
Step-by-step explanation:
The amount borrowed is subtracted from the amount paid back gives the remaining debt.
Therefore the amount to be paid back is 275
Jack's mother
gave him 50 chocolates to
party. He gave 3 chocolates to each
give to his friends at his
birthday
of his friends and still had 2 chocolates
left. Write an equation to determine the number of friends
(f) at Jack's party.
David rowed a boat upstream for three miles and then returned to point he started from. The entire journey took four hours. The speed of the stream is one mile per hour. Find David's speed in still water.
David's speed in still water 2 mile per hour , using downstream and upstream concept in river .
What is downstream and upstream in river?
Downstream : Towards the river where flow ends
In this river speed get added in rowing boat speed.
Upstream : Opposite to the flow of river
In this river speed gets subtracted from rowing boat speed.
In given que , one time boat is rowed by David in upstream and got back to original place i.e. case of downstream.
Speed of river = 1mile per hour
Let speed of David = x mile per hour.
Total time taken = 4 hour
As we know time = total distance / speed
Total distance covered by David = 3+3 = 6 miles
In upstream speed = x-1
In downstream speed = x+1
So, time = 3/(x-1 )+ 3/(x+1)
4/3 = 1/x-1 + 1/x+1
Solving this we get,
2x^2 - 3x - 2 = 0
Solution for this eq will be
x = 2, -1/2
But speed can't be negative.
So, x= 2mile per hour.
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question 2 a university surveys its student-athletes about their experience in college sports. the survey only includes student-athletes with scholarships. what type of bias is this an example of? 1 point
A university surveys its student-athletes about their experience in college sports. The survey only includes student-athletes with scholarships. This is an example of sampling bias.
In the field of statistics, sampling bias is a type of bias in which a sample is collected in such a way that some members of the intended population have a lower or higher sampling probability than others. It results in a biased sample of the population where all individuals, or instances, were not equally likely to have been selected. If this is not corrected, results can be erroneously attributed to the phenomenon under study rather than to the method of sampling. Here as the sample of the survey only includes the student athletes with scholarship, it becomes biased.
Therefore, sampling bias is the type of bias when a university surveys its student-athletes about their experience in college sports. the survey only includes student-athletes with scholarships.
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Consider the parent function f (x) below.
Answer:
see the attachment
Step-by-step explanation:
You want graphs of f(x -5) and f(x)+2 and their asymptotes, given exponential function f(x).
f(x-5)The subtraction of 5 from the argument x causes the graph to be shifted to the right 5 units. The horizontal asymptote at y=0 is unchanged.
f(x)+2The addition of 2 to every function value causes the graph to be shifted up 2 units. The horizontal asymptote is likewise shifted up 2 units to y=2.
The red and blue graphs are attached. The asymptotes are dashed lines.
there are 30 children in a class and they all have at least one cat or dog. 14 children have a cat, 19 children have a dog. what is the probability that a child chosen at random from the class has both a cat and a dog?
The probability that a child chosen at random from the class has both a cat and a dog is 1/10.
Suppose b is the total number of kids that have both:
• children having a cat Only must be 14 - b
• children having a dog Only must be 19 - b
We also get:
We also know there are 30 kids, therefore
⇒ (14 - b) + b + (19 - b) = 30
⇒ 33 - b = 30
⇒ b = 3
Consequently, we now understand:
3/30 = 1/10
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A small business earns a profit of $6500 in January and $17,500 in May. What is the rate of change in profit for this time period. Explain how you got it.
The rate of change in the profit for the five months earned by the given small business is $2750.
How to calculate the rate of change?The rate of change explains the relationship between two quantities.
Consider two quantities such profit and time in a small business.
Then, the rate of change in the profit is calculated by the ratio of change in the profit for the particular period to the time. I.e.,
rate of change in the profit = (change in the profit)/time
or
r = (p2 - p1)/(t2 - t1)
Where p1 is the profit gained at time t1 and p2 is the profit gained at time t2.
Calculation:Given that, a small business earns a profit of $6500 in January (the first month of the year) and $17,500 in May (the fifth month of the year).
So, here p1 = $6500; p2 = $17,500; t1 = 1; and t2 = 5
Then, the rate of change in the profit for this period is
r = (17,500 - 6500)/(5 - 1)
= 11000/4
= 2750
Therefore, the rate of change in the profit for the five months is $2750.
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Find the distance from point A(−9,−3) to the line y = x−6. Round your answer to the nearest tenth.
The distance is about
units.
The distance from point A(−9,−3) to the line y = x−6 is 8.5 units
What is slope ?
A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).
step 1
Find the slope of the perpendicular line to the given line
y=x-6 ---> given line
The slope is m=1
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
m1*m2 = -1
we have
m1=1
substitute
(1)*m2 = -1
so
m2 = -1
step 2
Find the equation of the perpendicular line to the given line
The equation in point slope form is
y-y1=m(x-x1)
we have
m=-1
(x1,y1)=(−9,−3)
substitute
y+3=-1(x+9)--> equation in point slope form
y+3= -x-9
y= -x-12---> equation in slope intercept form
step 3
Find the intersection point between the given line and the perpendicular line to the given line
we have the system of equations
y = x−6.
y= -x-12
Solve the system by graphing
The intersection point is (-3,-9)
see the attached figure
step 4
we know that
The distance between the point A and the point (-3,-9) is the same that the distance between point A and the line y=x-6
the formula to calculate the distance between two points is equal to
d=√[(y2-y1)² + (x2-x1)²]
substitute the values
d=√[(-9+3)² + (-3+9)²]
d= √72 units
simplify
d= 6√2 = 8.5 units
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the equation for the two lines of symmetry of a rectangle.
Answer:
180
Step-by-step explanation:
xdcjuggggggggggggggggggggg
Please hurry Describe this graph
The happening in the graph is that the speed of the roller skater increases and decreases with time
How to interpret the graphFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following axes
x-axis = Time
y-axis = Speed
The x-axis is continually increasing while the y-axis decreases and increases (as in a sine function)
This means that the speed increases and decreases with time
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An arithmetic sequence has first term 13 and common difference 6. Find the 25th term
of the sequence.
Answer:
a₂₅ = 157
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 13 and d = 6 , then
a₂₅ = 13 + (24 × 6) = 13 + 144 = 157
6ab + 2a²b + 5a²b² - 3ab - 6ab²+ a²b-2a²b²
please help.
Answer: 3a2b2+3a2b−6ab2+3ab
Step-by-step explanation:By simplifying,
6ab+2a2b+5a2b2−3ab−6ab2+a2b−2a2b2
= 3a2b2+3a2b−6ab2+3ab
Hope this help's You
a large stake was stocked with trout ten years ago. the change in the trout population each year is modeled by the function P(x)=8,500(0.88)x which statement describes 0.88 in the function
The value of 0.88 in the exponential function p(x) = 8500(0.88)ˣ is the rate of growth
Exponential FunctionAn exponential function is defined by the formula f(x) = aˣ, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.
The exponential function is an important mathematical function which is of the form
f(x) = aˣ
In the exponential function given;
p(x) = 8500(0.88)ˣ
Where;
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Please Help me on this question
Answer:
the answer is B
Step-by-step explanation:
Rewrite by separating off the final termn+1
∑ m(m+1)
m=1
The rewritten summation is [tex]\sum_{m=1}^{n}m(m+1)+(n+1)(n+2)[/tex].
A recursive function is a function that calculates subsequent terms by repeating or using its own prior terms, creating a succession of terms. By definition, the recursive function can be used to write the summation by separating the final term of the summation and adding a final term to the summation.
Given, the function is [tex]\sum_{m=1}^{n+1}m(m+1)[/tex].
First, we have to separate the final term from the given summation. The final term is m = n+1 which is present above the summation. For this replace the n+1 with n.
Then, add the term m(m+1) with m in the given summation replaced by n+1.
The new summation is rewritten as,
[tex]\begin{aligned}\sum_{m=1}^{n+1}&=\sum_{m=1}^{n}m(m+1)+(n+1)((n+1)+1)\\&=\sum_{m=1}^{n}m(m+1)+(n+1)(n+2)\end{aligned}[/tex]
The new summation is rewritten.
The complete question is -
Rewrite by separating off the final term [tex]\sum_{m=1}^{n+1}m(m+1)[/tex]
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picking 1 american man at a time, design a simulation to determine if we should be surprised if we select 20 or more men before finding a man with red-green color blindness.
On solving the provided question we can say that - as the probability the result will be either a red- or green-colorblind individual.
What is probability?A branch of mathematics known as probability measures the possibility of an event happening or a proposition being true. The probability of an occurrence is a number between 0 and 1, where roughly 0 denotes the event's improbability and 1 denotes certainty. A probability is a numerical representation of the possibility or probability that a specific event will take place. Probabilities can alternatively be stated as percentages ranging from 0% to 100%, or as percentages from 0 to 1.
In the US, there are more males than women who are colorblind to red and green = 0.07adults
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Randy starts biking at a rate of 6 miles per hour toward a store that is 20 miles away. Cali leaves the store when Randy starts biking. Cali bikes toward Randy along the same route at 2 miles per hour. How many hours will pass before they meet on the road?
PLEASE HELP
Answer:
5.5 hours
Step-by-step explanation:
6, 12, 18
20, 18, 16, 14, 12, 10, 8, 6, 4, 2
the national health and nutrition examination survey contains data on 2,263 u.s. adults. one of the variables is total cholesterol. total cholesterol levels less than 200 milligrams per deciliter (mg/dl) are considered desirable for adults. a reading between 200 and 239 mg/dl is considered borderline high and a reading of 240 mg/dl and above is considered high. does the data in this sample indicate that these individuals have average total cholesterol levels that are desirable?
Yes, the data in this sample indicate that these individuals have average total cholesterol levels that are desirable.
Average:
In math average refers mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.
Given,
Here we have the data of the national health and nutrition examination survey contains data on 2,263 US. adults. one of the variables is total cholesterol. total cholesterol levels less than 200 milligrams per deciliter (mg/dl) are considered desirable for adults. a reading between 200 and 239 mg/dl is considered borderline high and a reading of 240 mg/dl and above is considered high.
And we need to find that does the data in this sample indicate that these individuals have average total cholesterol levels that are desirable.
While we looking into the given question,
Total number pf participants = 2,263
Desirable level of cholesterol = less than 200 milligram
Border line level of cholesterol = Between 200 and 239 mg
Higher level of cholesterol = 240 mg
So, based on the given details, we know that at least 25% of people must have the desirable.
Therefore, the given level is a desirable one.
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What is the equation of a line perpendicular to y= 2z - 6 that passes through (5, 4)
Use the formula y = m x + b
Answer:
Step-by-step explanation:
balls
(a) if 2/3 of all kissing couples exhibit this right-leaning behavior, what is the probability that the number in a sample of 127 who do so differs from the expected value by at least as much as what was actually observed? (round your answer to four decimal places.)
The probability that the number in a sample of 127 who do so differs from the expected value is 0.6198.
How to calculate probability?
The critical value, according to the data, is 84. the following will be the mean:
= np = 127 × 2/3 = 84.6
The standard deviation is also 5.3748. The corresponding z score will be:
= (84 - 86.67)/5.3748
= -0.50.
Therefore, the left tailed area will be:
P(z < -0.50) = 0.3099
Since, it's two tailed, we'll multiply by 2. This will be:
= 2 × 0.3099
= 0.6198
In conclusion, the probability is 0.6198.
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Which of the is the inverse of (\f(x) = 4x+12\)? Select one: a. (\f(x) = (x/4)-3\) b. (\f(x) = 12x-4\) c. (\f(x) = (x/4)+3\) d. (\f(x) = 12x+4\)
The inverse function of f(x) = 4x + 12 is [tex]f^{-1}(x) = \frac{x}{4}-3[/tex] .
Option (A) is correct.
What is the inverse of a function?
The inverse of a function is a new function that "undoes" the original function. If f(x) is a function that takes in an input x and produces an output y, then the inverse function denoted as [tex]f^{-1}(x)[/tex], takes in an input y and produces an output x.
The inverse function of f(x) = 4x + 12 is denoted as [tex]f^{-1}(x)[/tex]. To find the inverse function, we can follow these steps:
Replace f(x) with y.
Interchange x and y.
Solve for y.
Following these steps, we get:
y = 4x + 12
x = 4y + 12
x - 12 = 4y
y = (x - 12)/4
Hence, the inverse function of f(x) = 4x + 12 is [tex]f^{-1}(x) = \frac{(x - 12)}{4}[/tex] = (x/4) - 3
Option (A) is correct.
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The ratio of cats to dogs in a room is 4:5, If there are 20 cats in the room, how many dogs are there
Answer: 25 dogs
Step-by-step explanation:
We know that every 4 cats will be with 5 dogs
So
First, take 20 divided by 4 = 5
Then take 5 times 5 = 25 dogs
Just one please help
[tex]\displaystyle\\\\ Answer: A=\frac{2P}{xV^3}[/tex]
Step-by-step explanation:
[tex]\displaystyle\\P=\frac{1}{2} xAV^3\\[/tex]
Multiply both parts of the equation by 2:
[tex]2P=xAV^3[/tex]
Divide both parts of the equation by xV³:
[tex]\displaystyle\\\frac{2P}{xV^3} =A[/tex]
[tex]\displaystyle\\\\Thus,\ A=\frac{2P}{xV^3}[/tex]
