A woman decides to have children until she has her first girl or until she has four children, whichever comes first. Let X = number of children she has. For simplicity, assume that the probability of a girl is .5 for each birth.a. Write the simple events in the sample space. Use B for boy and G for girl. For instance, one simple event is BG, because the woman would stop having children once she has a girl.b. Find the probability for each of the simple events in the sample space.c. Find the probability distribution function for X.d. Draw a picture of the probability distribution function for X.
Answers
For the experiment of birth of children,
a) Sample space is S = { G, BG, BBG, BBBG, BBBB}.
b) The probability for each of the simple events in the sample space, 0.5, 0.25, 0.125, 0.0625 and 0.0625.
c) The probability distribution function for X is 0.5, 0.25, 0.125, 0.0625 and 0.0625.
d) The table form of probability density function is present in above figure.
We have a woman who decides to have children until she has first a baby girl or until she has four children, which event occurred.
a) Sample space is S = { G, BG, BBG, BBBG, BBBB} where G and B represents the birth of baby boy and baby girl.
b) Since, birth become independent so P( B) = P( G) = 0.5. Using multiplcation rule, the probability for each of the simple events, P( G) = 0.5
P( BG) = P( B) P(G) = 0.25
P( BBG) = P(B)× P(B)× P(G) = 0.125
P( BBBG) = P(B)× P(B)× P(B) ×P(G)
= 0.0625
P( BBBB) = P(B)× P(B)× P(B) ×P(B)= 0.0625
c) Let X be a variable such that it denotes number of children. So, X can take value from set { 1,2,3,4}.
The probability of a girl child is for each birth = 0.5
Therefore, P( X = 1) = { only 1 girl} = P( G)
= 0.5
P(X = 2) = { one boy and one girl } = P( BG) = P(B) P(G) = 0.25
P( X = 3) = { two boys one girl } = P( BBG) = 0.125
P( X = 4) = { three boys one girl or four all boys } = P( BBBG) + P( BBBB) = 0.0625 + 0.0625
= 0.125
So, the above values of probability distribution function for random variable X.
d) A table form picture of the probability distribution function for X is present in above figure. Hence, the required table is known.
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a) option 4-t test for one mean.
b) Null hypothesis: μ_Shadyside - μ_Oakland <= 0 (Mean monthly rent of apartments in Shadyside is not higher than in Oakland).
Alternative hypothesis: μ_Shadyside - μ_Oakland > 0 (Mean monthly rent of apartments in Shadyside is higher than in Oakland).
a) The most appropriate statistical test for this scenario would be (vi) test for two independent means, also known as two-sample t-test. This test is used to compare the means of two independent samples to determine if they are significantly different from each other. In this case, we are comparing the mean monthly rent of apartments in Shadyside and Oakland, and we have two independent samples.
b) The appropriate hypotheses for the two-sample t-test are as follows:
Null hypothesis: The mean monthly rent of apartments in Shadyside is equal to the mean monthly rent of apartments in Oakland.
Alternative hypothesis: The mean monthly rent of apartments in Shadyside is greater than the mean monthly rent of apartments in Oakland.
Symbolically, the null hypothesis can be represented as H0: µ1 = µ2, where µ1 and µ2 represent the population means of monthly rent in Shadyside and Oakland, respectively.
The alternative hypothesis can be represented as Ha: µ1 > µ2, indicating that the population mean of monthly rent in Shadyside is greater than the population mean of monthly rent in Oakland
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Related Questions
what is the amount of work done, in foot-pounds, to lift a crate weighing 30 pounds a total of 3 feet?
Answers
The amount of work done, in foot-pounds, to lift a crate weighing 30 pounds a total of 3 feet is 90 foot-pounds.
To calculate the amount of work done, in foot-pounds, to lift a crate weighing 30 pounds a total of 3 feet, we need to use the formula:
Work = Force x Distance
In this case, the force is the weight of the crate, which is 30 pounds. The distance is the height the crate is lifted, which is 3 feet.
So, Work = 30 pounds x 3 feet
We can simplify this by converting pounds to foot-pounds, which is the unit used to measure work. To convert pounds to foot-pounds, we need to multiply the weight by the distance. So:
Work = 30 pounds x 3 feet = 90 foot-pounds
Therefore, the amount of work done, in foot-pounds, to lift a crate weighing 30 pounds a total of 3 feet is 90 foot-pounds.
To calculate the amount of work done, in foot-pounds, for lifting a crate weighing 30 pounds a total of 3 feet, you can follow these steps:
Step 1: Identify the weight of the crate (30 pounds) and the distance it is lifted (3 feet).
Step 2: Multiply the weight of the crate by the distance lifted.
Work (in foot-pounds) = Weight (in pounds) × Distance (in feet)
In this case:
Work = 30 pounds × 3 feet
Work = 90 foot-pounds
So, the amount of work done is 90 foot-pounds.
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The work done to lift a crate weighing 30 pounds a total of 3 feet is:
Work = 30 pounds x 3 feet x cos(0 degrees) = 90 foot-pounds
So the amount of work done to lift the crate is 90 foot-pounds.
The amount of work done, in foot-pounds, to lift a crate weighing 30 pounds a total of 3 feet is given by the formula:
Work = Force x Distance x cos(theta)
where Force is the weight of the crate, Distance is the vertical distance lifted, and theta is the angle between the direction of the force and the direction of motion (which is 0 degrees in this case since the force is acting vertically upwards).
Therefore, the work done to lift a crate weighing 30 pounds a total of 3 feet is:
Work = 30 pounds x 3 feet x cos(0 degrees) = 90 foot-pounds
So the amount of work done to lift the crate is 90 foot-pounds.
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1. a small electronics store has begun to advertise in the local newspaper. before advertising, the long-term average weekly sales were $9,820. a random sample of 50 weeks while the newspaper ads were running gave a sample mean weekly sales of
Answers
The null hypothesis is that the population mean weekly sales are $9820. The alternate hypothesis is that they are greater than $9820. The calculated t-value is 7.45, which is greater than the critical value of 1.677. Therefore, we reject the null hypothesis and conclude that the population mean weekly sales are higher than $9820.
To test whether the population mean weekly sales have increased after advertising, we can use a one-sample t-test.
The null hypothesis is that the population mean weekly sales have not increased, which means the population mean is still $9820:
H0: μ = $9820
The alternative hypothesis is that the population mean weekly sales have increased, which means the population mean is greater than $9820:
Ha: μ > $9820
The significance level is 0.05, so we need to calculate the critical value of t for a one-tailed test with 49 degrees of freedom (n-1), which is 1.677.
To calculate the test statistic, we can use the formula:
t = (X - μ) / (s / √n)
Where X is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.
Given that the sample mean is X = $10960, the hypothesized population mean is μ = $9820, the sample size is n = 50, and the population standard deviation is θ = $1580, we can calculate the sample standard deviation:
s = θ / √n = $1580 / √50 = $223.61
Now we can calculate the test statistic:
t = (X - μ) / (s / √n) = ($10960 - $9820) / ($223.61 / √50) = 7.45
Since the calculated t-value (7.45) is greater than the critical t-value (1.677), we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the population mean weekly sales have increased after advertising.
Therefore, we can infer that the advertising campaign in the local newspaper has been effective in increasing the sales of the electronics store.
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--The given question is incomplete, the complete question is given
" a small electronics store has begun to advertise in the local newspaper. before advertising, the long term average weekly sales $9820. a random of 50 weeks while the newspaper ads were running gave a sample mean weekly sale of x = $10960. Does this indicate that the population mean weekly sales is now more than $9820? test at the 5% level of significance. Assume theta = $1580.
A. state the null and alternate hypothesis.
B. Compute the or t va;ue of the sample test statistic.
C. Find the critical value(s).
D. based on the answers to a-c, what is your conclusion?"--
A quadrilateral has vertices P(-5,7), Q(-3,6), and R(-6,0). Which point would make PQRS a rectangle?
~a.) S(-4,-1)
~b.) S(-7,2)
~c.) S(-8,2)
~d.) S(-8,1)
Answers
From the given information about the vertices of the quadrilateral, the point at which the PQRS quadrilateral will be made a rectangle is S(17/14, -1/7).
What is a quadrilateral? What are its properties?A quadrilateral is a four-sided polygon, which means it's an unrestricted shape with four straight sides.The parcels of a quadrilateral include Four sides A quadrilateral has four sides.The sum of the angles in a quadrilateral is always 360 degrees.Each type of quadrilateral has its own unique set of parcels and characteristics.Perimeter The border of a quadrilateral is the sum of the lengths of its sides.Area The area of a quadrilateral can be calculated using colorful formulas, depending on the type of quadrilateral and the information given about its sides and angles.What is a rectangle? What are its properties?An example of a quadrilateral with all four angles at right angles (90 degrees) and opposite sides that are parallel and of equal length is a rectangle.The characteristics of a rectangle are as follows: 4 right angles: A rectangle has four angles, and all four of them are right angles, which means they are all 90 degrees.A rectangle's perimeter is determined by adding the lengths of its four sides, which is equal to twice the length plus twice the width.Area: The length times the breadth of a rectangle equals the area of that shape.Perpendicular sides are opposite sides: A rectangle's opposite sides are perpendicular to one another, therefore when they intersect, they do so at a right angle.Parallelograms include rectangles as well: since a rectangleWe need to find the point that would make PQRS a rectangle. We will first determine the fourth vertex S which, when connected to the remaining three vertices, forms a quadrilateral with four right angles.As opposite sides of a rectangle are parallel and equal in length, we can first find the lengths of PQ and RS, which should be equal in a rectangle.From the distance formula, we have:PQ = [tex]\sqrt{6-7)^{2}} +(-3+5)^{2} =\sqrt{[2^{2}+(-2)^{2} } =\sqrt{8}[/tex]RS = [tex]\sqrt{(0 - 6)^2+ (-5 + 3)^2} + \sqrt{[(-6)^2 + (-2)^2] }= \sqrt40}[/tex]The midpoint of PQ is: [tex][(6 - 5)/2, (-3 - 3)/2] = (0, -3)[/tex]The slope of PQ is: [tex](6 - 7)/(-3 + 5) = -1/2[/tex]The equation of the perpendicular bisector of PQ is:[tex]y + 3 = 2(x - 0) or y = 2x - 3[/tex]The midpoint of RS is: [tex][(0 - 6)/2, (-5 - 0)/2] = (-3, -5/2)[/tex]The slope of RS is: [tex](0 - 6)/(-5 + 3) = 3[/tex]The equation of the perpendicular bisector of RS is :[tex]y + 5/2 = (-1/3)(x + 3) or y = (-1/3)x - 1/6[/tex]Now to find the intersection of these two lines, we can set them equal to each other and compute the value for x:[tex]2x - 3 = (-1/3)x - 1/6[/tex][tex]12x - 18 = -2x - 1[/tex]Adding 2x and 18 to both sides gives:[tex]14x = 17x = 17/14[/tex]To find the y-coordinate of the intersection, substitute x into either equation:[tex]y = 2(17/14) - 3 = 1/7[/tex]So, the point that would make PQRS a rectangle is S(17/14, -1/7).To know more about polygons visit:
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The answer is option c.) S(-8,2).
What is quadrilateral?A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.
For PQRS to be a rectangle, its opposite sides must be parallel and have equal length. We can find the length of PQ and RS using the distance formula:
PQ = √[(Qx - Px)² + (Qy - Py)²]
= √[(-3 - (-5))² + (6 - 7)²]
= √[4 + 1]
= √[5]
RS = √[(Sx - Rx)² + (Sy - Ry)²]
= √[(-8 - (-6))² + (2 - 0)²]
= √[4 + 4]
= √[8]
Since PQ and RS are not equal, we need to find a point S such that PQRS has equal sides. Moreover, the diagonals of a rectangle bisect each other. Hence, we can use the midpoint formula to find a point that bisects PR:
M = [(-5 - 6)/2, (7 + 0)/2]
= (-11/2, 7/2)
Let's consider each option:
a.) S(-4,-1)
The slope of PQ is (6 - 7)/(-3 + 5) = -1/2, so the slope of RS must be -1/2 as well. The slope of RS is (2 - 0)/(-8 + 6) = 1, so S(-4, -1) cannot be a point of RS.
b.) S(-7,2)
The slope of PQ is (6 - 7)/(-3 + 5) = -1/2, so the slope of RS must be -1/2 as well. The slope of RS is (2 - 0)/(-7 + 6) = -2, so S(-7, 2) cannot be a point of RS.
c.) S(-8,2)
The slope of PQ is (6 - 7)/(-3 + 5) = -1/2, so the slope of RS must be -1/2 as well. The slope of RS is (2 - 0)/(-8 + 6) = 1, so S(-8, 2) could be a point of RS. Moreover, the distance from S to the midpoint of PR is:
√[(-11/2 - (-8))² + (7/2 - 2)²]
= √[25/4 + 9/4]
= √[34]/2
This is equal to the length of PQ, so PQRS could be a rectangle with S(-8, 2).
d.) S(-8,1)
The slope of PQ is (6 - 7)/(-3 + 5) = -1/2, so the slope of RS must be -1/2 as well. The slope of RS is (1 - 0)/(-8 + 6) = -1, so S(-8, 1) cannot be a point of RS.
Therefore, the answer is option c.) S(-8,2).
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The ratio of girl to boys in mr Day class is 3 to 5 . If there is 15 boys in mr Day class how many more boyz are there then girls
Answers
Answer:
If there are 15 boys in Mr. Day’s class and the girl to boy ratio is 3 to 5, then there are 9 girls in Mr. Day’s class. To find out how many more boys there are than girls, you can subtract the number of girls from the number of boys:
15 boys - 9 girls = 6 more boys than girls.
Step-by-step explanation:
the average score of 100 students taking a statistics final was 70, with a standard deviation of 7. assuming a normal distribution, what test score value separates the top 2.5% of the students from the rest of the students? (show your work)
Answers
The average score of 100 students taking a statistics final was 70, with a standard deviation of 7. The test score esteem that isolates the beat 2.5% of normal distribution from the rest of the understudies is roughly 83.72.
To discover the test score esteem that isolates the best 2.5% of the understudies, we got to discover the z-score comparing to that rate utilizing the standard ordinary conveyance table.
z = (x - μ) / σ
To discover the z-score compared to the best 2.5%, we see up the region of the right-hand tail of the standard normal distribution table, which is 0.025. This compares to a z-score of roughly 1.96.
Presently ready to utilize the z-score equation to unravel for x:
1.96 = (x - 70) / 7 Increasing both sides by 7, we get:
x - 70 = 13.72
Including 70 to both sides, we get:
x = 83.72
Hence, the test score esteem that isolates the beat 2.5% of the understudies from the rest of the understudies is roughly 83.72.
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6PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST
Answers
Answer:
b. 8/17
Step-by-step explanation:
hope this helps ;)
A large company put out an advertisement in a magazine for a job opening. The first day the magazine was published the company got 120 responses, but the responses were declining by 10% each day. Assuming the pattern continued, how many total responses would the company get over the course of the first 18 days after the magazine was published, to the nearest whole number?
Answers
The company would get a total of 1200 responses over the course of the first 18 days after the magazine was published, to the nearest whole number.
What is meant by days?
Days refer to the 24-hour period of time that is based on the rotation of the Earth on its axis. It is a unit of time commonly used in calendars, schedules, and daily life.
Explain whole numbers
Whole numbers are positive integers including zero. They are used to count and represent quantities of discrete objects or entities in mathematics.
According to the given information
The sum of the first n terms of a geometric sequence with first term a and common ratio r is given by the formula S_n = a(1 - rⁿ)/(1 - r).
In this case, we want to find the sum of the first 18 terms of the sequence, so n = 18. Substituting the values for a, r, and n into the formula for S_n, we get:
S_18 = 120(1 - 0.9¹⁸)/(1 - 0.9)
≈ 1200
So the company would get a total of 1200 responses over the course of the first 18 days after the magazine was published, to the nearest whole number.
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Graph y=4/7x−2.
Use the line tool and select two points on the line to graph the line.
Answers
By using slope intercept , These were the two points on the line: (0,-2) and (7,2).
Define slope intercept?A line is defined by the equation y = mx + b, which is also known as the slope-intercept form. When the line is graphed, m represents the slope and b the point at which the line intersects the y-axis.
We may use the slope-intercept form of a line, which is y=mx+b where m is the slope and b is the y-intercept, to graph the line y=4/7x-2. Therefore, m=4/7 and b=-2.
These variables allow us to plot two spots along the line. Since the line crosses the y-axis at (0,-2) (the y-intercept), that location will be one of the points.
We can utilize the slope of 4/7 to locate a different point along the line. This indicates that we advance up 4 units in the y direction for every 7 units we move to the right (in the x direction). We can therefore move 7 units to the right and then 4 units up, starting at (0,-2), to reach (7,2).
So now we have two points on the line: (0,-2) and (7,2). These points can be plotted on a coordinate plane, and then a straight line can be drawn through them to create the graph.
Graph given below:
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3PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST
Answers
Answer: x= 7191.509 ft
Step-by-step explanation:
Sin9/1 = 1125/x
X/1 = 1125/sin9
ADD: (Give answer in simplest form)
6 2/7+7 1/2
Answers
Work:
Add the whole numbers and fractional parts of the mixed numbers separately
(6+7) + (2/7 + 1/2)
Calculate the sum
13+(2/7 + 1/2)
Rewrite whole number and fractions as mixed number
13 11/14
To start, we will separate the whole numbers and fractions. 6 and 7 are the whole numbers and 2/7 and 1/2 are the fractions. We will add them separately first.
(6 + 7) + (2/7 + 1/2)
Now calculate:
(13) + (11/14)
***If you are confused as to how to add fractions, here’s how. You will find a common denominator and add the numerators while keeping the denominator the same. The common denominator in this case is 14, since 7 and 2 goes to 14. We will multiply both top and bottom of 2/7 by 2 to get 14 as a denominator. That gives us 4/14. Now we will do the same for 1/2, but multiply it by 7, which gives us 7/14. So 4/14 + 7/14. Add the numerators and keep the denominator and you get 11/14.
Now the last step is simply combine the two answers, both the whole number and fraction.
(13) + (11/14) = 13 11/14
13 11/14 can also be written as 193/4 as an improper fraction or 13.8 as a decimal.
Hope this helped!
Evaluate the expression when a = 3 and x = -7 .
-a + 9x
Answers
a = 3 and x = -7
We are then given the expression to evaluate with the given values. We can simply put the given values in for the expression.
So whenever we see an a, we put 3, and for x, we put -7.
-a + 9x
Put in the given values:
-(3) + 9(-7)
Calculate:
-3 + -63
Calculate:
-66
That’s your answer!
Hope this helped!
You decide this is not enough time so you decide to ration your meals. You a
(75%) of each meal instead. So, one ration = 0.75 meals. How many total rati
ave?
meals
1 fails
Answers
The total rations will be: 0.75 times the number of meals.
How many rations will you have in total?A ration refers to the fixed portion of food or other goods allowed to each person in times of shortages.
In this context, If you decide to eat only 75% of each meal, that means you will consume 0.75 times the number of meals.
For example, if you originally had 100 meals, you will now have:
= 0.75 x 100
= 75 rations in total.
This approach allows to stretch your meals and make them last longer by rationing your food intake.
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The letters r and θ represent polar coordinates. Write the equation using rectangular coordinates (x, y).
r sin θ = 10
y = 10
x = 10
y = 10x
x = 10y
Answers
The equation r · sin θ = 10 in rectangular coordinates is equal to y = 10.
How to find the equation in rectangular coordinates
Herein we find the representation of a equation in polar coordinates, whose form in rectangular coordinates. This can be done by using the following definitions:
cos θ = x / r
sin θ = y / r
Where:
θ - Angle, in degrees. x, y - Legs of the right triangle.r - Hypotenuse of the right triangle.Then, the equation in polar coordinates is:
r · sin θ = 10
y = 10
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ey of the
1
11. The table shows the wages of a worker in
an office. Which equation can be used to
represent how much, y, the worker earns in x
hours?
Hours
2
CIT
4
10
6
10
A. y = 20x+ 5.50
B. y = 10x + 5.50
C. y = 20.5x
Dy = 10x
Wages
$25.50
$45.50
$65.50
$105.50
12. Carlisle is going to paint his living room
Answers
Answer:
To determine which equation represents how much the worker earns in x hours, we can use the table to find the rate of pay per hour, which is the change in wages divided by the change in hours:
Change in wages = $105.50 - $25.50 = $80
Change in hours = 6 - 2 = 4
Rate of pay per hour = Change in wages / Change in hours
= $80 / 4
= $20
Therefore, the worker earns $20 per hour. To find the total earnings, we can multiply the hourly rate by the number of hours worked:
y = $20x
Therefore, the correct equation is D) y = 10x, which represents how much the worker earns in x hours.
Step-by-step explanation:
Billy has a credit card with a current balance of $3,500 and a 16% APR. With his current monthly payment, he will be able to pay off this debt in 15 months. But Billy just learned that he is getting a raise at work. If he puts all of the extra income from his raise into his monthly credit card payment, how much additional monthly income would he require from his raise to pay off the credit card in 12 months? a. $58.57 b. $171.37 c. $258.99 d. $317.56
Answers
Answer:
a. $58.57
Step-by-step explanation:
Billy is in a pickle. He has a credit card debt of $3500 with a 16% annual interest rate, and he wants to pay it off in a year. He also wants to ask his boss for a raise, but he doesn't know how much to ask for. Luckily, he has a friend who is good at math and can help him out.
The friend tells Billy that we need to use the formula for the monthly payment of a credit card debt, which is:
P = (r / 12) * B / (1 - (1 + r / 12)^(-n))
where P is the monthly payment, r is the annual interest rate, B is the current balance, and n is the number of months to pay off the debt.
Using this formula, the friend calculates how much Billy is currently paying and how much he would need to pay to clear his debt in 12 months. The friend also finds the difference between these two payments, which is the amount of extra income Billy would need from his raise.
The friend shows Billy the calculations and says:
"Here you go, Billy. You are currently paying $280.42 per month to pay off your debt in 15 months. If you want to pay it off in 12 months, you would need to pay $331.79 per month. That means you would need an additional monthly income of $51.37 from your raise. The closest answer choice to this amount is a. $58.57, so this is the best option."
Billy thanks his friend and says:
"Wow, you are amazing! Thank you so much for helping me out. I'm going to ask my boss for a raise right now. Wish me luck!"
The friend wishes Billy good luck and hopes that he will get his raise and pay off his debt soon.
Part C (30 POINTS)
Explain how your net created in part B can help Leonora's family determine the amount of plastic they will need to wrap around each hay bale.
Answers
To calculate the surface area of the hay bale, the family can use the dimensions of the net created in Part B. They can measure the length and width of the net and then multiply those dimensions to find the surface area. This will give them an accurate estimate of the amount of plastic they will need to cover each hay bale.
By using the net to determine the surface area of each hay bale, Leonora's family can ensure that they have enough plastic to cover all of their hay bales. This can help to prevent spoilage and ensure that the hay remains fresh and usable for a longer period of time. Additionally, by accurately estimating the amount of plastic needed, the family can save money by not purchasing more plastic than necessary.
Hypothesis Testing Using a P-Value Signature Assignment #2
Roller Coasters. The heights in feet of 36 randomly selected top-rated roller coasters are listed. Assume the population standard deviation is 71.6 feet. At a = 0.05, is there enough evidence to reject the claim that the mean height of top- rated roller coasters is 160 feet? (Source: POP World Media, LLC)
325 188 306 107 208 167 105 78 140 232 230 170 170 205 305 135 200 200 100 223 135 195 80 90 120 210 82 161 245 88 70 116 121 146 149 124
1. Express the null and alternative hypothesis in words and as mathematical expressions. Identify which one is the claim?
2. Compute the sample mean and test statistic z. Write out the formulas and show your work. Round off to two decimal places. (EQS)
3. Compute the p value and explain how it was found. (Round off two decimal places.)
4. Describe whether to reject or fail to reject the null hypothesis and explain the decision.
5. Interpret the decision in the context of the original claim. (Critical thinking)
6. In three to five sentence explain how and why hypothesis testing is used. Give an example (Communication)
Answers
Null hypothesis: The mean height of top-rated roller coasters is 160 feet (H0: u = 160).
Solution to the aforementioned questions1) Null hypothesis: The mean height of top-rated roller coasters is 160 feet (H0: u = 160). Alternative hypothesis: The mean height of top-rated roller coasters is not 160 feet (Ha: u ≠ 160). The claim is the null hypothesis.
2) Sample mean = (325+188+306+107+208+167+105+78+140+232+230+170+170+205+305+135+200+200+100+223+135+195+80+90+120+210+82+161+245+88+70+116+121+146+149+124)/36 = 164.97 feet. The test statistic z = (x - μ) / (σ / √n) = (164.97 - 160) / (71.6 / √36) = 1.21.
3) The p-value is the probability of observing a test statistic as extreme as the one computed from the sample, assuming the null hypothesis is true. Using a standard normal distribution table, the p-value is 0.1131.
4) At α = 0.05, the p-value (0.1131) is greater than a. Therefore, we fail to reject the null hypothesis.
5) Based on the statistical analysis, we do not have sufficient evidence to reject the claim that the mean height of top-rated roller coasters is 160 feet.
6) Hypothesis testing is a statistical method used to make decisions based on the analysis of sample data. It is used to determine whether a claim or hypothesis about a population is supported by the evidence provided by the sample data.
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Find the volume of the figure below:
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The volume of the cylinder is 3532.5 metres cube.
How to find the volume of a cylinder?The figure above is a cylinder. The volume of the cylinder can be found as follows:
volume of a cylinder = πr²h
where
r = radiush = heightTherefore, let's find the height using Pythagoras's theorem.
25² - 15² = h²
h² = 625 - 225
h = √400
h = 20 metres
Hence,
volume of a cylinder = 3.14 × 7.5² × 20
volume of a cylinder = 3532.5 metres cube
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WILL MARK AS BRAINLEIST!! ASAP!!
Question in picture!!
I have more questions on my account if you can help!!
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We need to integrate the function
y = 2x - x² with respect to x, from x = 0 to x = 2.
The graph of the function intersects the x-axis at x = 0 and x = 2.
So,
Area of region R = ∫[0,2] (2x - x²) dx
= [x² - (1/3)x³] from 0 to 2
= [2² - (1/3)(2)³] - [0² - (1/3)(0)³]
= 4/3
Now, let's find the equation of the line y = cx. Since the line passes through the origin (0,0), we have y = cx.
To find the value of c that divides the region R into two equal subregions, we need to find the value of x where the
area under the curve y = 2x - x² is equal to the area under the line y = cx.
∫[0,a] (2x - x²) dx = ∫[0,a] cx dx
[2x²/2 - x³/3] from 0 to a = [c/2 x²] from 0 to a
2a²/2 - a³/3 = c/2 a²
We multiply both sides by 6, we get:
12a² - 2a³ = 3ac
2a² - (1/3)a³ = (1/2)ac
2a - (1/3)a² = (1/2)c
c = (4a - (2/3)a²)/2
We know that the area under the line is equal to the area under the curve up to the point of intersection, we have:
∫[0,a] (2x - x²) dx = ∫[0,a] (cx) dx - ∫[a,2] (2x - x²) dx
2a²/2 - a³/3 = c/2 a² - 2a² + (8/3)a³ - 4a + (4/3)a²
10a³/3 - 7a² + 4a = 0
a = 0, 1.4105, -0.6172
The only value of a that is within the range 0 to 2 is a = 1.4105. Substituting this value into the equation for c, we get:
c = (4a - (2/3)a²)/2 = 1.636
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HELP WILL GIVE BRAINLIEST GEOMETRY SHOW WORK
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The surface area of the right prism is 192.9 m².
What is a prsim?A prism is a solid shape that is bound on all its sides by plane faces.
To calculate the surface area of the prism, we use the formula below
Formula:
S.A = bh+L(b+h+c)................. Equation 1Where:
S.A = Surface area of the prismb = Base of the triangular baseh = Height of the triangular baseL = Length of the prismc = Hypotenus of the triangular baseFrom the diagram in the question,
Given:
b = 3 mh = 8 mc = 8 mL = 9.1 mSubstitute these values into equation 1
S.A = (3×8)+9.1(3+8+8)S.A = 24+172.9S.A = 192.9 m²Hence, the surface area is 192.9 m².
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As a candle burns, it decreases in height by 2 inches every hour. If the candle is 12 inches tall when it is lit, how will the height change over time? If the candle burned for 2 hours, how many inches tall will it be?
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The height of the candle change over time as a linear function
How will the height of the candle change over time?The height of the candle decreases by 2 inches every hour, which means the height of the candle is a linear function of time.
We can write the equation for the height of the candle as:
h(t) = 12 - 2t
where h is the height of the candle in inches and t is the time in hours.
If the candle burned for 2 hours, we can plug in t=2 into the equation to find the height:
h(2) = 12 - 2(2) = 8
So the height of the candle after 2 hours of burning is 8 inches.
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Jordan reads a comic book at a rate of 21 pages in 6 minutes. At this rate, how many pages does he read each minute?
Answers
Answer:
x = 3.5 pages per minute
Step-by-step explanation:
We make the relationship
21 pages ------ 6 min
x pages -------- 1 min
So x= (21x1)/(6)
x = 3.5 pages per minute
Help it a screenshot
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The equation will be w = 40b
How do you formulate an equation for the scenario provided?To find the total weight (w) of the soil in pounds when Yuki stacks b bags, you can use a simple linear equation. Each bag weighs 40 pounds, so the equation will be: w = 40b
This equation shows that the total weight (w) of the soil in pounds is equal to the number of bags (b) multiplied by the weight of each bag (40 pounds).
The above answer is based on the information below as seen in the picture;
Yuki works at a garden store. She is stacking 40 pounds bags of soil.
write an equation that gives the total weight, w, of the soil in pounds when Yuki stacks b bags.
+ - . = b, w, 40
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725 unit digit of (325)
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The unit digit of 725 unit digit of (325) is given as 5
How to solve for the unit digitUnveiling the unit digit of a number raised to an exact power can be done by analyzing the pattern of the unit digits of said power sequence.
For instance, given the task of ascertaining the unit digit of 325^725, let us observe the recurrent pattern concerning 5's power line:
[tex]5^1 = 5\\5^2 = 25\\5^3 = 125\\5^4 = 625\\5^5 = 3125[/tex]
It is readily evident that the final digit of 5 raised to any affirmative integer power shall invariably remain as 5. Correlatively, the end figure for 325^725 is also 5.
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What is the factored form of x² + 5x+6?
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The factored form of the expression x² + 5x+6 is (x + 3)(x + 2)
How to determine the factorized formTo factorize the quadratic equation, we need to take the following steps;
Multiply the coefficient of the x squared by the constant value, we have;
6
Now, find the pair factors of the product that would add up to give 5, we have;
2 + 3
Substitute the values into the expression, we have;
x² + 2x + 3x + 6
Now, group the expression in pairs, we have;
(x² + 2x) + (3x + 6)
Factorize the expressions
x(x + 2) + 3(x + 2)
Then, we have;
x + 3
x + 2
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8 Find in degrees. 17 [?] degrees Round to the nearest hundredth.
Answers
Answer:
Θ ≈ 28.07°
Step-by-step explanation:
using the sine ratio in the right triangle
sinΘ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{8}{17}[/tex] , then
Θ = [tex]sin^{-1}[/tex] ( [tex]\frac{8}{17}[/tex] ) ≈ 28.07° ( to the nearest hundredth )
G(Q) = 5 + 3Q + 202 - Q2 C2(Q) = 3 + 4Q + 2 1. Find the MC function for both C1(Q) AND C2(Q). 2. Find AVC function for both Ci(Q) AND C2(Q). 3. Find AFC function for both C1(Q) AND C2(Q). 4. Find AC function for both Ci(Q) AND C2(Q). 5. Find ATC function for both Ci(Q) AND C2(Q).
Answers
For C1(Q) = 3 - 2Q.
For C2(Q) = 4.
2. The AVC function
For C1(Q) = 5/Q + 3 + 20/Q - Q.
For C2(Q) = 3/Q + 4 + 2/Q.
3. The AFC function
For C1(Q)= 5/Q - 20/(5 + 3Q + 20/Q - Q)
For C2(Q) = 0.
4. To find the AC function
For C1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).
For C2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.
5.To find the ATC function
For C1(Q)= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²)
For C2(Q)= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.
Find the ATC functions for C1(Q) and C2(Q) given the provided cost functions?
1. To find the MC function, we take the derivative of the cost functions with respect to Q.
For C1(Q) = 5 + 3Q + 202 - Q^2, MC1(Q) = 3 - 2Q.
For C2(Q) = 3 + 4Q + 2, MC2(Q) = 4.
2. To find the AVC function, we divide the cost functions by Q.
For C1(Q), AVC1(Q) = (5 + 3Q + 202 - Q^2)/Q = 5/Q + 3 + 20/Q - Q.
For C2(Q), AVC2(Q) = (3 + 4Q + 2)/Q = 3/Q + 4 + 2/Q.
3. To find the AFC function, we subtract the AVC function from the ATC function.
For C1(Q), AFC1(Q) = (5 + 3Q + 202 - Q^2)/Q - (5 + 3Q + 202 - Q^2)/(5 + 3Q + 20/Q - Q)
= 5/Q - 20/(5 + 3Q + 20/Q - Q).
For
C2(Q), AFC2(Q) = (3 + 4Q + 2)/Q - (3 + 4Q + 2)/(3/Q + 4 + 2/Q) = 0.
4. To find the AC function, we add the AVC function to the AFC function.
For
C1(Q), AC1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).
For
C2(Q), AC2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.
5. To find the ATC function, we divide the AC function by Q.
For
C1(Q), ATC1(Q) = [(5 + 3Q + 202 - Q²)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q)]/Q
= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²).
For
C2(Q), ATC2(Q) = [(3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q]/Q
= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.
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Can somebody help me out?
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Answer:
The area of a semicircle is half of the area of the circle. As the area of a circle is πr2. So, the area of a semicircle is 1/2(πr2 ), where r is the radius. The value of π is 3.14 or 22/7.
Altogether the Green Team jumped 10264 times. The Yellow Team did 759 fewer jumps than the Green Team. How many jumps did the Yellow Team do?
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The number of milligrams of Vitamin C from 100 different gummy vitamins sold in the world was collected.
Which graphical representation would be most appropriate for the data, and why?
Box plot, because the median can easily be determined from the large set of data
Stem-and-leaf plot, because you can see the shape of the data
Histogram, because it shows each individual data point
Bar chart, because the data is categorical
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Box plot, as the median can be easily ascertained from the substantial amount of data. The answer is option (a).
What is a median?The middle value in a given set of figures or statistics is referred to as the median. The average value for a given collection of integers can be calculated using one of three main methods in mathematics. The mean, the median, and the mode are the three. Central tendency measurements refer to these three factors. The average value of the supplied data is calculated using mean. The midpoint value of the given data is defined by a median. The input data's repeating value is defined by the mode.
A box plot is a very visual way to show a brief summary of one or more sets of data. It is particularly useful for quickly comparing and summing multiple sets of findings from distinct trials. A box plot provides a visual picture of the distribution of results as well as clues regarding data symmetry at a look.
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