The probability of getting 5 heads and 5 tails is 0.246
Given that,
No. of head = No of tail,
The probability of getting 5 heads and 5 tails
P(X = x ) = nCₓPˣQⁿ⁻ˣ
There x = 5, n=10 p= 1/2 and Q=1/2
P ( x = 1 ) = 10C₅(1/2)⁵(1/2)⁵
= 252 ( 0.000 9765625 )
P ( X = 5 )= 0.2460
First three flips are head stored no of Outcome 2^10 = 1024
X = {H,H,H....}
The remaining 7 position can be flued with Either head or tail
Therefore ,the possible favourable outcomes = 2^7
No of favourable outcomes
: P(X) =No of favorable outcomes /total no of outcomes
P(X) = 0.125
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How do you find the vertex angle of an isosceles triangle?.
Subtract the two congruent values for the base angles from 180° to determine the isosceles triangle's vertex angle measurement. For instance, if each base angle is 40°, the vertex angle is 100°, which is determined by subtracting 180° from (40° * 2) to arrive at 100°.
The angle created by two equal sides of an isosceles triangle is known as the "vertex angle." The isosceles triangle's vertex angle is BAC. Base angles: 4. The angles that include the base of an isosceles triangle are known as the "base angles."
Since the missing angle is not perpendicular to the two indicated sides, we must first add the two base angles together before subtracting the sum from 180 to arrive at the solution. The sum of the two base angles equals 140°. An isosceles triangle has angles that sum up to 180°. To get the amount of the remaining angle, we deduct 140 degrees from 180 degrees.
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HELP PLEASE!! 50 POINTS!!!!
The table defines the observed data values and the corresponding predicted values, based on a line of fit.
Observed Predicted
9 7.77
12 12.87
12 11.17
15 14.57
17 16.27
24 24.77
28 26.47
33 31.57
How many negative residuals does the data set have? How many positive residuals does the data set have?
2 negative residuals and 6 positive residuals
3 negative residuals and 5 positive residuals
5 negative residuals and 3 positive residuals
6 negative residuals and 2 positive residuals
Answer: 3 negative residuals and 5 positive residuals
Step-by-step explanation: When the observed number is lower than the predicted number then this is an example of a negative residual. The tricky thing is this doesn't make much sense you would think that this would be a positive residual but it's not to that's something you need to remember!
example
observed number: 10
predicted number: 10.5
this is a negative residual and it's the opposite for the positive residual
The data set has 2 negative residuals and 6 positive residuals. which is the correct answer would be an option (A).
What are the residuals?A residual is a difference between the observed value and the predicted value for a given data point. The sign of the residual indicates whether the predicted value is above or below the observed value.
The table defines the observed data values and the corresponding predicted values, based on a regression line of fit.
Observed Predicted
9 7.77
12 12.87
12 11.17
15 14.57
17 16.27
24 24.77
28 26.47
33 31.57
In this case, the residuals for the data points would be calculated as follows:
Observed value - Predicted value = Residual
9 - 7.77 = 1.23 (positive)
12 - 12.87 = -0.87 (negative)
12 - 11.17 = 0.83 (positive)
15 - 14.57 = 0.43 (positive)
17 - 16.27 = 0.73 (positive)
24 - 24.77 = -0.77 (negative)
28 - 26.47 = 1.53 (positive)
33 - 31.57 = 1.43 (positive)
Based on these calculations, there are 2 negative residuals (-0.87 and -0.77) and 6 positive residuals (1.23, 0.83, 0.43, 0.73, 1.53, and 1.43).
Therefore, the data set have 2 negative residuals and 6 positive residuals.
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A bakery sold a total of 200 cupcakes in a day, and 42 of them were chocolate flavored. What percentage of cupcakes sold that day were chocolate flavored?.
Percentage of cupcakes which was chocolate flavored = 21%. The formula to calculate percentage is (x/100 * total number of items = given no of items).
Let x be the percentage of chocolate flavored cupcakes
Therefore,
x% of 200 = 42
Since the total no. of cupcakes is 20.
=> x/100 * 200 = 42
=> x * 2 = 42
=> x =21
Hence the required percentage is 21 %.
A % is a number without dimensions. It is a ratio or a number that is written as a fraction of one hundred. The percentage sign (%) is the symbol used to represent a percentage. Pct and pc are two examples of the acronyms used. Typically, the relative amount of the entire number is expressed using the percentage.
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the 5x5 grid shown contains a collection of squares with sizes from 1x1 to 5x5. how many of these squares contain the black center square?
Using Counting principle,
The black center square contains total 330 small squares.
We start with lowest one i.e 1 × 1
Let’s consider any one face out of six faces of cube ,
1×1 squares = 25as one face of grid or cube is made up of 25 small squares.
2× 2 squares = 16If we are facing difficulty in visualising then
simply we draw a 5× 5 board on paper, just as seen in above picture :
and now check 2× 2 squares.
By using R1, R2 and all columns we shall be able to draw 4 such blocks.
Again, R2,R3 and R3, R4 and R4,R5 we can easily draw 4 squares each cash .
Thus, total square count of 2× 2 squares will be
= 16
similarly, we do it for 3× 3 and 4×4 and we will get 9 & 4 respectively.
For final one 5× 5 there is one big square
So, total squares for one face will be
= 25+16+9+4+1=55
Since, there are 6 such faces for a cube then
=>55× 6= 330
Hence, total squares contain the black center square is 330.
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find the lengths of the sides of the triangle of maximum area that can be drawn inside a circle of radius r with one vertex of the triangle at the center of the circle, and the other two vertices on the circle.
The lengths of the sides of a triangle are as follows:
base(b) = 2R and height(h) = R
What is the triangle's area?In a two-dimensional plane, a triangle's area is the area that it completely encloses. A triangle is a closed form with three sides and three vertices, as is common knowledge. The entire area occupied by a triangle's three sides is referred to as its area. Half of the product of the triangle's base and height provides the standard formula for calculating the area of the triangle.With one of the triangle's vertices in the circle's centre and the other two on the circumference, we must determine the lengths of the sides of the triangle with the largest possible area that can be drawn within.
Let,
b = base of triangle
h = height of triangle
R = Radius of circle
Area of triangle = bh/2
The area of a triangle is bh/2, but since b/2 is shared by a triangle, the maximum area is constrained by the height h.
This would be the perpendicular height to the base, which is the radius R
The base is two radii b=2R and height is h= R
Therefore, the lengths of the sides of a triangle are as follows:
base(b) = 2R and height(h) = R
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how many solutions does 8+x/6=x/6-4+5x/12
The equation 8+x/6=x/6-4+5x/12 has one solution x = 144/5 or 28.8
what is equation?Equation is a mathematical statement that shows that two mathematical expressions are equal
[tex]8 +\frac{x}{6} = \frac{x}{6} -4 + \frac{5x}{12}[/tex]
collect the like terms
8 +4 = [tex]\frac{x}{6} -\frac{x}{6} + \frac{5x}{12}[/tex]
12 = [tex]\frac{5x}{12}[/tex]
cross multiply
144 = 5x
Divide both side by 5
[tex]\frac{144}{5} = \frac{5x}{5}[/tex]
x = 144/5 or 28.8
Therefore, the equation has one solution which is x = 144/5 or 28.8
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In a certain company, the measured thickness m of a helicopter blade must not differ from the standard s by more than 0.14 millimeters. The manufacturing engineer expresses
Kthis as Im-s/s0.14. Find the limits of m if the standards is 18.92 millimeters.
What is the solution? Select the correct choice below and fill in any answer boxes within your choice.
If In a certain company, the measured thickness m of a helicopter blade must not differ from the standard s by more than 0.14 millimeters. The solution is 18.78 ≤m≤ 19.06.
How to find the limits?In order to find the limits we would have to add Standard 18.92 to the expression and as well less the standard from the expression 0.14.
Given data:
Manufacturing engineer expression /m-s/ ≤ 0.14
Standard = 18.92 millimeters
Hence,
Limit of m:
18.92 ± 0.14
m - 18.92 ≤ 0.14
= 19.06
And
-(m- 18.92) ≤ 0.14
m ≥ 18.78
So,
Solution =18.78 ≤m≤ 19.06
Therefore the solution is 18.78 ≤m≤ 19.06.
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The triangle shown,
What is y?
Answer:
y = 136 degrees
Step-by-step explanation:
We can see that both x and y lie on a straight line. Their two angles add up to be a straight line....
We already know the value of x (44)
x + y = 180 degrees
44 + y = 180
(Subtract from both sides)
y = 136
So, y is 136 degrees
This looks correct, since angle y seems to be an obtuse angle
As a borrower, you have the option to choose between two 30-year, monthly-payment loans: 7% interest rate with 3 points, versus 7.5% interest with one-half point.
(a) Which loan option would you choose if you had a 10-year expected prepayment horizon?
(b) Which would you choose if you expect to pay off this loan in 5 years?
If we had a 10-year expected prepayment horizon then Option 1 is preferred less expense and if we had a 5-year expected prepayment horizon then Option 2 is preferred less expense.
In the given question, as a borrower, we have the option to choose between two to 30-year, monthly-payment loans: 7% interest rate with 3 points, versus 7.5% interest with one-half point.
If we assume the pricipal loan amount as $100,000 based on the two option need to monthly instalements for 30 years & the equivalent amount for the respective points.
Under mortgage loan, 3 points on $100,000 is equal to $3,000 and for 1.5 points would be $1500.
Formula for calculating the monthly instalments would be
[tex]\text{EMI} = P\times \frac{r}{12}\times\left [ \frac{(1+r/12)^n}{(1+r/12)^n- 1} \right ][/tex]
where P is Principal , r is rate of interest, n = time period in months.
Using the above said formula we can compute EMI for both the options with interest rates as 7% and 7.5% respectively.
(a) We have to find which loan option would you choose if we had a 10-year expected prepayment horizon.
If repayment is 10 years then EMI under both the options would be:
Option 1: Interest rates as 7%
[tex]\text{EMI} = 100,000\times \frac{7}{1200}\times\left [ \frac{(1+7/1200)^{120}}{(1+7/1200)^{120}- 1} \right ][/tex]
EMI = $1161.08
Option 2: With interest rate as 7.5%.
[tex]\text{EMI} = 100,000\times \frac{7.5}{1200}\times\left [ \frac{(1+7.5/1200)^{120}}{(1+7.5/1200)^{120}- 1} \right ][/tex]
EMI = $1187.02
We can respond to both questions in the following problem using the EMI calculated and the comparable amounts for the respective options.
The total price for each option is as follows.
Particulars Option 1 Option 2
EMI x 12 x 10 139330 142442
Points 3000 1500
Total cost 142,330 143,942
The less expensive Option 1 is preferred.
(b) In this question we have find which would you choose if you expect to pay off this loan in 5 years.
If repayment is 5 years then EMI under both the options would be:
Option 1: Interest rates as 7%
[tex]\text{EMI} = 100,000\times \frac{7}{1200}\times\left [ \frac{(1+7/1200)^{60}}{(1+7/1200)^{60}- 1} \right ][/tex]
EMI = $1980.12
Option 2: With interest rate as 7.5%.
[tex]\text{EMI} = 100,000\times \frac{7.5}{1200}\times\left [ \frac{(1+7.5/1200)^{60}}{(1+7.5/1200)^{60}- 1} \right ][/tex]
EMI = $2003.79
We can respond to both questions in the following problem using the EMI calculated and the comparable amounts for the respective options.
The total price for each option is as follows.
Particulars Option 1 Option 2
EMI x 60 118807.20 120,227
Points 3000 1500
Total cost 121,807.20 121,727
The less expensive Option 2 is preferred.
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a basketball player claims to make 47% of her shots from the field. you want to simulate the player taking sets of 10 shots, assuming that her claim is true. suppose this player attempts 10 shots in a game and
Using simulation and Technics E and R,
he correct answer is option (b) and option (e).Use random two-digit numbers, where are a make and are a miss.
Simulation:
Simulation is a method of modeling random events so that the simulated results closely resemble the actual results. By observing simulated results, researchers gain insight into the real world.
Describe possible outcomes.Associates each result with one or more random numbers.Please select a random number source.Please select a random number. Note the "simulated" results, based onrandom numbers.
Repeat steps 4 and 5 several times. Preferably until the results show a stable pattern.Analyze simulated results and report results.We have been given that a basketball player claims to make 47% of her shots from the field.
Total number of shots in set taking by player = 10
let consider two events
A: She makes the shot
B: She miss the slot
Probability that she makes the slot , P(A) = 47%
= 0.47
Probability that she miss the slot , P(A) = 1 - 47%
= 57% = 0.53
Use TRD,
make slot = 00-46 and miss slot= 47-99
One trial = 10 shots
now, the possible options which may be right are option b and e .
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Complete question:
Select the best answer.
A basketball player claims to make 47% of her shots from the field. We want to simulate the player taking sets of 10 shots, assuming that her claim is true. To simulate the number of makes in 10 shot attempts, you would perform the simulation as follows:
(a) Use 10 random one-digit numbers, where 0-4 are a make and 5-9 are a miss.
(b) Use 10 random two-digit numbers, where 00-46 are a make and 47-99 are a miss.
(c) Use 10 random two-digit numbers, where 00-47 are a make and 48-99 are a miss.
(d) Use 47 random one-digit numbers, where 0 is a make and 1-9 are a miss.
(e) Use 47 random two-digit numbers, where 00-46 are a make and 47-99 are a miss.
Match the definitions on the left with the terms on the right.
Just want to make sure. Am I right??? Pls help Thxs!
The model represents the factorization of 2x2+5x+3. An algebra tile configuration. 4 tiles are in the factor 1 spot: 2 +x tiles, 2 + tiles. 2 tiles are in the factor 2 spot. : 1 +x tile, 1 + tile. 10 tiles are in the product spot in 4 columns with 2 rows. First row: 2 + x squared tiles, 3 + x tiles. Second row: 2 + x tiles, 3 + tiles. What are the factors of the polynomial?.
Required factors for the given polynomial 2x² + 5x + 3 is given by
(2x + 3) ( x+ 1).
As given in the question,
Given polynomial is equal to :
2x² + 5x + 3
Simplify the given polynomial by factorizing it:
2x² + 5x + 3
Standard form of quadratic equation is:
ax² + bx + c
Factors of the equation 2x² + 5x + 3 are:
x = (-b ± √b² -4ac )/2a
x = ( -5 ± √5² -4(2)(3) )/2(2)
= (-5 ± 1) /4
⇒(2x +3) (x+1) are the factors
Therefore, the required factors of the given polynomial is given by ( 2x + 3 ) ( x + 1 ).
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solve the following linear equation round to two decimal places if necessary. 3.8*-(-1-9.7*)=2.6+13.3* what is x
The value of x in linear equation 3.8x-(-1-9.7x)=2.6+13.3x is 8
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given linear equation is 3.8x-(-1-9.7x)=2.6+13.3x
3.8x+1+9.7x=2.6+13.3x
Add the x variable terms on left
13.5x+1=2.6+13.3x
Subtract 13.3x and 1 on both sides
13.5x-13.3x=2.6-1
0.2x=1.6
Divide both sides by 0.2
x=8
Hence, the value of x in linear equation 3.8x-(-1-9.7x)=2.6+13.3x is 8
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Is triangle ABC congruent to triangle AED?.
Triangles AED and ABC are congruent to one another according to SSS congruency.
Given,
The side BC is equal to side DE.
The side AC is equal to side AD.
∠BAC = ∠DAE
We have to find that whether triangle ABC congruent to triangle AED;
Here,
The side AB = 7 units.
The side AE = 7 units.
Therefore,
The side AB is equal to side AE.
The sum of all the angle of a triangle is 180°.
Consider the triangle ABC and triangle AED.
AB = AE
AC = AD
BC = DE
So, the triangle ABC is congruent to triangle AED by SSS congruency.
That is,
The triangle AED and triangle ABC are congruent by to each other by SSS congruency.
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The image for the question is attached below.
An important factor in selling a residential property is the number of people who look through the home. A sample of 21 homes recently sold in the Buffalo, New York, area revealed the mean number looking through each home was 25 and the standard deviation of the sample was 7 people.
Develop a 99% confidence interval for the population mean. (Use t Distribution Table.) (Round your answers to 2 decimal places.)
The 99% confidence interval for the population mean is (20.6568, 29.3432)
In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts. Therefore, it can be concluded that there is a 95% probability that the true value falls within that range if a point estimate of 10.00 is produced from a statistical model with a 95% confidence interval of 9.50 - 10.50.
Given:
Sample size = 21
Mean = 25
Standard deviation = 7
Confidence interval = 99%
α=1−0.99=0.01
α/2 = 0.005
Degrees of freedom(df)=n−1=21−1=20
Critical value(tc)=tα/2,df = t0.005,20 = 2.8433
Confidence Interval = mean +- tc * s/[tex]\sqrt{n}[/tex]
C.I = 25 ± 2.8433×7/[tex]\sqrt{21}[/tex]
C.I = (25 ± 4.3432)
C.I = (25−4.3432, 25+4.3432)
C.I = (20.6568, 29.3432)
99% confidence interval for the population average of the times homes are shown is (20.6568, 29.3432)
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The ratio of boy to girl in a chool play i 3:7 if there are 30 children in total how many boy are there
The total number of boys is 9.
What is a ratio?
An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could write the ratio as follows: 1: 3 if there is 1 boy and 3 girls.
Here, we have
The ratio of boys to girls in a school play is 3:7
Based on the given conditions, formulate: 30× 3 ÷ (3 + 7)
Calculate the product or quotient: 90/(3+7)
Calculate the sum or difference: 90/10
Hence, the total number of boys is 9.
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a box of snacks, contain 20 individual packages. The newly designed box contains 28 individual packages by what percentage did the number of individual packages increase.
The percentage that the number of individual packages increased by in the newly designed box is 40%
How to find the percentage increase?To find the percentage increase, you first need to find the increase in the number of individual packages in the newly designed box.
This increase is:
= Newly designed box quantity - old box of snacks
= 28 - 20
= 8 individual packages
The percentage increase would then be:
= Increase in packages / Number of packages in old box of snacks
= 8 / 20
= 40%
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What is true about the dilation it is a reduction with a scale?.
When the scale factor is between 0 and 1, a dilatation is considered a decrease.
What is scale factor?
The ratio of one object's scale to that of a new object, which has its representation but is larger, is known as a scale factor (bigger or smaller). A rectangle with sides of 2 cm and 4 cm, for instance, can be made larger by multiplying each side by a certain quantity, such asHow Can I Determine the Scale Factor?
When the new dimensions and the original dimensions are provided, the scaling factor can be determined. The following is a basic formula to determine a figure's scale factor: Scale factor is the product of the original shape's dimension and the new shape's dimension.Learn more about Scale Factor
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if both variables in a correlational study are non-numerical, the data can be organized in a matrix and then analyzed using a .
If both variable in a correlational study are non-numerical, the data can be organized in a matrix and then analyzed using a Chi-square hypothesis test.
A correlational study design investigates relationships between two variables (or more) without the researcher controlling or manipulating any of them.
Chi-square test for hypothesis tests about whether your data is as expected. The basic idea behind the test is to compare the observed values in your data to the expected values that you would see if the null hypothesis is true.
The Chi-square statistic compares the size of any discrepancies between the expected results and the actual results, given the size of the sample and the number of variables in the relationship.
Hence if both variables in a correlational study are non-numerical, the data can be organized in a matrix and then analyzed using a Chi-square hypothesis test.
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How many Great Balls could you purchase for $3,000 if each one costs $600?
Answer: 5 for 600 each
There are 50 great balls.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Cost of 1 great ball = $600
Total amount = $3000
So, number of Great balls
= 3000 / 600
= 50
hence, there are 50 great balls.
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A machine that is programmed to package 1.20 pounds of cereal is being tested for its accuracy in a sample of 36 cereal boxes, the sample mean filling weight is calculated as 1.22 pounds. The population standard deviation is known to be 0.06 pounds. Which of the following conclusions is correct with 95% confidence?? Select one: O A. The machine is operating improperly because the target is below the lower limit. O B. The machine is operating improperly because the target is above the upper limit. O C. The machine is operating properly because the interval contains the target. D. There is not enough information to make a conclusion.
The machine is operating properly because the interval contains the target.
Option (C) is the correct one.
Given, A machine that is programmed to package 1.20 pounds of cereal is being tested for its accuracy in a sample of 36 cereal boxes, the sample mean filling weight is calculated as 1.22 pounds.
the mean is 1.22 pounds the confidence level is 95%.
standard deviation = 0.06 pounds.
The critical value we will use is (1.22 - 0.06 , 1.22 + 0.06) when, the mean is 1.22.
As, the interval contains the target.
Hence, the machine is operating properly because the interval contains the target with 95% confidence.
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an urn contains two blue balls (denoted b1 and b2) and three white balls (denoted w1,w2, and w3). one ball is drawn, its color is recorded, and it is replaced in the urn. then another ball is drawn and its color is recorded. a. let b1w2 denote the outcome that the first ball drawn is b1 and the second ball drawn is w2. because the first ball is replaced before the second ball is drawn, the outcomes of the experiment are equally likely. the total number of possible outcomes of the experiment is b. consider the event that the first ball that is drawn is blue. what is the probability of the event? probability
(a) The total number of possible outcomes of the experiment is 25 outcomes .
(b) The probability of the event that the first ball drawn is blue is 2/5 .
In the question ,
it is given that ,
the number of blue balls in the urn = 2 ( b1 and b2)
the number of white balls in the urn = 3 (w1 , w2 and w3)
also given that ,
one ball is drawn, its color is recorded and is replaced in urn. then another ball is drawn and the color is recorded .
Part(a) ,
the total number of possible outcomes for experiment will be
b1b1, b1b2, b1w1, b1w2, b1w3
b2b1, b2b2, b2w1, b2w2, b2w3
w1b1, w1b2, w1w1, w1w2, w1w2
w2b1, w2b2, w2w1, w2w2, w2w3
w3b1, w3b2, w3w1, w3w2, w3w3 .
So , total number of outcomes is = 25 .
Part(b) ,
From Part(a) , we can see that the outcomes with first ball blue are
b1b1, b1b2, b1w1, b1w2, b1w3
b2b1, b2b2, b2w1, b2w2, b2w3,
the number of outcomes with first ball blue is = 10 .
So , the probability = (number of outcomes with first ball blue)/(total number of outcomes) .
= 10/25
= 2/5 .
Therefore , total number of outcomes is 25 and the probability that first ball is blue is 2/5 .
The given question is incomplete , the complete question is
An urn contains two blue balls (denoted b1 and b2) and three white balls (denoted w1,w2, and w3). one ball is drawn, its color is recorded, and it is replaced in the urn. then another ball is drawn and its color is recorded.
(a) let b1w2 denote the outcome that the first ball drawn is b1 and the second ball drawn is w2. because the first ball is replaced before the second ball is drawn, the outcomes of the experiment are equally likely. the total number of possible outcomes of the experiment is .
(b) consider the event that the first ball that is drawn is blue. what is the probability of the event ?
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BBQ Corp. had a 3:1 stock split ratio. Pre-split the company had 1.35 Million outstanding shares at a price of $72.45 per share.
What is the post-split market capitalization of BBQ corp.?
The pre-split market capitalization of BBQ corp. is $24,451,875.
Given that, BBQ Corp. had a 3:1 stock split ratio. Pre-split the company had 1.35 Million outstanding shares at a price of $72.45 per share.
What is the ratio?
The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Here, 3+1=4
Now, 1/4 × 1350000
= 337500 shares
So, capitalization is 337500×72.45
= $24,451,875
Therefore, the pre-split market capitalization of BBQ corp. is $24,451,875.
One difficulty in measuring the nesting success of birds is that the researchers must count the number of eggs in the nest, which is disturbing to the parents. Even though the researcher does not harm the birds, the flight of the bird might alert predators to the presence of a nest. To see if researcher activity might degrade nesting success, the nest survival of 102 nests that had their eggs counted, was recorded. Sixty-four of the nests failed (i.e. the parent abandoned the nest.) Assuming that it is reasonable to regard the 102 nests in the sample as representative of the population of nests for which the eggs have been counted, construct and interpret a 95% confidence interval for the proportion of nests that have eggs counted that are then abandoned. (0.5336, 0.7213) (0.5136, 0.7113) (0.5436, 0.7313) None of these
A 95% confidence interval for population proportion p is (0.5336, 0.7213).
Given,
One difficulty in measuring the nesting success of birds is that the researchers must count the number of eggs in the nest, which is disturbing to the parents. Even though the researcher does not harm the birds, the flight of the bird might alert predators to the presence of a nest. To see if researcher activity might degrade nesting success, the nest survival of 102 nests that had their eggs counted, was recorded. Sixty-four of the nests failed (i.e. the parent abandoned the nest.)
To find,
Assuming that it is reasonable to regard the 102 nests in the sample as representative of the population of nests for which the eggs have been counted, construct and interpret a 95% confidence interval for the proportion of nests that have eggs counted that are then abandoned;
n = 102
x = 64
Point estimate = sample proportion = [tex]\hat p[/tex] = x / n = 64/102 =0.627
1 - [tex]\hat p[/tex] = 1 - 0.627 = 0.373
[tex]Z\alpha/2[/tex] = 1.96
The margin of error = E
[tex]= Z\alpha / 2 * \sqrt((\hat p * (1 - \hat p)) / n) = 1.96 * (\sqrt(0.627*(0.373) /102 ) = 0.0934[/tex]
A 95% confidence interval for population proportion p is;
[tex]\hat p[/tex] - E < p < [tex]\hat p[/tex] + E
0.627 - 0.0934 < p < 0.627 + 0.0934
0.5336 < p < 0.7213
(0.5336, 0.7213)
Hence, a 95% confidence interval for population proportion p is (0.5336, 0.7213).
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in hypothesis testing, which hypothesis can be either one-sided or two sided? group of answer choices
Alternative hypothesis may be one-sided or two-sided.
b) alternative hypothesis.
What is meant by an alternative hypothesis?In statistical hypothesis testing, the alternative hypothesis is one of the suggested propositions in the hypothesis test. In general, the purpose of a hypothesis test is to demonstrate that, under the given conditions, there is sufficient evidence to support the believability of an alternate hypothesis rather than the test's exclusive statement (null hypothesis). Because it is based on a review of the literature and previous studies, it is usually congruent with the research hypothesis. However, the research hypothesis is sometimes congruent with the null hypothesis.
In statistics, alternative hypotheses are frequently denoted as Hₐ or H₁. In a statistical hypothesis test, hypotheses are developed to be compared.
In the field of inferential statistics, two competing hypotheses can be compared using explanatory and predictive power.
This is the two tailed test .
alternative hypothesis is ,
Hₐ :μ≠
For the left tail is
Hₐ : μ<
For the right tail is
Hₐ : μ >
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The complete question is :
"In hypothesis testing, which hypothesis can be either one-sided or two sided?
Group of answer choices
a.) null hypothesis
b.) alternative hypothesis"
PERSEVERE If three points a, b, and c lie on the same line, then b is between a and c if and only if
the distance from a to c is equal to the sum of the distances from a to b and from b to c. Write an
absolute value equation to represent the definition of betweenness.
An absolute value equation to represent the definition of betweenness will be;
⇒ B ∈ A,C ↔ AB +BC = AC
What is Absolute value equation?
An absolute value equation is a function that contains an algebraic expression within absolute value symbols.
Given,
There are three points a, b, and c lie on the same line, then b is between a and c if and only if the distance from a to c is equal to the sum of the distances from a to b and from b to c.
Now,
We need to find the absolute value function for this statement as;
In order to find the absolute value equation,
First we have to identify the symbols for the terms mentioned in the statement as;
Between = ∈
If and only if = ↔
Now, We have to divide the statement as two parts as;
First one is,
"c lie on the same line, then b is between a and c"
It can be written as,
⇒ B ∈ A,C
Then the second part is, "the distance from a to c is equal to the sum of the distances from a to b and from b to c."
Which can be written as
⇒ AB + BC = AC
When we combine it,
Then we get the absolute value equation as,
⇒ B ∈ A,C ↔ AB +BC = AC
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α and β are the roots of the equation 2x² - 3x + 4 = 0. Find α+β
Answer:
Step-by-step explanation:
ans is in the attachment.
How do you solve the number of solutions to an equation?.
the number of solutions to an equation can be solved by either elimination method or substitution method or by factorization
If solving an equation yields a statement that is true for a single value for the variable, like x = 3, then the equation has one solution. If solving an equation yields a statement that is always true, like 3 = 3, then the equation has infinitely many solutions.
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Which pair of triangle can be proven congruent by SAS?.
SAS can be used to show that the first pair of triangles are congruent.
Refer to the attachment for image:
What is SAS postulate?
According to the SAS postulate, two triangles have been shown to be congruent if their two sides and included angles are equal to those of another triangle's two sides and included angle.
According to the SAS postulate, the first pair of triangles is said to be congruent because each triangle's included angle is equal to two sides the included angle of the other triangle.
In the second image, the ASA postulate—not SAS—determines that the pair of triangles is congruent.
Since there is no SSA rule, the pair of triangles in the third figure cannot be said to be congruent through any postulate or theorem.
The pair of triangles in the fourth figure are congruent according to SSS postulate rather than SAS.
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which of the following does not need to be known in order to compute the p-value? a. null hypothesis b. test statistic c. standard deviation d. significance level e. sample size
Significance level does not need to be known in order to compute the p-value. Hence, Option (D) is correct
How to compute p- value ?A p-value is a statistical measurement that is used to check a hypothesis against actual data.When the null hypothesis is assumed to be true, a p-value calculates the likelihood of getting the results that were observed.The statistical significance of the observed difference increases with decreasing p-value.Statistical significance is typically defined as a p-value of 0.05 or less.P-value can be used for hypothesis testing instead of or in addition to predetermined confidence levels.Significance level does not need to be known in order to compute the p-value.
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