Construct an inscribed circle in triangle PQR by finding the incenter of the triangle.
Answers
9514 1404 393
Explanation:
You need to know these construction techniques:
bisect an anglecreate a perpendicular through a point not on a line1. Bisect vertex angle P (as the problem statement tells you)
2. Bisect vertex angle R. This angle is chosen because it is the largest angle in the triangle. Any angle can be used, but the construction is likely to be more accurately done for larger angles.
3. The point where the angle bisectors cross is the incenter. Label that point A. It will be used as the "off-line point" for the next step.
4. Create a perpendicular to line PQ through the point A. PQ is chosen because it is the segment opposite the largest angle. This gives you the most room for the construction, so it can be done with best accuracy. Mark the the point of intersection of the perpendicular with PQ as point B.
5. Using AB as the radius, draw the incircle centered at A.
It would look something like this. I don't know if this helps or not.
Related Questions
People were surveyed worldwide, being asked the question "How important is acquiring wealth to you?" of 1500 respondents in country A, 1185 said that it was of more than average importance. In country B, of 1302 respondents, 613 said it was of more than average importance.
1) (Round to three decimal places as needed):
a. The sample proportions for country A are: ___
b. The sample proportions for country B are: ___
2) What is the confidence interval for country A? Select the correct choice below and, if necessary, fill in the answer boxes within your choice.
a. The 90% confidence interval for country A is (__%, ___%) [Round to one decimal place as needed.]
b. The conditions for constructing a confidence interval are not satisfied.
3) Compare to the confidence interval for country B. Choose the correct answer below.
a. It is not possible to make a comparaison because the conditions for creating a confidence interval are not satisfied.
b. It appears that the proportion of adults who feel this way in country A is more than those in country B.
c. It appears that the proportion of adults who feel this way in country A is about the same as those in country B.
d. it appears that the proportion of adults who feel this way in country B is more than those in country A.
Answers
Answer:
1) A = 0.79
B = 0.4708
2) CI = (0.7728, 0.8072)
3) CI = (0.4481, 0.4935)
b. It appears that the proportion of adults who feel this way in country A is more than those in country B.
Step-by-step explanation:
1) Sample proportions for both Population A and B
For country A:
Sample size,n = 1500
Sample proportion = [tex] \frac{1185}{1500} = 0.79 [/tex]
For Country B:
Sample size,n = 1302
Sample proportion = [tex] \frac{613}{1302} = 0.4708 [/tex]
2) Confidence interval for country A:
Given:
Mean,x = 1185
Sample size = 1500
Sample proportion, p = 0.79
q = 1 - 0.79 = 0.21
Using z table,
90% confidence interval, [tex] Z _\alpha /2 = 1.64 [/tex]
Confidence interval, CI:
[tex] \frac{p +/- Z_\alpha_/2}{\sqrt{(p * q)/n}} [/tex]
[tex] = \frac{0.79 - 1.64}{\sqrt{(0.79 * 0.21)/1500}}, \frac{0.79 + 1.64}{\sqrt{(0.79 * 0.21)/1500}} [/tex]
[tex] CI = (0.7728, 0.8072) [/tex]
3) Confidence interval for country A:
Given:
Mean,x = 613
Sample size = 1302
Sample proportion, p = 0.4708
q = 1 - 0.4708 = 0.5292
Using z table,
90% confidence interval, [tex] Z _\alpha /2 = 1.64 [/tex]
Confidence interval, CI:
[tex] \frac{p +/- Z_\alpha_/2}{\sqrt{(p * q)/n}} [/tex]
[tex] = \frac{0.4708 - 1.64}{\sqrt{(0.4708 * 0.5292)/1302}}, \frac{0.4708 + 1.64}{\sqrt{(0.4708 * 0.5295)/1302}} [/tex]
[tex] CI = (0.4481, 0.4935) [/tex]
From both confidence interval, we could see that that the proportion of adults who feel this way in country A is more than those in country B.
Option B is correct.
if cos theta < 0 and cot theta > 0, then the terminal point determined by theta is in:
A. Quadrant 1
B. Quadrant 3
C. Quadrant 4
D. Quadrant 2
please help me !
Answers
Answer:
If cosine theta < 0 and cotangent theta > 0, then the terminal point determined by theta is in: quadrant 3.
Step-by-step explanation:
hope this helps you :) my answer is the Step-by-step explanation: and the answer :)
Considering the signals of the sine and the cosine of the trigonometric function, it is found that it's quadrant is given by:
B. Quadrant 3
What are the signals of the sine and the cosine in each quadrant?Q1: cos > 0, sin > 0.Q2: cos < 0, sin > 0.Q3: cos < 0, sin <0.Q4: cos > 0, sin < 0.In this problem, we have that the cosine is negative, and the cotangent is positive. Cotangent is cosine divided by sine, hence if it is positive, both cosine and sine have the same signal, since cos < 0, sine is negative, they are in third quadrant and option B is correct.
More can be learned about the quadrants of trigonometric functions at https://brainly.com/question/24551149
#SPJ2
The table shows some values of x and y that satisfy the equation y = acosxº + b
Х
0
30
180
60
90
120
150
y
10
4 + 373
7
4
1
4-373
-2
Find the value of y when x = 45
Answers
Answer:
Y = 3√2 +4
Step-by-step explanation:
y = acosxº + b
Let's look for the values of a and b first.
Let's get values of x and y and solve simultaneously
When x= 0 ,y=10
When x = 120, y= 1
10 =acos0 + b
10 = a +b..... equation 1
1 = acos120 + b
1= -0.5a + b ..... equation 2
10 = a +b
1= -0.5a + b
10-1= a +0.5a
9 = 1.5a
9/1.5 = a
6 = a
1= -0.5a + b ..... equation 2
1 = -0.5(6) +b
1= -3 + b
1+3 = b
4 =b
So
y = acosxº + b equal to
Y = 6cosx° + 4
So value of y when x= 45 is
Y= 6cos45° +4
Y =6(√2/2) +4
Y = 3√2 +4
The value of y when x = 45 degree is, [tex]y=3\sqrt{2}+4[/tex]
Given function is,
[tex]y = a cos(x)+ b[/tex]
From given table, It is observed that,
x = 0, y = 10 and x = 90, y = 4
Substitute above values in above equation.
[tex]a+b=10\\\\b=4[/tex]
[tex]a=10-b=10-4=6[/tex]
Now, our equation become,
[tex]y = 6 cos(x)+ 4[/tex]
Substitute x = 45 in above equation.
[tex]y=6cos(45)+4\\\\y=6*(\frac{\sqrt{2} }{2} )+4\\\\y=3\sqrt{2} +4[/tex]
Learn more:
https://brainly.com/question/13729598
Which statement represents a true conclusion, based on the Venn diagram? All real numbers are even numbers. All numbers that are multiples of three are even numbers. Some numbers that are multiples of three are also even numbers. No numbers that are multiples of three are also even numbers.
Answers
Answer:
Some number that are multiples of three are also even numbers
Step-by-step explanation:
In the picture
The statement represents a true conclusion, based on the Venn diagram is option A) Some numbers that are multiples of three are also even numbers
What are real numbers?The numbers which are not imaginary and can be quantified are real numbers.Real numbers can be positive or negative, and include the number zero. Imaginary numbers are numbers that cannot be quantified, like the square root of -1-2,-1.1 etc.What are even numbers?They are whole numbers that can be be divided by two into two equal value. examples 2,4,6,8 etc.
According to the question:-
A) All real numbers are even numbers.
B) All numbers that are multiples of three are even numbers.
C) Some numbers that are multiples of three are also even numbers
D) No numbers that are multiples of three are also even numbers.
OPTION C is the answer of the given question example 4*3,6*3 etc.
Learn more about whole numbers here: https://brainly.com/question/461046
#SPJ2
convert 0.34285714285 into an improper fraction
Answers
Answer:
34285714285/100000000000
Step-by-step explanation:
To write 0.34285714285 as a fraction you have to write 0.34285714285 as the numerator and put 1 as the denominator. Now you multiply the numerator and denominator by a number that makes the numerator to a whole number.
And finally, we have:
0.34285714285 as a fraction equals 34285714285/100000000000
Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. (Assume that n begins with 1.) 1, 1 3 , 1 5 , 1 7 , 1 9 , ...
Answers
Answer:
The general term for the sequence can be given by the following formula:
[tex]a_n=2\,n+9[/tex]
Step-by-step explanation:
If the sequence you typed starts with first term 11 and continues with terms 13, 15, 17, 19, We understand that the sequence is formed by adding 2 units to the previous term. So we are in the case of an arithmetic sequence with constant difference (d) = 2, and with first term 11.
Therefore, the nth term of this arithmetic sequence can be expressed by using the general form for an arithmetic sequence as:
[tex]a_n=a_1\,+\,(n-1)\,d\\a_n=11\,+\,(n-1)\,2\\a_n=11+2\,n-2\\a_n=2\,n+9[/tex]
In the questions below nine people (Ann, Ben, Cal, Dot, Ed, Fran, Gail, Hal, and Ida) are in a room. Five of them stand in a row for a picture. In how many ways can this be done if a) Ben is to be in the picture? b) Both Ed and Gail are in the picture? 4200 c) Neither Ed nor Fran are in the picture? 5040 d) Dot is on the left end and Ed is on the right end? 210 e) Hal or Ida (but not both) are in the picture? 4200 f) Ed and Gail are in the picture, standing next to each other? 960 g) Ann and Ben are in the picture, but not standing next to each other?
Answers
Answer:
Step-by-step explanation:
Ben is present in all pictures so rest of 4 persons to be selected from 8 persons , no of ways to do it is
⁸C₄ = 8 x 7 x 6 x 5 / 4 x 3 x 2 x 1
= 70 .
In one of these combination , we can get 5 ! ( five factorial )
Total no of permutations
= 70 x 5 !
= 8400 .
b ) Both Ed and Gail are present
The above derivation changes to the following .
Total no of permutations
= ⁷C₃ x 5 !
= 35 x 120
= 4200
c )
exclude 2 person from 9 to be selected
permutation
= ⁷C₅ x 5 !
= 21 x 120
= 2520
d )
rest of 3 person from 7 persons , no of permutations
⁷P₃ = 7 x 6 x 5 = 210
e )
Hal or Ida can occupy any of the 5 position which can be done in 5 ways .
when one position is occupied , the rest of 4 position can be occupied by 7 persons which can be done in
⁷P₄ ways
Total ways = 5 x ⁷P₄
= 5 x 840
= 4200
f )
They can occupy position like 1,2 or 2,3 or 3,4 or 4,5
Rest of the position can be occupied in ⁷P₃ ways
Total ways = 4 x ⁷P₃
= 4 x 210
= 840
They can also be exchanged mutually so no of ways
= 840 x 2 = 1680 .
g ) No of pictures in which Ann and Ben are present
two position to be selected out of 5 = ⁵P₂
Rest of position that can be shuffled = ⁷P₃
Total no of pictures in which both are present
= ⁵P₂ x ⁷P₃
= 20 x 210
= 4200
out of which they will be standing next to each other = 1680
no of pictures in which they will not be standing next to each other
= 4200 - 1680 = 2520. .
A basketball coach is looking over the possessions per game during last season. Assume that the possessions per game follows an unknown distribution with a mean of 56 points and a standard deviation of 12 points. The basketball coach believes it is unusual to score less than 50 points per game. To test this, she randomly selects 36 games. Use a calculator to find the probability that the sample mean is less than 50 points. Round your answer to three decimal places if necessary.
Answers
Answer:
The probability that the sample mean is less than 50 points = 0.002
Step-by-step explanation:
Step(i):-
Given mean of the normal distribution = 56 points
Given standard deviation of the normal distribution = 12 points
Random sample size 'n' = 36 games
Step(ii):-
Let x⁻ be the random variable of normal distribution
Let x⁻ = 50
[tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{50-56 }{\frac{12}{\sqrt{36} } }= -3[/tex]
The probability that the sample mean is less than 50 points
P( x⁻≤ 50) = P( Z≤-3)
= 0.5 - P(-3 <z<0)
= 0.5 -P(0<z<3)
= 0.5 - 0.498
= 0.002
Final answer:-
The probability that the sample mean is less than 50 points = 0.002
Answer:
56
2
.001
Step-by-step explanation:
The Central Limit Theorem for Means states that the mean of any sampling distribution of the means is equal to the mean of the population distribution. The standard deviation is equal to the standard deviation of the population divided by the square root of the sample size. So, the mean of this sampling distribution of the means with sample size 36 is 56 points and the standard deviation is 1236√=2 points. The z-score for 50 using the formula z=x¯¯¯−μσ is −3.
z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
-3.0 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001
-2.9 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.001 0.001 0.001
-2.8 0.003 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002
-2.7 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003
-2.6 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004
-2.5 0.006 0.006 0.006 0.006 0.006 0.005 0.005 0.005 0.005 0.005
Using the Standard Normal Table, the area to the left of −3 is approximately 0.001. Therefore, the probability that the sample mean will be less than 50 points is approximately 0.001.
Let x1 = 12, y1 = 15, and y2 = 3. Let y vary inversely with x. Find x2.
Answers
Answer:
x2 = 60
Step-by-step explanation:
If the variables x and y are inversely proportional, the product x * y is a constant.
So using x1 and y1 we can find the value of this constant:
[tex]x1 * y1 = k[/tex]
[tex]12 * 15 = k[/tex]
[tex]k = 180[/tex]
Now, we can use the same constant to find x2:
[tex]x2 * y2 = k[/tex]
[tex]x2 * 3 = 180[/tex]
[tex]x2 = 180 / 3 = 60[/tex]
So the value of x2 is 60.
Find f(x) - g(x) when f(x) = 2x^2 - 4x g(x) = x^2 + 6x
3x^2
x^2 + 2x
x^2 - 10x
3x^2 + 2x
Answers
Answer:
x^2 - 10x
Step-by-step explanation:
2x^2 - 4x - x^2 +6x
You subtract x^2 from 2x^2 and you get x^2
Then you add 6x and 4x together and get 10x
So then you have x^2 - 10x
(plus I took the test and this was the correct answer.)
An economist at Vanderbilt University devised a study to compare different types of online auctions. In one experiment he compared a Dutch auction to a first-place sealed bid auction. In the Dutch auction the item for sale starts at a very high price and is lowered gradually until someone finds the price low enough to buy. In the first-price sealed bid auction each bidder submits a single sealed bid before a particular deadline. After the deadline, the person with the highest bid wins. The researcher auctioned off collectible trading cards from the game Magic: The Gathering. He placed pairs of identical cards up for auction; one would go into Dutch auction and the other to the first-price sealed bid auction. He then looked at the difference in the prices he received on the pair. He repeated this for a total of 88 pairs.
[a] Explained why the data should be analyzed using paired samples as opposed to two independent samples.
[b] What makes a pair?
[c] What is the explanatory variable? Is it categorical or quantitative?
[d] What is the response variable? Is it categorical or quantitative?
[e] State the relevant hypotheses in words:
Null hypothesis:
Alternative hypothesis:
[f] Define the parameter of interest and give the symbol that should be assigned to it.
[g] State the relevant hypotheses in symbols (using a parameter):
Null hypothesis:
Alternative hypothesis:
[h] Assume the p-value is 0.17 (write a conclusion).
Answers
Answer:
Step-by-step explanation:
a. The data should be analyzed using paired samples because the economist made two measurements (samples) drawn from the same pair of identical cards. Each data point in one sample is uniquely paired to a data point in the second sample.
b. A pair is made up of two identical cards where one would go into Dutch auction and the other to the first-price sealed bid auction.
c. The explanatory variables are the types of online auction which are the Dutch auction and the first price sealed bid auction. The explanation variable here is categorical: the Dutch auction and the first price sealed bid auction.
d. The response variable which is also known as the outcome variable is prices for the 2 different auction for each pair of identical cards. This variable is quantitative.
e. Null Hypothesis in words: There is no difference in the prices obtained in the two different online auction.
Alternative hypothesis: There is a difference in the prices obtained in the two different online auction.
f. The parameter of interest in this case is the mean prices of pairs of identical cards for both auction and is assigned p.
g. Null hypothesis: p(dutch) = p(first-price sealed auction)
Alternative hypothesis: p(dutch) =/ p(first-price sealed auction)
h. Assuming the p-value is 0.17 at an assed standard 0.05 significance level, our conclusion would be to fail to reject the null hypothesis as 0.17 is greater than 0.05 or even 0.01 and we can conclude that, there is no statistically significant evidence to prove that there is a difference in the prices obtained in the two different online auction.
An insurance company examines its pool of auto insurance customers and gathers the following information: (i) All customers insure at least one car. (ii) 70% of the customers insure more than one car. (iii) 20% of the customers insure a sports car. (iv) Of those customers who insure more than one car, 15% insure a sports car. Calculate the probability that a randomly se
Answers
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
An insurance company examines its pool of auto insurance customers and gathers the following information: (i) All customers insure at least one car. (ii) 70% of the customers insure more than one car. (iii) 20% of the customers insure a sports car. (iv) Of those customers who insure more than one car, 15% insure a sports car. Calculate the probability that a randomly selected customer insures exactly one car, and that car is not a sports car?
Answer:
P( X' ∩ Y' ) = 0.205
Step-by-step explanation:
Let X is the event that the customer insures more than one car.
Let X' is the event that the customer insures exactly one car.
Let Y is the event that customer insures a sport car.
Let Y' is the event that customer insures not a sport car.
From the given information we have
70% of customers insure more than one car.
P(X) = 0.70
20% of customers insure a sports car.
P(Y) = 0.20
Of those customers who insure more than one car, 15% insure a sports car.
P(Y | X) = 0.15
We want to find out the probability that a randomly selected customer insures exactly one car, and that car is not a sports car.
P( X' ∩ Y' ) = ?
Which can be found by
P( X' ∩ Y' ) = 1 - P( X ∪ Y )
From the rules of probability we know that,
P( X ∪ Y ) = P(X) + P(Y) - P( X ∩ Y ) (Additive Law)
First, we have to find out P( X ∩ Y )
From the rules of probability we know that,
P( X ∩ Y ) = P(Y | X) × P(X) (Multiplicative law)
P( X ∩ Y ) = 0.15 × 0.70
P( X ∩ Y ) = 0.105
So,
P( X ∪ Y ) = P(X) + P(Y) - P( X ∩ Y )
P( X ∪ Y ) = 0.70 + 0.20 - 0.105
P( X ∪ Y ) = 0.795
Finally,
P( X' ∩ Y' ) = 1 - P( X ∪ Y )
P( X' ∩ Y' ) = 1 - 0.795
P( X' ∩ Y' ) = 0.205
Therefore, there is 0.205 probability that a randomly selected customer insures exactly one car, and that car is not a sports car.
what solid 3D object is produced by rotating the triangle about line m with a height of 8 and radius 4
Answers
Answer:
The diagram of the question is missing, I found a matching diagram, and it is attached to this answer
The 3D object produced is a cone with height 8 and diameter 8 (radius 4)
Step-by-step explanation:
A 3 dimensional solid figure can be formed when a 2 dimensional object is rotated about a line without displacing the object.
when the object in the diagram is rotated about line m, the rotation forms an object with a circular base of diameter 8 units (radius 4) from the base of the triangle and height 8 units, and the 3D object formed is called a cone.
The pie chart to the right shows how adults rate their financial shape. Suppose 4 people are chosen at random from a group of 1400. What is the probability that all four would rate their financial shape as excellent? (Make the assumption that the 1400 people are represented by the pie chart.)
Answers
Question Completion
PIE CHART NUMBERS:
Excellent 9% Good 41% Fair 36% Poor 13% Other 1%Answer:
0.000063
Step-by-step explanation:
Number of Respondents, n=1400
Probability that they would rate their financial shape as excellent = 0.09
Number of Those who would rate their financial shape as excellent
=0.09 X 1400
=126
Therefore:
The probability that 4 people chosen at random would rate their financial shape as excellent
[tex]=\dfrac{^{126}C_4 \times ^{1400-126}C_0}{^{1400}C_4} \\=\dfrac{^{126}C_4 \times ^{1274}C_0}{^{1400}C_4}\\=0.000063 $(correct to 6 decimal places)[/tex]
SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answers
Answer:
38 units
Step-by-step explanation:
We can find the perimeter of the shaded figure be finding out the number of unit lengths we have along the boundary of the given figure.
Thus, see attachment below for the number of units of each length of the figure that we have counted.
The perimeter of the figure = sum of all the lengths = 7 + 7 + 10 + 2 + 2 + 6 + 2 + 2 = 38
Perimeter of the shaded figure = 38 units
A triangular window has an area of 594 square meters. The base is 54 meters. What is the height?
Answers
Answer:
22 m
Step-by-step explanation:
Use the formula for the area of a triangle. Fill in the known values and solve for the unknown.
A = (1/2)bh
594 m^2 = (1/2)(54 m)h
h = (594 m^2)/(27 m) = 22 m
The height of the window is 22 meters.
What is the value of x to the nearest degree?
A.32
B.85
C.82
D.58
Answers
Answer:
m∠x ≈ 32°
Step-by-step explanation:
We can see that we have to use tan∅ to solve this (opposite over adjacent)
tan(x) = 7/11
x = tan^-1 (7/11)
x = 32.4712
Answer:
A.32
Step-by-step explanation:
tan(x) = 7/11
x = tan^-1 (7/11)
x = 32.4712
hey guys please help
Answers
Answer:
[tex]7.98 \:m[/tex]
Step-by-step explanation:
Area of a triangle is base times height divided by 2.
[tex]A= \frac{bh}{2}[/tex]
[tex]69.6= \frac{b \times 17.45}{2}[/tex]
[tex]69.6 \times 2= b \times 17.45[/tex]
[tex]139.2=b \times 17.45[/tex]
[tex]\frac{17.45b}{17.45}=\frac{139.2}{17.45}[/tex]
[tex]b=\frac{2784}{349}[/tex]
[tex]b=7.97707[/tex]
The appropriate unit is meters.
Answer:
7.98 m
Step-by-step explanation:
combine like terms to create an equivalent expression -1/2(-3y+10)
Answers
Answer:
3/2y - 5
Step-by-step explanation:
-1/2(-3y+10)
Expand the brackets.
-1/2(-3y) -1/2(10)
Multiply.
3/2y - 5
Answer:
[tex]= \frac{ 3y}{2} - 5 \\ [/tex]
Step-by-step explanation:
we know that,
[tex]( - ) \times ( - ) = ( + ) \\ ( - ) \times ( + ) = ( - )[/tex]
Let's solve now,
[tex] - \frac{1}{2} ( - 3y + 10) \\ \frac{3y}{2} - \frac{10}{2} \\ = \frac{ 3y}{2} - 5[/tex]
Determine if the expressions are equivalent.
when w = 11:
2w + 3 + 4 4 + 2w + 3
2(11) + 3 + 4 4 + 2(11) + 3
22 + 3 + 4 4 + 22 + 3
25 + 4 26 + 3
29 29
Complete the statements.
Answers
Answer:
Determine if the expressions are equivalent.
when w = 11:
2w + 3 + 4 4 + 2w + 3
2(11) + 3 + 4 4 + 2(11) + 3
22 + 3 + 4 4 + 22 + 3
25 + 4 26 + 3
29 29
Complete the statements.
Now, check another value for the variable.
When w = 2, the first expression is
11
.
When w = 2, the second expression is
11
.
Therefore, the expressions are
equivalent
.
Step-by-step explanation:
i did the math hope this helps
Answer:
Hii its Nat here to help! :)
Step-by-step explanation: A is 11 and b is 11.
C is Equal
Screenshot included.
A chi-square test for independence is being used to evaluate the relationship between two variables, one of which is classified into 3 categories and the second of which is classified into 4 categories. The chi-square statistic for this test would have df equal to ______.
Answers
Answer:
Degrees of freedom for independence in chi-square statistic
ν = ( r-1) (s-1) =6
Step-by-step explanation:
Explanation:-
Given data chi-square test for independence is being used to evaluate the relationship between two variables
Given "A" is classified into 3 categories
Second 'B' is classified into 4 categories
In this chi-square test, we test if two attributes A and B under consideration are independent or not
We will assume that
Null Hypothesis : H₀: The two variables are independent
Degrees of freedom in chi-square test for independence
ν = ( r-1) (s-1)
Given data 'r' = 3 and 's' = 4
Degrees of freedom for independence
ν = ( r-1) (s-1) = ( 3-1) ( 4-1) = 2×3 =6
Test statistic
χ ² = ∑ [tex]\frac{(O-E)^{2} }{E}[/tex]
This question is based on Chi-square test. Therefore, the chi-square statistic for this test would have df equal to [tex]X^{2} = \sum \dfrac{(O-E)^2}{E}[/tex].
Given:
Chi-square test for independence is being used to evaluate the relationship between two variables . Given "A" is classified into 3 categories . Second 'B' is classified into 4 categories
According to the question,
In this chi-square test, we would be test if two attributes A and B under consideration are independent or not.
Let assumed that, null Hypothesis : H₀: The two variables are independent
Now, degrees of freedom in chi-square test for independence is,
⇒ ν = ( r-1) (s-1)
It is given that, 'r' = 3 and 's' = 4.
Thus, degrees of freedom for independence is,
ν = ( r-1) (s-1) = ( 3-1) ( 4-1) = 2×3 =6
Therefore, test statistic be,
[tex]X^{2} = \sum \dfrac{(O-E)^2}{E}[/tex]
Therefore, the chi-square statistic for this test would have df equal to [tex]X^{2} = \sum \dfrac{(O-E)^2}{E}[/tex].
For more details, prefer this link:
https://brainly.com/question/23879950
Find the scale ratio for the map described below. 1 mm(map) equals 500 m (actual) The scale ratio is 1 to ? .
Answers
Answer:
1 : 500,000
Step-by-step explanation:
The scale of a map scale refers to the relationship (or ratio) between the distance on a map and the corresponding distance on the ground.
In the given map:
1 mm(map) = 500 m (actual)
1 meter = 1000 millimeter
Therefore:
500 meters = 1000 X 500 =500,000 millimeter
Therefore, the scale ratio of the map is:
1:500,000
Please answer this correctly
Answers
Answer:
1/2
Step-by-step explanation:
There is a 50/50 chance for the coin to land either heads or tails. Convert that to probability and it is 1/2.
The only time a coin would not be 50/50 chance is if the coin is weighted.
Answer:
1/2 is probability
becoz one side is head or one is tail
The period of a simple pendulum of length L feet is given by T=2πLg−−√~seconds. We assume that g, the acceleration due to gravity on the surface of the earth, is 32 feet per second per second. If the pendulum is that of a clock that keeps good time when L=4 feet, how much time will the clock gain in 24 hours if the length of the pendulum is decreased to 3.97 feet? (Use differentials and evaluate the necessary derivative at L=4 feet.)
Answers
Given that,
The acceleration due to gravity on the surface of the earth = 32 feet/s²
We need to calculate the time
Using formula of time period
[tex]T=2\pi\sqrt{\dfrac{l}{g}}[/tex]
On differentiating with respect to l
[tex]\dfrac{dT}{dL}=2\pi\times\dfrac{1}{2}(\dfrac{l}{g})^{-\frac{1}{2}}\times\dfrac{1}{g}[/tex]
[tex]\dfrac{dT}{dL}=\dfrac{\pi}{g}\times(\dfrac{g}{L})^{\frac{1}{2}}[/tex]
Put the value into the formula
[tex]\dfrac{dT}{dL}=\dfrac{\pi}{32}\times(\dfrac{32}{4})^{\frac{1}{2}}[/tex]
[tex]\dfrac{dT}{dL}=0.277\ sec[/tex]
If the length of the pendulum is decreased to 3.97 feet.
We need to calculate the time
Using formula of time period
[tex]\dfrac{dT'}{dL}=\dfrac{\pi}{g}\times(\dfrac{g}{L})^{\frac{1}{2}}[/tex]
Put the value into the formula
[tex]\dfrac{dT'}{dL}=\dfrac{\pi}{32}\times(\dfrac{32}{3.97})^{\frac{1}{2}}[/tex]
[tex]\dfrac{dT'}{dL}=0.278\ sec[/tex]
We need to calculate the gain time
Using formula for time
[tex]\dfrac{dT''}{dL}=\dfrac{dT'}{dL}-\dfrac{dT}{dL}[/tex]
Put the value into the formula
[tex]\dfrac{dT''}{dL}=0.278-0.277[/tex]
[tex]\dfrac{dT''}{dL}=0.001\ sec[/tex]
Hence, The clock gain the time in 24 hours is 0.001 sec.
plz help me divide and simplify
Answers
Answer:
Step-by-step explanation:
Given z = 4x – 6y, solve for y.
Answers
Answer:
Step-by-step explanation:
-6y+4x=z
-6y=z-4x
y=(z-4x)/-6
Answer:
[tex]y=\frac{z-4x}{-6}[/tex]
Step-by-step explanation:
A recent study conducted by a health statistics center found that 25% of households in a certain country had no landline service. This raises concerns about the accuracy of certain surveys, as they depend on random-digit dialing to houeholds via landlines. Pick five households form this country at random. Complete parts a) through c).
a) what is the probability that all five of them have a landline?
b) what is the probability that at least one of them does not have a landline?
c) what is the probability that at least one of them does have a landline?
Answers
Answer:
a) 23.73% probability that all five of them have a landline
b) 76.27% probability that at least one of them does not have a landline
c) 99.90% probability that at least one of them does have a landline
Step-by-step explanation:
For each household, there are only two possible outcomes. Either it has landline service, or it does not. The probability of a household having landline service is independent of other households. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
25% of households in a certain country had no landline service.
This means that 100-25 = 75% have, so [tex]p = 0.75[/tex]
Pick five households form this country at random.
This means that [tex]n = 5[/tex]
a) what is the probability that all five of them have a landline?
This is P(X = 5).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{5,5}.(0.75)^{5}.(0.25)^{0} = 0.2373[/tex]
23.73% probability that all five of them have a landline
b) what is the probability that at least one of them does not have a landline?
Either all have, or at least one does not have. The sum of the probabilities of these events is 100%.
From a), 23.73% probability that all five of them have a landline
100 - 23.73 = 76.27
76.27% probability that at least one of them does not have a landline
c) what is the probability that at least one of them does have a landline?
Either none have a landline, or at least one has. The sum of the probabilities of these events is 1. So
[tex]P(X = 0) + P(X \geq 1) = 1[/tex]
We want [tex]P(X \geq 1)[/tex]
Then
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.75)^{0}.(0.25)^{5} = 0.0010[/tex]
So
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0010 = 0.9990[/tex]
99.90% probability that at least one of them does have a landline
what are the formulas for right triangles
Answers
Answer:
The Pythagorean theorem is
a^2 + b^2 = c^2
where a and b are the lengths of the legs (the sides that form the right angle), and c is the length of the hypotenuse (the side opposite the right angle.)
Answer: Attached
Step-by-step explanation:
The sum of a number and its reciprocal is 41/20. Find the numbers. smaller value larger value
Answers
Answer:
The numbers are 5/4 and 4/5The smaller value is 4/5The larger value is 5/4Step-by-step explanation:
Let the number be x.
The reciprocal of the number will be 1/x
If the sum of the number and its reciprocal is 41/20, this can be represented as;
[tex]x+\frac{1}{x} = 41/20\\\frac{x^{2}+1}{x} = \frac{41}{20} \\20x^{2} +20 = 41x\\20x^{2} -41x+20 = 0\\[/tex]
Uisng the general formula to get x
x = -b±√b²+4ac/2a
x = 41±√41²-4(20)(20)/2(20)
x = 41±√1681-1600/40
x = 41±√81/40
x = 41±9/40
x = 50/40 or 32/40
x = 5/4 or 4/5
if the value is 5/4, the other value will be 4/5
The numbers are 5/4 and 4/5
The smaller value is 4/5
The larger value is 5/4
Answer:
a=5/4 or 4/5
Therefore, the smaller value = 4/5
The larger value = 5/4
Step-by-step explanation:
Let the number be represented by a
And it's reciprocal be represented by 1/a
So we have
a + 1/a = 41/20
Cross Multiply
20( a +1/a) = 41
20a +20/a =41
Find the LCM which is a
20a² + 20 = 41a
20a² + 20 - 41a =0
20a² - 41a +20 = 0
20a²-25a - 16a + 20 =0
5a(4a - 5) -4( 4a - 5) = 0
(5a - 4)(4a - 5) = 0
5a - 4 = 0
5a = 4
a = 4/5
or
4a - 5 = 0
4a =5
a = 5/4
Therefore, the number which is represented by a is
1) a = 4/5 while it's reciprocal which is 1/a is 5/4
or
2) a = 5/4 which it's reciprocal which is 1/a = 4/5
Therefore, the smaller value = 4/5
The larger value = 5/4
Elsa is framing some photos. If she has three frames and put two photos each frame, what fraction shows one photo
Answers
Answer:
1/6Step-by-step explanation:
Number of frames =3 frames
If each frames contain 2 photos, the total number of photos in all the 3 frames will be 3*2 = 6photos
Since we have 6 photos in total, the fraction that shows one photo will be ratio of one out of the six photos and this is represented as 1/6