Answer:
1.3859
Step-by-step explanation:
The formula for Margin of Error is given as:
Margin of Error = Critical value × Standard Error
Critical value = z score
In the question, we are given a confidence interval of 95%.
Z score for a 95% confidence level is given as: 1.96
Hence, critical value = 1.96
Standard Error = σ / √n
Where n = number of samples = 98 chicken eggs
σ = Standard deviation = 7 milligrams
Standard Error = 7/√98
Standard Error = 0.7071067812
Hence, Margin of Error = Critical value × Standard Error
Margin of Error = 1.96 × 0.7071067812
Margin of Error = 1.3859292911
Therefore, the margin of error corresponding to a 95% confidence interval for the true mean cholesterol content, μ, of all such eggs is approximately 1.3859
Which equation will solve the following word problem? Jared has 13 cases of soda. He has 468 cans of soda. How many cans of soda are in each case? 13(468) = c 468c = 13 468/13 = c 13 = c/468
Answer:
c = 468 / 13
Step-by-step explanation:
If c is the number of cans of soda in each case, we know that the number of cans in 13 cases is 13 * c = 13c, and since the number of cans in 13 cases is 468 and we know that "is" denotes that we need to use the "=" sign, the equation is 13c = 468. To get rid of the 13, we need to divide both sides of the equation by 13 because division is the opposite of multiplication, therefore the answer is c = 468 / 13.
Answer:
468/13 = c
Step-by-step explanation: Further explanation :
[tex]13 \:cases = 468\:cans\\1 \:case\:\:\:\:= c\: cans\\Cross\:Multiply \\\\13x = 468\\\\\frac{13x}{13} = \frac{468}{13} \\\\c = 36\: cans[/tex]
2⁶ × 2⁵ how do i simplify this?
Answer:
2^11
Step-by-step explanation:
since the bases are the same, we can add the exponents
a^b * a^c = a^(b+c)
2^6 * 2^5
2^(6+5)
2^11
For the regression equation, Ŷ = +20X + 200 what can be determined about the correlation between X and Y?
Answer:
There is a positive correlation between X and Y.
Step-by-step explanation:
The estimated regression equation is:
[tex]\hat Y=20X+200[/tex]
The general form of a regression equation is:
[tex]\hat Y=b_{yx}X+a[/tex]
Here, [tex]b_{yx}[/tex] is the slope of a line of Y on X.
The formula of slope is:
[tex]b_{yx}=r(X,Y)\cdot \frac{\sigma_{y}}{\sigma_{x}}[/tex]
Here r (X, Y) is the correlation coefficient between X and Y.
The correlation coefficient is directly related to the slope.
And since the standard deviations are always positive, the sign of the slope is dependent upon the sign of the correlation coefficient.
Here the slope is positive.
This implies that the correlation coefficient must have been a positive values.
Thus, it can be concluded that there is a positive correlation between X and Y.
Which relationships have the same constant of proportionality between y and x as the equation 3y=2x? SELECT 3 ANSWERS
*Correct Question:
Which relationships have the same constant of proportionality between y and x as the equation 3y=27x?
Answer:
A, B, C
Step-by-step explanation:
Given that [tex] 3y = 27x [/tex] , we can simplify to get a proportionality statement that exists between X and y. Thus
[tex] 3y = 27x [/tex]
Divide both sides by 3
[tex] \frac{3y}{3} = \frac{27x}{3} [/tex]
[tex] y = 9x [/tex]
Thus, we can say, y would always be 9 times the quantity of x.
From the options given, examine which options have this proportionality statement as well.
Option A, y = 9x is same as the statement.
Option B, 2y = 18x, conforms to the same statement. If we simply further, we would have y = 9x
Option C, the graph shows that when x = 1, y = 9. This also confirms to the same constant of proportionality in the given equation.
Option D and E do not have same constant of proportionality.
The right options are A, B, and C.
A bag contains two six-sided dice: one red, one green. The red die has faces numbered 1, 2, 3, 4, 5, and 6. The green die has faces numbered 1, 2, 3, 4, 4, and 4. A die is selected at random and rolled four times. You are told that two rolls were 1's and two were 4's. Find the probability the die chosen was green.
Answer:
the probability the die chosen was green is 0.9
Step-by-step explanation:
Given that:
A bag contains two six-sided dice: one red, one green.
The red die has faces numbered 1, 2, 3, 4, 5, and 6.
The green die has faces numbered 1, 2, 3, 4, 4, and 4.
From above, the probability of obtaining 4 in a single throw of a fair die is:
P (4 | red dice) = [tex]\dfrac{1}{6}[/tex]
P (4 | green dice) = [tex]\dfrac{3}{6}[/tex] =[tex]\dfrac{1}{2}[/tex]
A die is selected at random and rolled four times.
As the die is selected randomly; the probability of the first die must be equal to the probability of the second die = [tex]\dfrac{1}{2}[/tex]
The probability of two 1's and two 4's in the first dice can be calculated as:
= [tex]\begin {pmatrix} \left \begin{array}{c}4\\2\\ \end{array} \right \end {pmatrix} \times \begin {pmatrix} \dfrac{1}{6} \end {pmatrix} ^4[/tex]
= [tex]\dfrac{4!}{2!(4-2)!} ( \dfrac{1}{6})^4[/tex]
= [tex]\dfrac{4!}{2!(2)!} \times ( \dfrac{1}{6})^4[/tex]
= [tex]6 \times ( \dfrac{1}{6})^4[/tex]
= [tex](\dfrac{1}{6})^3[/tex]
= [tex]\dfrac{1}{216}[/tex]
The probability of two 1's and two 4's in the second dice can be calculated as:
= [tex]\begin {pmatrix} \left \begin{array}{c}4\\2\\ \end{array} \right \end {pmatrix} \times \begin {pmatrix} \dfrac{1}{6} \end {pmatrix} ^2 \times \begin {pmatrix} \dfrac{3}{6} \end {pmatrix} ^2[/tex]
= [tex]\dfrac{4!}{2!(2)!} \times ( \dfrac{1}{6})^2 \times ( \dfrac{3}{6})^2[/tex]
= [tex]6 \times ( \dfrac{1}{6})^2 \times ( \dfrac{3}{6})^2[/tex]
= [tex]( \dfrac{1}{6}) \times ( \dfrac{3}{6})^2[/tex]
= [tex]\dfrac{9}{216}[/tex]
∴
The probability of two 1's and two 4's in both dies = P( two 1s and two 4s | first dice ) P( first dice ) + P( two 1s and two 4s | second dice ) P( second dice )
The probability of two 1's and two 4's in both die = [tex]\dfrac{1}{216} \times \dfrac{1}{2} + \dfrac{9}{216} \times \dfrac{1}{2}[/tex]
The probability of two 1's and two 4's in both die = [tex]\dfrac{1}{432} + \dfrac{1}{48}[/tex]
The probability of two 1's and two 4's in both die = [tex]\dfrac{5}{216}[/tex]
By applying Bayes Theorem; the probability that the die was green can be calculated as:
P(second die (green) | two 1's and two 4's ) = The probability of two 1's and two 4's | second dice)P (second die) ÷ P(two 1's and two 4's in both die)
P(second die (green) | two 1's and two 4's ) = [tex]\dfrac{\dfrac{1}{2} \times \dfrac{9}{216}}{\dfrac{5}{216}}[/tex]
P(second die (green) | two 1's and two 4's ) = [tex]\dfrac{0.5 \times 0.04166666667}{0.02314814815}[/tex]
P(second die (green) | two 1's and two 4's ) = 0.9
Thus; the probability the die chosen was green is 0.9
hich statement best describes the domain and range of p(x) = 6–x and q(x) = 6x? p(x) and q(x) have the same domain and the same range. p(x) and q(x) have the same domain but different ranges. p(x) and q(x) have different domains but the same range. p(x) and q(x) have different domains and different ranges.
Answer:
[tex]p(x)[/tex] and [tex]q(x)[/tex] have the same domain and the same range.
Step-by-step explanation:
[tex]p(x) = 6-x[/tex] and
[tex]q(x) = 6x[/tex]
First of all, let us have a look at the definition of domain and range.
Domain of a function [tex]y =f(x)[/tex] is the set of input value i.e. the value of [tex]x[/tex] for which the function [tex]f(x)[/tex] is defined.
Range of a function [tex]y =f(x)[/tex] is the set of output value i.e. the value of [tex]y[/tex] or [tex]f(x)[/tex] for the values of [tex]x[/tex] in the domain.
Now, let us consider the given functions one by one:
[tex]p(x) = 6-x[/tex]
Let us sketch the graph of given function.
Please find attached graph.
There are no values of [tex]x[/tex] for which p(x) is not defined so domain is All real numbers.
So, domain is [tex](-\infty, \infty)[/tex] or [tex]x\in R[/tex]
Its range is also All Real Numbers
So, Range is [tex](-\infty, \infty)[/tex] or [tex]x\in R[/tex]
[tex]q(x) = 6x[/tex]
Let us sketch the graph of given function.
Please find attached graph.
There are no values of [tex]x[/tex] for which [tex]q(x)[/tex] is not defined so domain is All real numbers.
So, domain is [tex](-\infty, \infty)[/tex] or [tex]x\in R[/tex]
Its range is also All Real Numbers
So, Range is [tex](-\infty, \infty)[/tex] or [tex]x\in R[/tex]
Hence, the correct answer is:
[tex]p(x)[/tex] and [tex]q(x)[/tex] have the same domain and the same range.
What is the area of the house (including the drawing room, TV room, balcony, hallway, kitchen and bedroom)?
Answer:
The area of the house is A. 1,108
if z and (z+50) are supplement of each other find the value of z
Answer:
z=65
Step-by-step explanation:
supplementary angles means sum of those angles is 180 degrees
so,
z+z+50=180
2z=130
z=65
I did the best I could, I'm 12 don't judge me.
identify the decimals labeled with the letters A, B, and C on the scale below. Letter A represents the decimal Letter B represents the decimal Letter C represents the decimal
[tex]10[/tex] divisions between $20$ and $20.1$ so each division is $\frac{20.1-20.0}{10}=0.01$
A is 2nd division from $20.0$, so, A is $20.0+2\times 0.01=20.02$
similarly, C is one division behind $20.0$ so it is 19.99
and B is $20.14$
bananas cost $4 and apples close 0.60$ each if b represents the number of bunches of bananas and a represents the number of apple which of the following expressions represents the total cost? 1 4.60(b+a) 2 4b + 0.60 3 4.60 + a 4 4.60ab
Answer:
4b + .60a
Step-by-step explanation:
b represents the number of bunches of bananas
a represents the number of apple
Multiply the cost by the number purchased of each item and add them together
4b + .60a
Answer:
[tex]\huge\boxed{\$ (4 b + 0.60 a)}[/tex]
Step-by-step explanation:
Bananas represented by b
1 banana costs $4 so b bananas will cost $ 4 b
Apples represented by a
1 apples costs 0.60 $ so a apples will cost $ 0.60 a
Totally, they will cost:
=> $ (4 b + 0.60 a)
The diagonals of a rhombus bisect each other of measures 8cm and 6cm .Find its perimeter. please help !!!!!!!!!!!!!!!!!!!!!!!!
Answer:
20 cm
Step-by-step explanation:
20 cm
8/2 = 4
6/2 = 3
3 and 4 are the sides of the triangle (four triangles in rhombus)
a²+b²=c²
4³+3²=c²
c = 5
5 x 4 = 20
Hope this helped
Answer:
perimeter = 20 cm
Step-by-step explanation:
consider breaking the rhombus into four equal parts.
and that gives you a triangle.
(refer to image attached for more clarification)
let a = 3, b = 4
to get the side c, use Pythagorean theorem = c² = a² + b²
c = sqrt (3² + 4²)
side c = 5
therefore,
perimeter = 4 x sides (c)
perimeter = 4 x 5
perimeter = 20 cm
 evaluate the expression for r=-10 -54-r=
Answer:
To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. In the example above, the variable x is equal to 6 since 6 + 6 = 12. If we know the value of our variables, we can replace the variables with their values and then evaluate the expression.
Step-by-step explanation:
Evaluate Algebraic Expressions. ... To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number. To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations.
What is the x-value of point A?
━━━━━━━☆☆━━━━━━━
▹ Answer
x = 5
▹ Step-by-Step Explanation
The x-axis and y-axis are labeled on the graph. The x-axis is the horizontal axis. Between 4 and 6, there is a missing number. That number should be 5, leaving us with an x-value of 5 for Point A.
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Answer:
The x value is 5
Step-by-step explanation:
The x value is the value going across
Starting where the two axis meet, we go 5 units to the right
That is the x value
A company finds that the rate at which the quantity of a product that consumers demand changes with respect to price is given by the marginal-demand function Upper D prime (x )equals negative StartFraction 5000 Over x squared EndFraction where x is the price per unit, in dollars. Find the demand function if it is known that 1006 units of the product are demanded by consumers when the price is $5 per unit.
Answer:
q = 5000/x + 6
Step-by-step explanation:
D´= dq/dx = - 5000/x²
dq = -( 5000/x²)*dx
Integrating on both sides of the equation we get:
q = -5000*∫ 1/x²) *dx
q = 5000/x + K in this equation x is the price per unit and q demanded quantity and K integration constant
If when 1006 units are demanded when the rice is 5 then
x = 5 and q = 1006
1006 = 5000/5 +K
1006 - 1000 = K
K = 6
Then the demand function is:
q = 5000/x + 6
1 liter of ink can print 5000 pages of text. If you had 100 gallons of ink then how many pages
could you print?
How many variable terms are in the expression 3x3y + 5x2 − 4y + z + 9?
Answer:
4
Step-by-step explanation:
"4" is the number of variable terms that are in the expression 3x3y + 5x2 _ 4y + z + 9. The four variable terms in the expression are "xy", "x^2", "y" and "z". I hope that this is the answer that you were looking for and the answer has actually come to your desired help. If you need any clarification, you can always ask.
In tests of a computer component, it is found that the mean time between failures is 520 hours. A modification is made which is supposed to increase the time between failures. Tests on a random sample of 10 modified components resulted in the following times (in hours) between failures. 518 548 561 523 536 499 538 557 528 563 At the 0.05 significance level, test the claim that for the modified components, the mean time between failures is greater than 520 hours. Use the P-value method of testing hypotheses.
H0:
H1:
Test Statistic:
Critical Value:
Do you reject H0?
Conclusion:
If you were told that the p-value for the test statistic for this hypothesis test is 0.014, would you reach the same decision that you made for the Rejection of H0 and the conclusion as above?
Answer:
As the calculated value of t is greater than critical value reject H0. The tests supports the claim at ∝= 0.05
If the p-value for the test statistic for this hypothesis test is 0.014, then the critical region is t ( with df=9) for a right tailed test is 2.821
then we would accept H0. The test would not support the claim at ∝= 0.01
Step-by-step explanation:
Mean x`= 518 +548 +561 +523 + 536 + 499+ 538 + 557+ 528 +563 /10
x`= 537.1
The Variance is = 20.70
H0 μ≤ 520
Ha μ > 520
Significance level is set at ∝= 0.05
The critical region is t ( with df=9) for a right tailed test is 1.8331
The test statistic under H0 is
t=x`- x/ s/ √n
Which has t distribution with n-1 degrees of freedom which is equal to 9
t=x`- x/ s/ √n
t = 537.1- 520 / 20.7 / √10
t= 17.1 / 20.7/ 3.16227
t= 17.1/ 6.5459
t= 2.6122
As the calculated value of t is greater than critical value reject H0. The tests supports the claim at ∝= 0.05
If the p-value for the test statistic for this hypothesis test is 0.014, then the critical region is t ( with df=9) for a right tailed test is 2.821
then we would accept H0. The test would not support the claim at ∝= 0.01
Find the length of FV¯¯¯¯¯¯¯¯ A. 72.47 B. 77.71 C. 49.42 D. 56.84
Answer:
The answer is option AStep-by-step explanation:
Since it's a right angled triangle we can use trigonometric ratios here.
To find FV we use cosine
cos∅ = adjacent / hypotenuse
From the question
FV is the hypotenuse
TV is the adjacent
So we have
cos 43 = TV/FV
FV = TV/ cos 43
TV =53
FV = 53/ cos 43
FV = 72.4683
We have the final answer as
FV = 72.47Hope this helps you
Answer:
FV=72.47
Step-by-step explanation:
cos43=adj/hyp.=VT/FV
cos43=53/FV
FV=53/cos43
FV=72.46835= 72.47 rounded to the nearest hundredth
Suppose that it rains in Spain an average of once every 9 days, and when it does, hurricanes have a 2% chance of happening in Hartford. When it does not rain in Spain, hurricanes have a 1% chance of happening in Hartford. What is the probability that it rains in Spain when hurricanes happen in Hartford? (Round your answer to four decimal places.)
Answer:
I found the answer on Yahoo
Step-by-step explanation:
P[rains in spain] = 1/9
P[hurricane in hartford & rain in spain] = 0.03*1/9 = A
P[hurricane in hartford & no rain in spain] = 0.02*8/9
P[hurricane in hartford] = 0.03*1/9 + 0.02*8/9 = 0.19/9 = B
P[rain in spain | hurricane in hartford] = A/B = 3/19 <---------
Find the sum. 31.25 + 9.38
Answer:
40.63
Step-by-step explanation:
31.25+9.38= 40.63
Hope this helps
Answer: 40.63
Look at the image for shown work.
Convert 6 feet to miles ( round five decimal places
Answer:
0.00114
Step-by-step explanation:
Divide length value by 5280
Use the following cell phone airport data speeds (Mbps) from a particular network. Find the percentile corresponding to the data speed 4.9 Mbps.
0.2 0.8 2.3 6.4 12.3 0.2 0.8 2.3 6.9 12.7 0.2 0.8 2.6 7.5 12.9 0.3 0.9 2.8 7.9 13.8
0.6 1.5 0.1 0.7 2.2 6.1 12.1 0.6 1.9 5.5 11.9 27.5 0.6 1.7 3.3 8.3 13.8 1.3 3.5 9.8
14.6 10.1 14.7 11.8 14.8
Answer:
Thus percentile lies between 53.3% and 55.6 %
Step-by-step explanation:
First we arrange the data in ascending order . Then find the number of the values corresponding to the given value. Then equate it with the number of observations and x and then multiply it to get the percentile. n= P/100 *N
where n is the ordinal rank of the given value
N is the number of values in ascending order.
The data in ascending order is
0.1 0.2 0.2 0.2 0.3 0.6 0.6 0.6 0.7 0.8 0.8 0.8 0.9 1.3
1.5 1.7 1.9 2.2 2.3 2.3 2.6 2.8 3.3 3.5 5.5 6.1 6.4 6.9 7.5 7.9 8.3 9.8 10.1 11.8 11.9 12.1 12.3 12.7 12.9 13.8 13.8 14.6 14.7 14.8 27.5
Number of observation = 45
4.9 lies between 3.3 and 5.5
x*n = 24 observation x*n = 25 observation
x*45= 24 x*45= 25
x= 0.533 x= 0.556
Thus percentile lies between 53.3% and 55.6 %
9. There are 50 pupils in a class. Out of this
number, 1/10 speak French only and 4/5 of the remainder speak both French and
English. If the rest speak English only,
i) find the number of students who speak
Answer:
Step-by-step explanation:
50 : 10 = 5 speaks French only
50 -5= 45 the remainder
4/5 * 45= 36 speaks French and English
45 - 36= 9 speaks English only
The number of students who speak:
i) French only = 5 students,
ii) both French and English = 36 students,
iii) English only = 9 students.
Step 1: Find the number of students who speak French only.
Step 2: Find the remainder (students who speak both French and English) after subtracting the French-only speakers.
Step 3: Find the number of students who speak both French and English.
Step 4: Find the number of students who speak English only.
Let's calculate it step by step:
Step 1: Find the number of students who speak French only.
1/10 of 50 pupils speak French only:
French-only speakers = (1/10) * 50 = 5 students.
Step 2: Find the remainder (students who speak both French and English) after subtracting the French-only speakers.
Remaining students = Total students - French-only speakers
Remaining students = 50 - 5 = 45 students.
Step 3: Find the number of students who speak both French and English.
4/5 of the remaining students speak both French and English:
Both French and English speakers = (4/5) * 45 = 36 students.
Step 4: Find the number of students who speak English only.
To find the English-only speakers, subtract the total number of French-only speakers and both French and English speakers from the total number of students:
English-only speakers = Total students - (French-only speakers + Both French and English speakers)
English-only speakers = 50 - (5 + 36) = 50 - 41 = 9 students.
To know more about French:
https://brainly.com/question/34246494
#SPJ2
Complete question is:
There are 50 pupils in a class. Out of this number, 1/10 speak French only and 4/5 of the remainder speak both French and English. If the rest speak English only, find the number of students who speak
i) French only,
ii) both French and English,
iii) English only,
Find the side length, b.
Round to the nearest tenth.
Answer:
b ≈ 9.2
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
b² = a² + c² = 6² +7² = 36 + 49 = 85 ( take the square root of both sides )
b = [tex]\sqrt{85}[/tex] ≈ 9.2 ( to the nearest tenth )
Answer:
9.22
Step-by-step explanation:
Since it's a 90° triangle [tex]c^{2} =a^{2} +b^{2}[/tex].
In this example they labeled the hypotenuse as b instead of c are equation is still the same just put the correct variables in the right places.
[tex]b = \sqrt{6^{2} +7^{2} }[/tex]
b = 9.22
Find a vector equation and parametric equations for the line through the point (1,0,6) and perpendicular to the plane x+3y+z=5.
The normal vector to the plane x + 3y + z = 5 is n = (1, 3, 1). The line we want is parallel to this normal vector.
Scale this normal vector by any real number t to get the equation of the line through the point (1, 3, 1) and the origin, then translate it by the vector (1, 0, 6) to get the equation of the line we want:
(1, 0, 6) + (1, 3, 1)t = (1 + t, 3t, 6 + t)
This is the vector equation; getting the parametric form is just a matter of delineating
x(t) = 1 + t
y(t) = 3t
z(t) = 6 + t
The vector equation for the line through the point (1,0,6) and perpendicular to the plane x+3y+z=5 is v =(1+t)i + (3t)j + (6+t)k
The parametric equations for the line through the point (1,0,6) and perpendicular to the plane x+3y+z=5
x(t) = 1+ty(t) = 3tz(t) = 6+tThe parametric equation of a line through the point A(x, y, z) perpendicular to the plane ax+by+cz= d is expressed generally as:
A + vt where:
A = (x, y, z)
v = (a, b, c) (normal vector)
This can then be expressed as:
s = A + vt
s = (x, y, z) + (a, b, c)t
Given the point
(x, y, z) = (1,0,6)
(a, b, c) = (1, 3, 1)
Substitute the given coordinate into the equation above:
s = (1,0,6) + (1, 3, 1)t
s = (1+t) + (0+3t) + (6+t)
The parametric equations from the equation above are:
x(t) = 1+t
y(t) = 3t
z(t) = 6+t
The vector equation will be expressed as v = xi + yj + zk
v =(1+t)i + (3t)j + (6+t)k
Learn more here: brainly.com/question/12850672
Find an equation for the surface consisting of all points P in the three-dimensional space such that the distance from P to the point (0, 1, 0) is equal to the distance from P to the plane y
Answer:
x^2 +4y +z = 1
Step-by-step explanation:
Surface consisting of all points P to point (0,1,0) been equal to the plane y =1
given point, p (x,y,z ) the distance from P to the plane (y)
| y -1 |
attached is the remaining part of the solution
AB||CD. Find the measure of
Answer:
135 degrees
Step-by-step explanation:
3x+15 = 5x - 5 because of the alternate interior angles theorem.
20 = 2x
x = 10
3(10) + 15 = 30+15 = 45
Remember that a line has a measure of 180 degrees. So we can just subtract the angle we found from 180 degrees to get BFG.
180-45 = 135.
Solve for x. Question 12 options: A) 8 B) 5 C) 14 D) 10
Answer:
B) 5
Step-by-step explanation:
Proportions:
8 ⇒ 10
20 ⇒ 5x
5x = 20*10/8
5x = 25
x = 25/5
x = 5
Which of the following units is incommensurable with kilograms
Answer:
All units of measurement that are not based on or do not measure mass or weight and volume are incommensurable with kilograms.
Step-by-step explanation:
A measure unit is said to be incommensurable with another if it does not have the same measurement basis with the other measure unit. For example, a measure in time cannot be measured in kilograms because time is measured in hours, minutes, seconds, days, etc. But, if a measurement base can be applied to two or more measurement units, then the measurement units are commensurable with the measurement base.
Let A represent going to the movies on Friday and let B represent going bowling on Friday night. The P(A) = 0.58 and the P(B) = 0.36. The P(A and B) = 94%. Lauren says that both events are independent because P(A) + P(B) = P(A and B) Shawn says that both events are not independent because P(A)P(B) ≠ P(A and B) Which statement is an accurate statement? Lauren is incorrect because the sum of the two events is not equal to the probability of both events occurring. Shawn is incorrect because the product of the two events is equal to the probability of both events occurring. Lauren is correct because two events are independent if the probability of both occurring is equal to the sum of the probabilities of the two events. Shawn is correct because two events are independent if the probability of both occurring is not equal to the product of the probabilities of the two events.
Answer:
Shawn is correct because two events are independent if the probability of both occurring is equal to the product of the probabilities of the two events.
Step-by-step explanation:
We are given that A represent going to the movies on Friday and let B represent going bowling on Friday night. The P(A) = 0.58 and the P(B) = 0.36. The P(A and B) = 94%.
Now, it is stated that the two events are independent only if the product of the probability of the happening of each event is equal to the probability of occurring of both events.
This means that the two events A and B are independent if;
P(A) [tex]\times[/tex] P(B) = P(A and B)
Here, P(A) = 0.58, P(B) = 0.36, and P(A and B) = 0.94
So, P(A) [tex]\times[/tex] P(B) [tex]\neq[/tex] P(A and B)
0.58 [tex]\times[/tex] 0.36 [tex]\neq[/tex] 0.94
This shows that event a and event B are not independent.
So, the Shawn statement that both events are not independent because P(A)P(B) ≠ P(A and B) is correct.
Answer:
Shawn is correct
Step-by-step explanation:
