Answer:
True
Step-by-step explanation:
Coefficient of realism called alpha which is a decimal number between 0 and 1. This number provides the optimistic view. The number 1 - [tex]\alpha[/tex] is amount of emphasis that is placed in pessimistic outcome. If the coefficient of realism alpha is 1 then criterion of realism will yield same result as maxi max criterion.
need help asap! what is the value of x given that figure MNOP is a trapezoid with median QR
Answer:
x = 8
Step-by-step explanation:
To find the possible value of x in the given trapezoid MNOP with median QR, recall that one of the properties of a trapezoid is that the median length = ½ of the sum of the length of the parallel bases
Thus, ½ of [x + (3x + 8)] = 20
Let's find x
½*[x + (3x + 8)] = 20
½*[x + 3x + 8)] = 20
½*[4x +8] = 20
Multiply both sides by 2
4x + 8 = 20*2
4x + 8 = 40
Subtract 8 from both sides
4x = 40 - 8
4x = 32
Divide both sides by 4
x = 32/4
x = 8
Answer:
I think its 8 ♂️
Step-by-step explanation:
in QRS, m Q = 70°, m R = 44", and m S = 66º. Which side of QRS is the shortest?
Answer:
QS
Step-by-step explanation:
The side opposite to the smallest angle must be the shortest side. The smallest angle is ∠R so the opposite side is QS.
Answer:
Hey there!
Smaller angles are opposite smaller sides, so the side opposite to angle R would be the shortest. (Or side SQ)
Hope this helps :)
Can anyone please explain? Need some help :)
A regular hexagon is inscribed in a circle with a diameter of 12 units. Find the area of the hexagon. Round your answer to the nearest tenth. (there's no picture included)
Answer:
93.5 square units
Step-by-step explanation:
Diameter of the Circle = 12 Units
Therefore:
Radius of the Circle = 12/2 =6 Units
Since the hexagon is regular, it consists of 6 equilateral triangles of side length 6 units.
Area of the Hexagon = 6 X Area of one equilateral triangle
Area of an equilateral triangle of side length s = [tex]\dfrac{\sqrt{3} }{4}s^2[/tex]
Side Length, s=6 Units
[tex]\text{Therefore, the area of one equilateral triangle =}\dfrac{\sqrt{3} }{4}\times 6^2\\\\=9\sqrt{3} $ square units[/tex]
Area of the Hexagon
[tex]= 6 X 9\sqrt{3} \\=93.5$ square units (to the nearest tenth)[/tex]
The formula to convert Fahrenheit to Celsius is C - 5 (F - 32). Convert 30°C to
Fahrenheit. Round to the nearest degree.
A. 30°F
B. -1°F
C. 112°F
D. 86°F
Answer:
D. *6F
Step-by-step explanation:
C=(F-32)*5/9
30=(F-32)*5/9
F = (30*9)/5+32
F = 86
Write the equation in the form Ax + By = C. Find an equation of a line passing through the pair of points (4,7) and (3,4).
Answer:
[tex] 3x - y = 5 [/tex]
Step-by-step explanation:
The two pint equation of a line:
[tex] y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1) [/tex]
We have
[tex] x_1 = 4 [/tex]
[tex] x_2 = 3 [/tex]
[tex] y_1 = 7 [/tex]
[tex] y_2 = 4 [/tex]
[tex] y - 7 = \dfrac{4 - 7}{3 - 4}(x - 4) [/tex]
[tex] y - 7 = \dfrac{-3}{-1}(x - 4) [/tex]
[tex] y - 7 = 3(x - 4) [/tex]
[tex] y - 7 = 3x - 12 [/tex]
[tex] 5 = 3x - y [/tex]
[tex] 3x - y = 5 [/tex]
An appliance dealer sells three different models of upright freezers having 13.5, 15.9, and 19.1 cubic feet of storage. Let X = the amount of storage space purchased by the next customer to buy a freezer. Suppose that X has pmf:
Answer:
a) E(X) = 16.09 ft³
E(X²) = 262.22 ft⁶
Var(X) = 3.27 ft⁶
b) E(22X) = 354 dollars
c) Var(22X) = 1,581 dollars
d) E(X - 0.01X²) = 13.470 ft³
Step-by-step explanation:
The complete Correct Question is presented in the attached image to this solution.
a) Compute E(X), E(X2), and V(X).
The expected value of a probability distribution is given as
E(X) = Σxᵢpᵢ
xᵢ = Each variable in the distribution
pᵢ = Probability of each distribution
Σxᵢpᵢ = (13.5×0.20) + (15.9×0.59) + (19.1×0.21)
= 2.70 + 9.381 + 4.011
= 16.092 = 16.09 ft³
E(X²) = Σxᵢ²pᵢ
Σxᵢ²pᵢ = (13.5²×0.20) + (15.9²×0.59) + (19.1²×0.21)
= 36.45 + 149.1579 + 76.6101
= 262.218 = 262.22 ft⁶
Var(X) = Σxᵢ²pᵢ - μ²
where μ = E(X) = 16.092
Σxᵢ²pᵢ = E(X²) = 262.218
Var(X) = 262.218 - 16.092²
= 3.265536 = 3.27 ft⁶
b) E(22X) = 22E(X) = 22 × 16.092 = 354.024 = 354 dollars to the nearest whole number.
c) Var(22X) = 22² × Var(X) = 22² × 3.265536 = 1,580.519424 = 1,581 dollars
d) E(X - 0.01X²) = E(X) - 0.01E(X²)
= 16.092 - (0.01×262.218)
= 16.0926- 2.62218
= 13.46982 = 13.470 ft³
Hope this helps!!!
Which of the following theorems verifies that HIJ MLN?
Answer:
HL (try HL, I believe that's the right answer)
Answer:
HL
Step-by-step explanation:
BRO TRUST ME
Charlotte is running at a rate of 9 (km)/(h) what is charlotte speed in (m)/(s)
Answer:
2.5 meters per second
Step-by-step explanation:
9x1000=9000m/h
9000/60/60=2.5m/s
Answer:
2.5 m/s
Step-by-step explanation:
convert kilometers to meters and then use a conversion calc to do the rest
Not sure how to graph this
Answer:
y=2x+6
Step-by-step explanation:
The slope is 2x and the y-intercept is 6. It is shown how to graph it in the attachment.
George has opened a new store and he is monitoring its success closely. He has found that this store’s revenue each month can be modeled by r(x)=x2+5x+14 where x represents the number of months since the store opens the doors and r(x) is measured in hundreds of dollars. He has also found that his expenses each month can be modeled by c(x)=x2−3x+4 where x represents the number of months the store has been open and c(x) is measured in hundreds of dollars. What does (r−c)(3) mean about George's new store?
This is a great question!
When we are given ( r - c )( 3 ), we are being asked to take 3 as x in the functions r( x ) and c( x ), taking the difference of each afterwards -
[tex]r( 3 ) = ( 3 )^2 + 5( 3 ) + 14,\\x( 3 ) = ( 3 )^2 - 3( 3 ) + 4[/tex]
____
Let us calculate the value of each function, determine their difference, and multiply by 100, considering r( x ) and c( x ) are measured in hundreds of dollars,
[tex]r( 3 ) = 9 + 15 + 14 = 38,\\x( 3 ) = 9 - 9 + 4 = 0 + 4 = 4\\----------------\\( r - c )( 3 ) = 38 - 4 = 34,\\34 * 100 = 3,400( dollars )\\\\Solution = 3,400( dollars )[/tex]
Therefore, ( r - c )( 3 ) " means " that George's new store will have a profit of $3,400 after it's third month in business, given the following options,
( 1. The new store will have a profit of $3400 after its third month in business.
( 2. The new store will have a profit of $2400 after its third month in business.
( 3. The new store will sell 2400 items in its third month in business.
( 4. The new store will sell 3400 items in its third month in business.
The required answer is , [tex](r-c)(5)[/tex] means the revenue less expenses in 5 months i.e. the new store will have a profit of $ 5400 after 5 months.
Substitution:The substitution method is the algebraic method to solve simultaneous linear equations.
Given function is,
[tex]r(x) = x^2+5x+14[/tex]...(1)
And [tex]c(x) = x^2-4x+5[/tex]...(2)
Now, substituting the value into the equation (1) and (2).
[tex]r(5) = (5)^2+5(5)+14=64[/tex]
[tex]c(5) = (5)^2-4(5)+5=10[/tex]
Therefore,
[tex](r-c)(5)=r(5)-c(5)\\=64-10\\=54[/tex]
Now, [tex](r-c)(5)[/tex] means the revenue less expenses in 5 months i.e. the new store will have a profit of $ 5400 after 5 months.
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A man is twice the age of his son,in 20 years time, the son's age will be 2/3 of that his father. what is the son's present age?
Answer:
20 years old.
Step-by-step explanation:
Let us say that the man's age is represented by x and the son's age is represented by y.
As of now, x = 2y.
In 20 years, both ages will increase by 20. We can have an equation where the son's age increased by 20 equals 2/3 of the man's age plus 20.
(y + 20) = 2/3(x + 20)
Since x = 2y...
y + 20 = 2/3(2y + 20)
3/2y + 30 = 2y + 20
2y + 20 = 3/2y + 30
1/2y = 10
y = 20
To check our work, the man's age is currently double his son's, so the man is 40 and the son is 20. In 20 years, the man will be 60 and the son will be 40. 40 / 60 = 2/3, so the son's age is 2/3 of his father's.
So, the son's present age is 20 years old.
Hope this helps!
Express it in slope-intercept form.
Hey there! :)
Answer:
y = 1/4x - 3.
Step-by-step explanation:
Use the slope-formula to find the slope of the line:
[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Plug in two points from the line. Use the points (-4, -4) and (0, 3):
[tex]m = \frac{-3 - (-4)}{0 - (-4)}[/tex]
Simplify:
m = 1/4.
Slope-intercept form is y = mx + b.
Find the 'b' value by finding the y-value at which the graph intersects the y-axis. This is at y = -3. Therefore, the equation is:
y = 1/4x - 3.
Travis bought $9.45 worth of 49-cent stamps and 21-cent stamps. The number of 21-cent stamps was 5 fewer than the number of 49-cent stamps. Solve the equation 0.49s+0.21(s−5)=9.45 for s to find the number of 49-cent stamps Travis bought.
Answer:
15 49-cent stamps
Step-by-step explanation:
We can solve this problem with the equations 0.49(x) + 0.21(y) = 9.45 and x - 5 = y. Well, 0.49(15) + 0.21(10) = 9.45, so we know that there are 15 49-cent stamps and 10 21-cent stamps. The question is asking for the number of 49-cent stamps, so we can tell Travis bought 15 49-cent stamps.
Hope this helps! Plz give me brainliest, it will help me achieve my next rank.
The number of 49-cent stamps that Travis bought given the equation is 15.
What he number of 49-cent stamps Travis bought?Given this equation: 0.49s+0.21(s−5)=9.45 take the following steps to determine the value of s
Expand the bracket: 0.49s + 0.21s - 1.05 = 9.45Combine similar terms : 0.49s + 0.21s = 9.45 + 1.05Add similar terms: 10.50 = 0.70sDivide both sides of the equation by 0.70: s = 15To learn more about mathematical equations, please check: https://brainly.com/question/26427570
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Periodically, customers of a financial services company are asked to evaluate the company's financial consultants and services. Higher ratings on the client satisfaction survey indicate better service, with 7 the maximum service rating. Independent samples of service ratings for two financial consultants are summarized here. Consultant A has 10 years of experience, whereas consultant B has 1 year of experience. Use
α = 0.05
and test to see whether the consultant with more experience has the higher population mean service rating.
Consultant A Consultant B
n1 = 16
n2 = 10
x1 = 6.82
x2 = 6.28
s1 = 0.65
s2 = 0.75
(a)
State the null and alternative hypotheses.
H0:
μ1 − μ2 ≤ 0
Ha:
μ1 − μ2 = 0
H0:
μ1 − μ2 > 0
Ha:
μ1 − μ2 ≤ 0
H0:
μ1 − μ2 ≠ 0
Ha:
μ1 − μ2 = 0
H0:
μ1 − μ2 ≤ 0
Ha:
μ1 − μ2 > 0
H0:
μ1 − μ2 = 0
Ha:
μ1 − μ2 ≠ 0
(b)
Compute the value of the test statistic. (Round your answer to three decimal places.)
(c)
What is the p-value? (Round your answer to four decimal places.)
p-value =
(d)
What is your conclusion?
Reject H0. There is sufficient evidence to conclude that the consultant with more experience has a higher population mean rating.Do not reject H0. There is insufficient evidence to conclude that the consultant with more experience has a higher population mean rating. Do not Reject H0. There is sufficient evidence to conclude that the consultant with more experience has a higher population mean rating.Reject H0. There is insufficient evidence to conclude that the consultant with more experience has a higher population mean rating.
Answer:
A) Null hypothesis; H0: μ1 − μ2 ≤ 0
Alternative hypothesis; Ha: μ1 − μ2 > 0
B) Test statistic = t = 1.878
C) p-value is 0.038823.
D) Reject the Null hypothesis H0
Step-by-step explanation:
We are given;
α = 0.05
n1 = 16
n2 = 10
bar x1 = 6.82
bar x2 = 6.28
s1 = 0.65
s2 = 0.75
A) The hypothesis is as follows;
Null hypothesis; H0: μ1 − μ2 ≤ 0
Alternative hypothesis; Ha: μ1 − μ2 > 0
B) Formula yo determine the test statistic is;
t = ((bar x1) - (bar x))/√((s1)²/n1) + (s2)²/n2))
Plugging in the relevant values, we have;
t = (6.82 - 6.28)/√((0.65)²/16) + (0.75)²/10))
t = 0.54/√(0.02640625 + 0.05625)
t = 0.54/0.2875
t = 1.878
C) The formula for the degree of freedom is;
Δ = [(s1)²/n1) + (s2)²/n2))]²/[((s1²/n1)²/(n1 - 1)) + ((s2²/n2)²/(n1 - 1))
Plugging in the relevant values, we have;
Δ = [(0.65)²/16) + (0.75)²/10))]²/[((0.65²/16)²/(16 - 1)) + ((0.75²/10)²/(10 - 1))
Δ = 0.00683205566/(0.000046486 + 0.0003515625)
Δ ≈ 17
Thus, the P-value;
From online p-value calculator from t-score and DF which i attached, we have the p-value as;
The p-value is 0.038823.
D) The p-value result is significant at p < 0.05
Thus, we reject the Null hypothesis H0
A) Null hypothesis: μ1 − μ2 ≤ 0
B) Test statistic = t = 1.878
C) The p-value is 0.038823.
D) Reject the Null hypothesis H0.
HypothesisWhat all information we have ?
α = 0.05
n1 = 16
n2 = 10
bar x1 = 6.82
bar x2 = 6.28
s1 = 0.65
s2 = 0.75
Part A)
The hypothesis is as follows;
Null hypothesis; H0: μ1 − μ2 ≤ 0
Alternative hypothesis; Ha: μ1 − μ2 > 0
Part B)
The formula to determine the test statistic is :
t = ((bar x1) - (bar x))/√((s1)²/n1) + (s2)²/n2))
t = (6.82 - 6.28)/√((0.65)²/16) + (0.75)²/10))
t = 0.54/√(0.02640625 + 0.05625)
t = 0.54/0.2875
t = 1.878
The formula to determine the test statistic is t = 1.878.
Part C)
The formula for the degree of freedom is;
Δ = [(s1)²/n1) + (s2)²/n2))]²/[((s1²/n1)²/(n1 - 1)) + ((s2²/n2)²/(n1 - 1))
Δ = [(0.65)²/16) + (0.75)²/10))]²/[((0.65²/16)²/(16 - 1)) + ((0.75²/10)²/(10 - 1))
Δ = 0.00683205566/(0.000046486 + 0.0003515625)
Δ ≈ 17
Thus, the P-value is 0.038823.
Part D)
The p-value result is significant at p < 0.05 is :
Thus, we reject the Null hypothesis H0.
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Find a solution to the linear equation y=12x−24
Answer:
I didn't know which one you wanted...
Step-by-step explanation:
1. Finding the x an y-intercepts
To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.
x-intercept(s): (2,0)
y-intercept(s): (0,−24)
2. Finding the slope and y-intercept
Use the slope-intercept form to find the slope and y-intercept.
Slope: 12
y-intercept: −24
Translate the following argument in a standard form categorial syllogims then use venn diagram or rules for syllogim to determine whether each is valid or invalid.
All of the movies except the romantic comedies were exciting. Hence, the action films were exciting,because none of them is a romantic comedies.
Answer:
couldnt tell you
Step-by-step explanation:
jkj
The function defined by w(x)=-1.17x+1260 gives the wind speed w(x)(in mph) based on the barometric pressure x (in millibars,mb). a) Approximate the wind speed for a hurricane with the barometric pressure of 900mb. b) Write a function representing the inverse of w and interpret its meaning in context. c) Approximate the barometric pressure for a hurricane with speed 90 mph.
Answer:
a) 207 mph
b) x = (1260-w)/1.17
c) 1000 mb
Step-by-step explanation:
a) Put the pressure in the equation and solve.
w(900) = -1.17(900) +1260 = 207
The wind speed for a hurricane with a pressure of 900 mb is 207 mph.
__
b) Solving for x, we have ...
w = -1.17x +1260
w -1260 = -1.17x
x = (1260 -w)/1.17 . . . . inverse function
__
c) Evaluating the inverse function for w=90 gives ...
x = (1260 -90)/1.17 = 1170/1.17 = 1000 . . . millibars
The approximate barometric pressure for a hurricane with a wind speed of 90 mph is 1000 millibars.
Find the length of KC
Answer:
54
give me brainliest please please please and follow my page
Step-by-step explanation:
To find length of KC...we need to find the length of HM and MU first ...
so....HM= 96- 78 = 14
JU = 96 + HM = 96 + 14 = 110
....
KU = 110 - JK = 110 - 82 = 28
....
UN = 105+ 82 -( 96 + 14 )
187 - 110
= 77
UC = 77 - 51 = 26
KC = UC + KU = 26 + 28 = 54
The length of [tex]\overline{KC}[/tex] along line [tex]\overline{JN}[/tex] is given as 54 (Option A) See the computation below.
How do you compute the length of [tex]\overline{KC}[/tex]?To determine the length of [tex]\overline{KC}[/tex], the length of [tex]\overline{HM}[/tex] and [tex]\overline{MU}[/tex]must first be derived.
[tex]\overline{HM}[/tex] = 96 - 78
[tex]\overline{HM}[/tex] = 14
[tex]\overline{JU}[/tex] = 96 + [tex]\overline{HM}[/tex]
= 96 + 14
[tex]\overline{JU}[/tex]= 110
[tex]\overline{KU}[/tex] = 110 - [tex]\overline{JK}[/tex]
= 110 - 82
[tex]\overline{KU}[/tex]= 28
[tex]\overline{UN}[/tex] = 105+ 82 -( 96 + 14 )
=187 - 110
[tex]\overline{UN}[/tex]= 77
[tex]\overline{UC}[/tex] = 77 - 51
[tex]\overline{UC}[/tex]= 26
Thus,
[tex]\overline{KC}[/tex] = [tex]\overline{UC}[/tex] + [tex]\overline{KU}[/tex]
[tex]\overline{KC}[/tex]= 26 + 28
[tex]\overline{KC}[/tex]= 54
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In ABC,if sin A=4/5 and tan A=4/3, then what I s cos A?
Researchers studied the mean egg length (in millimeters) for a particular bird population. After a random sample of eggs, they obtained a 95% confidence interval of (45,60) in millimeters. In the context of the problem, which of the following interpretations is correct, if any?
A. We are 95% sure that an egg will be between 45 mm and 60 mm in length.
B. For this particular bird population, 95% of all birds have eggs between 45 mm and 60 mm.
C. We are 95% confident that the mean length of eggs for this particular bird population is between 45 mm and 60 mm.
D. We are 95% confident that the mean length of eggs in the sample is between 45 mm and 60 mm.
E. None of the above is a correct interpretation.
Answer:
C. We are 95% confident that the mean length of eggs for this particular bird population is between 45 mm and 60 mm.
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
For 95% confidence interval, it means that we are 95% confident that the mean of the population is between the given upper and lower bounds of the confidence interval.
For the case above, the interpretation of the 95% confidence interval is that we are 95% confident that the mean length of eggs for this particular bird population is between 45 mm and 60 mm.
Galina had two boxes with pieces of paper in each. In the first box, each piece of paper had one possible outcome from flipping a coin 4 times (e.g. HHTH). There was one piece of paper for every possible outcome.
How many pieces of paper were in the first box?
Answer:
B
Step-by-step explanation:
Which are the roots of the quadratic function f(b) = 62 – 75? Select two options.
b=573
Ob= -573
b=35
b= -35
Ob= 253
Answer:
[tex]b = 5 \sqrt{3} \ or\ b = -5 \sqrt{3}[/tex]
Step-by-step explanation:
Given
[tex]f(b) = b^2 - 75[/tex]
Required
Determine the roots
To get the root of the function, then f(b) must be 0;
i.e. f(b) = 0
So, the expression becomes
[tex]0 = b^2 - 75[/tex]
Add 75 to both sides
[tex]75 + 0 = b^2 - 75 + 75[/tex]
[tex]75 = b^2[/tex]
Take square roots of both sides
[tex]\sqrt{75} = \sqrt{b^2}[/tex]
[tex]\sqrt{75} = b[/tex]
Reorder
[tex]b = \sqrt{75}[/tex]
Expand 75 as a product of 25 and 3
[tex]b = \sqrt{25*3}[/tex]
Split the expression
[tex]b = \sqrt{25} *\sqrt{3}[/tex]
[tex]b = \±5 *\sqrt{3}[/tex]
[tex]b = \±5 \sqrt{3}[/tex]
[tex]b = 5 \sqrt{3} \ or\ b = -5 \sqrt{3}[/tex]
The options are not clear enough; however the roots of the equation are [tex]b = 5 \sqrt{3} \ or\ b = -5 \sqrt{3}[/tex]
find the area of the shaded region. 27.8 in and 150 degrees
Answer: 57769.8 in²
Let A be the area of the shaded region
We have a relation that can help us calculate its area
A= 0.5*(θ-sin(θ))*r² where r is the radius and θ the angle
A= 0.5*(150-sin(150°))* 27.8² =57769.79≈57769.8 in²
Answer:
818.4
Step-by-step explanation:
The graph of y =ex is transformed as shown in the graph below. Which equation represents the transformed function?
Answer:
B. e^x+3
Step-by-step explanation:
Y=e^x
the graph is moving 3 units up
y= y+3
y=e^x+3
answer = y=e^x+3
Answer: B
Step-by-step explanation:
How many bits does it take to identify uniquely every person in the United States (the current population is about 300 million)?
Answer:
what's a bit
Step-by-step explanation:
According to the Stack Overflow Developers Survey of 20184 , 25.8% of developers are students. The probability that a developer is a woman given that the developer is a student is 7.4%, and the probability that a developer is a woman given that the developer is not a student is 76.4%. If we encounter a woman developer, what is the probability that she is a student
Answer:
3.26%
Step-by-step explanation:
The computation of the probability that she is a student is shown below:
Percentage of student developers = 25.8% = SD
The Percentage of the developer is student = 7.4% = DS
The percentage of the developer is not student = 76.4% = ND
Based on this, the probability is
[tex]= \frac{SD \times DS}{SD \times DS + DS \times ND}[/tex]
[tex]= \frac{25.8\% \times 7.4\%}{25.8\% \times 7.4\% + 7.4\% \times 76.4\%}[/tex]
=3.26%
we simply considered all the elements
An object of height 2.50cm is placed 20.0cm from a converging mirror of focal length 10.0cm. What are the height and the magnification of the image formed?
First find the distance it is reflected:
D = 20.0 x 10.0 /(20-10) = 200/10 = 20cm away.
Now calculate the magnification: -20/ 20 = -1
Now calculate the height:
-1 x 2.50 = -2.50
The negative sign means the image is inverted.
The mirrored image would be inverted, 2.50 cm tall and 20 cm in front of the mirror.
If A and B are independent events, P(A) = 0.25, and P(B) = 0.3, what is P(AB)?
O A. 0.25
B. 0.3
C. 0.15
O D. 0.075
Answer:
[tex] P(A) = 0.25, P(B= 0.3[/tex]
And if we want to find [tex] P(A \cap B)[/tex] we can use this formula from the definition of independent events :
[tex] P(A \cap B) =P(A) *P(B) = 0.25*0.3= 0.075[/tex]
And the best option would be:
[tex] P(A \cap B) =0.075[/tex]
Step-by-step explanation:
For this case we have the following events A and B and we also have the probabilities for each one given:
[tex] P(A) = 0.25, P(B= 0.3[/tex]
And if we want to find [tex] P(A \cap B)[/tex] we can use this formula from the definition of independent events :
[tex] P(A \cap B) =P(A) *P(B) = 0.25*0.3= 0.075[/tex]
And the best option would be:
[tex] P(A \cap B) =0.075[/tex]
This is not an incomplete question, it has come from a very reliable source, please dont delete. If 60% of the students in Mr. Bobby's class are bio majors, which of the following could be the total number of students in his class? 28 32 35 39 PLZHELPTHANKS
Answer:
35 students
Step-by-step explanation:
Take the number of students in the class and multiply by 60% and see if you get an integer number
28 * .60 =16.8 not an integer
32 * .6 =19.2
35 * .6 =21 yes
39*.6 =23.4
Joan's Nursery specializes in custom-designed landscaping for residential areas. The estimated labor cost associated with a particular landscaping proposal is based on the number of planting trees, shrubs, and so on to be used for the project. For cost-estimating purposes, managers use two hours of labor time for planting of a medium-sized tree. Actual times from a sample of 10 plantintings during the past month follow (times in hours):
1.7, 1.5, 2.6, 2.2, 2.4, 2.3, 2.6, 3.0, 1.4, 2.3
With a 0.05 level of significance, test to see whether the mean tree-planting time differs from two hours.
A. State the null and alternative hypotheses.
B. Compute the sample mean.
C. Compute the sample standard deviation.
D. What is the p-value?
E. What is your conclusion?
Answer:
A) Null and alternative hypothesis
[tex]H_0: \mu=2\\\\H_a:\mu\neq 2[/tex]
B) M = 2.2 hours
C) s = 0.52 hours
D) P-value = 0.255
E) At a significance level of 0.05, there is not enough evidence to support the claim that the mean tree-planting time significantly differs from two hours.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the mean tree-planting time significantly differs from two hours.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=2\\\\H_a:\mu\neq 2[/tex]
The significance level is 0.05.
The sample has a size n=10.
The sample mean is M=2.2.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.52.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.52}{\sqrt{10}}=0.1644[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{2.2-2}{0.1644}=\dfrac{0.2}{0.1644}=1.216[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=10-1=9[/tex]
This test is a two-tailed test, with 9 degrees of freedom and t=1.216, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=2\cdot P(t>1.216)=0.255[/tex]
As the P-value (0.255) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
At a significance level of 0.05, there is not enough evidence to support the claim that the mean tree-planting time significantly differs from two hours.
Sample mean and standard deviation:
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{10}(1.7+1.5+2.6+. . .+2.3)\\\\\\M=\dfrac{22}{10}\\\\\\M=2.2\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{9}((1.7-2.2)^2+(1.5-2.2)^2+(2.6-2.2)^2+. . . +(2.3-2.2)^2)}\\\\\\s=\sqrt{\dfrac{2.4}{9}}\\\\\\s=\sqrt{0.27}=0.52\\\\\\[/tex]