Answer:
[tex]580\text{ miles per hour}[/tex]
Step-by-step explanation:
To solve this problem, we can use the formula [tex]d=rt[/tex], where [tex]d[/tex] is distance, [tex]r[/tex] is rate, and [tex]t[/tex] is time.
Let's start by calculating how long the small airplane takes to complete the journey. The distance is 1160 miles and the rate is 290 miles per hour. Therefore, we have:
[tex]1160=290t,\\t=\frac{1160}{290}=4\text{ hours}[/tex]
Since the Boeing 747 left 2 hours after the small airplane left, the small airplane has just [tex]4-2=2[/tex] hours left of travelling time.
Therefore, to arrive at the same time as the small airplane, the Boeing 747 must cover the same distance of 1160 miles in only 2 hours. Hence, the Boeing 747's speed must have been:
[tex]1160=2r,\\r=\frac{1160}{2}=\boxed{580\text{ miles per hour}}[/tex]
Write the equation of the line in fully simplified slope-intercept form.
Answer:
y = 6/5x-1
Step-by-step explanation:
We have two points so we can find the slope
(-5,-7) and (5,5)
The slope is
m = ( y2-y1)/(x2-x1)
= ( 5- -7)/( 5 - -5)
= (5+7)/(5+5)
= 12/10
= 6/5
The slope intercept form of a line is
y = mx+b
y = 6/5x+b
Using the point (5,5)
5 = 6/5(5)+b
5=6+b
b=-1
y = 6/5x-1
The scatterplot shows the number of bedrooms in a house and the selling price for that house.
Calculate the residual for the house with 6 bedrooms, to the nearest thousand.
The residual for the house with 6 bedrooms is ___
-30k
-26k
26k
30k
Answer:
-26k, -26,000 ; (B)
ED2021
The residual for the house with 6 bedrooms is -26k.
What is Scatterplots?Scatterplots are the plotting of set of points on a vertical axis and an horizontal axis. The shows the correlation extent between the numbers of the observed quantities.
Given is a scatterplot showing the selling price of houses with the number of bedrooms.
Equation of the line of best fit is given as,
y = 6.3x + 4.8
Residual = Actual value - Predicted value
From the scatterplot,
Actual selling price of house with 6 bedrooms = 40 × 10,000 = 400,000
Predicted selling price for 6 bedrooms = (6.3 × 6) + 4.8
= 42.6 × 10,000
= 426,000
Residual = 400,000 - 426,000
= -26,000
Hence the residual is -26k.
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consider the differential equation x3y ''' + 8x2y '' + 9xy ' − 9y = 0; x, x−3, x−3 ln(x), (0, [infinity]). Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval. The functions satisfy the differential equation and are linearly independent since W(x, x−3, x−3 ln(x)) = ≠ 0 for 0 < x < [infinity].
Verifying that a given expression is a solution to the equation is just a matter of plugging in the expression and its derivatives, and making sure that the given expressions are indeed linearly independent.
For example, if y = x, then y' = 1 and the other derivatives vanish. So the DE after substitution reduces to
9x - 9x = 0
which is true for all 0 < x < ∞.
To check for linear independence, you compute the Wronskian, which, judging by what you wrote, you've already done...
5
13
The probabilities that three men win their respective races are 1/3,3/5and 3/4.what is theprobability that
a) all of them win their races)
b) only one of them win his race?
Answer:
a
Step-by-step explanation:
1/3 x 3/5 x 3/4 =7/12 so therefore that's what the answer isn't
How many edges are there?
A. not enough information
B. 15
C. 7
D. 10
The number of edges in the given figure is 15. The correct option is B.
What is geometry?One of the first areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects.
The shape is made up of the triangular prism and the trapezoidal prism the total number of edges in the shape will be 15.
Therefore, the number of edges in the given figure is 15. The correct option is B.
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2/5 + 1/10= In simplest form
A. 3/15
B. 5/10
C. 1/4
D. 1/2
Answer:
1/2
Step-by-step explanation:
2/5 + 1/10
Get a common denominator of 10
2/5 * 2/2 + 1/10
4/10 + 1/10
5/10
simplify
Divide the top and bottom by 5
1/2
Answer:
[tex] \frac{1}{2} [/tex]
Answer D is correctStep-by-step explanation:
[tex] \frac{2}{5} + \frac{1}{10} \\ \frac{2 \times 2}{5 \times 2} + \frac{1}{10} \\ \frac{4}{10} + \frac{1}{10} \\ \frac{5}{10} \\ \frac{5 \div 5}{10 \div 5} \\ = \frac{1}{2} [/tex]
A company pays $20 per hour for up to 8 hours of work, and $30 per hour for overtime hours (hours beyond 8 hours). For up to 8 hours worked, the equation for total pay (y) for hours worked (x) is y = 20x. For over 8 hours worked, what is the equation for total pay (y) as a function of total hours worked (x)?
Answer: y = 30x
Step-by-step explanation:
Because we are talking about over 8 hours. The question states that you get 30$ per hour for overtime hours. That means if you work over 8 hours your dollars per hour increases to 30. So because the amount of dollars increases to 30 you can infer that all you have to do is make the same equation as the 20 dollar's per hour equation. Except you put 30 making it y = 30x.
Find the area of the sector round your answer to the nearest 10th
Answer:
63.4
Step-by-step explanation:
Area of sector=pi*r^2*(theta/360)
Area of sector=pi*121*(60/360)
Area of sector=63.4
Question Which of the following is a benefit of using email to communicate at work ? a) You can express yourself in a limited number of characters b) You don't have to worry about using proper grammar. c) You always get a response right away. d ) You can reach a large audience with one communication .
Answer:
d) you can reach a large audience with one communication
Step-by-step explanation:
common sense
write your answer as an integer or as a decimal rounded to the nearest tenth
Answer:
Step-by-step explanation:
CE and are the sides making up the sine of an angle.
CE is the side opposite the angle
DE is the side hypotenuse.
<D = 61 degrees
Sin(D) = opposite / hypotenuse
hypotenuse = 8
Sin(61) = 0.8746
CE = ?
sin(61) = CE / 8 multiply both sides by 8
8 sin(61) = CE
CE = 8 * 0.8746
CE = 6.9969
CE = 7.0
That 0 should be included in the answer, but I think it is safe to say that if you enter 7, you will get it right.
Answer:
7.0
Step-by-step explanation:
Trucks in a delivery fleet travel a mean of 120 miles per day with a standard deviation of 23 miles per day. The mileage per day is distributed normally. Find the probability that a truck drives less than 159 miles in a day. Round your answer to four decimal places.
Answer:
the probability that a truck drives less than 159 miles in a day = 0.9374
Step-by-step explanation:
Given;
mean of the truck's speed, (m) = 120 miles per day
standard deviation, d = 23 miles per day
If the mileage per day is normally distributed, we use the following conceptual method to determine the probability of less than 159 miles per day;
1 standard deviation above the mean = m + d, = 120 + 23 = 143
2 standard deviation above the mean = m + 2d, = 120 + 46 = 166
159 is below 2 standard deviation above the mean but greater than 1 standard deviation above the mean.
For normal districution, 1 standard deviation above the mean = 84 percentile
Also, 2 standard deviation above the mean = 98 percentile
143 --------> 84%
159 ---------> x
166 --------- 98%
[tex]\frac{159-143}{166-143} = \frac{x-84}{98-84} \\\\\frac{16}{23} = \frac{x-84}{14} \\\\23(x-84) = 224\\\\x-84 = 9.7391\\\\x = 93.7391\ \%[/tex]
Therefore, the probability that a truck drives less than 159 miles in a day = 0.9374
Differentiate the following Functions
5x^2-2xy + 4y^3= 5
Answer:
[tex]\displaystyle y' = \frac{y - 5x}{x + 6y^2}[/tex]
General Formulas and Concepts:
Algebra I
Terms/CoefficientsFactoringCalculus
Differentiation
DerivativesDerivative NotationImplicit DifferentiationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle 5x^2 - 2xy + 4y^3 = 5[/tex]
Step 2: Differentiate
Implicit Differentiation: [tex]\displaystyle \frac{dy}{dx}[5x^2 - 2xy + 4y^3] = \frac{dy}{dx}[5][/tex]Rewrite [Derivative Property - Addition/Subtraction]: [tex]\displaystyle \frac{dy}{dx}[5x^2] - \frac{dy}{dx}[2xy] + \frac{dy}{dx}[4y^3] = \frac{dy}{dx}[5][/tex]Rewrite [Derivative Property - Multiplied Constant]: [tex]\displaystyle 5\frac{dy}{dx}[x^2] - 2\frac{dy}{dx}[xy] + 4\frac{dy}{dx}[y^3] = \frac{dy}{dx}[5][/tex]Basic Power Rule [Chain Rule]: [tex]\displaystyle 10x - 2\frac{dy}{dx}[xy] + 12y^2y' = 0[/tex]Product Rule: [tex]\displaystyle 10x - 2\bigg[ \frac{dy}{dx}[x]y + x\frac{dy}{dx}[y] \bigg] + 12y^2y' = 0[/tex]Basic Power Rule [Chain Rule]: [tex]\displaystyle 10x - 2\bigg[ y + xy' \bigg] + 12y^2y' = 0[/tex]Simplify: [tex]\displaystyle 10x - 2y + 2xy' + 12y^2y' = 0[/tex]Isolate y' terms: [tex]\displaystyle 2xy' + 12y^2y' = 2y - 10x[/tex]Factor: [tex]\displaystyle y'(2x + 12y^2) = 2y - 10x[/tex]Isolate y': [tex]\displaystyle y' = \frac{2y - 10x}{2x + 12y^2}[/tex]Factor: [tex]\displaystyle y' = \frac{2(y - 5x)}{2(x + 6y^2)}[/tex]Simplify: [tex]\displaystyle y' = \frac{y - 5x}{x + 6y^2}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Book: College Calculus 10e
In a class of students, the following data table summarizes how many students have a cat or a dog. What is the probability that a student who has a cat also has a dog?
Has a cat Does not have a cat
Has a dog 7 6
Does not have a dog 8 2
A factory makes twenty-three million, five hundred fifty candies each month. This number in standard form is
Answer:
23,000,550
Step-by-step explanation:
A million has six zeroes, so twenty three million is
23,000,000
Since five hundred fifty is not in the thousands, it replaces the last trio of zeroes.
We have the number in standard form as
23,000,550
Answer:
23000550
Step-by-step explanation:
If the slope of a wheelchair ramp is 1/11 then what is the angle of inclination to the nearest tenth of a degree?
Answer
4.8 degrees to the nearest tenth.
Step-by-step explanation:
The slope = rise / run = opposite side / adjacent side.
So the angle of inclination is the angle whose tangent is 1/12.
To the nearest tenth of a degree it is 4.8 degrees.
Twenty students randomly assigned to an experimental group receive an instructional program; 30 in a control group do not. After 6 months, both groups are tested on their knowledge. The experimental group has a mean of 38 on the test (with an estimated population standard deviation of 3); the control group has a mean of 35 (with an estimated population standard deviation of 5). Using the .05 level, evaluate the researcher's hypothesis that the instructional program affects students' knowledge. What is the correct cutoff score(s)
Answer:
The solution according to the problem given is provided below in the explanation segment.
Step-by-step explanation:
According to the question,
[tex]H_o: \mu_1=\mu_2[/tex]
[tex]H_a: \mu_1 \neq \mu_2[/tex]
Level of significance,
[tex]\alpha = .05[/tex]
The test statistics will be:
⇒ [tex]Z = \frac{(\bar x_1 - \bar x_2)}{\sqrt{\frac{\sigma_1^2}{n_1} +\frac{\sigma_2^2}{n_2} } }[/tex]
[tex]=\frac{(38-35)}{\sqrt{\frac{(3)^2}{30} +\frac{(5)^2}{30} } }[/tex]
[tex]=2.82[/tex]
The p-value will be:
= [tex]0.0024[/tex]
Which expressions are equivalent to -6(b+2)+8
Choose all answers that apply:
A. -6b+2+8
B. -6b-4
C. None of the above
Answer:
B. -6b-4
Step-by-step explanation:
-6(b+2)+8
Distribute
-6b-12+8
Combine like terms
-6b-4
ko dung may tinh hay so sanh
3√7 vs 7√3
Answer:
what this makes bi sense haha
Step-by-step explanation:
but ok
Use the following information to answer the next six exercises. There are 23 countries in North America, 12 countries in South America, 47 countries in Europe, 44 countries in Asia, 54 countries in Africa, and 14 in Oceania (Pacific Ocean region).
Let A = the event that a country is in Asia.
Let E = the event that a country is in Europe.
Let F = the event that a country is in Africa.
Let N = the event that a country is in North America. Let O = the event that a country is in Oceania.
Let S = the event that a country is in South America.
18. What is the probability of drawing a red card in a standard deck of 52 cards?
19. What is the probability of drawing a club in a standard deck of 52 cards?
The probabilities we found in this exercise are.
0.2268 = 22.68% probability that a country is in Asia.0.2423 = 24.23% probability that a country is in Europe.0.2784 = 27.84% probability that a country is in Africa.0.1186 = 11.86% probability that a country is in North America.0.0722 = 7.22% probability that a country is in Oceania.0.0619 = 6.19% probability that a country is in South America.0.5 = 50% probability of drawing a red card in a standard deck of 52 cards.0.25 = 25% probability of drawing a club in a standard deck of 52 cards.In this exercise, probability concepts are used.
A probability is the number of desired outcomes divided by the number of total outcomes.
Total number of countries:
23 + 12 + 47 + 44 + 54 + 14 = 194
Let A = the event that a country is in Asia.
44 of the 194 countries are in Asia, thus:
[tex]P(A) = \frac{44}{194} = 0.2268[/tex]
0.2268 = 22.68% probability that a country is in Asia.
Let E = the event that a country is in Europe.
47 out of 194 countries are in Europe, thus:
[tex]P(E) = \frac{47}{194} = 0.2423[/tex]
0.2423 = 24.23% probability that a country is in Europe.
Let F = the event that a country is in Africa.
54 out of 194 countries are in Africa, thus:
[tex]P(F) = \frac{54}{194} = 0.2784[/tex]
0.2784 = 27.84% probability that a country is in Africa.
Let N = the event that a country is in North America.
23 out of 194 countries are in North America, thus:
[tex]P(N) = \frac{23}{194} = 0.1186[/tex]
0.1186 = 11.86% probability that a country is in North America.
Let O = the event that a country is in Oceania.
14 out of 194 countries are in Oceania, thus:
[tex]P(O) = \frac{14}{194} = 0.0722[/tex]
0.0722 = 7.22% probability that a country is in Oceania.
Let S = the event that a country is in South America.
12 out of 194 countries are in South America, thus:
[tex]P(S) = \frac{12}{194} = 0.0619[/tex]
0.0619 = 6.19% probability that a country is in South America.
18. What is the probability of drawing a red card in a standard deck of 52 cards?
In a standard deck of 52 cards, 26 are red, and thus:
[tex]p = \frac{26}{52} = 0.5[/tex]
0.5 = 50% probability of drawing a red card in a standard deck of 52 cards.
19. What is the probability of drawing a club in a standard deck of 52 cards?
In a standard deck of 52 cards, 13 are clubs, and thus:
[tex]p = \frac{13}{52} = 0.25[/tex]
0.25 = 25% probability of drawing a club in a standard deck of 52 cards.
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Land surveyors outlined a park as shown. What is the area of the park?
la cuadra se llama 6minutos
What type of line is PQ?
A. altitude
B. angle bisector
C. side bisector
D. median
The line PQ of the triangle is an altitude. The correct option is A.
What is the altitude of the triangle?
A line segment passing through a triangle's vertex and running perpendicular to the line containing the base is the triangle's height in geometry.
The extended base of the altitude is the name given to this line that contains the opposing side. The foot of the altitude is the point at where, the extended base and the height converge.
In the given triangle the line segment PQ is passing through a triangle's vertex and running perpendicular to the line containing the base is the triangle's height in geometry.
Therefore, the line PQ of the triangle is an altitude. The correct option is A.
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Seven and one-half foot-pounds of work is required to compress a spring 2 inches from its natural length. Find the work required to compress the spring an additional 3 inch.
Answer:
Apply Hooke's Law to the integral application for work: W = int_a^b F dx , we get:
W = int_a^b kx dx
W = k * int_a^b x dx
Apply Power rule for integration: int x^n(dx) = x^(n+1)/(n+1)
W = k * x^(1+1)/(1+1)|_a^b
W = k * x^2/2|_a^b
From the given work: seven and one-half foot-pounds (7.5 ft-lbs) , note that the units has "ft" instead of inches. To be consistent, apply the conversion factor: 12 inches = 1 foot then:
2 inches = 1/6 ft
1/2 or 0.5 inches =1/24 ft
To solve for k, we consider the initial condition of applying 7.5 ft-lbs to compress a spring 2 inches or 1/6 ft from its natural length. Compressing 1/6 ft of it natural length implies the boundary values: a=0 to b=1/6 ft.
Applying W = k * x^2/2|_a^b , we get:
7.5= k * x^2/2|_0^(1/6)
Apply definite integral formula: F(x)|_a^b = F(b)-F(a) .
7.5 =k [(1/6)^2/2-(0)^2/2]
7.5 = k * [(1/36)/2 -0]
7.5= k *[1/72]
k =7.5*72
k =540
To solve for the work needed to compress the spring with additional 1/24 ft, we plug-in: k =540 , a=1/6 , and b = 5/24 on W = k * x^2/2|_a^b .
Note that compressing "additional one-half inches" from its 2 inches compression is the same as to compress a spring 2.5 inches or 5/24 ft from its natural length.
W= 540 * x^2/2|_((1/6))^((5/24))
W = 540 [ (5/24)^2/2-(1/6)^2/2 ]
W =540 [25/1152- 1/72 ]
W =540[1/128]
W=135/32 or 4.21875 ft-lbs
Step-by-step explanation:
commission received
Answer:
Commission Received refers to a percentage amount received by the company (or) an individual on the total sales incurred. It is an indirect income/revenue recorded on the credit side of profit and loss account.
Step-by-step explanation:
mark me brainliest if my answer is correct
Plane P is a cross-section of the solid below. What shape is the cross section?
A. rectangle
B. not enough information
C. hexagon
D. pentagon
Answer:
C. Hexagon
Step-by-step explanation:
The answer is clearly C. Hexagon. This is because the question is referring to the shape shown on Plane P as if it were 2D. Therefore, the shape with 6 sides is a hexagon and cannot be anything else.
The shape is the cross-section is a hexagon.
What is a hexagon?In geometry, a hexagon may be described as a closed two-dimensional polygon with six aspects. The hexagon has 6 vertices and 6 angles also. Hexa means six and gonia approach angles.
All hexagons have six facets, regardless of the sort of hexagon it is. which means that normal hexagons, irregular hexagons, concave hexagons, and convex hexagons all have six facets.
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the perimeter of a square is less than or equal to 50 find the range of the value of the length of the square
Answer:
12.5 ≥ s >0
Step-by-step explanation:
The perimeter of a square is given by
P = 4s where s is the side length
50 ≥ 4s
Divide each side by 4
50/4 ≥ 4s/4
25/2 ≥ s
12.5 ≥ s
Can someone help me? I am struggling and I would be so happy if any of you helped me. Thank you for your help!
Answer:
Mean = 52
Standard Deviation = 13.64
Step-by-step explanation:
mean = 260/5
= 52
Standard Deviation = [tex]\sqrt{\frac{930}{5} }[/tex] = 13.64
I wasn't sure about my answer so used the Gauthmath app
Determine which type of error is most likely to arise from the following situations. a 1. the time in which individuals are contacted to take a survey occurs during work hours f 2. the last part of a newspaper article asks readers to mail or email the newspaper their opinion about universal health coverage 3. subjects are asked to recall how often they snacked between meals in the past 30 days 4. a survey to assess teachers' opinions about Common Core uses a member list for the largest teachers' union as the sampling frame a. question wording b. undercoverage c. processing error d. bad sampling method e. response error f. nonresponse g. random sampling error
Answer:
Determination of type of error arising from the situations
Situation Type of Error
1. Nonresponse
2. Bad sampling method
3. Question wording
4. Undercoverage
Step-by-step explanation:
Types of errors:
a. question wording means that the manner a question is worded elicits some particular responses, which may not accurately reflect reality.
b. undercoverage occurs when some elements of the target population is not represented on the survey frame.
c. processing error arises from data processing
d. bad sampling method is caused by the voluntariness of those who choose to respond.
e. response error is caused by a questionnaire that requires framing improvements, misinterpretation of questions by interviewers or respondents, and errors in respondents' statements.
f. nonresponse error arises as a result of incomplete information or partial response.
g. random sampling error arises from the limited sample size when compared with the population size.
What is the sum of 2 and 3 subtracted from the product of 2 and the difference of 7 and 4? The answer is 1, but how is it solved?
Answer: -1
Step-by-step explanation:
sum of 2 and 3 subtracted from the product of 2 difference of 7 and 4
(2+3) - 2 ( 7 - 4 ) = -1
(2+3)-2(7-4) =
5 - 2(3) =
5-6 = -1
The sum of 2 and 3 subtracted from the product of 2 and the difference of 7 and 4 is equivalent to 1.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have the sum of 2 and 3 subtracted from the product of 2 and the difference of 7 and 4
From the question, we can model the equation as -
x = 2 × (7 - 4) - (2 + 3)
x = 2(3) - 5
x = 6 - 5
x = 1
Therefore, the sum of 2 and 3 subtracted from the product of 2 and the difference of 7 and 4 is equivalent to 1.
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An article in the November 1983 Consumer Reports compared various types of batteries. The average lifetimes of Duracell Alkaline AA batteries and Eveready Energizer Alkaline AA batteries were given as 4.1 hours and 4.5 hours, respectively. Suppose these are the population average lifetimes.
Required:
Let x̄ be the sample average lifetime of 64 Duracell and ȳ be the sample average lifetime of 64 Eveready Energizer batteries. What is the mean value of x̄- ȳ(i.e., where is the distribution of -centered)?
Answer:
The mean is of -0.4 hours.
Step-by-step explanation:
To solve this question, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Mean of the sample of 64 Duracell:
By the Central Limit Theorem, 4.1 hours.
Mean of the sample of 64 Eveready:
By the Central Limit Theorem, 4.5 hours.
Mean of the difference?
Subtraction of normal variables, so we subtract the means.
4.1 - 4.5 = -0.4
The mean is of -0.4 hours.
For an avid bird watcher, the probability of spotting a California Condor while birdwatching in the Grand Canyon area is 0.3. The probability of being able to take a clear picture of the bird suppose one is able to spot it is 0.8. What is the probability that the bird watcher is able to take a clear picture of a California Condor
Answer:
the probability of taking a clear picture of a California candor is .24
