Answer:
a) 240 ways
b) 12 ways
c) 108 ways
d) 132 ways
e) i) 0.55
ii) 0.4125
Step-by-step explanation:
Given the components:
Receiver, compound disk player, speakers, turntable.
Then a purcahser is offered a choice of manufacturer for each component:
Receiver: Kenwood, Onkyo, Pioneer, Sony, Sherwood => 5 offers
Compact disc player: Onkyo, Pioneer, Sony, Technics => 4 offers
Speakers: Boston, Infinity, Polk => 3 offers
Turntable: Onkyo, Sony, Teac, Technics => 4 offers
a) The number of ways one component of each type can be selected =
[tex] \left(\begin{array}{ccc}5\\1\end{array}\right) \left(\begin{array}{ccc}4\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}4\\1\end{array}\right) [/tex]
[tex] = 5 * 4 * 3 * 4 = 240 ways [/tex]
b) If both the receiver and compact disk are to be sony.
In the receiver, the purchaser was offered 1 Sony, also in the CD(compact disk) player the purchaser was offered 1 Sony.
Thus, the number of ways components can be selected if both receiver and player are to be Sony is:
[tex] \left(\begin{array}{ccc}1\\1\end{array}\right) \left(\begin{array}{ccc}1\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}4\\1\end{array}\right) [/tex]
[tex] = 1 * 1 * 3 * 4 = 12 ways [/tex]
c) If none is to be Sony.
Let's exclude Sony from each component.
Receiver has 1 sony = 5 - 1 = 4
CD player has 1 Sony = 4 - 1 = 3
Speakers had 0 sony = 3 - 0 = 3
Turntable has 1 sony = 4 - 1 = 3
Therefore, the number of ways can be selected if none is to be sony:
[tex] \left(\begin{array}{ccc}4\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) [/tex]
[tex] = 4 * 3 * 3 * 3 = 108 ways [/tex]
d) If at least one sony is to be included.
Number of ways can a selection be made if at least one Sony component is to be included =
Total possible selections - possible selections without Sony
= 240 - 108
= 132 ways
e) If someone flips switches on the selection in a completely random fashion.
i) Probability of selecting at least one Sony component=
Possible selections with at least one sony / Total number of possible selections
[tex] \frac{132}{240} = 0.55 [/tex]
ii) Probability of selecting exactly one sony component =
Possible selections with exactly one sony / Total number of possible selections.
[tex] \frac{\left(\begin{array}{ccc}1\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) + \left(\begin{array}{ccc}4\\1\end{array}\right) \left(\begin{array}{ccc}1\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) + \left(\begin{array}{ccc}4\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}1\\1\end{array}\right)}{240} [/tex]
[tex] = \frac{(1*3*3*3)+(4*1*3*3)+(4*3*3*1)}{240} [/tex]
[tex] \frac{27 + 36 + 36}{240} = \frac{99}{240} = 0.4125 [/tex]
Solve this equation for x: 2x^2 + 12x - 7 = 0
What is the first step to solve this equation?
-combine like terms
-factor the trinomial
-isolate the constant term by adding 7 to both sides
Answer:
x=0.5355 or x=-6.5355
First step is to: Isolate the constant term by adding 7 to both sides
Step-by-step explanation:
We want to solve this equation: [tex]2x^2 + 12x - 7 = 0[/tex]
On observation, the trinomial is not factorizable so we use the Completing the square method.
Step 1: Isolate the constant term by adding 7 to both sides
[tex]2x^2 + 12x - 7+7 = 0+7\\2x^2 + 12x=7[/tex]
Step 2: Divide the equation all through by the coefficient of [tex]x^2[/tex] which is 2.
[tex]x^2 + 6x=\frac{7}{2}[/tex]
Step 3: Divide the coefficient of x by 2, square it and add it to both sides.
Coefficient of x=6
Divided by 2=3
Square of 3=[tex]3^2[/tex]
Therefore, we have:
[tex]x^2 + 6x+3^2=\frac{7}{2}+3^2[/tex]
Step 4: Write the Left Hand side in the form [tex](x+k)^2[/tex]
[tex](x+3)^2=\frac{7}{2}+3^2\\(x+3)^2=12.5\\[/tex]
Step 5: Take the square root of both sides and solve for x
[tex]x+3=\pm\sqrt{12.5}\\x=-3\pm \sqrt{12.5}\\x=-3+ \sqrt{12.5}, $ or $x= -3- \sqrt{12.5}\\$x=0.5355 or x=-6.5355[/tex]
Answer:
Step-by-step explanation:
Step 1: Isolate the constant term by adding 7 to both sides of the equation.
Step 2: Factor 2 from the binomial.
Step 3: 9
Step 3 b: 18
Step4: write the trinomial as the square root of a binomial.
Step 5: divide both sides of the equation by 2 Step
6: Apply the square root property of equality Step
7: subtract 3 from both sides of the equation.
What’s the correct answer for this?
Answer:
x = 12
Step-by-step explanation:
Since they are equidistant from the centre, they are equal in length i.e.
JK = LM
4x+37 = 5(x+5)
4x+37 = 5x+25
37-25 = 5x-4x
12 = x
OR
x = 12
Some parts of California are particularly earthquake-prone. Suppose that in one metropolitan area, 33% of all homeowners are insured against earthquake damage. Four homeowners are to be selected at random. Let X denote the number among the four who have earthquake insurance. A) Find the probability distribution of X.B) What is the most likely value for X?
C) What is the probability that at least two of the four selected have earthquake insurance?
Answer:
(a) The probability mass function of X is:
[tex]P(X=x)={4\choose x}\ (0.33)^{x}\ (1-0.33)^{4-x};\ x=0,1,2,3...[/tex]
(b) The most likely value for X is 1.32.
(c) The probability that at least two of the four selected have earthquake insurance is 0.4015.
Step-by-step explanation:
The random variable X is defined as the number among the four homeowners who have earthquake insurance.
The probability that a homeowner has earthquake insurance is, p = 0.33.
The random sample of homeowners selected is, n = 4.
The event of a homeowner having an earthquake insurance is independent of the other three homeowners.
(a)
All the statements above clearly indicate that the random variable X follows a Binomial distribution with parameters n = 4 and p = 0.33.
The probability mass function of X is:
[tex]P(X=x)={4\choose x}\ (0.33)^{x}\ (1-0.33)^{4-x};\ x=0,1,2,3...[/tex]
(b)
The most likely value of a random variable is the expected value.
The expected value of a Binomial random variable is:
[tex]E(X)=np[/tex]
Compute the expected value of X as follows:
[tex]E(X)=np[/tex]
[tex]=4\times 0.33\\=1.32[/tex]
Thus, the most likely value for X is 1.32.
(c)
Compute the probability that at least two of the four selected have earthquake insurance as follows:
P (X ≥ 2) = 1 - P (X < 2)
= 1 - P (X = 0) - P (X = 1)
[tex]=1-{4\choose 0}\ (0.33)^{0}\ (1-0.33)^{4-0}-{4\choose 1}\ (0.33)^{1}\ (1-0.33)^{4-1}\\\\=1-0.20151121-0.39700716\\\\=0.40148163\\\\\approx 0.4015[/tex]
Thus, the probability that at least two of the four selected have earthquake insurance is 0.4015.
In a religious survey of southerners, it was found that 65% believe in angels. If you have a random sample of 8 southerners: What is the probability that at most 3 of the southerners believe in angels
Answer:
10.60%
Step-by-step explanation:
We have to solve the above we have to apply bimonial and add each one, like this:
p (x <= 3) = p (x = 0) + p (x = 1) + p (x = 2) + p (x = 3)
p (x <= 3) = 8C0 * (0.65) ^ 0 * (0.35) ^ 8 + 8C1 * (0.65) ^ 1 * (0.35) ^ 7 + 8C2 * (0.65) ^ 2 * (0.35) ^ 6 + 8C3 * (0.65) ^ 3 * (0.35) ^ 5
p (x <= 3) = 8! / (0! (8-0)!) * (0.65) ^ 0 * (0.35) ^ 8 + 8! / (1! (8-1)!) * (0.65 ) ^ 1 * (0.35) ^ 7 + 8! / (2! (8-2)!) * (0.65) ^ 2 * (0.35) ^ 6 + 8! / (3! (8-3)!) * (0.65) ^ 3 * (0.35) ^ 5
p (x <= 3) = 0.1060
therefore the probability is 10.60%
Answer:
The probability that at most 3 of the southerners believe in angels is 10.61%
Step-by-step explanation:
Given;
65% believe in angels = p
then, 35% will not believe in angel = q
total sample number, n = 8
The probability that at most 3 southerners believe in angels is calculated as;
= p( non believe in angel) or p( 1 southerner believes and 7 will not believe) or p( 2 southerner believe and 6 will not believe) or p( 3 southerner believe and 5 will not believe)
= 8C₀(0.65)⁰(0.35)⁸ + 8C₁(0.65)¹(0.35)⁷ + 8C₂(0.65)²(0.35)⁶ + 8C₃(0.65)³(0.35)⁵
= 1(1 x 0.000225) + 8(0.65 x 0.000643) + 28(0.4225 x 0.00184) + 56(0.2746 x 0.00525)
= 0.1061
= 10.61%
Therefore, the probability that at most 3 of the southerners believe in angels is 10.61%
Marina had 24,500 to invest. She divided the money into three different accounts. At the end of the year, she had made RM1,300 in interest. The annual yield on each of the three accounts was 4%, 5.5%, and 6%. If the amount of money in the 4% account was four times the amount of money in the 5.5% account, how much had she placed in each account?
Answer:
See below
Bold parts are important parts. They are the equations.
Marina had RM24,500 to invest.
If the amount of money in the 4% account was four times the amount of money in the 5.5% account.
" At the end of the year, she had made RM1,300 in interest. The annual yield on each of the three accounts was 4%, 5.5%, and 6%."
"If the amount of money in the 4% account was four times the amount of money in the 5.5% account,"
a = 4b
Down is the equations.
let a = amt in the 4% acct
let b = amt in the 5.5% acct
let c = amt in the 6%
"Marina had RM 24,500 to invest."
a + b + c = 24500
Replace a with 4b in both equations, simplify
b = $2000 in the 5.5% investment
a = $8000 in the 4% acct
Hope this helps.
Marina invested $ 8000 at 4%, $ 2000 at 5.5%, and $ 14,500 at 6%.
Since Marina had $ 24,500 to invest, and she divided the money into three different accounts, and at the end of the year, she had made $ 1,300 in interest, and the annual yield on each of the three accounts was 4%, 5.5%, and 6%, to determine, if the amount of money in the 4% account was four times the amount of money in the 5.5% account, how much had she placed in each account, the following calculation must be performed:
4000 x 0.04 + 1000 x 0.055 + 19500 x 0.06 = 1385 8000 x 0.04 + 2000 x 0.055 + 14500 x 0.06 = 1300
Therefore, Marina invested $ 8000 at 4%, $ 2000 at 5.5%, and $ 14,500 at 6%.
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the mean for the scores 17,19,19,23,26
Answer:
the mean is 20.8.
Step-by-step explanation:
Add all the numbers to get 104. Then, divide it by how many score there were, 5. 104/4= 20.8
Solution,
Given data: 17,19,19,23,26
summationfX=104
N(total no.of items)=5
Now,
Mean=summation FX/N
=104/5
=20.8
hope it helps
Good luck on your assignment
two cars start at the same time, but travel In opposite direction. one car's average speed is 20 miles per hour. at the end of 4 hours, the two cars are 280 miles apart. find the average speed in mph of the car.
Answer: 50 MPH ON AVERAGE: ✌️
20 mph for four hours is 80 miles
200 miles divided by 4 hours is 50 mph
Answer:
50 mph :)
Step-by-step explanation:
20*4=80
280-80=200
200/4=50
answer 50 mph
the word bombard means
Answer:
Bombard means to rush, to overtake
Step-by-step explanation:
hope this helped a little !
Answer:
Rush overtake
Step-by-step explanation:
A friend gives you four baseball cards for your birthday. Afterward, you begin collecting them. You buy the same number of cards once each week. The equation y = 2x + 4 describes the number of cards, y, you have after x weeks.
Part 1 out of 3
Find and interpret the slope and the y−intercept of the line that represents this situation.
The slope is
, while the y−intercept is
. This equation represents starting with
cards and adding
cards each week.
Answer:
The slope is 2, while the y-intercept is 4. This equation represents starting with 4 cards and adding 2 cards each week.
Step-by-step explanation:
Given the equation which describes the number of cards, y, you have after x weeks: y=2x+4
Comparing this with the slope intercept form of the equation of the line: y=mx+b, where:
m is the slopeb is the y-intercept.We have that:
Slope
Slope, m=2.
A slope of 2 indicates that you buy 2 cards per week.
The y-intercept
The y-intercept of the line, b=4.
This is the starting value. In this case, it represents the number of cards you were given by your friend.
The slope is 2, while the y-intercept is 4. This equation represents starting with 4 cards and adding 2 cards each week.
Ariana is going to invest in an account paying an interest rate of 3.4% compounded monthly. How much would Ariana need to invest, to the nearest dollar, for the value of the account to reach $9,200 in 14 years?
Answer:
Ariana is going to invest P($) in an account paying an interest rate of 3.4% compounded monthly.
After 14 years, the amount of money in Adrina's account is calculated by:
A = P x (1 + rate)^(time)
or
A = P x (1 + 3.4/12)^(14 x 12)
or
9200 = P x (1 + 3.4/12)^(14 x 12)
=> P = 9200/[(1 + 3.4/12)^(14 x 12)]
=> P = 5791.044$
Hope this helps!
:)
The value of the account to reach $9,200 in 14 years is $5,791.
Calculation of the value of the account:Since interest rate of 3.4% compounded monthly. And, the amount is $9,200 in 14 years
So, the value should be
[tex]A = P \times (1 + rate)^{(time)}\\\\A = P \times (1 + 3.4/12)^{(14 \times 12)}\\\\9200 = P \times (1 + 3.4/12)^{(14 \times 12)}\\\\ P = 9200\div [(1 + 3.4/12)^{(14 \times 12)]}[/tex]
P = $5791
hence, The value of the account to reach $9,200 in 14 years is $5,791.
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what is 1/2*1^12 1/2
Answer: 0.5
Step-by-step explanation: I think that the answer.
A line passes through the point (3,-8) and has a slope of 3. Write an equation in point-slope form for this line.
Answer:
y+8 = 3(x-3)
Step-by-step explanation:
The point slope form of the equation for a line is
y-y1 = m(x-x1)
y- -8 = 3(x -3)
y+8 = 3(x-3)
Calculate the derivative indicated.
dy
1
where
y=51
+ 4x2
dx2
x=6
73
Answer:
8 5/648
Step-by-step explanation:
y = 5x ^ -3 + 4x^2
dy /dx = 5 * -3 x^ -4 + 4 * 2x ^ 1
= -15 x ^ -4 + 8x
Now take the second derivative
dy^2/ dx^2 = -15 * -4 x^-5 +8
= 60 x^ -5 +8
= 60 /x^5 +8
Evaluate at x = 6
= 60 / 6^5 +8
60/7776 +8
5/648 + 8
8 5/648
Please help! Correct answer only, please! Consider the matrix shown below: Find the determinant of the matrix C. Group of answer choices A. -14 B. 14 C. -22 D. The determinant cannot be found for a matrix with these dimensions.
Answer: d) determinant cannot be found
Step-by-step explanation:
You can only find the determinant of a SQUARE matrix.
In other words, the dimensions must be 2 × 2 or 3 × 3 or ... n × n
The dimensions of the given matrix is 2 x 3, so the determinant cannot be calculated.
Express the complex number in trigonometric form.
-6 + 6\sqrt(3) i
Answer:
12(cos120°+isin120°)Step-by-step explanation:
The rectangular form of a complex number is expressed as z = x+iy
where the modulus |r| = [tex]\sqrt{x^{2}+y^{2}[/tex] and the argument [tex]\theta = tan^{-1}\frac{y}{x}[/tex]
In polar form, x = [tex]rcos\theta \ and\ y = rsin\theta[/tex]
[tex]z = rcos\theta+i(rsin\theta)\\z = r(cos\theta+isin\theta)[/tex]
Given the complex number, [tex]z = -6+6\sqrt{3} i[/tex]. To express in trigonometric form, we need to get the modulus and argument of the complex number.
[tex]r = \sqrt{(-6)^{2}+(6\sqrt{3} )^{2}}\\r = \sqrt{36+(36*3)} \\r = \sqrt{144}\\ r = 12[/tex]
For the argument;
[tex]\theta = tan^{-1} \frac{6\sqrt{3} }{-6} \\\theta = tan^{-1}-\sqrt{3} \\\theta = -60^{0}[/tex]
Since tan is negative in the 2nd and 4th quadrant, in the 2nd quadrant,
[tex]\theta =180-60\\\theta = 120^{0}[/tex]
z = 12(cos120°+isin120°)
This gives the required expression.
Find the slope of the line on the graph. Write your answer or a whole number, not a mixed number or decimal
Answer:
-3/2
Step-by-step explanation:
The slope can be found through the equation y2 - y1 / x2 - x1
Finding two points on this line is what we start by doing.
Two points on the line I see are (0,-4) and (2, -7)
Plugging this into the slope formula gives us -7 - (-4) / 2 - 0
Solving this gives us -3 / 2 as the slope.
MIDDLE SCHOOL MATH BRAINLEIST AND 5 STARS AS SOON AS YOU ANSWER!!!!!!!! PLEASE HELP AND THANKS SO MUCH IM SUPER GRATEFUL!!!!!!!!!!!
Answer:
1.76
Step-by-step explanation:
The formula is l x w x h
2 x 2.2 x 0.2 = 0.88
The prisms are the same so
0.88 + 0.88 = 1.76
I need help not good at graphs
Answer:
a, b
Step-by-step explanation:
a and b cause all the data are not in a form of a line
What’s the correct answer for this?
｡☆✼★ ━━━━━━━━━━━━━━ ☾
A tangent meets with the radius to form a right angle
Thus, we can use Pythagoras' theorem
b^2 = c^2 - a^2
Sub the values in:
b^2 = 5^2 - 3^2
b^2 = 16
Square root for the answer:
b = 4
Thus, the answer is option A.
Have A Nice Day ❤
Stay Brainly! ヅ
- Ally ✧
｡☆✼★ ━━━━━━━━━━━━━━ ☾
Answer:
option 1 is the answer
Step-by-step explanation:
IN A CIRCLE , THE TANGENT IS THE PERPENDICULAR TO THE RADIUS DRAWN TO THE POINT OF CONTACT
SO AC ⊥ BC
ie angle ACB= 90 degree
therefore in triangle ABC , ACB = 90 DEGREE
By applying pythagorus theorem ,
AB^2 = AC^2 + BC^2
5^2 = r^2 + 3^2
25 -9 = r^2
16 = r^2
r = square root o f 16
therefore r= 4
please mark me as the brainliest...
Quadrilateral HIJK has sides measuring 12 cm, 26 cm, 14 cm, and 30 cm. Which could be the side lengths of a dilation of HIJK with a scale factor of 1.5?
Answer:
(C) 18cm, 39cm, 21cm and 45cm.
Step-by-step explanation:
The quadrilateral HIJK has sides measuring 12 cm, 26 cm, 14 cm, and 30 cm.
When HIJK is dilated with a scale factor of 1.5, the side lengths becomes:
12 X 1.5 =18 cm
26 X 1.5 =39 cm
14 X 1.5 =21 cm
30 X 1.5 =45 cm
A dilation of HIJK with a scale factor of 1.5 will give us the side lengths:
18cm, 39cm, 21cm and 45cm.
The correct option is C.
Are these calculated correctly?
14. Was the perimeter calculated correctly?
Length = 4 yards Breadth = 1 *2/5 yards = 7/5 yardsWe know that,
Perimeter of rectangle = 2 ( l + b )
= 2 ( 4 + 7 / 5 )
= 2 ( 20 + 7 / 5 )
= 2 × 27/5
= 54 / 5
= 1 * 4/5
No ...
Suppose a food scientist wants to determine whether two experimental preservatives result in different mean shelf lives for bananas. He treats a simple random sample of 15 bananas with one of the preservatives. He then collects another simple random sample of 20 bananas and treats them with the other preservative. As the bananas age, the food scientist records the shelf life of all bananas in both samples. The food scientist does not know the population standard deviations. What test should the food scientist run in order to determine if the two experimental preservatives result in different mean shelf lives for bananas
Answer:
The two sample t-test
Step-by-step explanation:
The appropriate test for thus is the two sample t test which is also known as the independent t test. This tests aims at determined whether there is a statistically significant difference between the means in two unrelated groups which in this context are a random sample with one type of preservative and another sample with another type of preservatives.
With this test, the researcher is able to compare the mean shelf lives of the bananas treated with the two different preservatives... The null hypothesis equalises the two means of the sample while the alternative does otherwise.
Marts is solving the equation S=2nrh+2nr2 for h. Which should be the result?
Step-by-step explanation:
Hope you understand this
HELP ASAP PLS! A random number generator is used to create a real number between 0 and 1, equally likely to fall anywhere in this interval of values. (For the instance, 0.3794259832... is a possible outcome). a. Sketch a curve of the probability distribution of this random variable, which is the continuous version of the uniform distribution. b. What is the mean of this probability distribution?
Answer:
a. Attached.
b. Mean = 0.5
Step-by-step explanation:
This random number generator con be modeled with an uniform continous random variable X that has values within 0 and 1, each with the same constant probability within this range.
The probability for the values within the interval [a,b] in a continous uniform distribution can be calculated as:
[tex]f(x)=\dfrac{1}{b-a}\;\;\;x\in[0; 1][/tex]
In this case, b=1 and a=0, so f(x)=1.
The sketched curve of the probability distribution of this random variable is attached.
The mean of this distribution can be calculated as the mean for any uniform distribution:
[tex]E(X)=\dfrac{a+b}{2}=\dfrac{0+1}{2}=0.5[/tex]
i need help quick! please!
Assume that random guesses are made for nine multiple choice questions on an SAT test, so that there are nequals9 trials, each with probability of success (correct) given by pequals0.35. Find the indicated probability for the number of correct answers.
Find the probability that the number x of correct answers is fewer than 4.
P(x<4)= ???
Answer: the probability that the number x of correct answers is fewer than 4 is 0.61
Step-by-step explanation:
Let x be a random variable representing the answers to the SAT questions. This is a binomial distribution since the outcomes are two ways. It is either the answer is correct or incorrect. Also, the probability of success or failure is constant for each trial. The probability of success, p = 0.35
The probability of failure, q would be 1 - p = 1 - 0.35 = 0.65
We want to determine P(x < 4)
n = number of trial = 9
x = 4
From the binomial distribution calculator,
P(x < 4) = 0.61
A Lake Tahoe Community College instructor is interested in the average number of days Lake Tahoe Community College math students are absent from class during a quarter that lasts 9 weeks. What is the population she is interested in
Answer:
All Lake Tahoe Community College math students
Step-by-step explanation:
From the question itself it is clear that the instructor is interested in the average number of days Lake Tahoe Community College math students are absent from class during a quarter that lasts 9 weeks, which clearly indicates that the teacher is interested in population of all Lake Tahoe Community College math students.
Use the set of data to calculate the measures that follow.
0, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 6
Choose each correct measure.
Mean =
Median =
Range =
Interquartile range =
ASAP NEED HELP?
Answer:
cbda
Step-by-step explanation:
What is the surface area of a triangular prism
Answer:
608 (D)
Step-by-step explanation:
To find the area of the prism, just add all the areas in the nets together.
The rectangle in the middle has an area of 192 because it is a 12x16 triangle so you multiply the sides.
Both the rectangles on the top and bottom have an area of 160 because they are both a 10x16. The total of the 2 rectangles would be 320 because 160+160=320.
The triangles on the right each have an area of 48 because the Base=12 and the Height= 8. The formula for finding the area of a triangle is 1/2(BH). 1/2(12*8)= 1/2(96)= 48. There are 2 triangles like this so the totla area of both triangles is 96.
To find the surface area, you just add them all up. 96+320+192= 608
Ocean fishing for billfish is very popular in the Cozumel region of Mexico. In the Cozumel region about 41% of strikes (while trolling) resulted in a catch. Suppose that on a given day a fleet of fishing boats got a total of 29 strikes. Find the following probabilities. a) 12 or fewer fish were caught.b) 5 or more fish were caught.c) between 5 and 12 fish were caught.
Answer:
a) 59.10% probability that 12 or fewer fish were caught.
b) 99.74% probability that 5 or more fish were caught.
c) 58.84% probability that between 5 and 12 fish were caught.
Step-by-step explanation:
I am going to use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 29, p = 0.41[/tex]
So
[tex]\mu = E(X) = np = 29*0.41 = 11.89[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = 2.6486[/tex]
Find the following probabilities.
a) 12 or fewer fish were caught.
Using continuity correction, this is [tex]P(X \leq 12 + 0.5) = P(X \leq 12.5)[/tex], which is the pvalue of Z when X = 12.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{12.5 - 11.89}{2.6486}[/tex]
[tex]Z = 0.23[/tex]
[tex]Z = 0.23[/tex] has a pvalue of 0.5910
59.10% probability that 12 or fewer fish were caught.
b) 5 or more fish were caught.
Using continuity correction, this is [tex]P(X \geq 5 - 0.5) = P(X \geq 4.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 4.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{4.5 - 11.89}{2.6486}[/tex]
[tex]Z = -2.79[/tex]
[tex]Z = -2.79[/tex] has a pvalue of 0.0026
1 - 0.0026 = 0.9974
99.74% probability that 5 or more fish were caught.
c) between 5 and 12 fish were caught.
Using continuity correction, this is [tex]P(5 - 0.5 \leq X \leq 12 + 0.5) = P(4.5 \leq X \leq 12.5)[/tex], which is the pvalue of Z when X = 12.5 subtracted by the pvalue of Z when X = 4.5. So.
From a), when X = 12.5, Z has a pvalue of 0.5910
From b), when X = 4.5, Z has a pvalue of 0.0026.
So
0.5910 - 0.0026 = 0.5884
58.84% probability that between 5 and 12 fish were caught.
the area of the base of a can is 45 square inches.its height is 12 inches.if 1/3 of the height is cut off,what will be the volume of the can?
Answer:
volume = 360 inches³
Step-by-step explanation:
The can itself is a cylinder. The volume of a cylinder can be calculated as follows
volume of a cylinder = πr²h
where
r = radius
h = height
1/3 of the height was cut off that means 1/3 × 12 = 4 inches of the height was cut off. The new height of the can will be 12 - 4 = 8 inches. Therefore,
volume = πr²h =
base area which is the area of a circle = πr² = 45 inches²
volume = 45 × 8
volume = 360 inches³
