Answer:
appropriately writing the proportion can reduce or eliminate steps required to solve it
Step-by-step explanation:
The proportion ...
[tex]\dfrac{A}{B}=\dfrac{C}{D}[/tex]
is equivalent to the equation obtained by "cross-multiplying:"
AD = BC
This equation can be written as proportions in 3 other ways:
[tex]\dfrac{B}{A}=\dfrac{D}{C}\qquad\dfrac{A}{C}=\dfrac{B}{D}\qquad\dfrac{C}{A}=\dfrac{D}{B}[/tex]
Effectively, the proportion can be written upside-down and sideways, as long as the corresponding parts are kept in the same order.
I find this most useful to ...
a) put the unknown quantity in the numerator
b) give that unknown quantity a denominator of 1, if possible.
__
The usual method recommended for solving proportions is to form the cross-product, as above, then divide by the coefficient of the variable. If the variable is already in the numerator, you can simply multiply the proportion by its denominator.
Example:
x/4 = 3/2
Usual method:
2x = 4·3
x = 12/2 = 6
Multiplying by the denominator:
x = 4(3/2) = 12/2 = 6 . . . . . . saves the "cross product" step
__
Example 2:
x/4 = 1/2 . . . . we note that "1" is "sideways" from x, so we can rewrite the proportion as ...
x/1 = 4/2 . . . . . . written with 1 in the denominator
x = 2 . . . . simplify
Of course, this is the same answer you would get by multiplying by the denominator, 4.
The point here is that if you have a choice when you write the initial proportion, you can make the choice to write it with x in the numerator and 1 in the denominator.
Edith is purchasing a car whose MSRP is $22,750. She has asked for an
upgrade to a premium package for which the cost is $5050. The delivery of
this vehicle is an additional $700. Edith will trade in her own car, and the
dealer has offered her $8000. If Edith agrees to this, what will be her total
price for the vehicle?
Answer:
Dear Yates
Answer to your query is provided below
Total Price for her vehicle will be $20600
Step-by-step explanation:
Edith's trading is worth $8000. So, without the package upgrade of the vehicle delivery charge, her cost is:
$22750 - $8000 = $14750.
Now, add the package upgrade ($5050) and the delivery charge ($800).
$14750 + $5050 + $800 = $20600.
The total cost price of the vehicle after all the expenses is given by the equation A = $ 20,500
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
The initial cost of the vehicle is = $ 22,750
Now , Edith has asked for an upgrade to a premium package for which the cost is $5050
So , the new cost of the vehicle = $ 22,750 + $ 5050 = $ 27,800
Now , the delivery charge of the vehicle = $ 700
And , the updated total price = $ 27,800 + $ 700 = $ 28,500
Now , the dealer has offered her $8000
So , the final price of the vehicle = updated total price - $ 8000
On simplifying the equation , we get
The final price of the vehicle A = $ 28,500 - $ 8,000
The final price of the vehicle A = $ 20,500
Hence , the final price of the vehicle is $ 20,500
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Boys to girls ratio is 2 to 3. There are 18 girls. What is total number of students
[tex]\frac{2}{3}=\frac{boys}{18}[/tex]
3*boys=2*18
3*boys=36
boys=12
12+18=30
total number of students: 30
Answer:
30 students
Step-by-step explanation:
2:3 = x:18
X = number of boys
[tex]\frac{2}{3} = \frac{x}{18}[/tex]
multiply 18 by both sides
18 × [tex]\frac{2}{3} = X[/tex]
X = 18 × [tex]\frac{2}{3} = 12[/tex]
18 + 12 = 30
6) The average Mathematics mark for Amin, Azman and Aziz is 73. Azman's mark is 35 more than
Amin while Aziz's is twice of Amin's. What is the Mathematics mark of Amin?
Answer:
46
Step-by-step explanation:
Azman=35+amin
Aziz=3×amin
therefore;35+amin+2amin+amin/3=73
219=35+4amin
219-35=4amin
184=4amin
Amin's mark=184÷4
=46
What is the sum of 2x^2-x and -x-2x^2-2
[tex]solution \\ {2x}^{2} - x + ( - x - {2x}^{2} - 2) \\ = {2x}^{2} - x - x - {2x}^{2} - 2 \\ = {2x}^{2} - {2x}^{2} - x - x - 2 \\ = - 2x - 2[/tex]
Hope it helps
Good luck on your assignment
Answer:
[tex] - 2x - 2[/tex]
Step-by-step explanation:
[tex]2 {x}^{2} - x + ( - x - 2 {x}^{2} - 2) \\ 2 {x}^{2} - x - x - 2 {x}^{2} - 2 \\ 2 {x}^{2} - 2 {x}^{2} - x - x - 2 \\ - 2x - 2[/tex]
hope this helps you.
brainliest appreciated
good luck!
have a nice day!
You have been assigned to determine whether more people prefer Coke or Pepsi. Assume that roughly half the population prefers Coke and half prefers Pepsi. How large a sample do you need to take to ensure that you can estimate, with 95% confidence, the proportion of people preferring Coke within 3% of the actual value? [Hint: proportion est. = 0.5] Round your answer to whole number
Answer:
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11[/tex]
And rounded up we have that n=1068
Step-by-step explanation:
For this case we have the following info given:
[tex] ME=0.03[/tex] the margin of error desired
[tex]Conf= 0.95[/tex] the level of confidence given
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
the critical value for 95% of confidence is [tex] z=1.96[/tex]
We can use as estimator for the population of interest [tex]\hat p=0.5[/tex]. And on this case we have that [tex]ME =\pm 0.03[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11[/tex]
And rounded up we have that n=1068
A restaurant sees about 600 orders on Tuesday. This is down from last Tuesday by about 0.85%. How many did they see last Tuesday
Answer:
Number of orders seen on last Tuesday = 605
Step-by-step explanation:
Number of orders seen on Tuesday = 600
It is given that it is 0.85% less than last Tuesday.
Let number of sales on last Tuesday = [tex]x[/tex]
As per question statement:
Number of order on last Tuesday - 0.85% of Number of order on last Tuesday = 600
OR
i.e. if we subtract 0.85% of x from x, it must be equal to 600.
[tex]x-\dfrac{0.85}{100}x =600\\\Rightarrow x-\dfrac{0.85}{100}x =600\\\Rightarrow \dfrac{100-0.85}{100}x =600\\\Rightarrow \dfrac{99.15}{100} \times x =600\\\Rightarrow x =\dfrac{600\times 100}{99.15}\\\Rightarrow x =\dfrac{60000}{99.15}\\\Rightarrow x \approx 605[/tex]
So, there were about 605 order seen last Tuesday.
Heights of Women. Heights of adult women are distributed normally with a mean of 162 centimeters and a standard deviation of 8 centimeters. Use the Table B.3 Areas under the Normal Curve (page 519 of the textbook) to find the indicated quantities: a) The percentage of heights less than 150 centimeters b) The percentage of heights between 160 centimeters and 180 centimeters
Answer:
a) 6.68% of heights less than 150 centimeters
b) 58.65% of heights between 160 centimeters and 180 centimeters
Step-by-step explanation:
When the distribution is normal, we use 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.
In this question, we have that:
[tex]\mu = 162, \sigma = 8[/tex]
a) The percentage of heights less than 150 centimeters
We have to find the pvalue of Z when X = 150. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{150 - 162}{8}[/tex]
[tex]Z = -1.5[/tex]
[tex]Z = -1.5[/tex] has a pvalue of 0.0668
6.68% of heights less than 150 centimeters
b) The percentage of heights between 160 centimeters and 180 centimeters
We have to find the pvalue of Z when X = 180 subtracted by the pvalue of Z when X = 160.
X = 180
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{180 - 162}{8}[/tex]
[tex]Z = 2.25[/tex]
[tex]Z = 2.25[/tex] has a pvalue of 0.9878
X = 160
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{160 - 162}{8}[/tex]
[tex]Z = -0.25[/tex]
[tex]Z = -0.25[/tex] has a pvalue of 0.4013
0.9878 - 0.4013 = 0.5865
58.65% of heights between 160 centimeters and 180 centimeters
A piece of wire 30 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle.
(a) How much wire should be used for the square in order to maximize the total area?m
(b) How much wire should be used for the square in order to minimize the total area? m
The length of wire used for the square in order to minimize the total area is 9.42m.
We are given that;
Length of wire= 30m
Now
Let the length of the wire used for the square x. The length of the wire used for the circle is 30-x.
The perimeter of the square is 4x and the perimeter of the circle is 2πr=2π(30-x)/(2π)=15-x/π.
The area of the square is [tex]x^2/16[/tex] and
the area of the circle is π(15-x/π)2/4π=225/π-(15x)/π2+[tex]x^2[/tex]/4π.
The total area is A=x2/16+225/π-(15x)/π2+[tex]x^2[/tex]/4π.
To maximize A, we take its derivative with respect to x and set it equal to zero: d[tex]A/dx=x/8-15/π^2+1/(4π)(x)=0[/tex]
Solving for x, we get x=120/(8+4π).
Therefore, 30-x=120/(8+4π)(3-π).
To minimize A, we take its derivative with respect to x and set it equal to zero:
[tex]dA/dx=x/8-15/π^2+1/(4π)(x)=0[/tex]
Solving for x, we get x=120/(8+4π)(3+π).
So, 30-x=120/(8+4π)(3-π).
Therefore, by area the answer will be approximately 9.42 m.
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If n is an even integer such that 5≤n≤12, then what is the mean of all possible values of n?
Answer:
9
Step-by-step explanation:
5≤n≤12
List all the even integers
6,8,10,12
Then find the mean
(6+8+10+12) /4
36/4
9
The mean is 9
For each ordered pair, determine whether it is a solution to x=-3.
Answer: no, no, no, yes
Step-by-step explanation:
x=-3 is a vertical line. It goes straight up and down at x=-3. In order for the points to be on this line, the x-axis has to be -3. Looking at all the choices, all points are not a solution with the exception of (-3,0) which is right on the line.
Answer:
no no no yes
Step-by-step explanation:
i think
Which has the lowest value: 1/20, 1/80, or 1/100?
Answer:
1/100
Step-by-step explanation:
Since the numerators are all the same, the lowest value will depend on the denominators. The greater the denominator, the lower the value. Thus, the answer is 1/100
what is the median of this set of measurements? 10cm, 15cm, 15cm, 18cm, 20cm.
Answer:
15 cm
Step-by-step explanation:
Median means middle number
10,15,15,18,20
Answer:
15 cm
Step-by-step explanation:
The median is the number in the middle of a data set.
First, arrange the data from least to greatest.
10 cm, 15 cm, 15 cm, 18 cm, 20 cm
Now, take one number off each end of the data set until the middle number is reached.
10 cm, 15 cm, 15 cm, 18 cm, 20 cm
15 cm, 15 cm, 18 cm
15 cm
Therefore the median of the set of measurements is 15 cm.
Based on the following construction which statement below must NOT be true?
Answer:
see below
Step-by-step explanation:
The construction makes ray BF a bisector of angle ABC. That bisector divides ABC into the two congruent angles DBF and EBF. As a consequence, angle EBF will be half of ABC, not equal to ABC.
What's the measure of Z1 if Z CBD = 75° and ZABC = 135°?
Answer:
60°
Step-by-step explanation:
∠ABC-∠CBD=∠1
[tex]135-75[/tex]
[tex]=60[/tex]
Answer:
Brainliest goes to me!
Step-by-step explanation:
angle abc = 135 degrees
part of it is angle 1 and the other part is angle cbd
<abc (135) = cbd (75) + <1
angle 1 = 60 degrees
If the price of a product is p (dollars), the number of units demanded is given by the equation q-pe-3p
(a) Find the price elasticity of demand by using the differentials definition of elasticity. Fully simplify your answer.
(b) Use your answer from part (a) to estimate the percent change in q when the price is raised from $2.00 to $2.10.
Answer:
[tex]\mathbf{E(p) = 1 - 3p}[/tex]
the estimate the percent change in q when the price is raised from $2.00 to $2.10 decreases by 25%
Step-by-step explanation:
Given that:
the number of units demanded [tex]q = pe^{-3p}[/tex]
Taking differentiations ; we have,
[tex]\dfrac{dq}{dp}=e^{-3p}+p(-3e^{-3p})[/tex]
[tex]\dfrac{dq}{dp}=(1-3)e^{-3p}[/tex]
Now; the price elasticity of demand using the differentials definition of elasticity is:
[tex]E(p) = \dfrac{dq}{dp}*\dfrac{p}{q}[/tex]
[tex]E(p) =[(1-3)e^{-3p}]*[\dfrac{p}{pe^{-3p}}][/tex]
[tex]\mathbf{E(p) = 1 - 3p}[/tex]
(b) Use your answer from part (a) to estimate the percent change in q when the price is raised from $2.00 to $2.10.
The estimate of the percentage change in price is :
[tex]=\dfrac{2.10-2.00}{2.00}*100 \%[/tex]
= 5%
From (a)
[tex]\mathbf{E(p) = 1 - 3p}[/tex]
Now at p = $2.00
E(2) = 1 - 3 (2.00)
E(2) = 1 - 6
E(2) = -5
The percentage change in q = -5 × 5%
The percentage change in q = -25%
Thus; we can conclude that the estimate the percent change in q when the price is raised from $2.00 to $2.10 decreases by 25%
on monday, it took 3 builders 5 1/2 hours to build a wall. an identical wall needs to be built on tuesday and 5 builders are available. each builder is paid £8.90 for each hour they work. work out how much each builder will be paid for the work completed on tuesday
Answer:
£29.37
Step-by-step explanation:
→ First step is to find the amount of hours it takes for 5 builders
[tex]\frac{3*\frac{11}{2} }{5} =\frac{33}{2} /5=\frac{33}{2} *\frac{1}{5} =\frac{33}{10} =3\frac{3}{10}[/tex]
→ Now we know how long 5 builder takes we need to multiply the hourly rate by their time worked
[tex]3\frac{3}{10} *8.90=\frac{33}{10} *8.90=3.3*8.90 = 29.37[/tex]
Answer:
Step-by-step explanation:
When the number of builders is increased, the hours worked will be reduced.
So, this is inverse proportion.
Number of hours worked by 5 builders = [tex]\frac{3*\frac{11}{2}}{5}\\\\[/tex]
[tex]=3*\frac{11}{2}*\frac{1}{5}\\\\=\frac{33}{10}\\\\=3\frac{1}{10}[/tex]
Amount received by each builder= 33/10 * 8.90
= £ 29.37
What is (2a)^2 ? Help please
Answer:
4a²
Step-by-step explanation:
(2a)²
Distribute the square to all the terms in the bracket.
2²a²
Solve the powers if possible.
4a²
Answer:
4a²
Step-by-step explanation:
=> [tex](2a)^2[/tex]
=> [tex](2^2*a^2)[/tex]
=> 4 * a²
=> 4a²
an oil company conducts a geological study that indicates that an exploratory oil well should have a 20% chance of striking oil. assuming independence, what is that probability that the third strike comes on the seventh well drilled
Answer:
4.92% probability that the third strike comes on the seventh well drilled
Step-by-step explanation:
For each drill, there are only two possible outcomes. Either it is a strike, or it is not. Each drill is independent of other drills. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
20% chance of striking oil.
This means that [tex]p = 0.2[/tex]
What is that probability that the third strike comes on the seventh well drilled
2 stikers during the first 6 drills(P(X = 2) when n = 6)[/tex]
Strike during the 7th drill, with 0.2 probability. So
[tex]P = 0.2P(X = 2)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{6,2}.(0.2)^{2}.(0.8)^{4} = 0.2458[/tex]
Then
[tex]P = 0.2P(X = 2) = 0.2*0.2458 = 0.0492[/tex]
4.92% probability that the third strike comes on the seventh well drilled
[tex]{f}^{4} = - 1[/tex]
O True
O False
?
Answer:
False.
Step-by-step explanation:
This statement is false, for any value of F because the power function with an even exponent is always positive or 0.
A tree and a flagpole are on the same
horizontal ground A bird on top of the
tree observes the top and bottom of the
flagpole below it at angles of 45° and bo'
respectively. if the tree is 10.65 mhigh,
Calculate Correct to 3
figis
the height of the flagpole
significant
ures
Answer:
The height of the flagpole = 4.50m (3signifiant figures)
Question:
A tree and a flagpole are on the same
horizontal ground. A bird on top of the
tree observes the top and bottom of the flagpole below it at angles of 45° and 60° respectively. If the tree is 10.65 m high, Calculate Correct to 3 significant figures the height of the flagpole.
Step-by-step explanation:
First we have to represent the above information with a diagram to enable us solve the question.
Then label them for easy identification.
To determine the distance between the tree and flagpole, we would apply tangent rule.
Let their distance = x
Tan60 = opposite/adjacent
Tan60 = 10.65/y
Tan60 × y = 10.65
y = 10.65/Tan60
y = 10.65/1.7321
y = 6.15m
See attachment for the concluding part
Simplify 5^2 · 5^9 1. 5^11 2. 5^18 3. 25^11 4. 25^18
Answer:
Answer choice 1
Step-by-step explanation:
[tex]5^2\cdot 5^9= \\\\5^{2+9}= \\\\5^{11}[/tex]
Therefore, the correct answer choice is choice 1. Hope this helps!
For a specific location in a particularly rainy city, the time a new thunderstorm begins to produce rain (first drop time) is uniformly distributed throughout the day and independent of this first drop time for the surrounding days. Given that it will rain at some point both of the next two days, what is the probability that the first drop of rain will be felt between 8: 40 AM and 2: 35 PM on both days? a) 0.2479 Web) 0.0608 om c) 0.2465 d) 0.9385 e) 0.0615 f) None of the above.
Answer:
b) 0.0608
Step-by-step explanation:
As it is mentioned that the next two days i.e 24 hours, the probability of the rain is uniformly distributed
Therefore the rain probability is
[tex]= \frac{T}{24}[/tex]
where,
T = Length of the time interval
Plus, as we know that rain is independent
So let us assume the rain between the 8: 40 AM and 2: 35 PM on single day is P1 and the time interval is 5 hours 55 minutes
i.e
= 5.91666 hours long.
So, P1 should be
[tex]= \frac{5.91666}{24}[/tex]
= 0.2465
Now we assume the probability of rain on day 2 is P2
So it would be same i.e 0.2465
Since these events are independent
So, the total probability is
[tex]= 0.2465 \times 0.2465[/tex]
= 0.0608
Hence, the b option is correct
Safety by-laws state that for a ladder to be stable, the angle the base of the ladder makes with the ground should be between 70° and 80'. A safety inspector at a construction site notices a painter on a 10-m ladder that is leaning against a wall. The base of the ladder is 1.5 m away from the wall. Does the inspector have cause to be concerned? Explain.
Cos(angle) = adjacent/hypotenuse
Cos(angle) = 1.5/10
Angle = arccos(1.5/10)
Angle = 81.37 degrees
Although the angle is close, it is over the 80 degrees, so the inspector should be concerned.
Which of the following is the simplified fraction that’s equivalent to 0.315? A) 35/999 B) 35/111 C) 105/333 D) 31/99
9514 1404 393
Answer:
B) 35/111
Step-by-step explanation:
[tex]0.\overline{315}=\dfrac{315}{999}=\boxed{\dfrac{35}{111}}[/tex]
The denominator of the fraction has as many 9s as the decimal has repeating digits. Here, the numerator and denominator both have factors of 9 that can be cancelled.
Evaluate the expression. 8! − 5!
Answer:
40200
Step-by-step explanation:
(8x7x6x5x4x3x2x1) - (5x4x3x2x1)
Or simply plug 8! - 5! into the calc.
Answer:
Step-by-step explanation:
40200
There are five faculty members in a certain academic department. These individuals have 4, 6, 7, 10, and 15 years of teaching experience. Two of these individuals are randomly selected to serve on a personnel review committee. What is the probability that the chosen representatives have a total of at least 16 years of teaching experience
Answer:
3/5Step-by-step explanation:
Probability is the likelihood or chance that an event will occur.
Probability = expected outcome of event/total outcome of event
Given 5 individuals with 4, 6, 7, 10, and 15 years of teaching experience.
Since two of these 5 individuals are randomly selected to serve on a personnel review committee, total possible outcome = 5C2 (randomly selecting 2 personnel out of 5 )
5C2 = [tex]\frac{5!}{(5-2)!2!}[/tex]
[tex]= \frac{5!}{3!2!}\\ = \frac{5*4*3!}{3!*2} \\= 10\ possible\ selections\ can\ be\ done[/tex]
To get the probability that the chosen representatives have a total of at least 16 years of teaching experience, first we need to find the two values that will give a sum of years greater that or equal to 16 years. The possible combination are as shown;
4+15 = 19years (first reps)
6+10 = 16years (second reps)
6+15 = 21years (third reps)
7+10 = 17 years (fourth reps)
7+15 = 22 years (fifth reps)
10+15 = 25 years (sixth reps)
This shows that there are 6 possible ways to choose the representatives that have a total of at least 16 years of teaching experience
Total outcome = 10
expected outcome = 6
Probability that the chosen representatives have a total of at least 16 years of teaching experience = [tex]\frac{6}{10} = \frac{3}{5}[/tex]
Find the midpoint of AB when A=(1,-2) B=(1,-1)
Answer:
Midpoint Of AB = ( 1+1/2 , -2-1/2)
= (2/2 , -3/2)
= ( 1 , -1.5)
Hope this helps
Please mark Branliest.
Answer:
-2,0
Step-by-step explanation:
X squared plus 5x plus 6 in a factor of binomials
Answer:
(x + 3)(x + 2)
Step-by-step explanation:
Given
x² + 5x + 6
Consider the factors of the constant term (+ 6) which sum to give the coefficient of the x- term (+ 5)
The factors are + 3 and + 2 , since
3 × 2 = 6 and 3 + 2 = 5 , thus
x² + 5x + 6 = (x + 3)(x + 2)
A committee of 15 members is voting on a proposal. Each member casts a yea or nay vote. On a random voting basis, what is the probability that the final vote count is unanimous?
Answer:
0.006% probability that the final vote count is unanimous.
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they vote yes, or they vote no. The probability of a person voting yes or no is independent of any other person. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Random voting:
So 50% of voting yes, 50% no, so [tex]p = 0.5[/tex]
15 members:
This means that [tex]n = 15[/tex]
What is the probability that the final vote count is unanimous?
Either all vote no(P(X = 0)) or all vote yes(P(X = 15)). So
[tex]p = P(X = 0) + P(X = 15)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{15,0}.(0.5)^{0}.(0.5)^{15} = 0.00003[/tex]
[tex]P(X = 15) = C_{15,15}.(0.5)^{15}.(0.5)^{0} = 0.00003[/tex]
So
[tex]p = P(X = 0) + P(X = 15) = 0.00003 + 0.00003 = 0.00006[/tex]
0.006% probability that the final vote count is unanimous.
Clarkson University surveyed alumni to learn more about what they think of Clarkson. One part of the survey asked respondents to indicate whether their overall experience at Clarkson fell short of expectations, met expectations, or surpassed expectations. The results showed that of the respondents did not provide a response, said that their experience fell short of expectations, and of the respondents said that their experience met expectations.A. If we chose an alumnus at random, what is the probability that the alumnus would say their experience surpassed expectations?B. If we chose an alumnus at random, what is the probability that the alumnus would say their experience met or surpassed expectations?
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is:
Clarkson University surveyed alumni to learn more about what they think of Clarkson. One part of the survey asked respondents to indicate whether their overall experience at Clarkson fell short of expectations, met expectations, or surpassed expectations. The results showed that 4% of respondents did not provide a response, 26% said that their experience fell short of expectations, 65% of the respondents said that their experience met expectations (Clarkson Magazine, Summer, 2001). If we chose an alumnus at random, what is the probability that the alumnus would say their experience surpassed expectations? If we chose an alumnus at random, what is the probability that the alumnus would say their experience met or surpassed expectations?
Solution:
Probability = number of favorable outcomes/number of total outcomes
From the information given,
The probability that respondents did not provide a response, P(A) is 4/100 = 0.04
The probability that a respondent said that their experience fell short of expectations, P(B) is 26/100 = 0.26
The probability that a respondent said that their experience met expectations, P(C) is 65/100 = 0.65
A) Adding all the probabilities, it becomes 0.04 + 0.26 + 0.65 = 0.95
Therefore, the probability,P(D) that a respondent said that their experience surpassed expectations is 1 - 0.95 = 0.05
B) The event of a randomly chosen respondent saying that their experience met expectations and that their experience surpassed expectations are mutually exclusive because they cannot occur together. It means that P(C) × P(D) = 0
Therefore, the probability of P(C) or P(D) is 0.65 + 0.05 = 0.7