Answer:
[tex]Pr = \frac{1}{2002}[/tex]
Step-by-step explanation:
See comment for complete question;
Given
[tex]n = 14[/tex]
[tex]r = 5[/tex] -- committee members
[tex]k = 4[/tex] ---- officers (i.e. president, CEO, COO and CFO)
Required
Probability of selecting 5 youngest qualified members
First, we calculate the number of ways the committee can be appointed;
Any 5 members can be part of the committee; This means that we won't consider the order.
So, the number of ways is:
[tex]^{14}C_5[/tex]
This gives:
[tex]^{14}C_5 = \frac{14!}{9!5!}[/tex]
So, we have:
[tex]^{14}C_5 = \frac{14*13*12*11*10*9!}{9!*5*4*3*2*1}[/tex]
[tex]^{14}C_5 = \frac{14*13*12*11*10}{5*4*3*2*1}[/tex]
[tex]^{14}C_5 = \frac{240240}{120}[/tex]
[tex]^{14}C_5 = 2002[/tex]
There can only be a set of 5 young people. So, the probability is:
[tex]Pr = \frac{1}{2002}[/tex]
a linear model is appropriate for the data in which scatterplot.?
Answer: (b) or 2
Step-by-step explanation: its the only one linear to the best possibility.
Which of the following rational functions is graphed below?
Answer:
the answer is d
Step-by-step explanation:
because when we put-1 from x the equation hasn't any value
A robot that makes _/6 of a boat per day will make 5 boats in 6 days
please i meed help!!! im stuck and cant concentrate
Total outcomes=6 i.e{1,2,3,4,5,6 }
No.of favourable outcomes = 3 i.e {I, 3,5}
P(odd)=3/6=1/2
Answer:
1/ 2
Step-by-step explanation:
[tex]probability \: of \:an \:event\: = \frac{number \: of \: favorable outcomes}{total \: number \: of \: outcomes} [/tex]
favorable outcomes = odd numbers
=1, 3, 5
number of favorable outcomes = 3
total outcomes
= 1, 2, 3, 4, 5, 6
total number of outcomes = 6
probability = 3/ 6
= 1/ 2
The graph below has the same shape as the graph of G(x) = x, but it is
shifted three units to the left. Complete its equation. Enter exponents using
the caret (-); for example, enter x as x^4. Do not include "G(x) =" in your
answer.
G(x) =
Answer:
G(x) = x+3
Step-by-step explanation:
The equation of the graph is G (x) = (x - 3)⁴
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
A relation between a set of inputs having one output each is called a function.
An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The graph of function G (x) is shown in image.
Here, the graph is 3 units left to function F (x) = x⁴.
The equation of the graph is G (x) = (x - 3)⁴
Hence, the equation of the graph is G (x) = (x - 3)⁴
To learn more on Graph click:
https://brainly.com/question/17267403
#SPJ7
Use the probability distribution for the random variable x to answer the question. x 0 1 2 3 4 p(x) 0.12 0.2 0.2 0.36 0.12 Calculate the population mean, variance, and standard deviation. (Round your standard deviation to three decimal places.)
Answer:
[tex]\mu =2.16[/tex] --- Mean
[tex]\sigma^2 = 1.4944[/tex] -- Variance
[tex]\sigma = 1.222[/tex] --- Standard deviation
Step-by-step explanation:
Given
[tex]\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ P(x) & {0.12} & {0.2} & {0.2} & {0.36} & {0.12} \ \end{array}[/tex]
Solving (a): The population mean
This is calculated as:
[tex]\mu = \sum x * P(x)[/tex]
So, we have:
[tex]\mu =0*0.12 + 1 * 0.2 + 2 * 0.2 + 3 * 0.36 + 4 * 0.12[/tex]
[tex]\mu =2.16[/tex]
Solving (b): The population variance
First, calculate:
[tex]E(x^2)[/tex] using:
[tex]E(x^2) = \sum x^2 * P(x)[/tex]
So, we have:
[tex]E(x^2) = 0^2*0.12 + 1^2 * 0.2 + 2^2 * 0.2 + 3^2 * 0.36 + 4^2 * 0.12[/tex]
[tex]E(x^2) =6.160[/tex]
So, the population variance is:
[tex]\sigma^2 = E(x^2) - \mu^2[/tex]
[tex]\sigma^2 = 6.16 - 2.160^2[/tex]
[tex]\sigma^2 = 6.160 - 4.6656[/tex]
[tex]\sigma^2 = 1.4944[/tex]
Solving (c): The population standard deviation
This is calculated as:
[tex]\sigma = \sqrt{\sigma^2}[/tex]
[tex]\sigma = \sqrt{1.4944}[/tex]
[tex]\sigma = 1.222[/tex]
Mr. Layton needs to buy some oil for his central heating. He can put up to 2500 litres of oil in his oil tank. There are already 750 litres of oil in the tank. Mr. Layton is going to fill the tank with oil. The price of oil is 58.4 p per litre. Mr. Layton gets 6% off the price of the oil. How much does Mr. Layton pay for the oil he needs to buy
Answer:
Step-by-step explanation:
If the tank holds 2500 liters and there are already 750 liters in there, he only needs to buy 1750 liters.
If he is saving 6%, he is still spending 94%, so
.94(58.4) = 54.896 (what he'll be paying per liter after the 6% comes off, then
54.896(1750) = $96,068
If f(1) =160 and f(n+1)=-2f(n),
What is f(4)?
Answer:
f(n+1=-2f(n)
f(x)=-2f(n)
f(4)
f(4)=-2f(4)
Answer:
f(4) = - 1280
Step-by-step explanation:
Using the recursive rule and f(1) = 60 , then
f(2) = - 2f(1) = - 2 × 160 = - 320
f(3) = - 2f(2) = - 2 × - 320 = 640
f(4) = - 2f(3) = - 2 × 640 = - 1280
The accompanying data represent the homework scores for material for a random sample of students in a college algebra course.
36
47
54
58
60
66
66
68
69
70
72
75
77
77
78
78
78
79
79
79
79
79
80
82
84
85
86
86
86
87
89
89
91
92
92
93
93
94
96
99
(a) Construct a relative frequency distribution with a lower class limit of the first class equal to 30 and a class width of 10.
(b) What is the probability a randomly selected student fails the homework (scores less than 70)? (The standard deviation is 13.64)
Simplify your answer to two decimal places.
Answer:
[tex]\begin{array}{ccc}{Class} & {Frequency} & {Relative\ Frequency} &{30-39} & {1} & {0.025} & {40-49} & {1} & {0.025} & {50 - 59} & {2} & {0.050} & {60 - 69} & {5} & {0.125} & {70 - 79} & {13} & {0.325} & {80 - 89} & {10} & {0.250} & {90 - 99} & {8} & {0.200} &{Total} & {40} & {1}\ \end{array}[/tex]
[tex]P(x < 70) = 0.225[/tex]
Step-by-step explanation:
Given
[tex]Lower = 30[/tex]
[tex]Width = 10[/tex]
Solving (a): The relative frequency table
First, we construct the frequency table using the given parameters.
[tex]\begin{array}{cc}{Class} & {Frequency} &{30-39} & {1} & {40-49} & {1} & {50 - 59} & {2} & {60 - 69} & {5} & {70 - 79} & {13} & {80 - 89} & {10} & {90 - 99} & {8} & {Total} & {40}\ \end{array}[/tex]
The relative frequency (RF) is calculated as:
[tex]RF = \frac{Frequency}{Total}[/tex]
Using the above formula to calculate the relative frequency, the relative frequency table is:
[tex]\begin{array}{ccc}{Class} & {Frequency} & {Relative\ Frequency} &{30-39} & {1} & {0.025} & {40-49} & {1} & {0.025} & {50 - 59} & {2} & {0.050} & {60 - 69} & {5} & {0.125} & {70 - 79} & {13} & {0.325} & {80 - 89} & {10} & {0.250} & {90 - 99} & {8} & {0.200} &{Total} & {40} & {1}\ \end{array}[/tex]
Solving (b): [tex]P(x < 70)[/tex]
To do this, we add up the relative frequencies of classes less than 70.
i.e.
[tex]P(x < 70) = [30 - 39] + [40 - 49] + [50 - 59] + [60 - 69][/tex]
So, we have:
[tex]P(x < 70) = 0.025 + 0.025 + 0.050 + 0.125[/tex]
[tex]P(x < 70) = 0.225[/tex]
what is defination of equation? And why is it called a equation.
An equation can be defined as a mathematical statement in which two expressions are set equal to each other. In simple words, equations mean equality i.e. the equal sign. Since equations are all about “equating one quantity with another”,they are simply known as equation
Answer:
In algebra, an equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value. ... For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
Nikola thinks that the model that reflects the growth of smartphones shipped from manufacturers to stores around the world may be logistic rather than exponential. Do you agree with Nikola
Answer:
When most people have a smartphone, that is, the variable starts getting closer to its capacity, the demand will start to have a slight decrease, until it stabilizes, so yes, Nikola is correct.
Step-by-step explanation:
Exponential model:
The variable keeps growing consistently, at a fixed rate.
Logistic model:
The variable starts growing, but as it approaches a limit, for example, the carry capacity of an environment, the growth rate starts to decrease, until the variable stabilizes at a fixed value.
Growth of smartphones shipped from manufacturers to stores around the world.
When most people have a smartphone, that is, the variable starts getting closer to its capacity, the demand will start to have a slight decrease, until it stabilizes, so yes, Nikola is correct.
Which statement is true regarding the functions on the
graph?
f(6) = g(3)
f(3) = g(3)
f(3) = g(6)
f(6) = g(6)
Answer:
f(3) = g(3)
Step-by-step explanation:
on the graph the only point, where both lines cross (both functions create the same functional value) is at x=3.
since both lines have the same y-value there, we express this in math by the "=" sign. and both functions have the same input value (x=3) there.
Suppose the mean income of firms in the industry for a year is 95 million dollars with a standard deviation of 11 million dollars. If incomes for the industry are distributed normally, what is the probability that a randomly selected firm will earn less than 114 million dollars
Answer:
95.73%
Step-by-step explanation:
Given data:
mean μ= 95
standard deviation, σ = 11
to calculate, the probability that a randomly selected firm will earn less than 114 million dollars;
Use normal distribution formula
[tex]P(X<114)=P(Z<\frac{X-\mu}{\sigma} )[/tex]
Substitute the required values in the above equation;
[tex]P(X<114)=P(Z<\frac{114-95}{11} )\\P(X<114)=P(Z<1.7272)\\P(X<114)=0.9573[/tex]
Therefore, the probability that a randomly selected firm will earn less than 114 million dollars = 95.73%
Your EZ Pass account begins with $80. It costs you $4/day. Write an equation
for the amount in your account (A) in terms of the number of days (D).
Answer:
The equation is [tex]A(d) = 80 - 4d[/tex]
Step-by-step explanation:
Linear function:
A linear function for the amount of money in an account after t days is given by:
[tex]A(d) = A(0) - md[/tex]
In which A(0) is the initial value and m is the daily cost.
Your EZ Pass account begins with $80. It costs you $4/day.
This means that [tex]A(0) = 80, m = 4[/tex]
So
[tex]A(d) = A(0) - md[/tex]
[tex]A(d) = 80 - 4d[/tex]
can someone tell me where i can get a graph that shows this:
Weight Not Over (lbs.) Price
0 $0
1 $2.69
2 $3.17
3 $3.65
4 $4.13
5 $4.61
6 $5.09
7 $5.57
8 $6.03
9 $6.49
10 $6.95
Answer:
Note: See the attached photo for the graph showing Weight Not Over (lbs.) vs Price($). The attached excel file also shows the same graph with the data used to draw it in the excel.
Step-by-step explanation:
In the attached graph, Weight Not Over (lbs.) is on the horizontal axis while Price ($) is on the vertical axis.
From the attached, it can be observed that the graph shows an upward trend. That implies that there is a positive relation between Weight Not Over (lbs.) and Price. That is, as Weight Not Over (lbs.) rises, the Price also rises.
if my child had 115 of 149 questions right what percentage is the grade
Answer:
77.18%
Step-by-step explanation:
115:149*100 =
(115*100):149 =
11500:149 = 77.18
What is the product?
(ay3)2 + 3y - 5)
Suppose a large telephone manufacturer has a problem with excessive customer complaints and consequent returns of the phones for repair or replacement. The manufacturer wants to estimate the magnitude of the problem in order to design a quality control program. How many telephones should be sampled and checked in order to estimate the proportion defective to within 9 percentage points with 89% confidence
Answer:
80 telephones should be sampled
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
89% confidence level
So [tex]\alpha = 0.11[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.11}{2} = 0.945[/tex], so [tex]Z = 1.6[/tex].
How many telephones should be sampled and checked in order to estimate the proportion defective to within 9 percentage points with 89% confidence?
n telephones should be sampled, an n is found when M = 0.09. We have no estimate for the proportion, thus we use [tex]\pi = 0.5[/tex]
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.09 = 1.6\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.09\sqrt{n} = 1.6*0.5[/tex]
[tex]\sqrt{n} = \frac{1.6*0.5}{0.09}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.6*0.5}{0.09})^2[/tex]
[tex]n = 79.01[/tex]
Rounding up(as 79 gives a margin of error slightly above the desired value).
80 telephones should be sampled
Find the length of side ab, give your answer to 1 decimal place 62 and 12
Answer:
Huh? is it triangle? and right triangle? if it is its 62^2 = 12^2 + x^2
Step-by-step explanation:
If f(x) = 4^x-8 and g(x) = 5x+6, find (f + g)(x)
A. (F+g)(x) = -4^x - 5x + 2
B.(F+g)(x) = 4^x + 5x - 2
C.(F+g)(x) = 4^x - 3x + 6
D.(F+g)(x) = 9x - 2
Hey there!
We are given two functions - one is Exponential while the another one is Linear.
[tex] \large{ \begin{cases} f(x) = {4}^{x} - 8 \\ g(x) = 5x + 6 \end{cases}}[/tex]
1. Operation of Function
(f+g)(x) is a factored form of f(x)+g(x). We can common factor out x. Therefore:[tex] \large{(f + g)(x) = f(x) + g(x)}[/tex]
2. Substitution
Next, we substitute f(x) = 4^x+8 and g(x) = 5x+6.[tex] \large{(f + g)(x) = ( {4}^{x} - 8) + (5x + 6)}[/tex]
3. Evaluate/Simplify
Cancel out the brackets and combine like terms.[tex] \large{(f + g)(x) = {4}^{x} - 8 + 5x + 6} \\ \large{(f + g)(x) = {4}^{x} + 5x - 8 + 6} \\ \large{(f + g)(x) = {4}^{x} + 5x - 2}[/tex]
4. Final Answer
(f+g)(x) = 4^x+5x-2Which descriptions from the list below accurately describe the relationship
between AABC and ADEF? Check all that apply.
E
37
B
10
8
5 37
4
534 D
A 3 C
53°
D
6
F
A. Same area
O B. Same size
C. Congruent
D. None of the above
Hi
Answer:
D. None of the above
Step-by-step explanation:
Both triangles have the same shape but different size. Their area cannot be the same. Also, the ratio of their corresponding side lengths are the same.
Thus:
8/4 = 10/5 = 6/3 = 2
This implies that both triangles are similar.
Therefore, both triangles cannot have the same area, they are not of the same size and cannot be congruent to each other.
Which rule describes the composition of transformations that maps ABC to A”B’C”
A line contains the points (3,1) and (-6,4) what is the equation for this line in slope intercept form
Answer:
y = (-1/3)x + 2
Step-by-step explanation:
Since points (3,1) and (-6,4) lie on y = (-1/3)x + c , it should satisfy the this equation. Thus, intercept is 2.
Answer:
m = -⅓
Step-by-step explanation:
m = (y2- y1)/(x2 - x1)
m = (4 -1)/(-6-3)
m = -⅓
15. Dravid is a famous cricket player. He has
so far scored 6980 runs in the test matches.
He wishes to complete 10,000 runs: How
many more runs does he need? *
4020 runs
3220 runs
2820 runs
O 3020 runs
Answer:
3020 runs
Step-by-step explanation:
Because he wants 10000 but only has 6980 so you have to minus 6980 from 10000. 10000-6980=3020
so 3020 is the answer
Answer:
3020 runs
Step-by-step explanation:
10,000-6980=3020
The PDF of the maximum
Let X and Y be independent random variables, each uniformly distributed on the interval (0, 1).
Let Z = max{X, Y}. Find the PDF of Z.
For 0 < z < 1
Let Z = max{2X, Y}. Find the PDF of Z.
For 0 < z < 1
For 1 < z < 2
Answer:
distinctly over here I think so
Verify the sine law by taking particular triangle in four quadrant.
Answer:
answer is in the picture above
What is the solution to the system of linear equations?
(-3,0)
(-3,3)
(0,2)
(3,1)
In golf, scores are often written in relationship to par, the average score for a round at a certain course. Write an integer to represent a score that is 7 under par.
Answer:
-7
Step-by-step explanation:
If it is 7 below (a key word, which you can connect to 'negative'), then you just write it as -7.
what was the original price of the car? MUST SHOW ALL STEPS OF THE PROCESS.
Answer:
19219.48
Step-by-step explanation:
16540x0.162+16540
The original price would be 100%
It was marked down 16.2%
100 % - 16.2% = 83.8%
The price you paid was 83.8% of the original price.
To find the original price divide the amount you paid by the percentage of the original price:
16,540 / 0.838 = 19.737.47
Original price: $19,737.47
Find the value of z such that 0.05 of the area lies to the right of z. Round your answer to two decimal places.
Answer:
[tex]z = 1.6[/tex]
Step-by-step explanation:
Given
[tex]Pr = 0.05[/tex]
Required
The z value to the right
The z value to the right is represented as:
[tex]P(Z > z)[/tex]
So, the probability is represented as:
[tex]P(Z > z) = 0.05[/tex]
From z table, the z value that satisfies the above probability is:
[tex]z = 1.645[/tex]
[tex]z = 1.6[/tex] --- approximated