Answer:
S = [0.2069,0.7931]
Step-by-step explanation:
Transition Matrix:
[tex]P=\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right][/tex]
Stationary matrix S for the transition matrix P is obtained by computing powers of the transition matrix P ( k powers ) until all the two rows of transition matrix p are equal or identical.
Transition matrix P raised to the power 2 (at k = 2)
[tex]P^{2} =\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right][/tex]
[tex]P^{2} =\left[\begin{array}{ccc}0.2203&0.7797\\0.2034&0.7966\end{array}\right][/tex]
Transition matrix P raised to the power 3 (at k = 3)
[tex]P^{3} =\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right][/tex]
[tex]P^{3} =\left[\begin{array}{ccc}0.2203&0.7797\\0.2034&0.7966\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right][/tex]
[tex]P^{3} =\left[\begin{array}{ccc}0.2086&0.7914\\0.2064&0.7936\end{array}\right][/tex]
Transition matrix P raised to the power 4 (at k = 4)
[tex]P^{4} =\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right][/tex]
[tex]P^{4} =\left[\begin{array}{ccc}0.2086&0.7914\\0.2064&0.7936\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right][/tex]
[tex]P^{4} =\left[\begin{array}{ccc}0.2071&0.7929\\0.2068&0.7932\end{array}\right][/tex]
Transition matrix P raised to the power 5 (at k = 5)
[tex]P^{5} =\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right][/tex]
[tex]P^{5} =\left[\begin{array}{ccc}0.2071&0.7929\\0.2068&0.7932\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right][/tex]
[tex]P^{5} =\left[\begin{array}{ccc}0.2069&0.7931\\0.2069&0.7931\end{array}\right][/tex]
P⁵ at k = 5 both the rows identical. Hence the stationary matrix S is:
S = [ 0.2069 , 0.7931 ]
¿Cuál es la fórmula para calcular el área de cualquier triangulo?
¡Hola! ¡Ojalá esto ayude!
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La fórmula para calcular el área de cualquier triángulo es:
base multiplicada por la altura y dividida por dos.
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Bh / 2.
Total length of a pole is 21.3 m. If 0.2m of the length of the pole is inside the ground. Find how much of its length is outside the ground
Answer:
21.1 mStep by step explanation
Total length of pole = 21.3 m
Length of pole inside the ground = 0.2 m
Let length of pole outside the ground be X,
So, according to the Question,
[tex]x + 0.2 = 21.3[/tex]
Move constant to R.H.S and change its sign
[tex]x = 21.3 - 0.2[/tex]
Calculate the difference
[tex]x = 21.1 \: m[/tex]
Hope this helps...
Good luck on your assignment...
Please help! Will give brainliest to correct answer! (1/3) - 50 POINTS - please no wrong answers.
Answer:
( 6, pi/6)
Step-by-step explanation:
( 3 sqrt(3), 3)
To get r we use x^2 + y ^2 = r^2
( 3 sqrt(3) )^2 + 3^2 = r^2
9 *3 +9 = r^2
27+9 = r^2
36 = r^2
Taking the square root of each side
sqrt(36) = sqrt(r^2)
6 =r
Now we need to find theta
tan theta = y/x
tan theta = 3 / 3 sqrt(3)
tan theta = 1/ sqrt(3)
Taking the inverse tan of each side
tan ^-1 ( tan theta) = tan ^ -1 ( 1/ sqrt(3))
theta = pi /6
what is the answer to 100×338
Answer:
33800
Step-by-step explanation:
100 x 338 = 33800
Answer:
33800
Step-by-step explanation:
338x10=3380 then 3380x10=33800
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Good luck with your assignment...
What is the simplified expression for 3 y squared minus 6 y z minus 7 + 4 y squared minus 4 y z + 2 minus y squared z?
WILL MARK BRAINLEST
Answer:
7y⁴- 10yz - y²z - 5
Step-by-step explanation:
First collect like terms
3y²+ 4y²- 6yz - 4yz - y²z - 7+2
7y⁴-10yz - y²z - 5
Answer:
Its C
Step-by-step explanation:
What is the slope of the line shown below (3,9) (1,1)
Answer:
slope m = 4Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points
[tex](3;\ 9)\to x_1=3;\ y_1=9\\(1;\ 1)\to x_2=1;\ y_2=1[/tex]
Substitute:
[tex]m=\dfrac{1-9}{1-3}=\dfrac{-8}{-2}=4[/tex]
Answer:
m=4
Step-by-step explanation:
Slope can be found using the following formula:
[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
where [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] are points on the line.
We are given the points (3,9) and (1,1). Therefore,
[tex]x_{1}=3\\y_{1}=9 \\x_{2}=1\\y_{2}=1[/tex]
Substitute each value into the formula.
[tex]m=\frac{1-9}{1-3}[/tex]
Subtract in the numerator first.
[tex]m=\frac{-8}{1-3}[/tex]
Subtract in the denominator.
[tex]m=\frac{-8}{-2}[/tex]
Divide.
[tex]m=4[/tex]
The slope of the line is 4.
A city council consists of eight Democrats and eight Republicans. If a committee of six people is selected, find the probability of selecting two Democrats and four Republicans.
(Type answer a fraction Simplify your answer.)
Answer:
The probability is [tex]P[ D n R] = 0.196[/tex]
Step-by-step explanation:
From the question we are told that
The number of Democrats is [tex]D = 8[/tex]
The number of republicans is [tex]R = 8[/tex]
The number of ways of selecting selecting two Democrats and four Republicans.
[tex]N = \left {D} \atop {}} \right. C_2 * \left {R} \atop {}} \right. C_1[/tex]
Where C represents combination
substituting values
[tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1[/tex]
[tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8!}{(8-2)! 2!} * \frac{8! }{(8-4)! 1 !}[/tex]
=> [tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8!}{(6)! 2!} * \frac{8! }{(6)! 1 !}[/tex]
=> [tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8 * 7 * 6!}{(6)! 2!} * \frac{8*7 *6! }{(6)! 1 !}[/tex]
=> [tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8 * 7 }{ 2*1 } * \frac{8*7 }{ 1 *1 }[/tex]
=> [tex]N = 1568[/tex]
The total number of ways of selecting the committee of six people is
[tex]Z = \left {D+R} \atop {}} \right. C_6[/tex]
substituting values
[tex]Z = \left {8+8} \atop {}} \right. C_6[/tex]
[tex]Z= \left {16} \atop {}} \right. C_6[/tex]
substituting values
[tex]Z= \left {16} \atop {}} \right. C_6 = \frac{16! }{(16-6) ! 6!}[/tex]
[tex]Z= \left {16} \atop {}} \right. C_6 = \frac{16 *15 *14 * 13 * 12 * 11 * 10! }{10 ! 6!}[/tex]
[tex]Z= \left {16} \atop {}} \right. C_6 = \frac{16 *15 *14 * 13 * 12 * 11 }{6* 5 * 4 * 3 * 2 * 1}[/tex]
[tex]Z= \left {16} \atop {}} \right. C_6 = 8008[/tex]
The probability of selecting two Democrats and four Republicans is mathematically represented as
[tex]P[ D n R] = \frac{N}{Z}[/tex]
substituting values
[tex]P[ D n R] = \frac{1568}{8008}[/tex]
[tex]P[ D n R] = 0.196[/tex]
What is the value of x?
Answer:
54
Step-by-step explanation:
x is half the difference of the two arcs:
x = (136 -28)/2 = 54
The value of x is 54.
Which of the following statements is correct about quadratic number patterns? A. The third difference is greater than zero. B. The first difference is constant. C. The difference between terms is always positive. D. The second difference is constant.
Answer: D.) The second difference is constant.
Step-by-step explanation:
The rate of change of a quadratic function is a linear function. The rate of change of that is constant, so second differences of a quadratic number pattern are constant.
Answer:
D.
Step-by-step explanation:
Which of the following algebraic expressions represents the statement given below?
A number is increased by five and squared.
A. x+5²
В.
x²+5
c. ° +5
D. (x+5)
Answer:
Let the number be x
The statement
A number is increased by five is written as
x + 5
Then it's squared
So we the final answer as
(x + 5)²Hope this helps
An experiment involves 17 participants. From these, a group of 3 participants is to be tested under a special condition. How many groups of 3 participants can
be chosen, assuming that the order in which the participants are chosen is irrelevant?
Answer: 680
Step-by-step explanation:
When order doesn't matter,then the number of combinations of choosing r things out of n = [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
Given: Total participants = 17
From these, a group of 3 participants is to be tested under a special condition.
Number of groups of 3 participants chosen = [tex]^{17}C_3=\dfrac{17!}{3!(17-3)!}\[/tex]
[tex]^{17}C_3=\dfrac{17!}{3!(17-3)!}\\\\=\dfrac{17\times16\times15\times14!}{3\times2\times14!}\\\\=680[/tex]
Hence, there are 680 groups of 3 participants can be chosen,.
The function f is defined as follows.
f(x) =4x²+6
If the graph of f is translated vertically upward by 4 units, It becomes the graph of a function g.
Find the expression for g(x).
G(x)=
Answer:
[tex]g(x)=4x^{2} +10[/tex]
Step-by-step explanation:
If we perform a vertical translation of a function, the graph will move from one point to another certain point in the direction of the y-axis, in another words: up or down.
Let:
[tex]a>0,\hspace{10}a\in R[/tex]
For:
y = f (x) + a: The graph shifts a units up.y = f (x) - a, The graph shifts a units down.If:
[tex]f(x)=4x^{2} +6[/tex]
and is translated vertically upward by 4 units, this means:
[tex]a=4[/tex]
and:
[tex]g(x)=f(x)+a=(4x^{2} +6)+4=4x^{2} +10[/tex]
Therefore:
[tex]g(x)=4x^{2} +10[/tex]
I attached you the graphs, so you can verify the result easily.
Circle the numbers divisible by 2.
320;5,763; 9,308; 5,857;3,219; 5,656; 83,001;53,634
81^x^2=27^x solve for x
Step-by-step explanation:
81^x² = 27^x
(3^4)^x² = (3^3)^x
3^(4x²) = 3^(3x)
4x² = 3x
4x² − 3x = 0
x (4x − 3) = 0
x = 0 or ¾
In 2005, there were 14,100 students at college A, with a projected enrollment increase of 750 students per year. In the same year, there were 42,100 students at college B, with a projected enrollment decline of 1250 students per year. According to these projections, when will the colleges have the same enrollment? What will be the enrollment in each college at that time?
Set up two equations and set equal to each other. Let number of years = x:
College A = 14100+750x
College B = 42100-1250x
Set equal:
14100 + 750x = 42100 - 1250x
Subtract 750x from both sides:
14100 = 42100 - 2000x
Subtract 42100 from both sides:
-28000 = -2000x
Divide both sides by -2000:
x = -28000 / -2000
x = 14
It will take 14 years for the schools to have the same enrollment.
Enrollment will be:
14100 + 750(14) = 14100 + 10500 = 24,600
Answer:
(a)2019 (14 years after)
(b)24,600
Step-by-step explanation:
Let the number of years =n
College A
Initial Population in 2005 = 14,100
Increase per year = 750
Therefore, the population after n years = 14,100+750n
College B
Initial Population in 2005 = 42,100
Decline per year = 1250
Therefore, the population after n years = 42,100-1250n
When the enrollments are the same
14,100+750n=42,100-1250n
1250n+750n=42100-14100
2000n=28000
n=14
Therefore, in 2019 (14 years after), the colleges will have the same enrollment.
Enrollment in 2019 =42,100-1250(14)
=24,600
Crime and Punishment: In a study of pleas and prison sentences, it is found that 45% of the subjects studied were sent to prison. Among those sent to prison, 40% chose to plead guilty. Among those not sent to prison, 55% chose to plead guilty.
(A) If one of the study subjects is randomly selected, find the probability of getting someone who was not sent to prison.
(B) If a study subject is randomly selected and it is then found that the subject entered a guilty plea, find the probability that this person was not sent to prison.
Answer:
(a) The probability of getting someone who was not sent to prison is 0.55.
(b) If a study subject is randomly selected and it is then found that the subject entered a guilty plea, the probability that this person was not sent to prison is 0.63.
Step-by-step explanation:
We are given that in a study of pleas and prison sentences, it is found that 45% of the subjects studied were sent to prison. Among those sent to prison, 40% chose to plead guilty. Among those not sent to prison, 55% chose to plead guilty.
Let the probability that subjects studied were sent to prison = P(A) = 0.45
Let G = event that subject chose to plead guilty
So, the probability that the subjects chose to plead guilty given that they were sent to prison = P(G/A) = 0.40
and the probability that the subjects chose to plead guilty given that they were not sent to prison = P(G/A') = 0.55
(a) The probability of getting someone who was not sent to prison = 1 - Probability of getting someone who was sent to prison
P(A') = 1 - P(A)
= 1 - 0.45 = 0.55
(b) If a study subject is randomly selected and it is then found that the subject entered a guilty plea, the probability that this person was not sent to prison is given by = P(A'/G)
We will use Bayes' Theorem here to calculate the above probability;
P(A'/G) = [tex]\frac{P(A') \times P(G/A')}{P(A') \times P(G/A') +P(A) \times P(G/A)}[/tex]
= [tex]\frac{0.55 \times 0.55}{0.55\times 0.55 +0.45 \times 0.40}[/tex]
= [tex]\frac{0.3025}{0.4825}[/tex]
= 0.63
Which of the following is best described as sets of three whole numbers (a, b, and c) that satisfy the equation ?
A.
The Pythagorean theorem
B.
Prime numbers
C.
Pythagorean triples
D.
Perfect squares
Answer:
Option C
Step-by-step explanation:
The whole numbers a,b and c such that [tex]a^2+b^2 = c^2[/tex] are Pythagorean triples satisfying the Pythagorean theorem.
Answer:
C
Step-by-step explanation:
a, b, and c are side lengths of the triangle.
The three side lengths that make up a right triangle are most commonly known as Pythagorean triples.
What is the cube of the square of the second smallest prime number?
Answer:8
Step-by-step explanation:
The smallest prime is 2
cube of 2 is equal to 8
2*2*2=8
Answer:
729
Step-by-step explanation:
The second smallest prime number is 3 (preceded by 2). We have (3^2)^3=3^6=729.
Hope this helped! :)
Explain how to find the range of a data set. What is an advantage of using the range as a measure of variation? What is a disadvantage?
Answer:
The range is found by subtracting the minimum data entry from the maximum data entry.
Step-by-step explanation:
The range is found by subtracting the minimum data entry from the maximum data entry.
It is easy to compute.
It uses only two entries from the data set.
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Consider the functions given below. SEE FILE ATTATCHED
Answer:
1. [tex] P(x) [/tex] ÷ [tex] Q(x) [/tex]---> [tex] \frac{-3x + 2}{3(3x - 1)} [/tex]
2. [tex] P(x) + Q(x) [/tex]---> [tex]\frac{2(6x - 1)}{(3x - 1)(-3x + 2)}[/tex]
3. [tex] P(x) - Q(x) [/tex]---> [tex] \frac{-2(12x - 5)}{(3x - 1)(-3x + 2)} [/tex]
4. [tex] P(x)*Q(x) [/tex] --> [tex] \frac{12}{(3x - 1)(-3x + 2)} [/tex]
Step-by-step explanation:
Given that:
1. [tex] P(x) = \frac{2}{3x - 1} [/tex]
[tex] Q(x) = \frac{6}{-3x + 2} [/tex]
Thus,
[tex] P(x) [/tex] ÷ [tex] Q(x) [/tex] = [tex] \frac{2}{3x - 1} [/tex] ÷ [tex] \frac{6}{-3x + 2} [/tex]
Flip the 2nd function, Q(x), upside down to change the process to multiplication.
[tex] \frac{2}{3x - 1}*\frac{-3x + 2}{6} [/tex]
[tex] \frac{2(-3x + 2)}{6(3x - 1)} [/tex]
[tex] = \frac{-3x + 2}{3(3x - 1)} [/tex]
2. [tex] P(x) + Q(x) [/tex] = [tex] \frac{2}{3x - 1} + \frac{6}{-3x + 2} [/tex]
Make both expressions as a single fraction by finding, the common denominator, divide the common denominator by each denominator, and then multiply by the numerator. You'd have the following below:
[tex] \frac{2(-3x + 2) + 6(3x - 1)}{(3x - 1)(-3x + 2)} [/tex]
[tex] \frac{-6x + 4 + 18x - 6}{(3x - 1)(-3x + 2)} [/tex]
[tex] \frac{-6x + 18x + 4 - 6}{(3x - 1)(-3x + 2)} [/tex]
[tex] \frac{12x - 2}{(3x - 1)(-3x + 2)} [/tex]
[tex] = \frac{2(6x - 1}{(3x - 1)(-3x + 2)} [/tex]
3. [tex] P(x) - Q(x) [/tex] = [tex] \frac{2}{3x - 1} - \frac{6}{-3x + 2} [/tex]
[tex] \frac{2(-3x + 2) - 6(3x - 1)}{(3x - 1)(-3x + 2)} [/tex]
[tex] \frac{-6x + 4 - 18x + 6}{(3x - 1)(-3x + 2)} [/tex]
[tex] \frac{-6x - 18x + 4 + 6}{(3x - 1)(-3x + 2)} [/tex]
[tex] \frac{-24x + 10}{(3x - 1)(-3x + 2)} [/tex]
[tex] = \frac{-2(12x - 5}{(3x - 1)(-3x + 2)} [/tex]
4. [tex] P(x)*Q(x) = \frac{2}{3x - 1}* \frac{6}{-3x + 2} [/tex]
[tex] P(x)*Q(x) = \frac{2*6}{(3x - 1)(-3x + 2)} [/tex]
[tex] P(x)*Q(x) = \frac{12}{(3x - 1)(-3x + 2)} [/tex]
Composite functions involve combining multiple functions to form a new function
The functions are given as:
[tex]P(x) = \frac{2}{3x - 1}[/tex]
[tex]Q(x) = \frac{6}{-3x + 2}[/tex]
[tex]P(x) \div Q(x)[/tex] is calculated as follows:
[tex]P(x) \div Q(x) = \frac{2}{3x - 1} \div \frac{6}{-3x + 2}[/tex]
Express as a product
[tex]P(x) \div Q(x) = \frac{2}{3x - 1} \times \frac{-3x + 2}{6}[/tex]
Divide 2 by 6
[tex]P(x) \div Q(x) = \frac{1}{3x - 1} \times \frac{-3x + 2}{3}[/tex]
Multiply
[tex]P(x) \div Q(x) = \frac{-3x + 2}{3(3x - 1)}[/tex]
Hence, the value of [tex]P(x) \div Q(x)[/tex] is [tex]\frac{-3x + 2}{3(3x - 1)}[/tex]
P(x) + Q(x) is calculated as follows:
[tex]P(x) + Q(x) = \frac{2}{3x - 1} + \frac{6}{-3x + 2}[/tex]
Take LCM
[tex]P(x) + Q(x) = \frac{2(-3x + 2) + 6(3x - 1)}{(3x - 1)(-3x + 2)}[/tex]
Open brackets
[tex]P(x) + Q(x) = \frac{-6x + 4 + 18x - 6}{(3x - 1)(-3x + 2)}[/tex]
Collect like terms
[tex]P(x) + Q(x) = \frac{18x-6x + 4 - 6}{(3x - 1)(-3x + 2)}[/tex]
[tex]P(x) + Q(x) = \frac{12x - 2}{(3x - 1)(-3x + 2)}[/tex]
Factor out 2
[tex]P(x) + Q(x) = \frac{2(6x -1)}{(3x - 1)(-3x + 2)}[/tex]
Hence, the value of P(x) + Q(x) is [tex]\frac{2(6x -1)}{(3x - 1)(-3x + 2)}[/tex]
P(x) - Q(x) is calculated as follows:
[tex]P(x) - Q(x) = \frac{2}{3x - 1} - \frac{6}{-3x + 2}[/tex]
Take LCM
[tex]P(x) - Q(x) = \frac{2(-3x + 2) - 6(3x - 1)}{(3x - 1)(-3x + 2)}[/tex]
Open brackets
[tex]P(x) - Q(x) = \frac{-6x + 4 - 18x +6}{(3x - 1)(-3x + 2)}[/tex]
Collect like terms
[tex]P(x) - Q(x) = \frac{-18x-6x + 4 + 6}{(3x - 1)(-3x + 2)}[/tex]
[tex]P(x) - Q(x) = \frac{-24x +10}{(3x - 1)(-3x + 2)}[/tex]
Factor out -2
[tex]P(x) - Q(x) = \frac{-2(12x -5)}{(3x - 1)(-3x + 2)}[/tex]
Hence, the value of P(x) - Q(x) is [tex]\frac{-2(12x -5)}{(3x - 1)(-3x + 2)}[/tex]
P(x) * Q(x) is calculated as follows:
[tex]P(x) \times Q(x) = \frac{2}{3x - 1} \times \frac{6}{-3x + 2}[/tex]
Multiply
[tex]P(x) \times Q(x) = \frac{12}{(3x - 1)(-3x + 2)}[/tex]
Hence, the value of P(x) * Q(x) is [tex]\frac{12}{(3x - 1)(-3x + 2)}[/tex]
Read more about composite functions at:
https://brainly.com/question/10687170
A regression model between sales (y in $1000), unit price (x1 in dollars), and television advertisement (x2 in dollars) resulted in the following function: Ŷ = 7 - 3x1 + 5x2 For this model, SSR = 3500, SSE = 1500, and the sample size is 18. If we want to test for the significance of the regression model, the critical value of F at the 5% level of significance is a. 3.29. b. 3.24. c. 3.68. d. 4.54.
Answer: C. 3.68
Step-by-step explanation:
Given that;
Sample size n = 18
degree of freedom for numerator k = 2
degree of freedom for denominator = n - k - 1 = (18-2-1) = 15
level of significance = 5% = 5/100 = 0.05
From the table values,
the critical value of F at 0.05 significance level with (2, 18) degrees of freedom is 3.68
Therefore option C. 3.68 is the correct answer
2| x-3| - 5 = 7 Helpp
Answer:
x = {9, -3}
Step-by-step explanation:
2| x-3| - 5 = 72| x-3| = 12| x-3| = 6x - 3 = ± 6 ⇒ x= 3+ 6= 9⇒ x= 3 - 6= -3Or it can be shown as:
x= {9, -3}a 12- inch ruler is duvided into 3 parts. the large part is 3 times longer than the small. the meddium part is times longer than then small, the medium part is 2 times long as the smallest .how long is the smallest part?
Answer:
2 inches
Step-by-step explanation:
x= smallest
3x=largest
2x=medium
x+3x+2x=12
6x=12
x=2
so smallest is 2
largest is 6 (3x)
medium is 4 (2x)
2+6+4=12
A newsletter publisher believes that 71q% of their readers own a personal computer. Is there sufficient evidence at the 0.010.01 level to refute the publisher's claim.
Required:
State the null and alternative hypotheses for the above scenario.
Answer:
Null - p= 71%
Alternative - p =/ 71%
Step-by-step explanation:
The null hypothesis is always the default statement in an experiment. While the alternative hypothesis is always tested against the null hypothesis.
Null hypothesis: 71% of their readers own a personal computer- p = 71%
Alternative hypothesis: Not 71% of their readers own a personal computer - p =/ 71%
Find the area of the kite below. POSSIBLE ANSWERS: 168 mm 2 or 216 mm 2 or 195 mm 2 or 228 mm 2
Answer:
168 mm²
Step-by-step explanation:
Let A be the area of this shape
the kite is made of two triangles
Let A' and A" be the areas of the triangles
let's calculate A' and A" :
The area of a triangle is the product of the base and the height over 2
A' = [tex]\frac{(12+12)*5}{2}[/tex] = 60 mm² A"= [tex]\frac{(12+12)*9}{2}[/tex] = 108 mm²Let's calculate A
A = A' + A" A = 108+ 60 A = 168 mm²Scatter plot show which type of correlation
Answer:
It is a negative correlation
Step-by-step explanation:
As the x value increases the y value decreases. This causes it to be a negative.
5x - y = -7
4x + 2y = – 14
Answer:
[tex]\boxed{\sf \ \ x=-2, \ y=-3 \ \ }[/tex]
Step-by-step explanation:
Hello,
I assume that you want to solve this system of two equations
(1) 5x - y = -7
(2) 4x + 2y = -14
We will multiply (1) by 2 and add to (2) so that we can eliminate the terms in y
2*(1)+(2) gives
10x - 2y + 4x + 2y = -7*2 -14 = -14 - 14 = -28
<=>
14x = - 28 we can divide by 14 both parts
x = -28/14 = -2
and then we replace x in (1)
5*(-2)-y=-7
-10-y=-7 add 7
-10-y+7=0
-3-y=0 add y
-3 = y
which is equivalent to y = -3
do not hesitate if you have any question
Answer:
x = -2, y = -3
Step-by-step explanation:
5x - y = -7
4x + 2y = – 14
Multiply the first equation by 2
2(5x - y) = 2*-7
10x -2y = -14
Add this to the second equation to eliminate y
10x -2y = -14
4x + 2y = – 14
---------------------------
14x = -28
Divide by 14
14x/14 = -28/14
x = -2
Now find y
4x+2y = -14
4*-2 +2y = -14
-8+2y = -14
Add 8 to each side
2y = -6
Divide by 2
2y/2 = -6/2
y = -3
Scores made on a certain aptitude test by nursing students are approximately normally distributed with a mean of 500 and a variance of 10,000. If a person is about to take the test what is the probability that he or she will make a score of 650 or more?
Answer:
0.0668 or 6.68%
Step-by-step explanation:
Variance (V) = 10,000
Standard deviation (σ) = √V= 100
Mean score (μ) = 500
The z-score for any test score X is:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
For X = 650:
[tex]z=\frac{650-500}{100}\\z=1.5[/tex]
A z-score of 1.5 is equivalent to the 93.32nd percentile of a normal distribution. Therefore, the probability that he or she will make a score of 650 or more is:
[tex]P(X\geq 650)=1-P(X\leq 650)\\P(X\geq 650)=1-0.9332\\P(X\geq 650)=0.0668=6.68\%[/tex]
The probability is 0.0668 or 6.68%
The probability that he or she will make a score of 650 or more is 0.0668.
Let X = Scores made on a certain aptitude test by nursing students
X follows normal distribution with mean = 500 and variance of 10,000.
So, standard deviation = [tex]\sqrt{10000}=100[/tex].
z score of 650 is = [tex]\frac{\left(650-500\right)}{100}=1.5[/tex].
The probability that he or she will make a score of 650 or more is:
[tex]P(X\geq 650)\\=P(z\geq 1.5)\\=1-P(z<1.5)\\=1-0.9332\\=0.0668[/tex]
Learn more: https://brainly.com/question/14109853
If w'(t) is the rate of growth of a child in pounds per year, what does 7 w'(t)dt 4 represent? The change in the child's weight (in pounds) between the ages of 4 and 7. The change in the child's age (in years) between the ages of 4 and 7. The child's weight at age 7. The child's weight at age 4. The child's initial weight at birth.
Complete Question
If w'(t) is the rate of growth of a child in pounds per year, what does
[tex]\int\limits^{7}_{4} {w'(t)} \, dt[/tex] represent?
a) The change in the child's weight (in pounds) between the ages of 4 and 7.
b) The change in the child's age (in years) between the ages of 4 and 7.
c) The child's weight at age 7.
d) The child's weight at age 4. The child's initial weight at birth.
Answer:
The correct option is option a
Step-by-step explanation:
From the question we are told that
[tex]w'(t)[/tex] represents the rate of growth of a child in [tex]\frac{pounds}{year}[/tex]
So [tex]{w'(t)} \, dt[/tex] will be in [tex]pounds[/tex]
Which then mean that this [tex]\int\limits^{7}_{4} {w'(t)} \, dt[/tex] the change in the weight of the child between the ages of [tex]4 \to 7[/tex] years
A gallup survey indicated that 72% of 18- to 29-year-olds, if given choice, would prefer to start their own business rather than work for someone else. A random sample of 600 18-29 year-olds is obtained today. What is the probability that no more than 70% would prefer to start their own business?
Answer:
The probability that no more than 70% would prefer to start their own business is 0.1423.
Step-by-step explanation:
We are given that a Gallup survey indicated that 72% of 18- to 29-year-olds, if given choice, would prefer to start their own business rather than work for someone else.
Let [tex]\hat p[/tex] = sample proportion of people who prefer to start their own business
The z-score probability distribution for the sample proportion is given by;
Z = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, p = population proportion who would prefer to start their own business = 72%
n = sample of 18-29 year-olds = 600
Now, the probability that no more than 70% would prefer to start their own business is given by = P( [tex]\hat p[/tex] [tex]\leq[/tex] 70%)
P( [tex]\hat p[/tex] [tex]\leq[/tex] 70%) = P( [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] [tex]\leq[/tex] [tex]\frac{0.70-0.72}{\sqrt{\frac{0.70(1-0.70)}{600} } }[/tex] ) = P(Z [tex]\leq[/tex] -1.07) = 1 - P(Z < 1.07)
= 1 - 0.8577 = 0.1423
The above probability is calculated by looking at the value of x = 1.07 in the z table which has an area of 0.8577.