Answer:
After 1st year, the age distribution will be
[tex]x_1 = \left[\begin{array}{ccc}1584\\36\\108\end{array}\right][/tex]
After 2nd year, the age distribution will be
[tex]x_2 = \left[\begin{array}{ccc}5256\\396\\27\end{array}\right][/tex]
Step-by-step explanation:
A population has the following characteristics.
A total of 25% of the population survives the first year. Of that 25%, 75% survives the second year.
The average number of offspring for each member of the population is 3 the first year, 5 the second year, and 3 the third year.
From the above information, we can construct a transition age matrix.
[tex]A = \left[\begin{array}{ccc}3&5&3\\0.25&0&0\\0&0.75&0\end{array}\right][/tex]
The population now consists of 144 members in each of the three age classes.
From the above information, we can construct the current age matrix.
[tex]x = \left[\begin{array}{ccc}144\\144\\144\end{array}\right][/tex]
How many members will there be in each age class in 1 year?
After 1st year, the age distribution will be
[tex]x_1 = A \cdot x[/tex]
[tex]x_1 = \left[\begin{array}{ccc}3&5&3\\0.25&0&0\\0&0.75&0\end{array}\right] \times \left[\begin{array}{ccc}144\\144\\144\end{array}\right][/tex]
The matrix multiplication is possible since the number of columns of first matrix is equal to the number of rows of second matrix.
[tex]x_1 = \left[\begin{array}{ccc}1584\\36\\108\end{array}\right][/tex]
After 2nd year, the age distribution will be
[tex]x_2 = A \cdot x_1[/tex]
[tex]x_2 = \left[\begin{array}{ccc}3&5&3\\0.25&0&0\\0&0.75&0\end{array}\right] \times \left[\begin{array}{ccc}1584\\36\\108\end{array}\right][/tex]
[tex]x_2 = \left[\begin{array}{ccc}5256\\396\\27\end{array}\right][/tex]
Factorizar e indicar cuántos factores primos tiene -3+3x^2+y-x^2*y-y^2+x^2*y
Claim: The mean pulse rate (in beats per minute) of adult males is equal to 69.3 bpm. For a random sample of 140 adult males, the mean pulse rate is 69.8 bpm and the standard deviation is 11.2 bpm. Complete parts (a) and (b) below.
a. Express the original claim in symbolic form.
_,_,bpm
Answer:
Part a
Null hypothesis: [tex] \mu = 69.3[/tex]
Alternative hypothesis: [tex]\mu \neq 69.3[/tex]
Part b
[tex] z = \frac{69.8- 69.3}{\frac{11.2}{\sqrt{140}}}= 0.528[/tex]
Step-by-step explanation:
For this case we have the following info given :
[tex] \bar X = 69.8[/tex] the sample mean
[tex] n= 140[/tex] represent the sample size
[tex] s = 11.2[/tex] represent the standard deviation
Part a
And we want to test if the true mean is equal to 69.3 so then the system of hypothesis:
Null hypothesis: [tex] \mu = 69.3[/tex]
Alternative hypothesis: [tex]\mu \neq 69.3[/tex]
Part b: Find the statistic
The statistic is given by:
[tex] z= \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And replacing the info we got:
[tex] z = \frac{69.8- 69.3}{\frac{11.2}{\sqrt{140}}}= 0.528[/tex]
Suppose that a random number generator randomly generates a number from 1 to 65. Once a specific number is generated, the generator will not select that number again until it is reset. If a person uses the random number generator 65 times in a row without resetting, how many different ways can the numbers be generated?
Answer:
65!
65! = 8. 2547650592 * 10^ 90 approximately
Step-by-step explanation:
A random number generator randomly generates a number from 1 to 65.
Once a specific number is generated, the generator will not select that number again until it is reset.
The number of ways it can be used is = 65!
65! = 8. 25476505* 10^ 90 approximately
Please answer this correctly
Answer:
540
Step-by-step explanation:
Since the surface area is 408, we can set up the equation
2*9*6 + 2*r*9 + 2*r*6 = 408
108 + 30r = 408
30r = 300
r = 10
The volume is length * width * height
9*6*10 = 540
Length of a rod: Engineers on the Bay Bridge are measuring tower rods to find out if any rods have been corroded from salt water. There are rods on the east and west sides of the bridge span. One engineer plans to measure the length of an eastern rod 25 times and then calculate the average of the 25 measurements to estimate the true length of the eastern rod. A different engineer plans to measure the length of a western rod 20 times and then calculate the average of the 20 measurements to estimate the true length of the western rod.
Answer:
b. The engineer who weighed the rod 25 times.
Step-by-step explanation:
Hello!
Full text:
Length of a rod: Engineers on the Bay Bridge are measuring tower rods to find out if any rods have been corroded from salt water. There are rods on the east and west sides of the bridge span. One engineer plans to measure the length of an eastern rod 25 times and then calculate the average of the 25 measurements to estimate the true length of the eastern rod. A different engineer plans to measure the length of a western rod 20 times and then calculate the average of the 20 measurements to estimate the true length of the western rod.
Suppose the engineers construct a 90% confidence interval for the true length of their rods. Whose interval do you expect to be more precise (narrower)?
a. Both confidence intervals would be equally precise.
b. The engineer who weighed the rod 25 times.
c. The engineer who weighed the rod 20 times.
X₁: Length of an eastern rod of the Bay Bridge
n₁= 25
X₂: Length of a western rod of the Bay Bridge
n₂= 20
Both Engineers will use their samples to estimate the population average length of the rods using a 90% CI.
Assuming the standard normal distribution, the confidence interval will be centered in the estimated mean.
X[bar] ± [tex]Z_{1-\alpha /2}[/tex]*(σ/√n)
And the width is determined by the semi amplitude:
↓d= [tex]Z_{1-\alpha /2}[/tex]*(σ/√↑n)
As you can see the sample size has an indirect relationship with the semi amplitude of the interval. This means, when the sample size increases, the semi amplitude decreases, and if the sample size decreases, the semi amplitude increases. Naturally this is leaving all other elements of the equation constant, this means, using the same confidence level and the same population standard deviation.
Since the first engineer took the larger sample, he's confidence interval will be narrower and more accurate.
Hope this helps!
A fraction with a zero in the numerator equals
Answer:Any legal fraction (denominator not equal to zero) with a numerator equal to zero has an overall value of zero. all have a fraction value of zero because the numerators are equal to zero.
The average score of all golfers for a particular course has a mean of 70 and a standard deviation of 3.5. Suppose 49 golfers played the course today. Find the probability that the average score of the 49 golfers exceeded 71.
what is 3 43/ 100 as a decimal number.
Answer:
3.43
Step-by-step explanation:
3 is the whole number and 43 out of 100 is a standard fraction that can simply be stated as 0.43. Hope this helps!
Answer:
3.43
Step-by-step explanation:
Used calculator.
Can someone plz help me solved this problem I need help ASAP plz help me! Will mark you as brainiest!
Answer:
8
Step-by-step explanation:
y²+by+16= (y+4)²
y²+by+16= y²+2*4*y+4²
y²+by+16= y²+8y+16
by=8y
b=8
Please help. I’ll mark you as brainliest if correct!!!!!
[tex]x^2+14x+40=0\\x^2+14x+40+9-9=0\\x^2+14x+49=9\\(x+7)^2=9\\\\D=7\\E=9[/tex]
Answer:
x^2+14x+40=0\\x^2+14x+40+9-9=0\\x^2+14x+49=9\\(x+7)^2=9\\\\D=7\\E=9
Step-by-step explanation:
A rectangle has a length of 60 in and a width of 8 in. Given a scale factor of 4in:5ft. What is the area of the rectangle?
Answer:
750ft²
Step-by-step explanation:
Area of rectangle = L*B
Before we find the area of the given rectangle, we need to convert the dimensions using the given scale.
Thus, dimensions of the given rectangle using the scale factor of 4in:5ft would be:
==> Length = 60in = (60*5)/4 = 75ft
Breadth or Width = 8in = (8*5)/4 = 10ft
Therefore, area of rectangle = L * B
= 75ft * 10ft
= 750 ft²
Area of rectangle = 750ft²
WILL GIVE BRAINLIEST ANSWER ASAP
Answer:
x = -6
Step-by-step explanation:
-2/3x + 9 = 4/3x - 3
First we need to simplify to where we have x on one side and a constant (number not connected to a variable) on the other side.
Subtract 4/3x from both sides:
-2/3x + 9 - 4/3x = -3
-6/3x + 9 = -3
Now subtract 9 from both sides:
-6/3x + 9 - 9 = -3 - 9
-6/3x = -12
Now turn -6/3 into a whole number to make things more simple:
-6/3 = -2
-2x = -12
Now divide both sides by -2 to get x by itself
-2x/-2 = -12/-2
x = -6
2. {5.0A.A.1, 5.0A.A.2} Write an expression to show....the product of eight
and two, minus the product of three and four. *
Answer:
[tex]\left ( 8\times 2 \right )-\left ( 3\times 4 \right )[/tex]
Step-by-step explanation:
Given: The statement is ' the product of eight and two, minus the product of three and four'
To find: expression for the given statement
Solution:
An algebraic expression is an expression consists of coefficients, variables, and the arithmetic operations.
Product of eight and two = [tex]\left ( 8\times 2 \right )[/tex]
Product of three and four = [tex]\left ( 3\times 4 \right )[/tex]
Therefore,
Product of eight and two, minus the product of three and four = [tex]\left ( 8\times 2 \right )-\left ( 3\times 4 \right )[/tex]
A classic counting problem is to determine the number of different ways that the letters of "misspell" can be arranged. Find that number.
Answer:
10,080 different ways that the letters of "misspell" can be arranged.
Step-by-step explanation:
Number of arrangents of the letters of a word:
A word has n letters.
The are m repeating letters, each of them repeating [tex]r_{0}, r_{1}, ..., r_{m}[/tex] times
So the number of distincts ways the letters can be arranged is:
[tex]N_{A} = \frac{n!}{r_{1}! \times r_{2}! \times ... \times r_{m}}[/tex]
In this question:
Misspell has 8 letters, with s and l repeating twice.
So
[tex]N_{A} = \frac{8!}{2!2!} = 10080[/tex]
10,080 different ways that the letters of "misspell" can be arranged.
Shari wrote the numbers from 1 to 16 on a card.
Next, she crossed out all the numbers which are factors of 80.
Then, she crossed out all the numbers which are multiples of 3.
How many numbers were not crossed out?
If a procedure meets all the conditions of a binomial distribution except that the number of trials is not fixed, then the geometric distribution can be used. The probability of getting the first success on the xth trial is given by
P
(
x
)
=
p
(
1
−
p
)
x
−
1
where
p
is the probability of success on any one trial.
Assume that the probability of a defective computer component is 0.21. Find the probability that the first defect is found in the fifth component tested.
(Round answer to four decimal places.)
P
(
5
)
=
Answer:
M.
Step-by-step explanation:
Suppose that the raw daily oxygen purities delivered by an air-products supplier have a standard deviation LaTeX: \sigma\approx.1 σ ≈ .1 (percent), and it is plausible to think of daily purites as independent random variables. Approximate the probability that the sample mean LaTeX: \frac{ }{X} X of n = 25 delivered purities falls within .03 (percent) of the raw daily purity mean, LaTeX: \mu μ .
Answer:
There is a probability of 86.6% that the sample mean falls within 0.03 percent of the raw purity mean.
Step-by-step explanation:
We have a population standard deviation of σ ≈ 0.1.
We have a sample of size n=25.
Then, we have a sampling distribution, which has a standard deviation for the sample mean that is:
[tex]\sigma_s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{0.1}{\sqrt{25}}=\dfrac{0.1}{5}=0.02[/tex]
Now, we can calculate a z-score for a deviation of 0.03 percent from the mean as:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{0.03}{0.02}=\dfrac{0.03}{0.02}=1.5[/tex]
Note: we considered that the margin is ±0.03.
Then, the probability is:
[tex]P(|X-\mu|<0.03\%)=P(|z|<1.5)=0.866[/tex]
What is the value of Y ? I’ll give you a brainslist !!!
[tex]answer \\ = 5 \sqrt{3} \\ please \: see \: the \: attached \: picture \: for \: \: full \: solution \\ hope \: it \: helps[/tex]
Answer:
[tex]5 \sqrt{3} [/tex]
First answer is correct
Step-by-step explanation:
[tex] \frac{5}{x} = \cos(60) \\ \frac{5}{x} = \frac{1}{2} \\ x = 10 \\ \frac{y}{x} = \sin(60 ) \\ \frac{y}{10} = \frac{ \sqrt{3} }{2} \\ 2y = 10 \sqrt{3} \\ y = \frac{10 \sqrt{3} }{2} \\ y = 5 \sqrt{3} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
If f(x) = (-x)^3, what is f(-2)?
-6
-8
8
6
Answer:
The answer is 8
Step-by-step explanation:
Plug -2 in for x. The double-negative inside the parenthesis makes it positive, then do the exponent.
Answer:
-(-2)^3 = 2^3 = 8
Answer is C
Step-by-step explanation:
So we plug in the numbers. We have -2 as x. (-(-2)^3 would be our thing. Thats because our x is the negative so the negative of -2 is 2.
2^3 = 8
therefore its 8
What is equivalent to
16x-12-24x+4
Answer:
-8x - 8
Step-by-step explanation:
You have to combine like term.
So you add 16x + -24x = -8x
And you add -12 + 4 = -8
Your answer would be -8x - 8
I hope this helps!
What is the length of the line?
Answer:
B) 5
Step-by-step explanation:
The points are (2,2) and (6,5). Subtract both Y's and X's and then square the answers and add. you should get 25, which has a square root of 5.
NEED GEOMETRY HELP ASAP PLEASE (12 POINTS)
Answer:
2 times the square root of 10
Step-by-step explanation:
If you make a right triangle and solve for the hypotenuse (the distance between P1 and P2), you will get 2 times the square root of 10.
Please mark this brainliest.
Answer: [tex]2\sqrt{10}[/tex]
Step-by-step explanation:
if you draw a triangle starting from P1 and go up to the y value of P2, the change in y is equal to 6.
From that point, go to the right until you hit P2 to get a change in x of 2.
Youre basically missing the hypotenuse of this triangle that you drew. Which is where the distance formula is derived from. 6^2 + 2^2 = s^2
You get √40 = s. It appears that they want you to simplify this square root. What are the two greatest numbers that multiply to equal 40 and atleast one of them has a perfect square root? That's 10 and 4. you can perfectly take the square root of 4, so go ahead and do that. Put that 2 outside of the square root. That gives you [tex]2\sqrt{10}[/tex]
M is the midpoint of st. Sm= 3x+16 and MT = 6x+4. Find the length of SM.
No figure required. If M is the midpoint of ST then SM=MT or
3x + 16 = 6x + 4
12 = 3x
x = 4
SM = 3(4)+16=28
Answer: 28
Which graph has the parent function 1/x?
Answer:
The graph of parent function [tex]f(x)=\frac{1}{x}[/tex] is a hyperbola.
Step-by-step explanation:
A rational function is described as the fraction of polynomials, where the denominator has degree of at least 1 .
Or it can be said that there must be a variable in the denominator.
The general form of a rational function is:
[tex]\text{Rational Function}= f(x)=\frac{p(x)}{q(x)}[/tex]
In this case the parent function provided is: [tex]f(x)=\frac{1}{x}[/tex].
The function is rational.
The graph of parent function [tex]f(x)=\frac{1}{x}[/tex] is a hyperbola.
The graph is attached below.
ASAP
What is the sum of 16.87 + (–98.35)?
–115.22
–81.48
81.48
115.22
Solution,
16.87+(-98.35)
=16.87-98.35
= -81.48
Hope it helps
Good luck on your assignment
Answer:-81.48
Step-by-step explanation:
16.87 + (–98.35)
-81.48
If you stumble in other questions like there you can use a calculator or ask me. :D hope that helps
In a class of 20 students 11 people have a brother 9 people have a sister 6 people have neither fill in the Venn diagram
Answer:
Draw a Venn diagram with the left circle labeled brother, and the right labeled sister. Label the middle both and fhe outisde neither. Put 5 in brother, 3 in sister, 6 in both and 6 in neithrr.
Step-by-step explanation:
11+9 = 20
20-6 = 14
20-14=6
There are 6 that have both
Find the measure of angle b
Answer: The measure of angle B is 31 degrees.
Step-by-step explanation:
180 -149 = 31
Answer:
31 degrees
Step-by-step explanation:
We can see that 149 degrees and b are on a line. If they are next to each other they are called adjacent angles. There is a rule that adjacent angles add up to 180 degrees. So we subtract 149 from 180 and we get 31 degrees for angle b.
Hope this helps! :)
The ratio of blue to red cars in a car park are 3:2 what percentage of cars are red? and blue?
Answer:40%
Step-by-step explanation:
For every 5 cars two are red. Percentage of red cars to blue is 2/5 * 100 = 40%
Which table represents a relation that is not function
Please urgent
Look at the row of numbers. What number should come next?
8, 4, 2, 1, 1/2, 1/4, ?
Answer:
1/8
Step-by-step explanation
Every time the number is divided by 2 like 8 divided by 2 is 4 and 4 divided by 2 is 2 and so on so if you divide 1/4 by 2 it would be 0.125 and that in fraction would be 1/8.
