the probability that a randomly-selected 2 year old male salamander will live to be three years old is 0.9 567 what is the possibility probability that two randomly selected two year old male salamanders with live to be three years old? what is the probability that nine randomly selected 2-year old male salamanders will live to be 3-years old? what is the probability that at least one of the nine randomly selected 2-year old male salamanders will not live to be 3 years old? would it be unusual if at least one of nine randomly selected 2 year old male salamanders did not live to be 3 years old?
Answer:
a. [tex]Probability = 0.9153[/tex]
b. [tex]Probability = 0.6714[/tex]
c. [tex]P(atleast\ one) = 0.99999999999[/tex]
d. It is not unusual
Step-by-step explanation:
Represent the given probability with P(T)
[tex]P(T) = 0.9567[/tex]
Solving (a): Probability two selected will live to be three years old
This is calculated as:
[tex]Probability = P(T) * P(T)[/tex]
[tex]Probability = 0.9567 * 0.9567[/tex]
[tex]Probability = 0.91527489[/tex]
[tex]Probability = 0.9153[/tex] --- Approximated
Solving (b): The probability that nine selected will live to be three years old
This is calculated as:
[tex]Probability = (P(T))^9[/tex]
[tex]Probability = 0.9567^9[/tex]
[tex]Probability = 0.67140097202[/tex]
[tex]Probability = 0.6714[/tex] --- Approximated
Solving (c): Probability that at least one of the nine selected will not live to be three years old
To solve this, we need to determine the probability that none of the 9 selected will live to be 3 years old.
But first, we need to solve the probability that a selected male will not live to be 3 years old.
This is represented as: P(T') and is calculated as thus:
[tex]P(T) + P(T') = 1[/tex]
[tex]P(T') = 1 - P(T)[/tex]
[tex]P(T') = 1 - 0.9567[/tex]
[tex]P(T') = 0.0433[/tex]
The probability that none of the nine will live to be 3 years old is:
[tex]P(none) = (P(T'))^9[/tex]
[tex]P(none) = 0.0433^9[/tex]
So, the required probability is calculated as thus;
[tex]P(atleast\ one) = 1 - P(none)[/tex]
[tex]P(atleast\ one) = 1 - 0.0433^9[/tex]
[tex]P(atleast\ one) = 0.99999999999[/tex]
Solving (d): Would (c) be unusual
This probability is calculated in (c) above.
[tex]P(atleast\ one) = 0.99999999999[/tex]
Because it approximates to 1, we can conclude that it is not unusual
Eddie is reading a novel gor englidh class he has read 24 out of 60 pages about what percent of the book has he read
Answer: 40%
Step-by-step explanation: We can also work this out in a simpler way by first converting the fraction 24/60 to a decimal. To do that, we simply divide the numerator by the denominator:
24/60 = 0.4
Once we have the answer to that division, we can multiply the answer by 100 to make it a percentage:
0.4 x 100 = 40%
help plessssssssssssss
Which graph represents the solution set of the equation 3y - x - 9 = 0?
Slope=
2.000
0.667
=0.333
x−intercept=
−1
9
=−9.00000
y−intercept=
3
9
=3
The required graph that represents the equation 3y - x - 9 = 0 is graph B. Option B is correct.
Which graph represents the solution set of the equation 3y - x - 9 = 0 is to determine.
The graph is a demonstration of curves that gives the relationship between the x and y-axis.
Given equation,
3y - x - 9 = 0
Rearranging the equation,
y = x/3 + 3
Since the slope of the equation is m = 1/3 and the intercept is positive
So graph A and C can be omitted because the intercept is negative.
Now, x intercepet,
put Y = 0
0 = x/3 + 3
-3 = x/3
x = -3 * 3
x = -9
So graph D is also omitted because the x-intercept is -1 which is wrong, So graph B is a correct option which has the x-intercept at x = -9.
Thus, the required graph that represents the equation 3y - x - 9 = 0 is graph B. Option B is correct.
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A line is drawn through (-7, 11) and (8.–9). The equation
y – 11 = -4/3 (x + 7) is written to represent the line. Which
equations also represent the line? Check all that apply.
y = -4/3x + 5/3
3y = -4x + 40
4x + y = 21
4x + 3y = 5
-4x + 3y = 17
Answer-9
Step-by-step explanation:
An executive for a large national restaurant chain with multiple locations in each of 513 counties wants to personally sample the cleanliness of the chain's restaurants throughout the country by visiting restaurants. The executive wants a good-quality sample but wants to minimize travel time and expenses. Which of the following sampling methods would b most appropriate? Select the correct answer below:
A. Obtain a convenience sample by visiting the 100 restaurants that are closest to the executive's office.
B. Obtain a systematic sample by selecting every 20th restaurant from a list that orders all restaurants by date of opening
C. Obtain a stratified sample by visiting I randomly selected restaurant ik every county.
D. Obtain a cluster sample by randomly selecting 20 counties and visiting every restaurant within those counties.
Answer:
D. Obtain a cluster sample by randomly selecting 20 counties and visiting every restaurant within those counties.
Step-by-step explanation:
Since this executive wants to minimize cost and expenses he should use a cluster sample of 20 counties and using the selected counties as a representative of the whole. Cluster sampling is a good and useful way of doing market research. It is more economical than other sampling methods and as the executive cannot get information on the whole population, he would be able to get information from the clusters.
7. The University of Texas at Austin has three times as many students enrolled as the University of
Miami. The University of California, Berkley has 3,000 more than twice the number of students as
the University of Miami. If the three schools have a total enrollment of 96,000 students, what is the
enrollment at each school?
a. Describe what the variables represent:
===xyz
b. Write the system of linear equations:
c. Write the Augmented Matrix for the system of linear equations then solve using the Gauss-Jordan
Elimination Method. Show all row operations and at least 5 of the resulting matrices. Use proper
notation. Write the solution as an ordered triple, if appropriate.
d. Now, answer the question in a complete sentence with proper grammar and correct spelling:
What is the enrollment at each school?
The variables x, y, and z represent the number of students enrolled at the University of Texas at Austin, the University of Miami, and the University of California, Berkley, respectively.
x = 3y ,z = 2y + 3000 and x + y + z = 96000 are the linear equations.
On solving the matrix , we get that x = 9000 y = 3000 and z = 31500.
The enrollment at each school is 9,000 for the University of Texas at Austin, 3,000 for the University of Miami, and 31,500 for the University of California, Berkeley.
b. Let's write the system of linear equations based on the given information:
x = 3y (Equation 1)
z = 2y + 3000 (Equation 2)
x + y + z = 96000 (Equation 3)
c. To solve this system of equations using the Gauss-Jordan Elimination Method, we need to write the augmented matrix and perform row operations. The augmented matrix is:
[1 -3 0 | 0]
[0 1 2 | 3000]
[1 1 1 | 96000]
Now, let's perform row operations to get the reduced row-echelon form:
1. R3 = R3 - R1 (subtracting row 1 from row 3)
2. R3 = R3 - R2 (subtracting row 2 from row 3)
3. R3 = R3/2 (dividing row 3 by 2)
4. R2 = R2 - 2R1 (subtracting 2 times row 1 from row 2)
5. R1 = R1 + 3R2 (adding 3 times row 2 to row 1)
After performing these row operations, we get the following resulting matrices:
[1 0 3 | 9000]
[0 1 2 | 3000]
[0 0 1/2 | 31500]
From the last matrix, we can determine the values of x, y, and z:
x = 9000
y = 3000
z = 31500
Therefore, the enrollment at each school is as follows:
The University of Texas at Austin has 9,000 students enrolled.
The University of Miami has 3,000 students enrolled.
The University of California, Berkley has 31,500 students enrolled.
d. The enrollment at each school is 9,000 for the University of Texas at Austin, 3,000 for the University of Miami, and 31,500 for the University of California, Berkeley.
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Seven tenths subtract five tenths
Answer:
[tex]\frac{1}{5}[/tex]
Step-by-step explanation:
Step 1: Write expression
[tex]\frac{7}{10} -\frac{5}{10}[/tex]
Step 2: Evaluate
[tex]\frac{2}{10}[/tex]
Step 3: Simplify
[tex]\frac{1}{5}[/tex]
Answer:
Step-by-step explanation:
The answer is two tenths it is like subtracting whole numbers but behind the decimal
Write the whole number that correctly completes the word problem:
During a 24-hour day, most people spend 2/3 the time awake. This amounts to how many
hours awake.
Answer:
2/3(two thirds) of the 24 hour day awake, amounts to 24 x 2 / 3 hours awake which is equal to 16 hours awake
Step-by-step explanation:
24 x 2/3
there are many ways to evaluate this mentally, if you know 8x3=24, for instance you can multiply top and bottom of 2/3 by 8 yo gey 24 x 16/24 which is 16 hours
If the hypothenuse of a right
triangle measures 17 meters,
and one leg measures 15 meters,
what is the length of the other
leg?
15
PLS FAST ITS DUE IN 5 MINS
Answer:
b = 8
Step-by-step explanation:
a² + b² = c²
15² + b² = 17²
225 + b² = 289
b² = 64
√b² = 64
b = 8
Please help with this question.
Answer:
$26.53
Step-by-step explanation:
1. Calculate how much the repairmen changed just for the labor
93.06-40=53.06
2. Divide by two
53.06/2=26.53
Hope this helped!
What is the answer for
9.85÷1.25
Answer:
7.88
Step-by-step explanation:
6 + 23 • 3 =? on e2020
Answer:
75
Step-by-step explanation:
Order of operations: BPEMDAS
Step 1: Write expression
6 + 23 · 3
Step 2: Multiplication
6 + 69
Step 3: Add
75
Answer:
75
Step-by-step explanation:
6 + 23 x 3
6+ 69
75
y = –y equals negative StartFraction 5 over 2 EndFraction minus 7.x – 7
x + 2y = 4
the answer is 2 because
Hi, I need help with this question, please
The interquartile range for this distribution is 23.
How to calculate the interquartile range of a grouped data set?In Mathematics, the first quartile and third quartile of a grouped data set with class interval can be calculated by using this formula;
First quartile (Q₁) = [tex]L+(\frac{\frac{N}{4} -F_c}{F_q} )C[/tex]
Third quartile (Q₃) = [tex]L+(\frac{\frac{3N}{4} -F_c}{F_q} )C[/tex]
Where:
L is the lower class boundary (LCB) of the quartile class.N represents the total frequency of the data set.C is the class width.Fc is the cumulative frequency before the quartile class.Fq is the frequency of the quartile class.For the first quartile (Q₁), we have:
First quartile (Q₁) = 1/4 × 100 = 25th observation.
[tex]20+(\frac{\frac{100}{4} -19}{30} ) \times 10\\\\20+(\frac{25-19}{30} ) \times 10[/tex]
First quartile (Q₁) = 20 + 2 = 22.
For the third quartile (Q₃), we have:
Third quartile (Q₃) = 3/4 × 100 = 75th observation.
[tex]40+(\frac{\frac{300}{4} -70}{10} ) \times 10\\\\40+(\frac{75-70}{10} ) \times 10[/tex]
Third quartile (Q₃) = 40 + 5 = 45.
Mathematically, the interquartile range (IQR) of a data set is the difference between third quartile (Q₃) and the first quartile (Q₁):
Interquartile range (IQR) of data set = Q₃ - Q₁
Interquartile range (IQR) of data set = 45 - 22
Interquartile range (IQR) of data set = 23.
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Mr. O’Connel purchased 12 bags of grass seed for $62.28. What was the price per bag of grass seed?
Answer:
$5.19
Step-by-step explanation:
62.28/12
Answer: The correct answer is $5.19
Step-by-step explanation:
Work out $216 as a percentage of $600
Answer:
36%
Step-by-step explanation:
Put it into a fraction:
216/600
Next divide:
216/600= 0.36
Turn the decimal into a percentage:
0.36 = 36%
216 as a percentage of 600 is equal to 36%.
Answer:
36%
Step-by-step explanation:
216 / 600
0.36
0.36 * 100 = 36%
Best of Luck!
The conventional algorithm for evaluating a polynomial anxn + an-1xn-1 + … + a1x + a0 at x = c can be expressed in pseudocode by
Procedure polynomial (c, a0, a1, …, an : real numbers)
power :=1
y :=a0
for i := 1 to n
begin
power := power * c
y := y + ai * power
end {y = ancn + an-1cn-1 +…+ a1c +a0}
where the final value of y is the value of the polynomial at x = c.
a. Evaluate 3x2 + x + 1 at x = 2 by working through each step of the algorithm showing the values assigned at each assignment step.
b. Exactly how many multiplications and additions are used to evaluate a polynomial of degree n at x = c? (Do not count additions used to increment the loop variable.)
Answer:
a.) value of polynomial at x=2 is 15
b,) exactly 2 multiplications and 1 addition are used to evaluate the polynomial
Step-by-step explanation:
a.)
at x = 2,
3x²+x+1
with n = 2, a₀=1, a₁=1, a₂=3 with c=2,
firstly we set power =1
y=1
for the first time through the loop;
we have i = 1
the power increases to 2
y = 1+1*2
= 3
i =2
then going through the loop for the last time
power = 2x2 = 4
y = 3+(3*4)
= 15
we stop here because polynomial is of degree 2
b.
while passing through the loop, each pass requires that we do 2 multiplications and 1 addition. so for the for loop we have n iterations with total being 2n multiplications and n additions.
How would you do these questions?
Part 1
Population = {1,2,4}
Sample 1 = {1,1}, probablity = 1/9
Sample 2 = {1,2}, probablity = 1/9
Sample 3 = {1,4}, probablity = 1/9
Sample 4 = {2,1}, probablity = 1/9
Sample 5 = {2,2}, probablity = 1/9
Sample 6 = {2,4}, probablity = 1/9
Sample 7 = {4,1}, probablity = 1/9
Sample 8 = {4,2}, probablity = 1/9
Sample 9 = {4,4}, probablity = 1/9
Each of the 9 samples has equal probablity of occuring, so that's why each probablity is 1/9
Note: it may be best to write the above in the form of a table
==================================================
Part 2
For each sample (1 through 9), compute the mean. So we'll add up the values and divide by 2
xbar represents the sample mean
Sample 1 = {1,1}, xbar = 1
Sample 2 = {1,2}, xbar = 1.5
Sample 3 = {1,4}, xbar = 2.5
Sample 4 = {2,1}, xbar = 1.5
Sample 5 = {2,2}, xbar = 2
Sample 6 = {2,4}, xbar = 3
Sample 7 = {4,1}, xbar = 2.5
Sample 8 = {4,2}, xbar = 3
Sample 9 = {4,4}, xbar = 4
----------
Now let's list out each possible xbar value and its associated probability
xbar = 1, probability = 1/9
xbar = 1.5, probability = 2/9
xbar = 2, probability = 1/9
xbar = 2.5, probability = 2/9
xbar = 3, probability = 2/9
xbar = 4, probability = 1/9
note how the probabilities listed above add to 9/9 = 1.
Again a table is ideal to help organize the data.
==================================================
Part 3
To calculate the value of mu_x, we add up all the xbar values found in part 2, and divide by 9
(1+1.5+2.5+1.5+2+3+2.5+3+4)/9 = 2.333
So mu_x = 2.333 approximately
----------
Calculating the standard deviation is a bit lengthier, but you subtract each data value from the mean, square each difference, and add up the squares.
Afterward, you divide by n = 9 to get the population variance. Apply the square root to get the population standard deviation.
Luckily a calculator or spreadsheet can make quick work of this. You should get roughly 0.88192 as the standard deviation.
==================================================
Part 4
The mean of the population {1,2,4} is (1+2+4)/3 = 2.3333 which matches with mu_xbar
The standard deviation of the population {1,2,4} is roughly 0.88191710368819 which matches with 0.88192 found earlier back in part 3.
6 square units
3 square units
5 square units
7 square units
4 square units
5 square units is the approximate area of the triangle. Option C is correct
Area of a triangleThe formula for calculating the area of a triangle is expressed as"
Area = 1/2 * base * height
From the given triangle, the base is RS and the height is TO where O is the midpoint of RS. =
Area of triangle RST = 1/2(RS)(TO)
Determine the distance RS and TO
RS = √(1-3)²+(-1-1)²
RS = √4+4
RS = 2√2 units
TO = √(-1-2)²+(2-0)²
TO = √9+4
TO = √13 units
Area of triangle RST = 1/2 * 2√2 * √13
Area of triangle RST = √26
Area of triangle RST = 5 square units
Hence the area of triangle RST is approximately 5 square units
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Please help me whoever answers first will get brainliest.
Which statement is true about the given expression?
3r2 – 11(2y + 1) + 4
OA. The "4" in the third term is a factor
OB. The "3" in the first term is an exponent.
OC. The "2" in the second term is a coefficient.
OD
The "11" in the second term is a constant,
Answer:
C
Step-by-step explanation:
It is C because the 2 is attached to the variable Y
seagull is flying at 125 feet above sea level. A dolphin is swimming 23 feet below sea level. What is the distance in feet between the seagull and dolphin?
Answer:
102 feet.
Step-by-step explanation:
-23ft + 125ft = 102 ft
How will the volume of a cube change if its edge becomes twice as long; 3 times as long; 10 times as long; n times as long?
Let, initial side is a.
When side is n times long, new side na.
Initial volume, [tex]V_i=a^3[/tex]
Final volume, [tex]V_f=(na)^3=n^3a^3[/tex]
Change in volume, [tex]V_f-V_i=\Delta V =a^3(n^3-1)[/tex]
For, n = 2 :
[tex]\Delta V = 7a^3[/tex]
n = 3 :
[tex]\Delta V = 26a^3[/tex]
n = 10 :
[tex]\Delta V = 999a^3[/tex]
Hence, this is the required solution.
John is 4 years younger than Mary, write an equation using x=John's age, M=Mary's age, and the number 4
What number should be added to both sides of the following equation to solve for x? x - 7 = 4 3 4 7 11
Answer:
The answer is 4
Step-by-step explanation:
This is because if u add 4 to seven it equals eleven so that is ur answer.
The point (5, -2) is translated by (x,y)→
(x - 4, y + 5), then rotated 90°
clockwise. What are the coordinates of the final image?
Answer:
(1,3)
Step-by-step explanation:
hope it's help ful
what is the distance between 1/3 and 2/3
Answer:
1/3
Step-by-step explanation:
is this a trick question? all you have to ask yourself is "what does it take to get from 1/3 to 2/3, or whats the difference between 1/3 and 2/3?" haha but here i guess!
PLEASe I’m BEGGING YOU IF YOU KNOW THIS 100% percent and get it correct I will Iove u forever even tho idk you but PLEASE
Answer:
The goal here is to simplify your answer, and so in order to do that, you must combine like terms.
Step-by-step explanation:
-x+ -9x= -10x
-7+6= -1
-10x-1 is the answer, hope this helps
If 3b – (6 – b) = –22, find the value of 7b.
Answer:
Step-by-step explanation:
first solve for b:
distribute the negative sign over the parentheses so:
3b-6+b=-22
combine like terms:
3b+b=-22+6
4b=-16
b=-4
2. Plug in the value of b
7b (replace b with -4)
7(-4)
=-28
A function h(x) is defined by the formula h(x)=x^3-3. What is the value of g(h(2))?
Answer:
g(h(2))= 5
Step-by-step explanation:
h(x)=x^3-3
g(2^3-3)
the 2 replaces the x
simplify
g(5)
