The equation for compound interest is A=P(1+rn)nt, where P is the initial amount invested, r is the interest rate as a decimal, n is the number of times compounded annually, and t is the number of years.
Determine the value of the account if the initial investment is $8,000 compounded monthly at a rate of 6% after 10 years.
$14,555.17
$8409.12
$8480.00
$14,326.78
Answers
Related Questions
Find the total surface area of a cone whose radius of base is 6cm and slant height is 8cm.
Answers
Answer:
The Total Surface Area of cone is 264 cm²
Step-by-step explanation:
Given:Radius (r) = 6 cm
Slant height (l) = 8 cm
To find TSA of cone
A = πr(l + r)
A = 22/7 × 6 × (8 + 6)
A = 22/7 × 6 × (14)
A = 22/7 × 84
A = 22 × 12
A = 264 cm²
Thus, The Total Surface Area of cone is 264 cm²
-TheUnknownScientist 72
If ST=17 and RT=41, find RS. Use the number line below.
Answers
The length of segment RS is given as follows:
RS = 24.
What does the angle addition postulate state?The angle addition postulate states that if two or more angles share a common vertex and a common angle, forming a combination, the measure of the larger angle will be given by the sum of the measures of each of the angles.
The segment RT is the combination of segments RS and ST, hence:
RT = RS + ST.
Hence the length of segment RS is given as follows:
41 = RS + 17
RS = 24.
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Which point maximizes the objective function, z = 3x + 5y? a. (1, 1) b. (2, 7) c. (5, 10) d. (6, 3)
Answers
To determine which point maximizes the objective function, we need to evaluate the objective function at each of the given points and then compare the results. The point that produces the highest value for z will be the solution.
a. (1, 1)
z = 3(1) + 5(1) = 8
b. (2, 7)
z = 3(2) + 5(7) = 41
c. (5, 10)
z = 3(5) + 5(10) = 55
d. (6, 3)
z = 3(6) + 5(3) = 33
Therefore, the point that maximizes the objective function is (5, 10) with a value of z = 55.
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The difference of two numbers is four. the sum of the lesser number and a half the greater number is 23. what is the product of the two numbers
Answers
The two numbers are 6.8 and 10.8. Thus the product of the two numbers will be 73.44.
What is the solution to the equation?In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.
Let the two numbers be 'x' and 'y', then the equations are given as,
x - y = 4 ...1
(x + y) + x/2 = 23
3x + 2y = 46 ...2
From equations 1 and 2, then we have
3(4 + y) + 2y = 46
12 + 3y + 2y = 46
5y = 34
y = 6.8
The value of 'x' is calculated as,
x - 6.8 = 4
x = 10.8
The product of two numbers is calculated as,
xy = 6.8 × 10.8
xy = 73.44
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(30 points)
A research company is performing an observational study of a certain endangered species of desert salamander to determine whether the species can survive in a new habitat.
Which reason provides a good rationale for avoiding randomization in this observational study?
(a). Placing a number of the endangered species in a new habitat where they may or may not survive is unethical.
(b). The observational study is too expensive to run.
(c). Food sources in the new habitat would not be the same as those in the species' present habitat.
(d). The species population may exceed expectations in the new habitat.
Answers
Placing a number of the endangered species in a new habitat where they may or may not survive is unethical. Option A
What does it mean to randomize a study?The random technique of assigning participants to treatment and control groups makes the assumption that each participant has an equal chance of being assigned to any group.
An observational study would involve the researchers observing the species in both its old and new habitats without altering any variables or introducing any novel situations. The researchers could gather data on the behavior and survival rates of the species in both habitats using this method without putting them in risk.
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(a) find the five-number summary, and (b) draw a box-and-whisker plot of the data. question content area bottom part 1 (a) min enter your response here (simplify your answer.) part 2 enter your response here (simplify your answer.) part 3 enter your response here (simplify your answer.) part 4 enter your response here (simplify your answer.) part 5 max enter your response here (simplify your answer.)
Answers
A five-number summary is a useful tool for summarizing a data set. It provides a quick and easy way to see the range of the data, the middle 50% of the data, and the median.
We have to find the five-number summary and draw a box-and-whisker plot of the given data. To find the five-number summary, we need to find the minimum, maximum, median, and first and third quartiles of the data. After that, we can create a box-and-whisker plot using these values.
The given data is not provided. Without the data, we cannot find the five-number summary and draw a box-and-whisker plot. However, we can discuss the steps involved in finding the five-number summary and drawing a box-and-whisker plot.
Let's consider a set of data:
12, 23, 34, 35, 46, 57, 58, 69, 70, 81, 92
To find the five-number summary of the above data, we follow the steps below:
Step 1: Arrange the data in ascending order
12, 23, 34, 35, 46, 57, 58, 69, 70, 81, 92
Step 2: Find the minimum and maximum values
Minimum value (min) = 12
Maximum value (max) = 92
Step 3: Find the median
The median is the middle value in the data. It is the value that separates the lower 50% of the data from the upper 50%. To find the median, we use the following formula:
Median = (n + 1)/2 where n is the number of observations in the data set.
Median = (11 + 1)/2
= 6
The 6th value in the data set is 57, which is the median.
Step 4: Find the first and third quartiles
The first quartile (Q1) is the value that separates the lower 25% of the data from the upper 75%.
To find Q1, we use the following formula:
Q1 = (n + 1)/4
Q1 = (11 + 1)/4
= 3
The 3rd value in the data set is 34, which is Q1.
The third quartile (Q3) is the value that separates the lower 75% of the data from the upper 25%.
To find Q3, we use the following formula:
Q3 = 3(n + 1)/4
Q3 = 3(11 + 1)/4
= 9
The 9th value in the data set is 70, which is Q3.
Now, we can use these values to draw a box-and-whisker plot. The box-and-whisker plot is a graphical representation of the five-number summary of the data. It consists of a box and two whiskers. The box represents the interquartile range (IQR), which is the range between Q1 and Q3. The whiskers represent the range of the data excluding outliers. The median is represented by a line inside the box.
In conclusion, the five-number summary is a useful tool for summarizing a data set. It provides a quick and easy way to see the range of the data, the middle 50% of the data, and the median. The box-and-whisker plot is a visual representation of the five-number summary. It is a useful tool for comparing data sets and identifying outliers.
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what is the answer to this question?
Answers
Answer:
A
Step-by-step explanation:
Proportions can be any number so other statements can't be always true
Answer:
A. Class X has a greater proportion of boys than Class Y
Step-by-step explanation:
- Before choosing any objective, first relate the two proportions.
Multiply class Y by 2:
\({ \rm{y = 2(4 : 5)}} \\ { \rm{y= 8:10}}\)
- So it can be related with class X as the ratios have a common proportion of girls; 10
\({ \rm{x= 9:{ \green{10}}}} \\ { \rm{y = 8:{ \green{10}}}}\)
- By observation, we see that class X has a greater number of boys than in class Y
\({ \boxed{ \red{ \delta}}}{ \underline{ \mathfrak{ \: ...creed}}}\)
3) A moving target at a police academy target range can be hit 88% of the time by a particular individual. Suppose that as part of a training exercise, eight shots are taken at a moving target. a) What 3 characteristics of this scenario indicate that you are working with Bernoulli trials? b) What is the probability of hitting the 6
th
target (Hint: think of this as a single trial)? c) What is the probability that the first time hitting the target is not until the 4 th shot?
Answers
a. The probability of success (hitting the target) is constant for each trial (88% or 0.88).
b. The probability of hitting the 6th target is:
P(X = 1) = C(1, 1) * 0.88^1 * (1 - 0.88)^(1 - 1) = 0.88
c. Using the binomial probability formula as before, with p = 0.88 and n = 3:
P(X = 1) = C(3, 1) * 0.88^1 * (1 - 0.88)^(3 - 1)
P(X = 2) = C(3, 2) * 0.88^2 * (1 - 0.88)^(3 - 2)
P(X = 3) = C(3, 3) * 0.88^3 * (1 - 0.88)^(3 - 3)
a) The three characteristics of this scenario that indicate we are working with Bernoulli trials are:
The experiment consists of a fixed number of trials (eight shots).
Each trial (shot) has two possible outcomes: hitting the target or missing the target.
The probability of success (hitting the target) is constant for each trial (88% or 0.88).
b) To find the probability of hitting the 6th target (considered as a single trial), we can use the binomial probability formula:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
where:
P(X = k) is the probability of getting exactly k successes,
C(n, k) is the binomial coefficient or number of ways to choose k successes out of n trials,
p is the probability of success in a single trial, and
n is the total number of trials.
In this case, k = 1 (hitting the target once), p = 0.88, and n = 1. Therefore, the probability of hitting the 6th target is:
P(X = 1) = C(1, 1) * 0.88^1 * (1 - 0.88)^(1 - 1) = 0.88
c) To find the probability that the first time hitting the target is not until the 4th shot, we need to consider the complementary event. The complementary event is hitting the target before the 4th shot.
P(not hitting until the 4th shot) = P(hitting on the 4th shot or later) = 1 - P(hitting on or before the 3rd shot)
The probability of hitting on or before the 3rd shot is the sum of the probabilities of hitting on the 1st, 2nd, and 3rd shots:
P(hitting on or before the 3rd shot) = P(X ≤ 3) = P(X = 1) + P(X = 2) + P(X = 3)
Using the binomial probability formula as before, with p = 0.88 and n = 3:
P(X = 1) = C(3, 1) * 0.88^1 * (1 - 0.88)^(3 - 1)
P(X = 2) = C(3, 2) * 0.88^2 * (1 - 0.88)^(3 - 2)
P(X = 3) = C(3, 3) * 0.88^3 * (1 - 0.88)^(3 - 3)
Calculate these probabilities and sum them up to find P(hitting on or before the 3rd shot), and then subtract from 1 to find the desired probability.
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For a project in his Geometry class, Fwam uses a mirror on the ground to measure the height of his school building. He walks a distance of 7. 15 meters from the building, then places a mirror flat on the ground, marked with an X at the center. He then walks 2. 45 more meters past the mirror, so that when he turns around and looks down at the mirror, he can see the top of the school clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1. 55 meters. How tall is the school? Round your answer to the nearest hundredth of a meter
Answers
the height of the school building is approximately 8.08 meters. Fwam used a mirror on the ground to measure the height of his school building. The method he used is called the mirror method,.
which involves using the reflection of the top of the building in a mirror to calculate the building's height. We can use some basic trigonometry to solve this problem.
First, we need to draw a diagram of the situation. The mirror on the ground, the point where Fwam is standing, and the top of the building form a right triangle. The distance from Fwam's eyes to the mirror is the height of the triangle, and the distance from Fwam to the mirror and from the mirror to the top of the building are the two legs of the triangle.
Using the Pythagorean theorem, we can write:
distance from Fwam to the top of the building = √\((distance from Fwam to the mirror)^2 + (distance from the mirror to the top of the building)^2\)
distance from Fwam to the top of the building = √\((7.15 + 2.45)^2 + 1.55^2\)
distance from Fwam to the top of the building = √65.343
distance from Fwam to the top of the building ≈ 8.08 meters
Therefore, the height of the school building is approximately 8.08 meters.
In summary, Fwam used the mirror method to measure the height of his school building. By using some basic trigonometry, we can calculate the distance from Fwam's eyes to the top of the building, which is the height of the building. We round the result to the nearest hundredth of a meter to get our final answer.
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. The height of a cell phone tower is 200 ft tall. The tower is secured by 3 wires, stretching from the
top of the tower to spots on the ground 50 ft away from the base of the tower. Each wire creates a
right triangle with the tower and the ground. What is the length of each wire to the nearest foot?
Answers
The length of each of the wires is 206.16 ft
How to determine the length of the wires?The length talks about how long the wires are from the top of the phone tower.
The given parameters are
height of the phone tower = 200 feet
The distance from the base to where it is pinned = 50 feet
Recall, each of them forms a right angled triangle
To find the lengths we use the Pythagoras rule
a²=b²+c²
Where a, b, c are the sides of each of the right angled triangles
a²=200²+50²
a²= 40,000+ 2500
Add together to have
a²=42,500
Taking the squares of both sides we have
a=√42500
a=206.16 feet
In conclusion each of the wires is 206.16 feet long
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What is the value of x in the equation 2(x+8) - 4x = 10x +4? A.5 B.1 C.8 D.12
Answers
Answer:
x = 1
Step-by-step explanation:
2 (x=8) -4 = 10x +4
2x+16-4x=10x+4
-2x+16=10x+4
-2x-10x=4-16
-12x=-12
x = 1
URGENT PLEASE ANSWER WILL MARK BRAINLIEST FOR THE FIRST RIGHT ANSWER
Write 3 key characteristics of a direct variation.
Answers
Answer:
1) The rate of change is constant ($$ 2) The line passes through the origin (0, 0). 3) The equation of the direct variation is $$ y =1 x or simply $$
Answer:
1) The rate of change is constant ($$ 2) The line passes through the origin (0, 0). 3) The equation of the direct variation is $$ y =1 x or simply $$
Step-by-step explanation:
I know this because I done this last week
A mathematics teacher wanted to see the correlation between test scores and homework. The homework grade (x) and test grade (y) are given in the accompanying table. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. Using this equation, find the projected test grade, to the nearest integer, for a student with a homework grade of 80.
Regression Equation:
Final Answer:
Answers
The linear regression equation for the model is Y = ( 0.9629 )X - 2.759 where the slope of the equation is m = 0.9629
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of the line be represented as A
Now , the homework grade is represented as x
The values of x = { 71 , 72 , 62 , 80 , 85 , 74 , 90 , 83 , 62 }
And , the test grade is represented as y
The values of y = { 63 , 75 , 58 , 77 , 71 , 65 , 95 , 68 , 57 }
From the linear regression calculator , the equation of line is given as
y = mx + b where m is the slope and b is the y-intercept
Y = ( 0.9629 )X - 2.759 be equation (1)
where the slope is m = 0.9629
And , Y = Test grade ; X = homework grade
Now , for a student with a homework grade of 80
Substitute the value of x as 80 , we get
Y = ( 0.9629 )X - 2.759
when X = 80 , we get
Y = ( 0.9629 ) ( 80 ) - 2.759
Y = 77.032 - 2.759
On simplifying the equation , we get
Y = 74.273
Y = 74
Therefore , the test grade Y of the student is 74
Hence , the linear regression equation is Y = ( 0.9629 )X - 2.759
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At Smith Mountain Lake Boat Rentals, it cost $25 per hour to rent a pontoon boat, plus a one-time charge for cleaning. The Bengal family rented a boat from 11 am - 6:30 pm and paid $226.50. If the Jones family rented a boat from 8 am- 1pm, how much did the pay?
Answers
Answer: $164
Step-by-step explanation:
25*7=175
175+12.5
226.50-187.50
5*25=125+39
Jones family payed $164
Match the correct equation to the statement.
1. tan x has a vertical asymptote at x =
2. cotx has a vertical asymptote at x =
A) pi/2-n(pi)
B)n(pi)
C)n(pi/2)
D)pi/2+n(pi)
Answers
Answer:
1234
Step-by-step explanation:
Consider the following set of equations:
Equation R: −3y = −3x − 9
Equation S: y = x + 3
Which of the following best describes the solution to the given set of equations?
a
No solution
b
One solution
c
Infinite solutions
d
Two solutions
Answers
The solution to the given set of equations is Infinite solutions.
We have the equation
R: -3y = -3x -9
S: y = x + 3
Now, solving the equation R and S as
-3y = -3x - 9
3y = 3x + 9
_________
0 = 0 + 0
0 = 0
Also, -3/1 = 3/(-1) = 9/(-3)
-3/1 = -3/1 = -3/1
Thus, the equation have Infinite many solutions.
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solve this please! thanks dude
Answers
Answer:
9^8
Step-by-step explanation:
please mark me as brainlest
Answer:
9to the 8th
Step-by-step explanation:
9^8
if the variance of a distribution is 16, the mean is 12, and the number of cases is 24, the standard deviation is select one: a. 4 b. 6 c. 8 d. 12
Answers
The standard deviation is (a).4
Given that the variance of a distribution is 16, the mean is 12, and the number of cases is 24.
A standard deviation (SD) is a measure of how dispersed the data is in relation to the mean. Whereas, variance is a measure of how data points differ from the mean.
The formula for variance can be expressed as the square of the standard deviation (SD). Therefore, the formula for standard deviation is the square root of the variance.
SD = sqrt(variance)
SD = sqrt(16)
SD = 4
Hence, the standard deviation for the given data is 4.
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A magician asks a volunteer to think of two different positive integers without telling her what they are. She then asks him to calculate x, the sum of the larger number with the square of the smaller, and y, the difference between the numbers. The volunteer tells her that x = 9 and y = 3. Find the original numbers.
Answers
Answer:
the original numbers are 5 and 2
Step-by-step explanation:
fistly it says inorder to find x one has to add the larger number to the square of the smaller number. So in this case start off with smaller guesses of positive integers as it is simpler that way.
the first guesses that would end up giving you 9 as an answer is 5 and 2
5+(2×2)=9So now that the integers chosen fit in when calculating x we have to check if it also checks out in calculating y.
For y the difference between the 2 integers have to give an answer of 3. after calculations it the numbers comply to the statement for y;
5-2=3hence the answers are 5 and 2
Age
Pete is ten years older than his brother Jeff.
In five years, Pete will be twice as old as
Jeff. How old will Pete be in five years.
Answers
Answer:
20 years
Step-by-step explanation:
jeff's age = x
pete's age = x+10
in 5 years time
2(x+5) = x+10+5
thus x=5 therefore
pete's age in 5 years will be 20
write code to assign x and y coordinates to currcoord, and store currcoord in locations. input first receives an x value, then a y value. input example: 12 32 88 2 -1 -1
Answers
It will be feasible to create a coordinate code that looks like this using the knowledge of the Python computational language:
Writing coordinate code in python:
def __init__(self, x, y):
self.x = x
self.y = y
def getX(self):
directly
return self.x
def getY(self):
return self.y
def __str__(self):
return '<' + str(self.getX()) + ',' + str(self.getY()) + '>'
class Coordinate(object):
def __init__(self,x,y):
self.x = x
self.y = y
def getX(self):
return self.x
def getY(self):
return self.y
def __str__(self):
return '<' + str(self.getX()) + ',' + str(self.getY()) + '>'
def __eq__(self, other):
if other.x == self.x and other.y == self.y:
return True
else:
return False
def __repr__(self):
return "Coordinate"+ str((self.x, self.y))
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#1 Which equation is the correct stope intercept form equation for the
table below?
X
Y
0
y 8x=2
y 8.8x*2
y 8.5x=2
y=2x-8.8
5
40.5
10
125.5
Answers
Answer:
THE 4 ONE
Step-by-step explanation:
if x=2 what is the value of 5X-7+ 22
x=
Answers
Answer:
25
Step-by-step explanation:
5(2)-7+22
10-7+22
25
In order to prove the triangles pictured below as congruent BY SAS, we would need to know ___
a. AB≅AD
b. angle BAC≅angle DAC
c. angle ABC≅angle ADC
d. angle BCA≅angle DCA
Answers
Answer: D
Step-by-step explanation: i got it right
Which equations and/or functions represent the graphed line? Select three options.
f(x)=1/5x-4
f(x)=1/2x+2
f(x)=1/2+1
y-3=1/2(x-2)
y-1=1/2(x+2)
Answers
Answer:
The second one, the fourth one, and the fifth one.
f(x)=(1/2)x+2
y-3=1/2(x-2)
y-1=1/2(x+2)
The three equations that represent the graphed line are:
f(x) = (1/2)x + 2
y - 1 = (1/2)(x + 2)
y - 3 = (1/2)(x - 2)
To identify which equations and/or functions represent the graphed line, we can compare the given equations with the characteristics of the graph.
The graphed line appears to have a slope of 1/2 and passes through the point (0, 1). Let's check the options:
f(x) = (1/5)x - 4: This equation has a slope of 1/5, not 1/2, so it does not represent the graphed line.
f(x) = (1/2)x + 2: This equation has the correct slope of 1/2, but it does not pass through the point (0, 1), so it does not represent the graphed line.
f(x) = (1/2) + 1: This equation is not in slope-intercept form and does not represent the graphed line.
y - 3 = (1/2)(x - 2): This equation has the correct slope of 1/2 and passes through the point (2, 3). However, it does not pass through the point (0, 1), so it does not represent the graphed line.
y - 1 = (1/2)(x + 2): This equation has the correct slope of 1/2 and passes through the point (−2, 1) (after rearranging to slope-intercept form). It also passes through the point (0, 1), which matches the graph.
The three equations that represent the graphed line are:
f(x) = (1/2)x + 2
y - 1 = (1/2)(x + 2)
y - 3 = (1/2)(x - 2)
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Probability and likelihood
a team of scientists is studying the animals at a nature reserve. They capture the animals, mark them so they can identify each animal, and then release them back into the park. The table gives the number of animals they’ve identified. Use this information to complete the two tasks that follow.
animal total in park number marked
elk 5,625 225
wolf 928 232
cougar 865 173
bear 1,940 679
mountain goat 328 164
deer 350 105
moose 215 86
part a
what is the probability of the next elk caught in the park being unmarked? write the probability as a fraction, a decimal number, and a percentage.
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characters used: 310 / 15000
part b
describe the likelihood of the next elk caught being unmarked.
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part c
describe a simulation that you can use to model this situation.
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part d
what is the probability of the next wolf caught in the park being unmarked? write the probability as a fraction, a decimal number, and a percentage.
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characters used: 54 / 15000
part e
describe the likelihood of the next wolf caught being unmarked.
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part f
describe a simulation that you can use to model this situation. The simulation should be different from the one in part c.
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part g
in the unit, you found the probability of a compound event by identifying the sample space. However, it is also possible to find the probability of a compound event without finding the sample space. To do this, multiply the probability of the first event by the probability of the second event. For example, the probability of flipping heads twice on a coin is. Using this idea, what is the probability that the next cougar and bear caught will both be unmarked?
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part h
describe the likelihood that the next cougar and bear caught are both unmarked.
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part i
describe a simulation that you can use to model this event.
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part j
using the method described in part g, what is the probability that the next mountain goat, deer, and moose caught are all unmarked?
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part k
describe the likelihood that the next mountain goat, deer, and moose caught are all unmarked.
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part l
describe a simulation that you can use to model this event. Your simulation should be different from the one in part i.
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characters used: 0 / 15000
Answers
Part g, h, i, j, k, and l:
Since the information for the other parts is not provided, it is not possible to calculate the probabilities, describe the likelihood, or propose simulations for those events.
Part a:
To find the probability of the next elk caught in the park being unmarked, we need to calculate the ratio of unmarked elks to the total number of elks.
Total number of elks: 5,625
Number of marked elks: 225
Number of unmarked elks: Total number of elks - Number of marked elks = 5,625 - 225 = 5,400
Probability = Number of unmarked elks / Total number of elks = 5,400 / 5,625
As a fraction: 5,400/5,625
As a decimal: 0.96
As a percentage: 96%
Part b:
The likelihood of the next elk caught being unmarked is high, as 96% of the elks captured so far have been unmarked.
Part c:
One possible simulation to model this situation is as follows:
Create a sample space consisting of 5,625 elks.
Randomly select an elk from the sample space.
Determine if the elk is marked or unmarked.
Repeat steps 2 and 3 for a desired number of simulations to observe the distribution of marked and unmarked elks.
Part d:
To find the probability of the next wolf caught in the park being unmarked, we need to calculate the ratio of unmarked wolves to the total number of wolves.
Total number of wolves: 928
Number of marked wolves: 232
Number of unmarked wolves: Total number of wolves - Number of marked wolves = 928 - 232 = 696
Probability = Number of unmarked wolves / Total number of wolves = 696 / 928
As a fraction: 696/928
As a decimal: 0.75
As a percentage: 75%
Part e:
The likelihood of the next wolf caught being unmarked is high, as 75% of the wolves captured so far have been unmarked.
Part f:
One possible simulation to model this situation is as follows:
Create a sample space consisting of 928 wolves.
Randomly select a wolf from the sample space.
Determine if the wolf is marked or unmarked.
Repeat steps 2 and 3 for a desired number of simulations to observe the distribution of marked and unmarked wolves.
Part g, h, i, j, k, and l:
Since the information for the other parts is not provided, it is not possible to calculate the probabilities, describe the likelihood, or propose simulations for those events.
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Find the logarithmic function f(x)=log a (x-h) that describes each graph.
PLEASE HELP 100 POINTS+BRAINLIEST
Answers
just an addition to the decent reply above
\(\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{\textit{we will be using this rule}}{a^{log_a x}=x} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\)
\(f(x)=\log_a(x-h) \\\\[-0.35em] ~\dotfill\\\\ 1=\log_a(\frac{3}{2}-h)\implies a^1=a^{\log_a(\frac{3}{2}-h)}\implies a^1=\cfrac{3}{2}-h\implies a=\cfrac{3}{2}-h \\\\[-0.35em] ~\dotfill\\\\ -1=\log_a(3-h)\implies a^{-1}=a^{\log_a(3-h)}\implies a^{-1}=3-h\implies \cfrac{1}{a}=3-h \\\\\\ 1=(3-h)a\implies 1=(3-h)\left( \cfrac{3}{2}-h \right)\implies 1=(3-h)\left( \cfrac{3-2h}{2} \right) \\\\\\ 2=(3-h)(3-2h)\implies 2=9-9h+2h^2\implies 0=2h^2-9h+7\)
\(0=(h-1)(2h-7)\implies \boxed{h= \begin{cases} 1\\\\ \frac{7}{2} \end{cases}}\hspace{5em}a=\cfrac{3}{2}-h\implies \boxed{a= \begin{cases} \frac{1}{2} ~~ ~~ \checkmark\\\\ -2 ~~ \bigotimes \end{cases}} \\\\\\ ~\hfill {\Large \begin{array}{llll} f(x)=\log_{\frac{1}{2}}(x-1) \end{array}} ~\hfill\)
now, why we didn't use the negative value for the base "a"?
from the standpoint of a negative value raised to some exponent, is perfectly fine, however if we plug that in the change of base rule, we run into a really hot pickle.
Answer:
\(f(x)=\log_{\frac{1}{2}}(x-1)\)
Step-by-step explanation:
Use the given points to assist in determining the logarithmic function of the given graph in the form:
\(f(x)=\log_a(x-h)\)Substitute the given points (³/₂, 1) and (3, -1) into the formula to create two equations:
\(\log_a\left(\dfrac{3}{2}-h\right)=1\)
\(\log_a\left(3-h\right)=-1\)
\(\boxed{\begin{minipage}{4 cm}\underline{Low law}\\\\$\log_ab=c \iff a^c=b$\\ \end{minipage}}\)
Apply the log law and rearrange each equation to isolate a:
Equation 1
\(\begin{aligned}\log_a\left(\dfrac{3}{2}-h\right)&=1\\\\\implies a^1&=\dfrac{3}{2}-h\\\\ a&= \dfrac{3}{2}-h\end{aligned}\)
Equation 2
\(\begin{aligned}\log_a\left(3-h\right)&=-1\\\\\implies a^{-1}&=3-h\\\\ \dfrac{1}{a}&=3-h\\\\a&=\dfrac{1}{3-h}\end{aligned}\)
Substitute the first equation into the second to eliminate a:
\(\dfrac{3}{2}-h=\dfrac{1}{3-h}\)
Solve for h:
\(\implies \dfrac{3}{2}-h=\dfrac{1}{3-h}\)
\(\implies \dfrac{3-2h}{2}=\dfrac{1}{3-h}\)
\(\implies (3-h)(3-2h)=2\)
\(\implies 9-9h+2h^2=2\)
\(\implies 2h^2-9h+7=0\)
\(\implies 2h^2-2h-7h+7=0\)
\(\implies 2h(h-1)-7(h-1)=0\)
\(\implies (2h-7)(h-1)=0\)
\(\implies h=\dfrac{7}{2},\;1\)
Substitute both values of h into the equations for a:
\(h=\dfrac{7}{2}\implies a=\dfrac{3}{2}-\dfrac{7}{2}=-2\)
\(h=\dfrac{7}{2}\implies a=\dfrac{1}{3-\dfrac{7}{2}}=-2\)
\(h=1\implies a=\dfrac{3}{2}-1=\dfrac{1}{2}\)
\(h=1\implies a=\dfrac{1}{3-1}=\dfrac{1}{2}\)
Therefore, the two values of h given is two possible values of a. Since a is the base of the function, and the bases of logarithmic function cannot be negative, the value of a cannot be -2. Therefore, the only valid value of a is ¹/₂.
Similarly, logs of negative numbers are undefined, therefore the value of h cannot be ⁷/₂ since this would make the argument negative for the points given. Therefore, the only valid value of h is 1.
Inputting the found values of a and h into the given formula, the logarithmic function of the given graph is:
\(f(x)=\log_{\frac{1}{2}}(x-1)\)HI PLEASE ANSWER THIS QUESTION THANK YOU SO MUCH!
Mr. Avanzado has an underground in his house. What unit ofmeasure will he use to find its volume?
A. mm3
B. cm3
C. dm3
D. m3
2.What is the best unit of measure to use in finding the volumeof a rectangular pencil case?
A. mm3
B. cm3
C. dm3
D. m3
3.What is the formula to be used in finding the volume of a cube?
A. V = s x s or s2
B. V = s x s x s or s3
C. V = l x w x h
D. V = s + s + s
(NO TROLLS PLEASE)
Answers
1. m³
2. cm³
3. s³
What is Unit?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
1. Volume is measure in m³
2. volume of a rectangular pencil case in cm³
3. V = s x s x s or s³
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What types of bees live in a hive?
you are now a fiftynaire
Answers
Answer:
the queen, the workers, and the drones. :)
What is the 27th term of arithmetic sequence with the equation f(n) = -n + 8?
Answers
The 27th term of the given arithmetic sequence is -19.
What is arithmetic sequence?An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference. The explicit formula for any arithmetic series is given by the formula,
aₙ = a₁ + (n-1)d
where d is the difference and a₁ is the first term of the sequence.
Given that the nth term of an arithmetic sequence can be found using the function, f(n) = -n + 8. Now, the value of the 27th term of the arithmetic sequence can be found as,
f(n) = -n + 8
f(27) = -(27) + 8
f(27) = -27 + 8
f(27) = -19
Hence, the term is -19.
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