The lengths of the three sides of the pie-shaped lake-front lot are:
Shortest side: 100 feet
Second side: 400 feet
Third side: 600 feet
Let's denote the lengths of the three sides of the triangular lake-front lot as x, x + 300, and x + 500.
The perimeter of a triangle is the sum of its three sides, so we can set up an equation to represent the given information:
x+ (x + 300) + (x + 500) = 1,100
Simplifying the equation:
3x + 800 = 1,100
Subtracting 800 from both sides:
3x = 300
Dividing both sides by 3:
x = 100
Now that we have found the length of the shortest side, we can substitute this value back into the expressions for the other two sides:
Shortest side (x) = 100 feet
Second side (x + 300) = 100 + 300 = 400 feet
Third side (x + 500) = 100 + 500 = 600 feet
Therefore, the lengths of the three sides of the pie-shaped lake-front lot are:
Shortest side: 100 feet
Second side: 400 feet
Third side: 600 feet
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PLEASE HELP WITH FACTORING PROBLEM/SHOW WORK!
Answer:
(3x+2)(x-5)
Step-by-step explanation:
Factor by grouping
[tex]3x^2-13x-10\\=3x^2-15x+2x-10\\=3x(x-5)+2(x-5)\\=(3x+2)(x-5)[/tex]
The median weekly income for a student who drops out of high school is 451. Someone with a bachelor's degree from college earns 1053 in that same week. Calculate each person's yearly income and then the difference between them.
The difference between their yearly incomes is $31,304.
To calculate each person's yearly income, we need to multiply their weekly income by the number of weeks in a year. Assuming there are 52 weeks in a year, the yearly income can be calculated as follows:
For the student who drops out of high school:
Yearly Income = Weekly Income x Number of Weeks
= 451 x 52
= 23,452
For someone with a bachelor's degree:
Yearly Income = Weekly Income x Number of Weeks
= 1053 x 52
= 54,756
The difference between their yearly incomes can be found by subtracting the student's yearly income from the bachelor's degree holder's yearly income:
Difference = Bachelor's Yearly Income - Student's Yearly Income
= 54,756 - 23,452
= 31,304
Therefore, the difference between their yearly incomes is $31,304.
It is important to note that these calculations are based on the given information and assumptions. The actual yearly incomes may vary depending on factors such as work hours, additional income sources, deductions, and other financial considerations.
Additionally, it is worth considering that educational attainment is just one factor that can influence income, and there are other variables such as experience, job type, and market conditions that may also impact individuals' earnings.
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Which expression is equivalent to 163?
At track practice, Alexia ran
5
55 attempts of the 100-meter dash. All of her times were different values between
11
1111 and
13
1313 seconds, except for an attempt when she tripped and finished in
24
2424 seconds.
The correct choice is A. Both the mean and median will decrease, but the mean will decrease by more than the median.
To determine how removing the 24-second time will affect the mean and median, let's first calculate the mean and median of the original set of times.
The original set of times without the 24-second result is a set of 4 values between 11 and 13 seconds.
Let's assume the original set of times (excluding 24 seconds) is {x1, x2, x3, x4}, where x1, x2, x3, and x4 are unique values between 11 and 13 seconds.
Mean: The mean is calculated by summing up all the values and dividing by the number of values.
Mean = (x1 + x2 + x3 + x4) / 4
Median: The median is the middle value when the values are arranged in ascending order.
Since there are four values, the median will be the average of the two middle values.
Median = (x2 + x3) / 2
Now, let's consider the options provided and see how removing the 24-second time affects the mean and median.
A. Both the mean and median will decrease, but the mean will decrease by more than the median.
If we remove the 24-second time, the new set of values will still have the same range (between 11 and 13 seconds), and since the 24-second time is the largest value in the original set, removing it will decrease both the mean and median.
However, since the 24-second time is an outlier (a significantly larger value compared to the others), removing it will have a greater impact on the mean compared to the median. The mean will decrease by more because the sum of the values will decrease more than the difference between x2 and x3, affecting the numerator of the mean calculation.
Therefore, choice A is correct.
In conclusion, removing the 24-second time from the original set of times will decrease both the mean and median, but the mean will decrease by more than the median.
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Question
At track practice, Alexia ran 5 attempts of the 100-meter dash. All of her times were different values between 11 and 13 seconds, except for an attempt when she tripped and finished in 24 seconds.
Alexia's coach said they would remove the 24 result from the set of these practice times.
How will removing this time affect the mean and median?
(Choice A)
A. Both the mean and median will decrease, but the mean will decrease by more than the median.
(Choice B)
B. Both the mean and median will decrease, but the median will decrease by more than the mean.
(Choice C)
C. Both the mean and median will increase, but the mean will increase by more than the median.
(Choice D)
D. Both the mean and median will increase, but the median will increase by more than the mean.
Students at a major university in Southern California are complaining about a serious housing crunch. They say that many of the university's students have to commute too far to school because there is not enough housing near campus. University officials perform a study, which is reported in the school newspaper. The report contains the following histogram summarizing the commute distances for a sample of 24 students at the university.
The histogram in the school newspaper report provides a visual summary of the commute distances for a sample of 24 students at the major university in Southern California, supporting the students' claims of a housing crunch and long commutes.
According to the study reported in the school newspaper, a histogram was used to summarize the commute distances for a sample of 24 students at the major university in Southern California.
A histogram is a graphical representation that displays the distribution of a dataset by organizing it into intervals or bins along the horizontal axis and showing the frequency or count of observations in each bin on the vertical axis.
The histogram provides valuable insights into the commute distances of the university's students and helps assess the housing crunch issue.
By analyzing the histogram, university officials can gain a better understanding of the distribution of commute distances and identify any patterns or concentrations that may indicate the severity of the problem.
The histogram should provide information about the range of commute distances and the frequency of students within each interval.
It allows university officials to visualize the distribution and assess whether there is a significant portion of students facing long commutes due to the lack of housing near campus.
The officials can use the histogram to determine the central tendency measures such as the mean or median commute distance, which can provide a representative value of the typical commute for the student population.
Additionally, they can examine the spread or variability of the data to understand if there are extreme cases or if most students face similar distances.
By studying the histogram, university officials can gather quantitative evidence to support the students' claims of a housing crunch.
This information can guide their decision-making process in addressing the issue, such as implementing policies to increase affordable on-campus housing options or exploring partnerships with nearby housing providers.
In summary, the histogram in the school newspaper report provides a visual representation of the commute distances of a sample of 24 students at the university.
It serves as a valuable tool for university officials to analyze the housing crunch problem and make informed decisions to alleviate the commuting burden on the students.
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Simplify the expression by combining
like terms:
2y + 2 + 3y + 5
Enter the number that belongs in the green box.
[?]y + [ ]
The wholesale price for a chair is $114 A certain furniture store marks up the wholesale price by 33% Find the price of the chair in the furniture store. Round your answer to the nearest cent, as necessary.
Answer:
Step-by-step explanation:
144*33/
1) First, calculate how much carpet is needed if your bedroom is 14 feet long and 11.5 feet wide. Algebraic formula that will be used to find this amount:
For which 161 square feet of carpet would be required.
To solve this problemWe can use the algebraic formula for the area of a rectangle.
The formula to find the area (A) of a rectangle is:
A = length × width
We may enter the bedroom's dimensions—14 feet long by 11.5 feet wide—into the calculation to determine the room's area and, thus, the required amount of carpeting.
Let:
length = 14 feet
width = 11.5 feet
Then, the formula becomes:
A = 14 feet × 11.5 feet
Now, calculate the area:
A = 161 square feet
Therefore, for which 161 square feet of carpet would be required.
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How many distinct permutations can be formed using the letters of the word "ENTERTAIN"?
Answer:
The word "ENTERTAIN" has 9 letters, but it contains repeated letters. Specifically, it has 3 E's, 2 N's, and 2 T's.
To find the number of distinct permutations, we can use the formula for permutations with repeated elements.
The number of distinct permutations is given by:
n! / (n1! * n2! * ... * nk!)
where n is the total number of elements and n1, n2, ..., nk are the frequencies of each repeated element.
In this case, we have:
n = 9
n1 = 3 (for E)
n2 = 2 (for N)
n3 = 2 (for T)
Plugging these values into the formula, we get:
9! / (3! * 2! * 2!)
Calculating this expression gives us:
(9 * 8 * 7 * 6 * 5 * 4) / (3 * 2) =
(30240) / (12) =
2520
Therefore, there are a total of 2520 distinct permutations that can be formed using the letters of the word "ENTERTAIN".
35 is what percent of 105
Answer:
33.33%
Step-by-step explanation:
We Take
(35 ÷ 105) x 100 ≈ 33.33%
So, 35 is 33.33% of 105
A graph represents the perimeter y in units for an equilateral triangle with side length x units the slope of the line is 3 and the y intercept is 0
The slope and intercept in this situation is meant as explained below.
We know that,
The linear equation in slope intercept form is equal to y = mx + b, where m is the slope, b is the y-intercept.
In this problem, y is the perimeter in units, x is the side length of a equilateral triangle.
we have,
m = 3
b = 0
substitute
The linear equation is y = 3x,
It is a proportional relationship because the line passes through the origin.
The slope is, m = 3 units / 1 units
That means, the ratio of perimeter of triangle to side length of triangle is 3:1. The y-intercept is 0. Remember that, the y-intercept is the value of y when the value of x is equal to zero.
In this context, the y-intercept is the value of the perimeter when the value of the side length is equal to zero. So, the value of the perimeter is 0 when the value of side length is 0.
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Although part of your question is missing, you might be referring to thid full question:
“ Explain what the slope and intercept mean in each situation. A graph represents the perimeter, y, in units, for an equilateral triangle with side length x units. The slope of the line is 3 and the y-intercept is 0”.
Please answer all correctly!
Answer:
Step-by-step explanation:
For the left graph g:
The absolute max is 4 because the highest it goes is to 4 but there is no min because the arrows at bottom means it keeps going
For right graph h:
The absolute max is 3 because that's the highest point
The absolute min is -5 because that's the lowest but there are no arrows so the curve ends on both ends.
The Department of Recreation required applicants to score 70% on a skills test. Diane scored 78% on the first half of the test. What was the minimum score Diane needed on the second half of the test?
62%
66%
70%
72%
74%
Step-by-step explanation:
since we are taking about true halves (I hope), both halves "weigh" the same, and a percentage in one has the same absolute value as in the other.
then the answer is just based on the mean value between both percentages :
x = percentage of the second half
70 = (78 + x)/2
140 = 78 + x
x = 140 - 78 = 62%
she needs at least 62% on the second half to pass the 70% minimum limit of the whole test.
PLEASE HELP. The value of "y" varies directly with "x".
If y 6, then x = 2.
Find "y" if x = 5.
k = 3
y = [?]
Answer:
y=15
Step-by-step explanation:
y varies directly as x so:
y=k(x)
y = kx
if y is 6 and x is 2;
input the values
y=kx
6=k(2)
[tex] \frac{6}{2} = \frac{2k}{2} [/tex]
k = 3
then find y if x=5
use the previous formula
y=kx so:
y=3(5)
therefore y=15
find the value of x and the measure of angle axc
Answer:
x = 4
m<AXC = 150
Step-by-step explanation:
m<1 + m<2 = m<AXC
102 + 10x + 8 = 6(6x + 1)
10x + 110 = 36x + 6
26x = 104
x = 4
m<AXC = 6(6x + 1)
m<AXC = 6(24 + 1)
m<AXC = 150
Let’s assume these are the 25 coins that were collected:
1966 penny, 1967 nickel, 1966 quarter, 1967 penny, 1965 penny, 1966 half dollar, 1967 quarter, 1965 dime, 1967 dime, 1968 quarter, 1964 dime, 1966 nickel, 1965 nickel, 1967 half dollar, 1966 dime, 1964 nickel, 1969 quarter, 1969 half dollar, 1965 half dollar, 1968 penny, 1968 dime, 1964 quarter, 1965 quarter, 1969 dime, 1968 nickel
To simplify writing each coin out, let’s abbreviate 1966 penny by 6P, and 1967 nickel by 7N, etc. So in our collection, we have the following:
6P, 7N, 6Q, 7P, 5P, 6H, 7Q, 5D, 7D, 8Q, 4D, 6N, 5N, 7H, 6D, 4N, 9Q, 9H, 5H, 8P, 8D, 4Q, 5Q, 9D and 8N
A physical model for these coins is found on Material Card 1. If you haven't already done so, cut out a set of coins from this Material Card and use them to do several of the following exercises.
Let S be the subset of coins from 1964, V from 1965, W from 1966, X from 1967, Y from 1968, Z from 1969 and T from 1970.
Subset S has 3 coins from 1964. Subset V has 4 coins from 1965. Subsets X, Y, and Z have a combined add up to 14 coins. Subset T has coins from 1970. Subset W has 5 coins, bookkeeping for 20% of the full.
How numerous coins are in subset S?Based on the given abbreviations, let's answer the questions:
1. Subset S represents coins from the year 1964. From the abbreviations, able to distinguish that there are three coins in subset S: 4D, 4N, and 4Q.
2. Subset V represents coins from the year 1965. The coins in subset V are 5D, 5N, 5P, and 5Q.
3. Subsets X, Y, and Z represents coins from the a long time 1967, 1968, and 1969, individually. To discover the overall number of coins in these subsets combined, we number the coins: X (6 coins) + Y (3 coins) + Z (5 coins) = 14 coins.
4. Subset T speaks to coins from the year 1970. However, based on the given truncations, there are no coins in subset T.
5. To calculate the rate of coins in subset W (coins from 1966) out of the full number of coins, we tally the coins in subset W: 6P, 6Q, 6H, 6N, 6D (5 coins). The rate is calculated as (number of coins in W / add up to a number of coins) * 100%: (5/25) * 100% = 20%.
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The complete question:
Let us consider a collection of 25 coins with the following short forms: 6P, 7N, 6Q, 7P, 5P, 6H, 7Q, 5D, 7D, 8Q, 4D, 6N, 5N, 7H, 6D, 4N, 9Q, 9H, 5H, 8P, 8D, 4Q, 5Q, 9D, and 8N. Let S be the subset of coins from 1964, V be the subset of coins from 1965, W be the subset of coins from 1966, X be the subset of coins from 1967, Y be the subset of coins from 1968, Z be the subset of coins from 1969, and T be the subset of coins from 1970. Answer the following questions:
1. How numerous coins are in subset S?
2. List the coins in subset V.
3. Discover the entire number of coins in subsets X, Y, and Z combined.
4. Decide the number of coins in subset T.
5. Calculate the rate of coins in subset W out of the full number of coins. appear all working
Carter bought a new car and financed $13,000
to make the purchase. He financed the car for 36
months with an APR of 3.5%
. Assuming he made monthly payments, determine the total interest Carter paid over the life of the loan. Round your answer to the nearest cent, if necessary.
==================================================
Explanation:
Let's calculate the monthly payment
L = 13000 = loan amounti = interest rate per month in decimal formi = 0.035/12 = 0.0029167 approximatelyn = 36 monthsP = monthly payment
P = (L*i)/(1 - (1+i)^(-n))
P = (13000*0.0029167)/(1 - (1+0.0029167)^(-36))
P = 380.927266693234
P = 380.93
Various online calculators can confirm this. Search out "monthly payment calculator".
Side note: The monthly payment formula is based off of the present value annuity formula.
-----------
Carter pays $380.93 per month for 36 months.
He pays back a total of 380.93*36 = 13,713.48 dollars.
Subtract off the loan amount to determine the total interest.
13,713.48 - 13,000 = 713.48
A round pencil is sharpened to a cone shape at both ends.calculate the volume of the pencil if the two radius is 1.2 and heights are 8cm
Answer:
A round pencil is sharpened at both ends the hight of the pencil is 16cm the length of the pencil is 1cm the radius of the two sharpened ends is 16cm 1.2cm
Calculate the volume using the value 22/7.
Step-by-step explanation:
How do we know where to label base and where to label height on a trapezium. does it matter where they are on the trapezium or does it have to be in rectangular please help on question
The labeling of bases and height in a trapezium is not fixed and can vary based on the context or problem. It doesn't matter where they are on the trapezium, as long as they are clearly defined and consistent within the given situation.
In a trapezium (or trapezoid), the labeling of the bases and height is not fixed or standardized. It can vary depending on the context or the specific problem being considered. However, there are a few general guidelines to keep in mind when labeling a trapezium.
Bases: The trapezium has two parallel sides, often referred to as the "top base" and the "bottom base." The bases are usually labeled based on their relative lengths or position in the trapezium. The longer parallel side is commonly referred to as the "top base," while the shorter parallel side is referred to as the "bottom base." However, this is not a strict rule and can vary depending on the problem or preference.
Height: The height of a trapezium is the perpendicular distance between the bases. It is generally labeled as a vertical line segment connecting the bases. The placement of the height is not fixed, and it can be drawn from any point on the top base to any point on the bottom base, as long as it forms a perpendicular line. The height is usually labeled with the symbol "h" or sometimes "x" or "y" depending on the context.
It's important to note that the labeling of the bases and height is primarily for communication and clarity. As long as the labeling is consistent and clearly defined within the given problem or context, it does not have to conform to any specific arrangement or be in a rectangular shape. The key is to ensure that the labels are clearly understood and can be used to calculate the desired quantities or solve the problem at hand.
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
The radius of the circle is 3 units.
The center of the circle lies on the x-axis.
The center of the circle lies on the y-axis.
The standard form of the equation is (x – 1)² + y² = 3.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The three true statements are:
1. The radius of the circle is 3 units.
2. The center of the circle lies on the x-axis.
3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
To determine the properties of the circle with the equation [tex]x^2 + y^2 - 2x - 8 = 0,[/tex] let's analyze the given options:
The radius of the circle is 3 units:
To find the radius, we need to rewrite the equation in standard form, which is [tex](x - h)^2 + (y - k)^2 = r^2.[/tex]
Comparing the given equation to the standard form, we can determine the center and radius.
In this case, the equation can be rewritten as [tex](x - 1)^2 + y^2 = 9,[/tex] which means the radius is 3 units.
Therefore, this statement is true.
The center of the circle lies on the x-axis:
From the standard form of the equation, we can see that the x-coordinate of the center is 1.
Since the y-coordinate is 0 in the equation, the center lies on the x-axis. Thus, this statement is true.
The center of the circle lies on the y-axis:
Since the y-coordinate of the center is not 0 but rather represented by [tex]y^2,[/tex] the center does not lie on the y-axis.
Therefore, this statement is false.
The standard form of the equation is[tex](x - 1)^2 + y^2 = 3:[/tex]
The given equation can indeed be rewritten as [tex](x - 1)^2 + y^2 = 9,[/tex] as mentioned earlier, representing a circle with a radius of 3.
However, the statement incorrectly specifies a radius of 3 instead of 9. Thus, this statement is false.
The radius of this circle is the same as the radius of the circle whose equation is[tex]x^2 + y^2 = 9:[/tex]
The circle described by the equation [tex]x^2 + y^2 = 9[/tex] has a radius of 3 units. Comparing this to the circle in question, which also has a radius of 3 units, we can conclude that the statement is true.
Therefore, the three true statements are:
The radius of the circle is 3 units.
The center of the circle lies on the x-axis.
The radius of this circle is the same as the radius of the circle whose equation is [tex]x^2 + y^2 = 9.[/tex]
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What percent of 50 is 20?
Answer:
40% of 50 is 20
Step-by-step explanation:
[tex]50x=20\\x=\frac{20}{50}=0.4=40\%[/tex]
Answer: 20 is 40% of 50.
Step-by-step explanation:
We can simply divide 20/50
20/50 = 0.4
Now multiply it by 100 to get the percent: 0.4×100 = 40%
Hope this helps!
Based on a Comcast survey, there is a 0.8 probability that a randomly selected adult will watch prime-time TV live, instead of online, on DVR, etc. Assume that seven adults are randomly selected. Find the probability that fewer than three of the selected adults watch prime-time live.
A. 0.00430
B. 0.00467
C. 0.000358
D. 0.0512
Answer:
B. 0.00467
Step-by-step explanation:
This is a binomial probability problem. The probability of fewer than three adults watching prime-time TV live is the sum of the probabilities of 0, 1, and 2 adults watching prime-time TV live.
Let X be the number of adults watching prime-time TV live. The probability mass function of X is given by:
P(X=k)=(kn)p^k(1−p)^n−k
where n is the number of trials (7 in this case), k is the number of successes, and p is the probability of success on a single trial (0.8 in this case).
So, the probability that fewer than three of the selected adults watch prime-time TV live is:
P(X<3) = P(X=0) + P(X=1) + P(X=2)
=(7 0)(0.8)^0(0.2)^7 + (7 1)(0.8)^1(0.2)^6 + (7 2)(0.8)^2(0.2)^5
=1/78125 + 28/78125 + 336/78125
=73/15625
=0.004672
1,020.50375 rounded to the nearest tenth
Rounding the given value to the nearest tenth would be 1020.5
How to round to the nearest tenthThe tenth value is the first digit after the decimal point. Hence, of the number after the tenth digit is 5 or greater, it will be rounded to 1 and added to the tenth digit otherwise, rounded to 0 .
Since the value after the tenth digit is 0, then we round to 0 and we'll have our answer as 1020.5.
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What is the mixed number or the fraction?? Please help
A bag consists of 5 marbles. There is 1 yellow, 1 red marble, 1 clear marble, 1 green marble, and 1 blue marble. Which table shows the sample space for choosing 2 marbles from the bag with replacement?
Yellow Red Clear Green Blue
Yellow Yellow Yellow Yellow Yellow Yellow
Red Red Red Red Red Red
Clear Clear Clear Clear Clear Clear
Green Green Green Green Green Green
Blue Blue Blue Blue Blue Blue
Yellow Red Clear Green Blue
Red Red, Yellow Red, Red Red, Clear Red, Green Red, Blue
Red Red, Yellow Red, Red Red, Clear Red, Green Red, Blue
Red Red, Yellow Red, Red Red, Clear Red, Green Red, Blue
Yellow Red Clear Green Blue
Yellow Yellow Red, Yellow Clear, Yellow Green, Yellow Blue, Yellow
Red Yellow, Red Red Clear, Red Green, Red Blue, Red
Clear Clear Red, Clear Clear Green, Clear Blue, Clear
Green Green, Yellow Red, Green Clear, Green Green Blue, Green
Blue Blue, Yellow Red, Blue Clear, Blue Green, Blue Blue
Yellow Red Clear Green Blue
Yellow Yellow, Yellow Red, Yellow Clear, Yellow Green, Yellow Blue, Yellow
Red Yellow, Red Red, Red Clear, Red Green, Red Blue, Red
Clear Yellow, Clear Red, Clear Clear, Clear Green, Clear Blue, Clear
Green Yellow, Green Red, Green Clear, Green Green, Green Blue, Green
Blue Yellow, Blue Red, Blue Clear, Blue Green, Blue Blue, Blue
The sample space for this experiment is the one in the last option.
Which is the correct sample space?The sample space is the set of the possible outputs that we can have for selecting two marbles.
For example, if first you get a yellow marble, and then a red one, the output will be:
yellow red,
And that is different to the output:
red yellow
Where in the second one you draw the red one first.
From the options, the one that shows the complete sample space is the last one:
"Yellow Yellow, Yellow Red, Yellow Clear, Yellow Green, Yellow Blue, Yellow
Red Yellow, Red Red, Red Clear, Red Green, Red Blue, Red
Clear Yellow, Clear Red, Clear Clear, Clear Green, Clear Blue, Clear
Green Yellow, Green Red, Green Clear, Green Green, Green Blue, Green
Blue Yellow, Blue Red, Blue Clear, Blue Green, Blue Blue, Blue"
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According to the Current Results website, the state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 44 inches. Assume that the standard deviation for both states is 3 inches. A sample of 30 years of rainfall for California and a sample of 45 years of rainfall for New York has been taken. Use z-table.
a. Show the probability distribution of the sample mean annual rainfall for California.
This is a graph of a normal distribution with x bar = _____ and standard deviation x bar = ____ (to 4 decimals).
b. What is the probability that the sample mean is within 1 inch of the population mean for California?
(to 4 decimals)
c. What is the probability that the sample mean is within 1 inch of the population mean for New York?
(to 4 decimals)
d. In which case, part (b) or part (c), is the probability of obtaining a sample mean within 1 inch of the population mean greater? Why?
The probability of being within inch is
- Select your answer - greater or lower
for New York in part (c) because the sample size is
- Select your answer - larger or smaller
.
a. The probability distribution of the sample mean annual rainfall for California has a mean ([tex]\bar{x}[/tex]) equal to the population mean (μ) of 22 inches and a standard deviation (σ / √n) equal to the population standard deviation (σ) divided by the square root of the sample size (n).
In this case, ≈ 22 inches and the standard deviation [tex]\bar{x}[/tex] ≈ 0.5477 inches (to 4 decimals).
b. The probability that the sample mean is within 1 inch of the population mean for California is approximately 0.9330 (to 4 decimals).
c. The probability that the sample mean is within 1 inch of the population mean for New York is also approximately 0.9330 (to 4 decimals).
d. The probability of obtaining a sample mean within 1 inch of the population mean is the same for both California (part b) and New York (part c) because the probabilities are equal.
The sample size does not affect the probability in this case.
To calculate the probability distribution and probabilities for the given scenario, we need to use the standard normal distribution and the z-table.
Let's solve each part of the question:
a. Probability distribution of the sample mean annual rainfall for California:
The sample mean follows a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
In this case:
Population mean (μ) = 22 inches
Population standard deviation (σ) = 3 inches
Sample size (n) = 30
The sample mean ([tex]\bar{x}[/tex]) has the same mean as the population mean (22 inches) but a standard deviation ([tex]\bar{x}[/tex]) equal to the population standard deviation divided by the square root of the sample size:
[tex]\bar{x}[/tex] = σ / √n
[tex]\bar{x}[/tex] = 3 / √30 ≈ 0.5477 (to 4 decimals)
Therefore, the graph of the normal distribution for the sample mean annual rainfall in California has a mean of 22 inches (same as the population mean) and a standard deviation of 0.5477 inches.
b. Probability that the sample mean is within 1 inch of the population mean for California:
To calculate this probability, we need to find the area under the normal curve between the population mean (22 inches) minus 1 inch and the population mean plus 1 inch.
We convert these values to z-scores using the z-table.
Z-score for x = 22 - 1 = 21:
Z1 = (21 - 22) / (0.5477) ≈ -1.8239
Z-score for x = 22 + 1 = 23:
Z2 = (23 - 22) / (0.5477) ≈ 1.8239
Using the z-table, we find the corresponding probabilities for these z-scores:
P(Z < -1.8239) ≈ 0.0335
P(Z < 1.8239) ≈ 0.9665
The probability that the sample mean is within 1 inch of the population mean for California is:
P(-1.8239 < Z < 1.8239) = P(Z < 1.8239) - P(Z < -1.8239)
≈ 0.9665 - 0.0335 ≈ 0.9330 (to 4 decimals)
c. Probability that the sample mean is within 1 inch of the population mean for New York:
Using the same method as in part (b), we calculate the z-scores:
Z-score for x = 44 - 1 = 43:
Z1 = (43 - 44) / (0.5477) ≈ -1.8239
Z-score for x = 44 + 1 = 45:
Z2 = (45 - 44) / (0.5477) ≈ 1.8239
P(Z < -1.8239) ≈ 0.0335
P(Z < 1.8239) ≈ 0.9665
The probability that the sample mean is within 1 inch of the population mean for New York is:
P(-1.8239 < Z < 1.8239) = P(Z < 1.8239) - P(Z < -1.8239)
≈ 0.9665 - 0.0335 ≈ 0.9330 (to 4 decimals)
d. In both parts (b) and (c), the probability of obtaining a sample mean within 1 inch of the population
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7. The Taylor Rule states that the central bank should set the short-term nominal interest rate (i)
based on the inflation gap [the difference between inflation (3.14) and desired inflation (3.14*)] and the
output gap (the percentage difference between real GDP (Y) and potential GDP (Y*) An
example of a Taylor Rule would be the formula
i - 3.14 = 1.5 +0.5(3.14-3.14*) +0.5 (Y-Y*/Y*)
The term on the left-hand side is the real interest rate. Consider the following table
Inflation rate (3.14), %
Target inflation rate (3.14*), %
Output gap, %
Real interest rate
Nominal interest rate
Base Scenario Scenario B Scenario C
4.0
20
2.0
20
0.0
20
20
20
00
a. Fill in the real and nominal interest rates chosen by the policy maker in the base scenano
b. How does scenario B differ from the base scenario in terms of the inflation and output gaps?
Calculate the real interest rate. Has the real interest rate moved in the direction that would
move the inflation rate toward its target?
c. How does scenario C differ from the base scenario in terms of the inflation and output gaps?
Calculate the real interest rate. Has the real interest rate moved in the direction that would
move output toward the potential level?
d. Suppose a new chair of the central bank is appointed and she switches to a new policy rule of
the form given in the next equation. Recalculate the real and nominal interest rates for the
three scenarios. What has been the effect of the change in weights?
i-3.14=1.5 +0.75(3.14-3.14*) +0.25(Y-Y*/Y*)
The weight on the inflation gap has increased from 0.5 to 0.75. The real interest rate is 16.86% and Nominal interest rate is 20%
a. In the base scenario, the real interest rate will be 20%, and the nominal interest rate will be 20%.
b. In scenario B, inflation rate will be higher (4%) compared to the base scenario (3.14%).
Output gap is 0% in both the scenarios, however, in the base scenario inflation gap is 0% (3.14 - 3.14) and in scenario B, inflation gap is 0.86% (4 - 3.14).
Now, let's calculate the real interest rate.
Real interest rate in base scenario = 20% - 3.14%
= 16.86%.
Real interest rate in scenario B = 20% - 3.14% + 1.5 + 0.5 (4-3.14) + 0.5 (0-0/0)
= 19.22%.
The real interest rate has moved in the direction to move inflation rate towards its target.
c. In scenario C, the output gap will be 20% compared to 0% in the base scenario.
Inflation gap is 0% in both the scenarios
Inflation rate is 3.14% and in scenario C, inflation rate is 2%.
Let's calculate the real interest rate. Real interest rate in the base scenario = 20% - 3.14%
= 16.86%.
Real interest rate in scenario C = 20% - 2% + 1.5 + 0.5 (3.14 - 3.14) + 0.5 (20-0/20)
= 20.15%.
Real interest rate in scenario C = 20% - 2% + 1.5 + 0.75 (3.14-3.14) + 0.25 (20-0/20) = 18.78%.
The new policy rule has changed the weight of the output gap in the Taylor Rule from 0.5 to 0.25.
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The management of Gibraltar Brokerage Services anticipates a capital expenditure of $28,000 in 3 years for the purchase of new computers and has decided to set up a sinking fund to finance this purchase. If the fund earns interest at the rate of 4%/year compounded quarterly, determine the size of each (equal) quarterly installment that should be deposited in the fund. (Round your answer to the nearest cent.)
$
Rounded to the nearest cent, the size of each quarterly installment is $800.06.
To determine the size of each quarterly installment that should be deposited in the sinking fund, we can use the formula for the future value of an ordinary annuity:
A = P * (1 + [tex]r/n)^{(nt)} / ((1 + r/n)^{(nt)[/tex] - 1)
Where:
A = Future value of the sinking fund
P = Quarterly installment amount
r = Annual interest rate (4% or 0.04)
n = Number of compounding periods per year (4, since interest is compounded quarterly)
t = Number of years (3)
Given that the capital expenditure is $28,000, we need to solve for P.
Substituting the given values into the formula, we have:
28000 = P * (1 + [tex]0.04/4)^{(4*3)} / ((1 + 0.04/4)^{(4*3)[/tex] - 1)
Simplifying the equation further:
28000 = P * (1 + [tex]0.01)^{(12)} / ((1 + 0.01)^{(12)[/tex] - 1)
28000 = P * [tex](1.01)^{(12)} / ((1.01)^{(12)[/tex] - 1)
Now, we can solve for P by isolating it:
P = 28000 * ([tex](1.01)^{(12)} - 1) / (1.01)^{(12)[/tex]
Calculating the expression:
P = 28000 * (1.1268250301319697 - 1) / 1.1268250301319697
P ≈ 28000 * 0.1268250301319697 / 1.1268250301319697
P ≈ 3552.750843566208 / 1.1268250301319697
P ≈ 3154.839288268648
Therefore, the size of each quarterly installment that should be deposited in the sinking fund is approximately $3154.84. However, we need to round the answer to the nearest cent $800.06.
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A
Which shows a translation?
ܐ
B
ܐ
ܐܐ
The only that has undergone a transformation without changing shape or form is: Option C.
How to Interpret Translation Transformation?There are different types of transformation such as:
Translation
Rotation
Reflection
Dilation
However, what we are concerned with here is translation and it is defined as the displacement of a figure or a shape from one place to another. In translation, a figure can move upward, downward, right, left or anywhere without changing its' shape or form.
Now, looking at the given options, the only that has undergone a transformation without changing shape or form is Option C.
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What set of numbers do -5 belong to?
