As a result, when a park's size is 3/5 square miles and its length is 7/8 miles, the park's width is equal to 24/35.
what is rectangle ?A quadrilateral having four right angles, or rectangle, in Euclidean plane geometry. A quadrilateral that is equiangular, or one in which all of the angles are equal, is another way to describe it. Also possible is a straight angle in the parallelogram. With four sides that are of the same size, a square is a rectangle. Four 90-degree vertices and equal parallel sides make up a quadrilateral with a rectangle-like shape. Its equirectangular rectangle moniker derives from this. The term "parallelogram" also refers to a rectangle, which has equal and parallel opposite sides.
given
Area of a park with a rectangular shape is equal to 3/5 of a mile squared.
A rectangular park is 7/8 of a mile long.
3/5 = 7/8 * Park's rectangular width
As a result, when a park's size is 3/5 square miles and its length is 7/8 miles, the park's width is equal to 24/35.
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Vanessa is buying a house next year. She applies for a $300,000 loan to be paid in 30 years. Her credit score is 550 Using the table, how much bigger will her monthly payment be than if her score were 850?O $745O $42O $258O $97
$745 is bigger will her monthly payment of credit score.
How does a credit score operate and what is it?
A consumer's creditworthiness is indicated by a credit score, which ranges from 300 to 850. The better a borrower seems to potential lenders, the higher their score.
A credit score is based on a person's credit history, which includes the number of open accounts, total amounts owed, payment history, and other elements.
We are given a table in which we are specified different monthly payments for different credit scores for a $300,000 loan.
Monthly payment if her credit score is 550 = $2,487
Monthly payment if her credit score is 850 = $1,742
Her monthly payment will be bigger by = Monthly payment if her credit score is 550 - Monthly payment if her credit score is 850 = $2,487 - $1,742 = $745
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1 week is 5 miles 2 weeks is 6 miles 3 weeks is 7 miles 4 weeks is 8 miles write an equation while w is weeks and m is miles m=w...
Answer: w=m+4
Step-by-step explanation: Every week there are 4 more miles than the number of weeks. Ex. 1 week / 5 miles 5-1=4.
anybody pls help i dont know how to do this
The value of the expression → q(p(-2)) will be → -1.5.
What are functions?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.Any subset of the Cartesian product of two sets X and Y defines a binary relation R ⊆ X × Y between these two sets.A binary relation is univalent (also called right-unique) if -[tex]${\displaystyle \forall x\in X,\forall y\in Y,\forall z\in Y,\quad ((x,y)\in R\land (x,z)\in R)\implies y=z.}[/tex]
A binary relation is total if -[tex]${\displaystyle \forall x\in X,\exists y\in Y,\quad (x,y)\in R.}[/tex]
In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given are the graphs of two function as shown in the image.
We have to find -
q(p(-2))
Now, we can see from the graph that -
p(-2) = 0
Then, q(p(-2)) will be -
q(0) = - 1.5
Therefore, the value of the expression → q(p(-2)) will be → -1.5.
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10. A company sold a total of $1440 in gift bears for Valentine's Day. If the gift bears cost $15 apiece, how many gift bears did it sell? A. 15 B. 96 C. 144 D. 1440
Answer:A
Step-by-step explanation:
1440:15=96
the following is a list of grades that students received on a recent probability and statistics exam: 77, 78, 81, 62, 63, 65, 82, 93, 94, 88, 92, 76, 64, 77, 79, 90, 92, 94, 96, 95, 91, 88, 76, 89, 93, 99 the teacher wants to display scores in equal ranges. which of the following displays would represent the data in this way? bar chart box plot circle graph
histogram
A average histogram is the best way to display this data in equal ranges as it shows a visual representation of the frequency of scores within each range.
1. Calculate the minimum and maximum values of the data set: min = 62, max = 99
2. Divide the range of the data set into equal ranges, e.g. 0-20, 21-40, 41-60, 61-80, 81-100
3. Count the number of scores that fall within each range
4. Plot the data on a histogram, with the range of each interval as the x-axis and the frequency of scores within each interval as the y-axis.
A histogram is the best way to represent this set of data in equal ranges. To create a histogram, we first calculate the minimum and maximum values of the data set (62 and 99). Then we divide the range of the data set into equal ranges, such as 0-20, 21-40, 41-60, 61-80, 81-100. We count the number of scores that fall within each range, and then plot the data on a histogram, with the range of each interval as the x-axis and the frequency of scores within each interval as the y-axis. This helps to easily show the distribution of scores within each range.
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In the 2011 regular season, Seattle Mariners won 61
games, scored
671 runs and their winning percentage was 0.406. Using
the winning percentage, determine how many runs they
should have allowed.
671 runs and their winning percentage was 0.406. They should have allowed the runs are 333.42.
how many runs they should have allowed?The Mariners just need ten games to clinch their first postseason berth since the momentous 2001 campaign. On paper, the route there appears to be quite straightforward, with many factors going Seattle's way.
Felix Hernandez now holds the record for most victories in Seattle Mariners history with 169 victories as of November 2022. With a total of 145 games won, Hernandez is followed in this position by Jamie Moyer.
671 runs and their winning percentage was 0.406.
671 * 0.406 = 272.42
272 + 61 =333.42
They should have allowed the runs are 333.42.
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Here's a plot showing the interest rate on a 3-month bond from 1950 to 1980, and a regression model fit to the relationship between the Rate (in %) and Years since 1950. Complete parts a through d. a) What is the correlation between rate and year? b) Interpret the slope and intercept. On average, interest rates during this period at about % per year, starting from an interest rate of about c) What does this model predict for the interest rate in the year 2000? %
a) Positive correlation. b) Slope = 0.02, Intercept = 3.17; rate increases ~2%/yr, starting at 3.17%. c) Predicts interest rate of 5.17% in 2000.
a) The correlation between rate and year can be determined by constructing a scatter plot. From the given plot, we can see that there is a positive correlation between the two variables, meaning that as the year increases, the rate increases as well.
b) The regression model fit to the data provides the slope and intercept of the line of best fit. The slope is 0.02, which means that the rate is increasing by 0.02% per year. The intercept is 3.17, which means that the interest rate starts at 3.17% in 1950.
c) The model predicts that the interest rate in the year 2000 will be 5.17%. This can be calculated by plugging in 2000 for the year in the model equation (Rate = 0.02*Year + 3.17).
d) In summary, the regression model fit to the data shows that on average, interest rates during this period increased by about 0.02% per year, starting from an interest rate of about 3.17% in 1950. The model predicts that the interest rate in the year 2000 will be 5.17%.
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Use the number line to find the missing value. (-6)+_=-3
Answer:
3
Step-by-step explanation:
Let x represent the missing value.
(-3) = x + (-6)
Add 6 to both sides.6 + (-3) = x + 6 + (-6)
+6 will eliminate -6 on the left side of the equation.3 = x
If $2000 is invested at an interest rate of 4.5% per year, compounded continuously, find the value of the investment after the given number of years. (Round your answers to the nearest cent.) a) 2 years
b) 4 years c) 12 years
a) 2 years: The value of the investment after 2 years would be $2090.45.
b) 4 years: The value of the investment after 4 years would be $2186.63.
c) 12 years: The value of the investment after 12 years would be $2712.20.
a) 2 years: Value = 2000 x e^(0.045 x 2) = $2090.45
b) 4 years: Value = 2000 x e^(0.045 x 4) = $2186.63
c) 12 years: Value = 2000 x e^(0.045 x 12) = $2712.20
The value of a continuously compounded interest rate can be calculated using the formula: Value = P x e^(r x t), where P is the principal amount, r is the interest rate per year, and t is the time in years.
Using this formula, the value of a $2000 investment with an interest rate of 4.5% after 2 years would be $2090.45. This can be calculated by plugging the values into the formula: Value = 2000 x e^(0.045 x 2) = $2090.45.
The value of the same investment after 4 years would be $2186.63, which can be calculated in the same way: Value = 2000 x e^(0.045 x 4) = $2186.63.
The value of the same investment after 12 years would be $2712.20, which can be calculated by plugging the values into the formula: Value = 2000 x e^(0.045 x 12) = $2712.20.
Continuously compounded interest rates are a great way to earn money on investments, as the compounding of interest leads to higher returns over time.
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Carolyn has $2.55 in her purse in nickels and dimes. The number of nickels in nine less than three times the number of dimes. Find the number of each type of coin
This is a system of equations problem. Let x be the number of dimes and y be the number of nickels.
From the problem, we know the following:
x + y = n (where n is the total number of coins)
y = 3x - 9 (because the number of nickels is three times the number of dimes minus nine)
We also know that the total value of the coins is $2.55 and that a dime is worth $0.10 and a nickel is worth $0.05. So we can create an equation using the total value of the coins:
0.10x + 0.05y = 2.55
Now we have a system of three equations and three variables. To solve for x, y and n, we can use substitution or elimination method.
First equation and second equation:
x+3x-9 = n
4x-9=n
4x = n+9
x = (n+9)/4
By substituting the value of x in equation 3
0.10*(n+9)/4 + 0.05*(3*(n+9)/4-9) = 2.55
Solving this equation we get n = 63
Thus, x = (63+9)/4 = 18 dimes
y = 3x - 9 = 3*18 - 9 = 45 nickels
So, Carolyn has 18 dimes and 45 nickels.
let e be the amount in dollars that edison spends on salad and pizza. if edison buys s bowls of salad and p slices of pizza, then the total amount of money he spends (e) can be represented by the equation
The total amount of money that Edison spends on salad and pizza is equal to e.
e = s * $2 + p * $3
This equation can be used to calculate the amount of money Edison spends on salad and pizza. The first part of this equation, s * $2, calculates the cost of the bowls of salad. The cost of one bowl of salad is $2, and the number of bowls of salad that Edison buys is represented by s.
The second part of this equation, p * $3, calculates the cost of the slices of pizza. The cost of one slice of pizza is $3 and the number of slices of pizza that Edison buys is represented by p.
When added together, the total amount of money that Edison spends on salad and pizza is equal to e. For example, if Edison buys four bowls of salad (s=4) and six slices of pizza (p=6), the total amount of money he spends (e) is equal to (4 * $2) + (6 * $3) = $24.
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Find the height of the triangle.
Answer:
6 cm
Step-by-step explanation:
a = 1/2bh
42 = 1/2(14)h
42 = 7h Divide both sides by 7
6 = h
answer now its timed
Answer:
24
Step-by-step explanation:
Because of similar triangles,
UV/UG = UW/UH
132/24 = 132/UH
UH = 24
Answer:
24
Step-by-step explanation:
GU.U.V=HU. UW
24×132=HU×132
3168=132HU
HU=24
Which of the following series can be used with the limit comparison test to determine whether the series 5 + 2 η converges or diverges? η3 + 3n2 A ΟΣ B ΟΣ Σ1 η 1η 2 00 1 D n1 1 What are all values of p for which the series Ž (–1)n+1 will converge? n 1 A -1
1 only C) p > 0 D) p < 0 Which of the following conditions are necessary to conclude that the series an converges using the alternating series test? 1. The terms an alternate in sign for all n > N for some positive integer N. II. lim an = 0 III. (antil N for some positive integer N. 1200 A I only B I and II only с II and III only D) I, II, and 111
If your limitation is non-zero and finite, the series conduct similarly so their succession will bear similarly as well. Limit Comparison Test: Let ∞∑n=1an and ∞∑n=1bn be positive-termed series. If limn→∞ an b n=c, where c is limited, and c>0, then either both sequences join or both diverge.
What is meant by limit comparison?You compare two series a (subscript n) and b (subscript n) with a n greater than or equal to 0 and b n greater than 0 in the limit comparison test. When n reaches infinity, c = lim a n/b n follows. Both series will either converge or diverge if c is positive and finite. The original series is divergent, according to the limit comparison test. The limit in question does not exist, hence the limit comparison test does not apply. The original series converges, as demonstrated by the comparison test. It is possible to demonstrate how the original series deviates using the comparison test.To learn more about limit comparison, refer to:
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Given, y<−x+a and y>x+bIn the xy-plane, if (0,0) is a solution to the system of inequalities above, which of the following relationship between a and b must be true?A. a > bB. b > aC. |a| > |b|D. a = - b
We can conclude that an is a positive number and that b is a negative amount from the aforementioned inequalities.
What is positive number?Anything more than zero is considered to be positive. By placing a plus sign (+) in front of a number, positive numbers can be identified. Numbers are believed to be positive if no symbol is present. Positive numbers on a number line are those that are placed after zero.Positive numbers only exist above zero. The + sign or no sign at all can be used to denote positive integers. Negative numbers are all those below zero. Always use a - sign in front of negative numbers when writing them down. 0 has neither a positive nor a negative value. With such qualities, it is the only number.Given,
y<-x + a and y > x + b
The above inequalities have a solution of (0,0) as indicated.
[tex]& \Rightarrow 0 < 0+a \text { and } 0 > 0+b \\[/tex]
[tex]& \Rightarrow a > 0 \text { and } b < 0[/tex]
As a result, we can infer from the aforementioned inequalities that b is a negative quantity and an is a positive number.
As a result, a>b can be considered to be true.
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Ask a question about your assignment
The length of diagonal JL of the rectangle is equal to 93
What is a rectangle?A quadrilateral is a shape with two opposed sides that are equal and parallel. It is a polygon with four sides and four 90-degree angles. The shape of a rectangle is two dimensional.
The diagonal is the line that passes across the middle of a square, rectangle, or other geometric shape and connects one corner to the opposing corner. Every square with two diagonals is an equal-sized square.
Considering the problem, in a rectangle, the length of the diagonals are equal hence we can say that JL = IK = 93
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The length of the diagonal JL in the rectangle is 93 units.
How to find the side of a rectangle?A rectangle is a quadrilateral with opposite sides parallel to each other and opposite sides equal to each other.
The angle in a rectangle is 90 degrees each. The sum of angles in a triangle is 360 degrees.
The diagonals of a rectangle are congruent. The diagonal of a rectangle bisects each other.
The opposite central angles are equal in the diagonals.
Therefore, the diagonal IK is congruent to diagonal JL.
Hence,
IK = JL = 93 units.
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Bronx 2 Middle School took their fifth grade scholars on a field trip to the Math Museum. General admission tickets to the Math Museum costs $16 for adults and $9 for children. In total, Bx2MS spent a total of $776 on tickets. If eight adults attended this field trip, how many children attended?
The number of the children that attended is 72.
How many children attended?We have to note that we have to put the sentence that we have been given into an equation so that we can be able to answer the question that we have been given here.
We are told that; General admission tickets to the Math Museum costs $16 for adults and $9 for children. In total, Bx2MS spent a total of $776 on tickets. The adults that attended were eight in number. Let the number of the children be X
16(8) + 9X = 776
128 + 9X = 776
776 - 128 = 9X
X = 72
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I have equal numbers of nickels, dimes, and quarters. If these coins have a total value less than $10, I have at most? of each coin.
Answer:
24
Step-by-step explanation:
Try 1 of each:
1 nickel is worth $0.05
1 dime is worth $0.10
1 quarter is worth $0.25
Add them up: $0.05 + $0.10 + $0.25 = $0.40
Divide $10 by $0.40:
$10/$0.40 = 25
25 coins of each will give a total value of $10.
That means you can only have up to 24 coins of each.
Answer: 24
which of these features lets you control how long user-level and event-level data is stored by analytics?
Data Retention Settings. This feature allows you to specify how long user-level and event-level data is stored by analytics before being automatically deleted. You can set up data retention periods for different types of data, such as individual user data, event data, and session data.
Data Retention Settings is a feature available in many analytics platforms that allows you to control how long user-level and event-level data is stored. This helps ensure that the data stored is only relevant to your project. You can set up different data retention periods for different types of data, such as individual user data, event data, and session data. This allows you to specify how long the data should be stored before being automatically deleted. Data retention settings are important as they help protect user privacy and ensure that only the data necessary for your project is stored. They also help you manage your storage costs by allowing you to set a maximum amount of data that can be stored for a certain period of time. Data Retention Settings is a valuable tool for managing the data collected by your analytics platform.
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The complete question is
which of these features lets you control how long user-level and event-level data is stored by analytics Data Retention Policies.
please help!! i don’t understand this question
The Polynomial 4 will be 3x^2 - 2. The solution is obtained using arithmetic operations.
What are arithmetic operations?
There are four basic operations which are listed as follows:
Addition(‘+’): This operation deals with finding the sum.Subtraction(‘-’): This operation deals with finding the difference. Multiplication(‘×’): This operation deals with finding the product.Division(‘÷’): This operation deals with finding the quotient.⇒Polynomial 1 = x^2 - x^2 + x + x + x + x - 1 + 1 - 1
⇒Polynomial 1 = 4x - 1
⇒Polynomial 2 = x + x + x - x - x^2 - x^2 - 1 + 1 - 1
⇒Polynomial 2 = 2x - 2x^2 - 1
⇒Polynomial 2 = -2x^2 + 2x - 1
⇒Polynomial 3 = 1 + 1 + 1 + 1 - x - x + x - x^2 + x^2 - x^2
⇒Polynomial 3 = 4 - x - x^2
⇒Polynomial 3 = -x^2 - x + 4
We are given sum of all four expressions = 5x
So,
4x - 1 + (-2x^2 + 2x - 1) + (-x^2 - x + 4) + Polynomial 4 = 5x
On simplifying the equation,
⇒4x - 1 - 2x^2 + 2x - 1 - x^2 - x + 4 + Polynomial 4 = 5x
⇒5x - 3x^2 + 2 + Polynomial 4 = 5x
⇒Polynomial 4 = 5x - (5x - 3x^2 + 2)
⇒Polynomial 4 = 5x - 5x + 3x^2 - 2
⇒Polynomial 4 = 3x^2 - 2
Hence, polynomial 4 is 3x^2 - 2 which will be 3 big black squares and 2 small white squares.
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On a test, for every correct answer the student gets 2 points and for every
incorrect answer the student loses 1 point
Corinne got the first two questions correct and missed the next three.
She will receive a grade of zero if she answers
O
question(s)
correctly
incorrectly
# 1
correctly
incorrectly
Answer: she will receive a grade of zero if she gets one more question incorrect.
Step-by-step explanation: She gets 2 questions correct which equals 4 points and 3 questions wrong which is minus 3 points
4-3=1 so if she were to get one more incorrect she would receive a zero
The graph shows the proportional relationship between time, in minutes, spent skateboarding and the number of calories burned.
The proportional relationship between time spent skateboarding and the number of calories burned will be y = 10x.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Let 'x' be the number of minutes and 'y' be the number of calories burned. And at x = 0, the value of y is also zero. Then we have
0 = m(0) + c
c = 0
Then the equation is given as,
y = mx
At x = 5, the value of y is 50. Then we have
50 = m(5)
5m = 50
m = 50 / 5
m = 10 calories per minute
The proportional relationship between time spent skateboarding and the number of calories burned will be y = 10x.
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The missing graph is attached below.
An unbiased statistic is a statistic whose mean value is ____ the population characteristic estimated
equal to the population characteristic mean that it is estimating. It is not affected by any outside biases, making it a reliable and accurate measure.
An unbiased statistic is a statistic which is not affected by any outside biases. This means that the value of the statistic is equal to the population characteristic that it is estimating. For example, the mean of a sample is an unbiased estimate of the population mean. Unbiased statistics provide reliable and accurate measures, as they are not affected by any external influences. This makes them a valuable tool for researchers, as they can use them to accurately represent the population that they are studying. Unbiased statistics are essential for drawing valid conclusions from statistical data.
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Lower limit= Q₁-1.5xIQR Upper limit= Q3 +1.5xIQR IQR = Q3 - Q₁
The manager of a local fast-food chain wants to improve the service provided to customers who use the drive-up
window. As a first step in this process, the manager records how long it takes from the time the customer first
enters the drive-in window until they are served their food at the final window. Below are the times (in minutes) fo
the 30 customers (in order):
2 2 3 4 4 6 8 9 10 10 10 10 10 11 11
13 13 13 13 14 14 14 15 18 18 20 20 23 37 41
(a) Calculate the median.
(b) Calculate the first and third quartile.
QI=
Q3=
(c) Calculate the interquartile range.
IQR=
Lower=
(d) Calculate the lower and upper limits.
Upper=
The median is the middle value of a data set, the first quartile (Q1) is the median of the lower half of the data set, while the third quartile is the upper half. The interquartile range (IQR) is the difference between the first and third quartiles.
What is an interquartile range?The interquartile range (IQR) is a measure of variability defined as the difference between a data set's 75th percentile (Q3) and 25th percentile (Q1). It is often referred to as the midspread or the middle 50% of a data set. The interquartile range (IQR) is a measure of the dispersion of the middle 50% of values in a data set that is commonly used in descriptive statistics.
In the given question, the median is the data set's midway value. The data must first be organized in ascending or descending order before the median can be calculated. Because the data set is already in order in this example, the median may be computed simply locating the data set's middle value. The supplied data set's median is 10 minutes.
The first quartile (Q1) is the median of the data set's bottom half. To compute Q1, first organize the data in ascending or descending order. The lower part of the data set has values ranging from 2 to 11. This subset's median time is 6.5 minutes, which is in the top quartile.
The third quartile (Q3) is the median of the data set's upper half. To compute Q3, first organize the data in ascending or descending order. The upper part of the data set has values ranging from 13 to 41. This subset's median is 14.5 minutes, which is in the third percentile.
The difference between the first and third quartiles is defined as the interquartile range (IQR). The data must first be organized in ascending or descending order before the IQR can be calculated. The supplied data set's IQR is 14.5 - 6.5 = 8 minutes.
The first quartile minus 1.5 times the interquartile range is the lower limit. The data must first be organized in ascending or descending order before the lower limit can be calculated. The supplied data set has a lower limit of Q1 - 1.5 x IQR = 6.5 - (1.5 x 8) = -5.5 minutes.
The third quartile plus 1.5 times the interquartile range is the top limit. The data must first be organized in ascending or descending order before the upper limit can be calculated. The presented data set has an upper limit of Q3 + 1.5 x IQR = 14.5 + (1.5 x 8) = 23.5 minutes.
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The Wall Street Journal reported that 33% of taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized
deductions on their federal income tax return. The mean amount of deductions for this population of taxpayers was $16,562.
Assume that the standard deviation is a $2167. Use z-table.
a. What is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample
mean within $157 of the population mean for each of the following sample sizes: 30, 50, 100, and 400? Round your answers to
four decimals.
n=30
7=50
n=100
n = 400
b. What is the advantage of a larger sample size when attempting to estimate the population mean? Round your answers to four
decimals.
A larger sample increases
population mean. In this instance, the probability of being within ±157 of 4 ranges from
for a sample of size 400.
the probability that the sample mean will be within a specified distance of the
for a sample of size 30 to for a sample size of 400
Answer: 33
Step-by-step explanation: because like its 33% and its a number between them + its in the range of sample
fill in the blaank. suppose smith and jones begin by producing 0 computers and 220 calculators per hour. if they wish to produce 2 computers and 200 calculators per hour efficiently, then smith should spend___, and jones should spend___.
smith should spend 12 min to make computer and 48 min to make calculator and jones should spend 1 hour to make calculators.
the production rate of producing calculators by smith=100 per hour.
the production rate of producing computer by smith=10 per hour.
the production rate of producing calculators by jones=120 per hour
the production rate of producing computer by jones=6 per hour.
the time spend to make one calculator by smith=60/100=0.6min
the time spend to make one computer by smith=60/10=6 min
the time spend to make one calculator by jones=60/120=0.5 min
the time spend to make one computer by jones=60/6=10 min
both produce 220 calculator per hour,
so, one calculator makes in 60/220 =0.272min
time spent to make 200 calculators=0.272*220= approx. 1 hour
time spent to make 2 computers=0 hour
so, according to above calculations.
smith should spend 12 min to make computer and 48 min to make calculator and jones should spend 1 hour to make calculators.
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A group of tourists spent three days hiking from the beginning to the end of the trail. On the first day, they hiked 1/8 of the trail. On the second day, they hiked 4/7 of the remaining trail. On the third day, they hiked 1/3 of the remaining trail plus the last 8 km. How many km long is the trail.
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The length of the trail is given as follows:
32 km.
How to obtain the length of the trail?The length of the trail is obtained applying the proportions in the context of this problem.
The fractions hiked each day are given as follows:
First day: 1/8.Second day: 4/7 of the remaining 7/8.Third day: 1/3 of the remaining plus 8 km.The total fraction after the second day is given as follows:
1/8 + 4/7 x 7/8 = 5/8.
On the third day, one third of the remaining was hiked, hence:
5/8 + 1/3 x 3/8 = 6/8.
Meaning that the remaining distance of 8 km is 2/8 = 1/4 of the total distance, hence:
x/4 = 8
x = 32 km.
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uses similar triangles to explain why the slope is the same between any two distinct points on a nonvertical line in the coordinate plane and graphs and analyzes linear equations
hence we can use similarity of triangle to find out the slopes, and it will be same.
We can use the graph given to draw two similar triangles and then use ten to find the slope.
the Pythagorean theorem.
if ABC is a triangle with AC as the hypotenuse and angle B is 90 degree then we have
[tex](AC)^2=(AB)^2+(BC)^2[/tex]
Refer to the diagram, we have
AD=44 UNIT
BD=1 UNIT (on graph)
and from Pythagorean theorem.
[tex]AB=\sqrt{(AD)^2+(BD)^2} \\\\AB=\sqrt{44^2+1}\\ \\AB=44.01 UNIT[/tex]
Now for triangle
FA=44+44=88
CF=2BD
[tex]AC=\sqrt{88^2+4} \\\\AC=88.02[/tex]
AC= 2AB
thus, all sides of ACF is twice of each corresponding sides of ADB. THUS BY SSS similarity
we have ΔADB ~ ΔAFC.
slope of hypotenuse of a right-angled triangle is the ratio of base and its height.
As base of AFC is twice of base of ADB and height of ADB.
thus, both triangles have same slope.
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What is the slope of the line? m=
The slope of the line is given by the equation m = -3
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 line be represented as A
Now , the value of A is
Let the first point be represented as P ( 2 , -1 )
Let the second point be represented as Q ( 1 , 2 )
Now , the slope of the line between the points is
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 2 - ( -1 ) ) / 1 - 2
Slope m = 3 / -1
Slope m = -3
Hence , the slope of the line is decreasing as m = -3 and has a negative value
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Kaylee works in an office building across town. To get to the office in the morning, Kaylee walks to the bus stop a few blocks away. Then she takes the bus, staying on through several stops before getting off and walking the rest of the way. Which graph could show Kaylee's distance from the office over time?
The graph that represents the situation is added as an attachment
How to determine the graph of the situationFrom the question, we have the following parameters that can be used in our computation:
Bus stop = Few stepsBus = several stopsWalks the restThis means that the graph would be represented using a distance/time graph
Such that the distance would be on the y-axis and the time would be on the x-axis
See attachment for the graph
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