There is a 21.19% chance that the daily production falls within 32.3 and 36.9 liters.
To find the probability that the daily production of a herd of cows is between 32.3 and 36.9 liters, we need to use the normal distribution properties.
Given that the mean daily production of the herd of cows is 30 liters and the standard deviation is 8.2 liters, we can standardize the distribution and use the standard normal distribution table or calculator. We calculate the z-scores for the values 32.3 and 36.9, which tells us how many standard deviations away from the mean each value is.
Using a standard normal cumulative distribution function, we can find that the probability of the daily production falling between 32.3 and 36.9 liters is approximately 0.2119. This means that there is a 21.19% chance that the daily production falls within this range.
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The probability that daily production is between 32.3 and 36.9 liters is 0.18949 or 18.9%.
To determine the probability that the herd's daily production will be between 32.3 and 36.9 liters, we must compute the z-scores for each number and use a standard normal distribution table to calculate the area under the curve between those z-scores.
To find out the z - scores we need use z-score formula:
Z = X−μ / σ
where μ is the mean, σ is the standard deviation and X is the observed value. In the problem μ is 30 liters, X₁ = 32.3 liters & X₂ = 36.9 liters and σ = 8.2 liters.
Substituting the values in the equation to find the z-score for 32.3 liters is:
z₁ = (32.3 - 30) / 8.2 = 0.2804
z₁ = 0.28049
Substituting the values in the equation to find the z-score for 36.9 liters is:
z₂ =( 36.9 - 30) / 8.2 = 0.8414
z₂ = 0.8414
We can determine the area under the curve between these two z-scores using a conventional normal distribution table. The area between z = 0.28049 and z = 0.8414 and the probability is approximately 0.1894.
As a result, the probability that the herd's daily output is between 32.3 and 36.9 liters is about 0.1894.
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Kiran swims z laps in the pool. Clare swims 18 laps, which is 9/5
times as many laps as Kiran. How many laps did Kiran swim?
Equation:
Solution: z=
we use linear equation in one variable to solve the problem. Kiran swam 10 laps in the pool.
Let's represent the number of laps Kiran swam as "z".
We know that Clare swam 18 laps, which is 9/5 times as many laps as Kiran. We can represent this relationship with the following equation:
18 = (9/5)z
To solve for z, we can isolate it by multiplying both sides of the equation by the reciprocal of 9/5, which is 5/9:
18 * (5/9) = (9/5)z * (5/9)
10 = z
Therefore, Kiran swam 10 laps in the pool.
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suppose that prior to conducting a coin-flipping experiment, we suspect that the coin is fair. how many times would we have to flip the coin in order to obtain a 98% confidence interval of width of at most .15 for the probability of flipping a head? (note that the z-score was rounded to three decimal places in the calculation) a) 241 b) 185 c) 238 d) 188 e) 247 f) none of the above
The minimum number of coin flips required to obtain a 98% confidence interval width of at most 0.15 is 188.
Hence option d is correct.
We'll use the formula for the confidence interval of a proportion, which is given by:
CI = p-hat ± (z * sqrt(p-hat * (1-p-hat) / n))
Here, p-hat represents the sample proportion (observed proportion of heads), z is the z-score for the desired confidence level (98% in this case), and n is the number of coin flips.
We want to find the minimum number of coin flips (n) needed to obtain a confidence interval width of at most 0.15. Since we suspect that the coin is fair, we'll assume p-hat = 0.5.
For a 98% confidence interval, the z-score (rounded to three decimal places) is 2.576.
Now, we'll set up the inequality:
0.15 >[tex]= 2 * (2.576 * \sqrt{(0.5 * (1-0.5) / n))}[/tex]
Squaring both sides and solving for n, we get:
n >= [tex]((2.576 * \sqrt{(0.25))^2) / (0.15/2)^2}[/tex]
n >= 188.423
Since the number of coin flips must be a whole number, we'll round up to the nearest integer, which is 188.
Hence option d is correct.
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Can someone help me pls!!!
Answer: Yes
Step-by-step explanation: SSS criteria
Mr. Lowe is a school librarian. His computer kept track of the number of books checked out
each month during the last school year.
Books checked out
4,247. 4,983. 6,214. 7,500. 3,500. 2,500. 5,000. 3,876. 4,753. 2,712.
Which box plot represents the data?
Answer:
A (top)
Step-by-step explanation:
You want to know which box plot represents the data in the given list.
MedianThe difference between the box plots is the location of the median.
When the data is sorted into order, it is ...
{2500, 2712, 3500, 3876, 4247, 4753, 4983, 5000, 6214, 7500}
There are an even number of elements in this list, so the median is the average of the middle two:
median = (4247 +4753)/2 = 9000/2 = 4500
The median is represented by the line inside the box of the box plot. The plot with its median at 4500 is the top one (shown in the attachment).
The top box plot represents the data.
<95141404393>
What is the dividend yield on Stock A that sells at
$20/share, when Company A pays a quarterly
dividend of $0.10 per share?
dividend yield = [?] %
Give your answer as a percent rounded to the
nearest tenth.
The calculated value of the dividend yield on Stock A is 2%.
Calculating the dividend yield on the StockThe dividend yield is a ratio that indicates how much a company pays out in dividends relative to its stock price.
To calculate the dividend yield on Stock A, we need to divide the annual dividend per share by the stock price per share and then multiply by 100 to express it as a percentage.
Annual dividend per share = Quarterly dividend per share x 4
Annual dividend per share = $0.10 x 4 = $0.40
Now, we can calculate the dividend yield on Stock A:
Dividend yield = Annual dividend per share / Stock price per share x 100%
Dividend yield = $0.40 / $20 x 100%
Dividend yield = 2%
Therefore, the dividend yield on Stock A is 2%.
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Write an inequality relating the given side lengths. If there is not enough information to reach a conclusion write “no conclusion”
(25,26,27,28)
The inequality relating the figures are
25 XZ > AC
26. DF < FD
27. 38 > x > 11
28. 37/3 > x > 7/3
How to find xIn the figure, the angles are related from the concept that one angle in a triangle must be greater than zero and less than 180.
In addition, when other dimensions are equal the side having greater length will have greater angle facing it.
27. since side 18 > side 12 we have that
5x - 10 > 45
5x > 45 + 10
5x > 55
x > 11
each angle must be less than 180
Also, 5x - 10 < 180
5x < 180 + 10
5x < 190
x < 38
The range of values of x is 38 > x > 11
28. since side 9 > side 6
30 > 3x - 7
30 + 7 > 3x
37 > x
x < 37/3
each angle must be greater than 0
3x - 7 < 0
3x > 7
x > 7/3
The range of values of x is 37/3 > x > 7/3
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9) Given f-¹(x)=-3x+2, write an equation
that represents f(x).
as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so for this inverse, since finding the inverse of the inverse, will give us the original function :)
[tex]f^{-1}(x)=-3x+2\implies y~~ = ~~-3x+2\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~-3y+2} \\\\\\ x-2=-3y\implies \cfrac{x-2}{-3}=y\implies \cfrac{2-x}{3}=y=f(x)[/tex]
a prism has three rectangular faces. its other faces are in the shape of
Answer: All the faces are rectangular.
Step-by-step explanation: A prism with three rectangular faces is called a rectangular prism. Therefore, the other faces are in the shape of rectangles.
there are three urns that contain a mixture of black and red balls as shown in table 1: no. of red balls no. of black balls urn 1 7 3 urn 2 2 8 urn 3 5 5 table 1: distribution of colored balls in each urn two urns are chosen at random and two balls are randomly chosen from each of the two urns. what is the probability that all four chosen balls are red?
The probability that all four chosen balls are red is 14/6075.
What is probability?Probability is a way to gauge how likely or unlikely something is to happen. It is a number between 0 and 1, where 0 denotes an improbable event and 1 denotes an inevitable one.
According to question:Let's first find the probability of choosing two red balls from each of the two urns separately and then multiply the results.
The probability of choosing two red balls from urn 1 is:
P(2 red balls from urn 1) = (7/10) * (6/9) = 7/15
Similarly, the probability of choosing two red balls from urn 2 is:
P(2 red balls from urn 2) = (2/10) * (1/9) = 1/45
And the probability of choosing two red balls from urn 3 is:
P(2 red balls from urn 3) = (5/10) * (4/9) = 2/9
Now, we need to find the probability of choosing two urns out of three, and since the order in which we choose the urns does not matter, we can use combinations:
Number of ways to choose two urns out of three = C(3, 2) = 3
Therefore, the probability of choosing two urns out of three is 3/3 = 1.
Finally, we need to multiply the probability of choosing two red balls from each of the two urns and the probability of choosing two urns out of three:
P(all four balls are red) = P(2 red balls from urn 1) * P(2 red balls from urn 2) * P(2 red balls from urn 3) * P(choose two urns out of three)
= (7/15) * (1/45) * (2/9) * 1
= 14/6075
Therefore, the probability that all four chosen balls are red is 14/6075.
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Integers can be represented by repeatedly adding or subtracting the number 1. For example, the integer 3 can be represented as 0 + 1 + 1 + 1, and the integer -3 can be represented as 0 - 1 - 1 - 1. Hence, the definition "an integer is the number 0 or any number obtained by repeatedly adding 1 to this number" is true.
"An integer is the number 0 or any number obtained by repeatedly adding 1 to this number" is not entirely true.
True that integers can be represented by repeatedly adding or subtracting the number 1,
The fact that integers can also be negative and can be obtained by repeatedly subtracting 1 from 0 or another negative integer.
The definition does not account for the fact that integers can be represented using other operations, such as multiplication or division. The integer 12 can be represented as 4 x 3 or as 24 ÷ 2.
A more accurate definition of an integer is a whole number that can be positive, negative, or zero.
Integers can be represented using addition, subtraction, multiplication, or division, and can be used to represent quantities such as counts, distances, temperatures, and other measurable quantities.
The original definition is a useful way to understand how integers can be represented using addition and subtraction, it is not a complete or entirely accurate definition of what integers are.
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Bernard used a stopwatch to time how many seconds he could balance a spoon on his nose. The first attempt lasted 5 1/3 seconds. The second attempt lasted 5 5/9 seconds. The third attempt lasted 5 1/2 seconds.
Which list orders the times from shortest to longest ?
List orders the times from shortest to longest
5 1/3 seconds
5 1/2 seconds
5 5/9 seconds
What is Decimal?A decimal is a way of representing numbers using a base-10 positional notation system, where each digit represents a power of 10. It is written as a whole number followed by a decimal point and a series of digits representing fractions of 1.
According to the given information:
To order the times from shortest to longest, we need to convert them into a common format, such as a decimal or a common denominator.
First, let's convert the times to a common denominator of 9:
5 1/3 seconds = 16/3 seconds = 48/9 seconds
5 5/9 seconds = 50/9 seconds
5 1/2 seconds = 9/2 seconds = 45/9 seconds
Now we can order the times from shortest to longest:
48/9 seconds = 5 1/3 seconds
45/9 seconds = 5 1/2 seconds
50/9 seconds = 5 5/9 seconds
Therefore, the correct list in order from shortest to longest is:
5 1/3 seconds
5 1/2 seconds
5 5/9 seconds
So Bernard's first attempt was the shortest, his third attempt was the second longest, and his second attempt was the longest.
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you roll a 6-sided dice. what is the probability that you rolled a 5, given that the number rolled was greater than 3?
The probability that you rolled a 5, given that the number rolled was greater than 3, is 1/3 or approximately 0.333.
We need to find the probability that you rolled a 5, given that the number rolled was greater than 3. Let's break this down step by step:
1. Identify the total number of outcomes: Since it is a 6-sided dice, there are 6 possible outcomes (1, 2, 3, 4, 5, and 6).
2. Determine the number of outcomes greater than 3: The outcomes greater than 3 are 4, 5, and 6. There are 3 possible outcomes that satisfy this condition.
3. Identify the number of outcomes that result in rolling a 5: There is only 1 outcome that results in rolling a 5.
4. Calculate the probability: To find the probability, divide the number of outcomes that result in rolling a 5 (1) by the total number of outcomes greater than 3 (3).
Probability = (Number of outcomes with a 5) / (Number of outcomes greater than 3) = 1/3
So, the probability that you rolled a 5, given that the number rolled was greater than 3, is 1/3 or approximately 0.333.
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The probability that the number rolled was a 5, given that it was greater than 3, is [tex]$\frac{1}{3}$[/tex].
The number rolled was greater than 3, it must be either a 4, 5, or 6.
The probability that the number rolled was a 5, given that it was greater than 3.
Let [tex]$A$[/tex] be the event that the number rolled is a 5 and let [tex]$B$[/tex] be the event that the number rolled is greater than 3.
Then, we want to find. [tex]$P(A|B)$[/tex], the probability of [tex]$A$[/tex] given [tex]$B$[/tex].
By Bayes' theorem, we have:
Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes, describes the probability of an event, based on prior knowledge of conditions that might be related to the event.
The risk of developing health problems is known to increase with age, Bayes' theorem allows the risk to an individual of a known age to be assessed more accurately by conditioning it relative to their age, rather than simply assuming that the individual is typical of the population as a whole.
One of the many applications of Bayes' theorem is Bayesian inference, a particular approach to statistical inference.
The probabilities involved in the theorem may have different probability interpretations.
Bayesian probability interpretation, the theorem expresses how a degree of belief, expressed as a probability, should rationally change to account for the availability of related evidence.
Bayesian inference is fundamental to Bayesian statistics, being considered by one authority as; "to the theory of probability what Pythagoras's theorem is to geometry."
[tex]$P(A|B) = \frac{P(B|A)P(A)}{P(B)}$[/tex]
[tex]$P(A) = \frac{1}{6}$[/tex], since there is only one way to roll a 5 on a 6-sided die.
[tex]$P(B) = \frac{3}{6} = \frac{1}{2}$[/tex], since there are three outcomes (4, 5, or 6) that satisfy. [tex]$B$[/tex], out of a total of six possible outcomes.
[tex]$P(B|A)$[/tex], the probability of rolling a number greater than 3, given that the number rolled is a 5, note that. [tex]$B$[/tex] is true only if the number rolled is a 4, 5, or 6.
Since there is only one way to roll a 5, and only one of these three outcomes satisfies. [tex]$A$[/tex], we have:
[tex]$P(B|A) = \frac{1}{1} = 1$[/tex]
Substituting these values into Bayes' theorem, we get:
[tex]$P(A|B) = \frac{P(B|A)P(A)}{P(B)} = \frac{1 \cdot \frac{1}{6}}{\frac{1}{2}} = \frac{1}{3}$[/tex]
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a motor boat traveling at 18 miles per hour traveled the length of a lake in one-quarter of an hour less time than it took when traveling at 12 miles per hour. what was the length in miles of the lake?
The length of the lake in miles for the given situation of travelling motor boat is equal to 9 miles.
Let us consider the length of the lake be d in miles.
Number of miles motor boat travelled per hour = 18 miles
When the motor boat travels at 18 miles per hour,
The time it takes to travel the length of the lake is,
t₁ = d/18
When the motor boat travels at 12 miles per hour,
The time it takes to travel the length of the lake is,
t₂ = d/12
Time it takes to travel the length of the lake at 18 miles per hour
= one-quarter of an hour less than the time it takes at 12 miles per hour,
⇒ t₁ = t₂ - 1/4
Substituting the expressions for t₁ and t₂ from above, we get,
⇒ d/18 = d/12 - 1/4
Simplify this equation by multiplying both sides by the least common multiple of the denominators,
least common multiple = 36
⇒ 2d = 3d - 9
Solving for d, we get,
⇒ d = 9
Therefore, the length in miles of the lake is 9 miles.
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Write the equation for the following graph.
Step-by-step explanation:
the equation for the following graph os (-3,-5) & (1,1)
Interpret the probability. In 100 trials of this experiment, it is expected about (Round to the nearest whole number as needed.) to result in exactly 15 flights being on time
Hence, it is expected that 14 flights will arrive on time out of the 100 trials of this experiment.
What is the probability?The probability of an occurrence is a number used in mathematics to describe how likely it is that the event will take place. In terms of percentage notation, between 0% and 100% it is expressed as a number between 0 and 1, or . The higher the likelihood, the more likely it is that the event will take place.
What is the trials?when we refer to an experiment or trial, we mean a random experiment. When difference between a trial and an experiment, think of the experiment as a larger entity created by the fusion of several trials.
Unless otherwise stated,A trial is any specific outcome of a random experiment. In other words, a trial of the experiment is what we call when we conduct an experiment.
according to question, the number of on-time flights in 100 trials as a binomial random variable with parameters n = 100 (the number of trials) and p (the chance of success, i.e., a flight being on time), presuming that the probability of a flight being on time is the same in all trials.
The expected number of on-time flights in 100 trials is E(X) = np if the same of a flight being on time is p. Given that E(X) = 15, we determine p ,
E(X) = n p = 15 n = 100
p = [tex]\frac{E(X)}{n} = \frac{15}{100}[/tex] = 0.15
Therefore, it is probability that 0.15 %of flights will arrive on time.
To determine the expected number of trials from a total of 100
Using the probability mass function of the binomial distribution, we can get the expected probability of trials out of 100 that result in precisely 15 flights departing on time:
[tex]P(X = 15)=(100 choose 15) * 0.15^{15} * 0.85^{85}[/tex]
We can calculate this 0.144 get using a calculator.
therefore it is expected that 14 flights will arrive on time out of the 100 trials of this experiment. It should be noted that while this is an expected value, random fluctuation may cause the actual number of on-time flights in each trial to deviate somewhat from this figure.
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select the location -2 and -9 on the number line. select the places on the number line to plot the points.
-2: | -2 |
-9: | -9 |
past data shows that the standard deviation of apartments for rent in the area is $200. suppose we want a 98% confidence interval with margin of error of 50. what sample size do we need?
A sample size of 87 is required to obtain a 98% confidence interval with a margin of error of 50.
How to calculate sample size?To calculate the sample size required for a 98% confidence interval with a margin of error of 50, we need to use the following formula:
n = [Z*(σ/ME)]^2
where:
n = the sample size needed
Z = the Z-score for the desired confidence level (98% or 2.33)
σ = the standard deviation of apartments for rent in the area ($200)
ME = the margin of error ($50)
Plugging in the given values, we get:
n = [2.33*(200/50)]^2
n = [9.32]^2
n ≈ 86.7
Since we cannot have a fractional sample size, we round up to the nearest whole number to get the final answer.
Therefore, a sample size of 87 is required to obtain a 98% confidence interval with a margin of error of 50, given that the standard deviation of apartments for rent in the area is $200.
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2. Find the area of the circle. Use 3.14 for r. Round to the nearest unit.
18 cm
01,017 cm²
0254 cm²
057 cm²
028 cm²
(1 point)
The area of the circle for given problem will be approx. 254 [tex]cm^2[/tex].
How to find the area of circle?The formula for finding the area of a circle is given by:
Area =[tex]\pi* r^2[/tex]
where "π" (pi) is a mathematical constant approximately equal to 3.14159, and "r" represents the radius of the circle.
Measure the radius (r) of the circleSquare the radius: (r * r)Multiply the squared radius by π (pi):[tex]\pi* r^2[/tex].The result is the area of the circle.Given,
Find the radius (r) of the circle. The radius is half of the diameter, so divide the diameter by 2:
Radius (r) = Diameter / 2 = 18 cm / 2 = 9 cm
Area = [tex]\pi * r^2[/tex] = [tex]3.14*(9 \;cm)^2[/tex] = [tex]254.34 \;cm^2[/tex] (rounded to two decimal places)
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Correct Question: Find the area of the circle with Diameter =18 cm(refer to image). Use 3.14 for π.( Round to the nearest unit).
find the average rate of change of the car's position on the interval . include units on your answer.
The average rate of change of the car's position on the interval is ∆P/∆t.
To find the average rate of change of the car's position on the interval, follow these steps:
Identify the interval: First, determine the specific interval for which you need to find the average rate of change (e.g.,
between times t1 and t2).
Calculate the change in position:
Determine the car's position at both the beginning and end of the interval (e.g., positions P1 and P2).
Then, subtract the initial position (P1) from the final position (P2) to find the change in position (∆P).
Calculate the change in time: Subtract the initial time (t1) from the final time (t2) to find the change in time (∆t).
Calculate the average rate of change: Divide the change in position (∆P) by the change in time (∆t) to find the average
rate of change.
The average rate of change of the car's position on the interval is ∆P/∆t. Include units in your answer (e.g., meters per
second or miles per hour) to indicate the car's rate of change in position.
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I need some help please
Answer: it is 3/2x x + 0
Step-by-step explanation:
you do rise over run which is 3 up and 2 over in this case. and the 0 is the y intercept but its at the center also known as the origin so its 0
Answer:
Step-by-step explanation:
x^2+y^2+12x+12y+12=0
Answer: the equation represents a circle centered at (-6, -6) with radius 2.
Step-by-step explanation:
x^2 + 12x + 36 + y^2 + 12y + 12 - 36 = 0
Simplifying, we get:
(x + 6)^2 + y^2 - 12 = 0
For the y terms, we add (12/2)^2 = 36 to both sides to get:
x^2 + 12x + 36 + y^2 + 12y + 36 - 24 = 0
Simplifying, we get:
(x + 6)^2 + (y + 6)^2 = 4
Therefore, the equation represents a circle centered at (-6, -6) with radius 2.
Answer: 0
Step-by-step explanation:
what is inches to feet
Answer: 12 inches is one foot
Step-by-step explanation: hope that this is what you were asking ;)
The equation y = 2x + 3
represents the cost y (in dollars) of mailing a package that weighs x pounds.
a. Use a graph to estimate how much it costs to mail
the package.
b. Use the equation to find exactly how much it costs
to mail the package.
Thus, the price for the to mail the package of weight 1.126 lb is found as: $5.25.
Explain about the slope intercept form:Simply put, the slope-intercept form is the way to write a line's equation so that the y-intercept (where its line crosses its vertical y-axis) and slope (steepness) are instantly visible. This form is frequently known as the y = mx + b form. One of the line types that is taught in algebra schools the most is this one.
Draw a line connecting the points (because x and y are weights and costs, respectively, they must be positive; as a result, the function's graph only includes the section in Quadrant I):
Given equation:
y = 2x + 3
Put x = 0 , y = 3 ;(0,3)
Put y = 0, x = -1.5 ; (-1.5, 0)
when weight x = 1.126lb.
cost y (in dollars) and weighs x pounds.
y = 2(1.126) + 3
y = 5.252
y ≈ 5.25
Thus, the price for the to mail the package of weight 1.126 lb is found as: $5.25 .
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Complete question:
The equation y = 2x + 3 represents the cost y (in dollars) of mailing a package that weighs x pounds.
Use a graph to estimate how much it costs to mail the package for the weight of 1.126 lb.
1. suppose we know that the average weight of coyotes is 14.5kg with a standard deviation of 4kg. what is the probability of trapping a coyote that is 17kg or larger?
The probability of trapping a coyote that is 17kg or larger, given an average weight of 14.5kg and a standard deviation of 4kg is approximately 0.2743 or 27.43%.
To solve the problem, we first need to standardize the weight of the coyote using the formula:
z = (x - μ) / σ
Where:
x = the weight of the coyote we want to find the probability for (17kg in this case)
μ = the population mean (14.5kg in this case)
σ = the population standard deviation (4kg in this case)
z = the standardized score
Substituting the given values in the formula, we get:
z = (17 - 14.5) / 4
z = 0.625
Next, we need to find the probability of getting a coyote weighing 17kg or more, which is equivalent to finding the area under the normal distribution curve to the right of z = 0.625. We can use a standard normal distribution table or a calculator to find this probability.
Using a calculator, we can use the cumulative distribution function (CDF) of the standard normal distribution. The CDF gives the area under the curve to the left of a specified z-score. Since we want the area to the right of z = 0.625, we can subtract the CDF from 1 to get the area to the right.
Using a standard normal distribution table or calculator, we find that the CDF for z = 0.625 is approximately 0.734. Therefore, the area to the right of z = 0.625 is 1 - 0.734 = 0.266 or 26.6%.
Thus, the probability of trapping a coyote that is 17kg or larger is approximately 0.266 or 26.6%.
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Using a standard normal distribution table or a calculator, the probability of trapping a coyote that is 17kg or larger is approximately 0.266 or 26.6%.
What exactly is a standard normal distribution?The standard normal distribution is a probability distribution that is used to calculate probabilities associated with a random variable that has a normal distribution with mean 0 and standard deviation 1. Any normally distributed random variable can be standardized by subtracting its mean and dividing by its standard deviation to obtain a new variable with mean 0 and standard deviation 1.
In this case, we are given that the weight of coyotes has a normal distribution with a mean of 14.5kg and a standard deviation of 4kg. We want to find the probability of trapping a coyote that is 17kg or larger.
To calculate this probability, we need to standardize the weight of a 17kg coyote using the formula:
z = (× - μ) / σ
where:
x is the value we want to standardize (in this case, 17kg),
μ is the mean of the distribution (14.5kg),
σ is the standard deviation of the distribution (4kg).
Substituting the values we have:
[tex]z =\frac{(17 - 14.5)}{4} = 0.625[/tex]
This value of 0.625 is the z-score for a coyote weighing 17kg. The z-score represents the number of standard deviations that a particular value is above or below the mean.
Next, we need to find the probability of a randomly selected coyote weighing 17kg or larger, which can be calculated using the standard normal distribution table or a calculator.
The standard normal distribution table gives the probability associated with a given z-score. However, since the table only gives probabilities for z-scores less than 0, we need to use the fact that the standard normal distribution is symmetric about the mean (0) to find the probability of a z-score greater than 0.625.
Specifically, we can use the property that:
P(Z > z) = 1 - P(Z < z)
where Z is a standard normal random variable and z is a z-score. This formula tells us that the probability of a z-score greater than a certain value is equal to 1 minus the probability of a z-score less than that value.
Using this formula, we can calculate:
P(Z > 0.625) = 1 - P(Z < 0.625)
We can look up the value of P(Z < 0.625) in a standard normal distribution table or calculate it using a calculator. For example, using a standard normal distribution table, we can find that P(Z < 0.625) = 0.734.
Substituting this value into the formula, we get:
P(Z > 0.625) = 1 - 0.734 = 0.266
Therefore, the probability of trapping a coyote that is 17kg or larger is approximately 0.266 or 26.6%.
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A bottle of water that is 80°F is placed in a cooler full of ice. The temperature of the water decreases by 0. 5°F every minute. What is the temperature of the water, in degrees Fahrenheit, after 5 1/2
minutes? Express your answer as a decimal
After 5 and a half minutes, the temperature of the water will be 77°F.
In this scenario, we are given that the initial temperature of the water is 80°F. We also know that the temperature of the water decreases by 0.5°F every minute. We want to find out what the temperature of the water will be after 5 and a half minutes.
To solve this problem, we need to use a bit of math. We know that the temperature of the water is decreasing by 0.5°F every minute. So after 1 minute, the temperature of the water will be 80°F - 0.5°F = 79.5°F. After 2 minutes, the temperature will be 79.5°F - 0.5°F = 79°F. We can continue this pattern to find the temperature after 5 and a half minutes.
After 5 minutes, the temperature of the water will be 80°F - (0.5°F x 5) = 77.5°F. And after another half minute (or 0.5 minutes), the temperature will decrease by another 0.5°F, so the temperature will be 77.5°F - 0.5°F = 77°F.
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Madison made the following table to record the height of each person in her family. About how much taller is her mom than Jade? Be sure to round to the nearest half or whole.
{1}{2} foot
1, 1{2} feet
0 feet
1 foot
As per the data mentioned in the table, Jade's mom is 0.7 ft or 1 ft taller than jade.
Describe mixed fractions.Mixed numbers represent whole numbers and proper fractions together. Usually represents a number between any two integers. Hybrid numbers are made by combining three parts:
An integer, a numerator, and a denominator. The numerator and denominator are part of the correct fraction giving the mixed number.
Height of jade's mom = 5⁵/₈ ft
Jade's height = 4⁵/₆
The difference in their heights is:
= (45/8) - (29/6)
= (270 - 232)/48
= 38/48
= 0.7 ft
0.7 ft ≈ 1 ft
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3. Technology required. Here are the data for the population f, in thousands, of a city d decades after 1960 along with the graph of the function given by f(d) = 25 - (1.19)ª. Elena thinks that shifting the graph off up by 50 will match the data. Han thinks that shifting the graph of f up by 60 and then right by 1 will match the data. a. What functions define Elena's and Han's graphs? b. Use graphing technology to graph Elena's and Han's proposed functions along with f. population (thousands) c. Which graph do you think fits the data better? Explain your reasoning.
The relationship between the functions are indicated in the attached graph. see further explanation below.
a. Elena's graph is obtained by shifting the original function f up by 50 units, so her function is g(d) = f(d) + 50 = 75 - (1.19)ª.
Han's graph is obtained by shifting the original function f up by 60 units and then to the right by 1 unit, so his function is h(d) = f(d - 1) + 60 = 85 - (1.19)^(a-1).
b. Using graphing technology, we can graph the three functions f, g, and h to compare how well they fit the given data. Here's an example graph:
graph of f, g, and h
c. From the graph, it appears that Han's function h fits the data better than Elena's function g. The graph of h seems to align more closely with the plotted data points than the other two functions. Moreover, the shift to the right and up of the graph of f seems to better capture the overall trend of the data, as it appears that the population increased and shifted slightly to the right over time.
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The right triangle shown is enlarged such that each side is multiplied by the value of the hypotenuse, 3y. Find the expression that represents the perimeter of the enlarged triangle. TRIANGLE AND ANSWER CHOICES BELOW!
Answer:
c.
Step-by-step explanation:
The original triangle has two sides with length 4x each, and the hypotenuse has length 3y.
After the enlargement, each of the sides with length 4x becomes 3y × 4x = 12xy, and the hypotenuse becomes 3y × 3y = 9y^2.
Therefore, the perimeter of the enlarged triangle is the sum of the lengths of its three sides:
12xy + 12xy + 9y^2 = 24xy + 9y^2 = 9y^2 + 24xy
So the answer is (C) 9y^2 + 24xy.
You roll a six sided die 30 times. A 5 is rolled 8 times. What is the theoretical probability of rolling a 5? What is the experimental probability of rolling a 5?
The theoretical and experimental probability of rolling a 5 are 1/6 and 4/15 respectively.
How do we derive the probability?We will calculate the theoretical probability by substituting 30 for the number of favorable outcomes as the die is rolled 30 times with one option each for 30 rolls and 180 for total number of outcomes in theoretical probability formula.
P(Theoretical probability of rolling a 5) = 30/180
P(Theoretical probability of rolling a 5) = 1/6.
The experimental probability is calculated by substituting 8 for the number of time the event occurs and 30 for the total number of trials.
P(Experimental probability of rolling a 5)= 8/30
P(Experimental probability of rolling a 5) =4/15
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Choose Yes or No to tell whether the Addition Property of Inequality can be used to solve each statement. W – 4 > –10 12 ≥ 20x 7y10 ≤ 5. 5 –3. 25 < x – 9. 75
According to the given inequality,
W – 4 > –10 uses Addition Property
12 ≥ 20x not uses Addition Property
7y10 ≤ 5. 5 –3. 25 < x – 9. 75 uses Addition Property
Let's analyze each given inequality to see whether we can use the Addition Property of Inequality to solve them.
W – 4 > –10: We can use the Addition Property of Inequality to solve this inequality. To do this, we need to add 4 to both sides of the inequality, which gives us: W – 4 + 4 > –10 + 4, or W > –6.
12 ≥ 20x: We cannot use the Addition Property of Inequality to solve this inequality since we need to isolate "x" on one side of the inequality. To do this, we would need to subtract 12 from both sides of the inequality, which is not allowed under the Addition Property of Inequality.
7y + 10 ≤ 5.5 – 3.25x: We cannot use the Addition Property of Inequality to solve this inequality either since we need to isolate "y" on one side of the inequality.
To do this, we would need to subtract 10 from both sides of the inequality, which is not allowed under the Addition Property of Inequality.
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