Answers
The required expression equal to [tex]$\csc\left(\frac{4\pi}{9}\right)$[/tex] using a cofunction is: [tex]\begin{equation}\frac{1}{\cos\left(\frac{5\pi}{18}\right)}\end{equation}[/tex]
How to deal with trigonometric equation?Trigonometry is the study of angles and the angular relationships between planar and three-dimensional figures. The cosecant, cosine, cotangent, secant, sine, and tangent are the trigonometric functions—also known as the circular functions—that make up trigonometry.
According to question:The cofunction of sine is cosine, which means:
[tex]$\begin{equation}\csc(\theta) = \frac{1}{\sin(\theta)} = \frac{1}{\cos\left(\frac{\pi}{2}-\theta\right)}\end{equation}[/tex]
Therefore, we can express [tex]$\csc\left(\frac{4\pi}{9}\right)$[/tex] as:
[tex]$\begin{equation}\csc\left(\frac{4\pi}{9}\right) = \frac{1}{\sin\left(\frac{4\pi}{9}\right)} = \frac{1}{\cos\left(\frac{\pi}{2}-\frac{4\pi}{9}\right)}\end{equation}[/tex]
Simplifying the argument of the cosine function:
[tex]$\begin{equation}\frac{\pi}{2}-\frac{4\pi}{9} = \frac{5\pi}{18}\end{equation}[/tex]
Substituting this back into the equation, we get:
[tex]$\begin{equation}\csc\left(\frac{4\pi}{9}\right) = \frac{1}{\cos\left(\frac{5\pi}{18}\right)}\end{equation}[/tex]
Therefore, an expression equal to [tex]$\csc\left(\frac{4\pi}{9}\right)$[/tex] using a cofunction is:
[tex]\begin{equation}\frac{1}{\cos\left(\frac{5\pi}{18}\right)}\end{equation}[/tex]
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Related Questions
In the slope-intercept form y = m x + b, what does the m and the b stand for? a. m = slope, b = y-intercept c. m = variable, b = slope b. m = y-intercept, b = slope d. m = slope, b = variable Please select the best answer from the choices provided
Answers
Answer: Choice A
Step-by-step explanation:
M= slope
B= y-intercept
90 percent% of seven7 years
Answers
The value of the given percent that satisfied the relation through which it justified it is 6.3 years.
What about percent?
Percent: A percent is a way of expressing a number as a fraction of 100. The symbol for percent is "%". For example, if you say that 50% of a group are females, it means that 50 out of every 100 people in the group are female. Percentages are often used to describe the proportion of something or to compare different quantities.
According to the given information:
90 % of 7 years
⇒ [tex]\frac{90}{100}[/tex] x 7 years
⇒ [tex]\frac{630}{100}[/tex]
⇒ 6.3 years
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An airplane cruises at an altitude of 35,000 feet. It begins its descent at a rate of 1,200 feet per minute. Find a linear model
in the form h(t) = mt+b where h represents the altitude of the plane, in feet, after t minutes into its descent.
Answers
h(t) = mt + b
where h is the altitude, t is the time in minutes, m is the slope, and b is the y-intercept (the altitude when the plane begins its descent).
Since the plane is descending at a constant rate of 1,200 feet per minute, the slope of the linear model is -1,200. This is because as time increases, the altitude decreases at a rate of 1,200 feet per minute.
To find the y-intercept, we need to know the altitude of the plane when it begins its descent. The problem states that the plane is cruising at an altitude of 35,000 feet, so this is the y-intercept.
Therefore, the linear model for the altitude of the plane during its descent is:
h(t) = -1,200t + 35,000
where h is the altitude in feet and t is the time in minutes since the beginning of the descent.
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Help guys small math problem PLEASE ASAP !!
Answers
Step-by-step explanation:
F'(x) = f(x + h)² - 5(x + h) + 3 - (x² - 5x + 3)
---------------------------------------------------
h
F'(x) = x² + 2xh + h² - 5x - 5h + 3 - x² + 5x - 3
--------------------------------------------------------
h
F'(x) = 2xh + h² - 5h
-----------------------
h
F'(x) = h(2x + h - 5)
----------------------
h
F'(x) = 2x + h - 5
Lim
h---0
= 2x + 0 - 5
= 2x - 5
Question 20 options: The time a student sleeps per night has a distribution with mean 6.1 hours and a standard deviation of 0.6 hours. Find the probability that average sleeping time for a randomly selected sample of 36 students is more than 6 hours per night. Answer: (round to 4 decimal places)
Answers
The probability that the average sleeping time for a randomly selected sample of 36 students is more than 6 hours per night is 0.8413.
Describe Probability?Probability is a branch of mathematics that deals with the measurement of the likelihood or chance of an event occurring. It is used to quantify uncertainty and make predictions based on incomplete information. In general, probability is defined as a number between 0 and 1, where 0 represents an event that is impossible, and 1 represents an event that is certain to occur.
The basic concept of probability is based on the ratio of the number of favorable outcomes to the total number of possible outcomes. For example, if we toss a fair coin, the probability of getting heads is 1/2 or 0.5, since there is one favorable outcome (heads) out of two possible outcomes (heads or tails).
We can use the central limit theorem to approximate the distribution of the sample mean, assuming that the sample size is large enough. Since the sample size is n=36, we can assume that the sample mean has a normal distribution with mean μ=6.1 and standard deviation σ/√n=0.6/√36=0.1.
Let X be the sample mean sleeping time per night. Then we need to find the probability P(X > 6), which can be transformed into a standard normal distribution using the formula:
Z = (X - μ) / (σ/√n)
where Z is the standard normal variable.
Substituting the given values, we get:
Z = (6 - 6.1) / (0.1) = -1
Now we need to find the probability that Z is greater than -1. Using a standard normal distribution table or calculator, we can find that the probability is approximately 0.8413.
Therefore, the probability that the average sleeping time for a randomly selected sample of 36 students is more than 6 hours per night is 0.8413.
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What kind of triangle whose sides are 53,28,45.
Answers
So, the given triangle is a scalene right triangle.
what is triangle ?
With three consecutive sides and three angles, a triangle is an enclosed plane shape. It is one of the fundamental geometric shapes and is frequently used in physics, maths, and engineering. A triangle's total angles are always 180 degrees. Triangles come in a variety of shapes, such as equilateral triangles, which have three equal sides and angles, isosceles triangles, which have two equal sides and angles, and scalene isosceles (all sides and angles are different).
To determine the type of triangle based on the given side lengths, we can use the following rules:
If all three sides are equal, it's an equilateral triangle.
If two sides are equal, it's an isosceles triangle.
If all three sides are different, it's a scalene triangle.
We can also use the Pythagorean theorem to determine if the triangle is a right triangle. According to this theorem, in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side.
Let's check the sides of the given triangle using these rules:
The three sides are different, so it's a scalene triangle.
To check if it's a right triangle, we can find the longest side (53) and see if it satisfies the Pythagorean theorem with the other two sides. Using a calculator, we find that [tex]28^2 + 45^2 = 784 + 2025 = 2809[/tex], and [tex]53^2 = 2809.[/tex]Therefore, the triangle is a right triangle.
So, the given triangle is a scalene right triangle.
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As a salesperson at Trading Cards Unlimited, Justin receives a monthly base pay plus commission on all that he sells. If he sells $400 worth of merchandise in one month, he is paid $384. If he sells $700 of merchandise in one month, he is paid $447.
Answers
Step-by-step explanation:
As a salesperson at Trading Cards Unlimited, Justin receives a monthly base pay plus commission on all that he sells. If he sells $400 worth of merchandise in one month, he is paid $384. If he sells $700 of merchandise in one month, he is paid $447.
Answer:
Step-by-step explanation:
To solve this problem, we can set up a system of two equations with two variables. Let x be Justin's base pay for the month and y be the commission rate he receives for each dollar of merchandise sold. Then we have:
400y + x = 384 (equation 1)
700y + x = 447 (equation 2)
To solve for x and y, we can use the method of substitution. Solving equation 1 for x, we get:
x = 384 - 400y
Substituting this expression for x into equation 2, we get:
700y + (384 - 400y) = 447
Simplifying and solving for y, we get:
300y = 63
y = 0.21
Substituting this value of y into equation 1, we can solve for x:
400(0.21) + x = 384
x = 304.80
Therefore, Justin's base pay for the month is $304.80 and he receives a commission of 21% on all merchandise sold.
Suppose that defined population is all brown eyed people in a survey is being conducted which of these is an example of selection bias
Answers
Answer:
I will try my best with the given info
Step-by-step explanation:
Selection bias occurs when the selection of the sample is not random and is instead influenced by factors that are not related to the study objective. Here are some examples of selection bias in a survey of brown-eyed people:
A survey that only includes brown-eyed people from a specific geographic location, such as a single city or state. This would not be representative of the entire population of brown-eyed people.
A survey that only includes brown-eyed people who are members of a particular organization or club. This would not be representative of the entire population of brown-eyed people, as it would exclude those who are not members of the organization or club.
A survey that only includes brown-eyed people who have a certain level of education or income. This would not be representative of the entire population of brown-eyed people, as it would exclude those with different levels of education or income.
A survey that only includes brown-eyed people who are willing to participate in the study. This could result in a biased sample, as those who are not willing to participate may have different characteristics than those who are willing to participate.
In general, any selection process that is not random and does not provide equal opportunity for all members of the population to be included in the study can result in selection bias.
10.08 is what percent of 56?
Answers
Answer: 18%
Step-by-step explanation:
Answer:
18%
Step-by-step explanation:
To find what percent 10.08 is of 56, we can use the following formula:
[tex]p=\frac{x * 100}{y}[/tex]
where x is 10.08 and y is 56:
[tex]p = \frac{10.08 * 100}{56}[/tex]
which p is 18%
A sample of size n=77 is drawn from a population whose standard deviation is σ=50.
Find the margin of error for a 90% confidence interval for μ.
Answers
If we take multiple samples of the same size and calculate their means, 90% of the resulting sample which is 69.3 means will fall within 9.02 units of the true population mean for standard deviation.
The following formula must be used to determine the margin of error for a 90% confidence interval for the population mean ():
Margin of error = [tex]z * (/n)[/tex].
where is the population standard deviation, n is the sample size, and z is the critical value from the standard normal distribution with a 90% confidence level.
The matching z-value is 1.645 because a 90% confidence interval is what we are looking for. Thus, the margin of error can be determined as follows:
Margin of error: (50 / 77) / 1.645 = 9.02
This indicates that 90% of the sample means obtained when calculating the means of several samples of equal size will be within 9.02 units of the actual population mean.
It is significant to remember that the margin of error lowers with sample size and rises with confidence level. A bigger sample size in this situation would lead to a smaller margin of error, whereas a greater confidence level would lead to a larger margin of error.
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PLEASE IM FAILING AND IM GONNA GET HELD BACK PLEASEPLEASE...Which two ordered pairs represent a proportional relationship? A. (3, 2) and (6, 6) B. (4, 2) and (6, 4) C. (5, 3) and (6, 4) D. (3, 2) and (6, 4)
Answers
Answer:
D
Step-by-step explanation:
If you flip the X and Y axis you get the same answer
A graph of a function f(x) undergoes a sequence of transformations to form a new function f(x)= -2f(x+6)-8, which transformation are part of the sequence?
Chose all that apply
A.) f(x) reflected over x-axis
B.) f(x) reflected over y-axis
C.) f(x) stretched vertically
D.) f(x) stretched horizontally
E.) f(x) shifted right 6 units
F.) f(x) shifted down 8 units
Answers
A because the first number outside the parentheses is negative, C because the number is between bigger or equal to one, and F because of the negative 8. Keep in mind it does not go right 6 units, it goes left, if it was a minus sign it would be right, two negatives equal a positive.
this is a composite functions question please can you help to solve it with or without working out
Answers
Therefore, the solution to fg(x) = gf(x) for the composite functions is x = -1/4.
What is function?A function is a mathematical rule that assigns a unique output for every input in a given set. In other words, it is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. A function can be represented using a formula, a graph, or a table of values. Functions are widely used in mathematics, science, engineering, economics, and many other fields to describe the relationship between variables and to make predictions based on data.
Here,
To solve fg(x) = gf(x), we need to find f(g(x)) and g(f(x)), and then set them equal to each other.
f(g(x)) = f(x + 1)
= 2(x + 1)²
= 2(x² + 2x + 1)
= 2x² + 4x + 2
g(f(x)) = g(2x²)
= 2x² + 1
Now we can set them equal to each other and solve for x:
2x² + 4x + 2 = 2x² + 1
Subtracting 2x² from both sides, we get:
4x + 2 = 1
Subtracting 2 from both sides, we get:
4x = -1
Dividing both sides by 4, we get:
x = -1/4
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Examine the pattern and determine how many shaded squares then unshaded squares will be in the 100x100 square in the sequence shown in the diagram on the right.
Answers
There are 2500 Shaded squares and 7500 unshaded squares in the 100x100 square, based on the given sequence in the diagram.
1. First, analyze the given diagram and observe the pattern. Notice that there are alternating shaded and unshaded squares, with the shaded squares being on the main diagonal.
2. Next, identify the sequence in the pattern. It appears that there is a continuous increase of shaded squares, starting from 1 and increasing by 2 each time. This forms an arithmetic sequence: 1, 3, 5, 7, and so on.
3. To find the number of shaded squares in the 100x100 square, calculate the sum of the first 50 terms of the sequence (since there are 100 rows/columns and each shaded area covers 2 rows/columns). The formula for the sum of an arithmetic sequence is: Sn = n * (a1 + an) / 2, where Sn is the sum of the sequence, n is the number of terms, a1 is the first term, and an is the last term.
4. In our case, n = 50, a1 = 1, and an = 99 (the 50th term in the sequence). Plugging these values into the formula, we get: S50 = 50 * (1 + 99) / 2 = 50 * 100 / 2 = 2500.
5. Thus, there are 2500 shaded squares in the 100x100 square.
6. To find the number of unshaded squares, subtract the number of shaded squares from the total number of squares in the 100x100 square. The total number of squares is 100 * 100 = 10,000.
7. Now, calculate the number of unshaded squares: 10,000 - 2500 = 7500.
In conclusion, there are 2500 shaded squares and 7500 unshaded squares in the 100x100 square, based on the given sequence in the diagram.
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The population of Winnemucca Nevada can be modeled by P=6191(1.04)^1 , what is the growth rate (r) represented as a percentage?
a. 106%
b. 96%
c. 4%
d. 1.04%
Answers
The grοwth rate (r) represented as a percentage is 4%, which is οptiοn (c).
What is the percentage?A percentage is a number οr ratiο expressed as a fractiοn οf 100. It is οften denοted using the percent sign, "%", althοugh the abbreviatiοns "pct.", "pct" and sοmetimes "pc" are alsο used. A percentage is a dimensiοnless number; it has nο unit οf measurement.
The given pοpulatiοn grοwth mοdel is:
P = 6191(1.04)¹
Here, P represents the pοpulatiοn after οne year, 6191 represents the initial pοpulatiοn, and 1.04 is the grοwth factοr.
The grοwth factοr is calculated as:
grοwth factοr = 1 + grοwth rate
where the grοwth rate is a decimal representatiοn οf the percentage increase in pοpulatiοn.
Sο, in this case, we can calculate the grοwth rate as:
grοwth rate = grοwth factοr - 1 = 1.04 - 1 = 0.04
Tο cοnvert this tο a percentage, we multiply by 100:
grοwth rate as a percentage = 0.04 * 100% = 4%
Therefοre, the grοwth rate (r) represented as a percentage is 4%, which is an οptiοn (c).
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A friend is curious what the probability of it snowing today is. What would the complement of this event be? explain how you would calculate the complement of an event. 
Answers
Answer:
Step-by-step explanation:
compliment of an event A is probability of not happening A
Hope the picture helps :)
Dana had an equal number of red beads and yellow beads. After using 500 red beads to make necklaces, she had 3 times as many yellow beads as red beads. How many yellow beads does she have?
Answers
Answer:2000
Step-by-step explanation:
Dana has 1500 yellow beads when Dana had an equal number of red beads and yellow beads.
Dana had an equal number of red beads and yellow beads, so let's say she had x red beads and x yellow beads.
After using 500 red beads to make necklaces, she was left with x - 500 red beads.
Since she now had 3 times as many yellow beads as red beads, she had a total of 3 * (x - 500) = 3x - 1500 yellow beads.
We know that the total number of yellow beads is x, so we can set the two expressions equal to each other:
x = 3x - 1500
Solving for x, we get:
2x = 1500
x = 750
Therefore, Dana had x = 750 yellow beads.
Since she now has 3 times as many yellow beads as red beads, she has a total of 3 * 750 = 1500 yellow beads.
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A triangle has sides with lengths of 63 inches, 73 inches, and 98 inches. Is it a right triangle?
Answers
Thus, the given side of triangle with lengths of 63 inches, 73 inches, and 98 inches does not form a right triangle.
Explain about the features of right triangle:A triangle is considered to be correct when one of its angles is 90 degrees. Moreover, a right angle is one that measures 90 degrees or more.
The non-right angle measurements of right triangles must add up to 90 degrees, which is a crucial condition. This results from the fact that a triangle's total number of angles equals 180 degrees.
In right triangle, the longest side is called hypotenuse.
Then,
hypotenuse H = 98 inches
Let Side S1 = 63 inches,
Let Side S2 = 73 inches,
Then, Pythagorean theorem must satisfy for right triangle
H² = (S1)² + (S2)²
98² = (63)² + (73)²
9604 = 3969 + 5329
9604 = 9298
But, 9604 ≠ 9298
Thus, the given side of triangle with lengths of 63 inches, 73 inches, and 98 inches does not form a right triangle.
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Find the values of m and b
Answers
The values of m and be for the line given, can be found to be:
m - 3 / 5b - 5How to find the values of m and b on a line ?First, we need to pick two points from the line which would be ( 0, 5 ) and ( -5, 2 ).
To find the values of m (slope) and b (y-intercept) for a line with the given coordinates (0, 5) and (-5, 2), we can use the slope formula and the point-slope form of a linear equation.
Calculate the slope (m) using the slope formula:
m = (y2 - y1) / (x2 - x1)
m = (2 - 5) / (-5 - 0)
m = (-3) / (-5)
m = 3/5
Find the y-intercept (b) using the point-slope form. The y - intercept is the point where the line crosses the y axis. This means that the value of x at this point would be 0.
The y - intercept can therefore be seen from the point ( 0, 5 ) which means that 5 is the y - intercept or b.
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answers
The graph of the given values of x and y coordinates shows the straight line. Thus, the function is said to be linear function.
Explain about the linear or non linear function:A linear function is one whose graph on a Cartesian plane is a straight line. The line is always straight even though it can travel in any direction.
The form of a non-linear function is not a straight line.There are no exponents higher than one for the linear functions. Some of them only have the single variable x, which would be equal to x to the first power, if they have any variables at all.In its most basic form, a linear function is stated as y = a + bx, where this one and b are both constants.Given table:
x y
-2 -7
-1 -4
0 -1
1 2
2 5
Plot the coordinates on graph:
(-2, -7), (-1, -4),(0,-1),(1,2),(2,5)
The graph of the given values of x and y coordinates shows the straight line. Thus, the function is said to be linear.
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Complete question:
Explain, if the given table shows linear or non linear function?
x y
-2 -7
-1 -4
-0 -1
1 2
2 5
simplify 22 - (-24) + (-32)
Answers
Simplify
22 - (-24)
Swap since they are both negatives.
22-(-24) =
22+(24)
22+24
= 46
Which now add in the negative 32 to the problem
46 + (-32)
Recreate the problem to make it more simple:
46 - 32
= 14
Which measurement is not equal to one mile
Answers
Thus, the parking space is longer than length of the truck by 42 inches.
Explain about the unit conversion:The same attribute is expressed using a unit conversion, but in a different measurement equivalent. For instance, time can always be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or another type of measurement unit instead of miles.
Using conversion factors, existing units, and or the fact that a unit of measure cancels out another unit of measure, a unit cancellation table is created.
Given data:
Length of the parking space = 60 feet
Length of truck = 6 yard.
Convert yards in feet
1 yard = 3 feet
Multiply both side by 6.
6*1 yard = 6*3 feet
6 yard = 18 feet
Difference = 60 - 18 = 42 feet.
The parking space is longer than length of the truck by 42 inches.
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Discount questions…..
Answers
Mr Leonard will receive a discount of £45.84 on his oil purchase.
How is discount calculated?We must first determine the entire amount of oil Mr. Leonard intends to buy in order to determine the discount he will receive.
There are currently 450 liters in the tank, which has a capacity of 1200 liters. Therefore, Mr. Leonard needs to buy an extra 750 liters (1200 - 450 = 750).
The total cost of the oil before the discount must then be determined.
With a litre costing 81.5p, the price for 750 liters of oil would be:
750 liters x 81.5 pence per liter = £611.25.
We must multiply the entire cost of the oil by the discount rate (7.5 percent, or 0.075), in order to determine the discount:
£611.25 x 0.075 = £45.84
Therefore, Mr Leonard will receive a discount of £45.84 on his oil purchase.
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The total amount of oil that can be added to the tank is 1200 liters, and there are already 450 liters in the tank. Therefore, the tank can hold an additional 750 liters of oil.
Mr. Leonard will get a discount of [tex]£45.84[/tex] on this purchase.
The price of oil is 81.5p per litre. So, the cost of 750 liters of oil would be:
[tex]750 * 81.5p = £ 611.25[/tex]
As Mr. Leonard is a loyal customer and gets a discount of 7.5% on the price of oil, he will get a discount of:
[tex]7.5% of £611.25 = £45.84[/tex]
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HELP PLSSSSSSSSSSSSSSSsss
Answers
Answer:
G
Step-by-step explanation:
The diagonal of a square is equal to the diameter of the circle in this case
d = 16 cm
r = 0,5 × d
r = 0,5 × 16 = 8 cm
The circumference of the circle is equal to:
[tex]c = 2\pi \times r[/tex]
[tex]c = 2\pi \times 8 = 16\pi \: {cm}^{2} [/tex]
12a+14=302
♀️♀️♀️♀️♀️♀️
Answers
Answer
a=24
Step-by-step explanation:
12 times 24 equals 288 plus 14 equals 302
obby needs to change the oil in his car. Bobby has 4 quarts of oil. Each quart is equal to 4 cups. How many cups of oil does Bobby have?
Answers
Answer: 16
Step-by-step explanation:
4*4 = 16
The yearbook team is also designing a page for each
graduate. This page will have five different sections
and will be 8 in. wide and 10 in. tall.
Answers
Step-by-step explanation:
you dind't but what we had to anwser
The distribution of weights of pumpkins from a harvest is approximately normal with a mean of 8.3 pounds and a standard deviation of 1.68 pounds. Find the value of the interquartile range (IQR) for the mean of 15 pumpkins. Express the answer as a decimal value rounded to the nearest thousandth.
Answers
The value of the interquartile range (IQR) for the mean of 15 pumpkins is approximately 0.585 pounds.
What is mean?
In statistics, the mean (also known as the arithmetic mean or average) is a measure of central tendency that represents the sum of a set of numbers divided by the total number of numbers in the set.
To find the IQR for the mean of 15 pumpkins, we need to first find the standard error of the mean, which can be calculated using the formula:
SEM = σ / sqrt
where SEM is the standard error of the mean, σ is the standard deviation, and n is the sample size.
Substituting the given values, we get:
SEM = 1.68 / sqrt(15) = 0.433
The interquartile range (IQR) for the mean can be calculated as:
IQR = 1.35 * SEM
where 1.35 is the multiplier for the IQR based on the normal distribution.
Substituting the value of SEM, we get:
IQR = 1.35 * 0.433 = 0.585
Rounding to the nearest thousandth, we get the final answer as:
IQR ≈ 0.585
Therefore, the value of the interquartile range (IQR) for the mean of 15 pumpkins is approximately 0.585 pounds.
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If GH is a diameter of circle F, find the measurement of the minor arc JI.
A. 51 degrees
B. 102 degrees
C. 112 degrees
D. 258 degrees
Answers
Answer:
B) 102
Step-by-step explanation:
To find x, we need to simplify and solve the equation (5x+6)=(7x-12):
5x + 6 = 7x - 12 // distribute the 5 and 7
6 + 12 = 7x - 5x // group the x terms and constants
18 = 2x
Now, we can solve for x by dividing both sides by 2:
18/2 = x
9 = x
Therefore, x is 9.
To find the solution if x = 9, we can simply substitute 9 for x in the given expressions:
(5x+6) = (5(9) + 6) = 51
(7x-12) = (7(9) - 12) = 51
Therefore, both expressions are equal to 51 when x = 9.
solve the Systens of equations
x+y-z =3
4x-y+z=-13
x-3y+2z=-28
Answers
As a result, the system of equations has the following solution: x=-2,y=16,z=11.
In order to resolve the equation system:
x + y - z = 3
x - 3y - 2z = -28 and 4x - y + z = -13
The elimination strategy can be used to find the values of x, y, and z. In order to remove z, we can first add the first and second equations:
3 - 13x + y - z + 4x - y + z
Define elimination method?A approach for solving systems of linear equations is the elimination method. The addition method is another name for it. We change an equation system so that one variable "cancels out" in order to solve it by elimination. In this approach, one of the variables is removed by adding or subtracting from the equations. After removing one variable, we can find a solution for the remaining one.
When we simplify this equation, we obtain:
5x = -10
When we multiply both sides by 5, we get:
x = -2
Knowing x now allows us to solve for y by substituting it into the first equation:
-2 + y - z = 3
When we simplify this equation, we obtain:
y - z = 5
In order to solve for z, we may now enter x and y into the third equation:
-2 - 3y + 2z = -28
When we simplify this equation, we obtain:
-3y + 2z = -26
by replacing y - z = 5 to this equation gives us:
-3y + 2(y - 5) = -26
When we simplify this equation, we obtain:
-y - 10 = -26
To both sides of the equation, add 10, and we get:
-y = -16
Adding -1 to both sides gives us:
y = 16
Knowing x and y now allows us to solve for z by substituting them into the first equation:
-2 + 16 - z = 3
When we simplify this equation, we obtain:
z = 11
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