Answer: Mike is ( 3x + 4 ) years old
Step-by-step explanation:
K -> x y/o
L -> 3x y/o
M -> (3x + 4) y/o
The number of employees for a certain company has been decreasing each year by 5%. If the company cumently has 860 employees and this rate continues, find the number of employees in 10 years
The number of employees in 10 years will be approximately
(Round to the nearest whole number as needed)
Based on the exponential decay equation, the number of employees for the company that has been decreasing yearly by 5%, will in 10 years be approximately 515.
What is exponential decay equation?The exponential decay equation or function gives the value in t years that has a constant ratio of decrease.
Exponential decay equation is one of the two exponential functions. The other is the exponential growth equation.
The annual decrease in the number of employees = 5%
The current number of employees in the company = 860
The expected time = 10 years.
The exponential decay equation is as follows, y = 860 x 0.95^10.
y = 860 x 0.95^10 = 515
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I NEED YOUR HELP ASAP!!
To create a modified box plot for a data set, determine the outliers of the data set and the smallest and largest numbers in the data set that are not outliers. Next, determine the median of the first half of the data set, the median of the entire data set, and the median of the second half of the data set.
What are the values that are needed to create a modified box plot for this data set?
19, 15, 22, 35, 16, 22, 4, 22, 24, 16, 17, 21
Enter your answers in the blanks in order from least to greatest.
Smallest number in the data set that is not an outlier is 15, Median of the first half is 17, Median of the entire data set is 20.5. Median of the second half is 22. Largest number in the data set that is not an outlier is 35.
Give a short note on Median?
In statistics, the median is a measure of central tendency that represents the middle value in a dataset. To find the median, the data must first be sorted in ascending or descending order. If the dataset contains an odd number of values, the median is the middle value. If the dataset contains an even number of values, the median is the average of the two middle values.
The median is a useful measure of central tendency in datasets that are skewed or have outliers, as it is less sensitive to extreme values than the mean. It is also useful in datasets with non-numeric values, such as rankings or survey responses.
To create a modified box plot, we need the following values:
The smallest number in the data set that is not an outlier: 15
The median of the first half of the data set: 17
The median of the entire data set: 20.5
The median of the second half of the data set: 22
The largest number in the data set that is not an outlier: 35
So the values needed to create a modified box plot for this data set are: 15, 17, 20.5, 22, 35.
Im a trapezoid measuring 8cm, 10cm, 16 cm and 10cm on its sides. What is my Perimeter? 1-5 po lhat
Answer:
See Below.
Step-by-step explanation:
To find the perimeter of a trapezoid, you simply add up the lengths of all four sides.
In this case, the trapezoid has sides of 8 cm, 10 cm, 16 cm, and 10 cm.
Perimeter = 8 cm + 10 cm + 16 cm + 10 cm
Perimeter = 44 cm
Therefore, the perimeter of the trapezoid is 44 cm.
Hi. Please help me convert this non-linear to linear form y=mx+c. The answer is square root of y= 6/p x - 2/q .
Thank you so much.
Answer: To convert the given equation, √y = (6/p)x - (2/q), into the linear form y = mx + c, we can use the following steps:
Square both sides of the equation to eliminate the square root:
√y = (6/p)x - (2/q)
√y^2 = (6/p)x - (2/q)^2
Simplifying the right-hand side, we get:
y = (36/p^2)x - (4/q) + 4/q^2
Rearrange the equation to the form y = mx + c:
y = (36/p^2)x + (4/q^2 - 4/q)
So the linear form of the given non-linear equation is y = (36/p^2)x + (4/q^2 - 4/q).
Step-by-step explanation:
I need help, what does this mean
Answer:
2125 ft/min
33,000 ft
y = -2125x + 33,000
Step-by-step explanation:
A. -2125 feet per minute. You get this number when you divide 17,000 by 8 (rise over run). You could also use the formula y2-y/x2-x1 with the points (0, 33,000) and (8, 17,000).
B. 33,000 feet is the height of the plane before it starts descending, so it must be the starting value.
C. Plug in the values you got for A and B into the slope formula y = mx + b
y = -2125x + 33,000
What property of real numbers does each statement demonstrate? (3 + 4) + 1 = 3 + (4 + 1)
Answer: Associative property
Step-by-step explanation:
The definition of the associative property is the answer is the same no matter how the terms are grouped. Hope this helped!
What is the solution to 3(2k + 3)= 6-(3k -5)
Answer:
[tex]\frac{11}{8}[/tex]
Step-by-step explanation:
3(2k+3)=6-(3k-5)
6k +9=6-3k+5
6k+3k=6+5
8k=11
k=[tex]\frac{11}{8}[/tex]
Answer: I think it is k=2/9
Step-by-step explanation:
A triangle is equal in area to a rectangle which measures 10cm by 9cm. If the base of the triangle is 12cm long, find its altitude
Answer:
h = 15 cm
Step-by-step explanation:
Area of triangle equals the area of rectangle. As the dimensions of the rectangle is given, we can first find the area of the rectangle.
[tex]\boxed{\bf Area \ of \ the \ rectangle = length * width}[/tex]
= 10 * 9
= 90 cm²
Area of triangle = area of rectangle
= 90 cm²
base of the triangle = b = 12 cm
[tex]\boxed{\bf Area \ of \ triangle = \dfrac{1}{2}bh}[/tex] where h is the altitude and b is the base.
[tex]\bf \dfrac{1}{2} b* h = 90 \\\\\dfrac{1}{2}*12* h = 90[/tex]
[tex]\bf h = \dfrac{90*2}{12}\\\\\boxed{\bf h = 15 \ cm}[/tex]
Ryan buys some jumpers to sell on a stall. He spends £190 buying 80 jumpers. He sells 50% of the jumpers for £12 each. He then puts the rest of the jumpers on a Buy one get one half price offer. He manages to sell half the remaining jumpers using this offer. How much profit does Ryan make?
Ryan makes a profit of £240. the total sales now amount to £600. By subtracting the cost of the jumpers, i.e. £190, from the total sales, we calculate that Ryan makes a profit of £240.
Ryan spends £190 to buy 80 jumpers. He sells 50% of the jumpers, i.e. 40 jumpers, at £12 each. This brings the total sales to £480. Then, he puts the remaining 40 jumpers on a Buy one get one half price offer. He sells 20 of the remaining jumpers using this offer. Therefore, the total sales now amount to £600. By subtracting the cost of the jumpers, i.e. £190, from the total sales, we calculate that Ryan makes a profit of £240.
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Simplify.
Remove all perfect squares from inside the square root. Assume x is positive.
20x8 =
The simplified form of the given expression as required to be determined in the task content is; 2x⁴√5.
What is the simplified form of the given expression?It follows from the task content that the Simon form of the given expression √20x⁸ is required to be determined from the task content.
On this note, since the given expression is; √20x⁸.
We have that; = √ (4 × 5 × x⁸)
Therefore, since 4 and x⁸ are perfect squares; it follows that we have;
= 2x⁴ √5.
Ultimately, the simplified form of the given expression as required to be determined is; 2x⁴ √5.
Complete question; The correct expression is; √20x⁸.
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Which of the following is equivalent to the inequality 2x + 13 < 5x - 20?
F. x >-11
G. x<?
H. x>;
J. x < 11
K. x > 11
Answer:
k
Step-by-step explanation:
2x+13<5x−20
Subtract 5x from both sides.
Combine 2x and −5x to get −3x.
Subtract 13 from both sides.
Subtract 13 from −20 to get −33.
Divide both sides by −3. Since −3 is negative, the inequality direction is changed.
x>11
a general principle in the field of tests and measurements is that longer tests tend to be more reliable than shorter ones. in your opinion, is that principle illustrated by the reliability coefficients shown in the table?
This principle is validated by the data shown in the table.
Tests and measurements is an essential aspect of the education process as it enables educators to gauge the level of knowledge and skills their students have acquired. The principle that longer tests tend to be more reliable than shorter ones has some merit because it allows educators to assess a broader range of skills and knowledge, which increases the validity of their assessments.In my opinion, the principle that longer tests tend to be more reliable than shorter ones is illustrated in the reliability coefficients shown in the table. This is because the data shows that the reliability coefficients for longer tests are consistently higher than those for shorter tests. Additionally, the results for the 10-item test indicate a higher reliability coefficient compared to the 5-item test, which supports the notion that longer tests are more reliable than shorter ones.The table displays that the longer tests have higher reliability coefficients compared to the shorter tests. For example, in the 5-item test, the reliability coefficient is .45, while the 10-item test's reliability coefficient is .73. This shows that the 10-item test is more reliable than the 5-item test, as the higher reliability coefficient indicates that the assessment is consistent in measuring the skill or knowledge it is intended to measure. As a result, this principle is validated by the data shown in the table.
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Suppose f is a continuous function defined on a rectangle R=[a,b]X[c,d]. What is the geometric interpretation of the double integral over R of f(X,y) if f(X,y)>0
If f(x,y) > 0 and is a continuous function defined over a rectangle R=[a,b]x[c,d], then the double integral over R of f(x,y) can be interpreted as the volume of a solid that lies in the first octant and under the graph of the function f(x,y) over the region R.
The geometric interpretation of the double integral over R of f(x,y) if f(x,y) > 0, where f is a continuous function defined on a rectangle R = [a,b] × [c,d] is given as follows:
The double integral of f(x,y) over R, if f(x,y) > 0, gives the volume under the graph of the function f(x,y) over the region R in the first octant.
Consider a point P (x, y, z) on the graph of f(x, y) that is over the region R, and let us say that z = f(x,y). If f(x,y) > 0, then P is in the first octant (i.e. all its coordinates are positive).
As a result, the volume of the solid that lies under the graph of f(x,y) over the region R in the first octant can be found by integrating the function f(x,y) over the rectangle R in the xy-plane, which yields the double integral.
The following formula represents the double integral over R of f(x,y) if f(x,y) > 0:
∬Rf(x,y)dydx
The geometric interpretation of the double integral over R of f(x,y) if f(x,y) > 0 is given by the volume of the solid that lies under the graph of the function f(x,y) over the region R in the first octant.
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An avid gardener wants to know which of two brands of fertilizer is best for her tomatoes. The two brands of fertilizer are A and B. She plants five pairs of tomato plants in two rectangular planters and places them beside one another. She gives each set of tomato plants the same amount of water each day, only she gives one set of plants fertilizer A and the other set of plants fertilizer B. At the end of the growing season, she counts the number of tomatoes each plant has yielded. Assume that all conditions for inference have been met. The rectangular planters are lined up so that plant 1 is beside plant 6, and plant 2 is beside plant 7, and so on. The yield for the five pairs of tomato plants are given. Plant 1 2 3 4 5 Yield with Fertilizer A 7 6 5 8 10 Plant 6 7 8 9 10 Yield with Fertilizer B 4 7 6 5 3 The gardener believes that fertilizer A enhances the yield of her tomatoes more than fertilizer B. She uses the following order of subtraction when determining the difference in the yields for the two brands: A- B (a) We would like to carry out a t test for the population mean difference. Calculate the point estimate. (b) Calculate the standard deviation of the differences. (Round your answer to three decimal places.) (c) Calculate the test statistic. (Round your answer to two decimal places.)
(a) Point estimate (mean difference): 2.2 tomatoes. (b) The standard deviation of differences: Approximately 3.47. (c) The test statistic: Approximately 1.38.
To perform a t-test for the population mean difference, follow these steps:
(a) Calculate the point estimate (mean difference): The point estimate is the mean difference between the yields of fertilizer A and fertilizer B.
Mean difference = (Sum of differences) / Number of pairs
Using the given data gives:
Mean difference = ((7-4) + (6-7) + (5-6) + (8-5) + (10-3)) / 5
Subtracting gives:
Mean difference = (3 - 1 - 1 + 3 + 7) / 5
Solving gives:
Mean difference = 11 / 5
Dividing gives:
Mean difference = 2.2
(b) Calculate the standard deviation of the differences:
To calculate the standard deviation of the differences, we need to calculate the squared differences, find their sum, divide by (n-1), and then take the square root.
Squared differences:[tex](3 - 2.2)^2, (-1 - 2.2)^2, (-1 - 2.2)^2, (3 - 2.2)^2, (7 - 2.2)^2[/tex]
Solving gives:
Sum of squared differences = (0.64 + 12.96 + 12.96 + 0.64 + 21.16)
Solving gives:
The sum of squared differences = 48.36
The standard deviation of the differences [tex]= \sqrt{48.36 / 4}[/tex]
Solving gives:
The standard deviation of the differences [tex]= \sqrt{2.09}[/tex]
Rounded to three decimal places
The standard deviation of the differences ≈ 3.47
c) Calculate the test statistic:
The test statistic (t) = (Point estimate - Null hypothesis value) / (Standard deviation /√(sample size))
Let's assume the null hypothesis is that there is no difference between the two fertilizers
(i.e., mean difference = 0).
[tex]t = (2.2 - 0) / (3.47 / \sqrt5)[/tex]
Substituting [tex]\sqrt 5 = 2.236[/tex]
t = 2.2 / (3.47 / 2.236)
Rounded to two decimal places
t ≈ 1.378
So, the test statistic is approximately 1.378.
The gardener can compare this test statistic to critical values from the t-distribution to determine whether the difference between the two fertilizers is statistically significant at a certain significance level. If the calculated test statistic is greater than the critical value, she ma
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In a distribution of 387 values with a mean of 72, at least 344 fall within the interval 64-80. Approximately what percentage of values should fall in the interval 56-88? Use Chebyshev’s theorem. Round your k and s values to one decimal place and final answer to two decimal places.
The required percentage of values that should fall in the interval 56-88 is approximately 74.37%.
Chebyshev’s Theorem:Chebyshev's Theorem states that, for any given data set, the proportion (or percentage) of data points that lie within k standard deviations of the mean must be at least (1 - 1/k2), where k is a positive constant greater than 1.Calculation:Given,Mean (μ) = 72N (Total number of values) = 387Interval (x) = 64-80 and 56-88Minimum values (n) = 344Minimum percentage (p) = (344 / 387) x 100 = 88.85%From the given data we have,1. Calculate the variance of the distribution,Variance = σ2 = [(n × s2 ) / (n-1)]σ2 = [(344 × 42) / 386]σ2 = 18.732. Calculate the standard deviation of the distribution,σ = √(18.73)σ = 4.33. Calculate k = (|x - μ|) / σ for the given interval 56-88,Here, x1 = 56, x2 = 88, k1 = |56-72| / 4.33 = 3.7, k2 = |88-72| / 4.33 = 3.7Thus, k = 3.74. Calculate the minimum percentage of values within the interval 56-88 using Chebyshev's Theorem,p = [1 - (1/k2)] x 100p = [1 - (1/3.7)2] x 100p = 74.37% (approximately)Therefore, the required percentage of values that should fall in the interval 56-88 is approximately 74.37%.
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B=6,c=7.5 what is A in Pythagorean therom
Answer: 4.5
Step-by-step explanation:
A^2 +B^2 =C^2
A^2 + 6^2 =7.5^2
A^2 + 36= 56.25
A^2= 20.25
A= square root of 20.25
A= 4.5
Prove that sum of measure of three angles of triangle is 180
Proved that the sum of measure of three angles of triangle is 180 using the Polygon Angle Sum Theorem
To prove that the sum of the measures of three angles of a triangle is 180 degrees, we can use the Polygon Angle Sum Theorem, which states that the sum of the measures of the interior angles of a polygon with n sides is equal to (n-2) times 180 degrees.
A triangle is a polygon with three sides, so we can apply the Polygon Angle Sum Theorem to a triangle to find the sum of its interior angles. Using n=3, we have:
Sum of measures of interior angles of triangle = (n-2) × 180 degrees
= (3-2) × 180 degrees [since we are dealing with a triangle]
= 1 × 180 degrees
= 180 degrees
Therefore, the sum of the measures of the interior angles of a triangle is 180 degrees. This means that the sum of the measures of the three angles in a triangle is always 180 degrees, regardless of the size or shape of the triangle.
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Write a quadratic function in standard form to represent the data in the table.
Ordered pairs arranged in a table. From left to right the pairs are: 2, 3, and 4, 1, and 6, 3, and 8, 9, and 10, 19.
y = x2 − x +
Use substitution to solve -4x + y = 3, 5x - 2y = -9
Using the substitution method, the solution of the system of equations -4x + y = 3 and 5x - 2y = -9 is (x, y) = (1, 7)
We can solve this system of equations using the substitution method by solving for one variable in terms of the other in one equation, and then substituting that expression into the other equation. Here's how:
-4x + y = 3 (Equation 1)
5x - 2y = -9 (Equation 2)
Solving Equation 1 for y, we get:
y = 4x + 3
Now, we substitute this expression for y into Equation 2 and solve for x:
5x - 2(4x + 3) = -9
5x - 8x - 6 = -9
-3x = -3
x = 1
We have found the value of x to be 1. Now, we substitute this value back into Equation 1 to find the value of y:
-4(1) + y = 3
y = 7
Therefore, the solution to the system of equations is (x, y) = (1, 7)
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Will give brainiest
Write the equation of the circle using the center and any one of the given points A, B, or C
Answer:
To write the equation of a circle given its center and a point on the circle, we need to use the standard form of the equation of a circle, which is:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center of the circle and r is the radius.
Let's use point A as the point on the circle. We are given that the center of the circle is (4, -2) and point A is (6, 1). We can use the distance formula to find the radius of the circle:
r = √[(6 - 4)^2 + (1 - (-2))^2] = √[4^2 + 3^2] = 5
Now we can substitute the center and radius into the standard form equation:
(x - 4)^2 + (y + 2)^2 = 5^2
Simplifying and expanding the right-hand side, we get:
(x - 4)^2 + (y + 2)^2 = 25Therefore, the equation of the circle is (x - 4)^2 + (y + 2)^2 = 25 and we used point A to find it.
find the length of the cord pt.3
According to the circle theorem, we can find the length of the cord, x = 4 units.
Define circle theorem?Geometrical assertions known as "circle theorems" set forward significant conclusions pertaining to circles. These theorems provide significant information regarding several aspects of a circle.
A circle's chord is a line segment that hits the circle twice on its edge, separating it into two equal pieces. The circle is divided into two equal pieces by the longest chord of the circle, which runs through its centre.
Here in the given circle,
As per the intersecting chords theorem,
AB × CB= BE × BD
⇒ 6 × 6 = 9× x
⇒ x = 36/9=4
Therefore, the length of the chord, x = 4 units.
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Salaries for teachers in a particular state have a mean of $ 52000 and a standard deviation of $ 4800. a. If we randomly select 17 teachers from that district, can you determine the sampling distribution of the sample mean? Yes If yes, what is the name of the distribution? normal distribution The mean? 52000 The standard error? b. If we randomly select 51 teachers from that district, can you determine the sampling distribution of the sample mean? ? If yes, what is the name of the distribution? The mean? The standard error? C. For which sample size would I need to know that population distribution of X, teacher salaries, is normal in order to answer? ? v d. Assuming a sample size of 51, what is the probability that the sampling error is within $1000. (In other words, the sample mean is within $1000 of the true mean.) e. Assuming a sample size of 51, what is the 90th percentile for the AVERAGE teacher's salary? f. Assuming that teacher's salaries are normally distributed, what is the 90th percentile for an INDIVIDUAL teacher's salary?
a. Yes, the sampling distribution of the sample mean is a normal distribution with a mean of $52000 and a standard error of $\frac{4800}{\sqrt{17}}$.
b. Yes, the sampling distribution of the sample mean is a normal distribution with a mean of $52000 and a standard error of $\frac{4800}{\sqrt{51}}$.
c. You would need to know that the population distribution of X, teacher salaries, is normal in order to answer the questions regarding any sample size.
d. Assuming a sample size of 51, the probability that the sampling error is within $1000 is approximately 0.84 or 84%.
e. Assuming a sample size of 51, the 90th percentile for the average teacher's salary is approximately $54488.
f. Assuming that teacher's salaries are normally distributed, the 90th percentile for an individual teacher's salary is approximately $56396.
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Can someone help me with this math problem pls! #Percents
Answer: $3.64
Step-by-step explanation:
At the store, you buy four toys for $1.5, which means you pay $1.5 * 4, or $6.
Then, you calculate the sales tax, which is 6%, which means you multiply $6 by (100% + 6%), or $6*(1.06) which is $6.36.
Finally, if you hand the cashier $10, and you spent $6.36, your change is $10 - $6.36, which is $3.64.
Given the lengths of two sides of a triangle, write an equality to indicate between which two numbers the length of the third side must fall.
The sides are:
8 and 13
I will award brainliest to the first correct answer with a decent explanation
The length of the third side must fall between 8 and 13. This is because the sum of the lengths of any two sides of a triangle must always be greater than the length of the third side.
Line A has a y-intercept of 3 and is perpendicular to the line given by
y = 5x + 2.
What is the equation of line A?
Give your answer in the form y = mx + c, where m and c are integers or
fractions in their simplest forms.
Answer:
Step-by-step explanation:
The given line is y = 5x + 2. We know that any line perpendicular to this line will have a slope that is negative reciprocal of 5. The negative reciprocal of 5 is -1/5.
Line A is perpendicular to y = 5x + 2, so it has a slope of -1/5. We also know that the y-intercept of line A is 3. Therefore, the equation of line A can be written as:
y = (-1/5)x + 3
or in the form y = mx + c, where m = -1/5 and c = 3.
Here is a scale drawing of a garden. Tom wants to plant a tree in the garden according to the following rules: It must be 4 m from A and 2 m from CD. Place a cross where Tom can plant the tree. D 2.5 cm A 4 cm C B 1 cm represents 2m
Answer:
the cross is the blue color
Y=3x+3 what is the slope and y intercept
Answer:
y-intercept is (0,3) and the slope is 3
Step-by-step explanation:
Answer: the slope is 3x while 3 is the y-intercept.
Step-by-step explanation:
Bella is splitting her rectangular backyard into a garden in the shape of a trapezoid and a fish pond in the shape of a right triangle. What is the area of her garden?
The Area of Bella's garden as required to be determined in the task content is the difference of the area of the rectangular backyard and the right triangular fish pond.
What is the area of Bella's trapezoidal garden?It follows from the task content that the area of Bella's trapezoidal garden is to be determined from the given information.
Since the garden and the fish pond are from the rectangular backyard; the sum of their areas is equal to the area of the backyard.
Ultimately, the area of the garden is the difference of the area of the rectangular backyard and the right triangular fish pond.
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48 identical looking bags of lettuce were delivered to Circle J grocers. Unfortunately, 12 of these bags of lettuce are contaminated with listeria. Joe, from Joes Cafe randomly selects 4 bags of the lettuce for his cafe. Let X equal the number of the selected packets which are contaminated with listeria. a. How many possible ways are there to select the 4 out of 48 packets (order does not matter) without replacement? b. What is the probability thatX=0
c. What is the probability thatX=4? d. What is the probability thatx>2? e. What is the expected value ofX? f. What is the standard deviation ofX? g. What is the probability that X is smaller than its expected value?
h. What is the probability thatX=5?
Probability that X = 5:Since, Joe selects only 4 bags of lettuce. X can't be 5.P(X=5) = 0Hence, the probability that X = 0 is 0.3164 and the probability that X = 5 is 0.
The given problem can be solved using the concept of binomial distribution.
In the given question, there are 48 bags of lettuce out of which 12 bags are contaminated with listeria.
Joe selects 4 bags of lettuce. X is the random variable which represents the number of contaminated bags of lettuce selected by Joe. X can take values from 0 to 4. (as Joe selects only 4 bags).
Part A)Number of ways to select 4 bags of lettuce out of 48:This can be solved using the concept of combinations. The formula to calculate the number of combinations is[tex]:nCr = n! / r!(n-r)![/tex]Here, n = 48 and r = 4.
Number of ways = 48C4 = 194,580
Part B)Probability that X = 0:This can be calculated using the formula for the binomial distribution :
[tex]P(X = r) = nCr * p^r * q^(n-r)[/tex]
Here, p = probability of selecting contaminated bag = 12/48 = 0.25q = probability of selecting non-contaminated bag = 1-0.25 = 0.75Also, n = 4 and r = [tex]0P(X=0) = 4C0 * 0.25^0 * 0.75^4= 0.3164[/tex]
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when performing a hypothesis test based on a 95% confidence level, what are the chances of making a type ii error?
When performing a hypothesis test based on a 95% confidence level, the chances of making a type II error are 5%.
The process of hypothesis testing is used to determine whether or not a given statistical hypothesis is valid. The objective of this method is to determine whether the null hypothesis can be accepted or rejected based on the sample data obtained.
Hypothesis testing can be used to evaluate two hypotheses. The null hypothesis is the one that must be accepted or rejected, while the alternative hypothesis is the one that must be supported. In other words, hypothesis testing is a way of determining whether the null hypothesis is reasonable or not.
The Type II error is defined as the error that occurs when the null hypothesis is not rejected even though it is incorrect. In hypothesis testing, this type of error is referred to as a beta error or a false-negative error. The chances of making a Type II error depend on several factors, including the sample size, the level of significance, and the power of the test. When the level of significance is lowered to 0.05, the chances of making a Type II error are 5%.
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