The two possible locations for the fourth vertex are (4, -4) and (-3, -1).
What is quadratic equation?
it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form.
To find the location of the fourth vertex of the square, we need to use the fact that a square has four equal sides and four right angles.
The first two vertices given are (4, 3) and (-3, 3), which lie on a horizontal line segment of length 7.
The third vertex is (-3, -4), which is 7 units away from the first two vertices and lies on a vertical line segment.
Since the square has four equal sides, the distance between the third vertex and the fourth vertex must also be 7 units.
And since the square has four right angles, the fourth vertex must be located on a vertical line passing through the first two vertices or on a horizontal line passing through the third vertex.
So, there are two possible locations for the fourth vertex:
(4, -4): This point is located 7 units below the first vertex (4, 3) on the vertical line passing through it.
(-3, -1): This point is located 7 units to the right of the third vertex (-3, -4) on the horizontal line passing through it.
Therefore, the two possible locations for the fourth vertex are (4, -4) and (-3, -1).
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A bag contains 41 U.S. quarters and nine Canadian quarters. (The coins are identical in size.) If six quarters are randomly picked from the bag, what is the probability of getting at least one Canadian quarter? (Round your answer to one decimal place.
%
Answer:
The coins are picked without replacement.
The probability of picking at least one Canadian quarter is 1 minus the probability of picking 6 U.S. quarters:
[tex]1 - ( \frac{41}{50} )( \frac{40}{49} )( \frac{39}{48} )( \frac{38}{47} )( \frac{37}{46} )( \frac{36}{45} ) [/tex]
[tex] = 1 - .28296 = .71704[/tex]
So the probability of picking at least one Canadian quarter is about 71.7%.
50 Points! Multiple choice algebra question. Shen is simplifying the expression (3x^4+4x^2) (x^3-2x^2-1). Which of the following shows the correct product. Photo attached. Thank you!
So, multiple choice algebra questions. the correct answer would be option D: [tex]3x^7 - 6x^6 - 11x^4 + 4x^5 - 4x^2[/tex].
To simplify the given expression [tex](3x^4+4x^2) (x^3-2x^2-1)[/tex], we can use the distributive property of multiplication to multiply each term of the first expression by each term of the second expression. This gives us:
[tex](3x^4+4x^2) (x^3-2x^2-1) \\= 3x^4(x^3) + 3x^4(-2x^2) + 3x^4(-1) + 4x^2(x^3) - 4x^2(2x^2) - 4x^2(1)[/tex]
Simplifying each term, we get:
[tex]= 3x^7 - 6x^6 - 3x^4 + 4x^5 - 8x^4 - 4x^2[/tex]
So, the correct answer would be option D: [tex]3x^7 - 6x^6 - 11x^4 + 4x^5 - 4x^2.[/tex]
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Prove that
sin 2x
1+ cos2x
= tan x
The statement that (sin 2x) / (1 + cos 2x) = tan x can be proven.
How to prove the mathematical statement ?To prove that (sin 2x) / (1 + cos 2x) = tan x, we will use trigonometric identities.
(sin 2x) / (1 + cos 2x)
(2sin x × cos x) / (1 + (cos²x - sin²x))
(2sin x × cos x) / (cos²x + 2sin x × cos x + sin²x)
We can rewrite the denominator using the Pythagorean identity sin²x + cos²x = 1:
(2sin x × cos x) / (1 + 2sin x × cos x)
(2sin x × cos x) × (1 - 2sin x × cos x) / (1 - (2sin x × cos x)²)
((2sin x × cos x) - (4sin²x × cos²x)) / (1 - 4sin²x × cos²x)
(2sin x - 4sin²x) / (1/cos²x - 4sin²x)
Since tan x = sin x / cos x, we can rewrite the expression:
(2tan x - 4tan²x) / (sec²x - 4tan²x)
(2tan x - 4tan²x) / (1 + tan²x - 4tan²x)
(2tan x - 4tan²x) / (1 - 3tan²x)
2tan x × (1 - 2tan²x) / (1 - 3tan²x)
tan x
So, we have proved that (sin 2x) / (1 + cos 2x) = tan x.
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PLEASE HELPPPPPP ME PLEASE
If the the a is greater than 1, compared to the parent function the C. Stretched vertically.
How to find the comparison ?The equation y = ax^2 + c represents a quadratic function where "a" is the coefficient of the x^2 term and "c" is a constant term. The parent function of this quadratic function is y = x^2.
If the equation of a quadratic function is given in the form y = ax^2 + c and "a" is greater than 1, then the graph of the function will be stretched vertically and the vertex will be shifted up or down depending on the value of "c".
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Trangle ABC has an area 25 square feet and perimeter of 65.5 feet of triangle ABC is dilated by a factor of 5/2 to create now calculate the area of trangle DEF using the scale factor
So, the area of triangle DEF is 312.5 square feet, using the scale factor of 5/2.
What is dilation?the context of mathematics and geometry, dilation is a transformation that changes the size of an object. It is a type of transformation that scales an object by a certain factor, without changing its shape or orientation.
In other words, dilation involves multiplying the coordinates of a geometric figure by a fixed constant, which results in an enlarged or reduced version of the original figure. The constant is known as the dilation factor or the scale factor, and it can be any real number greater than zero.
For example, if we dilate a circle by a scale factor of 2, every point on the circle will be moved twice as far away from the center, resulting in a new circle with a diameter twice as large as the original.
Let's start by using the formula for the perimeter of a triangle:
[tex]Perimeter of triangle ABC = AB + BC + AC = 65.5 feet[/tex]
We can also use Heron's formula to find the area of triangle ABC:
[tex]Area of triangle ABC = \sqrt(s(s-AB)(s-BC)(s-AC))[/tex]
where s is the semi perimeter of the triangle:
[tex]s = (AB + BC + AC) / 2[/tex]
We can use these equations to solve for the side lengths of triangle ABC:
[tex]AB + BC + AC = 65.5[/tex]
[tex]s = (AB + BC + AC) / 2[/tex]
[tex]25 = \sqrt(s(s-AB)(s-BC)(s-AC))[/tex]
Solving for AB, BC, and AC gives us:
AB = 15
BC = 20
AC = 30.5
Now, let's dilate triangle ABC by a factor of 5/2 to create triangle DEF. This means that each side of triangle ABC will be multiplied by 5/2 to get the corresponding side length of triangle DEF.
DE = AB * (5/2) = 37.5
EF = BC * (5/2) = 50
DF = AC * (5/2) = 76.25
Now we can use Heron's formula again to find the area of triangle DEF:
s = (DE + EF + DF) / 2 = 81.875
Area of triangle DEF = sqrt(s(s-DE) (s-EF) (s-DF)) = 312.5 square feet
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please help me in this question
Answer:
step by step explanation:
All you have to do is expand and reduce the expressions
then evaluate -2 being a root of the expressions
To do that you need to substitute -2 into the simplified expressions
if the result comes as zero then f(-2) is factor of f(x) according to the factor theorem.
Example 1.
simplify (-5x-2)(7x-4)-2x+3
if you substitute f(x) as f(-2)
then substitute x with -2
when you simply and evaluate the expression you will get that the expression is equal to -137
which means -2 isn't a root since the expression must be equal to 0
-2 is not a root
do the same for the other expressions
Can you find X? Show how did u find
Answer:
x=90°
Step-by-step explanation:
As in the angle, there is a box giving us info that x has to be 90°.
But to be sure that there is no mistake we have to do the following:
Look at all the other angles (see what kind of angles they are).Add all the angles up to 360°( in this case as the angle we are looking for is on a straight line which gives straight line=180°).Checking and comparing the two answers.So we are looking at the surroundings of angle x (which is on a straight line) we see that it is a right angle and look at the angle on the same line is a right angle too.
The equation right angle=90° helps us see that because there are two right angles on a 180° line (90°+90°+180°).
Therefore the answer is:
x=90°
In a survey, 150 shoppers were asked whether they have access to a computer at home and if they have a personal e-mail account. Their responses are summarized in the following table. E-Mail account No e-mail account Computer access at home 44 22 No computer access at home 7 77 (a) What percentage of the shoppers have an e-mail account? (b) What percentage of the shoppers do not have computer access at home?
In linear equation, 44% of the shoppers have an e-mail account and 56% of the shoppers do not have computer access at home.
What is a linear equation in mathematics?
A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.
Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.
Total number of the shoppers who were surveyed = 150
a). Number of shoppers who have an e-mail account = Shoppers who have email accounts and computer access at home + Shoppers who have email accounts but no computer access at home
= 44 + 22
= 66
Percentage of the shoppers having an e-mail account = 66/150 * 100
= 44%
b). Total number of shoppers who do not have computer access at home
= 7 + 77
= 84
Percentage of the shoppers having computer access at home
= 84/150 * 100 = 56%
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"The quotient of 30 and a number is decreased by 2." please help
This sentence relating to the quotient can be expressed mathematically as:
(30 / x) - 2
What is the explanation for the above response?
This sentence can be expressed mathematically as:
(30 / x) - 2
where x represents the unknown number.
The word "quotient" indicates that we are dividing 30 by the unknown number x. The phrase "is decreased by 2" means that we need to subtract 2 from the quotient.
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what is the range of the function in the graph?
A. 6≤e≤12
B. 40≤f≤100
C. 6≤f≤12
D. 40≤e≤100
The range of the function in the graph is 6≤e≤12. So correct option is A.
Describe Range?In mathematics, range is a term used to refer to the set of all possible output values of a function. It is the set of values that the function can take as its input varies over its entire domain. In other words, the range of a function is the set of all output values that can be obtained by evaluating the function for all possible input values.
For example, consider the function f(x) = x². The domain of this function is all real numbers, but the range is only non-negative real numbers, since x² is always non-negative for any real number x.
The range of a function can be determined by analyzing its graph, which is a visual representation of the function. The range corresponds to the set of all y-values that appear on the graph. For instance, the range of the function f(x) = sin(x) is the closed interval [-1, 1], since the sine function oscillates between -1 and 1 as its input varies over all real numbers.
Sometimes, it is useful to restrict the domain of a function in order to obtain a specific range. This process is called domain restriction or range selection. For example, the inverse function of f(x) = x² can be obtained by restricting the domain of f to non-negative real numbers, which ensures that the inverse function is also a function. The resulting function is f^-1(x) = √x, whose domain is non-negative real numbers and range is the same as the domain of f.
The range of the function in the graph is 6≤e≤12. So correct option is A.
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Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.
The shaded area covers around 0.8664 square feet of space.
What is the typical normal distribution where the standard deviation is 0 and the mean 1?The mean and standard deviation of the standard normal distribution are 0 and 1, respectively. The standard deviation shows how much a particular measurement deviates from the mean, and the standard normal distribution is centred at zero.
Using a conventional normal distribution table, we must first determine the areas to the left of z= -1.5 and z=1.5, and then subtract those two areas to determine the area of the shaded zone.
Using a standard normal distribution table, we find that the area to the left of z= -1.5 is 0.0668, and the area to the left of z=1.5 is 0.9332. As a result, the darkened region's area is:
0.9332 - 0.0668 = 0.8664
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a private student loan at 4.25%, but the rate for such a loan could be 12.59%. Under the same circumstances as Self Check 2 ($10,000 principal, no interest paid while in school) and a rate of 12.59%, what would the principal be when you make your first payment 51 months later? What are some recent examples of community change that involves a clash between different cultures that helped disadvantaged communities and the populations.?
The principal when making the first payment 51 months later on a private student loan with a principal of $10,000 and a rate of 12.59% would be $15,307.13.
What is the principal?To calculate the principal when making the first payment 51 months later on a private student loan with a principal of $10,000 and a rate of 12.59%, we first need to calculate the amount of interest that has accrued over the 51 months.
Using the formula:
Interest = Principal x Rate x Time
where Principal = $10,000,
Rate = 12.59% per year,
Time = 51/12 years (since the interest is compounded monthly):
Interest = $10,000 x 0.1259 x (51/12)
= $5,307.13
So the total amount owed after 51 months would be:
Total amount owed = Principal + Interest
= $10,000 + $5,307.13
= $15,307.13
Therefore, the principal when making the first payment 51 months later on a private student loan with a principal of $10,000 and a rate of 12.59% would be $15,307.13.
As for recent examples of community change that involves a clash between different cultures that helped disadvantaged communities and the populations, one example is the Black Lives Matter movement, which has brought attention to systemic racism and police brutality in the United States. Another example is the #MeToo movement, which has raised awareness about sexual harassment and assault and has led to changes in workplace policies and cultural attitudes toward these issues.
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nvrm i got it i am him
can u slove ASAP please
Answer:
B) 352
Step-by-step explanation:
45% = 0.45
640 x 0.45= 288
288 is how many students walked to school
So to find how many took the bus to school
640- 288= 352
What is the perimeter of the trapezoid?
A certain coin is a circle with diameter 18 mm. What is the exact area of either face of the coin in terms of pie?
Answer:
[tex]81\pi[/tex] [tex]mm^2[/tex]
Step-by-step explanation:
Let's recall the formula for the area of a circle:
[tex]A = \pi r^2[/tex]
We are given the diameter, but the formula uses the radius. Since the radius is equal to one-half of the diameter, we can find the radius by doing this:
[tex]r = \frac{1}{2}d=\\\\r=\frac{1}{2}(18)= \\\\r=9[/tex]
Now that we've found the radius is 9 mm, let's substitute the values into the formula for the area of a circle. We have:
[tex]A = \pi r^2=\\A=\pi (9^2)=\\A=\pi (81)=\\A=81\pi[/tex]
So, we've found that the exact area, in terms of pi, of either face of the coin is [tex]81\pi[/tex] [tex]mm^2[/tex].
To find the area of the coin/a circle use this equation:
(a = area, r = radius, d = diameter)
[tex]\text{a = r}^2[/tex]
So we need to do for the radius.
[tex]\text{r} = \dfrac{\text{d}}{2}[/tex]
[tex]\text{r} = \dfrac{18}{2}[/tex]
[tex]\text{r} = 9[/tex]
Then solve
[tex]\text{a = 9}^2[/tex]
[tex]\boxed{\bold{a = 81}}[/tex]
question attached
A. 5
B. 16
C. function is not defined for this value
D. 9
F(4)=9 is the value for this function.
What is piecewise function?A function that is defined by numerous smaller functions across various time intervals is known as a piecewise function. The domain of a function is the sum of all the smaller domains, and each sub-function has its own formula and domain. The input value and the function that establishes that interval determine the function's output.
The typical functional notation, which represents the body of a function as an array of functions and related subdomains, can be used to define piecewise functions. Together, these subdomains must encompass the entire domain; frequently, it is also necessary for them to be pairwise disjoint, or constitute a partition of the domain.
x=4 is bigger than or equal to 0 because it.
we use the third function definition
F(x)=x+5.
Therefore, F(4)=4+5=9.
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help with statistics
Statistics is a branch of mathematics that involves the collection, analysis, interpretation, presentation, and organization of data. It is used in a wide range of fields such as science, engineering, social sciences, business, economics, and more.
What is statistics?In statistics, data is collected through various methods such as surveys, experiments, and observations. This data is then analyzed using statistical methods to extract meaningful insights, identify patterns and relationships, and make informed decisions.
Some common statistical techniques include descriptive statistics, inferential statistics, hypothesis testing, regression analysis, and probability theory. These techniques are used to help researchers and analysts to understand and draw conclusions about data, and to test whether their conclusions are statistically significant.
Statistics has many practical applications, such as market research, medical research, quality control, risk assessment, and many others. It plays a critical role in modern society, helping individuals and organizations make informed decisions based on data-driven insights.
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find the value for each variable in simplest radical form
The values are;
1. x = 6 ,y = 6√2
2. x = 9√2, y = 18
3. x = y = 9
4. x = 12, y = 12√2
5. x = y = 4√2
6. x = y =( 3√2)/2
What trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
There are some special angles , in which 45 is part of them.
sin 45 = 1/√2
cos 45 = 1/√2
tan 45 = 1
1. x = 6 ( isosceles triangle)
y = 6 × √2 = 6√2
2. x = 9√2 ( isosceles triangle)
y = 9√2 × √2 = 9×2 = 18
3. x = 9√2/√2 = 9
x = y = 9 ( isosceles triangle)
4. x = 12 ( isosceles triangle)
y = 12×√2 = 12√2
5. x = 8/√2 = 8√2/2 = 4√2
x = y = 4√2( isosceles triangle)
6. x = 3/√2 = (3√2)/2
x = y =( 3√2)/2 ( isosceles triangle)
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Create a Truth Table for
(A ⋀ B) → C
The truth table is given above for (A ⋀ B) → C.
What is the logical statement?
A logical statement, also known as a proposition or a statement of fact, is a declarative sentence that is either true or false, but not both. It is a statement that can be evaluated based on the available information or evidence to determine its truth value. In other words, a logical statement is a statement that can be either true or false, but not both.
To create a truth table for the logical statement (A ⋀ B) → C, we need to consider all possible combinations of truth values for propositions A, B, and C.
There are 2 possible truth values (true or false) for each proposition, so there are 2³ = 8 possible combinations.
We can organize these combinations into a table as follows:
| A | B | C | (A ⋀ B) | (A ⋀ B) → C |
|---|---|---|---------|-------------|
| T | T | T | T | T |
| T | T | F | T | F |
| T | F | T | F | T |
| T | F | F | F | T |
| F | T | T | F | T |
| F | T | F | F | T |
| F | F | T | F | T |
| F | F | F | F | T |
In this table, the column labeled (A ⋀ B) represents the truth value of the conjunction of A and B (i.e., A AND B), and the column labeled (A ⋀ B) → C represents the truth value of the conditional statement (A ⋀ B) → C.
The symbol "T" represents "true" and the symbol "F" represents "false".
Hence, The truth table is given above for (A ⋀ B) → C.
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Problem 1: Find the Area and round to the nearest tenth.
Answer:
39.96
Step-by-step explanation:
the shape is a parallelogram ao the formula is base x height
A=10.8 x 3.7
A=39.97
2. Violet is baking cupcakes for a bakesale. The equation for her profit, p, based on the
number of cupcakes she sells, c, is based on the equation p = 2.75c-24. What is the best
nterpretation of the number -24.
A. How many cupcakes she sold.
B. How much it cost to buy the ingredients for the cupcakes.
C. How much each cupcake cost.
D. What her profit is.
Answer: The best interpretation of the number -24 in the equation p = 2.75c-24 is option D: What her profit is.
The equation is in slope-intercept form, where the coefficient of c (2.75) represents the profit per cupcake and the constant term (-24) represents the fixed costs or expenses that Violet incurs regardless of how many cupcakes she sells.
In this case, the constant term of -24 represents the fixed costs such as the cost of ingredients, supplies, and other expenses that Violet incurs to make the cupcakes. This cost is subtracted from the total revenue generated by selling cupcakes to determine the profit. Therefore, the number -24 represents the fixed costs or expenses and its inclusion in the equation allows us to determine Violet's profit as a function of the number of cupcakes sold.
Step-by-step explanation:
2À candy company claims that its jelly bean mix contains 15% blue jelly beans. Suppose that the candies are packaged at random in small bags containing about 200 jelly beans. What is the probability that a bag will contain more than 20% blue jelly beans?
We find that P(Z > 2.46) is roughly 0.007 using a calculator or a basic normal distribution table. The probability that a bag will contain more than 20% blue jellybeans is therefore approximately 0.007 or 0.7%.
Define probability?The probability of an event is the ratio of good outcomes to all other potential outcomes. The number of successful outcomes for an experiment with 'n' outcomes can be expressed using the symbol x.
Here in the question,
We can utilise the binomial distribution formula to resolve this issue. In a bag of 200 jelly beans, let X represent the proportion of blue jelly beans. Following that, X exhibits a binomial distribution with parameters of n = 200 and p = 0.15, where p is the likelihood of drawing a blue jellybean.
The formula for determining the likelihood of finding more than 20% blue jellybeans in a bag is:
P (X > 0.2 × 200) = P (X > 40)
Since n is large (200) and p is not too near to 0 or 1, we can utilise the usual approximation to the binomial distribution. We may determine the equivalent mean and standard deviation of the normal distribution by using the mean and variance of the binomial distribution:
μ = np = 200 × 0.15 = 30
σ = √ (np(1-p)) = √ (200 × 0.15 × (1-0.15)) = 4.07
Then, we can standardize the random variable X as:
Z = (X - μ) / σ
So, we have:
P(X > 40) = P((X - μ) / σ > (40 - μ) / σ)
= P(Z > (40 - 30) / 4.07)
= P(Z > 2.46)
We find that P(Z > 2.46) is roughly 0.007 using a calculator or a basic normal distribution table. The likelihood that a bag will contain more than 20% blue jellybeans is therefore approximately 0.007 or 0.7%.
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Find the volume of this sphere.
Use 3 for TT.
-d=6in
V ≈ [?] in ³
V = πr³
Enter
Answer: Spheres aren’t three-dimensional—they are two-dimensional. This is evident from the fact that in order to specify a point on a sphere, you only need two pieces of information, such as latitude and longitude.
If you include the interior of the sphere, this is instead called a closed ball, and that is three-dimensional. You can specify a point in the closed ball in all sorts of different ways; one of the most convenient would be latitude, longitude, and distance from the center. However, other than convenience, there is no reason to prefer one coordinate system over any other.
(This fact has nothing to do with spheres or closed balls—that is just a statement that is generally true. People who insist that “the three dimensions” are length, width, and height don’t know what they are talking about.)
Step-by-step explanation:
In the year 2000, the population of Mexico was about 100 million, and it was growing by 1.53% per year. At this growth rate, the function f(x) = 100(1.0153)x gives the population, in millions, x years after 2000. Using this model, in what year would the population reach 106 million? Round your answer to the nearest year.
Answer:
2004
Step-by-step explanation:
Question 6(Multiple Choice Worth 5 points) (Statistical Measurements LC) Which of the following is a statistical question that can result in numerical data? What is the name of your favorite pizza store? How many hours this week did you spend on homework? O How many times did you go swimming this year? How many pink erasers do the students in your class have?
The statistical question that can result in numerical data is "How many hours this week did you spend on homework?"
Identifying the statistical question that can result in numerical data?The statistical question that can result in numerical data is "How many hours this week did you spend on homework?"
This is because the question is asking for a numerical response that can be measured and counted. The other options are not statistical questions that can result in numerical data.
"What is the name of your favorite pizza store?" is a question that asks for a categorical response, "How many times did you go swimming this year?" is a question that asks for a countable response, And "How many pink erasers do the students in your class have?" is a question that asks for a discrete numerical response.Read more about statistical question at
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A large production facility uses two machines to produce a key part for its main product. Inspectors have expressed concern about the quality of the finished product. Quality-control investigation has revealed that the key part made by the two machines is defective at times. The inspectors randomly sampled 35 units of the key part from each machine. Of those produced by machine A, 5 were defective. Seven of the 35 sampled parts from machine B were defective. The production manager is interested in estimating the difference in proportions of the populations of parts that are defective between machine A and machine B. From the sample information, compute a 98% confidence interval for this difference.
The range of the 98% confidence interval for the percentage of faulty components that differ between machines A and B is about between -0.2448 and 0.1305. (rounded to 4 decimal places).
How can you figure up a confidence interval for the proportional difference?Define the populations of interest and the characteristic you want to compare (e.g., proportion of success or failure).Collect random samples from each population and record the number of occurrences of the characteristic of interest in each sample.Calculate the sample proportions ([tex]p_1 \;and \;p_2[/tex]) by dividing the number of occurrences by the sample size for each population.Calculate the standard error (SE) of the difference in proportions using the sample proportions, sample sizes, and appropriate formula (SE = [tex]\sqrt{ [(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)}[/tex], where[tex]p_1 \;and \;p_2[/tex] are the sample proportions and[tex]n_1 \;and \;n_2[/tex] are the sample sizes for the two populations, respectively).Determine the appropriate critical value from the probability distribution (e.g., standard normal distribution for large sample sizes or t-distribution for small sample sizes) based on the desired confidence level.Calculate the margin of error (ME) by multiplying the standard error by the critical value (ME = critical value * SE).Construct the confidence interval by adding and subtracting the margin of error from the sample statistic (e.g., the difference in sample proportions, or the ratio of sample proportions).Interpret the confidence interval, stating that we can be [confidence level]% confident that the true population parameter falls within the calculated interval.Given:
Sample proportion from machine A ([tex]p_1[/tex]) = 5/35 = 0.14285714285714285
Sample proportion from machine B ([tex]p_2[/tex]) = 7/35 = 0.2
Sample size from machine A ([tex]n_1[/tex]) = 35
Sample size from machine B ([tex]n_2[/tex]) = 35
Standard error (SE) = [tex]\sqrt{ [(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)}[/tex]
= [tex]\sqrt{[0.14285714285714285 * (1 - 0.14285714285714285) / 35] + [0.2 * (1 - 0.2) / 35] }[/tex]
= 0.07058061453775912 (rounded to 11 decimal places)
Margin of error (ME) = Critical value * Standard error
= 2.660 * 0.07058061453775912 (using z-score for a 98% confidence level)
= 0.18765117789861733 (rounded to 11 decimal places)
Confidence interval (CI) = Sample statistic ± Margin of error
= [tex](p_1 - p_2) \pm ME[/tex]
= (0.14285714285714285 - 0.2) ± 0.18765117789861733
= -0.05714285714285715 ± 0.18765117789861733
The 98% confidence interval for the difference in proportions of defective parts between machine A and machine B is approximately -0.2448 to 0.1305 (rounded to 4 decimal places).
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2. center (5, -6), radius 4
Answer:
(x - 5)² + (y + 6)² = 16
Step-by-step explanation:
assuming you require the equation of the circle
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
here (h, k ) = (5, - 6 ) and r = 4 , then
(x - 5)² + (y - (- 6) )² = 4² , that is
(x - 5)² + (y + 6)² = 16
Translate in two ways each of these statements into logical expressions using predcates quantifiers and logical connective first let the domain consist of the students in your class and second let it consist of all people a) everyone in your class has a cellular phone
For all x, P(x) (using universal quantifier ∀) and It is not the case that there exists an x such that ~P(x) (using negation ¬ and existential quantifier ∃)
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
Let S be the set of students in your class and P(x) be the predicate "x has a cellular phone". Then, we can represent the statement "everyone in your class has a cellular phone" as:
1. For all x in S, P(x) (using universal quantifier ∀)
2. It is not the case that there exists an x in S such that ~P(x) (using negation ¬ and existential quantifier ∃)
If we want to represent the same statement for all people, we can use the same predicate P(x) and consider the domain of all people. Then, the statement "everyone has a cellular phone" can be represented as:
For all x, P(x) (using universal quantifier ∀)
It is not the case that there exists an x such that ~P(x) (using negation ¬ and existential quantifier ∃)Let S be the set of students in your class and P(x) be the predicate "x has a cellular phone". Then, we can represent the statement "everyone in your class has a cellular phone" as:
For all x in S, P(x) (using universal quantifier ∀)
It is not the case that there exists an x in S such that ~P(x) (using negation ¬ and existential quantifier ∃)
If we want to represent the same statement for all people, we can use the same predicate P(x) and consider the domain of all people. Then, the statement "everyone has a cellular phone" can be represented as:
1. For all x, P(x) (using universal quantifier ∀)
2. It is not the case that there exists an x such that ~P(x) (using negation ¬ and existential quantifier ∃)
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Jackson had $104,292.12 in a savings account with simple interest. He had opened the
account with $80,040 exactly 3 years earlier. What was the interest rate?
Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r
is the interest rate expressed as a decimal, and t is the time in years.
Answer: Using the formula i = prt, we have:
i = (104292.12 - 80040) = 24252.12
p = 80040
t = 3
Substituting these values, we get:
24252.12 = 80040 * r * 3
Solving for r, we get:
r = 0.101 or 10.1%
Therefore, the interest rate is 10.1%.
Step-by-step explanation: