Answer: We can begin by factoring the quadratic expression in the numerator and denominator of the left-hand side of the inequality:
x^2 - 1 = (x + 1)(x - 1)
x^2 + 5x + 4 = (x + 1)(x + 4)
Substituting these expressions into the inequality, we get:
(x + 1)(x - 1)/(x + 1)(x + 4) ≤ 0
We can simplify this expression by canceling out the common factor of (x + 1) from both the numerator and the denominator:
(x - 1)/(x + 4) ≤ 0
To solve this inequality, we can use a sign chart or test values. Here's a sign chart:
x x - 1 x + 4 (x - 1)/(x + 4)
-4 -5 0 +
-1 -2 3 -
1 0 5 0
4 3 8 +
The inequality is satisfied when (x - 1)/(x + 4) is less than or equal to 0, which occurs when x is between -4 and -1, or when x is equal to 1. Therefore, the solution to the inequality is:
-4 ≤ x < -1 or x = 1
Step-by-step explanation:
Lin plans to swim 12 laps in the pool. She has swum 9.75 laps so far.
How many laps does she have left to swim? Use y
for the number of laps that Lin has left to swim.
Lin plans to swim 12 laps and has already swum 9.75 laps, so the number of laps she has left to swim can be found by subtracting 9.75 from 12:
y = 12 - 9.75
Simplifying the right side:
y = 2.25
Therefore, Lin has 2.25 laps left to swim.
Solve x^2 + 6x + 9 = 0 by graphing. Please enter the number part of your answer only.
If your answer has two numbers, enter them like this: x = 6 and -1 should be entered as "6, -1" (no quotes).
Answer:
-3
Step-by-step explanation:
You want the graphical solution to x² +6x +9 = 0.
GraphThe graph of the expression on the left shows it has a value of 0 when x = -3.
The solution is x = -3.
__
Additional comment
A graphing calculator is very helpful when you want a graphical solution.
If you want to graph this by hand, you can rewrite it as ...
(x +3)² = 0
The graph of (x +3)² is a graph of the parent function y = x² after it has been shifted left 3 units. The graph will go through points (-5, 4), (-4, 1), (-3, 0), (-2, 1), (-1, 4). Of course the point at (-3, 0) indicates the solution is x=-3.
One computer can process a payroll in 6 hours a new computer can do it in 4 hour how long would it take both computers together
Both computers working together can process the payroll in 2.4 hours.
Let's denote the time it takes for both computers working together to process the payroll as "t".
We can use the formula:
work done = rate x time
where "work done" is the same in both cases, as they are processing the same payroll. Therefore, we can set up an equation using the rates :
1/6 + 1/4 = 1/t
We can simplify the left-hand side of the equation:
2/12 + 3/12 = 1/t
5/12 = 1/t
Multiplying both sides by 12t:
5t = 12
t = 12/5
t = 2.4
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Find the number of possibilities in each scenario
Find the number of ways 4 members from a family’s of 5 can line up for a photo shoot
There are [tex]5[/tex] ways to choose 4 members from a family of 5 to line up for a photo shoot.
What is the number of possibilities?The problem you are describing is a classic example of a combination problem, specifically choosing a certain number of items from a larger set without regard to the order in which they are arranged.
The formula to calculate the number of ways to choose "r" items from a set of "n" items without replacement is given by the combination formula, also known as "n choose r" or denoted as C(n, r). The formula is:
[tex]C(n, r) = n! / (r! \times (n - r)!)[/tex]
where "!" denotes the factorial of a number, which is the product of all positive integers up to that number.
In your case, you are choosing 4 members from a family of 5 for a photo shoot, and the order in which they line up does not matter. So you need to find C(5, 4).
Plugging the values into the formula:
[tex]C(5, 4) = 5! / (4! \times (5 - 4)!) = 5! / (4! \times 1!) = (5 \times 4 \times 3 \times 2 \times 1) / ((4 \times 3 \times 2 \times 1) \times 1) = 5[/tex]
Therefore, there are [tex]5[/tex] ways to choose 4 members from a family of 5 to line up for a photo shoot.
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The average age in a sample of 90 students at City College is 20. As a result of this sample, it can be concluded that the average age of all the students at City College:
If the sample is not truly representative, the conclusion may not accurately reflect the actual average age of all the students at the college.
Based on the given information, it can be concluded that the average age of all the students at City College is likely around 20. However, it's important to note that this conclusion is only valid if the sample of 90 students is representative of the entire student population at City College. If the sample is not truly representative, the conclusion may not accurately reflect the actual average age of all the students at the college.
The average age in a sample of 90 students at City College is 20. However, based on this sample alone, it cannot be conclusively determined that the average age of all the students at City College is also 20. This is because the sample may not be fully representative of the entire student population. More information or a larger sample would be needed to make a more accurate conclusion about the average age of all students at City College.
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If the sample of 90 students is representative of the entire student population at City College, then we can conclude that the average age of all students is approximately 20 years old.
Based on the given information, the average age in a sample of 90 students at City College is 20.
To determine if this sample can be used to conclude the average age of all students at City College, we need to consider these terms:
Sample:
A subset of a population, which in this case is the group of 90 students at City College.
Population:
The entire group of students at City College that we want to make a conclusion about.
Average (Mean) Age:
The sum of ages divided by the total number of students, in this case, 20 years.
Representativeness:
How well the sample reflects the characteristics of the entire population.
If the sample of 90 students is representative of the entire student population at City College, then we can conclude that the average age of all students is approximately 20 years old.
However, if the sample is not representative, the conclusion may not be accurate.
To make a more accurate conclusion, it is important to ensure that the sample is representative by using a larger sample size or random sampling methods.
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perform the operation form the sum 3a^2-ab-2b^2 and 2a^2 +5ab "-3b^2." subtract a^2 "-3ab-4b^2" i searched up it wont work but help me please
The result of the operation 3a²-ab-2b² and 2a² +5ab "-3b² is
4a² + 7ab - b².
What is an algebraic expression?
An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations. It may also include exponents and/or roots. Algebraic expressions are used to represent quantities and relationships between quantities in mathematical situations, often in the context of problem-solving.
Let's simplify the expressions and then perform the given operation:
3a² - ab - 2b² + 2a² + 5ab - 3b² - (a² - 3ab - 4b²)
Combining like terms within parentheses:
3a² - ab - 2b² + 2a² + 5ab - 3b² - a² + 3ab + 4b²
Combining like terms outside parentheses:
4a² + 7ab - b²
Therefore, the result of the operation is 4a² + 7ab - b².
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This is for the unit 4 lesson 7 Triangles Unit Test please help. Identify the combination of angle measures that could form a triangle
The combination of angle measures that could form a triangle are (a) 22, 140, 18 degrees and (c) 55, 67, 58 degrees.
In a triangle, the sum of the three interior angles is always equal to 180 degrees. Therefore, if the sum of the given angle measures is equal to 180 degrees, they could form a triangle.
For option a) 22 + 140 + 18 = 180, so the given angles could form a triangle.
For option b) 72 + 92 + 46 = 210, which is greater than 180, so the given angles could not form a triangle.
For option c) 55 + 67 + 58 = 180, so the given angles could form a triangle.
Therefore, the correct options are (a) 22,140,18 degrees and (c) 55,67,58 degrees
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The given question is incomplete, the complete question is:
Identify the combination of angle measures that could form a triangle
a) 22,140,18 degrees
b) 72,92,46 degrees
c) 55,67,58 degrees
2. There are 80 girls in the sophomore class of 200 students. Find the ratio of girls to non-girls.
Answer: 2 girls to 3 non-girls
Step-by-step explanation:
80 are girls
120 are boys (200-80)
80:120
simplify
2:3
Hello solve this, what is 9 x 5/7
Answer: 6 3/7
Step-by-step explanation:
9/1 x 5/7
If we multiply the numerators and denominators, we get 45/7 or 6 3/7 as a mixed number.
Answer:
[tex]\frac{45}{7}[/tex] or 6.4285
Step-by-step explanation:
First, multiply 9 and 5, which gives you 45.
9(5)=45
Then, divide 45 by 7.
45/7=6.4285
That gives you [tex]\frac{45}{7}[/tex] or 6.4285
Hope this helps!
Please help Thank you
The values of trigonometric-ratios in the given triangle whose legs are 4 and [tex]4\sqrt{3}[/tex] are:
a)sinθ=0.5
b)cosθ=0.866
c)tanθ=0.577
What is trigonometric-ratios ?
A right angle triangle has six trigonometric ratios: Sin, Cos, Tan, Cosec, Sec, and Cot. Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent are their respective acronyms. These ratios show the ratio of various sides depending on the angle selected.
Given sides of triangle: 4 and [tex]4\sqrt{3}[/tex]
hypotenuse=[tex]\sqrt{perpendicular^{2}+base^{2} }[/tex]
=[tex]\sqrt{4^{2}+\((4\sqrt{3}) ^{2} }[/tex]
=[tex]\sqrt{16+48}[/tex]
=8
a)Sin θ=[tex]\frac{side opposite to the given angle}{hypotenuse}[/tex]
Sin θ=[tex]\frac{4 }{8}[/tex]
Sin θ=[tex]\frac{1}{2}[/tex]
Sin θ=0.5
b)Cos θ=[tex]\frac{side adjacent to the given angle}{hypotenuse}[/tex]
=[tex]\frac{4\sqrt{3} }{8}[/tex]
=[tex]\frac{\sqrt{3} }{2}[/tex]
=[tex]\frac{1.732}{2}[/tex]
Cos θ=0.866
c)tan θ=[tex]\frac{side opposite to the given angle}{side adjacent to the given angle}[/tex]
=[tex]\frac{4}{4\sqrt{3} }[/tex]
=[tex]\frac{1}{\sqrt{3} }[/tex]
tan θ=0.577
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for which data frequency is seasonality not a problem? group of answer choices monthly. weekly. annual. daily. quarterly.
Seasonality may be less of a problem for annual data frequency as there may be less variation due to the longer time interval.
What is annual data frequency?Annual data frequency refers to data that is collected and reported on an annual basis. This means that the data points in the dataset represent a full year's worth of data, with one data point for each year. Annual data is often used in economic indicators, such as gross domestic product (GDP) or unemployment rates, and can provide insights into long-term trends and changes over time.
What is GDP?GDP stands for Gross Domestic Product, which is a measure of the total value of goods and services produced within a country's borders during a specific time period, typically a year. It is used as an indicator of a country's economic health and growth. GDP is calculated by adding up the total spending on consumption, investment, government spending, and net exports (exports minus imports) during the period.
According to the given informationSeasonality may still be a problem for data frequencies of monthly, weekly, daily, and quarterly as certain patterns or fluctuations may occur within each of these time intervals. Seasonality may be less of a problem for annual data frequency as there may be less variation due to the longer time interval.
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Solve for length of segment d.
= 4 cm
b = 12 cm
c = 6 cm
4. ? =
].d
Enter the segment length tha
belongs in the green box.
If two segments intersect inside
or outside a circle: ab = cd
Answer: Using the given information and the formula ab = cd, we can write:
d = (ab) / c
We are given b = 12 cm and c = 6 cm. To find ab, we can use the Pythagorean theorem:
a^2 + b^2 = c^2
where a is the unknown length we want to find. Substituting the given values, we get:
a^2 + 12^2 = 6^2
a^2 + 144 = 36
a^2 = -108 (which is not a possible solution)
This means that the given values do not form a valid triangle. Therefore, we cannot find the length of segment d using the given information.
Step-by-step explanation:
Determine whether the given set S is a subspace of the vector space V. Note: Pn(R) is the vector space of all real polynomials of degree at most n and Mn(R) is the vector space of all real n x n matrices = OA. V is the vector space of all real-valued functions defined on the interval [a, b], and S is the subset of V consisting of those functions satisfying f(a) = f(b). B. V = P5(R), and S is the subset of V P5(R) consisting of those polynomials satisfying p(1) > p(0). C. V = C3(1), and S is the subset of V consisting of those functions satisfying the differential equation y'" + 2y = x2. D. V = Mn(R), and S is the subset of all skew-symmetric matrices. VE. V = C2(I), and S is the subset of V consisting of those functions satisfying the differential equation y" – 4y' + 3y = 0. F. V = R", and S is the set of solutions to the homogeneous linear system Ax = 0 where A is a fixed m X n matrix. OG. V = R", and S is the set of vectors (x1 , X2, X3 ) in V satisfying x1 – 4x2 + x3 = 3
S is a subspace of the vector space V.
For four conditions are satisfied,
The set S is a subspace of C3(1)
The set S is a subspace of Mn(R)
The set S is a subspace of C2(I)
The set S is a subspace of [tex]R^n[/tex]
The set S is not a subspace of P5(R) because it is not closed under scalar multiplication.
If p(x) is a polynomial in S, then 2p(x) may not satisfy the condition. [tex]p(1) > p(0).[/tex]
The set S is a subspace of C3(1).
The differential equation [tex]y\prime\prime\prime + 2y = x^2[/tex] is linear and homogeneous, so the sum of two solutions is also a solution, and a constant multiple of a solution is also a solution.
S is closed under linear combinations.
The set S is a subspace of Mn(R) because it is closed under addition and scalar multiplication.
If A and B are skew-symmetric matrices, then[tex](A + B)^T = A^T + B^T = -A - B = -(A + B), so A + B[/tex]is skew-symmetric. Similarly, if c is a scalar, then [tex](cA)^T = cA^T = -cA, so c A[/tex] is skew-symmetric.
S is a subspace of C2(I) because it is closed under addition and scalar multiplication.
If y1 and y2 are solutions to[tex]y\prime\prime - 4y\prime+ 3y = 0, then y1\prime\prime - 4y\prime + 3y1 = 0[/tex] and [tex]y2\prime\prime - 4y2\prime + 3y2 = 0[/tex].
Adding these equations gives [tex](y1 + y2)\prime\prime - 4(y1 + y2)\prime + 3(y1 + y2) = 0,[/tex] so [tex]y1 + y2[/tex]is also a solution.
Similarly, if c is a scalar, then [tex](cy)\prime\prime - 4(cy)\prime + 3(cy) = c(y\prime\prime - 4y\prime+ 3y) = 0[/tex], so cy is also a solution.
The set S is a subspace of [tex]R^n[/tex]because it is the null space of a fixed matrix A.
The null space of a matrix is always closed under addition and scalar multiplication.
The set S is not a subspace of [tex]R^n[/tex]because it is not closed under addition. If (1, 1, 0) and (0, 2, 1) are in S, then their sum (1, 3, 1) is not in S because. [tex]1 - 4(3) + 1 \neq 3.[/tex]
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find the measurement of angle A and round the answer to the nearest tenth.
(Show work if you can plsss).
Answer:
40.8°
Step-by-step explanation:
SohCahToa
use tan
tan^-1(19/22)
=40.81508387
=40.8
Answer:
Step-by-step explanation:
Here,
Opposite side is 19
Adjacent side is 22
To find : The value of Angle A, that is X°.
Formula
Tan X° = Opposite side/Adjacent side
Tan X° = 19/22 = 0.863 ( approximately )
X° = Tan inverse (0.863)
X° = 40.79° ~ 40.8°
Rounding off this to nearest tenth is 41°.
Hence,
X° = 41°
That is,
Angle A is 45°.
which expressions are equivalent to 8 13 ?
The next four equivalent fractions of 8/13 are:
16/2624/3932/5240/65What are some equivalent fractions of 8/13?Equivalent fractions are fractions that represent the same value but have different numerator and denominator. To find equivalent fractions of 8/13, we can multiply both the numerator and the denominator by the same non-zero integer.
In this case, we multiplied the numerator and denominator by 2, 3, 4, and 5, respectively, to obtain the next four equivalent fractions: 16/26, 24/39, 32/52, and 40/65. These fractions have different numerators and denominators, but they are equivalent to 8/13 as they represent the same value or amount.
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Jessica wants to add a border around the edge of the solar panels to help protect them from weather events. Write the standard form expression that represents the amount of border material Jessica will need. Enter the correct answer in the box.
answer : 8c^2 + 24c - 6
The standard form expression that represents the amount of border material Jessica will need is 2L + 2W - 2x - 2y = -2B
To create this expression, we need to consider a few things. Firstly, we need to know the length and width of the solar panels. Let's say the length of the solar panel is L and the width is W. We also need to know the width of the border that Jessica wants to add. Let's call this value B.
The total amount of material needed for the border will be the sum of the material needed for the four sides of the solar panel. Each side will need a length of B, so the total length of the material needed will be 2B + 2L + 2W.
However, we can simplify this expression by putting it into standard form. Standard form expressions are written in a specific way that makes them easier to read and work with. In standard form, the expression is written as Ax + By = C, where A, B, and C are constants and x and y are variables.
To put the expression 2B + 2L + 2W into standard form, we need to group the variables together and move the constants to the other side of the equation. This gives us the expression 2L + 2W - Ax - By = -2B, where A and B are both equal to -2, and C is equal to -2B.
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Answer:
8c^2 + 24c - 6
Step-by-step explanation:
I got it right on edmentum
Can someone help with this? Find the area of the shaded region. Anything helps, thank you
Thus, the Area of shaded region for the given sector of circle is found as:
1.14 sq. cm.
Explain about the sector of circle:Two radii that meet at the centre to form a sector define a circle. The sector is the portion of the circle created by these two radii. Knowing a circle's central angle measurement and radius measurement are both crucial for solving circle-related difficulties.
Given:
radius r = 2 cminternal angle Ф = 90 degreesArea of shaded region = area of sector - area of triangle
Area of shaded region = Ф/360° * (πr²) - 1/2*base*height
Area of shaded region = 90/360° * (3.14*2²) - 1/2*2*2
Area of shaded region = 1/4*3.14*4 - 2
Area of shaded region = 3.14 - 2
Area of shaded region = 1.14 sq. cm
Thus, the Area of shaded region for the given sector of circle is found as:
1.14 sq. cm.
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in how many ways can you divide 5 people into two groups, where the first group has 2 people and the second has 3?
There are 10 ways to divide 5 people into two groups where the first group has 2 people, and the second group has 3 people.
There are two ways to divide 5 people into two groups where the first group has 2 people and the second has 3. The first way is to choose 2 people out of the 5 for the first group, which can be done in 5C2 ways, and then the remaining 3 people form the second group. The second way is to choose 3 people out of the 5 for the second group, which can be done in 5C3 ways, and then the remaining 2 people form the first group. Therefore, the total number of ways to divide 5 people into two groups with a group of 2 people and a group of 3 people is 5C2 + 5C3, which equals 10 + 10, or 20.
The formula for combinations is:
C(n, r) = n! / (r!(n-r)!)
where C(n, r) is the number of ways to choose r items from a set of n items, n! represents the factorial of n, and r! represents the factorial of r.
In this case, you want to choose 2 people from a set of 5. So, n = 5 and r = 2. Plug the values into the formula:
C(5, 2) = 5! / (2!(5-2)!)
C(5, 2) = 5! / (2!3!)
C(5, 2) = 120 / (2*6)
C(5, 2) = 120 / 12
So, there are 10 ways to divide 5 people into two groups where the first group has 2 people, and the second group has 3 people.
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Topic 7: Tangents
For questions 19-20, determine if AB is tangent to circle C.
Based on the definition of the tangent of a circle and the Pythagorean triple of a right triangle, AB is not tangent to circle C in both question 19 and 20.
What is the Tangent of a Circle?In geometry, the tangent of a circle is a line that intersects the circle at exactly one point, which is called the point of tangency. This line is perpendicular to the radius of the circle at that point. This means that it forms a right angle at that point.
19. If AB is tangent to circle C, the lengths of the triangle ABC will form a Pythagorean triple. Let's check:
4.8² + 7.2² = 12²
74.88 = 144 [not true} Therefore, AB is not tangent to circle C.
20. Also, we will have the following:
15² + 11.2² = 6.8²
350.44 = 46.24 [not true].
AB is not tangent to circle C.
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A bookstore had 90 copies of a magazine. Yesterday, it sold 1/6 of them. Today, it sold 2/5 of the remaining copies. How many copies does the bookstore still have
Therefore , the solution of the given problem of unitary method comes out to be 45 copies of the magazine are still available at the bookstore.
Definition of a unitary method.Use the tried-and-true core approach, the real variables, nor any useful information you learn from the general and detailed questions to finish the project expression. Customers may be given another chance to taste the products in response. If these improvements don't happen, we'll miss out on significant advancements in programming comprehension.
Here,
Let's figure out how many issues of the magazine are still available in the store.
Given: There were 90 copies in all when the bookstore opened.
1/6 of the total copies were sold at the bookstore yesterday.
=> 15 copies were sold yesterday = (1/6) * 90.
=> Total copies - Copies sold yesterday = 90 - 15 = 75 Remaining copies after yesterday's sale
=> 2/5 of the remaining copies were sold in the bookstore today.
30 copies were sold today, which
=> (2/5) * 75.
The quantity of copies left after today's sale equals the quantity left after yesterday's sale. - Today's sales of copies:
=> 75 - 30 = 45
45 copies of the magazine are still available at the bookstore.
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please help it’s a review question but i don’t get it
Possible translations such that the graph passes through the point (1,2) are given as follows:
Translate the graph one unit right and one unit up.Translate the graph three units right and two units down.What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.Two possible translations for the function to pass through the point (1,2) are given as follows:
Translate the graph one unit right and one unit up, considering that the function passes through the point (0, 1), hence x + 1, y + 1.Translate the graph three units right and two units down, considering that the function passes through the point (-2, 4).More can be learned about translations at brainly.com/question/28174785
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g fit the logistic regression model to predict diabetic status based on age and glucose levels. what is the odds of ratio of being diabetic for older adults compared to adults while controlling for glucose levels? round your answer to 0.01.
To calculate the odds ratio of being diabetic for older adults compared to adults while controlling for glucose levels in a logistic regression model, we exponentiate the coefficient estimate for Age. For example, if the estimate is 0.05, the odds ratio is 1.65.
To obtain the odds ratio for older adults compared to adults while controlling for glucose levels in a logistic regression model predicting diabetic status based on age and glucose levels, we would need to look at the coefficient estimate for the age variable. Let's say the logistic regression model is
logit(P(Diabetic)) = β_0 + β_1Age + β_2Glucose
where P(Diabetic) is the probability of being diabetic, Age is the age in years, and Glucose is the glucose level in mg/dL. β_1 represents the coefficient estimate for Age.
To calculate the odds ratio for older adults (e.g., those who are 10 years older than the average age in the sample) compared to adults while controlling for glucose levels, we can exponentiate the coefficient estimate for Age and round to 0.01. That is
OR = exp(β_1*10)
For example, if the coefficient estimate for Age is 0.05, then:
OR = exp(0.05*10) = 1.65
This means that for every 10-year increase in age, the odds of being diabetic compared to non-diabetic increase by a factor of 1.65 while holding glucose levels constant.
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a doctor can complete 3 examinations in 2 hours. how many examinations can the doctor complete in 4 hours? hint: use the proportion 3 exams : 2 hours :: x exams : 4 hours. 5 exams 5 exams 6 exams 6 exams 7 exams 7 exams 8 exams
Answer:
6 examinations
Step-by-step explanation:
We Know
A doctor can complete 3 examinations in 2 hours.
How many examinations can the doctor complete in 4 hours?
We see
4 hours is 2 hours times 2
We take
3 x 2 = 6 examinations
So, the doctor can complete 6 exams in 4 hours.
Complex numbers [tex]z[/tex] and [tex]w[/tex] satisfy [tex]|z|=|w|=1, |z+w|=\sqrt{2}[/tex].
What is the minimum value of [tex]P = |w-\frac{4}{z}+2(1+\frac{w}{z})i|[/tex]?
Okay, here are the steps to find the minimum value of P:
1) Given: |z|=|w|=1 (z and w are complex numbers with unit modulus)
|z+w|=sqrt(2)
Find z and w such that these conditions are satisfied.
Possible solutions:
z = 1, w = i (or vice versa)
z = i, w = 1 (or vice versa)
2) Substitute into P = |w-\frac{4}{z}+2(1+\frac{w}{z})i|
For the cases:
z = 1, w = i: P = |-1-4+2(1+i)i| = |-5+2i| = sqrt(25+4) = 5
z = i, w = 1: P = |1-\frac{4}{i}+2(1+\frac{1}{i})i| = |-3+2i| = sqrt(9+4) = 5
3) The minimum value of P is 5.
So in summary, the minimum value of
P = |w-\frac{4}{z}+2(1+\frac{w}{z})i|
is 5.
Let me know if you have any other questions!
The arrival times of vehicles at the ticket gate of a sports stadium may be assumed to be poisson with a mean of 25 veh/hr. It takes an average of 1. 5 min for the necessary tickets to be bought for occupants of each car. (a)what is the expected length of queue at the ticket gate, not including the vehicle being served? (b)what is the probability that there are no more than 5 cars at the gate, including the vehicle being served? (c)what will be the average waiting time of a vehicle?
(a) The expected length of the queue, not including the vehicle being served, is 0.625 vehicles.
(b) The probability that there are no more than 5 cars at the gate, including the vehicle being served, is approximately 0.0176.
(c) The average waiting time of a vehicle at the ticket gate is 1.5 minutes or 0.025 hours.
(a) To find the expected length of the queue at the ticket gate, we need to calculate the expected number of vehicles waiting in the queue at any given time. This can be found by using the Little's Law, which states that the expected number of customers in a stable system is equal to the arrival rate multiplied by the average time spent in the system.
In this case, the arrival rate is 25 vehicles per hour, and the average time spent in the system is the time it takes to buy the tickets, which is 1.5 minutes or 0.025 hours. Therefore, the expected number of vehicles waiting in the queue is
E[N] = λW = 25 x 0.025 = 0.625 vehicles
So the expected length of the queue, not including the vehicle being served, is 0.625 vehicles.
(b) To find the probability that there are no more than 5 cars at the gate, including the vehicle being served, we need to use the Poisson distribution with a mean of 25 vehicles per hour. Let X be the number of vehicles arriving in an hour, then X Poisson(25).
P(X ≤ 5) = ∑ P(X = k) for k = 0 to 5
= ∑ (e^(-λ) × λ^k / k!) for k = 0 to 5
= e^(-25) × (25^0 / 0!) + e^(-25) × (25^1 / 1!) + ... + e^(-25) × (25^5 / 5!)
Using a calculator or software, this probability is found to be approximately 0.0176.
(c) The average waiting time of a vehicle can be found by dividing the expected number of vehicles waiting in the queue by the arrival rate. From part (a), we know that the expected number of vehicles waiting in the queue is 0.625 vehicles. The arrival rate is 25 vehicles per hour. Therefore, the average waiting time of a vehicle is
W = E[N] / λ = 0.625 / 25 = 0.025 hours or 1.5 minutes
So the average waiting time for a vehicle at the ticket gate is 1.5 minutes.
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I will be given brainliest!!!!
Answer:2/3
Step-by-step explanation:
its the only possible answer because it needs to have a scale factor below one as A'B'C'D' is smaller than ABCD
Answer: 2/3
Step-by-step explanation:
The corresponding side of AD is A'D'.
AD = 30
A'D' = 20
Scale factor = 2/3 because AD * 2/3 = A'D'
If I'm wrong, please tell me.
The Hack family is planning a trip to a theme park next fall for nights. After much research, they have found several deals for lodging at the theme park. They have narrowed it down to three hotels: the Contemporary Resort, the Fun Times Resort, and The Princess Resort. Based on the rates in the table below, which is the best deal?
the Princess Resort is the best deal with a total cost of $657 for a four-night stay.
What is Total fixed cost?
Total fixed cost refers to the cost of all fixed assets which incur a fixed cost irrespective of the level of production in a company.
The Contemporary Resort costs $239 per night, so the total cost for four nights would be:
$239 × 4 = $956.
The Fun Times Resort costs $189 per night, so the total cost for four nights would be:
$189 × 4 = $756.
The regular cost is $219 per night, so the total cost for three nights would be:
$219 × 3 = $657. But since they get the fourth night free, the total cost for four nights would be:
$657 + $0 = $657.
Comparing the three options, the Princess Resort is the best deal with a total cost of $657 for a four-night stay.
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Which of the following phrases can be used to represent -11?
the opposite of -11
eleven greater than zero
eleven below zero
positive eleven
Thx
Answer:
Eleven below Zero
Step-by-step explanation:
Every number below zero (less than zero) is a negative number.
A triangle has two legs measuring 21 cm and 20 cm. Which of the following leg measurement will make a right triangle?
The leg measurement will make a right triangle is 21 cm.
What is hypotenous?The longest side of a right-angled triangle, i.e. the side opposite the right angle, is called the hypotenuse in geometry.
Pythagorean theorem :
If p be the length of the hypotenuse of a right-angled triangle, q and r be the lengths of the other two sides, then
p² = q² + r²
The lengths of the other two sides of the given right-angled triangle are 20 cm and 21 cm. Put these values in the above theorem to get the desired result.
Now, p² = (20)² + (21)²
= 400 + 441 = 841
i.e. p = √(841) = 29
Therefore the length of the hypotenuse is 29 cm. The right angle traingle is 21 cm.
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we wish to estimate the proportion of all college students who are working while going to school to within 4% at the 90% confidence level. we believe the true proportion is around 40%. how large a sample should we take to get the desired accuracy?
To estimate the sample size required for estimating the proportion of college students who are working while going to school with a desired accuracy of 4% at a 90% confidence level, we can use the following formula:
n = (Z^2 * p * (1-p)) / (E^2)
where:
n is the sample size
Z is the Z-score corresponding to the desired confidence level (90% confidence level corresponds to a Z-score of 1.645)
p is the estimated proportion (or expected proportion) of the population
E is the desired margin of error
Given:
Desired accuracy (E): 4% or 0.04
Confidence level (Z-score): 1.645 (corresponding to 90% confidence level)
Estimated proportion (p): 0.40 (or 40%)
Plugging the values into the formula, we get:
n = (1.645^2 * 0.40 * (1-0.40)) / (0.04^2)
n = 0.1239 / 0.0016
n ≈ 77.4375
Rounding up to the nearest whole number, the estimated sample size required to achieve the desired accuracy is 78.
So, a sample size of at least 78 college students would be needed to estimate the proportion of college students who are working while going to school with a margin of error of 4% at a 90% confidence level, assuming an estimated proportion of 40%.