In hyperbolic geometry, the angle sum of a triangle is always less than 180 degrees.
A lune is a wedge of a sphere with angle θ, represented by L(θ) in the proof.
α, β, and γ are the three angles of the triangle.
4πr²+4area[αβγ]=2L(α)+2L(β)+2L(γ)
2(2πr²+2area[αβγ])=2(L(α)+L(β)+L(γ))
2πr²+2area[αβγ]=L(α)+L(β)+L(γ)
At this point, we need to use a theorem that states that a lune whose corner angle is θ radians has an area of 2θr².
2πr²+2area[αβγ]=2αr²+2βr²+2γr²
2πr²+2area[αβγ]=2r²(α+β+γ)
π+area[αβγ]r²=α+β+γ
At this point, it is clear that the sum of the angles is equal to π plus the area[αβγ]r² (which cannot be zero).
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(a) Write 130% as a decimal.
(a) 130% =
Answer: 1.3
Step-by-step explanation:
We know that in order to convert from percentages to decimals, we divide by 100. Therefore, 130 percent is the same as 1.3.
Answer: 1.3
Step-by-step explanation:
100% is equal to 1. Now we just have to find the value of 30%. Divide 1 by 10 and multiply by 3 to get 0.3. Since 0.3 is 30% and 1 is 100%, 130% = 1 + 0.3 = 1.3.
An easier way of converting is dividing the percentage by 100.
if trap is an isosceles trapezoid, what is the value of x?
The value of X is 22.
What is value?Value is regard that something is held to deserve, the important worth or usefullness of something.
The calculation is as follows:
In the case of an isosceles trapezoid if there is any lower base angle is supplementary to any upper base angle.
So,
6x + 2x + 4 = 180
8x + 4 = 180
8x = 176
x = 22
Therefore we can conclude that The value of X is 22.
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in which section of the graph does the actual solution to the system lie? 1 2 3 4; consider this system of inequalities. x + y โค โ3 y < which graph shows the solution for this system?; modeling with systems of linear inequalities ; consider the system of inequalities and its graph; consider the system of inequalities and its graph y x/4; a school is planning for an addition; which graph represents the system of inequalities y 34x 2y โ 1 โฅ 2x; which graph represents the solution set of the system of inequalities? (x+y 12y โฅxโ4)
The graph of the system of inequalities y ≤ –0.75x , y ≤ 3x – 2 is attached.
Actual solution of the inequalities in the graph is shown by common shaded region of both the inequalities below A(-0.533 , 0.4 ).
As shown in the question,
Given system of inequalities are :
y ≤ –0.75x
y ≤ 3x – 2
Graph of the inequalities is attached.
For first inequality :
y ≤ –0.75x
When x = 0
y ≤ 0
when y =0 ⇒ x ≤ 0
For second inequality :
y ≤ 3x – 2
x = 0⇒ y ≤ -2
when y =0 ⇒x ≥ 2/3
Actual solution by converting into equalities
y = -0.75x
Substitute in second equation
-0.75x = 3x -2
⇒ 3.75x =2
⇒ x= 0.5333
⇒ y= -0.4
Graph below ( 0.533 , -0.4 ) represents the actual solution.
Therefore, the actual solution of the attached graph of the inequalities is region below ( 0.533 , -0.4 ) common shaded region.
The complete question is :
Consider the system of inequalities and its graph. y ≤ –0.75x , y ≤ 3x – 2 In which section of the graph does the actual solution to the system lie? 1 2 3 4.
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Classify the polynomial 5x3 + 4x − 2 by degree.
A. cubic
B. constant
C. quartic
D. linear
Classifying the polynomial 5x³ + 4x − 2 by degree gives a degree of
A. cubicHow to determine the degree of the polynomialAn equation made up of variables, exponents, and coefficients along with operations and the equal sign is known as a polynomial equation.
Sums of terms of the form kxⁿ, where k is any number and n is a positive integer, make up polynomials.
The degree refers to the highest exponents which is a positive integer
examining the function the degree is 3 and referred to as cubic
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Four students were given paint supplies for an art project. The table shows the amount of paint used by each student.
Student 1 Student 2 Student 3 Student 4
seventeen twentieths 1 and one fourth 65% 0.20
Which student used the least amount of paint for their art project?
Student 1
Student 2
Student 3
Student 4
Student 4 used the least amount of paint for the art project
How to determine which student used the least amount of paint?Given:
Student 1 used seventeen twentieths => 17/20
Student 2 used 1 and one-fourth => 1 1/4 = 5/4
Student 3 used 65% = 65/100
Student 4 used 0.20 = 20/100
Since the amount of paint used for the art project has been expressed in fractions. Find the LCM:
17/20, 5/4, 65/100, 20/100
The LCM of 20, 4 and 100 is 100
Student 1: 17/20 = 85/100
Student 2: 5/4 = 125/100
Student 3: 65/100
Student 4: 20/100
Thus, student 4 used the least amount of paint
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Answer: Student 4 (d)
Step-by-step explanation:
Brainliest?
6) Pamela wants to buy a new Mercedes. The Mercedes wheel has a radius of
15", what is the area of the Mercedes wheel? (State answer to nearest tenth.)
Answer:
706.5 inches^2.
Step-by-step explanation:
The area of a circle is given by the formula A = πr^2, where A is the area of the circle, r is the radius of the circle, and π is a mathematical constant approximately equal to 3.14.
To find the area of a Mercedes wheel with a radius of 15 inches, we can substitute these values into the formula:
A = πr^2 = π(15 inches)^2 = 706.5 inches^2
Rounding to the nearest tenth, the area of the Mercedes wheel is approximately 706.5 inches^2.
A businessman borrowed P9000 from a bank to fix his car. The bank charges 7% simple interest per year.
What is the total amount that the businessman has to pay the bank after two years?
The total amount that the businessman has to pay the bank after two years is P10260
How to determine the amount to pay back at the bank?From the question, we have the following parameters that can be used in our computation:
Principal, P = P9000
Rate, r =7%
Time = 2 years
The amount to pay back is calculated using the following amount equation
A = P + PRT
Substitute the known values in the above equation, so, we have the following representation
A = 9000 + 9000 * 7% * 2
Evaluate the sum of products
A = 10260
Hence, the amount to pay back at the bank is P10260
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please I need help, only complete answers please, if you can do it in that photo the answers would help me a lot please
The z-scores of the monthly utility bills for the value of x as $60, $71 and $9 are -1.25, 0.125, and 2.25 respectively.
What is Z-score?
A Z-score helps us to understand how far is the data from the mean. It is a measure of how many times the data is above or below the mean. It is given by the formula,
Z = (X - μ)/σ
Where Z is the Z-score,
X is the data point,
μ is the mean and σ is the standard variable.
As it is given that the standard deviation of the monthly utility bills is $8, while the mean is $70. Therefore, the z-score can be written as,
A.) X= 60
z= (60- 70 )/8 = -1.25
B.) X = 71
z = ( 71 -70)/8 = 0.125
C.) X = 92
z= (92 - 70)/8 = 2.25
Hence, the z-scores of the monthly utility bills for the value of x as $60, $71 and $9 are -1.25, 0.125, and 2.25 respectively.
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Find the sixth number in this sequence. (a.) The fourth number is equal to 3x10. (b.) The second number is equal to 10+6. (c.) The Third number is halfway between the second and fourth numbers. (d.) The fifth number is 7 more than the fourth number.
The sixth number of the arithmetic progression is 44
What is arithmetic progression?Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value.
For example 3, 8 , 13, 18, 23 is an arithmetic progression with common difference of 5
The nth term of a sequence is given as a1+(n-1)d
where a1 is the first number
Therefore
a5= 37
a4= 30
a2= 16
a3 = (30+16)÷2 = 46÷2= 23
therefore common difference = 23-16 = 7
a1 = 16-7= 9
therefore a6 = fifth number + common difference
a6= 37+7= 44
therefore the sixth number is 44
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T/F alma corp. issues 1,000 shares of $10 par common stock at $14 per share. when the transaction is journalized, credit(s) are made to
Cash is debited for increasing assets and credited for increasing stockholder equity by crediting common stock and paid-in capital.
Given,
Alma corp. issues 1,000 shares of $10 par common stock at $14 per share.
We have to find the credits made to when the transaction is journalized;
The journal entry is displayed below;
Cash; 1,000 shares at $14 = 1000 × 14 = $14,000
To Common Stock ; 1,000 shares at $10 = 1000 × 10 = 10,000
To Paid in capital in excess of par value; 3,000 shares at $4 = 14,000 - 10,000 = 4,000
Being documented as the common stock's issue
Here, cash is debited because it increased assets and credited because it increased stockholder equity by purchasing common shares and paying for capital.
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Its Kumon So It Is Very Easy.
Answer: It's kumon?
Step-by-step explanation:
3. What are the slope and y-intercept of the
line described by y = 3x - 6?
A. m= -3; b = -6
C. m = -6; b=3
B. m= 3; b= -6
D. m = 6; b = -3
Answer:
Slope is 3, y-intercept is -6
Step-by-step explanation:
y=3x-6
The equation of a line is y=mx+b, so in this case,
m = 3
b = -6
Tiana is toid to carry out the following polynomial division:
(2x³+4x² - 9x -18) + (x + 5)
quotient (answer without remainder
remainder(written as a fraction)
When the polynomial (2x³+4x² - 9x -18) is divided by x+5, the quotient is 2x²-6+21 and the remainder is -123/(x+5).
What is polynomial?Polynomials are sums of k-x^n terms, where k can be any number and n can be any positive integer. 3x+2x-5, for example, is a polynomial. Polynomials are introduced. This video defines words such as degree, standard form, monomial, binomial, and trinomial. A polynomial is an equation made up of variables, constants, and exponents that are mixed using mathematical operations including addition, subtraction, multiplication, and division (No division operation by a variable).
Here,
Dividend=(2x³+4x² - 9x -18)
Divisor=(x+5)
On dividing them using long division,
quotient=2x²-6+21
remainder=-123/(x+5)
The quotient is 2x²-6+21 and remainder is -123/(x+5) for the polynomial (2x³+4x² - 9x -18) when divided by x+5.
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which of the following is equivalent to an odd function mcq
Therefore, the option (B) f(x) = [tex]x^{} +x^{3} +x^{5}[/tex] is an example of odd function in the mcq
What is function?An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). Functions are essential for building physical relationships in both math and science.
Here,
We can see ,
For (A), the function f(x)=f(x)f(x) is an even function.
For (B), f(x)=f(x), where f(x) is an unusual function.
For (C), f(x) is a function that is neither odd nor even.
For (D), f(x) is a function that is neither odd nor even.
Therefore, the option (B) is an example of odd function in the mcq
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3. The point (−5,3) is on the terminal arm of an angle θ in the standard position.
(a) Find θ
Answer:
Step-by-step explanation:
suppose man paints on a she paper 25 in wide by 15 in high. He then places this sheet on a mat so that a uniform wide strip of the mat shows all around the picture. The perimeter of the mat is 96 in How wide is the strip of the mat showing around the picture?
When the mat's perimeter is 96 inches, the strip that shows around the picture is 4 inches broad.
What is perimeter?The perimeter of a shape is the distance around its edge. The perimeter of a form is the length of its contour. To calculate the perimeter of a rectangle or square, sum the lengths of all four sides. The perimeter of a shape is the distance around its exterior. Perimeter is calculated by summing the lengths of all the sides of a form.
Here,
length of paper, l=25 inch
width of paper, w=15 inch
perimeter=96 inch
Let x be the strip of mat,
l=25+2x
w=15+2x
perimeter=2(l+w)
96=2*(25+2x+15+2x)
48=40+2x
2x=8
x=4 inch
The strip of the mat showing around the picture is 4 inch wide when the perimeter of the mat is 96 inch.
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the exponential model a=368.3e ^0.002t describes the population, a, of a country in millions, t years after 2003. use the model to determine the population of the country in 2003
the population of the country in 2003 is, 368.3 million.
What is exponential?
The exponential is an example of a mathematical function that is useful in determining if something is increasing or decreasing exponentially is the exponential function. As implied by its name, an exponential function uses exponents. But take note that an exponential function does not have a variable as its exponent and a constant as its base (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).
The population's description is provided by the exponential model a = 368.3e0.002t.
"a" denotes a nation's population in millions,
following 2003 by t years.
We must ascertain the country's population in 2003.
At 2003, t = 0.
In the exponential model above, enter t = 0.
a = 368.3e^0.002(0) (0)
a = 368.3e^0
a = 368.3
Hence, the population of the country in 2003 is, 368.3 million.
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the graph below shows two different types of plans published by a cell phone company. ryan claims that the cost of plan a and plan b differ a lot. which statement best explains why ryan was misled by the graph? a.) the scale of intervals on the horizontal axis is inconsistent. b.) the graph of plan a shows a gradual increase in price. c.) the graph of plan b shows a rapid increase in price. d.) the scale of intervals on the vertical axis is inconsistent.
Answer:
d.) the scale of intervals on the vertical axis is inconsistent.
Step-by-step explanation:
FILL IN THE BLANK. the___prompts the user to select a model, allowing the user to access the database and select data for the decision process or to set criteria for selecting such data.
The Dialog module prompts the user to select a model, allowing the user to access the database and select data for the decision process or to set criteria for selecting such data .
Given :
prompts the user to select a model, allowing the user to access the database and select data for the decision process or to set criteria for selecting such data.
Dialog module :
The dialog module provides dialog awareness for the Kamailio proxy. It's functionality is to keep track of the current dialog , to offer information about them .
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Match the equation with its graph
Y=2/5x-1
Answer:
the second one
Step-by-step explanation:
When Mara started at her current job, her employer gave her 3 days of paid vacation with a promise of 4 additional paid vacation days for each year she remains with the company to a maximum of 5 workweeks of paid vacation time.
If Mara's annual vacation time is viewed as an arithmetic sequence, give the first term and common difference?
When will she reach the maximum number of paid vacation days allowed?
linear equation
An equation with a maximum power of 1 for a variable is called a linear equation.
How to form a linear equation based on a given situation?
The total number of paid holidays is y.
Also, let x be the number of years Mara worked for the company.
4 days of fixed paid vacation. The additional number of years of paid leave is 3 days.
So, the linear equation that forms is
y = 3x + 4... (1)
Five years from now, how many days of paid vacation will she take?
Substitute the value of x = 5 into equation (i).
y = 3(5) + 4
y = 15 + 4
y = 19
Mara therefore has 19 days of paid leave after her five years of service.
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A piñata is a container filled with toys and candy and is broken open by hitting it with a stick. Sophia is trying to break the piñata. The probability that she will break the piñata on the first hit is 0.7. She will continue to hit the piñata until it breaks. If she does not break the piñata on a particular hit, the piñata is weakened and the probability that she will break it on the next hit is 0.1 greater than the probability on the previous hit. For example, if the piñata does not break on the first hit, the probability that it will break on the second hit is 0.8.
(a) Calculate the probability that Sophia docs.not break the piñata on the first hit and does break the piñata on the second hit. Let the random variable X represent the number of hits required for Sophia to break the piñata.
(b) Complete the probability distribution of X in the table below Probability of x 0.7
The probability that Sophia does not break the piñata on the first hit and does break the piñata on the second hit is of:
0.24 = 24%.
How to calculate the probability?In the context of a problem, a probability is calculated as the division of the number of desired outcomes divided by the number of total outcomes.
In the context of this problem, these probabilities are given by the percentages/proportions stated in the problem.
The probability that Sophia does not break the piñata on the first hit and does break the piñata on the second hit is calculated considering these two outcomes given as follows:
First outcome -> does not break -> 0.3 probability.Second outcome -> breaks -> 0.8 probability.The probability is calculated as the multiplication of these outcomes, as follows:
p = 0.3 x 0.8 = 0.24 = 24%.
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Question is attached
Answer:
56°
Step-by-step explanation:
the measurement of angle O is less than 90°, but not 62°, and angle O is larger than angle R, so angle O is not 28°, so the only other option less than 90° is 56°
Enter the ordered pair for the vertices for (Ry-axis o T(2,0))(QRST).
On solving the provided question, we got to know the vertices those are - Q' = (-3, 3), R' = (-5, -3), S' = (-2, -2), T' = (0, 1)
what is vertices?As kids learn about the characteristics of 3D forms, vertices, faces, and edges start to appear often in geometry. Here's what it means and how to figure out how many vertices, faces, and edges each form has. The most popular forms' edge, face, and vertex counts are also included.
[tex]The coordinates of the vertices of the quadrilateral are;[/tex]
[tex]T(-2, 1), Q(1, 3), S(0, -2), R(3, -3)[/tex]
T
The coordinates of the vertices of the quadrilateral are;
[tex]T(2, 0)QRST, gives;\\ T(2, 0)QRST→ T(-2 + 2, 1), Q(1 + 2, 3), S(0 + 2, -2), R(3 + 2, -3)\\ T(2, 0)QRST→ T(0, 1), Q(3, 3), S(2, -2), R(5, -3)\\[/tex]
For the next process R y-axis which is the reflection about the y-axis, the preimage (x, y) becomes the image (-x, y)
Therefore, we have;
[tex]R y-axis(T(0, 1), Q(3, 3), S(2, -2), R(5, -3)) = T'(0, 1), Q'(-3, 3), S'(-2, -2), R'(-5, -3)\\ From which we get (Ry-axis T(2, 0))(QRST = T'(0, 1), Q'(-3, 3), S'(-2, -2), R'(-5, -3).[/tex]
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I can’t find the answer
Answer:
C. 225m^2
Step-by-step explanation:
Let's find the area of the shaded region. There are 5 whole squares shaded. There are 8 half squares shaded. (Each pair of triangles makes a whole square.) We have 4 more whole squares.
There are a total of 9 whole squares shaded.
The length of the side of the entire shape is 25m. The entire shape is divided into 25 squares. 25/5 = 5.
Each small square has an area:
A_smallsquare
= 5×5
= 25m^2
A_shaded
= 25 × 9
= 225m^2
YodelAir operates a charter jet service out of an airport in a secluded mountain ski resort. The chief safety officer for YodelAir uses a normal distribution with a
mean of 629 m and a standard deviation of 120 m to model the takeoff distance of the company's X15 jets in wintry weather.
Use this table or the ALEKS calculator to find the percentage of takeoff distances between 467 m and 611 m according to the model. For your intermediate
computations, use four or more decimal places. Give your final answer to two decimal places (for example 98.23%).
By "standard deviation", 30.62% the percentage of takeoff distances .
How to interpret a standard deviation?
The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean.
Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.
X ~ N ( µ = 628 , σ = 80 )
P ( 464 < X < 592 ) = ?
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 464 - 628 ) / 80
Z = -2.05
Z = ( 592 - 628 ) / 80
Z = -0.45
P ( -2.05 < Z < -0.45 )
P ( 464 < X < 592 ) = P ( Z < -0.45 ) - P ( Z < -2.05 )
P ( 464 < X < 592 ) = 0.3264 - 0.0202
P ( 464 < X < 592 ) = 0.3062
= 30.62%
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The table to the right shows binned data for the percentages of high school graduates who took a national ___ in 2016 among the 50 states and the District of Columbia. Make a histogram of the data.Test Takers by State Percentage of high school graduates Number of states s 20% 2 21-40% 13 41-60% 4 61-80% 7 81-100% 25 O A. 0 B. O C. D. 30- a Number of states Number of states 0 0 100 Percentage of students 100 Percentage of students 0 100 Percentage of students 0- 0 100 Percentage of students
Number of states , 100 Percentage of students 0- 0 100 Percentage of students 20 21- 40 41- 60 61- 80 81- 100
1. Draw a horizontal axis with percentages of students (0 - 100%) marked along the axis.
2. Draw a vertical axis with number of states (0 - 25) marked along the axis.
3. Divide the horizontal axis into sections, with each section corresponding to one of the percentage ranges in the table (20%, 21-40%, 41-60%, 61-80%, 81-100%).
4. For each section, draw a rectangle with a height that corresponds to the number of states in that range. For example, for the 81-100% section, the rectangle should have a height of 25.
5. Label each rectangle with the corresponding percentage range.
The final result should be a histogram that shows the percentage of high school graduates who took a national test in 2016 among the 50 states and the District of Columbia.
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Assume this year's flu vaccine has a 80% chance of being effective. If the vaccine is given to 337 randomly selected people, answer the following.
a) The wording for the random variable is given as follows:
n X = the number of 337 randomly selected people who get the vaccine and do not get the flu;
b) The symbol is: n = 337.
c) The symbol is: p = 0.8.
d) P(X = 265) = 0.0426.
e) P(X < 265) = 0.2451.
f) P(X > 265) = 0.7123.
g) P(X = 268) = 0.0545.
h) P(X < 268) = 0.3859.
i) P(X > 268) = 0.5596.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].The parameters for the binomial distribution in this problem are given as follows:
n = 337, p = 0.8.
Hence the mean and the standard deviation for the approximation are given as follows:
[tex]\mu = 337 \times 0.8 = 269.6[/tex][tex]\sigma = \sqrt{337 \times 0.8 \times 0.2} = 7.34[/tex]Using continuity correction, the probability that exactly 265 people do not get the flu is the p-value of Z when X = 265.5 subtracted by the p-value of Z when X = 264.5.
X = 265.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (265.5 - 269.6)/7.34
Z = -0.56
Z = -0.56 has a p-value of 0.2877.
X = 264.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (264.5 - 269.6)/7.34
Z = -0.69
Z = -0.69 has a p-value of 0.2451.
Hence:
0.2877 - 0.2451 = 0.0426.
Then:
e) P(X < 265) = 0.2451 -> p-value of Z when X = 264.5.
f) P(X > 265) = 1 - 0.2877 = 0.7123 -> one subtracted by the p-value of Z when X = 265.5.
For exactly 268, we have the same logic as follows:
X = 265.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (268.5 - 269.6)/7.34
Z = -0.15
Z = -0.15 has a p-value of 0.4404.
X = 267.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (267.5 - 269.6)/7.34
Z = -0.29
Z = -0.29 has a p-value of 0.3859.
Hence:
0.4404 - 0.3859 = 0.0545.
Then:
h) P(X < 268) = 0.3859 -> p-value of Z when X = 267.5.
i) P(X > 268) = 1 - 0.4404 = 0.5596.
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2.
Possible choices for correct answer:
a.
Using linear first order method, solve the following IVP:
(x(xy'-1) In(x) = 2y,
y(e) = 0.
b.
C.
d. None of the above
y=(ln(x)-1)²-In(x)
y=(In(x)-1)²
y=(In(x))²-In(x)
The IVP has only one solution with the initial condition y(0)=1 which corresponds to C=2
How to use linear first order method?You should understand that the square root of a number y is a non-negative number.
To this effect, take C = -2 - 1/2In(1+x) + c/2 and this is a negative value in the neighborhood of x=0
On the other hand, the square root of y(x) = -1/2In(1+x)-2)²
⇒√y(x) = -1/2In(1+x) -2.
This is also non-negative in the neighborhood
Note that √y(x) = 1/2In(1+x) +2
And y(x) is not a solution of the original IVP
In conclusion, The IVP has only one solution with the initial condition y(0)=1 which corresponds to C=2
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A national businessman magazine reports that the mean age of retirement for women executives is 61.0. A women’s rights organization believes that this value does not accurately depict the current trend in retirement. to test this the group pulled a simple random sample of 95 recently retired will make executives and found that they have a mean age of retirement at 61.5 and the standard deviation is 2.5 years. is there is sufficient evidence of support the organization belief at the a=0.05 significance level?
P-value >= 0.05 and adequate evidence supporting the organization's opinion at the a=0.05 significance level prevent the null hypothesis from being rejected.
What is null hypothesis ?A common statistical theory called the null hypothesis asserts that there is no statistical relationship or significance between two sets of observed data and measured events for a given single observed variable.
The alternative and null hypotheses are listed below. μ = 61
61 Alternative Hypothesis
Rejection Area
For = 0.05, this test has two tails.
Z has a critical value between -1.96 and 1.96.
Reject H0 thus if z -1.96 or z > 1.96
The test statistic is z = (xbar - mu)/(sigma/sqrt(n)) z = (61.5 - 61)/(2.5/sqrt(95)) z = 1.95.
P-value P-value for the method is 0.0512.
Failure to reject the null hypothesis because P-value >= 0.05.
Approach to the Rejection Zone
Failure to reject the null hypothesis because the test statistic z is within the crucial value range.
P-value >= 0.05 and adequate evidence supporting the organization's opinion at the a=0.05 significance level prevent the null hypothesis from being rejected.
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