Solving the system of equations, it is found that a viable time that the trains are side by side is given by:
15 seconds
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the equations are:
[tex]y=14t^2[/tex]
[tex]y=130t+1200[/tex]
They will be side by side when:
[tex]14t^2=130t+1200[/tex]
[tex]14t^2-130t-1200=0[/tex]
It's solution is a quadratic function with coefficients a = 14, b = -130, c = -1200, hence:
[tex]\Delta=(-130)^2-4(14)(-1200)=84100[/tex]
[tex]x_1=\dfrac{130+\sqrt{84100} }{28}=1.5[/tex]
[tex]x_2=\dfrac{130-\sqrt{84100} }{28}=-5.71[/tex]
Time is a non-negative measure, hence 15 seconds is correct.
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Question 24 (2 points)
Suppose a race takes place involving 15 participants. In how many different ways can
the top three finishers be arranged?
3
15
455
2730
Answer: The top three finishers can be arranged in 15 x 14 x 13 ways, since there are 15 choices for the first place, 14 choices for the second place (since one person has already been selected for first place), and 13 choices for the third place (since two people have already been selected for first and second place).
So the answer is:
15 x 14 x 13 = 2730
Therefore, the top three finishers can be arranged in 2730 different ways. Answer: 2730.
Step-by-step explanation:
Answer:
[tex]2730[/tex]
Step-by-step explanation:
We can solve this problem without using any complex formulas, though there is a formula for solving such problems
Out of the 15 participants, only one participant can be in first place but this can be any one of the participants
So choice for first place = 15 participants
Once a participant has won in the first place, there are 14 remaining participants who can come second place
For third place there are only 13 participants who can make it
The total number of ways in which top three participants can be arranged is
15 x 14 x 13 = 2730 ways
The formula is
[tex]P(n, r ) = \dfrac{n!}{(n-r)!}[/tex]
where n is the population to be considered; here n = 15
r = number of items to be considered ; here r = 3
[tex]P(n, r)[/tex] sometimes written as [tex]_nP_r[/tex] represents the number of subsets r that can be taken from a larger set n when the order of the subset matters.
using the formula we get
[tex]P(n, r ) = \dfrac{15!}{(15-3)!} = \dfrac{15!}{12!} = 15 \times \ 14 \times 13 = 2730[/tex]
For the graph, find the average rate of change on the intervals given
See attached picture
The average rate of change on the intervals [0, 3], [3, 5], [5, 7], and [7, 9] are 2, -1.5, 1, and -1.5, respectively.
What is the average rate in math?It expresses how much the function changed per unit on average during that time period. It is computed by taking the slope of the straight line connecting the interval's endpoints on the function's graph.
To calculate the average rate of change for the intervals shown in the graph, we must first determine the slope of the line connecting the endpoints of each interval.
0-3 interval:
Because the interval's endpoints are (0, 1) and (3, 7), the slope of the line connecting them is:
slope = (y change) / (x change) = (7 - 1) / (3 - 0) = 2
pauses [3, 5]:
Because the interval's endpoints are (3, 7) and (5, 4), the slope of the line connecting them is:
slope = (y change) / (x change) = (4 - 7) / (5 - 3) = -1.5
[5–7] Interval:
Because the interval's endpoints are (5, 4) and (7, 6), the slope of the line connecting them is:
slope = (y change) / (x change) = (6 - 4) / (7 - 5) = 1
Interval 7 and 9:
Because the interval's endpoints are (7, 6) and (9, 3), the slope of the line connecting them is:
slope = (y change) / (x change) = (3 - 6) / (9 - 7) = -1.5
As a result, the average rate of change on the intervals [0, 3], [3, 5], [5, 7], and [7, 9] is 2, -1.5, 1, and -1.5.
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pseudoinverse [[1,1,0,1],[1.5,0.5,0,1],[2,1,0,1],[2.5,2,0,1],[0,0,0,1],[0,0,0,0.5],[0,0,2,1],[0,0,2.5,2]]
The pseudoinverse of the given matrix is:A+ = [tex][[-2.00, 0.50, 0.00, -1.00][/tex], [ [tex]0.00, -1.00, 0.00, 1.00], [ 1.00, -0.50, 0.00, 0.00], [ 0.50, -0.50, 0.00,[/tex][tex]0.00], [ 0.00, 0.00, 0.50, 0.00], [ 0.00, 0.00, -2.00, 1.00], [ 0.00, 0.00, 0.75, -0.50], [ 0.00, 0.00, -1.50, 1.00]].[/tex]
The Moore-Penrose pseudoinverse is a tool used to solve a system of linear equations when the rank of the matrix is less than the number of columns. When a matrix has a rank that is less than the number of columns, it is said to be "singular", meaning that it has no unique solution. To solve this problem, the Moore-Penrose pseudoinverse uses a combination of inverse matrix and transpose matrix operations to calculate a solution that is as close as possible to the true solution. The pseudoinverse is defined mathematically as[tex]A+ = (A*A)^-1A*,[/tex] where A is the original matrix and A* is its transpose. The pseudoinverse of the given matrix is:A+ = [[-2.00, 0.50, 0.00, -1.00], [ 0.00, -1.00, 0.00, 1.00], [ 1.00, -0.50, 0.00, 0.00], [ 0.50, -0.50, 0.00, 0.00], [ 0.00, 0.00, 0.50, 0.00], [ 0.00, 0.00, -2.00, 1.00], [ 0.00, 0.00, 0.75, -0.50], [ 0.00, 0.00, -1.50, 1.00]].It is calculated by taking the inverse of the matrix multiplication of the transpose of the matrix and the original matrix, and then multiplying that by the original matrix transpose. This process allows for the calculation of the closest solution possible to the original set of equations given by the matrix.
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High school students across the nation compete in a financial capability challenge each year by taking a nation financial capability challenge exam(URGENT)
The standard deviation that the student would have in order to be publicly recognized is given as 1.17
How to solve for the standard deviationWe would have to assume that the students score follows a normal distribution
This is given as
X ~ (μ, σ)
(μ, σ) are the mean and the standard deviation
1 - 12 percent =
0.88 = 88 percent
using the excel function given as NORMS.INV() we would find the standard deviations
=NORM.S.INV(0.88)
= 1.17498
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A student would have to score approximately 0.89 standard deviations above the mean to be in the top 12% and be publicly recognized.
How do we calculate?we can use the empirical rule to estimate the number of standard deviations a student has to score above the mean to be in the top 12 percent, assuming it is a normal distribution
The empirical rule states that for a normal distribution:
Approximately 68% of the data falls within one standard deviation of the mean.Approximately 95% of the data falls within two standard deviations of the mean.Approximately 99.7% of the data falls within three standard deviations of the mean.we will use the complement rule since our aim is to find the number of standard deviations a student has to score above the mean to be in the top 12%.
The complement of being in the top 12% is being in the bottom 88%.
From the empirical rule, we have that 68% of the data falls within one standard deviation of the mean.
Therefore, the remaining 32% (100% - 68%) falls outside one standard deviation of the mean.
Since we want to find the number of standard deviations a student has to score above the mean to be in the bottom 88%, we can assume that the remaining 32% is split evenly between the two tails of the distribution.
Applying the z-score formula:
z = (x - μ) / σ
The z-score for a cumulative area of 0.44 is approximately -0.89 found by looking up the z-score corresponding to the cumulative area of 0.44 (half of 0.88) in a standard normal distribution table.
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Monique and Tara each make an ice-cream sundae. Monique gets 2 scoops of Cherry ice-cream and 1 scoop of Mint Chocolate Chunk ice-cream for a total of 71 g of fat. Tara has 1 scoop of Cherry and 2 scoops of Mint Chocolate Chunk for a total of 61 g of fat. How many grams of fat does 1 scoop of each type of ice cream have?
The factors in the word problem for the amount of fat in the ice cream
combination are given by the fat in each constituent.
The amount of fat in Cherry ice-cream is 27 grams.The amount of fat in the Mint Chocolate Chunk ice-cream is 17 grams.Reasons:
The given parameters are;
Let C represent the amount of fat in Cherry ice-cream, and let M represent
the amount of fat in Mint Chocolate Chunk ice-cream, we get;
2·C + M = 71...(1)
C + 2·M = 61...(2)
Multiplying equation (1) by 2 and then subtracting equation (2) from the
result gives;
2 × (2·C + M) = 2 × 71
4·C + 2·M = 142...(3)
(4·C + 2·M) - (C + 2·M) = 142 - 61
3·C = 81
[tex]C=\dfrac{81}{3} =27[/tex]
The amount of fat in Cherry ice-cream C = 27 grams
2 × 27 + M = 71
M = 71 - 2 × 27 = 17
The amount of fat in the Mint Chocolate Chunk ice-cream, M = 17 grams
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label each example with the type of variable that best represents it. labels can be used more than once.
Answer:
Step-by-step explanation:
perpendicular y= 1/2 x +4 (-8, 3)
show your work by the way
this is for normal math class 9th grade.
Answer:
To find the perpendicular line to the line y = 1/2x + 4 that passes through the point (-8, 3), we can follow these steps:
Determine the slope of the given line. The line y = 1/2x + 4 is in slope-intercept form (y = mx + b), where the slope is m = 1/2.
Find the negative reciprocal of the slope from step 1 to obtain the slope of the perpendicular line. The negative reciprocal of 1/2 is -2, so the slope of the perpendicular line is -2.
Use the point-slope form of a line (y - y1 = m(x - x1)) and plug in the slope from step 2 and the point (-8, 3) to find the equation of the perpendicular line.
y - 3 = -2(x + 8)
Simplifying this equation gives:
y = -2x - 13
Therefore, the equation of the perpendicular line passing through (-8, 3) is y = -2x - 13.
I will mark you brainiest!
What is the length of AC in the given triangle?
A) 126.6
B) 99.6
C) 66.9
D) 57.1
Answer:
We can use the Law of Cosines to find the length of side AC:
cos(A) = (b² + c² - a²) / 2bc
cos(A) = (85² + 530² - 850²) / (2 × 85 × 530)
cos(A) = -0.3589 (using a calculator)
Since the cosine of an angle is negative in the second quadrant, we have:
A = 180° - cos⁻¹(-0.3589)
A = 114.49°
Now we can use the Law of Cosines again to find the length of AC:
a² = b² + c² - 2bc cos(A)
AC² = 85² + 530² - 2 × 85 × 530 cos(114.49°)
AC ≈ 99.6
Therefore, the length of AC is approximately 99.6. Answer: (B)
the function f is defined by f of x is equal to 3 divided by the square root of x minus 2 divided by x cubed for x > 0. g
The required value of the function (f + g)(x) for given f(x) and g(x) as ( 3 / √x ) - ( 2 / x³ ) and √(5x - 7) is equals to ( 3 / √x ) - ( 2 / x³ ) + √(5x - 7).
Function f(x) is equals to,
( 3 / √x ) - ( 2 / x³ ) for all x > 0
Function g(x) is equals to,
g(x) = √(5x - 7)
To get the value of (f + g)(x),
Substitute the value of f(x) and g(x) and add the functions f(x) and g(x) together,
Sum of f(x) and g(x) is equals to,
(f + g)(x)
= f(x) + g(x)
= ( 3 / √x ) - ( 2 / x³ ) + √(5x - 7)
Therefore, value of the function (f + g)(x) is equals to ( 3 / √x ) - ( 2 / x³ ) + √(5x - 7).
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The above question is incomplete, the complete question is:
The function f is defined by f of x is equal to 3 divided by the square root of x minus 2 divided by x cubed for x > 0, g as a function of x is equal to the square root of quantity 5 x minus 7 Find (f + g)(x).
Mrs. Young has p goats and q cows on his farm. He has 23 fewer cows than goats.
What are the missing values in the table?
PLSSSS QUICK
Step-by-step explanation:
35:12
40:17
45:22
50:27
55:32
LI Annexure A shows Rhandzu's grade 11 school timetable for 2023. Learners are given 5 minutes to change from one lesson to the other. Use ANNEXURE A to answer the questions that follow. 1.1.1 Determine how l
ong the second break is. 1.1.2 How many subjects is Rhandzu doing? 1.1.3 Determine the number of days in an eight-day cycle that Rhandzu has Mathematical Literacy. Explain why it is important to schedule breaks on the time-table. 1.1.4
The answer of the given question based on determining the second break in the break is 1.1.1 The second break is from 11:25 AM to 11:40 AM, which means it is 15 minutes long , 1.1.2 Rhandzu is doing 8 subjects , Rhandzu has Mathematical Literacy on Day 3 and Day 7, which means it is a 4-day cycle.
What is Sepedi Home Language?Sepedi is Bantu language spoken in South Africa by Pedi people. It is one of the 11 official languages of South Africa and is primarily spoken in northern parts of country, like Limpopo, Gauteng, and Mpumalanga provinces.
Sepedi is also known as Sesotho sa Leboa and is closely related to Sesotho (Southern Sotho) and Setswana (Tswana). Sepedi Home Language refers to study of Sepedi as first language or mother tongue in South African schools. It is an important subject in South African education system, as it helps to preserve and promote use of indigenous languages and cultural heritage.
1.1.1 The second break is from 11:25 AM to 11:40 AM, which means it is 15 minutes long.
1.1.2 Rhandzu is doing 8 subjects, which are English Home Language, Mathematics, Life Orientation, Physical Sciences, Life Sciences, Agricultural Sciences, Mathematical Literacy, and Sepedi Home Language.
1.1.3 Rhandzu has Mathematical Literacy on Day 3 and Day 7, which means it is a 4-day cycle. Therefore, in an eight-day cycle, Rhandzu would have Mathematical Literacy on Day 3, Day 7, Day 3 again, and Day 7 again.
It is important to schedule breaks on the time-table because they allow students to rest and recharge between lessons. Breaks can also help students to stay focused and engaged during lessons by giving them time to process and reflect on what they have learned. Additionally, breaks can provide opportunities for social interaction and physical activity, which can have a positive impact on students' well-being and academic performance.
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The second break is from 11:25 AM to 11:40 AM, which means it is 15 minutes long , Rhandzu is doing 8 subjects , Rhandzu has Mathematical Literacy on Day 3 and Day 7, which means it is a 4-day cycle.
What is Sepedi Home Language?Sepedi is Bantu language spoken in South Africa by Pedi people. It is one of the 11 official languages of South Africa and is primarily spoken in northern parts of country, like Limpopo, Gauteng, and Mpumalanga provinces.
Sepedi is also known as Sesotho sa Leboa and is closely related to Sesotho (Southern Sotho) and Setswana (Tswana). Sepedi Home Language refers to study of Sepedi as first language or mother tongue in South African schools. It is an important subject in South African education system, as it helps to preserve and promote use of indigenous languages and cultural heritage.
1.1.1 The second break is from 11:25 AM to 11:40 AM, which means it is 15 minutes long.
1.1.2 Rhandzu is doing 8 subjects, which are English Home Language, Mathematics, Life Orientation, Physical Sciences, Life Sciences, Agricultural Sciences, Mathematical Literacy, and Sepedi Home Language.
1.1.3 Rhandzu has Mathematical Literacy on Day 3 and Day 7, which means it is a 4-day cycle. Therefore, in an eight-day cycle, Rhandzu would have Mathematical Literacy on Day 3, Day 7, Day 3 again, and Day 7 again.
It is important to schedule breaks on the time-table because they allow students to rest and recharge between lessons. Breaks can also help students to stay focused and engaged during lessons by giving them time to process and reflect on what they have learned. Additionally, breaks can provide opportunities for social interaction and physical activity, which can have a positive impact on students' well-being and academic performance.
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How many degrees are in 5/8 of a circle
Answer:
225 degrees
Step-by-step explanation:
It is: 5/8 of 360 = 225 degrees.
5/8 of a circle is equivalent to 225 degrees.
Given,
5/8 of a circle.
Now,
A full circle represents 360 degrees .
So,
1 complete circle = 360 degrees
Let 5/8 of a circle represents x degrees,
1 complete circle = 360 degrees
5/8 of circle = x degrees
Cross multiply,
x = 5/8 * 360
x = 225 degrees.
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CAN SOMEONE HELP WITH THIS QUESTION?✨
The red car is traveling at a pace of about speed of 56.67 feet per second along the road.
How are speed and math related?The mathematical relationship between speed, distance, and time will be explained here. A moving body's speed is the distance it covers in a given amount of time. The speed is calculated using the time in hours and the distance in kilometers per hour. If the distance is in m and the time is in seconds, the speed is m/sec.
Let x represent the distance the red automobile has traveled from where it started, and y represent the separation it has from the police car. We learn the following from the Pythagorean theorem:
[tex]x^2 + y^2 = d^2[/tex]
where d is the separation between the two vehicles.
When we divide the two sides by the passage of time, we obtain:
[tex]2x(dx/dt) + 2y(dy/dt) = 2d(dd/dt)[/tex]
Given that dy/dt = -85 ft/s, we need to get dx/dt.
The police car is also mentioned as being 50 feet off the side of the road. Hence, we can state that [tex]d = sqrt(x^2 + (y - 50)^2)[/tex].When we differentiate this phrase according to time, we get:
[tex]dd/dt = (1/2)*(x^2 + (y - 50)^2)^(-1/2)*(2x*dx/dt + 2(y - 50)*dy/dt)[/tex]
By changing the specified values, we obtain
[tex]-85 = (1/2)*sqrt(x^2 + (180 - 50)^2)^(-1/2)*(2x*dx/dt + 2(180 - 50)*(-85))[/tex]
If we condense this phrase, we get:
[tex]dx/dt = 170/3 ≈ 56.67 ft/s[/tex].
The red car is therefore traveling at a pace of about 56.67 feet per second along the road.
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I NEED THE ANSWER ASAP
PLEASSEEEE
IM BEGGING
Penelope and Artemis worked a total of 70 hours this week. Penelope worked 2 hours less than twice what Artemis worked.
1) Let P= hours Penelope worked and A= hours Artemis worked. Write a system of equations for this scenario.
2) Determine how many hours Penelope and Artemis worked.
Answer:
P + A = 70
2P = A + 2
1) P + A = 70
2P = A + 2
2) Solve the system of equations:
Subtract P from both sides of the first equation:
A = 70 - P
Substitute A for 70 - P in the second equation:
2P = (70 - P) + 2
Simplify:
2P = 72 - P
Add P to both sides of the equation:
3P = 72
Divide both sides of the equation by 3:
P = 24
Substitute P for 24 in the first equation:
A = 70 - 24
A = 46
Penelope worked 24 hours and Artemis worked 46 hours.
A major cab company in Chicago has computed its mean fare from O'Hare Airport to the Drake Hotel to be $27.87, with a standard deviation of $3.50. Based on this information, complete the following statements about the distribution of the company's fares from O'Hare Airport to the Drake Hotel.
(a) According to Chebyshev's theorem, at least __of the fares lie between 20.87 dollars and 34.87 dollars.
(b) According to Chebyshev's theorem, at least 84% of the fares lie between ____
and ____. (Round your answer to 2 decimal places.)
(c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 99.7% of the fares lie between _____ and ______.
(d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately ____ of the fares lie between 20.87 dollars and 34.87 dollars.
The percentage of fares for a cab company in Chicago that fall within certain standard deviation ranges from the mean fare from O'Hare Airport to the Drake Hotel is calculated Using Chebyshev's theorem:
What is standard deviation?
Standard deviation is a measure of the amount of variation or dispersion of a set of data values from their mean (average) value. In other words, it measures how spread out the data is from the average.
(a) According to Chebyshev's theorem, at least 75% of the fares lie between 20.87 dollars and 34.87 dollars.
(b) According to Chebyshev's theorem, at least 84% of the fares lie between $18.37 and $37.37. (Round your answer to 2 decimal places.)
(c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 99.7% of the fares lie between $14.37 and $41.37.
(d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 95% of the fares lie between 20.87 dollars and 34.87 dollars.
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a homogeneous wire is bent into the shape shown. determine the x coordinate of its centroid by direct integration. express your answer in terms of a.
The x coordinate of the centroid of the wire with y=kx^(3/2) and x and y intercept a is 0.546a. The y coordinate is 8a/5.
To find the centroid of the wire, we need to find the area and first moments of the wire, which are given by:
Area, A = ∫y dx, where x ranges from -a to a
First moment with respect to x, Mx = ∫xy dx, where x ranges from -a to a
Then the x coordinate of the centroid is given by:
xc = Mx / A
We can start by finding the area:
A = ∫y dx = ∫kx^(3/2) dx = (2/5)kx^(5/2) + C
At x = a, y = 0, so C = - (2/5)ka^(5/2)
At x = -a, y = 0, so A = 2(2/5)ka^(5/2) = (4/5)ka^(5/2)
Now we need to find the first moment with respect to x:
Mx = ∫xy dx = ∫kx^(5/2) dx = (2/7)kx^(7/2) + C'
At x = a, y = 0, so C' = - (2/7)ka^(7/2)
At x = -a, y = 0, so Mx = 0
Therefore, the x coordinate of the centroid is:
xc = Mx / A = 0 / [(4/5)ka^(5/2)] = 0
This means that the centroid lies on the y-axis. To find its y coordinate, we can use the formula:
yc = ∫x dy / A = ∫x (dy/dx) dx / A
Using the equation y = kx^(3/2), we can find dy/dx:
dy/dx = (3/2)kx^(1/2)
Substituting this into the formula for yc and simplifying, we get:
yc = (4/5)ka^(5/2) / (5/8)ka^(5/2) = (8/5)a
Therefore, the coordinates of the centroid are (0, 8/5 a), and the y coordinate is (8/5)a.
To find the x coordinate of the centroid, we need to use the formula:
xc = (1/A) ∫x y dx
We already found the expression for the area A, so we just need to evaluate the integral:
xc = (1/A) ∫x y dx = (1/A) ∫x kx^(3/2) dx
Integrating this by substitution with u = x^(1/2), we get:
xc = (2/5a^(5/2)) ∫u^4 du = (2/5a^(5/2)) (u^5/5) + C
where C is a constant of integration.
At x = a, y = 0, so u = a^(1/2) and C = -(2/25)a^(5/2).
At x = -a, y = 0, so the contribution to the integral is zero.
Therefore, the x coordinate of the centroid is:
xc = (2/5a^(5/2)) (u^5/5) - (2/25a^(5/2)) = (2/25)a(5√2 - 1)
Plugging in a = 1, we get:
xc = 0.546a
So the x coordinate of the centroid is 0.546 times the x and y intercept value a.
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_____The given question is incomplete, the complete question is given below:
a homogeneous wire is bent into the shape shown of graph y = kx^(3/2), x and y intercept is 'a'. determine the x coordinate of its centroid by direct integration. express your answer in terms of a. Also find y- coordinate.
Select the description of the graph created by the equation 3x2 – 6x + 4y – 9 = 0.
Parabola with a vertex at (1, 3) opening left.
Parabola with a vertex at (–1, –3) opening left.
Parabola with a vertex at (1, 3) opening downward.
Parabola with a vertex at (–1, –3) opening downward.
Answer is C. Parabola with a vertex at (1, 3) opening downward.
the value of the given test statistic lies between the given cutoffs -2.58 and 2.58. it falls in acceptance region.
Here the values -0.94 and 2.12 falls between the points -2.58 and 2.58. The area between is the acceptance region. So we cannot reject the null hypothesis.
The given is an example for two tailed test. A two tailed test is used to determine whether the value is greater than or less than the mean value of the population. It represents the area under both tails or sides on a normal distribution curve.
Here the value of the test statistic lies between -2.58 and 2.58. So the values less than -2.58 and greater than 2.58 fall in the rejection region, where the null hypothesis can be rejected.
a) -0.94 falls between -2.58 and 2.58. So it is in the acceptance region. So null hypothesis is accepted.
b) 2.12 lies between -2.58 and 2.58. It is also in acceptance region. So null hypothesis is accepted.
So in both cases null hypothesis cannot be rejected.
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The complete question is :
f the cutoffs for a z test are -2.58 and 2.58, determine whether you would reject or fail to reject the null hypothesis in each of the following cases and explain why:
a. z = −0.94
b. z = 2.12
In the isosceles trapezoid, what is the length of LA?
A) 15
B) 17
C) 16
Answer:
A) 15 idek
Step-by-step explanation:
A textbook store sold a combined total of 228 psychology and biology textbooks in a week. The number of psychology textbooks sold was 58 more than the number of biology textbooks sold. How many textbooks of each type were sold?
Number of psychology textbooks sold:
Number of biology textbooks sold:
The number of textbooks sold were;
Psychology textbooks : 143
Biology textbooks: 85
How to determine the valueFirst, we have to determine the algebraic expression.
Let the number of biology textbooks by y
The number of psychology textbooks be 58 + y
The total number of textbooks is 228
Now, substitute the values
58 + y + y = 228
collect the like terms
y + y = 228 - 58
add or subtract the like terns
2y = 170
Divide by the coefficient of y
y = 170/2
y = 85 textbooks
Psychology textbooks = 58 + y = 58 + 85 = 143 textbooks
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I need help with this
The line segment AB and CB are perpendicular to each other.
How to determine if a line is perpendicular?Check whether the slopes of the lines are the negative reciprocals of one another to see if they are perpendicular to one another. The steps are as follows:
Using the following formula, get the slope of the first line:slope is equal to (y-change) / (change in x)where the "change in y" refers to the difference between the y-coordinates of two points on the line, and the "change in x" refers to the difference between the x-coordinates of the same two places.Using the same formula, determine the slope of the second lineTake the first slope's negative reciprocal by turning it upside down and altering its sign. For instance, the negative reciprocal of the first line's slope of 2/3 is -3/2.Check if the second slope is equal to the negative reciprocal of the first slope. If it is, then the lines are perpendicular.Learn more about Coordinates here:
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Mr yaro left sunyani at 8:30 am. He arrived in Accraat 4.58pm . How long did the journey takes?
Answer:
4 hours and 28 minutes
How do you use the discriminant only to determine the number and type of solutions for the following quadratic equation?
To use the discriminant to determine the number and type of solutions for a quadratic equation, we simply need to calculate b² - 4ac and examine the value.
The discriminant of a quadratic equation is a value that can be used to determine the nature and number of solutions for the equation. The discriminant is found by calculating b² - 4ac, where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.
If the discriminant is positive, then the equation has two real solutions. If the discriminant is zero, then the equation has one real solution (a double root). If the discriminant is negative, then the equation has no real solutions but two complex solutions.
If it is positive, there are two real solutions; if it is zero, there is one real solution; if it is negative, there are no real solutions.
For example, consider the quadratic equation 2x² + 4x + 3 = 0. The coefficients are a = 2, b = 4, and c = 3. The discriminant is b² - 4ac = 4² - 4(2)(3) = 16 - 24 = -8. Since the discriminant is negative, the equation has no real solutions but two complex solutions.
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Question 14 (2 points)
Suppose you flip a coin and then roll a die. You record your result. What is the
probability you flip heads and roll a 6?
1/12
1/4
1/2
9/12
Answer:
1/12
Step-by-step explanation:
Assuming both the die and coin are fair, there is a 1/2 chance of flipping heads and a 1/6 chance of rolling a specific number on the die.
Multiplying, 1/2 * 1/6 is 1/12.
Hope this helps!
Rae's unpaid credit card balance was $1,603. Her APR is 28.6%. What is her new
balance after she makes one new transaction for $51? Round answer to the
hundredths place. If answer doesn't have a hundredths place then include a zero so
that it does. Use a word not a symbol for the units.
$2010.458 is her new balance after she makes one new transaction for $51.
What does a credit balance mean?
The amount that the credit card company owes you is shown as a credit balance on your billing statement. Each payment you make results in credits being added to your account.
When you return something you purchased with your credit card, you can receive an additional credit.
Credit balance = $1,603
APR = 28.6%
= 28.6% * $1,603
= 458.458
Credit balance = $1,603 + 458.458
= $2061.458
net balance = $2061.458 - 51
= $2010.458
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if you have 96 houses and you sell 1/4 of the houses you have one six remaining what are the total number houses you have left
Step-by-step explanation:
that does not make any sense at all. if you copied this correctly, then many greetings to your teacher. this, as it is written, is not possible.
you have 96 houses.
when you sell 1/4 of the houses, (= 96 × 1/4 = 24) you have 3/4 of the houses left (= 96 × 3/4 = 96 - 96 × 1/4 = 72).
so, what you have left are 3/4 of the houses. NOT 1/6.
3/4 is NOT 1/6.
1/6 of the original 96 houses is
96 × 1/6 = 96/6 = 16 houses
but if 72 (the remaining houses after the first sell of 1/4) is supposed to be 1/6, then the total number of houses at the beginning would have been
72 × 6 = 432 houses. NOT 96.
so, you see, this is again NOT possible. no matter how we twist and turn it.
Let p be the largest prime with 2010 digits. What is the smallest positive integer k such that p^2-k is divisible by 12?
For the largest prime with 2010 digits, the smallest positive integer k such that p²-k is divisible by 12 is mod 24.
First, we need to find the largest prime number with 2010 digits. We know that a prime number greater than 5 must end in either 1, 3, 7, or 9. Therefore, we can start with the number 9 followed by 2009 nines, which gives us a 2010-digit number. We then check whether this number is prime or not using a primality test.
Next, we need to find the smallest positive integer k such that p^2 - k is divisible by 12. We can rewrite this as k ≡ p² (mod 12).
Since p is odd, we know that p² ≡ 1 (mod 8), and since 12 = 3 × 4, we can use the Chinese Remainder Theorem to solve the congruence system k ≡ 1 (mod 8) and k ≡ 1 (mod 3).
Using the fact that 8 and 3 are coprime, we can solve for k using the formula k ≡ a_1N_1y_1 + a_2N_2y_2, where N_1 = 3, N_2 = 8, a_1 = 1, a_2 = 1, y_1 = [tex]3^{(-1)}[/tex] (mod 8) = 3, and y_2 = [tex]2^{(-1)}[/tex] (mod 3) = 2.
Plugging in the values, we get k ≡ 25 (mod 24).
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h=p√m2+n find the value of h when p = 3, n=20 , m=6
Answer:
We can substitute the given values of p, m, and n into the formula for h:
h = p√(m^2 + n)
h = 3√(6^2 + 20)
h = 3√(36 + 20)
h = 3√56
We can simplify this by factoring 56 into its prime factors:
h = 3√(2^3 × 7)
h = 3 × √(2^2 × 7) × √2
h = 3 × 2√7
Therefore, when p = 3, n = 20, and m = 6, the value of h is 6√7 or approximately 13.42.
6TH GRADE MATH PLS HELPPPP! TYSM
Answer:
slope is 1 1/4
Step-by-step explanation:
5/4 = 1 1/4 simplified
A penny has a diameter of 0.750 inches. What is the area of a penny to the nearest hundredth?
The area of a penny is .001m²
What exactly is a circle's area?The quantity of space contained within a circle's perimeter is known as its area. The area that the circle occupies is that which lies inside its perimeter. It is also known as the total number of square units included within that circle. In square units, the area of a circle is equal to πr²or πd²/4 where (Pi) = 22/7 or 3.14.
r stands for circle radius.
circle's diameter is given as d.
Diameter of Penny is 0.750 inches
Converting inch into meter
1 inch=0.0254 meter
0.750 inch= 0.01905 meter
Area of a circle is =π×r²
=π×(0.01905)²
=.001139≈ .001m²
A penny's surface area is.001 m² to the nearest tenth.
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