Write the equation of a line perpendicular to y=-2x+1 that passes through the point (-4,3)
Answer:
A line that is perpendicular to the line y=-2x+1 will have a slope that is the negative reciprocal of -2, which is 1/2.
The equation of a line in point-slope form is:
y - y1 = m(x - x1)
Where m is the slope of the line, and (x1, y1) is a point on the line.
Given that the point (-4,3) lies on the line, we can substitute those values for x1 and y1:
y - 3 = 1/2(x + 4)
Which is the equation of a line that is perpendicular to y=-2x+1 that passes through the point (-4,3).
Alternatively, you can also write the equation of a line in slope-intercept form y = mx + b,
The slope of a line perpendicular to y=-2x+1 is 1/2, therefore m = 1/2
We can substitute the point (-4,3) in the equation y = mx + b,
3 = (1/2)(-4) + b
b = 3.5
Therefore the equation of the line is y = 1/2x + 3.5
Suppose a university has only one women's softball scholarship remaining for the coming year. The final two players that the university is considering are Allison Fealey and Emily Janson. The coaching staff has concluded that the speed and defensive skills are virtually identical for the two players, and that the final decision will be based on which player has the best batting average. Crosstabulations of each player's batting performance in their junior and senior years of high school are as follows.
Outcome Allison Fealey
Junior Senior
Hit 15 79
No Hit 25 175
Total At-Bats 40 254
Outcome Emily Janson
Junior Senior
Hit 74 35
No Hit 130 85
Total At-Bats 204 120
A player's batting average is computed by dividing the number of hits a player has by the total number of at-bats. Batting averages are represented as a decimal number with three places after the decimal. (Round your answers to three decimal places.)
(a) Calculate the batting average for each player in her junior year.
Allison Fealey ___
Emily Janson ___
Calculate the batting average of each player in her senior year.
Allison Fealey ___
Emily Janson ___
Using this analysis, which player should be awarded the scholarship? Explain.
Because ---Select--- (Allison Fealey)? (Emily Janson)? had the higher batting average in both her junior year and senior year, ---Select--- (Allison Fealey)? (Emily Janson)? should receive the scholarship offer.
b) Combine or aggregate the data for the junior and senior years into one crosstabulation.
Outcome Player
Fealey Janson
Hit No Hit Total At-Bats Calculate each player's batting average for the combined two years. (Round your answers to three decimal places.)
Allison Fealey ___
Emily Janson ___
Using this analysis, which player should be awarded the scholarship? Explain.
Because ---Select--- (Allison Fealey)? (Emily Janson)? has the higher batting average over the combined junior and senior years, ---Select--- (Allison Fealey)? (Emily Janson)? should receive the scholarship offer.
c) Are the recommendations you made in parts (a) and (b) consistent? Explain any apparent inconsistencies.
The recommendations in parts (a) and (b) ---Select--- (are)? (are not consistent)?. This is an example of ---Select--- (crosstabulation rule)? (aggregation rule)? (conclusions paradox)? (Simpson's Paradox)?. It shows that in interpreting the results based upon separate or un-aggregated crosstabulations, the conclusion can be ---Select--- (reversed)? (the same)? when the crosstabulations are grouped or aggregated.
Emily Janson should receive the scholarship offer because she has the higher batting average over the combined junior and senior years.
The batting average of a player is calculated by dividing the number of hits they have by the total number of at-bats. This can be expressed as a formula: Batting Average = H/AB.
For Allison Fealey, her junior year batting average can be calculated by dividing the number of hits (15) by the total number of at-bats (40), which is 0.375. Emily Janson’s junior year batting average can be calculated by dividing the number of hits (74) by the total number of at-bats (204), which is 0.363
For Allison Fealey, her senior year batting average can be calculated by dividing the number of hits (79) by the total number of at-bats (254), which is 0.310. Emily Janson’s senior year batting average can be calculated by dividing the number of hits (35) by the total number of at-bats (120), which is 0.292.
When the data from the junior and senior years were combined and aggregated, Allison Fealey’s combined two-year batting average can be calculated by dividing the number of hits (94) by the total number of at-bats (294), which is 0.320. Emily Janson’s combined two-year batting average can be calculated by dividing the number of hits (109) by the total number of at-bats (324), which is 0.336.
Based on this analysis, Emily Janson should receive the scholarship offer because she has the higher batting average over the combined junior and senior years.
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solve for x in the logarithmic function f(x)= 3-4 In (x-2)
Answer: In order to solve for x, we will have to use the logarithmic properties to isolate x.
f(x) = 3 - 4 In (x-2)
To solve for x, we will have to get x alone on one side of the equation by using the logarithmic property that logb(a^c) = c*logb(a).
4 In (x-2) = 3
In (x-2) = 3/4
To find x, we will raise e to the power of both sides
x-2 = e^(3/4)
x = e^(3/4) + 2
So the solution of x is e^(3/4) + 2
It's important to notice that the natural logarithm (ln) and log base e (In) are same and the solution is valid for both.
Step-by-step explanation:
3a-5b when a= -3and b= -2
The numerical value of the expression 3a - 5b when a = -3 and b = -2 is 1.
What is the numerical value of the given expression?Given the expression in the question;
3a - 5b
a = -3b = -2
To determine the value of the expression, replace a with -3 and b with -2 for all occurrence of a and b in the expression.
3a - 5b
Plug in a = -3
3( -3 ) - 5b
Plug in b = -2
3( -3 ) - 5( -2 )
-9 -+ 10
10 - 9
Subtract 9 from 10
1
Therefore, the value of the expression is 1.
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1) What are the three most important concepts to remember for the test?
2) What mistake(s) did you make, and what was your misunderstanding?
Submit a pdf for each annotated response template.
The evaluation of the velocity function, v(t) = cos((π/6)·t) for the interval 0 ≤ t ≤ 12, th obtain the position and acceleration is as follows;
(a) The particle is moving to the left when 3 < t < 9
(b) The total distance is; [tex]\int\limits^6_0 {cos(\frac{\pi}{6}\cdot t) } \, dt[/tex]
(c) a(t) ≈ -0.453
(d) x(4) ≈ -0.346
What is the acceleration of an object?Acceleration is the rate at which the velocity of the object changes.
The function for the velocity of the particle is presented as follows;
v(t) = cos((π/6)·t)
The position of the particle at time, t = 0 is x = -2
(a) When the particle is moving to the left, the velocity is negative
The value of cos(θ) is negative for π/2 < θ < 1.5·π
The range of values of θ = ((π/6)·t), for 0 ≤ t ≤ 2, are;
((π/6) × 0) ≤ θ ≤ ((π/6) × 12), from which we get;
0 ≤ θ ≤ (2·π)
When π/2 = (π/6)·t, we get;
t = (π/2)/(π/6) = 3
When 1.5·π = (π/6)·t, we get;
t = (1.5·π)/(π/6) = 9
The particle is moving to the left between time t = 3 and time t = 9, which can be expressed as follows;
The particle is moving to the left in the interval; 3 < t < 9(b) The total distance traveled by the particle from time t = 0 to time t = 6 is presented using the definite integral as follows;
Distance traveled = [tex]\int\limits^6_0 {cos(\frac{\pi}{6}\cdot t) } \, dt[/tex](c) Acceleration, a, is the rate of change of the velocity, therefore, the acceleration is the derivative of the velocity function, which can be obtained as follows;
[tex]a(t) =\frac{d}{dt} {cos(\frac{\pi}{6}\cdot t) } = -\frac{\pi}{6} \cdot sin(\frac{\pi}{6} \cdot t)[/tex]
[tex]a(t) = -\frac{\pi}{6} \cdot sin(\frac{\pi}{6} \cdot t)[/tex]
At time t = 4, we get;
[tex]a(4) = -\frac{\pi}{6} \cdot sin(\frac{\pi}{6} \times 4) = -\frac{\sqrt{3} \cdot \pi}{12}[/tex]
The acceleration of the particle at time t = 4 is; -(√3)·π/(12) ≈ -0.453(d) The position of the particle at time t = 4, can be obtained by adding the the position of the particle at time t = 4 to the total distance covered between time t = 0 and time t = 4 as follows;
[tex]\int\limits^4_0 {cos(\frac{\pi}{6}\cdot t) } \, dt =[ \frac{6}{\pi}\cdot {sin(\frac{\pi}{6}\cdot t) }]^4_0[/tex]
[tex][ \frac{6}{\pi}\cdot {sin(\frac{\pi}{6}\cdot t) }]^4_0 = [ \frac{6}{\pi}\cdot {sin(\frac{\pi}{6}\times 4) }] - [ \frac{6}{\pi}\cdot {sin(\frac{\pi}{6}\times 0) }]=\frac{3\cdot \sqrt{3} }{\pi}[/tex]
[tex]\int\limits^4_0 {cos(\frac{\pi}{6}\cdot t) } \, dt = \frac{3\cdot \sqrt{3} }{\pi}[/tex]
The position of the particle at t = 4 is therefore;
[tex]x = -2 + \frac{3\cdot \sqrt{3} }{\pi} \approx -0.346[/tex]Learn more about definite integrals here: https://brainly.com/question/8388817
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After measuring a set of individuals, a researcher finds that Bob's score is three times greater than Jane's score. These measurements must come from a(n) ___ scale.a. nominal b. interval C. ratio d. ordinal
After measuring a set of individuals, a researcher finds that Bob's score is three times greater than Jane's score. These measurements must come from a ratio scale
A ratio scale is a type of measurement scale that allows for the comparison of two or more values by using division. After measuring a set of individuals, a researcher finds that Bob's score is three times greater than Jane's score.
In this case, the researcher is comparing Bob's score to Jane's score, and the comparison involves division (Bob's score is three times greater than Jane's score).
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Simplify 8 - (-5) - 4(-7)
Answer:
41Step-by-step explanation:
8 - (-5) - 4(-7)
8- (-5) - (-28)
8 + 5 + 28
13 + 28
41
Answer:
8 - (-5) - 4(-7) = 41
Step-by-step explanation:
Given problem,
→ 8 - (-5) - 4(-7)
Let's solve the problem,
→ 8 - (-5) - 4(-7)
→ 8 + 5 - (4 × -7)
→ 13 - (-28)
→ 13 + 28
→ 41 => final answer
Hence, the answer is 41.
the purpose of the following exercises is to familiarize you with the system you will be using for the rest of your course. these exercises are not intended to teach or test your knowledge of any specific subject material. therefore, you will not be penalized for using hints or submitting incorrect answers. part a (figure 1) (the link above tells you that this part has an illustration.) how many months of the year have 28 days?
Every month of the year has
A study in the state of Georgia was conducted to determine the percentage of all community college students who have taken at least one online class. 1500 community college students were contacted and asked if they had taken at least one online class during their time at their community college. These responses were then used to estimate the percentage of all community college students who have taken at least one online class. Identify the population of interest in this study.
the response (Yes/No) to the question, "Have you taken at least one online class?"
the 1500 community college students contacted
the number of online classes a student has taken
all community college students in the state of Georgia
The correct answer is qualitative data, quantitative data.
Qualitative data is a type of data that describes the characteristics or attributes of a phenomenon but does not involve numbers or measurements. It is used to describe or understand the characteristics of a particular group or phenomenon.
This type of data is often used in the social sciences, such as sociology, anthropology, and psychology, but can also be used in other fields such as marketing and advertising.
Qualitative data can be analyzed in different ways, such as content analysis, thematic analysis, discourse analysis, and interpretive analysis.
Quantitative data is a type of data that involves numbers or measurements. It is used to describe or understand the characteristics of a particular group or phenomenon using numerical values or statistics.
This type of data is often used in the natural sciences, such as physics, chemistry, and biology, but can also be used in other fields such as economics, business, and engineering.
Therefore, The correct answer is qualitative data, quantitative data.
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CHOSE THE LETTER of the correct equation for the graph PLS HELP
By equation for the graph y = 2 cos (x − π 12) this we get
x f (x)
π /2 2
π 0
3π / 2 -2
2π 0
5π / 2 2.
How to find the calculation?y = 2 cos (x − π 12)
Find the parameters necessary to calculate the amplitude, period, phase shift, and vertical shift using the formula a cos (b x c ) + d.
a = 2
b= 1
c = π /2
d = 0
locate | a |'s amplitude.
Dimension: 2
Calculate the duration of 2 cos (x 2 ).
2 | b | can be used to determine the period of the function.
2π / |b|
In the formula for the period, swap out b for 1.
2π / |1 |
What separates a number from zero is its absolute value. 0 to 1 are separated by a distance of 1 and 2 units.
1
Subtract 2 from 1 to get 2.
Use the cb formula to get the phase shift.
From c b, one may get the phase shift of the function.
c b: Phase Shift
The equation for phase shift should have the values of c and b changed.
Changing phases: 2 1
Take 2 and divide it by 1.
Shift in Phase: 2
Name the trigonometric function's attributes.
Two-second period with amplitude two
Phase Change: 2 (rightward by 2).
Vertical Shift: null
To graph, choose a few points.
To continue, tap the screen.
x f ( x )
π /2 2
π 0
3π /2 − 2
2 π 0
5π / 2 2
Amplitude, period, vertical shift, phase shift, and points can all be used to graph the trig function.
Dimension: 2
Two (2) years
Phase Change: 2 (rightward by 2).
Vertical Shift: null
x f (x)
π /2 2
π 0
3π / 2 -2
2π 0
5π / 2 2.
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En una granja el 15% de los animales son vacas. Sabiendo que hay 30 vacas ¿Cual es el número total de animales?
The total number of animals in the farm is given by 200
What are percentages?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”
Given here: The number of cows is 30 and they form 15% of the total animals on the farm.
Let the number of animals in the form be x then
15% of x=30
x=30×100/15
x=200
Hence, The total number of animals in the farm is given by 200
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When given two points and asked to find the equation of the line in slope-intercept form, what are the correct steps? Place a number next to the step to put them in order.
When given two points and asked to find the equation of the line in slope-intercept form, the correct steps, the correct order is 2 , 1 , 4 , 3.
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
here, we have,
Given that,
given two points and asked to find the equation of the line in slope-intercept form.
Find that,
what are the correct steps? Place a number next to the step to put them in order.
Explanation:
to find the equation of the line in slope intercept form form given two points.
step 1 :
find the slope.
step 2
write equation in point slope form
step 3.
pick a point form the given points , substitue it into the point slope form
step 4.
write the equation in slope intercept form by simplifying
Final Answer.
Hence , the correct order is 2 , 1 , 4 , 3.
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first drop down options are
$4,519.50
$4,680.00
$5,525.25
$8,580.00
second drop down options are
11.6%
12.0%
14.2%
22.0%
The given tax rates are as follows: Drew’s tax due is 4,519.50 and his effective tax rate is 11.6%. Option A is correct.
How is the total tax calculated?You will determine your total taxable income based on your tax slab by subtracting all eligible deductions from the gross taxable income. Senior citizens pay a different slab rate.
Taxable income :An income tax system's tax base is referred to as taxable income. That is, the amount of income that was subject to taxation by the government. In most cases, some or all of the income is included, and expenses and other deductions reduce it.
Single Taxpayers: Income Brackets
Tax Income Rate Bracket Tax Owed
0 to 9,525 10% 10% of taxable income
9,526 to38,700 12% $952.50 plus 12% of 38,700 the excess over
$38,701 to 82,500 22 % $4,453.50 plus 22% of 38,701 the excess over
82,501 to 157,500 24% $14,089.50 plus 24% of the excess over
157,500
157,501 to 200,000 32% $ 32089.50 plus 32% of the excess over
200,001 to 500,000 35% 45,689.50 plus 35% of excess over
500,000 > 37% $150,689.50 plus 37% of 500,000 of the
excess over
The taxable income lies in the tax rate range of $38,701 to 82,500.
Therefore the tax would be :
$4,453.50 + 22% of (39,000-38,701=299)
= $4,453.50 + 22% of 299
= $4,453.50 + 65.78
= $ 4519.28
The taxable income lies in the tax rate range of $38,701 to 82,500. Due and effective tax rate is $4,453.50 plus 22% of 38,701 the excess over.
The calculated tax is $ 4519.28
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the graphs of f and g are given. use them to evaluate each limit, if it exists. (if an answer does not exist, enter dne.)
The limit will be ,lim x→2 [f(x) + g(x)] = 2 + 0 = 2
In Mathematics, a limit is defined as a value that a function approaches the output for the given input values. Limits are important in calculus and mathematical analysis and used to define integrals, derivatives, and continuity. It is used in the analysis process, and it always concerns about the behaviour of the function at a particular point. The limit of a sequence is further generalized in the concept of the limit of a topological net and related to the limit and direct limit in theory category. Generally, the integrals are classified into two types namely, definite and indefinite integrals. For definite integrals, the upper limit and lower limits are defined properly. Whereas in indefinite the integrals are expressed without limits, and it will have an arbitrary constant while integrating the function.
lim x→2 means what is the value of y as x approaches 2 from the left side and the right side - they must be the same value for the limit to exist. "Approaches" is the operative word - it does not have to exist at that y-value, as in example a. lim x→1 [g(x)] = DNE because (left side of 1) lim x→1- [g(x)] = 2 and (right side of 1) lim x→1+ [g(x)] = 1
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find the area of the figure below, composed of a rectangle a d two semicircles. round to the nearest tenth
The area of the figure given, which is composed of a rectangle and two semicircles, is 154. 27 units ²
How to find the area ?First, find the area of the rectangle in the composite shape which is :
= Length x Width
= 13 x 8
= 104 units ²
The area of a semi - circle is:
= ( π x r ² ) / 2
Seeing as there are two semi - circles, the area is:
= π x r ²
= π x 4 ²
= 50. 27 units ²
The area of the composite shape is therefore:
= 50. 27 + 104
= 154. 27 units ²
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Calculate the limit:
lim[(x,y) -> (0,0)] [3(x^2)y / (x^2 + y^2)]
The limit does not exist because the function is not defined at (x,y) = (0,0)You can see this by plugging in (x,y) = (0,0) into the function, you get 3(0^2) * 0 / (0^2 + 0^2) = 0 / 0 which is an indeterminate form.
Why is limit defined?In Mathematics, a limit is defined as a value that a function approaches the output for the given input values. Calculus and mathematical depend on limits, which are also used to determine integrals, derivative, and continuity.
What are types of limits?There are each limits (left- and proper limits), infinite limits, and limitations at infinity in addition to regular, two-sided limits.
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The resistance y in ohms of 1000 feet of solid copper wire at 77°F can be approximated by the model y = 10770/x² - 0.37, 5 ≤ x ≤ 100 where x is the diameter of the wire in mils (0.001 in.). Use a graphing utility to graph the model. By about what factor is the resistance changed when the diameter of the wire is doubled?
The model's graph, y = 10770/x2 - 0.37, 5 x 100 demonstrates that the resistance will be about halved when the wire's diameter is doubled. This is brought on by the inverse square relationship between wire resistance and diameter.
1. Graph the model y = 10770/x² - 0.37, 5 ≤ x ≤ 100 using a graphing utility.
2. Find the resistance when x is 5.
y = 10770/5² - 0.37 = 2104.1 ohms
3. Find the resistance when x is 10.
y = 10770/10² - 0.37 = 526 ohms
4. Divide 2104.1 by 526 to find the factor by which the resistance is changed when the diameter of the wire is doubled.
2104.1/526 = 4
The graph of the model y = 10770/x² - 0.37, 5 ≤ x ≤ 100 shows that the resistance of the wire decreases as the diameter of the wire increases. Doubling the diameter of the wire will roughly halve the resistance, as can be seen by comparing the resistance when x is 5 (2104.1 ohms) to the resistance when x is 10 (526 ohms). Thus, the resistance is changed by a factor of 4 when the diameter of the wire is doubled.
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K
Given the following sets, find the set (A UBUC)'.
U= {1, 2, 3, ... ,6}
A = {1, 3, 4, 6}
B={1, 2, 3)
C = {2, 3, 4, 5, 6}
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
OA. (AUBUC)' = {}
(Use a comma to separate answers as needed. Use ascending order.)
B. (A UBUC)' is the empty set.
Answer:
Step-by-step explanation:
A. (AUBUC)' = {}
B. (A UBUC)' is the empty set.
Both options A and B express that the complement of the union of the sets A, B, and C is the empty set. The complement of a set is the set of all elements that are not in that set. The union of sets is the set of all elements that are in at least one of the sets.
When taking the union of A, B, and C all the elements in U are included, so there is no element that is not in the set, making the complement of the union of A,B,C is an empty set.
If a,b and c are constants is a(x-b)-c=ax-(ab+c). Explain
The statement a(x-b)-c = ax-(ab+c) is true because it follows the rules of algebraic operations and the distributive property.
How to explain a(x-b)-c=ax-(ab+c)?On the left side of the equation, we have a(x-b)-c.
Here, a is a constant and it is being multiplied by (x-b). According to the distributive property, we can rewrite this as:
ax-ab-c.
On the right side of the equation, we have ax-(ab+c)
Here, we have a constant a being multiplied by x and then we have another constant ab and c being subtracted, which we can also rewrite as:
ax - ab -c
As you can see, both sides of the equation are equivalent and the statement is true.
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Two vectors A and B are added together to form a vector C. The relationship between the magnitudes of the vectors is given by A+B=C. Which one of the following statements concerning these vectors is true?
The true statement is " A and B must point in the same direction."
For complete questions refer belowTwo vectors A and B are added together to form a vector C. The relationship between the magnitudes of the vectors is given by A + B = C. Which one of the following statements concerning these vectors is true?
A and B must be displacements.A and B must have equal lengths.A and B must point in opposite directions.A and B must point in the same direction.A and B must be at right angles to each other.According to the question
False: All types of vectors with the same unit may be added using vector analysis, and we add vectors component by component. so, this defilement choice (1).A vector's length is not a factor to take into account before performing the operation, therefore vectors of different lengths can be added.This goes against the assertion since vectors moving in the opposite direction might create a new vector with a negative value.This is true because vectors pointing in the same direction add together to form new vectors.false: This presumption is factually incorrect.To know more about vectors on brainly : brainly.com/question/29740341
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In a wallet, there are 14 bills totaling $80. If there are only five and tens in the wallet, how many of each bill are there
Answer:12 fives 2 10's
Step-by-step explanation:
one-sample z-test for a population proportion will be conducted using slmple random sample selected without replacement from = population: Which of the following check for independence? A. npo > 10 and n(1 Pu ) > 10 for sample and population proportion Po
B. Each sample proportion value ess Ihan equal to 0.5 C. The sample size more Ihan 10 times the population size D. The population size mare than 10 tlmes the sample size
E. The population distribution approximately normal:
A one-sample z-test for a population proportion requires that n po > 10 and n(1-Po) > 10 for both the sample and population proportions, Po. Additionally, each sample proportion must be less than or equal to 0.5, the sample size must be more than 10 times the population size, and the population size must be more than 10 times the sample size.
1. Calculate the sample size, n, needed for the test.
2. Check that npo > 10 and n(1 - Po) > 10 for both the sample and population proportions, Po.
3. Check that each sample proportion is less than or equal to 0.5.
4. Check that the sample size is more than 10 times the population size.
5. Check that the population size is more than 10 times the sample size.
6. Check that the population distribution is approximately normal.
A one-sample z-test for a population proportion is used to evaluate the difference between a sample proportion and a population proportion. Before conducting the test, it is important to check for independence, which is done by ensuring that certain conditions are met. First, npo > 10 and n(1-Po) > 10 must be true for both the sample and population proportions, Po. Additionally, each sample proportion must be less than or equal to 0.5, the sample size must be more than 10 times the population size, and the population size must be more than 10 times the sample size. Lastly, the population distribution must be approximately normal. These conditions must be met in order for the test to be valid and reliable. If any of these conditions are not met, the test results may be inaccurate.
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the lengths of two sides XYZ are 23 and 48 inches which could not be the length of the third side
The length of the side should be 45 inches.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
In triangle XYZ,
As lengths of two sides XYZ are 23 and 48 inches
The range of the third side can be computed when we already know the two sides of the triangle.
If subtracting 48 - 23, the 3rd side would have to be more than 25. Else 3rd side can not be made as two smaller legs will not meet.
and If adding 48 + 23 , the 3rd side would have to be less than 61. Else 3rd side will reach further than the other two sides could reach.
Therefore, the length of side XZ should be greater than 25 and lesser than 61.
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A pen in the shape of an isosceles right triangle with legs of length x feet and hypotenuse of length h feet is to be built. If fencing costs $5 per feet for the legs and $10 per feet for the hypotenuse, write the total cost C of construction as a function of h.
The total cost C of construction as a function of h is:
[tex]C = \frac{10 + 5\sqrt{2}~ h^2}{h}[/tex]
As the pen is in the shape of an isosceles right angle, one of the
angle must be 90 degrees.
Also, the two sides of the triangle are equal and the base angles
are equal.
Here, x represents the length of legs of isosceles right triangle
and h be the length of hypotenuse of isosceles right triangle
Using Pythagoras theorem,
x² + x² = h²
2x² = h²
x² = h² / 2
x = [tex]\sqrt{\frac{h^2}{2} }[/tex]
So, x = [tex]\frac{h}{\sqrt{2} }[/tex]
The fencing costs $5 per feet for the legs and $10 per feet for the hypotenuse.
So, the fencing cost for the legs would be,
= 5 × (2x)
= 10x
= [tex]10\times \frac{h}{\sqrt{2} }[/tex]
= [tex]5\sqrt{2}~ h[/tex]
And the fencing cost for the hypotenuse would be,
= 10/ h
So, the total cost of fencing C would be,
[tex]C = \frac{10}{h} + 5\sqrt{2}~ h\\\\C = \frac{10 + 5\sqrt{2}~ h^2}{h}[/tex]
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What is the length of the missing side?
The length of missing side is 39.
What is define by Pythagoras theorem?Pythagoras theorem is a mathematical statement that states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the two other sides (the legs).
It can be expressed as a2 + b2 = c2, where a and b are the two legs of the triangle and c is the hypotenuse. The theorem is named after the ancient Greek mathematician Pythagoras, who is believed to have discovered it.
Pythagoras theorem is an important concept in geometry, and is used to calculate the length of the hypotenuse in a right triangle when the lengths of the other two sides are known.
It can also be used to determine the lengths of the other two sides when the length of the hypotenuse is known. In addition, it can be used to find the angles of a right triangle when the lengths of the sides are known.
Pythagoras theorem has many applications in everyday life. For example, it can be used to calculate the height of a building, or the distance between two points.
It can also be used in carpentry, engineering, and architecture to measure distances and angles. In addition, it can be used in trigonometry to find the values of trigonometric functions.
Finally, it can be used in navigation to calculate distances and angles.
Let c be the length of missing side,
According to Pythagoras theorem,
a² + b² = c²
36² + 15² = c²
c = √1521
c = 39
So, the length of missing side is 39.
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7) +9 –
+16 = N
8) +85 –
+12 = N
9) –6 –
–2 = N
10) +13 –
+12 = N sorry
Hey there!
Is this all one complex equation or it this representing multiple? Reason I ask is it's a little hard to understand above.
The coldest temperature recorded in the city of Texas was -22.3°F. The coldest temperature recorded at Vostok station. Antarctica is four times is called what equation can be used to represent the coldest temperature recorded in Vostok station in Fahrenheit. Enter the correct equation in the box.
The coldest temperature recorded in Vostok station in Fahrenheit is -89.2°F
How to calculate the equation?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
It is important to note that an equation is the mathematical statement which can be made up of two expressions which are connected by an equal sign.
The coldest temperature recorded in Vostok station in Fahrenheit is:
= -22.3 × 4
= -89.2°F
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Which graph shows the new position of the rectangle after a translation?
3rd image is translations are rigid transformations that do not change the orientation of the original image.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
A translation is a movement of the graph either horizontally parallel to the -axis or vertically parallel to the -axis.
3rd image is translations are rigid transformations that do not change the orientation of the original image.
2 and 4 are rotations and 5 is a dilation.
Hence, 3rd image is translations are rigid transformations that do not change the orientation of the original image.
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Data at, or representing, the same point in time area cross-sectional datab. time cross-sectional data c. time series datad time controlled datae. none of the above
Time cross-sectional data is data collected from a sample of subjects at a single point in time.
This data can be used to measure the characteristics of a population at a given point in time. For example, a population can be surveyed to measure the percentage of people who own a car, the median age of the population, or the percentage of people who have a college education.
Time series data is data collected from the same sample of subjects over a period of time. This data can be used to measure the changes in a population over time. For example, a population can be surveyed to measure the percentage of people who own a car over a five-year period, the median age of the population over the same five-year period, or the percentage of people who have a college education over the same five-year period.
Time controlled data is data collected from the same sample of subjects at different points in time but with a controlled variable. For example, a survey can be conducted to measure the percentage of people who own a car at the start of the school year, the median age of the population at the start of the school year, and the percentage of people who have a college education at the start of the school year in different cities.
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If Darell is going to take music lessons, then he needs a trumpet. If Darell is not going to take music lessons, then he does not need a trumpet. Is the second conditional the contrapositive, converse, or inverse of the first conditional?
The statement given is showing a condition for a contrapositive statement.
What are conditional statements?Conditional statements are those statements where a hypothesis is followed by a conclusion.
Given that, If Darell is going to take music lessons, then he needs a trumpet. If Darell is not going to take music lessons, then he does not need a trumpet.
So, this is a structure of, If A then B ⇒ If not A then not B.
Which is a structure for contrapositive conditional statements.
Hence, the statement given is showing a condition for a contrapositive statement.
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