the equation of the required line is 3xâ2y+1=3x1â2y1+1.
(i) We are given the parallel line of the given equation, that is yâ2x=0.
So, the equation of the required line will be yâ2x=c, where c is a constant.
Let the point of intersection of the two lines be (x1, y1).
Then, substituting the values of x1 and y1 in the equation yâ2x=c, we get
y1â2x1=c
or, c=y1â2x1
Hence, the equation of the required line is yâ2x=y1â2x1.
(ii) We are given the perpendicular line of the given equation, that is 2x+yâ5=0.
So, the equation of the required line will be 3xâ2y+1=c, where c is a constant.
Let the point of intersection of the two lines be (x1, y1).
Then, substituting the values of x1 and y1 in the equation 3xâ2y+1=c, we get
3x1â2y1+1=c
or, c=3x1â2y1+1
Hence, the equation of the required line is 3xâ2y+1=3x1â2y1+1.
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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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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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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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Mr. Mogi borrowed $9000 for 10 years to make home
improvements. If he repaid a total of $20,000 at what
interest rate did he borrow the money?
The interest rate that Mr. Mogi borrowed the money, given the amount borrowed and the amount repaid, is 17. 8%
How to find the interest rate ?To find the interest rate that Mr. Mogi borrowed the money at, first find the amount he paid per year:
= Total payment / Number of years
= 20, 000 / 10
= $ 2, 000 per year
You can then use the RATE function on Spreadsheet to find the interest:
NPER = 10 years
PMT = $ 2, 000
PV = 9, 000
FV = $ 20, 000
The interest rate would be 17. 8%
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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:
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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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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Let (lim)f(x) = 7 and (lim)g(x) = -2. Find lim [f(x) - g(x)].
lim [f(x) - g(x)] is9.
What is a limit of a function?Generally, In mathematics, a limit is a value that a function "approaches" as the input of the function "approach" some value.
More formally, given a function f(x) and a value L, we say that "the limit of f(x) as x approaches a is L" if the values of f(x) can be made arbitrarily close to L by taking x sufficiently close to a, but not equal to a.
In other words, the limit of a function describes the behavior of the function as the input gets arbitrarily close to a particular value, but doesn't necessarily equal that value
The limit of the difference between the two functions is the difference of their individual limits. So,
lim [f(x) - g(x)] = lim f(x) - lim g(x)
= 7 - (-2)
= 9.
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Morgan ran 5 miles in 57 days and a half minutes. How long did it take her to run each mile
Answer:
70
Step-by-step explanation:
The time that should take her to run each mile is approx 11.5 minutes.
Given that,
She runs 5 miles in 57 and a half minutes.
Based on the above information,
The time that should be taken by her is
= 57.5 ÷ 5 miles
= 11.5 minutes.
Therefore we can conclude that the time that should take her to run each mile is approx 11.5 minutes......
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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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
find a polynomial polynomial the sum or difference of terms which have variables raised to non-negative integer powers and which have coefficients that may be real or complex that represents the perimeter perimeter the length of the outer edge of a shape. of the rectangle rectangle a quadrilateral containing four right angles. .
The perimeter of a rectangle can be represented by a polynomial expression. The expression will consist of two terms, one representing the width and one representing the length. Each term will contain a variable, which is to the power of one, multiplied by a coefficient. The sum of the two terms produces the perimeter of the rectangle.
For example, if the width of the rectangle is w and the length is l, then the polynomial expression for the perimeter would be: P = w + l. This expression can also be written in expanded form as: P = w + w + l + l.
By adding more terms to this polynomial expression, the perimeter of more complex rectangles can be found. For example, if the rectangle is not a perfect square, then two additional terms can be added to the polynomial expression. One term will represent the extra width and one term will represent the extra length. By adding these two additional terms, the perimeter of the rectangle can be calculated.
In conclusion, the perimeter of a rectangle can be represented as a polynomial expression, which consists of terms that have variables raised to the power of one and are multiplied by coefficients. By adding more terms to the expression, the perimeter of more complex rectangles can be found.
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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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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
Many people have misconceptions about how profitable small, consistent investments can be. In a survey of 1010 randomly selected U.S. adults (Associated Press, October 29, 1999), only 374 responded that they thought that an investment of $25 per week over 40 years with a 7% annual return would result in a sum of over $100,000 (the correct amount is $286,640). Is there sufficient evidence to conclude that less than 40% of U.S. adults are aware that such an investment would result in a sum of over $100,000? Test the relevant hypotheses using α =.05.
No, there is not. We do not have sufficient evidence to conclude that less than 40% of U.S. adults are aware that such an investment would result in a sum of over $100,000.
Two-Proportion Z-Test ResultsTo test the hypothesis that less than 40% of U.S. adults are aware that such an investment would result in a sum of over $100,000, we can use a two-proportion z-test. The null hypothesis is that the proportion of U.S. adults who are aware of the investment's outcome is equal to or greater than 40%, and the alternative hypothesis is that the proportion is less than 40%.
The test statistic is calculated as:
z = (p1 - p2) / √(p(1-p)(1/n1 + 1/n2))
where p1 is the proportion of U.S. adults in the sample who are aware of the investment's outcome (374/1010), p2 is the proportion assumed in the null hypothesis (0.4), and n1 and n2 are the number of observations in the sample and population, respectively.
Using these values, the test statistic is:
z = (0.369 - 0.4) / √(0.4(1-0.4)(1/1010)) = -1.08
Using a two-sided test with a significance level of 0.05, we can look up the critical value in a standard normal table or using software and find that the critical value is ±1.96. Since -1.08 is between -1.96 and 1.96, we fail to reject the null hypothesis.
Therefore, we do not have sufficient evidence to conclude that less than 40% of U.S. adults are aware that such an investment would result in a sum of over $100,000.
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(50 POINTS AND BRAINLYEST)
The side length of the square is 14 units long, what is the diameter of the circular base of the cylinder from the picture in number 1?
Answer: the diameter of the circle is about 19.8
Step-by-step explanation:
Since the length of the square is 14 units, we can use the Pythagorean theorem to find the diagonal:
14^2 + 14^2 = c^2
196 + 196 =c^2
392 = c^2
c = about 19.8
Answer:
19.8
Step-by-step explanation:
The diameter of the base of the cylinder is equal to the diagonal of the inscribed square and is equal to the hypotenuse of an equilateral triangle into which the square is divided by diagonals ... By the Pythagorean theorem, the diameter (hypotenuse) is equal to the square root of the sum of the squares of the legs and is equal to 19.8
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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480,000 in scientific notation.
The number 480,000 in scientific notation is 4.8 * 10⁵
How to determine the scientific notation of the number
From the question, we have the following parameters that can be used in our computation:
Number = 480,000
Multiply the number by 1
So, we have the following representation
Number = 480000 * 1
Express 1 as 10⁵/10⁵
Som we have
Number = 480000 * 10⁵/10⁵
This gives
Number = 4.8 * 10⁵
Hence, the expression is 4.8 * 10⁵
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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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4) Estimate the sum. Round each num
1/2 + 2/1/20
4
4
8
The sum is approximately
Submit
The sum of expression 1/2 + 2/(1/2) is obtained to be option B: 4.
What is sum?
The outcome of adding two or more numbers or phrases is known as the sum in mathematics. The sum is a method of bringing things together as a result. To put it another way, adding two or more numbers together results in a new result or total.
The fractional expression is - 1/2 + 2/(1/2)
Apply the fraction reciprocal rule -
If there is a fraction in denominator then it is reciprocated and multiplied.
= 1/2 + 2/(1/2)
= 1/2 + 2(2/1)
= 1/2 + 4
Now, take the LCM and multiply it with the numerators -
= 1/2 + 4
Find the sum of the numbers -
= (1 + 8)/2
= 9/2
= 4.5
When estimated and rounded the number is equivalent to 4.
Therefore, the fractional expression results in 4.
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Estimate the sum. Round the number.
1/2 + 2/(1/2)
The sum is approximately -
A: 0
B: 4
C: -4
D: 8
what number is equal to 4 hundreds + 3 tens + 7 ones + 6 hundredths + 8 thousandths
Answer:
Four hundred thirdy seven and six hundred and eight thousandths.
437.068
Step-by-step explanation:
Hope it helps! =D
The number formed by these terms is 437.068.
To solve this problem, we first need to understand the place value system and what each term represents.
As per the place value system used in decimals:
- Hundreds: It is the third digit to the left of the decimal point and each unit represents 100.
- Tens: It is the second digit to the left of the decimal point and each unit represents 10.
- Ones: It is right next to the decimal point, all the digits to the left of it are the ones. Each unit represents 1.
- Hundredths: It is the second digit to the right of the decimal point and each unit represents 0.01.
- Thousandths: It is the third digit to the right of the decimal point and each unit represents 0.001.
In the given context, we know that there are 4 hundreds, 3 tens, 7 ones, 6 hundredths, and 8 thousandths.
To start, we calculate each term separately:
- 4 hundreds = 4 x 100 = 400
- 3 tens = 3 x 10 = 30
- 7 ones = 7 x 1 = 7
- 6 hundredths = 6 x 0.01 = 0.06
- 8 thousandths = 8 x 0.001 = 0.008
After evaluating each term separately, we sum them up together for the final answer:
- Sum = 400 + 30 + 7 + 0.06 + 0.008 = 437.068
Hence, the number formed by these terms is 437.068.
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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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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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imagine that you have a tennis ball and a baseball at different locations. the center of the tennis ball is at <-3,-1,0>m, and the center of the baseball is at <3,5,0>m. the position vector of the baseball is . the position vector of the tennis ball is . the position vector of the tennis ball relative to the baseball is . which of the following images best corresponds to the described geometry?
So, the two balls are located on the same plane, the x-y plane, with the baseball at <3,5,0>m and the tennis ball at <-3,-1,0>m, with the vector pointing from baseball to the tennis ball is <-6,-6,0>m.
The position vector of the baseball is <3,5,0>m. The position vector of the tennis ball is <-3,-1,0>m.
The position vector of the tennis ball relative to the baseball is the vector pointing from the baseball to the tennis ball and it is calculated by subtracting the position vector of the baseball from the position vector of the tennis ball: <-3,-1,0>m - <3,5,0>m = <-6,-6,0>m
So the two balls are located on the same plane, the x-y plane, with the baseball at <3,5,0>m and the tennis ball at <-3,-1,0>m, with the vector pointing from baseball to the tennis ball is <-6,-6,0>m.
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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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an individual who exhibits a mixture of schizophrenic symptoms most likely has undifferentiated schizophrenia. T/F
False. Undifferentiated schizophrenia is a type of schizophrenia where a person displays general symptoms of the disorder such as hallucinations and delusions, but does not meet the criteria for any of the other subtypes of schizophrenia.
A person exhibiting a mixture of schizophrenic symptoms would likely be diagnosed with schizophrenia, but not as specifically undifferentiated schizophrenia.This disorder is characterized by a mixture of positive and negative symptoms, including delusions, hallucinations, disorganized speech, disorganized behavior, lack of emotion, and social withdrawal. However, a person who exhibits a mixture of schizophrenic symptoms could have any type of schizophrenia, not just undifferentiated schizophrenia. For example, a person could have paranoid schizophrenia, disorganized schizophrenia, or catatonic schizophrenia. To diagnose schizophrenia, a doctor must analyze the patient's symptoms and determine which type of schizophrenia they have.
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Insert < or > between the pair of integers to make a true statement.
-12 -5
Help me please. asap!
Answer:
-12 < -5
Step-by-step explanation:
its simple math. -12 is less than -5 because its more negative.
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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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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