Answer:
22
Step-by-step explanation:
(8 + 20) - ((8 * 9) ÷ 12)
Using PEMDAS, let us find the product to get;
(8 + 20) - (72/12)
Next operation is to divide what is in the bracket to get:
(8 + 20) - 6
Next operation is addition of the bracket content to get; 28 - 6
Next operation is to carry out subtraction to get: 22
Thus, the total number of days taken to make the batch of pens is 22.
Graph the rational function Start by drawing the vertical and horizontal asymptotes. Then plot two points on each piece of the graph. Finally, click on the graph-a-function button X ?
The horizontal and vertical asymptotes for the function f(x) =6/(-2x +1) is equal to y = 0 and x = 1/2 respectively.
Graph is attached.
As given in the question,
Given function is :
f(x) =6 /(- 2x +1)
f(x) = y
Degree of the numerator is zero
Degree of the denominator is 1.
Degree of denominator is greater than the degree of numerator.
Function represent the horizontal asymptotes for y =0
To get the vertical asymptotes equate denominator equals to zero
(- 2x +1) = 0
⇒2x = 1
⇒x = 1/2
Vertical asymptotes is given by x =1/2.
Graph is attached.
Therefore , the horizontal and vertical asymptotes for the given function is equal to y=0 and x =1/2 respectively.
The above question is incomplete, the complete question is:
Graph the rational function. f(x) =6 /(- 2x +1) Start by drawing the vertical and horizontal asymptotes. Then plot two points on each piece of the graph. Finally, click on the graph-a-function button X.
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an application is using a two-dimensional list defined as follows: write a statement that creates an empty two-dimensional list named values with 4 rows and 3 columns. write nested loops that get an integer value from the user for each element in the list, example: values
Complete Question :
An application is using a two-dimensional list defined as follows: 1. Write a statement that creates an empty two-dimensional list named values with 4 rows and 3 columns. 2. Write nested loops that get an integer value from the user for each element in the list, for example: values= [[1, 2, 3], [10, 20, 30], [100, 200, 300],[1000, 2000, 3000]] 3. Write a function named row_values that accepts values as argument and returns the sums of each row and displays the result as a list named row 4. Write a function named column_values that accepts values as arguments and returns the sums of each column and displays the result as a list named column 5. Write a function called sum_values that sums all the elements of the array and displays the result.
Sum of rows : [ 6, 60, 600, 6000 ]
Sum of columns : [ 1111, 2222, 3333]
Sum of all elements : 6666
The nested loops are :
Enter a number at row 0, and column 0 : 1
Enter a number at row 0, and column 1 : 2
Enter a number at row 0, and column 2 : 3
Enter a number at row 1, and column 0 : 10
Enter a number at row 1, and column 1 : 20
Enter a number at row 1, and column 2 : 30
Enter a number at row 2, and column 0 : 100
Enter a number at row 2, and column 1 : 200
Enter a number at row 2, and column 2: 300
Enter a number at row 3, and column 0 : 1000
Enter a number at row 3, and column 1 : 2000
Enter a number at row 3, and column 2 : 3000
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Zareen has 24 minutes to work on her math homework, and each problem is taking her of a minute, on average, to complete. Which expression can be used to determine the number of math problems she will be able to complete in the time she has?
By using division, it can be concluded that
Number of math problem she can be able to complete within given time is [tex]24 \div \frac{2}{3}[/tex]
This is the required expression
What is division?
Division is the process by which value of single unit can be calculated from the value of multiple unit.
The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula for division
Divisor x Quotient + Remainder = Dividend.
This is a word problem on division
Zareen has 24 minutes to work on her math homework
Fraction of time taken to do each sum =[tex]\frac{2}{3}[/tex]
Number of math problem she can be able to complete within given time is
[tex]24 \div \frac{2}{3}[/tex]
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Through C construct a parallel to AB.
Through A construct a parallel to BC.
Through B construct a parallel to AC.
Extend these lines to form a new triangle.
What relationship exists between the
two triangles?
A
C
B
Answer:
new triangle is similar to and 2 times the size of the original
Step-by-step explanation:
You want to construct a new triangle with the sides of the existing one being midsegments of the new one. Then you want to know the relationship between the triangles.
ConstructionThe attachment shows the described construction.
RelationshipThe sides of the original triangle are midsegments of the new triangle, so the new triangle is ...
scaled up by a factor of 2 (has 4 times the area)similar to the originalrotated 180° about the common centroid of the two trianglesSolve the system if we x-3y=0 and 3x-6y=9 by combining the equations.
Step-by-step explanation:
Hope u get it x=3×3
x=9
It didn't include in the photo
A reactor coolant tank is being filled with coolant at the rate of 400 gallons per hour with t>0 measure in hours. If the tank originally contained 200 gallons of coolant, approximately how many gallons are in the tank after 8 hours?
The gallons after 8 hours will be 3400 gallons.
How to illustrate the expression?Expression refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.
Numbers, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations.
In this case, the reactor coolant tank is being filled with coolant at the rate of 400 gallons per hour with t>0 measure in hours.
Therefore, the gallons after 8 hours will be:
= 200 + 400(8)
= 200 + 3200
= 3400 gallons.
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Write another division problem that has a quotient of 3 and a remainder of 28.
Division problem with quotient of 3 and a remainder of 28 are-
43 / 157 = 3, leaving a difference of 28.Three times 37 yields three, leaving a leftover of 28.Explain the term quotient of the division?The quotient is the result of dividing two numbers by each other. As in the case of 8 ÷ 4 = 2, when the division produced the number 2, the outcome is the quotient.In this example, the number being divided (15) is known as the dividend, as well as the number being divided by (3 in this instance) is known as the divisor. The quotient is the outcome of the division. Observe how 15 ÷ 3 = 5 is a correct equation even if you change the quotient and divisor. 15 ÷ 5 = 3.The given data is-
quotient=3remainder=28To estimate:
division problem?
43 / 157 = 3, leaving a difference of 28.Three times 37 yields three, leaving a leftover of 28.To know more about the quotient of the division, here
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find two polynomials whose difference is 2x^2 + x + 4
The two polynomials whose difference is 2x^2 + x + 4 are
6x² + 3x + 5 and 4x² + 2x + 1.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
The difference between the two polynomials is 2x² + x + 4.
The two polynomials are:
6x² + 3x + 5 _____(1)
4x² + 2x + 1 ______(2)
The difference between (1) and (2)
6x² + 3x + 5 - 4x² - 2x - 1
2x² + x + 4
Thus,
The two polynomials are 6x² + 3x + 5 and 4x² + 2x + 1.
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The Picture and Sound electronics store has hired Brennan to work in the warehouse. He uses a pulley with a hand crank to lift heavy boxes. He turns the crank 15 times to lift a box 15 feet. He turns the crank 45 times to lift a box 45 feet.
In this relationship, x represents the number of times Brennan turns the crank to lift a box, and y represents the height the box has been lifted (in feet).
Graph two points for this relationship and the line passing through them.
The graph (created with MS Excel) of the height the box is lifted to the number of times Brennan turns the crank to lift the box which is the graph of the proportional relationship, y = x, is attached.
What is a proportional relationship?A proportional relationship is one in which one variable (the output variable) is a constant multiple of the another variable known as an input variable.
The number of times Brennan turns the crank = x
The height to which the box is lifted = y
The points on the graph are; (15, 15), and (45, 45)
The ratio of the y-values to the x-values is 15/15 = 45/45 = 1, which indicates that the relationship is a proportional relationship
A point on the graph of a proportional relationship is the point (0, 0), therefore, the points on the graph are; (0, 0), (15, 15), and (45, 45)
Please find attached the graph of the proportional relationship between the number of times Brennan turns the crank to the height to which the box is lifted created with MS Excel
The relationship between the variables x and y is; y = x
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Find composition of A and B
A ={(1;2);(-3;0);(4;7)}
B ={(2;1);(0;3);(4;-3)}
A o B=
The composition of A and B represents by the set A o B = {(2,2),(4,0)}
What is a set of ordered pair?
An ordered pair in mathematics is a set of two things. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples, or 2-length sequences.
Given sets are
A = {(1,2), (-3,0), (4,7)}
B = {(2,1), (0,3), (4,-3)}
The inputs of B are 2, 0, and 4.
The outputs of B are 1, 3, and -3.
The inputs of A are 1, -3, and 4.
The outputs of A are 2, 0, and 7.
The composition can be written as A o B = A(B(x)
A(B(2)) = A(1) = 2
A(B(0)) = A(3) = not valid [Since 3 is not an input of A].
A(B(4)) = A(-3) = 0
The composition is {(2,2), (4,0)}.
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A graphing calculator is recommended.
Three students, Linda, Tuan, and Javier, are given five laboratory rats each for a nutritional experiment. Each rat's weight is recorded in grams. Linda feeds her rats Formula A, Tuan feeds his rats Formula B, and Javier feeds his rats Formula C. At the end of a specified time period, each rat is weighed again, and the net gain in grams is recorded. Using a significance level of 10%, test the hypothesis that the three formulas produce the same mean weight gain. (Let 1 = Linda's rats, 2 = Tuan's rats and 3 = Javier's rats.)
Weights of Student Lab Rats
Linda's rats Tuan's rats Javier's rats
46.3 49.8 53.3
42.3 42.7 43.1
44.1 41.8 40.2
48.7 48.9 47.7
40.8 46.5 51.5Enter an exact number as an integer, fraction, or decimal.
df(num) =
Enter an exact number as an integer, fraction, or decimal.
df(denom) =
State the distribution to use for the test.
A. F2, 12
B. F12, 2
C. F14, 2
D. F14, 12
E. F2, 14
What is the test statistic? (Round your answer to two decimal places.)
What is the p-value? (Round your answer to four decimal places.)
Explain what the p-value means for this problem.
A. If H0 is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value.
B. If H0 is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value.
C. If H0 is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.
D. If H0 is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.
Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write appropriate conclusions.
(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)
α =
(ii) Decision:
reject the null hypothesisdo not reject the null hypothesis
(iii) Reason for decision:
Since α < p-value, we do not reject the null hypothesis.
Since α > p-value, we reject the null hypothesis.
Since α < p-value, we reject the null hypothesis.
Since α > p-value, we do not reject the null hypothesis.
(iv) Conclusion:
There is sufficient evidence to conclude that there is a difference among the different nutritional formulas for rats with respect to weight gain.
There is not sufficient evidence to conclude that there is a difference among the different nutritional formulas for rats with respect to weight gain.
The graph representation of the given distribution is attached below.
The term graph in math refers the visual representation of the collection of data that has the x and y coordinate values.
Here we have given that Three students, Linda, Tuan, and Javier, are given five laboratory rats each for a nutritional experiment. Each rat's weight is recorded in grams and we need to find the graphical representation of the distribution.
Here by using the values in the foregoing ANOVA table are quickly produced by the calculator, including the test statistic and the p-value of the test calculator shows :
=> F=0.66853555
=> p = 0.530548
And the FACTOR df =2 and SS=23.212
=> MS = 11.606
Here the ERROR df = 12
=> SS=208.324
=> MS = 17.36
Here by using the f distribution for the test of three different means.
Then the value of the test statistic (F-value) is 0.668 and the p -value for the test is 0.5301
When we plot the graph for the distribution then we get he graph like the following.
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Write the expression \[\frac{4+6a}{5}-\frac{1+3a}{4}\] as a single fraction.
The expression [tex]\[\frac{4+6a}{5}-\frac{1+3a}{4}\][/tex] as a single fraction is [tex]\frac{9a-11}{20}[/tex]
What is algebraic expression ?
In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.
According to question
⇒ [tex]\[\frac{4+6a}{5}-\frac{1+3a}{4}\][/tex]
⇒ taking LCM of 4, 5 = 20
now [tex]\[\frac{4(4+6a)-5(1+3a)}{20}[/tex]
⇒ (16 +24a - 5 - 15a)/20
⇒ ((24a - 15a) - (16-5))/20
⇒ (9a - 11)/20
hence, the expression [tex]\[\frac{4+6a}{5}-\frac{1+3a}{4}\][/tex] as a single fraction is [tex]\frac{9a-11}{20}[/tex]
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A laser rangefinder is locked on a comet approaching Earth. The distance g(x) , in kilometers, of the comet after x days, for x in the interval 0 to 42 days, is given by g(x)=300,000csc(π42x) .
a. The blue line represents g(x) = 250,000csc(π30x).
b. g(5) = 25,000 km. This is the distance of the comet from Earth after 5 days.
c. The minimum distance between the comet and Earth is 250,000 km, which occurs when x = 0. This corresponds to the constant csc(π30x).
d. The equation has a vertical asymptote at x = 30/π.
Write the solution to following questions:a. Graph the value of x on the range [0,35].b. Analyze g(5) and explain the results.c. What is the shortest path the comet must take to reach Earth? When does this take place? What equation constant does this match up to?d. Find any vertical asymptotes and explain their significance.a. Graph g(x):
To graph g(x), we can plot several points on the interval [0,35] and then connect them to form a graph of the function. For example, we can plot the points (0,250,000), (5,50,000), (10,25,000), (15,16,667), (20,12,500), (25,10,000), (30,8,333) and (35,7,143). Connecting these points will give us a graph of the function g(x).
b. Evaluate g(5):
The value of g(5) can be found by plugging in x = 5 into the equation: g(5) = 250,000 csc(π30*5) = 50,000 km. This means that after 5 days, the comet will be 50,000 km away from Earth.
c. Minimum distance between the comet and Earth:
The minimum distance between the comet and Earth can be found by taking the derivative of the equation and setting it to 0.
d. Vertical Asymptotes:
The vertical asymptotes of g(x) occur at x = 0 and x = 30. This means that the comet approaches an infinitely large distance from Earth at x = 0 and x = 30.
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Graph the solution of the inequality on a number line.
2(x − 3) – 5x < x-2
Ο
Α.
OB.
OC
OD.
℗
-5 -4 -3 -2 -1 0 1 2
←
+1
-5 -4 -3 -2 -1 0 1
#2
0111
1
-5 -4 -3 -2 -1 0
2
3 4 5
3 4 5
3 4
+
5
4
110111
-5 -4 -3 -2 -1 0 1 2 3 4 5
Answer:
Choice D : x > - 1
Step-by-step explanation:
Left hand side (LHS) of the inequality can be siimplified
[tex]2\left(x-3\right)-5x = 2x - 6 - 5x = -3x -6\\\\[/tex]
Inequality becomes
[tex]-3x-6 < x-2[/tex]
Move x to the left side and -6 to the right side:
[tex]-3x - x < -2 + 6\\\\-4x < 4\\\\[/tex]
Multiply both sides by -1(the inequality sign changes to >)
[tex]4x > -4\\\\[/tex]
Divide both sides by 4:
[tex]x > -1[/tex]
The number line corresponding to this is the fourth choice
Given the points (1, -4) and (4, 5), construct two equations in point slope form using each of the points. Construct and upload the graph of the line. Show your work and upload your graph for your teacher to review.
The equation of line passes through the points (1, -4) and (4, 5) will be;
⇒ y = 3x - 7
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (1, -4) and (4, 5).
Now,
Since, The equation of line passes through the points (1, -4) and (4, 5)
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (5 - (-4)) / (4 - 1)
m = 9 / 3
m = 3
Thus, The equation of line with slope 3 is,
⇒ y - (-4)= 3 (x - 1)
⇒ y + 4 = 3x - 3
⇒ y = 3x - 3 - 4
⇒ y = 3x - 7
Therefore, The equation of line passes through the points (1, -4) and (4, 5) is given as;
⇒ y = 3x - 7
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HELP ASAP
3. If the aspect ratio of a tire is 50%, width 10 inches, and the rim diameter is 19 inches, what is the tire diameter?
a. 59in b. 35.8in
d. 49in
4. The standard print paper is 11" by 8.5 in. What is the aspect ratio of a standard print paper?
a. 11:8
c. 8.5
c. 29 in
b. 22:17
d. 11
3) The tire diameter using the aspect ratio is; 29 inches
4) The aspect ratio of a standard print paper is; 22:17
How to solve aspect ratio problems?The aspect ratio is defined as the relationship between the width and height.
Now, in this case, the aspect ratio must be in whole numbers and not decimals and as such we can solve as follows;
3) We are told that the aspect ratio of a tire is 50%.
Thus, the aspect ratio is; 50/100 = 1/2 or 1:2.
Now, we are told that width 10 inches, and the rim diameter is 19 inches, then it means that the tire diameter = 10/2 + 19 + 10/2 = 29 inches
4) The standard print paper is 11" by 8.5. This can also be written as;
11 by 17/2 or 11 * 2 : 17
= 22:17
This then gives us the aspect ratio.
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exercise 28 a sample of 20 joint specimens of a particular type gave a sample mean proportional limit stress of 8.52 mpa and a sample standard deviation of 0.78 mpa.
A 95% % lower confidence bound for the true average proportional limit stress of all such joints is 8.01.
In the given question, a sample of 20 joint specimens of a particular type gave a sample mean proportional limit stress of 8.52 mpa and a sample standard deviation of 0.78 mpa.
We have to calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints.
Sample size: n = 13
Sample mean: x’ = 8.52 mps
Sample standard deviation: s = 0.78 mps
95% lower confidence bound for the true average proportional limit stress of all such joints
Level of Significance (α) = 1-95% = 5% = 0.05
α/2 = 0.025
So the value of t(α/2) = 1.8
The confidence interval = x’± t(α/2)*s/√n
Now putting the value:
The confidence interval = 8.41± (1.8)*(0.78)/√12
The confidence interval = 8.41± (1.8)*(0.226)
The confidence interval = 8.41± 0.4068
The confidence interval = (8.41- 0.4068, 8.41+ 0.4068)
The confidence interval = (8.01, 8.82)
A 95% % lower confidence bound for the true average proportional limit stress of all such joints is 8.01.
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The right question is:
A sample of 12 joint specimens of a particular type gave a sample mean proportional limit stress of 8.41 mpa and a sample standard deviation of 0.78 mpa.
Calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints. (Round your answer to two decimal places.)
a line passes through the point (-6,3) and has a slope of 3/2
The equation of slope intercept form is y = 3/2x + 12 if a line passes through the point (-6,3) and has a slope of 3/2.
Define slope intercept form.The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation. The slope, m, is a measure of how steep a line is. The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables.
Given
A line passes through the point (-6,3)
and has a slope of 3/2
Slope intercept form
y = mx + b
Equation,
y - 3 = 3/2(x - (-6))
y - 3 = 3/2(x+6)
2y - 6 = 3x + 18
2y = 3x + 24
y = 3/2x + 12
The equation of slope intercept form is y = 3/2x + 12 if a line passes through the point (-6,3) and has a slope of 3/2.
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what is 309x317/9-4+7/8x3
[tex]340.11[/tex] or [tex]\frac{32651}{96}[/tex].
Step-by-step explanation:1. Write the expression.[tex]\frac{(\frac{309*317}{9-4+7})}{8x3}[/tex]
3. Solve the main denomonator.[tex]\frac{(\frac{309*317}{9-4+7})}{24}[/tex]
4. Solve the secondary denominator.[tex]\frac{(\frac{309*317}{12})}{24}[/tex]
5. Solve the secondary numerator.[tex]\frac{(\frac{97953}{12})}{24}[/tex]
6. Solve the main numerator.[tex]\frac{(8162.75)}{24}[/tex]
7. Simplify the fraction.[tex]340.11[/tex] or [tex]\frac{32651}{96}[/tex].
Find the value of each of these quantities a) P(6,3) c) P(8,1) e) P(8,8) b) P(6,5) d) P(8,5) f) P(10,9)
The values for the given data set is as follows 120 , 720 , 8 ,40320 , 6720 ,3628800 respectively.
The formula to calculate the permutation is , P = n! / ( n - r )!. Using this formula we get the result as,
P(6,3) = 6! / (6−3)!
= 6! / 3!
= 120
P(8,1) = 8! / (8 - 1)!
= 8! / 7!
= 8
P(6,5) = 6! / (6-5)!
6! / 1!
720
Similarly ,
P(8,8)= 40320
P(8,5) = 6720
P(10,9) = 3628800
A permutation is a specific arrangement of items. Set members or elements are arranged in a sequence or linear order here.
For example, the permutation of set A=1,6 is 2, as in 1,6,1.
There are no alternative ways to arrange the items in set A, as you can see.
In permutation, the elements must be organised in a specific sequence, whereas in combination, the order of the elements is irrelevant. Read also: Permutation And Combination
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a)the perimeter of a rectangle is 56 m and it's length is 18cm find its breadth
If the perimeter of the rectangle is 56m with length 18m the breadth is 10m
How to determine the breadth of the rectangle?You should know that the breath of the rectangle is the two shorter sides of the rectangle.
The perimeter of the rectangle is the distance round the rectangle
In every rectangle, there are 2 Lengths and 2 breadths
This implies that the perimeter is
P= L+B+L+B
P=2L+2B
This implies that
56=2(18)+2B
⇒56=36+2B
56-36=2B
20=2B
Making B the subject of the relation we have
B=20/2
B=10m
Therefore the breadth of the rectangle is 10m
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for the independent-measures t test, which of the following describes the estimated standard error of the difference in sample means (whose symbol is
For an independent-measures t test, the option that describes the estimated standard error of the difference in sample means is D. an estimate of standard distance between the difference in the sample mean and the difference in the corresponding population mean.
What is a T test?A statistical test called a t test is employed to compare the means of two groups. It is frequently employed in hypothesis testing to establish whether a procedure or treatment actually affects the population of interest or whether two groups differ from one another.
The Independent Samples t Test compares the means of two separate groups to see if there is statistical support that the population mean values are statistically significantly different. A parametric test is called the Independent Samples t Test. For instance, you could determine whether first-year graduate salaries varied by gender using an independent t-test.
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Complete question
for the independent-measures t test, which of the following describes the estimated standard error of the difference in sample means (whose symbol is
a. a weighted average of the two sample
b. the difference between the standard deviationa
c. The variance
d. an estimate of standard distance between the difference in the sample mean and the difference in the corresponding population mean.
Can anyone help me ASAP?
Answer:
Equation 1 - x + 4y = 12
Equation 2 - 2x + 4x = 16
Cost of 1 Cheeseburger - $4
Cost of 1 Taco - $2
Step-by-step explanation:
Cheeseburger(x) and Taco(y)
x + 4y = 12 and 2x + 4y = 16
x = - 4y + 12
2(- 4y + 12) + 4y = 16
- 8y + 24 + 4y = 16
- 4y = - 8
y = 2
x + 4(2) = 12
x + 8 = 12
x = 4
Consider square ABCD. What is the angle of rotation about the center that maps AB to BC?
Recall that rotations are counterclockwise.
The angle of rotation is 90 degrees.
What is a square?
In a square, all the sides are equal in length and all the angles are right angles (90 degrees). The center of a square is the point that is equidistant from all four vertices, and it is also the point of intersection of the diagonals of the square.
The angle of rotation about the center that maps AB to BC is 90 degrees.
If we rotate the square about its center, the sides of the square will rotate to new positions. For example, if we rotate the square 90 degrees counterclockwise (as specified in the question), side AB will rotate to the position of side BC.
The angle of rotation that maps AB to BC is the angle through which the square was rotated.
Hence, the angle of rotation is 90 degrees.
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each year, 40% of a salmon population is extracted from a farming pond. at the beginning of the next year, the pond is stocked with an additional fixed amount of n caught wild salmon. let pn denote the amount of fish at the beginning of the n-th year assume that the initial salmon population on the pond is p0=5000
a. Write a recursion to describe Pn. b. Determine the value of N so the amount of fish remains constant at the beginning of each year.
(a) [tex]p_{n} =p_{n-1}-0.4p_{0} +n[/tex]
(b) [tex]n = {\frac{p_{n-1} -p_{n} }{0.4p_{0}} }[/tex]
Given,
Initial salmon population [tex]p_{0}=5000[/tex]
Extraction rate = 40% per year
(a) Formula for recursion,
For the first year,
[tex]p_{1} =p_{0} -0.4p_{0}+n[/tex]
For the second year,
[tex]p_{2} =p_{1} -0.4p_{0} +n[/tex]
For the n'th year,
[tex]p_{n} =p_{n-1}-0.4p_{0} +n[/tex]
(b) The value of n,
From the above equation,
[tex]p_{n} =p_{n-1}-0.4p_{0} +n[/tex]
[tex]n = {\frac{p_{n-1} -p_{n} }{0.4p_{0}} }[/tex]
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Each year, 40% of the salmon population is extracted from a farming pond.
a. The recursion to describe Pn is Pn = 0.6 Pn-1 + N.
b. The value of N is 3000.
What is recursion?According to the recursion equation, the quantity of fish at the start of the nth year. Pn, is equal to 0.6 times the quantity at the start of the year before, Pn-1, plus the constant quantity of wild salmon that is restocked every year, N.
b. We can set the recursion equation equal to the initial population of 5000 fish in order to get the value of N that ensures the quantity of fish stays constant at the start of each year. Now we have the equation.
0.6Pn-1 + N = 5000. Solving for N gives us N = 3000.
Therefore, a. Pn = 0.6 Pn-1 + N. b. 3000.
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What is the product?
2•[-1]
[0]
Answer:
-2
Step-by-step explanation:
A firm manufactures two products; the net profit on product 1 is Rupees 3 per
unit and Rupees 5 per unit on product 2. The manufacturing process is such that
each product has to be processed in two departments D1 and D2. Each unit of
product1 requires processing for 1 minute at D1 and 3 minutes at D2; each unit
of product 2 requires processing for 2 minutes at D1 and 2 minutes at D2.
Machine time available per day is 860 minutes at D1 and 1200 minutes at D2.
How much of product 1 and 2 should be produced every day so that total profit
is maximum. Make the mathematical model for the given problem.
To answer this question we need to make use of Linear Programming
The solution is:
x = 170 units
y = 345 units
z(max) = 2235 rupees
To solve a linear programming problem, we need to formulate the model
The Objective Function
Let´s call x the number of product 1 manufactured
and y the number of product 2 manufactured
Then the Objective Function is:
z = 3× x + 5×y to be maximize
The set of constraints are:
D1 D2
( min. ) ( min. )
Product 1 (x) 1 3
Product 2 (y) 2 2
Availability 860 1200
First constraint:
Time available in D1: 860 minutes
1×x + 2×y ≤ 860
Second constraint:
Time available in D2: 1200 minutes
3×x + 2×y ≤ 1200
General constraint: x ≥ 0 ; y ≥ 0 integers ( we will assume only complete products at the end of the period no fractions )
Then the model is:
z = 3× x + 5×y to be maximize
Subject to:
1×x + 2×y ≤ 860
3×x + 2×y ≤ 1200
x ≥0 y ≥ 0 integers
With the help of Avtomat we get the solution:
x = 170 units
y = 345 units
z(max) = 2235 rupees
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11. A triangle has a base length of 3.9 cm and a height of 9 cm. Which dimensions could
be the measurements of a similar triangle?
The dimensions that could be the measurements of a similar triangle are; base = 7.8 cm and height = 18 cm
How to Identify a similar triangle?Two triangles are said to be similar provided that they have the same ratio of corresponding sides and an equal pair of corresponding angles.
Now, we are given the side lengths of the triangle as a base length of 3.9 cm and a height of 9 cm.
Thus, this means that a similar triangle will have same ratio of side lengths. Thus;
If new height is h and new base is b, then we have;
9/h = 3.9/b
Thus,
h/b = 9/3.9
If we multiply the right side top and bottom by 2, then we have;
h/b = 18/7.8
18 and 7.8 cm could be similar dimensions.
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PLEASE ANSWERE ASAP
If BC = 16.7 ft, what is AY?
The length of segment AY is 16.7 ft if the length of segment BC is 16.7 ft
How to determine the length of the side length AYFrom the question, we have the following parameters that can be used in our computation:
BC = 16.7 ft
The measures of the angles are not given
However, the marks on the side lengths imply that:
The points A, B and C divides the line segments XY, XZ and YZ into equal segmentsThe parallel segments are equal segmentsUsing the above as a guide, we have the following:
AY = BC
This is because these segments are parallel segments
Recall that parallel segments are equal segments
Substitute the known values in the above equation, so, we have the following representation
AY = 16.7
Hence, the length of AY is 16.7 ft
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Find m/S
U
10x + 8
11x + 2
T
S
Q. Find the measure of the angle indicated in the following parallelogram.
The measure of the angle S is 112° in the following parallelogram.
What is parallelogram?
A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of a polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. In a parallelogram, the opposing sides are of equal length, and the opposite angles are of equal size. A parallelogram has adjacent angles that add up to 180 degrees.
Given, ∠T= 11x + 2
∠V = 10x + 8
From the above definition, opposite angles are equal
So, ∠T = ∠V
or, 11x + 2 = 10x + 8
or, 11x - 10x = 8 - 2
or, x = 6
∠V= 10x + 8 = 10*6 + 8 = 68 degree
From the above definition, adjacent angles add up to 180 degrees
∠V + ∠S = 180°
or, 68° + ∠S =180°
or, ∠S = 180° - 68° = 112°
Hence, the measure of the angle S is 112°.
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