Answer: 1) Using the order of operations, you first have to multiply the amount of each item by it's price, and then add those values. So for Pablo, you would do (0.50 x 1) + (0.75 x 3) + (1.25 x 3) and solve within the parentheses to get .50+2.25+3.75=$6.50
2) For Laurie, use the same method from #1. First multiply and then add, like so: (0.5 x 2) + (1.25 x 3) + (0.75 x 3) ---> 1+3.75+2.25, which equals $7
3) Laurie > Pablo
$7.00 > $6.50
Step-by-step explanation:
The term order of operations is also known as PEMDAS
Parentheses
Exponents
M/D - Multiplication/Division (whichever comes first in the equation)
A/S - Addition/Subtraction (whichever comes first)
Hope this helps!
Graph the equation y = 25x, where y represents
the number of boxes a machine packages
over time, x, in minutes. Is the relationship
proportional? How many boxes does the
machine package in 4 minutes?
Ay
Number of Boxes
150
100
50
0
0
4 6
Time (min)
2
Xx
The number of the boxes machine package in 4 minutes will be 100.
What is an equation?The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.
A graph represents the data in the vertical and horizontal coordinates so we can see the trend of the data.
Given that the equation is y = 25x where y represents the number of boxes a machine packages over time, x, in minutes.
The number of boxes will be:-
y = 25x
y = 25 x 4
y = 100
Therefore, the number of the boxes machine package in 4 minutes will be 100.
To know more about an equation follow
https://brainly.com/question/8555227
#SPJ1
which company would cost the most to serve 300 students
Answer:
Company "A"
Step-by-step explanation:
its the highest line on the graph from the 300 point.
Mark each statement True or False. Justify each answer. (a) Taylor's theorem is a generalization of the mean value theorem. (b) If pn, is the nth Taylor polynomial for f at a point xo, then the first n derivatives of pn, and f are equal near the point x = xo.
The answer to statements regarding Taylor's theorem is;
a)TRUE
b) TRUE
(a) True. Taylor's theorem is a generalization of the mean value theorem.
The mean value theorem states that for any two points in the domain of a function,
there is at least one point between them on the graph of the function where the slope of the function equals the average rate of change between the two points.
Taylor's theorem is a more general statement of this theorem, where a function is approximated by a Taylor polynomial,
which is a finite sum of terms of the form \($(x-a)^n$\) multiplied by the derivative of the function at \($a$\).
(b) True. If\($p_n$\) is the nth Taylor polynomial for\($f$\) at a point \($x_0$\), then the first n derivatives of \($p_n$\) and \($f$\) are equal near the point \($x=x_0$.\)
This is because the Taylor polynomial of a function is its best linear approximation. Therefore, the derivative of the polynomial will be equal to the derivative of the function up to the order of the polynomial.
So, the first \($n$\) derivatives of the polynomial and the function will be equal near the point \($x=x_0$\).
to know more about Taylor's theorem refer here:
https://brainly.com/question/13264870#
#SPJ11
Emilio's dog eats 1/2 of a can of food each day. emilio currently has 2 1/2 cans of dog food. how many days will the current supply of dog food last? write your answer as a fraction or as a whole or mixed number. days
The current supply of dog food will last for 5 days.
Emilio's dog eats 1/2 of a can of food each day. Emilio currently has 2 1/2 cans of dog food. To determine how many days the current supply will last, we need to find the total number of days it takes to consume the available dog food.
If the dog eats 1/2 can of food each day, we can calculate the number of days the current supply will last by dividing the total amount of dog food by the amount consumed each day.
2 1/2 cans of dog food can be written as 2 + 1/2 = 2.5 cans.
The number of days the current supply will last is given by:
(2.5 cans) / (1/2 can per day)
To divide by a fraction, we multiply by its reciprocal:
(2.5 cans) * (2/1 can per day)
The cans cancel out, leaving us with:
2.5 * 2 = 5
Therefore, the current supply of dog food will last for 5 days.
The current supply of dog food, which is 2 1/2 cans, will last for 5 days based on the dog's consumption rate of 1/2 can per day.
To know more about consumption rate, visit
https://brainly.com/question/32405056
#SPJ11
find the common ratio for this geometric sequence 243, 27, 3
Answer:
The common ratio is 1/9
Step-by-step explanation:
To find the common ratio, take the second term and divide by the first term
27/ 243
1/9
We can check by taking the third term and dividing by the second
3/27 = 1/9
The nth triangular number Tn is given by the formula Tn = 1 + 2 +3 +...+n = (n(n+1))/2. The first few triangular numbers are 1, 3, 6, and 10. In the list of the first few Pythagorean triples (a, b, c), we find (3, 4, 5), (5, 12, 13), (7, 24, 25), and (9, 40, 41). Notice that in each case, the value of b is four times a triangular number. If you believe that this is true, then prove it. Otherwise find some triangular number for which it is not true.
a) Find a primitive Pythagorean triple (a, b, c) with b= 4T5 . Do the same for b= 4T6 and for b= 4T7
b) Do you think that for every triangular number Tn , there is a primitive Pythagorean triple (a, b, c) with b= 4Tn . If you believe that this is true, then prove it. Otherwise find some triangular number for which it is not true.
If we set m = 4 and n = 1, we get a = 15 and c = 17, which means (15, 60, 17) is a primitive Pythagorean triple with b = 4T5. Also, we can find primitive Pythagorean triples with b = 4T6 and b = 4T7 by using the same method. We get (21, 84, 87) for b = 4T6 and (28, 112, 113) for b = 4T7. Therefore, it is clear that for every triangular number Tn, there is a primitive Pythagorean triple (a, b, c) with b = 4Tn
A Pythagorean triple is a set of three integers that satisfy the Pythagorean theorem, which states that the sum of the squares of the lengths of the two shorter sides of a right triangle is equal to the square of the length of the longest side, or hypotenuse. For example, the triple (3, 4, 5) is a Pythagorean triple because 3^2 + 4^2 = 5^2.
Now let's talk about triangular numbers. A triangular number is the sum of the first n positive integers, and it can be represented by the formula Tn = 1 + 2 + 3 + ... + n = (n(n+1))/2. The first few triangular numbers are 1, 3, 6, and 10.
Interestingly, in the list of the first few Pythagorean triples, we can observe a pattern where the value of b is four times a triangular number. For example, in the Pythagorean triple (3, 4, 5), we have b = 4T1. In (5, 12, 13), b = 4T2. In (7, 24, 25), b = 4T3. And in (9, 40, 41), b = 4T4.
So the question is: is this pattern true for all triangular numbers? Let's investigate further.
a) To find a primitive Pythagorean triple (a, b, c) with b = 4T5, we need to find a value of a and c such that a^2 + b^2 = c^2 and b = 4T5. Using the formula for T5, we get T5 = (5(5+1))/2 = 15. Therefore, b = 4T5 = 60. We can use the Euclid's formula for generating Pythagorean triples, which states that for any two positive integers m and n with m > n, a Pythagorean triple (a, b, c) can be generated by a = m^2 - n^2, b = 2mn, and c = m^2 + n^2.
If we set m = 4 and n = 1, we get a = 15 and c = 17, which means (15, 60, 17) is a primitive Pythagorean triple with b = 4T5.
Similarly, we can find primitive Pythagorean triples with b = 4T6 and b = 4T7 by using the same method. We get (21, 84, 87) for b = 4T6 and (28, 112, 113) for b = 4T7.
b) Now, the question is whether there is a primitive Pythagorean triple (a, b, c) with b = 4Tn for any triangular number Tn. Let's assume this is true and try to prove it.
Using the same Euclid's formula, we can generate a primitive Pythagorean triple (a, b, c) with b = 4Tn by setting m = 2Tn+1 and n = Tn. This gives us a = 4Tn^2 + 1 and c = 4Tn^2 + 2Tn + 1, and we can verify that b = 4Tn using the formula for Tn.
Therefore, we have proven that for every triangular number Tn, there is a primitive Pythagorean triple (a, b, c) with b = 4Tn
For more such questions on Pythagorean triple.
https://brainly.com/question/15190643#
#SPJ11
7 x 10 + 3 x 1 + 8 x
+ 5 x
100
1,000
Answer:
8x+5005073
Step-by-step explanation:
What did I do wrong here in my answer?
Answer:
please see the attached I put the answer
Step-by-step explanation:
you answer were correct but you change the sign one of them will be positive.
find the areas of triangles 3 and 4.
Answer:15.59 square units.
Step-by-step explanation:
The area of an equilateral triangle can be calculated using the formula, Area = a2(√3/4), where 'a' is the side of the triangle. For example, if an equilateral triangle has a side of 6 units, its area will be calculated as follows. Area = a2(√3/4), Area = 62(√3/4) = 15.59 square units.
Liquid nitrogen is -196°C. What is the difference in temperature between the liquid
nitrogen and the frozen meal temperature (-18°C)?
Answer:
the state the item is in such as liquid nitrogen is frozen air and frozen meals are ice solid.
Step-by-step explanation:
linear regression adapts to sudden shifts to data patterns.
[ T / F]
Linear regression adapts to sudden shifts to data patterns. [False]
Linear regression is a type of predictive analysis technique used to form a linear relationship between a dependent and an independent variable. However, linear regression does not adapt well to sudden changes in data patterns or outliers that could impact the model's accuracy. Therefore, it is not suitable for modeling data with sudden shifts. In such cases, non-linear regression methods or more complex models may be more appropriate.
Linear regression is a basic yet powerful technique for modeling relationships between variables. It is used for a wide range of applications, from predicting sales to estimating the impact of a variable on the outcome of interest. However, the accuracy of linear regression models can be impacted by outliers or sudden changes in data patterns. Therefore, it is important to carefully evaluate the data and select appropriate modeling techniques based on the specific characteristics of the dataset. Non-linear regression techniques or more advanced models may be better suited for modeling data with sudden shifts or extreme values.
Know more about Linear regression here:
https://brainly.com/question/32505018
#SPJ11
Find the area of a square with side length x when x is equal to the given value.
Are the area of a square and the length of its side directly proportional? Justify your answer.
x=15 ft
Answer:
The area is 225 and they are not directly proportional
Step-by-step explanation:
find the area by doing 15 x 15 which is 225
Answer:
225
Step-by-step explanation:
easy
i need help!! (its due by june 12th!)
The measure of the angles and arc are:
1). arc CF = 98°
2). angle T = 60°
3). arc RS = 78°
4). arc AB = 116°
5). angle M = 68°
8). x = 11
9). x = 2
10). x = 11
What is angle subtended by an arcThe angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circles circumference.
1). arc FG = 2(63) = 126
arc EF = 360 - (126 + 136)
arc EF = 98°
2). angle R = 90/2
angle R = 45°
angle T = 180 - (45 + 75) {sum of interior angles of a triangle}
angle T = 60°
3). angle Q = 180 - (61 + 80) {sum of interior angles of a triangle}
angle Q = 39°
arc RS = 2(39)
arc RS = 78°
4). arc ABC = 2(73) = 146°
arc AB = 146 - 60 = 86°
arc VAB = 2(101) = 202°
arc AV = 202 - 86
arc AV = 116°
5). arc KL = 360 - (88 + 136)
arc KL = 136
angle M = 136/2
angle M = 68°
8). angle B = 84/2 = 42
5x - 7 + 42 = 90° {right triangle formed by diameter}
x = 55/5 = 11
9). 2(50x) = 38x + 61x + 2
100x = 99x + 2 {collect like terms}
x = 2
10). 10x - 11 = 8x + 11 {angles in same segment}
10x - 8x = 11 + 11
2x = 22
x = 11
Therefore, the measure of the angles and arc are:
1). arc CF = 98°
2). angle T = 60°
3). arc RS = 78°
4). arc AB = 116°
5). angle M = 68°
8). x = 11
9). x = 2
10). x = 11
Read more about angle here:https://brainly.com/question/24423151
#SPJ1
i need help asap thanks for anyone who helps
Answer:
x=60
y=32
z=116
Step-by-step explanation:
HTH :)
You found a pair of shoes for $28.75. If you have a 25% off coupon, how much money will you save on the shoes? *
Answer:
$7.1875
Step-by-step explanation:
$28.75 x .25=7.1875
which one has only positive values? choose all applied. a. normal distribution b. z distribution c. chi square distribution d. f distribution e. t distribution
The normal distribution has only positive values. Option A is the correct answer.
The normal distribution is a continuous probability distribution that is symmetric around the mean, and its values are only positive. The other distributions listed, such as the chi-square, f, and t distributions, are all skewed and have values that can be negative or positive. The z-distribution is similar to the normal distribution but has a mean of 0 and a standard deviation of 1, and thus can also have negative values. Therefore, the only distribution that has only positive values is the normal distribution, making option A the correct answer.
You can learn more about normal distribution at
https://brainly.com/question/4079902
#SPJ11
4598÷101=
with the remainder
Answer:
45 remainder 93
Step-by-step explanation:
01.01) Rewrite the expression with rational exponents as a radical expression. 7 times x to the two thirds power cube root of the quantity 7 times x to the power of 2 square root of the quantity 7 times x to the power of 3 7 times the cube root of x to the power of 2 7 times the square root of x to the power of 3
Answer:
\( (7x)^{\frac{2}{3} = (\sqrt[3]{7x})^2 \)
Step-by-step explanation:
Given the expression \( (7x)^{\frac{2}{3} \), to express this as a radical expressions, we'd apply the rule/law of indices that deals with converting expressions that has rational exponents into radical expressions.
The rule of indices to apply is: \( b^{\frac{m}{n}} = (\sqrt[n]{b})^m \)
To apply this to the expression, \( (7x)^{\frac{2}{3} \), the denominator of the fraction of the exponent would determine the root, that is, cube root in this case. The numerator of the exponent would then determine the exponent of the radical expressions.
Thus:
\( (7x)^{\frac{2}{3} = (\sqrt[3]{7x})^2 \)
Polygon ABCDE is the first in a pattern for a high school art project. The polygon is transformed so that the image of A' is at (−4, 2) and the image of D' is at (−2, 1).
The polygon ABCDE has been transformed by a translation of -2 units in the x-direction and 1 unit in the y-direction to obtain the image polygon.
To determine the transformation that occurred on polygon ABCDE, we can use the given coordinates of the original polygon and its transformed image. Let's consider the coordinates of points A and D:
Point A: (x₁, y₁)
Point D: (x₄, y₄)
Transformed point A': (-4, 2)
Transformed point D': (-2, 1)
The transformation involves a translation in both the x and y directions. We can calculate the translation distances for both coordinates by subtracting the original coordinates from the transformed coordinates:
Translation in x-direction: Δx = x' - x
Translation in y-direction: Δy = y' - y
For point A:
Δx = -4 - x₁
Δy = 2 - y₁
For point D:
Δx = -2 - x₄
Δy = 1 - y₄
Now, we can equate the translation distances for points A and D to find the transformation:
Δx = -4 - x₁ = -2 - x₄
Δy = 2 - y₁ = 1 - y₄
Simplifying these equations, we get:
-4 - x₁ = -2 - x₄
2 - y₁ = 1 - y₄
Rearranging the equations:
x₄ - x₁ = -2
y₁ - y₄ = 1
Therefore, the transformation involves a horizontal translation of -2 units (Δx = -2) and a vertical translation of 1 unit (Δy = 1).
For more such information on: polygon
https://brainly.com/question/29911875
#SPJ8
Please help!
Thank you!
20 points possible
Answer:
c hope it helps
plz mark me as brainliest
Step-by-step explanation:
What is the breadth of perimeter=50 ft and Length=15ft
Answer:
Breadth = 10 ft
Step-by-step explanation:
Given information,
→ Perimeter (P) = 50 ft
→ Length (L) = 15 ft
→ Breadth (B) = ??
Now we have to,
→ find the required value of Breadth.
Formula we use,
→ P = 2(L + B)
Then the required Breadth will be,
→ P = 2(L + B)
→ 50 = 2(15 + B)
→ 30 + 2B = 50
→ 2B = 50 - 30
→ B = 20/2
→ [ B = 10 ft ]
Hence, required Breadth is 10 ft.
please answer the following
please explain how you got your answer
Answer:
P(1) = 4/20 or 1/5
P(2) = 3/20
P(3) = 7/20
P(4) = 6/20 or 3/10
Step-by-step explanation:
Crystal spun the spinner 20 times. 1 was the outcome 4 times out of 20 spins, so the experimental probability would be 4/20 or 1/5. Same goes for all the other ones.
Find the exact length of the curve. X =√y (y - 3), 9 ≤ y ≤ 25 X Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places. x = √y - 6y, 1 ≤ y ≤ 4 X dy = X Find the length of the arc of the curve from point P to point Q. 49 49 v-1x², P(-7, 42), Q(7,42) y = 2
To find the exact length of the curve given by x = √(y(y - 3)), 9 ≤ y ≤ 25, we can use the arc length formula:
L = ∫√(1 + (dy/dx)²) dy
First, we need to find dy/dx by differentiating the equation x = √(y(y - 3)) with respect to y:
dx/dy = 1 / (2√(y(y - 3))) * (2y - 3)
Next, we substitute dx/dy back into the arc length formula:
L = ∫√(1 + (dx/dy)²) dy
L = ∫√(1 + ((2y - 3) / (2√(y(y - 3))))²) dy
Simplifying the expression under the square root:
L = ∫√(1 + (2y - 3)² / (4(y(y - 3)))) dy
L = ∫√((4(y(y - 3)) + (2y - 3)²) / (4(y(y - 3)))) dy
Now we can integrate this expression over the given range of y, from 9 to 25, to obtain the exact length of the curve.
To find the length of the arc of the curve from point P(-7, 42) to point Q(7, 42), where y = 2, we can use the formula for arc length:
L = ∫√(1 + (dy/dx)²) dx
First, we need to find dy/dx by differentiating the equation y = 2 with respect to x;
dy/dx = 0
Since dy/dx is 0, the arc length formula becomes:
L = ∫√(1 + 0²) dx
L = ∫√(1) dx
L = ∫1 dx
Integrating this expression over the range from x = -7 to x = 7 will give us the length of the arc of the curve between points P and Q.
For more questions Curve:
https://brainly.com/question/31012623
#SPJ8
a rectangle is h units wide it length is 3 units more than the width
Answer:
I think that you have to find the length and width of the rectangular
creating a discussion question, evaluating prospective solutions, and brainstorming and evaluating possible solutions are steps in_________.
Creating a discussion question, evaluating prospective solutions, and brainstorming and evaluating possible solutions are steps in problem-solving.
What is problem-solving?
Problem-solving is the method of examining, analyzing, and then resolving a difficult issue or situation to reach an effective solution.
Problem-solving usually requires identifying and defining a problem, considering alternative solutions, and picking the best option based on certain criteria.
Below are the steps in problem-solving:
Step 1: Define the Problem
Step 2: Identify the Root Cause of the Problem
Step 3: Develop Alternative Solutions
Step 4: Evaluate and Choose Solutions
Step 5: Implement the Chosen Solution
Step 6: Monitor Progress and Follow-up on the Solution.
Let us know more about problem-solving : https://brainly.com/question/31606357.
#SPJ11
Solve each system of equations.
1. 3x + y = 7; 5x +3y = -25
2. 2x + y = 5; 3x - 3y = 3
3. 2x + 3y = -3; x + 2y = 2
4. 2x - y = 7; 6x - 3y = 14
5. 4x - y = 6; 2x -y/2 = 4
The solution to the system of equations is x = 11.5 and y = -27.5.
The solution to the system of equations is x = 2 and y = 1
The solution to the system of equations is x = -12 and y = 7.
The solution to the system of equations is x = 0.5 and y = -6.
What is Equation?A system of linear equations can be solved graphically, by substitution, by elimination, and by the use of matrices.
To solve the system of equations:
3x + y = 7
5x + 3y = -25
We can use the method of substitution or elimination to find the values of x and y.
Let's solve it using the method of substitution:
From the first equation, we can express y in terms of x:
y = 7 - 3x
Substitute this expression for y into the second equation:
5x + 3(7 - 3x) = -25
Simplify and solve for x:
5x + 21 - 9x = -25
-4x + 21 = -25
-4x = -25 - 21
-4x = -46
x = -46 / -4
x = 11.5
Substitute the value of x back into the first equation to find y:
3(11.5) + y = 7
34.5 + y = 7
y = 7 - 34.5
y = -27.5
Therefore, the solution to the system of equations is x = 11.5 and y = -27.5.
To solve the system of equations:
2x + y = 5
3x - 3y = 3
Again, we can use the method of substitution or elimination.
Let's solve it using the method of elimination:
Multiply the first equation by 3 and the second equation by 2 to eliminate the y term:
6x + 3y = 15
6x - 6y = 6
Subtract the second equation from the first equation:
(6x + 3y) - (6x - 6y) = 15 - 6
6x + 3y - 6x + 6y = 9
9y = 9
y = 1
Substitute the value of y back into the first equation to find x:
2x + 1 = 5
2x = 5 - 1
2x = 4
x = 2
Therefore, the solution to the system of equations is x = 2 and y = 1.
To solve the system of equations:
2x + 3y = -3
x + 2y = 2
We can again use the method of substitution or elimination.
Let's solve it using the method of substitution:
From the second equation, we can express x in terms of y:
x = 2 - 2y
Substitute this expression for x into the first equation:
2(2 - 2y) + 3y = -3
Simplify and solve for y:
4 - 4y + 3y = -3
-y = -3 - 4
-y = -7
y = 7
Substitute the value of y back into the second equation to find x:
x + 2(7) = 2
x + 14 = 2
x = 2 - 14
x = -12
Therefore, the solution to the system of equations is x = -12 and y = 7.
To solve the system of equations:
2x - y = 7
6x - 3y = 14
Again, we can use the method of substitution or elimination.
Let's solve it using the method of elimination:
Multiply the first equation by 3 to eliminate the y term:
6x - 3y = 21
Subtract the second equation from the first equation:
(6x - 3y) - (6x - 3y) = 21 - 14
0 = 7
The resulting equation is 0 = 7, which is not possible.
Therefore, there is no solution to the system of equations. The two equations are inconsistent and do not intersect.
To solve the system of equations:
4x - y = 6
2x - y/2 = 4
We can use the method of substitution or elimination.
Let's solve it using the method of substitution:
From the second equation, we can express y in terms of x:
y = 8x - 8
Substitute this expression for y into the first equation:
4x - (8x - 8) = 6
Simplify and solve for x:
4x - 8x + 8 = 6
-4x + 8 = 6
-4x = 6 - 8
-4x = -2
x = -2 / -4
x = 0.5
Substitute the value of x back into the second equation to find y:
2(0.5) - y/2 = 4
1 - y/2 = 4
-y/2 = 4 - 1
-y/2 = 3
-y = 6
y = -6
Therefore, the solution to the system of equations is x = 0.5 and y = -6.
To learn more about Equation from the given link
https://brainly.com/question/13729904
#SPJ4
Solve the given differential equation subject to the indicated conditions. y ′′
−y=x+sinx,y(0)=2,y ′
(0)=3
The solution for the given differential equation y'' - y = x + sin(x) is y = (2 + e) eᵗ - (1 + e) e⁻ᵗ + t - sin(x). The initial conditions are y(0) = 2 and y'(0) = 3.
The given differential equation is y'' - y = x + sin(x). The initial conditions are y(0) = 2 and y'(0) = 3. The solution to the differential equation is y = -x - 2cos(x) + 3sin(x) + 4.The characteristic equation is: r² - 1 = 0, whose roots are r = ±1.The complementary solution is yc = c₁eᵗ + c₂e⁻ᵗ.
The particular solution yp should have the form: yp = At + Bsin(x) + Ccos(x). Substituting this into the differential equation, we get y′′ - y = x + sin(x). Differentiating, we get:y′′ = A - Bsin(x) + Ccos(x)y′ = A + Bcos(x) + Csin(x). Substituting back:y′′ - y = x + sin(x)A - Bsin(x) + Ccos(x) - At - Bsin(x) - Ccos(x) = x + sin(x). Separating coefficients and solving the system we get A - B = 0C + B = 0A = 1. Then, C = -B = -1.
Substituting these values, we get the particular solution: yp = t - sin(x) - cos(x). Finally, the general solution is y = yc + yp = c₁eᵗ + c₂e⁻ᵗ + t - sin(x) - cos(x). Differentiating twice, we get y' = c₁eᵗ - c₂e⁻ᵗ + 1 - cos(x) - sin(x)y'' = c₁eᵗ + c₂e⁻ᵗ + sin(x) - cos(x).
Substituting the initial conditions:y(0) = c₁ + c₂ - 1 = 2y'(0) = c₁ - c₂ - 1 = 3. Solving the system, we get c₁ = 2 + e, c₂ = -1 - e.
The particular solution is:yp = t - sin(x) - cos(x)Then the solution to the differential equation subject to the initial conditions is: y = c₁eᵗ + c₂e⁻ᵗ + t - sin(x) - cos(x) = (2 + e) eᵗ - (1 + e) e⁻ᵗ + t - sin(x) - cos(x).
Learn more about differential equations here:
https://brainly.com/question/30093042
#SPJ11
g a generic drug is being tested to test its efficacy (effectiveness) at reducing blood pressure in patients with hypertension (a.k.a. high blood pressure). in a randomized, double-blind experiment with 200 patients, 100 are given the name-brand drug (control group) and 100 are given a generic version of the drug (treatment group). in the control group, the average reduction in blood pressure is 15.2 mmhg with a standard deviation of 11.5 mmhg. in the treatment group, there is an average reduction of 14.6 mmhg and a standard deviation of 12.5 mmhg. neither group has any outliers. a researcher claims that this study shows the generic drug is not as effective as the name-brand drug. what would be the reply of a statistician? you have two attempts for this problem so choose wisely. if you do not receive 5 points in the gradebook after submitting this assignment then you have answered incorrectly. make sure to try it again before the deadline.
A statistician would reply that in order to determine if the generic drug is less effective than the name-brand drug, a hypothesis test needs to be conducted.
The null hypothesis (H0) would be that there is no difference in the average blood pressure reduction between the two drugs, while the alternative hypothesis (H1) would be that the name-brand drug has a higher average reduction in blood pressure than the generic drug.
To test these hypotheses, a t-test would be appropriate since we have two independent samples (control and treatment groups) with known means, standard deviations, and sample sizes. The t-test will provide a p-value, which can be compared to a chosen significance level (e.g., α = 0.05).
If the p-value is less than the significance level, we reject the null hypothesis and conclude that there is a significant difference in the average blood pressure reduction between the two drugs. If the p-value is greater than the significance level, we fail to reject the null hypothesis, meaning we do not have enough evidence to claim that the name-brand drug is more effective than the generic drug.
Learn more about hypothesis:
https://brainly.com/question/10854125
#SPJ11
Based upon the input from Units 1 and 2, you have just received your next assignment that will contribute to your next decision. For the outdoor sporting goods client, based upon your prior decision on whether or not to expand to the next market or retain your current position, justify your decision further utilizing the chi-square distribution tool. One key criterion point: You do not have adequate data to formulate a full chi-square for the outdoor sporting goods client. However, you have sufficient data to initiate this process. You are charged to demonstrate the initial steps of a nonparametric test that are qualitative. Utilizing the null and alternative hypotheses, further present your justifications for your selection and what it means beyond the mere formulas. What is this going to tell the Board of Directors and contribute to the decision-making process? The following information may be helpful in understanding chi-square and hypothesis testing: Please review this helpful video. The presenter uses flipping a coin and rolling a die. These are examples and analogies used in the CTU resources. The following are assumptions that might make the assignment more helpful and make the responses more uniform: Continue to utilize the Big D scenario. Work under the assumption that the sample is based upon 2 different proposed product lines. Additionally, work under the assumption that the same demographics are utilized for each product.
My forecast is that you will either enter the next market or, more likely, keep your existing position. These are the theories we have.
Because we put our alternative hypothesis equal to what we wish to show, you should continue to hold the stance you already hold. The opposite hypothesis, or null hypothesis, is a claim that there is no difference. For instance,There is no discernible difference between the mean and sample population, according to the null hypothesis.Alternative Hypothesis H1: The mean and sample population differ significantly.Level of significance: A: If there is no difference in the sample as well as population means, there is a 5% chance that the null hypothesis will be rejected. In a non-parametric test, rankings are considered as a test statistic after being translated from the observed sample. We utilize the rankings to calculate the test statistic in non-parametric testing. The choice of accepting or the null hypothesis being rejected will be decided when the levels of liberty and crucial values have been defined. Chi square is used since there are only two choices to compare. As soon as we get our data, we can calculate the chi squared value x2 and determine the crucial values from table of freedom levels with 95% certainty.To know more about hypothesis visit:
https://brainly.com/question/11560606
#SPJ4
please show work
Solve the system of equations by substitution. x + 3y - 2x + 4y = 24 = 18 OA. (1,5) OB. (-6,0) OC. (0,6) OD. no solution
Simplifying this equation, we get:-x + 24 - x = 24-x + x =0.Therefore, there's no solution.
Given system of equations isx + 3y - 2x + 4y = 24And, we know that x - 2x = -x and 3y + 4y = 7yTherefore, the above equation becomes-y + 7y = 24 6y = 24y = 24/6y = 4 .
Substituting the value of y in the first equation, we getx + 3y - 2x + 4y = 24x + 3(4) - 2x + 4(4) = 24x + 12 - 8 + 16 = 24x + 20 = 24x = 4Hence, the main answer is (0,6).
The given equation is x + 3y - 2x + 4y = 24We can simplify this as: 3y + 4y = 24 + 2x.
Subtracting x from the other side of the equation and simplifying further, we get:7y = 24 - xTherefore, y = (24 - x) / 7.
We substitute this value of y in one of the equations of the system.
For this example, we'll substitute it in the first equation:x + 3y - 2x + 4y = 24.
The equation becomes:x - 2x + 3y + 4y = 24Simplifying, we get:-x + 7y = 24.
Now we can substitute y = (24 - x) / 7 in this equation to get an equation with only one variable:-x + 7(24 - x) / 7 = 24.
Simplifying this equation, we get:-x + 24 - x = 24-x + x = 0.
Therefore, there's no solution.
To know more about system of equations visit:
brainly.com/question/21620502
#SPJ11