Use the given feasible region to find the maximum possible value of the objective function. f=5x+6y
Answers
The maximum value above is 46 at (2, 6). The production output goal which refers to the maximisation of profits relative to production is described by the objective function.
The production output goal which refers to the maximisation of profits relative to production is described by the objective function, which is a mathematical equation. The quantity of the final result is then calculated using the correlation between the variables. In other words, it's a formula that companies employ to meet their production and profitability objectives.
F = 5x + 6y
The coordinates of the feasible region are (0, 6), (1, 6.5) and (2, 6)
Substitute (0, 6), (1, 6.5) and (2, 6) in the above equation
F(0, 6) = 5(0) + 6(6) = 36
F(1, 6.5) = 5(1) + 6(6.5) = 44
F(2, 6) = 5(2) + 6(6) = 46
The maximum value above is 46 at (2, 6)
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Related Questions
Find the value of x
Answers
The value of x in the intersecting secants in a circle is 0.5
Finding the value of x in the intersecting secantsFrom the question, we have the following parameters that can be used in our computation:
intersecting secants
Using the theorem of intersecting secants, we have teh following equation
2 * (x + 2) = 1 * (1 + 4)
Evaluating the like terms
So, we have
2 * (x + 2) = 1 * 5
Divide both sides by 2
This gives
x + 2 = 2.5
Evaluating the like terms
So, we have
x = 0.5
Hence, the value of x is 0.5
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Help I need help with this now
Answers
The volume of the rectangular prism is 90 units³
We have,
The figure shown has the dimensions:
L = Length = 5 units
W = Width = 6 units
H = Height = 3 units
Now,
The volume of the rectangular prism.
= L x W x H
= 5 x 6 x 3
= 90 units³
Thus,
The volume of the rectangular prism is 90 units³
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Help pldssssssss………………..
Answers
The missing value for the quadratic function is given as follows:
y = -3.
How to obtain the quadratic function?As a function of it's roots x* and x**, the quadratic function is defined as follows:
y = a(x - x*)(x - x**)
In which a is the leading coefficient.
The roots of the function are the values of x when y = 0, hence:
x* = -4, x** = -2.
Thus:
y = a(x + 4)(x + 2)
y = a(x² + 6x + 8).
When x = 0, y = -8, hence the leading coefficient a of the function is given as follows:
8a = -8
a = -1.
Hence:
y = -x² - 6x - 8;
The missing value is the value of y when x = -1, hence:
y = -(-1)² - 6(-1) - 8
y = -3.
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what is the abgle of elevation from the ground to the top of a 45 foot tree from 65 feet away
Answers
The angle of elevation from the ground to the top of a 45 foot tree from 65 feet away is 33.41 degrees.
To find the angle of elevation from the ground to the top of a tree, we need to use some trigonometry. We can use the tangent function, which relates the opposite and adjacent sides of a right triangle.
Let's call the angle of elevation θ. We can draw a right triangle with the height of the tree (45 feet) as the opposite side and the distance from the tree to the observer (65 feet) as the adjacent side. Then, we can use the formula:
tan(θ) = opposite / adjacent
Plugging in the values we have:
tan(θ) = 45 / 65
We can solve for θ by taking the inverse tangent of both sides:
θ = arctan(45 / 65)
Using a calculator, we get:
θ ≈ 33.41 degrees
Therefore, the angle of elevation from the ground to the top of the tree is approximately 33.41 degrees.
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A study is conducted to determine if the age at which an individual can receive a driver's license should be increased. One
hundred people at a local high school are asked to take a survey.
The survey is composed of 5 statements to which people respond on a scale of 1-5. A response of 5 indicates strong
agreement with the statement and a response of 1 indicates strong disagreement with the statement. The results to the
statement, "The age at which an individual can receive a driver's license should not be increased." shows an average
response score of 1.5 and a standard deviation of 0.3.
One conclusion in the report of the study states that there may be a causal relationship between the age of those surveyed and
their responses.
Which statement regarding the report is true?
A)The report inaccurately stated the results of the survey because the majority of those surveyed were likely
teenagers.
B)The report accurately stated the results because the sample size was sufficient.
C)The report accurately stated the results of the survey because the majority obse surveyed were likely teenagers.
Reading Off
D)The report inaccurately stated the results because teenagers are likely to oppose an increase in the age
requirement.
Answers
Answer: B) The report accurately stated the results because the sample size was sufficient.
Step-by-step explanation:
The given statement in the report about a possible causal relationship between age and responses cannot be determined solely based on the information provided. However, the statement can be considered accurate because the sample size of 100 people from a local high school was sufficient to provide reliable results. The fact that the majority of those surveyed were teenagers does not make the report inaccurate or unreliable. The mean response score of 1.5 and the standard deviation of 0.3 are valid indicators of the attitudes of the surveyed group towards the age at which an individual can receive a driver's license.
Identify the pairs of supplementary angles.
Choose all that apply.
A. RQS and SQR
B. SQT and SQR
C. TQP and RQP
D. SQR and RQP
E. PQR and RQP
F. SQT and TQP
G. TQP and PQT
H. SQR and TQP
Answers
The pairs of angles that are supplementary angles include the following:
SQT and SQR = Option B
TQP and RQP = Option C
SQR and RQP = Option D
SQT and TQP = Option F
What are supplementary angles?A supplementary angle is the angle that makes up to 180° when both are summed up together.
The angles that are chosen above include the following:
<SQT = 165°
<SQR = 15°
The addition of the both angles = 180°, and therefore is an example of a supplementary angle.
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Given: a || b
Find the missing angle measures in the diagram. Explain how you find each angle measure. (please explain how you got the answer)
Answers
The angle measure explained in the solution.
Given that, a || b, we need to find the missing angles,
∠1 = 42° [vertically opposite angles]
∠3 = 62° [vertically opposite angles]
∠2 = 180°-(∠1+62°) [angle in a straight line]
∠2 = 76°
∠4 = ∠2 [vertically opposite angle]
∠4 = 76°
∠4 = ∠9 = 76° [alternate angles]
∠9 = ∠12 = 76° [vertically opposite angle]
∠3 = ∠ 6 = 62° [alternate angles]
∠ 6 = ∠7 = 62° [vertically opposite angle]
∠3 + ∠5 = 180° [consecutive angles]
∠5 = 118°
∠5 = ∠8 = 118° [vertically opposite angle]
∠4 + ∠10 = 180° [consecutive angles]
∠10 = 104°
∠10 = ∠11 [vertically opposite angle]
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Need help fast please!
Answers
The value of -5/6 ÷( -1/4) is 3 1/3
What are fractions?A fraction is a part of a whole. it consist of upper part( numerator) and lower part denominator.
In a simple fraction, both numerator and denominator are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
Solving -5/6 ÷( -1/4)
-5/6 × -4/1
= 20/6
= 10/3
= 3 1/3
therefore the value of the expression is 3 1/3
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Convert the polar coordinates (6
Answers
The polar coordinates in rectangular coordinates are (3√2, 2√6)
Given are polar coordinates (6√2, 7π/3), we need to convert it into, rectangular coordinates.
so, (r, θ) = (6√2, 7π/3)
x = rcosθ
y = rsinθ
r = 6√2, θ = 7π/3
x = 6√2 cos 7π/3 = 3√2
y = 6√2 sin 7π/3 = 2√6
Hence, the polar coordinates in rectangular coordinates are (3√2, 2√6)
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Write an essay describing how you would implement subtraction as a money lesson. You must add the lesson plan for this lesson to support your discussion in your essay. Your essay must not be longer than 3 pages. And if you use ideas from the internet, did not forget to reference it as far as possible. Also, if you are going to do this lesson in your class, you are welcome to add images to your assignment of what you did with the learners. (But this is not a requirement). I will be posting the rubric for the assignment along with the slides tomorrow morning. Due date: Tuesday the 25th of April 2023 su wil mo follo toric
Answers
The implementing of subtraction as a money lesson need a starting with concrete examples and building students' understanding of the concept in scenarios.
How can we implement subtraction as a money lesson?As a mathematical concept, subtraction is useful in real-life scenarios including managing money. To implement it, we must note that it important to start with concrete examples that students can relate to like making purchases or earning an allowance.
We can provide the students with a set amount of money and ask them to subtract the cost of various items from it to determine how much they have left. For example, if a student has $10 and wants to buy a $3 toy, they would need to subtract $3 from $10 to determine that they have $7 remaining.
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please help find the equations of the following lines
Answers
The line equations according to its features are, respectively:
Case C: y = - 2
Case D: x = - 7
Case E: y = - x + 1 / 2
Case F: y = - (1 / 3) · x + 20 / 3
Case G: y = 4 · x + 17
How to determine the equation of lines
In this question we must determine five line equations based on its features. The equation of the line can be found by understanding the following features:
A line can be found by knowing a slope and a point.Two lines are parallel when both lines have the same slope.Two lines are perpendicular when the product of the slopes of both lines is equal to - 1.There are two forms of the equation of the line:
Slope-intercept
y = m · x + k
Standard
a · x + b · y + c = 0
Where:
x - Independent variable.y - Depedent variable.m - Slopek - Intercepta, b, c - Standard coefficients.Now we proceed to determine the equation of each line:
Case C: m = 0, (x, y) = (- 7, - 2)
- 2 = 0 · (- 7) + k
k = - 2
y = - 2
Case D: m = 0, (x, y) = (- 7, - 2)
x = - 7
Case E: k = 1 / 2, m = - 1
y = - x + 1 / 2
Case F: Parallel to x - 3 · y = 9, (x, y) = (2, 6)
x - 3 · y = 9
3 · y = 9 - x
y = 3 - (1 / 3) · x
m = - 1 / 3
6 = - (1 / 3) · 2 + k
6 = - 2 / 3 + k
k = 20 / 3
y = - (1 / 3) · x + 20 / 3
Case G: Perpendicular to y + (1 / 4) · x - 5 = 0, (x, y) = (- 3, 5)
y + (1 / 4) · x - 5 = 0
y = - (1 / 4) · x + 5
m = - 1 / 4
m' = 4
5 = 4 · (- 3) + k
5 = - 12 + k
k = 17
y = 4 · x + 17
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Graph the image of AWXY after the
following sequence of
transformations:
Translation 18 units left and 8
units down
Reflection across the line y = x
Answers
Note that the graph of WXY when reflected to W'X'Y' is attached accordingly.
What is reflection in math?A reflection in mathematics is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a fixed point set; this set is known as the axis or plane of reflection. A figure's reflection image is its mirror image in the axis or plane of reflection.
A line of reflection is required to accomplish a geometric reflection; the resulting orientation of the two figures is opposite.
The distance between the corresponding portions of the figures is the same. Ordered pair rules reflect along the x-axis (x, -y), the y-axis (-x, y), and the line y=x (y, x).
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4) Create a check register using graph paper and enter the following transactions.
a. Your balance on 10/01 is $1,863.90.
b.
On 10/3, you write check 621 for $71.10 to the Telephone Company.
c. On 10/7, you write check 622 for $500.00 to Banner Reality for rent.
d.
On 10/8, you write check 623 for $51.12 to Electric Company for utility bill.
e.
On 10/10, you write check 624 for $25.00 to Cathy Santoro for piano lesson.
On 10/15, you deposit your paycheck of $650.00
f.
g.
h.
i.
j.
On 10/16, you write check 625 for $200.00 to Don's Day Camp.
On 10/18, you write check 626 for $90.00 to Ed's Sporting Goods.
On 10/21, you write check 627 for $49.00 to Maple Place Garage.
On 11/15, you deposit your paycheck of $400.00.
Answers
A table representing the transactions based on the question prompt is given below:
The Check Register TableDate Transaction Type Check No. Description Debit (-) Credit (+) Balance
10/01 Starting Balance - - - - $1,863.90
10/03 Check 621 Telephone Company $71.10 - $1,792.80
10/07 Check 622 Banner Reality (Rent) $500.00 - $1,292.80
10/08 Check 623 Electric Company $51.12 - $1,241.68
10/10 Check 624 Cathy Santoro (Piano) $25.00 - $1,216.68
10/15 Deposit - Paycheck - $650.00 $1,866.68
10/16 Check 625 Don's Day Camp $200.00 - $1,666.68
10/18 Check 626 Ed's Sporting Goods $90.00 - $1,576.68
10/21 Check 627 Maple Place Garage $49.00 - $1,527.68
11/15 Deposit - Paycheck - $400.00 $1,927.68
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Find a polynomial function f(x) of degree 3 with zeros, 2, -3 , 5 and f(3)=6
Answers
A polynomial function f(x) of degree 3 with given zeros, 2, -3 , 5 and condition f(3)=6 is given by f(x) = -1/2 (x-2)(x+3)(x-5).
Degree of the polynomial function is equal to 3.
Zero's of the polynomial function is equal to 2, -3 , 5 .
And f(3) = 6
If 2, -3, and 5 are zeros of f(x), then we can write function as,
f(x) = a(x-2)(x+3)(x-5)
where a is some constant.
To determine the value of a, we can use the fact that f(3) = 6.
Substituting x = 3 into the equation above, we get,
f(3) = a(3-2)(3+3)(3-5)
= -12a
Here we have,
f(3) = 6, so we can set these two expressions equal to each other and solve for a,
⇒ -12a = 6
⇒ a = -1/2
Now we can substitute this value of a back into the equation for f(x) that we found earlier,
⇒ f(x) = -1/2 (x-2)(x+3)(x-5)
Therefore, a polynomial function f(x) of degree 3 with zeros 2, -3, 5, and f(3) = 6 is equal to f(x) = -1/2 (x-2)(x+3)(x-5).
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The right triangle with vertices (0, 0), (0, 3) and (-4, 0) is revolved around the x-axis to form a three-dimensional solid.
What is the volume of the resulting solid? Round to the nearest thousandth
Answers
The volume of the resulting solid revolved around the x-axis is equal to 28.274 cubic units (round to the nearest thousandth).
Vertices of the right triangle are,
(0, 0), (0, 3) and (-4, 0)
To obtain the solid formed by revolving the given right triangle about the x-axis, use the disk method.
The cross-sectional area of the solid at a given height is a circle with radius = distance between the x-axis and the upper edge of the triangle at that height.
The height of the triangle is 3 units,
and the base of the triangle is 4 units.
So, the equation of the hypotenuse of the right triangle can be found as follows,
y = (3/4)x + 3
Now, let us consider a horizontal slice of the solid at a distance y units above the x-axis.
The radius of the circle at this height is ,
r = y - 3
The area of the circle at this height is ,
A = πr²
= π(y - 3)²
The limits of integration are y = 0 the x-axis to y = 3 the height of the triangle.
Using the disk method, the volume of the solid is,
V = [tex]\int_{0}^{3}[/tex] π(y - 3)²dy
Evaluating the integral, we get,
⇒ V = π /3 ( y - 3 )³[tex]|_{0}^{3}[/tex]
⇒ V = π/3 [( 3- 3 )³ - ( 0 -3)³ ]
⇒ V = (π /3) ( 27)
⇒V = 9π
⇒V = 9 (3.1415)
Rounding to the nearest thousandth gives,
V ≈ 28.274
Therefore, the volume of the solid formed by revolving the given right triangle about the x-axis is approximately 28.274 cubic units.
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Offering 100 points to the first correct answer. Need ASAP - Please!!
The lengths of two sides of a triangle are shown.
Side 1: 8x2 − 5x − 2
Side 2: 7x − x2 + 3
The perimeter of the triangle is 4x3 − 3x2 + 2x − 6.
Part A: What is the total length of the two sides, 1 and 2, of the triangle? Show your work. (4 points)
Part B: What is the length of the third side of the triangle? Show your work. (4 points)
Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer. (2 points)
Answers
Te polynomials are closed under addition and subtraction
What is the total length of the two sides, 1 and 2, of the triangle?This is calculated as
Length 1 and 2 = 8x^2 − 5x − 2 + 7x − x^2 + 3
Evaluate
Length 1 and 2 = 7x^2 + 2x + 1
What is the length of the third side of the triangle?This is calculated as
Third side = Perimeter - Length 1 and 2
So, we have
Third side = 4x^3 − 3x^2 + 2x − 6 - 7x^2 - 2x - 1
Evaluate
Third side = 4x^3 − 10x^2 − 7
Polynomials are closed under addition and subtraction?Yes, the answers for Part A and Part B show that the polynomials are closed under addition and subtraction
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Given that cos x = 3/5 and 0
Answers
Answer:
What do we have to do in this? Find x? Let me know I'll explain it in the comment section
PLEASE SOMEONE HELP ME!! ANSWER BELOW
Answers
A. The slope of the linear function is given as follows: m = 2.
B. The slope means that the number of races increases by two when the number of track meets increases by one.
C. The y-intercept of 5 means that when there are 5 races when there are 0 track races.
D. The slope-intercept definition of the linear function is given as follows: y = 2x + 5.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change of the output variable relative to the input variable.b is the intercept, representing the value of y when x assumes a value of zero.The input and output variables for this problem are given as follows:
Input x: number of track meets.Output y: number of races.Two points in the function are given as follows:
(0,5) and (1,7).
Hence the slope and the intercept are given as follows:
Slope of 2, as when x increases by one, y increases by two.Intercept of 5, as when x = 0, y = 5.Meaning that the function is defined as follows
y = 2x + 5.
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I need help with this to find x and y value pls explain me with reasons.
Answers
The x and y values in the triangle are:
x = 58°
y = 26°
How to find x and y values in the triangle?Trigonometry deals with the relationship between the ratios of the sides of a triangle with its angles.
To find the x and y values in the triangle, check the attached image for labeling.
In the image:
Triangle ABC is isosceles. Thus,
t = 61° (base angles of isosceles triangles are equal)
x + t + 61 = 180 (sum of angles in a triangle is 180°)
x + 61 + 61 = 180
x = 180 - 61 - 61
x = 58°
x + v = 180 (sum of angles on a straight line is 180°)
58 + v = 180
v = 180 - 58
v = 122°
In triangle ACD:
32 + v + y = 180 (sum of angles in a triangle is 180°)
32 + 122 + y = 180
y = 180 - 32 - 122
y = 26°
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I need assistance please.
Your Assignment
Mr. Paulsen challenges Olivia and Angelica to move figure ABCDE onto figure A"B"C"D"E" using a series of two different transformations. They give two different answers.
Answer the questions to investigate ways to transform ABCDE.
1. Olivia finds a combination of two different transformations that moves ABCDE onto A"B"C"D"E". What is one way she might have done this? (3 points)
2. Angelica reflects ABCDE over the y-axis and translates it up 8 units. Does her transformed figure match A"B"C"D"E"? If not, describe how her transformed figure compares to A"B"C"D"E". (3 points)
3. Michael says he can move ABCDE onto A"B"C"D"E" with one transformation by translating ABCDE diagonally so that it moves 8 units up and 10 units right. Is he correct? Explain why or why not. (4 points)
Answers
One way Olivia might have moved ABCDE onto A"B"C"D"E" is by first reflecting ABCDE over the x-axis, and then translating it 4 units to the left and 6 units down.
1) This would map point A to A", B to B", C to C", D to D", and E to E", creating A"B"C"D"E".
2) Angelica's transformation does not result in a figure that matches A"B"C"D"E". Reflecting ABCDE over the y-axis would map point A to A", B to E", C to D", D to C", and E to B", so the shape would be flipped horizontally. Translating it up 8 units would then shift the shape up, but it would still be horizontally flipped, so it would not match A"B"C"D"E".
3) Michael's claim is not correct. Translating ABCDE diagonally 8 units up and 10 units right would move point A to point J, which is not on A"B"C"D"E". The other points would also not be in their correct positions, so the resulting shape would not match A"B"C"D"E". To get to A"B"C"D"E" with one transformation, Michael would need to use a combination of translation, rotation, and/or reflection.
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I keep coming up with 75. The answer is 85.5. How do you get it?picture below of problem.
10A) A large company is trying to determine the mean number of bags of dog food sold per day in
its stores. The dot plot shows the mean number of bags sold per day from 40 samples of 25
stores (rounded to the nearest 10 bags).
Means of Samples
0
50
100
150
Bags of Dog Food Sold per Day
How many bags of dog food sold per day is an appropriate estimate of the population mean?
Round to the nearest tenth.
10B) Find and interpret the variability in the distribution.
Answers
To find the variability in the distribution of the means, we need to calculate a measure of spread, such as the standard deviation. We can use the dot plot to estimate the standard deviation of the distribution.
From the dot plot, we see that the range of the means is from 0 to 150 bags of dog food sold per day. The midpoint of this range is 75, which we can use as an estimate of the population median. We can estimate the standard deviation by calculating the distance between the median and the quartiles.
From the dot plot, we can see that the lower quartile (Q1) is around 60, and the upper quartile (Q3) is around 110. Therefore, the interquartile range (IQR) is:
IQR = Q3 - Q1 = 110 - 60 = 50
We can use the IQR to estimate the standard deviation by assuming that the distribution is approximately normal and using the empirical rule, which states that:
Approximately 68% of the data falls within one standard deviation of the mean.
Approximately 95% of the data falls within two standard deviations of the mean.
Approximately 99.7% of the data falls within three standard deviations of the mean.
Since the IQR is about half of the range, we can estimate the standard deviation as:
SD ≈ IQR / 1.35 ≈ 50 / 1.35 ≈ 37
Therefore, an appropriate estimate of the standard deviation of the distribution of means is 37, rounded to the nearest whole number.
Interpretation: The variability in the distribution of means is relatively large, with a standard deviation of approximately 37 bags of dog food sold per day. This means that the mean number of bags sold per day can vary by as much as 37 bags from one sample to another.
Find the value of x and y.
3x=8-(2y)
Answers
Answer:
3x = 6y
Step-by-step explanation:
8 - 2y = 6y and 3x is by itself so it would be 3x is equal to 6y.
If there is a polynomial of a higher degree than a quadratic, it might have more than two solutions. For example, a cubic polynomial could have up to three solutions.
The polynomial equation 20z3−11z2−3z=0 is factorable. Factor the polynomial completely and set each of the factored terms equal to zero, just like you would with a quadratic equation. What are the solutions to the given polynomial equation?
Answers
The preceding polynomial equation has three solutions: z = 0, z = 3/4, and z = -1/5.
First, we can factor out a common factor of z:
z(20z² - 11z - 3) = 0
Now we need to factor the quadratic expression in the parentheses.
We can use the quadratic formula or factor by grouping to do this. Factoring by grouping yields:
z(20z² - 11z - 3) = 0
z(4z - 3)(5z + 1) = 0
Setting each of the factored terms equal to zero, we have:
z = 0, 3/4, -1/5
Therefore, the solutions to the given polynomial equation are z = 0, z = 3/4, and z = -1/5.
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How does increasing the distance between charged objects affect the electric force between them?
The electric force increases because the distance has an indirect relationship to the force.
The electric force increases because the distance has a direct relationship to the force.
The electric force decreases because the distance has an indirect relationship to the force.
The electric force decreases because the distance has a direct relationship to the force.
Answers
The effect of increasing the distance e between charged object is that , the electric force decreases because the distance has an indirect relationship to the force.
What is coulomb's law?Coulomb's law states that the force between two charged bodies is directly proportional to the product of the charge and inversely proportional to the square of the distance between them.
Coulomb's law can therefore be expressed mathematical as;
F = Q1Q2/r²
where r is the distance between charge Q1 and Q2
This means that since the force is inversely proportional to the square of distance, force will decrease as distance is increasing.
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How do I solve this?
Answers
Answer: 1/5
Step-by-step explanation:
In this case, you multiple the exponents together because you are raising a power to a power:
25^(-3/2 * 1/3)
25^(-3/6)
25^(-1/2)
Next, when the power is negative, we can get rid of it by changing the whole number to its reciprocal (divide the number by one):
1/(25^(1/2))
Now, when an exponent is a fraction, the numerator is what the base is raised to and the denominator is what the base is rooted to:
1/(sqrt(25))
Now, simplify:
1/5
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Answers
Car Make and Model that i choose is Toyota RAV4
The Cost of this car as of today is about $27,000
To know the value of car after one year will be:
20% of $27,000
= $5,400.
So the car value will be:
$27,000 - $5,400
= $21,600 after year 1
3. Value of car after second year of ownership:
15% of $27,000
= $4,050.
So, the car value will be:
$21,600 - $4,050
= $17,550 after year 2.
4 The Exponential Function If the car continues to decrease in value by 15% each yea will be
V(x) = 27,000 x (0.85)ˣ
V(5) = 27,000 x (0.85)⁵
= 27,000 x 0.44370
= $11979.9
Therefore, the value of the car after owning it for five years is $11979.9
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See text below
Car Value: Exponential
1. Pick a car that you would be interested in buying someday. Research the cost of buying this car.
Car Make and Model:
Cost of this car as of today:
2. Cars depreciate in value over time, which means they lose a certain percent of their value each year. A car typically decreases in value by 20% within the first year. If the car you picked above decreased in value by 20% in its first year, how much will it be worth one year after owning it?
Value of car after one year:
3. Each year after the first year, a car typically decreases around 15% in value. How much will your car be worth after owning it for 2 years?
Value of car after second year of ownership:
4. If your car continues to decrease in value by 15% each year, write the equation of the exponential function that models its value x years after you purchased it.
Exponential Function:
Use your exponential function to calculate the predicted value of your car after you own it for five years.
Value after five years of ownership:
= 8; = 2 P(7 ≤ x ≤ 10) =
Answers
The indicated probability for the given mean and standard deviation for P(7 ≤ x ≤ 10) is equal to 0.6915 approximately.
Mean = 8
Standard deviation = 2
Standardize the distribution using the formula,
z = (x - μ) / σ
where μ is the mean and σ is the standard deviation.
Substituting the given values, we get,
z = (x - 8) / 2
We want to find P(7 ≤ x ≤ 10),
which is the same as finding the probability that z is between,
z = (7 - 8) / 2
= -0.5
and
z = (10 - 8) / 2
= 1
Using a standard normal table .
Find the area under the standard normal distribution curve between -0.5 and 1.
P(-0.5 ≤ z ≤ 1) ≈ 0.6915
Attached table.
This implies,
P(7 ≤ x ≤ 10) ≈ 0.6915.
Therefore, the probability that x is between 7 and 10 is approximately 0.6915.
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The above question is incomplete, the complete question is:
Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Enter a number. Round your answer to four decimal places.)
μ = 8; σ = 2
P(7 ≤ x ≤ 10) =
SOMEONE PLEASE HELP!!!!
Answers
The expression is simplified to √5
How to determine the valueFrom the information given, we have that;
logₐ x = 3
logₐ y = 4
logₐ z = 5
Given that the expression is;
logₐ [tex]\sqrt[4]{\frac{y^3z^6}{x^4z^-^2} }[/tex]
Now, we have to substitute the value of the logarithm into the expression.
We have;
[tex]\sqrt[4]{\frac{4^35^6}{3^45^-^2} }[/tex]
Find the value of the index forms and substitute;
[tex]\sqrt[4]{\frac{64(625)}{81(1/25)} }[/tex]
Multiply the values and expand the bracket
3(5)/3(5^⁻²/4)
multiply the values
15/3(5^-1/2)
Find the square root of the denominator, we have
15/3(√5)⁻¹
5/√5
Rationalize the surd form, we get;
5√5/5
Then, we have;√5
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helppppppppppppppppppppp!PLEASE THE ONLY THNG S THS !!!AM BEGGNG YOU SOMEBODY!!PLEASE
Answers
The cost of one hour of television each day is $1.
We have,
The average electricity bill reduced to $130 to $40.
Number of days in month= 30 days
So, the cost of one hour of television is
= (130- 40) /30
= 90 /30
= $30
Thus, the cost of one hour of television is $ 30.
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Prove that the roots of x^2 +(1-k)x+k-3=0 are real for all real values of k
Answers
The discriminant is positive for all values of k, thus, the roots are always real.
How to prove that all the roots are real?For a quadratic equation:
0 = ax^2 + bx +c
The discriminant is defined as:
D = b^2 - 4ac
If the discriminant is positive, then the roots are real.
Here we have:
x^2 +(1-k)x+k-3
Then:
a = 1
b = (1 - k)
c = k - 3
The discriminant is:
D = (1 - k)^2 - 4(k - 3)
D = 1^2 - 2k + k^2 - 4k + 12
D = k^2 - 6k + 13
Now notice that the vertex of this quadratic is at:
k = 6/2 = 3
Evaluating there we get:
D = 3^2 - 6*3 + 13
D = 9 - 18 + 13 = 4
So the discriminant is positive for all values of k, meaning that all the roots are real.
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