It is true to say that when utilizing MATLAB's built-in ode solver, the function for one's states the variable for the state derivatives must be set as column vectors.
The Ordinary Differential Equation (ODE) solvers in MATLAB solve initial value problems with a varient state of properties. They consider state spaces as a column vector. For example, two solve a second degree ODE, It's two states in state space has to be arranges in a 1x2 column vector to pass it into a ODE solver.
Initial value problems with different attributes can be solved using theODE solvers in MATLAB.
Here the first ODE is of third order, so it will be converted to three equivalent first order ODEs. The second ODE is second order, so it will be converted to two equivalent first order ODEs.These solver can be used to solve the different type like the differential algebraic equations (DAEs), problems involving a mass matrix, and fully implicit problems. ODE45, is most frequently used ODE solver in MATLAB.It used to compare methods of orders four and five to determine an estimate error.
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On Sunday a local hamburger shop sold 356 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Sunday
The number of hamburgers sold on Sunday was 89
How many hamburgers were sold on SundayLet's assume that the number of hamburgers sold on Sunday was x.
According to the problem, the number of cheeseburgers sold was three times the number of hamburgers sold.
Therefore, the number of cheeseburgers sold can be expressed as 3x.
The total number of hamburgers and cheeseburgers sold was 356.
Therefore, we can write an equation to represent this information:
x + 3x = 356
Simplifying the left-hand side of the equation, we get:
4x = 356
Dividing both sides by 4, we get:
x = 89
Therefore, the number of hamburgers sold on Sunday was 89, and the number of cheeseburgers sold was 3 times that, or 267.
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BRAINLIST!
PLS SHOW ALL STEPS!! WE ARE DOING A CLASS JAM BOARD AND I NEED THIS DONE! I WILL MAKE YOU A BRAINLIST!
Step-by-step explanation:
Ok do what you need to do is label the line opposite the square angle as H for the hypotenuse. Then label the line opposite the circular angle as O for the opposite. And finally, the last line remaining should be labelled as A for Adjacent. Does this help?
help. the picture is attached below, when i search it up it’s trying to solve it.
The value of the expression, -0.4·(3·x - 2) + (2·x + 4)/3 when x = 4 is 0
-0.4 × (3 × 4 - 2) + (2 × 4 + 4)/3 = 0
What is a mathematical expression?A mathematical expression comprises, variables, and or numbers, which could include indices, joined together by mathematical operators.
The value of the expression -0.4·(3·x - 2) + (2·x + 4)/3 for x = 4 can be found by plugging in x = 4 into the expression as follows;
Where; x = 4
-0.4·(3·x - 2) + (2·x + 4)/3 = -0.4 × (3 × 4 - 2) + (2 × 4 + 4)/3
-0.4 × (3 × 4 - 2) + (2 × 4 + 4)/3 = -0.4 × (12 - 2) + (8 + 4)/3
-0.4 × (12 - 2) + (8 + 4)/3 = -0.4 × 10 + 12/3 = -4 + 4 = 0
Therefore;
The value of the expression, -0.4·(3·x - 2) + (2·x + 4)/3 for x = 4 is zero
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The area of the small triangle is_______
The area of the medium triangle is______
The area of the large triangle is______
The area of the small triangle is 4 sq.cm.. The area of the medium triangle is 12 sq.cm. The area of the large triangle is 24 sq. cm.
Explain about the triangle:With three sides, three angles, and three vertices, a triangle is a closed, two-dimensional object. A polygon also includes a triangle.
A triangle's internal angles are always added together to equal 1800.Any two triangle sides added together will always have a length larger than the third side.Half of a product of a triangle's base and height makes up its surface area.Given data:
Dimensions-
small triangle: base = 2 cm, height = 4cmmedium triangle: base = 4 cm , height = 6 cmLarger triangle: base = 6 cm ,height = 8 cmarea of triangle = 1/2 *base * height
The area of the small triangle = 1/2*2*4 = 4 sq.cm.
The area of the medium triangle = 1/2*4*6 = 12 sq.cm.
The area of the large triangle = 1/2*6*8 = 24 sq. cm
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Complete question:
Dimensions-
small triangle: base = 2 cm, height = 4cm
medium triangle: base = 4 cm , height = 6 cm
Larger triangle: base = 6 cm ,height = 8 cm
The area of the small triangle is_______
The area of the medium triangle is______
The area of the large triangle is______
The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 10 to 14.5 on the number line. A line in the box is at 12.5. The lines outside the box end at 5 and 20. The graph is titled Fast Chicken.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
Which drive-thru typically has less wait time, and why?
Fast Chicken, because it has a smaller median
Fast Chicken, because it has a smaller mean
Super Fast Food, because it has a smaller median
Super Fast Food, because it has a smaller mean
The correct answer is: Fast Chicken, because it has a smaller median.
What is median?
Median is a measure of central tendency that represents the middle value in a dataset when the values are arranged in order of magnitude. To find the median, you need to arrange the values in order from smallest to largest and then find the middle value.
Based on the information provided, the drive-thru restaurant with less wait time is Fast Chicken, as it has a smaller median wait time of 12.5 minutes compared to the median wait time of 12 minutes for Super Fast Food. The mean wait time is not given, and even if it were, the median is a better measure of central tendency to compare in this scenario, as the box plots suggest some potential outliers.
Therefore, the correct answer is: Fast Chicken, because it has a smaller median.
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The Johnson family lives 432 miles from the beach. They drive 52% of the distance before stopping for lunch. About how many miles do they drive before lunch? Explain how you can use mental math to find the answer.
Which are the coordinates of the vertex of F(x)=x^2-2x-3
Therefore , the solution of the given problem of coordinates comes out to be (1, -4) are the coordinates of the vertex of the function F(x) = x² - 2x - 3.
What does coordinate plane actually mean?When used in connection with particular other algebraic components on this place, such as Euclidean space, a parameter can reliably detect placement using a number of qualities or coordinates. Coordinates, which appear as collections of numbers when traversing in reflected space, can be utilised to identify particular places or things. Using the two y & x measurements, one can find something over both sides.
Here,
The formula x = -b/2a can be used to determine the vertex of a quadratic function with the form
F(x) = ax² + bx + c. A and B are equal in the given function
=> F(x) = x² - 2x - 3.
With these values entered into the formula, we obtain:
=> x = -b/2a x = -(-2)/(2*1)
=> x = 2/2 x = 1
Consequently, the vertex's x-coordinate is 1.
Now, we can enter the value of x into the following function, F(x), to determine the vertex's y-coordinate:
=> F(1) = 1² - 2(1) - 3
=> F(1) = 1 - 2 - 3
=> F(1) = -4
Therefore, the vertex's y-coordinate is -4.
As a result, (1, -4) are the coordinates of the vertex of the function
=> F(x) = x² - 2x - 3.
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Mrs. Hanson is filling containers in her bakery with flour. How much flour will fit into two of the containers?
The flour will fit into two of the container is 144 inches.
What is the volume of cuboids?
A cuboid is a six-sided solid known as a hexahedron. Quadrilaterals make up its faces. Cuboid is short for "like a cube". A cuboid is similar to a cube in that a cuboid can become a cube by varying the lengths of the edges or the angles between the faces.
Here, we have
Given: Mrs. Hanson is filling containers in her bakery with flour.
we have to find how much flour will fit into two of the containers.
Volume of cuboid = length × breadth × height
Length = 6 inches
Breadth = 3 inches
Height = 8 inches
The flour will fit into two of the containers = length × breadth × height
= 6 ×3 × 8
= 144 inches
Hence, The flour will fit into two of the container 144 inches.
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Which sum is equivalent to 9c-12-15c-8-3c
The equivalent sum to the given equation is -9c - 20.
An algebraic expression is consists of variables, numbers with various mathematical operations.
Equivalent sums refers to addition or subtraction from the other number to maintain the same total value.
= 9c-12-15c-8-3c
To find the equivalent sum, first we can simplify this expression by first combining like terms:
= 9c - 15c - 3c - 12 - 8
= (9c - 15c - 3c) - (12 + 8) (grouping the like terms)
Solving the expression for terms c and for constant terms,
= -9c - 20
Therefore, the equivalent sum is -9c - 20.
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Can someone help with this fast!?!!
The total cost b(x), in dollars, for renting a bowling lane for x hours is shown: b(x) = 3x + 15. What does b(3) represent?
A. The number of dollars it costs to rent the bowling lane for 3 hours.
B. The number of games you can bowl for a cost of $3.
C. The number of hours the bowling lane can be rented for a cost of $3.
D. The number of games you can bowl in 3 hours.
As a result, the response is A .The number of dollars it costs to rent the bowling lane for 3 hours.
Define dollar?The US, Canada, Australia, and some nations in the Pacific, Caribbean, Southeast Asia, Africa, and South America all use the dollar as their primary unit of exchange It is a type of paper money, currency, and monetary unit used in the United States that is equivalent to 100 cents
The total cost (in dollars) for renting a bowling alley for x hours is represented by the function b(x) = 3x + 15.
We change x in the function to 3 to obtain b(3).
B(3) = 3(3) + 15 = 9 + 15 = 24 is the result.
Therefore, b(3) is the amount of money required to rent the bowling alley for three hours.
As a result, the response is A.
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what is the probability that at least one customer arrives at the shop during a one-minute interval? 0.736 0.368 0.632 0.264
Probability about at least one customer arrives at the shop while a one-minute interval is almost 0.632 or 63.2%.
How to calculate probability?The probability that at least one customer arrives at the shop during a one-minute interval can be calculated using the Poisson distribution, which is commonly used to model the arrival of events over a given time period.
Let's assume that the average number of customers arriving at the shop per minute is [tex]l[/tex]. Poisson probability mass function is;
[tex]P(X = k) = (e^{-l} * l^k) / k![/tex]
where X is the random variable representing the number of customers arriving in a one-minute interval, and k is the number of customers that arrive.
To find the probability of at least one customer arriving, we need to calculate the probability of X being greater than or equal to 1. That is,
[tex]P(X > = 1) = 1 - P(X = 0)[/tex]
When [tex]l[/tex] is relatively small, we can use approximation:
[tex]P(X = 0) = e^{-l[/tex]
Therefore,
[tex]P(X > = 1) = 1 - P(X = 0)[/tex]
[tex]≈ 1 - e^{-l[/tex]
We don't have the value of [tex]l[/tex], but assuming an average arrival rate of 1 customer per minute (i.e., [tex]l[/tex] = 1), we get:
[tex]P(X > = 1) = 1 - e^{-1[/tex]
≈ 0.632
Therefore, the probability about at least one customer arrives at the shop while a one-minute interval is almost 0.632 or 63.2%.
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An article on the relation of cholesterol levels in human blood to aging reports that average cholesterol level for women aged 70-74 was found to be 230m/dl. If the standard deviation was 20mg/dl and the distribution normal, what is the probability that a given woman in this age group would have a cholesterol level
a) Less than 200mg/dl
b) More than 200mg/dl
c) Between 190mg/dl and 210mg/dl
d) Write a brief report on the guidance you would give a woman having high cholesterol level in this age group
a) The probability of a given woman in this age group having a cholesterol level less than 200mg/dl is 6.68%.
b) The probability of a given woman in this age group having a cholesterol level more than 200mg/dl is 93.32%.
c) The probability of a given woman in this age group having a cholesterol level between 190mg/dl and 210mg/dl is 15.87%.
d) If a woman in this age group has a cholesterol level higher than 230mg/dl, it is considered high and puts her at risk of heart disease
To calculate the probability of a given woman in this age group having a cholesterol level less than 200mg/dl, we need to find the z-score first. The z-score is the number of standard deviations that a given value is from the mean. The formula to calculate the z-score is:
z = (x - μ) / σ
where x is the given value, μ is the mean, and σ is the standard deviation.
For a cholesterol level of 200mg/dl, the z-score is:
z = (200 - 230) / 20 = -1.5
We can then use a z-table or calculator to find the probability of a z-score being less than -1.5, which is 0.0668 or approximately 6.68%.
Next, to find the probability of a given woman in this age group having a cholesterol level more than 200mg/dl, we can use the same process but subtract the probability of a z-score being less than -1.5 from 1 because the total probability is always 1.
So, the probability of a given woman in this age group having a cholesterol level more than 200mg/dl is:
1 - 0.0668 = 0.9332 or approximately 93.32%.
Finally, to find the probability of a given woman in this age group having a cholesterol level between 190mg/dl and 210mg/dl, we need to find the z-scores for both values.
For a cholesterol level of 190mg/dl, the z-score is:
z = (190 - 230) / 20 = -2
For a cholesterol level of 210mg/dl, the z-score is:
z = (210 - 230) / 20 = -1
We can then use the z-table or calculator to find the probability of a z-score being between -2 and -1, which is 0.1587 or approximately 15.87%.
Finally, a brief report on the guidance that you would give a woman having high cholesterol levels in this age group is:
It is essential to make lifestyle changes such as eating a healthy diet, exercising regularly, quitting smoking, and managing stress to lower cholesterol levels.
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A rod of length L is placed along the X-axis between X=0 and x=L. The linear density (mass/length) rho of the rod varies with the distance x from the origin as rho=a+bx. (a) Find the SI units of a and b. (b) Find the mass of the rod in terms of a,b and L.
(a) The linear density (mass/length) rho has SI units of kg/m. Since rho = a + bx, the SI units of a must be kg/m and the SI units of b must be kg/m^2.
(b) To find the mass of the rod, we need to integrate the linear density function over the length of the rod:
m = ∫₀ᴸ ρ(x) dx
Substituting in ρ(x) = a + bx:
m = ∫₀ᴸ (a + bx) dx
m = [ax + (1/2)bx²] from 0 to L
m = aL + (1/2)bL²
Therefore, the mass of the rod in terms of a, b, and L is m = aL + (1/2)bL².
(a) In this problem, rho (ρ) represents linear density, which has units of mass per length. In SI units, mass is measured in kilograms (kg) and length in meters (m). Therefore, the units of linear density are kg/m. Since ρ = a + bx, the units of a and b must be consistent with this equation. The units of a are the same as those of ρ, so a has units of kg/m. For b, since it is multiplied by x (which has units of meters), b must have units of kg/m² to maintain consistency in the equation.
(b) To find the mass of the rod, we need to integrate the linear density function over the length of the rod (from x=0 to x=L). Let's set up the integral:
Mass (M) = ∫(a + bx) dx, with limits from 0 to L
Now, we can integrate:
M = [a * x + (b/2) * x²] evaluated from 0 to L
Substitute the limits:
M = a * L + (b/2) * L²
So, the mass of the rod in terms of a, b, and L is:
M = aL + (bL²)/2
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sue works 5 out of the 7 days of the week. how many possible schedules are there to work on tuesday or friday or both?
Sue works 5 out of 7 days a week, which implies that she has two days off. We need to discover how numerous conceivable plans there are for her to work on Tuesday or Friday or both.
There are two cases to consider:
1. Sue works on Tuesday as it were, Friday as it were, or both Tuesday and Friday.
2. Sue does not work on Tuesday or Friday.
For the primary case, there are three conceivable outcomes:
1. Sue works on Tuesday as it were and has Friday off.
2. Sue works on Friday as it were and has Tuesday off.
3. Sue works on both Tuesdays and Fridays.
For the moment case, there are two conceivable outcomes:
1. Sue works on one of the other 5 days of the week and has both Tuesday and Friday off.
2. Sue has Tuesday and Friday off.
In this manner, there are added up to 3 + 2 = 5 conceivable plans for Sue to work on Tuesday or Friday or both.
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The sum of first two angles is 120 degree and that of last two angles is 130 degree. Find all the angles in degrees.
The four angles are: A = 110 degrees, B = 10 degrees, C = 120 degrees, D = 120 degrees
What are angles ?Angles are geometric shapes created when two lines, rays, or line segments cross at a single point.
The two lines or line segments that make up the angle are referred to as the sides or arms of the angle, and this shared point is known as the vertex of the angle.
The amount of rotation required to shift one side to overlap with the opposite side determines the magnitude of an angle.
Angles are commonly expressed in degrees, with 360 degrees representing a full rotation around a point.
Acute angles (less than 90 degrees),
right angles (exactly 90 degrees),
obtuse angles (more than 90 degrees but less than 180 degrees), and straight angles (exactly 180 degrees) are some frequent forms of angles.
What are degrees ?
Angles are measured in degrees, a unit of measurement. 1/360th of a full revolution around a point is equivalent to one degree (1°).
Two perpendicular lines can be used to create a right angle, which has a 90 degree angle.
A straight angle, created by a straight line, has a degree value of 180.
Angles, rotations, and slopes are frequently measured in degrees in the fields of mathematics, physics, engineering, and several others.
The freezing point of water is 0 degrees Celsius (or 32 degrees Fahrenheit), whereas the boiling point is 100 degrees Celsius. In daily life, degrees are frequently used to express temperatures. (or 212 degrees Fahrenheit).
According to question :-
Let the four angles be A, B, C, and D. We know that:
A + B + C + D = 360 (the sum of all angles in a quadrilateral is 360 degrees)
We also know that:
A + B = 120 (the sum of the first two angles is 120 degrees)
C + D = 130 (the sum of the last two angles is 130 degrees)
We can use these equations to solve for the individual angles. First, we can rearrange the equation A + B = 120 to get:
A = 120 - B
Similarly, we can rearrange the equation C + D = 130 to get:
D = 130 - C
Substituting these expressions for A and D in terms of B and C into the equation A + B + C + D = 360, we get:
(120 - B) + B + C + (130 - C) = 360
Simplifying, we get:
250 - B + C = 360
Subtracting 250 from both sides, we get:
C - B = 110
Now we have two equations with two unknowns:
C + B = 130 (from the equation C + D = 130)
C - B = 110
We can add these equations to eliminate B and get:
2C = 240
Dividing by 2, we get:
C = 120
Substituting this value for C into either of the equations above, we get:
B = 10
Now we can use the equation A + B = 120 to find A:
A + 10 = 120
A = 110
Finally, we can use the equation A + B + C + D = 360 to find D:
110 + 10 + 120 + D = 360
D = 120
Therefore, the four angles are:
A = 110 degrees
B = 10 degrees
C = 120 degrees
D = 120 degrees
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The graph of a linear function is shown on the coordinate grid.
What is the y-intercept of the graph of this function?
PLEASE HELP! WILL GIVE BRAINLY ANSWER
Answer:
[tex]\dfrac{4}{3}[/tex]
Step-by-step explanation:
We can find the y-intercept of this line by:
1) finding the slope using the given points
[tex]m = \dfrac{8-(-7)}{4-(5)}[/tex]
[tex]m = \dfrac{8+7}{4+5}[/tex]
[tex]m = \dfrac{15}{9}[/tex]
[tex]m=\dfrac{5}{3}[/tex]
2) forming an equation for the line using point slope form
[tex]y - b = m(x - a)[/tex] where [tex](a,b)[/tex] is a point on the line
... using the point (4,8)
[tex]y - 8 = \frac{5}{3}(x - 4)[/tex]
3) plugging 0 in for x to get the y-intercept
[tex]y - 8 = \frac{5}{3}(0 - 4)[/tex]
[tex]y - 8 = \frac{5}{3}(-4)[/tex]
[tex]y = 8 -\frac{20}{3}[/tex]
[tex]y = \frac{24}{3} -\frac{20}{3}[/tex]
[tex]\boxed{y=\dfrac{4}{3}}[/tex]
n.2 multi-step word problems with positive rational numbers jvu you have prizes to reveal! go to your game board. on friday night, suzie babysat her cousin for 3 1 2 hours and earned $8.50 per hour. on saturday, she babysat for her neighbors for 4 1 2 hours. if she made a total of $72.50 from both babysitting jobs, how much did suzie earn per hour on saturday?
Answer:
$9.50
Step-by-step explanation:
You want Suzie's hourly rate on Saturday if she babysat for 3.5 hours on Friday, earning 8.50 per hour, and for 4.5 hours on Saturday, earning a total of 72.50 from both jobs.
EarningsFor (hours, rates) of (h1, r1) and (h2, r2), Suzie's total earnings for the two jobs are ...
earnings = h1·r1 +h2·r2
Filling in the known values, we can find r2:
72.50 = 3.5·8.50 +4.5·r2
72.50 = 29.75 +4.5·r2 . . . . . . . simplify
42.75 = 4.5·r2 . . . . . . . . . . . subtract 29.75
9.50 = r2 . . . . . . . . . . . . divide by 4.5
Suzie earned $9.50 per hour on Saturday.
__
Additional comment
The steps of the "multistep" problem are ...
find Friday's earningssubtract that from the total to find Saturday's earningsdivide by Saturday's hours to find the hourly rateEffectively, these are the steps to solving the equation we wrote.
For which equations is 8 a solution? Select the four correct answers. x + 6 = 2 x + 2 = 10 x minus 4 = 4 x minus 2 = 10 2 x = 4 3 x = 24 StartFraction x Over 2 EndFraction = 16 StartFraction x Over 8 EndFraction = 1
The equations for which 8 is a solution are: x - 4 = 4, 2x = 16, x/2 = 16, and x/8 = 1.
What is equation?An equation is a mathematical statement that shows that two expressions are equal to each other. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The goal is usually to solve for the value of the variable that makes the equation true.
In the given question,
The equations in which 8 is a solution are:
x - 4 = 8 (which simplifies to x = 12)
2x = 16 (which simplifies to x = 8)
x/2 = 16 (which simplifies to x = 32)
x/8 = 1 (which simplifies to x = 8)
Therefore, the correct answers are:
x - 4 = 8
2x = 16
x/2 = 16
x/8 = 1.
The equations for which 8 is a solution are: x - 4 = 4, 2x = 16, x/2 = 16, and x/8 = 1.
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x² - 16x + 64 = 0 is the equation whose solution is 8.
How to check for which equations is 8 a solution?
To check if 8 is a solution for each equation, we substitute x = 8 into each equation and see if the equation is true or not.
x + 6 = 8 + 6 = 14
and
2x + 2 = 2(8) + 2 = 18, which is not equal to the value of (x+6).
Therefore, 8 is not a solution to this equation.
4x - 4 = 4(8) - 4 = 28,
and
10 - 2x = 10 - 2(8) = -6, which is not equal to 28.
Therefore, 8 is not a solution to this equation.
2x - 4 = 2×8-4 = 12
and
3x-24 = 3×8-24 = 0 which is not equal to 12. Therefore, 8 is not a solution to this equation.
Now,
x² - 16x + 64 = 0 (which can be factored as (x-8)² = 0)
x = 8 (which is always true)
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Correct question is "For which equations is 8 a solution? Select the correct answers from the following,
1) x + 6 = 2 x + 2
2) 10 - 2x = 4 x - 4
3) 2 x-4 = 3 x - 24
4) x² - 16x + 64 = 0
Akira and Desmond order eggs for $4. 45, pancakes for $4. 05, and 2 mugs of cocoa for $1. 10 each. The tax is $0. 85. How much change should they get from $15. 00?
Answer:
$3.45
Step-by-step explanation:
A primary credit cardholder's card has an APR of 22. 99%. The current monthly balance, before interest, is $4,528. 34. Determine how much more the cardholder will pay, making monthly payments of $200, until the balance is paid off, instead of paying off the current balance in full
The cardholder will pay an additional $1,471.66 in interest by making monthly payments of $200 until the balance is paid off instead of paying off the current balance in full.
First, we need to calculate the total interest that will accrue on the current balance of $4,528.34. We can do this using the formula
Interest = Balance x (APR/12)
where APR is the annual percentage rate and is divided by 12 to get the monthly interest rate. Plugging in the values, we get:
credit card Interest = $4,528.34 x (22.99%/12) = $87.80
So the total interest that will accrue on the current balance is $87.80.
Next, we need to calculate how long it will take to pay off the balance by making monthly payments of $200. We can use a credit card repayment calculator to do this, but we'll use a simplified formula here
Months = -log(1 - (Balance x (APR/12))/Payment) / log(1 + (APR/12))
where Payment is the monthly payment amount. Plugging in the values, we get
Months = -log(1 - ($4,528.34 x (22.99%/12))/$200) / log(1 + (22.99%/12)) = 29.6 months
So it will take about 30 months (or 2.5 years) to pay off the balance by making monthly payments of $200.
Finally, we can calculate how much more the cardholder will pay in total by subtracting the current balance from the total amount paid over 30 months
Total amount paid = $200 x 30 = $6,000
Total interest paid = $6,000 - $4,528.34 = $1,471.66
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given that the absolute value of the difference of the two roots of $ax^2 + 5x - 3 = 0$ is $\frac{\sqrt{61}}{3}$, and $a$ is positive, what is the value of $a$?
The value of "a" is approximately 1.83 given that the absolute value of the difference of the two roots of the quadratic equation "ax squared plus 5x minus 3 equals 0" is the square root of 61 divided by 3, and "a" is positive.
We are given that the absolute value of the difference between the two roots of the quadratic equation "ax squared plus 5x minus 3 equals 0" is the square root of 61 divided by 3, and "a" is positive. We need to find the value of "a".
Let the two roots of the equation be r1 and r2, where r1 is not equal to r2. Then, we have:
|r1 - r2| = √(61) / 3
The sum of the roots of the quadratic equation is given by r1 + r2 = -5 / a, and the product of the roots is given by r1 × r2 = -3 / a.
We can express the difference between the roots in terms of the sum and product of the roots as follows:
r1 - r2 = √((r1 + r2)² - 4r1r2)
Substituting the expressions we obtained earlier, we have:
r1 - r2 = √(((-5 / a)²) + (4 × (3 / a)))
Simplifying, we get:
r1 - r2 = √((25 / a²) + (12 / a))
Taking the absolute value of both sides, we get:
|r1 - r2| = √((25 / a²) + (12 / a))
Comparing this with the given expression |r1 - r2| = √(61) / 3, we get:
√((25 / a²) + (12 / a)) = √(61) / 3
Squaring both sides and simplifying, we get:
25 / a² + 12 / a - 61 / 9 = 0
Multiplying both sides by 9a², we get:
225 + 108a - 61a² = 0
Solving this quadratic equation for "a", we get:
a = (108 + √(108² + 4 × 61 × 225)) / (2 × 61)
Since "a" must be positive, we take the positive root:
a = (108 + √(108² + 4 × 61 × 225)) / (2 × 61) ≈ 1.83
Therefore, the value of "a" is approximately 1.83.
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The question is -
Given that the absolute value of the difference of the two roots of the quadratic equation "ax squared plus 5x minus 3 equals 0" is the square root of 61 divided by 3, and "a" is positive, what is the value of "a"?
Find the volume
of the figure below:
Step-by-step explanation:
Use Pythagorean theorem to find the base of the right triangle
221^2 = 195^2 + b^2
b = 104 km
triangle area = 1/2 base * height = 1/2 * 104 * 195 = 10140 km^2
Now multiply by the height to find volume
10140 km^2 * 15 km = 152100 km^3
The function f is given by f(x) = 10x + 3 and the function g is given by g(x) = 2×. For each question, show your reasoning
1. Which function reaches 50 first
2. Which function reaches 100 first?
1. x = 4.7 for f(x) and x = 25 for g(x), f(x) reaches 50 first.
2. x = 9.7 for f(x) and x = 50 for g(x), f(x) reaches 100 first.
1. Which function reaches 50 first?
To answer this, we need to solve for x in each function when the output is 50:
For f(x): 50 = 10x + 3
47 = 10x
x = 4.7
For g(x): 50 = 2x
x = 25
Since x = 4.7 for f(x) and x = 25 for g(x), f(x) reaches 50 first.
2. Which function reaches 100 first?
Similarly, we'll solve for x in each function when the output is 100:
For f(x): 100 = 10x + 3
97 = 10x
x = 9.7
For g(x): 100 = 2x
x = 50
Since x = 9.7 for f(x) and x = 50 for g(x), f(x) reaches 100 first.
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Please help, I’ve given up on trigonometry
Answer:
6.02
Step-by-step explanation:
sin 37=x/10
x/10=sin 37
x=10(sin 37)
x=6.02
in an analysis testing differences between an experimental and a control group on the dependent variable, a p-value of 0.07 means there is a
A control group on the dependent variable, P-value is higher than the usual cutoff of 0.05 for rejecting the null hypothesis that there is no difference between the groups, this is frequently regarded as evidence that the difference between the groups is not statistically significant.
In an analysis testing difference between an experimental and a control group on the dependent variable, a p-value of 0.07 means that there is a 7% chance of obtaining a difference as large or larger than the observed difference between the two groups, assuming that there is no true difference between the groups in the population.
Interpreted as evidence that the difference between the groups is not statistically significant, since the p-value is greater than the conventional threshold of 0.05 for rejecting the null hypothesis of no difference between the groups.
Statistical significance does not necessarily imply practical significance, and there may still be a meaningful difference between the groups that is not detected by the statistical test.
Additionally, the interpretation of a p-value depends on the study design, sample size, and other factors, and should be considered in conjunction with other information about the study.
True difference between the groups in the population, a p-value of 0.07 indicates that there is a 7% chance of finding a difference as large or larger than the observed difference between the two groups in an analysis testing the difference between an experimental and a control group on the dependent variable.
P-value is higher than the usual cutoff of 0.05 for rejecting the null hypothesis that there is no difference between the groups, this is frequently regarded as evidence that the difference between the groups is not statistically significant.
It's crucial to remember that statistical significance does not always imply practical relevance.
There could still be a significant difference between the groups that is not shown by statistical analysis.
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KKIC
8. The area of a circle can be found using the formula A = (pi)r^2. Find the area of the circle with a radius of 3xy^3.
The area of circle is with radius 3xy³ is 9πx²y⁶.
What is area?Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, A = πr2.
Define radius of a circle?Radius of a circle is the distance from the center of the circle to any point on it's circumference. It is usually denoted by 'R' or 'r'.This quantity has importance in almost all circle-related formulas. The area and circumference of a circle are also measured in terms of radius. Circumference of circle = 2π (Radius)
area of circle=πr²
=π×(3xy³)²
=9πx²y⁶
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∠A=6x−2
∘
start color #11accd, angle, A, end color #11accd, equals, start color #11accd, 6, x, minus, 2, degrees, end color #11accd \qquad \green{\angle B} = \green{4x +48^\circ}∠B=4x+48
∘
, angle, B, equals, start color #28ae7b, 4, x, plus, 48, degrees, end color #28ae7b
Solve for xxx and then find the measure of \blueD{\angle A}∠Astart color #11accd, angle, A, end color #11accd:
The given information describes the measures of two angles, A and B. Angle A is represented as ∠A and has a measure of 6x-2 degrees. Angle B is represented as ∠B and has a measure of 4x+48 degrees. These measures are respectively shown in the colors #11accd and #28ae7b.
The question gives us two equations, one for angle A and one for angle B, in terms of x. We will have to solve for x and then find the measure of angle A.
To solve for x, we can set the expressions for ∠A and ∠B equal to each other and solve for x
∠A = ∠B
6x - 2 = 4x + 48
Subtracting 4x from both sides we get
2x - 2 = 48
Adding 2 to both sides we get
2x = 50
Dividing by 2 we get
x = 25
Now that we have found the value of x, we can substitute it into the expression for ∠A
∠A = 6x - 2
∠A = 6(25) - 2
By multiplying 6 with 25 we get
∠A = 150 - 2
By Subtracting we get
∠A = 148
Hence, the measure of angle A is 148 degrees.
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Evaluate the following.
Write an exponential function of the form y = ab^x that has the given points
(−1,6 3/4), (2, 1-4)
Answer:
Step-by-step explanation:
y = abx
a is the y-intercept
y = 16bx
Now substitute 2 for x and 1296 for y
1296 = 16(b)2
81 = b2
b = 9
y = 16(9)x
The table shows the results for spinning the spinner 50 times. What is the relative frequency for the event "spin a 1"?
Outcome. | 1 | 2| 3 |4
Frequency|16| 16|16|2
Number of trials
50
The relative frequency for the event "spin a 1" is
The relative frequency of spinning a 1 is 0.32 or 32%.
The given table shows the results of spinning a spinner 50 times. The outcomes of the spins are listed in the first column, and the frequencies are listed in the second column. To find the relative frequency of spinning a 1, we need to divide the frequency of spinning a 1 by the total number of trials (50).
According to the table, the frequency of spinning a 1 is 16. Therefore, the relative frequency of spinning a 1 can be calculated as follows:
Relative frequency of spinning a 1 = (frequency of spinning a 1) / (total number of trials)
Relative frequency of spinning a 1 = 16 / 50
Relative frequency of spinning a 1 = 0.32 or 32%
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Which of the following choices describes the function?
an exponential function that is decreasing.
a quadratic function that is increasing then decreasing.
a quadratic function that is decreasing then increasing.
None of these choices are correct.
Answer: The function that is an exponential function that is decreasing is described as:
an exponential function that is decreasing.
A quadratic function that is increasing then decreasing would have a U-shaped graph, and a quadratic function that is decreasing then increasing would have an inverted U-shaped graph. However, neither of these options describes an exponential function that is decreasing.
Therefore, the correct choice is: an exponential function that is decreasing.
Step-by-step explanation: