Answers
hope this helps:)
Related Questions
2/3 - 5/9=
in simplest form
Answers
Answer:
Step-by-step explanation:
2/3 - 5/9 = 1/
9
≅ 0.1111111
Answer: 1/9
Step-by-step explanation:
How do you solve quadratic equations with answers?
Answers
Answer:
Step-by-step explanation:
How to solve a quadratic equation using the Quadratic Formula.
Write the quadratic equation in standard form, ax2 + bx + c = 0. Identify the values of a, b, c.
Write the Quadratic Formula. Then substitute in the values of a, b, c.
Simplify.
Check the solutions.
The four methods for solving a quadratic issue are the quadratic formula, using square roots, factoring, and completing the square.
What is meant by quadratic equations?A quadratic equation in algebra is any equation that can be written in standard form as where x stands for an unknown value, a, b, and c stand for known numbers, and where a ≠ 0.
Problems involving squares and quadrangles and quadratic equations are closely related. In actuality, the word quadratic comes from the Latin word quadratus, which means square.
The quadratic formula, using square roots, factoring, and completing the square are the four ways to solve a quadratic problem. An overview of all the many approaches to solving a quadratic equation is what I'd want to discuss right now.
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What goes on the X and y-axis of a graph?
Answers
The x-axis should contain the independent variable (also known as the "explanatory variable"), and the y-axis should contain the dependent variable (also known as the "response variable").
Definition of X and Y Graph?
The x-axis and the y-axis, which together make up a graph's coordinate plane, can be used to define an x and y graph.
The y-axis and the x-axis each stand in for one of the two axes: the horizontal or horizontally oriented. The origin, or point of reference for the plane, is the intersection of the x- and y-axes.
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The x-axis (horizontal line) of the graph should have the independent variable, and the y-axis should have the dependent variable (vertical line). At the origin, the location of the coordinates, the x and y axes intersect (0,0).
What is represented by the x-axis? The x-axis (horizontal line) of the graph should have the independent variable, and the y-axis should have the dependent variable (vertical line).At the origin, the location of the coordinates, the x and y axes intersect (0,0).A point's horizontal location is shown by the x-axis; its vertical position is indicated by the y-axis; and its exact center point is referred to as the origin.The line that runs vertically from bottom to top on a graph is known as the y-axis.The coordinate measurement axis is parallel to this axis.Y-coordinates are the numerical values plotted along the y-axis.The x-coordinate comes first in ordered pairs, followed by the y-coordinate, and is written in parentheses: (x, y).To learn more about X and y-axis refer
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3.) Katy Perry's bank granted her a single-payment loan of $4,400 at an interest rate of 6% exact interest to buy
a new sound system. The term of the loan is 172 days. What is the exact interest and what is the maturity value
of the loan?
Answers
The interest on the loan is: $375.44
The maturity value is: $4,775.44.
How to Calculate Maturity Value and Interest on a Loan?Maturity value and interest on a loan can be calculated as follows:
Maturity value: it is the amount of the loan plus the interest charged on it. It can be calculated using the formula:
MV = P + I
where MV is the maturity value, P is the principal (original loan amount), and I is the interest charged on the loan.
Interest: it is the amount charged by the lender for the use of their money. It can be calculated using the formula:
I = P * r * t
where I is the interest, P is the principal, r is the interest rate, and t is the term of the loan (in years or days).
Therefore:
Exact interest: 4,400 * 6% * 172/365 = $375.44
Maturity value: 4,400 + 375.44 = $4,775.44
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Mr chua bought a vanguard sheet with dimension 75 cm by 90 cm . He cut squares of identical size from the vanguard sheet such that there was no wastage
(a) What was the largest possible length of the side of each square he cut out?
(b) What was the total number of squares he cut out?
Answers
(A) - The largest possible length of the side of each square is 15 cm.
(B) - The total number of squares he cut out is 6750 / 225 = 30 squares.
Explanation:
(a) To find the largest possible side length of each square, we need to determine the greatest common factor of the length and width of the vanguard sheet.
The greatest common factor of 75 and 90 is 15, so the largest possible length of the side of each square is 15 cm.
(b) To find the total number of squares he cut out, we need to divide the area of the vanguard sheet by the area of each square.
The area of the vanguard sheet is 75 cm * 90 cm = 6750 square cm.
The area of each square is 15 cm * 15 cm = 225 square cm.
So the total number of squares he cut out is 6750 / 225 = 30 squares.
75 cm and 90 cm have a GCD of 15 cm, so the largest possible side length of each square is 15 cm.
(b) To find the total number of squares he cut out, we divide the area of the Vanguard sheet by the area of each square:
Area of Vanguard sheet = 75 cm * 90 cm = 6750 square cm
Area of each square = 15 cm * 15 cm = 225 square cm
Total number of squares = 6750 / 225 = 30
So, Mr. Chua cut out 30 squares of side length 15 cm from the Vanguard sheet
Laurie sold a house and made a commission of $14,050. She charges her customers a commission fee of 2. 5% on the selling price of the house. How much was the selling price of the house Laurie sold?
Answers
The selling price of the house that Laurie sold was $562,000.
The selling price is the amount paid by the customer to purchase the goods. The actual selling price is the amount paid by the customer for a product or service. This is the price that is more than the cost of products and includes a proportion of profit.
The cost price of an item is the amount spent to buy it or the price at which it is manufactured.
Let's call the selling price of the house "P".
The commission fee of 2.5% on the selling price of the house is equal to 0.025 * P.
Since Laurie made a commission of $14,050, we can set up the following equation:
0.025 * P = 14050
Dividing both sides by 0.025:
P = 14050 / 0.025 = 562000
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If we were constructing a box with length l , width w , and height = 8 cm, where the length of the box is twice the width, which could we use as a volume function?A)V = 16W2B)V =8w2C)V =16I2D)V = 16I
Answers
We can use (A) V = 16lw as a volume function.
Because the volume of a rectangular box is given by the product of its length, width, and height. In this case, the height is fixed at 8 cm, so the volume would be calculated as V = 16 x l x w, where l = 2w.
A three-dimensional space's volume is measured. t is frequently expressed numerically using units derived from SI (such the cubic Meter and litre) or by different imperial or US customary units (such as the gallon, quart, cubic inch). Volume and length (cubed) are related concepts.
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three sandwiches were given to each adult and two sandwiches were given to each child that went on the field trip. there were 40 people on the bus and a total of 89 sandwiches were given out. how many adults and how many children were on the trip ? (PLEASE HELP)
Answers
Answer:
the number of children on the trip=31
The number of adult=9
Step-by-step explanation:
Let's call the number of adults on the trip "a" and the number of children on the trip "c".
We know that:
a + c = 40 (the total number of people on the trip)
And:
3a + 2c = 89 (the total number of sandwiches given out)
We can use the first equation to solve for one variable in terms of the other:
a = 40 - c
And substitute this into the second equation:
3(40 - c) + 2c = 89
Expanding and simplifying:
120 - 3c + 2c = 89
120 - c = 89
Subtracting 120 from both sides:
-c = -31
So c = 31, the number of children on the trip.
And the number of adults on the trip, a = 40 - c = 40 - 31 = 9.
Explain why each of the following expressions makes no sense. (dot product )(a) u\bullet(v\bulletw)(b) (u\bulletv)+w(c) ?u\bulletv?(d) k\bullet(u+v)
Answers
All the given statements does not make sense by the definition of dot product.
(a) (dot product)(a): The dot product is a mathematical operation and doesn't take any arguments or values, so this expression doesn't make sense as written.
(b) u\bullet(v\bulletw): The dot product is associative, meaning that u\bullet(v\bulletw) = (u\bullet v)\bullet w. However, the expression itself is not well defined, since the inner expression v\bullet w doesn't specify what values v and w represent.
(c) (u\bullet v) + w: The dot product is an scalar product, meaning it results in a scalar value, and adding a scalar to a vector does not make sense mathematically.
(d) k\bullet(u+v): The dot product is between two vectors, and the expression k\bullet(u+v) implies that the dot product is between a scalar (k) and a vector (u+v). This does not make mathematical sense, as the dot product is only defined between two vectors of the same dimension.
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How To Convert 24 °C to °F
Answers
Answer: 75.2 °F
Step-by-step explanation: (24°C × 9/5) + 32 = 75.2°F
The calculation would be (24 x 9/5) + 32 = 75.2°F.
How To Convert 24 °C to °F?To convert 24°C to°F, you can use the following formula is°F = (°C x 9/5) + 32Celsius (°C) and Fahrenheit (°F) are both units used to measure temperature.The formula for converting from Celsius to Fahrenheit is based on the relationship between the two temperature scales.To convert from Celsius to Fahrenheit, you need to multiply the temperature in Celsius by 9/5, and then add 32.The result will be the temperature in Fahrenheit.For example, to convert 24°C to°F, the calculation would be (24 x 9/5) + 32 = 75.2°F.This conversion formula is commonly used in various industries, such as meteorology, chemistry, and thermodynamics, to convert temperatures between Celsius and Fahrenheit.It's important to keep in mind that the temperature scales are not linear, meaning that the same difference in temperature will represent a different change in the two temperature scales.To learn more about Celsius to Fahrenheit:
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pls help Use your response to question 1 to write a recursive definition for the amount of medication in Aldi’s bloodstream after each dose of medication. Is your definition arithmetic, geometric, or neither? Explain.
Answers
The sequence is neither arithmetic nor geometric.
What does mathematical sequence mean?Informally, a sequence in mathematics is a list of items that are in some order (or events). It possesses members, much like a set (also called elements, or terms). The length of the series is the number of ordered elements in the sequence, which could be unlimited.
Also, Arithmetic sequences, geometric sequences, quadratic sequences, and special sequences are the four primary categories of distinct sequences you need to be familiar with.
Squares, rectangles, circles, cones, cubes, and other shapes that can be created using geometry are known as geometric forms. In structural, civil, and architectural engineering, geometric forms are frequently used.
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The sequence from response to question 1 is neither arithmetic nor geometric.
How to identify the type of sequence ?The sequence in mathematics is the order of value of items or events. Usually, it contains a number or a series of numbers with a length of series that can be unlimited.
If the sequence has common differences from one value to another it can be considered as an arithmetic sequence, for example, 2,4,6,8. If the sequence has common ratios from one value to another it can be considered as a geometric sequence, for example, 2,4,8,16.
Since the response in question 1 doesn't have either common differences or common ratios, so it is neither arithmetic nor geometric.
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how many kilograms are in a pound
Answers
0.453592 kilograms are in a pound.
How many kilograms are in a pound?
One pound is approximately equal to 0.45359237 kilograms (kg). The conversion of the pound to kilograms is done by multiplying the given pound value and 0.45359237. Also, one kilogram is approximately equal to 2.2046226218 lbs.One litre of water has a mass of almost exactly one kilogram when measured at its maximal density, which occurs at about 4 °C. It follows, therefore, that 1000th of a litre, known as one millilitre (1 mL), of water has a mass of about 1 g; 1000 litres of water has a mass of about 1000 kg (1 tonne or megagram).Pounds and kilograms are both units for measuring mass. Pound refers to an imperial system of measuring weight or mass. Kilogram, on the other hand, was adopted under the SI or International System of Units in 1959.To learn more about pound refers to:
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axial force of 103 kn. if a safety factor against yielding of 1,5 is required, a) what is the lowest necessary yield strength for the axle material?
Answers
The lowest necessary yield strength for the axle material is 113.88 M/mm^2.
Torsional moment of Mv = 2×10^7 Nmm.
Bending moment of Mb = 1×10^7 Nmm
Axial force = 10^3 kN
Axial Stress = Axial Force/(πd^2/4)
Axial Stress = 10^3 × 10^3/(π(100)^2/4)
Axial Stress = 4 × 10^6/3.14 × 10^4
Simplifying
Axial Stress = 1.274 × 10^2
Axial Stress = 127.4
The combined tension of a torsional moment and a bending moment is known as shear stress.
τ = 16/πd^3√(Mv^2 + M^2)
τ = 16/π(100)^3√[(2×10^7)^2 + (1×10^7)^2]
τ = 16/π(10)^6√[4×10^14 + 10^14]
τ = 16/π(10)^6√[5×10^14]
After solving, we get
τ = 113.88 M/mm^2
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The complete question is:
The figure shows a circular axial made of steel that is loaded by a torsional moment of Mv=2×10^7 Nmm, a bending moment of Mb = 1×10^7 Nmm and an axial force of 10^3 kN. If a safety factor against yielding of 1,5 is required, what is the lowest necessary yield strength for the axle material?
Deshawn wrote the following rule for the translation shown. What was his error?
T(-4, -3)(JKL)
Answers
The rule for the translation is (-3, -4).
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
A translation is a movement of the graph either horizontally parallel to the -axis or vertically parallel to the -axis.
JKL is the original figure.
J'K'L' is the transformed figure after applying cetain rule.
We obtain J'K'L' by translating the original image left 3 units and down by 4 units.
The rule should be (-3, -4)
Hence, the rule for the translation is (-3, -4).
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flip a coin. if you have flipped t tails, you need to flip t 1 consecutive heads to win the game. what is the probability to win the game?
Answers
The probability of winning the game, given t tails, is equal to [tex]0.5^t[/tex] .It's important to note that the outcome of each flip is independent.
The probability of winning the game in which you have flipped t tails and need to flip t consecutive heads can be calculated as follows:
Each flip of the coin has a probability of 0.5 of landing heads and 0.5 of landing tails. So, for the first flip, the probability of flipping a head is 0.5. For the second flip, the probability of flipping two heads in a row is
[tex]0.5 * 0.5 = 0.25[/tex]
For the third flip, the probability of flipping three heads in a row is
[tex]0.5 * 0.5 * 0.5 = 0.125[/tex] , and so on.
Therefore, the probability of winning the game, given t tails, is equal to 0.5^t. For example, if you have flipped 2 tails, the probability of winning the game by flipping 2 consecutive heads is
[tex]0.5 * 0.5 = 0.25.[/tex]
It's important to note that the outcome of each flip is independent, so the probability of winning the game given t tails is constant regardless of the number of tails flipped prior to the current flip.
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help me pass alegbra class. the second screenshot is question 6.
Answers
The linear system of equations in the question are resolved as follows;
Question 4
The true statements are;
The point satisfies both equation 1 and 2The point is a solution to the systemQuestion 6
Solution: (1.5, -1.375)What is a linear system of equation?A linear system consists of two or more linear equations that operate simultaneously.
Question 4;
The system of equations is presented as follows;
Equation 1: 10·x - 2·y = 15
Equation 2: 4·x + y = 6
Plugging in the values of x = 1.5, y = 0, we get;
10 × 1.5 - 2 × 0 = 15
4 × 1.5 + 0 = 6
The point (1.5, 0), satisfies both equations in the system of equations, therefore, the point (1.5, 0) is a solution of the system of equations.
The true statements are therefore;
The point satisfies both equation 1 and 2The point is a solution of the systemQuestion 6;
The linear system of equation is presented as follows;
-4·x - 8·y = 5
x = 4·y + 7
The substitution method can be used by plugging in the value of x = 4·y + 7, in equation (1) as follows;
-4·x - 8·y = 5
-4·(4·y + 7) - 8·y = -24·y - 28 = 5
Adding 28 to both sides, we get;
-24·y - 28 + 28 = 5 + 28
-24·y + 0 = 5 + 28 = 33
-24·y = 33
y = 33/(-24) = -11/8
y = -11/8 = -1.375
x = 4 × (-11/8) + 7
x = -11/2 + 7 = (-11 + 14)/2 = 3/2
x = 3/2 = 1.5
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A sequence can be generated by using an=an−1+17, where a1=15 and n is a whole number greater than 1.
What are the first 5 terms in the sequence?
32, 49, 66, 83, 100
17, 32, 47, 62, 77
15, 32, 49, 66, 83
15, 30, 45, 60, 75
Answers
Answer:
Step-by-step explanation:
A sequence can be generated by using an=an−1+17, where a1=15 and n is a whole number greater than 1. The first 5 terms in the sequence are:
a2 = a1 + 17 = 15 + 17 = 32
a3 = a2 + 17 = 32 + 17 = 49
a4 = a3 + 17 = 49 + 17 = 66
a5 = a4 + 17 = 66 + 17 = 83
So the first 5 terms in the sequence are:
15, 32, 49, 66, 83
pls help I can't figure out the problem and I need help it worth a lot of points in my grade
Answers
Answer:
Perimeter 18.42
Area 20.13
Step-by-step explanation:
Perimeter:
This is the distance around the figure.
The distance around the triangle is 9.
The distance around the 1/2 circle
c= 2[tex]\pi[/tex]r
c [2(3.14)(3)]/2
c = 9.42
9.42 + 9 = 18.42
Area:
triangle
a = 1/2(bh)
a - 1/2 (3)(4)
a = 6
circle
a = 1/2([tex]\pi r^{2}[/tex])
a = 1/2(3.14)(9)
a = 14.13
6 + 14.13 = 20.13
Whats the slope and y-intercept
2x-6y=24
I think I know the intercept I just don't know the slope.
Answers
Answer:
x-6y=-24
Step-by-step explanation:
do it
Answer:
Step-by-step explanation:
The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.
To find the slope and y-intercept of the equation 2x - 6y = 24, you can first isolate y by adding 6y to both sides and then dividing both sides by -6. This gives you: y = (-1/3)x + 4
So, the slope is -1/3 and the y-intercept is 4.
please help I would really be happy
Answers
Jackson invested $320 in an account paying an interest rate of 3. 2% compounded
continuously. Assuming no deposits or withdrawals are made, how long would it
take, to the nearest tenth of a year, for the value of the account to reach $410?
Answers
If Jackson invested $320 in an account paying an interest rate of 3. 2% compounded continuously, assuming no deposits or withdrawals are made, it would take: 3.37 years
for the value of the account to reach $410
To solve this problem, we can use the formula for continuously compounded interest:
A = P * e^(rt)where A is the final amount, P is the initial amount (320), r is the interest rate (3.2%), and t is the time in years.
Solving for t, we get:
t = (ln(A/P)) / (r)Plugging in the values, we get:
t = (ln(410/320)) / (0.032)Approximating this, we get:
t = 3.37 years, rounded to the nearest tenth of a year.So it would take about 3.4 years for the value of the account to reach $410.
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There i a pattern 1 tree then 2 bead. If there are a total of 42 tree and bead, how many tree and how bead will you need?
Answers
If there is a pattern 1 tree then 2 bead. If there are a total of 42 tree and bead, then 84 bead is needed to complete the pattern as 42 tree and 84 bead.
What is pattern?A recurring arrangement of numbers, forms, colours, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series.Sequences and patterns. Patterns are common, repeatable sorts of practises or guidelines. Patterns can help us anticipate the future or what has already happened. come following a series of integers that are ordered specifically. A sequence is the name given to this collection of integers.Learn more about patterns refer to :
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Se conoce el peso ideal de un niño de 5 años en Colombia es de 20Kg. Escriba una frase que indique a cuántos kilogramos está cada niño, por debajo, por encima del peso ideal.
a. Juan pesa 22kg b. Mario pesa 18Kg c. Pedro pesa 26kg d. Alfredo pesa 20Kg
Answers
a) Juan, 2 kg de encima
b) Mario, 2 kg por debajo
c) Pedro, 5 kg por encima
d) Alfredo, Tiene el peso preciso
Qué se entiende por diferencia en matemáticasOperaciones aritméticas incluyen suma, resta, multiplicación y división
La diferencia en matemáticas es una operación aritmética de resta entre dos números grandes con un número pequeño para que el resultado sea siempre positivo.
La diferencia en matemáticas es también la diferencia de valor entre dos números
Ejemploa) la edad de Dewi = 25 años
edad de Adi = 51 años
entonces
Diferencia de edad entre A y B
= (51 – 25) años
= 26 años
Entonces la diferencia en sus edades es 26 años
b) El dinero de A = IDR 13,000.00
Dinero de B = IDR 10,500.00
entonces diferencia en su dinero es
= 13.000,00 IDR – 10.500,00 IDR
= 2.500,00 IDR
Entonces, la diferencia o la diferencia en su dinero es IDR 2,500.00
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On a coordinate plane, a curved line with minimum values of (negative 2, 0) and (2.4, negative 51) and a maximum value of (negative 0.75, 6), crosses the x-axis at (negative 2, 0), (0, 0), and (3.5, 0), and crosses the y-axis at (0, 0).
Which statement is true about the end behavior of the graphed function?
As the x-values go to positive infinity, the function's values go to negative infinity.
As the x-values go to zero, the function's values go to positive infinity.
As the x-values go to negative infinity, the function's values are equal to zero.
As the x-values go to negative infinity, the function's values go to positive infinity.
Answers
The truth about the end behavior of the graph is
D. As the x-values go to negative infinity, the function's values go to positive infinity.What is end behavior?The end behavior of function typically says the characteristics of the function at the ends
How to find the end behavior of polynomial functionExamining the given graph it can be deduced that end behavior is described as
x ⇒ -∞ f(x) ⇒ ∞
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Answer:
Step-by-step explanation:
The truth about the end behavior of the graph is
D. As the x-values go to negative infinity, the function's values go to positive infinity.
How do I find the measure of angle ABE?? 43
Answers
The required measure of supplementary angle ∠ABE is 137°.
What are the angle?Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
The measure of a supplementary angle to an angle with measure x is defined as 180°-x. Therefore, the measure of the supplementary angle ∠ABE to an angle with a measure 43° is:
∠ABE = 180° - 43° = 137°
Thus, the required measure of supplementary angle ∠ABE is 137°.
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Tramaine is using a carton of chicken stock that contains 4 1/2 pints of chicken stock. He will use the 3/5 carton to make a stew and he will use the rest of the carton to make rice. How many pints of chicken
stock with Tramaine use for each dish?
Answers
Using the given fractions, we can see that for the stew they use (27/10) pints and for the rice (18/10) pints.
How many pints of chicken stock with Tramaine use for each dish?
We know that the carton has a volume of:
(4 + 1/2) pints of chicken stock.
He uses 3/5 of the carton to make a stew, so he uses:
(3/5)*(4 + 1/2) pints = (12/5 + 3/10) pints
= (27/10) pints.
And the rest, (2/5) of the carton, is used to make rice, then:
(2/5)*(4 + 1/2) pints = (8/5 + 2/10) pints = (18/10) pints.
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if you must use a 1/4 inch diameter mill, then the best surface tolerance and finish would be gotten if all inside vertical corners had a fillet radius with the minimum requirement of: (a) < 0.25 inch (b) > 0.125 inch (c) < 0.125 inch (d)
Answers
The best surface tolerance and finish would be gotten if all inside vertical corners had a fillet radius of (b) > 0.125 inches.
The choice of fillet radius is an important factor in determining the surface tolerance and finish of a machined part. A fillet radius is a rounded corner between two flat surfaces. A fillet radius that is too small can result in a rough surface, while a fillet radius that is too large can weaken the part.
In this scenario, a 1/4 inch diameter mill is being used, so the best surface tolerance and finish would be achieved if the fillet radius is greater than 0.125 inch, but less than 0.25 inch. This will ensure that the part is not weakened and the surface is smooth. The exact value of the fillet radius will depend on the specific requirements of the machining process.
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Complete Question:
If you must use a 1/4 inch diameter mill, then the best surface tolerance and finish would be gotten if all inside vertical corners had a fillet radius with the minimum requirement of:
(a) < 0.25 inch
(b) > 0.125 inch
(c) > 0.25 inch
(d) = 0.25 inch
(e) = 0.125 inch
(f) < 0.125 inch
When Kyle doesn't study for his tests, he has a 45% chance of passing. If Kyle didn't study for15 tests this semester, what is the probability he passed at this semester?
Answers
The probability that Kyle will pass all 15 tests if he does not study for them is approximately 0.0017.
This is because the probability of passing each individual test without studying is 0.45, and the probability of passing all tests without studying is equal to 0.45 multiplied by itself 15 times, which is 0.0017. This means that the odds of Kyle passing all 15 tests without studying are very slim.
Even if he has a good understanding of the material and has been able to recall the information without studying, it is very unlikely that he will be able to do so for all 15 tests. It is therefore recommended that Kyle studies for his tests in order to increase his chances of passing them.
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(exercise 2: find the critical points of the gompertz equation (1). (is y = 0 a critical point? does it solve the algebraic equation you get?).dy = ry In(K/y
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y = k asymptotically stable critical point because f'(k) < 0 and f'(0) > 0. So y = 0 is an an asymptotically unstable critical point.
The Gompetz equation is dy/dt = ry In(K/y).
In order to find critical points equate dy/dt equal to zero
dy/dt = 0
ry In(k/y) = 0
Here, k and r are constants
y In(k/y) = 0
y = 0
In (k/y) = 0
Eliminating In
k/y = e^0
k/y = 1
Multiply by y on both side, we get
k = y
y = 0 and y = k
The critical points are 0 and k
Since zero is a critical point
dy/dt = f(y)
dy/dt = ry In(k/y)
Differentiation on both side
f'(y) = ry In(k/y) - ry × y/k × k/[tex]y^2[/tex]
f'(y) = r In(k/y) - r
f'(k) = r In(k/k) - r
f'(x) = -r < 0
So that, y = k asymptotically stable critical point because f'(k) < 0
f'(0) > 0
That means y=0 is asymptotically unstable critical point.
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how many turning points does -3x^{3} 2 have
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The polynomial -3x^3 + 2 has only one turning point.
A turning point is a point on a curve where the curve changes direction, either from going up to going down or vice versa. In other words, it is a point where the first derivative of the curve changes sign.
For the polynomial -3x^3 + 2, the first derivative is given by:
d/dx (-3x^3 + 2) = -9x^2
Since the first derivative is a monotonically decreasing function (that is, its slope is always negative), the polynomial -3x^3 + 2 has only one turning point.
Slope of first derivative
d²(-3x^3 + 2)/dx² = -18x
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