Answers
1) 6 3/7
2) 7 1/2
3) 2 7/13
4) 4
Find the quotient (same page as find the product) :
1) 3
2) 3/19
3) 18/35
4) 4 4/9
Find the quotient (beginning of the other page) :
1) 11 3/7
2) 35/43
3) 24/25
4) 6
Find the quotient (end of the other page) :
1) 2
2) 5 1/11
3) 11 1/2
4) 4 9/34
Related Questions
at a local book store, fiction books were on sale. Some were priced at $6 and some at $8. Marci bought 10 books and spent a total of $68.00. How many $6 books did she buy?
Answers
Answer:
6 $6 books
Step-by-step explanation:
Using the information, we can create a system of equations.
We can let x represent the total number of $6 Marci bought and y represent the total number of $8 books she bought.
Because the total number of books is 10, one equation we have is x + y = 10.
Because the total cost of both types of books is $68, our other equation is 6x + 8y = 68.
We can solve with substitution by isolating y in the first equation and plugging it into the second equation:
[tex]x+y=10\\y=-x+10\\\\6x+8(-x+10)=68\\6x-8x+80=68\\-2x+80=68\\-2x=-12\\x=6[/tex]
Thus, the total number of $6 books Marci bought was 6.
Find an expression which represents the difference when (−5x+7) is subtracted from (9x+5) in simplest terms.
Answers
14x - 2
To find the difference between (−5x+7) and (9x+5), we need to subtract the first expression from the second.
(9x+5) - (-5x+7)
= 9x + 5 + 5x - 7 [Distribute the negative sign to (-5x+7)]
= 14x - 2
Therefore, the difference between (−5x+7) and (9x+5) is 14x - 2.
See image below!!
The food service manager conducted a random survey of 200 students to determine their preference for new lunch menu items. There are 1,500 students in the school. Select all the manager’s predictions that are supported by the data.
Answers
1 & 3 are true, 2/4/5 are false
[tex]f(x) = \frac{ {x}^{3} + 1 }{ {x}^{3} - 2} [/tex]
Find the inverse
Answers
Answer:
Step-by-step explanation:
[tex]f^-1[/tex][tex]\sqrt[3]{1/-1+x | + | 2x/-1+x}[/tex]
Arthur is building a rectangular sandbox for his son. The area of the sandbox is 17 23/32 square feet. If the length of the sandbox is 3 3/8 feet, what is the width of the sandbox?
Answers
Answer:
5 1/4 feet----------------------------------
Area of a rectangle is the product of it width and length:
A = wlGiven the length and area of a rectangle, find the missing width:
w = A/lw = 17 23/32 : 3 3/8 = (17*32 + 23)/32 : (3*8 + 3)/8 = 567/32 : 27/8 =567/32 * 8/27 = 21/4 = 5 1/4There are 150 players on the high school football team. 30% of the players are on the freshman team, and the rest of them are on either JV or varsity.
How many players are on the freshman team?
Answers
what conclusions can you draw about the sugar content of the cereals at Supermarket Eats? Which of the cereals would you be willing to purchase and which ones would you avoid? Explain your reasoning below.
Answers
When choosing cereals at Supermarket Eats, it is important to read the nutrition labels and choose cereals that are lower in added sugars and higher in fiber.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants
Based on general nutrition guidelines, it is recommended to choose cereals that are lower in added sugars and higher in fiber.
If the cereals at Supermarket Eats have nutrition labels, it is important to read them carefully to determine the sugar content per serving size. According to the American Heart Association, it is recommended that men limit their intake of added sugars to no more than 9 teaspoons per day, and women limit their intake to no more than 6 teaspoons per day. Choosing cereals that have less than 5 grams of added sugars per serving is a good rule of thumb.
In terms of fiber content, it is recommended to choose cereals that have at least 3 grams of fiber per serving. This will help to keep you feeling full and satisfied, and promote healthy digestion.
Therefore, When choosing cereals at Supermarket Eats, it is important to read the nutrition labels and choose cereals that are lower in added sugars and higher in fiber.
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the measure of three interior angle of a triangle are in the ratio 2፡3፡4. what is the measure of the smallest and largest interior angles of triangle?
Answers
Answer:
Below
Step-by-step explanation:
The interior angles of ANY triangle add up to 180 degrees
you want to divide this 180 into 2 + 3 + 4 = 9 parts
180 / 9 = 20 degrees for each part
2 parts = 2 * 20 = 40 °
4 parts = 4 * 20 = 80 °
The net of a right circular cylinder is shown.
net of a cylinder where the radius of each circle is labeled 4 meters and the height of the rectangle is labeled 8 meters
What is the surface area of the cylinder? Use π = 3.14 and round to the nearest whole number.
251 m2
301 m2
502 m2
804 m2
Answers
The area of each circular base is πr^2, where r is the radius. In this case, the radius is 4 meters, so the area of each circular base is:
π(4)^2 = 16π
The lateral surface area is the area of the rectangle that forms the curved surface of the cylinder. The height of the rectangle is the same as the height of the cylinder, which is 8 meters, and the base of the rectangle is the circumference of the circle, which is 2πr. So, the lateral surface area is:
8(2πr) = 16πr
Substituting r = 4, we get:
16π(4) = 64π
Adding the areas of the two circular bases and the lateral surface area, we get:
16π + 16π + 64π = 96π
Using π = 3.14 and rounding to the nearest whole number, the surface area of the cylinder is:
96π ≈ 301 square meters
Answer:
The first person to answer was correct, the answer is 301 m squared.
Step-by-step explanation:
I took the quiz so you don't have to! <3
On a coordinate plane, a parabola with a solid boundary line opens down. It goes through (negative 2, 0), has a vertex at (2, 12), and goes through (6, 0). Find the symbol and coefficients for the standard form of the inequality represented by the graph. y the boundary line. a = b = c =
Answers
Therefore , the solution of the given problem of inequality comes out to be y - 12 = -(3/4)(x - 2)².
What is an inequality?Without the equal sign, an association or collection of numbers can be a disparity in mathematics. Equity always comes after equilibrium. When standards are still incompatible, inequality results. Fairness and disparity have different variable characteristics. Because parts aren't always similar or close to one another, we decided to select the most common symbol (). It is also possible to use disparities of any size to assess values.
Here,
We must recast the parabola's equation in this form in order to determine the inequality's standard form. The vertex version of a quadratic equation is as follows:
=> y = a(x - h)² + k
where (h, k) is the parabola's apex. Inputting the numbers provided yields:
=> y = a(x - 2)² + 12
We can use the information that the parabola passes through (-2, 0) and to determine the value of a. (6, 0). When we enter these values into the formula, we obtain:
=> 0 = a(-2 - 2)² + 12
=> 0 = 16a + 12
=> a = -3/4
The parabola's solution is as follows:
=> y = -(3/4)(x - 2)²
We need to separate y on one side in order to determine the inequality's standard form:
=> y - 12 = -(3/4)(x - 2)²
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an
How was Malaka's father finally able to move to the
United States?
O He saved enough money to afford the cost of moving.
He was accepted to UCLA's School of Management.
He studied and was able to pass the TOEFL.
He received a teaching job at UCLA.
Answers
Answer:
B
Step-by-step explanation:
He was accepted to UCLA's School of Management
Write a word problem involving percents for which the percent is about one half and the whole is known. Write a percent equation for the problem and then use it to solve the problem
Answers
The purchase cost is $40. Question: What is the discount price of shoes if they were originally $80 and are currently on sale for 50% off. % formula: Sale price equals 50% of $80.
The word puzzle asks you to determine the sale price of shoes that are being offered at a 50% discount. The percent equation, which asserts that the percent of the whole is equal to the part over the entire, or percent = part/whole, may be used to solve this problem. In this instance, the sale price is the component we are interested in, the initial price of $80 is the component as a whole, and 50% is the percentage. With these numbers as inputs, we can calculate the sale price as 50% of $80. When we solve for the sale price, we arrive at $40. Hence, the sneakers are $40 on sale.
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Write a word problem involving percents for which the percent is about one half and the whole is known. Write a percent equation for the problem and then use it to solve the problem. If a store has a sale on shoes for 50% off and the original price is $80, what is the sale price?
Help with work shown all of them
Answers
The expression are simplified to ;
7. 16 + 8g
8. 4h - 20g
9. -35 + 7n
10. 16m + 8
13. -56n + 7m
14. -36 - 6d
15. -8c - 4d
16. -6f + 10g
What are algebraic expressions?Algebraic expressions are defined as expressions that are usually made up of terms, variables, constants, factors and coefficients.
These expressions are identified with mathematical or arithmetic operations, such as;
AdditionMultiplicationSubtractionBracketDivisionParentheses, etcFrom the information given, we need to expand the bracket to determine the expressions, we have;
a. -7(8n - m)
expand the bracket
-56n + 7m
b. (6+d)(-6)
expand the bracket
-36 - 6d
c. (4c + 2d) - 2
expand the bracket
-8c - 4d
d. -2(3f - 5g)
expand the bracket
-6f + 10g
e. (2 + g) 8
expand the bracket
16 + 8g
f. 4(h - 5g)
expand the bracket
4h - 20g
g. -7(5 - n)
expand the bracket
-35 + 7n
h. 8(2m + 1)
expand the bracket
16m + 8
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Step-by-step explanation:
13. -7(8n-m)= -56n+7m
14. (6+d)(-6)= -36-6d
15. (4c+2d)(-2)= -8c-4d
16. -2(3f-5g)= -6f+10g
7. (2+g)8= 16+8g
8. 4(h-5g)= 4h-20g
9. -7(5-n)= -35+7n
10. 8(2m+1)= 16m+8
What are the angles of a triange if the sides are 11, 10, 17
Answers
In the following question, among the conditions given, This triangle must be a non-Euclidean triangle, which is not possible to draw on a flat plane without distorting its shape. Therefore, there are no valid angles for this triangle.
To find the angles of a triangle when given the lengths of its sides, we can use the Law of Cosines, which states that:
c^2 = a^2 + b^2 - 2ab*cos(C)
where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides.
Using this formula, we can find the cosine of each angle and then use the inverse cosine function (cos^-1) to find the measure of each angle.
Let's use this formula to find the angles of the triangle with sides of 11, 10, and 17:
c^2 = a^2 + b^2 - 2ab*cos(C)
For the side opposite angle C = 17:
17^2 = 10^2 + 11^2 - 2(10)(11)cos(C)
289 = 121 + 100 - 220cos(C)
cos(C) = (121 + 100 - 289)/(21011)
cos(C) = -0.4
We get a negative value for the cosine of angle C. This means that the triangle cannot be a standard triangle in the Euclidean plane, as the Law of Cosines requires that the cosine of an angle be between -1 and 1. This triangle must be a non-Euclidean triangle, which is not possible to draw on a flat plane without distorting its shape.
Therefore, there are no valid angles for this triangle.
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A parallelogram of base 12cm has an area 108sq. Cm. Find the height
Answers
The height of the parallelogram is 9 cm.
To find the height of a parallelogram with a given base and area, we can use the formula:
Area = base x height
In this case, we are given that the base of the parallelogram is 12 cm and the area is 108 sq. cm. Substituting these values into the formula, we get:
height = 108/12
Simplifying this expression, we get:
height = 9cm
A parallelogram is a four-sided polygon with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length and parallel to each other. The opposite angles are also equal in measure, meaning that the adjacent angles are supplementary (their sum is 180 degrees).
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342×38 without using a calculator
Answers
Answer:
12996
Step-by-step explanation:
342
× 38
-----
2052 (2 x 342)
13680 (3 x 342, plus a zero)
-----
12996
Therefore, 342 × 38 = 12,996.
Demonstrate your knowledge by giving clear, concise solutions to each problem. Be sure to include all
relevant drawings and justify your answers (show all your work). You may show your solution in more
than one way to investigate beyond the requirements of the problem. (21 pts)
1. a. Tell how you know that a system of linear equations has no solutions. (3 pts)
b. Write a system of two linear equations that has no solution. (3 pts)
c. Tell how you know that a system of two linear equations has more than one solution. How
many solutions will such a system have? Justify your answer. (3 pts)
d. Write a system of two linear equations that has more than one solution. (3 pts)
e. Write a system of linear equations that has only one solution. (3 pts)
f. Solve the system of equations in part e in at least two ways. (3 pts)
g. Write a word problem that can be solved using a system of two linear equations. Solve the
problem and give the meaning of the answer. (3 pts)
Answers
The solutions of a system of linear equations are as follows;
1. Their slope is the same but their y-intercept are different
b. y = 3·x + 2 and y = 3·x + 5
c. The equations are the same
d. y = 3·x + 2 and y = 9·x + 15
e. y = 3·x + 2, and y = 8·x + 5
f. x = 0, y = 0
g. Please see the following section
What is a system of linear equations?A system of linear equations are equations that have the same variables.
1. a. A system of linear equations have no solution if the equations in the system of equations have the same slope
b. y = 3·x + 2, and y = 3·x + 5
c. A system of two linear equations has more than one solution if the equations in the system are the same
The number of solutions = Infinite number of solutions
d. y = 3·x + 5, 3·y = 9·x + 15
e. y = 3·x + 5, y = 8·x + 5
f. y = 3·x + 5, y = 8·x + 5
Therefore; 3·x + 5 = 8·x + 5
3·x = 8·x
3·x - 8·x = 0
-5·x = 0
x = 0/(-5) = 0
x = 0
y = 3·x + 5
y = 3 × 0 + 5 = 5
y = 5
The solution is therefore;
x = 0, y = 5
g. A customer wants to spend a total of ¢50 to buy drawing pads and pencils. The cost of the pencil the customer intends to buy is ¢2, and the cost of each drawing pad is ¢8. The number of pencils and the number of drawing pads the customer buys are the same.
How many drawing pads and pencils does the customer buy.
Let x represent the number of drawing pad the customer buys and let y represent the number pencils the customer buys, we get;
8·x + 2·y = 50
x = y
Therefore;
8·x + 2·x = 50
10·x = 50
x = 50/10
x = 5
Therefore; y = 5
The number of drawing pads and pencils the customer buys are 5 each.
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PLSSSSSSSSSS HELPPPPPPPPPPPP!!!!!!!!!!!!!!!!!!!!!!!!
How is the quotient of 8,552 and 16 determined using an area model?
Enter your answers in the boxes to complete the equations.
8,552 ÷ 16 = (___÷ 16) + (480 ÷ 16) + (___ ÷ 16) + (8 ÷ 16)
8,552 ÷ 16 = ___ +30 + ___ + 8/16
8,552 ÷ 16 = ___ 1/2
Answers
Answer:
Step-by-step explanation:
Hi there I am able to help so when you do 8,552/16 it is best to reverse it then add the expression, what I mean by that is translating expressions. the answer would be 444.23 then you would want to add (480/16) no mental math how you would do this is the recalabric way, take 480/16 and put in an a fraction to make it work easier than the rest of your problems you would do the same things its simple, just repeat what I did to all the other problems,
regards, me
In my class of 25 students, I have 5 times slots to fill with student presentations. If there is only one student per time slot, in how many ways can the 5 time slots be filled?
Answers
If one student can fill 5 slots with student presentations, then 25 students might be able to fill the slots in 125 different ways.
To calculate the number of ways in which a student can fill a specific slot, the simple arithmetic operation of multiplication is used. In the given question it is already given that there are 25 students in a class and one of the student has filled the slots in 5 different ways. This means that each student will be able to fill the slots in 5 different ways.
Hence total number of ways in which all the students might be able to fill the slots is given as product of total students and number of slots filled.
Total number of ways = 25*5 = 125 ways
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I NEED HELP PLEASE ! I NEED SOMEONE TO EXPLAIN IT GOOD!
Answers
The expression -3¾ + 1/2 is represented on the number line.
What is a number line?Real numbers are represented by a number line, which is a representation of a graduated straight line, in elementary mathematics.
Every point on a number line is thought to represent a real number, and every real number is thought to represent a point.
Number lines are horizontal lines with uniformly spaced numerical increments.
So, first solves the expressions as follows:
-3¾ + 1/2
-12+3/4 + 1/2
-9/4 + 1/2
-9 + 2/4
-7/4
Now plot -7/4 on the number line as follows:
(Refer to the number line attached below)
Therefore, the expression -3¾ + 1/2 is represented on the number line.
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exponential law of heating and cooling
Answers
Part A: k = 8.4, to find the value of k, we must solve for k in the equation.
Part B: 193°F is the temperature of the water after 4.5 minutes.
What is initial temperature?Initial temperature is the temperature of a system before it undergoes a change. It can be calculated by subtracting the change in temperature from the final temperature.
Part A: k = 8.4
To find the value of k, we must solve for k in the equation.
We are given the temperature of the room (67°F) and the initial temperature of the water (208°F).
We are also given the temperature of the water after 3 minutes (193°F). We can plug these values into the equation and solve for k:
T-Ta = k(To-T)
193-67 = k(208-193)
126 = 15k
k = 126/15
k = 8.4
Part B: 193°F
To find the temperature of the cup of water after 4.5 minutes, we can plug the k-value we found in Part A into the equation, along with the given temperature of the room (67°F) and the initial temperature of the water (208°F).
T-Ta = k(To-T)
T = Ta + k(To-T)
T = 67 + 8.4(208-T)
T = 67 + 1747.2 - 8.4T
9.4T = 1814.2
T = 193
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Part A: k = 8.4, to find the value of k, we must solve for k in the equation.
Part B: 193°F is the temperature of the water after 4.5 minutes.
What is initial temperature?The temperature of a system at the start of a shift is called the initial temperature. You can figure it out by deducting the final temperature from the temperature difference.
Part A: k = 8.4
We must answer for k in the equation in order to determine its value.
We are informed of the room's temperature (67°F) and the water's starting temperature (208°F).
After three minutes, we are also told the water's temperature (193°F). We can solve for k by entering these numbers into the equation:
T-Ta = k(To-T)
193-67 = k(208-193)
126 = 15k
k = 126/15
k = 8.4
Part B: 193°F
We can enter the k-value we discovered in Part A, the given room temperature (67°F), and the starting temperature of the water (208°F) into the equation to determine the temperature of the cup of water after 4.5 minutes.
T-Ta = k(To-T)
T = Ta + k(To-T)
T = 67 + 8.4(208-T)
T = 67 + 1747.2 - 8.4T
9.4T = 1814.2
T = 193
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The complete question is,
EXIT TICKET
After heating up in a teapot, a cup of hot water is poured at a temperature of 208^0F . The cup sits to cool in a room at a temperature of 67^0 F. Newton's Law of Cooling explains that the temperature of the cup of water will decrease proportionally to the difference between temperature of the water and the temperature of the room, as given by the formula shown below.
Part A: If the cup of water reaches the temperature of 193^0 F after 3 minutes. Find the value of k, to the room, as given by the formula shown below. nearest thousandth.
Part B: Use the resulting equation to determine the Fahrenheit temperature of the cup of water, to the nearest degree, after 4.5 minutes.
The length of a rectangle is 1 ft more than double the width, and the area of the rectangle is 28 ft². Find the dimensions.
Answers
28= (1+2x)(x)
28=x+2x²
2x²+x-28 = 0
2x²+8x-7x-28 =0
2x(x+4) -7(x+4) =0
(x+4)(2x-7) = 0
x = -4 and 7/2
dimensions can't be negative
length=1+2×7/2 =1+7 = 8ft
width= 7/2ft
A physics exam consists of 9 multiple-choice test that has 7 questions. Each of the questions has 5 choices, with one correct choice per question. If you select one of these options per question and leave nothing blank, in how many ways can you answer the questions?
A.) 78,125
B.) 16,807
C.) 35
D.) 12
Answers
Using expression 5⁷ x 9, there are 59,049,125 ways to answer all 9 tests if you select one option per question and leave nothing blank.
What exactly are expressions?
In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, and exponentiation) that represents a value or a quantity.
Expressions can be simple or complex, and they can contain one or more variables. For example, "2x + 3" is a simple expression that contains the variable x.
Now,
To solve this problem, we can use the multiplication principle of counting, which states that if there are m ways to do one thing and n ways to do another thing, then there are m x n ways to do both things.
For each of the 9 tests, there are 5 choices for each of the 7 questions. Therefore, there are 5 x 5 x 5 x 5 x 5 x 5 x 5 possible ways to answer the questions on each test. Using the multiplication principle, we can find the total number of ways to answer all 9 tests by multiplying the number of ways to answer each test together:
5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 = 5⁷ x 9 = 59,049,125
Therefore,
there are 59,049,125 possible ways ways to answer all 9 tests if you select one option per question and leave nothing blank.
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6. Assume that the life of a packaged magnetic disk exposed to corrosive gases has a Weibull distribution with β = 0. 5 and the mean life is 600 hours. A) Determine the probability that a disk lasts at least 500 hours. B) Probability that a disk fails before 400 hours
Answers
A) Determine the probability that a disk lasts at least 500 hours.= 0.275
B) Probability that a disk fails before 400 hours=0.685
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
Remind the formula for CDF of Weibull random variable X
[tex]F(x)=1-e^{-(x/\delta)^{\beta}[/tex]
Now apply this formula for the Weibull variable X with the parameters β=0.5 and δ to be deduced from the mean of 600. The formula for the mean is:
[tex]600=\delta\Gamma(1+2)=\delta*2!\\\\\delta=300\\Finally\\\\P(x > 500)=1-F(500)=e^({-5/3})^{0.3}=0.275\\\\p(x < 400)=f(400)=0.685[/tex]
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find the missing angle
answer as soon as possible <3
Answers
Answer:
This is the answer!!!
31
28 students are divided into
7 groups for a party game.
32 students would create
how many groups of the
same size?
Answers
Answer:
If 28 students are divided into 7 groups, then each group will have 28/7 = 4 students.
To find out how many groups would be created if there were 32 students, we can use the same ratio:
32 students divided into groups of 4 students each would give us:
32/4 = 8 groups.
Therefore, if there were 32 students, they would be divided into 8 groups of the same size.
could anyone help me please :(
Answers
a) We need to find the values of x for which the denominator, cos(x), is equal to zero. b) vertical asymptotes at x = π/2, x = 3π/2, x = -π/2, x = -3π/2, and so on.
Describe Tangent Function?The tangent function is periodic, with a period of π radians (or 180 degrees). This means that the tangent function repeats itself every π radians, or every 180 degrees. The tangent function is also an odd function, which means that it is symmetric about the origin.
The graph of the tangent function has a characteristic shape with multiple cycles between consecutive vertical asymptotes. The graph passes through the origin and intersects the x-axis at the vertical asymptotes. The tangent function has a maximum and a minimum value between any two consecutive vertical asymptotes. However, it does not have a maximum or minimum value over its entire domain.
a) To determine the exact location of the asymptotes of the tangent function using the identity tan(x) = sin(x)/cos(x), we need to find the values of x for which the denominator, cos(x), is equal to zero. These values of x correspond to the vertical asymptotes of the tangent function.
Since cos(x) = 0 when x = π/2 + kπ, where k is an integer, the vertical asymptotes of the tangent function occur at these values of x. We can also write this as x = kπ/2, where k is an odd integer.
b) From the graph of the tangent function, we can see that there are vertical asymptotes at x = π/2, x = 3π/2, x = -π/2, x = -3π/2, and so on. These correspond to the values of kπ/2, where k is an odd integer. We can also write the set of vertical asymptotes as:
{x | x = kπ/2, k ∈ Z and k is odd}
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Im having trouble, I subtracted 90 with 40 but I dont understand. What are the values of x and y?
Answers
The value of x = 50°
What is the triangle?
A triangle is a 3 line segments with a closed diagram. It has 3 vertices, 3 sides and 3 angles. The sum of all interior angles is 180°.
Given figure y° = 40° and right angle triangle.
So, all interior angles sum is 180°.
90° + y° + x° = 180°
90° + 40° + x° = 180°
x° = 50°
Therefore, the value of x = 50°
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A day’s production of n manufactured parts contains x parts that do not conform to customer requirements. Assume that the selected parts are independent. What is the probability that the second nonconforming part is obtained in y tests?
Please choose n between 15 and 25
Please choose x between 11 and 14
Please choose y between 3 and 10
Then solve the problem. Formula: P(X = k) = (k-1) choose (r-1) * p^r * (1-p)^(k-r)
Answers
The P(2nd non-conforming part is obtained in y tests) is given by (n-x) / n * (1-x/n)^(y-1).
The probability that the second nonconforming part is obtained in y tests is given by the formula P(X = k) = (k-1) choose (r-1) * p^r * (1-p)^(k-r).Solution:Given, n = between 15 and 25x = between 11 and 14y = between 3 and 10To find: The probability that the second nonconforming part is obtained in y testsFormula used:P(X = k) = (k-1) choose (r-1) * p^r * (1-p)^(k-r)Where X represents the number of trials, p represents the probability of success, k represents the number of successful outcomes, and r represents the number of trials.Possible values of x:n - xLet the probability of obtaining a non-conforming part be p, then the probability of obtaining a conforming part would be 1-p.Number of non-conforming parts in n: n-xProbability of selecting the non-conforming part p = x/nProbability of selecting the conforming part 1-p = (n-x)/nP(2nd non-conforming part is obtained in y tests) = P(y-th trial is non-conforming) = P(y-1 conforming trials followed by a non-conforming trial)P(2nd non-conforming part is obtained in y tests) = (n-x) / n * (x/n)^(1-1) * (1-x/n)^(y-1)Therefore, P(2nd non-conforming part is obtained in y tests) = (n-x) / n * (x/n)^(0) * (1-x/n)^(y-1)P(2nd non-conforming part is obtained in y tests) = (n-x) / n * (1) * (1-x/n)^(y-1)Hence, P(2nd non-conforming part is obtained in y tests) is given by (n-x) / n * (1-x/n)^(y-1).
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A firm has classified its customers in two ways: according to whether the account is overdue and whether the account is new (less than 12 months) or old. An analysis of the firm's records provided the input for the following table of joint probabilities: One account is selected at random. If the account is overdue, what is the probability that it is new? If the account is new, what is the probability that it is overdue?
Answers
The probability that it is new is 0.0833.
The probability that it is overdue is 0.25.
How to calculate conditional probability?To solve this problem, use conditional probability.
Let A be the event that the account is new, and B be the event that the account is overdue.
A) To find the probability that an account is new given that it is overdue, calculate:
P(New | Overdue) = P(New and Overdue) / P(Overdue)
P(New | Overdue) = 0.05 / (0.05 + 0.55) = 0.0833 or 8.33%
So the probability that the account is new, given that it is overdue, is 8.33%.
B) To find the probability that an account is overdue given that it is new, calculate:
P(Overdue | New) = P(Overdue and New) / P(New)
P(Overdue | New) = 0.05 / (0.05 + 0.15) = 0.25 or 25%
So the probability that the account is overdue, given that it is new, is 25%.
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The complete question is:
A firm has classified its customers in two ways: according to whether the account is overdue and whether the account is new (less than 12 months) or old. An analysis of the firm's records provided the input for the following table of joint probabilities: One account is selected at random. If the account is overdue, what is the probability that it is new? If the account is new, what is the probability that it is overdue?