The seller purchased the product at a cost of 7500 and sold it for 7950, which resulted in a gain of 6%. So, the cost price is 7500.
In business, it is essential to keep track of cost prices and profit margins to ensure profitability. If the selling price is 7950 and the gain is 6%, we can use the following formula to calculate the cost price:
Cost price = Selling price / (1 + Gain%)
Substituting the given values, we get:
Cost price = 7950 / (1 + 0.06)
Cost price = 7500
Therefore, the cost price of the product is 7500, the gain percentage is calculated based on the cost price and not the selling price.
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The measure of the angle turns through 3/5 of 360°, true or false
Answer:
false, 216° turns 3/5 in a 360° rotation
An airliner carries 200 passengers and has doors with a height of 74 in. Heights of men are normally distributed with a mean of 69.0 in and a standard deviation of 2.8 in. Complete parts (a) through (d).
(A) If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending.
The probability that a male passenger can fit through the doorway without bending is approximately 0.9599, or 95.99%.
What is probability?
Probability is a branch of mathematics that deals with the study of random events and their likelihood of occurrence. It is used to quantify uncertainty and to make informed decisions in the face of incomplete or uncertain information.
We can assume that the heights of male passengers follow a normal distribution with a mean of 69.0 in and a standard deviation of 2.8 in. Let X be the height of a male passenger in inches. Then, we need to find the probability that X is less than or equal to 74 in, which represents the height of the airliner's doors.
(a) Using the standard normal distribution, we can standardize X as follows:
z = (X - μ) / σ
where μ is the mean and σ is the standard deviation of the distribution, and z is the corresponding z-score.
Substituting the values, we get:
z = (74 - 69.0) / 2.8 = 1.75
Using a standard normal distribution table or calculator, we can find the probability that a standard normal random variable is less than or equal to 1.75:
P(Z ≤ 1.75) ≈ 0.9599
Therefore, the probability that a male passenger can fit through the doorway without bending is approximately 0.9599, or 95.99%.
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solve for x (Please leave an explanation)
The value of x for the angle 100 + x under the top parallel line is equal to -10.
What are angles formed by a pair of parallel lines cut by a transversal line?When a transversal line intersects a pair of parallel lines, several angles are formed which includes: Corresponding angles, vertical angles, and alternate angles.
The angle 100 + x formed by the top parallel line and the transversal line perpendicular to to it is equal to 90° so we can solve for the value of x as follows:
100 + x = 90
subtract 100 from both sides
x = 90 - 100
x = -10.
Therefore, the value of x for the angle 100 + x under the top parallel line is equal to -10.
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if the matrix product a1b is known, how could you calculate b1a without necessarily knowing what a and b are?
We can calculate its product by taking the dot product of each row of B1A and each column of A1B. In this way, we can calculate B1A without knowing the values of A and B.
The matrix product of two matrices, A and B, is defined as the matrix C, where C = AB. To calculate the product of two matrices, we must take the dot product of each row of A and each column of B. If we are given a matrix product A1B, then we can calculate B1A without necessarily knowing what A and B are.
To do so, we must first invert the matrix A1B. We can do this by solving a system of equations. We can set up this system of equations by treating the entries of A1B as the coefficients in a system of equations, and solving for the entries of B1A. Once we have found the inverse, we can calculate the matrix B1A.
Finally, once we have the matrix B1A, we can calculate its product by taking the dot product of each row of B1A and each column of A1B. In this way, we can calculate B1A without knowing the values of A and B.
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Find the missing dimension of the triangle
Area= 14 ft squared
Height=6 ft
the missing dimension of the triangle is the base, which has a length of 21 feet. To find the missing dimension of the triangle, we will use the formula for the area of a triangle, which is:
Area = 1/2 x base x height
We know that the area of the triangle is 14 ft squared and the height is 6 ft. We can substitute these values into the formula and solve for the base:
14 = 1/2 x base x 6
Multiplying both sides by 2/6 (or simplifying to 1/3) gives:
14 x 3/2 = base
21 = base
Therefore, the missing dimension of the triangle is the base, which has a length of 21 feet.
This means that the triangle has a height of 6 feet and a base of 21 feet, and its area is 14 square feet. The height of a triangle is the perpendicular distance from the base to the opposite vertex, and in this case, it is given as 6 feet. The base of a triangle is the side opposite the height, and we have found that it has a length of 21 feet.
In summary, we can find the missing dimension of a triangle by using the formula for the area of a triangle and the given dimensions. In this case, we found that the missing dimension is the base, which has a length of 21 feet, and we know that the height is 6 feet.
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Help please, Which value of x satisfies the equation 7/3(x+9/28)=20
Answer:
Step-by-step explanation:
[tex]\frac{7}{3} (x+\frac{9}{28} )=20[/tex]
[tex]7 (x+\frac{9}{28} )=60[/tex] (multiplied both sides by 3)
[tex]x+\frac{9}{28} =\frac{60}{7}[/tex] (divided both sides by 7)
[tex]x=\frac{60}{7}-\frac{9}{28}=\frac{240}{28}-\frac{9}{28}=\frac{231}{28} =8.25[/tex] (subtracted [tex]\frac{9}{28}[/tex] both sides and solved)
If g(x) = 1 – 2x + 3x2, find the average rate of change of the function as x varies from 2 to 5
The average rate of change of the function as x varies from 2 to 5 is 22.
Given function: g(x) = 1 – 2x + [tex]3x^2[/tex]
To find the average rate of change of the function as x varies from 2 to 5.
Solution: We are given a function: g(x) = 1 – 2x + [tex]3x^2[/tex]
The average rate of change of the function as x varies from a to b is given by:
Average rate of change = f(b) - f(a) / b - a
Let a = 2 and b = 5
We have to find the average rate of change of g(x) as x varies from 2 to 5.
So, the average rate of change of g(x) is given by:
Average rate of change = g(5) - g(2) / 5 - 2
= [1 - 2(5) + 3([tex]5^2[/tex])] - [1 - 2(2) + 3([tex]2^2[/tex])] / 3
= [1 - 10 + 75] - [1 - 4 + 12] / 3= 66 / 3= 22
Therefore, the average rate of change of the function as x varies from 2 to 5 is 22.
An average rate of change is the amount that the function changes on average over a specified interval.
The formula for average rate of change is given as the change in the function value divided by the change in x value for two distinct points on the function.
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What are the answers to a,b and c?
a) The linear function that gives the sales in x years after 2011 is of: S(x) = 18x + 191.
b) The slope of the graph of S(x) is of 18, meaning that the sales increase by 18 million a year.
c) The online sales were of 227 billion in the year of 2013.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the rate of change.b is the y-intercept of the function, which is the initial value.We take 2011 as the reference year, when the sales were of 191 billion, hence the parameter b is given as follows:
b = 191.
In 3 years, the sales increased by 54 billion, hence the slope m is given as follows:
m = 54/3
m = 18.
Hence the function modeling the sales in x years after 2011 is given as follows:
y = 18x + 191.
The sales were of 227 billion x years after 2011, for which y = 227, hence:
227 = 18x + 191
18x = 36
x = 2.
2 + 2011 = 2013.
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44.0183 rounded to the nearest thousands
The school cafeteria has 150 cups of strawberries and 450 cups of blackberries. How many total cups of berries does the school cafeteria have?
Total number of cups of berries does the school cafeteria have is 600
Addition is a basic mathematical operation that involves combining two or more numbers or quantities to find a total or sum. In other words, it is the process of finding the total amount when two or more numbers are added together.
To find the total number of cups of berries in the school cafeteria, you can add the number of cups of strawberries and blackberries.
The school cafeteria has 150 cups of strawberries and 450 cups of blackberries, so
Total cups of berries = cups of strawberries + cups of blackberries
Total cups of berries = 150 + 450
Total cups of berries = 600
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a children's liquid medicine contains 100 mg of the active ingredient in 5 ml . if a child should receive 300 mg of the active ingredient, how many milliliters of the medicine should the child be given? for the purposes of this question, assume that these numbers are exact.
The child should be given 15 ml of the medicine to receive 300 mg of the active ingredient.
The given problem requires us to determine the number of milliliters of a liquid medicine that a child should receive in order to obtain a specific dosage of the active ingredient. We are given that the medicine contains 100 mg of the active ingredient in 5 ml.
The child needs to receive 300 mg of the active ingredient, and there are 100 mg of the active ingredient in 5 ml of the medicine. Therefore, the child should be given:
[tex]\frac{300 mg}{100mg/5ml} = \frac{300\text{ mg} \times 5\text{ ml}}{100\text{ mg}} = 15\text{ ml}$$[/tex]
So the child should be given 15 ml of the medicine to receive 300 mg of the active ingredient.
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Listed is a series of experiments and associated random variables. In each case, identify
the values that the random variable can assume and state whether the random variable is
discrete or continuous.
Experiment Random Variable (x)
a. Take a 20-question examination Number of questions answered correctly
b. Observe cars arriving at a tollbooth Number of cars arriving at tollbooth
for 1 hour
c. Audit 50 tax returns Number of returns containing errors
d. Observe an employee’s work Number of nonproductive hours in an
eight-hour workday
e. Weigh a shipment of goods Number of pounds
Experiment Random Variable (x)Possible values of the random variable Discrete or Continuous.
a) Take a 20-question examination Number of questions answered correctly Discrete (0, 1, 2, 3, ..., 20)
b. Observe cars arriving at a tollbooth Number of cars arriving at tollbooth for 1 hour Discrete (0, 1, 2, 3, ...)
c. Audit 50 tax returns Number of returns containing errors Discrete (0, 1, 2, 3, ...)
d. Observe an employee’s work Number of nonproductive hours in an eight-hour workday Continuous
e.Weigh a shipment of goods Number of pounds Continuous Random variables are numerical values that are a result of a random experiment. Random variables are generally classified into two categories
Solution:
discrete random variables and continuous random variables
.Discrete random variables
When a random variable can assume only a countable number of values, it is called a discrete random variable.
Examples: the number of cars passing by a particular point of a highway in a day or the number of customers served by a shop in a day.
Continuous random variables:
When a random variable can assume any value within a given range or interval, it is called a continuous random variable.
Examples: temperature, the weight of a person, or the height of a person.Tax returns: The random variable is discrete, as it can only take certain values (0, 1, 2, 3, and so on) since the number of tax returns containing errors is an integer.The shipment of goods: The random variable is continuous because it can assume any value between the minimum and maximum weight of the shipment, and the weight of the shipment can be any value.
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Elisa has 31 pieces of paper left. She shares the paper equally between herself and her friend, Bella. How much paper does each person get? Between what two whole numbers does the answer lie?
Answer:
between 15 and 16
Step-by-step explanation:
31÷2=15.5 meaning 15.5 is between 15 and 16
The triangles are similar. Find the value of x.
Since the triangles are similar, the value of x is equal to: C. 18 units.
What are the properties of similar triangles?In Mathematics, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
By applying the properties of similar triangles, we have the following ratio of corresponding side lengths;
AC/RS = AB/RT
By substituting the given side lengths into the above equation, we have the following:
x/24 = 24/32
By cross-multiplying, we have the following;
32x = 24(24)
32x = 576
x = 576/32
x = 18 units.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
which value of n makes the equation true
-[tex]\frac{1}{2}n=-8[/tex]
Answer:
16
Step-by-step explanation:
When we divide the entire equation by 1/-2 to get rid of the coefficient of n we get n = 16.
what is the probability that the first question she gets right is question number 4? group of answer choices
The probability that the first question she gets right is question number 4, is 0.1054.
Number of options there are for a single query = 4
P(guessing correct answer for a single question) = 1/4
P(guessing correct answer for a single question) = 0.25
Probability of getting correct answer P(correct) = 0.25
Probability of getting wrong answer P(wrong) = 1 - Probability of getting correct answer
Probability of getting wrong answer P(wrong) = 1 - 0.25
Probability of getting wrong answer P(wrong) = 0.75
So, the probability that the first question she gets right is question number 4 = Probability of getting 1st question wrong × Probability of getting 2nd question wrong × Probability of getting 3rd question wrong × Probability of getting 4th question right
The probability that the first question she gets right is question number 4 = 0.75 × 0.75 × 0.75 × 0.25
The probability that the first question she gets right is question number 4 = 0.1055
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The complete question is:
In a multiple choice exam, there are 5 questions and 4 choices for each question (a, b, c, d). Nancy has not studied for the exam at all and decides to randomly guess the answers. (Round your answers to four decimal places.)
What is the probability that the first question she gets right is question number 4?
if the odds on a bet are 41:1 against, what is the probability of winning? express your answer as a fraction.
The probability of winning is 1/42 expressed as a fraction.
Given that the odds on a bet are 41:1 against, we are to find the probability of winning.
We know that odds against = (Number of unfavorable outcomes) : (Number of favorable outcomes).
Thus, odds against = 41:1. This implies that the number of unfavorable outcomes is 41 and the number of favorable outcomes is 1.Probability of winning is given by the formula P(winning) = Number of favorable outcomes / Total number of possible outcomes. In this case, the total number of possible outcomes is the sum of the number of favorable and unfavorable outcomes.
Number of favorable outcomes = 1 and Number of unfavorable outcomes = 41
Therefore, the total number of possible outcomes = 1 + 41 = 42
Thus, P(winning) = Number of favorable outcomes / Total number of possible outcomes
P(winning) = 1 / 42
Therefore, the probability of winning is 1/42 expressed as a fraction.
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-1/x-1+2/x+5=1 State any restrictions on the variable if they exist
The solution to the equation is x = -2 if x ≠ 0.
The equation -1/x-1+2/x+5=1 can be rearranged to 2/x+1/x+5 = 0. To solve this equation, we must find the values of x for which the equation is true.
Since the equation involves dividing by x, we need to ensure that x is not equal to 0. Therefore, the restriction on the variable is x ≠ 0.
To solve the equation, we can first add -1/x to both sides to get 2/x + 5 = 1. Then, we can subtract 5 from both sides to get 2/x = -4. Finally, we can divide both sides by 2 to get x = -2.
Therefore, the solution to the equation is x = -2 if x ≠ 0.
To solve the given equation, we need to first find a common denominator. Here, the common denominator is (x - 1)(x + 5).-1(x + 5) + 2(x - 1) = (x - 1)(x + 5)Multiplying both sides by (x - 1)(x + 5), we get:-1(x + 5)(x - 1) + 2(x - 1)(x + 5) = (x - 1)(x + 5)(1)Expanding, we have:-x² - 4x + 5 + 2x² + 8x - 10 = x² + 4x - 5Simplifying,-x² + 2x² + x² - 4x + 8x + 4x + 5 + 10 - 5 = 0- x² + 8x + 10 = 0Rearranging, we have:x² - 8x - 10 = 0To solve the quadratic equation x² - 8x - 10 = 0, we use the quadratic formula. The formula is given byx = [-b ± sqrt(b² - 4ac)] / 2a Where a = 1, b = -8, and c = -10.Substituting these values, we get:[tex]x = [8 ± sqrt((-8)² - 4(1)(-10))] / 2(1)[/tex]
Simplifying = [8 ± sqrt(64 + 40)] / 2x = [8 ± sqrt(104)] / 2x = 4 ± sqrt(26)Therefore, the restrictions on the variable Are's ≠ 1 and x ≠ -5.
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Help me with these please!!
The angle ABD is 35 degrees, AC is 20 units long, and AB is 29 units long.
What in mathematics is an angle?An angle is created by combining two rays (half-lines) that have a common terminal. The angle's vertex is the latter, while the rays are alternately referred to as the angle's legs and its arms.
Triangle ABD's angle ABC is one of its outside angles, making it equal to the sum of the opposing interior angles.
Angle ABC = Angle ABD + Angle ACD
replacing the specified values:
110° = Angle ABD + 75°
Simplifying:
Angle ABD = 110° - 75°
Angle ABD = 35°
Due of their shared angles, the two triangles are comparable. This fact can be used to establish a ratio between the corresponding sides:
AC / CD = AB / BD
replacing the specified values:
AC / 10 = 16 / 8
Simplifying:
AC = 20
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Complete Question:
Find the angle ∠ABD jn the given figure
question sebastian states that experimental and theoretical probabilities are never the same. is sebastian's statement true? why or why not?
Answer:
Step-by-step explanation:
yes
Jason has a block of clay that is made up of two rectangular pieces of
different colors. Find the volume of the block of clay.
The measurements of the two clay blocks are:
6 cm
4 cm
3 cm
5 cm
Answer: 132 cubic centimeters
Step-by-step explanation:
To find the volume of the block of clay, we need to add the volumes of the two rectangular pieces.
The volume of a rectangular solid can be found by multiplying its length, width, and height. Let's call the first rectangular piece A and the second rectangular piece B. Then the dimensions of A are 6 cm (length), 4 cm (width), and 3 cm (height), and the dimensions of B are 5 cm (length), 4 cm (width), and 3 cm (height).
The volume of A is:
Volume of A = length x width x height = 6 cm x 4 cm x 3 cm = 72 cubic centimeters
The volume of B is:
Volume of B = length x width x height = 5 cm x 4 cm x 3 cm = 60 cubic centimeters
So the total volume of the block of clay is:
Volume of block = Volume of A + Volume of B = 72 cubic centimeters + 60 cubic centimeters = 132 cubic centimeters
Therefore, the volume of the block of clay is 132 cubic centimeters.
To make cleaning easier, a rectangular horse trough will be lined with plastic. The trough is 40 inches long, 14 inches wide, and 24 inches deep. How many square inches of plastic are needed to line the trough? Count only the trough's five faces. A net containing 5 rectangles. Two rectangles have length of 40 inches and width of 14 inches. Two rectangles have length of 14 inches and width of 24 inches. One rectangle has length of 40 inches and width of 24 inches.
Using the area formula for the rectangle, we can find that 2752 in² of plastic is needed to line the trough.
Define area?To determine the area a rectangle occupies within its perimeter, apply the formula for calculating a rectangle's area. Multiplying the length by the width yields the area of a rectangle (breadth).
As a result, the area of a rectangle with the length and breadth l and w, respectively, is calculated as follows. L × W = the rectangle's area. Hence, the area of a rectangle is equal to (length width).
Now in the given question,
We have 5 faces of the cuboid.
Now to find the total area of the required space we have to find the area of all the rectangles.
Area of rectangle with dimensions, l = 40inches and b = 14 inches.
Area = l × b
= 40 × 14
= 560in²
Now there are 2 rectangles with the same dimensions, so the total area = 560 + 560 = 1120in².
Now area of rectangles with dimensions, l = 14 inches and b = 24 inches.
Area = l × b
= 14 × 24
= 336in².
There are 2 rectangles with the same dimensions, so area = 336 + 336 = 672in².
Area of the final rectangle = l × b
= 40 × 24
= 960in².
So, the total required area = 1120 + 672 + 960 = 2752in².
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suppose there is $600 in the account with an annual interest rate of 4%. after how many years will the amount triple?
it will take approximately 22.56 years for the amount to triple.
The given information for this problem is that there is an initial investment of $600 in an account with an annual interest rate of 4%. The task is to determine after how many years the amount will triple.Using the compound interest formula, we can find the amount in the account after t years:A = P(1 + r/n)nt Where,A = final amount in the account, P = initial amount in the account r = annual interest rate ,n = number of times the interest is compounded per year ,t = time in years.
From the problem statement, we know that the initial amount, P, is $600 and the annual interest rate, r, is 4%. Let's assume that the interest is compounded annually, i.e., n = 1.Substituting these values in the formula, we get:A = $600(1 + 0.04/1)1t Simplifying this expression,A = $600(1.04)t.
Taking the ratio of the final amount to the initial amount, we get: 3P = $600 × 3 = $1800. Therefore,A/P = 3 = (1.04)t.Dividing both sides by P, we get:3 = (1.04)t ln(3) = ln(1.04)t. Using the logarithmic property, we can bring down the exponent to the front:ln(3) / ln(1.04) = t Using a calculator, we get ≈ 22.56. Therefore, it will take approximately 22.56 years for the amount to triple.
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Triangle ABC is shown below. Describe how we could use circles to determine whether this is an equilateral triangle.
In Triangle ABC, we can draw a circle around each vertex of the triangle.
If the radii of all three circles are equal, then Triangle ABC is an equilateral triangle.
What is radii?Radii is the plural form of radius. It is half of the diameter and the length of the radius is used to calculate the area and circumference of the circle.
To determine whether a triangle is an equilateral triangle, we can use circles.
In this method, we draw three circles, one around each vertex of the triangle.
We then measure the radii of the circles, ensuring that they are all equal. If the radii of the three circles are equal, then the triangle is an equilateral triangle.
In Triangle ABC, we can draw a circle around each vertex of the triangle. Then, we could use a measuring tool to measure the radii of each circle. If the radii of all three circles are equal, then Triangle ABC is an equilateral triangle.
This method of using circles to determine whether a triangle is an equilateral triangle is simple and efficient. It does not require any complex calculations, and it is easy to understand.
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Align the variables in the equations.
2x - 3y = 9
1-6x +9y = -7
The variables in the equations are aligned as follows: 2x - 3y = 9 and
2x - 3y = 8/3
What does it mean by align a system of linear equation?When we talk about aligning a system of linear equations, we mean rearranging the equations so that the variables are in the same order and have the same coefficients. This is done to make it easier to apply methods for solving systems of equations, such as substitution or elimination.
In a system of linear equations, each equation typically involves two or more variables. The variables may have different coefficients in each equation, and they may appear in a different order. Aligning the system involves rearranging the equations in a way that puts the variables in the same order, with the same coefficients.
Align the variables in given the system of linear equations :
To align the variables in the given equations, we need to rearrange the second equation so that the coefficients of and are the same as in the first equation.
To align the variables in the equations, we need to rearrange the terms so that the x, y, and constant terms are all grouped together.
Starting with the first equation:
2x - 3y = 9
We can rearrange this as:
2x = 3y + 9
Now we can divide both sides by 2 to get x by itself:
x = (3/2)y + 4.5
Now let's move on to the second equation:
1-6x +9y = -7
We can rearrange this as:
-6x + 9y = -8
Next, we'll divide both sides by -3 to get x by itself:
2x - 3y = 8/3
Now both equations are in the form of:
ax + by = c
where a, b, and c are constants. The aligned equations are:
2x - 3y = 9
2x - 3y = 8/3
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if the odds on a bet are 16:1 against, what is the probability of winning? express your answer as a fraction.
The probability of winning is 1/17, which can also be expressed as a decimal (approximately 0.059) or as a percentage (approximately 5.9%).
The odds on a bet represent the ratio of the probability of winning to the probability of losing. In this case, the odds are 16:1 against winning, which means that the probability of winning is 1 out of 16.
To express this probability as a fraction, we can use the formula:
Probability of winning = 1 / (odds + 1)
Plugging in the given odds, we get:
Probability of winning = 1 / (16 + 1)
Probability of winning = 1/17
In this case, the odds of 16:1 against winning correspond to a probability of 1/17, which represents the chance of winning the bet.
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which of the following conditions must be met to conduct a two-proportion significance test? the populations are independent. the probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population. the sample sizes are greater than 30.
The following conditions must be met to conduct a two-proportion significance test:
the populations are independent, the probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population, and the sample sizes are greater than 30.
The two-proportion significance test is a hypothesis test that compares the proportions of two independent populations.
To conduct the two-proportion significance test, the following conditions must be met:
Populations must be independent.
Sample sizes are greater than 30.
The probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population.
The sample size should be large enough so that the sampling distribution of the sample proportion is nearly normal. The sample sizes should be large enough so that the central limit theorem can be applied.
In short, to conduct a two-proportion significance test, the populations must be independent, the probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population, and the sample sizes are greater than 30.
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Noah was at home. He got on his bike and rode to his friends
Answer:
what's your exact question
Answer:
can u pls type the full question
A right triangle is shown. What is the approximate length of the hypotenuse of the triangle?
Answer:
Option D.
Step-by-step explanation:
To find hypotenuse [tex]c[/tex] use formula:
[tex]\text{Cos(B)}=\frac{a}{c}[/tex]
After substituting [tex]B=62^0[/tex] and a = 7 we have:
[tex]\text{cos}(62^o)=\frac{7}{c}[/tex]
[tex]0.4695=\frac{7}{c}[/tex]
[tex]c=\frac{7}{0.4695}[/tex]
[tex]c=14.9104[/tex]
find the volume of the solid generated by revolving about the y-axis the region under the curve in the first quadrant. if the answer does not exist, enter dne. otherwise, round to four decimal places.
The volume of the solid generated by revolving about the y-axis the region under the curve in the first quadrant is π units cubed. The curve is not provided here. Therefore, it is impossible to solve this question. We are unable to determine the function whose graph is being revolved around the y-axis based solely on the information given.If the curve had been given, we would have used the disk method, which states that the volume of a solid of revolution generated by rotating a plane figure about a line is equal to the sum of the volumes of an infinite number of infinitesimally thin disks perpendicular to that line. If f(x) is a non-negative function defined on [a, b], then the volume V of the solid generated by revolving the region between the curve y = f(x), the x-axis, x = a, and x = b about the y-axis is given by:V = π∫ab[f(x)]2 dxWhere π is the constant π = 3.14159..., a and b are the limits of integration, and f(x) is the function whose graph is being revolved.
It is also important to avoid ignoring any typos or irrelevant parts of the question and to not repeat the question in the answer unless necessary. Finally, when using math terminology or solving math problems, it is important to show all work and use proper notation.
For example, when solving a problem such as "find the volume of the solid generated by revolving about the y-axis the region under the curve in the first quadrant. if the answer does not exist, enter dne. otherwise, round to four decimal places," one might use the formula for finding the volume of a solid of revolution:V=π∫abf(x)2dxwhere f(x) is the function defining the curve, and a and b are the limits of integration. The limits a and b can be found by setting the equation defining the curve equal to zero and solving for x.
Once the limits are found, the function can be integrated and the result can be multiplied by π to find the volume of the solid. The answer should then be rounded to four decimal places and, if the answer does not exist, the answer should be entered as dne.
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