Mr. Ferrell can cut 6 and 2/3 pieces that are one-eighth foot long from a 5/6 foot long piece of cardboard.
What is common factor?A number is said to be a common factor if it can divide two or more integers without producing a residue. Common factors are used in fraction operations to simplify fractions and carry out operations like addition, subtraction, multiplication, and division.
Finding a common denominator is necessary, for instance, when adding or subtracting fractions. A multiple of all the fractions' denominators is referred to as a common denominator. We can determine the shared characteristics of the denominators and utilise the lowest common multiple (LCM) as the common denominator to obtain a common denominator.
Given that, one-eighth foot long pieces can be cut from a 5/6 foot long piece of cardboard.
First, we need to convert 5/6 feet into eighths of a foot:
5/6 feet = (5/6) * 8 eighths = 40/48 eighths
Next, we need to divide 40/48 by 1/8 to find the number of one-eighth foot long pieces that can be cut:
(40/48) ÷ (1/8) = (40/48) * (8/1) = 320/48 = 6 2/3 pieces
Hence, Mr. Ferrell can cut 6 and 2/3 pieces that are one-eighth foot long from a 5/6 foot long piece of cardboard.
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Write and solve an equation to answer the following question. The Smith family rented a recreational vehicle for a seven-day vacation. The cost to rent the recreational vehicle was $80 plus $0.50 per mile. How many miles were driven if the total cost was $1350?
Answer: 2540
Step-by-step explanation: 1350-80=1270. 1270/0.5=2540
solve simultaneously 4x-y=3x+1y 4x+3y=x+6y
(x, y) = (0,0) is the solution of the system of equations.
simultaneous equationSimultaneous equations are a set of two or more equations that contain multiple variables, which must be solved at the same time. The solution to the system of equations is the set of values of the variables that satisfy all of the equations in the system simultaneously.
The given system of equations is:4x - y = 3x + y
4x + 3y = x + 6y
Simplifying the first equation by moving all the y-terms to the left-hand side and all the x-terms to the right-hand side, we get:
4x - 3x = y + y
x = 2y
Substituting this value of x into the second equation, we get:
4(2y) + 3y = (2y) + 6y
8y + 3y = 8y
11y = 0
y = 0
Substituting y = 0 into the equation x = 2y, we get:
x = 2(0)
x = 0
Therefore, the solution to the system of equations is:
x = 0 and y = 0
Hence, (x, y) = (0,0) is the solution of the system of equations.
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National Collegiate Athletic Association (NCAA) statistics show
that for every 75,000 high school seniors playing basketball, about 2250 play
college basketball as first-year students. Write the ratio of the number of first-
year students playing college basketball to the number of high school seniors
playing basketball.
Answer: 100:3
Step-by-step explanation:
Answer:
the ratio of first-year college basketball players to high school seniors playing basketball is 3:100.
Step-by-step explanation:
The problem states that for every 75,000 high school seniors playing basketball, about 2,250 play college basketball as first-year students. To write the ratio of first-year college basketball players to high school seniors playing basketball, we need to compare the two quantities.
The ratio is a way of expressing the relationship between two numbers as a fraction or a pair of numbers separated by a colon (:). In this case, we want to express the ratio of the number of first-year college basketball players to the number of high school seniors playing basketball.
To write the ratio, we start by putting the number of first-year college basketball players (2,250) in the numerator of a fraction. We put the number of high school seniors playing basketball (75,000) in the denominator of the same fraction.
So the ratio can be expressed as:
2,250/75,000
To simplify this fraction, we can divide both the numerator and denominator by a common factor. In this case, both 2,250 and 75,000 are divisible by 750. Dividing both numbers by 750 gives:
2,250/75,000 = 3/100
phoebe has a hunch that older students at her very large high school are more likely to bring a bag lunch than younger students because they have grown tired of cafeteria food. she takes a simple random sample of 80 sophomores and finds that 52 of them bring a bag lunch. a simple random sample of 104 seniors reveals that 78 of them bring a bag lunch.Do these data give convincing evidence to support Phoebe’s hunch?
Yes, the data give convincing evidence to support Phoebe's hunch. As the result of the test is a p-value that is 0.1 of less than 0.05.
What is p-value?The p-value is the probability of obtaining a result as extreme or more extreme given that the null hypothesis is true. The p-value is calculated by comparing the test statistic to the probability distribution under the null hypothesis.
The ratio of seniors bringing a bag lunch= 78/104 or 0.75,
while the ratio of sophomores bringing a bag lunch= 52/80 or 0.65.
This indicates that the proportion of seniors bringing a bag lunch is higher than the proportion of sophomores bringing a bag lunch.
Further, the difference between the proportions is
0.75-0.65 = 0.1,
which is a large enough difference to be considered significant.
The result of the test is a p-value of less than 0.05, which is statistically significant and indicates that the difference in the proportions is due to the different ages, and not due to chance.
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Calculate the final value in cell D2 using the following formula: "price - price* discount". Use a formula with cell reference (B1, etc. ).
Product – Toys
Price - $114. 99
Discount – 12%
The final value in cell D2 using the following formula:
price - price× discount = $ 101.19
Take the original price. Multiply that by the discount percentage and divide the result by 100. Subtract the result from the original price. this is your final price
According to the Question:
The final value in cell D2 using the following formula:
(price - price) × discount.
Given that:
Price = $114.99
Discount = 12%
By the above formula:
(price - price) × discount.
= ($114.99 - $114.99) × 12%
= $101.19
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5my × 5ym = ?
Can you multiply two terms with the same 2 coefficients in different positions like the example above?
Answer:
In the example given, 5my × 5ym, you can simplify it using the commutative property of multiplication as follows:
5my × 5ym = 5 × 5 × m × m × y × y
= 25m²y²
So, the answer is 25m²y².
Suppose Elena has $5 and sells pens for $1.50 each. Her goal is to save $20 to buy a t-shirt. She does not spend any money while she is saving money.
Let p represent the number of pens Elena sells. Write an expression for how much money she saves in total after selling p pens.
Write an equation using your answer from question 1, showing that she saves exactly $20.
Solve the equation you wrote from question 2. What do you notice about your value for p?
What if Elena wants to have some money left over? Write an inequality using your expression from question 1 to show this.
Write down other values for p where Elena would have money left over.
Write an inequality using p, to describe the values of p where she would be able to buy the tshirt and still have money left over.
In conclusion the values of p that satisfy this inequality are p = 11, p = 12, p = 13, etc. The equation showing that Elena saves exactly $20 is:
5 + (1.5)p = 20
Why it is?
The expression for how much money Elena saves after selling p pens is:
Total money saved = 5 + (1.5)p
The equation showing that Elena saves exactly $20 is:
5 + (1.5)p = 20
Solving the equation:
5 + (1.5)p = 20
(1.5)p = 15
p = 10
We notice that the value of p is a whole number, which makes sense since Elena cannot sell a fractional number of pens.
If Elena wants to have some money left over, we can write the inequality:
5 + (1.5)p > 20
Some values for p where Elena would have money left over are p = 11, p = 12, p = 13, etc.
To describe the values of p where Elena would be able to buy the t-shirt and still have money left over, we can write the inequality:
5 + (1.5)p > 20
(1.5)p > 15
p > 10
Therefore, the values of p that satisfy this inequality are p = 11, p = 12, p = 13, etc.
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The access code for a car's security system consist of six digits. The first digit cannot be zero and the last digit must be even. How many different codes are available?
If an access code for a car's security system consist of six digits and the first digit cannot be zero and the last digit must be even, then the number of different codes available are 4,500,000
Since the first digit cannot be zero, we have 9 choices for the first digit. For each of these 9 choices, there are 10 possibilities for the second digit (0-9).
Similarly, there are 10 possibilities for the third digit, 10 for the fourth digit, 10 for the fifth digit, and 5 (0, 2, 4, 6, 8) for the last digit.
Therefore, the total number of possible access codes is:
9 x 10 x 10 x 10 x 10 x 5 = 4,500,000
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Someone please help me ASAP!! It’s due today!! Show work please! I will mark brainliest if it’s done correctly
Answer:
D
Step-by-step explanation:
First set up the fraction [tex]\frac{9}{40}[/tex] , and next divide 9 ÷ 40 = 0.225. Lastly, multiply 0.225 × 100 = 22.5%.
Hope this helps.
Tanya is making a scale drawing of her house. She is using a 6 inch line on her drawing to represent the 30 foot width of her house. Tanya's room is 12 feet by 12 feet. What will be the length of the lines she uses to represent her room on the scale drawing?
Answer:2.4 inches
Step-by-step explanation:
if 6 is for 30 feet, we can use a proportional statement to find what the length of the line will be for a room that is 12 feet.
Stefanie bought a package of pencils for 1. 75$ and some erasers that cost 0. 25 each. She paid a total of 4. 25 for these items, before tax. Exactly how many erasers did stefanie buy?
Stefanie bought a package of pencils for 1. 75$ and some erasers that cost 0. 25 each. She paid a total of 4. 25 for these items, before tax. Stefanie bought total 10 erasers.
Equation:
In mathematics, an equation is a formula that connects two expressions with the equal sign = to indicate that they are equal.
According to the Question:
The number of erasers bought by Stefanie:
Let we denote the number of erasers bought by her by x (an unknown variable)
Then we will have:
Total amount before tax = cost of one package of pencil + cost of erasers
$4.25 = $1.75 + X × $0.25
⇒ 4.25 = 1.75 + 0.25x
Now,
we will perform subtraction by 1.75 and division by 0.25 on both sides.
4.25 = 1.75 + 0.25x
Subtracting 1.75 both side:
4.25 -1.75 = 0.25x
⇒ 2.5 = 0.25x
Dividing by 0.25 on both sides:
2.5/0.25 = 0.25x/0.25
⇒ x = 10
Thus, Stefanie bought total 10 erasers.
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At a party to celebrate a successful school play, the drama club bought 999 large pizzas. Each pizza had sss slices. All together, there were 727272 slices of pizza for the club to share.
Write an equation to describe this situation.
How many slices does each pizza have?
Answer:
Step-by-step explanation:
Let's use "n" to represent the number of slices in each pizza. Then the equation to describe the situation is:
999n = 727272
To solve for "n", we divide both sides by 999:
n = 727272/999
Using a calculator or long division, we get:
n ≈ 728.56
Therefore, each pizza has approximately 728 slices.
one number is 13 les then a certain number let g repersent the larger number. repersent the sum of the two numbers
We will consider two cases: n is even and n is odd. In this step, you will complete the proof of the first case. Proof. Case 1: n is even Let n be an even integer. By the definition of even, for some integer k. This follows that nº + 17n - 1 = 2:( 2k )+1 Since is an integer, n^3+17n + 1 must be an integer. Since na +17n – 1 equals times an integer plus n+ 17n – 1 is 2
We will consider two cases: n is even and n is odd. In this step, you will complete the proof of the first case. Proof. Case 1: n is even Let n be an even integer. By the definition of even, for some integer k. This follows that `nº + 17n - 1 = 2:( 2k )+1`
Since is an integer, `n^3+17n + 1` must be an integer. Since `na +17n – 1` equals times an integer plus `n+ 17n – 1` is 2The solution explains the concept of even integer. Let n be an even integer, and by the definition of even, for some integer k. This follows that `nº + 17n - 1 = 2:( 2k )+1`.Since 2k is an integer, n^3 + 17n + 1 must also be an integer. This is because even times even is even and even times odd is even, which means that (2k + 1) is always odd. The integer n^3 can be written as (n*n*n). Given that n is an even integer, it follows that n*n is even. And since an even number times an even number is always even, it follows that (n*n*n) is even. Since the sum of an even number and an odd number is always odd, adding 1 to n^3 + 17n gives an odd number, and thus an integer, as desired. The equality `na +17n – 1 = 2` is not needed in this proof.
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Blaine works for a battery manufacturing company. he wants to develop a method to test the batteries made each day to determine if they work. which method would provide the most valid results?
Random sampling 50 batteries throughout the day and testing to see if they would provide most valid results.
A sample is described as a smaller, more manageable representation of a larger group. A smaller population with characteristics of a larger one. A sample is used in statistical analysis when the population size is too large to include all participants or observations in the test.
The sample may be biased if it is taken from the first 25 batteries made each day or the last 25 batteries made each day.
The first and last battery made each day could not be an accurate representation of the total quality of the batteries produced that day if the battery manufacturing process is not consistent thought the day.
Although the battery quality can change during the day, sampling the first 50 batteries produced each day may also add bias into the sample.
The ideal course of action is to randomly select 50 batteries throughout the day, since this helps to ensure that the sample is reflective of the general calibre of batteries manufactured that day.
A more accurate image of the quality of the batteries manufactured can be obtained using this method, which is also more likely to capture any variations in battery quality over the day.
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Use spherical coordinates to find the volume of the region outside the cone phi = pi /4 and inside the sphere rho = 4 cos phi. The volume is ____ . (Type an exact answer, using pi as needed.)
The volume is 63.717 cubic units
The limits of integration for rho are 0 and 4 cos phi, since the sphere has radius 4 cos phi. The limits for phi are π/4 and π/2, since we want to consider the region outside the cone but inside the sphere, and phi is the angle between the positive z-axis and the position vector of a point. Finally, the limits for theta are 0 and 2π, since theta is the azimuthal angle and we want to integrate over the entire azimuthal angle.
Thus, the volume of the region is given by:
V = 8 x ∫(0 to 2π) ∫(π/4 to π/2) ∫(0 to 4 cos phi) ρ² sin phi dρ dphi dtheta
Simplifying the integral using basic calculus, we get:
V = 8 x (64/3 - 16/3√2π) = 63.717
Therefore, the volume of the region outside the cone phi = π/4 and inside the sphere rho = 4 cos phi is 8(64/3 - 16/3√2π), which is an exact answer using π as needed.
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Draw a diagram to help you set up an equation(s). Then solve the equation(s). Round all lengths to the neatest tenth and all angles to the nearest degree.
Answer:
Were sorry! Answer is not available right now check in later.
Step-by-step explanation:
Find the equation of the straight line passing through the point (3,5) which is perpendicular to the line y=3x+2
Answer:
y = -1/3x +6
Step-by-step explanation:
You want the equation of the line through the point (3, 5) and perpendicular to y = 3x +2.
Slope-intercept formThe slope-intercept form of the equation of a line is ...
y = mx +b
where m is the slope, and b is the y-intercept.
Comparing this to the given equation, we see that m=3 for the given line.
Perpendicular linesThe slopes of perpendicular lines are opposite reciprocals of one another. This means the slope of the line we want is ...
desired slope = -1/m = -1/3
Y-interceptThe slope-intercept equation above can be solved for b to give ...
b = y -mx
Then the y-intercept for the line we want is ...
b = 5 -(-1/3)(3) = 5 +1 = 6
The equation of the desired line is y = -1/3x +6.
__
Additional comment
Once you understand how to find the slope of the given line and of the desired line, you can write down the desired equation in point-slope form.
Given slope = 3; perpendicular slope = -1/3
Point-slope equation: y -k = m(x -h) . . . . line through (h, k) with slope m
y -5 = -1/3(x -3) . . . . . line through (3, 5) with slope -1/3
The only "work" required is to rearrange this equation to whatever form you may want. In standard form it is x +3y = 18.
Write down the smallest possible answer.
The answer of the given factor and multiplication term for the positive integers are 3.
What about integers?Positive, negative, and zero digit whole numbers are all included in the category of integers. They can be stated without any fractional or decimal components and are a subset of the real numbers. On a number line, integers can be visualized as positive numbers to the right of zero and negative numbers to the left.
Define Multiplication term:In mathematics, a multiplication term is a mathematical expression that involves the multiplication of two or more factors. The factors can be numbers, variables, or a combination of both. Multiplication terms are commonly represented using the multiplication symbol "×" or the dot "." symbol.
For example, in the expression 2x × 3y, the multiplication term is 2x × 3y, which involves the multiplication of the factors 2x and 3y.
According to the given information:If you want to find the smallest possible value of the given term we have that,The smallest factor of 15 is 1.
The smallest multiple of 3 is 3so, the smallest answer is 1x3 = 3.
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Riley started selling bracelets. During the first month she sold 400 bracelets at $10 each. She tried raising the price, but for every $0. 50 she raised the price, she sold 8 fewer bracelets. What price should she charge in order to make the highest possible gross income?
$17.5 price should she charge in order to make the highest possible gross income.
Given two points are (400, 10) and (392, 10.5)
slope = (10.5-10)/(392 -400) = 0.5/ - 8 = -0.0625
Equation is
p -10 = -0.0625(x-400)
p-10 = -0.0625x + 25
p = -0.0625x + 35
find revenue as
R=x*p
-0.0625x² + 35x
To maximize,
R'(x) =0
-0.125x + 35 = 0
35/0.125 = x
280 = x
when x is equal to 280, find
p= -0.0625(280) + 35
p= -17.5 +35
p= 17.5
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Find the magnitude and direction of the vector <2,7>. Round angles to the nearest degree and other values to the nearest tenth. 7.3; 73°7.3; 74°7.4; 73°7.4; 74
The magnitude of the vector is approximately 7.3 and the direction of the vector is approximately 74 degrees which is option B.
We have,
To find the magnitude and direction of the vector <2, 7>, we can use trigonometric concepts. Let's break down the steps:
Magnitude (Length) of the Vector:
The magnitude of a vector <x, y> is given by the formula:
Magnitude = √(x² + y²)
For the given vector <2, 7>:
Magnitude = √(2² + 7²) = √(4 + 49) = √53 ≈ 7.3 (rounded to the nearest tenth)
Direction (Angle) of the Vector:
The angle θ that the vector makes with the positive x-axis can be found using trigonometric functions:
θ = arctan(y / x)
For the given vector <2, 7>:
θ = arctan(7 / 2) ≈ 74° (rounded to the nearest degree)
Thus,
The magnitude of the vector is approximately 7.3 and the direction of the vector is approximately 74 degrees which is option B.
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Customer five had a $5.00 off coupon, but still has to pay the 4.5% sales tax. How much do they end up paying?
Sure, I can help you with this. To calculate the amount that Customer five will end up paying with their $5.00 off coupon and 4.5% sales tax, we will use the following formula: final amount = original amount - coupon - (original amount * tax rate).
In this case, the original amount is $5.00, the coupon is $5.00, and the tax rate is 4.5%. Plugging these values into the formula, we get:
final amount = 5.00 - 5.00 - (5.00 * 0.045)
final amount = 5.00 - 5.00 - 0.225
final amount = 4.775
Therefore, Customer five will end up paying $4.775 after their coupon and the sales tax.
A triangle has one side that measures 1 1/2 inches and another side that measures 2 1/4 inches. The angle between these sides measures 60°. Draw the triangle in the space below. Label the given side lengths and angle measure on the figure. Is it possible to draw a different triangle with those measurements
the given side that measures 2 1/4 inches with the corresponding length measurement. Label the angle between these sides as 60°.
What is triangle?A triangle is a polygon with three sides, three vertices, and three angles. The sum of the interior angles of a triangle is always 180 degrees, and the longest side of a triangle is opposite to the largest angle, and the shortest side is opposite to the smallest angle. Triangles can be classified according to their side lengths and angles. For example, an equilateral triangle has three equal sides and three equal angles of 60 degrees each, while an isosceles triangle has two equal sides and two equal angles. A scalene triangle has no equal sides or angles. Triangles are important in geometry and have many applications in mathematics and other fields, such as architecture, engineering, physics, and computer graphics.
by the question.
Draw a straight-line segment and label it as the given side that measures 1 1/2 inches.
From one endpoint of the first line segment, draw another line segment that forms a 60° angle with the first line segment. Label this second line segment as the given side that measures 2 1/4 inches.
Draw a third line segment that connects the endpoints of the first two-line segments. This will complete the triangle.
To label the triangle, label the given side that measures 1 1/2 inches with the corresponding length measurement, and label the given side that measures 2 1/4 inches with the corresponding length measurement. Label the angle between these sides as 60°.
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consider a european put option on a non-dividend paying stock with a current stock price of $100 and 4 years until expiration. the strike price of the option is unknown you are given that: ape(s,t) as -05 determine a numerical value for: ape(s,t) da please round your numerical answer to the nearest integer.
The strike price of the option is $101.5, rounded to the nearest integer, whicch is given as the APE(s,t)= -0.5.
What is asset price elasticity?The asset price elasticity (APE) of a European Put Option at time 't' is the ratio of the change in the option price to the change in the stock price, given that all other factors remain constant.
The APE(s,t) of a European put option is calculated using the formula APE(s,t) = -S+Ke-rτ.
In this case, the current stock price is $100 and the time until expiration is 4 years.
We can solve for K, the strike price of the option, given the APE(s,t) is -0.5.
K = S + APE(s,t) + reτ
K = 100 - 0.5 + (0.5 x 4)
K = 101.5
The strike price of the option is $101.5, rounded to the nearest integer.
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what is 1 half of 68 ?
Answer:
34
Step-by-step explanation:
1/2 multiplied by 68=34
34 is 1 half of 68 .
Here, we have,
given that,
what is 1 half of 68
we know that,
Half of a number can be found by dividing the number by 2.
i.e. we have to find half of 68,
for that, we need to divide 68 by 2
so, we get,
To find half of 68:
68 / 2 = 34
Therefore, half of 68 is 34.
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16^(3x-1) = 32. pls help
Answer:x=33/4096=0.008
Step-by-step explanation: 1.1 16 = 24
(16)3 = (24)3 = 212
Equation at the end of step
1
:
((212 • x) - 1) - 32 = 0
STEP
2
:
Equation at the end of step 2
4096x - 33 = 0
STEP
3
:
Solving a Single Variable Equation:
3.1 Solve : 4096x-33 = 0
Add 33 to both sides of the equation :
4096x = 33
Divide both sides of the equation by 4096:
x = 33/4096 = 0.008
a random sample of 15 recent college graduates found that starting salaries for attorneys in new york city had a mean of $102,342 and a standard deviation of $21,756. there are no outliers in the sample data set. construct a 95% confidence interval for the average starting salary of all attorneys in the city.
The correct option is C, A 95% confidence interval for the average starting salary of all attorneys in the city is (91331.94, 113352.06)
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
∝= [tex]\frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a p-value of 1-∝.
So it is z with a value of, so [tex]1-0.025=0.975,Soz= 1.96[/tex]
Now, find M as such
[tex]M= z*\frac{1}{\sqrt{n} } *[/tex]σ
In which is the standard deviation of the population and n is the size of the sample.
[tex]M= 1.96* \frac{21756}{\sqrt{15}} =11010.06[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 102342 - 11010.06 = 91331.94.
The upper end of the interval is the sample mean added to M. So it is 102342 + 11010.06 = 113.352.06.
So the correct answer is:
(91331.94, 113352.06)
Standard deviation is a measure of how much the values in a data set vary from the average or mean value. It is a statistical measure that indicates the extent to which the values are spread out from the mean. A low standard deviation indicates that the values are clustered around the mean, while a high standard deviation indicates that the values are more widely spread out.
Standard deviation is commonly used in statistics and probability theory to measure the uncertainty or risk associated with a particular event or outcome. It is also used in fields such as finance, economics, and engineering to analyze data and make predictions. Standard deviation can provide valuable insights into the distribution of data and help identify trends and patterns in the data set.
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Complete Question:
A random sample of 15 recent college graduates found that starting salaries for attorneys in New York City had a mean of $102,342 and a standard deviation of $21,756. There are no outliers in the sample data set. Construct a 95% confidence interval for the average starting salary of all attorneys in the city. Group of answer choices
A). (89869.82, 114814.18)
B). (90292.73, 114391.27)
C). (91331.94, 113352.06)
D). (90371.37, 114312.63)
Calculate the area and perimeter of this rectangle.
Answer:
Area: 391.92 ft²
Perimeter: 84.4 ft
Step-by-step explanation:
Area of rectangle = L × W
We Take
13.8 × 28.4 = 391.92 ft²
Find the Perimeter of the Rectangle
We Take
28.4 + 13.8 + 28.4 + 13.8 = 84.4 ft
So, Area: 391.92 ft²
Perimeter: 84.4 ft
Answer:
Area = 391.92 square feet
Perimeter = 84.4 feet
Step-by-step explanation:
The area of a rectangle is the product of its width and length.
The perimeter of a rectangle is twice the sum of its width and length.
Given the width of the rectangle is 28.4 feet and its length is 13.8 feet:
[tex]\begin{aligned}\textsf{Area of the rectangle}&=\sf width \times length\\&=28.4 \times 13.8\\&=391.92 \sf \;\;square\;feet\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Perimeter of the rectangle}&=\sf 2(width +length)\\&=2(28.4 +13.8)\\&=2(42.2)\\&=84.4 \sf \;\;feet\end{aligned}[/tex]
Find M BC using picture below
Based on the picture, we can use the Pythagorean theorem to find MBC. Therefore, MBC is equal to [tex]7[/tex]√2.
What three categories of theorems are there?Theorem of Linear Pairs Two angles are supplementary if they create a linear pair. Additional theorem, Two angles are congruent if they are supplements of the same angle.
Theorem of congruent complements an of thes., but it will be the first of a series of events that will result in a new set of rules and the.
First, we can find AB:
AB = √(AD² + BD²)
= √ [tex](3^2 + 4^2)[/tex]
= √[tex](9 + 16)[/tex]
= √ [tex]25[/tex]
[tex]= 5[/tex]
Next, we can find AC:
AC = √(AD² + CD²)
= √[tex](3^2 + 8^2)[/tex]
= √ [tex](9 + 64)[/tex]
= √[tex]73[/tex]
Finally, we can find BC:
[tex]BC = √(AB^2 + AC^2)[/tex]
= √(5² + (√73)²)
= √(25 + 73)
= √98
= 7√2
Therefore, m Bc is = 7√2
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an urn contains p black balls, q white balls, and r red balls; and n balls are chosen without replacement. a. find the joint distribution of the numbers of black, white, and red balls in the sample. b. find the joint distribution of the numbers of black and white balls in the sample. c. find the marginal distribution of the number of white balls in the sample.
a. The joint distribution of the numbers of black, white, and red balls in the sample is given by P(x, y, z) = nCx * nCy * nCz / (p + q + r)Cn, where x is the number of black balls, y is the number of white balls, z is the number of red balls, and n is the total number of balls chosen.
b. The joint distribution of the numbers of black and white balls in the sample is given by P(x, y) = nCx * nCy / (p + q)Cn, where x is the number of black balls, y is the number of white balls, and n is the total number of balls chosen.
c. The marginal distribution of the number of white balls in the sample is given by P(y) = nCy / qCn, where y is the number of white balls, and n is the total number of balls chosen.
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