The domain of the function is positive integers. The function () = 200 + 16 represents the daily cost of production in a factory, where x is the number of complete products manufactured.
Since the production of products cannot be negative or fractional, the domain of the function is restricted to non-negative integers.
Therefore, the domain of the function is the set of positive integers:
{1, 2, 3, 4, ...}
Any value outside this set would not make sense in the context of the problem, as a fraction or a negative number of products cannot be produced.
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The December 31 inventory count of computer supplies shows $660 still available.
Accounting problem
Please help this is due by 11:59 PM
In the Closing Entries, the Income summary, computer service revenue, and retained earnings are given.
What is a Statement of Income?A Statement of Income, also known as an Income Statement or Profit and Loss Statement (P&L), is a financial statement that reports a company's revenues, expenses, and net income or net loss over a specific period of time, usually a month, quarter, or year.
The statement shows the company's ability to generate revenues and manage expenses during the period being reported
It is an essential tool for analyzing a company's financial performance and is used by investors, creditors, and management to make decisions about the company's operations.
The journal entries, adjusted balances, closing entries, unadjusted trial balances, and statements of income have all been solved in the images below.
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What is the multiplicative rate of change of the
function?
1/3
2/3
2
9
The multiplicative rate of change of a function is calculated by taking the ratio of the change in the output to the change in the input, which in this case would be 2.
The multiplicative rate of change of a function is the rate at which the output of the function changes in relation to the input. It is calculated by taking the ratio of the change in the output to the change in the input. The formula for this is:
Multiplicative Rate of Change = (Change in Output)/(Change in Input)
For example, if a function f(x) has an input of 3 and an output of 9, then the multiplicative rate of change of the function would be 2. This can be calculated by taking the difference between the output and the input, which is 9 - 3 = 6, and dividing it by the difference between the input and the output, which is 3 - 0 = 3. Thus, the multiplicative rate of change of the function is 6/3 = 2.
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complete question:
What is the multiplicative rate of change of the function f(x) = 3x?
Hey triangle area with three sides 26 feet18 feet and 9 feet
The area of the triangle with sides 26 feet, 18 feet, and 9 feet is approximately 125.6 square feet.
To find the area of a triangle while given three aspects, we are able to use Heron's formula, which states that the region of a triangle with facets a, b, and c is given by means of:
area = √(s(s-a)(s-b)(s-c))
where s is the semiperimeter, calculated as:
s = (a + b + c) / 2
plugging inside the given values, we get:
s = (26 + 18 + 9) / 2 = 26.5
area = √26.5(26.5-26)(26.5-18)(26.5-9))
area = √(26.50.58.5×17.5)
area = √(15793.75)
area ≈ 125.6 square feet
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What coordinates on the unit circle are associated with the angle measure? Drag coordinates into each box to match the angle measure.
Angle measure [tex]\frac{23 \pi}{3}[/tex] is associated with the coordinate [tex]\left({\frac{1}{2}}\;-{\frac{\sqrt{3}}{2}}\right)$[/tex]
Angle measure [tex]-\frac{3 \pi}{4}[/tex] is associated with the coordinate [tex]\left(-{\frac{\sqrt{2}}{2}},-{\frac{\sqrt{2}}{2}}\right)[/tex]
Angle measure 150° is associated with the coordinate [tex]\left(-{\frac{\sqrt{3}}{2}},{\frac{1}{2}}\right)$[/tex]
What is angle measure coordinate?An angle is fοrmed when twο lines οr rays meet at a cοmmοn pοint. The cοmmοn pοint is knοwn as the vertex.
In geοmetry, an angle measure can be defined as the measure οf the angle fοrmed by the twο rays οr arms at a cοmmοn vertex.
Angles are measured in degrees (°) using a prοtractοr. A prοtractοr is a measuring device that is used tο calculate οr draw angles in terms οf degrees.
Check the figure given in the attachment to better understand
Angle measure [tex]\frac{23 \pi}{3}[/tex] is associated with the coordinate [tex]\left({\frac{1}{2}}\;-{\frac{\sqrt{3}}{2}}\right)$[/tex]
Angle measure [tex]-\frac{3 \pi}{4}[/tex] is associated with the coordinate [tex]\left(-{\frac{\sqrt{2}}{2}},-{\frac{\sqrt{2}}{2}}\right)[/tex]
Angle measure 150° is associated with the coordinate [tex]\left(-{\frac{\sqrt{3}}{2}},{\frac{1}{2}}\right)$[/tex]
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Gender Selection The Genetics and IVF Institute conducted a clinical trial of the YSORT method designed to increase the probability of conceiving a boy. As of this writing, 291 babies were born to parents using the YSORT method, and 239 of them were boys. 291/239= a. What is the best point estimate of the population proportion of boys born to parents using the YSORT method? b. Use the sample data to construct a 99% confidence interval estimate of the proportion of boys born to parents using the YSORT method. c. Based on the results, does the YSORT method appear to be effective? Why or why not? Theoretical probability is u. population proportion is o. 90% confidence interval
the 99% confidence interval estimate for the proportion of boys born to parents using the YSORT method is: (0.7584, 0.8820)
what is an algebraic expression?
An algebraic expression is a mathematical phrase consisting of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
a. The point estimate of the population proportion of boys born to parents using the YSORT method can be calculated as the ratio of the number of boys to the total number of babies:
239/291 ≈ 0.8202
Therefore, the best point estimate of the population proportion of boys born to parents using the YSORT method is approximately 0.8202.
b. To construct a 99% confidence interval estimate of the proportion of boys born to parents using the YSORT method, we can use the following formula:
p ± z*sqrt(p(1-p)/n)
where p is the point estimate of the population proportion, z* is the critical value from the standard normal distribution for the desired confidence level (99% in this case), and n is the sample size.
Using the values from part (a), we have:
p = 0.8202
n = 291
z* = 2.576 (from the standard normal distribution table for a 99% confidence level)
Plugging in these values, we get:
0.8202 ± 2.576sqrt(0.8202(1-0.8202)/291)
Simplifying, we get:
0.8202 ± 0.0618
c. Based on the results, the YSORT method appears to be effective in increasing the probability of conceiving a boy. The point estimate of 0.8202 is significantly higher than the theoretical probability of 0.5 for a randomly selected baby to be a boy.
Therefore, the 99% confidence interval estimate for the proportion of boys born to parents using the YSORT method is: (0.7584, 0.8820)
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please help me with this question
Answer:
V = 3 * 3 * 7 + 2 * 3 * 5 = 63 + 30 = 93 just adding 2 segments
Evaluate x2 + 2(y ÷ w) for w = 2, x = 5, y = −8
The value of the expression x² + 2y ÷ 2w + 3z for w = 2, x = 5, y = 8, and z = 3 will be; ⇒ 3.15
Mathematical expression is defined as the collection of numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is;
⇒ x² + 2y ÷ 2w + 3z
And, The values are w = 2, x = 5, y = 8, and z = 3.
Now,
The expression is;
⇒ x² + 2y ÷ 2w + 3z
Substitute all the values of w = 2, x = 5, y = 8, and z = 3 in above equation, we get;
⇒ x² + 2y ÷ 2w + 3z
⇒ 5² + 2 × 8 ÷ 2 × 2 + 3 × 3
⇒ 25 + 16 ÷ 4 + 9
⇒ 41 ÷ 13
⇒ 3.15
Thus, The value of the expression x² + 2y ÷ 2w + 3z for w = 2, x = 5, y = 8, and z = 3 will be;
⇒ 3.15
The complete question is-
What is the value of x2 + 2y ÷ 2w + 3z for w = 2, x = 5, y = 8, and z = 3?
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What is the equation of this graphed line?
Enter your answer in slope-intercept form in the box.
Answer:
y = -1/3x - 5
Step-by-step explanation:
The slope-intercept form is y = mx + b
m = the slope
b = y-intercept
Slope = rise/run or (y2 - y1) / (x2 - x1)
Points (-6, -3) (6, -7)
We see the y decrease by 4, and the x increase by 12, so the slope is
m = -4/12 = -1/3
Y-intercept is located at (0, -5)
So, our equation is y = -1/3x - 5
Please help
A rock is dropped from a height of 100 feet. Calculate the time between when the rock was dropped and when it landed. If we choose "down" as positive and ignore air friction, the function is h(t)=16t^2-100
T= 2. 5 seconds
t = 10 seconds
t = 12. 5 seconds
t = 6. 25 seconds
When "down" is positive and air friction is disregarded, the time it takes for the rock to touch the ground may be calculated using the formula [tex]h(t)=16t2-100[/tex] to be roughly 6.25 seconds.
the formula[tex]h(t)=16t2 - 100[/tex]when a rock is dropped from a height of 100 feet, and assuming that "down" is positive and air friction is neglected, represents the height of the rock at time t in seconds.
As the rock will land at the value of t when h(t) = 0, we must determine that value in order to determine how long it takes for the rock to land.
When we set h(t) to 0 we obtain 0 = 16t2 - 100.
[tex]16t^2 = 100 \st^2 = 100/16 \st^2 = 6.25 \st = ±√6.25[/tex]
The only viable answer in this case is[tex]t = 6.25 = 2.5[/tex] seconds since time cannot be negative. As a result, there was a 2.5 second delay between when the rock was dropped and when it landed.
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4. A stone nudged off the Royal Gorge Bridge near Cañon City, Colorado, falls 1053 feet before hitting water. Because its speed increases as it falls, the distance it travels each second increases. During the first second, it drops 16 feet. During the next second, it drops an additional 48 feet. During the third second, it drops another 80 feet. The distances traveled each second form an arithmetic sequence:
16, 48, 80, ...
Part I: How far does the stone fall during the 5th second? Find and use the explicit formula.
a. What is the first term of the sequence? _____
b. What is d, the common difference? _____
c. Write the explicit formula in function notation. Use f(n) = f(1) + (n – 1)d, where f(1) represents the first term. _______________
d. Use the explicit formula to find the distance the stone travels in the 5th second.
a. The first term of the sequence is 16.
b. the common difference is d = 32
c. the explicit formula is f(n) = 16 + (n - 1)32
d. the stone falls a distance of 144 feet during the 5th second.
How to find the first term in the sequencea. The first term of the arithmetic sequence is given to be 16.
b. To find the common difference, we can subtract the second term from the first term, then the third term from the second term:
48 - 16 = 32
80 - 48 = 32
Therefore, the common difference is d = 32.
c. Using f(n) = f(1) + (n - 1)d,
where
f(1) = 16 and d = 32,
we can write the explicit formula for the distance traveled during the nth second as:
f(n) = 16 + (n - 1)32
d. To find the distance traveled during the 5th second, we plug in n = 5 into the explicit formula:
f(5) = 16 + (5 - 1)32
f(5) = 16 + 4*32
f(5) = 16 + 128
f(5) = 144
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Let (Xn)n≥0 be a branching process (as described in lectures) with X_0 = 1. Let Z denote the common offspring distribution (iid for all individuals) and suppose that Z ∼ Poisson(γ). Write down a general expression for P(X_n = i|X_n−1 = j) for the case that i ∈ N and j > 0.
Hint: Distribution of the sum of independent Poisson distributed RVs is?
The probability as a function of the sum of independent Poisson distributed random variables. We can then obtain the desired expression for P(X_n = i|X_n−1 = j) as follows:P(X_n = i|X_n−1 = j) = P(Z_1 + ... + Z_j = i) = (1/i!)×(γi)×e{-γ}.
What is expression?Expression in math is a combination of numbers, variables, operations and symbols that represent a mathematical relationship or value. Expressions can be used to represent equations, functions, and sequences, and can be evaluated for a result. Expressions can include constants, variables, operators, functions, and other mathematical expressions.
The general expression for P(X_n = i|X_n−1 = j) is given by P(X_n = i|X_n−1 = j) = P(Z_1 + ... + Z_j = i), where Z_1, ..., Z_j are independent and identically distributed Poisson random variables with parameter γ. This follows from the fact that the offspring of each individual follows the same Poisson distribution, and the total number of offspring is the sum of the offspring of each individual. Therefore, we can express the probability as a function of the sum of independent Poisson distributed random variables. We can then obtain the desired expression for P(X_n = i|X_n−1 = j) as follows:
P(X_n = i|X_n−1 = j) = P(Z_1 + ... + Z_j = i) = (1/i!)×(γi)×e{-γ}.
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A triangular bandana has an area of 86 square inches. The height of the triangle is 5 3/8
inches. Enter and solve an equation to find the length of the base of the triangle. Use b to represent the length of the base.
An equation to find the length of the base of the triangle is 86 = ?
The length of the base of the triangle is ? inches
Answer the word problem UvU
A triangular bandana has an area of 86 square inches. The height of the triangle is 5 3/8 inches. An equation to find the length of the base of the triangle is 86 = 1/2 * b * 43/8
The length of the triangle's base is 32 inches.
We know that the formula for calculating the area of a triangle is:
1/2 * base * height = area
We also know that the triangle's height is 5 3/8 inches, which may be expressed as a mixed number:
Height = 5 + 3/8 inch = 43/8 inch
Let b be the base of the triangle.
Substituting these numbers into the area formula yields:
86 = 1/2 * b * 43/8
To find b, multiply both sides of the equation by 2/43:
86 * 2/43 = 2/43 * 1/2 * b * 43/8
4 = b/8
b = 32
As a result, the length of the triangle's base is 32 inches.
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GIVING 75 POINTS URGENTTTT please help me thanksssss
Matching each number with its name, 1,254 :: whοle number
What is whοle numbers?Whοle numbers are a set οf numbers including all natural numbers and 0. They are a part οf real numbers that dο nοt include fractiοns, decimals, οr negative numbers. Cοunting numbers are alsο cοnsidered as whοle numbers.
Whοle numbers are pοsitive integers (including zerο) withοut any fractiοnal οr decimal parts. They are used tο cοunt whοle οbjects οr things, and cannοt represent a part οf a whοle. Examples are 0, 1, 2, 3, 4, 5, and sο οn.
0.143143143.... :: repeating decimal
0.123456789..... :: nοn-terminating/nοn-repeating
0.13 :: terminating
1,254 :: whοle number
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work out the length and width
Answer:
The dimensions of the rectangle are 5 by 24.
Step-by-step explanation:
Sometimes it's easy to finish solving the system and think that the x and y coordinates are your answer. Remember what the question is asking for - the dimensions of the rectangle.
Determine if the following numbers are rational or irrational.
1. √25
2.4.31
3.-2/2
4. √18
5.7
6. Pi
7.√50
8.-5
9. 1/3
10. 0
Answer:check explanation
Step-by-step explanation:1. √25 is a rational number because it is equal to 5, which is a rational number.
2. 4.31 is a rational number because it can be expressed as the ratio of two integers (431/100).
3. -2/2 is a rational number because it can be simplified to -1, which is a rational number.
4. √18 is an irrational number because it cannot be expressed as the ratio of two integers. It is approximately equal to 4.242640687119285.
5. 7 is a rational number because it can be expressed as the ratio of two integers (7/1).
6. Pi is an irrational number because it cannot be expressed as the ratio of two integers or as a terminating or repeating decimal. It is approximately equal to 3.141592653589793.
7. √50 is an irrational number because it cannot be expressed as the ratio of two integers. It is equal to √(25*2) which simplifies to 5√2.
8. -5 is a rational number because it can be expressed as the ratio of two integers (-5/1).
9. 1/3 is a rational number because it can be expressed as the ratio of two integers (1/3 = 0.33333...).
10. 0 is a rational number because it can be expressed as the ratio of two integers (0/1).
Typically, the y-value in a function is called the ______.
a. output
b. axis
c. expression
d. variable
e. input
Write all the factors of 15 .
Use commas to separate them.
Answer: 1, 3, 5 and 15
Step-by-step explanation:
trust me bro
Please solve with proof
Yes, the Median of a triangle is also an altitude and the triangle is isosceles.
What is the altitude of a triangle?The altitude of a triangle is the perpendicular line segment drawn from the vertex of the triangle to the side opposite to it
A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side.
In an isosceles triangle, two sides that are equal meet at a vertex that lies directly above the base midpoint. Because of this altitude from the vertex bisect the base at midpoint median to the base from the vertex.
Therefore, Median of a triangle is also an altitude and the triangle and it is isosceles.
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A poster storage tube in the shape of a cylinder has a diameter of inches and a volume ofcubic inches.
What is the height of the poster storage tube in inches?
ANSWER IS ON VERY BOTTOM.
The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height. We are given the diameter of the cylinder, which is 4 inches, so the radius is half of that, or 2 inches. We are also given the volume of the cylinder, which is V = cubic inches.
Substituting these values into the formula, we get:
cubic inches = π(2 inches)^2h
Simplifying, we have:
cubic inches = 4πh
To solve for h, we can divide both sides by 4π:
h = cubic inches / 4π
Using a calculator to evaluate this expression, we get:
h = 5.027 inches (rounded to three decimal places)
Therefore, the height of the poster storage tube is approximately 5.027 inches.
The height of the poster storage tube in inches is 40 inches.
What is Volume?Volume of a three dimensional shape is the space occupied by the shape.
Given that,
A poster storage tube in the shape of a cylinder.
Volume = 122.5π inches³
Diameter = 3.5 inches
Radius = Diameter / 2 = 1.75 inches
Volume of the cylinder = π r² h
where r is the radius of the base and h is the height of the cylinder.
Substituting,
π (1.75)² h = 122.5π
(1.75)² h = 122.5
h = 122.5 / (1.75)²
h = 40 inches
Hence the height of the cylinder is 40 inches.
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The complete question is as follows :
A poster storage tube in the shape of a cylinder has a diameter of 3.5 inches and a volume of 122.5 (pi) cubic inches. What is the height of the poster storage tube in inches?
Consider the figure below.
What are the coordinates of Point S after a dilation with the center at the origin and a scale factor of 12?
Responses
(2,−1)
( 2 , − 1 )
(4,−2)
( 4 , − 2 )
(8,−4)
( 8 , − 4 )
(16,−8)
On solving the question we have that As a result, the coordinates of coordinates point S after dilation with the origin as the Centre and a scale factor of 12 are (24, 12). Option (D) (16,-8), however, is incorrect.
what are coordinates?In geometry, a coordinate system is a method that uses one or more numbers or coordinates to determine the precise location of points or other physical objects on a basis, such as Reference frame. Pairs of figures called coordinates are employed in order to locate a point or item on a double plane. The x and y parameters of a location on a 2D plane are two integers that describe its position. a set of digits which represent precise positions. In most cases, the figure has two numbers. The first number represents the front-to-back distance, while the second column represents the top-to-bottom distance. As in (12.5), there are 12 divisions below and 5 units above.
To determine the image of point S after dilation with the origin as the centre and a scale factor of 12, multiply S's coordinates by the scale factor of 12.
As a result, the coordinates of point S after dilation are as follows:
S' = (12 × 2, 12 × −1)
S' = (24, −12)
As a result, the coordinates of point S after dilation with the origin as the centre and a scale factor of 12 are (24, 12).
Option (D) (16,-8), however, is incorrect.
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helpp -3(0.75x-2y)+6(0.5x-2y) ?????
Label the drawing or write the segment
The side opposite to angle B is AC. The side adjacent to angle B is BC. The hypotenuse is segment AB.
What is adjacent side and hypotenuse?A pair of sides are referred to as neighboring if they have a shared angle. The term "hypotenuse" refers to a right-angled triangle's longest side as compared to the base and perpendicular lengths. The right angle, the largest angle of the three angles in a right triangle, lies opposite the hypotenuse side. In essence, only the right triangle possesses the hypotenuse feature, not any other triangles.
From the figure we observe that the side opposite to angle B is AC.
The angle adjacent to angle B is BC.
The hypotenuse is segment AB.
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A number is called ‘interesting’ if it is divisible by 11,111. How many 10-digit interesting numbers are there?
Please help I will award brainliest
if there are 6 consecutive numbers and 10 is the smallest one, what is their sum?
Hence, 75 is the result of adding the six consecutive integers starting at 10.
What are consecutive numbers?Numbers that follow one another sequentially are known as consecutive numbers. Every time there are two numbers, there is a 1 difference.
We can find the sum of these numbers by adding them up if there are six consecutive numbers and 10 is the smallest one.
The six numbers in order are x, x+1, x+2, x+3, x+4, and x+5. We are aware that x equals 10 because 10 is the smallest number.
The six numbers are therefore 10, 11, 12, 13, 14, and 15.
We simply put them together to determine their sum:
10 + 11 + 12 + 13 + 14 + 15 = 75
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What is the answer for this question?
The figure similar to figure E after dilation is figure F.
What are transformations?The transformation, or f: X X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the picture X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one way or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point. Two-dimensional mathematical figures move about a coordinate plane according to transformations.
We know that when a figure is dilated the ratio of their sides are same, that is they are proportional.
From the graph we observe that the line passes through the point F and E. Thus, the sides of the figure are proportional or in linear relation with each other.
Hence, the figure similar to figure E after dilation is figure F.
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PLS ANSWER will give brainliest‼️‼️
4.) You decide to paint your room, too.
Your room has 300 square feet of wall space to paint. Sam says it took her 10 minutes to paint 25 square feet. At this rate, how many hours would it take Sam to paint your room?
Answer: 2 hours
Step-by-step explanation: (10 min) / (25 square feet) = (X minutes) / (300 square feet)
Cross-multiply to solve, as we always do with proportions:
10 * 300 = 25 * x
3000 = 25X
3000/25 = 25X /25
120 = X
120 minutes * (1 hour / 60 minutes) = 2 hours
A rectangle has side lengths of x cm and (x+y) cm, where x and y are both positive. The rectangle has an area of 57 cm squared and a perimeter of 44 cm. work out the values of x and y
The value of x and y for the rectangle has side lengths of x cm and (x+y) cm are found as : x = 3 and y = 16.
Explain about the area of rectangle?The total of a rectangle's four sides is its perimeter. The equation Perimeter of Rectangle = 2 (Length + Width) is used to calculate it. The region contained within the boundaries of a rectangle is its area, which may be determined using the formula area of rectangle = length width.Dimensions are:
Length L = x cmWidth w = (x + y) cmArea = 57 cm squared perimeter = 44 cm.Then,
Area = l*w
57 = x(x + y) ....eq 1
Perimeter = 2(l + w)
44 = 2(x + x + y)
22 = 2x + y
y = 22 - 2x ...put in eq 1
57 = x(x + y)
57 = x(x + 22 - 2x)
57 = x(22 - x)
Simplifying:
57 = 22x - x²
Or.
x² - 22x + 57
Factorizing using quadratic formula:
x = 19 ans x = 3
For x = 19
y = 22 - 2*19
y = 22 - 38 (negative value not possible)
So, x = 3
y = 22 - 2*3
y = 22 - 6
y = 16
Thus, the value of x and y for the rectangle has side lengths of x cm and (x+y) cm are found as : x = 3 and y = 16.
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Please Urgent! Find the EXACT value of tan(A-B) if cscA= -17/15where A is in Quadrant III and sinB=12/13 where B is in Quadrant I.Assume all angles are measured from standard position.tan(A-B) = ?
The value of tan(A - B) will be 15/8.
As mentioned, cscA= -17/15 and A is in Quadrant III and sinB=12/13 where B is in Quadrant I To find tan(A - B), we need to have the values of sin (A - B) and cos (A - B).We know that, sin(A - B) = sinAcosB - cosAsinB and cos(A - B) = cosAcosB + sinAsinB.Since we have the values of sinA, cosA, and sinB, let's find the values of cosA and cosB.First, let's find cosA. We know that cscA = 1/sinA. Therefore, sinA = -15/17.Since A is in Quadrant III, sinA < 0, cosA < 0, and tanA > 0.
By using the Pythagorean identity sin^2A + cos^2A = 1, we get cosA = -8/17.Next, let's find cosB. We know that sin^2B + cos^2B = 1.
Therefore, cosB = sqrt(1 - sin^2B) = 5/13.
Since B is in Quadrant I, sinB > 0, cosB > 0, and tanB > 0.
Now, we have sinA, cosA, sinB, and cosB.
Using the values of sinA, cosA, sinB, and cosB, let's find sin(A - B) and cos(A - B).
sin(A - B) = sinAcosB - cosAsinB= (-15/17)(12/13) - (-8/17)(5/13)= -180/221
cos(A - B) = cosAcosB + sinAsinB= (-8/17)(12/13) + (-15/17)(5/13)= -96/221
Finally, tan(A - B) = sin(A - B) / cos(A - B)= (-180/221) / (-96/221)= 15/8. Therefore, tan(A - B) = 15/8.
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Let x be a random variable distributed as normal(5,4). Find the probabilities of the following events: (i) p(x::; 6). (ii) p(x > 4 ). (iii) p( ix- 5 1 > 1
From the given information provided, the probability of P(X ≤ 6), P(X˃ 4) and P(|X- 5| ˃ 1) is 0.6915, 0.6915 and 0.3829 respectively.
(i) To find P(X ≤ 6), we need to standardize the value of 6 using the formula:
Z = (X - μ) / σ
where μ = 5 and σ = 2 (since the standard deviation is the square root of the variance, which is 4).
So, we have:
Z = (6 - 5) / 2
Z = 0.5
We can then look up the probability of Z ≤ 0.5 in a standard normal distribution table, or use a calculator to find:
P(X ≤ 6) = P(Z ≤ 0.5) = 0.6915
(ii) To find P(X > 4), we again need to standardize the value of 4:
Z = (4 - 5) / 2
Z = -0.5
Then, we can use the fact that the total area under a normal distribution curve is 1 to find the probability of X being greater than 4:
P(X > 4) = 1 - P(X ≤ 4) = 1 - P(Z ≤ -0.5)
Using a standard normal distribution table:
P(X > 4) = 0.6915
(iii) To find P(|X - 5| > 1), we first need to transform this inequality into a standard normal distribution by standardizing both sides:
|X - 5| > 1
implies:
X - 5 > 1 or
X - 5 < -1
which gives:
X > 6 or X < 4
We can then standardize each inequality separately. For X > 6, we have:
Z = (6 - 5) / 2
Z = 0.5
and for X < 4, we have:
Z = (4 - 5) / 2 = -0.5
Then, using the fact that the total area under a normal distribution curve is 1, we can find the probability of both events occurring:
P(|X - 5| > 1) = P(X > 6 or X < 4) = P(Z > 0.5 or Z < -0.5)
Since the standard normal distribution is symmetric around 0:
P(Z > 0.5 or Z < -0.5) = 2 × P(Z < -0.5)
Using a standard normal distribution table:
P(|X - 5| > 1) = 0.3829
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Rafael spins the pointers of the top spinners shown at the right. Find the probability of each possible sum.
After addressing the issue at hand, we can state that Keep in mind that any probability model must have these probabilities sum up to 1, as is the case here.
What is probability?Calculating the probability that an event will occur or that a statement is true is the subject of probability theory in mathematics. A risk is a number between 0 and 1, where 1 denotes certainty and an approximate probability of 0 denotes how likely an event appears to be to occur. A mathematical representation of the likelihood that an event will take place is called probability. You can also express probabilities as percentages ranging from 0% to 100% or as integers between 0 and 1. the proportion of equally plausible options that actually occur when compared to all possible outcomes, leading to a certain event.
A probability model for selecting a bead can be defined as follows:
Let the actions of choosing a glass, wood, or brass bead be represented by G, W, and B, respectively. We can suppose that the likelihood of choosing a particular type of bead is inversely correlated with the quantity of that type of bead in the box. As a result, we have:
P(W) = 96/300 = 8/25 P(B) = 144/300 = 12/25 with P(G) = 60/300 = 1/5
Keep in mind that any probability model must have these probabilities sum up to 1, as is the case here.
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The correct question is -
Write a probability model for choosing a bead.
Choosing Beads
Glass 60
Wood 96
Brass 144