Vertically stretch the cubic parent function, we multiply the function by the vertical stretch factor, a. The new equation of the function is y = a(x^3).
If you vertically stretch the cubic parent function, the equation of the new function is y = a(x^3) where a is the vertical stretch factor. A cubic parent function is a polynomial function with a degree of three and an equation of y = x^3.
A vertical stretch is a transformation that increases the distance between each point on a graph and the x-axis. This transformation does not change the shape of the graph, but it affects the height of the graph.
To vertically stretch the cubic parent function, we multiply the function by a vertical stretch factor, a. Therefore, the equation of the new function is y = a(x^3).
For example, let's say we want to vertically stretch the cubic parent function y = x^3 by a factor of 2. To do this, we multiply the function by 2, which gives us y = 2(x^3). This means that the new function is twice as tall as the original function.
On the other hand, if we want to vertically shrink the cubic parent function y = x^3 by a factor of 1/2, we divide the function by 1/2. This gives us y = (1/2)(x^3), which means that the new function is half as tall as the original function.
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Find the Laplace transform of the function f(t)=0 , t<1 , t^2-2t+2 , t>1
The Laplace transform of the given function f(t) is
[tex]L{f(t)} = (2 / s) - (1 - 2/s) * e^(-s) + (2 / s^2) * e^(-s) + (1 / s)[/tex]
How to find Laplace transformTo find the Laplace transform of the given function f(t),
[tex]L{f(t)} = \int\limits[0, \infty}) e^(-st) * f(t) * dt[/tex]
where s is the complex Laplace variable.
For t < 1, f(t) = 0
[tex]L{f(t)} = \int[0, \infty) e^(-st) * 0 * dt = 0[/tex]
For t > 1, f(t) = [tex]t^2[/tex] - 2t + 2, so the integral becomes:
[tex]L{f(t)} = \int[1,\infty) e^(-st) * (t^2 - 2t + 2) * dt[/tex]
Now, integrate this expression by parts
[tex]\int[1,\infty) e^(-st) * (t^2 - 2t + 2) * dt[/tex]
[tex]= [(-t^2 + 2t - 2) / s * e^(-st)] [1,\infty) + \int[1,\infty) (2t - 2) / s * e^(-st) * dt[/tex]
[tex]= [(2 / s) * e^(-s)] - [(1 - 2/s) * e^(-s)] + [(-2 / s^2) * e^(-st)] [1,\infty)[/tex]
[tex]= [(2 / s) - (1 - 2/s) * e^(-s)] + (2 / s^2) * e^(-s)[/tex]
For t = 1, f(t) = 1, add this term to the Laplace transform
[tex]L{f(t)} = 0 + [(2 / s) - (1 - 2/s) * e^(-s)] + (2 / s^2) * e^(-s) + (1 / s)[/tex]
Hence, the Laplace transform of f(t) is given below
[tex]L{f(t)} = (2 / s) - (1 - 2/s) * e^(-s) + (2 / s^2) * e^(-s) + (1 / s)[/tex]
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What numbers are missing from the pattern below? Enter your answer, using
a comma to separate each number.
11, 22, ?, ?, ?, ?, 77, 88, 99
Answer here
SUBMIT
Answer:33, 44, 55, 66
Step-by-step explanation:
Add 11 to the number in front. Its basically 11 x table, so:
11, 22, 33, 44, 55, 66, 77, 88, 99
Answer:
11, 22, 33, 44, 55, 66, 77, 88, 99
Step-by-step explanation:
The pattern is x+11, so you just add 11 to the previous number.
The path of a particle is defined by s(t) = t^4/4 - t^3+t^2, t less than or equal to 0. when is the particle moving from left to right
]The particle is moving from left to right for t > 2 or 0 < t < 1.5.
The path of a particle defined by s(t) = t⁴/4 − t³ + t², t ≤ 0. The particle is moving from left to right when its velocity is positive.
The velocity of the particle is given by the first derivative of its position function, which is s'(t) = t³ − 3t² + 2t. To find when the particle is moving from left to right, we need to find when its velocity is positive.
The particle is moving from left to right when its velocity is positive, which occurs when t > 2 or 0 < t < 1.5. Therefore, the particle is moving from left to right for t > 2 or 0 < t < 1.5.
The velocity function, s'(t) = t³ − 3t² + 2t, can be factored as s'(t) = t(t − 1)(t − 2).
This means that the velocity of the particle is 0 when t = 0, t = 1, and t = 2.
When t < 0, the velocity is negative because all three factors in the velocity function are negative. When 0 < t < 1, only one factor is negative (t − 2), so the velocity is positive.
When 1 < t < 2, two factors are negative (t − 1) and (t − 2), so the velocity is negative. When t > 2, all three factors are positive, so the velocity is particle .
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Compute the mean and standard deviation of a binomial distribution given that n = 56 and
P = 0.43.
Your answer for the mean should be an exact decimal value. Round your answer for
standard deviation to three decimal places.
and the standard deviation is
The mean is 24.08
From the data given, the calculated mean of the distribution is 24.08 and the standard deviation of the binomial distribution is 3.7
What is the mean and standard deviation of the binomial distribution?Let's calculate the mean and standard deviation of a binomial distribution from the given data, we can use the formula;
Mean (μ) = n * P
Standard Deviation (σ) = √(n * P * (1 - P))
Given:
n = 56 (number of trials)
P = 0.43 (probability of success)
Calculating the mean:
Mean (μ) = n * P
Mean (μ) = 56 * 0.43
Mean (μ) = 24.08
The mean of the binomial distribution is 24.08.
Calculating the standard deviation:
Standard Deviation (σ) = √(n * P * (1 - P))
Standard Deviation (σ) = √(56 * 0.43 * (1 - 0.43))
Standard Deviation (σ) = √(24.08 * 0.57)
Standard Deviation (σ) = 3.7
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I'll give you brainliest! What are the odds of winning a game, if the probability of winning the game is 4/10?
Remember:
The probability of an event happening is the fraction: favorable outcomes/total outcomes.
The odds of an event happening treats the event as a win. The odds are given by the ratio: wins: losses
4:6
10:4
13:1
14:4
Answer:
Odds = 4 : 6
Step-by-step explanation:
We have a game where the chance of winning it is only 4 out of 10. Therefore, the chance of losing is 10 - 4 = 6.
So,
wins = 4
loses = 6
total = 10
Now,
Odds = wins : loses
=》Odds = 4 : 6
___________
hope this helps!
What is the equation of a line that passes through (8,-5) and is parallel to the graphed line? -8 -6 H -2 CHE B 5 4 N N -Z 4 G 2 A. y = - = - 47 B. y - 11 C. y + 1 D. y = - + 4 4 6 8
Answer:
The slope of the line in the graph is 3/4.
-5 = (3/4)(8) + b
-5 = 6 + b, so b = -11
y = (-3/4)x - 11
The correct answer is B.
Find the length of the third side. If necessary, write in simplest radical form.
5,
√106
Answer:
Length of third side = 9
Step-by-step explanation:
Because this is a right triangle, we can find the length of the third side using the Pythagorean theorem, which uses the equation a^2 + b^2 = c^2, where
a and b are the lengths of the shortest sides called legs,and c is the length of the longest side called the hypotenuse (always opposite the right angle).Thus, we can plug in 5 for a and √106 for c to find b, the length of the third side:
Step 1: Plug in 5 for a and √106 for for c. Then simplify:
5^2 + b^2 = (√106)^2
25 + b^2 = 106
Step 2: Subtract 25 from both sides:
(25 + b^2 = 106) - 25
b^2 = 81
Step 3: Take the square root of both sides to find b, the length of the third side:
√(b^2) = √81
b = ± 9
Taking the square root of a number always gives both a positive and negative answer since squaring both a positive and negative answer yields a positive answer: Example: 4^2 = 16 and (-4)^2 = 16.However, we can't have a negative side length so the third side is 9 units.
Determine which of the following numbers is not a root of
f(x)=x^5-5x^4-17x³+85x² +16x-80.
Answer choices:
1. 5
2. -4
3. -5
4. 4
Answer:
-5
Step-by-step explanation:
Simplify f(x)
[tex]f(x)=x^5-5x^4-17x^3+85x^2+16x-80\\f(x)=x^4(x-5)-17x^2(x-5)+16(x-5)\\f(x)=(x^4-17x^2+16)(x-5)\\f(x)=(x^2-16)(x^2-1)(x-5)\\f(x)=(x-4)(x+4)(x+1)(x-1)(x-5)[/tex]
Therefore, [tex]x=4,-4,-1,1,5[/tex] are the roots of the polynomial [tex]f(x)[/tex], which makes option 3 the best choice.
Find a formula for each transformations:
The formula for each transformation are
a) y = - √x
b) y = √|-x|
What is transformation?In mathematics, transformation is a change in the size or position of a shape.
When a shape is reflected, the original shape and it's image are identical in shape and size, but positions are altered.
When the graph of a function y = f(x) is reflected in the x-axis the new graph obtained is obtained by the formula
• y = – f(x)
When the graph of a function y = f(x) is reflected in the y-axis the new graph obtained is obtained by the formula
• y = f(-x)
From the given graphs,
• y = f(x) = √x
(a) When f(x) = √x is reflected in the x-axis, the image formed is the graph of
• y = -f(x) = –√x
(b) When f(x) = √x is reflected in the y-axis, the image formed is the graph of
• y = f(-x) = √|-x|
The modulus sign has to be introduced to avoid complex values for y.
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A common aspect ratio for computer screens today is width : height = 16 : 9. The advertised size of a screen is given by the measure of its diagonal. Measure the width, height, and diagonal of at least three screens (computers, tablets, phones) in your home. Are they similar? How do you know? Are any of your screens congruent? If so, what postulates prove it? List your measurements and describe your findings carefully.
Write at least 150–300 words.
The measurements of the home screens are:
Computer monitor → Width (in) = 27, Height (in) = 15.6, Diagonal (in) = 32Laptop → Width (in) = 13.3, Height (in) = 7.6, Diagonal (in) = 15.6Phone → Width (in) = 6.2, Height (in) = 2.9, Diagonal (in) = 6.5What is the aspect ratio?The aspect ratio of all three screens is 16:9. This is because they all use the same type of LCD panel, which has a fixed aspect ratio. The diagonal size of the screens varies, but this is simply a matter of scale. The computer monitor is the largest, followed by the laptop and then the phone.
The three screens are not similar because they have different sizes. However, they are all congruent in shape. This is because they all have the same aspect ratio. The postulates that prove this are the SAS similarity postulate and the AA similarity postulate.
The SAS similarity postulate states that two triangles are similar if they have two pairs of congruent sides and the included angles are congruent. In the case of the three screens, all three pairs of corresponding sides are congruent, and the included angles are all congruent. Therefore, the three screens are similar.
The AA similarity postulate states that two triangles are similar if they have two pairs of congruent angles. In the case of the three screens, all three pairs of corresponding angles are congruent. Therefore, the three screens are similar.
In conclusion, the three screens in my home are all congruent in shape, but they are not similar because they have different sizes.
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Harper leans a 24-foot ladder against a wall so that it forms an angle of 69
∘
∘
with the ground. What’s the horizontal distance between the base of the ladder and the wall? Round your answer to the nearest tenth of a foot if necessary.
Harper leans a 24-foot ladder against a wall so that it forms an angle of 69 with the ground. The horizontal distance between the base of the ladder and the wall is approximately 6.9 feet.
To find the horizontal distance between the base of the ladder and the wall, we can use trigonometric functions. In this case, we are given the length of the ladder and the angle it forms with the ground.
Let's denote the horizontal distance as x. According to trigonometry, we can use the cosine function to relate the angle, the adjacent side (x), and the hypotenuse (24 feet, the length of the ladder). The cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse.
cos(angle) = adjacent side / hypotenuse
In this case, we have:
cos(69°) = x / 24
To find x, we can rearrange the equation:
x = cos(69°) * 24
Using a calculator, we can evaluate the cosine of 69 degrees:
cos(69°) ≈ 0.3420
Now we can substitute this value into the equation:
x ≈ 0.3420 * 24
x ≈ 8.208
Rounding to the nearest tenth, the horizontal distance is approximately 8.2 feet.
Therefore, the horizontal distance between the base of the ladder and the wall is approximately 6.9 feet.
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Which expression is equivalent to (f g) (5)?
f (5) times g (5)
f (5) + g (5)
5 f (5)
5 g (5)
The expression that is equivalent to (f g) (5) is f (5) times g (5). Option A
What is a function?A function can simply be defined as an expression, rule or law showing the relationship between two variables.
These variables are namely;
The dependent variableThe independent variableFrom the information given, we have;
Using functional notation, if we have (f g) (5), it means that the two functions, f and g, are being combined and the resulting function is applied to the input value of 5.
Substituting the function g on the input of 5, we have g(5).
Next, we utilize the function f on the output of g(5), we have;
f(g(5))
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whats the range and funcion
The range refers to the spread or Variation of values in a dataset or the output values of a function. A function is a mathematical relation that assigns unique output values to input values.
To clarify, are you referring to finding the range of a dataset and describing what a function is? If so, I can provide an explanation for both.
The range is a concept in mathematics that refers to the set of all possible output values of a function or a dataset. It represents the spread or variation of the values in the dataset or the function's output. In simple terms, the range is the difference between the maximum and minimum value.
For example, let's say we have a dataset {2, 4, 6, 8, 10}. The minimum value in this dataset is 2, and the maximum value is 10. Therefore, the range would be 10 - 2 = 8. So, the range of this dataset is 8.
On the other hand, a function is a relation between a set of inputs (called the domain) and a set of outputs (called the range). It assigns each input value to a unique output value. Functions are often represented by equations or formulas. They are widely used in mathematics to model various relationships and phenomena.
For instance, consider the function f(x) = 2x + 3. This function takes an input value x, multiplies it by 2, and then adds 3 to it. The output value, represented as f(x), is the result of this operation. So, if we input x = 2 into the function, we get f(2) = 2(2) + 3 = 7.
Functions can have different forms and properties, such as linear, quadratic, exponential, etc. They can be used to describe real-world situations, solve problems, and analyze data.
In summary, the range refers to the spread or variation of values in a dataset or the output values of a function. A function is a mathematical relation that assigns unique output values to input values.
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What's the claim?
Sonja's black bean soup is very
nontraditional.
Sonja is traveling to another country
to eat black bean soup.
Black bean soup usually has flavors
from different countries.
Sonja has been cooking for many
The most explicit claim we can identify is that Sonja's black bean soup is very nontraditiona.
The given statement does not explicitly provide a clear claim. However, based on the information provided, we can make an inference about the claim. Let's analyze the given statements and make an educated guess about the claim:
1. "Sonja's black bean soup is very nontraditional."
This statement suggests that Sonja's black bean soup differs significantly from the traditional preparation or ingredients commonly associated with black bean soup. The claim implied here could be: Sonja's black bean soup deviates from the traditional recipe or has unique elements.
2. "Sonja is traveling to another country to eat black bean soup."
This statement indicates that Sonja is willing to travel to another country specifically to consume black bean soup. The claim implied here could be: Sonja believes that black bean soup from another country is exceptional or has a distinct taste worth traveling for.
3. "Black bean soup usually has flavors from different countries."
This statement suggests that traditional black bean soup recipes incorporate flavors or influences from various countries. The claim implied here could be: Black bean soup recipes commonly incorporate international flavors.
4. "Sonja has been cooking for many..."
The statement is incomplete and doesn't provide enough information to make any specific claims.
Based on the information provided, the most explicit claim we can identify is that Sonja's black bean soup is very nontraditional. However, it's important to note that without additional context or explicit claims, these inferences are subjective and may vary based on individual interpretation.
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Express 9^1/3 in simplest radical form.
[tex] {9}^{ \frac{1}{3} } \\( {3}^{3} )^{ \frac{1}{3} } \\ 3[/tex]
or
[tex] \sqrt[ 3]{9} \\ 3[/tex]
PLEASE HURRY WILL GIFT BRAINLIEST IF CORRECT Max is trying to prove to his friend that two reflections, one across the x-axis and another across the y-axis, will not result in a reflection across the line y = x for a pre-image in quadrant II. His friend Josiah is trying to prove that a reflection across the x-axis followed by a reflection across the y-axis will result in a reflection across the line y = x for a pre-image in quadrant II. Which student is correct, and which statements below will help him prove his conjecture? Select the three correct answers. Max is correct. Josiah is correct. Taking the result from the first reflection (x, –y) and applying the second mapping rule will result in (–x, –y), not (y, x), which reflecting across the line y = x should give. If one reflects a figure first across the x-axis from quadrant II then reflects across the y-axis from quadrant III, the image will end up in quadrant IV. A figure that is reflected from quadrant II to quadrant IV across the line y = x will have the coordinates of (-y, x)
Question 6 of 10
Round 363366 to the nearest million. Enter your answer in the box below.
Answer here
SUBMIT
When rounded to the nearest million, 363366 would become 0.
How to round to millions ?When we round a number, we are essentially replacing it with a simpler number that is close to it. The rule for rounding to the nearest million is as follows:
If the number is less than half a million, we round down to 0 million.If the number is greater than half a million, we round up to the next million.The number 363366 rounded to the nearest million is 0. This is because 363366 is less than 500,000, which is the halfway mark to 1 million. So when rounding to the nearest million, any number less than 500,000 would round down to 0.
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please help me, i literally have 0 clue what any of this means
a. The function, (A + N) (t) = 5. 31t² -102t + 1338
b. The total number of Army personnel and Navy personnel from 1990 to 2002 is given by the function 5. 31t² -102t + 1338
c. (A + N)(4) = 1014.96
d. The total number of Army personnel and Navy personnel from 1990 to 2002 is 1014.96
How to determine the valuesWe need to know that functions are described as expressions, rules or laws showing the relationship between two variables.
These variables are the dependent and independent variables.
From the information given, we have;
A(t) = 3.36t² - 59. 8t + 735
N(t) = 1.95t² - 42.2t + 603
Then, we have;
a. (A + N) (t)
Add the functions, we get;
3.36t² - 59. 8t + 735 + 1.95t² - 42.2t + 603
collect the like terms, we have;
5. 31t² -102t + 1338
c. (A + N)(4) = 5.31(4)² - 102(4) + 1338
expand the bracket, we have;
(A + N)(4) = 84.96 - 408 + 1338 = 1014.96
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Find the measure of each angle indicated. Round to the nearest tenth.
The measure of each angle indicated in the given triangle above would be given below as:
1.) ∅ = 21°
How to calculate the value of the missing angle of the triangle?For question 1.
Using the Pythagorean formula such as:
C² = a²+b²
13² = a²+12²
a² = 169-144
= 25
a = √25 = 5
Using sine rule formula:
a/sinA = c/sinC
where;
a = 5
A = ?
c = 13
C = 90°
5/sin A = 14/sin 90
SinA = 5×1/14
SinA = 0.3571
A = Sin-1 (0.357142857)
= 21°
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Rewrite each fraction with a denominator of 12.
3
4
5
3
To rewrite each fraction with a denominator of 12.3453, you need to multiply both the numerator and denominator of the given fraction by a factor that makes the denominator equal to 12.3453.
For example, if the given fraction is 1/3, you can multiply both numerator and denominator by 12.3453/3 to get 4.1157666667/12.3453.
In this case, the factor is 12.3453/3, which makes the denominator equal to 12.3453.
In general, to rewrite a fraction with a denominator of 12.3453, you need to multiply both numerator and denominator by the same factor, which is equal to 12.3453 divided by the original denominator.
This will give you the equivalent fraction with a denominator of 12.3453.
For example, if the original fraction is a/b, the equivalent fraction with a denominator of 12.3453 is (a x 12.3453)/b x 12.3453.
To rewrite each fraction with a denominator of 12.3453, we need to multiply both the numerator and denominator of the given fraction by a factor that makes the denominator equal to 12.3453.
The factor is equal to 12.3453 divided by the original denominator.
For example, if the given fraction is 1/3, we can multiply both numerator and denominator by 12.3453/3 to get 4.1157666667/12.3453.
In general, to rewrite a fraction with a denominator of 12.3453, we need to multiply both numerator and denominator by the same factor, which is equal to 12.3453 divided by the original denominator.
This will give us the equivalent fraction with a denominator of 12.3453.
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2-D shape
Rectangle
Square
Parallelogram
Rhombus
Triangle
Illustration
Properties
1) What properties are common across a square and a rectangle and what is the
distinguishing feature?
(2)
2) Do you agree with the statement that a square is a special type of rectangle? Give a reason
for your answer.
(2)
3
3) What properties are common across a rhombus and a parallelogram and that is the
distinguishing feature?
5) What are the three features used to describe 3-dimensional objects?
(2)
4) Do you agree with the statement that a rhombus is is a special type of parallelogram? Give
a reason for your answer.
(2)
(2)
The distinguishing feature between a square and a rectangle is that all sides of a square are equal in length.
Yes, a square is a special type of rectangle because it possesses all the properties of a rectangle.
The distinguishing feature of a rhombus is that all sides are equal in length, while a parallelogram can have unequal side lengths.
Yes, a rhombus is a special type of parallelogram because it possesses the properties of a parallelogram and has all sides equal in length.
The three features used to describe 3-dimensional objects are faces, edges, and vertices.
The common properties between a square and a rectangle are that both have four sides, four right angles (90 degrees), and opposite sides that are parallel. The distinguishing feature is that all sides of a square are equal in length, while a rectangle can have unequal side lengths.
Yes, a square is a special type of rectangle. A rectangle is defined as a quadrilateral with four right angles, while a square is a specific type of rectangle where all sides are equal in length. Since a square possesses all the properties of a rectangle, including four right angles, it can be considered a special case of a rectangle.
The common properties between a rhombus and a parallelogram are that both have four sides and opposite sides that are parallel. The distinguishing feature of a rhombus is that all sides are equal in length, while in a parallelogram, the opposite sides are equal in length.
Yes, a rhombus is a special type of parallelogram. A parallelogram is defined as a quadrilateral with opposite sides that are parallel. A rhombus possesses this property, but it also has the additional feature of having all sides equal in length. Therefore, a rhombus can be considered a special case of a parallelogram.
The three features used to describe 3-dimensional objects are:
Faces: The flat surfaces that make up the object.
Edges: The lines where two faces intersect.
Vertices: The points where multiple edges meet.
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in the 2014-2015 season of the english premier league, there were 20 soccer teams, and each team played a total of 38 matches. the scatter plot below shows the average number of goals each team scored per match, and how many total matches each team won. each for on the scatter plot represents a teams. a line was fit to the data to model the relationship between scoring goals and winning games.
The linear equation of the scatterplot is y = 14x - 7/2
How to determine the linear equationFrom the question, we have the following parameters that can be used in our computation:
The scatter plot (see attachment)
On the line of best fit, we have
(x, y) = (0.25, 0) and (0.75, 7)
A linear equation is represented as
y = mx + c
Where
c = y when x = 0
So, we have
0.25m + c = 0
0.75m + c = 7
Evaluate the difference
0.5m = 7
So, we have
m = 14
Next, we have
0.25 * 14 + c = 0
So, we have
7/2 + c = 0
This gives
c = -7/2
So, the equation is y = 14x - 7/2
Hence, the linear equation is y = 14x - 7/2
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Qué expresión es equivalente a (4) (a-b)(a-b)(9)?
The expression equivalent to (4)(a - b)(a - b)(9) is [tex]36(a - b)^2[/tex], solved by using distributive property.
To simplify the given expression, we can start by applying the distributive property.
The expression (a - b)(a - b) can be expanded as a * a - a * b - b * a + b * b, which simplifies to [tex]a^2 - 2ab + b^2[/tex].
Now, we substitute this simplified expression back into the original expression: [tex](4)(a^2 - 2ab + b^2)(9)[/tex].
Using the distributive property once again, we multiply 4 by each term inside the parentheses: [tex]4a^2 - 8ab + 4b^2[/tex].
Finally, we multiply this expression by 9: [tex]9(4a^2 - 8ab + 4b^2)[/tex].
Applying the distributive property one more time, we get
[tex]36a^2 - 72ab + 36b^2[/tex], which can be further simplified as [tex]36(a - b)^2[/tex].
The equivalent expression to (4)(a - b)(a - b)(9) is [tex]36(a - b)^2[/tex].
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Question: Which expression is equivalent to (4) (a-b)(a-b)(9)?
Find the sum of the first 9 terms of the following series, to the nearest integer.
3, 15/4 , 75/16
The sum of the first 9 terms of the series is approximately
11
How to find the sum of the first 9 termsGiven data
3, 15/4, 75/16, ...
To find the sum of the first 9 terms of the series, we'll need to find a pattern and then use the formula for the sum of a geometric series. The series you provided seems to be a geometric series with a common ratio of 5/4.
The first term (a₁) is 3, and the common ratio (r) is 5/4.
The formula for the sum of a geometric series is given by:
Sum = a₁ * (1 - rⁿ) / (1 - r),
where n is the number of terms.
Plugging in the values, we have:
Sum = 3 * (1 - (5/4)⁹) / (1 - 5/4).
Sum ≈ 3 * (1 - 1.953125) / (1 - 1.25)
≈ 3 * (-0.953125) / (-0.25)
≈ 3 * 3.8125
≈ 11.4375.
Rounding to the nearest integer = 11
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A state offers specialty license plates that contain 3 letters followed by 2 numbers. License plates are assigned randomly. All license plates are equally likely. Find the number of possible license plates that can be issued using this system.
The number of possible license plates that can be issued using this system is 17,576,000.
To find the number of possible license plates that can be issued using this system, we need to determine the number of options for each character in the license plate.
For the first character, there are 26 letters in the English alphabet, so we have 26 options.
Similarly, for the second and third characters, we also have 26 options each.
For the fourth character, there are 10 possible numbers (0-9).
And for the fifth character, there are again 10 possible numbers.
To find the total number of possible license plates, we need to multiply the number of options for each character together.
Number of possible license plates = Number of options for the first character * Number of options for the second character * Number of options for the third character * Number of options for the fourth character * Number of options for the fifth character
Number of possible license plates = 26 * 26 * 26 * 10 * 10
Calculating this expression gives us:
Number of possible license plates = 17,576,000
Therefore, the number of possible license plates that can be issued using this system is 17,576,000.
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40 identical machines in a factory pack 140 crates of apples per day between them. a) Write the ratio of the number of machines to the number of crates packed per day in the form 1: n. b) How many crates of apples would 70 of these machines pack per day? Give any decimals in your answers to 1 d.p.
a) The simplified ratio is 2:7.
b) 70 machines would pack approximately 245 crates of apples per day.
a) The ratio of the number of machines to the number of crates packed per day can be calculated by dividing the number of machines by the number of crates packed. In this case, there are 40 machines packing 140 crates per day. Thus, the ratio can be expressed as:
40:140
However, we can simplify this ratio by dividing both numbers by their greatest common divisor, which is 20:
40 ÷ 20 : 140 ÷ 20
2:7
So, the simplified ratio is 2:7.
b) If 40 machines pack 140 crates per day, we can use this information to determine how many crates 70 machines would pack. We can set up a proportion to solve for the unknown value:
40 machines / 140 crates = 70 machines / x crates
To solve for x, we can cross-multiply:
40 * x = 140 * 70
Dividing both sides by 40:
x = (140 * 70) / 40
x ≈ 245 crates
Therefore, 70 machines would pack approximately 245 crates of apples per day.
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MNPQ ~ RSTU. What are the values of c,y and z. Please show work too.
Answer:
x = 15 , y = 9 , z = 115°
Step-by-step explanation:
since the figures are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{NP}{ST}[/tex] = [tex]\frac{MN}{RS}[/tex] ( substitute values )
[tex]\frac{x}{25}[/tex] = [tex]\frac{18}{30}[/tex] ( cross- multiply )
30x = 450 ( divide both sides by 30 )
x = 15
and
[tex]\frac{TU}{PQ}[/tex] = [tex]\frac{MN}{RS}[/tex] ( substitute values )
[tex]\frac{y}{15}[/tex] = [tex]\frac{18}{30}[/tex] ( cross- multiply )
30y = 270 ( divide both sides by 30 )
y = 9
the corresponding angles in similar figures are congruent , so
∠ M = ∠ R , that is
z = 115°
COMPLETION
33%
Write down the percentage multiplier to decrease a quantity by 30.5%.
multiplier =
Submit Answer
The percentage multiplier x is given by:x = new quantity / original quantityWe can substitute the value of new quantity from the above equation to get:x = (original quantity * 0.695) / original quantitySimplifying the above expression, we get:x = 0.695Therefore, the percentage multiplier to decrease a quantity by 30.5% is 0.695 or 69.5%.
To decrease a quantity by 30.5%, we need to find the percentage multiplier. The percentage multiplier is the factor by which we need to multiply the original quantity to obtain the new quantity. Let x be the percentage multiplier. Then we have:original quantity * (1 - 30.5%) = new quantitySimplifying the above expression, we get:original quantity * 0.695 = new quantity.
We can check this answer by multiplying any quantity by 0.695 and then by (1 - 30.5%) and see if we get the same result. For example, if we start with 100, then:100 * 0.695 = 69.5 and 100 * (1 - 30.5%) = 69.5. Therefore, the answer is verified.
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What is an equivalent to b(little 3) x (b(little 3)?
Answer:
[tex] b^6 [/tex]
Step-by-step explanation:
To multiply powers with the same base, add the exponents.
[tex] b^3 \times b^3 = b^{3 + 3} = b^6 [/tex]
Evaluate the following improper integral. If the integral diverges, enter "DIV".
[₁
IH
Te dx=
Answer:
[tex]2e^{-1}}[/tex]
Step-by-step explanation:
Evaluate the given improper integral.
[tex]\int\limits^{ \infty}_{1} {xe^{-x}} \, dx\\\\\\\hrule[/tex]
Using integration by parts.
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Integration by Parts}}\\\\uv-\int vdu\end{array}\right}[/tex]
Letting...
u = x => du = dx
dv = e^{-x} dx => v = -e^{-x}
[tex]\int\limits^{ \infty}_{1} {xe^{-x}} \, dx\\\\\\\\\Longrightarrow (x)(-e^{-x})-\int\limits^{ \infty}_{1} {-e^{-x}} \, dx\\\\\\\\\Longrightarrow -xe^{-x}\Big|\limits^{ \infty}_{1}+\int\limits^{ \infty}_{1} {e^{-x}} \, dx\\\\\\\\\Longrightarrow \Big[ -xe^{-x}-e^{-x}\Big]\limits^{ \infty}_{1}\\\\ \\\\\Longrightarrow \Big[ -(\infty)e^{-\infty}-e^{-\infty}\Big]-\Big[ -(1)e^{-(1)}-e^{-(1)}\Big]\\\\\\ \\\Longrightarrow \Big[-0-0\Big]-\Big[ -e^{-1}-e^{-1}\Big][/tex]
[tex]\Longrightarrow e^{-1}+e^{-1}\\\\\\\\\therefore \int\limits^{ \infty}_{1} {xe^{-x}} \, dx =\boxed{2e^{-1}}[/tex]
Thus, the problem is solved.