A basis {p(x),q(x)} for the vector space {f(x) € P3[x] | f'(1) = f(1)} where P3[x] is the vector space of polynomials in with degree less than 3. p(x) = ,q(x) = is {p(x) = x² - 1, q(x) = x² + x - 2}
Polynomial Space Basis SearchThe vector space {f(x) € P3[x] | f'(1) = f(1)} consists of polynomials of degree less than 3 with the property that their derivative at x = 1 is equal to the polynomial itself evaluated at x = 1. To find a basis for this space, we can start by finding a set of two polynomials that satisfy this property, and that are linearly independent.
One possible choice for p(x) is x² - 1, and one possible choice for q(x) is x² + x - 2. These polynomials satisfy the required property (i.e., their derivatives at x=1 are equal to the polynomials themselves evaluated at x=1), and they are linearly independent because their leading terms (x² in both cases) are distinct.
Thus, {p(x) = x² - 1, q(x) = x² + x - 2} is a basis for the vector space {f(x) € P3[x] | f'(1) = f(1)}.
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Let X be a random variable whose distribution is Normal, with a mean of 100 and a standard deviation of 10. The proportion of observations above 115 is equal to the proportion below what value? Use the fact that the normal distribution is symmetric about the mean.
The value for which the proportion of observations below it is equal to the proportion of observations above 115 is 85.
The normal distribution, also known as the Gaussian distribution or the bell curve, is a continuous probability distribution that describes the distribution of many real-world phenomena such as height, weight, IQ scores, and financial returns. It is a symmetric distribution with a bell-shaped curve that is centered on the mean and characterized by its mean and standard deviation.
Since the normal distribution is symmetric about the mean, the proportion of observations above 115 is equal to the proportion of observations below 100 - (115 - 100) = 85.
So, the value for which the proportion of observations below it is equal to the proportion of observations above 115 is 85.
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At a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is 44
The probability of not ordering nonalcoholic beverages is 66.
What is the probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favourable outcomes / Number of samples
Given that at a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is 44%.
The probability of not ordering the beverages will be:-
P = 100% - 44%
P = 66%
Therefore, the probability of not ordering nonalcoholic beverages is 66.
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Find: (6m^5+3-m^3-4m)-(-m^5+2m^3-4m+6)
The simplification of the algebraic expression results in 7m^5 - 3m^3 - 3.
What are algebraic expressions?Algebraic expressions are mathematical expressions that consist of integers, variables, and arithmetic operations. To simplify algebraic expressions, some mathematical properties are being used such as distributive property in opening the brackets and additional property in adding like terms together.
Given that:
= (6m^5+3-m^3-4m)-(-m^5+2m^3-4m+6)
Apply distributive property
= 6m^5 + m^5 - m^3 -2m^3 - 4m + 4m + 3 - 6
Add like terms
= 7m^5 - 3m^3 - 3
Therefore, we can conclude that the simplification of the algebraic expression results in 7m^5 - 3m^3 - 3.
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I NEED THE ANSWER ASAP
You then need to write an equation of a line using slope-intercept format goes through the point (4,2) and is parallel to y = 1/2x - 3
An equation of a line using slope-intercept format goes through the point (4, 2) and is parallel to y = 1/2x - 3 is y = x/2.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y represents the data points.From the information provided above, we have the following slope and data points on the line:
Points = (4, 2).Slope, m = 1/2.In Geometry, two (2) lines are parallel under the following conditions:
m₁ = m₂ ⇒ 1/2 = 1/2
At data point (4, 2), a linear equation of this line can be calculated in point-slope form as follows:
y - 2 = 1/2(x - 4)
y - 2 = x/2 - 2
y = x/2 - 2 + 2
y = x/2
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15.0782 to one decimal place
Answer:
15.1
Step-by-step explanation:
15.0782 is between 15.0 and 15.1. It is closer to 15.1
An ice cream factory makes 150 quarts of ice cream in 5 hours how many quarts could be made in 36 hours what’s was the rate per day
1080 quarts can be made in 36 hours.
The rate per day is 30 quarts.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
150 quarts of icecream = 5 hours
This can be written as,
5 hours = 150 quarts
Divide both sides by 5.
1 hour = 30 quarts
Multiplying 36 on both sides.
36 hours = 36 x 30 quarts
36 hours = 1080 quarts
Thus,
1080 quarts can be made in 36 hours.
30 quarts per day.
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In an orchestra, the ratio of trombones to violas is 1 to 3.
Answer:
3 trombones
Step-by-step explanation:
9 divided by three is 3.
For the following exercises, find the measure of the angle between the three-dimensional vectors a and b. Express the answer in radians rounded to two decimal places, if it is not possible to express it exactly 135. a = (3. -1,2), b = (1,-1,-2) 136. a = (0,-1, -3), b = (2,3,-1)
The angle between the 3D vectors a = (3, -1, 2) and b = (1, -1, -2) is 2.23 radians. The angle between a = (0, -1, -3) and b = (2, 3, -1) is 2.43 radians.
The angle between two vectors a and b in three-dimensional space can be found using the dot product formula:
cos(θ) = (a * b) / (||a|| * ||b||)
Where ||a|| and ||b|| represent the magnitude (length) of vectors a and b, respectively, and "*" represents the dot product of the two vectors. The dot product is given by:
a * b = a1 * b1 + a2 * b2 + a3 * b3
Where a1, a2, and a3 are the components of vector a, and b1, b2, and b3 are the components of vector b. The angle θ is then calculated using the inverse cosine function:
θ = arccos(cos(θ))
Finally, the angle θ is expressed in radians.
For the first problem, we have:
a = (3, -1, 2)
b = (1, -1, -2)
So, we have:
a * b = 3 * 1 + (-1) * (-1) + 2 * (-2) = 3 - 1 - 4 = -2
||a|| = [tex]\sqrt{(3^2 + (-1)^2 + 2^2)} = \sqrt{(14)}[/tex]
||b|| = [tex]\sqrt{(1^2 + (-1)^2 + (-2)^2) }= \sqrt{(6)}[/tex]
cos(θ) = [tex](-2) / (\sqrt{(14)} * \sqrt{(6)} ) = -\sqrt{(2)} / \sqrt{(21)[/tex]
θ = arccos[tex](-\sqrt{(2)} / \sqrt{(21)})[/tex] = 2.23 radians (rounded to two decimal places)
For the second problem, we have:
a = (0, -1, -3)
b = (2, 3, -1)
So, we have:
a * b = 0 * 2 + (-1) * 3 + (-3) * (-1) = -3
||a|| = [tex]\sqrt{(0^2 + (-1)^2 + (-3)^2)} = \sqrt{(10)}[/tex]
||b|| = [tex]\sqrt{(2^2 + 3^2 + (-1)^2)} = \sqrt{(14)}[/tex]
cos(θ) = [tex]-3 / (\sqrt{(10)} * \sqrt{(14)}) = -3 / \sqrt{(140)}[/tex]
θ = arccos[tex](-3 / \sqrt{(140)})[/tex] = 2.43 radians (rounded to two decimal places)
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PLEASE HELP MY HW IS LATE
The following information can be extracted from the system of triangles ABC and DEF:
Case A: 3 / 5 = y / z
Case D: m ∠ C = m ∠ F
Case E: Δ ABC ~ Δ DEF
How to interpret a system of two similar triangles
In this problem we find a representation of a system with two similar triangles, that is, two triangles with two congruent internal angles and proportional sides. Then, the following relationships are derived below:
m ∠ A = m ∠ D
m ∠ B = m ∠ E
m ∠ C = m ∠ F
AB / DE = BC / EF = AC / DF
6 / 10 = y / z = x / w
3 / 5 = y / z = x / w
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Explain how to rewrite the function shown in order to determine the transformation of the parent function. Then, describe the transformation of the graph compared to the parent function. y=3sqaure root-8x-4
The parent function of the function f(x) = 3√(-8x - 4) will be h(x) = √x.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The function is given below.
f(x) = 3√(-8x - 4)
Simplify the function, then we have
f(x) = 3√(-8x - 4)
f(x) = 6√- (2x + 1)
Divide the equation by 6, then we have
g(x) = √(-2x - 1)
Replace -(2x + 1) with x, then we have
h(x) = √x
The parent function of the function f(x) = 3√(-8x - 4) will be h(x) = √x.
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Answer:
Rewrite the equation by factoring –8 from the radicand and taking the cube root to get –2 in front of the radical symbol.
The graph is reflected over the x-axis.
The graph is also reflected over the y-axis.
The graph is vertically stretched by a factor of 2.
The graph is translated ½ unit to the left.
Step-by-step explanation: All possible answers for edge
the ratio in the simplest form 3:9
Answer:
1:3
Step-by-step explanation:
the greatest common factor is 3 so to simplify divide both sides by 3.
the number of faculty for a variety of private colleges that offer only bachelor's degrees is listed below. 285 125 120 128 135 138 155 226 389 116 154 310 204 206 162 165 135 77 248 225 264 318 176 221 210 93 176 276 What is the class width for a frequency distribution with 9 classes? The class width is_____
The class width for a frequency distribution with 9 classes is 35.
What is range of the data?The difference between the highest and lowest values for a given data collection is the range in statistics. In statistics, we must put the given values, set of data, or set of observations in ascending order in order to determine the range. That indicates that you should start by writing the observations from lowest to highest value. The formula must now be used to determine the range of observations.
The range of the data is given as:
Range = highest value - lowest value
Range = 389 - 77
Range = 312
The class width for a frequency distribution with 9 classes is:
Class width = 312 / 9 = approx. 35.
Hence, the class width for a frequency distribution with 9 classes is 35.
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Solve for x
12 + x = 15
Answer: x = 3
Step-by-step explanation: just isolate the variable x
So subtract 12 on both sides of the equation and you are left with x is equal to 3
Hope this helped
How many hours do I need to work to make 35$
How many hours do I need to work to make $94
How many hours do I need to work to make $540
Explain:
Step-by-step explanation:
Is some of the problem missing? impossible to answer unless we know how much they make an hour
GDrag expressions and value to represent the situation and the unknown in the diagram
Expressions using words: 2/5 as the sum of 4 and 8.
Expression with using numbers: 2/5 x(8+4)
Value = 12 2/5.
What is Fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
First, the Expressions using words
2/5 of the product of 8 and 4.
4 times as mush as 2/5 of 8.
2/5 as the sum of 4 and 8.
Now, Expression with using numbers
2/5 + (8+4)
2/5 x (8 x 4)
4 x (2/5 x 8)
2/5 x(8+4)
Values are: 2 2/5, 4 2/5, 32 2/5, 12 2/5.
Now, the Answers is
Expressions using words: 2/5 as the sum of 4 and 8.
Expression with using numbers: 2/5 x(8+4)
Value = 12 2/5.
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ana opened a bank account with $1000 that earns interest, compounded continuously, at an annual rate of r
After 1 year of time period, Ana would have $1051.7 in her account, including interest.
Ana opened a bank account with $1000 that earns interest, compounded continuously, at an annual rate of r. To calculate the amount of money in the account after t years, we can use the formula:
[tex]A = P * e^{(rt)}[/tex]
where A is the amount in the account after t years, P is the initial deposit (in this case, $1000), r is the annual interest rate, and e is the mathematical constant approximately equal to 2.718.
For example, if the interest rate is 5% (r = 0.05), after 1 year, the amount in the account would be:
[tex]A = \$1000 * e^{(0.05 * 1)} = \$1000 * 1.0517[/tex]
[tex]A = \$1051.7[/tex]
So, after 1 year, Ana would have $1051.7 in her account, including interest. The higher the interest rate and the longer the time period, the more money Ana would have in her account due to the compounding effect.
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In 1903, Crayola's very first box of crayons had 8 colors. Today there are 120 Crayola crayon colors to choose from. find the percent change.
Answer:
Step-by-step explanation:
To find the percent change, we can use the formula:
percent change = (final value - initial value) / initial value * 100
In this case, the initial value is 8 and the final value is 120. Plugging in the values, we get:
percent change = (120 - 8) / 8 * 100 = 1,400%
So, the percent change in the number of Crayola crayon colors is 1,400%. This represents a significant increase from the initial 8 colors in 1903.
find the value of x and please show process!
The cost of tuition at a state college is $8,500 and is increasing by 3% each year. what is the cost of the tuition after 6 years?
Answer: $51,000
Step-by-step explanation:
At first, I multiplied 8,500 times 3 then the outcome I got was 25,500 so now I'm going to try multiplying 8,500 times 6 which equals 51,000 but I'm sorry if I got the answer wrong
The angles in a straight line are X degree, 3x degree and 6x degree. find the measure of each angle.
Answer:
"18", "54", and "108"
Step-by-step explanation:
Angles:A straight line has an angle of 180 degrees. It can be seen as "half a circle", which has an angle of... 360 degrees, and since it's half, it's just 180 degrees.
Now we're also given the angles that compose the straight line (x, 3x, and 6x), and by adding these angles together, we should get the angle of the straight line. So that means that: [tex]x+3x+6x=180[/tex]
Now from here we can just combine them all into one term:
[tex]10x=180[/tex]
Now divide both sides by 10:
[tex]x=18[/tex]
Our angles are equal to "x", "3x", "6x", and to calculate their value, we just plug in "18" as x giving us: "18", "3(18)", "6(18)" which simplifies to the angles: "18", "54", "108"
Problem 1:
The US Department of Energy conducts weekly surveys of approximately 900 gasoline stations to
determine the average price per gallon of regular gasoline in the U.S. On December 29, 2003, the average price was $1.478 per gallon.
a. Identify the population.
b. Identify the sample.
c. Identify the parameter.
d. What is the statistic?
e. If the 900 gasoline stations were randomly selected from the gasoline stations in Minnesota.
Is this a good sample? Explain.
The population is 900 gasoline stations. The sample is 800. The parameter is price of gasoline. The statistics is for 900 stations and not all stations.
What is average?The ratio of the sum of the values in a particular set to all the values in the set is the mean value, which is the definition of the average. The average formula has numerous practical uses. If we were asked to determine the average male height in India or the average age of the men and women in a group, we would add up all the data and divide it by the total number of data points.
The population is 900 gasoline stations.
The sample is 800.
The parameter is price of gasoline.
The statistics is for 900 stations and not all stations.
The sample selected is a good sample as it covers most of the gas stations.
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A student takes ten exams during a semester and receives the following grades: 90, 85, 97, 76, 89, 58, 82, 102, 70, and
67. Find the five-number summary used in a boxplot. Which boxplot best represents the data?
+
a.
b.
C.
d.
++++
50 55 60 65 70 75 80 85 90 95 100 105
+4
+ +
+
+++
50 55 60 65 70 75 80 85 90 95 100 105
4
4++
50 55 60 65 70 75 80 85 90 95 100 105
◆
50 55 60 65 70 75 80 85 90 95 100 105
Quadrile 1: 70 Quartile 3: 90 Median: 83.5 Lowest: 58 The average of the five summaries is maximum: 102.
what is mean ?The mean of even a dataset, often described as the mean and median, is the sum including all values divided by the overall number of values (as opposed to the geometric mean). This represents the most often used indicator of central tendency and is constantly referred to as the "mean." This is obtained by dividing the number of values contained within the dataset by the sum of all the values. Calculations can be conducted using either raw data or data that has been integrated into frequency tables. A number's average is called to as its average. Simple statistics can be used to determine: After adding up all the digits, divide by the number of digits total. the sum divided by the number.
given
The first quartile, median, third quartile, and maximum are the five summaries that make up the distribution of the ordered observation.
Five-number formula overview
Minimum: The first piece of the set
(n+1)/4 is the first quartile.
Average: (n+1)/2
Quartile three: 3(n+1)/4
Maximum: The set's final component
The five-digit grade summary (90, 85, 97, 76, 89, 58, 82, 102, 70, 67)
58 minimum
70 in the top quartile
Average: 83.5
90th percentile:
The most: 102
Quadrile 1: 70 Quartile 3: 90 Median: 83.5 Lowest: 58 The average of the five summaries is maximum: 102.
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SOMEONE HELPPPPP MEEEEEE PLEASE
Answer:
a.) (1,4), (-2,3), (0,4)
b.) (4,1), (3,-2), (4,0)
Step-by-step explanation:
a. When we want to find the reflection over the Y axis, that means the X coordinate signs reflect. For A, it says (-1,4). To reflect it, we reflect the X coordinate, so now it's (1,4) instead. You'll do that to the other two.
b. When rotating, you would switch the numbers of the coordinates and switch the sign of X. For the first one (-1,4), we'll switch it to (1,4). Not we'll switch the numbers around to make it (4,1). You'll do that for the other two
Parallelogram EFGH has vertices E(1, 3), F(3, 5), and G(4, 2). What are the coordinates of point H?
The coordinates of the point H of the parallelogram is H ( 2 , 0 )
What is a Parallelogram?A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure
The four types are parallelograms, squares, rectangles, and rhombuses
Properties of Parallelogram
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent.
Same-Side interior angles (consecutive angles) are supplementary
Each diagonal of a parallelogram separates it into two congruent triangles
The diagonals of a parallelogram bisect each other
Given data ,
Let the parallelogram be represented as EFGH
Now , the coordinates of the parallelogram is given by
Substituting the values in the equation , we get
The coordinate of E = E ( 1 , 3 )
The coordinate of F = F ( 3 , 5 )
The coordinate of G = G ( 4 , 2 )
The coordinate of H = H ( x , y )
Now , the difference in the x coordinates of F and G = ( 4 - 3 ) = 1
The difference in the y coordinates of F and G = ( 2 - 5 ) = -3
So , the coordinates of the point H = x coordinate of E + 1 and y coordinate of E - 3
On simplifying the equation , we get
The coordinate of H = H ( 2 , 0 )
Hence , the coordinates of the parallelogram is H ( 2 , 0 )
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FIND MULTIPLICITY AND ZEROS OF THE GRAPH!
Answer: The Zeros Are(in order) -3,-2,-1,1, 1.5 ALL have a multiplicity of 1.
Step-by-step explanation: Since the 0's cross the graph and don't "bounce" on the x-axis, they're all for a multiplicity of 1.
Find the value of x of the triangle below
Angles in a triangle add to 180 degrees
make a little equation for that
58 + 42 + x = 180
simplify
100 + x = 180
x = 180 - 100
x = 80
Hope this helps,
- Jeron :- )
if you can run 1 1/2 miles in 15 minutes how long would it take to run 1 mile
Answer:
Step-by-step explanation:
How many adults binge drink four times per month?
A. 1 in 10
B. 1 in 6
C. 1 in 4
D. 1 in 8
Answer:
C.
Step-by-step explanation:
Its more likely to happen
what is the equation of a line with a y-intercept of -3 and a slope of -4/5
Answer:
Below
Step-by-step explanation:
y= mx + b is the slope intercept form of a line
m = slope and b = y-axis intercept
Plug in the given values
y = -4/5 x -3
You are a loan officer at the West Elm Savings and Loan. Mr. and Mrs. Brady are in your office to apply for a mortgage loan on a house they want to buy. The house has a market value of $180,000. Your bank requires 1/5
The amount of the down payment for the house, given the market value and the amount your bank requires is $ 36, 000
How to find the down payment ?The bank that you work for requires that for mortgage loans, the applicants ( in this case Mr. and Mrs. Brady) , should be able to pay 1 / 5 of the market value of the property as down payment.
The down payment is therefore :
= Market value of house x Requirement of bank
= 180, 000 x 1 / 5
= 180, 000 / 5
= $ 36, 000
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The rest of the question is:
Your bank requires 1/5 of the market value as a down payment.
What is the amount (in $) of the down payment?