Polynomials p(x) and q(x) can be written as linear combinations of {1, x, [tex]x^2[/tex], 1 - [tex]x^3[/tex]}, we conclude that p(x) and q(x) are in the span of β.
We need to determine if there exist constants a, b, c, and d such that
p(x) = a(1) + b(x) + c([tex]x^2[/tex]) + d(1 - [tex]x^3[/tex])
q(x) = a(1) + b(x) + c([tex]x^2[/tex]) + d(1 - [tex]x^3[/tex])
Substituting p(x) into the equation, we have
3 - [tex]x^2[/tex] - 2[tex]x^3[/tex] = a(1) + b(x) + c([tex]x^2[/tex]) + d(1 - [tex]x^3[/tex])
Grouping the coefficients of the same powers of x, we get
3 = d
0 = b - d
-1 = c - d
-2 = -d
Hence, d = -3, b = -3, c = -2, and a = 6
Therefore,
p(x) = 6(1) - 3(x) - 2([tex]x^2[/tex]) - 3(1 -[tex]x^3[/tex])
Now, substituting q(x) into the equation, we get
3x^3 = a(1) + b(x) + c([tex]x^2[/tex]) + d(1 - [tex]x^3[/tex])
Grouping the coefficients of the same powers of x, we get
0 = d
0 = b
0 = c
3 = a
Therefore,
q(x) = 3(1 - [tex]x^3[/tex])
Since p(x) and q(x) can be written as linear combinations of {1, x, [tex]x^2[/tex], 1 - [tex]x^2[/tex]}, we conclude that p(x) and q(x) are in the span of β.
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To determine if a vector field is conservative, we need to check if it satisfies the following condition:
∇ x F = 0
where F is the vector field and ∇ x F is the curl of F.
Let's calculate the curl of the given vector field F:
∇ x F =
| i j k |
| ∂/∂x ∂/∂y ∂/∂z |
| 0 ez*7 xe^z |
= (7 - 0) i - (0 - 0) j + (xe^z - 7e^z) k
= (7 - 0) i + (xe^z - 7e^z) k
Since the curl of F is not equal to zero, the vector field is not conservative.
Therefore, there does not exist a function f such that F = ∇f, and we enter "dne" as the answer.
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Sketch the curve y = \sqrt{x+3} .
Find the area bounded by the curve, X-axis and Y-axis.
I get the first part but not the second part.
The area bounded by the curve, x-axis and y-axis of the function y = √(x + 3) is 2√3
How to determine the area bounded by the curve, x-axis and y-axis?The curve is given as:
y = √(x + 3)
The area bounded by the curve, x-axis and y-axis is when x = 0 and y = 0
When y = 0, we have:
0 = √(x + 3)
This gives
x = -3
So, we set up the following integral
A = ∫ f(x) d(x) (Interval a to b)
This gives
A = ∫ √(x + 3) d(x) (Interval -3 to 0)
When the above is integrated, we have:
A = 1/3 * [2(x + 3)^(3/2)] (Interval -3 to 0)
Expand
A = 1/3 * [2(0 + 3)^3/2 - 2(-3 + 3)^3/2]
This gives
A = 1/3 * 2(3)^3/2
Apply the law of indices
A = 2(3)^1/2
Rewrite as:
A = 2√3 or 3.46
Hence, the area bounded by the curve, x-axis and y-axis of the function y = √(x + 3) is 2√3
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Can someone please help
Solving the given equation, the value of v that makes the statement true is:
A. v = 8.
What is the given equation?The equation is:
[tex]12 = 12 + \frac{v - 8}{2}[/tex]
Hence:
[tex]\frac{v - 8}{2} = 0[/tex]
Applying cross multiplication:
v - 8 = 0
v = 8.
Hence option A is correct.
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In a recent poll, 230 people were asked if they liked dogs, and 90% said they did. Find the margin of error of this poll, at the 99% confidence level.
The margin of error of this poll is
Given that 230 people were asked if they liked dogs, and 90% said they did.
In a random sample, a margin of error is a statistical measure that takes into account the discrepancy between actual and expected results.
Sample size (N)=230
Sample proportion [tex](\hat{p})[/tex] = 90% = 0.90 and
confidence interval = 99%
The critical value at 99% confidence interval with α=0.01 is
[tex]\begin{aligned}Z_{c}&=Z_{1-\frac{\alpha}{2}}\\ &=Z_{1-\frac{0.01}{2}}\\ &=Z_{0.995}\\ &=2.576\end[/tex]
This value is taken from the Standard normal distribution table.
Now, we will calculate the margin of error (E) by using the formula
[tex]E=Z_{c}\sqrt{\frac{\hat{p}(1-\hat{p})}{N}}[/tex]
Substituting the values in the formula, we get
[tex]\begin{aligned}E &=2.576\times \sqrt{\frac{0.90(1-0.90)}{230}}\\ &=2.576\times \sqrt{\frac{0.09}{230}}\\ &=2.576\times\sqrt{0.00039}\\ &=2.576\times 0.0197\\ &=0.0507\end[/tex]
Hence, the margin of error when 230 people were asked if they liked dogs, and 90% said they did is 0.0507.
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Which expression could help you find the distance between –1 and 3 on the number line?
Answer:
|-1| + |3|
Step-by-step explanation:
We can use absolute values to find the distance between positive and negative numbers on a number line.
|-1| + |3| =
Keep in mind that
- the absolute value of a positive number is positive and
- the absolute value of a negative number is positive
1 + 3 =
4 units
How much does a $5.40 lunch cost if it is discounted by 10%
Answer:
$4.86
Step-by-step explanation:
Original price: $5.40
Discount: 10%
Discount amount:
10% of $5.40 = 0.1 × $5.40 = $0.54
Discounted price:
$5.40 - $0.54 = $4.86
Answer:
$4.86
Step-by-step explanation:
There are two approaches to this problem.
1:
You can multiply the original value by 10% and subtract it from the original value. In this case, $5.40-(5.40×10%). This becomes $5.40-$0.54. This is $4.86.
2:
You can simply multiply the original value by 90%. In this case, $5.40×90%. This also becomes $4.86.
There were 50,000 bacteria in a petri dish yesterday at noon, and 40,000 bacteria at noon today. if the trend continues, on what day at noon can you expect to find less than 5,000 bacteria?
Answer:
900
Step-by-step explanation:
A zoologist researched the feeding habits of lemurs. she collected data by studying the lemurs in a zoo exhibit for a one-month period and drew conclusions based on her data. what kind of statistical study did the zoologist conduct?
The kind of statistical study the zoologist conducted was D. observational study.
What is observational study in research?An observational study serves as a study whereby the researcher simply observes the subjects without interfering with it.
This is different from carrying out experiment on them or just a theoretical approach.
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CHECK THE COMPLETE QUESTION BELOW:
A zoologist researched the feeding habits of lemurs. She collected data by studying the lemurs in a zoo exhibit for a one-month period and drew conclusions based on her data. What kind of statistical study did the zoologist conduct? A. survey B. theoretical study C. experiment D. observational study
solve this pls>>>>>>>there’s a pic
Answer:
x = 5, 1
Step-by-step explanation:
To solve for x, you must factor the equation. The factored equation will be: (x - 1) (x - 5) = 0. After factoring, isolate the two factored equations: (x - 1) = 0 and (x - 5) = 0. Then solve for x for both the equations which should get you to x = 5, 1.
PLEASE HELP NOW
Which formula can be used to find the volume of the cylinder? Check all that apply. A = ( d )( h ) V = B( h ) V = ( l )( w )( h ) V = 2( r )( h ) V = (pi) (r squared) (h)
Answer:
V= (pi) (r squared) (h)
Step-by-step explanation:
This is confusing me please someone help
Answer:
The distance from the plane to the observer tower is 7.7 kmStep-by-step explanation:
We are given two sides and one angle opposite to one of the known sides.
In order to find the missing side we need to use the law of sines.
Step 1Find the angle opposite to the second known side, let it be x.
sin 68°/7.5 = sin x /5.2sin x = 5.2 sin 68°/7.5sin x = 0.64 (rounded)x = arcsin 0.64x = 39.8°Step 2Find the missing third angle y, using angle sum theorem:
68° + 39.8° + y = 180°107.8° + y = 180°y = 180° - 107.8°y = 72.2°Step 3Find the required side length z, the distance from the plane to the observer tower, using the law of sines again.
Note. At this point you can use the law of cosines as we have found the angle between the known sides.
sin 68°/7.5 = sin 72.2°/zz = 7.5 sin 72.2°/sin 68°z = 7.7 km (rounded)
So the required distance is 7.7 km
which unit of measure would be appropriate for the volume of a sphere with aradius of 2 meters?
Answer:
The unit of measuring volume of the sphere is cubic meters.
From Andys house to Billys hometown you can travel by 3 roads. And to get from Billys hometown to Willies's house you can travel by 5 roads. How many possible wats are there to travel from andys house to willies house?
Using the Fundamental Counting Theorem, there are 15 ways to travel from Andy's house to Willie's house.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For this problem, the parameters are:
[tex]n_1 = 3, n_2 = 5[/tex].
Hence the number of ways is:
N = 3 x 5 = 15.
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Tara has 4 and 4 over 5 feet of rope.
part a: how many 2 over 5 foot pieces can tara cut from the 4 and 4 over 5 feet of rope? show your work. (5 points)
part b: using the information in part a, interpret the meaning of the quotient in terms of the two fractions given. (5 points)
the answer box is a writing thing so might have to explain it differently
Part A - Tara cuts [tex]12[/tex] pieces of [tex]2/5[/tex] from [tex]4\frac{4}{5}[/tex] feet of rope.
Part B - The quotient means the amount of foot pieces so it is [tex]12[/tex] foot pieces.
How can we find the foot pieces of [tex]2/5[/tex] from [tex]4\frac{4}{5}[/tex] rope. ?
from part A
we solve the fraction
[tex]4\frac{4}{5} =24/5[/tex] rope
And Tara needs to pieces of [tex]2/5[/tex] foot
So we need to divide
[tex]\frac{24/5}{2/5} \\=\frac{24}{5} *\frac{5}{2} \\=\frac{24}{2} \\=12[/tex]
For part B
When we using the information from part A we decide that the quotient means the amount of foot pieces Tara can cut from the [tex]4\frac{4}{5}[/tex] feet of rope.
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Meg plotted the graph below to show the relationship between the temperature of her city and the number of sweaters sold at a store:
Part A: In your own words, describe the relationship between the temperature of the city and the sale of sweaters in the city. (5 points)
Part B: Describe how you can make the line of best fit. Write the approximate slope and y-intercept of the line of best fit. Show your work, including the points that you use to calculate slope and y-intercept. (5 points)
PLEASE HELP WITH PART B ASAP
The explanation about the graph is illustrated below.
How to illustrate the graph?The graph shows 0 to 30 on the x-axis at increments of 5 and 0 to 12 on the y-axis at increments of 1. The label on the x-axis is Temperature in degrees C, and the label on the y axis is the Number of Sweaters Sold.
If you will draw lines through, (12.5,6) and (15,4), it will best represent a line of best fit, because most of the points on the same and opposite sides of line are equidistant from each other.
Equation of line passing through (12.5,6) and (15,4) A line of best is the line that passes through all or some points or only through a single point, which describes the relationship between x and y values of data set
4x + 5y = 80
5y = -4x + 80.
y = -4x/5 + 16
Slope = -4/5 and y intercept is 16.
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solve each equation round to the nearest ten-thousandth in (x+21)=7
The solution to the equation (x+21)=7 is x = -14
How to solve the equation?The equation is given as:
(x+21)=7
Remove the brackets
x + 21 = 7
Subtract 21 from both sides
x + 21 - 21 = 7 - 21
Evaluate the expression
x = -14
Hence, the solution to the equation (x+21)=7 is x = -14
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Calculate the mean and standard deviation for the average yards rushed by
each player. Then graph the data (use the mean for each player and SD for error bars).
Compare and contrast the mean rushing yards Dillon and Corey.
What does the SD indicate about the mean rushing yards for each player?
Question:
A sample of cans of peaches was taken from a warehouse, and the content of each can mearsed for weight. the sample means was 486g with stand deviation 6g. state the weight percentage of cans with weight:
Draw normal curve to help - split into 8 section ( i can't draw it here)
a) 34.13% of cans will be between 480g and 486g.
b) 13.59 + 2.15 + 0.13= 15.87% of cans greater than 492g.
Look at the Stand Dev Graph where the give you the number
Step-by-step explanation:
Let me give you a different question and i will answer it, which you help you answer your question.
One student can paint a wall in 12 minutes. Another student can paint the same wall in 24minutes. Working together, how long will it take for them to paint the wall?
Answer:
8 minutes.
Step-by-step explanation:
We work in fractions of the wall they can paint in 1 minute, so
1/12 + 1/24 = 1/x where x is the time it takes when working together.
Multiplying through by 24x:
2x + 1x = 24
3x = 24
x = 8 minutes.
4.10.1 checkup, answer questions about the unit circle
Using the unit circle, the correct answer regarding the comparison of angles w and t is given by:
a. t > w.
What is the unit circle?For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].
From this, we get that the sine is represented by the vertical axis. As we advance into the second quadrant, as the angle increases, sine decreases. Hence, since sin w > sin t, we have that t > w and option a is correct.
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Solve this system of equations using the substitution method
y = 2x + 17
y = 6x - 3
Step-by-step explanation:
well, as you can witness both of the equations are equal to y, so you're free to reckon that they are equal as well
[tex]6x - 3 = 2x + 17 = = = > \\ 4x = 20 = = = > x = 5 \: and \: \\ y = 6(5) - 3= = = > y = 27[/tex]
Answer:
<3
Step-by-step explanation:
5, 27 is right on acellus
x=5
y=27
Use the drop-down menus to complete each equation so the statement about its solution is true. CLEAR CHECK No Solutions 3x 9 4x x
The complete equation so that the statement is true is 3x+9+4x+x= 8x + 1
How to complete the equation?The equation is given as:
3x+9+4x+x=
Represent the blank with y
So, we have:
3x + 9 + 4x + x = y
Evaluate the like terms
8x + 9 = y
For the equation to have no solution the value of y and 8x + 9 must not be equal.
Take for instance
y = 8x + 1
So, we have:
8x + 9 = 8x + 1
Subtract 8x from both sides
9 = 1
The above equation is false because 1 and 9 are not equal
Hence, the complete equation so that the statement is true is 3x+9+4x+x= 8x + 1
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Complete question
Use the drop-down menus to complete each equation so the statement about its solution is true.
No Solutions
3x+9+4x+x=
1.rani was selling flowers. each day she made 7 bouquets by arranging 8 roses and 6 marigolds in each bouquet. each bouquet was sold for rs.85. a) find the number of marigolds used in a day. b) find the total number of flowers used by using suitable property of whole numbers. c) if she sold 42 bouquets in a whole week, find the amount she earned. 2. by suitable rearrangement, find the value of a) 819 + 364 + 181 + 436 b) 20 x 348 x 50 3. using suitable property find the value of 492 x 13 + 492 x 37 4. a) name the property 86 + 65 = 65 + 83 b) the multiplicative identity of whole numbers is ______ 5. find the next two numbers in the pattern 1,1,2, 3,5,8, ______, ________
1.(a) The number of marigolds used in a day is 42.
(b) The total number of flowers used by using suitable property of whole numbers is 98.
(c) She earned Rs. 3570
2.(a) The value of [tex]819 + 364 + 181 + 436[/tex] is 1800.
(b) The value of [tex]20 \times 348 \times 50[/tex] is 348000.
3. The value of [tex]492 \times 13 + 492 \times 37[/tex] is 24600.
4.(a) Name the property 86 + 65 = 65 + 86 is commutative property.
(b) The multiplicative identity of whole numbers is 1.
5. The next two numbers in the pattern 1,1,2, 3,5,8 are 13 and 21.
1. (a) The number of marigolds used in a day is 42.
Rani made 7 bouquets on each day by arranging 8 roses and 6 marigolds in each bouquet. So number of marigolds used in a day is 7×6 = 42.
(b) The total number of flowers used by using suitable property of whole numbers is 98 flowers used by using distributive property.
What is distributive property of whole numbers?
The distributive property of multiplication states that when multiplying a number by the sum/difference of 2 numbers, the final value is equal to the sum/difference of each addend multiplied by the third number.
Distributive property = a×(b+c) = a×b+a×c
Total number of flowers = 7×(8+6) = 7×14 = 98.
(c) If she sold 42 bouquets in a whole week, find the amount she earned is rs.3570.
Each bouquet was sold for Rs.85. Then she earned a whole week off = 42×85 = rs.3570.
2. (a) By suitable rearrangement, the value of 819 + 364 + 181 + 436 is 1800.
Rearrangement of the given numbers = (819+181)+(364+436)
= 1000+800
= 1800
(b) By suitable rearrangement, the value of 20 x 348 x 50 is 348000.
Rearrangement of the given numbers = 348×(50×20)
= 348×1000
= 348000
3. Using suitable property find the value of 492 x 13 + 492 x 37 is 24600 by using distributive property.
By using distributive property = 492 x 13 + 492 x 37
= 492×(13+37)
= 492×50
= 24600
4. (a) Name the property 86 + 65 = 65 + 86 is commutative property.
What is commutative property?
This law simply states that with addition and multiplication of numbers, you can change the order of the numbers in the problem and it will not affect the answer.
By using commutative property, a+b = b+a
86 + 65 = 65 + 86
151 = 151
(b) The multiplicative identity of whole numbers is 1.
Multiplying a whole number by 1 equals that identical number, the whole number 1 is called the multiplicative identity.
5. The next two numbers in the pattern 1,1,2, 3,5,8,?,? are 13 and 21.
Just add the no before the given no then you will get the pattern. example first no=1 and no before it is 0
1+0=1
1+1=2
2+1=3
3+2=5
5+3=8
8+5=13
Hence, The next two numbers for the given series are 13 and 21.
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What is the nature of the solution set to the following system of equations?
4x + 3y = 2
3x − 2y = 10
The solution to the system of equations is one solution at (2, -2)
How to determine the solution set?The system of equations is given as:
4x + 3y = 2
3x − 2y = 10
Multiply (1) by 2 and (2) by 3.
So, we have:
8x + 6y = 4
9x − 6y = 30
Add both equations
17x = 34
Divide by 17
x = 2
Substitute x = 2 in 3x − 2y = 10
3(2) − 2y = 10
Solve for y
y = -2
Hence, the solution to the system of equations is one solution at (2, -2)
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Who am I ?
- My thousands digit is 4
- My hundreds digit is 4 less than the digit in the thousands place
- The sum of my tens digit and ones digit is 7
- My tens digit is 3 more than my ones digit
- The digits in the thousands period have a sum of 10
- My first digit is half the digit that immediately follows it.
I am the number_______________
I am the number 4052. It is rather confusing and i cannot promise that it is correct. Hope it helps : )
A worker at a shoe factory is required to box at least
8
pairs of shoes per minute, but is not allowed to box more than
12
pairs of shoes per minute. According to this information, what is a possible amount of time, in minutes, that it could take the worker to box
168
pairs of shoes?
The possible amount of time, in minutes, that it could take the worker to box 168 pairs of shoes is between 14 minutes to 21 minutes.
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
A worker at a shoe factory is required to box at least 8 pairs of shoes per minute, and not more than 12 pairs of shoes per minute.
For 168 pairs of shoe:
Maximum time = 168 pair / 8 pairs per minute = 21 minutes
Minimum time = 168 pair / 12 pairs per minute = 14 minutes
The possible amount of time, in minutes, that it could take the worker to box 168 pairs of shoes is between 14 minutes to 21 minutes.
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A card is randomly chosen from the cards in the image. Find the probability of choosing the cards with either Q or R on them.
P(Q or R) = ________
The probability of choosing cards either Q or R when a card is drawn from a deck of 8 cards is 0.25.
Given that a card is randomly chosen from 8 cards shown in figure.
We have to calculate the probability of choosing either Q or R when a card is drawn from those 8 cards.
Probability means calculating the likeliness of happening an event among all the events possible. It lies between 0 and 1. It cannot be negative.
Number of cards=8
Number of repeated cards=0
Number of cards showing Q and R =1 each.
Probability of getting Q or R is P(X=Q)+P(X=R)
= 1/8+1/8
=2/8
=1/4
=0.25
Hence the probability of getting either P or Q when a card is drawn from 8 cards is 0.25.
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The equation -2x − y = -4 shows the budget for spending on supplies over the next few weeks. If the total money (y) decreases every week (x), how many weeks will it take for the budget money to run out?
The number of weeks it will take for the budget money to run out is; 2 weeks.
How many weeks will it take for the money to run out?The number of weeks it would take for the budget money to decrease till it runs out as required in the task can be interpreted as the x-value which corresponds to a Y-value of zero.
Hence, by setting y=0; we have;
-2x -0 = -4
-2x = -4
Divide both sides of the equation by; -2.
x = 2
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One of the reasons to use the bootstrap method is because the formula for the confidence interval is too hard to derive. Group of answer choices True False
The confidence interval formula is extremely complicated to derive, which is one of the justifications for using the bootstrap approach. this statement is true.
What purposes serve the bootstrap method?A resampling technology named the bootstrap can be used to sample a dataset using replacement to calculate statistics on a group. Estimating summary statistics like the mean or standard deviation may be done using it.
The advantages of the bootstrap methodThe benefits of bootstrapping include its simplicity in estimating standard errors and confidence intervals as well as its cost-effectiveness in avoiding the need to conduct the operation to get additional groups of sampled data.
Therefore it can be concluded that the said query statement is true.
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Determine the area of the figure.
Answer: 3x - 6 (in^2)
Step-by-step explanation:
base * height / 2
=
3 ( 2x - 4) / 2 (in^2)
= 3x - 6 (in^2)
Answer: 3x-6 in^2
Step-by-step explanation:
There is no way to figure out what x is without additional information, so you have to leave the answer in this form
Solve F=gm1*m2/d2 for g
The expression for g in terms of other variables is g = Fd^2/m1m2
Subject of formulaGiven the expression below as shown
F=gm1*m2/d2
We are to make g the subject of the formula
F=gm1*m2/d2
Cross multiply
Fd2 = gm1m2
Divide both sides by m1m2
Fd^2/m1m2 = g
g = Fd^2/m1m2
Hence the expression for g in terms of other variables is g = Fd^2/m1m2
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Help me solve this problem on arithmetic and geométrica sequences
Answer:
math math math math math math math math math math