Answer:
b = -10
Step-by-step explanation:
Two vectors are orthogonal if and only if their dot product is zero. The dot product of v and w is given by:
(v · w) = (5i + 2j) · (4i + bj) = 5 * 4 + 2 * b = 20 + 2b.
For v and w to be orthogonal, we need the dot product to be zero, which means 20 + 2b = 0, so:
2b = -20
b = -10
Therefore, b = -10 makes the vectors v and w orthogonal.
which value is a solution for the equation cot x/2=1?
The solution for the equation is [tex]x=\frac{\pi }{2} +2\pi n[/tex] ,for any integer n.
What is an equation?An equation is the statement that asserts th equality of the two expressions with 'equal to' (=) sign.
cot [tex]\frac{x}{2} =1[/tex],
Taking inverse on both sides we get,
[tex]\frac{x}{2}[/tex] = [tex]cot^{-1} (1)[/tex]⇒[tex]\frac{x}{2}=\frac{\pi}{4}[/tex]
⇒[tex]x=\frac{\pi }{2}[/tex].
cot is positive in first and third quadrant. To find the second solution add π to it.
[tex]\frac{x}{2} =\pi +\frac{\pi }{2}[/tex]
[tex]x=\frac{5\pi }{2}[/tex]
to find period for cot([tex]\frac{x}{2}[/tex])
The periodic function can be calculated by [tex]\frac{\pi }{|b|}[/tex], replace b with [tex]\frac{1}{2}[/tex]
we get [tex]2\pi[/tex]. we get period for cot([tex]\frac{x}{2}[/tex]) is [tex]2\pi[/tex] so values will repeat every
radians in both directions.
[tex]x=\frac{\pi }{2} +2\pi n, \frac{5\pi }{2} +2\pi n,[/tex] for any integer n.
consolidating we get,
[tex]x=\frac{\pi }{2} +2\pi n[/tex], for any integer.
Hence, the solution for the equation cot [tex]\frac{x}{2}[/tex]= 1 is [tex]x=\frac{\pi }{2} +2\pi n[/tex]
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Show that the function f ∶ R^2 → R given by f(x, y) = e^x does not have
any local or global extrema.
The required function f ∶ R² → R given by f(x, y) = eˣ does not have any local or global extrema.
What is a global extreme point?A global extreme point, also known as a global maximum or minimum, is the highest or lowest value that a function attains over its entire domain. In other words, it is the maximum or minimum value of the function over the whole range of inputs, rather than just a specific interval or region.
Here,
The function f(x, y) = eˣ only depends on x and is not a function of y. This means that it does not have any extrema since its value can be arbitrarily close to zero or arbitrarily close to infinity for different x-values, and therefore it does not attain a maximum or minimum value. This holds both locally and globally.
Thus, the required function f ∶ R² → R given by f(x, y) = eˣ does not have any local or global extrema.
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50 POINTS!!! GIVING BRAINLIEST TO CORRECT ANSWER
Answer:
reflection over the x axis
vertical stretch of 2
vertical translation down 1 unit
Step-by-step explanation:
-2 [tex]\sqrt[3]{x}[/tex] -1
The negative in front is a reflection over the x axis
The 2 is a vertical stretch of 2
The subtraction of 1 at the end is a vertical translation down 1 unit
Let A and B be any two events. Which of the following statements, in general, are false? P(A∣B)+P(A∣B)=1
Option A and B : This statements is generally false in probability theory.
A. P(A ∪ B) = P(A) + P(B) - This statement is generally false in probability theory. This is known as the inclusion-exclusion principle, which states that the probability of the union of two events is equal to the sum of their individual probabilities minus the probability of their intersection.
B. P(A | B) = P(A) - This statement is generally false in probability theory. In general, P(A | B) is not equal to P(A) because the occurrence of event B affects the probability of event A.
C. P(A ∩ B) = P(A)P(B) - This statement is generally true in probability theory. This is known as the independent events rule, which states that the probability of the intersection of two independent events is equal to the product of their individual probabilities.
D. P(A | B) + P(A' | B) = 1 - This statement is generally true in probability theory.
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Let A and B be any two events. Which of the following statements, in general, are false? P(A∣B)+P(A∣B)=1
A. P(A ∪ B) = P(A) + P(B)
B. P(A | B) = P(A)
C. P(A ∩ B) = P(A)P(B)
D. P(A | B) + P(A' | B) = 1
Circle all the equations that represent the relationship between the price of oranges last week, x, and the price of oranges this week, y.
A. y=1/5x B. y=6/5x C. y=x+1/5x D. y=x+2 E. y=1.2x
Answer: The equation that represents the relationship between the price of oranges last week, x, and the price of oranges this week, y is:
y = x + 1/5x
The equation states that the price of oranges this week is equal to the price of oranges last week plus 1/5 of the price of oranges last week.
Step-by-step explanation:
100 POINTS HELP How would a delivery on products listed as a $5000 Unearned Revenue credit be recorded on an accounting worksheet?
A. a $5000 Adjustment debit
B. a $5000 Trial Balance debit
C. an increase in T.B. revenue
D. a $5000 Adjusted T.B. credit
Answer: A
Step-by-step explanation:
If there is a $5000 Unearned Revenue credit on the accounting worksheet, it means that the company has received payment for products or services that have not yet been delivered. Therefore, when the delivery is made, an adjusting entry is needed to reflect the change in the company's financial statements.
The adjusting entry would be a debit to the Unearned Revenue account for $5000 and a credit to the Revenue account for $5000, reflecting the delivery of the products and the recognition of revenue. The entry would be recorded in the Adjustment column of the worksheet.
Therefore, the correct answer is option A, a $5000 Adjustment debit.
Answer:
A. a $5000 Adjustment debit
Step-by-step explanation:
The delivery of products listed as a $5000 Unearned Revenue credit would be recorded on an accounting worksheet with a $5000 Adjustment debit.
Unearned revenue is a liability account that represents payments received from customers for goods or services that have not yet been provided. When the delivery is made and the products are provided, the unearned revenue is "earned" and the revenue is recognized in the accounting records.
To record the delivery and recognize the revenue earned, the company would make an adjusting entry to decrease the unearned revenue account and increase the revenue account. Since the unearned revenue account has a credit balance, the adjusting entry would require a debit to reduce the balance. This would result in a $5000 Adjustment debit to Unearned Revenue and a $5000 Adjustment credit to Revenue.
Fill in the blank question.
Be Precise A standard shower drain can drain water at the rate of 480 gallons in 23
hour. Create three different rates, using the same or different units, that are all equivalent to this rate. Be precise in the units you choose. Then find the unit rate, in gallons per minute.
Answer:
see image for answer
Step-by-step explanation:
see image for answe
Name the second largest of the four angles named in the figure (not drawn to scale) if the side included by <1 and <2 is 11 cm the side included by <2 and <3 is 16 cm and the side included by <3 and <1 is 14 cm
The second largest of the four angles is angle ∠1
Relationship of sides to interior angles in a triangle:Triangle is a closed polygon that is formed by connecting 3 line segments which are called sides of the triangle. In a triangle, the shortest side will always be placed opposite the smallest interior angle. Similarly, the longest side will always be opposite the largest interior angle.
Here we have
The side included by <1 and <2 is 11 cm
The side included by ∠2 and ∠3 is 16 cm
The side included by ∠3 and <1 is 14 cm
As we can observe angle ∠4 is an obtuse angle
Hence, ∠4 is the largest angle among the 4 angles
As we know the shortest side is placed opposite the smallest interior angle and the longest side is opposite the largest interior angle.
From the given data,
The side included by ∠2 and ∠3 is the longest side
Hence, the largest angles among ∠1, ∠2, and ∠3 are the angles ∠1
Therefore,
The second largest of the four angles is angle ∠1
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The width of a rectangle is 4y-3.5 feet and the length is 3.5y+10 feet. Find the perimeter of the rectangle.
6
3
3
C
C
6
6
C
C
3
3
6
Solve for c.
= √ [?]
C =
Enter the number
that goes beneath
the radical symbol.
Answer:
10
Step-by-step explanation:
100 POINTS HELP PLEASE
Answer:
The $19,000 in expenses should be entered by the accountant as a debit in the following journal entry:
Date Account Account Number Debit Credit
1 - Oct Expenses 19000 5050
Oxana's account has an annual interest rate of 7.1% compounded monthly. What is the annual percentage yield for Oxana's account?
Answer: The annual percentage yield (APY) takes into account both the interest rate and the frequency of compounding. It is a measure of the effective rate of return over a year, taking into account the effect of compounding.
In Oxana's account, with a 7.1% interest rate
Step-by-step explanation:
Determine the monthly payment for the installment loan.
Amount Financed (P) = $15,000
Annual Percentage Rate (R) = 5%
Number of Payments per Year (N) = 12
Time in Years (T) = 3
The monthly payment is $_____?
(Round to the nearest cent as needed.)
The monthly payment is $453.125.
How to calculate simple interest amount?If the initial amount (also called as principal amount) is P, and the interest rate is R% annually, and it is left for T years for that simple interest, then the interest amount earned is given by:
[tex]I = \dfrac{P \times R \times T}{100}[/tex]
Given;
Amount Financed (P) = $15,000
Annual Percentage Rate (R) = 5%
Number of Payments per Year (N) = 12
Time in Years (T) = 3
Now, monthly payment;
=(p*i*(1+i)^n)/((1+i)^n-1)
=15000(0.05/12)(1+0.05/12)^36/(1+0.05/12)^36-1
= 72.5/0.16
=453.125
Therefore, the monthly payment by 5% interest will be $453.125.
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The manager of a bookshop ordered 70 copies of Teen magazine;
s of these were charged at £1.90 each and the remainder, t, were
charged at a discounted price of £1.70 p each.
The bill for all 70 copies was £124.
How many magazines were charged at the discounted price?
Answer:
Let's call the number of magazines charged at £1.90 each "x".
So, the number of magazines charged at £1.70 each is "t=70-x".
The total cost of the x magazines is x * £1.90, and the total cost of the t magazines is t * £1.70.
The total bill for all 70 magazines is £124, so we can write an equation:
x * £1.90 + t * £1.70 = £124
x * £1.90 + (70-x) * £1.70 = £124
Expanding the equation, we get:
x * £1.90 + 70 * £1.70 - x * £1.70 = £124
x * £1.90 - x * £1.70 = £124 - 70 * £1.70
x * (£1.90 - £1.70) = £124 - 70 * £1.70
x * £0.20 = £124 - 70 * £1.70
x = (£124 - 70 * £1.70) / £0.20
Now that we have an expression for x, we can use a calculator to solve for it.
x = (124 - (70 * 1.70)) / 0.20 = 40.
So, 40 magazines were charged at £1.90 each and 70 - 40 = 30 magazines were charged at £1.70 each.
Mr. Tabor believes that less than 75% of the students at his school completed their math homework last night. The math teachers inspect the homework assignments from a random sample of 50 students at the school.The math teachers inspect the homework assignments from a random sample of 50 students at the school. Only 68% of the students completed their math homework.We want to test H0:p=0.75;Ha:p<0.75H0:p=0.75;Ha:p<0.75, where pp = the true proportion of the students at Mr. Tabor’s school who completed their math homework last night. A significance test yields a PP-value of 0.1265.What it would mean for the null hypothesis to be true in this setting?
The required explanation for hypothesis test is described.
How take hypothesis test?When the null hypothesis is true in this setting, it means that the true proportion of students at Mr. Tabor's school who completed their math homework last night is equal to 0.75, or 75%. This is the value that Mr. Tabor initially believed, but the sample data suggests that only 68% of the students completed their homework.
A PP-value is the probability of observing a sample proportion as extreme or more extreme than the sample proportion, given that the null hypothesis is true. In this case, the PP-value of 0.1265 is not small enough to reject the null hypothesis. A commonly used significance level is 0.05, which means that if the PP-value is less than 0.05, the null hypothesis would be rejected.
So, given the PP-value of 0.1265, which is greater than 0.05, we cannot reject the null hypothesis and must conclude that there is not enough evidence to suggest that the true proportion of students who completed their homework is less than 0.75. This means that, based on the sample data, the null hypothesis that the true proportion is equal to 0.75 is not ruled out, and there is not enough evidence to support the alternative hypothesis that the true proportion is less than 0.75.
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Miguel has $30. He spends $6.75 on a movie ticket, $3.70 for snacks, and $1.25 for bus fare each way.
How much money does Miguel have left?
a) Factorise x²-2x-3
b) Hence, simplify
2x-1
x²-2x-3
1
X-3
Answer:
x²-2x-3 using factorisation method
Step-by-step explanation:
x²-3x+1x-3
x(x-3) 1(x-3)
(x+1) (x-3)
x=-1,x=+3
Harry invests a lump sum of money in a bond fund with a fixed annual interest rate of 7% that is compounded continuously.
After 17 years, the balance reaches $10,775.05. How much was initially invested?
The initial investment was $4,176.69
What is investment?Investment is the dedication of money to purchase of an asset to attain an increase in value over a period of time.
To find initially invested we can use the formula for continuously compounded interest to find the initial investment:
A = Pe^(rt)
Where:
A is the final balance ($10,775.05)P is the initial investmentr is the annual interest rate (7%)t is the number of years (17)So, solving for P:
P = A / e^(rt)
P = $10,775.05 / e^(0.07 * 17)
P = $10,775.05 / 2.56724943786794
P = $4,176.69
Therefore, the initial investment was $4,176.69.
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Quadrilateral BCDE has vertices B(-1, -1), C(6, -2), D(5, -9), and E(-2, -8). Determine the most precise classification of BCDE.
a
Square
b
Parallelogram
c
Rectangle
d
Rhombus
The most precise classification of BCDE is a square.
What are Quadrilaterals?Quadrilaterals are four sided polygons which also have four vertices and four angles.
Sum of all the interior angles of a quadrilateral is 360 degrees.
We have to find the length of adjacent sides of the quadrilateral BCDE.
If they are equal, then the quadrilateral is either square or rhombus.
If they are not equal, then they are either rectangle or parallelogram.
B(-1, -1), C(6, -2), D(5, -9), and E(-2, -8)
BC = [tex]\sqrt{(6--1)^2+(-2--1)^2}[/tex] = √50
CD = [tex]\sqrt{(5-6)^2+(-9--2)^2}[/tex] = √50
Adjacent sides are equal. So it is either square or rhombus.
If it is rhombus, length of diagonals BD and CE are not equal.
If it is square, length of diagonals BD and CE are equal.
BD = [tex]\sqrt{(5--1)^2+(-9--1)^2}[/tex] = √100 = 10
CE = [tex]\sqrt{(-2-6)^2+(-8--2)^2}[/tex] = √100 = 10
Length of diagonals are same. So it is a square.
Hence the given quadrilateral is a square.
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Determine whether each of the equations in Problems 1 through 8 is exact. If it is exact, find the solution. 1. (2x + 3) + (2y - 2)y' = 0 2. (2x + 4y) + (2x - 2y)y' = 0 3. (3x2 - 2xy + 2) + (6y2 - x2 + 3) y' = 0 dy ax + by 4. dx bx + cy dy ax - by 5. dx 6. (ye"y cos(2x) -2e* sin(2x)+2x)+(xey cos(2x) -3) y'=0 7. (y/x+6x) +(In x - 2)y' = 0, > 0 8. у dy + 0 (x2 + y2)3/2 (x2 + y2)3/2 dx bx - cy x
None of the equations in Problems 1 through 8 is exact, so they cannot be solved using the method of integration factors.
If an ODE is exact, it can be solved using the method of integration factors.
Here is the determination of whether each of the equations in Problems 1 through 8 is exact, and if it is, finding the solution:
1. (2x + 3) + ( 2y - 2)y' = 0
This equation is not exact.
2. (2x + 4y) + ( 2x - 2y)y' = 0
This equation is not exact.
3. (3x^2 - 2xy + 2) + ( 6y^2 - x^2 + 3) y' = 0
This equation is not exact.
4. dx/dt = bx + cy, dy/dt = ax - by
This system of ODEs is not exact.
5. dx/dt = bx - cy, dy/dt = ax + by
This system of ODEs is not exact.
6. (ye^(2x) -2e^(2x)x sin(2x)+2x)+(xe^(2x)y cos(2x) -3) y'=0
This equation is not exact.
7. (y/x+6x) +(In x - 2)y' = 0, x > 0
This equation is not exact.
8. (y^2)dy/dx + 0 = (x^2 + y^2)^(3/2)
This equation is not exact.
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I need help with this its due by 12:00 pleaseee
the best answer i got for a is 5 days (1.5 hours a day)
b was 3 days (an hour a day) but I am not that sure but thats the best answer I could come up with
NO LINKS!!! URGENT HELP PLEASE!!!
1. Sketch several rectangles with a perimeter of 20 meters. Include some with small areas and some large areas, Label the dimensions of each rectangle.
In the image you can see some rectangles with different dimensions, to scale.
What is a rectangle?A rectangle is a geometric figure that is characterized by:
has four angleshas four sidesIt has two sides (base and top) that are longer than the other two sides.How to find the perimeter of a rectangle?To find the perimeter of a rectangle we must add all its sides. In this case we must illustrate a 20 m rectangle so we can draw the following variants:
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simplify 6 - (2 - 4x)
Someone please help mee
The table shows the amounts of each day is attached below.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The total amount of snow that falls in three days equals the sum of the amount of snow that falls each day, then
s1 + s2 + s3 = Ts
Here s1 is the snow that fell on day 1, s2 on day 2, s3 on day 3 and Ts is the total amount of snow that fell over the three days.
We need to calculate the amount of snow that fell on the first two days by multiplying the total snow by the given fractions, like this:
s1 = 1/6 * 2 = 1/3
s2 = 7/12*2 = 7/6
Now ,
1/3+ 7/6+ s3 = 2
1.5 + s3 = 2
1.5 - 1.5 + s3 = 2 - 1.5
s3 = 2 - 1.5
s3 = 1/2
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find the intersection of the set of odd integers between 0 and 20 and the set of multiples of 5 between 0 and 35 inclusive.
The intersection of the set of integers and multiples of 5 will be (5,15).
What exactly are integers?
In mathematics, integers are the collection of positive and negative numbers. Integers, like whole numbers, do not include the fractional element. Thus, integers are numbers that can be positive, negative, or zero, but not fractions. On integers, we can do all arithmetic operations such as addition, subtraction, multiplication, and division. Integers include numbers such as 1, 2, 5, 8, -9, -12, and so on. "Z" is the symbol for integers.
Now,
Odd Integers between 0 and 20=1,3,5,7,9,11,13,15,17,19
Multiples of 5 between 0 and 35=5,10,15,20,25,30,35
Then the common integers are=5,15
Hence,
The intersection of the set of integers multiples of 5 will be (5,15).
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What Is The Difference Between Apparent Capacity And Actual Capacity Of A Glass Vessel? IN SURFACE AREA AND VOLUME!!?
Hence, the cylinder's content determines the apparent volume of the glassware, and also the difference between the cylinder as well as spherical volumes determines the glass's true capacity.
What can be termed Capacity?Capacity can be defined as the amount which can be held by any kind of vessel. This can depend upon their depth as well as their size.
Actual capacity is the volume of liquid that a glass vessel can contain while it is only partially filled, as opposed to capacity, which refers to the volume of liquid when the glass vessel is fully filled to the brim.
The distinction between both apparent capacity versus Actual capacity in parameters of surface area, as well as volume, is that the former refers to the entire surface area proportional volume of the vessel, whilst the latter refers to the surface area but instead the volume of the liquid that could also fit.
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can someone tell me how solve this problem?
Using the midpoint formula we will see that the coordinates of B are (-9, 1)
How to find the coordinates of point B?We know that for two points (x, y) and (a, b) the midpoint is at:
( (x + a)/2, (y + b)/2)
In this case if the coordinates of B are (x, y), we can write the equation:
(-2, 4) = ( (x + 5)/2, (7 + y)/2)
We can solve these two equations to find the coordinates of point B, we will get:
(x + 5)/2 = -2
x + 5 = -4
x = -4 - 5 = -9
And:
(7 + y)/2 = 4
7 + y = 4*2 = 8
y = 8 - 7 = 1
The coordinates of B are (-9, 1)
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HELP PLEASE ITS DUE TMR
The value of the given expression is -6
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.
f(-2) value is the value of f(x) when x= -2
From the graph ,
f(-2)= 0
g(7)=2
Given:
-5 * f(-2) - 3*g(7)
= -5*0 - 3*2
First multiplication ,then subtraction from left to right
= 0- 3*2
=0-6
= -6
So, the value of the given expression is -6
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A numbler of workers must weed a large Wheat Field. The number of daisies iwill it takes them variesation inversely with the number of workers. If it takes 6 days for 10 workers to weed the field, how lowly manely days would the weadingg take if there were twelve workers?
Answer: Let x be the number of days it takes for y workers to weed the field. Then, we know that x and y are inversely proportional, meaning that x * y = k, where k is a constant.
Since it takes 6 days for 10 workers to weed the field, we have:
6 * 10 = k
So, k = 60.
Now, to find the number of days it would take if there were 12 workers, we can plug in y = 12 and solve for x:
x * 12 = 60
x = 60/12
x = 5
Therefore, it would take 5 days for 12 workers to weed the field.
Step-by-step explanation:
9. Alicia had 3 feet of wood. She used
8
3 feet of wood. Estimate the amount of
4
wood Alicia has left.
Answer: Alicia had 3 feet of wood and she used 3 feet, so she has 3 - 3 = 0 feet of wood left.
Since we are asked to estimate the amount of wood, we could round 3 to the nearest whole number and say that Alicia has approximately 0 feet of wood left.
Step-by-step explanation: