The LU factorization of the matrix is:
[-5 0 4] [1 0 0] [ -5 0 4 ]
[10 2 -5] = [1 0 0] [ 0 2 3 ] [ 0 2 3 ]
[10 10 16] [-2 5/2 1] [ 0 0 9 ]
To compute the LU factorization of a matrix, we need to decompose it into an upper triangular matrix U and a lower triangular matrix L, where L is a unit lower triangular matrix (i.e., its diagonal entries are all 1).
We begin with the given matrix:
[-5 0 4]
[10 2 -5]
[10 10 16]
First, we use row operations to transform the matrix into an upper triangular matrix. Let's use Gaussian elimination to reduce the matrix to row echelon form.
Let's add 2 times the first row to the second row to eliminate the entry in the (2,1) position:
[-5 0 4]
[0 2 3]
[10 10 16]
Next, let's add 2 times the first row to the third row to eliminate the entry in the (3,1) position:
[-5 0 4]
[0 2 3]
[0 10 24]
subtract 5 times the second row from the third row to eliminate the entry in the (3,2) position:
[-5 0 4]
[0 2 3]
[0 0 9]
We now have an upper triangular matrix U. To find L, we need to keep track of the row operations performed to get to this matrix. Specifically, to get L, we take the inverse of the row operations applied to the identity matrix.
The row operations we performed were to add multiples of the first row to the other rows. So, to get L, we apply the inverse row operations and write the multipliers as entries in L below the diagonal:
[1 0 0]
[-2 1 0]
[-2 5/2 1]
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the drawing shows an isosceles triangle
40 degrees
can you find the size of a
Angle "a" in the given isosceles triangle is 40 degrees.
To find the size of angle "a" in the isosceles triangle with a 40-degree angle, we can use the properties of isosceles triangles. In an isosceles triangle, the two equal sides are opposite the two equal angles.
Since the given angle is 40 degrees, we know that the other two angles in the triangle are also equal. Let's call these angles "b" and "c." Therefore, we have:
b = c
Since the sum of the angles in a triangle is always 180 degrees, we can write the equation:
40 + b + c = 180
Since b = c, we can rewrite the equation as:
40 + b + b = 180
Combining like terms, we have:
2b + 40 = 180
Subtracting 40 from both sides, we get:
2b = 140
Dividing both sides by 2, we find:
b = 70
Therefore, both angles "b" and "c" are 70 degrees.
Now, we can find angle "a" by subtracting the sum of angles "b" and "c" from 180 degrees:
a = 180 - (b + c)
= 180 - (70 + 70)
= 180 - 140
= 40
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Kurt Busch won the 59th Daytona 500 in February. If he paid back a $8,700 loan with $30 interest at 8%, what was the time of the loan?
The time of the loan when Kurt Busch paid back the $8,700 loan with $30 interest at 8% was approximately 6.204 months.
The time of the loan when Kurt Busch paid back a $8,700 loan with $30 interest at 8%, we can use the formula for simple interest:
Interest = Principal × Rate × Time
The principal is $8,700, the interest is $30, and the rate is 8% or 0.08 (in decimal form).
We need to find the time of the loan.
Rearranging the formula, we have:
Time = Interest / (Principal × Rate)
Substituting the given values into the equation:
Time = $30 / ($8,700 × 0.08)
Calculating the expression inside the parentheses first:
$8,700 × 0.08 = $696
Now, divide $30 by $696:
Time = $30 / $696
Time ≈ 0.0431 years
Since we want to find the time in months, we need to convert years to months.
There are approximately 12 months in a year.
Time ≈ 0.0431 × 12
≈ 0.517 years
≈ 0.517 × 12 months
≈ 6.204 months
It's worth noting that in this calculation, we assumed the interest was calculated based on the entire duration of the loan, and not on a partial period.
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Winning the jackpot in a particular lottery requires that you select the correct five numbers between 1 and 37 and, in a separate drawing, you must also select the correct single number between 1 and 47. Find the probability of winning the jackpot.
The probability of winning the jackpot is ?
Answer:
To calculate the probability of winning the jackpot in this particular lottery, we need to determine the probability of selecting the correct five numbers between 1 and 37 and the correct single number between 1 and 47.
The probability of selecting the correct five numbers between 1 and 37 can be calculated as follows:
P(correct five numbers) = 1 / (total possible combinations of five numbers)
In this case, there are C(37, 5) possible combinations of five numbers, which represents the number of ways to choose five numbers out of 37. The formula for calculating combinations is given by:
C(n, k) = n! / (k! * (n - k)!)
Plugging in the values:
C(37, 5) = 37! / (5! * (37 - 5)!)
The probability of selecting the correct single number between 1 and 47 is:
P(correct single number) = 1 / (total possible numbers between 1 and 47)
Since there are 47 possible numbers to choose from, the probability is:
P(correct single number) = 1 / 47
To calculate the probability of winning the jackpot, we multiply the probability of selecting the correct five numbers by the probability of selecting the correct single number:
P(jackpot) = P(correct five numbers) * P(correct single number)
P(jackpot) = (1 / C(37, 5)) * (1 / 47)
Calculating this expression will give you the probability of winning the jackpot in this particular lottery.
fill in the bank. In the triangle below, x = . Round your answer 2 decimal places
The calculated value of x in the triangle is 23.57 degrees
How to calculate the value of xFrom the question, we have the following parameters that can be used in our computation:
The right triangle
From the triangle, we have
Angle x
Also, we have the following sides in relation to x
Opposite = 6
Hypotenuse = 15
This means that we make use of the sine ratio
i.e. sin = opposite/hypotenuse
So, we have
sin(x) = 6/15
Evaluate
sin(x) = 0.4
Take the arc sin of both sides
x = 23.57
Hence, the value of x is 23.57 degrees
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Graph the line with slope 1/3 and y-intercept −2.
The graph of the function y = 1/3x - 2 is added as an attachment
Sketching the graph of the functionFrom the question, we have the following parameters that can be used in our computation:
Slope = 1/3y-intercept = -2So, the equation is
y = 1/3x - 2
The above function is a linear function that has been transformed as follows
Vertically stretched by a factor of 1/3Shifted down by 2 unitsNext, we plot the graph using a graphing tool by taking note of the above transformations rules
The graph of the function is added as an attachment
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help i needa graduate
Answer: A
Step-by-step explanation:
for a function y = Asin(bx + c), an amplitude equals to |A| (10 in this case), and the period equals to 2π/b (1/2 * π in this case).
Answer:
[tex]\textsf{A)} \quad \rm amplitude = 10, \; period=\dfrac{1}{2}\pi[/tex]
Step-by-step explanation:
The sine function is periodic, meaning it repeats forever.
The general formula for a sine function is:
[tex]\boxed{y = A \sin(B(x + C)) + D}[/tex]
where:
|A| is the amplitude (height from the mid-line to the peak).2π/B is the period (horizontal length of one cycle of the curve).C is the phase shift (horizontal shift - positive is to the left).D is the vertical shift.Given function:
[tex]y=-10\sin 4x[/tex]
Comparing the given function with the general formula:
|A| = |-10| = 10B = 4C = 0D = 0Therefore, the given function has no horizontal or vertical shift.
The amplitude of the function is 10.
The period of the function is:
[tex]\textsf{Period}=\dfrac{2\pi}{B}=\dfrac{2\pi}{4}=\dfrac{1}{2}\pi[/tex]
Which expression is equivalent to the area of square A, in square centimeters? 3 squares are positioned to form a triangle. The small square is labeled 24 centimeters, medium square is 45 centimeters, and large square is not labeled. One-half (24) (45) 24 (45) (24 + 45) squared 24 squared + 45 squared
The expression that is equivalent to the area of square A is 2601.
To determine the expression that is equivalent to the area of square A, let's analyze the given information.
We have three squares positioned to form a triangle. The small square has a labeled side length of 24 centimeters, the medium square has a labeled side length of 45 centimeters, and the side length of the large square is not labeled.
Since the small and medium squares form a right triangle, we can use the Pythagorean theorem to find the length of the hypotenuse, which corresponds to the side length of the large square. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Applying the Pythagorean theorem, we have:
(24^2) + (45^2) = c^2
Simplifying this equation:
576 + 2025 = c^2
2601 = c^2
Taking the square root of both sides, we find:
c = √2601
c = 51
Therefore, the side length of the large square (square A) is 51 centimeters.
Now, to find the area of square A, we can use the formula for the area of a square, which is the side length squared:
Area of square A = (51^2) = 2601 square centimeters.
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Answer
The answer is D
Step-by-step explanation:
on edge 2023
MARK BRAINLIEST
Show that the following number is rational by writing it as a ratio of two integers.
52.4726172617261…
We have expressed the number 52.4726172617261... as the ratio 527261/10000, showing that it is a rational number.
To show that the number 52.4726172617261... is rational, we can express it as a ratio of two integers. Let's denote this number as x.
Let's first observe the repeating pattern in the decimal part of the number, which is 7261. This pattern repeats indefinitely. We can write this decimal part as the fraction 7261/10000, where the numerator represents the repeating pattern and the denominator represents the number of decimal places in the pattern.
Next, we need to consider the non-repeating part of the number, which is 52. We can write this as the fraction 52/1.
Now, let's combine the non-repeating and repeating parts to express the entire number as a fraction:
x = 52 + 7261/10000
To simplify this expression, we can find a common denominator of 10000 for both fractions:
x = (52 * 10000 + 7261) / 10000
This can be further simplified to:
x = (520000 + 7261) / 10000
Performing the addition:
x = 527261 / 10000
Therefore, we have expressed the number 52.4726172617261... as the ratio 527261/10000, showing that it is a rational number.
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Explain the relationship of acute and equilateral triangles. Can an equilateral sometimes be acute
The relationship between acute and equilateral triangles is equilateral triangle is consistently acute, not every acute triangle is equilateral.
An equilateral triangle is always acute as all of its angles measure less than 90 degrees.
How to determine the relationshipAn acute-angled triangle is one where all three angles are less than 90 degrees in measure. Alternatively, an equilateral triangle is a three-sided polygon in which all three sides and angles are congruent, with each angle measuring 60 degrees.
An equilateral triangle is always acute as all of its angles measure less than 90 degrees. As an equilateral triangle comprises three angles of 60 degrees each, all angles in the triangle are acute.
To put it simply, while an equilateral triangle is consistently acute, not every acute triangle is equilateral. Acute-angled triangles exhibit different side measurements and angles, as long as all the angles measure less than 90 degrees.
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A plane is 121 miles north and 183 miles east of an airport. Find , the angle the pilot should turn in order to fly directly to the airport. Round your answer to the nearest tenth of a degree.
The pilot should turn approximately 34.4 degrees to fly directly to the airport.
To find the angle the pilot should turn in order to fly directly to the airport, we can use trigonometry. In this case, we have a right triangle formed by the plane's northward distance, eastward distance, and the direct path to the airport.
Let's label the sides of the triangle:
The northward distance is the opposite side (O) and measures 121 miles.
The eastward distance is the adjacent side (A) and measures 183 miles.
The direct path to the airport is the hypotenuse (H), which represents the shortest distance between the plane and the airport.
To find the angle, we will use the inverse tangent function (arctan), which relates the lengths of the sides of a right triangle to the angle between the hypotenuse and the adjacent side.
The formula for the angle is: θ = arctan(O / A)
Substituting the values, we have: θ = arctan(121 / 183)
Calculating this using a calculator, we find that the angle is approximately 34.4 degrees.
Therefore, the pilot should turn approximately 34.4 degrees to fly directly to the airport.
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[tex]\lim_{x,y \to \infty} \frac{x+y}{x^{2} +y^{2}-xy }[/tex]
To evaluate the limit [tex]\sf \lim_{x,y \to \infty} \frac{x+y}{x^{2} +y^{2}-xy} \\[/tex], we can analyze the behavior of the expression as both [tex]\sf x \\[/tex] and [tex]\sf y \\[/tex] approach infinity.
Let's consider the numerator [tex]\sf x + y \\[/tex] and the denominator [tex]\sf x^{2} + y^{2} - xy \\[/tex] separately.
For the numerator, as both [tex]\sf x \\[/tex] and [tex]\sf y \\[/tex] approach infinity, their sum [tex]\sf x+y \\[/tex] will also approach infinity.
For the denominator, we can rewrite it as [tex]\sf (x-y)^2 + 2xy \\[/tex]. As [tex]\sf x[/tex] and [tex]\sf y[/tex] approach infinity, the terms [tex]\sf (x-y)^2 \\[/tex] and [tex]\sf 2xy \\[/tex] will also approach infinity. Therefore, the denominator will also approach infinity.
Now, let's consider the entire fraction [tex]\sf \frac{x+y}{x^{2} +y^{2}-xy} \\[/tex]. Since both the numerator and denominator approach infinity, we have an indeterminate form of [tex]\sf \frac{\infty}{\infty} \\[/tex].
To evaluate this indeterminate form, we can apply techniques such as L'Hôpital's rule or algebraic manipulations. However, in this case, we can simplify the expression further.
By dividing both the numerator and denominator by [tex]\sf x^{2} \\[/tex], we get:
[tex]\sf \lim_{x,y \to \infty} \frac{\frac{x}{x^{2}} + \frac{y}{x^{2}}}{1 + \frac{y^{2}}{x^{2}} - \frac{xy}{x^{2}}} \\[/tex]
As [tex]\sf x[/tex] approaches infinity, the terms [tex]\sf \frac{x}{x^{2}} \\[/tex] and [tex]\sf \frac{y}{x^{2}} \\[/tex] both approach zero. Similarly, the term [tex]\sf \frac{y^{2}}{x^{2}}[/tex] and [tex]\sf \frac{xy}{x^{2}} \\[/tex] also approach zero.
Therefore, the limit simplifies to:
[tex]\sf \lim_{x,y \to \infty} \frac{0 + 0}{1 + 0 - 0} = \frac{0}{1} = 0 \\[/tex]
Hence, the limit [tex]\sf \lim_{x,y \to \infty} \frac{x+y}{x^{2} +y^{2}-xy} \\[/tex] is equal to 0.
At an amusment park, the cost for an adult admission is a, and for a child the cost is c. For a group of six that included two children, the cost was $325.94. For a group of five that included three children, the cost was $256.95. All ticket prices include tax.
Part A / Write a system of equations in terms of a and c, that models this situation.
Part B / Use your systems of equations to determine the exact cost of each type of ticket algebraically
Part C / Determine the cost for a group of four that includes three children
A part-time hotel desk clerk made $9230.60 last year. If she claimed herself
as an exemption for $3650 and had a $5700 standard deduction, what was
her taxable income last year?
A. $0
B. $119.40
C. $3530.60
D. $5580.60
No taxes would be owed in this scenario as the taxable income is zero.
To calculate the hotel desk clerk's taxable income, we need to subtract her exemptions and deductions from her total income.
Total Income: $9230.60
Exemption: $3650
Standard Deduction: $5700
Taxable Income = Total Income - Exemption - Standard Deduction
Taxable Income = $9230.60 - $3650 - $5700
Taxable Income = $9230.60 - $9350
Taxable Income = -$119.40
Since the result is negative, it means that her taxable income is zero (0). In the US tax system, if the taxable income is negative, it is considered as zero taxable income. Therefore, the correct answer is:
A. $0
No taxes would be owed in this scenario as the taxable income is zero.
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Use the identity 2 sinz cos z = sin(2x) to find the power series expansion of sin² z at z=0.
(Hint: Integrate the Maclaurin series of sin(2x) term-by-term.).
7=0
The power series expansion of sin²x at x = 0 is given by:
sin²x = 4x² - 32x⁴/3 + 64x⁶/5! - 512x⁸/7! + ...
To find the power series expansion of sin²x at x = 0, we can utilize the identity 2sin(x)cos(x) = sin(2x) and the Maclaurin series expansion of sin(2x).
The Maclaurin series expansion of sin(2x) is given by:
sin(2x) = 2x - (2x)³/3! + (2x)⁵/5! - (2x)⁷/7! + ...
To find sin²x, we square the Maclaurin series of sin(2x) term-by-term:
(sin(2x))² = (2x)² - 2(2x)⁴/3! + (2x)⁶/5! - 2(2x)⁸/7! + ...
Now, let's simplify the expression:
(2x)² = 4x²
(2x)⁴ = 16x⁴
(2x)⁶ = 64x⁶
(2x)⁸ = 256x⁸
Substituting these values back into the expansion:
(sin(2x))² = 4x² - 2(16x⁴)/3! + (64x⁶)/5! - 2(256x⁸)/7! + ...
Simplifying further:
(sin(2x))² = 4x² - 32x⁴/3 + 64x⁶/5! - 512x⁸/7! + ...
This expansion represents sin²x as an infinite sum of terms involving powers of x.
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Your taxable wages for Social Security purposes are $1100. How much is your Social Security tax if you have previous taxable wages of $102,000?
If you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.
To calculate the Social Security tax, we need to know the tax rate for Social Security and the taxable wages. Let's assume the Social Security tax rate is 6.2% for both the employee and the employer.
Given that your taxable wages for Social Security purposes are $1,100, and your previous taxable wages are $102,000, we can determine the Social Security tax amount.
First, we need to calculate the Social Security tax on the previous taxable wages of $102,000. Multiply $102,000 by 6.2% (0.062) to find the Social Security tax for that amount:
Social Security tax = $102,000 x 0.062 = $6,324
Next, we calculate the Social Security tax on the current taxable wages of $1,100. Multiply $1,100 by 6.2% to find the tax amount:
Social Security tax = $1,100 x 0.062 = $68.20
Therefore, if you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.
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Enter the number that belongs in the green box
Suppose sin (in picture), where
Find exact values for each of the following.
The exact values of the given Trigonometric functions of ∠A are as follows: cos(A) = 4/5tan(A) = 3/4sec(A) = 5/4csc(A) = 5/3cot(A) = 4/3.
Suppose sin (in the picture) as shown below: In the above image, we have a right triangle with sides opposite, adjacent, and hypotenuse such that: opposite = a = 3; adjacent = b = 4; hypotenuse = c = 5.
The sine of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the hypotenuse.
Hence, the sine of ∠A in this triangle is given by: sin(A) = opposite/hypotenuse = a/c = 3/5
Now, we are required to find the exact values of the following trigonometric functions of ∠A in terms of fractions, radicals, and/or pi.1. cos(A)cos(A) = adjacent/hypotenuse = b/c = 4/5Therefore, cos(A) = 4/5.2. tan(A)tan(A) = opposite/adjacent = a/b = 3/4
Therefore, tan(A) = 3/4.3. sec(A)sec(A) = 1/cos(A) = 1/(4/5) = 5/4Therefore, sec(A) = 5/4.4. csc(A)csc(A) = 1/sin(A) = 1/(3/5) = 5/3Therefore, csc(A) = 5/3.5. cot(A)cot(A) = 1/tan(A) = 1/(3/4) = 4/3Therefore, cot(A) = 4/3.
Thus, the exact values of the given trigonometric functions of ∠A are as follows: cos(A) = 4/5tan(A) = 3/4sec(A) = 5/4csc(A) = 5/3cot(A) = 4/3.
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The profit resulting from manufacturing and selling a product is represented by the function P(x) = -30(x - 500)² + 1000,
where x is the number of products manufactured and P(x) is the profit generated. What is the maximum profit?
$200
$1000
none of the answer choices
O $500
O There is no maximum profit.
The maximum profit is $1000. Therefore, the correct answer is:
$1000
To find the maximum profit, we need to determine the maximum point on the profit function, which corresponds to the vertex of the parabola. In this case, the profit function is given by:
P(x) = -30(x - 500)² + 1000
To find the maximum point, we can note that the vertex of a parabola in the form of y = a(x - h)² + k is located at the point (h, k). Comparing this with our profit function, we can see that the vertex is located at (500, 1000).
Therefore, the maximum profit is $1000. Therefore, the correct answer is:
$1000
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Use the graph to solve the given system of equations by plotting both lines and the point of intersection by moving the dots to the correct location,, then enter your solution below.
y=−3x−9
3x+4y=−9
Answer:
(x, y) = (-3, 0)
Step-by-step explanation:
You want a graphical solution to the system of equations ...
y = -3x -93x +4y = -9GraphA graph of the system is attached. The lines intersect at (-3, 0).
The solution to the equations is (x, y) = (-3, 0).
<95141404393>
The solution to the system of equations is x = -3 and y = 0.
The given system of equations is:
Equation 1: y = -3x - 9
Equation 2: 3x + 4y = -9
To find the solution to this system, we need to find the values of x and y that satisfy both equations simultaneously.
We can start by substituting Equation 1 into Equation 2:
3x + 4(-3x - 9) = -9
Simplifying the equation:
3x - 12x - 36 = -9
Combine like terms:
-9x - 36 = -9
Now, let's isolate the variable x:
-9x = -9 + 36
-9x = 27
Divide both sides of the equation by -9 to solve for x:
x = 27 / -9
x = -3
Now that we have the value of x, we can substitute it back into Equation 1 to find the value of y:
y = -3(-3) - 9
y = 9 - 9
y = 0
Therefore, the solution to the system of equations is x = -3 and y = 0.
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The original plan for assigning telephone numbers that you investigated in
Applications Task 4 was implemented in
1947. At that time, the supply of numbers was expected to last for 300 years. However, by the 1970s the numbers were already starting to run out. So, the numbering plan
had to be modified. In this task, you will count the number of different phone numbers that were available in 2012.
a. For three-digit area codes, the first digit cannot be a 0 or a 1. Assuming no additional restrictions, how many three-digit area codes are possible under
this plan?
b. Certain area codes are classified as "Easily Recognizable Codes" (BRCs).
ERCs designate special services, like 888 for toll-free calls. The requirement for an ERC is that the second and third digit of the area code must be the same. The first digit again cannot be a 0 or a 1. How many ERCs are there?
c. Consider the seven digits after the area code. As with the area code, the first digit of the three-digit local prefix cannot be a 0 or a 1. The remaining six digits for the local number have no restrictions. How many of these seven-digit phone numbers are possible?
d. Assuming only the 0 and 1 restrictions in Parts a and c, how many ten-digit phone numbers are possible?
a. Assuming no additional restrictions, there are 800 possible three-digit area codes.
b. Considering ERCs, there are 80 ERCs.
c. For the seven digits after the area code, there are [tex]8 \times 10^6 = 8,000,000[/tex] possible seven-digit phone numbers.
d. Assuming only the 0 and 1 restrictions from parts a and c, the number of possible ten-digit phone numbers is 800 [tex]\times[/tex] 8,000,000 = 6,400,000,000.
a. For three-digit area codes, the first digit cannot be 0 or 1.
Assuming no additional restrictions, there are 8 possibilities for the first digit (2-9) and 10 possibilities for each of the remaining two digits (0-9). Therefore, the total number of three-digit area codes possible under this plan is [tex]8 \times 10 \times 10 = 800.[/tex]
b. For an ERC (Easily Recognizable Code), the second and third digits of the area code must be the same, and the first digit cannot be 0 or 1. There are 8 possibilities for the first digit (2-9) and 10 possibilities for the third digit (0-9).
Since the second digit must be the same as the third digit, there is only 1 possibility.
Therefore, the total number of ERCs is [tex]8 \times 1 \times 10 = 80.[/tex]
c. For the seven digits after the area code, the first digit of the three-digit local prefix cannot be 0 or 1.
There are 8 possibilities for the first digit (2-9) and 10 possibilities for each of the remaining six digits (0-9).
Therefore, the total number of seven-digit phone numbers possible is 8 * [tex]10\times 10 \times 10 \times 10 \times 10 \times 10 = 8,000,000.[/tex]
d. Assuming only the 0 and 1 restrictions from parts a and c, the number of possible ten-digit phone numbers can be calculated by multiplying the number of possibilities for each digit position.
For the area code (part a), there are 800 possibilities.
For the seven digits after the area code (part c), there are 8,000,000 possibilities.
Therefore, the total number of ten-digit phone numbers possible is 800 * 8,000,000 = 6,400,000,000.
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A company is trying to determine the crossover point for two different manufacturing processes. Process A has a fixed cost of $50,000 and a variable cost of $10 per unit produced. Process B has a fixed cost of $30,000 and a variable cost of $15 per unit produced. The selling price for the product is $25 per unit. The company wants to know at what production volume the total cost of each process will be equal, and which process should be chosen above that volume.
Answer:
To determine the crossover point, we need to find the production volume at which the total cost of each process is equal. Let's denote the production volume as "x."
For Process A:
Fixed cost = $50,000
Variable cost = $10 per unit
Total cost for Process A = Fixed cost + (Variable cost * x)
For Process B:
Fixed cost = $30,000
Variable cost = $15 per unit
Total cost for Process B = Fixed cost + (Variable cost * x)
The selling price for the product is $25 per unit.
To find the crossover point, we'll equate the total costs of both processes and solve for "x."
Total cost for Process A = Total cost for Process B
$50,000 + ($10 * x) = $30,000 + ($15 * x)
Now, let's solve this equation to find the crossover point:
$50,000 + $10x = $30,000 + $15x
$10x - $15x = $30,000 - $50,000
-$5x = -$20,000
x = -$20,000 / -$5
x = 4,000
Therefore, the crossover point occurs at a production volume of 4,000 units.
To determine which process should be chosen above that volume, we'll compare the total costs of each process at a production volume greater than 4,000 units.
For Process A:
Total cost for Process A = $50,000 + ($10 * x)
Total cost for Process A = $50,000 + ($10 * 4,000)
Total cost for Process A = $50,000 + $40,000
Total cost for Process A = $90,000
For Process B:
Total cost for Process B = $30,000 + ($15 * x)
Total cost for Process B = $30,000 + ($15 * 4,000)
Total cost for Process B = $30,000 + $60,000
Total cost for Process B = $90,000
At a production volume greater than 4,000 units, both Process A and Process B have the same total cost of $90,000. Therefore, either process can be chosen above that volume without any cost advantage.
Shan works in a factory and is paid $12.20 per hour. If he works more than 36 hours in a week he is paid overtime at 1.5 times the basic rate. a If he works a 42 hour week calculate his wage for that week b The week after he earned $585.60. How many hours overtime did Shan work?
Answer:
The answer should be ( he worked 8 hours over time)
Step-by-step explanation:
Graphing Linear Inequalities and Systems of Linear Inequalities in Real-World Situations - Item 7607Question 1 of 7
Which inequality describes the graph?
On a coordinate plane, a line goes through (0, negative 2) and (2, 2). Everything to the left of the line is shaded.
CLEAR CHECK
y≥−2+2x
y–2≥−2x
y≤2x–2
y>2x–2
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Answer:
4-1/4
Step-by-step explanation:
just Tixes by your denominator to get your number
Mr Dieter wants to title the family room it is basement he has selected a pattern of square tiles that measure 9 inches by 9 inches each the shape of the floor would be tiled is shown below
Mr. Dieter will need to purchase 528 square tiles that measure 9 inches by 9 inches each to tile the family room in his basement.
As we can see in the image provided, the shape of the floor is a rectangle with dimensions 16 feet by 18 feet. To title the family room using square tiles that measure 9 inches by 9 inches each, we need to convert the dimensions from feet to inches. 1 foot is equal to 12 inches, so we have:
16 feet x 12 inches/foot = 192 inches
18 feet x 12 inches/foot = 216 inches
Now we can divide the length and width of the floor by the length and width of each tile to find out how many tiles are needed. Since each tile measures 9 inches by 9 inches, we have:
192 inches ÷ 9 inches = 21.33 tiles ≈ 22 tiles needed for the length
216 inches ÷ 9 inches = 24 tiles needed for the width
Therefore, we need 22 tiles for the length and 24 tiles for the width, which gives us a total of:
22 tiles x 24 tiles = 528 tiles
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Find the score (X value) that corresponds to each of the following z-scores.
z = 1.00: X=
z = 0.20: X=
z = 1.50: X=
z = -0.50: X=
z= -2.00:X=
z = -1.50: X=
For z-score of 1.00, the corresponding X value is 0.8413.
For z-score of 0.20, the corresponding X value is 0.5793.
For z-score of 1.50, the corresponding X value is 0.9332.
For z-score of -0.5, the corresponding X value is 0.3085.
For z-score of -2.00, the corresponding X value is 0.0228.
For z-score of -1.50, the corresponding X value is 0.0668
What is the score (x value) that corresponds to the z-score?
The score (x value) that corresponds to each of the z-score is determined by looking up these values or scores in normal distribution chart.
For z-score of 1.00, the corresponding X value is determined as;
X = 0.8413
For z-score of 0.20, the corresponding X value is determined as;
X = 0.5793
For z-score of 1.50, the corresponding X value is determined as;
X = 0.9332
For z-score of -0.5, the corresponding X value is determined as;
X = 0.3085
For z-score of -2.00, the corresponding X value is determined as;
X = 0.0228
For z-score of -1.50, the corresponding X value is determined as;
X = 0.0668
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Consider the following pair of equations:
y = 3x + 3
y = x − 1
Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form.
Find the roots of quadratic equation: 2x2 + 5x + 2 = 0?
A. -2, -1/2
B. 4, -1
C. 4, 1
D. -2, 5/2
Answer:
A
Step-by-step explanation:
2x² + 5x + 2 = 0 ← in standard form
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 2 × 2 = 4 and sum = + 5
the factors are + 4 and + 1
use these factors to split the x- term
2x² + 4x + x + 2 = 0 ( factor the first/second and third/fourth terms )
2x(x + 2) + 1(x + 2) = 0 ← factor out (x + 2) from each term
(x + 2)(2x + 1) = 0 ← in factored form
equate each factor to zero and solve for x
x + 2 = 0 ( subtract 2 from both sides )
x = - 2
2x + 1 = 0 ( subtract 1 from both sides )
2x = - 1 ( divide both sides by 2 )
x = - [tex]\frac{1}{2}[/tex]
the roots are x = - 2, - [tex]\frac{1}{2}[/tex]
what is the nat term of the sequence -3, 0, 5, 10, 25, 5, 47 ?
The nth term of the sequence -3, 0, 5, 10, 25, 5, 47 can be represented by the piecewise function:
nth term =
-3 + (n - 1) * 5, if n mod 5 ≤ 5
5 + (n - 1) * 15, if n mod 5 > 5
To find the nth term of a sequence, we need to identify the pattern or rule that governs the sequence. Upon analyzing the given sequence -3, 0, 5, 10, 25, 5, 47, we can observe the following:
The sequence starts with -3 and increases by 5 each time, except for the 5th term, where it increases by 15 (from 10 to 25). After the 5th term, the sequence starts again with 5 and continues to increase by 15 each time.
Based on this pattern, we can divide the sequence into two parts:
Part 1: -3, 0, 5, 10, 25 (increasing by 5 each time)
Part 2: 5, 20, 35, 50, 65 (increasing by 15 each time)
Now, to determine the nth term, we can consider the formula for arithmetic sequences:
nth term = first term + (n - 1) * common difference
For Part 1, the first term is -3 and the common difference is 5. Thus, the nth term for Part 1 is given by:
nth term = -3 + (n - 1) * 5
For Part 2, the first term is 5 and the common difference is 15. Therefore, the nth term for Part 2 can be expressed as:
nth term = 5 + (n - 1) * 15
However, since the sequence alternates between Part 1 and Part 2, we need to determine which part the nth term falls into. For that, we can use modular arithmetic:
If n mod 5 is less than or equal to 5, then the nth term is from Part 1.
If n mod 5 is greater than 5, then the nth term is from Part 2.
Let's calculate a few terms to illustrate this:
For n = 1, the sequence starts with -3, so the 1st term is -3.
For n = 2, we are still in Part 1, so the 2nd term is 0.
For n = 3, Part 1 continues, so the 3rd term is 5.
For n = 4, we are still in Part 1, so the 4th term is 10.
For n = 5, Part 1 ends, and the 5th term is 25.
For n = 6, the sequence starts with 5 in Part 2, so the 6th term is 5.
For n = 7, Part 2 continues, so the 7th term is 20.
For n = 8, we are still in Part 2, so the 8th term is 35.
Based on this analysis, we can conclude that the nth term for the given sequence is:
If n mod 5 ≤ 5:
nth term = -3 + (n - 1) * 5
If n mod 5 > 5:
nth term = 5 + (n - 1) * 15
Therefore, depending on the value of n and the remainder when divided by 5, we can use the appropriate formula to calculate the nth term.
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54
Mark this and return
-5-
3-
2+
1-
-5-4-3-2-11-
+2+
-3+
4+
91
1 2 3 4 5 x
•
Which explains why the graph is not a function?
O It is not a function because the points are not
connected to each other.
O It is not a function because the points are not
related by a single equation.
It is not a function because there are two different x-
values for a single y-value.
It is not a function because there are two different y-
values for a single x-value.
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D.It is not a function because there are two different y-values for a single x-value.
A function is a relation where each input(x) has a single output(y).
From the given graph we can see that there are 2 different values of y
i.e. y=-2 and y=4 for single x=4.
Therefore, D is the right answer.
The graph is not a function because it is not a function because there are two different y-values for a single x-value.
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Question
Which explains why the graph is not a function?
A.It is not a function because the points are not connected to each other.
B.It is not a function because the points are not related by a single equation.
C.It is not a function because there are two different x-values for a single y-value.
D.It is not a function because there are two different y-values for a single x-value
A is the point on X-anis whose abscissa is 6 and Bis the point on Y-anis whose ordinate is - 8. Find the distance between AB.
A coordinate plane is a two-dimensional grid that has an x-axis (horizontal) and a y-axis (vertical). A point on the coordinate plane has an x-coordinate (abscissa) and a y-coordinate (ordinate) that show its position on the grid. The distance between two points can be found by using the distance formula, which is derived from the Pythagorean theorem. The distance formula is:
d=(x2−x1)2+(y2−y1)2
where d is the distance, (x1,y1) and (x2,y2) are the coordinates of the two points. In this problem, the coordinates of point A are (6,0) and the coordinates of point B are (0,−8). Plugging these values into the formula, we get:
d=(0−6)2+(−8−0)2
d=36+64
d=100
d=10
Therefore, the distance between A and B is 10 units.
