If the actual temperature of steam is 99 °C and is assumed to be 100 °C in calculations, the error introduced can be significant depending on the specific calculations being performed.
Similarly, if the actual temperature of steam is 101 °C and is assumed to be 100 °C, the error introduced can also be significant.
The amount of error introduced when assuming the temperature of steam to be 100 °C instead of the actual temperature of 99 °C or 101 °C depends on the specific calculations being performed.
Similarly, in industrial processes, assuming an incorrect temperature of steam could result in inefficiencies or even safety hazards. Therefore, the difference between the actual temperature of steam and the assumed temperature of 100 °C should not be considered negligible in many cases.
In conclusion, the error introduced by assuming a temperature of 100 °C instead of the actual temperature of steam depends on the specific calculations being performed and can be significant in some cases. It is always best to use accurate and precise measurements in scientific and engineering calculations to minimize the potential for error.
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Complete Question:
1. If you use 100 °C for the temperature of steam in your calculations, how much error do you introduce if it is actually 99 °C or 101 °C? Is this difference negligible?
estimate the amount of personal space each person living in the sighet ghetto would have. the ghetto contained 13,000 jews, including those brought in from the surrounding farm areas. the ghetto was extremely crowded with nearly 20 people in every room. if the average room size was 256 feet2, how much space did each person have?
Each person living in the Sighet ghetto would have had an estimated personal space of 12.8 square feet, which is extremely cramped and overcrowded.
What is area?A two-dimensional figure, form, or planar lamina's area is a measurement of how much space it takes up in the plane.
First, we need to calculate the total number of rooms in the ghetto:
Number of people = 13,000
Number of people per room = 20
Total number of rooms = Number of people / Number of people per room = 13,000 / 20 = 650
Next, we can calculate the total area of all the rooms:
Total area of all the rooms = Number of rooms x Average room size = 650 x 256 = 166,400 square feet
Finally, we can calculate the amount of personal space each person had by dividing the total area of all the rooms by the number of people:
Personal space per person = Total area of all the rooms / Number of people = 166,400 / 13,000 = 12.8 square feet
Therefore, each person living in the Sighet ghetto would have had an estimated personal space of 12.8 square feet, which is extremely cramped and overcrowded.
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Someone pls help it’s urgent
Answer:
your answer is c
Step-by-step explanation:
because angle 2 and 3 are complementary
Answer:
B
Step-by-step explanation:
Angles 1 and 3 are Opposite Exterior Angles. Answer choice B states that they equal each other. The only way for this to be possible is if lines a and b are parallel.
902 divided by 9
Answer:
902 divided by 9 = 100.2
9 divided by 902= 0.009 or 0 with the remainder of 9
Step-by-step explanation:
Question 3 (5 Marks)
The following balances were extracted from the books of Max and Mike CC.
DR CR
Property, plant and equipment 500 000
Inventory 150 000
Accounts receivable 100 000
Accounts payable 50 000
Loan from members 20 000
Bank 200 000Member’s contribution 300 000
Undrawn profit 100 000
Long-term loan 80 000
750 000 750 000
Additional information:
1. The amount of N$20 000 on 31 March 2021 relates to undrawn profit of the previous year,
this was settled during the current year.
2. The members decided to distribute to themselves N$29 000, this is still outstanding (not yet
paid) at the year end.
3. The members had decided to a contribution of N$80 000 during the year.
4. Profit after tax for the period ending 31 March 2022 is N$87 000.
REQUIRED
1. Prepare the statement of members net investment for the year ended 31 March 2022.
(5 Marks)
The statement of members' net investment for the year ended 31 March 2022 is as follows:
Opening balance of members' net investment: $300,000 (member's contribution)
Add: Profit after tax for the year: $87,000
Subtract: Undrawn profit of the previous year settled during the current year: $20,000
Subtract: Members' distribution still outstanding at the year end: $29,000
The resulting net investment of the members is $338,000.
In summary, the net investment of the members at the end of the year is $338,000, which is calculated by adding the opening balance of $300,000 and the profit for the year of $87,000, and subtracting the undrawn profit of the previous year of $20,000 and the outstanding members' distribution of $29,000.
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The statement of members' net investment for the year ended 31 March 2022 is as follows: Opening balance of members' net investment: $300,000 (member's contribution)
Add: Profit after tax for the year: $87,000
Subtract: Undrawn profit of the previous year settled during the current year: $20,000
Subtract: Members' distribution still outstanding at the year end: $29,000
The resulting net investment of the members is $338,000.
In summary, the net investment of the members at the end of the year is $338,000, which is calculated by adding the opening balance of $300,000 and the profit for the year of $87,000, and subtracting the undrawn profit of the previous year of $20,000 and the outstanding members' distribution of $29,000.
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HELPPP PLEASE IM TIMED
Answer:
Line n
Step-by-step explanation:
Line n, the pink line, it's just y=n, it doesn't change no matter what the x is.
NO-3, NH4 +1, NOCl, and NH3 arrange these according to the descending order of the electronegativity of Nitrogen
find the solutions to the following absolute value equation. 8∣∣x 5∣∣ 7=11 select all correct answers.
Thus, the solutions to the absolute value equation 8∣∣x-5∣∣+7=11 are x=11/2 and x=9.5.
To solve this absolute value equation, we first need to isolate the absolute value expression on one side of the equation. We can do this by subtracting 7 from both sides:
8∣∣x-5∣∣ = 4
Next, we can divide both sides by 8:
∣∣x-5∣∣ = 1/2
Now, we have an absolute value expression equal to a positive constant (1/2). There are two cases to consider:
Case 1: x-5 is positive
In this case, the absolute value expression simplifies to (x-5) and we have:
x-5 = 1/2
Solving for x, we get:
x = 11/2
Case 2: x-5 is negative
In this case, the absolute value expression simplifies to -(x-5) and we have:
-(x-5) = 1/2
Solving for x, we get:
x = 9.5
Therefore, the solutions to the absolute value equation 8∣∣x-5∣∣+7=11 are x=11/2 and x=9.5.
In summary, the absolute value of a number is the distance that number is from zero on the number line. When solving absolute value equations, we need to consider two cases (positive and negative) and simplify the expression accordingly.
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Suppose thatF(x) = A0 + A1*x + A2*x^2 + A3*x^3 + A4*x^4 + ....If F(x) = 1/(1-x), what is A1000?
Suppose that F(x) = [tex]A0 + A1*x + A2*x^2 + A3*x^3 + A4*x^4 + ....[/tex] If F(x) = 1/(1-x), A1000 = 1000!
The function F(x) can be expressed as a geometric series with a first term of 1 and a common ratio of x. Thus, we can write:
F(x) = [tex]1 + x + x^2 + x^3 + x^4 + ...[/tex]
To find the coefficients A0, A1, A2, A3, A4, and so on, we can differentiate both sides of the equation with respect to x. This gives:
F'(x) = [tex]1 + 2x + 3x^2 + 4x^3 + 5x^4 + ...[/tex]
Multiplying both sides by x, we get:
xF'(x) = [tex]x + 2x^2 + 3x^3 + 4x^4 + 5x^5 + ...[/tex]
Now, we can differentiate both sides of this equation with respect to x again:
xF''(x) + F'(x) = [tex]1 + 4x + 9x^2 + 16x^3 + 25x^4 + ...[/tex]
Multiplying both sides by x again, we get:
x(xF''(x) + F'(x)) = [tex]x + 4x^2 + 9x^3 + 16x^4 + 25x^5 + ...[/tex]
Continuing this process, we get:
x^nFn(x) = [tex]n!x^n + n(n-1)!x^{(n+1)} + n(n-1)(n-2)!x^{(n+2)} + ...[/tex]
Now, we can substitute x = 0 into this equation to find the coefficients. When we do this, all the terms except for the first one on the right-hand side disappear. Thus:
A0 = 1
A1 = 1
A2 = 2
A3 = 6
A4 = 24
We can see that the coefficients are the factorials of the index, so:
An = n!
Therefore, A1000 = 1000!
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Find i (the rate per period) and n (the number of periods) for the following loan at the given annual rate. Quarterly payments of $1000 are made for 10 years to repay a loan at 10.7% compounded quarterly. is Type an integer or a decimal.) n=
Thus, the rate per period (i) is 0.02675 or 2.675%, and the number of periods (n) is 40.
For this problem, we can use the formula for the present value of annuity:
PV = PMT * ((1 - (1 + i)^(-n)) / i)
Where PV is the present value of the loan, PMT is the quarterly payment, i is the rate per quarter, and n is the total number of quarters.
We know that the quarterly payment is $1000 and the annual rate is 10.7%, compounded quarterly. To find the quarterly rate, we need to divide the annual rate by 4 (since there are 4 quarters in a year):
i = 10.7% / 4 = 0.02675
Next, we need to find the total number of quarters, which is 10 years * 4 quarters per year = 40 quarters:
n = 40
Now we can solve for the present value of the loan:
PV = $1000 * ((1 - (1 + 0.02675)^(-40)) / 0.02675) = $70,401.41
So the rate per period (i) is 0.02675 or 2.675%, and the number of periods (n) is 40.
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In JKL, m L = 53, m J = 90 and KL = 11 ft. What is the length of side JL?
The length of JL is approximately 8.29 ft.
What is the Pythagorean theorem?The Pythagorean theorem says that the sum of the square of the perpendicular and the base will be equal to the square of the hypotenuse of the right-angle triangle.
Since JKL is a right triangle, we can use the Pythagorean theorem to find the length of JL.
Let's label the sides of the triangle: JL = a, LK = b, and JK = c.
By the Pythagorean theorem, we have:
c² = a² + b²
In this case, we know that m L = 53 and m J = 90, so m K = 180 - m L - m J = 37.
Using the sine function, we have:
sin 53 = b/c
c = b/sin 53
Using the sine function again, we have:
sin 37 = a/c
a = csin 37 = (b/sin 53)sin 37
Finally, we can use the Pythagorean theorem to find a:
a² = c² - b² = (b/sin 53)² - b^2
Simplifying this expression, we get:
a² = b² x (1/sin² 53 - 1)
Now we can plug in the given value for KL and solve for b:
b = KL/cos 53 = 11/cos 53
Plugging in this value for b, we get:
a² = (11/cos 53)² x (1/sin² 53 - 1)
Simplifying this expression, we get:
a = 11/tan 53 = 11/1.327 = 8.29 ft
Therefore, the length of JL is approximately 8.29 ft.
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For any real number x, [x] denotes the largest integer less than or equal to x. For example, [4.2] = 4 and [0.9] = 0. If S is the sum of all integers k with 1 <= k <= 999999 and for which k is divisible by [sqrt k], then S equals
The value of S, the sum of all integers k with 1 <= k <= 999999 and for which k is divisible by [sqrt k], is 666167.
To find the value of S, we need to check which integers between 1 and 999999 are divisible by their respective largest integer less than or equal to their square root.
For example, for the number 36, [sqrt 36] = 6, so we need to check if 36 is divisible by 6.
Similarly, for the number 100, [sqrt 100] = 10, so we need to check if 100 is divisible by 10. We need to perform this check for all integers between 1 and 999999 and add up the ones that are divisible.
We can simplify this process by noting that for any integer n, [sqrt n] is either equal to the integer part of sqrt n or one less than the integer part of sqrt n.
Therefore, we only need to check if each integer n is divisible by either floor(sqrt n) or floor(sqrt n) - 1.
We can then use a loop to iterate through all integers between 1 and 999999 and add up the ones that are divisible.
The resulting sum is 666167.
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What percentage (to the nearest tenth) of the total hours were completed by the students other than Lee?
The percentages of the students are
Sally = 25.5%
Min-juin = 32.8
Felicia = 13.6%
How to find the percentages of the studentsTo solve for percentage we use the formula
(a particular part) / total sum * 100
The total sum
= 6.5 + 6.0 + 7.7 + 3.2
= 23.5 hours
Sally
= 6 / 23.5 * 100 = 25.5%
Min-juin
= 7.7 / 23.5 * 100
= 32.8
Felicia
= 3.2 / 23.5 * 100
= 13.6%
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Directions - Create a Phythagorean Theorem equation for the diagram, then solve for the unknown side. If necessary, round to two decimal places.
Answer:
[tex]x^{2} +6^{2} =9^{2}[/tex]
x=6.71
Step-by-step explanation:
The pythagorean theorem is a^2 + b^2 = c^2 where c is the longest side (hypotenuse).
For this right triangle, 9 = c, the hypotenuse. It's across from the right angle.
So [tex]x^{2} +6^{2} =9^{2}[/tex]
Solve for x
x^2 + 36 = 81
x^2 = 81-36
x^2 = 45
take square root of both sides
x = 6.7082039325
so rounded, x=6.71
Two angles are congruent. One angle measures (2x − 3)°. The other angle measures (x + 9)°. What is the measure of one of these angles?
One angle measures (2x - 3)°.
The other angle measures (x + 9)°.
Since the angles are congruent, we can set up the equation:
2x - 3 = x + 9
2x - x - 3 = x + 9 - x
x - 3 = 9
x = 12
Now that we have found the value of x, we can substitute it back into one of the angle measures to find the measure of one of the angles.
Using the expression (2x - 3)°:
Angle measure = (2(12) - 3)°
Angle measure = (24 - 3)°
Angle measure = 21°
Therefore, one of the angles measures 21°.
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find the following product and write in rectangular form [4(cos30 isin30)][3(cos210 i sin 210)]
The product of [4(cos30° + i sin30°)][3(cos210° + i sin210°)] can be written in rectangular form as -6 - 3sqrt(3)i. This means that the product is a complex number with a real part of -6 and an imaginary part of -3sqrt(3).
To find the product, we first multiplied the magnitudes of the two complex numbers, which were 4 and 3, and then added their angles, which were 30° and 210° for the first and second complex numbers, respectively. We then used the trigonometric identities for cosine and sine to simplify the expression and obtain the rectangular form of the product.
It's important to note that complex numbers are useful in a variety of fields, including mathematics, physics, and engineering, where they can be used to represent quantities that have both a magnitude and a direction, such as electric fields and quantum mechanical states. The rectangular form of a complex number makes it easier to perform calculations and visualize the complex plane, where the real and imaginary axes correspond to the horizontal and vertical axes, respectively.
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The bottom of the inside of a rectangular prism is completely covered with a layer of letter cubes, as shown.
A rectangular prism is shown. The bottom of the inside of the prism is completely covered with a layer of letter cubes. The figure is not drawn to scale. The layer of letter cubes is five cubes long in the front and back and three cubes wide on the left and right. [3]
The edges of each letter cube are
1
1
2
inches long.
Part A
What are the length and the width, in inches, of the bottom of the inside of the prism?
The length and width of the bottom of the inside of the rectangular prism are 10 inches and 6 inches, respectively.
The rectangular prism has a layer of letter cubes covering the bottom, and each letter cube has edges that measure 1 inch, 1 inch, and 2 inches long. The layer of letter cubes is five cubes long in the front and back and three cubes wide on the left and right. To find the length and width of the bottom of the inside of the prism, we need to determine the total length and width covered by the layer of letter cubes.
The length is determined by multiplying the number of cubes in the front and back by the length of each cube, which gives 5 cubes × 2 inches/cube = 10 inches. The width is determined by multiplying the number of cubes on the left and right by the width of each cube, which gives 3 cubes × 2 inches/cube = 6 inches.
Therefore, the length and width of the bottom of the inside of the rectangular prism are 10 inches and 6 inches, respectively.
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evaluate the integral. 1∫0 3dx √1+7x
To evaluate the integral 1∫0 3dx √1+7x, we can use the substitution method. Let u = 1 + 7x, then du/dx = 7 and dx = du/7. When x = 0, u = 1 and when x = 3, u = 22. Substituting these into the integral, we get:
1∫0 3dx √1+7x = 1/7 ∫1 22 √u du
To solve this integral, we can use the power rule for integrals, which states that ∫x^n dx = (1/(n+1))x^(n+1) + C. Applying this rule with n = 1/2 and u as the variable, we get:
1/7 ∫1 22 √u du = 1/7 * (2/3) * (22^(3/2) - 1^(3/2))
Simplifying this expression, we get:
1∫0 3dx √1+7x = (2/21) * (22^(3/2) - 1)
Therefore, the value of the integral 1∫0 3dx √1+7x is (2/21) * (22^(3/2) - 1).
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In preparation for a local infrastructure initiative, the city government sent out a survey asking registered voters whether they would support the initiative on the next ballot. The results indicated that 46% of voters would support the initiative. The survey had a margin of error of 1. 9%. If the maximum number of voters who support the initiative is 130,802, what is the population of the city?
The population of the city, applying the proportions in the context of the problem, is given as follows:
273,073.
How to obtain the maximum population?The maximum population of the city is obtained applying the proportions in the context of the problem.
The results indicated that 46% of voters would support the initiative. The survey had a margin of error of 1.9%, hence the maximum proportion is given as follows:
0.46 + 0.019 = 0.479.
(maximum proportion is the estimate plus the margin of error).
The maximum number of voters who support the initiative is 130,802, hence the population is obtained as follows:
0.479p = 130802
p = 130802/0.479
p = 273,073.
(The amount who supports is equivalent to 47.9% = 0.479 of the population p).
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what growth model is appropriate for the number of arrests grew for several years, but now has been decreasing
The appropriate growth model for the given scenario would be a logistic growth model where the growth rate slows down as the variable approaches its carrying capacity, which is the maximum value it can reach.
A logistic growth model is appropriate for situations where the growth rate of a variable initially increases and then slows down as it approaches a maximum value or carrying capacity. In the given scenario, the number of arrests initially grew for several years, but has been decreasing recently, suggesting that it may have reached a saturation point. Thus, a logistic growth model would be appropriate to model the trend of the number of arrests.
In a logistic growth model, the growth rate slows down as the variable approaches its carrying capacity, which is the maximum value it can reach. In the case of the number of arrests, the carrying capacity could be the maximum number of arrests that can be made in a given period, which might be limited by factors such as the number of police officers, the number of crimes committed, or the effectiveness of law enforcement policies. As the number of arrests approaches this limit, the growth rate slows down, eventually leading to a plateau or a decline in the number of arrests.
Overall, a logistic growth model would be appropriate for the given scenario as it takes into account the saturation point and provides a better fit to the trend of the number of arrests over time.
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(05.02 MC) f sin(y°) = cos(x°), which of the following statements is true?
y = w and ΔABC ~ ΔCDE
y = x and ΔABC ~ ΔCDE
y = w and ΔABC ≅ ΔCDE
y = x and ΔABC ≅ ΔCDE
The statement that truly represent the diagram is
y = w and Δ ABC ~ Δ CDE
How to identify the true statementsThe two triangles depicted are similar triangles and similar triangle is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
Examining the figure shows that pair of congruent angles are
angle y = angle w (alternate angles)
angle D = angle B (right triangle)
angle x = angle z (alternate angles)
similar triangles is represented by ~ and only the first option match the description
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find bases for the four fundamental subspaces of the matrix a. a = 1 6 4 0 3 0
the bases for the four fundamental subspaces of a are:
col(a) = span{(1 0), (6 3), (4 0)}
null(a) = {(-6 0 1)}
row(a) = spam{(1 6 4), (0 3 0)}
null([tex]a^T[/tex]) = {(-1/2 1)}
To find the bases for the four fundamental subspaces of the matrix a = [[1 6 4] [ 0 3 0]] , we need to find the column space, nullspace, row space, and left nullspace of a and determine bases for each subspace.
The column space of a is the span of its columns. So, we can write the column space as:
col(a) = span{(1 0), (6 3), (4 0)}
To find a basis for the nullspace of a, we need to solve the equation ax=0 where 0 is the zero vector. This gives us the system of equations:
x₁ + 6x₂ + 4x₃ = 0
3x₂ = 0
The general solution to this system is (x₁ x₂ x₃) = t(-6 0 1) where t is a scalar. So, a basis for the nullspace of a is: {(-6 0 1)}
The row space of a is the span of its rows. So, we can write the row space as:
row(a) = spam{(1 6 4), (0 3 0)}
To find a basis for the left nullspace of a, we need to solve the equation ya=0 where 0 is the zero vector. This gives us the system of equations:
y₁ = 0
6y₁ + 3y₂ = 0
4y₁ = 0
The general solution to this system is (y₁ y₂) = t(-1/2 1) where t is a scalar. So, a basis for the left nullspace of a is: {(-1/2 1)}
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a computer that costs $4600 new has a book value of $3000 after 2 years. find the value of the computer after 3 years by using the exponential model y
The value of the computer with initial value $4600 after 3 years using the exponential model is equal to $2422.39 (approximately).
Cost of new computer = $4600
Book value after 2 years = $3000
use the exponential model,
y = a × [tex]e^{(-kt)}[/tex]
where y is the value of the computer after t years,
a is the initial value of the computer when t=0,
k is a constant,
and e is the base of the natural logarithm.
Find the value of k using the information given,
y(2) = 3000
⇒3000 = a × [tex]e^{(-2k)}[/tex]
y(0) = 4600
⇒ 4600 = a × e⁰
⇒ 4600 = a
Dividing the two equations, we get,
⇒3000/4600 = [tex]e^{(-2k)}[/tex]
⇒0.6522 = [tex]e^{(-2k)}[/tex]
Taking the natural logarithm of both sides, we get,
⇒ -2k = ln (0.6522 )
Solving for k, we get,
⇒ k = -0.4276 /2
⇒ k = - 0.2138
So the exponential model for the value of the computer is,
y = 4600 × [tex]e^{(-0.2138 \times t)}[/tex]
To find the value of the computer after 3 years, we can plug in t=3,
y(3) = 4600 × [tex]e^{(-0.2138 \times 3)}[/tex]
= 4600 × [tex]e^{(-0.6413)}[/tex]
= 4600 × 0.5266
= 2422.39
Therefore, the value of the computer after 3 years using the exponential model is approximately $2422.39.
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if x and y are rational numbers then 3x 2y is also a rational number.
Yes, if x and y are rational numbers, then 3x + 2y is also a rational number. This can be proven using the definition of rational numbers and the closure properties of addition and multiplication.
A rational number is defined as any number that can be expressed as the ratio of two integers, where the denominator is not zero. For example, 3/4, 7/2, and -5/6 are all rational numbers.
Now, let's assume that x and y are rational numbers. Then, by definition, we can write x = p/q and y = r/s, where p, q, r, and s are integers and q and s are not zero.
Using this notation, we can write:
3x + 2y = 3(p/q) + 2(r/s)
= (3p/q) + (2r/s)
= (3ps + 2rq) / qs
Since p, q, r, and s are all integers and qs is not zero, (3ps + 2rq) / qs is also a ratio of two integers where the denominator is not zero. Therefore, 3x + 2y is a rational number.
In conclusion, we can say that if x and y are rational numbers, then 3x + 2y is also a rational number. This result follows directly from the definition of rational numbers and the closure properties of addition and multiplication.
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30 POINTS
USE THE MATRICES TO SHOW THAT MATRIX MULTIPLICATION IS ASSOCIATIVE
(AB) C = 7 1 2
3 1 -4
A (BC) = 7 1 2
3 1 -4
The above shows that the matrix multiplication is associative.
What is a matrix?A matrix is described as a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.
We have that (AB)C =
[(7 1) (1 -2 5)] (2)
[(3 1) (2 4 1)] (-1)
= [(7(1) + 1(2)) (-2(1) + 1(4)) (5(1) + 1(0))]
[(3(1) + 1(2)) (-2(3) + 1(2)) (5(1) + 1(0))]
= [(9) (2) (5)]
[(5) (-4) (5)]
(AB)C = 7 1 2
3 1 -4
If we also solve A (BC), it will also give us 7 1 2
3 1 -4
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PLEASE ONLY ANSWER IF YOU KNOW!!!! :)
(it's so annoying when people only "give an answer" to be able to ask a question. PLS DO NOT DO THAT!! THANK YOU.)
The equations of the functions are f(x) = 200(2.25)ˣ and f(x) = 100(0.84)ˣ
The values of a and b are 8 and 4.2
How to find the equations of the functions a and bFor problem card 1
An exponential function is represented as
f(x) = abˣ
Where
a = y-intercept
b = rate
Using the data card, we have
a = 200
So, we have
y = 200bˣ
Solving for b, we have
200b² = 1012.5
b² = 5.0625
b = 2.25
So, the function is f(x) = 200(2.25)ˣ
For problem card 2
An exponential function is represented as
f(x) = abˣ
Where
a = y-intercept
b = rate
Using the data card, we have
a = 100
So, we have
y = 100bˣ
Solving for b, we have
[tex]100b^{\frac14} = 50[/tex]
[tex]b^{\frac14} = 0.5[/tex]
b = 0.84
So, the function is f(x) = 100(0.84)ˣ
Finding the values of a and bAn exponential function is represented as
f(x) = abˣ
Where
a = y-intercept
b = rate
So, we have
a = 8
So, we have
y = 8bˣ
Solving for b, we have
b² = 18
b = 4.2
Hence, the values of a and b are 8 and 4.2
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a man shares $100 between his son and daughter in the ratio 9:7 how much more money does his son receive than his daughter?
Answer: To determine how much more money the son receives than the daughter, we need to calculate the amounts each of them receives based on the given ratio.
The total ratio is 9 + 7 = 16.
Let's find out the share of the son and daughter:
Son's share = (9/16) * $100
Daughter's share = (7/16) * $100
Calculating these amounts:
Son's share = (9/16) * $100 = $56.25
Daughter's share = (7/16) * $100 = $43.75
The son receives $56.25, and the daughter receives $43.75. To find out how much more money the son receives than the daughter, we subtract the daughter's share from the son's share:
Son's share - Daughter's share = $56.25 - $43.75 = $12.50
Therefore, the son receives $12.50 more than the daughter.
The son receives $12.5 more than the daughter in this question about sharing money in a given ratio.
Explanation:To find out how much more money the son received than the daughter, we need to calculate the difference between the amounts they received.
Let's first calculate the total ratio.
9 + 7 = 16
Now, we can divide $100 in the ratio 9:7.
Son's share = (9/16) * $100 = $56.25
Daughter's share = (7/16) * $100 = $43.75
The son received $56.25 and the daughter received $43.75. Therefore, the son received $12.5 more than the daughter.
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At the beginning of an experiment, the number of bacteria in a colony was counted at time t = 0. The
number of bacteria in the colony t minutes after the initial count is modeled by the function
b (t) = 4(2). What is the average rate of change in the number of bacteria for the first 5 minutes of the
experiment?
Select from the drop-down menus to correctly complete the sentence.
The average rate of change in the number of bacteria for the first 5 minutes of the experiment is
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The average rate of change for the number of bacteria for the first 5 minutes of the experiment is given as follows:
24.8 bacteria per minute.
How to obtain the average rate of change?The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function.
The function for this problem is given as follows:
[tex]b(t) = 4(2)^t[/tex]
The initial number of bacteria is given as follows:
[tex]b(0) = 4(2)^0 = 4[/tex]
The number of bacteria after 5 minutes is given as follows:
[tex]b(5) = 4(2)^5 = 128[/tex]
Hence the average rate of change is given as follows:
(128 - 4)/(5 - 0) = 24.8 bacteria per minute.
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A triangle has vertices at B(-3,0), C(2, -1), D(-1, 2). Which transformation would produce an image with vertices B"(-2, 1), C"(3, 2), D"(0, -1)? (x,y) → (X, -y). (x,y) → (X + 1, y + 1) (x,y) → (-x, y). (x,y) → (X + 1, y + 1) (x,y) → (X. -Y). (x,y) → (X + 2, Y + 2) (x,y) → (-x, y). (x,y) → (X + 2, Y + 2)
The transformation that would produce an image with vertices B"(-2, 1), C"(3, 2), D"(0, -1) from the original vertices B(-3,0), C(2, -1), D(-1, 2) is the transformation (x,y) → (X + 1, y + 1).
By applying the transformation (x,y) → (X + 1, y + 1), each point's x-coordinate is shifted one unit to the right (X = x + 1), and each point's y-coordinate is shifted one unit upward (Y = y + 1). This results in the image with the given coordinates B"(-2, 1), C"(3, 2), D"(0, -1).
The other transformations listed do not match the given image coordinates and would not produce the desired result.
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Answer:
(x, y) → (x, −y) → (x + 1, y + 1)
Step-by-step explanation:
Reflect the vertices over the x-axis by applying the transformation (x, y) → (x, -y):
B'(-3, 0) → B'(-3, 0)
C(2, -1) → C(2, 1)
D(-1, 2) → D(-1, -2)
Translate the reflected vertices by (1, 1):
B'(-3, 0) → B″(-3 + 1, 0 + 1) → B″(-2, 1)
C(2, 1) → C″(2 + 1, 1 + 1) → C″(3, 2)
D(-1, -2) → D″(-1 + 1, -2 + 1) → D″(0, -1)
So, the correct sequence of transformations is:
(x, y) → (x, -y) → (x + 1, y + 1)
(Image provided for more proof)
Find the x- and y-intercept in 3x + 2y = 24 provide work
The x-intercept is (8, 0).
The y-intercept is (0, 12).
We have,
To find the x-intercept, we set y = 0 and solve for x:
3x + 2(0) = 24
3x = 24
x = 8
To find the y-intercept, we set x = 0 and solve for y:
3(0) + 2y = 24
2y = 24
y = 12
Thus,
The x-intercept is (8, 0).
The y-intercept is (0, 12).
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a bag contains 7 white marbles, 4 blue marbles, and 3 yellow marbles. if a marble is drawn from the bag, replaced, and another marble is drawn, what is the probability of drawing first a white marble and then a yellow marble?
Answer:
Step-by-step explanation:
the percetnage is 45%