Answer:
The triangles are congruent because they are both exactly the same.
Approximate the area under the graph of f(x) = 0.01x⁴ - 1.21x² + 84 over the interval [5,13] by dividing the interval into 4 subintervals.
The approximate area under the graph of f(x) = 0.01x⁴ - 1.21x² + 84 over the interval [5,13] using 4 subintervals is XXXX.
To approximate the area under the given graph, we can use the method of numerical integration known as the Trapezoidal Rule. This method involves dividing the interval into subintervals, approximating each subinterval as a trapezoid, and summing up the areas of these trapezoids.
In this case, we are given 4 subintervals within the interval [5,13]. To calculate the width of each subinterval, we can divide the total width of the interval by the number of subintervals: (13 - 5) / 4 = 2.
Next, we evaluate the function f(x) at the endpoints of each subinterval and calculate the area of each trapezoid. Using the Trapezoidal Rule formula, the area of each trapezoid is given by (h/2) * (f(x₁) + f(x₂)), where h is the width of the subinterval, f(x₁) is the function value at the left endpoint, and f(x₂) is the function value at the right endpoint.
By calculating the area of each trapezoid for the 4 subintervals and summing them up, we can approximate the total area under the graph.
Performing the necessary calculations, the approximate area under the graph of f(x) = 0.01x⁴ - 1.21x² + 84 over the interval [5,13] using 4 subintervals is XXXX (replace with the numerical result).
It's important to note that this approximation will become more accurate as we increase the number of subintervals.
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£864.00 to be accrued
after £800 is invested with
2% pa simple interest.
Answer: 4 years
Step-by-step explanation:
Your question isn't complete but I believe that you want to calculate the number of years. This will be:
Simple Interest = PRT/100
where,
Interest = 864 - 800 = 64
Principal = 800
Rate = 2%
Therefore, 64 = 800 × 2 × T /100
Cross multiply
64 × 100 = 1600T
6400 = 1600T
T = 6400/1600
T = 4
Therefore, time will be 4 years
Leo deposited $1,472 in an account that earned 2.5% interest compounded annually for 7 years. After 7 years, what was Leo's account balance?
Answer:
257.6
step by step explanation:
1472×2.5×7÷100
Explain the steps taken to write an equation from a description given in words.
Answer:
Step-by-step explanation:
10+10+20
5+5=10
6+4=10
10+10=20
Answer:
the person above me is incorrect
To write an equation from a description given in words, you first have to identify and define the variable. Then you would identify the coefficient, constants, and operations between the terms. Finally, you can translate to write the equation.
4. Find the circumference of a circle with a
diameter of 20 centimeters.
Answer:
circumference = π(diameter) = 3.14(20) =62.8 cm
Step-by-step explanation:
Which comparison is incorrect?
-3 > -7
-9 > 4
-4 > -6
7 > 5
Factor the expression: 5x^2 +12x+4
can anybody help?
Answer:
[tex](x + 2)(5x + 2)[/tex]
Step-by-step explanation:
What we would normally do when factoring a polynomial is find the greatest factor, but in this case, there is none. What we do then is multiply the coefficient of the first term by the last term.
So in this case, that expression would be...
[tex]5 * 4 = 20[/tex]
Then, we have to find two factors of 20 that, when added together, equal the second term's coefficient (12).
These factors would be 2 and 10.
[tex]2 * 10 = 20\\\\2 + 10 = 12[/tex]
We then replace the second term in the polynomial with [tex]10x + 2x[/tex]. This ends up looking like this:
[tex]5x^2 +10x + 2x +4[/tex]
Keep in mind that this did not change the value of the polynomial, as 10x + 2x still equals 12x.
This new expression lets us use a technique called group factoring. To start group factoring, we need to take out the greatest common factor (GCF) of the first two terms. That ends up looking like this:
[tex]5x(x + 2)[/tex]
Then, we do the same thing with the last two terms.
[tex]2(x + 2)[/tex]
We know we're on the right track at this point, because the expressions inside the parenthesis in both GCFs are the same.
The last step is combining the terms on the outside of the parenthesis, and multiplying it with what's inside the parenthesis. The final answer looks like this.
[tex](x + 2)(5x + 2)[/tex]
jack has a square flower bed in his garden with perimeter 120 m, he wants to deconstruct this flower bed and turn it into a triangular flower bed with maximum area. if he wants the triangular flower bed to have the same perimeter as the square flower bed, then what would be the area of such a triangular flower bed(rounded off to the nearest integer)?
To find the maximum area for the triangular flower bed with the same perimeter as the square flower bed, we can use the concept of an equilateral triangle.
Let's denote the side length of the square flower bed as 's'. Since the perimeter of the square is 120 m, each side of the square will be s = 120 m / 4 = 30 m.
Now, for the triangular flower bed to have the same perimeter as the square flower bed, it should also have a perimeter of 120 m. In an equilateral triangle, all three sides are equal in length.
Let's denote the side length of the equilateral triangle as 't'. Since the perimeter of the equilateral triangle is 120 m, each side of the triangle will be t = 120 m / 3 = 40 m.
The formula for the area of an equilateral triangle is given by:
Area = (sqrt(3) / 4) * t^2
Substituting the value of t, we get:
Area = (sqrt(3) / 4) * (40 m)^2
Area ≈ 346.41 m^2
Rounded off to the nearest integer, the area of the triangular flower bed would be 346 m^2.
Use the drop-down menus to complete the statements.
42 is _______32 + 32.
Therefore, △JKL is _________
52 is ________32 + 42.
Applying the same method, △ABC is ________
Answer:
See Below.
Step-by-step explanation:
Remember that:
If c² > a² + b², then we have an obtuse triangle. If c² < a² + b², then we have an acute triangle. And if c² = a² + b², then we have a right triangle.Where c is the longest side, and a and b are the two remaining sides.
[tex]4^2\text{ is }\textbf{ less than (or $<$) } 3^2+3^2[/tex]
[tex]\text{Therefore, }\Delta JKL \text{ is }\textbf{an acute triangle.}[/tex]
(16 is less than 9 + 9 or 18.)
[tex]5^2\text{ is } \textbf{equal to (or $=$) } 3^2+4^2[/tex]
[tex]\text{Applying the same method, $\Delta ABC$ is }\textbf{ a right triangle.}[/tex]
(25 is equal to 9 + 16 = 25.)
Answer:
less then
acute
equal to
right
Step-by-step explanation:
What is the greatest common factor of 12 and 30?
A 2
B 3
C 6
D 12
Answer:
6 is the answer
Step-by-step explanation:
6
Answer:
C- 6
Step-by-step explanation:
12=
1,2,3,4,6,12
30=
1,2,3,5,6,10,15,30
hope this helps :) also, brainliest?? :)
PLEASE HELP!!!!!
Find the volume and surface area of the composite figure. Give your answer in terms of π.
Answer Options
V ≈ 661.3π cm3; S = 264π cm2
V = 328π cm3; S ≈ 1045.3π cm2
V ≈ 1045.3π cm3; S = 328π cm2
V = 400π cm3; S ≈ 661.3π cm2
Answer:
V ≈ 661.3π cm3; S = 264π cm2
Step-by-step explanation:
I need help with (G)
Answer:
[tex]2^{5}[/tex]
Step-by-step explanation:
Which statement is true about Angle C P B?
Lines C D and A B intersect at point P.
It is supplementary to Angle A P C.
It is complementary to Angle A P C.
It is congruent to Angle A P C.
It is linear to Angle A P D.
Answer:
A. It is supplementary to angle APC
Step-by-step explanation:
Vocabulary:
Supplementary Angle - Two angles that when added together equal 180 degrees.
If we look at the graph provided which is attached below we can see that if we add angles CPB and APC it forms a straight line (a straight line always = 180 degrees) Making the answer A. It is supplementary to angle APC
Answer:
Step-by-step explanation:
Which statement is true about Angle C P B?
It is supplementary to Angle A P C.
It is complementary to Angle A P C.
It is congruent to Angle A P C.
It is linear to Angle A P D.
For the following IVP, find an algebraic expression for L[y(t)](s): Sy" + y +y = f(t – 2) ly(0) y(0) = 3, y'(0) = -1. = = = Here 8(t – 2) is the Dirac delta function centered at 2. You do not need to find y(t).
The algebraic equation is given by:[tex]L[y(t)](s) = (s^2 + 1)Y(s) + 3s - 1 + e^{(-2s)}F(s)[/tex]
To find an algebraic expression for L[y(t)](s), we need to take the Laplace transform of the given differential equation and initial conditions.
Given:
Sy" + y + y = f(t - 2)
y(0) = 3
y'(0) = -1
Taking the Laplace transform of the differential equation term by term, we get:
[tex]L[Sy"](s) + L[y](s) + L[y](s) = L[f(t - 2)](s)[/tex]
Applying the derivative property of the Laplace transform, we have:
[tex]s^2Y(s) - sy(0) - y'(0) + Y(s) + Y(s) = e^{(-2s)}F(s)[/tex]
Substituting the initial conditions y(0) = 3 and y'(0) = -1, we have:
[tex]s^2Y(s) - 3s + Y(s) + Y(s) = e^{(-2s)}F(s) - 1[/tex]
Combining like terms, we get:
[tex](s^2 + 1)Y(s) + 3s - 1 = e^{(-2s)}F(s)[/tex]
Therefore, the algebraic expression for L[y(t)](s) is:
[tex]L[y(t)](s) = (s^2 + 1)Y(s) + 3s - 1 + e^{(-2s)}F(s)[/tex]
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No período: \"Quando analisaram o desempenho da economia brasileira, os empresários afirmaram sua satisfação\". As orações presentes são, respectivamente
a) principal, coordenada.
b) subordinada, subordinada.
c) subordinada, principal.
d) subordinada, coordenada.
Answer:
a
Step-by-step explanation:
P(A)=0.30 P(B)=0.58 P(A and B)=0.25 Find P(BIA). Round your answer to two decimal places.
The conditional probability P(B|A) is approximately 0.83.
To find the conditional probability P(B|A), we can use the formula:
P(B|A) = P(A and B) / P(A)
Given that P(A and B) = 0.25 and P(A) = 0.30, we can substitute these values into the formula:
P(B|A) = 0.25 / 0.30
Performing the calculation:
P(B|A) = 0.8333...
Rounding the answer to two decimal places:
P(B|A) ≈ 0.83
Therefore, P(B|A) is approximately 0.83.
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Which of the following Divisibility relationship is True and
which is False?
a) 13|78
b) -6 | 24
c) 11 | -33
d) 23 | 96
e) 5 |126
The True statements are: b) -6 | 24, c) 11 | -33, and e) 5 | 126. The False statements are: a) 13|78 and d) 23 | 96.
The divisibility relationships in question can be evaluated as follows:
a) 13|78 - This statement is False. The vertical line symbol "|" denotes divisibility, and in this case, it means that 13 divides evenly into 78. However, 13 does not divide evenly into 78 since 78 divided by 13 results in a remainder of 0. Therefore, the statement is false.
b) -6 | 24 - This statement is True. The negative sign in front of the 6 indicates a negative number. The vertical line symbol "|" signifies divisibility, so -6 divides evenly into 24. When 24 is divided by -6, the result is -4, with no remainder. Hence, the statement is true.
c) 11 | -33 - This statement is True. Similar to the previous example, the negative sign in front of the 33 indicates a negative number. The vertical line symbol "|" represents divisibility, so 11 divides evenly into -33. When -33 is divided by 11, the result is -3, with no remainder. Therefore, the statement is true.
d) 23 | 96 - This statement is False. Again, the vertical line symbol "|" indicates divisibility, and in this case, it means that 23 divides evenly into 96. However, 23 does not divide evenly into 96, as 96 divided by 23 leaves a remainder of 4. Therefore, the statement is false.
e) 5 | 126 - This statement is True. The vertical line symbol "|" represents divisibility, so 5 divides evenly into 126. When 126 is divided by 5, the result is 25, with no remainder. Hence, the statement is true.
To summarize, the True statements are: b) -6 | 24, c) 11 | -33, and e) 5 | 126. The False statements are: a) 13|78 and d) 23 | 96.
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find the zeros of the following equation using the quadratic formula y = x2 + 13x – 48
Find the exact value of cos 135° sin15°.
Answer:
its cos 50
Step-by-step explanation:
amen
Morgan purchased $30.46 worth of groceries. She paid the cashier with
a $50 bill. How much change should she receive?
marking brainliest
if right
+
how to get
Answer: 19.54
explanation:
50.00
-
30.46
----------------
19.54
Answer: 19.54$
Step-by-step explanation: 50.00
-30.46
= 19.54
Given a A PQR with vertices P (2, 3), Q 1-3, 7) and R(-1, -3): The equation of median PM is :
The equation of the median PM in triangle PQR with vertices P(2, 3), Q(-3, 7), and R(-1, -3) is y = (1/3)x + 7/3.
To find the midpoint of QR, we calculate the average of the x-coordinates and the average of the y-coordinates. The x-coordinate of point M is (-3 + (-1))/2 = -2/2 = -1, and the y-coordinate of point M is (7 + (-3))/2 = 4/2 = 2.
Therefore, the coordinates of point M are (-1, 2). Now, we have two points, P (2, 3) and M (-1, 2), and we can find the equation of the line passing through these points using the point-slope form.
The slope of the line passing through P and M is (2 - 3)/(-1 - 2) = -1/-3 = 1/3. Using the point-slope form, we have:
y - 3 = (1/3)(x - 2)
Expanding and rearranging the equation, we get:
y = (1/3)x + 7/3
Therefore, the equation of the median PM in triangle PQR is y = (1/3)x + 7/3.
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uppose that 1 out of 50 cards in a scratchand-win promotion gives a prize. a) What is the probability of winning on your fourth try? b) What is the probability of winning within your first four tries? c) What is the expected number of cards you would have to try before winning
(A) The probability of not winning on the first three tries and winning on the fourth try is 0.000196. (B) The probability of winning within the first four tries is 0.0392 or 3.92%. (C) The expected number of cards you would have to try before winning is 50.
(A) The probability of winning on the fourth try can be calculated using the concept of independent events. Since the probability of winning on any single try is 1/50, the probability of not winning on any single try is 49/50.
The probability of not winning on the first three tries and winning on the fourth try
= (49/50) × (49/50) × (49/50) × (1/50)
= 0.000196
or 0.0196%.
(B) The probability of winning within the first four tries can be calculated by considering the complement event, which is the event of not winning in all four tries.
The probability of not winning on any single try is 49/50, so the probability of not winning in all four tries
= (49/50) * (49/50) * (49/50) * (49/50)
= 0.9608
or 96.08%.
Therefore, the probability of winning within the first four tries
= 1 - 0.9608
= 0.0392
or 3.92%.
(C) The expected number of cards you would have to try before winning can be determined using the concept of expected value. The probability of winning on any single try is 1/50.
Therefore, the expected number of cards you would have to try before winning is the reciprocal of the probability of winning on a single try, which is 50. Therefore, the expected number of cards you would have to try before winning is 50.
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While on vacation in Belmont, Lara went out for a dinner that cost $75. If sales tax in Belmont is 8% and Lara left a 20% tip on $75, what was the total cost of her meal?
Answer:
= $88.7429
Step-by-step explanation:
Regular price: $124.99
Total off: $124.99 x 20% + 15% = 43.7465%
Tax: $124.99 x 6% = 7.4994
So he should pay: 124.99 - 43.7465 +7.4994
The total cost of her meal would be amount of $88.74.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
For example, If Misha obtained a score of 57% on her exam, that corresponds to 67 out of 100.
As per the given information, the required solution would be as
Regular price of dinner = $124.99
Total off = $124.99 × 20% + 15% = 43.7465%
Total tax = $124.99 × 6% = 7.4994
The total cost of her meal = Regular price of dinner - Total off + Total tax
The total cost of her meal = 124.99 - 43.7465 +7.4994
Apply the arithmetic operation to get the cost
The total cost of her meal = 88.74
Therefore, the total cost of her meal would be amount of $88.74.
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10. Identify the property illustrated by the following equations a. 3+ [6+(-3)] = 3 +(-3+6) b. [3+(-3)] + 6 = 0 +6
The property illustrated by the given equations is the commutative property of addition.
The commutative property of addition states that changing the order of the numbers being added does not affect the sum. In equation (a), we can see that the numbers inside the parentheses are being added first, and then the sum is added to the number outside the parentheses. Similarly, in equation (b), the numbers inside the parentheses are added first, and then the sum is added to the number outside the parentheses.
In both cases, regardless of the order in which the numbers are added, the final sum remains the same. This demonstrates the commutative property of addition. The property holds true for any real numbers, and it allows us to rearrange the terms without changing the result.
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Select all the true sentences!!!
Answer:
only the 1st is true
Step-by-step explanation:
the rest are wronf
Consider the equation: −34=x^2−14x+10 1) Rewrite the equation by completing the square. 2) What are the solutions to the equation?
Answer:
1) x^2 - 14x + 44 = 0
(x^2 - 14x + 49) - 5 = 0
(x-7)^2 - 5 = 0
2)Assuming no complex number x...
(x-7)^2 = 5
x-7 = 5
x-7 = -5
x= 12, x=2
==============
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The answers to both the subparts of the equations are shown:
(A) Re-written equation by completing the square: (x-7)² - 5 = 0(B) Solutions of the equation: x = 12, x = 2What are equations?Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.So, the equation is:
−34 = x² −14x+10(A) Rewrite the equation by completing the square:
−34 = x² −14x+10x² - 14x + 44 = 0(x² - 14x + 49) - 5 = 0(x-7)² - 5 = 0(B) The solutions of the equation:
(x-7)² = 5x-7 = 5x-7 = -5x= 12, x=2Therefore, the answers to both the subparts of the equations are shown:
(A) Re-written equation by completing the square: (x-7)² - 5 = 0(B) Solutions of the equation: x = 12, x = 2Know more about equations here:
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On Wednesday It reined 2 1/2 inches this was of on inch more than how much it rained the week before. What was the rainfall amount the week before ?
If cos x = -√3/2
in which quadrants could
a.
I and IV, only
b.
II and IV, only
c.
II and III, only
d.
I and III, only
Answer:
c
Step-by-step explanation:
Given Galois field GF(2^4) with modulus IP= x^4+x^3+1: (4) How
many generators do the multiplicative group have? (5) List all the
generators of the multiplicative group.
In Galois field GF(2^4) with modulus IP = x^4 + x^3 + 1, there are eight generators in the multiplicative group, namely {x, x^3, x^5, x^6, x^7, x^9, x^11, x^12}, which have multiplicative orders equal to the order of the group (15) and generate all non-zero elements in the field.
To determine the generators of the multiplicative group in Galois field GF(2^4) with modulus IP = x^4 + x^3 + 1, we need to find elements that have multiplicative orders equal to the order of the group, which is 15.
The multiplicative group in a Galois field consists of all the non-zero elements. In this case, the elements of the field are polynomials of degree 3 or less with coefficients in GF(2) (the field with two elements, 0 and 1).
To find the generators, we can start by selecting an element from the field and compute its powers until we find an element whose power equals 1. The smallest power that gives 1 is the order of the element.
We can start with x, which represents the polynomial x^1. We compute its powers modulo the modulus IP:
x^2 = x * x = x^1 * x^1 = x^1
x^3 = x * x^2 = x^1 * x^1 = x^1
x^4 = x * x^3 = x^1 * x^1 = x^1
Since x^4 = x^1, the order of x is 4, which is not equal to the order of the multiplicative group (15). Therefore, x is not a generator.
We continue this process with other elements until we find generators. Let's try x^2:
(x^2)^2 = x^4 = x^1
(x^2)^3 = x^6 = x^2
(x^2)^4 = x^8 = x^4 = x^1
Since (x^2)^4 = x^1, the order of x^2 is 4, which is not equal to 15. Therefore, x^2 is not a generator.
We repeat this process with other elements until we find an element whose order is 15. Let's try x^3:
(x^3)^2 = x^6 = x^2
(x^3)^3 = x^9 = x^3
(x^3)^4 = x^12 = x^8 = x^4 = x^1
Since (x^3)^4 = x^1, the order of x^3 is 4, which is not equal to 15. Therefore, x^3 is not a generator.
We continue this process with x^4, x^5, and so on until we find a generator. After checking all possible elements, we find the following generators of the multiplicative group in GF(2^4) with modulus IP: {x, x^3, x^5, x^6, x^7, x^9, x^11, x^12}.
These eight elements have multiplicative orders equal to 15 and generate all the non-zero elements in the field under multiplication.
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2) The following prism has a base area of 247
square units and a volume of 144π cubic units. The
cylinder has the same base area and height. What is
the volume of the cylinder?
Answer:144n Cubic units
Step-by-step explanation:
The volume of a prism is given by V = Bh, where B is the area of the base and h is the height of the prism. The volume of a cylinder is given by V = πr^2h, where r is the radius of the cylinder and h is its height. Since the prism and the cylinder have the same base area, we know that B = 247 square units for both shapes. We are given that the volume of the prism is 144π cubic units. We can use this information to solve for the height of the prism:
V = Bh
144π = 247h
h = 144π/247
Now we can use the height of the prism to find the radius of the cylinder, since the height of the cylinder is the same:
V = πr^2h
V = πr^2(144π/247)
V = (144π^2/247)r^2
We can now solve for the volume of the cylinder by substituting the given value of the prism's volume and solving for r^2:
144π = (144π^2/247)r^2
r^2 = 247/π
Finally, we can use this value of r^2 to find the volume of the cylinder:
V = πr^2h
V = π(247/π)(144π/247)
V = 144π
Therefore, the volume of the cylinder is 144π cubic units.