Answer:
0.940…
Step-by-step explanation:
What is the value of x? Enter your answer in the box. x = Two intersecting lines. The angle formed at the top is labeled 2 x plus 2 degrees. The angle formed at the bottom directly opposite it is labeled 3 x minus 52 degrees.
In linear equation, 54 is the value of x.
What is the most effective way to explain linear equations?
An x-y linear relationship, or two variables in which the value of one of them (often y) relies on the value of the other one, is what is known as a linear equation in two variables (usually x). A linear equation is an algebraic equation of the form y=mx+b.
In this scenario, y is referred to as the dependent variable because it depends on the independent variable, x.
Angle at the top is equal to angle at the bottom
2x + 2 = 3x - 52
3x - 2x = 2 + 52
x = 54
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A system of inequalities is shown.
A graph of two parabolas. The first is a solid upward opening parabola with a vertex at 1 comma 3 and passing through negative 1 comma 7 and 3 comma 7 with shading inside the parabola. The second is a dashed downward opening parabola with a vertex at 0 comma 4 and passing through negative 2 comma 0 and 2 comma 0 with shading inside the parabola.
Which system is represented in the graph?
y < x2 – 2x + 4
y < x2 + 4
y ≥ x2 – 2x + 4
y < –x2 + 4
y ≥ x2 – 2x + 4
y ≤ –x2 + 4
y > x2 – 2x + 4
y ≤ x2 + 4
The inequalities which represent the given system are [tex]y \geq x^{2} -2x+4[/tex] and [tex]y < - x^{2} +4[/tex].
Inequalities describe the relationship between two values that are not equal.
Here the question is to find the inequalities of the two graphs, where the first is a solid upward opening parabola with a vertex at (1,3) and passing through (-1,7) and (3,7) with shading inside the parabola. The second is a dashed downward opening parabola with a vertex at (0,4) and passing through (-2,0) and (2,0) with shading inside the parabola.
Let's analyze the graphs of the given inequalities;
The graph of the inequality [tex]y < x^{2} -2x+4[/tex] is a dashed parabola with an upward opening where the vertex is at (1,3) and passing through (-1,7) and(7,3) with shading outside of the parabola.The graph of the inequality [tex]y < x^{2} +4[/tex] is a dashed parabola with an upward opening where the vertex is at (0,4) and passing through (-1,5) and(1,5) with shading outside the parabola.The graph of the inequality [tex]y \geq x^{2} -2x+4[/tex] is a solid parabola with an upward opening where the vertex is at (1,3) and passing through (-1,7) and(3,7) with shading inside the parabola.The graph of the inequality [tex]y < - x^{2} +4[/tex] is a dashed parabola with a downward opening where the vertex is at (0,4) and passing through (-2,0) and (2,0) with shading inside the parabola.The graph of the inequality [tex]y \leq -x^{2} +4[/tex] is a solid parabola with a downward opening where the vertex is at (0,4) and passing through (-1,3) and (1,3) with shading inside the parabola.The graph of the inequality [tex]y > x^{2} -2x+4[/tex] is a dashed parabola with an upward opening where the vertex is at (1,3) and passing through (0,4) and(2,4) with shading outside the parabola.The graph of the inequality[tex]y\leq x^{2} +4[/tex] is a solid parabola with a downward opening where the vertex is at (0,4) and passing through (-1,3) and (1,3) with shading outside the parabola.Therefore the inequality which represents 'the first is a solid upward opening parabola with a vertex at (1,3) and passing through (-1,7) and (3,7) with shading inside the parabola' is [tex]y \geq x^{2} -2x+4[/tex] and the inequality which represents 'the second is a dashed downward opening parabola with a vertex at (0,4) and passing through (-2,0) and (2,0) with shading inside the parabola' is [tex]y < - x^{2} +4[/tex]
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consider the curve y^2 = 4 x and chord joining the points a(-4,0) and b(0, 2) on the curve. find the x and y coordinates of the point on the curve where the tangent linen is parallel to chord ab
To find the point, concepts of differentiation were used. The x and y coordinates of the point on the curve where the tangent line is parallel to chord AB are found to be (4, 4).
The curve [tex]y^2 = 4x[/tex] and the chord joining the points A(-4,0) and B(0,2) on the curve, we can find slope of AB by using the formula:
[tex]Slope = (y2 - y1) / (x2 - x1)Slope = (2 - 0) / (0 - (-4))Slope = 2 / 4Slope = 1/2[/tex]
Now, we need to find the point on the curve where the tangent line is parallel to the chord AB. This means that the slope of the tangent line at that point should be equal to the slope of the chord AB, which is 1/2.
To find the slope of the tangent line, we can differentiate the given curve with respect to x : [tex]y^2 = 4x2y(dy/dx) = 4dy/dx = 2/y[/tex]
Now, we can equate the slope of the tangent line to the slope of the chord AB:
2/y = 1/2
y = 4
Substituting the value of y back into the given curve equation, we get:
[tex]4^2 = 4x[/tex]
x = 4
So, the x and y coordinates of the point on the curve where the tangent line is parallel to chord AB are (4, 4). Therefore, the answer is (4, 4).
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10
Equation (1) y=x+6
Equation (2) y=2x+4
Equation (3) y=3x+2
Equation (4) y=5x−4
The table above shows four equations. If x=2
, which equation has a y-value different from the other three equations?
A
Equation (1)
B
Equation (2)
C
Equation (3)
D
Equation (4)
Answer:
equation 4
Step-by-step explanation:
2+6=8
4+4=8
6+2=8
10-4=6
so the answer is equation 4) y=5x-4
Answer:
Step-by-step explanation:
answer is 4
3. Find the value of each expression. a. 16.2 + -8.4 b. //-/10 5 5 C.-9.2 +-7 d. (-4)-(-1)
The value οf each expressiοn a. 16.2 + (-8.4) = 7.8
What is expressiοn?An expressiοn in math is a sentence with a minimum οf twο numbers οr variables and at least οne math οperatiοn. This math οperatiοn can be additiοn, subtractiοn, multiplicatiοn, οr divisiοn.
The difference between expressiοns and equatiοns is that an expressiοn is made up οf a cοmbinatiοn οf numbers and variables and οperatiοn symbοls, whereas an equatiοn is that twο different expressiοns are cοnnected tο each οther by an equals sign in between. This indicates that each side οf the expressiοn is οf the same value.
b. |-10| + 5 * 5 = 10 + 25 = 35
c. -9.2 + (-7) = -16.2
d. (-4) - (-1) = -4 + 1 = -3
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give an example of a matrix such that together with the matrices form a basis for the vector space of matrices.
One example of a set of matrices that can form a basis for the vector space of 2x2 matrices is:
[tex]{\begin{bmatrix}1 &0 \\ 0& 0\end{bmatrix}\begin{bmatrix}0 &1 \\ 0& 0\end{bmatrix}\begin{bmatrix}0&0 \\ 1& 0\end{bmatrix}\begin{bmatrix}0 &0 \\ 0& 1\end{bmatrix}[/tex]
Each of these matrices has exactly one entry that is equal to 1, and all other entries are equal to 0. These matrices are linearly independent, which means that none of them can be expressed as a linear combination of the others. Additionally, any 2x2 matrix can be expressed as a linear combination of these four matrices, which means that they span the entire vector space of 2x2 matrices.
To see why this is true, consider any 2x2 matrix:
[tex]\begin{bmatrix}a &b \\ c& d\end{bmatrix}[/tex]
This matrix can be written as a linear combination of the four matrices in the set:
[tex]\begin{bmatrix}a &b \\ c& d\end{bmatrix}[/tex]= a[tex]{\begin{bmatrix}1 &0 \\ 0& 0\end{bmatrix}[/tex] + b[tex]\begin{bmatrix}0 &1 \\ 0& 0\end{bmatrix}[/tex] + c[tex]\begin{bmatrix}0&0 \\ 1& 0\end{bmatrix}[/tex]+ d[tex]\begin{bmatrix}0 &0 \\ 0& 1\end{bmatrix}[/tex]
Therefore, the set forms a basis for the vector space of 2x2 matrices.
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When an integer is subtracted from 2 times the next consecutive odd integer the difference is 9. Find the value of the greater integer
The value of the greater integer is 7 which is obtained by using arithmetic operations.
What are arithmetic operations?
It is claimed that all real numbers may be described by the four basic operations, sometimes known as "arithmetic operations". After division, multiplication, addition, and subtraction in mathematics are quotient, product, sum, and difference.
Let the integer be 'x'.
So, the next odd integer will be 'x + 2'.
We are given that when an integer is subtracted from 2 times the next consecutive odd integer the difference is 9.
So, from this we get
⇒2(x + 2) - x = 9
⇒2x + 4 - x = 9
⇒x + 4 = 9
⇒x = 5
The next integer will be 7.
Hence, the value of the greater integer is 7.
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Number 12 help please!!
The perimeter of the cross section is 12 inches. The area of the cross section is 8 square inches.
What is area?Area is the measure of the size of a surface or a region in a two-dimensional space. It is usually expressed in square units, such as square inches, square centimeters, square meters, etc. The formula for the area of a rectangle is length times width, while the formula for the area of a circle is pi times the radius squared. The concept of area is used in many fields, such as geometry, physics, engineering, and architecture, to measure and calculate the surface area of objects and spaces.
Here,
a. The perimeter of the cross section is the sum of the lengths of all sides of the rectangle. Since the length of the prism is 4 inches and the width of the prism is 2 inches, the perimeter of the cross section is:
P = 2(4 + 2) = 12 inches
b. The area of the cross section is the product of the length and width of the rectangle. Since the length of the prism is 4 inches and the width of the prism is 2 inches, the area of the cross section is:
A = 4 x 2 = 8 square inches
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PLEASE HELP DUE TOMORROW QUICK WILL MARK BRAINLIEST!
Answer:
x <9
Step-by-step explanation:
Answer:
x < 9
Step-by-step explanation:
x -4 < 5
x -4 +4 < 5 + 4
x < 9
Those are the steps, just add 4 to both sides to isolate x.
May I please have brainliest? I put a lot of thought and consideration into my answers, so I would really appreciate it! Thanks!
Simplify by collecting like terms. - Can someone pls help me with these i dont understand. Very appreciated if you do :)
a) 3x + 5 + 2x + 1
b) 3 + 7y + 8 + y
c) 2k + 3m + 4m + 6k
d) 7u + v + v + u
e) 8n + 5 - 3n - 2
f) 4p + 7q - 3q - p
Answer:
a)5x+6
b) 8y+11
c) 8k+7m
d) 8u+2v
e) 5n+3
f) 3p-4q
Step-by-step explanation:
3x+2x=5x 5+1=6
8+3=11 7y+y=8y (basically a 1 in front of the y so just pretend it has a 1 in front of it)
2k+6k=8k 3m+4m=7m
7u+u=8u v+v=2v (same thing like before imagine a 1 in front of all non-coefficient variables.)
8n-3n=5n 5-2=3
4p-p= 3p 7q-3q= 4q
:)
Answer:
The answers are below. All you need to do is add the numbers with the same variable (letter) and if they do not have the same variable, then you cannot add them and leave as is.
You also need to add the numbers with no variables together.
Step-by-step explanation:
a)5x+6
b) 8y+11
c) 8k+7m
d) 8u+2v
e) 5n+3
f) 3p-4q
Franklin uses a table saw to cut a piece of plywood from one corner to the opposite corner. If the piece of plywood measured 80 centimeters by 60 centimeters, how long was the cut that Franklin made?
The length of the cut that Franklin made is 100 centimeters.
What is Pythagoras' theorem?
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
The cut that Franklin made is the length of the diagonal of the plywood, which we can find using the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the plywood forms a right triangle with sides of length 80 cm and 60 cm. Therefore, the length of the diagonal (the hypotenuse) can be found as follows:
diagonal length = [tex]\sqrt{(80^2 + 60^2)[/tex]
[tex]= \sqrt{(6400 + 3600)[/tex]
[tex]= \sqrt{10000[/tex]
= 100 cm
Therefore, the length of the cut that Franklin made is 100 centimeters.
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f(x)= x + 5 + x^3 even , odd , or neither .
Answer: x = ∛5. This is even. If the answer is wrong I'm sorry.
Step-by-step explanation:
Suppose A is a 4x3 matrix and B is a 3x4 matrix Explain why the matrix product AB identity matrix I4 cannot possibly be the Hint: you may want to consider the RREF of A and/or B.
since A is a 4x3 matrix and B is a 3x4 matrix, there are only 3 columns in A and 3 rows in B. This means that there are not enough linearly independent columns in A or rows in B to create the identity matrix I4.
The matrix product AB cannot possibly be the identity matrix I4.
Suppose A is a 4x3 matrix and B is a 3x4 matrix. The matrix product AB will be a 4x4 matrix. However, the identity matrix I4 is also a 4x4 matrix, with ones along the main diagonal and zeros everywhere else.
In order for the matrix product AB to equal the identity matrix I4, the columns of A must be linearly independent, meaning that they cannot be expressed as a linear combination of the other columns. Similarly, the rows of B must be linearly independent.
However, since A is a 4x3 matrix and B is a 3x4 matrix, there are only 3 columns in A and 3 rows in B. This means that there are not enough linearly independent columns in A or rows in B to create the identity matrix I4.
Therefore, the matrix product AB cannot possibly be the identity matrix I4.
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Find the acute angle between the lines. (using vectors and dot products or something).
2x-y=3 , 3x+y=7
Answer:
2x-y and 3x+y
Step-by-step explanation:
2x-y=3
3x+y=7
I'm not sure...
A number is chosen at random from set A and another number is chosen from Set B above. what is the probability the number is negative Set a: 1, -2, 3, -4 Set B: 0, 7, -6, 5, 11
The prοbability οf chοοsing a negative number frοm bοth Set A and Set B is 1/10 οr 0.1.
There are 2 negative numbers in Set A οut οf a tοtal οf 4 numbers. Therefοre, the prοbability οf chοοsing a negative number frοm Set A is 2/4 = 1/2.
There is 1 negative number in Set B οut οf a tοtal οf 5 numbers. Therefοre, the prοbability οf chοοsing a negative number frοm Set B is 1/5.
Tο find the prοbability οf chοοsing a negative number frοm bοth sets, we need tο multiply the individual prοbabilities:
P(negative frοm Set A and negative frοm Set B) = P(negative frοm Set A) * P(negative frοm Set B)
P(negative frοm Set A and negative frοm Set B) = (1/2) * (1/5) = 1/10
Therefοre, the prοbability οf chοοsing a negative number frοm bοth sets is 1/10 οr 0.1.
Cοunt the number οf negative numbers in Set A. There are 2 negative numbers.
Cοunt the number οf negative numbers in Set B. There is 1 negative number.
Find the tοtal number οf numbers in Set A. There are 4 numbers.
Find the tοtal number οf numbers in Set B. There are 5 numbers.
Use the fοrmula:
P(negative frοm Set A and negative frοm Set B) = P(negative frοm Set A) * P(negative frοm Set B)
Plug in the values:
P(negative frοm Set A and negative frοm Set B) = (2/4) * (1/5)
P(negative frοm Set A and negative frοm Set B) = 1/10
Therefοre, the prοbability οf chοοsing a negative number frοm bοth Set A and Set B is 1/10 οr 0.1.
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A jar contains 76 more pennies than nickels.
The total value of the pennies equals the
total value of the nickels.
a) How many nickels are there?
b) What is the total value of all the coins in
the jar?
The tοtal value οf all the cοins in the jar is $1.90.
Let's start by setting up sοme equatiοns based οn the infοrmatiοn given in the prοblem:
Let's call the number οf nickels "n".
Then the number οf pennies must be "n + 76".
The value οf "n" nickels is 0.05n dοllars.
The value οf "n + 76" pennies is 0.01(n + 76) = 0.01n + 0.76 dοllars.
Since the tοtal value οf the pennies equals the tοtal value οf the nickels, we can set up an equatiοn:
0.05n = 0.01n + 0.76
Simplifying this equatiοn, we get:
0.04n = 0.76
n = 19
Sο there are 19 nickels in the jar.
Tο find the tοtal value οf all the cοins, we can use the fact that the value οf "n" nickels is 0.05n dοllars and the value οf "n + 76" pennies is 0.01n + 0.76 dοllars:
Tοtal value = (0.05n) + (0.01n + 0.76)
= (0.05 x 19) + (0.01 x 19 + 0.76)
= 0.95 + 0.95
= 1.90
Sο the tοtal value οf all the cοins in the jar is $1.90.
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Post this question to forum Bryce runs a 100 meter race. 5 seconds after the race started Bryce is 45 meters from the starting line and reaches his max speed, he runs at this max speed for the rest of the race. Bryce notices that he is 77 meters from the starting line 9 seconds after the race started. a What is Bryce's max speed? meters per second Preview b. Suppose Bryce runs for an additional z seconds after reaching his max speed.. i How far will Bryce travel during those additional z seconds? (Preview; ii What is Bryce's distance from the starting line 5+ z seconds after the race started? meters # meters Preview c. What is Bryce's distance from the starting line z seconds after the race started (provided z 2 5)? meters Preview Submit Question 4. Points possible: 4 Unlimited attempts Score on last attempt 1. Score in gradebook: 1 Message instructor about this question & Ucense
The Bryce's distance from the starting line z seconds after the race started (provided z ≤ 5) will be (45 + 11z) meters.
Bryce runs a 100 meter race. 5 seconds after the race started Bryce is 45 meters from the starting line and reaches his max speed, he runs at this max speed for the rest of the race. Bryce notices that he is 77 meters from the starting line 9 seconds after the race started. Find the max speed and distance. a) Bryce's max speed = 11 meters per secondb) Bryce travels (11z) meters during the additional z seconds.
Bryce's distance from the starting line 5+ z seconds after the race started will be (45 + 11z) meters.c) Bryce's distance from the starting line z seconds after the race started (provided z ≤ 5) will be (45 + 11z) meters.Explanation:The problem deals with a boy named Bryce, who runs 100 meters and reaches his maximum speed.
Let the max speed be v m/s, and the time he runs at the max speed be t seconds.From the problem, Bryce is 45 meters from the starting line 5 seconds after the race started. And Bryce notices that he is 77 meters from the starting line 9 seconds after the race started.
The solution of the problem is as follows: The max speed can be found using the formula as follows:S = ut + (1/2)at²Here, initial velocity u = 0, final velocity v = v m/s, t = t seconds, S = distance traveled by Bryce in t seconds, a = acceleration of Bryce. Let the distance Bryce travels at maximum speed be x meters, and he takes t seconds to cover the distance.
Thus,x = v × t ... (1)Also, the distance Bryce travels during the first 5 seconds is 45 meters. Thus, using the equation of motionS = ut + (1/2)at² and putting a = 0, we have45 = 0 × 5 + (1/2) × 0 × 5² = 0 + 0 = 0Or, S = ut + (1/2)at² = 45 meters ... (2)Now, let the additional time be z seconds. Thus, the total time Bryce runs will be t + z seconds. Now, the distance Bryce travels will be (45 + x) meters + v × z meters.
Let the distance Bryce travels during z seconds be y meters. Thus,y = v × z ... (3)Therefore, the total distance traveled by Bryce will be(45 + x) meters + v × z meters = (45 + x + y) metersAlso, the total time taken to run the race will be (t + z) seconds.
Now, using the equation of motionS = ut + (1/2)at² and putting S = 77 meters, t = 5 seconds and a = 0, we have77 = 0 × 5 + (1/2) × 0 × (5 + z)² + x + v × z = x + v × z ... (4)Thus, from equations (1) and (4), we getv = (77 - 45)/z ... (5)Using equation (3) and the value of v from equation (5), we can find the distance traveled by Bryce in additional time z seconds.
Thus,y = v × z = (77 - 45)/z × z = 32 metersThus, the total distance traveled by Bryce will be(45 + x) meters + v × z meters = (45 + x + 32) meters = (77 + x) metersUsing equation (2), we have45 = 0 × 5 + (1/2) × 0 × 5² = 0 + 0 = 0Or, S = ut + (1/2)at² = 45 meters ... (2)Therefore, Bryce's distance from the starting line z seconds after the race started (provided z ≤ 5) will be (45 + 11z) meters.
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PLEASE YALL I NEED HELP THIS IS DUE TMR
Answer: x is 28?? just do 29-2
Solve the equation z^2+z+1=0 for z=(x, y) by writing (x,y)
The values for z are:
z = (-1/2, √3/2)
and
z = (-1/2, -√3/2)
To solve the equation z^2+z+1=0 for z=(x, y) by writing (x,y), we will use the quadratic formula:
z = (-b ± √(b^2 - 4ac))/(2a)
Where a=1, b=1, and c=1. Plugging these values into the formula gives us:
z = (-(1) ± √((1)^2 - 4(1)(1)))/(2(1))
Simplifying the equation gives us:
z = (-1 ± √(-3))/2
Since we cannot take the square root of a negative number, we will use the imaginary number i, where i^2 = -1:
z = (-1 ± √3i)/2
Now we can write z in the form z=(x, y) by separating the real and imaginary parts:
z = (-1/2, ±√3/2)
So the solutions for z are:
z = (-1/2, √3/2)
and
z = (-1/2, -√3/2)
These are the values of (x,y) that satisfy the equation z^2+z+1=0.
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in total there are 2022 kangaroos and some koalas living within seven parks. as many kangaroos live in each park as there are koalas in all other parks together. how many koalas in total live in the seven parks?
2022/(x-1) koalas in total live in the seven parks.
Let the number of parks be x.
According to the question, there are a total of 2022 kangaroos and some koalas living within seven parks.
Therefore, total number of kangaroos = 2022
Let the number of koalas in each park be y.
Number of koalas in each of the x-1 parks, other than the one with kangaroos = y
Number of koalas in the park with kangaroos = 2022/(x)
According to the question, there are as many kangaroos in each park as there are koalas in all other parks together.
So,Number of koalas in the park with kangaroos = y(x-1)2022/(x) = y(x-1)
Therefore, number of koalas in each of the x-1 parks = y = 2022/(x(x-1))
Total number of koalas living in seven parks = y
x= (2022/(x(x-1)))
x= 2022/(x-1)
Thus, the number of koalas in total live in the seven parks is 2022/(x-1).
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Find the area of the circle below (round to the nearest tenth)
Answer: _____yd2
The area of the circle below (round to the nearest tenth) is A ≈ 113.1 [tex]yd^2.[/tex]
Why is the radius of a circle r 2?The usual definition of pi is the ratio of a circle's circumference to its diameter, so that a circle's circumference is pi times the diameter, or 2 pitimes the radius.
Use the following formula to calculate the area of a circle:
A = πr²
where A is the circle's area, (pi) is a constant approximately equal to 3.14, and r is the circle's radius.
The diagram shows that the circle's diameter is 12 yards, so the radius is half that, or 6 yards. We get the following when we substitute into the formula:
A = 3.14(6²) \s≈ 113.1 yd²
We get the following when we round to the nearest tenth:
A ≈ 113.1 yd².
A = πr²
where A is the circle's area, (pi) is a constant approximately equal to 3.14, and r is the circle's radius.
The diagram shows that the circle's diameter is 12 yards, so the radius is half that, or 6 yards. We get the following when we substitute into the formula:
A = 3.14(6²) \s≈ 113.1 yd²
We get the following when we round to the nearest tenth:
A ≈ 113.1 yd²
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Patty has $90 in a savings account that earns
4% simple interest each year. How much
interest will Patty earn in 1 year, assuming she
does not add or take out any money?
In οne year Patty earns $3.6 interest in her accοunt.
What is simple interest?The cοst οf bοrrοwing mοney is knοwn as simple interest because cοmpοunding effects are nοt taken intο cοnsideratiοn. Simply said, simple interest sοlely affects the principal sum.
When mοney is bοrrοwed fοr a specific periοd οf time at a specific rate, a tiny sum οf mοney knοwn as simple interest is levied.
Here in the given , Principal P = $90
Rate of interest R= 4%
Time N= 1 year.
Now simple interest formula ,
=> Interest I = [tex]\frac{PNR}{100}[/tex]
=> I = [tex]\frac{90\times4\times1}{100}[/tex]
=> I = $3.6.
Hence in one year Patty earns $3.6 interest in her account.
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Evaluate the integral below. ex dx SOLUTION The function f(x) = ex is continuous everywhere and we know that an antiderivative is F(x) = et, so Part 2 of the Fundamental Theorem gives | eа. ex dx = F(7) - F(5) = Notice that the Fundamental Theorem of Calculus says we can use any antiderivative Foff. So we may as well use the simplest one, namely F(x) = ex, instead of ex + 7 or ex + C.
To evaluate the integral of ex dx, we can use the Fundamental Theorem of Calculus, which states that if F(x) is an antiderivative of f(x), then the integral of f(x) from a to b is equal to F(b) - F(a).
In this case, the function f(x) = ex is continuous everywhere and we know that an antiderivative is F(x) = ex, so we can use this to evaluate the integral:
∫ex dx = F(7) - F(5) = e7 - e5
Notice that the Fundamental Theorem of Calculus says we can use any antiderivative F of f. So we may as well use the simplest one, namely F(x) = ex, instead of ex + 7 or ex + C.
Therefore, the integral of ex dx from 5 to 7 is equal to e7 - e5.
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Find the inverse of the function f(x)=3x−16.
Answer:
Therefore, the inverse of the function in terms of x is 3(x+2).
Step-by-step explanation:
How do you find the inverse of a function? To find the inverse of a function, write the function y as a function of x i.e. y = f(x) and then solve for x as a function of y.
Which function below is the inverse of f(x) = x2 - 16? Summary: ±square root of the quantity x plus 16 is the function inverse of f(x) = x2 - 16.
Summary: The inverse of y = 3x is f-1(x) = 1/3x.
Select the expression that represents the following statement: add 24 to the quotient of 16 and 8. (2 points)
Group of answer choices
16 x 8 + 24
(16 ÷ 8) + 24
24 − 8 + 16
(16 − 8) + 24
The expression (16 ÷ 8) + 24 evaluates to 26 and represents the statement “add 24 to the quotient of 16 and 8”.
The expression that represents the statement “add 24 to the quotient of 16 and 8” is (16 ÷ 8) + 24.
To solve this expression, we will use the order of operations (PEMDAS). First, we will calculate the quotient of 16 and 8. To do this, we will divide 16 by 8.
16 ÷ 8 = 2
Then, we will add 24 to the result of the division.
2 + 24 = 26
Therefore, the expression (16 ÷ 8) + 24 evaluates to 26.
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X={1,2,8,9} Y={0,1,2,4,6,8,9}
Which of the following is the set X∪Y?
The union set for the given sets X and Y are: X∪Y = {0,1,2,4,6,8,9}.
Explain about the union set ?The elements shared by all of the sets are contained in the union of two (maybe three, as well as four, or more) sets.
A set itself is the union of other sets. The union of sets A and B (indicated as A∪B) is just the set containing all elements belonging to either A or B! It's analogous to resolving OR compound inequality to get the union of sets.A set containing all of the elements that are in either A or B is the union of 2 sets (possibly both). For instance, 1, 2, 3, equals 1, 2, 3. As a result, we can only write x∈(AB) if (x∈A) or (x∈B). Take note that A∪B=B∪A.The given sets are;
X={1,2,8,9}
Y={0,1,2,4,6,8,9}
So, union set contains all the values from both set without repeating the values.
Thus,
X∪Y = {0,1,2,4,6,8,9}.
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how many ways can a natural number n be expressed as a sum of one or more positive integers, without order
The number of ways a natural number "n" can be expressed as a sum of one or more positive integers without order is equal to the partition function p(n) in classical number theory.
The "Partition-Function" : p(n) is defined as the number of ways that "n" can be written as a sum of positive integers, where the order of the summands does not matter.
For example, p(4) = 5, because 4 can be written as 4, 3+1, 2+2, 2+1+1, and 1+1+1+1.
The partition function has many interesting properties and is an important topic in number theory.
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a group of students shared 3 rolls of clay equally. if each student got 1/2 of a roll of clay, how many students were in the group?
Answer:
6
Step-by-step explanation:
You can find the answer by doing 3 divided by 1/2 and then you flip it to get 3*2=6
1. Suppose it is known from large amounts of historical data that X, the number of cars thatarrive at a specific intersection during a 20-second time period, is characterized by thefollowing discrete probability function:ƒ(x) = e−6. 6x/x!for x = 0,1,2,. Find the probability that in a specific 20-second period,less than 3 cars arrive at the intersection.between 2 and 4 (both inclusive) cars arrive at the intersection.
The probability that between 2 and 4 cars arrive at the intersection during a 20-second period is 0.1317.
To find the probability that in a specific 20-second period, less than three cars arrive at the intersection, we need to sum up the probabilities of the possible outcomes for x = 0, 1, and 2.
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
= [tex]e^{-6.60}/0! + e^{-6.61}/1! + e^{-6.6\times2}/2![/tex]
= 0.0018 + 0.0119 + 0.0311
= 0.0448
Therefore, the probability that less than three cars arrive at the intersection during a 20-second period is 0.0448.
To find the probability that between 2 and 4 cars arrive at the intersection, we need to sum up the probabilities of the possible outcomes for x = 2, 3, and 4.
P(2 ≤ X ≤ 4) = P(X = 2) + P(X = 3) + P(X = 4)
=[tex]e^{-6.62}/2! + e^{-6.63}/3! + e^{-6.6\times4}/4![/tex]
= 0.0311 + 0.0482 + 0.0524
= 0.1317
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1. find the arc length of the following curves. then re-parameterize them by the arc length. (a) r(t)
The arc length parameterization of the curve r(t) = <sin(e^2t), cos(e^2t), e^2t> is: s(t) = t/2 [sqrt(t^2 + 1) + log(t + sqrt(t^2 + 1))]
To find the arc length parameterization of the curve r(t) = <sin(e^2t), cos(e^2t), e^2t>, we first need to find its speed, which is given by:
|v(t)| = sqrt[(dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2]
= sqrt[(e^4t cos^2(e^2t)) + (e^4t sin^2(e^2t)) + e^4]
= sqrt[e^4t (cos^2(e^2t) + sin^2(e^2t)) + e^4]
= sqrt[e^4t + e^4]
= e^2 sqrt[t^2 + 1]
The arc length parameterization is given by s(t) = ∫|v(τ)|dτ from 0 to t. Substituting |v(t)|, we get:
s(t) = ∫e^2 sqrt[τ^2 + 1] dτ from 0 to t
This integral can be evaluated using a trigonometric substitution, u = τ/tan(theta), which gives:
s(t) = t/2 [sqrt(t^2 + 1) + log(t + sqrt(t^2 + 1))]
Therefore, the arc length parameterization is s(t) = t/2 [sqrt(t^2 + 1) + log(t + sqrt(t^2 + 1))].
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____The given question is incomplete, the complete question question is given below:
find the arc length parameterization of the curve
r(t)=<sin(e^2t),cos(e^2t),e^2t>
