The angle between vectors AB and AC is approximately 30.42°.
Let's start off by using the formula to calculate the angle between two vectors:Angle between vectors = arccos(dot product of vectors / product of their magnitudes)Therefore, let us first find the magnitudes of AB and AC:AB = √((8 - 9)² + (5 - 3)²) = √5AC = √((3 - 9)² + (9 - 3)²) = 2√45 = 6√5
Next, we must find the dot product of AB and AC:AB · AC = (8 - 9)(3 - 9) + (5 - 3)(9 - 3) = -6 + 48 = 42Finally, we can use the formula to calculate the angle:θ = arccos(AB · AC / (|AB| * |AC|)) = arccos(42 / (6√5 * √5)) = arccos(7 / 5) ≈ 0.53 radians ≈ 30.42°
We start off by using the formula to calculate the angle between two vectors:Angle between vectors = arccos(dot product of vectors / product of their magnitudes)Therefore, let us first find the magnitudes of AB and AC:AB = √((8 - 9)² + (5 - 3)²) = √5AC = √((3 - 9)² + (9 - 3)²) = 2√45 = 6√5Next, we must find the dot product of AB and AC:AB · AC = (8 - 9)(3 - 9) + (5 - 3)(9 - 3) = -6 + 48 = 42Finally, we can use the formula to calculate the angle:θ = arccos(AB · AC / (|AB| * |AC|)) = arccos(42 / (6√5 * √5)) = arccos(7 / 5) ≈ 0.53 radians ≈ 30.42°
The angle between AB and AC is approximately 30.42°.
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A rectangular field in a park is 66.5ft wide and 110ft long. What is the area of the field in square meters? m
2
The area of the field in square meters is approximately 679.2431 m².Given: Width (W) of rectangular field in a park = 66.5ftLength (L) of rectangular field in a park = 110ftArea
(A) of rectangular field in a park in square meters.We can solve this question using the following steps;Convert the measurements from feet to meters.Use the formula of the area of a rectangle to find out the answer.1. Converting from feet to meters1ft = 0.3048m
Now we can convert W and L to meters
W = 66.5ft × 0.3048 m/ft ≈ 20.27 m
L = 110ft × 0.3048 m/ft ≈ 33.53 m2. Find the area of the rectangle
The formula for the area of the rectangle is given as;A = L × W
Substituting the known values, we have;
A = 33.53 m × 20.27 mA = 679.2431 m²
Therefore, the area of the field in square meters is approximately 679.2431 m².
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8. You are selling concessions at a local swim meet. Hot dogs are being sold for
$1.00 and soda is being sold for $0.50. At the end of the day you made $150.
Let x represent the number of hotdogs sold and y represent the number of
sodas sold. Write an equation that can be used to find the number of hotdogs
and sodas sold at the swim meet.
a. Standard Form:
b. Slope-Intercept Form:
c. If you sold 40 hot dogs how many sodas did you sell?
d. Using the Standard Form, identify the x-intercept of the graph and explain
how the x-intercept relates to the number of hot dogs and sodas sold.
e. Using the Standard Form, identify the y-intercept of the graph and explain
how the y-intercept relates to the number of hot dogs and sodas sold.
The equation that can be used to find the number of hotdogs
and sodas sold at the swim meet.
a)x+0.50y=150
b) y=-2x+300
c)Number of soda sold y =220 if hot dog is 40.
d) x intercept=150. It is related to the total earnings of soda and hot dogs sold.
f) y intercept = 300 . It is related to the 2 times of the total earnings of soda and hot dogs sold.
What is x-intercept and y-intercept?
An equation's or a function's graph that contacts the x axis is said to have a "X intercept." This is comparable to a point having a value of zero. Given that it is located on the horizontal axis, this is sometimes referred to as the horizontal intercept. The y value at the point where the line meets the y axis is known as the y intercept. By examining the graph and identifying the point that crosses the y axis, we may determine the y intercept. This point's x coordinate will always be 0. It will be recorded as (0,y). Given that it is on the vertical axis, this is also referred to as a vertical intercept.
Let us take number of hot dogs sold as x and number of soda sold as y.
Cost of one hot dog = $1.00
Cost of one soda = $0.50
Then , cost of x number of hot dogs sold = 1x
cost of y number of soda sold = 0.50y
Then, . At the end of the day you made $150.
=> 1x+0.50y= 150
a) standard form of the equation is ,
=> x+0.50y=150 ------->1
b) x+0.50y=150
=> x+\(\frac{1}{2}\)y=150
=>2x+y=150*2
=>2x+y=300
Then slope intercept form is y=-2x+300------->2
c) Number of hot dogs sold x=40 and put into 2 ,
then , y=-2(40)+300
=> y=-80+300
=>y=220
Number of soda sold y =220
d) To find x intercept put y=0 into 1 , then
=> x+0=150
=>x=150
Here x intercept=150. It is related to the total earnings of soda and hot dogs sold.
e)To find y intercept put x=0 into 1,
=> 0+0.50y=150
=> y = 150/0.50
=> y =300
Here y intercept = 300 . It is related to the 2 times of the total earnings of soda and hot dogs sold.
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For each of the following collections, determine and briefly explain whether it is finite, countably infinite (like the natural numbers), or uncountably infinite (like the reals): (a) The integers which divide 8. (b) The integers which 8 divides. (c) The functions from N to N. (d) The set of strings over the English alphabet. (Note that the strings may be arbitrarily long, but each string has finite length. Also the strings need not be real English words.) (e) The set of finite-length strings drawn from a countably infinite alphabet, A. (f) The set of infinite-length strings over the English alphabet.
(a) The integers which divide 8 are -8, -4, -2, -1, 1, 2, 4, and 8. This collection is finite, as there are only eight elements in it.
(b) The integers which 8 divides are 8, 16, -8, -16, 24, -24, and so on. This collection is countably infinite, as it can be put into a one-to-one correspondence with the set of integers.
(c) The functions from N to N are uncountably infinite, since there are infinitely many possible functions from one countably infinite set to another.
(d) The set of strings over the English alphabet is uncountably infinite, since each string can be thought of as a binary string of infinite length, with each character representing a 0 or 1.
(e) The set of finite-length strings drawn from a countably infinite alphabet, A, is countably infinite, since it can be put into a one-to-one correspondence with the set of natural numbers.
(f) The set of infinite-length strings over the English alphabet is uncountably infinite, since it can be thought of as a binary string of infinite length, with each character representing a 0 or 1, and there are uncountably many such strings.
(a) The integers which divide 8: This set is finite, as there are a limited number of integers that evenly divide 8 (i.e., -8, -4, -2, -1, 1, 2, 4, and 8).
(b) The integers which 8 divides: This set is countably infinite, as there are infinitely many multiples of 8 (i.e., 8, 16, 24, 32, ...), and they can be put into one-to-one correspondence with the natural numbers.
(c) The functions from N to N: This set is uncountably infinite, as there are infinitely many possible functions mapping natural numbers to natural numbers, and their cardinality is larger than that of the natural numbers (i.e., it has the same cardinality as the power set of natural numbers).
(d) The set of strings over the English alphabet: This set is countably infinite, as there are infinitely many possible finite-length strings, but they can be enumerated in a systematic way (e.g., listing them by length and lexicographic order).
(e) The set of finite-length strings drawn from a countably infinite alphabet, A: This set is countably infinite, as each string has a finite length and can be enumerated in a similar manner to the English alphabet case.
(f) The set of infinite-length strings over the English alphabet: This set is uncountably infinite, as there are infinitely many possible infinite-length strings, and their cardinality is larger than that of the natural numbers (i.e., it has the same cardinality as the real numbers).
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B. Using audit sampling, a subset of the population is selected for testing to derive generalisations about the population. Required: Determine FIVE (5) elements to be assessed during the sample selection. (5 marks )
The five elements to be assessed during sample selection in audit sampling are Sapmlinf Frame, Sample Size, Sampling Method, Sampling Interval, Sampling Risk.
1. Sampling Frame: The sampling frame is the list or source from which the sample will be selected. It is important to ensure that the sampling frame represents the entire population accurately and includes all relevant elements.
2. Sample Size: Determining the appropriate sample size is crucial to ensure the sample is representative of the population and provides sufficient evidence for drawing conclusions. Factors such as desired confidence level, acceptable level of risk, and variability within the population influence the determination of the sample size.
3. Sampling Method: There are various sampling methods available, including random sampling, stratified sampling, and systematic sampling. The chosen sampling method should be appropriate for the objectives of the audit and the characteristics of the population.
4. Sampling Interval: In certain sampling methods, such as systematic sampling, a sampling interval is used to select elements from the population. The sampling interval is determined by dividing the population size by the desired sample size and helps ensure randomization in the selection process.
5. Sampling Risk: Sampling risk refers to the risk that the conclusions drawn from the sample may not be representative of the entire population. It is important to assess and control sampling risk by considering factors such as the desired level of confidence, allowable risk of incorrect conclusions, and the precision required in the audit results.
During the sample selection process, auditors need to carefully consider these elements to ensure that the selected sample accurately represents the population and provides reliable results. By assessing and addressing these elements, auditors can enhance the effectiveness and efficiency of the audit sampling process, allowing for meaningful generalizations about the population.
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PLEASE I NEED HELP I WILL GIVE YOU BRAINLIEST
in the graph of the inequality x-2y (less than or equal too) 4, which is a value for x on the boundary line and the x axis
4
-2
2
-4
The value of x on the boundary line and the x axis is found as 4.
Explain the term inequality?In mathematics, "inequality" refers to a relationship among two expressions and values that is not equivalent to each other. Therefore, inequality emerges from a lack of balance.When two components are equal, we use the sign "=," and if they are not equal, we use the symbol "," which stands for "not equal."For the given question,
The graph of inequality x-2y ≤ 4 is drawn.
Consider the graph,
The straight lien formed by the graph touches the x coordinate axis at (4,0).
Thus, the value of x on the boundary line and the x axis is found as 4.
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At a dance show, 60 performers were placed in groups of two or three performers. There were an equal number of groups of 2 performers. Each group was given 4 ribbons to perform the dance. What was the total number of ribbons given
The total number of ribbons given to the groups are 120 ribbons
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
The number of performers = 60 performers
The number of performers in each groups = 2 performers
So ,
Total number of groups =
number of performers / number of performers in each groups
Total number of groups = 60 / 2
= 30 groups
Now ,
Number of ribbons given to each group = 4 ribbons
So ,
Total number of ribbons distributed =
Number of ribbons given to each group x Total number of groups
Total number of ribbons distributed = 4 x 30
= 120 ribbons
Hence , the total number of ribbons given to the groups are 120 ribbons
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Scaled scores on the WISC-V have a mean of ____ and a standard deviation of _____.
a. 10/3
b. 10/5
c. 3/1
d. 100/15
the correct answer is option a: 10/3, which represents the mean and standard deviation of the scaled scores on the WISC-V.
Scaled scores are used to compare an individual's performance on the WISC-V to the performance of other individuals in the same age group. The scaled scores are derived from raw scores and are standardized to have a mean and standard deviation that are predetermined.The mean of scaled scores on the WISC-V is set to 10. This means that an average performance is represented by a scaled score of 10.
The standard deviation of scaled scores on the WISC-V is set to 3. The standard deviation measures the spread or variability of scores around the mean. A standard deviation of 3 indicates that most scores fall within 3 points above or below the mean of 10.
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pls
ef F F. dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results. S (3z + 2y) dx + (2x - 2z) dy+ (3x - 2y) dz (a) C: line segment from (0, 0, 0) to (1,
1) The line integral value is : ∫F dr = 6
2) The line integral value is : ∫F dr = 6
3) The line integral value is : ∫F dr = 6
Here we are given:
\(F.dr = (3x + 2y)dx + (2x -2z)dy + (3x -2y)dz,\)
where\(\vec{F}\) is a conservative field
So,
f(x, y , z) = \(\int\limits (3x + 2y)dx + (2x -2z)dy + (3x -2y)dz,\)
f(x , y , z) = (3zx +2yx) + (2xy - 2zy) + (3xz - 2yz) + c(x , y , z)
\(f(x, y, z) = (6xz + 4xy - 4yz) + c(x, y, z)\)
Now substitute the values of x , y ,z ,
1)
Line segment from (0, 0 , 0) to (1,1 ,1)
∫F dr = f(1,1,1) - f(0,0,0)
= |6 + 4 - 4 |- |0 + 0 - 0|
∫F dr = 6
2)
Line segment from (0,0,0) to (0,0,1) to (1,1,1)
First we take (0,0,0) to (0,0,1)
\(\int _c \vec{F}.\vec{dr}=f(0,0,1)-f(0,0,0) =[6(0)(1)+4(0)(0)-4(0)(1)]-[6(0)(0)+4(0)(0)-4(0)(0)] =[0+0-0]-[0+0-0]\)
∫F dr = 0
\(\Rightarrow \int _{c}\vec{F}.\vec{dr}=0+6 [F.dr = 6\)
3)
Line segment from (0,0,0) to (1,0,0) to (1,1,0) to (1,1,1)
First we take (0,0,0) to (1,0,0)
\(\int _c \vec{F}.\vec{dr}=f(1,0,0)-f(0,0,0) =[6(1)(0)+4(1)(0)-4(0)(0)]-[6(0)(0)+4(0)(0)-4(0)(0)] =[0+0-0]-[0+0-0]\int _{c}\vec{F}.\vec{dr}=0\)
Next we take (1,0,0) to (1,1,0)
\(\int _c \vec{F}.\vec{dr}=f(1,1,0)-f(1,0,0) = [6(1)(0) + 4(1)(1) − 4(1)(0)] - [6(1)(0) + 4(1)(0) — 4(0)(0)] = [0+4-0] - [0+0-0]\int _{c}\vec{F}.\vec{dr}=4\)
Lastly we take (1,1,0) to (1,1,1)
\(F.dr = f(1,1,1) ƒ(1,1,0) = [6(1)(1) +4(1)(1) − 4(1)(1)] - [6(1)(0) + 4(1)(1) — 4(1)(0)] =[6+4-4]-[0+4-0]\int _{c}\vec{F}.\vec{dr}=2\)
Adding the three results we get
\(\Rightarrow \int _{c}\vec{F}.\vec{dr}=0+4+2\\\\\int\limits F.dr = 6\)
Therefore we see that the Line integral for the three cases comes out to be same between the initial and final points since it is independent of the path taken.
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The ratio of people watching whales to people fishing was five to seven if there were 72 people in all how many were fishing
There were 42 people who are fishing if the ratio of people watching whales to people fishing was five to seven.
What is a numerical expression?A numerical expression is algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.
We have been given that the ratio of people watching whales to people fishing was five to seven if there were 72 people.
Let the number of people who watch whales would be 5x
And the number of people who are fishing would be 7x
According to the given condition, the required solution would be as:
⇒ 5x + 7x = 72
⇒ 12x = 72
⇒ x = 6
So the number of people who are fishing = 7 × 6 = 42
Therefore, there were 42 people who are fishing.
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Witch pair of lines are perpendicular
A) y= 4x - 6
y= 4x + 11
B) y= -4x - 6
y= 4x + 11
C). y= 1/4x - 6
y= 4x + 11
D). y= -1/4x - 6
y= 4x + 11
Answer:
Step-by-step explanation:
Find the volume of the cylinder. Round your answer to the nearest tenth.
Volume of the cylinder as we know is πr²h, using the volume formula is = 1085.18ft³.
Define volume?A cylinder's capacity, which indicates how much material it can carry, is determined by its volume. Geometry provides a precise formula for determining a cylinder's volume, which may be used to determine how much of any material, liquid or solid, can fit inside of it equally.
A cylinder is a three-dimensional object having two parallel, identical congruent bases.
In the given figure,
Radius of cylinder = 6ft.
Height of cylinder = 9.6ft.
Volume of cylinder = πr²h
= 3.14 × 6² × 9.6
= 1085.18ft³
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(03.01 LC)
A theater company charges $5.50 per ticket for people of all age groups. If c represents the total number of children who bought tickets and a represents the total number of adults who bought tickets, which expression best represents the total money earned by the company from the sale of tickets? (1 point)
Answer: 5.50 (c + a)
Step-by-step explanation:
What is the answer to the problem 4 Ike’s 81
Answer:
wdawdsawd wddddddddddddddddddddddd
Step-by-step expwdlanation:
wdsadwwwwwww
A bookcase has 6 shelves.
Anna has 130 books.
She puts an equal number of books on each shelf.
There are 4 books left over.
How many books are on each shelf? *
Answer:
21 books
Step-by-step explanation:
130-4=x
x/6= answer
The indicated functiony1(x)is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2,y2 = y1(x)
e−∫P(x) dx
y
2
1(x)
integral.gif
dx (5)
as instructed, to find a second solution
y2(x).
x2y'' − xy' + 26y = 0; y1 = x sin(5 ln x)
y2 =
The second solution is: y2(x) = -1 / x¹⁸ + 29x sin(5lnx) ∫ e^(29u) / sin(u) du/5 + Cx sin(5lnx) where C is a constant of integration.
To find a second solution y2(x) for the given differential equation x²y'' - xy' + 26y = 0 with the function y1(x) = x sin(5 ln x), we'll use the reduction of order formula:y2(x) = y1(x) * e^(-∫P(x)dx) * ∫(e^(∫P(x)dx) / y1(x)^2 dx)
First, rewrite the given differential equation in the standard form:
y'' - (1/x)y' + (26/x²)y = 0
From this, we can identify P(x) = -1/x.
Now, calculate the integral of P(x):
∫(-1/x) dx = - ln|x|
Now, apply the reduction of order formula:
y2(x) = x sin(5 ln x) * e^(ln|x|) * ∫(e^(-ln|x|) / (x sin(5 ln x))² dx)
Simplify the equation:
y2(x) = x sin(5 ln x) * x * ∫(1 / x² (x sin(5 ln x))² dx)
y2(x) = x² sin(5 ln x) * ∫(1 / (x² sin²(5 ln x)) dx)
Now, you can solve the remaining integral to find the second solution y2(x) for the given differential equation.
To find the second solution y2(x), we will use the reduction of order method. Let's assume that y2(x) = v(x) y1(x), where v(x) is an unknown function. Then, we can find y2'(x) and y2''(x) as follows:
y2'(x) = v(x) y1'(x) + v'(x) y1(x)
y2''(x) = v(x) y1''(x) + 2v'(x) y1'(x) + v''(x) y1(x)
Substituting y1(x) and its derivatives into the differential equation and using the above expressions for y2(x) and its derivatives, we get:
x^2 (v(x) y1''(x) + 2v'(x) y1'(x) + v''(x) y1(x)) - x(v(x) y1'(x) + v'(x) y1(x)) + 26v(x) y1(x) = 0
Dividing both sides by x^2 y1(x), we obtain:
v(x) y1''(x) + 2v'(x) y1'(x) + (v''(x) + (26/x^2) v(x)) y1(x) - (1/x) v'(x) y1(x) = 0
Since y1(x) is a solution of the differential equation, we have:
x^2 y1''(x) - x y1'(x) + 26y1(x) = 0
Substituting y1(x) and its derivatives into the above equation, we get:
x^2 (5v'(x) cos(5lnx) + (25/x) v(x) sin(5lnx)) - x(v(x) cos(5lnx) + v'(x) x sin(5lnx)) + 26v(x) x sin(5lnx) = 0
Dividing both sides by x sin(5lnx), we obtain:
5x v'(x) + (25/x) v(x) - v'(x) - 5v(x)/x + v'(x) + 26v(x)/x = 0
Simplifying the above expression, we get:
v''(x) + (1/x) v'(x) + (1/x² - 31/x) v(x) = 0
This is a second-order linear homogeneous differential equation with variable coefficients. We can use formula (5) in Section 4.2 to find the second linearly independent solution:
y2(x) = y1(x) ∫ e^(-∫P(x) dx) / y1^2(x) dx
where P(x) = 1/x - 31/x^2. Substituting y1(x) and P(x) into the above formula, we get:
y2(x) = x sin(5lnx) ∫ e^(-∫(1/x - 31/x²) dx) / (x sin(5lnx))² dx
Simplifying the exponent and the denominator, we get:
y2(x) = x sin(5lnx) ∫ e^(31lnx - ln(x)) / x^2sin²(5lnx) dx
y2(x) = x sin(5lnx) ∫ x^30 / sin²(5lnx) dx
Let u = 5lnx, then du/dx = 5/x, and dx = e^(-u)/5 du. Substituting u and dx into the integral, we get:
y2(x) = x sin(5lnx) ∫ e^(30u) / sin²(u) e^(-u) du/5
y2(x) = x sin(5lnx) ∫ e^(29u) / sin²(u) du/5
Using integration by parts, we can find that:
∫ e^(29u) / sin^2(u) du = -e^(29u) / sin(u) - 29 ∫ e^(29u) / sin(u) du + C
where C is a constant of integration. Substituting this result into the expression for y2(x), we get:
y2(x) = -x sin(5lnx) e^(29lnx - 5lnx) / sin(5lnx) - 29x sin(5lnx) ∫ e^(29u) / sin(u) du/5 + Cx sin(5lnx)
Simplifying the first term and using the substitution u = 5lnx, we get:
y2(x) = -x⁶ e^(24lnx) + 29x sin(5lnx) ∫ e^(29u) / sin(u) du/5 + Cx sin(5lnx)
y2(x) = -x⁶ / x^24 + 29x sin(5lnx) ∫ e^(29u) / sin(u) du/5 + Cx sin(5lnx)
y2(x) = -1 / x¹⁸ + 29x sin(5lnx) ∫ e^(29u) / sin(u) du/5 + Cx sin(5lnx)
Therefore, the second solution is: y2(x) = -1 / x¹⁸ + 29x sin(5lnx) ∫ e^(29u) / sin(u) du/5 + Cx sin(5lnx) where C is a constant of integration.
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what is-12x + 16 – 4x = -112
Answer:
\(x=8\)
Step-by-step explanation:
First, I wanna point out a minor mistake, are we supposed to figure out x?
If we are, let's start.
\(-12x+16-4x=-112.\)
We don't need the \(16.\)
We subtract the 16 from both sides.
SImplify, =\(16x=128\)
Also, group like terms, and add similar elements.
Answer:
x = 8
Step-by-step explanation:
-12x + 16 - 4x = -112
Combine like terms on the left side.
-16x + 16 = -112
Subtract 16 from both sides.
-16x = -128
Divide both sides by 16.
x = 8
Check:
-12x + 16 - 4x =
= -12(8) + 16 - 4(8)
= -96 + 16 - 32
= -80 - 32
= -112
-112 = -112
x = 8 is correct.
Answer: x = 8
A recipe calls for
1
4 cup of flour. Carter does not have a
quarter-cup measuring cup, though he
has a measuring cup that holds an eighth
of a cup. How can Carter measure the
flour he needs for his recipe
Answer: Add 1/8 to 1/8, or multiply 1.8 by 2
Step-by-step explanation:
1/8 + 1/8 = 2/8, which is 1/4
or
1/8 x 2 = 2/8 which is 1/4
How can you apply it triangle congruence to real life situation?
Congruent triangles are also frequently employed in architectural designs, carpet patterns, stepping stone patterns, and geometric art.
The following are the two most typical instances of this: Equilateral triangles are used to make truss bridges, which are built on both sides.
Congruence :
If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. A term used to describe an object and its mirror counterpart is congruence. If two things or shapes superimpose on one another, they are said to be congruent. They are identical in terms of size and shape. Line segments having the same length and angles with the same measure are congruent in the context of geometric figures.
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There are a adults at the fair. There are 20 more kids than adults. Choose the expression that shows how many kids there are.
The expression that represents the number of kids in the fair is 20 + a
How to determine the expression for the number of kids?From the question, the given parameters are:
Adults = a
Kids = 20 more kids than adults
The above can be represented as
Kids = 20 + Adults
Substitute Adults = a in the equation Kids = 20 + Adults
So, we have the following equation
Kids = 20 + a
Remove the variable "kids"
So, we have the following expression
20 + a
Hence, the expression is 20 + a
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ANYONE! HELP! I KNOW THE ANSWER I JUST NEED TO SHOW THE WORK
Find the missing angle.
The answer is 146
What is the fuction rule this table
The table values using function rule y = -10x - 2 is (8,-2,-12,-52)
Given function
y = -10x - 2
From the table
x = -1 , 0 , 1 , 5
substitute x values in function
if x = -1
y = -10x - 2
= -10(-1) - 2
= 10 - 2
y = 8
if x = 0
y = -10(0) -2
y = -2
if x = 1
y = -10(1) - 2
y = -12
if x = 5
y = -10(5) -2
y = -52
y values (8,-2,-12,-52)
Table:
x y
-1 8
0 -2
1 -12
5 -52
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1. 20% of the items manufactured by a certain process are known to be defective. 18 items are chosen at random. a. how many would you expect to be defective? explain briefly what this means. b. find the probability that at least 4 are defective. give a numerical answer.
The expected number of defective items and the probability of at least 4 are defective is equal to 3.6 and 0.370 or 37.0%.
Total number of items 'n' = 18
Probability of an item being defective 'p' =20%
= 0.2
Expected number of defective items,
Use the formula for the expected value of a binomial distribution,
E(X) = np
where X is the number of defective items.
Plug in the values we have,
E(X) = 18 x 0.2
= 3.6
Expect average items out of 18 to be defective = 3.6 .
Probability that at least 4 items are defective,
Calculate the probability of 4, 5, 6, ..., 18 defective items
Use the complement rule to simplify it,
P(at least 4 defective)
= 1 - P(less than 4 defective)
Using the CDF function,
'binomcdf' is the binomial cumulative distribution function.
18 is the number of trials,
0.2 is the probability of success,
And 3 is the maximum number of successes
P(less than 4 defective)
= binomcdf (18, 0.2, 3)
= P(X <= 3)
=\(\sum_{x=0}^{3}\) ¹⁸Cₓ × (0.2)^x × (0.8)^(18-x)
= ¹⁸C₀× (0.2)^0 × (0.8)^(18-0) + ¹⁸C₁× (0.2)^1 × (0.8)^(18-1) + ¹⁸C₂× (0.2)^2 × (0.8)^(18-2) + ¹⁸C₃× (0.2)^3 × (0.8)^(18-3)
= (0.8)^(18) + 18× (0.2) × (0.8)^(17) + 153 × (0.04) × (0.8)^(16) + 1632× (0.008) × (0.8)^(15)
= 0.630
Plug in the values,
P(at least 4 defective)
= 1 - 0.630
= 0.370
Therefore, the expected items to be defective and probability that at least 4 items out of 18 are defective is equal to 3.6 and 0.370 or 37.0%.
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The slope of a line is 7/8 The y-intercept of the same line is 4
Complete the slope-intercept form equation
Answer:
y = -7/8x + 4
Step-by-step explanation:
Slope-intercept form :
y = mx + b
m = slopeb = y-interceptHence, the equation formed is :
y = -7/8x + 4Find the circumference of the circle below. (Use 3.14 for Pi)
The answer is 75.36 m
Please see the attached picture for full solution
Hope it helps
Answer:
\(75.36m\)
Step-by-step explanation:
\(c = 2\pi \: r \\ = 2 \times 3.14 \times 12 \\ = 75.36m\)
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BRAINLIEST FOR THE CORRECT AWNSER! The slope of the line below is –3. Use the coordinates of the labeled point to find a point-slope equation of the line.
Answer: y+7 = 3(x-5) A
Step-by-step explanation: Plug in the points into y-y1= m(x-b)
Match each of the following differential equations with a solution from the list below. 1. y" +y=0 2. y" 1ly' + 28y = 0 3. y" + 11y' + 28y = 0 4. 2x²y" + 3xy' = y A. y = cos(2) B.y = e^-4x C. y = e^7x 1 Dy 1/2
The following differential equations with a solution
y" + y = 0 corresponds to solution A: y = cos(2)
y" + y' + 28y = 0 corresponds to solution B: y = e^(-4x)
y" + 11y' + 28y = 0 corresponds to solution C: y = e^(7x)
2x^2y" + 3xy' = y corresponds to solution D: y = x^(1/2)
1. y" + y = 0:
This is a second-order homogeneous differential equation with constant coefficients. The characteristic equation is r^2 + 1 = 0, which has complex roots r = ±i. The general solution is therefore a linear combination of sine and cosine functions:
y = c1 cos(x) + c2 sin(x)
Using the initial condition y(0) = 1, we can solve for the constants to get:
y = cos(x)
2. y" + y' + 28y = 0:
This is a second-order homogeneous differential equation with constant coefficients. The characteristic equation is r^2 + r + 28 = 0, which has complex roots given by the quadratic formula:
r = (-1 ± sqrt(1 - 4*28)) / 2 = (-1 ± 7i) / 2
The general solution is therefore a linear combination of exponential and sine/cosine functions:
y = e^(-x/2) (c1 cos(7x/2) + c2 sin(7x/2))
Using the initial condition y(0) = 1, we can solve for the constants to get:
y = e^(-4x)
3. y" + 11y' + 28y = 0:
The characteristic equation is r^2 + 11r + 28 = 0, which can be factored as (r + 4)(r + 7) = 0. The roots are r = -4 and r = -7. Therefore, the general solution is a linear combination of exponential functions:
y = c1 e^(-4x) + c2 e^(-7x)
Using the initial condition y(0) = 1, we can solve for the constants to get:
y = e^(7x)
4. 2x^2y" + 3xy' = y:
Dividing both sides by x^2 and letting z = y/x^(1/2). Then, we get:
z' + (1/4x)z = 0
This is a first-order homogeneous differential equation with an integrating factor of e^(1/4 ln x) = x^(1/4). Multiplying both sides by the integrating factor, we get:
x^(1/4) z' + (1/4)x^(-3/4)z = 0
The left-hand side is the derivative of (x^(1/4) z), so we can integrate both sides to get:
x^(1/4) z = c1
Solving for z, we get:
z =c1/x^(1/4)
Substituting back for y, we get:
y = x^(1/2) z = c1 x^(1/4)
Using the initial condition y(1) = 1, we can solve for the constant to get:
y = x^(1/2)
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Lines AB and CD are parallel. If ∠3 measures (3x + 20)°, and ∠4 measures 70°, which equation could be used to solve for x
Answer:
(3x + 20)° + 70° = 180°
Step-by-step explanation:
Identify whether the following data set is unimodal, bimodal, multimodal, or has no mode. Assume the data set is a sample and find the modes, if any exist.28,30,23,41,24,35,41,30,35,33,31
1. Order the data:
\(23,24,28,30,30,31,33,35,35,41,41\)2. Identify the mode: the number in the data set that occurs most frequently.
For the given data set, the next are the modes:
30
35
41
The three modes have a frequency of 2.
Then, the given data set is polimodal and its modes are: 30, 35 and 4110 points first person
Answer:
Step-by-step explanation:
a=20
b=70
c=20
d=70
e=110
Answer:
A. 20
B. 70
C.20
D.70
E. 110
Step-by-step explanation:
Hope this helps
pls tell me if im wrong
find the area of this circle please
Answer:
It is B
Step-by-step explanation:
If the diameter of the circle is 16 inches, then the radius is half of that or 8 inches. The area of a circle can be calculated using the formula A = πr^2, where r is the radius of the circle. Substituting the value for the radius into this formula gives A = π * 8^2 = 64π ≈ 201.06 square inches. So the closest would be B