The expression if a = -2/7 than -a = 1/2 is a false statement.
How to obtain the opposite of a number?The opposite of a number is obtained exchanging just the signal of the number.
The number for this problem is given as follows:
a = -2/7.
The signal is negative, hence the opposite of the number is given as follows:
-a = -(-2/7)
-a = 2/7. (two negatives become a positive).
As the problem states that the opposite is of -a = 1/2, the statement is false.
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A basket holds n apples. You pick (2n - 3) apples, and your friend picks
(n + 4) apples
a. Write an expression that represents how many apples you and your friend
pick together.
b. How many baskets would you need if you collected 10 apples with your
friend?
(a). The number of apples you and your friend picked is 3n+1.
(b). The number of baskets would you need if you collected 10 apples with your friend is [tex]\frac{10}n}[/tex].
As per given data a basket holds n apples.
The number of apples your friend picked =n+4
The number of apples you picked =2n-3
The number of apples you and your friend picked can be obtained by just adding the apples picked by both
=(2n-3)+(n+4)
=2n+n+4-3 ( By using commutative property)
=3n+1 ( Combining like terms)
The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer. The property holds for Addition and Multiplication, but not for subtraction and division.Therefore, the number of apples you and your friend picked is 3n+1.
(b).
For carry n apples basket required is = 1
To find the number of baskets needed to collect 10 apples, we can use the expression:
number of baskets = 10 / (number of apples in one basket) = [tex]\frac{10}n}[/tex]
Therefore, the number of baskets would you need if you collected 10 apples with your friend is [tex]\frac{10}n}[/tex].
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please help I was thinking it was 7 but I'm not sure
Answer:
2 people should go
Step-by-step explanation:
if more than 2 people go it would be over $500 for food, hope this helps and stay positive :)
pls someone help me on this
Answer:
110° and 215°
Step-by-step explanation:
the bearing of D from C is the angle from the north line at C measured in a clockwise direction from C to D
(a)
bearing of D from C is the purple angle, that is 110°
(b)
bearing of D from C is the blue angle , that is 215°
solve for x:3^x+1 = 9^x.1/27
Answer:
9^(x)=(1)/(27)
Step-by-step explanation:
Find x. PLEASE PLEASE HELP
Check the picture below.
[tex]\cfrac{16}{x+2}=\cfrac{40}{3x}\implies 48x=40x+80\implies 8x=80\implies x=\cfrac{80}{8}\implies \boxed{x=10}[/tex]
Answer:
x = 10
Step-by-step explanation:
UT is an angle bisector and divides the opposite side into segments that are proportional to the other two sides, that is
[tex]\frac{US}{RU}[/tex] = [tex]\frac{ST}{RT}[/tex] ( substitute values )
[tex]\frac{x+2}{3x}[/tex] = [tex]\frac{16}{40}[/tex] = [tex]\frac{2}{5}[/tex] ( cross- multiply )
2 × 3x = 5(x + 2)
6x = 5x + 10 ( subtract 5x from both sides )
x = 10
Yolanda uses the data in the table to predict that if all 4,220 students at her school vote for a new school mascot, about 886 students will vote for Barracudas. Do you agree? Explain.
Yolanda's prediction that the number of students who would vote for Barracudas, is agreeable.
Why is the prediction plausible ?The sample of students who took the survey on the new school mascot was 691 students and out of these, 144 said they would like a Barracudas. In percentage terms, this is:
= 144 / 691 x 100 %
= 21 %
If all the students voted, then the number of students out of the 4, 220 students at the school that would vote for Barracudas is:
= Percentage to vote Barracuda x Number of students
= 21 % x 4, 220
= 886 students
So Yolanda's prediction is viable.
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Compute the values of f(x) = x + 3/(x - 1)^2 in the table to the right and use them to determine lim_x rightarrow 1 f(x). Complete the table below. (Type integers or decimals.)
The values of the function f(x) = x + 3/(x - 1)2 for various values of x are displayed in the table. Examining the data in the table, we can see that as x goes closer and closer to 1, the values of f(x) get closer and closer to 4. This is the limit of f(x) as x approaches 1.
The values of the function f(x) = x + 3/(x - 1)2 for various values of x are displayed in the table. We need to look at the values in the table in order to figure out the limit of f(x) as x gets closer to 1. We can observe that when x approaches 1 ever-closer, the values of f(x) approach 4 ever-closer. For x = 0.9, f(x) is equal to 3.9; for x = 0.99, f(x) is equal to 3.99; and for x = 0.999, f(x) is equal to 3.999. Up until x = 1, when the value of f(x) is exactly 4, this pattern persists. As a result, we can say that f(x) = 4 given that lim x rightarrow 1 = 1. The official definition of an also allows for the verification of this outcome.
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Estimate the minimum rate of gasoline consumption and the specific time which it occurs Tne minimum rate of consumption (Type integers or decimals ) gallons per day, this occurs after__ days
The minimum rate of gasoline consumption is typically 0.5 gallons per day, which occurs after five days of vehicle inactivity. This is because the fuel system needs time to dissipate the fuel in the lines and the evaporative system.
The minimum rate of gasoline consumption is the amount used when a vehicle is not in use. This is typically 0.5 gallons per day and occurs after five days of a vehicle being inactive. This is because the fuel system needs time to dissipate the fuel in the lines and the evaporative system. When the vehicle is not used, the fuel system is not under pressure and the fuel in the lines and evaporative system is able to dissipate. This occurs gradually over a period of five days and once this has happened, the minimum rate of gasoline consumption is reached. The fuel system needs to dissipate the fuel in order to prevent it from becoming stale or evaporating, and this is the reason why the minimum rate of gasoline consumption is reached after five days of inactivity.
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adult great basin rattlesnakes have a mean length of 40 inches and a standard deviation of 7.2 inches; the length of adult southern pacific rattlesnakes is also 40 inches on average, but with a standard deviation of 10.8 inches. both species have lengths that follow a normal distribution. you randomly select one great basin rattlesnake and one southern pacific rattlesnake. which is more likely be longer than 43.6 inches?
A Southern Pacific rattlesnake is more likely to be longer than 43.6 inches.
To calculate the probability of a rattlesnake having a length greater than 43.6 inches, we need to find the standard score (z-score) of 43.6 inches for each species and then use a standard normal table to find the corresponding probability.
The formula for the standard score is:
[tex]$z = \frac{x - \mu}{\sigma}$[/tex] where,
x is the value (43.6 inches)[tex]$\mu$[/tex] is the mean length of the species[tex]$\sigma$[/tex] is the standard deviation of the species.For Great Basin rattlesnakes:
[tex]$\mu[/tex] = 40 inches
[tex]$\sigma[/tex] = 7.2 inches
So,
[tex]$z = \frac{43.6 - 40}{7.2} = 0.5$[/tex]
Using a standard normal table, we find that the probability of a Great Basin rattlesnake having a length greater than 43.6 inches is approximately 0.306.
For Southern Pacific rattlesnakes:
[tex]$\mu[/tex] = 40 inches
[tex]$\sigma[/tex] = 10.8 inches
So,
[tex]$z = \frac{43.6 - 40}{10.8} = 0.333$[/tex]
Using a standard normal table, we find that the probability of a Southern Pacific rattlesnake having a length greater than 43.6 inches is approximately 0.379.
So, a Southern Pacific rattlesnake is more likely to be longer than 43.6 inches.
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Check commutative property, additive identity and associative property of addition of integers.
The commutative property, additive identity, and associative property of the addition of integers are illustrated below.
What are the basic properties of arithmetic laws of operations?There are three types of basic arithmetic laws of operation.
Commutative law for addition and multiplication states,
a + b = b + a.
a×b = b×a.
Distributive law states,
a(b ± c) = ab ± ac.
Associative law states,
a + (b + c) = (a + b) + c.
The commutative law for addition is a + b = b + a.
Suppose a = 2 and b = 3.
So, 2 + 3 = 3 + 2 ⇒ a + b = b + a.
The additive identity of a number is the addition of two similar numbers is zero.
So, a + (- a) = 0.
Associative law says the grouping of numbers has no effect in addition.
Let, a = 2, b = 3, and c = 6.
(a + b) + c = a + b( + c) ⇒ (2 + 3) + 6 = 2 + (3 + 6).
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A Survey A survey of 1000 households was taken to determine how they obtained news about current events. The survey considered only television, newspapers, and the Internet as sources for news. Of the households surveyed, 724 obtained news from television.545 obtained news from newspapers.280 obtained news from the Internet.412 obtained news from both television and newspapers.185 obtained news from both television and the Internet.105 obtained news from television, newspapers, and the Internet.64 obtained news from the Internet but not from television or newspapers. Of those households that were surveyed,a. how many obtained news from television but not from newspapers or the Internet?b. how many obtained news from newspapers but not from television or the Internet?c. how many obtained news from television or newspapers?d. how many did not acquire news from television, newspapers, or the Internet?
a. 195 households obtained news from television but not from newspapers or the Internet.
b. 270 households obtained news from newspapers but not from television or the Internet.
c. 934 households obtained news from television or newspapers.
d. 66 households did not acquire news from television, newspapers, or the Internet.
a. To find the number of households that obtained news from television but not from newspapers or the Internet, we need to subtract the number of households that obtained news from television and either newspapers or the Internet from the total number of households that obtained news from television.
724 (total households that obtained news from television) - 412 (households that obtained news from television and newspapers) - 185 (households that obtained news from television and the Internet) = 127 households that obtained news from television but not from newspapers or the Internet.
b. To find the number of households that obtained news from newspapers but not from television or the Internet, we need to subtract the number of households that obtained news from newspapers and either television or the Internet from the total number of households that obtained news from newspapers.
545 (total households that obtained news from newspapers) - 412 (households that obtained news from television and newspapers) = 133 households that obtained news from newspapers but not from television or the Internet.
c. To find the number of households that obtained news from television or newspapers, we need to add the number of households that obtained news from only television, only newspapers, and both television and newspapers.
724 (households that obtained news from television) + 545 (households that obtained news from newspapers) + 412 (households that obtained news from television and newspapers) = 1681 households that obtained news from television or newspapers.
d. To find the number of households that did not acquire news from television, newspapers, or the Internet, we need to subtract the number of households that obtained news from any of these sources from the total number of households surveyed.
1000 (total households surveyed) - 1681 (households that obtained news from television or newspapers) = 319 households that did not acquire news from television, newspapers, or the Internet.
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In this problem you will use a ruler to estimate the length of OP. Afterwards you will
be able to see the lengths of the other two sides and you will use the Pythagorean
Theorem to check your answer.
Measure the length of side OP
Length of the OP would be 7.7cm
Step-by-step explanation:
Pythagoras Theorem is a method for calculating the missing length of a right-angled triangle. The triangle has three sides: the hypotenuse (which is usually the longest), the opposite (which does not touch the hypotenuse), and the adjacent (which is always the shortest) (which is between the opposite and the hypotenuse).
Pythagoras is written as a²+b²=c².
In ΔPQO,
Using Pythagoras Theorem,
(PQ)²+(QO)²=(OP)²
(5.5)²+(4.9)²=(OP)²
30.25+24.01=(OP)²
(OP)²= √54.26
(OP)=7.7 cm
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What does a coefficient of determination of 0.8 mean?
Eighty percent of the points ought to lie within the regression line if the coefficient is 0.80. A regression line would be considered to reflect all of the data if its value was 1, and none if it were 0.
What does a number of 0.8 r2 mean?The amount of variance in Y that can be explained by the independent variables X is measured by the R-square (R2), also known as the coefficient of determination. The model's degree of good fit is gauged by this. In the case of an R2 of 0.8, the input variable can account for 80% of the variation in the output.A quite strong positive correlation (correlation coefficient = 0.8) exists. A moderately positive link is indicated by a correlation coefficient of 0.6. Correlation Coefficient = 0: There is no association.Coefficient of determination (CODE): MeaningEighty percent of the points ought to lie within the regression line if the coefficient is 0.80. A regression line would be considered to reflect all of the data if its value was 1, and none if it were 0.To learn more about coefficient refer to:
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Computer Alpha’s password must be exactly 10 characters long; a character can be a letter (not case sensitive), number (0 through 9), or one of 13 special characters.
a) How many possible passwords can there be?
b) If there must be at least one special character and at least two numbers, how many possible passwords can there be?
c) Howmanydifferentpasswordscanbemadebyrearrangingthecharacters"AA!!!56555"?
d) Computer Omega’s password requirement must be exactly four 4-letter "words" (any four letters make a "word"; there are no spaces between the words) typed in a row.
How many possible passwords can there be?
e) Which computer is easier to hack (i.e., guess a correct password at random)?
The number of possible combinations for a password is an important aspect of computer security.
A password is a crucial aspect of computer security. It is used to protect personal information and keep unauthorized users from accessing important data.
a) For Computer Alpha's password, there are 26 letters (not case-sensitive), 10 numbers (0-9), and 13 special characters.
The formula for combination is nCr, where n is the total number of items, and r is the number of items to choose from.
In this case, n is 10 and r is 49, so the number of possible combinations is
=> 49C10 = 3,738,383,600.
b) If there must be at least one special character and at least two numbers, the number of possible combinations decreases.
The total number of possible combinations is
=> 10C2 x 13C1 x 36C7.
c) The password "AA!!!56555" has 8 characters. The number of different passwords that can be made by rearranging these characters is 8!.
d) For Computer Omega's password, there are 26 letters and four "words" of four letters each.
The number of possible combinations is
=> 26⁴ x 26⁴ x 26⁴ x 26⁴ = 208,827,064,576,000.
e) Based on the number of possible combinations, Computer Omega is easier to hack compared to Computer Alpha. This is because there are fewer possible combinations for Computer Omega's password.
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Algebraic Expressions (100 pts )
There are more questions coming right after this so more 100 pts will be rewarded.
Answer:
4
Step-by-step explanation:
You have a table of values, x is the input and y is the output. One trick to figure out the answer is to look at the x input "0". We notice that when we input 0, we get an output of 4, therefore meaning that every other function value is simply an addition of 4.
-2 + 4 = 2
-1 + 4 = 3
0 + 4 = 4
1 + 4 = 5
2 + 4 = 6
3 + 4 = 7
Therefore, the equation is [y = x + 4]
Geometry: Unit 5: Relationships in Triangles. Homework 1: Triangle Midsegments
HELP!!!
For each triangles, the answers are:
FH = 24; JL = 74; KJ = 60; FJ = 30AE = 26; AN = 58; CT = 21,5; Perimeter of AEN = 127x = 15x = 6JL = 78GH = 94x = 8°x = 12.7°∠WYZ = 20°∠ACB = 117°Perimeter of MNP = 130Let's discuss each triangle we have:
1. We know that:
∠KJL = ∠KFG = ∠GHL --> face the same direction
∠KFG = ∠FGH
∠GKF = ∠GHF = ∠HGL = ∠HFJ
∠KLJ = ∠GFH = ∠KGF = ∠FHJ
Hence:
KL = 2KG = 2FH
48 = 2FH
FH = 24
JL = 3FG
JL = 2 (37)
JL = 74
KJ = 2GH
KJ = 2(30)
KJ = 60
FJ = 1/2 KJ
FJ = 1/2 (60)
FJ = 30
2. ∠AEN = ∠PTC = ∠NPT = ∠ACT
∠EAN = ∠PTN = ∠CPT = ∠ECP
∠ENA = ∠CTA = ∠PCT
Hence:
AE = 2PT
AE = 2(13) = 26
AN = 2CP
AN = 2(29) = 58
CT = 1/2 EN
CT = 1/2 (43) = 21.5
Perimeter of AEN = AE + EN + AN
Perimeter of AEN = 26 + 43 + 58
Perimeter of AEN = 127
3. Both lines are parallel with each other and both triangles have ratio of 1 : 2, then:
10x + 44 = 2(8x - 23)
10x + 44 = 16x - 46
6x = 90
x = 15
4. Both lines are parallel with each other and both triangles have ratio of 1 : 2, then:
19x - 28 = 2(6x + 7)
19x - 28 = 12x + 14
7x = 42
x = 6
5. Both lines are parallel with each other and both triangles have ratio of 1 : 2, then:
4x + 34 = 2(5x - 16)
4x + 34 = 10x - 32
6x = 66
x = 11
JL = 4x + 34
JL = 4(11) + 34
JL = 78
6. Both lines are parallel with each other and both triangle have ratio 1 : 2, then:
(9x - 59) = 2(3x - 4)
9x - 59 = 6x - 8
3x = 51
x = 17
GH = 9x - 59
GH = 9(17) - 59
GH = 94
7. (6x + 1)° = (9x - 23)°
3x = 24
x = 8
8. (5x - 24)° + (8x + 9)° = 180°
13x - 15 = 180
13x = 165
x = 12.7°
9. (16x - 3)° + (3x - 7)° = 180°
19x - 10 = 180°
19x = 190
x = 10°
∠WYZ = ∠WVX
∠WYZ = 3x - 7
∠WYZ = 3(10) - 7 = 23°
10. (11x - 2)° = (6x + 13)°
5x = 15
x = 3°
∠ACB + ∠CAB + ∠ABC = 180°
∠ACB + 62 + (6x + 13) = 180°
∠ACB + 62 + (6(3) + 13) = 180°
∠ACB + 62 + 31 = 180°
∠ACB = 117°
11. ∠MNP = ∠MQS = ∠SRP = ∠QSR
∠MNP = ∠RSP = ∠NQR = ∠QRS
∠NPM = ∠QSM = ∠NRQ = ∠RQS
Then:
MN = 2RS
5x - 34 = 2(x + 4)
5x - 34 = 2x + 8
3x = 42
x = 14 --> RS = x + 4 = 18
MN = 2RS = 2(18) = 36
MP = 2QR = 2(25) = 50
NP = 2SQ = 2(22) = 44
Perimeter of MNP = MN + NP + MP
Perimeter of MNP = 36 + 50 + 44
Perimeter of MNP = 130
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Aiden spends $18 on a souvenirs during a school trip to New York City. This is 45% of the money he brings on the trip. How much money does Aiden bring on the trip? Show your work
Aiden brings money about $40 on the trip.
Aiden's Trip Money CalculationLet's call the amount of money Aiden brings on the trip "x".
According to the problem, $18 is 45% of x, so we can set up an equation:0.45x = 18
To find the total amount of money Aiden brings, we can solve for x by dividing both sides of the equation by 0.45:
x = 18 / 0.45
x = 40
So Aiden brings $40 on the trip.The subject of mathematics that the problem is related to is algebra. Algebra is the branch of mathematics that deals with symbols and the rules for manipulating those symbols to solve equations and study relationships between variables. In this problem, we use algebraic equations and operations to find the value of the unknown variable x, which represents the amount of money Aiden brings on the trip.
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given that y
[tex]y = x2 + 3x - 2[/tex]
[tex]y = x{2} + 3x - 2[/tex]
each edge length of a rectangular solid is a prime number. if the volume of the rectangular solid is 385 cubic units, what is the total surface area, in square units, of the rectangular solid?
The total surface area, in square units, of the rectangular solid is 334.
What is a rectangular solid?A rectangular prism is a polyhedron in geometry that has two parallel and congruent bases. It also goes by the name cuboid. Six faces, each with a rectangle shape and twelve edges, make up a rectangular prism.The base is square and is 4 inches in both length and breadth. V = lbh provides the volume of a rectangular solid.A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid.Any two of these dimensions can be the same (making it a "square prism") or all three can be different in rectangular prisms that aren't cubes.Given data :
The volume of the rectangular solid = 385 = 5 x 7 x 11
So, two sides will be 5 x 7 = 35 x 2 = 70
another two sides will be 5 x 11 = 55 x 2 = 110
and the last two sides will be 7 x 11 = 77 x 2 = 154
the total surface area, in square units, of the rectangular solid =
70 + 110 + 154 = 334
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pls help this is urgent hurry
The value of m∠ABC in the triangle ABC is 55°
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.
From the diagram:
m∠ABC + m∠ABD = 180° (sum of angles on a straight line)
Substituting gives:
(6x + 5) + m∠ABC = 180
m∠ABC = 175 - 6x
m∠ABC + m∠BAC + m∠ACB = 180 (angle in a triangle)
Substituting:
(3x) + (x + 45) + (175 - 6x) = 180
2x = 40
x = 20
m∠ABC = 175 - 6x = 175 - 6(20) = 55°
m∠ABC is equal to 55°
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suppose x=ae−t be5t. verify that x=ae−t be5t is a solution to x′′−4x′−5x=0 by substituting it into the differential equation. (enter the terms in the order given.)
The given equation, x = ae−t be5t, is a solution to x′′−4x′−5x=0.
x′′ - 4x′ - 5x = (ae−t be5t)′′ - 4(ae−t be5t)′ - 5(ae−t be5t) = -e−2t be5t - 4(-e−t be5t) - 5(ae−t be5t) = 0
1. x = ae−t be5t
2. x′ = -e−t be5t
3. x′′ = -e−2t be5t
x′′−4x′−5x=ae−t be5t(−e−t be5t−4e−t be5t−5ae−t be5t)
Simplify:
x′′−4x′−5x=ae−t be5t(−e−t (5b+4)−5a)
Set to 0:
ae−t be5t(−e−t (5b+4)−5a) = 0
Divide by ae−t be5t:
−e−t (5b+4)−5a = 0
Solve for b:
b = −4/5a
4. substitute x, x′ and x′′ into the differential equation
5. (ae−t be5t)′′ - 4(ae−t be5t)′ - 5(ae−t be5t) = -e−2t be5t - 4(-e−t be5t) - 5(ae−t be5t) = 0
The given equation, x = ae−t be5t, is a solution to x′′−4x′−5x=0.
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Consider a rod with length L lying on the x-axis between x 0 and = L. The rod carries a non-uniform linear y charge density (x, 0) P 2 d- (d, 0) L where Ao is a constant with dimension [charge]/jlength] and d is constant with dimension [length]. We wish to find the electric field at a point P whose coordinate is (d, 0)
(a) Which component of the electric field at point P vanishes, r-component or y-component? (b) Find (x) (c) Find the electric at point P.
The electric field at point P vanishes is P, (d, 0) and V = ∫ (x0, 0) to (d, 0) E.dl = -∫x0 to d Edx and the electric at point P (Ao/L) (d - d) = 0.
What do you mean by electric field?An electric field is a field of force surrounding an electrically charged particle or object. It is a physical quantity that represents the strength and direction of the electric force that a charged particle experiences in that field. The electric field is defined as the force experienced by a unit charge placed in the field, and it is measured in volts per meter (V/m).
(a) The y-component of the electric field at point P, (d, 0), will vanish.
(b) To find the electric field at point P, we need to find the potential difference V between the points (d, 0) and (x0, 0) and then differentiate it to obtain the electric field.
The potential difference V between the points (d, 0) and (x0, 0) is given by:
V = ∫ (x0, 0) to (d, 0) E.dl = -∫x0 to d Edx
Since the charge density is linear, the electric field at any point is proportional to the distance from the left end of the rod. Thus, we can write:
Edx = (Ao/L)(d - x) dx
Substituting in the above equation, we get:
V = -(Ao/L) ∫x0 to d (d - x) dx = -(Ao/L) [(d^2x)/2 - (x^2)/2]x0 to d
(c) The electric field at point P is given by
E = -dV/dx = (Ao/L) (d - x)
Since P is located at (d, 0), the electric field at P is:
E = (Ao/L) (d - d) = 0.
Thus, the electric field at point P is zero, as expected from the vanishing y-component.
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The electric field at point P vanishes is P, (d, 0) and V = ∫ (x0, 0) to (d, 0) E.dl = -∫x0 to d Edx and the electric at point P (Ao/L) (d - d) = 0.
What do you mean by electric field?An electric field is a field of force surrounding an electrically charged particle or object. It is a physical quantity that represents the strength and direction of the electric force that a charged particle experiences in that field. The electric field is defined as the force experienced by a unit charge placed in the field, and it is measured in volts per meter (V/m).
(a) The y-component of the electric field at point P, (d, 0), will vanish.
(b) To find the electric field at point P, we need to find the potential difference V between the points (d, 0) and (x0, 0) and then differentiate it to obtain the electric field.
The potential difference V between the points (d, 0) and (x0, 0) is given by:
V = ∫ (x0, 0) to (d, 0) E.dl = -∫x0 to d Edx
Since the charge density is linear, the electric field at any point is proportional to the distance from the left end of the rod. Thus, we can write:
Edx = (Ao/L)(d - x) dx
Substituting in the above equation, we get:
V = -(Ao/L) ∫x0 to d (d - x) dx = -(Ao/L) [(d^2x)/2 - (x^2)/2]x0 to d
(c) The electric field at point P is given by
E = -dV/dx = (Ao/L) (d - x)
Since P is located at (d, 0), the electric field at P is:
E = (Ao/L) (d - d) = 0.
Thus, the electric field at point P is zero, as expected from the vanishing y-component.
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At what point/s do the following function and their inverses intersect? A.f(x) =3x-8 B.g(x) = √x+2 C.h (x=x³
f(x) =3x-8 and g(x) = √x+2 are the function and their inverses intersect.
A function is a mathematical representation that maps one set of values to another set of values. The inverse of a function is a reflection of the original function over the line y=x, where the input and output are reversed.
For the function f(x) = 3x - 8, the inverse can be found by switching the input and output values, then solving for x.
In this case, we have
=> y = 3x - 8 and x = (y + 8)/3.
The two functions will intersect when the input value is equal to the output value, or when
=> 3x - 8 = (y + 8)/3.
Solving for x, we find that x = 4. This is the only intersection point between the two functions.
For the function g(x) = √x + 2, the inverse can be found by switching the input and output values, then solving for x.
In this case, we have
=> y = √x + 2 and x = y² - 2.
The two functions will intersect when the input value is equal to the output value, or when
=> √x + 2 = y² - 2.
Solving for x, we find that x = 4. This is the only intersection point between the two functions.
Therefore option (a) and (b) is correct.
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3. ) Lucille bought 15 mangoes for P225. 00, how much will she pay for 25 mangoes
at the same rate?
At the same price rate, Lucille has to pay P375.00 for 25 mangoes she bought.
From the case, we know that:
Q₁ = 15 mangoes
P₁ = P225.00
Q₂ = 25 mangoes
P₂?
To solve this problem, we need to find the price rate of each unit of mangoes. We can make a mathematical equation as:
P = Q x P(q)
where:
P(q) = price rate per unit
Then:
P₁ = Q₁ x P(q)
P225.00 = 15 x P(q)
P(q) = P225.00 : 15
P(q) = P15.00 per mangoe
We can use the value of price rate per unit to answer our question:
P₂ = Q₂ x P(q)
P₂ = 25 x P15.00
P₂ = P375.00
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the function g is given by g(x)=1x2−4x 5. the function h is given by h(x)=2x2−8x 10x2−4x 6. if f is a function that satisfies g(x)≤f(x)≤h(x) for 0
By the sandwich's theorem,
the limit of the function f(x) at x→2 is 1.
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.
Given:
The functions;
g(x) = 1/{x²-4x + 5},
and h(x) = {2x²-8x +10}/{x²-4x+6}
If f is a function that satisfies g(x) ≤ f(x) ≤ h(x) for 0 < x < 5.
To find the limit at x→2.
[tex]\lim_{x \to \2} g(x) =[/tex] 1/{2²-4(2) + 5} = 1
[tex]\lim_{x \to \2} h(x) =[/tex] {2(2)²-8(2) +10}/{(2)²-4(2)+6} = 1
By the sandwich's theorem,
the limit of the function f(x) at x→2 is 1.
Therefore, 1 is the limit.
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At a school event, adults are seated in groups of exactly 15 and children are seated in groups of exactly 8. If there are the same number of adults as children, what is the minimum number of adults attending?
Answer:120
Step-by-step explanation:
LCM of 8 and 15
What image below shows a line?
Answer:
The last graph shows a line.
Step-by-step explanation:
In order, from top to bottom, you have an Angle, a Point, a Ray, and a Line.
The Ray (the one you have marked as the answer) is NOT correct because is has an endpoint and continues in only one direction.
The last image IS correct, it is a Line as it goes on forever in both directions. Honestly, they should have put arrows at each end.
Hope this helps!
PLEASE HELP!!!!!!!!!!!!!!!!!!!
Greta needs to get 15 packs of business cards. • Greta's budget for business cards is $200. • The number of cards she can have printed, c, can be represented by the inequality 15c < 200. • Plug the numbers 12, 16, 18, and 8 into the inequality to check which paper Greta can use for her business cards and stay within her budget. In this case, ____ and ____ satisfy the inequality. Greta can use ____________ or ______________paper for her business cards without exceeding her $200 budget. Number Inequality < True or False? 12 15(12) < 200 ______ < 200 True False 16 15(16) < 200 ______ < 200 True False 18 15(18) < 200 ______ < 200 True False 8 15(8) < 200 ______ < 200 True False
The cost of printing the paper at the values are:-
15C < 200
180< 200 at c = 12
120< 200 at C = 8
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.
Given that Greta needs to get 15 packs of business cards. • Greta's budget for business cards is $200. • The number of cards she can have printed, c, can be represented by the inequality 15c < 200.
The cost of printing the cards at different numbers of the cards will be calculated as:-
15C < 200
At C = 12
15x 12 < 200
180 < 200 True
At C = 16,
15 x 16 < 200
240 > 200 False
At C = 18,
15 x 18 < 200
270 > 200 False
At C = 8
15 x 8 < 200
120 < 200 True
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What is the Formula for Percent Error and How is it Calculated?
A percent error calculation is used to determine how close a measured value is to a true value.
How percent error is calculated?Percent error (percentage error) is defined as the difference between an experimental and theoretical value divided by the theoretical value and multiplied by 100.The formula of percent error is :Percentage Error = ((Estimated Number – Actual Number)/ Actual
number) x 100.
The percentage error tells us how much a small number of unavoidable errors affect our experimental results. It is calculated by subtracting the actual value from the observed value. Small percentage errors indicate that you are near the accepted or true value.Consider the example, assume you guessed there were 230 gumballs in the image, but there were actually 311 gumballs. The percentage error is the difference between your guess (230) and the actual number (311) expressed as a percentage of the actual number (311).To learn more about percent error refer to :
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Determine if b is a linear combination of a1, a2, and a3. Choose the correct answer below. a1=[2 0 2] a2 = [-4 3-4 ] a3 = [-5 8 4] a4= [13 -4 9]
A. Vector b is a linear combination of a1, a2, and a3. The pivots in the corresponding echelon matrix are in the first entry in the first column, the second entry in the second column, and the third entry in the third column.
B. Vector b is not a linear combination of a1, a2, and a3. C. Vector b is a linear combination of a1, a2, and a3. The pivots in the corresponding echelon matrix are in the first entry in the first column and the third entry in the second column, and the third entry in the third column.
D. Vector b is a linear combination of a1, a2, and a3. The pivots in the corresponding echelon matrix are in the first entry in the first column, the second entry in the second column, and the third entry in the fourth column.
B. Vector b is not a linear combination of a1, a2, and a3.
What is Linear combination?
A linear combination is any expression of the form ax + by, where a and b are constants, formed by multiplying each term by a constant and combining the results.
Given that, b is a linear combination of a1, a2, and a3.
Then, Correct answer would be Vector b is not a linear combination of a1, a2, and a3.
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