Overall velocity FORWARDS in m/s is 1.66
What is velocity?Velocity is a vector expression of the displacement that an object or particle undergoes with respect to time . The standard unit of velocity magnitude (also known as speed ) is the meter per second (m/s). Alternatively, the centimeter per second (cm/s) can be used to express velocity magnitude. The direction of a velocity vector can be expressed in various ways, depending on the number of dimensions involved.
Let the forward displacement of the person is taken as positive and backward displacement is taken as negative;
You walk forward 10 meters;
displacement = = 10 meter
You walk backward 5 meters;
displacement = = -5 meter
You walk forward 10 meters,
displacement = = 10 meter
Total displacement = s =
s = 15 -5 +15
s = 25 meter
Total time taken is given;
t = 15 second
Average velocity = total displacement/total time
Average velocity = 25/15
Average velocity = 1.66
Therefore, the velocity will be 1.66 m/s
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Is X² and 2x like terms?
No, X² and 2x are not like terms. Like terms are terms that have the same variables and exponents, but different coefficients. X² and 2x have the same variable (x) but different exponents (2 and 1, respectively).
Like terms are terms that have the same variables and exponents, but different coefficients. X² and 2x are not like terms because they have the same variable (x) but different exponents (2 and 1, respectively). When two terms have the same variable and exponent, they are considered like terms. For example, 3x² and 4x² are like terms because they have the same variable (x) and exponent (2). However, if the terms have different variables or different exponents, they are not like terms. For example, X² and 2y are not like terms because they have different variables (x and y). Similarly, 2x and x² are not like terms because they have different exponents (1 and 2, respectively). To sum up, like terms must have the same variables and exponents in order to be considered as such.
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Are these shapes similar? Justify your answer.
Two figures are considered to be "similar figures" if they have the same shape, congruent corresponding angles (meaning the angles in the same places of each shape are the same) and equal scale factors.
What is congruent?The term “congruent” means exactly equal shape and size. This shape and size should remain equal, even when we flip, turn, or rotate the shapes. In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.The term “congruent” means exactly equal shape and size. This shape and size should remain equal, even when we flip, turn, or rotate the shapes.In geometry, congruent means identical in shape and size. Congruence can be applied to line segments, angles, and figures.similar to or in agreement with something, so that the two things can both exist or can be combined without problems.To learn more about congruent refer to:
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Last week, Alex took 90 selfies and Vic took 75 selfies. Today,
they each decided that some of these selfies were not very good
and deleted them. Alex deleted three times as many selfies
as Vic. Now, Alex has half as many selfies as Vic. How many
selfies did Alex delete?
The number of selfies deleted by Alex is 63.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Given that, last week, Alex took 90 selfies and Vic took 75 selfies.
Let the number of selfies deleted by Vic be s.
Alex deleted three times as many selfies as Vic.
So, the number of selfies deleted by Alex =3s
Alex has half as many selfies as Vic.
Now, 90-3s = 1/2 (75-s)
180-6s=75-s
5s=105
s=21
The number of selfies deleted by Alex =3s
= 63
Therefore, the number of selfies deleted by Alex is 63.
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the numbers $1, 2, 3, \dots, 8$ are used once each to form four two-digit numbers. what is the largest number of primes that could possibly be among these four numbers?
Four two-digit numbers are constructed from numbers 1, 2, 3, ..., 8. The largest number of primes that could possibly formed among those four numbers is 3 numbers.
A prime number is a whole number greater than 1 which only divisible by 1 and itself. Example of prime numbers are 2, 3, 5, 7, ...
We want to form 4 two-digit numbers from, 1, 2, 3, 4, 5, 6, 7, 8.
Recall that: other than 2, all even numbers are not prime since they are divisible by 2. Hence, from those numbers, we look at which odd two-digit numbers are prime.
We have four odd numbers in the list that can construct two-digit odd numbers: 1, 3, 5, 7.
However, two-digit numbers with 5 as its second digit is not prime since they are exactly divisible by 5.
Therefore, now we only have 3 numbers (1, 3, 7) that can construct two-digit odd numbers. Hence, the largest number of primes that could possibly formed is 3 numbers.
Example, the constructed four two-digit numbers are:
47, 53, 61, 28
47, 53, and 61 are prime, while 28 is not.
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Let g be a vertical shrink by a factor of 1/3 followed by a translation 3 units right
of the graph of f(x) = srqt of x + 5.
Answer:
g(x) = ([tex]\sqrt{x-3}[/tex])/3 + 5
Step-by-step explanation:
f(x) = [tex]\sqrt{x}[/tex] + 5
[tex]\sqrt{x}[/tex] + 5 ==> 1/3 * [tex]\sqrt{x}[/tex] + 5 ==> vertical shrink is when the function's y-coordinates shrink from the y-intercept (5 is the y-int) by a factor of 1/3
[tex]\sqrt{x}[/tex]/3 + 5 ==>( [tex]\sqrt{x-3}[/tex])/3 + 5 ==> in order to translate the graph 3 units to the right, subtract x by 3 since x is being affected when the graph moves left/right. In addition, x now has to be 3 units greater in order for the function to have the same value:
[tex]\sqrt{4-3}[/tex] = [tex]\sqrt{1}[/tex]
4 > 1 and 4 = 1 + 3
Hence, g(x) = ([tex]\sqrt{x-3}[/tex])/3 + 5
Where is log x defined?
Log x is defined for all positive real numbers (x>0). Exponential functions increase exponentially (x^y) and logarithmic functions decrease logarithmically (log x).
Log x is defined as the inverse of the exponential function. Exponential functions increase exponentially (x^y) and logarithmic functions decrease logarithmically (log x). The logarithm of a number is the exponent to which another fixed number must be raised to produce that number. Log x is defined for all positive real numbers (x>0). This means that any number that is greater than 0 can have a logarithm associated with it. For example, log 10 = 1 because 10^1 is equal to 10. The logarithm of a number can also be expressed in terms of other logarithms. For example, log 10 = log 10^2 = 2 log 10. Log x can also be used to solve equations and find the value of unknown variables.
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You are given quadrilateral PQRS, such that
ABCD = T (0, -8)(Ro 180°(R y-axis (PQRS)))
What are the new coordinates for ABCD?
On solving the provided question, we can say that from the graphs
the new coordinates for ABCD (-1,-2),(2,-3),(-4,-6),(-3,8)
What is graphs?Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle
here,
ABCD = T (0, -8)(Ro 180°(R y-axis (PQRS)))
from the graphs
the new coordinates for ABCD
(-1,-2),(2,-3),(-4,-6),(-3,8)
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please answer quick , and explain
Calculate the areas of each simpler figure, then sum the areas to determine the overall area of the composite figure.
What does Area of Composite Shapes mean?As specified by any composite shape, the area of composite shapes is the space it occupies. The assemblage of simple shapes creates a composite shape. As a result, the area of the composite shape is calculated by separately adding each of the fundamental shapes.Simple geometric forms are assembled into a composite figure. Divide a composite figure or other figure with an atypical shape into straightforward, non-overlapping figures to determine its area. Calculate the areas of each simpler figure, then sum the areas to determine the overall area of the composite figure.To learn more about areas refer to:
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pls helppp
One-third of the cars in the parking
lot are silver. There are 165 cars in
the lot. How many cars are silver?
Answer: 55
Step-by-step explanation:
Its 55 because 55 is one third of 165! Hope this helps :)
A door manufacturer specifies the width of a front-entrance door as 36 inches with a tolerance of ±0.0625 inches. When designing a prefabricated home, what should you ensure the width of the door opening is greater than?
- 33.75 inches
- 35.9375 inches
- 36.0625 inches
- 37.0625 inches
- 38.75 inches
Based on mathematical operations, when designing a prefabricated home, you must ensure that the width of the door opening is greater than A. 33.75 inches, given the sample mean of 36 inches with a tolerance (margin of error) of ±0.0625 inches.
What is the margin of error?The margin of error is the tolerance level that creates the confidence interval for the sample mean.
With a sample mean of 36 inches for the door opening and a tolerance level of ±0.0625 inches, the width can be designed to measure between 35.9375 inches and 36.0625 inches.
This measurement implies that the upper limit for the width (confidence interval) is 36.0625 inches while the lower limit is 35.9375 inches.
Thus, the width of the door opening must be greater than Option A.
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Is 4x² 3x 7 a polynomial?
Yes, 4x² 3x 7 is a polynomial because it is an algebraic expression composed of constants, variables, and exponents, with the variables being multiplied together.
Step 1: 4x² 3x 7 can be expanded as 4x² + 3x - 7.
Step 2: 4x² + 3x - 7 can be further expanded into 4x2 + 3x - 7.
Step 3: Simplify the expression by combining like terms: 4x2 + 3x - 7 = 4x2 + 3x - 7.
Step 4: The final result is 4x2 + 3x - 7, which is a polynomial.
A polynomial is an algebraic expression composed of constants, variables, and exponents, with the variables being multiplied together. 4x² 3x 7 is an example of a polynomial. To expand this polynomial, we start by combining the like terms, 4x² and 3x, to get 4x2 + 3x. Then, we add the constant, -7, to get 4x2 + 3x - 7. This final expression is a polynomial because it has constants, variables, and exponents, and the variables are multiplied together. Therefore, 4x² 3x 7 is a polynomial.
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-178 = -5x +4(-4x-13)
Answer: To solve for x, you can first simplify the right side of the equation by distributing the negative 4x:
-178 = -5x + (-16x - 52)
Next, combine like terms on the right side:
-178 = -21x - 52
Then add 52 to both sides:
-126 = -21x
Finally, divide both sides by -21 to solve for x:
x = 6
Step-by-step explanation:
statistics uses methods that generalize results obtained from a sample to the population and measure the reliability of the results. t or f
Inferential statistics use techniques that extrapolate results from a sample to the population and assess the accuracy of the findings.
What is the difference between a population and a sample?The entire group about whom you want to make conclusions is referred to as a population.
The particular group from which you will gather data is known as a sample. The sample size is always smaller than the population as a whole.
It is crucial to separate, handle, and organize all data that is given to us in order to streamline work. Descriptive statistics refer to the reading of the given data that supports characterizing or supplying the well-behaved data for analysis.
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the hair on your head grows 1in 1 inch per month discreet or continuous
Answer: Continuous
Step-by-step explanation: I say it is continuous as the hair will grow continuously but we can't determine how exactly it'll grow 1 inch a month and the inches won't be integers if the hair is grown more than an inch.
two distinct circles and a square lie in the plane. what is the maximum number of points of intersection of two or more of these three figures?
The maximum number of points of intersection of two distinct circles and a square is 18.
The maximum possible intersection points of a circle and a line is 2. A square comprises 4 line segments, hence, the maximum possible intersection points of a circle and a square is 2 x 4 = 8 points.
The condition for 8-point intersection is that the diameter of the circle must be between s and s√2, where s is the length of the sides of the square, or it can be written as:
s < d < s√2
In the problem, there are two circles and a square. Let's denote the circles as C1 and C1, while the square as S
- Maximum number of intersection points of C1 and C2 is 2
- Maximum number of intersection points of C1 and S is 8
- Maximum number of intersection points of C2 and S is 8
Hence, the maximum possible intersection points of these figures is 2 + 8 + 8 = 18 points.
The possible construction where these three figures have maximum intersection points is depicted on the attached picture.
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Rewrite 15x4y3 − 45x3y4 using a common factor.
Answer:
The other form of 15x^4y^3 − 45x^3y^4 is 15x^3y^3(x - 3y)
The endpoints of AB are given. Find the coordinates of the midpoint M. Then find AB. A(-3, 5), B(3, 5)
Answer:
Step-by-step explanation:
The difference between the x coordinates is 6, (difference between -3 and 3). Half of 6 is 3. Add this to the lowest value (-3) to get to zero.
Repeating the exercise for the Y coordinates we get a difference of 0 (there's no difference between the values 5 & 5). So adding this difference (0) to the lowest value (5) we get 5 still.
So the midpoint is (0,5)
In a 3 out of n system, in which each component has probability 0. 9 of functioning, what is the smallest value of n needed so that the probability that the system functions is at least 0. 90?
The smallest value of n needed so that the probability that the system functions is at least 0.90 is 12. Probability is a measure of the likelihood of an event occurring. In a mathematical sense, probability is a value between 0 and 1 that represents the chance of a particular event happening.
In a 3 out of n system, the probability that the system functions is given by the formula:
P(function) = [tex]1 - (1 - p)^3 * (1 - (1 - p)^(^n^ - ^3^))[/tex]
where p is the probability that each component functions (in this case, 0.9) and n is the total number of components.
To find the smallest value of n that satisfies the condition P(function) ≥ 0.9, we can rearrange the formula to:
n ≥ 3 + log(1 - 0.9) / log(1 - 0.9)
By solving this equation, we find that the smallest value of n that satisfies the condition is n ≥ 12.
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Which number is between pie 21 and 3 Irrational over 2
33.72 is the number between pie 21 and 3 Irrational over 2.
What is Number system?A number system is defined as a system of writing to express numbers.
We have to find the number between pie 21 and 3 Irrational over 2
The value of pie 21 is 65.94
3/2 is the other irrational number.
The value of 3/2 is 1.5
The number between 65.94 and 1.5 is
65.94+1.5/2
67.44/2
33.72
Hence, 33.72 is the number between pie 21 and 3 Irrational over 2.
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in most cases, the product of a monomial and a binomial is a ___.
In most cases, the product of a monomial and a binomial is a trinomial.
A monomial is an algebraic expression that is a single term, such as 2x or 5y^3. A binomial is an algebraic expression that is a sum or difference of two terms, such as x+y or 2x-3y. When a monomial is multiplied by a binomial, the result is an expression with three terms, which is called a trinomial.
For example, when we multiply the monomial 2x with the binomial x+y, we get:
(2x)(x+y) = 2x^2 + 2xy
This is a trinomial because it has three terms: 2x^2, 2xy and the constant term is missing.
It's worth noticing that, this is a general rule but not always true, there are some cases when the product of a monomial and a binomial is a binomial, like when the monomial has a factor that cancels out one of the terms in the binomial.
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What are the 7 properties of logarithms?
properties of logarithms -Logarithm Base Properties
Product Property
Quotient Property
Power rule
Change of Base rule
Reciprocal rule
Exponent law vs Logarithm law
Natural Logarithm properties.
properties of logarithms functions are used to solve logarithm problems. We have learned many properties in basic math such as commutative, associative and distributive, which are applicable for algebra.
The properties of logarithms are used to simplify the complex problems involving logarithmic functions. These properties help in converting the functions into easily computable parts.
The logarithmic number is associated with exponent and power, such that if x n = m, then it is equal to log x m=n. Hence, it is necessary that we should also learn exponent law.
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Fill in the Blanks
Evaluate the following trigonometric expressions.
a. 2 cos^2(pi/8) -1=
b. 2tan(11/pi)/1-tan^2(11pi/12)=
2 cos^2(pi/8) -1= ,
x=(2n + 1) π/4 + π/8, where n is an integer.
What is meant by integer?
An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction.Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples.The Latin word integer, from the prefix in ("not") plus tangere, means "whole" or (literally) "untouched" ("to touch").An integer is any number that may be expressed without using any fractions. Since there are no fractions in integers, they are essentially entire numbers that can be positive, zero, or negative.An integer field can have 3, 5, 10, or 20 digits, with length being defined in terms of the number of digits. One byte of storage is required for a 3-digit field.x=(2n + 1) π/4 + π/8, where n is an integer.
We use the double angle identity 2[tex]cos^{2}[/tex]A−1 = cos2A
if x − π/8 =A, then 2[tex]cos^{2}[/tex] (x− π/8) −1 = cos(2(x − π/8)) = cos(2x − π/4)
Hence cos(2x − π/4) = 0
and 2x − π/4 = (2n + 1) π/2, where n is an integer
or 2x = (2n+1) π/2 + π/4
or x = (2n + 1) π/4 + π8, where n is an integer.
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I need the work and the answer to the problem
Answer:
3.7 L
Step-by-step explanation:
How do you find f (- 2 on a graph?
To find the value of f(-2) on a graph, you would locate the point (-2, y) on the graph, where y is the value of the function at x = -2. The value of y is the y-coordinate of the point on the graph.
In a cartesian coordinate system, the x-axis and y-axis are perpendicular to each other. The x-axis is the horizontal axis and the y-axis is the vertical axis. When a function is graphed, the x-coordinate is input into the function and the y-coordinate is the output of the function. So, when you are trying to find the value of f(-2) on a graph, you are looking for the y-coordinate of the point where x = -2. To find this point, you would move horizontally along the x-axis until you reach the value of -2. Then, you would move vertically from that point until you reach the point on the graph. The y-coordinate of that point is the value of f(-2)
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how to tell the difference between no solution, infinite solutions, and one solution
Answer:if you try to solve the equation and get a variable or a number equal to itself.
Step-by-step explanation:
PLEASE HELP ASAP!!!!!!!!
Bilquis invested $6,900 in an account paying an interest rate of 5\tfrac{1}{8}5 8 1 % compounded continuously. Sophie invested $6,900 in an account paying an interest rate of 4\tfrac{3}{4}4 4 3 % compounded monthly. After 18 years, how much more money would Bilquis have in her account than Sophie, to the nearest dollar?
The amount of money Bilquis have more than Sophie when compounded continuously is given by the equation A = $ 42
What is Compound Interest?Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.
The formula for calculating Compound Interest is
A = P ( 1 + r/n )ⁿᵇ
where A = Final Amount
P = Principal
r = rate of interest
n = number of times interest is applied
b = number of time periods elapsed
Given data ,
Let the compound interest amount of Bilquis be represented as B
Let the compound interest amount of Sophie be represented as S
The amount of money invested by Bilquis and Sophie is = $ 6,900
The rate of interest of Bilquis = 5 1/8 = 5.125 %
The rate of interest of Sophie = 4 3/4 = 4.75 %
The time period b = 18 months = 1.5 years
So , the amount after compound interest A = P ( 1 + r/n )ⁿᵇ
Substituting the values in the equation , we get
The amount with Bilquis after 18 months B = Pe^rt ( compounded continuously )
The amount with Bilquis after 18 months B = 6900 ( 2.71828 )^(0.05125)(1.5 )
On simplifying the equation , we get
The amount with Bilquis after 18 months B = $ 7451.36
And ,
The amount with Sophie after 18 months S = Pe^rt ( compounded continuously )
The amount with Sophie after 18 months S = 6900( 2.71828 )^(0.0475)(1.5 )
On simplifying the equation , we get
The amount with Sophie after 18 months S = $ 7409.56
So , the difference in amount is A = amount with Bilquis after 18 months B - amount with Sophie after 18 months S
On simplifying the equation , we get
The difference in amount is A = 7451.36 - 7409.56
The difference in amount is A = $ 41.8
So , The difference in amount is A = $ 42
Hence , Bilquis had $ 42 more than Sophie
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What are 3 algebraic expressions?
The 3 algebraic expressions are simple linear expression, linear expression and a product of two binomials.
Here are five examples of algebraic expressions:
1. 2x + 3: This is a simple linear expression that involves a variable (x) and two constants (2 and 3).
2. 4y - 7: Similar to the first example, this is also a linear expression, involving a variable (y) and two constants (4 and 7).
3. 3x^2 + 4x - 5: This is a quadratic expression, involving a variable (x) raised to the power of 2, a constant (3), a variable (x) and a constant (-5).
4. (x + 2)(x - 3): This is a product of two binomials, each one is a linear expression and the result of the product is a quadratic expression.
5. (3x + 4)/(x-2): This is a quotient of two expressions, the numerator is a linear expression and the denominator is a linear expression.
It's important to note that these are just a few examples and there are many different types of algebraic expressions, each with their own unique characteristics and properties. Algebraic expressions can become more complex as the student progresses, but the basic idea remains the same.
Therefore, The 3 algebraic expressions are simple linear expressions, linear expressions and a product of two binomials.
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(+5) Find the arc length of AB to the nearest tenth. Show work.
А
8
30⁰
5 cm
Answer:
Step-by-step explanation:
a
Which of the following equations is equivalent to -5(x-1)=2x+15
Select one:
-7x =14
-7x =20
-7x =10
-7x =16
Answer:
-7x = 10
Step-by-step explanation:
step 1: multiply each term inside the parentheses by -5, to get:
-5x + 5 = 2x + 15
you can subtract 2x from each side of the equation to get:
-7x + 5 = 15
now you subtract 5 from each side to get:
-7x = 10