Therefore the correct answer is A. Adam earns $5.25 more per hour than Kim.
Define percentage.A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Define Fraction.Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
Adam earns $186 for 8 hours of work, so his hourly rate is $186/8 = $23.25 per hour
Kim earns $54 for 3 hours of work, so her hourly rate is $54/3 = $18.00 per hour
Kim earns $125 for 7 hours of work, so her hourly rate is $125/7 = $17.86 per hour
Kim earns $216 for 12 hours of work, so her hourly rate is $216/12 = $18.00 per hour
Adam earns $23.25 per hour and Kim earns $18.00 per hour on average.
Adam earns $23.25 - $18.00 = $5.25 more per hour than Kim.
Therefore the correct answer is A. Adam earns $5.25 more per hour than Kim.
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What is the angle of turn clockwise from South East to North?
N
A 45°
B 135°
C 225°
D 315°
The angle of a turn clockwise from South East to North is Option B 135°.
When determining the angle of turn, it is important to consider the direction of rotation (in this case, clockwise) and the starting and ending points (in this case, South East to North).
If we imagine the compass as a clock, with North at the 12 o'clock position, South at the 6 o'clock position, East at the 3 o'clock position, and West at the 9 o'clock position. Then South East would be at the 4:30 position and the North would be at the 12 o'clock position. To rotate from 4:30 (South East) to 12 o'clock (North) in a clockwise direction, we would have to rotate 135 degrees. Thus, the angle of a turn clockwise from South East to North is 135 degrees.
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Subtract -2a+7b=-5 from the other equation so the b-terms become opposites
When subtracted -2a+7b=-5 from the other equation so the b-terms become opposites, we get 2a -7b = 5 as the result.
What is equation?In mathematics, an equation is an expression or a statement made up of two algebraic expressions with the same value that are separated by the equal sign. It is a mathematically quantified version of an otherwise expressed statement. Equations can take many different forms. Equations are used to compare two expressions.
To Subtract -2a+7b=-5 from the other equation so the b-terms become opposites, we need to make +7b to -7b
This is only possible when the other term has 14,
Lets solve
2a + 7b = - 5
- 4a + 14b = -10
-2a -7b = 5
Thus, when subtracted -2a+7b=-5 from the other equation so the b-terms become opposites, we get 2a -7b = 5 as the result.
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Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form. 4,\, 5,\, 6,\, ... 4,5,6,...
The given sequence is arithmetic because the difference between consecutive terms is constant. The common difference is 1, since the difference between each pair of consecutive terms is 1 (e.g., 5 - 4 = 6 - 5 = 1). The common difference can be expressed in simplest form as 1/1 = 1.
Answer:
it is arithmetic, 6-5=1, 5-4=1
Does anybody know what the answer to this question?
The simplified form of the given fraction is, [tex]\frac{1}{x^2y}[/tex].
What is simplified form of the expression?
If a fraction's top and bottom have only the number one in common, then it is expressed in its simplest form. The top and bottom cannot be divided further and remain whole numbers, in other words. The phrase "lowest terms" is another term for the simplest form.
Consider, the given expression
[tex]\frac{(\frac{1}{x^2}-\frac{2}{y} )}{y-2x^2}[/tex]
We have to find the simplified form of the given expression.
Taking cross multiplication of numerator of the above fraction.
[tex]\frac{(\frac{y-2x^2}{x^2y} )}{y-2x^2}[/tex]
Using: [tex]\frac{(\frac{a}{b} )}{c} = \frac{a}{b}*\frac{1}{c}[/tex]
⇒ [tex]\frac{(\frac{y-2x^2}{x^2y} )}{y-2x^2} = \frac{y-2x^2}{x^2y} *\frac{1}{y-2x^2} = \frac{1}{x^2y}[/tex]
Hence, the simplified form of the given fraction is, [tex]\frac{1}{x^2y}[/tex].
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9) Express the roots of the equation 2x² + 4x + 5 = 0 in simplest a + bi form.
2x2+4x5=0 is a quadratic equation that can be solved. 2 x 2 + 4 x - 5 = 0. To find the answers, start with the quadratic formula.
What is the quadratic equation of 2x² 3x 5 0?Using the quadratic formula, determine the roots of the quadratic equations 2x2-3x-5= 0. The equation's roots must be located. As a result, the equation's roots are 5/2 and -1. Which equation with 2 as a root must be identified. As a result, 2 is not a root of x2-4x + 5= 0.
Since 2 is not a root, x2 + 3x-12= 0 cannot be solved. Thus, 2 is the root of the equation 2x2-7x + 6= 0. The roots of the quadratic equation ax2 + bx + c= 0 are real and equivalent if the discriminant is equal to zero (b2-4ac=0), a, b, and c are real values, and a0. The roots in this situation arex= -b/2a.
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hi how do you solve x/5 + 6 < 2
Answer:
x < -20
Step-by-step explanation:
To solve x/5 + 6 < 2,
First subtract 6 from both sides of the equation.
This makes x/5 < -4.
Then multiply both sides of the equation by 5.
This makes x < -20.
Therefore, the solution to the equation is x < -20.
After my salary was increased by $16\%,$ it was $\$52{,}200$. What was my salary before the increase
%, a relative figure signifying hundredths of any amount. Before the raise, I was making $45,000.
What is percentage?A percentage that represents a tenth of a quantity. In essence, percentages are fractions with a denominator of 100. The percent symbol (%) is placed next to a number to indicate that it is a percentage. For instance, you would have received a 75% on the examination if you correctly answered 75 out of 100 questions (75/100).
Calculating a percentage involves dividing an item by its sum and multiplying the result by 100.
Considering the query
It was $52,200 after a 16% raise in my pay.
In light of the conditions stated, come up with
[tex]$=\frac{52200}{1+16 \%}$$=\frac{52200}{1+0.16}$$=\frac{52200}{1.16}$$=\frac{5220000}{116}$[/tex]
= $45000
Before the raise, I was making $45,000.
Therefore, the answer is $45,000.
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what is x^2(2x^2+8)?
Answer:
2[tex]x^{4}[/tex] + 8[tex]x^{2}[/tex]
Step-by-step explanation:
[tex]x^{2}[/tex](2[tex]x^{2}[/tex] + 8) When you are multiplying powers that have the same bases, you add the exponents.
Can you help me do this exercice that I don't know how to do it, can you help me for this homework ?
After simplifying each expression, we get (2+5a - 10 b), (8a² - 15ca +2c),
(11- 2a+b) and (a+ b) respectively.
What is simplification?
The word simplify means to write an expression, equation or problems
in the simplest form so as to easy to evaluate it. we simplify an expression by removing the parenthesis and collecting like terms.
How can we simplify the expression given in question?
exercise 1.
given, A = 7 - 4a + 7a - 3b -5 -7b +2a
We collect the like term and get
A= 7 - 5 -4a +7a +2a -3b- 7b
A = 2 + 5a -10b
next, given B = 4a × 2a -5c - c +8c -3c × 5a
B = 8a² -6c +8c - 15ca
B = 8a² -15ca +2c
exercise 2.
given, A = 7 + [(2- a) -( 2+a) +9] + (b-5)
at first, we remove the parenthesis and get
A= 7 + [2-a - 2 -a+ 9] +b- 5
A = 7 + 9- 2a +b- 5
after collecting the like term
A = 11- 2a + b
given, B = 15 - [(7-b) - 9- (a-17)]
B = 15 - [7- b- 9 - a+17]
B = 15 - [15 - b -a]
after removing the parenthesis
B = b +a
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−8≤2−10
Can you please help me find it?
Answer:
-8 [tex]\leq[/tex] -8
Step-by-step explanation:
-8[tex]\leq[/tex]2-10
-8[tex]\leq[/tex]-8
Answer:
-8
Step-by-step explanation:
-8≤2-10
2-10 = -8
-8≤-8
A line is drawn so that is passed through the points (2, -1) and (0, 5). What is the slope of the line
If a line is drawn so that it passes through the point [tex](2,-1)[/tex] and [tex](0,5)[/tex] , then slope of line is -3 .
What is Slope ?
The slope of a line is defined as measure of steepness and direction of line. The slope of line in a plane help in predicting whether lines are parallel, perpendicular, or none without using a compass.
The slope of line passes through points [tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2} ,y_{2} )[/tex] is calculated by formula ⇒ [tex]Slope = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex] ;
the points are given as [tex](2,-1)[/tex] and [tex](0,5)[/tex] ;
So , on substituting the values in the slope formula ,
we get ;
[tex]Slope = \frac{5 -(-1) }{0 -2 }[/tex] ;
= [tex]\frac{6}{-2}[/tex]
= -3 .
Therefore , the required slope of the line is -3 .
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Why is a 5th interval called perfect?
The 5th interval is called perfect
Interval notation is a method to represent an interval on a number line.
The 5th interval is called perfect
Interval notation is a method to represent an interval on a number line. In other words, it is a way of writing subsets of the real number line. An interval comprises the numbers lying between two specific given numbers. For example, the set of numbers x satisfying 0 ≤ x ≤ 5 is an interval that contains 0, 5, and all numbers between 0 and 5.
Interval Notation is a way of expressing a subset of real numbers by the numbers that bound them. We can use this notation to represent inequalities. We know an interval expressed as 1 < x < 5 denotes a set of numbers lying between 1 and 5.
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Saad yearly income is rs 236000.How much income tax he paid
Saad's income tax will be N.I.L.
Here, saad's yearly income is Rs 2,36,000.
The rate of income tax on his income will be nil because,
INCOME TAX RATE
0-2,50,000 NIL
2,50,000-5,00,000 5%
5,00,001-10,00,000 20%
More than 10,00,000 30%
Computation of tax liability of Saad
Tax on 1st 2,36,000 = N.I.L
As his income is less than 2,50,000 no income tax shall be charged to saad's income.
Therefore, the tax liability of saad would be 0.
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The linear function F is defined as f(x) = -2x + 3. Consider the graph of y = f(x) in the xy-Plane.
If the function g(x) = f (x) + k, where k = 2, describe the changes to the slope and y-intercept of this transformation.
The changes to the slope and to the intercept of the linear function after the transformation g(x) = f(x) + k, in which k = 2, are given as follows:
The slope remains constant.The intercept is increased by two.What is the definition of a linear function?The slope-intercept definition of a linear function is presented as follows:
y = mx + b.
In which the coefficients are given as follows:
m is the slope.b is the y-intercept.The function f(x) in this problem is given as follows:
f(x) = -2x + 3.
Meaning that it has a slope of -2 and and intercept of 3.
The function g(x) is defined as follows:
g(x) = f(x) + k.
Since k = 2, we have that:
g(x) = f(x) + 2
g(x) = -2x + 3 + 2
g(x) = -2x + 5.
Hence the slope and the intercept are given as follows:
Slope of -2, which is the same as f(x).Intercept of 5, which is an increase of 2 compared to the intercept of f(x).More can be learned about linear functions at https://brainly.com/question/24808124
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What is the equation of the straight line shown below? Give your answer in the form y = mx + c, where m and c are integers or fractions in their simplest forms. Y 14- 13- 12- 11- 10- 9 8- 97654 MNE 7- 6- 5- 4- 3- 2- 1- -10-9-8-7-6-5-4-3-2 0 1 2 3 4 5 6 7 8 9 10 x -1 -2- -3- بنا -4- 56 -5- -6+
Answer:
y = 2x + 10
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 5, 0) and (x₂, y₂ ) = (0, 10) ← 2 points on the line
m = [tex]\frac{10-0}{0-(-5)}[/tex] = [tex]\frac{10}{0+5}[/tex] = [tex]\frac{10}{5}[/tex] = 2
the line crosses the y- axis at (0, 10 ) ⇒ c = 10
y = 2x + 10 ← equation of line
Which statement about the order of operations is TRUE?
Complete all subtraction operations before addition.
Simplify operations within the innermost grouping symbols first.
Complete all division operations before multiplication.
Simplify exponents before operations in grouping symbols.
4382 round 1 significant figure
Answer:
4382 contains 4 significant figures, 4382 round to 1 significant figure is 4000.
Rewrite 14x4y3 − 42x3y4 using a common factor.
The expression 14x⁴y³ - 42x³y⁴ is rewritten to 14x³y³(x - y)
What is an algebraic expression?
An algebraic expression can be described as a mathematical expression that is made up of terms, coefficients, variables, factors and constants.
They are also made up of some arithmetic operations, such as;
SubtractionMultiplicationDivisionBracketParenthesesAddition, etcFrom the information given, we have the algebraic expression;
14x⁴y³ - 42x³y⁴
Now, factor the common numbers, we have;
14(x⁴y³ - 3x³y⁴)
Factor the common variables, we get;
14x³y³(x - y)
Hence, the expression is 14x³y³(x - y)
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what is the least common denominator 5/8 and 3/4
Answer:
The least common denominator is 8, you need to multiply the 3 by 2.
Answer:
8
Step-by-step explanation:
What is the secret calculator app?
The secret calculator app is used to protect confidential Photos, Videos, Documents, Passwords, Notes, Contacts and To Dos.
The term calculator is referred as a device that performs arithmetic operations on numbers and it does the basic calculators can do only addition, subtraction, multiplication and division mathematical calculations.
Here we need to find definition and the usage of secret calculator app.
As per the definition of calculator here we know that the app is used to acts like a photo vault to store all password protected files, and can only be viewed inside the app.
As the user who is unaware of this app you will never expect a simple calculator looking app is used to hide files.
Here if you want to access this you will need the password to open the photos from your child.
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You want to ride your bike down the street to your friend's house, which is 340 meters from your house. The trip takes you 68 seconds from start to finish. How fast are you traveling on your bike?
The speed of the Bike is 5 meters per second
What is speed?Speed is a scalar quantity that describes how fast an object is moving . It is defined as the distance an object travels divided by the time it takes to travel that distance. The units of speed are typically meters per second (m/s) or kilometers per hour (km/h).
To find out how fast you are traveling on your bike, you can use the formula:
Speed = [tex]\frac{Distance}{Time}[/tex]
In this case, the distance is 340 meters and the time is 68 seconds. So, you can plug these values into the formula and get:
Speed = 340 meters / 68 seconds
Speed = [tex]\frac{340 meters}{68 seconds}[/tex] = 5 meters per second
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A straw is placed inside a rectangular box that is 2 inches by 1 inches by 3 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in the simplest radical form.
The length of the straw is 3.74 inches.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
In rectangular box,
Length (l) = 2 inches
Width (w) = 1 inches
Height (h) = 3 inches
Here, The straw is said to fit into the box diagonally from the bottom.
So, the length (s) of the straw is calculated as:
⇒ s = √ l² + w² + h²
⇒ s = √ 2² + 1² + 3²
⇒ s = √ 4 + 1 + 9
⇒ s = √ 14
⇒ s = 3.74 inches
Thus, The length of straw = 3.74 inches
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The length of the straw will be 3.7416 inches long in radical form.
What is Length of diagonal in cuboid?If a cuboid has length = l units, breadth = b units, and height = h units, then we can evaluate the length of the diagonal of a cuboid using the formula : X²=l²+b²+h²
Here,
As per the question the length of the straw is equal to length of the diagonal of Rectangular box.
l= 3 inch , b= 2 inch , h= 1 inch
Let us consider the length of the straw be 'x'.
As, Diagonal of Cuboid is,
X²=14
X=√14
i.e. X=3.7416
We get, X= 3.7416 (in radical form)
Hence, the length of the straw will be 5.91607 inches.
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What are the factors of 2x^2 7x 3?
The factors of 2[tex]x^{2}[/tex] + 7x + 3 are ( x + 3) and (2x + 1)
Now, According to the question:
The given function is :
f(x) = [tex]2x^2+7x+3[/tex]
To find the factors of [tex]2x^2+7x+3[/tex] we need to split the middle term, that is, 7x.
7x = 6x + x
Therefore, 2[tex]x^{2}[/tex] + 7x+ 3 can be written as 2[tex]x^{2}[/tex] + 6x + x + 3 .
On taking '2x' common from first two terms and +1 from next two terms we get
2x (x + 3) +1 (x + 3)
(x + 3) (2x + 1)
Thus, the factors of 2x2 + 7x + 3 are (x+3) and (2x+1)
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The complete question is this:
What are the factors of 2x^2+7x +3?
Help please
Determine the sum of the measures of the interior angles of a dodecagon (12-sided polygon).
540°
360°
1,800°
2,160°
Answer:
Below
Step-by-step explanation:
Formula for sum of interior angles of a n - gon
(n-2) * 180
for this 12 sided 'gon
(12-2) * 180 = 1800°
( and for a 'regular' dodecagon each would be 1800/12 = 150°
Answer:
Option C) 1,800°
Step-by-step explanation:
To Find : Interior Angles of a Decagon
In order to find interior angles of any polygon we usually use the formula
(n-2)x180
Over Here it is a 12 sided polygon
So,
(12-2)x180
10x180
1800
Hence the interior angles of a decagon is 1800°
How do you solve 3 to the power of 3?
As per the power rule of exponents, the solution of 3 to the power of 3 is 27.
The term exponent in math is defined as a number shows how many times the number is multiplied by itself.
Here we have to solve 3 to the power of 3.
Here according to the Power Rule of Exponents then we have the rule as
=> aⁿ = a × a × a... (n times)
Therefore, the given expression is written as
=> 3³
Now, based on the power of exponent rule it can be rewritten as,
=> 3 × 3 × 3
Then we have to multiply the values then we get
=> 27
Therefore, the value of 3 raised to 3rd power is 27.
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Select the correct answer. Solve the quadratic equation by factoring.
9x -16 = 0
Answer:
x = 16/9
Step-by-step explanation:
9x -16 = 0
9x = 16
x = 16/9
Let's check
9(16/9) -16 = 0
144/9 - 16 = 0
16 - 16 = 0
0 = 0
So, x = 16/9 is correct!
Answer:
Step-by-step explanation:
9x = 16
x = 16/9
What is the probability that this year's graduation will fall on the birthday of exactly one of the 68 Seniors? What is the probability that there is more than one such Senior?
The probabilities are given as follows:
Birthday of one student: 0.1550 = 15.50%.Birthday of more than one student: 0.0152 = 1.52%.What is the binomial distribution formula?The mass probability formula, giving the probability of x successes, is of:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.The parameter values for this problem are given as follows:
n = 68, as the class is composed by 68 Seniors.p = 1/365, as the year has 365 days, hence the probability of a person having a given day as a birthday is of 1/365.Hence the probability of one senior having the birthday on the same day as the graduation is of:
P(X = 1) = 68 x 1/365 x (364/365)^67 = 0.1550.
The probability of more than one is given as follows:
P(X > 1) = 1 - P(X <= 1).
In which:
P(X <= 1) = P(X = 0) + P(X = 1)
Hence:
P(X = 0) = (364/365)^68 = 0.8298.P(X = 1) = 68 x 1/365 x (364/365)^67 = 0.1550.Finally:
P(X <= 1) = 0.8298 + 0.1550 = 0.9848.P(X > 1) = 1 - P(X <= 1) = 1 - 0.9848 = 0.0152.More can be learned about the binomial distribution at https://brainly.com/question/24756209
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Write an equation for the parabola that passes through (-2,7), (1, 10), and (2,27)
An equation for the parabola is y=.
Answer: To find an equation for a parabola that passes through three specific points, we can use the method of algebraic manipulation.
Since the parabola is symmetric about the y-axis, the equation of the parabola will have the form y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.
Given three points (-2,7), (1, 10), and (2,27), we can use the vertex form of the equation and substitute the x, y values of the three points to find the values of a, h and k
y = a(x-h)^2 + k
Since it is passing through (-2,7), we can substitute the values of x and y in the equation and get
7 = a(-2 - h)^2 + k
It passing through (1, 10), we can substitute the values of x and y in the equation and get
10 = a(1 - h)^2 + k
It passing through (2,27), we can substitute the values of x and y in the equation and get
27 = a(2 - h)^2 + k
Now we have three equations with three variables, we can solve it using any of the techniques such as substitution, elimination or matrix. But the final equation will be in the form of y= a(x-h)^2 + k
Here, x= (-2, 1, 2) and y = (7, 10, 27) . Therefore it has a unique parabola passing through these points.
Step-by-step explanation:
What phrases can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created
Negative Slope can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created.
In the given question, we have to find what phrases can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created.
As we know that,
(1) Negative Slope: A line with a negative slope is one that is moving from left to right in a downward direction. The rise to run ratio of the line, in other words, is negative.
(2) Decreasing Function: For a given function, y = F(x), the function is known as an increasing function if the value of y increases as the value of x increases, and the function is known as a decreasing function if the value of y decreases as the value of x increases.
(3) Constant Slope: Small slopes correspond to low speeds, negative slopes to high speeds, and constant slopes (straight lines) to steady speeds.
Hence, Negative Slope can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created.
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A quadrilateral
is a polygon with four sides. Consider
the quadrilateral and the dashed segment. What is the sum
of the measures of the four interior angles of this quadrilateral?
Draw a different quadrilateral. Can you guess the sum
of the measures of its angles? Is it possible to generalize about
the angles of a quadrilateral?
The sum of the measures of the four interior angles of a quadrilateral is always 360°
What is a quadrilateral?A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles.
Given is, A quadrilateral is a polygon with four sides. Consider the quadrilateral and the dashed segment
If we draw one diagonal to quadrilateral we will get two triangles i.e. △ABC and △ACD and we know that sum of the angles of a triangle is 180°
Sum of angles of quadrilateral ABCD = sum of angles of △ABC + sum of the angles △ACD
= 180° + 180°
= 360°
If we take examples of a square or a rectangle, we know that they are also a quadrilateral and also their each angle is right angle, i.e. 90°
Therefore, the sum of their interior angles will = 90×4 = 360°
Hence, we can say that the sum of the measures of the four interior angles of a quadrilateral is always 360°
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