Tom had 60 dollars as his pocket money initially.
Let's assume that Tom had x dollars as his pocket money.
He spent 2/3 of his pocket money on apples, which means he spent (2/3)x dollars on apples.
He had 1/3 of his pocket money left after buying the apples.
Out of the remaining money, he spent 1/4 on bananas, which means he spent (1/4)(1/3)x = (1/12)x dollars on bananas.
The total amount spent on apples and bananas is given as $45. So, we can write the equation:
(2/3)x + (1/12)x = 45
Multiplying both sides by 12 to get rid of the fractions:
8x + x = 540
Simplifying, we get:
9x = 540
Dividing both sides by 9:
x = $60
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exercise 3.2.5: facts about power sets - true or false. help outline let x be a finite set. for each statement, indicate whether the statement is true or false, or whether more information about x is required to determine if the statement is true.
The given facts about power sets: Statement 1: False, Statement 2: True, Statement 3: True.
Statement 1: The power set of X is a subset of X. False. The power set of X, denoted by P(X), is a set containing all subsets of X. However, X is not a subset of P(X).
Statement 2: The cardinality of P(X) is greater than the cardinality of X. True. Since the power set of X contains all subsets of X, it has a higher cardinality than X. This can be proven with the equation |P(X)| = 2^|X|.
Statement 3: The cardinality of the power set of the empty set is 1. True. The empty set, denoted by Ø, has no elements, and therefore the power set of the empty set, P(Ø), has one element, which is the empty set itself. Therefore, |P(Ø)| = 1.
In conclusion, each statement is either true or false depending on the given information.
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If 3 −2√5 and 6 + ???? are roots of P(x), what other numbers must
also be roots?
There is no one definite answer.
Given information: If 3 −2√5 and 6 + ???? are roots of P(x), what other numbers must also be roots?To find out the other roots of P(x), we have to make use of the Fundamental theorem of algebra which states that every polynomial of degree n has n roots, both real and complex.In order to find out the other roots, we have to divide the polynomial P(x) by its given roots i.e (x-(3-2√5))(x-(6+????)) = 0Let's begin by solving the first root:Since, If 3 −2√5 is the root, thus we can write, x - (3 - 2√5) = 0Or, x - 3 + 2√5 = 0Or, x = 3 - 2√5Similarly, for the second root, 6 + ???? ,
we can write: x - (6 + ???? ) = 0Or, x = 6 + ????Now, Let's combine these two roots and write the polynomial in factored form. Using these two roots, we can write the equation as below: Thus, P(x) = (x - 3 + 2√5)(x - 6 - ???? ) = 0We have found the other roots to be: Other roots = (x - 3 + 2√5)(x - 6 - ???? ) = 0Where ???? can be any value. Therefore, there is no one definite answer.
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write an equation of the line that passes through (-1,0) and (0,0)
y=
Answer:
y = 0
Step-by-step explanation:
the 2 points (- 1, 0 ) and (0, 0 ) both have the same y- coordinate.
this indicates the line is horizontal with equation
y = c ( c is the value of the y- coordinates the line passes through )
both points have a y- coordinate of 0 , then
y = 0 ← equation of line
Mr. Moore has a rectangular prism shaped planter box to grow herbs inside his house. The dimensions of the planter box are 4. 5 feet long, 2 feet wide, and 1. 5 feet tall. How any cubic feet of soil does Mr. Moore need in order to fill the planter box
Mr. Moore needs 13.5 cubic feet of soil to fill the planter box.
To calculate the volume of the rectangular prism planter box, we need to multiply the length, width, and height of the box.
Volume = length x width x height
V = 4.5 ft x 2 ft x 1.5 ft
V = 13.5 cubic feet
Therefore, Mr. Moore needs 13.5 cubic feet of soil to fill the planter box.
It is important to note that the volume of the box represents the amount of space inside the box and does not take into account any obstructions or irregularities that may be present inside the box.
Thus, the actual amount of soil required may be slightly different from the calculated value. Additionally, it is always a good idea to add some extra soil to account for settling and to ensure that the planter box is completely filled.
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the two line segments below each have the same length l. if you were to calculate the integral the contour integer of the dot product of vector b with respect to vector s for each path, which one would yield b times l?
In response to the given question, we can state that To compute the function contour integral and establish the value of b times l for each path, the precise path of the line segments must be specified.
what is function?Mathematicians examine numbers and complex variations, equations and associated structures, forms and their locations, and prospective positions for these things. The term "functioning" signifies the connection between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and results in which each input leads to a single, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used this to denote functions (x). The symbol for admission is an x. The four primary types of usable functions are on operations, one-to-one capabilities, so multiple functionality, in capabilities, and then on functions.
It is impossible to predict which path would provide a contour integral of b times l for the dot product of vector b with respect to vector s without knowing the precise trajectories of the line segments.
The contour integral of a vector field F's dot product with respect to a curve C is given by:
∫C F · ds
To compute the contour integral and establish the value of b times l for each path, the precise path of the line segments must be specified.
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For each ordered pair (x, y), determine whether it is a solution to the inequality y > 0.
(x,y)
(6, 38)
(-4, - 13)
(-1, 8)
(3, 26)
The ordered pairs (6, 38), (-1, 8), and (3, 26) are solutions to the inequality y > 0, while (-4, -13) is not a solution.
Define in short the solution to the inequality?An inequality is a mathematical statement that compares two values and shows the relationship between them using symbols like "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to).
For the given ordered pairs:
(6, 38): The y-coordinate (38) is greater than 0, this ordered pair is a solution to the inequality y > 0.
(-4, -13): The y-coordinate (-13) is not greater than 0, this ordered pair is not a solution to the inequality y > 0.
(-1, 8): The y-coordinate (8) is greater than 0, this ordered pair is a solution to the inequality y > 0.
(3, 26): The y-coordinate (26) is greater than 0, this ordered pair is a solution to the inequality y > 0.
Therefore, the ordered pairs (6, 38), (-1, 8), and (3, 26) are solutions to the inequality y > 0, while (-4, -13) is not a solution.
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In8=2.08 in exponential form
can yall help me with this this is due on Saturday pls help me!!!
Therefore , the solution of the given problem of fraction comes out to be Y is therefore equivalent to 26/5.
A fraction is what?Any combination of like-sized pieces or portions can represent a whole. Standard English defines "quantity" as "a portion" of a particular measure. 8, 3/4. Wholes also include fractions. In mathematics, numerals are expressed by the ratio of quotient to ratio. Every one of these fractions of integers are simple fractions. The fraction contains a fraction, but the fraction's remainder is a challenging fraction. because the values, 4.91, and numerators of real fractions can vary.
Here,
We can begin by isolating the variable with one side of the solution in order to solve for y. The reciprocal of fraction on the left side of the equation can be used to add both sides of the equation to achieve this:
=> 2/5 = (y - 4)/3
=> 3 * 2/5 = y - 4 [add 3 to both ends]
=> 6/5 = y - 4 [simplify]
=> y = 6/5 + 4 [Adjust both ends by 4]
=> y = 6/5 + 20/5 Using the denominator 5 as the corresponding fraction, write 4.
=> y = 26/5
Y is therefore equivalent to 26/5.
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Which of the following is a rational number?
Answer:
-77
Step-by-step explanation:
What is Radical? The radical of a number is the same as the root of a number. The root can be a square root, cube root, or in general, nth root. Thus, any number or expression that uses a root is known as a radical. The term radical is derived from the Latin word Radix which means root.
(Taken from Online)
(35 points!)
Which is CLOSEST to the curve of best fit for the data shown?
(a). y = -10x^2 - 0.5x + 8
(b). y = -2x^2 + 0.2x +23
(c). y = -8x^2 - 0.5x + 9
(d). y = -5x^2 - 18x + 66
The CLOSEST to the curve of best fit for the data shown is:
(c). y = -8x^2 - 0.5x + 9
How to interpret the line of best fit?The line of best fit is defined as a straight line that is drawn to pass through a set of plotted data points that produces the best and most approximate relationship between such given data points.
From the given graph, we see that:
at x = 1, y = 0
Thus:
a) -10x² - 0.5x + 8
Plugging x = 1:
-10(1)² - 0.5(1) + 8
= -10 - 0.5 + 8 = -2.5
b) y = -2x² + 0.2x + 23
At x = 1:
y = -2(1)² + 0.2(1) + 23
y = 21.2
c) y = -8x² - 0.5x + 9
At x = 1:
y = -8(1)² - 0.5(1) + 9
y = -8 - 0.5 + 9
y = 0.5
d) y = -5x² - 18x + 66
At x = 1:
y = -5(1)² - 18(1) + 66
y = 43
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A group of friends wants to go to the amusement park. They have no more than $125 to spend on parking and admission. Parking is $9, and tickets cost $20 per person, including tax. Write and solve an inequality which can be used to determine
�
p, the number of people who can go to the amusement park.
Answer:
Hello, your answer is 10
Step-by-step explanation:
Have a good day UwU
The box plot shows a comparison of the heights of gymnasts and basketball players. The mean absolute deviation for each group is approximately 2.
How many mean absolute deviations describe the difference between the two medians?
See image below:
Please give me an answer, work doesn't have to be shown at all, thank you so much.
Answer:
6.75 in
Analysis:
[tex]\text{The average heights of gymnasts is 60 in, the other is 75 in.}[/tex]
[tex](60+75)\div2=6.75 \ \text{in}[/tex]
HELP PLEASE
NUMBER 18
Answer is (1,1)
i. The points of intesection of the common chords of the curve x² + y² = 4 and y² = 3x are
(1, √3) and (1,-√3)ii. The points of intesection of the common chords of the curve x² + y² = 4 and x² - 4y + 1 = 0 are
(√3, 1) and (-√3, 1)What are common chords of a circle?The common chords of circles are the chords that pass through the points of intersection of the curves.
i. Given the curve x² + y² = 4 and y² = 3x. We desire to find their points of intesection of the common chords. We proceeds as follows.
Since x² + y² = 4 and y² = 3x. Substituting the second equation into the first, we have
x² + y² = 4 and y² = 3x.
x² + 3x = 4
Re-arranging, we have
x² + 3x - 4 = 0
Factorizing the quadratic equation, we have
x² - x + 4x - 4 = 0
x(x - 1) + 4(x - 1) = 0
(x + 4)(x - 1) = 0
⇒ x + 4 = 0 and x - 1 = 0
⇒ x = - 4 and x = 1
Now, y² = 3x.
⇒ y = ±√3x
So.substituting x = -4 into the equation, we have
y = ±√3x
y = ±√(3 × -4)
= ±√(-12)
Since the square root is negative, this answer is invalid.
Substituting x = 1 into y, we have
y = ±√3x
y = ±√3(1)
y = ±√3
So, the points of intersection are (1, √3) and (1,-√3)
ii. Given the curve x² + y² = 4 and x² - 4y + 1 = 0. We desire to find their points of intesection of the common chords. We proceeds as follows.
Since x² + y² = 4 and x² - 4y + 1 = 0. From the second equation, we have
x² = 4y - 1
Substituting this equation into the first, we have
x² + y² = 4 and x² = 4y - 1
y² + 4y - 1 = 4
Re-arranging, we have
y² + 4y - 1 - 4 = 0
y² + 4y - 5 = 0
Factorizing the quadratic equation, we have
y² - y + 5x - 5 = 0
y(y - 1) + 5(y - 1) = 0
(y + 5)(y - 1) = 0
⇒ y + 5 = 0 and y - 1 = 0
⇒ y = - 5 and y = 1
Now, x² = 4y - 1
⇒ x = ±√(4y - 1)
So, substituting y = -5 into the equation, we have
x = ±√(4y - 1)
x = ±√[(4 × -5) - 1)]
= ±√(- 20 - 1)
= ±√-21
Since the square root is negative, this answer is invalid.
Substituting y = 1 into x, we have
x = ±√(4y - 1)
x = ±√(4(1) - 1)
x = ±√(4 - 1)
x = ±√3
So, the points of intersection are (√3, 1) and (-√3, 1)
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A shop is having a sale. All items are reduced by 20%. Work out the price of an item that is normally £120
The price of an item that is normally £120 after a 20% discount is £96.
To find the price of an item that is normally £120 after a 20% discount,
Calculate the discount amount: To find the discount amount, multiply the original price (£120) by the discount rate ( 20% ) in decimal form:
Discount amount = Original price x Discount rate
= £120 x 0.2
= £24
Calculate the sale price: To find the sale price, subtract the discount amount from the original price:
Sale price = Original price - Discount amount
= £120 - £24
= £96
Therefore, the sale price is £96
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How can I solve this?
In conclusion, we need to identify the set of values of x for which either f(x)=-1/4 or f(-x)=-1/4 in order to solve to the equation f(|x|)=-1/4.
How is a function solved?The expression f(|x|)=-1/4 indicates that the absolute value of x's function f is equal to 1/4. Any x values that satisfy this equation are what we are trying to find. We can rewrite the equation as f(x)=-1/4 when x is positive and f(-x)=-1/4 when x is negative because the absolute value of x is always positive.
We must search for values of x such that f(x)=-1/4 or f(-x)=-1/4 in order to identify the answers. Without knowing more about the function, f may be anything, hence we cannot know the precise solutions.
Therefore, we can state that x or -x is a solution to the equation if there is a value of x such that f(x)=-1/4 or f(-x)=-1/4.
As a result, we must identify the range of x values for which either f(x) or f(-x) = 1/4.
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Please ASAP Help
Will mark brainlest due at 12:00
Answer:
Plot the point on 1
Step-by-step explanation:
Answer: 1
Step-by-step explanation: There are 10 space on the number line between the two pts. Since we are finding a 1:4 ratio we will need to divide these 10 space by 5.
[tex]10/5=2[/tex]
Which means that the point is two spaces away from T. Which is point 1 on the number line.
please help i will give points
The value of m, n and w are 92, 48 and 88 respectively
What is sum of angle in a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon( 3sided polygon). The sum of angles In a polygon is 180. i.e A+B +C = 180
In the triangle above, The triangle is divided into two.
42+36+w = 180
88+w = 180
w = 180 - 88
w = 92°
From the law of the law of exterior angle of a triangle which states that; The exterior angle of a triangle is equal to the sum of opposite angles.
Therefore;
92 = n + 44
n = 92-44
n = 48°
w = 180-92( angles on a straight line)
w = 88°
Therefore the value of m, n, w are 92, 48 and 88 respectively
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Which set of ordered pairs does NOT represent a function?ResponsesA(-4, 2), (-3, 2), (-2, 2), (-1, 2), (0, 2), (1, 2)(-4, 2), (-3, 2), (-2, 2), (-1, 2), (0, 2), (1, 2)
B(0, 1), (2, 2), (4, 8), (-2, 7), (5, 8)(0, 1), (2, 2), (4, 8), (-2, 7), (5, 8)
C(0, 1), (2, 2), (4, 8), (2, 7), (5, 8), (7, 9)(0, 1), (2, 2), (4, 8), (2, 7), (5, 8), (7, 9)
D(1, 4), (3, 7), (5, 8), (4, 9), (6, 2), (7, 8), (2, 5)(1, 4), (3, 7), (5, 8), (4, 9), (6, 2), (7, 8), (2, 5)
E(-3, 6), (2, 7), (0, 5), (1, 5), (4, 9), (5, 4)
The set of ordered pairs in option C does not represent a function.
What is a function?
A function is a mathematical expression, rule, or law that describes the relationship between an independent variable and a dependent variable.
We know that in a function each input has only one output.
So, on evaluating the options, we get
Option A
This represents a function as each input has only one output.
Option B
This represents a function as each input has only one output.
Option C
This does not represent a function as input 2 has two different outputs which are 2 and 7.
Option D
This represents a function as each input has only one output.
Option E
This represents a function as each input has only one output.
Hence, the set of ordered pairs in option C does not represent a function.
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Question: Which set of ordered pairs does NOT represent a function?
A. (-4, 2), (-3, 2), (-2, 2), (-1, 2), (0, 2), (1, 2)
B. (0, 1), (2, 2), (4, 8), (-2, 7), (5, 8)
C. (0, 1), (2, 2), (4, 8), (2, 7), (5, 8), (7, 9)
D. (1, 4), (3, 7), (5, 8), (4, 9), (6, 2), (7, 8), (2, 5)
E. (-3, 6), (2, 7), (0, 5), (1, 5), (4, 9), (5, 4)
Find the exact value using the sum/difference formula.
sin 140 degrees cos 50 degrees-cos 140 degrees sin 50 degrees
how do you delete your account?
Answer: go to your profile and you'll see the account or profile I
think, and you go to settings and it it will probably say something like delete the account or give you the choice to.
Step-by-step explanation:
Answer:
I think that you click on your profile picture, then go to your settings from there, and then you eventually find the cancel account or delete account choice.
Step-by-step explanation:
you do the above
The width of a box is two-third of it's length and height is one-third of it's length. If the volume of the box is 384 cubic meter, find the dimensions of the box.
Answer:
Length - 12 m, width - 8m, height - 4 m
--------------------------------------
The relation between dimensions of the box:
w = (2/3)l;h = (1/3)l;V = 384 m³.Use volume equation and find the value of l:
V = lwh384 = l*(2/3)l*(1/3)l384 = 2/9l³l³ = 384*9/2l³ = 1728l = ∛1728l = 12 mFind the width and height:
w = (2/3)*12 = 8 mh = (1/3)*12 = 4 mI NEED HELP ON THIS ASAP!
simplify 3 c -9 d+7 c+5 d
Pricing Math Quiz
QUESTION 4 of 10: You make a corn dip appetizer that feeds four. The key ingredients and prices are: corn $0.77, sour cream $0.96, cheese
$1.11, seasoning $0.44. What is the total food cost?
Answer:
13 dollars and 12 cents
Step-by-step explanation:
I added all of the ingredient prices in parenthesis then multiplies it by 4. :)
a weather ballon ascends at a constant rate. the height of the ballon 8 minutes after beginning to ascend is 2,320 feet. the height 15 minutes after ascending is 4,350 feet. what is the change in the elevation of the ballon per minute
Answer:
290 feet/minute
Step-by-step explanation:
2320/9 = 290
4350/15 = 290
Which pair of angles are corresponding?
A. <1 and <3
B. <3 and <4
C. <1 and <8
D. <2 and <6
Answer:
2 and 6
Step-by-step explanation:
2 and 6 is the correct option
Pls awnser all they easy (brainlist)
The given expressiοn is equivalent tο -19.5b - 6.9.
What is an expressiοn?A finite cοmbinatiοn οf symbοls that are well-fοrmed in accοrdance with cοntext-dependent principles is referred tο as an expressiοn οr mathematical expressiοn. Unknοwn variables, integers, and arithmetic οperatοrs are the cοmpοnents οf an algebraic expressiοn.
Here, we have
Given: 3(-4.5b-2.1)-(6b+0.6)
We have tο find the expressiοn that is equivalent tο the given expressiοn.
= 3(-4.5b-2.1)-(6b+0.6)
= -13.5b - 6.3 - 6b - 0.6
= -19.5b - 6.9
Hence, the given expressiοn is equivalent tο -19.5b - 6.9.
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Answer the question with an explanation!!
Answer: 212.5
Step-by-step explanation: you find a base to multiply it with the height so like this 17X25=425 now you have to divided it into a half because it's a triangle 425 divided by 2 = 212.5
Maggie has a bag of different colored marbles the probability of picking an orange marble is 3 out of 10 what is the probability that Maggie will not pick an orange marble is it 3% ,7%, 30%, or 70%
Answer:
70%
Step-by-step explanation:
3 out of the 10 marbles are not orange, so 7/10 chance you don't, and then you can multiply by 10, and then you have 70 percent
The sum of the areas of the two squares on the legs ( a and b ) equals the area of the square on the hypotenuse ( c )?
Answer: A^2 + B^2 = C^2
Step-by-step explanation:
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