Maurice is a distance of 232 miles away from his starting point.
What is the final distance of Maurice from his starting point by using vectors and Pythagorean theorem?
Let suppose the existence of a coordinate system whose orthogonal axes are represented by north and east directions, which means that both north and east directions have positive signs. Then, the vector position of Maurice relative to his starting point is:
r = ∑ Δx i + ∑ Δy j
Where:
Δx - Net change in the east direction.Δy - Net change in the north direction.Then, the vector position of Maurice relative to his starting point is:
r = (- 168) i + (- 262 + 422) j
r = - 168 i + 160 j
And the distance is found by using the Pythagorean theorem:
r = √[(Δx)² + (Δy)²]
r = √[(- 168)² + 160²]
r = 232
Maurice is a distance of 232 miles away from his starting point.
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Decide which of the two given prices is the better deal.
The same kind of water is sold in two types of bottle. Which type has the lower unit price?
Five 10-oz bottles for $2.30
Seven 12-oz bottles for $4.20
Select one:
A.
not enough information
B.
Five 10-oz bottles
C.
equal value
D.
Seven 12-oz bottles
Five 10-oz water bottles will have a lower unit price. The correct option is B.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that there are two conditions for water bottles Five 10-oz bottles for $2.30 and Seven 12-oz bottles for $4.20. The water bottle having the lower price will be:-
Five 10-oz bottles = $2.30
One 10- oz bottle = 2.30 / 5 = $0.46
Seven 12-oz bottles = $4.20
One 12-oz bottles = $4.20 / 7 = $0.6
Therefore, five 10-oz water bottles will have a lower unit price. The correct option is B.
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How much interest would you pay on a loan of 8000 for 6 months at 14 percent interest
[tex]6000 + \frac{14 \\ }{100} \times 6000 = 6840 \times 6 = 41040[/tex]
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(answer reported if incorrect)
Based on the fact that Shannon has created 4 levels for her game after 8 weeks, the equation for the relationship between x and y is y = 2x
What is the proportional relationship?y is used to denote the number of weeks it takes to program the number of levels which is 8 weeks.
x is the number of levels that Shannon would have made for the game which is 4 levels.
The relationship between y and x is:
= y / x
= 8 weeks / 4 levels
= 2 weeks per level
The relationship can then be shown as:
y = 2x
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Select all expressions below that are equivalent to (25/50)^15
A. (25^15/50^15)
B. 25^15/50
C. (50/25)^-15
D. (0.5)^15
E. 2^15
F. (25^5/50^5)^3
(hint: 4 of them are correct)
.
The response to a question has three alternatives: A, B, and C. A sample of 120 responses provides 57 A, 26 B, and 37 C responses. Show the frequency and relative frequency distributions
Here is a table that shows the frequency and the relative frequency distributions:
Class Frequency Relative frequency
A 57 0.475
B 26 0.217
C 37 0.308
Total 120 1
What is the frequency and relative frequency?Frequency measures the number of times a response is observed in a dataset. For example, the frequency of A is 57. Relative frequency measures how often a value appears relative to the sum of the total values. The sum of relative frequency is equal to 1.
Relative frequency = frequency / total frequency
A = 57 / 120 = 0.475
B =26 / 120 = 0.217
C = 37 / 120 = 0.308
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2198290.45 divided by 1.08
A standard die is rolled. Find the probability that the number rolled is greater than 2.
Answer:
2/3
Step-by-step explanation:
To find this, we need to find out how many numbers are greater than 2 but no more than 6. This set includes 3, 4, 5, 6; there are 4 numbers that qualify for this. This means that out of all 6 numbers, 4 numbers are in the probability, so our answer would be 4/6 = 2/3
Answer:
2/3
Step-by-step explanation:
The probability of a die getting 3,4,5,6 over a 1 or 2 is 4 chances out of the 6 chances in a die, or 2/3.
Can someone help with this question?✨
Answer:
13
Step-by-step explanation:
According to the Pythagorean principle
[tex]c^{2} = a^{2} +b^{2}[/tex]
[tex]c^{2} = (5^{2} ) + (12^{2} ) = 25 +144= 169\\c= \sqrt{169 } = 13[/tex]
30-12 (mod 6) pls I need solution class ss1
Answer:
30
Step-by-step explanation:
Divide
[tex]\frac{12}{6}\\\\\bold{Long\:division}\\6 \times 2 = 12\\= 2[/tex]
[tex]\mathrm{2\:remainder\:0}[/tex]
Simplify the rest of the expression
[tex]= 30 - 0\\= 30[/tex]
Hope this helps!
Which number set is the most reasonable to describe an adult's weight?
O Integers
O Irrational numbers
O Rational numbers
O Whole numbers
Answer:
rational numbers
Step-by-step explanation:
An adult's weight can be a non-integer, but is likely of the form of a decimal.
This matches best with the set of rational numbers (of which we take the positive ones).
The dance team lines up in 4 rows of 6 dancers each. How many dancers are on the dance team?
? dancers
6 6 6 6
4 rows →. ^
6 dancers in each row
HELP PLEASEEEEEEE!!!!!!!!
It should be noted that two perfect squares so that the square root will fall between consecutive numbers of 0.4 and 0.5 include 0.2025 and 0.2209.
How to illustrate the information?It should be noted that based on the information, we want to find two perfect squares so that the square root will fall between consecutive numbers of 0.4 and 0.5.
In this case, it should be noted that 0.45 × 0.45 = 0.2025. It should be noted also that 0.47 × 0.47 = 0.2209.
As a result, 0.2025 and 0.2209 are two perfect squares such that the square root will lie between consecutive numbers of 0.4 and 0.5.
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1.1. Describe, explain and give examples of three important mathematical ideas:
(a) prime numbers (3)
(b) rational numbers (3)
(c) irrational numbers (3
Answer:
=The numbers which donot have factors and can be only divided by themselves are know as prime numbers.Eg: 2,3,5,7
= A number that can be represented as the quotient p/q of two integers such that q ≠ 0 are known as rational numbers. Eg 4/8,5,-10
=An irrational number is a number that cannot be expressed as a fraction for any integers.Eg -0.25,3.5
Complete the truth table for the statement ~Q ^ P.
A truth table is a breakdown of a logic function by listing all possible values the function can attain.
This tool generates truth tables for propositional logic formulas. You can enter logical operators in several different formats. For example, the propositional formula p ∧ q → ¬r could be written as p /\ q -> ~r, as p and q => not r, or as p && q -> !r. The connectives ⊤ and ⊥ can be entered as T and F.
P Q (Q ∧ P)
F F F
F T F
T F F
T T T
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1. find three consecutive integers such that twice the least integer is 12 more than the greater integer.
2. The perimeter of a rectangle is 150 cm the length is 15cm greater than the width. Find all of the dimensions, please.
Answer: offf
Step-by-step explanation:off
A table with 1 column. The column has a header of "Scores" with the following numbers: 56, 82, 90, 83, 79, 59, 71, 66, 53, 94, 78, 80, 67, 65, 86, 76, 83, 92, 69, 69, 91, 68, 78, 87, 87, 81, 87, 76, 96, and 83.
Based on the scores given in the table, the mean of the scores can be found to be 78
How to find the mean?The mean of the scores can be found by adding all the scores together and then dividing the sum by the number of scores in the table.
The sum of the scores is:
= 56+ 82 + 90 + 83 + 79 + 59 + 71 + 66 + 53 + 94 + 78 + 80 + 67 + 65 + 86 + 76 + 83 + 92 + 69 + 69 + 91 + 68 + 78 + 87 + 87 + 81 + 87 + 76 + 96 + 83
= 2,332
The mean is:
= 2,332 / 30
= 77.73
= 78
Question is:
What is the mean of the scores?
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How many cookies will Tanya have if she bakes
12 more batches?
y = 70 + 18(x)
Enter the correct answer.
000
?
DONE
Tanya will then have 286 cookies after baking 12 more batches.
What is the linear equation formula?A linear equation's slope-intercept form is y = mx + b. The variables in the equation are x as well as y. The integers m and b represent the the line's slope (m) and the value of y when x is 0 respectively (b). Because (0,y) is the point when the line crosses the y-axis, the value of y when x is 0 is known as the y-intercept.
Which equations are linear?A linear equation with one variable is one with only one variable. It has the formula Ax + B = 0, where A and B can be any two real numbers as well as x is an unknown variable with a single solution. 9x + 78 = 18, for example, is a one-variable linear equation.
According to the given data:y = 70 + 18(x)
x = 12 batches.
substituting the value in the equation:
y = 70 + 18(x)
y = 70 + 18(12)
= 70 + 216
y = 286.
Tanya will then have 286 cookies after baking 12 more batches.
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1. A rectangle has a length that is three feet more than twice its width.
(a) If the width of the rectangle is represented
by the variable w, give an expression for
the length of the rectangle in terms of w.
(b) What would the perimeter of this
rectangle be if the width was 10 feet?
(c) The perimeter of the rectangle is 78 feet. Set up an equation using w that models this
situation. Solve it and state the values for both the width and the length of the rectangle.
Part a: Expression for length; l = 2w + 3.
Part b: Perimeter equation; P = 2(l + 10).
Part c: Length of rectangle = 29 feet.
What is defined as the rectangle?A rectangle is a the kind of quadrilateral, a two-dimensional shape with four sides as well as four vertices. The rectangle's four angles are all right angles as well as equal to 90 degrees.The given conditions are-
Let 'l' be the length of the rectangle.
Let 'w' be the width of the rectangle.
Part a: expression for the length of a rectangle in the terms of w.
Length is three feet more than twice its width.
l = 2w + 3
Thus, the expression of l in terms of w is: l = 2w + 3.
Part b: Perimeter equation.
The width is given as 10 feet.
The formulae of perimeter if rectangle is;
P = 2(l + w)
Put the value;
P = 2(l + w)
P = 2(l + 10)
Thus, the equation for perimeter is P = 2(l + 10)
Part c: Length of rectangle.
perimeter of rectangle = 78 units.
P = 2(l + w)
w = 10 feet.
78 = 2(l + 10)
l + 10 = 39
l = 29
Thus, the length of the rectangle is found as 29 feet.
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A glass pitcher contains 65 ounces of juice which is poured equally into six glasses. How many ounces of juice does each glass contain?
Answer: 10.83334 ounces or 10 5/6
Step-by-step explanation:
Essentially you would divide 65 into six groups. Because you are dividing the amount of liquid into six cups. Hope this answers your question, ask me any other questions you might have.
Find the y-intercept of the line on the graph
Since no equation of the line, or graph is provided in the question statement, considering the line to be [3x +4y = 12], the y-intercept of the line is 3.
As per question statement, we are supposed to determine the y-intercept of the line on the graph, but no equation of the line, or graph is provided. Hence, we considered the equation of a random line, say,
[3x +4y = 12] and then, determine it's y-intercept.
To solve this question, we can use two methods:
One method is by converting the given equation into the format of the standard equation of a line, and then comparing it to the standard equation to determine the y-intercept, i.e.,
The standard equation of line is (y = mx + c), where, "m" is the slope of the line, and "c" is the y-intercept. Converting [3x +4y = 12] to the form of the standard equation, we get,
[tex]3x+4y=12\\or,4y=-3x+12\\or,y=\frac{-3x+12}{4}\\ or,[y=(\frac{-3}{4})x+3]...(i)[/tex]
Now comparing (i) to the standard equation of line, we can identify that
(c = 3), i.e., y-intercept of the line [3x +4y = 12] is 3.
Another way we can determine the y-intercept of a line is by, substituting (x = 0) and then solving the equation for "y".
Y-Intercept: The y-intercept is the point on a cartesian plane, where a graph crosses the y-axis, i.e., the value of y when (x = 0).To learn more about Y-Intercepts, click on the link below.
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Evaluate ƒ(x) = 3x + 8 for x = 1.
Answer:
f(1) = 11
Step-by-step explanation:
ƒ(x) = 3x + 8 for x = 1.
f(1) = 3(1) + 8
f(1) = 3+ 8
f(1) = 11
I hope this helps!
Elena gives the following transformation to show that the two figures are similar by transforming ABCD into EFGD
It should be noted that the information regarding the transformation illustrates that Elena is wrong.
How to explain the information?A point, line, or geometric figure can be transformed in a way that affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
It should be noted that the first step makes the figures be the same by size but the second step, reflection over line AE doesn't map them together.
In this case, the correct line of reflection would be a vertical line through point D.
Therefore, it should be noted that the information regarding the transformation illustrates that Elena is wrong.
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Elena gives the following sequence of transformations to show that the two figures are similar by
transforming ABCD into EFGD.
1. Dilate using center D and scale factor 2.
2. Reflect using the line AE.
GIVING BRAINIEST IF CORRECT!!!!!!!
Express in simplest form
Answer:
Step-by-step explanation:
-3√(4)(10) - √(16)(10)
-3(2)√(10) - 4√(10)
-6√(10) - 4√(10)
-10√(10)
help help help.......
A store is having a sale on walnuts and chocolate chips. For 5 pounds of walnuts and 3 pounds of chocolate chips, the total cost is $13. For 2 pounds of walnuts and 6 pounds of chocolate chips, the total cost is 16. Find the cost for each pound of walnuts and each pound of chocolate chips.
Answer:
c= 1 w =1.25
Step-by-step explanation:
10w +6c = 26- 2w +6c= 16 Subtration = 8w = 10 = 10/8 = 1.25 = w =1.25 12(1.25)+ 6c = 16 = 2.5 + 6c = 8.5 Subtration = 6c = 8.5 -2.5 = 6c = 6 = c= 6/6 = 1 c= 1
The length of a rectangular photograph is 9 in more than the width. If the area is 90 in2, what are the dimensions of the photograph?
Part 1 of 2
The photograph is
Part 2 of 2
The photograph is
in wide.
in ng.
X
X
MacBook Air
Submit Assignm
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The photograph is 6 inches wide and 15 inches long.
Need help with #9! Intermediate Algebra.
Answer:12.35 = t
Step-by-step explanation:
95 + t + 3.5 = 110.85
where t = tax
12.35 = t
A farmer sells an average of 15g bushels of corn
each day. What integer represents the change in
bushels of corn in his inventory after 6 days?
According to the solving his unused inventory will have = x - [tex]\frac{468}{5}[/tex]
What is mixed fraction?A mixed fraction is defined by its quotient as well as remainder. 2/3, for example, is a mixed fraction in which 2 is the quotient and 1 is the remainder. A mixed fraction is thus the product of a whole number as well as a proper fraction.
What is an example of a simple fraction?If the only common factor of a fraction's numerator and the denominator is 1, the fraction is considered to be in its simplest form. For example,89, because 1 is the sole common factor in this fraction of 8 and 9. We simplify fractions simply because it is usually easier to work with or compute fractions when they are in their simplest form.
According to the given data:Every day, a farmer sells on average of 15 3/5 bushels of maize.
Converting mixed fraction to proper fraction;
[tex]15\frac{3}{5}[/tex] this can be written as [tex]\frac{78}{5}[/tex]
Assume he has a total of x bushels.
As a result, he will sell in 6 days.
= 6 x [tex]\frac{78}{5}[/tex]
= [tex]\frac{468}{5}[/tex]
So,
According to the solving his unused inventory will have = x - [tex]\frac{468}{5}[/tex]
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I understand that the question you are looking for is:
A farmer sells an average of 15 3/5 bushels of corn each day. What integer represents the change in bushels of corn in his inventory after 6 days.
HELP PLEASEEEEE!!!!!!
Answer:
Step-by-step explanation:
(0.1)²=0.01
(0.2)²=0.04
(0.3)²=0.09
(0.4)²=0.16
(0.5)²=0.25
(0.6)²=0.36
(0.7)²=0.49
(0.8)²=0.64
√0.5 or √0.50 is between √0.49 and √0.64
or
0.7 and 0.8
(0.01)²=0.0001
(0.02)²=0.0004
(0.03)²=0.0009
(0.04)²=0.0016
(0.05)²=0.0025
so √0.002 or √0.0020 is between √0.0016 and √0.0025
or between 0.04 and 0.05
Find the distance between the two points
(-1,1)
(2,-4)
✓ [?]
Enter the number that
goes beneath the
radical symbol.
Enter
The distance between the two points is √ [37]
given,
A(-4,1) ; B(2,0)
For the distance,
d(A,B) = √(x B - x A)² + (y B - y A)²
d(A,B) = √(2+4)² + (0-1)²
= √6² + 1² = √36 + 1
= √37
therefore the distance between the two point is √37.
Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on a coordinate plane or x-y plane.
We can apply the Pythagoras theorem to derive the distance between two points formula. We can take the line joining the two points as the hypotenuse of a right triangle formed in the cartesian plane. The length of the hypotenuse can be calculated using the Pythagorean theorem and the given coordinates of two points to derive the distance between two points formula.
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