with two straight cuts, we can divide a flat pancake into four pieces: [asy] size(4 cm); draw(circle((0,0),1)); draw(rotate(45)*(1,0)--rotate(200)*(1,0),dashed); draw(rotate(150)*(1,0)--rotate(330)*(1,0),dashed); [/asy] what is the fewest number of straight cuts that will divide a flat pancake into $16$ pieces? (the pieces do not need to be the same shape or size.)
The fewest number of straight cuts needed to divide a flat pancake into 16 pieces is 5. This can be done by cutting the pancake into 4 pieces, then the 4 pieces into 4, and the resulting 16 pieces into 2.
The fewest number of straight cuts needed to divide a flat pancake into 16 pieces is 5. To do this, start by making one straight cut to divide the pancake into two equal pieces. Then make two more cuts, spaced evenly around the circumference, to divide the pancake into 4 equal pieces. Next, make two more cuts, spaced evenly around the circumference, to divide the 4 pieces into 4 even smaller pieces. Finally, make one last cut, spaced evenly around the circumference, to divide the 16 pieces into 2 equal pieces, giving you a total of 16 pieces. With this method, you can divide a flat pancake into 16 pieces with just 5 straight cuts.
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X is a positive integer.
33 + x is a positive integer.
Work out the four possible values of x, writing your values in ascending order.
smallest
value
largest
value
The possible values of x such that 33+x remains a positive integer in ascending order are 1,3,11 and 33.
An integer is a whole number irrespective of the sign that the integer is all whole numbers that are going from 0 to infinite or 0 to minus infinite.
Integer; ....-2, -1, 0, 1, 2, .....
Given the expression, 33+x
Now positive integers are whole numbers ( 1,2,3,...)
To 33/x be the whole number and x is also a positive integer.
33/1 = 33 (1,3 Positive integer)
33/3 = 11 (3,11 Positive integer)
33/11 = 3 (11,3 Positive integer)
33/33 = 1 (33,1 Positive integer)
Hence "The possible values of x such that 33+x remains a positive integer in ascending order are 1,3,11 and 33".
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Would anyone know this ?
There are two possible options for points and distances:
M = - 14, AM = 0, MB = 49, AB = 49M = 6, AM = 20, MB = 29, AB = 49How to determine the coordinates of point M and distances between points
In this problem we need to determine the location of point M and distances between points A, M and B. This can be done by means of differences on number line and algebraic equations:
M - A = x² - x
M - (- 14) = x² - x
M + 14 = x² - x
M = x² - x - 14
B - M = 5 · x + 4
35 - M = 5 · x + 4
M = 31 - 5 · x
Then, we eliminate M and find the solutions to the resulting quadratic equation:
x² - x - 14 = 31 - 5 · x
x² + 4 · x - 45 = 0
(x + 9) · (x - 5) = 0
x = - 9 or x = 5
Finally, we determine the possible values for M based on the fact that M is between - 14 and 35:
x = - 9
M = 31 - 5 · x
M = 31 - 5 · (- 9)
M = 31 - 45
M = - 14
AM = - 14 - 14
AM = 0
MB = 35 - (- 14)
MB = 49
x = 5
M = 31 - 5 · x
M = 31 - 5 · 5
M = 31 - 25
M = 6
AM = 6 - (- 14)
AM = 20
MB = 35 - 6
MB = 29
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Charles is going to purchase a new car that has a list price of $21,450. He is planning on trading in his good-condition 2004 Dodge Neon and financing the rest of the cost over three years, paying monthly. His finance plan has an interest rate of 12. 28%, compounded monthly. Charles will also be responsible for 6. 88% sales tax, a $1,089 vehicle registration fee, and a $124 documentation fee. If the dealer gives Charles 80% of the listed trade-in price on his car, once the financing is paid off, what percent of the total amount paid will the interest be? (Consider the trade-in to be a reduction in the amount paid. ) Dodge Cars in Good Condition Model/Year 2004 2005 2006 2007 2008 Viper $7,068 $7,225 $7,626 $7,901 $8,116 Neon $6,591 $6,777 $6,822 $7,191 $7,440 Intrepid $8,285 $8,579 $8,699 $9,030 $9,121 Dakota $7,578 $7,763 $7,945 $8,313 $8,581 a. 17. 64% b. 15. 67% c. 16. 70% d. 12. 86% Please select the best answer from the choices provided A B C D
Percent of the total amount a per the given list price, documentation fee , registration fee and other payment paid by Charles is given by :
Option c. 16.70%
Cost of his old 2004 Dodge Neon = $6591
Sales tax = 6.88%
Dealer gives 80% trade in price on hos car
After tax selling price of the car
= 6,591 × (80/100) × [ 1 - (6.88/100) ]
= $4910.03
= $4,910
Vehicle registration amount = $1,089
List price of car = $21,450
Documentation fee = $124
Total cost of the car
= $21,450 + $1,089 + $124
= $22,663
Net amount Charles needs to pay
= $22,663 - $4,910
= $17,753
Monthly payment at the rate of 12.28% compounded monthly for 3 years
= 17753 [ 12.28%( 1+ 12.28%)^3 / [( 1+ 12.28%)^3 -1 ]
= $592
Total amount paid by Charles
= $592 × 36
= $21,312
Total interest paid by Charles
= $21,312 - $17,753
= $3,559
Percent of the total amount
= ( $3,559 / $21,312 ) × 100
= 16.699%
= 16.70%
Therefore, the percent of the total amount paid by Charles is equal to Option c. 16.70%.
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Help please! God bless the person who helps
Answer:
3/2
Step-by-step explanation:
slope is rise over run:
3/2
Payton did not spend $15.00 at the grocery store. Write an inequality to represent the amount Payton spent. Then wrote two examples of amounts Payton might have spent.
A possible inequality to represent the amount Payton spent is x >15, and two examples of the possible amount of money Payton spent are $30 and $6.
What is inequality?This is a mathematical expression that represents a situation using symbols such as ≥ (greater or equal to) or < (less than).
What is a possible inequality in this case?A possible inequality is 15 >x or 15 <x, which means the amount of money spent was less than or more than 15.
Some possible values within this range are:
$10
$2
$6
$30
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Please help me mark u brainliest anuthing please i beg u :
in the interval 0 x 360 find the values of x for which tan x =-0. 6745
The required values of x in the interval 0° ≤ x ≤ 360° are 146.1° and 326.1°, when the value of tan x is given.
The interval of angle is given as 0° ≤ x ≤ 360°.
The value of x for which tan x is given as, tan x = - 0. 6745.
We have tan negative in two of the four axes, they are second (90° - 180°) and fourth quadrants (270° - 360°).
So, tan x = - 0. 6745
x = tan⁻¹ (- 0. 6745) = -33.9
As periodicity of tan x is 180°, x = 180-33.9 = 146.1°
x = 360-33.9 = 326.1°
Thus, the required values of x in the interval 0° ≤ x ≤ 360° are 146.1° and 326.1°, when the value of tan x is given.
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if distance between points p(3,a) and q(3,1 is 4 units find the value of a
Answer: -3 AND 7
Step-by-step explanation: very important to include the and, as it that point could be to the right or left of (3,1)
What is the midpoint to this line segment?
Answer:
I think 5
Step-by-step explanation:
16. Jake borrowed money to purchase a new bike. He has paid back $65 of the money he
borrowed, but he still owes $185. What was the total amount Jake originally borrowed?
Answer: $250
Step-by-step explanation:
If Jake still owes $185 and only just paid back $65, you need to add 185 and 65 together to get the total amount that he borrowed.
How to factor -25-15mn
The factorization of -25-15mn is -5(5+3mn)
What is factorization?Factorising is the reverse process of expanding brackets. To factorise an expression fully, means to put it in brackets by taking out the highest common factors. The simplest way of factorising is: Find the highest common factor of each of the terms in the expression.
For example 5( 3x+ 2y+ 4z) can be expanded into 15x + 10y + 20z and moreover 15x + 10y + 20z can be transformed by finding the factors between each terms, here the factor is 5; 5( 3x + 2y +4z)
Similarly to factorize -25-15mn we find the factor that is common to -25 and - 15 . The common factor is -5.
therefore factorizing -25-15mn we bring -5 out of -25 and -5
= -5( 5+3mn)
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the tortoise and the hare are having a race. in this tale, the tortoise moves at feet per hour while the hare moves at feet per hour. the tortoise takes hours longer than the hare to finish. what was the distance of the race?
Distance of the race is 500 feet.
Given that tortoise moves at 50 feets per hour and hare moves at 250 feets per hour.
So speed of tortoise = 50 feets per hour.
Speed of hare = 250 feets per hour.
Let hare takes T hours to complete the race
Than tortoise will take (T + 8) hours to complete the race.
Total distance traveled by hare = speed * time = 250T
Total distance traveled by tortoise = speed * time = 50(T + 8)
Total distance traveled by both is same.
250T = 50(T + 8)
250T = 50T + 400
250T – 50T = 400
200T = 400
T = 2 hours
So, total distance of the race = 250T = 250 * 2 = 500 feet.
Therefore, total distance of the race is 500 feet.
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please help for algebra 1
Answer:
A: first choice
x^4
Step-by-step explanation:
When you divide two powers with the same base, you subtract the exponents, not divide.
The step x^8/x^4 is correct.
The next step should be x^(8 - 4), not x^8/4.
The correct simplification is x^4.
Answer:
A: first choice
x^4
Need asap pls broooo
The angles in the quadrilateral are as follows:
g = 116 degrees
h = 64 degrees
How to find the angles of a quadrilateral?A quadrilateral is a polygon with 4 sides. The sum of angles in a quadrilateral is 360 degrees.
Therefore, let's find the angles g and h in the quadrilateral. According to the diagram, the quadrilateral has opposite side parallel to each other.
Therefore, the diagram can be regarded as a parallelogram.
Hence, adjacent angles of the diagram are supplementary.
Supplementary angles add up to 180 degrees.
Therefore,
116 + h = 180
h = 180 - 116
h = 64 degrees.
Therefore,
64 + g = 180
g = 180 - 64
g = 116 degrees.
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Find the Area of the figure below, composed of a parallelogram and two semicircles.
Round to the nearest tenths place.
16
5
18
The area of figure composing a parallelogram and two semicircles is 399.06 units².
What is a parallelogram?
A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.
The base of the parallelogram is = 18 units
The height of the parallelogram is = 11 units
The area of a parallelogram is given as -
Area = Base × Height
Area = 18 × 11
Area = 198 units²
The diameter of the semicircle is = 16 units
The radius of semicircle is = 8 units
The area of the semicircle is given as -
Area = (1/2)πr²
Area = (1/2)π(8)²
Area = (1/2)π × 64
Area = 32π units²
The total area of the figure is given as -
Total Area = Area of Parallelogram + 2 (Area of semi-circle)
Total Area = 198 + 2(32)π
Total Area = 198 + 64π
Total Area = 198 + 201.06
Total Area = 399.06 units²
Therefore, the area of the figure is 399.06 units².
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A right triangle has a hypotenuse that is 21 inches long and a leg that is 15 inches long. How long is the other leg of the triangle?
Answer: In a right triangle, the length of the hypotenuse is the square root of the sum of the squares of the other two legs. So, using the Pythagorean theorem, the other leg would be the square root of (21^2 - 15^2) = (441 - 225) = 216 = 14.69 inches.
Step-by-step explanation:
what expressions are equivalent to 3 (9p+2r)
Answer:
greetings
27p+6r, is an expression which is equivalent to 3 (9p+2r).
The distance from where Chris lives to willow lake is 48 miles.
Chris will take the train to willow lake. The train goes 60 miles an hour. If Chris takes the 2:20 train, about what time will he get to willow lake?
If Chris takes the 2:20 train, then he will get to willow lake at 2:28.
If Chris takes the 2:20 train, then we have to find at what time he will get to willow lake.
The distance from where Chris lives to willow lake is 48 miles.
Chris will take the train to willow lake. The train goes 60 miles an hour.
The distance = 48 miles
The speed of train = 60 miles an hour
Time = distance/speed
Time = 48/60
Time = 0.8 minutes
The train reach after 8 minutes in willow lake.
So the train reach 2:28.
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Find the reflection of point A over the y-axis.
A (-3,-9)
The coordinates of point A after a reflection over the y-axis are given as follows:
A(3,-9).
How to obtain the coordinates of point A?The original coordinates of A are given as follows:
A(-3,-9).
The rule for a reflection over the y-axis is given as follows:
(x,y) -> (-x,y).
Meaning that the x-coordinate has the signal exchanged while the y-coordinate remain constant, hence the coordinates of point A after a reflection over the y-axis are given as follows:
A(3,-9).
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You buy 4 mall candle and 2 large candle for $14. Your friend buy 5 mall candle and 3 large candle for $20. What i the cot of each mall candle? of each large candle?
The cost of 1 mall candle = $1 while the cost of 1 large candle = $5
Let the cost of 1 mall candle = x
Let us assume that the cost of 1 large candle = y
So, in case 1,
As I can buy,
4 mall candles and 2 large candles for $14
So, framing the equation,
We can rewrite it as:
4x+2y = 14-------(1)
As my friend can buy 5 mall candles and 3 large candles for $20
Now again framing the equation,
We can write it as:
5x+3y=20 -------(2)
From (1) and (2), for determining the value of x, we will first make the coefficient of y equal in both cases.
So, multiply the first equation by 3 and the second by 2
We will get,
12x+6y=42 -----(3)
10x+6y=40------(4)
Now subtracting (4) from (3)
We will get,
2x=2
=>x=1
So, for determining the value of y,
We will put the value of x in (1)
So, 4x+2y = 14-------(1)
=> 4+2y=14
=>2y=10
=>y=5
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The cost of a small candle is equal to $1, and the cost of each large candle is $5..
When I buy the candles,
Cost of 4 small and 2 large candles = $14
but when my friend purchse the candles , cost of 5 small and 3 large candles= $ 20 .
Let the cost of each small candle and each large candle be $x and $y respectively.
From first condition, when I can buy the candles,
Cost of 4 smalll candles = $4x
Cost of 2 large candles= $2y
=> $4x + $2y = $14
Reduce the equation, 2x + y = 7 ---(1) ( since, divided by 2)
In case Second, when my friend buy the candles,
Cost of 5 small candles= $5x
Cost og 3 large candles= $ 3x
=> $5x + $3y = $20 or 5x + 3y = 20 --(2)
Now, equation (1) and (2) made a system of linear equations. Linear equations are in two variables x and y . To solve the system of linear equation, we can use Elimination Method,
To make the same cofficient of y variable in both equtions, multiply the equation (1) by 3
=> 3(2x + y ) = 3× 7
=> 6x + 3y = 21 --(3)
Subtracts the eqution (2) from (3) to eliminate y,
=> 6x + 3y - ( 5x + 3y) = 21 - 20
=> 6x + 3y - 5x - 3y = 21 - 20
=> x = 1
from (1) , 2x + y = 7 => 2×1 + y = 7
=> y = 5
Hence, the cost of one small candle and one large candle are $1 and $5.
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Select the correct answer from each drop-down menu.
The given equation has been solved in the table.
Step
Statement
& +5 – 5 = 23 – 5
į = 18
4. 5 = 4. 18
= 72
Use the table to complete each statement.
In step 2, the
In step 4, the
property of equality was applied.
property of equality was applied.
© 2020 Edmentum. All rights reserved.
In step 2. the addition property of equality was applied.
In step 2. the subtraction property of equality was applied.
We have solved the equation x/4 + 5 = 23.
In step second we subtract 5 on both side, this is the property of equality of addition.
In step 3 the expression is x/4 = 23
In step 4 we multiply 4 on both side, again using the property of equality of subtraction.
Now the value of x is 72.
Hence, using the property of equality in step 2 and 4 we solve the equation.
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The complete question is given below:
graph y=|x+4|
Please help!!
The graph for the points (-6, 2), (-5, 1), (-4, 0), (-3, 1) and (-2, 2) is plotted as below.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given function is y=|x+4|.
Graph the absolute value using the vertex and a few selected points.
Plot the points (-6, 2), (-5, 1), (-4, 0), (-3, 1) and (-2, 2)
Therefore, the graph for the points (-6, 2), (-5, 1), (-4, 0), (-3, 1) and (-2, 2) is plotted as below.
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data collected at the same, or approximately the same point in time are a. time series data. b. approximate data. c. approximate time series data. d. cross-sectional data.
Data collected at the same, or approximately the same point in time are Cross- sectional data
In statistics and econometrics, cross-sectional data, or a cross section of a study population, is a type of data gathered by monitoring numerous subjects (such as individuals, firms, countries, or regions) at one point or throughout the course of time. It's also possible that the analysis disregards variations in time. Cross-sectional data analysis often entails contrasting the variations among pre-selected respondents.
For instance, if we wanted to determine the prevalence of obesity in a population, we could randomly select a sample of 1,000 people (also referred to as a cross section of that population), measure their height and weight, and then determine what proportion of that sample falls under the definition of obesity. With the use of this cross-sectional sample, we are able to get a current picture of that group. Be aware that based on a single cross-sectional sample, we cannot determine whether the prevalence of obesity is rising or falling; we can only describe the current proportion.
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PLEASE SOMEONE HELP ME!!
I need this turned in by 10
Slope-intercept form (y=mx+b) of linear equations highlights the slope (m) and the y-intercept (b) of a line.
Define slope -intercept form?
The steepness of line is a slope (m). The point on the line is in the form of (x1, y1). The Point Slope Form Formula is, y – y1 = m (x – x1).Point-Slope Form of a LineSubstitution method = plug in the slope and the (x, y) point values into y = mx + b, then solve for b. Point-slope form = y − y 1 = m ( x − x 1 ) , where ( x 1 , y 1 ) is the point given and m is the slope given.A simple definition of point-slope form is an equation of a line written using one point on the line and the slope of the line. The point form is written as (x,y) and the slope is the rise over run, or the ratio of the change in the y values over the change in the x values.
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let p be the set of all people and let t(x,y) be the statement x trusts y. write the given statement using variables, quantifiers and symbols only
The given statement using variables, quantifiers and symbols only ∀x ∈ p, ∃y ∈ p, t(x,y).
Predicate variables are quantified using quantifiers. It contains a formula, a type of statement whose veracity depends on the values of various parameters.
A predicate turns into a proposition when we give it a definite value. Another way to put it is that the predicate will turn into a proposition if it is quantified.
Therefore, the phrase "quantify" refers to quantifiers like "all" or "some."
The two basic categories of quantifiers are existential and universal quantifiers.
Additionally, it demonstrates whether the predicate is true or false for all conceivable values or for specific value(s) inside the realm of discourse.
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Only variables, quantifiers, and symbols are used in the following statement: ∀x ∈ p, ∃y ∈ p, t(x,y).
Only variables, quantifiers, and symbols are used in the supplied statement.
Quantifiers are used to quantify predicate variables. It includes a formula, which is a sort of assertion whose truth is determined by the values of several factors.
When we assign a definite value to a predicate, it becomes a proposition. Another way to say it is that if the predicate is quantified, it becomes a proposition.
As a result, the term "quantify" refers to quantifiers such as "all" or "some."
Existential and universal quantifiers are the two primary types of quantifiers.
It also shows whether the predicate is true or false for all possible values or for specified value(s) inside the scope of discourse.
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GEOMETRY
this triangle has a depression of 10 degrees and it’s 1150 feet long. i’m supposed to find the height but i don’t know how !? pls help
I think this is it if not I'm sorry
78264 in
ec
19. Lennon bought two books for $21.00. One book
cost $8.00. Solve the equation 21 = b + 8 to find
b, the cost of the other book.
Answer:
b = 13
Step-by-step explanation:
21 = b + 8 Subtract 8 from both sides
21 - 8 = b + 8 - 8
13 = b
Answer: 13
Step-by-step explanation:
He bought two books for $21, and one of the books was $8. With this, we know that if we subtract 8 from 21, we can get "b", or the cost of the other book
21 = b + 8
-8 -8
13 = b
b = 13
Therefore, b = 13, or $13 for the other obok
What is the answer? Please explain how you got the answer too!!
The correct sentence to describe in the parent function is,
⇒ Shifted up.
⇒ Horizontal stretch
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
We have to given that;
The function is,
⇒ f (x) = x
Here, The graph of the parent function of f (x) = x is shown in figure.
Hence, We get;
The correct sentence to describe in the parent function is,
⇒ Shifted up.
⇒ Horizontal stretch
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a logarithm is defined as the power to which a base must be raised in order to equal a given number, why can't we have negative bases
Negative bases are not often used in logarithms because they produce complex results. For example, if the base is negative and the exponent is positive, the result will be a complex number.
Logarithms are generally used to solve equations or simplify complex problems. Having a negative base would complicate this process, as it would introduce complex numbers or even imaginary numbers into the equation. Consequently, it is not feasible to use negative bases with logarithms. Furthermore, if both the base and the exponent are negative, the result is undefined. This means that it is not possible to evaluate the expression. Therefore, for these reasons, it is usually not practical to use negative bases when working with logarithms.
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Brainly to correct answer
Jaidon counted dishes in the kitchen cabinet. The table shows what was found.
Plates 10
Bowls 8
Cups 14
Write a ratio to compare plates to all dishes.
10:14
10 over 22
32 to 10
10 over 32
Answer:
10/32
Step-by-step explanation:
10+8+14 = all dishes = 32
10 = how many plates
In a ratio: 10/32