The probability of at least two people bringing the same item is 0.19.
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
Given that, The organizer of a potluck dinner sends 6 people a list of 10 different recipes and asks each person to bring one of the items on the list.
The probability of two people bringing the same item can be calculated using the formula P(A∩B) = P(A) × P(B).
In this case, P(A) and P(B) are both 1/10, because each person has the same chance of choosing any one of the 10 items on the list.
Therefore, the probability of two people bringing the same item is 1/100. To calculate the probability of at least two people bringing the same item, we can use the formula P(A∪B) = P(A) + P(B) - P(A∩B).
In this case, P(A∪B) = 1/10 + 1/10 - 1/100 = 0.19.
Hence, the probability of at least two people bringing the same item is 0.19.
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7. Determine if each sequence represents a function. Explain why
or why not. If it is a function, identify its domain and range.
Create a mapping to verify your answer.
a. 2, 4, 6, 8, 10, ...
b. 1, 0, 1, 0, 1, ...
c. 0, 5, 10, 15, 20, ...
Only a and c represent function
How is a sequence defined?
In mathematics, a sequence is a list of items that is in order (or events). It has members and is similar to a set (also called elements, or terms). The number of ordered elements determines the length of the sequence (potentially infinite).
a. The sequence 2, 4, 6, 8, 10, ... represents a function. The domain of the function is the set of natural numbers, and the range is the set of even natural numbers. We can create a mapping by using the rule "multiply by 2" to match each input value of the domain with its corresponding output value in the range. For example, 2 maps to 4, 4 maps to 8, 6 maps to 12, and so on.
b. The sequence 1, 0, 1, 0, 1, ... does not represent a function. The reason is that for any given input value, the output value is not unique. For example, the input value of 1 maps to both 1 and 0, which means that the function is not well-defined.
c. The sequence 0, 5, 10, 15, 20, ... represents a function. The domain of the function is the set of natural numbers, and the range is the set of multiples of 5. We can create a mapping by using the rule "multiply by 5" to match each input value of the domain with its corresponding output value in the range. For example, 0 maps to 0, 1 maps to 5, 2 maps to 10, and so on.
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express the following as a ratio in it's simplest form: 48 seconds: 1 minute
Answer:
4:5
Step-by-step explanation:
We know that 1 minute is equals to 60 seconds.
So the ratio is now:
48 seconds : 60 seconds
We need to simplify the ratio in its simplest form. 12 goes into both 48 and 60 so:
48/12 = 4 seconds
60/12 = 5 seconds
So the ratio 48 seconds: 1 minute in its simplest form is:
4 seconds : 5 seconds
please help me. i have no idea what to do
Answer:
F
Step-by-step explanation:
(x + 2)² + (y - 3)² = 37
intersection points with the x-axis means that their y-values are 0 !
that is the whole trick, as I am sure you experienced already with lines and y-intersects (x = 0) and x-intersects (y =0).
so, we need to solve for x, when y = 0 :
(x + 2)² + (-3)² = 37
x² + 4x + 4 + 9 = 37
x² + 4x - 24 = 0
the solution to a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = (-4 ± sqrt(4² - 4×1×-24))/(2×1) =
= (-4 ± sqrt(16 + 96))/2 = (-4 ± sqrt(112))/2 =
= (-4 ± sqrt(16×7))/2 = (-4 ± 4×sqrt(7))/2 =
= -2 ± 2×sqrt(7)
x1 = -2 + 2×sqrt(7)
x2 = -2 - 2×sqrt(7)
so, F is the right answer.
work out the answer to these simultaneous equations
y=4x
y=x² - 12
A man is x years old and his son is y years old. what is their average age
Answer:(x+y)/2
Step-by-step explanation:
A factory can produce two products x and y with a profit approximated by p=14x+22y-900.
The vertices of the feasible region are (0,100) (0,700) (400,500)
The minimum profit is (0,100) and the maximum profit is (400,500)
Given that, P=14x+22y-900 where p is the profit
y > x +100 y must exceed the production of x by at least 100 units
x+2y<1400
x>0
y>0
We cannot produce negative quantities
Substitute y = x+100 into x+2y <1400
x+2(x+100) < 1400
x+2x+200 <1400
3x+200<1400
Subtract 200 from each side
3x<1200
Divide by 3
x<400
y = x+100
y = 400+100
y = 500
(400,500)
y > x +100
when x=0 y > 100
x+2y <1400
0+2y <1400
2y <1400
y <700
When x=0 y = 700
a) The vertices of the feasible region are (0,100) (0,700) (400,500)
b) Maximum and minimum profit occur at the vertices.
P=14x+22y-900
P(0,100) = 14(0) +22(100)-900 =2200-900=1300
P(0,700) = 14(0) +22(700)-900 =15400-900=14500
P(400,500) = 14(400) +22(500)-900 =5600+11000-900=15700
Thus, The vertices of the feasible region are (0,100) (0,700) (400,500)
The minimum profit is (0,100) and the maximum profit is (400,500)
Complete question: A factory can produce two products, x and y, with a profit approximated by P=14x+22y-900. The production of y must exceed the production of x by at least 100 units. Moreover, production levels are limited by the formula x+2y<1400.
a) Identify the vertices of the feasible region.
b) What production levels yield the maximum profit, and what is the maximum profit?
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What is the length of the side opposite?.
A right triangle's hypotenuse is its longest side, its "opposite" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question.
The side opposite the right angle is always the hypotenuse of a right triangle. In a right triangle, it is the longest side. The opposing and neighboring sides are the other two sides. The labels on these sides relate to an angle.
One side is opposite the other at a specific angle. The non-hypotenuse side that lies next to a particular angle is known as the neighboring side. The terms hypotenuse, opposite, and adjacent are used to define the trigonometric functions sine, cosine, and tangent.
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Julia parcourt 1200 km par mois en voiture. Elle possède
une voiture à essence qui consomme 6 L d'essence par 100 km.
Je raisonne
Pour réduire son impact écologique et économiser,
Julia s'informe sur les voitures hybrides. Elle apprend
qu'une voiture hybride consommerait
d'essence de moins que sa voiture actuelle.
Si le prix d'un litre d'essence est de 1,30 $ pendant
toute l'année, combien Julia économiserait-elle
en essence par année si elle remplaçait sa voiture
actuelle par une voiture hybride?
Answer:
Julia parcourt 1200 km par mois en voiture, donc elle parcourt 1200 x 12 = 14400 km par an.
Sa voiture actuelle consomme 6 L d'essence par 100 km, donc elle consomme 6/100 x 14400 = 864 L d'essence par an.
Si elle remplaçait sa voiture actuelle par une voiture hybride qui consomme moins d'essence, elle économiserait 864 L d'essence par an.
Si le prix d'un litre d'essence est de 1,30 $, alors Julia économiserait 864 x 1,30 = 1129,20 $ par an si elle remplaçait sa voiture actuelle par une voiture hybride.
What are all the prime numbers between 36 and 50?.
The ratio 800g : 1kg can be written in the form 1:n.
Find the value of n.
Please help
The value of n is 1/8. A ratio in math displays how many times one number is contained in another.
What is a ratio?A ratio in math displays how many times one number is contained in another. The ratio of oranges to lemons, for instance, is eight to six if there are eight oranges and six lemons in a bowl of fruit. In a similar way, the ratio of oranges to all other fruits is 8:14, while the ratio of lemons to oranges is 6:8.
The ratio shows how many times one value is contained in another value.
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
800g : 1kg = 1 : n
This can be written as,
800g/1kg = 1/n
Cross multiply.
n = 1kg/800g
[ 1 kg = 1000g ]
n = 1000g/8000g
n = 1/8
Thus,
The value of n is 1/8.
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A rectangle has an area of 209 square yards and a height of 19 yards. What is the length of the base?
The length of the base of the rectangle is B = 11 yards
What is the Area of a Rectangle?The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle
Area of Rectangle = Length x Width
Given data ,
Let the area of the rectangle be represented as A
Now , the value of A is
Let the base of the rectangle be represented as B
Area of rectangle A = 209 yards²
The length of the rectangle L = 19 yards
And , Area of Rectangle = Length x Width
Substituting the values in the equation , we get
Area of Rectangle = 19 x B
209 = 19 B
Divide by 19 on both sides of the equation , we get
B = 209 / 19
B = 11 yards
Hence , the length of the base of rectangle is 11 yards
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-2x -y=6
-2x +8y=-30
Answer : -4
explained:
you would have to sub 2 from -2x and -30(-30 - 2 = -32) to get x by it self then divide 8 by 8(equals) x then divide -32 with 8 = -4
your welcome!
The atomic radius of metal x is 135 picometers (pm) and a crystal of metal x has a unit cell that is face-centered cubic. Calculate the density of metal x (atomic weight = 42. 3 g/mol).
We have that the Density of metal X is mathematically given as
∅ = 5048.33 Kg/[tex]m^{3}[/tex]
Density is a word we use to describe how much space an object or substance takes up (its volume) in relation to the amount of matter in that object or substance (its mass). Another way to put it is that density is the amount of mass per unit of volume. If an object is heavy and compact, it has a high density.
Density of metal,
Generally the equation for the side of fcc is mathematically given as
fcc = 2 × [tex]\sqrt{2}[/tex] × radius of metal
fcc = 2 × 1.414 × 135
fcc = 381.78 × [tex]10^{-12}[/tex] m.
where, volume of 1 unit cell of fcc
fccV = ( 381.78 × [tex]10^{-12}[/tex] ) ^3
fccV = 55,646,713.615752 × [tex]10^{-36}[/tex] [tex]m^{3}[/tex]
And
weight of 1 atom
Wa = molecular weight / avagadro number
Wa = 42.3/(6.023 × [tex]10^{23}[/tex])
Wa = 7.023 × [tex]10^{-23}[/tex] gm/atom
Therefore, density is
∅ = (28.0923 × [tex]10^{-26}[/tex]) / (55,646,713.615752 × [tex]10^{-36}[/tex] )
∅ = 5048.33 Kg/[tex]m^{3}[/tex]
Therefore, we have that the Density of metal X is mathematically given as ∅ = 5048.33 Kg/[tex]m^{3}[/tex]
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which of the following is not a polynomial identity
Option B does not represent a polynomial identity.
What is a polynomial identity?Polynomial identities are equations that are true for all possible values of the variable. The polynomial identities are -
(x + y)² = x² + 2xy + y²(x – y)² = x² – 2xy + y²(x²– y²) = (x + y)(x – y)(x + a)(x + b) = x²+ (a + b)x + ab.(x + y + z)²= x² + y² + c² + 2xy + 2yz + 2zx.(x + y)³ = x³ + y³ + 3xy (x + y)(x – y)³ = x³ – y³ – 3xy (x – y)(x³ + y³) = (x + y)(x² – xy + y²)Given are the equations as shown in the image.
The equation that is not a polynomial identity is option B.
Therefore, Option B does not represent a polynomial identity.
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Can you find the sin of a right angle?.
Sine of a right-angled triangle is 1 i.e., sin 90°=1
One of the three fundamental functions in trigonometry, along with cosine and tan functions, is the sine function. The ratio of the opposite side of a right triangle to its hypotenuse is known as the sine x or sine theta.
Let the base of the triangle be ‘x’ and the perpendicular be ‘y’ and θ be the angle
Sine acts as the ratio of the lengths of the opposing side and the hypotenuse side for any right-angled triangle measured from any angle.
sin θ =y/1
When the angle measurement hits the positive y-axis, it will have reached 90°, starting with the first quadrant. Since it now contacts the circle's rim, the value of y changes to 1. Consequently, y's value is changed to 1.
sin θ =y/1=1/1
Therefore, sin 90°=1/1
or, sin 90°=1
Hence, proved.
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Terry hared an apartment with three other people each peron paid an equal hare of the rent together they pay $1,095 per month how much doe Terry pay per month?
If everyone paid equal share of amount of rent, then Terry paid $365 per month.
A property is considered to be rented out if it is occupied by someone other than the owner and the tenant consistently pays the owner a set rent. A person is renting when they desire to pay a landlord to live on that landlord's property. The term "letting" refers to the process of someone transferring ownership of their property in return for cash.
The total amount per month for the rent is given as $1095.
Since there are three persons including Terry, The rent is divided equally among all three people.
So, the toal amount should be divided by three to get individual amount
= 1095 / 3
= $365
Hence Terry paid $365 per month as the apartment rent.
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What is the quotient 3x3 10x2 10x 4 )/( x 2?.
After solving, the quotient (3x^3 + 10x^2 + 10x + 4) ÷ (x + 2) is 3x^2 + 4x + 2.
In the question, we have to find the quotient (3x^3 + 10x^2 + 10x + 4) ÷ (x + 2).
The polynomial is 3x^3 + 10x^2 + 10x + 4.
We have to divide the given equation by x + 2 to find the quotient.
Four operations, namely divide, multiply, subtract, and bring down, can be used to break down the division process into phases.
1: Find the appropriate integer to use as the divisor for the given number.
2: Multiply the integer (quotient) and divisor to obtain the amount to be deducted from the payout.
3: Deduct the amount from the dividend.
4: Bring down the balance and any additional digits from the dividend in step four.
5: Continue the procedure outlined above until the remainder equals zero or less than the divisor.
x+2 ) 3x^3 + 10x^2 + 10x + 4 ( 3x^2 + 4x + 2
3x^3 + 6x^2
- -
___________
4x^2 + 10x
4x^2 + 8x
- -
______________
2x + 4
2x + 4
- -
____________
0
Hence, the quotient (3x^3 + 10x^2 + 10x + 4) ÷ (x + 2) is 3x^2 + 4x + 2.
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The complete question is:
What is the quotient (3x^3 + 10x^2 + 10x + 4) ÷ (x + 2)?
Which equation represents the graph?
Answer:D y=-2x-1
Step-by-step explanation:
To solve this problem, we first need to look at the direction of the line to determine whether the slope is positive or negative. Since the left portion of the line is Quadrant 2 and the right portion in quadrant 4, the slope will be negative. Anytime the line looks like \ it will be negative, while / is positive. This immediately eliminates answers A and C. Now, our next order of business is to find the slope of the line. To do this, we need to pick two points on the line and use the equation (y2-y1)/(x2-x1). Any points on the line will work, so even if you do not use the same as me, you still should get the same answer (this is a good way to check!)
point 1: (-2,3)
point 2: (0,-1)
(-1 - 3) / (0 - -2) = (-1 - 3) / (0 + 2) = -4/2 = -2
Since the slope is -2, we know the answer is d. Hope this helps
What is the general form of linear equation class 10?.
The general form of linear equation is expressed in the form of ax+b=0 where a and b are the integers and X is the variable and has the only one solution and the general form of a linear equation in two variables is ax + by + c = 0, where a and b cannot be zero simultaneously.
An equation is a statement that two mathematical expressions having one or more variables are equal And the equations in which the powers of all the variables involved are one are called linear equations. The degree of a linear equation is always one.
Define Linear Equation in One Variable
A linear equation with one variable is one with a single variable of order 1 or less. Where x is the variable, it has the form a x +b = 0.
There is just one solution to this equation. Examples include:
3x = 1
22x-1=0
4x+9=-11
A simple equation is deemed to be a linear equation of two variables when it is given the form ax+by+c=0, according to the Linear Equations in Two Variables CLass 10 textbook. A, B, and C in this scenario should all be constants or real integers, such 2, 3, 4, etc. The a and b coefficients of x and y in this situation shouldn't be equal to zero. Given that a, b, and c are real values, the two unknown variables in this case would be x and y. An illustration of a two-variable linear equation is 4x+5y+3=12.
therefore , the general form of linear equation in one variable and intwo variable are ax+b=0 and ax+by+c=0
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What is the image of (-5, -1) after a reflection over the y-axis?
Answer:
5, -1
Step-by-step explanation:
Hope it helps! =D
xiv 2. Complete the table. Make drawings if needed. a. b. C. d. e. Rectangle Length: 4 cm Width: 2 cm Length: 3 cm Width: 2 cm Length: 5 cm Width: 4 cm Length: 6 cm Width: 3 cm Length: 7 cm Width: 6 cm 0 1 2 3 Perimeter Area Enlarge by: 2 times Length: Width: 3 times Length: Width: 4 times Length: Width: 2 times Length: Width: 3 times Length: Width: 4 5 6 7 8 9 Perimeter Are 10 11 12
Answer:
bsbsnhs
Step-by-step explanation:
gsgdhbdjdnndnsnnsbsbdnhidfgdhhdjjdndjsjkekkekekekkekkekejekkdir
How many solutions does Y =- 3x 7 have?.
The equation, Y = - 3x + 7 has infinitely many solutions.
Here we are given the equation y = - 3x + 7.
Now this equation has 2 variables. when an equation has 2 variables, there must be at least 2 equations for the system to have a unique solution, hence the given equation cannot have 1 unique solution.
If we plot this equation on the graph we will see that it makes a never-ending line.
Here for every value of x, we get a different value of y, which can be easily seen in the graph.
Therefore we cannot conclude that this will have no solution. Hence since there can be infinite possible answers to the above equation, this has infinitely many solutions.
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Correct Question
How many solutions does Y = - 2x + 3 have?
acide whether the two expressions are equivalent and explain your reasoning.
5x + 2-3x and 2x+2
3(x-1)+2 and 3x+2
4 (2x - 2) and -2 (4-4x)
Equivalent: Yes or No
Equivalent: Yes or No
Equivalent: Yes or No
Justification:
Justification:
Justification
When two expressions can be written similarly or when they can be combined into a single, simpler expression, they are said to be equivalent.
What is the best way to tell if two expressions are comparable to one another?
Let's evaluate each expression pair separately.
8. (n2+4)-n2 and 4n. (n2+4)-n2 = n2+ 4 - n2 = 4, which is not the same as 4n.
NOT THE SAME
9. The product of 3x + 5 and 2(x + 3) 2(x + 3) equals 2x + 6, not 3x + 5.
NOT THE SAME
10. 15 - 6x and 15(1 - 6x) (1 - 6x)
In other words, 15(1 - 6x) = 15 - 90x, which is not equal to 15 - 6x, is NOT EQUAL.
11. (y + y + 2 + y) + 3y and 6y + 2 (y + y + 2 + y) + 3y equals y+y+y+y +2 + 3y, which equals 3y + 2 + 3y and 6y + 2.
It is equivalent to the other phrase.
EQUIVALENT
12. 8y - 3 + 10y and 3 (6 - 1)
8y - 3 + 10y = 8y + 10y - 3 = 18y - 3 3(6 - 1) = 3(5) = 15
Both of the expressions are incompatible.
NOT THE SAME.
Only the expressions shown in position 11 are equivalent.
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Whats 2/3 + 3/5 in fractions
Answer:
19/15
2/3+3/5
Multiply each by 3
10/15+9/15=19/15
[tex] = \frac{2}{3} + \frac{3}{5} \\ [/tex]
[tex] = \frac{2}{3} \times \frac{5}{5} + \frac{3}{5} \times \frac{3}{3} \\ [/tex]
[tex] = \frac{10}{15} + \frac{9}{15 \\ } [/tex]
[tex] = \frac{10 + 9}{15} \\ [/tex]
[tex] = \frac{19}{15} \\ [/tex]
[tex] = 1 \frac{4}{15} \\ [/tex]
The box-and-whisker plot below represents some data set. What is the value of the upper quartile?
The value of the upper quartile is 65.
In the box plot, what is the upper quartile?The lower quartile, which is represented by the left border of the box, is the value that the first 25% of the data falls within. 25% of the data are to the right of the upper quartile value, which is indicated by the upper quartile at the right border of the box.
The left whisker represents the bottom 25% of the data, the left half of the box represents the second 25%, the right half of the box represents the third 25%, and the right whisker represents the top 25%.
The value of the upper quartile is 65.
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Please help !!
Consider the line y = -2-4x.
What is the slope of a line perpendicular to this line?
What is the slope of a line parallel to this line?
Slope of a perpendicular line:
Slope of a parallel line:
For the line y = -2-4x, the slope of a line parallel to this line is -4 and the slope of a line perpendicular to this line is 1/4.
What is slope?
A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
The equation for the line is - y = -2 - 4x.
The slope of a line is represented by the coefficient of the x term. In this case, the slope of the line y = -2 - 4x is -4.
The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line. The negative reciprocal of -4 is 1/4.
So, the slope of a line perpendicular to y = -2 - 4x is 1/4.
The slope of a line parallel to a given line is the same as the slope of the given line.
So the slope of a line parallel to y = -2 - 4x is -4.
Therefore, the parallel and perpendicular slope is -4 and 1/4 respectively.
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The figure shows a line graph and two shaded triangles that are similar:
Which statement about the slope of the line is true?
A.) It is 1/6 throughout the line.
B.) It is 6 throughout the line.
C.) The slope from point O to point A is 1/6 times the slope of the line from point A to point B.
D.) The slope from point O to point A is six times the slope of the line from point A to point B.
Answer: A). It is 1/6 throughout the line
Step-by-step explanation:
Help pleaseee!! I need it done before Monday
In point-slope form, the equation of the line through the indicated points is y - 2 = -4/3. ( x - 4 ).
What is the formula for the line passing through the specified points?Y - Y1 = m is the line's equation in point slope form (x – x1).As a result, the equation for a line passing through the origin and having a slope of m is given by y - 0 = m(x = 0), which equals y = mx. Given the information in the query;
A Point (4, 2)
x₁ = 4
y₁ = 2
B Point (1, 6)
x₂ = 1
y₂ = 6
We start by figuring out the line's slope.
Slope m is equal to (y2 - y1)/(x2 - x1)
Slope: m = (6 - 2) ( 1 - 4 )
(4)/ Slope m ( -3)
Slope m=-4/3
Then, simplify the point slope formula y - y1 = m(x - x1) using the slope -4/3 and point (4,2).
y - y₁ = m(x - x₁)
y - 2 = -4/3( x - 4 ) ( x - 4 )
As a result, y - 2 is the equation of the line in point-slope form that passes through the indicated places.
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The vertices of ΔABC are A(−5,4), B(−2,3), and C(−3,2). If ΔABC is reflected across the line y=−1 to produce the image ΔA'B'C', find the coordinates of the vertex C'.
The coordinates of the vertex C' will be (-5, -4). And the graph is given below.
What is a transformation of a point?A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.
The reflection does not change the shape and size of the geometry. But flipped the image.
The vertices of ΔABC are A(−5,4), B(−2,3), and C(−3,2). If ΔABC is reflected across the line y = −1 to produce the image ΔA'B'C'.
Then the coordinate of the triangle ΔA'B'C' will be given as,
(x', y') = (x, -y - 2)
A' = (-5, -4 - 2) = (-5, -6)
B' = (-2, -3 - 2) = (-5, -5)
C' = (-3, -2 - 2) = (-5, -4)
The coordinates of the vertex C' will be (-5, -4). And the graph is given below.
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32% of the field i red. If the field i 600 quare feet, how many quare feet of the field i red?
So, 32% of the field is red, which is equivalent to 192 square feet.
To find out how many square feet of the field is red, we need to use the percentage of the field that is red in the calculation. We know that 32% of the field is red, and the total size of the field is 600 square feet.
To calculate the number of square feet of the field that is red, we can use the following formula:
(32/100) * 600 square feet = 192 square feet
This calculation shows us that 32/100 of the field is red. To express this fraction in decimal we divide 32 by 100, which equals 0.32. To find the area of the field that is red, we then multiply 0.32 by 600 square feet.
So, the field has 192 square feet of the field is red.
Another way to think about it is: 32% is equal to 0.32, so we can multiply 600 square feet by 0.32, which also gives us 192 square feet.
Therefore, 32% of the field is red, which is equivalent to 192 square feet.
To learn more about Percentages
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