The slope formula generally used in the 7th grade is as follows -
1. The Point slope form -
Suppose you are given two points (x1,y1) and (x2,y2) or a graph consisting of two points whose slope is asked, then you use this method.
These points are often intercepts of the x and/or y axes.
Here you can use the formula for the equation of the slope which is -
m= (y2−y1) / (x2−x1).
2. The Slope-intercept Form-
Here, you are given the linear equation that is in the form y=mx+b.
If not you can manipulate it into that form.
Now, the slope here is m which is the coefficient of x.
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if we take a sample of ice from 10 meters beneath the surface and find that it is 1,000 years old, where would we need to look for ice that is about 10,000 years old?
Answer: 100 meters
Step-by-step explanation:
10 meters = 1,000 years old
50 meters = 5,000 years old
and so 100 meters = 10,000 years old
hope this helps you!
Helpppppppppppppppppp
Answer:
B
Step-by-step explanation:
Aaron deposits $20,000 in a bank account that earns 5.9%
compounded quarterly. The amount of money, A, in the
account can be determined by the formula
A = 20,000 (1 + 0.059) 41
where t is the number of years that the money is in the
bank. How much money does Aaron have after 10 years?
$17,972.10
0 $30,872.31
O $13,804.20
O $35,924.64
Answer:
Answer:A=20000(1+0.059)^10A=$35,480.49
Step-by-step explanation:
What is the slope of the line through − 5 − 10 and − 1 5?
Slope is a measure of how much a line changes in the y-direction for every unit of change in the x-direction. It is typically represented by the m in the equation y = mx + b. Line through points -5, -10, and -1 has a slope of 5.
Slope is calculated by taking the difference in the y-coordinates divided by the difference in the x-coordinates of two points on a line. Since we only have one point, we cannot calculate the slope .The slope of a line is equal to the change in y divided by the change in x. We can calculate the slope by subtracting the y-coordinates and then dividing by the difference of the x-coordinates. In this case, the change in y is (10 - (-5)) = 15 and the change in x is (5 - (-1)) = 6. Therefore, the slope of the line is 15/6 = 5.
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new legislation is passed requiring a riparian zone by the family's waterway. this will reduce the size of their field by 15% how much money will the family lose per year by having this riparian zone on their farm
The amount of money lost per year is 15x
Where 100x can be any amount
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Let the total amount of money earned in a year from the field = 100x
The new field area.
= 100% - 15%
= 85%
Now,
The amount of money earned in a year from the new field area.
= 85% of 100x
= 85x
Now,
The amount of money lost per year.
= 100x - 85x
= 15x
Thus,
If 15% of the field is reduce the amount of money lost per year is 15x
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Who do you solve y= -5/2x-7
Answer:
To solve the equation y = -5/2x - 7, we can first multiply both sides of the equation by 2x + 7, which is the denominator of the fraction on the right-hand side. This gives us the equation 2xy + 7y = -5, which we can rearrange to isolate the variable y on one side of the equation. Dividing both sides of the equation by 2x + 7, we get y = -5 / (2x + 7). This is the solution to the original equation.
Step-by-step explanation:
Simplify each term.
y= −5 x2 −7
Solve the problem.
The area of a rectangle is 30m2 - 20m - 10. Find the length if the width is 5m - 5.
The length of the rectangle is 6m - 2.
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
Area = 30m² - 20m - 10
Width = 5m - 5
Now,
Area = Length x Width
30m² - 20m - 10 = Length x (5m - 5)
10(3m² - 2m - 1) = Length x (5m - 5)
10(3m² - (3 - 1)m - 1 = Length x (5m - 5)
10 (3m² - 3m + m - 1) = Length x (5m - 5)
10 (3m(m - 1) + 1(m - 1)) = Length x (5m - 5)
10 (3m + 1)(m - 1) = Length x 5(m - 1)
(m - 1) gets canceled.
10(3m - 1) = Length x 5
2(3m - 1) = Length
Length = 6m - 2
Thus,
6m - 2 is the length of the rectangle.
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Triangle EFG is similar to triangle HIJ.find the measure of side HI round answer to nearest ten
Since the ΔEFG is similar to ΔHIJ, so side HI is equivalent to the measure of length of segment [EF] divided by the scale factor [K].
What is Parallelogram? What is triangle?In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. TThe sum of all the angles of a triangle is 180 degrees. Mathematically - ∠x + ∠y + ∠z = 180°There are different types of triangles such as -equilateral triangle, scalene triangle, isosceles triangle etc.
We have triangle ΔEFG is similar to triangle ΔHIJ.
Since ΔEFG is similar to triangle ΔHIJ, then we can write -
EF/HI = FG/IJ = EG/HJ = K [constant]
Since the side lengths are not given, we can write -
EF/HI = K
HI = EF/K
Therefore, since the triangles ΔEFG is similar to ΔHIJ, the side HI is equivalent to HI = EF/K.
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vertex of g(x)=-2x^2 - 14x +12
The vertex of the function g(x)=-2x²- 14x +12 is (-7/2, 25/2).
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
The given function is g(x)=-2x²- 14x +12
We need to find the vertex of the function.
y=-2x²- 14x +12
To make it a perfect square we are adding and subtracting (7/2)²
y=-2x²- 14x +(7/2)²+12-49/4
y=-2(x+7/2)²+25/2
x+7/2=0
Subtract 7/2 on both sides
x=-7/2
and y=25/2
Hence, the vertex of the function g(x)=-2x²- 14x +12 is (-7/2, 25/2).
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Please help me pretty please man
Answer:25
Step-by-step explanation:
just think its so easy
Answer:
25
Step-by-step explanation:
Three packages of chicken and 4 cases of barbecue sauce cost $40 five packages of chicken and 2 cases of barbecue sauce cost $34
Answer: .
Step-by-step explanation: ..
i need help with my Math homework please
Answer: I may not be much of a help, but....
Step-by-step explanation: Count up each year by 2%, and then do the rounding! I really do hope this helps!
Answer:
Step-by-step explanation:
per year=2%5 years=10%6 years=12%7 years=14%8 years=16%So basically ur adding 2 % every year.
a ball of radius 16 has a round hole of radius 5 drilled through its center. find the volume of the resulting solid.
The volume of the resulting solid is 16623 when a circular hole of radius 5 has been bored through the center of a ball with a radius of 16.
Given that,
A circular hole of radius 5 has been bored through the center of a ball with a radius of 16.
We have to determine the resulting solid's volume.
We know that,
Volume of the original ball= 4/3πr³
Radius r=16
Volume v₁=4/3π(16)³ = 16384π/3
Volume of hole = 4/3πr³
Radius r=5
Volume v₂=4/3π(5)³ = 500π/3
Volume of the resulting solid = v₁-v₂
= 16384π/3 - 500π/3
= 15882π/3
= 16623
Therefore, The volume of the resulting solid is 16623 when a circular hole of radius 5 has been bored through the center of a ball with a radius of 16.
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the foci of an ellipse are (5,0) and (-5,0), and the vertices are (8,0) and (-8,0). find an equation of the ellipse. then sketch the conic section and bring the sketch to your discussion section. which form (below) does the equation of the given ellipse fit?
according to the question
given data in the question,
the foci of an ellipse are (5,0) and (-5,0)
and vertices are (8,0) and (-8,0)
** Standard Form of an Equation of an Ellipse is
where Pt (h k) is the center. (a variable positioned to correspond with major axis)
a and b are the respective vertices distances from center
and are the foci distances from center: a > b
Recommend sketching it...Foci (-5,0) (5,0) and Vertices (8,0) (-8,0).
then using √(64+b^2 )=5 to find b
64 - b^2 = 25, b = √ 39
**** The standard form of the equation is an ellipse
where Pt (h, k) is the center. (variable aligned to match long axis)
a and b are the respective vertex distances from the center.
and are the distances from the center to the focal point.
a > b
hyperbolic equations in normal form,
C (h, k) and 2b units up and down from the centre at vertex 'b' Horizontal axis length
Focus units up and down from the center along x = h
& asymptotes straight line through C (h, k) with slope m = b/a
after that.
C (h, k) and corner 'a' are units left and right of the center, 2a is the length of the horizontal axis
The focal points are units left and right of the center along y = k.
asymptotes straight line through C (h, k) with slope m = b/a
parabolic vertex form open to the top (a>0) or bottom (a<0 x=removed>0) or left (a<0),
where (h, k) is the vertex and y = k is the line of symmetry.
The standard form is where the focus is (h + p, k )
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** Standard Form of an Equation of an Ellipse is
where Pt (h k) is the center. (a variable positioned to correspond with major axis)
a and b are the respective vertices distances from center
and are the foci distances from center: a > b
Recommend sketching it...Foci (-5,0) (5,0) and Vertices (8,0) (-8,0).
then using √(64+b^2 )=5 to find b
64 - b^2 = 25, b = √ 39
**** The standard form of the equation is an ellipse
where Pt (h, k) is the center. (variable aligned to match long axis)
a and b are the respective vertex distances from the center.
and are the distances from the center to the focal point.
a > b
hyperbolic equations in normal form,
C (h, k) and 2b units up and down from the center at vertex 'b' Horizontal axis length
Focus units up and down from the center along x = h
& asymptotes straight line through C (h, k) with slope m = b/a
after that.
C (h, k) and corner 'a' are units left and right of the center, 2a is the length of the horizontal axis
The focal points are units left and right of the center along y = k.
asymptotes straight line through C (h, k) with slope m = b/a
parabolic vertex form open to the top (a>0) or bottom (a<0 x=removed>0) or left (a<0),
where (h, k) is the vertex and y = k is the line of symmetry.
The standard form is where the focus is (h + p, k )
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The equation of the ellipse with foci as (5,0) and (-5,0) is
[tex]\frac{x^2}{49}+\frac{y^2}{24}=1[/tex]
What is an ellipse simple definition?A plane section of a right circular cone that is a closed curve is produced by a point moving in such a way that the sum of its distances from two fixed points is a constant.
How do you know if an equation is an ellipse?Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 is the equation in standard form for a conic section. Here, A, B, C, D, E, and F are all real integers, and A 0, B 0, and C 0. The conic section is an ellipse if B2 - 4AC 0.
where the center is Pt(h,k). (a variable placed such that it lines up with the main axis)
The relative vertices' distances from the center are a and b.
the foci's separations from the center are: a > b
It's suggested that you sketch it: Vertices (-7,0), Focus (-5,0), and (5,0). (7,0).
then finding b
when 49 - b2 = 25.
The relative vertices' distances from the center are a and b.
furthermore,
the foci's separations from the center are: a > b
The equation for an opening up and down hyperbola
having C(h,k), vertices "b" units up and down from the center, and a transverse axis length of 2b.
Foci
29 units away from the center, along x = h
& Asymptotes Lines Through C(h,k), Slope m = b/a
Equation of a Hyperbola Opening Right and Left Standard Form:
with C(h,k), vertices 'a' units to the right and left of the center, and 2a the transverse axis length
y = k along 29 units to the right and left of the center
& Asymptotes Lines through C(h,k), slopes m = b/a
is the vertex form of a Parabola with an opening up (a>0) or down (a0).
where the vertex is (h,k), and the line of symmetry is (x = h).
The conventional form is with (h,k + p) as the main focus.
the vertex form of a Parabola opening right(a>0) or left(a0).
where y = k is the Line of Symmetry and (h,k) is the vertex
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What is the perimeter of the entire design? 46 cm 64 cm 108 cm 147 cm
Option B is correct, the perimeter of the entire design is 64cm.
In the design, there are two congruent trapezoids stitched together.
So, the given length = 14cm & base = 9cm
There are 4 bases and 2 lengths.
So, the perimeter of a trapezoid is
= length + base
= 14 x 2 + 9 x 4
= 64 cm.
So, the perimeter of the entire design is 64 cm.
The perimeter of a trapezoid is the sum of the lengths of every facet of the trapezoid. A trapezoid is a quadrilateral that has aspects parallel to each different and non-parallel aspects termed bases and legs respectively. The perimeter of a trapezoid is defined as the overall length of the boundary of the trapezoid. A trapezoid is a -dimensional shape (2nd shape) and an irregular polygon. thus, the perimeter of the trapezoid is calculated by including the period of all its aspects.
The perimeter of a trapezoid is expressed in linear units like, 'inches', 'feet', 'meters' or 'centimeters', and many others. The formulation of the perimeter of a trapezoid is a simple one wherein the duration of all 4 sides is added. study the trapezoid ABCD given below wherein aspects AB and CD (bases) are parallel to each other while ad and BC (legs) are non-parallel sides.
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Complete question: -
Cameron makes a quilt design using four congruent What is the perimeter of the entire design? triangles as shown below.
46 cm 64 cm 108 cm 147 cmWhich equation represents a line passing through the point (8,33) with a slope of 3?
The slope intercept form of equation of required line is y = 3x + 9
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Here,
Slope = 3
The line passes through (8, 33)
Equation of required line
y - 33 = 3(x - 8)
y - 33 = 3x - 24
y = 3x - 24 + 33
y = 3x + 9
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When is -2x^3-13x^2+8x+52 ≥ 0?
Answer:
x ≤ -13/2 ∨ -2≤ x ≤ 2
Step-by-step explanation:
-x²(2x + 13) + 4(2x+ 13) ≥ 0
(2x+13)(-x²+4) ≥ 0
(2x+13)(2+x)(2-x) ≥ 0
2x + 13 ≥ 0
2x ≥ -13
2/2 x ≥ -13/2
x ≥ -13/2
2+ x ≥ 0
x ≥ -2
2 - x ≥ 0
-x ≥ -2
x ≤ 2
-13/2. -2. 2
- +. +. +
- - +. +
+. +. +. -
+. - +. -
x ≤ -13/2 ∨ -2≤ x ≤ 2
Mary used a sample of 68 large u. S. Cities to estimate the relationship between crime (annual property crimes per 100,000 persons) and income (median annual income per capita, in dollars). Her estimated regression equation was crime = 428 + 0. 050 income. If income decreases by 1000, we would expect that crime will:.
The required expected crime when income decreases by 1000 is 50.
What is annual property crimes ?In property crime, a victim's property is taken or obliterated, without the utilization or danger of power against the person in question. Local misdemeanors incorporate thievery and robbery as well as defacing and incendiary.
According to question:We have,
crime = 428 + 0. 050 income
If the income goes down by 1, crime goes down by 0.050.
Similarity, if income goes down by 1000, crime goes sown by 0.050(1000)
⇒ 50
Thus, the expected crime is 50.
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An airplane descends at a rate of 25 feet per minute. What is the airplane's change in
altitude after 10 minutes? Interpret the product.
Answer:
-250 feet
Step-by-step explanation:
-25x10=-250
needs to buy some food. At the nearest store, bags of food cost $. How much would spend on of food?
when a single card is drawn from a standard 52-card deck, what is the probability that it will be a king or a diamond?
The probability that it will be a king or a diamond is 4/13
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Here, we have
There are 52 cards, of which 4 are kings.
There are 52 cards, of which 13 are diamonds.
But there are only 3 cards that are kings which are not diamonds, and only 12 cards that are diamonds but not kings, there’s one card that is both a king and a diamond.
So, there are 3/52+12/52=15/52 chances of drawing a card that is king or diamond but not both.
There are 3/52+12/52+1/52=16/52 chances of drawing a card that is king or diamond or both.
Hence, the probability that it will be a king or a diamond is 4/13.
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If g(x) = (x + 1)2, complete each part below.
a. g(5)
b. g(2m + 4)
c. x if g(x) = 9
A) g(5)=(5+1)2
6*2
12
b) (2m+4)2
4m+8
C) (9+1)2
10*2
20
How many elements are required to construct a quadrilateral uniquely * 5 Elements 4 Elements 6 Elements 3 elements?
The minimum number of elements required for the construction of a quadrilateral uniquely are 5 elements.
Explanation:
The minimum number of elements required for the construction of a quadrilateral uniquely are as follow:
Total number of elements present in the quadrilateral are ten.Name of the quadrilateral elements are ; four sides, four angles , and two diagonals.If we take two elements it is not possible to construct a quadrilateral.If we consider three elements again we are not able to construct a quadrilateral.If we take any four elements all four vertices will not intersect each other and quadrilateral will not formed.Minimum four sides and one diagonal or four sides one angle that at least 5 elements are required to construct a quadrilateral.Therefore, minimum 5 elements are required to construct a unique quadrilateral.
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bolivian coffee sells for $4.59 per pound, and colombian coffee sells for $5.95 per pound. how many pounds of each coffee should be mixed to produce 4000 pounds of mixture that will sell for $5.10 per pound?: * a) bolivian: 2500 pounds; columbian: 1500 pounds b) bolivian: 2000 pounds; columbian: 2000 pounds c) bolivian: 2250 pounds; columbian: 1750 pounds d) bolivian: 1500 pounds; columbian: 2500 pounds e) bolivian: 1000 pounds; columbian: 3000 pounds
The required pounds of Bolivian coffee and Colombian coffee are 2500 and 1500 respectively.
How we use the linear equation of two variable to solve this problem?
A equation is supposed to be linear equation in two factors in the event that it is written as ax + by + c=0, where a, b and c are genuine numbers and the coefficients of x and y, i.e an and b separately, are not equivalent to nothing. For instance, 10x+4y = 3 and - x+5y = 2 are direct conditions in two factors.
According to question:Let x be the pound of Bolivian coffee and y is that of Colombian coffee.
Bolivian coffee sells for $4.59 per pound, and Colombian coffee sells for $5.95 per pound and whole mixture sells for $5.10.
So, 4.59x + 5.95y = 5.10(4000)
4.59x + 5.95y = 20400--------------------(1)
and x + y = 4000-----------------------------(2)
On solving above two equation, we get
x = 2500 pounds and y = 1500 pounds
Thus, required pounds of two coffees are 2500 and 1500.
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a rectangular poster is to contain square inches of print. the margins at the top and bottom of the poster are to be inches, and the margins on the left and right are to be inch. what should the dimensions of the poster be so that the least amount of poster is used?
The Poster Dimensions of rectangle will be:
W = 18 inches
Y = 36 inches
Area can be defined as the amount of space covered by a plane of a particular shape. It is measured in "number" of square units (square centimeters, square inches, square feet, etc.). The area of a rectangle is the number of unit squares that fit in the rectangle. Examples of rectangles are flat surfaces such as laptop monitors, chalkboards, and painting canvases. You can use the rectangle area formula to find the space occupied by these objects.
Now,
Let's say the printable area of a rectangular poster is 512 square inches
"x". " and "y" - the dimensions of the printed area of the poster
A(p) = printed area of the poster = x × y
512 = x × y ⇒ y = 512/x
Therefore, The total area of the poster is:
A( t) = ( y + 4 ) × ( x + 2 )
⇒ A(t) = yx +2y +4x + 8 and y = 512/x
Total Area of x or Total poster area as x function:
A(x) =( 512/x)*x + 2* (512/x) + 4*x + 8
A(x) = 512 + 1024/x + 4 *x + 8
⇒ A(x) = 520 + 1024/x + 4*x
Differentiating both sides of the equation gives:
A´(x) = - 1024/x² + 4
A´(x) = 0
⇒ - 1024 /x² = -4
⇒ 4*x² = 1024
⇒ x² = 1024/4
⇒ x² = 256
or, x = 16 inches
and y = 512/x
⇒ y = 512/16
⇒ y = 32 inches
So x is found, the y dimension of the print area, Than n is the dimension of the poster:
Therefore,
w = x + 2 ⇒ w = 16 + 2 w = 18 in
And,
Y = y + 4 ⇒ Y = 32 + 4 Y = 36 in
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what is 75 divided by 688
Answer: 0.109011627907
Step-by-step explanation:75 divided by 688 =0.109011627907
Bilquis owns a food truck that sells tacos and burritos. She sells each taco for $4 and each burrito for $6.25. Bilquis must sell a minimum of $630 worth of tacos and burritos each day. Write an inequality that could represent the possible values for the number of tacos sold, tt, and the number of burritos sold, bb, that would satisfy the constraint.
The inequality that could represent the possible values for the number of tacos sold and the number of burritos sold is 4t + 6.25b ≥ 630.
What inequality that could represent the possible values for the number of tacos sold?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
The inequality that could represent the possible values for the number of tacos sold and the number of burritos sold will be:
4(t) + 6.25(b) ≥ 630.
4t + 6.25b ≥ 630.
Therefore, the inequality is 4t + 6.25b ≥ 630..
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Given a fixed point and a fixed line, a parabola consists of all points that are equidistant to the fixed point and the fixed line.
True
False
It is true that given a fixed point and a fixed line, a parabola consists of all points that are equidistant to the fixed point and the fixed line.
A parabola is a quadratic function graph .A parabola is a curve equation in which a point on the curve is equidistant from a fixed point and a fixed line.
The fixed point is known as the parabola's focus, and the fixed line is known as the parabola's directrix. It is also worth noting that the fixed point does not lie on the fixed line.
A parabola is a locus of any point that is equidistant from a given point (focus) and a given line (directrix). The parabola is a significant curve of the coordinate geometry's conic sections.
The general equation of a parabola is: y = a(x-h)² + k or x = a(y-k)² +h, where (h,k) denotes the vertex.
The standard equation of a regular parabola is y² = 4ax.
It's true that given a fixed point and a fixed line, a parabola consists of all points that are equidistant to the fixed point and the fixed line.
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when a fair die is tossed twice, what is the probability that the same number appears twice (round off to second decimal place)?
The probability that the same number appears twice is 0.16
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
The fair die is thrown twice.
The total number of outcomes if a fair die is tossed twice is 36.
The favorable number of outcomes, which also contains six, is six.
Following is a calculation of the likelihood of the same number appearing twice.
Probability = (Number of possible outcomes)/(Total number of outcomes)
= 6/36
= 0.16
So, the probability is 0.16
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Are 2 congruent triangles always similar?
Answer: There are only a few similar congruent triangles.
Step-by-step explanation: