A bicycle lock has a four-digit code. The possible digits, 0 through 9, cannot be repeated. What is the probability that the lock code will begin with the number 5? . What is the probability that the lock code will not contain the number 0? .
The probability that the lock code will begin with the number 5 is:
0.1The probability that the lock code will not contain the number 0 is:
0.6What is Probability?This refers to the use of permutations to find the possible occurrence of events.
The total number of elements is 10
Hence, the total codes is 5040.
P(five)= n(first number)/n(all codes)= 1/10= 0.1
Next,
P(codes without zero)= n(codes without zero)/n(all codes)
(9*8*7*6)/(10*9*8*7)=6/10=0.6
=0.6
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Triangle DEF is congruent to GHJ by the SSS theorem. Which rigid transformation is required to map DEF onto GHJ?
dilation
reflection
rotation
translation
Answer: The correct option is 4, i.e., translation.
Explanation:
It is given that the triangle DEF is congruent to GHJ by the SSS theorem.
From the given figure it is noticed that the triangle DEF and GHI are isosceles triangle.
Reason for correct option:
In transition the side and angles of the shape are not effected and the figure transfers from one place to another place without making any other change.
Since the both triangle are congruent and the position of all sides and angles are same, therefore option 4 is correct.
Reason for incorrect option:
In dilation the size of the figure is either stretched or compressed according to the scale factor k. But in the given figure the size of both triangles are same it means option A is incorrect.
In reflection the distance of all the point in preimage and all the image are same from the central line. Any central line does not exist in given figure. SO, the option B is incorrect.
In rotation the side length and angles are not affected but the position are not same, therefore the option C is incorrect.
Answer: Translation
Step-by-step explanation:
Given: Triangle DEF is congruent to GHJ by the SSS theorem.
From the given picture two sides of both triangles are equal therefore, the triangle DEF and GHI are isosceles triangle.
We know that a transition is a kind of rigid motion used in geometry to trace a function that moves an object a particular distance that maps produces images.
Since the both triangle are congruent and just position of triangle GHJ is shifted to the right and down.
Therefore, the transition is rigid transformation which is required to map DEF onto GHJ
Using the given points, determine the slope.
(0, 32) and (100, 212)
The slope is the change in y divided by the change in x.
The slope is the ratio of rise to run.
so:If 7 is added to twice a number and this sum is multiplied by 5 â, the result is the same as if the number is multiplied by 6 and 11 is added to the product. what is theâ number?
(2x+7)*5 = 6x+11
10x+35 = 6x+11
4x+35 =11
4x=-24
x=-6
the number is -6
Find the surface area of the figure below. Leave answer in terms of π.
A. 1060π in2
B. 1160π in2
C. 1260π in2
D. 1000π in2
Solve the equation. 8d + 3d – 3d – 8 = 3d
Answer:
1.6
Step-by-step explanation:
If 3x² -6=y for all real numbers x, then x² - 2 =
Find the 6th term of a geometric sequence t3=444 t7=7104
Answer:
3552
Step-by-step explanation:
In pentagon ABCDE, angle A= 87, angle B=125, angle C= 63, angle D=169. Find angle E
Find the measures of all of the angles in the parallelogram.
Find the equation of the linear function which passes through the points (-1, 3) and (4, -2). give your answer in y = mx + b form.
Hello : let
A(-1,3) B(4,-2)
the slope is : (YB - YA)/(XB -XA)
(-2-3)/(4+1) = -1
an equation is : y=ax+b a is a slope
y = -x +b
the line through
point B(4,-2) : -2 = -1(4)+b
b = 2
the equation is : y =-x+2
Find the dot product, a • b. a = 6i + 5j, b = -5i + 4j
Answer:
the answer is -10
8. Find the congruence transformation that maps ∆ABC to ∆A’B’C’. Explain your reasoning
In this case, to flip any of the points to map up accurately to the other points, we would have to do a transformation of reflection about the y-axis. The reason behind this is that out of other transformation process, we can only achieve the image of triangle ∆A’B’C’ through reflection.
Dilation will not work since it only changes the size of the object. The shape and position will not affected.
A translation will not work because although the shape can move, it still needs to flip to achieve triangle ∆A’B’C’.
A rotation will also not work because when you rotate it, the shape will still not map over the new one.
Therefore the only answer to this question would be to
reflect triangle ∆ABC about the y-axis.
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What is the simplified form of the expression?
5(14 - 2)2 ÷ 2
In two or more complete sentences describe how to determine the appropriate model for the set of data, (0,2), (2,3), (5,4), (10,5).
what is the slope of a line that is parellel to the line represented by the equation y=2/5x+4/5
The base edge of an oblique square pyramid is represented as x cm. If the height is 9 cm, what is the volume of the pyramid in terms of x?
3x2 cm3
9x2 cm3
3x cm3
x cm3
Hence, the volume of pyramid is:
3x^2 cm^3
Step-by-step explanation:We know that a volume(V) of a oblique square pyramid with height 'h' and base area A is given by the help of formula:
[tex]V=\dfrac{1}{3}\times (Ah)[/tex]
Now, according to the ques we have:
The base edge of an oblique square pyramid is represented as x cm.
The height is 9 cm.
Hence, the base area (A) is calculated as:
[tex]A=x^2[/tex]
( Since the base is in the shape of a square and we know that the area of square with side length s is given as:
[tex]Area=s^2[/tex] )
So, the volume of the pyramid is calculated as:
[tex]V=\dfrac{1}{3}\times (x^2\times 9)\\\\V=3x^2 \ cm^3[/tex]
Hence, the volume of pyramid is:
3x^2 cm^3
A pyramid is a solid shape with several triangles and a base. The volume of the pyramid in terms of x is 3x^2 cm3
How to calculate the volume of a pyramid?The volume(V) of an oblique square pyramid with height 'h' and base area A is expressed according to the formula:
V = Bh/3
B is the base area = x * x = x^2
h is the height = 9cm
Substitute
V = x^2*9/3
V = 3x^2cubic cm
Hence the volume of the pyramid in terms of x is 3x^2 cm3
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#27 how do I find x?
E to F is 6 F to G is x
and overall distance from e to g is 1.6x
so:
6+x = 1.6x
subtract x from each side
6 = 0.6x
now divide both sides by .6
x = 6/0.6 = 10
x = 10
Zeus Industries bought a computer for $2740. It is expected to depreciate at a rate of 24% per year. What will the value of the computer be in 3 years?
Round to the nearest penny. Do not type the "$" sign in your answer
I need help with this problem
a basketball player has already scored 56 points in a game the team record for point a in a game is 72 which equation would allow you to find out how many more points the player needs to tie the record
Answer: The player needs 16 more points to tie the record.
Step-by-step explanation:
Let the number of points the player needs to tie the record be 'x'.
Number of points that a basketball player has already scored = 56
Number of points a team need for record in a game = 72
According to question, it becomes,
[tex]x+56=72\\\\x=72-56\\\\x=16[/tex]
Hence, the player needs 16 more points to tie the record.
Aunt Mary is 6 times as old as Jane. If Aunt Mary is 72 years old, how old is Jane?
Joey has a full 40 coins consisting of only quarters and nickels if the total value is $5.00 how many of each does joey have.
The following is an arithmetic sequence.
-3, 3, -3, 3
true false
If a and b are positive numbers such that 2b=3a, what's the value of ((a+b)/b)? I know you can plug in numbers for this, but i'm interested in solving this algebraically. Thanks.
What is the solution to this system of equations 2x-7=y y=2x+3
Answer:
No solution
Step-by-step explanation:
[tex]2x-7=y[/tex]
[tex]y=2x+3[/tex]
To solve the system of equations, we use substitution method
Lets substitute the second equation y=2x+3 for y in the first equation and solve for x
[tex]2x-7=2x+3[/tex]
Lets solve for x
subtract 2x on both sides
[tex]2x-2x-7=2x-2x+3[/tex]
[tex]-7=+3[/tex] is false
So, no solution for this system of equations
(05.01 MC)
The table and the graph below each show a different relationship between the same two variables, x and y:
How much more would the value of y be on the graph than its value in the table when x = 12?
20
30
60
70
For the table, y = 25x.
When x = 12, y = 25*12 = 300
For the graph, y = 30x
When x = 12, y = 30*12 = 360
When x = 12, the value of y on the graph is 60 more than its value in the table.
Answer:
The correct option is C. The value of y be on the graph than is 60 more than the y value in the table when x = 12.
Step-by-step explanation:
If a line passing through two points then the equation of line is
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
From the given table it is clear that the line passing thought the points (4,100) and (5,125).
[tex]y-100=\frac{125-100}{5-4}(x-4)[/tex]
[tex]y-100=25(x-4)[/tex]
[tex]y-100=25x-100[/tex]
[tex]y=25x[/tex]
The value of this function at x=12 is
[tex]y=25(12)=300[/tex]
From the given table it is clear that the line passing thought the points (0,0) and (2,60).
[tex]y-0=\frac{60-0}{2-0}(x-0)[/tex]
[tex]y=30x[/tex]
The value of this function at x=12 is
[tex]y=30(12)=360[/tex]
The difference between y value in the graph and in the table at x=12 is
[tex]360-300=60[/tex]
The value of y be on the graph than is 60 more than the y value in the table when x = 12. Therefore the correct option is C.
Rewrite using standard notation: 2.43 × 104
A: 24,300
B: 2,430
C: 2.43
D: 0.000243
Rex weighed 80 pounds a year ago. Now he weighs 92 pounds. What is the percent increase in his weight?
(A)12%
(B)13%
(C)15%
(D)16%