The largest possible last digit in the string of 2002 digits and number divisible by 19 or 31 is 9.
Given the first digit of a string of 2002 digits is 1 and the two digit number formed by consecutive digits within the string is divisible by 19 or 31.
We have to tell the last largest digit of such number.
Two digit numbers divisible by 19=19,38,57,76,95.
Two digit numbers divisible by 31=31,62,93,124
Number started with 1 =19
Last digit is 9
We have said that the number should be divisible by 19 or 31 not from both and started with 1.
Hence the largest possible last digit and number divisible by 19 or 31 in this string is 9.
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The triangles are congruent by the SSS congruence theorem.
Triangles A B C and F E D are shown. Triangle A B C is reflected across A C and then is shifted down and to the left to form triangle F E D.
Which rigid transformation(s) can map TriangleABC onto TriangleFED?
reflection, then dilation
reflection, then translation
rotation, then translation
rotation, then reflection
The rigid transformations that maps ΔABC onto ΔFED by reflection then translation.
The correct option is (B).
What is Translation?Translation is also another form of transformation whereby all the points of a figure are shifted at exactly the same distance and in the same direction without being resized, reflected nor rotated.
given:
ΔABC ≅ ΔFED are congruent by the SSS Congruence Theorem.
Hence, the rigid transformations that maps ΔABC onto ΔFED by reflection then translation.
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Answer:
B
Step-by-step explanation:
Find the tangent of angle Θ in the triangle below.
A. 12/13
B. 12/5
C. 5/12
D. 13/12
E. 5/13
Answer:
tanΘ = [tex]\frac{5}{12}[/tex]
Step-by-step explanation:
tanΘ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{5}{12}[/tex]
Given that ΔJKL ≅ ΔUVW and ΔUVW ≅ ΔABC, complete the following statements.
Triangle JKL is congruent to triangle
.
Side LK corresponds to sides
.
Angle JLK corresponds to angles
.
Step-by-step explanation:
JKL is congruent to ABC
side LK corresponds to WV and CB
angle JLK corresponds to angle UWV and angle ACB
PROBLABILITY!!!
(I added the picture needed)
1.Create a sample space and find the product of each combination. What is the probability that a person wins the game? Express your answer as a fraction in lowest terms and as a percent rounded to the nearest tenth.
(answer to this one is 9/28 and 32.1%)
2. You realize a short time into the carnival that you don’t have enough prizes to last the entire event. You call your teacher, and she suggests that you change the winning number so that a participant will win only 25% of the time. What number will that be? Support your answer.
3. Participants achieving a winning score of 36 or higher in four consecutive attempts will receive a large prize! What is the probability of this occurring?
4. After changing the game rules, participants and the crowd are disappointed when the first five games yield scores of 12, 18, 30, 28, and 24. What statement can you recommend the teacher posts to reassure everyone that the game is fair?
Based on the rules of the game, the probability that a person wins the game is 3/8 or 37.5%.
If participants can only win 25% of the time, the number that they need to get would be 32 or higher.
The probability of a winning score of 36 or higher in four consecutive attempts is 1/1,296.
To show that the game is fair, the teacher can post that every number apart from 24 and 30 has an equal chance of appearing.
What is a good sample space to represent the data?There are 6 sides to dice and 4 cards. The sample space is:
Dice Card Product Frequency of Product
1 5 5 1
1 6 6 1
1 7 7 1
1 8 8 1
2 5 10 1
2 6 12 1
2 7 14 1
2 8 16 1
3 5 15 1
3 6 18 1
3 7 21 1
3 8 24 2
4 5 20 1
4 6 24 1
4 7 28 1
4 8 32 1
5 5 25 1
5 6 30 2
5 7 35 1
5 8 40 1
6 5 30
6 6 36 1
6 7 42 1
6 8 48 1
Total 24
24 and 30 have frequencies of 2 as they appear twice.
From the table, in order to win, a player needs to get 28 or higher.
There are only 8 numbers that are 28 or higher but including the chance that 30 has a relative frequency of 2, we have 9 chances to win the game. The probability is:
= 9 / 24
= 3 / 8
How can a player win 25% of the time?If people are to win only 25% of the time, this means that the number of products that can be picked is:
= 25% x 24
= 6
To find the winning number, count down from the highest product 6 times to get 32.
A person therefore needs to get 32 or above to win 25% of the time.
What is the probability of winning the large price?The probability of getting 36 or higher is:
= Chance of 36 + chance of 40 + chance of 42 + chance of 48
= 1 / 24 + 1/24 + 1/24 + 1/24
= 1 / 6
The probability of repeating this 4 times is:
= 1 / 6 x 1 / 6 x 1/ 6 x 1 / 6
= 1 / 1,296
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Pls see below very short question
Answer:
[tex]f(x)=2(2)^{0.5x}-3[/tex]
Step-by-step explanation:
Parent function:
[tex]g(x)=2^x[/tex]
Properties of the given parent function:
y-intercept at (0, 1)horizontal asymptote at y = 0As x → -∞, y → 0As x → ∞, y → ∞Given form of function f(x):
[tex]f(x)=a(b)^{kx}+c[/tex]
If the parent function is [tex]g(x)=2^x[/tex] then b = 2:
[tex]\implies f(x)=a(2)^{kx}+c[/tex]
From inspection of the graphed function f(x):
y-intercept at (0, -1)horizontal asymptote at y = -3Therefore, the y-intercept has shifted 2 units down, yet the asymptote has shifted 3 units down. This implies that there has been a vertical shift of 3 units down and a vertical stretch.
The vertical shift is denoted by the variable "c" so c = -3:
[tex]\implies f(x)=a(2)^{kx}-3[/tex]
The vertical stretch is denoted by the variable "a". To find value of a, substitute the point of the y-intercept into the equation:
[tex]\begin{aligned}f(0) & = -1\\\implies a(2)^{k \times 0}-3 & =-1\\a-3 & = -1\\a-3+3 & = -1+3\\a & = 2\end{aligned}[/tex]
Therefore, as a = 2:
[tex]\implies f(x)=2(2)^{kx}-3[/tex]
From inspection of the given graph, the curve passes through point (4, 5). Substitute this point into the equation to find the value of k:
[tex]\begin{aligned}f(4) & = 5\\\implies 2(2)^{4k}-3 & =5\\2(2)^{4k}& =8\\(2)^{4k}& =4\\(2)^{4k}& =2^2\\4k & = 2\\k & = 0.5\end{aligned}[/tex]
Therefore, the equation of the function f(x) is:
[tex]\implies f(x)=2(2)^{0.5x}-3[/tex]
12 cans of soup each can is a cylinder with a radius of 3.5 cm and a height of 10 cm. the cans may be arranged in any way. the company would like to minimize the packaging costs involved with the creation of the container.
Answer:
2 layers, 3×2 cans per layer
Step-by-step explanation:
Factors of 12: 1, 2, 3, 4, 6, 12
The box can have 1 layer of 12 cans, 2 layers of 6 cans each, or 3 layers of 4 cans each.
In each case below, the total surface area is 2(LW + LH + WH)
1 layer, 12×1 cans
L = 84 cm; W = 7 cm; H = 10 cm
SA = 2996 cm²
1 layer, 6×2 cans
L = 42 cm; W = 14 cm; H = 10 cm
SA = 2248 cm²
1 layer, 4×3 cans
L = 28 cm; W = 21 cm; H = 10 cm
SA = 2156 cm²
2 layers, 6×1 cans per layer
L = 42 cm; W = 7 cm; H = 20 cm
SA = 2548 cm²
2 layers, 3×2 cans per layer
L = 21 cm; W = 14 cm; H = 20 cm
SA = 1988 cm² <--------------- smallest surface area
3 layer, 4×1 cans per layer
L = 28 cm; W = 7 cm; H = 30 cm
SA = 2492 cm²
3 layers, 2×2 cans per layer
L = 14 cm; W = 14 cm; H = 30 cm
SA = 2072 cm²
Determine the equation, in both factored and standard forms of the following parabola
The standard form of the equation of the parabola is y + 3 = (1/3) · (x - 3)² and The factored form of the equation of the parabola is y = (1/3) · x · (x - 6).
How to derive the two forms of the equation of the parabola
Mathematically speaking, parabolae are defined by second order polynomials. The standard form of the equation of the parabola is defined by:
y - k = C · (x - h)² (1)
Where C is the vertex constant.
And the factored form has this form:
y = k · (x - r₁) · (x - r₂) (2)
First, we determine the standard form of the equation of the parabola: (h, k) = (3, - 3) and (x, y) = (0, 0)
0 - (- 3) = C · (0 - 3)²
3 = 9 · C
C = 1/3
Then, the standard form of the equation of the parabola is y + 3 = (1/3) · (x - 3)². Now we proceed to determine the factored form of the parabola: (r₁ = 0, r₂ = 6), (h, k) = (3, - 3)
- 3 = k · (3 - 0) · (3 - 6)
- 3 = k · 3 · (- 3)
- 3 = - 9 · k
k = 1/3
The factored form of the equation of the parabola is y = (1/3) · x · (x - 6).
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Parent function Y equals 0.5 square root X is..
-increasing
-decreasing
-constant
Using translation concepts, it is found that:
The parent function y = [tex]0.5^x[/tex] is decreasing across it's domain because it's base, b, is such that 0 < |b| < 1.The function f shifts the parent function 8 units up.The function f shifts the parent function 5 units right.What is a translation?
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The parent function is:
[tex]y = 0.5^x[/tex]
It has a base with absolute value between 0 and 1, hence it is decreasing.
The changes to the function are given as follows:
y -> y + 8, hence the function was shifted 8 units up.x -> x - 5, hence the function was shifted 5 units right.More can be learned about translation concepts at https://brainly.com/question/4521517
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If the length of the hypotenuse of the right triangle whose legs measure 6 feet and 4 square root of 3 feet
The hypotenuse of the right triangle, with legs of 6 and 4√3 feet is 2√21 feet, computed using the Pythagoras Theorem.
The Pythagoras Theorem states that in a right triangle, the square of the hypotenuse is always equal to the sum of the squares of the other two legs.
If the hypotenuse is taken as a, and the two legs are taken as b and c, then by the Pythagoras Theorem, we can write that:
a² = b² + c².
In the question, we are given that a right triangle, has legs of lengths 6 feet and 4√3 feet each, and we are asked to find the length of the hypotenuse.
Thus, taking b = 6 and c = 4√3, in the above equation, we get:
a² = 6² + (4√3)²,
or, a² = 36 + 48,
or, a² = 84,
or, a² = (2√21)²,
or, a = 2√21.
Thus, the hypotenuse of the right triangle, with legs of 6 and 4√3 feet is 2√21 feet, computed using the Pythagoras Theorem.
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Will give 15 points. Rewrite each expression using the property indicated.
I. commutative: 4 x 5
2. associative: (12 x 7) x 8
3. identity: 32 x1
4.distributive: 6 x (8-5)
5.associative: (3+4) + 5
6.zero: 0 x 4
HELP HELP HELP
If you know algebra 1 then you can do these 5 quick algebra 1 questions for 50 points!
Only answer if you know the answer to all questions please! ;)
1. x = a
2. y = b
3. A vertical line has an undefined slope.
4. rise/run or Change in y/change in x (m) = y2 - y1 / x2 - x1
5. Rewrite the equation in slope-intercept form to determine the y-intercept.
What is the Equation of a Line?In slope-intercept form, the equation of a line in slope-intercept form is, y = mx + b, where m is the slope and the y-intercept = b.
1. The slope of a vertical line is undefined, therefore, the equation for a vertical line is given as: x = a, where a is the value of the x-intercept.
A vertical line that contains (a, b) will have the equation, x = a.
2. The slope of a horizontal line is 0, therefore, the equation of the horizontal line is, y = b, where b is the y-intercept.
A horizontal line that contains (a, b) will therefore have the equation, y = b.
3. A vertical line has an undefined slope.
4. For example, if we have the two points (3, 3) and (0, 5), two methods to find the slope are:
rise/run
or
Change in y/change in x (m) = y2 - y1 / x2 - x1 = 5 - 3 / 0 - 3 = 2/-3 = -2/3.
5. If we have an equation in point-slope form, for example, y - 3 = 2(x - 4), to find the coordinates of its y-intercept, rewrite the equation in slope-intercept form to determine the y-intercept:
y - 3 = 2x - 8
y = 2x - 8 + 3
y = 2x - 5
The y-intercept is -5, thus, the coordinates would be: (0, -5).
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write an equation for the graph below in terms of x
The linear equation for the graph in terms of x is given by: y = -0.5x - 3.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Looking at the graph, when x = 0, y = -3, hence the y-intercept is of b = -3. The graph also passes through point (2,-4), hence the slope is given by:
m = (-4 - (-3))/(2 - 0) = -1/2 = -0.5.
Hence the equation is:
y = -0.5x - 3.
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Find the surface area of the regular pyramid.
Answer:
384mmStep-by-step explanation:
The surface area of a square pyramid is 1/2 the product of its base perimeter & slant height.
SA = area of base + 1/2 (perimeter of base * slant height)
So, we can substitute 12 and 10 into this equation.
The area of the base is 12*12 (144). The perimeter of the base is 48mm.
144 + 1/2(48*10) = Surface Area.
144 + 240 = Surface Area.
384mm = Surface Area.
Hope that helps :)
i am not able to solve this problem
The length of the board is 0.665 meters wide. When the boarder is added in all 4 edges, the length decrease by 0.05 meters on both side. So, the remaining length across is 0.665 - 0.5 x 2 = 0.565, so b.
*but maybe it's not a rectangle*
samanth drew this pictogram
Answer:
la verdad noce no me acuerdo
Answer:
4
Step-by-step explanation:
There are 6 grey diamonds in the row labelled "cat".
Each diamond means two hours.
6 × 2 = 12
Samanth's table shows that cats sleep 12 hours.
Tony is going to use a circle that means 3 hours.
12 ÷ 3 = 4
Tony needs 4 circles to show 12 hours.
4 × 3 = 12
Tony will use 4 circles.
Find the value of the expression (x2−4)3x when x = 5.
Answer:
315
Step-by-step explanation:
You plug 5 in for x
(5^2-4)3(5) = 315
Answer:
(5^2−4)3(5)
25-4(3)(5)
15*21=315
Hope This Helps!!!
Write the expression two-cubed times seven as a numerical expression.
Answer:
See below
Step-by-step explanation:
2^3 is two cubed ...now multiply times 7
7 * 2^3
Factor the expression. q²r+ blank s^2t)(blankq^4r^2-6q^2rs^2t+blanks^4t^2
The equivalent expression of (q² − r²s) (q⁴ + q²r²s + r⁴s²) is q⁶ - r⁶s³
How to factor the expression?The expression is given as:
(q² − r²s) (q⁴ + q²r²s + r⁴s²)
Expand the expression
(q² − r²s) (q⁴ + q²r²s + r⁴s²) = q²(q⁴ + q²r²s + r⁴s²) − r²s(q⁴ + q²r²s + r⁴s²)
Open the brackets
(q² − r²s) (q⁴ + q²r²s + r⁴s²) = q⁶ + q⁴r²s + q²r⁴s² -q⁴r²s - q²r⁴s² - r⁶s³
Evaluate the like terms
(q² − r²s) (q⁴ + q²r²s + r⁴s²) = q⁶ - r⁶s³
Hence, the equivalent expression of (q² − r²s) (q⁴ + q²r²s + r⁴s²) is q⁶ - r⁶s³
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Complete questionFactor the expression. (q² − r²s) (q⁴ + q²r²s + r⁴s²)
A square piece of card has a square of side 2 cm cut out from
each of its corners. The remaining card is then folded along
the dotted lines shown to form an open box whose total
internal surface area is 180 cm².
What is the volume of the open box in cm³?
A 100 B 128 C 162 D 180 E 200
Answer:
E) 200
Step-by-step explanation:
Let the length of the side after cutting the corners =x cm
Length of the side before cutting the corners = x + 4 cm
Area of square before cutting = (x + 4)² square cm
Area of that square that was cut = 2*2 = 4 cm²
Area of 4 squares cut from all 4 corners = 4 * 4 = 16 cm²
Area of internal surface area = 180 square cm
(x + 4)² - 4*4 = 180
x² + 2*4*x + 4² - 16 = 180
{expand using the identity (a + b)² = a² + 2ab + b²) }
x² + 8x + 16 -16 = 180
x² + 8x - 180 = 0
x² + 18x - 10x - 180 = 0
x( x + 18) - 10(x + 18) = 0
(x + 18) (x - 10) = 0
x - 10 = 0 {Ignore x +18 = 0}
x = 10
Open box:length = x = 10 cm
breadth = x = 10 cm
height = 2 cm
Volume of open box = length * breadth * height
= 10 * 10 * 2
= 200 cm³
Write the standard form of the equation of the line through the pair of points (3,5) and (1,5).
The standard form of the equation of the line passing through the points (3,5) and (1,5) is given by
(Simplify your answer.)
Answer:
y = 5
Step-by-step explanation:
The standard form of a linear equation is Ax + By=C
But let's start with the slope-intercept form: y = mx+b, where m is the slope and b the y-intercept (the value of y when x=0).
M, the slope, may be calculated by using the Rise/Run between the two given points: (1,5) and (3,5):
Rise = (5-5) = 0 [Note that the value of y does not change when x = 1 or 3.]
Run is = (3-1)=2
Rise/Run (slope, m) is (0/2) or 0. [y does not change as a function of x. It is a flat, horizontal line]
The equation becomes y = (2/3)x + b
We need to find a value of b, the y-intercept, that forces the line to go through both points. This can be done by entering one of the points into the equation and solving for b:
y = (0)x + b
I'll use (1,5)
5 = (0)*(1) + b
b = 5
The equation becomes y = (0)x + 5 or y = 5
Standard form of the equation is Ax + By = C
A is 0, B is 1 and C is 5
y = 5
helllppppppppppp please
Answer:
4
Step-by-step explanation:
to find the x intercept of a line in standard form we can simply set y as 0 and find x
4x - 7(0) = 16
4x = 16
x = 4
the answer is 4
Find a number between 2- and 2.1251:
8
Uh
cals 1/2
10. MA bisects segment CB at midpoint M. Based on the definition of angle bisector and midpoint, find the value
of x and the following measures.
Middle
x =
MB.=
CM =
CB =
x+6
(92)
M
2r-4
B
Answer:
x = 10MB = 16CM = 16CB = 32Step-by-step explanation:
There are two different relations here that can be used to write equations for the value of x:
a perpendicular to a line creates a linear pair of right anglesa midpoint divides a segment into two congruent segmentsValue of xUsing the angle relation, we have ...
∠CMA ≅ ∠BMA
(9x)° = 90°
x = 90/9 = 10
Segment lengthsUsing the found value of x in the expressions for the segment lengths, we find ...
MB = 2x -4 = 2(10) -4 = 16
CM = x +6 = 10 +6 = 16 . . . . . . . congruent to MB, as it should be
CB = CM +MB = 16 +16 = 32
Can someone explain 03.05 Polynomial Identities and Proofs for me?
The polynomial Identities and an example of a proof of an identity have been explained below.
What are polynomial Identities and Proofs?Polynomial identities are defined as equations that are always true, regardless of the variable values. These polynomial identities are used while factorizing the polynomial or expanding the polynomial. These polynomial identities are;
(a + b)² = a² + b² + 2ab
(a - b)² = a² + b² - 2ab
(a + b)(a - b) = a² - b²
(x + a)(x + b) = x² + x(a + b)+ ab
Let us prove the polynomial identity (a + b)² = a² + b² + 2ab.
Now, (a + b)² is simply the product of (a + b) and (a + b).
That is; (a + b)² = (a + b) × (a + b)
This can simply be imagined to be a square whose side are (a + b) with its' area equal to (a + b)²
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The process of inferring conclusions about a population from data on selected individuals is called statistical _____.
inferential statistics is the answer.
Statistics is the study and manipulation of data, including ways to gather, review, analyze, and draw conclusions from data. The two major areas of statistics are descriptive and inferential statistics.
Inferential statistics use measurements from the sample of subjects in the experiment to compare the treatment groups and make generalizations about the larger population of subjects. There are many types of inferential statistics and each is appropriate for a specific research design and sample characteristics.
The most common methodologies in inferential statistics are hypothesis tests, confidence intervals, and regression analysis.
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77 = 88 because they both equal 1. Peter takes one part away from each. Will the results be equal? Use the drop-down menus to complete an explanation.
Yes, the results will be equal as it follows from the task content that both numbers were equal initially.
What will he the equality verdict on both results?As evident in the task content, it follows that the numbers 77 and 88 although, not equal in the real sense, are equal according to the task content.
Hence, it follows that when equal parts are taken away from the two numbers, they would still be equal as both numbers were equal initially.
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Find m, given that the three angles of a triangle are (m+18), (2m+28) and (3m+47).
Step-by-step explanation:
As all angles in a triangle add up to 180°
we can write:
(m+18)+(2m+28)+(3m+47) = 180
6m + 93 = 180
6m = 180 - 93
6m = 87
m = 87 / 6
m = 14.5
If m(arc BY)= 44, enter the
mZY AC.
(The figure is not drawn to scale.)
Answer: [tex]68^{\circ}[/tex]
Step-by-step explanation:
Assuming AC is a tangent, this means [tex]m\angle BAC=90^{\circ}[/tex].
Since arc BY measures 44 degrees, by the inscribed angle theorem, [tex]m\angle BAY=22^{\circ}[/tex].
This means [tex]m\angle YAC=90^{\circ}-22^{\circ}=68^{\circ}[/tex]
what is the negative-2y+13 answer?
The negative of the expression -2y+13 is 2y-13.
Given Expression:-2y+13
We know that an expression is a combination of numbers, variables, symbols, indeterminants, etc. It is not expressed in equal to form. It expresses a relationship but we cannot find the value of variable because it is usually not present in equal to form.
We have to find the negative of the expression -2y+13 and to find out that we need to just put a negative mark in front of the expression and then adjust the expression for finding the negative of that expression.
Negative of -2y+13=-(-2y+13)
=2y-13.
Negative of an expression expresses opposite thing.
Hence the negative of -2y+13 is 2y-13.
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Find the volume of a cylinder with a radius of 4.8 cm and a height of 14.6 cm. [Use it =
3.14]
56.2 cm³
1056.24 cm³
O 156.2 cm³
820 cm³
Answer:
1056.24 cm^3
Step-by-step explanation:
The volume of a cylinder is [tex]\pi r^2h[/tex]. The problem says to use [tex]\pi[/tex]=3.14
Plug in your numbers [tex]3.14*4.8^2*14.6=1056.24[/tex]