The first digit of a string of 2002 digits is a 1. Any two-digit number formed by consecutive digits within this string is divisible by 19 or 31. What is the largest possible last digit in this string

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).

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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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*

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

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.

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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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:

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):

Therefore, 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]

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

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

The linear equation for the graph in terms of x is given by: y = -0.5x - 3.

A linear function is modeled by:

y = mx + b

In which:

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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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]

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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The polynomial Identities and an example of a proof of an identity have been explained below.

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 rigid transformations that maps ΔABC onto ΔFED by reflection then translation.

The correct option is (B).

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:

Answer:

See below

Step-by-step explanation:

2^3    is   two cubed     ...now multiply times 7

7 * 2^3    

Answer:

Step-by-step explanation:

There are two different relations here that can be used to write equations for the value of x:

Using the angle relation, we have ...

  ∠CMA ≅ ∠BMA

  (9x)° = 90°

  x = 90/9 = 10

Using 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

The equivalent expression of (q² − r²s) (q⁴ + q²r²s + r⁴s²) is  q⁶  - r⁶s³

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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Factor the expression. (q² − r²s) (q⁴ + q²r²s + r⁴s²)

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.

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

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.

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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Yes, the results will be equal as it follows from the task content that both numbers were equal initially.

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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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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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

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

           length =  x = 10 cm

          breadth = x = 10 cm

         height  = 2 cm

Volume of open box = length * breadth * height

                                  = 10 * 10 * 2

                                  = 200 cm³

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

Answer:

tanΘ = [tex]\frac{5}{12}[/tex]

Step-by-step explanation:

tanΘ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{5}{12}[/tex]

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]

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.

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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Answer:

Step-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 :)

Using translation concepts, it is found that:

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:

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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!!!