Amy, bill and cara each played a game. amy's score was ten times bill's score. cara's score was half of amy's score. write down the ration of amy's score to bill's score to cara's score. give your answer in its simplest form

The number of unique permutations that may be made from all of the letters in each word 210.

The number of alternative arrangements of such an object in different orders or sequences is referred to as its permutation. These are typically computed using factorials, as denoted by the symbol. Only natural numbers are utilized in factorials.

Assume we wish to find the number of various permutations of n objects, where p items are one type, q items are another, r items are yet another, and so on.

For the word 'UNUSUAL' there are 7 letters. Then there are 7! possibilities.

We have to divide this by the number of possibilities where letters would replace the same letters.

there are letter U repeated 3 time so 3!

= [tex]\frac{7!}{3!}[/tex]

= 210

the number of unique permutations that may be made from all of the letters in each word 210.

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The value of the algebraic expression -2y³ + y² - 3y + 4, when y = 3 is evaluated as: -50.

An algebraic expression contains a variable. To find the value or evaluate the algebraic expression, plug in the the value of the variable and solve accordingly.

Given the algebraic expression,

-2y³ + y² - 3y + 4, when y = 3

Substitute the value of y into the algebraic expression:

-2(3)³ + (3)² - 3(3) + 4

Evaluate the exponents in the expression:

-2(27) + 9 - 9 + 4

-54 + 9 - 9 + 4

Add together to get the value of the algebraic expression:

-54 + 0 + 4

-54 +  4

= -50

In summary, the value of the algebraic expression -2y³ + y² - 3y + 4, when y = 3 is evaluated as: -50.

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Answer:

[tex]x^3y^{12}[/tex]

Step-by-step explanation:

[tex]\left(xy^4\right)^3\\\left(xy^4\right)^3=x^3\left(y^4\right)^3\\=x^3\left(y^4\right)^3\\=(y^4)^3\\=(y)^{4\times 3}\\= y^{12}\\= x^3y^{12}[/tex]

[tex]\textsf{Hi Brainy User, I'm Here to Help you!}[/tex]

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

[tex]\textsf{By using the \textbf{Exponent Property}, we can simplify this.}[/tex]

[tex]\textsf{This is what it states:}[/tex]

[tex]\sf{(x^m)^n=x^{(m*n)}}[/tex]

[tex]\textsf{Multiply:}[/tex]

[tex]\sf{(xy^4)^3=x^3y^{3*4}=x^3y^{12}}[/tex]

[tex]\Large\overbrace{\underbrace{\boldsymbol{\rm{Reflection - RoSe}}}}^\star_\star[/tex]

Answer: AED and BEC are isosceles triangles

Definition: A quadrilateral having two and only two sides parallel is called a trapezoid.

Formula: distance between two points =√(x1-x2)^2-(y1-y2)^2

Given,

ABCD is a trapezoid

AC and BD are diagonals

E is the intersection of two diagonals

A(0,0), B(3,3), C(9,3), D(12,0), E(6,2)

distance between BE=√10

distance between CE=√10

BE=CE

Similarly, AE=DE

Therefore, AED and BEC are isosceles triangles

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Answer:

13.85 million $

Step-by-step explanation:

the man just add 12.35 and 1.5

therefore = 13.85 million $

Answer:

Step-by-step explanation:

slope = (y2-y1) ÷ (x2-x1)

    = ((-7)-(-19)) ÷ ((-2) - (1))

    = 12 ÷ -3

 m  = -4

Answer:

C. 6

Step-by-step explanation:

$20 - $13 + $2 - $8 + $5 =

= $7 + $2 - $8 + $5

= $9 - $8 + $5

= $1 + 5

= $6

The co-ordinates of the image after translation are R"(2,1),S"(-1,7) and T"(2,7).

A translation is a geometric change in Euclidean geometry that involves moving each point in a figure, shape, or space by the same amount in one direction. A translation can also be thought of as moving the origin of the coordinate system or as adding a constant vector to each point.

When a point is rotated 90° counter clockwise, the co-ordinates of the point say A(x ,y) changes to A"(y,-x).

The given co-ordinates are:  R(-7, - 5), S(-1,- 2), and T(-1.- 5 ).

So when this co-ordinates are translated by rotating 90° counterclockwise.

R(-7, -5) →R'(5,-7)

S(-1,- 2) →S'(2,-1)

T(-1.- 5) →T'(5,-1)

Now the figure is translated 3 units left and 8 units up the new co-ordinates is given by (x-3,y+8).

So when this co-ordinates are translated the new co-ordinates are:

R'(5,-7)→R"(2,1)

S'(2,-1)→S"(-1,7)

T'(5,-1)→T"(2,7)

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The value of sinФ = 0.139 for the given cosФ = 0.139 and tanФ > 0.

The given trigonometric function is-

cosФ = 0.139.

We know the relation of sin and cos functions.

sin²Ф + cos²Ф = 1

Thus,

sinФ = √(1 - cos²Ф)

Put the value of cosФ = 0.139

sinФ = √(1 - 0.139²)

sinФ = √0.981

sinФ = 0.139

Thus, the value of the trigonometric function sinФ = 0.139.

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Answer:   4*8 - 4*1

Or you could write it as 4(8) + 4(-1)

The distributive property in general is a(b+c) = ab+ac. We multiply the outer term 'a' with each term inside.

The minimum cost is $210.

Forgetting the situation for just a second, we can take a look atthe equation.

c(x)=x^2-40x+610

It is a parabola that opens upward and has a minimum value.

That minimum value will be the minimum cost of the taco stand.

The equation x=-b/2a gives you the axis of symmetry of theparabola. Basically, it goes right down the middle of the parabola,right through its minimum

In the equation  c(x)=x^2-40x+610, a=1 and b=-40

x=-b/2a

x=-(-40/2(1)) = 20

So 20 tacos should be sold to achieve the minimum cost.

To find the cost, return to the original equation.

c(x)=x^2-40x+610

c(20)=(20)^2-40(20)+610 = 210

So the minimum cost is $210.

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.

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The minimum cost of the function is $210.

A function is defined as the representation of  a set of variables known as the domain which are mapped onto another set of variables called the range.

The most common function is of the form y = f(x) , where x is the independent variable and y is the dependent variable and f(x) is the function.

The given function is of the form:

c(x) = x² - 40 x + 610

To find the maximum or minimum point of the function we find the second degree derivative of the function.

c'(x)=2x -40

Now we find the second degree derivative.

c"(x) = 2 > 0 so we know that c(x) is minimum at x for c'(x)=0.

Therefore c'(x) = 0

or , 2x-40 = 0

or , x = 20

Now the minimum value of the function is

c(20) = 20² - 40 (20) + 610

or, c(20) = 400 - 800 + 610

or, c(20) = 210

Hence the minimum value of the function is $210.

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Based on the number of people employed in education and health service industries in 2009, the number of new jobs that will be gained between 1/2009 and 1/2016 is b. 2,826,800 people.

The number of total jobs in 2016 can be found as:

= Number of jobs in education and health service industries x (1 + rate of increase)

= 19,200,000 x (1 + 14.8%)

= 19,200,000 x 1.148

= 22,041,600 people

The number of new jobs are:

= 22,041,600 people - 19,200,000

= 2,841,600 people

= 2,826,800 people approximate

Graph and options for the question are:

Education and Health Services - All Employees, 2000-2009 A line graph titled Education and Health Services, All Employees, 2000 to 2009, where the x-axis shows years and the y-axis shows all employees, in thousands. Line starts at 15,000 on January 2000, and increases gradually to 16,000 on January 2002, 17,200 on January 2005, 18,100 on January 2007, and 19,200 on January 2009.

a. 21,926,800

b. 2,826,800

c. 16,273,200

d. 1,790,600

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Answer:

b on edge

Step-by-step explanation:

Using the given linear function, it is found that:

a) The initial height of the balloon is of 6 feet, as before the balloon was released t = 0 and h(0) = 6.

b) The values of t must be greater than or equal to 0, because a negative time does not does not make sense for the given situation. The graph would start at the origin and would only go to the right, in a positive direction.

A linear function is modeled by:

y = mx + b

In which:

For this problem, the linear function is:

h(t) = 2t + 6.

From the y-intercept, it is found that:

The initial height of the balloon is of 6 feet, as before the balloon was released t = 0 and h(0) = 6.

Since time cannot be negative, the domain is t ≥ 0, and:

The values of t must be greater than or equal to 0, because a negative time does not does not make sense for the given situation. The graph would start at the origin and would only go to the right, in a positive direction.

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Answer:

x = five over two and x = −3

Step-by-step explanation:

Let's solve your equation step-by-step.

2x2+x=15

Step 1: Subtract 15 from both sides.

2x2+x−15=15−15

2x2+x−15=0

Step 2: Factor left side of equation.

(2x−5)(x+3)=0

Step 3: Set factors equal to 0.

2x−5=0 or x+3=0

x=5/2 or x=−3

Answer: to the nearest hundredth

I hope this helps!

Answer:

its true, true, false, false

Step-by-step explanation:

a is true b is true c is false and d is false

Answer:

25

Step-by-step explanation:

By the segment addition postulate,

[tex]XY+YZ=XZ \\ \\ 8a+6a=2a+50 \\ \\ 14a=2a+50 \\ \\ 12a=50 \\ \\ a=\frac{25}{6} \\ \\ \therefore YZ=6(25/6)=25[/tex]

The complete statement is 5 + 7

The commutative property of addition is a mathematical rule stating that a change in the order or arrangement of the numbers being added does not affect the sum.

It is also important to note the following sign changes;

(-) (-) = +

(+) (+) = +

(-)(+) = -

(+)(-) = -

Given the expression;

5 - ( -7)

We know that the signs (-)(-) is equivalent to (+) sign

Substitute into the expression;

5 + 7

Thus, the complete statement is 5 + 7

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Answer:

The equation in slope intercept form of the line that is parallel to the group in each equation and passes through the given point (3,-7) is y = -2/7x - 6.14

Step-by-step explanation:

It is given that the line that is parallel to the group in each equation and passes through the given point 7y= -2x + 5; (3,-7) and we need to write the equation in slope intercept form of the same line.

Now,

The slope of parallel lines is the same. By changing the equation to slope-intercept form, get the slope in the first line;

=> 7y= -2x + 5

=> y= -2/7x + 5/7

So, the slope = -2/7

Further,

Given the point and the knowledge that the second line would similarly have a slope of -2/7 and the point is (3, -7). With these numbers, we can construct an equation in the slope-intercept form and apply it to get the y-intercept;

=> y = mx + b

=> -7 = -2/7 × 3 + b

=> -7 + 2/7 × 3 = b

=> b = -6.14

Now, put the value of y-intercept back into the equation;

=> y = -2/7x - 6.14

Therefore, the equation in slope intercept form of the line that is parallel to the group in each equation and passes through the given point (3,-7) is y = -2/7x - 6.14

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Given data,

First take work sheet 4.

Based on the given conditions formulate :

                  = [tex]\sqrt{16}[/tex]

Factor and rewrite the radicand in exponential form,

                 = [tex]\sqrt{4^{2} }[/tex]

Simplify the radical form,

                = 4

Therefore,         [tex]\sqrt{16} = 4[/tex]

Based on the given conditions formulate :

          = [tex]\sqrt{49}[/tex]

Factor and rewrite the radicand in exponential form,

           = [tex]\sqrt{7^{2} }[/tex]

Simplify the radical form,

          = 7

Therefore,      [tex]\sqrt{49} = 7[/tex]

Factor and rewrite the radicand in exponential form,

                 = [tex]\sqrt{5^{2} }[/tex]

Simplify the radical form,

                  = 5

Therefore,         [tex]\sqrt{25} = 5[/tex]

Factor and rewrite the radicand in exponential form,

              = [tex]\sqrt{12^{2} }[/tex]

Simplify the radical form,

              = 12

Therefore,          [tex]\sqrt{144} = 12[/tex]

Factor and rewrite the radicand in exponential form,

               = [tex]\sqrt{10^{2} } +\sqrt{7^{2} }[/tex]

Simplify the radical form,

               = 10+7

               = 17

Therefore,    [tex]\sqrt{100} +\sqrt{49} = 17[/tex]

Factor and rewrite the radicand in exponential form,

                = [tex]\sqrt{14^{2} }[/tex]

Simplify the radical form,

                = 14

Therefore,        [tex]\sqrt{196} = 14[/tex]

Factor and rewrite the radicand in exponential form,

                     = [tex]3^{2}[/tex] x [tex]\sqrt{11^{2} }[/tex]

Simplify the radical form,

                     = 9 x 11

                     = 99

Therefore,         [tex]3^{2}[/tex] x [tex]\sqrt{121} = 99[/tex]

Factor and rewrite the radicand in exponential form,

               = [tex]\sqrt{13^{2} }[/tex] x [tex]\sqrt{6^{2} }[/tex]

Simplify the radical form,

                 = 13 x 6

                 = 78

Therefore,      [tex]\sqrt{169}[/tex] x [tex]\sqrt{36} = 78[/tex]

Factor and rewrite the radicand in exponential form,

             = [tex]\sqrt{4^{2} }[/tex] x [tex]\sqrt{5^{2} }[/tex]

Simplify the radical form,

             = 4 x 5

             = 20

Therefore,     [tex]\sqrt{16}[/tex] x [tex]\sqrt{25}[/tex] = 20

Given data,

First take work sheet 5.

Therefore,

                     [tex]\sqrt{400} = 20[/tex]

Therefore,

                     [tex]\sqrt{2500} = 50[/tex]

Therefore,

                     [tex]\sqrt{6400} = 80[/tex]

Therefore,

                   [tex]\sqrt{900} = 30[/tex]

Hence,

              [tex]\sqrt{16} = 4\\\sqrt{49} = 7\\\sqrt{25} = 5\\\sqrt{144} = 12\\\sqrt{100} + \sqrt{49} = 17\\\sqrt{196} = 14\\[/tex]

               [tex]3^{2}[/tex] x [tex]\sqrt{121}[/tex] = 99

             [tex]\sqrt{169}[/tex] x [tex]\sqrt{36}[/tex] = 78

              [tex]\sqrt{16}[/tex] x [tex]\sqrt{25}[/tex] = 20

                 [tex]\sqrt{400} = 20\\\sqrt{2500} = 50\\\sqrt{6400} = 80\\\sqrt{900} = 30[/tex]

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Answer: somehow got that v

Step-by-step explanation:

f=

x6+8x5+17x4−8x3−45x2+27

x

Answer:

[tex]\sf 22\dfrac{1}{2}\; years[/tex]

Step-by-step explanation:

[tex]\textsf{First convert all mixed fractions to improper fractions: }\\\\3\dfrac{2}{3} = \dfrac{3 \times 3 + 2}{3}= \dfrac{11}{3}\\\\18\dfrac{5}{6 } = \dfrac{18 \times 6 + 5}{6} = \dfrac{113}{6}[/tex]

Let Carlo's age be C

Carlo's age = sister's age + 11/3

[tex]\sf == > C = \dfrac{113}{6} +\dfrac {11}{3}\\\\\textsf{Multiply both sides by 6 to eliminate the denominator}\\\\\sf 6C = 6\cdot\dfrac{113}{6} + 6\cdot\dfrac {11}{3}\\\\[/tex]

[tex]\sf == > C = \dfrac{113}{6} +\dfrac {11}{3}\\\\\textsf{Multiply both sides by 6 to eliminate the denominator}\\\\\sf 6C = 6\cdot\dfrac{113}{6} + 6\cdot\dfrac {11}{3}\\\\\sf 6C = 113 + 22 = 135\\[/tex]

[tex]\textsf {Divide both sides by 6}\\\\\sf C = \dfrac{135}{6} \\\\\textsf {Reduce $\dfrac{135}{6}$ by dividing numerator and denominator by 3}\\\\== > C = \dfrac{135 \div 3}{6\div3} = \dfrac{45}{2}[/tex]

[tex]\textsf{So Carlo's age is $\dfrac{45}{2}$ or $22\dfrac{1}{2}$ years}[/tex]

The image of 3 and the image of -2 are 2 and 7, respectively

The equation of the function is given as

f(x) = x^2 - 2x - 1

To determine the image of 3 and the image of -2, we set x to the following values

x = 3 and -2

Substitute x = 3 and -2 in the equation f(x) = x^2 - 2x - 1

So, we have

f(3) = (3)^2 - 2(3) - 1 = 2

f(-2) = (-2)^2 - 2(-2) - 1 = 7

Hence, the image of 3 and the image of -2 are 2 and 7, respectively

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When the train on one route stop there every 9 minutes and trains on the other route stop there every 6 minutes, the time when they will stop at same time is 18 minutes.

From the information, the train on one route stop there every 9 minutes and trains on the other route stop there every 6 minutes.

Therefore, the time when will they stop at same time will be the lowest common multiple for 9 and 6. This is 18. Therefore, 18 minutes is the appropriate answer.

Therefore, the the time when they will stop at same time is 18 minutes.

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Trains on two different routes at the same train station. Train on one route stop there every 9 minutes and trains on the other route stop there every 6 minutes. When will they stop at same time?

The required solution of the number to the nearest 10 , 100 and 1000 is 1260, 1300, 1000.

A number that is easily multiplied, divided, etc., and especially a number that ends in zero.

Given:

A school has 1256 pupils write this number to the nearest 10 , 100 and 1000

According to given question we have

⇒ Round off to 10 for 1256 is 1250 or 1260 but nearest to 1256 is 1260.

⇒  So, round off to the nearest 10 is 1260.

⇒ Round off to 100 for 1256 is 1200 or 1300 but nearest to 1260 is 1300.

⇒  So, round off to the nearest 100 is 1300.

⇒  Round off to 1000 for 1256 is 1000 or 2000 but nearest to 1256 is 1000.

⇒  So, round off to the nearest 1000 is 1000.

∴  The answer is 1260,1300,1000.

Therefore, the required solution of the number to the nearest 10 , 100 and 1000 is 1260, 1300, 1000.

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Answer:

3645, 10935

Step-by-step explanation:

1215*3 = 3645

3645*3= 10935

The slope Intercept and the standard form of the equation are y = -1/2x - 3 and x + 2y = -6

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

The given parameters are

y= -3 and x=-6

The above represent the y and the x intercepts

i.e.

y-intercept = -3

x-intercept = -6

A linear equation is represented as

y = mx + c

Where

c = y-intercept = -3

So, we have

y = mx - 3

At x-intercept = -6, we have

y = 0

So, we have

0 = m(-6) - 3

This gives

m = -1/2

So, we have

y = -1/2x - 3 --- slope-intercept form

Multiply through by 2

So, we have

2y = -x - 6

Rewrite as

x + 2y = -6 ----- standard form

Hence, the slope Intercept and the standard form of the equation are y = -1/2x - 3 and x + 2y = -6

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