a combination lock requires three selections of numbers, each from 1 through 35. suppose the lock is constructed in such a way that no number may be used twice in a row, but the same number may occur both first and third. for example, 20 13 20 would be acceptable, but 20 20 13 would not. how many different combinations are possible? to answer this question, note that some combinations will consist of three different numbers, whereas in others the first and third numbers can be the same. the total number of combinations is

The area of the given polygon is 30 square units.

The area of a triangle can be calculated using the formula 1/2[x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)] where (x₁, y₁), (x₂, y₂) and (x₃, y₃) are the coordinates of its vertices. This formula is also useful in finding the area of any polygon with given coordinates.

The area of the given polygon can be calculated by the expression of the area of triangle as 1/2[x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)].

The given polygon can be divided into two ΔABC and  ΔACD,

Then, the area is given as follows,

Area of ΔABC +  Area of ΔACD

= 1/2|[-3(4 - 1) + -3(1 - 1) + 7(1  - 4)]| + 1/2|[-3(1 - 4) + 7(4 - 1) + 7(1 - 1)]|

= 1/2 × 30 + 1/2 × 30

= 30

Hence, the area of the given polygon is 30 square units.

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The equation of line passing through points [tex](x_{1} ,y_{1} )[/tex] = (4,19) and [tex](x_{2},y_{2})[/tex] =

( 8,23 ) is represented in the slope intercepted form as y = x + 15

When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilise the slope intercept formula,

y = mx + b. (0, b) The symbol b in the formula stands for the y value of the y intercept point.

According to the given information

We are given with two points

[tex](x_{1} ,y_{1} )[/tex] = (4,19)

[tex](x_{2},y_{2})[/tex] = ( 8,23 )

So

Now we need to find the slope of the given line having the above coordinate points

m = [tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]

Putting the values

We get

m = [tex]\frac{23-19}{8-4}[/tex]

m = [tex]\frac{4}{4}[/tex]

m = 1

Equation of line passing through points [tex](x_{1} ,y_{1} )[/tex] = (4,19) and having

slope = 1

[tex]y-y_{1} = m(x-x_{1})[/tex]

y - 19 = x - 4

y = x + 15

So

The equation of line passing through points [tex](x_{1} ,y_{1} )[/tex] = (4,19) and [tex](x_{2},y_{2})[/tex] =

( 8,23 ) is represented in the slope intercepted form as y = x + 15

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a. To find the value of the home in the year 2000, we need to find how many 16-year intervals have passed between 1992 and 2000. Since 2000 is 8 years after 1992, we have that $\frac{8}{16} = \frac{1}{2}$ 16-year intervals have passed. This means that the value of the home has doubled once since 1992, so it is now worth $136,500 * 2 = $273,000.

b. The growth in housing value as a function of time in t years since 1992 can be represented by the equation $V(t) = 136,500 * 2^{\frac{t}{16}}$, where $V(t)$ is the value of the home in t years after 1992 and 2 is the factor by which the value has doubled every 16 years.

c. The growth in housing value as a function of time in d decades since 1992 can be represented by the equation $V(d) = 136,500 * 2^{\frac{d * 10}{16}}$, where $V(d)$ is the value of the home in d decades after 1992 and 2 is the factor by which the value has doubled every 16 years.

d. To find the value of the home 1.5 decades after 1992, we can use the equation $V(d) = 136,500 * 2^{\frac{d * 10}{16}}$. Plugging in $d = 1.5$, we get $V(1.5) = 136,500 * 2^{\frac{1.5 * 10}{16}} = 136,500 * 2^{0.9375} = $351,284.375.

Answer: Simplify each radical, then combine.

Exact Form:

2√6+ 3.85

Decimal Form:

8.74897948

The linear function that represents c, the total cost, when x tickets are ordered is

c=5.50+20.50x

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form.

Let

The overall price is c.

the quantity of tickets, x

the price of one ticket, excluding service charges, is z.

Knowing this

108=5.50+5z

finding z

z=20.50

therefore

The linear equation equals

c=5.50+20.50x

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Answer: a= 16

Step-by-step explanation:

a^2 + 30^2 = 34^2

a^2 + 900 = 1,156

a^2 = 256

a = 16

Answer:

Step-by-step explanation:

As the ticket prices at an outdoor theatre performance are $2.50 for children and $5.00 for adults. one evening, $6350 is collected from a total of 1900 people attending. There are 640 adult and 1260 childrens.

Given in the questions:

Ticket price in outdoor Theater = $2.50

For Children = $5.00

Total tickets collected in evening = $6350(collected from 1900 people)

Let p be the adult and

1900 - p be the children's who attained the show.

Now,

   2.5 × (1900- p) +5p = 6350

⇒ 4750 - 2.5p +5p =6350

⇒ 2.5p = 1600

⇒ p = 1600/2.5

⇒ p = 640

Since,

p = 640

Therefore,

   1900 - p = children

⇒ Children = 1900 - 640

⇒ Children = 1260

Therefore, there are total 640 adults and 1260 children's in the theater.

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Out of the 750 registered voters in the precinct, 480 people actually voted in the primary selection.

We have 750 registered voters in one precinct and in a primary selection 64 out of 100 voters actually voted.

Out of 100 people, only 64 voted. So, the percentage of people voted can be calculated as follows -

64 = x% of 100

64 = x/100 x 100

x = 64%

So -

64% 0f 750

(64/100) x 750

480

Therefore, 480 people out of 750 registered voters in one precinct actually voted.

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Answer: 72 cm

Step-by-step explanation:

78 is the hypotenuse, so that it will be the c

30^2 + b^2 = 78^2

900 + b^2 = 6084

b^2 = 5184

b= 72cm

Answer:

20T+12L[tex]\geq[/tex]200

T+L[tex]\leq[/tex]18

Step-by-step explanation:

Therefore ,Since 2.7406 > 2.023, reject H0 and conclude that the mail-order business is not achieving its goal.

A test statistic is a statistic used for testing statistical hypotheses. A test statistic, which is a tally of a data set that can be used to conduct the test and boils the data down to a single figure, is a common way to characterize a hypothesis test.

Here,

a) H0 : u > 6 days

Ha :  u < 6 days

Thus,

n=39

x'=6.65

α=1.5

b) test statistics = Z

Z=[tex]\frac{x'-u}{\alpha /\sqrt{n } }[/tex]

Z=[tex]\frac{6.65-6}{1.5 /\sqrt{39 } }[/tex]

Z=2.71

c) p value =P(Z<2.71)

p value = 1 - P(Z<2.71)

p value = 0.9966

Since 2.71 > 2.023, reject H0 and conclude that the mail-order business is not achieving its goal.

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Answer:

Here are six equivalent expressions to 12x - 6:

6(2x - 1)

3(4x - 2)

2(6x - 3)

1(12x - 6)

4(3x - 1)

(12x - 6) + 0

These expressions are all equivalent to 12x - 6 because they all have the same value, regardless of the value of x. This is because the terms on the right side of the equation cancel out, leaving only the constant value on the left side. For example, in the first expression, 6(2x - 1), the 2x and -1 terms cancel out, leaving only 6. This is the same for the other expressions listed above.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Here are six equivalent expressions to the given expression:

Note that in each of the above expressions, the value of 12x - 6 is preserved, but the terms and the order of operations may be different. For example, in the second expression, the subtraction has been expressed as addition with a negative number, and in the fourth and sixth expressions, the subtraction has been expressed as multiplication with a fraction.

Answer:

A fraction bar separates the numerator and denominator of a fraction. It indicates that a division of the numerator by the denominator will be performed.

Step-by-step explanation:

In math, a fraction bar can be defined as a visual representation of fractions that helps in comparing fractions and carrying out operations with fractions. Fraction bars or fraction strips are a part-to-whole representational model. Each part of a fraction bar represents one unit out of a whole.

Answer:To separate the top and bottom numbers.

Step-by-step explanation:In math, a fraction bar can be defined as a visual representation of fractions that helps in comparing fractions and carrying out operations with fractions.

Answer:

C. Drawing a line perpendicular to [tex]\overline{AC}[/tex] through point [tex]B[/tex]

Step-by-step explanation:

The triangles formed by the perpendicular can be proved congruent by HL, and thus [tex]\angle A \cong \angle C[/tex] by CPCTC.

Answer:

Step-by-step explanation:

x=23

I think

5x+-3=5x+20

add 3 on both sides canceling the -3 so then you get

5x=5x+23

subtract the 5x from both sides so then you get

x=23

By using $9,455 dollars we can get 151 bags of chips and $7,600 dollars we can get 122 bags of chips and 16000 bags for $1,000,000 dollars.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that you can buy 2 bags of chips for $125.

We need to find how many bags of chips we can get by $9,455 dollars,

$7,600 dollars and $1,000,000 dollars.

2/125=x/9455

Apply cross multiplication

2×9455=125x

18900=125x

Divide both sides by 125

x=151

So 151 bags we can get by using $9,455 dollars.

Now for $7,600 dollars.

2/125=x/7,600

2(7600)=125x

15200=125x

x=121.6 =122

So 122 bags we can get by using $7,600 dollars.

Now for $1,000,000

2/125=x/1,000,000

2000000=125x

Divide both sides by 125

16000=x

16000  bags for $1,000,000

Hence, 151 bags we can get by using $9,455 dollars, 122 bags we can get by using $7,600 dollars and 16000  bags for $1,000,000

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If a  traveler is walking on a moving walkway airport. The traveler's speed off the walkway is 5 ft/sec and the speed of the moving walkway is 3 ft/sec.

Speed can simply be defined as how fast an object move.

Let t represent the traveler's speed in ft/sec

Let w represent the walkway's speed in ft/sec

So,

t-w =2

t+w=8

Add the equation

2t =10

Divide both side by 2t

t= 10/2

t=5fr/sec ( traveler's speed )

Speed of moving walkway

t+w =8

5+w=8

w=8-5

w=3ft/sec

Therefore the traveler's speed off the walkway is 5 ft/sec and the speed of the moving walkway is 3 ft/sec.

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The value of the variable 'x' is less than 3 and the value of the variable 'r' is greater than negative 5.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequalities are given below.

-2r < 10 and -6 < -2x

The value of the variable 'r' is given as,

-2r < 10

2r > -10

r > - 10/2

r > - 5

The value of the variable 'x' is given as,

-6 < -2x

2x < 6

x < 6 / 2

x < 3

The value of the variable 'x' is less than 3 and the value of the variable 'r' is greater than negative 5.

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The horizontal asymptote of function f(x) is y=6.5, which is a straight line, which means that even if time is infinite, the pH of the mouth will not rise above 6.5, which is the normal pH of the mouth.

A function's horizontal asymptote is a horizontal line with which the function's graph appears to coincide but does not actually coincide. The horizontal asymptote is used to determine the behavior of the function.

When either lim x f(x) = k or lim x - f(x) = k, the horizontal asymptote of a function y = f(x) is a line y = k. . It is commonly abbreviated as HA. In this case, k is a real number that the function approaches when x is extremely large or extremely small.However, the maximum number of asymptotes that a function can have is 2.

Given,

[tex]f(x)=\frac{6.5x^2-89.4x+3734}{x^2+576}[/tex]

The horizontal asymptote of the function f(x) can be determined by

[tex]y=\lim_{x \to \infty} f(x)\\\\=\lim_{x \to \infty}\frac{6.5x^2-89.4x+3734}{x^2+576}\\\\=\lim_{x \to \infty}\frac{x^2(6.5-\frac{89.4}{x}+\frac{3734}{x^2})}{x^2(1+\frac{576}{x^2})}\\\\=\lim_{x \to \infty}\frac{(6.5-\frac{89.4}{x}+\frac{3734}{x^2})}{(1+\frac{576}{x^2})}\\\\=\frac{(6.5-\frac{89.4}{ \infty}+\frac{3734}{ \infty})}{(1+\frac{576}{ \infty})}\\\\=\frac{6.5-0+0}{1+0}\\\\=\frac{6.5}{1}=6.5[/tex]

Thus, the horizontal asymptote of function f(x) is y=6.5 which is straight line which means even the time reaches infinity the pH of mouth will not increase more than 6.5, which is the normal pH of mouth.

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Your question is incomplete, here is the complete question.

The function [tex]f(x)=\frac{6.5x^2-89.4x+3734}{x^2+576}[/tex] models the pH level f(x) of a mouth x minutes after eating food containing sugar. The graph of this function is shown.

What is the equation is the horizontal asymptote associated with is function? Describe what this means in terms of mouth's pH level over time.

The coordinates of midpoint D from the given triangle ABC is (-4x, 0).

A midpoint of a line segment is the point on a segment that bisects the segment into two congruent segments.

The formula to find the midpoint of line segment is (x, y) = [(x1+x2)/2, (y1+y2)/2]

From the given figure, the coordinates are A(-6x, 4y) and B(-2x, -4y) and C(8x, -2y)

D(x, y)=[(-6x-2x)/2, (4y-4y)/2]

= (-4x, 0)

Therefore, the coordinates of midpoint D is (-4x, 0).

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Answer: A song costs 0.99$, and an album 9.99$

Step-by-step explanation:

14.94=5x+1y

22.95=3x+2y

29.88=10x+2y

22.95=3x+2y

subtract

6.93=7x

x=0.99$

y=9.99

The expression that does not factor on the mentioned is m² + 1.

Because other expression can be factored, while m² + 1 has no factor form. For make it clear we can calculate to find the form expression and find the calculate power or result.

m³ + 1 =

m³ - 1 =

m² - 1 =

        and then it could be, m² - 1 = (m + 1)(m - 1).

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Answer:

1/w^4

Step-by-step explanation:

The gradient of the vector field F(x , y , z) = ⟨−7y , −7x , 9z⟩ be

F'(x , y , z) = < 0 , 0 , 9 > i.e. F'(x , y , z) = 9k.

Given, a vector field F(x , y , z) = <-7y , -7x , 9z>.

we have to find the gradient of the vector field F = ∇V.

Also, the function V satisfies the condition V(0 , 0 , 0).

As, we know to find the gradient of the vector field F(x , y , z) we differentiate the vector field or differentiate the vector field partially.

F(x , y , z) = <-7y , -7x , 9z>

F(x , y , z) = -7yi - 7xj + 9zk

On differentiating, we get

F'(x , y , z) = <d(-7y)/dx , d(-7x)/dy , d(9z)/dz>

F'(x , y , z) = < 0 , 0 , 9 >

F'(x , y , z) = 9k

So, the gradient of the vector field F(x , y , z) be, 9k

Hence, the gradient of the vector field F(x , y , z) be

F'(x , y , z) = < 0 , 0 , 9 >

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Answer:

2

Step-by-step explanation:

The way to find the absolute value of a number is to remove the negative symbol (-) if it has one.

The number 2 does not have one, so just leave it as it is.

Another way to think about it is, how far is 2 from 0 on a number line? Well, 2 is obviously 2 units away from 0.

The triangle with sides measuring 3, 4, 5 will form a Right Nagle Triangle

What is Pyhtagorean Theorem?

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship in Euclidean geometry between the three sides of a right triangle. It indicates that the area of the hypotenuse square is equal to the sum of the areas of the squares on the other two sides.

Solution:

(i) 4, 11, 20

20² = 4² + 11²

400 = 16 + 121

400 ≠ 137 #Not a right angle triangle

(ii) 16, 21, 25

25² = 16² + 21²

625 = 256 + 441

625 ≠ 697 #Not a right angle triangle

(iii) 5, 13, 25

25² = 5² + 13²

625 = 25 + 169

625 ≠ 194 #Not a right angle triangle

(iv) 3, 4, 5

5² = 3² + 4²

25 = 9 + 16

25 = 25 #Right angle triangle

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Both equations are satisfying by substituting (5, 0) in the system of inequalities.

What is a system of inequalities?

"A system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system."

Given

System of inequalities graphed equation

y ≤ 2x + 2.................(1)

y ≥ -5x + 4................(2)

Substituting the point (5, 0) in equations 1 and 2

y ≤ 2x + 2

⇒ 0 ≤ 2(5) + 2

⇒ 0 ≤ 27

It is true

y ≥ -5x + 4

⇒ 0 ≥ -5(5) + 4

⇒ 0 ≥ -25 + 4

⇒ 0 ≥ -21

It is also true

In this option, Both equations are satisfying by substituting (5, 0)

Both equations are not satisfying by substituting (0, 5)

Hence, Both equations are satisfying by substituting (5, 0) in the system of inequalities given.

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Answer: 18 plums cost 12 dollar means
1 plum costs 18 divide by 12
That means 1 dollar and 50 cents for 1 plum
that is 1 plum for 2 dollar

Answer:

Step-by-step explanation:

the answer its 3