#8 Tessa has a plan for a set of stairs made of concrete, as shown. Each stair is 1 point the same width and height and is taller than the previous one by the same amount. What is the volume of concrete needed for the set of stairs?
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I think the answer would be B. The range is then total price of the tickets purchased and includes all whole numbers from 1 to 4.

Answer:

The first term is 10.

The second term is 16

The third term is 22.

We can see that the first term plus 6, is:

10 + 6 = 16

Then the first term plus 6 is equal to the second term.

And the second term plus 6 is:

16 + 6 = 22

Then the second term plus 6 is equal to the third term.

A) As we already found, the recursive rule is:

Aₙ = Aₙ₋₁ + 6

B) The explicit rule is:

Aₙ = A₁ + (n - 1)*6

Such that A1 is the first term, in this case A₁ = 10

Then:

Aₙ = 10 + (n - 1)*6

C)

Now we want to find A₅, then:

A₅ = 10 + (5 - 1)*6 = 34

There are 34 chairs in row 5.

D)

Here we have 17 rows, then we can have 17 terms, this means that the total number of chairs will be:

C = A₀ + A₁ + ... + A₁₆

This summation can be written as:

∑ 10 + (n - 1)*6        such that n goes from 0 to 16.

The formula  for the sum of the first N terms of a sum like this is:

S(N) = (N)*(A₁ + Aₙ)/2

Then the sum of the 17 rows gives:

S(17) = 17*(10 + (10 + (17 - 1)*6)/2 = 986 chairs.

There are total 986 chairs in the considered auditorium and there are 34 chairs in the fifth row.

A rule defined such that its definition includes itself.

Example: [tex]F(x) = F(x-1) + c[/tex] is one such recursive rule.

For this case, we're provided that:

Seats in rows are 10 in front, 16 in second, 22 in third, and so on.

10 , 16 , 22 , .....

16 - 10 = 6

22 - 16 = 6

...

So consecutive difference is 6

If we take [tex]T_i[/tex] as ith term of the series then:

[tex]T_2 - T_1 = 6\\T_3 - T_2 = 6\\T_4 - T_3 = 6 \\T_5 - T_4 = 6\\\cdots\\T_{n} - T_{n-1} = 6[/tex]

Thus, the recursive rule for the given series is [tex]T_{n} - T_{n-1} = 6[/tex] or [tex]T_n = T_{n-1} + 6[/tex]

From this recursive rule, we can deduce the explicit formula as:
[tex]T_n = T_{n-1} + 6\\T_n = T_{n-2} + 6 + 6\\\cdots\\T_n = T_{n-k} + k \times 6\\T_n = T_1 + 6(n-1)\\T_n = 10 + 6(n-1) \: \rm (as \: T_1 = 10)\\[/tex]

Thus, the explicit rule for this series is [tex]T_n = 10 + 6(n-1)[/tex]

For 5th row, putting n = 5 gives us:

[tex]T_n = 10 + 6(n-1) = 6n + 4\\T_5 = 6(5) + 4 = 34[/tex]

If the auditorium has 17 rows, then total chairs are:

[tex]T = T_1 + T_2 + \cdots + T_{17} = \sum_{n=1}^{17} T_n\\\\T = \sum_{n=1}^{17} (10 + 6(n-1))\\\\T = \sum_{n=1}^{17} (6n + 4)\\\\T = 6\sum_{n=1}^{17} n + \sum_{n=1}^{17}4 = 6\sum_{n=1}^{17} n + 4 \times 17\\\\T = 6\left( \dfrac{17(18)}{2}\right) + 68 = 918 + 68\\\\T = 986[/tex]

(it is because [tex]\sum_{k=1}^n k = 1 + 2 + \cdots + n = \dfrac{n(n+1)}{2}[/tex] )

Thus, there are total 986 chairs in the considered auditorium. There are 34 chairs in the fifth row. The recursive rule for this series is: [tex]T_n = T_{n-1} + 6[/tex] The explicit rule for this series is: [tex]T_n = 6n + 4[/tex].

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[tex]\frac{-3 - (-4)}{1 - (-5)}[/tex]

= [tex]\frac{-3 + 4}{1 + 5}[/tex]

= 1/6

Answer:

find the answer of the rectangle (7×3=21)

than find the area if one triangle and do 7/2 to get base then multiply 1/2base×height. because there are two triangles add the area to itself then add it to the area of the rectangle. the two triangles shoukd equal 21 together and 21 plus 21 equals 42.

Step-by-step explanation:

im sorry if this is incorrect but it should be right

Answer:

dkeekek

Step-by-step explanation:

kddeejwkwnqnnwwnwwnwnwnwwnw

Answer:

use pythagoras theorem for solving this

value of x is 12 cm

Answer:

49

Step-by-step explanation:

7^2 mean 7x7 which is 49

Answer:

41.4 in

Step-by-step explanation:

(sin 80) opposite      =    x

          hypotenuse        42

x = 42 * sin (80)  = 41.4 in

Answer:

He should buy about 2 quart of stain

Step-by-step explanation:

Find the diagram attached

First we need to find the area of the given ramp

The ramp consists of two identical triangles, a larger and small rectangles

Since area of triangle  = 1/2 * base * height

Area of the identical triangles = 1/2 * 25ft * 25/12 ft (Note that 1ft = 12in)

Area of the 2 identical triangles = 2* 625/24ft² = 625/12 ft²

Area of the large rectangle = Length * Width

Area of the large rectangle = 25 1/12 * 5

Area of the large rectangle = 301/12 * 5

Area of the large rectangle = 1505/12 ft²

Area of the small rectangle = 25/12 * 5

Area of the small rectangle = 125/12 ft²

Area of the figure = 625/12 + 1505/12 + 125/12

Area of the figure = (625+1505+125)/12

Area of the figure = 2255/12

Area of the figure = 187.917

Area of the figure = 187.917ft²

Since  a quarter steam covers a 100' square fee, then;

1 quarter = 100ft²

x = 187.917ft²

Cross multiply

100 * x = 187.917

100x =187.917

x = 187.917/100

x = 1.87917

x ≈ 2

Hence he should buy about 2 quart of stain

Answer:

= $88.7429

Step-by-step explanation:

Regular price: $124.99

Total off: $124.99 x 20% + 15% = 43.7465%

Tax: $124.99 x 6% = 7.4994

So he should pay: 124.99 - 43.7465 +7.4994

The total cost of her meal would be amount of $88.74.

The percentage is defined as a ratio expressed as a fraction of 100.

For example, If Misha obtained a score of 57% on her exam, that corresponds to 67 out of 100.

As per the given information, the required solution would be as

Regular price of dinner = $124.99

Total off =  $124.99 × 20% + 15% = 43.7465%

Total tax = $124.99 × 6% = 7.4994

The total cost of her meal = Regular price of dinner - Total off + Total tax

The total cost of her meal = 124.99 - 43.7465 +7.4994

Apply the arithmetic operation to get the cost

The total cost of her meal = 88.74

Therefore, the total cost of her meal would be amount of $88.74.

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Answer: x = -5

New Equation (after substituting) 4x = 3x - 5

Subtract 3x from both sides

x = -5

Answer:

P(-3) = -1

Step-by-step explanation:

So just substitute the value of x in the equation:

Value of x is (-3)

So:

P(x) = -2(1 - x)2 +5

P(-3) = -2(1-(-3)) 2 + 5

P(-3) = -2(4) 2 + 5

P(-3) = -8 + 2 + 5

P(-3) = -6 + 5

P(-3) = -1

Answer:

The real answer is (-20, 8).

Step-by-step explanation:

I just did the unit test practice or whatever and used the answer above and got it wrong. This is the correct answer.

Answer:

-822

Step-by-step explanation:

i just typed it in the calculator

but if you're doing it by hand, 1st multiply 4*12*3*6 and then subtract 42 from it

Answer:

x= 114, y= 66

Step-by-step explanation:

Opposite angles of a parallelogram are equal

Option B is correct, x ≤ 2  is the domain of the function shown on the graph.

A relation is a function if it has only One y-value for each x-value.

We have to find the domain of the given graph.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis.

The graph has x values less than or equal to two.

x ≤ 2 is the domain of the given function.

Hence, option B is correct, x ≤ 2  is the domain of the function shown on the graph.

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yah it's not probably it's not 2 mmmm

Answer:

150.72

Step-by-step explanation:

C = 2*pi * r

C = 2* 3.14 * 6

C = 37.68

1 revolution = 37.68

4 revolutions = 4 * 37.68

4 revolutions = 150.72

Answer:

C. 2:5

Step-by-step explanation:

Find perimeter of each...

a. 10+25+21.5=56.5

b. 4+10+8.6=22.6

b:a

22.6:56.6

simplify

11.3 will go into both for..

2:5

Answer:

[tex]y=0.01(4)^x[/tex]

Step-by-step explanation:

Therefore, the decimal representations of irrational numbers satisfy conditions 1 and 2; that is, irrational numbers are decimals that do not terminate and do not repeat. Knowing these properties, it is now possible for us to construct irrational numbers in decimal form at will.

for spanish people

Por lo tanto, las representaciones decimales de números irracionales cumplen las condiciones 1 y 2; es decir, los números irracionales son decimales que no terminan y no se repiten. Conociendo estas propiedades, ahora es posible para nosotros construir números irracionales en forma decimal a voluntad.

Answer:

∠ W = 51°

Step-by-step explanation:

Since WX is the diameter , then

∠ WYX = 90° ( angle in a semicircle )

The sum of the 3 angles in a triangle = 180° , then

x + x + 12 + 90 = 180

2x + 102 = 180 ( subtract 102 from both sides )

2x = 78 ( divide both sides by 2 )

x = 39

Then

∠ W = x + 12 = 39 + 12 = 51°

Answer:

A

Step-by-step explanation:

Answer:

The probability of getting a white or green gumball is 35.64%.

Step-by-step explanation:

1. calculate the total number of gumballs in the gumball machine

35 + 22 + 30 + 14 = 101 gumballs

2. calculate the number of white and green gumballs combined

22 + 14 = 36 w/g gumballs

3. divide the number of white and green gumballs combined by the total number of gumballs in the gumball machine

36 / 101 = 0.3564

Answer: the probability of getting a white or green gumball is 35.64% (0.3564).

Probability is the chance of occurring an event from the total possible outcomes.

The probability of getting a white or a green gumball is 57/101.

It is the chance of occurring an event from the total possible outcomes.

We have,

Green gumballs = 35

White gumballs = 22

Purple gumballs = 30

Blue gumballs = 14

Total gumballs = 35 + 22 + 30 + 14 = 101

The combination is given by:

= [tex]^nC_{r}[/tex]

= n! / r! (n-r)!

The probability of choosing a white gumball:

= [tex]\frac{^{22}C_{1}}{^{101}C_{1} }[/tex]

= 22 / 101

The probability of choosing a green gumball:

= [tex]\frac{^{35}C_{1}}{^{101}C_{1} }[/tex]

= 35 / 101

The probability of getting a white or a green gumball:

= 22/101 + 35 / 101

= (22 +35) / 101

= 57 / 101

Thus the probability of getting a white or a green gumball is 57/101.

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Answer:

1

Step-by-step explanation:

Answer:

if its not a fraction or a number that can be written as a fraction, its an irrational

Answer:

10 days

Step-by-step explanation:

Mogaka and Ondiso working together can do a piece of job in 6 days. Mogaka working alone takes 5 days longer than Ondiso. How many days does it take Ondiso to do the work alone?

Let us represent :

The number of days

Mogaka worked alone = x

Ondiso worked alone = y

Total days worked together = T

Mogaka and Ondiso working together can do a piece of job in 6 days.

Hence,

1/x + 1/y = 1/T

Mogaka working alone takes 5 days longer than Ondiso.

x = y + 5

Therefore:

1/y + 5 + 1/y = 1/6

Multiply all through by (y+5)(y)

= y + y + 5 = (y+5)(y)/6

= 2y + 5/1 = (y+5)(y)/6

Cross Multiply

6( 2y + 5) = (y+5)(y)

12y + 30 = y² + 5y

= y² + 5y - 12y - 30 = 0

= y² - 7y - 30 = 0

Factorise

= y² +3y - 10y - 30 = 0

y(y + 3) - 10(y + 3) = 0

(y + 3)(y -10)= 0

y + 3 = 0, y = -3

y - 10 = 0

y = 10 days

Note that

The number of days Ondiso worked alone = y

Hence, it takes 10 days for Ondiso to work alone

Answer:

2 6/7 units

Step-by-step explanation:

You substitute 5/7 in for x

4(5/7) = 20/7 = 2 6/7 units

You can also add 5/7 + 5/7 + 5/7 + 5/7 to check your work

Answer:

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

Step-by-step explanation:

Given,

Width of the rectangular prism

= x

Length of the rectangular prism

[tex] = {x}^{2} y[/tex]

Height of the rectangular prism

[tex] = {y}^{2} [/tex]

Therefore,

Volume of the rectangular prism

= Width × Length × Height

[tex] = x \times {x}^{2} y \times {y}^{2} [/tex]

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

Hence,

The required volume of the rectangular prism is

Option J:

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