Determine the number of possible settings for a row of five -on Gg switches under each condition

Answer:

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] (3n + 7)

Step-by-step explanation:

We require to find the first term a₁ and the common difference d

The n th term is given by 3n + 2, thus

a₁ = 3(1) + 2 = 3 + 2 = 5

a₂ = 3(2) + 2 = 6 + 2 = 8

d = 8 - 5 = 3

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ], substitute values

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ (2 × 5) + 3(n - 1) ] = [tex]\frac{n}{2}[/tex] (10 + 3n - 3) = [tex]\frac{n}{2}[/tex] (3n + 7)

Answer:

Sn = (3/2)n² + (7/2)n

Step-by-step explanation:

Sn = (n/2)[2a + (n-1)d]

a = 3(1)+2 = 5

d = second term - 5 = 3(2)+2 - 5 = 3

Sn = (n/2)[2(5) + (n-1)(3)]

= (n/2)[10 + 3n - 3]

= (n/2)(7 + 3n)

Sn = (3/2)n² + (7/2)n

Answer:

-7/4

Step-by-step explanation:

Did you mean -7?

The best scenario for an exponential function is Option B, as it describes a consistent percentage decrease annually, which is characteristic of exponential decay.

The situation that is best modeled by an exponential function is Option B, which describes the amount of a substance remaining after x years if it is decreasing at a rate of 25% annually. This exemplifies an exponential decay scenario where the rate of change of a quantity is directly proportional to its current value. Over time, the substance decreases by a consistent percentage, which is characteristic of exponential decay functions.

A key feature of exponential relationships is that they describe processes where the change at any given point is proportional to the current amount, which fits the description of a substance decreasing by a consistent percentage each year.

Answer:y=-24

Step-by-step explanation:

Move all terms not containing

y

to the right side of the equation.

D. (-2,-1)

Hope it helps you.

Answer:

D

Step-by-step explanation:

Given the 2 equations

y = 2x + 3 → (1)

y = - [tex]\frac{1}{2}[/tex] x - 2 → (2)

Since both equations express y in terms of x, equate the right sides

2x + 3 = - [tex]\frac{1}{2}[/tex] x- 2

Multiply through by 2 to clear the fraction

4x + 6 = - x - 4 ( add x to both sides )

5x + 6 = - 4 ( subtract 6 from both sides )

5x = - 10 ( divide both sides by 5 )

x = - 2

Substitute x = - 2 into (1) for corresponding value of y

y = 2(- 2) + 3 = - 4 + 3 = - 1

Solution is (- 2, - 1 ) → D

The dimensions of the rectangle shown on the coordinate plane is The base is 9 units and the height is 4 units.

Option: B.

Step-by-step explanation:

We are given with the coordinate points of a rectangle.

The points are  (1, -1), (10, -1), (10, -5), (1, -5).

From the given graph, the bigger side is the base and the height is the smaller side.

The points  (1, -1), (10, -1) and (1, -5), (10, -5) can be used to find the base of the rectangle.

The points (10, -1), (10, -5) and  (1, -1), (1, -5) can be used to find the height of the rectangle.

Let us find the base using coordinate point (1, -5), (10, -5) .

Since the base runs horizontally on the x-axis, we have to find the run.

run = [tex]x_2-x_1[/tex].

run = 10-1.

run (base)= 9 units.

Let us find the base using coordinate point (10, -1), (10, -5) .

Since the height runs vertically on the y-axis, we have to find the rise.

rise = [tex]y_2-y_1[/tex].

rise = -5-(-1).

rise=-5+1.

rise (height)= 4 units.      ( Units are always measured in positive.)

∴ The base is 9 units and the height is 4 units.

Answer:

domain={0,3}

range={1,9}

Step-by-step explanation:

Answer:

The number of square tiles required to cover the bathroom floor is approximately 31.

Step-by-step explanation:

The dimensions of the rectangular floor of the bathroom are:

Length = 10.5 ft.

Breadth = 6.5 ft.

The dimensions of the square tiles are:

Side = 1.5 ft.

The area of the rectangular floor of the bathroom is:

[tex]Area\ of Bathroom\ floor=Length\times Breadth\\=10.5\times6.5\\=68.25[/tex]

The area of 1 square tile:

[tex]Area\ of\ 1\ square\ tile=(SIde)^{2}\\=(1.5)^{2}\\=2.25[/tex]

The number of tiles required to cover the bathroom floor is:

[tex]Number\ of\ tiles=\frac{Area\ of\ bathroom\ floor}{Area\ of\ 1\ square\ tile} \\=\frac{68.25}{2.25}\\ =30.3333\\\approx31[/tex]

Thus, the number of square tiles required to cover the bathroom floor is approximately 31.

Answer:

the answer is to 72 divided by 1/3 is 216

The result of the division 72 divide by 1/3 is : 216.

Here, we have,

given that,

What is 72 divide by 1/3

we know that,

72 divide by 1/3 is the same thing as 72 times 3/1.

i.e. 72 ÷ 1/3

=> 72 × 3/1

now, we know that,

So 72 x 3 = 216

=> 216/1

And 216 divided by 1 is 216.

so, we get,

Hence, The result of the division 72 divide by 1/3 is : 216.

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Answer:

x = 4.5.

Step-by-step explanation:

5(2x + 1) = 50

10x + 5 = 50

10x = 50 -  5

10x = 45

x = 4.5.

Answer:

<ABC = 98.

Step-by-step explanation:

We know that the triangle is lying on a flat line, which is 180 degrees. We know that angle ABC and angle CBD are supplementary as they both use line ABD as their transversal.

Set up the equation (3 + 5x) + 82 = 180.

Solve for x, and you get 19.

Plug it back in to (3 + 5x), we get <ABC = 98.

Answer:

The answer is 24

Step-by-step explanation:

If each person eats 1/3 of the pizza then that means it takes 3 people to eat a whole pizza so you multiply three times 8 and you get twenty four.

Answer:

There will be 6 necklaces

Step-by-step explanation:

102/17 is 6

Answer:Juanita can make 6 bracelets.

Step-by-step explanation:

Divide 102 and 17 then you should get 6.

Answer:

32 cups of water is needed to fill a 2 gallon water tank.

Step-by-step explanation:

Here, the amount of water to be filled in the fish tank = 2 gallons

The utensil to measure water   =  a measuring cup

Now, as we know:

1 quart  = 0.25 gallons

⇒ 4 pints =  1  gallons

⇒ 8 pints =  2 gallons

Also, 1 pint  = 0.5 quart

⇒ 2 pints =  1 quarts

⇒ 8 pints =  4 quarts

⇒ 16 pints =  8 quarts

Again,  1 cup = 0.5 pint

⇒ 2 cup  = 1  pint

⇒ 32 cup  = 16  pints

Hence, 32 cups of water is needed to fill a 2 gallon water tank.

Answer:

6

Step-by-step explanation:

hello :

the nth term is : Bn= B1×R^n-1

calculate B3  (when n=3)    R= -1/3   B1 = 54

B3 =54×(-1/3)^(3-1)

B3 =54×(1/9)=6

Knowing about geometric sequences we have that its third term will be given by 6

Geometric Progression (PG) is a numerical continuity in which the division of a term with its previous one, except the first, will result in a single value, the so-called ratio (q), that is: PG: (a1, a2, a3, a4, ..., an), where q = (a2/a1 = a3/a2 = a4/a3,.

Given that:

The formula of the term will be:

[tex]Bn= B1*R^n-1[/tex]

Calculated the B3 we have:

[tex]B3 =54*(-1/3)^{(3-1)}\\B3 =54*(1/9)=6[/tex]

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The height of the redwood tree can be determined through trigonometry, using the tangent of the angles given and the distances provided. The height of the tree from point B is found to be 1.8 feet, and the total height of the tree from point A is found to be approximately 30.9 feet.

In this question, we can use trigonometry to solve the problem. From point B, we see two angles. The smaller angle, 85.8°, is the angle from the line extending to the tree and line AB, and the greater angle is 90°. Therefore, the angle between the line extending to the top of the tree and line AB is (90-85.8)= 4.2°.

Using the tangent function, which is the ratio of the opposite side to the adjacent side in a right triangle, we can solve for h. Tan 4.2° = h/24.8 feet. Solving for h gives us h = 24.8 feet * tan 4.2°. Using a calculator, we find that h is approximately 1.8 feet.

Similarly, let's calculate the height from point A. From point A, the angle of elevation to the top of the tree is 10.4°. The distance from the tree to point A is the sum of the length of AB (24.8 feet) and the length from B to the tree (h/tan 85.8°). So, the total height of the tree is h (from point B) + distance from A to the tree * tan 10.4°. This calculation gives us h = 1.8 feet + (24.8 feet + 1.8 feet/tan 85.8°)*tan 10.4°. After doing the calculations, we find that the height of the tree is approximately 30.9 feet when rounded to one decimal place.

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The angles of a triangle always add to 180°. In the triangle with 35°, we know that the other angle is 55° since 180 - 90 - 35 = 55. Know we know that 55° angle, 60° angle and the unknown angle will add to 180° because they form a flat line. So 180 - 60 - 55 = 65. Next, we subtract 65° and 90° from 180° to get the last unknown angle, which is 25°. Lastly we subtract 25° from 180 because the x angle and the 25° angle form a a flat line. 180 - 25 = 155.

I believe the measure of angle x is 155°.

The required value of the exterior angle x = 155°

A figure of angle in triangles is shown in which the value of x is to be determined.

The angle can be defined as the one line inclined over another line.

From the image attached below From the orange triangle,
The sum of the interior angle of a triangle is 180°,
35 + 90 + z =180
z = 180 -90 - 35
z = 55
Now, the sum of the angle
z + y + 60 = 180
55 + y + 60 = 180
y = 180 -60 - 55
y = 65

Now angle x can be given as the sum of the remote angle is equal to exterior angle x.
35 + z + y = x
35 + 55 + 65 = x
x = 155

Thus, the required value of the exterior angle x = 155°

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Answer:

y=-1/3x-8

Step-by-step explanation:

y-y1=m(x-x1)

y-(-9)=-1/3(x-3)

y+9=-1/3x+3/3

y+9=-1/3x+1

y=-1/3x+1-9

y=-1/3x-8

The final price of a $1049 television on a 12% sale, with a 4.5% sales tax, is $964.66.

The final price on a $1049 television that is on sale for 12% off can be found by deducting the discount from the original price, and then adding the sales tax on the discounted price.

First, let's find the discount: 12% of $1049 is (12/100)*1049 = $125.88. So, the price after discount would be 1049 - 125.88 = $923.12.

Next, we need to add the 4.5% sales tax. Sales tax is calculated on the discounted price, so 4.5% of $923.12 is (4.5/100)*923.12 = $41.54.

Finally, we add the tax to the discounted price to get the final price: $923.12 + $41.54 = $964.66. So, the final price of the television is $964.66.

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Answer:

$366.66

Step-by-step explanation:

You start with a credit card balance of $1950. If you reduce this balance by 13% each month for 12 months, using the formula for geometric series (a(r^n)), your final balance at the end of 12 months will be approximately $452.98.

The student's question is asking about reducing a credit card debt balance by a fixed percent each month. In this case, the student is reducing their debt by 13% every month for 12 months. To get a clear picture, let's go through this step by step.

Initially, the credit card balance is $1950. In the first month, the student reduces the debt by 13% which is $253.5. So, the remaining balance at the end of first month would be $1950 - $253.5 = $1696.5

This process is repeated each month. For example, in the second month, the student reduces the new amount of $1696.5 by 13%. The debt will continue to decrease in this manner each month.

To calculate the balance at the end of 12 months, we would use the formula for geometric series: a(r^n), where 'a' is the initial amount of debt($1950), 'r' is the percentage (1 - 13% or 0.87) and 'n' is the number of months (12).

Your final balance at the end of 12 months would be $1950*(0.87^12) which approximately equals $452.98. Hence, by reducing your debt by 13% each month for 12 months, your balance will be approximately $452.98. But remember, maintaining steady payments and not adding to the balance by new purchases is also important in managing credit card debt.

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Answer:

country a = 19,812 cars

country b = 6,604 cars

Step-by-step explanation:

a = country a

b = country b

the 2 eqations are:

a + b = 26,416

a = 3b

now substitute 3b for a in the first equation:

3b + b = 26,416

add the variables:

4b = 26,416

now divide 26,416 by 4 (26,416/4)

b = 6,604

so country b has 6,604 cars

to find country b, substitute the number of cars in country b (which is 6,604) in the second equation:

a = 3b

a = 3 × 6,604

a = 19,812

so country a has 19,812 cars

Answer:

y = 30

Step-by-step explanation:

If y varies directly with x, then you can make a ratio:

24/8

Simplify the ratio:

3/1

Y is always the first number/ on top in a ratio, that's where I get 24 over 8

3/1 means that y is triple x

so 10 * 3 is 30

The midpoint of AB is point G

The complete question has been attached below. As you can see, we have a line segment which is defined as a part of a line that is bounded by two different points that are at the end of the segment. So here we know that:

Therefore, the midpoint can be calculated as:

[tex]M:midpoint \\ \\ \\ M=\frac{A+B}{2} \\ \\ M=\frac{-6+8}{2} \\ \\ M=1[/tex]

So the midpoint is [tex]M=1[/tex] that matches point G. Finally:

Conclusion: The midpoint of AB is point G

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Brandus bought a total of 7/12 pounds of meat by adding together 1/3 pound of ground turkey and 1/4 pound of ground beef.

To find out how much meat Brandus bought, you need to add the weights of the ground turkey and the ground beef. Brandus bought 1/3 pound of ground turkey and 1/4 pound of ground beef.

Convert the fractions to have a common denominator:

1/3 = 4/12 (multiply both the numerator and the denominator by 4)

1/4 = 3/12 (multiply both the numerator and the denominator by 3)

Add the two amounts:

4/12 + 3/12 = 7/12

Hence, Brandus bought 7/12 pounds of meat in total to make sausages.

Yo sup??

cot(7π/6)=cot(π+π/6)

=cot(π/6)

=√3

Hope this helps

Answer:

[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Using the trigonometric identity

cot x = [tex]\frac{1}{tanx}[/tex]

Consider tan([tex]\frac{7\pi }{6}[/tex] )

[tex]\frac{7\pi }{6}[/tex] is an angle in the third quadrant where tan > 0

Thus tan([tex]\frac{7\pi }{6}[/tex] ) = tan([tex]\frac{7\pi }{6}[/tex] - π ) = tan([tex]\frac{\pi }{6}[/tex] ) = [tex]\frac{1}{\sqrt{3} }[/tex]

Hence

cot([tex]\frac{7\pi }{6}[/tex] ) = [tex]\frac{1}{\frac{1}{\sqrt{3} } }[/tex] = [tex]\sqrt{3}[/tex]

Answer:

- 3

Step-by-step explanation:

hello:

-2-17+12-(-4)=(-2-17)+(12+4)= -19+16= -3

Answer:

-3

Step-by-step explanation:

-2-17+12-(-4)

From BODMAS, we begin witht the bracket

=-2-17+12+4

= -2-17+16

= -19+16

= -3

Answer:

1.Distribute values

(3x+12)-(2x+8)

2.Add common terms

x+4