Write the first five terms of the sequence:
a(1) = 1, a(n) = 5(n-1), n ≥ 2

Answer:

5

Explanation:

When we divide A by B, we are calculating how many Bs fit into A. So, if we want to know how many 2/5s fit into 2 yds, we need to divide 2 by 2/5. So:

So, 2 yds of rope can be divide into 5 ropes of 2/5 yd.

The area of the first and second circles is 36π m² and 9π m², respectively.

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If the first marble is not reinserted into the bag before the second draw, there is 1/15 probability of drawing two pink marbles.

When the result of one event affects the result of another, two events are said to be dependent. The likelihood of two connected events is the sum of the probabilities of the occurrences X and Y that happen after X.

It is given that there are two yellow, three pink and 5 blue marbles.

So, in the first draw, the probability of drawing pink marble is the ratio of the number of pink marbles to the total number of marbles in the bag.

[tex]p_1=\frac{3}{10}[/tex]

Now, in the second draw, the probability of drawing pink marbles will be affected as it is not kept back. So, in the second draw, the probability of drawing pink marble is the ratio of the number of remaining pink marbles to the remaining number of marbles in the bag.

[tex]p_2=\frac{2}{9}[/tex]

Given that both occurrences occur concurrently, multiply the likelihood of the first event by the probability of the second event.

[tex]p=p_1\times p_2\\\\=\frac{3}{10}\times\frac{2}{9}\\\\ =\frac{1}{15}[/tex]

So, If the first marble is not reinserted into the bag before the second draw, there is 1/15 probability of drawing two pink marbles.

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If in lixue's garden the green pepper plants grew 5 inches in 3/4 months then at this rate they can grow 0.555 feet in one month

The problem is solved as per the unitary method

In lixue's garden the green pepper plants grew 5 inches in 3/4 months.

In 3/4 months the green pepper grew by 5 inches.

3/4 months can be written as 0.75 months

in 1 month the green pepper plant will grow by (5/0.75) 1

The green pepper plant will grow by 6.66 inches

1 foot is equals to 12 inches

1 inch = 1/12 foot

6.666 inches = (1/12) 6.666

= 0.0833 x 6.666

= 0.555

the plant grew 0.555 feet in 1 month

Therefore, if in lixue's garden the green pepper plants grew 5 inches in 3/4 months then at this rate,they can grow 0.555 feet in one month

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The most appropriate choice for function and domain and range of a function will be given by -

Domain of y = [tex]\mathbb{R} -[/tex] {[tex]-\frac{1}{2}[/tex]}

Range = [tex]\mathbb{R}-[/tex]{[tex]\frac{1}{2}[/tex]}

What is a function and domain and range of a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

The set of  values for which the function is defined is the domain of the function and the values obtained on substituting the values of domain in the function is the range of the function.

y = [tex]\frac{x -5}{2x + 4}\\[/tex]

For domain of y

y is not defined if 2x  +4 = 0

y is not defined if [tex]x = -\frac{1}{2}[/tex]

Domain of y = [tex]\mathbb{R} -[/tex] {[tex]-\frac{1}{2}[/tex]}

For range of y

let [tex]\frac{x -5}{2x + 4}\\[/tex] = z

[tex]x - 5 = z(2x +4)\\x - 5 = 2zx + 4z\\x - 2zx = 4z + 5\\x(1 - 2z) = 4z + 5\\x = \frac{4z + 5}{1 - 2z}[/tex]

If y = [tex]\frac{1}{2}[/tex]

[tex]\frac{x-5}{2x + 4} = \frac{1}{2}\\2x - 10 = 2x + 8\\-10 = 8\\[/tex]

Not possible

[tex]\frac{1}{2}[/tex] is not in the range of y

Range = [tex]\mathbb{R}-[/tex]{[tex]\frac{1}{2}[/tex]}

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Answer:

6

Step-by-step explanation:

4-x/3=2

4-6/3=2

Given:

A U.S. Geological Survey map has a scale of 1:24200

There are two buildings that are 3.38 miles apart.

We will find how they are inches apart on the map

First, convert from miles to inches

1 mile = 63 360 inches

So, 3.38 miles = 3.38 * 63 360 inches = 214156.8 inches

The map has a scale of 1:24200

So, using the ratio and the proportions, we will find the length on the map as follows:

Rounding to the nearest hundredth

So, the answer will be: 8.85 inches

Step-by-step explanation:

option D is correct..

can we become friends???

Answer:

y = -2x.

Step-by-step explanation:

2y = x - 3

y = 1/2x - 3/2

- so, the slope of this line is 1/2

and the slope of a line perpendicular to it is - 1/ 1/2

= -2.

Using the point slope form of a line the equation of the required line is

y - y1 = m(x - x1)

m = -2, x1 = -1 and y1 = 2.

So,

y - 2 = -2(x - (-1))

y - 2 = -2x - 2

y = -2x - 2 + 2

y = -2x.

The lengths of the two pieces of a wire will be 19,19.

A square is a closed, two-dimensional object with four equal sides and four vertices. On either side, it has parallel sides.

The square of a square's side determines its area.

Given data -

Length of a wire = 38 m

As the wire is divided into two pieces,

Let the length of two pieces of wire be x and y m respectively.

As per given data, x + y = 38

Therefore, y = 38 - x    

As each piece is bent into a square, area of squares will be

[tex](x/4)^{2}[/tex]  and  [tex](y/4)^{2}[/tex]

Therefore, the sum of areas of two squares will be A = [tex](x/4)^{2}[/tex] +      [tex](y/4)^{2}[/tex]

A = [tex]x^{2}[/tex]/16 + [tex]y^{2}[/tex]/16

A = [tex]x^{2}[/tex]/16 + [tex](38-x)^{2}[/tex]/16

By differentiating, we will get

A' = [tex]\frac{2x}{16}[/tex] - [tex]\frac{2(38-x)}{16}[/tex]

In order to minimize the the sum of the areas of the two squares, we will take A' = 0

0 = x - (38 - x)

2x = 38

x = 19

Therefore y = 19

The length of two pieces of a wire should be 19 m each.

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Answer:

96

Step-by-step explanation:

Answer:

1) 267.45

2) 18.48

3) 3472

Answer:

The right answer choices are B, C, and F

Answer:

{1, -5/6}

Step-by-step explanation:

(6a+5)(a-1) = 0

6a+5 = 0 (or) a-1 = 0

a = -5/6 (or) a = 1

The expression that is equivalent to \frac{9^5}{9^3} is 9^2.

It should be noted that an expression is simply used to shoe the relationship between the variables that are illustrated.

In this case the given expression is 9^5 / 9^3. It should be noted that when dividing powers, we have to subtract them. Therefore, 5 - 3 = 2.

The value will be:

= 9^5 / 9^3

9^2

The expression is 9^2.

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The price after the discount but before tax, to the nearest dollar and cent, is $18.4.

Given Information:

Price on the tag = $23

Amount of Discount =20%

A % or Percentage is a figure or ratio that is stated as a fraction of 100 (from the Latin per centum, "by a hundred").  A % lacks dimensions and has no associated unit of measurement.

Percentage Formula =[tex]\frac{value}{Total value} *100[/tex]

Calculating the discount,

There is a 20 % discount on the camera

So, the amount of discount by using the percentage formula = [tex]\frac{20*23}{100} = 4.6[/tex]

Hence, the amount of discount is $4.6

Subtracting the discount to calculate the price after the discount =

Initial Price - Discount amount = $23-$4.6 = $18.4

Thus, the price after the discount is $18.4

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Step-by-step explanation:

146 × 48 = 48 × 146

due to the commutative law of multiplication the sequence of the operands of a multiplication does not matter.

a × b = b × a

this bases on the fact that a multiplication is nothing else than a special kind of addition

a × b = add a b times; or add b a times.

and as already the addition follows the commutative law

a + b = b + a

so, does then the multiplication.

Answer:

-6<v<3

Step-by-step explanation:

hope this helps

Using limit definition of the derivative, The value of f'(3) is 2.

By determining the limit of a slope expression, one can get the instantaneous rate of change (derivative).

The derivative of a function f at x is the instantaneous rate of change of the function at x since the derivative is defined as the limit that determines the slope of the tangent line to a function.

Given function

f(x) = x² - 4x.

derivate with respect to x

f'(x) = 2x - 4

put x = 6

f'(x) = 2(3) - 4

= 6-4

=2

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Answer:

a value that is not yet shown

Step-by-step explanation:

Mark me as branlist to help

Answer:

Step-by-step explanation:

2100 - 1900 =  200

660(200) + 14,400

p = 146400

146,400 people

The answer is B

Yes it is possible for a rectangle to have irrational sides and rational area.

What are rational numbers?

Ration numbers is an ordered pair of integers a, b written in the form a/b where b is not equal to zero.

We are given that sides of rectangle are irrational can the rectangle have rational area

Let us consider that sides of the rectangle be [tex]2\sqrt{2}[/tex] and [tex]\sqrt{2}[/tex]

Hence the area of the rectangle is the product of sides which is [tex]4[/tex] sq. units

Which is a rational number

Hence, Yes it is possible for a rectangle to have irrational sides and rational area

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The fractional equivalent of the repeating decimal n = 0.1515... is 5/33, with two repeating digits.

A fractional equivalent is a fraction that shares the same equivalent value with a decimal.

For instance, the equivalent fraction of 0.1515 is 303/2000.  But for a repeating decimal like 0.1515..., the equivalent fraction is 5/33.

When numbers or values are said to be equivalent, it means that they are equal.

By their nature, repeating decimals continue endlessly.

Let x = 0.1515... equation 1

100x = 15.1515... equation 2

Subtract equation 1 from equation 2:

100x = 15.1515...

    x =   0.1515...

99x = 15

x = 15/99

x = 5/33

Thus, n = 0.1515... as a repeating decimal or 5/33 as a fraction.

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Answer:

Rational

Step-by-step explanation:

there are very few irrational numbers, such as

[tex] \sqrt{2} [/tex]

or π

most of irrational numbers have a lot of decimal digits. And also numbers with 2 decimal digits are all rational because you can write them as

[tex] \frac{49}{100} [/tex]

Answer:

Option D.

Step-by-step explanation:

We are given with three function.

Plug in x=-2 in first functionf(x)= 3 so f(-2) = 3Plug in x=-2 in second function.

Given that g(x)=2x + 1,

therefore, the value of g(a+h) and g(a) can be written as,g(x)=2x + 1g(a+h)=2(a+h) + 1     
   = 2a + 2h + 1

g(x) = 2x + 1g(a) = 2(a) + 1   
   = 2a + 1

Now, the value of g(a+h)-g(a) will be,

g(a+h) - g(a)= (2a + 2h + 1) - (2a + 1)= 2a + 2h + 1 - 2a - 1= 2h

Hence, the value of g(a+h)-g(a) is 2h.

The value of the quotient expression 546 ÷ 13 is 42

The expression is given as

546 divided by 13

Rewrite the expression as

546 ÷ 13

By the standard algorithm, we have

The expression can be solved using a calculator and with the use of standard algorithm i.e. partial decomposition

By the rule of partial decomposition, we have

a ÷ b = (c ÷ d) ÷ b

Where

a = c + d

Next, we expand the expression as follows:

546 ÷ 13 = (520 + 26) ÷ 13

Remove the brackets

So, we have

546 ÷ 13 = 520 ÷ 13 + 26 ÷ 13

Evaluate the quotients

So, we have

546 ÷ 13 = 40 + 2

Evaluate the sum

So, we have

546 ÷ 13 = 42

Hence, the solution of 546 ÷ 13 is 42

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