The total population of students was 380. Based on the data, what is the best approximation for the total number of students who have a cell phone plan with company Y?

The total number of books that we had in out bookcase when we were 11 years old was 2,187 books.

Suppose the initial term of a geometric sequence is [tex]a[/tex]

and the term by which we multiply the previous term to get the next term is [tex]r[/tex]

Then the sequence would look like

[tex]a, ar, ar^2, ar^3, \cdots[/tex]

(till the terms to which it is defined)

Thus, the nth term of such sequence would be

[tex]T_n = ar^{n-1}[/tex] (you can easily predict this formula, as for nth term, the multiple r would've multiplied with initial terms n-1 times).

Lets suppose its initial term is  [tex]a[/tex] , multiplication factor is  [tex]r[/tex]

and let it has total n terms, then, its sum is given as:

[tex]S_n = \dfrac{a(r^n-1)}{r-1}[/tex]

(sum till nth term)

For this case the initial number of books (2) is multiplied by 3 each year.

So we got:

a = 2,

r = 3

Since a = 2 was for age 5, and  if we take age 5 at 1st position, then age 11 is at the 7th position.

The number of books we read at each age is a geometric sequence with initial term 2 and multiplication factor 3.

The sum of its term(which would make it geometric series) will give the total number of books we will have.

Since age 11 is at 7th position, so n = 7

Thus, the total number of books we had in the bookcase when we were 11 years old is:

[tex]S_n = \dfrac{a(r^n-1)}{r-1}\\\\S_7 = \dfrac{2((3)^7-1)}{3-1} = 2187[/tex]

We could've derived it without formula as:

Their sum is 2187.

Thus, the number of books that we had in out bookcase when we were 11 years old was 2187 books.

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Answer:

Step-

Honey it c !!!!………!l║.by-step explanation:

The explicit formula for the given "geometric-sequence" is aₙ = 4 × 2ⁿ⁻¹, and the eight term is 512, Option(c) is correct.

To find the explicit formula for a geometric-sequence, we need to find the common ratio between any two consecutive terms.

In this sequence, we can see that each term is obtained by multiplying the previous term by 2. So, the "common-ratio" is 2.

We also know the "first-term" is 4, so we use the formula for the nth term of a geometric sequence which is : aₙ = a₁ × rⁿ⁻¹,

Substituting the values,

We get,

⇒ a₈ = 4 × 2⁽⁸⁻¹⁾

⇒ a₈ = 4 × 2⁷

⇒ a₈ = 512,

Therefore, the correct answer is (c) aₙ = 4 × 2ⁿ⁻¹; 512.

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The given question is incomplete, the complete question is

Find the explicit formula for the geometric sequence. Then find a₈.

4, 8, 16, 32, 64,....

Which Answer is Correct:

(a) aₙ = 4 × rₙ - 1; 1024

(b) aₙ = a₁ × 2ⁿ⁻¹; 256

(c) aₙ = 4 × 2ⁿ⁻¹; 512

(d) aₙ = 2 × 4ⁿ⁻¹; 512

Answer:

y-4=-7(x-1) OR y-(-10)=-7(x-3)

Step-by-step explanation: The point-slope form is [tex]y_[/tex]-[tex]y_{1}[/tex]=[tex]m_[/tex]([tex]x_[/tex]-[tex]x_{1}[/tex])

In slope-intercept form, the equation would be y = -7x + 11

You could find the slope by using the slope equation, [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex].

Using that, you would get -7. Thus by inserting one of the points and the slope in the point-slope equation, you will get your answer.

Answer:

Value of blank 1 is 2

Value of blank 2 is 10

Step-by-step explanation:

We are given that a and b are the lengths of legs of right angle in right angled triangle .

b = 3

We are also given that c is the hypotenuse

c = hypotenuse = 7

To find the value of 'a' we will use Pythagoras theorem

[tex]Hypotenuse^2 = perpendicular^2 +base^2\\c^2=a^2+b^2\\7^2=a^2+3^2\\7^2-3^2=a^2\\\sqrt{7^2-3^2}=a\\\sqrt{40}=a\\2\sqrt{10}=a\\[/tex]

Value of blank 1 is 2

Value of blank 2 is 10

Answer:

66 units

Step-by-step explanation:

just addition

Answer:

66 units

Step-by-step explanation:

The perimeter of a two dimensional object is all of its sides added together:

6+14+10+17+4+3+8+4=

20+10+17+4+3+8+4=

30+17+4+3+8+4=

47+4+3+8+4=

51+3+8+4=

54+8+4=

62+4=

66 units

Answer:

A) Suppose we have an onedimensional situation.

in the 0 of our x-axis, we have a fruit tree, and we want to rest at a distance no bigger than 6 ft of the tree, then all the possible positions of our resting place are:

x ∈(-6ft, 6ft)

we can write this as: IxI < 6ft

b) now we think the opposite situation, we want to rest at least 6ft away from the tree, then we have that:

x ∉  [-6ft, 6ft].

or IxI > 6ft.

So you can see that the difference in those two cases is if we want to be "inside a given range" (for the first case) or "outside a given range" (for the second case).

Answer:

the answer is -15°F

1st: draw a number line

2nd: start at -2

3rd: go back 13 spaces toward the negitive

4th: u get your answer= -15°F

Answer:

A

Step-by-step explanation:

15 boxes multiplied by 2 is 30, 1/3 times 30 is 10

Answer:

$43,200

Step-by-step explanation:

25% is 1/4 of the total dollar value, to find the answer we need to multiply 10,800 by 4 (it is 1/4, and the answer will be equivalent to the 4/4)

10,800 * 4 = 43,200

The total dollar value of the art that he sells is 43200 dollars.

Percentage is the value per hundredth.We can also convert percentages into decimals by dividing he percentage value by 100.

According to the given question Pierre, an art dealer, earns 25% commission of the dollar value of the art pieces that he sells at the Bizzell Gallery. Pierre earns $10,800.

∴ 25% of the total value is 10800 dollars.

Assuming total value to be x dollars.

So, (25/100)x = 10800

(1/4)x = 10800

x = 10800 × 4

x = 43200 dollars.

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Answer:

-1/5x -4/5 = y

Step-by-step explanation:

f(x) = -5x -4

y = -5x-4

Switch x and y

x = -5y -4

Solve for y

Add 4

x+4 = -5y

Divide by -5

-1/5x - 4/5 = -5y/-5

-1/5x -4/5 = y

Answer:

f(x) = -5x - 4

let f(x)= y

y = -5x -4

x = -5y - 4

-5y = x+4

y = - (x +4)/5

The inverse of f(x) is -(x +4)/5

Hope this helps.

Answer:

2nd option is the correct answer.

Step-by-step explanation:

[tex] \because \bigg(x + \frac{b}{2a}\bigg) ^2 = \frac{-4ac+b^2}{4a^2}\\\\

\therefore \bigg(x + \frac{b}{2a}\bigg) ^2 = \frac{b^2-4ac}{4a^2}\\\\

\therefore \bigg(x + \frac{b}{2a}\bigg) = \pm \sqrt {\frac{b^2-4ac}{4a^2}} \\\\

\purple {\boxed {\bold {\therefore x + \frac{b}{2a}= \frac{\pm\sqrt{b^2-4ac}}{2a}}}} \\\\[/tex]

Answer:

B

Step-by-step explanation:

Answer:

Congruent angles

Step-by-step explanation:

Angle bisectors, divides the given angle into two equal parts

thus if value of angle is x then angle bisector will divide this angle into  parts

of equal value x/2 .

_______________________

complementary angles are two angles whose sum is 90 degrees.

since we do not the value of angle we cannot say with certainty that the angles are complementary

Congruent angles are angles who have the same angular measurement.

since, in above problem we have seen that angle bisector divides the angle in two equal parts.

hence angles are equal and thus they are congruent angle.

Congruent angles is the correct answer.

_______________________________________

vertical angles are angle opposite two one another when two line cross each other.

Since in the problem line is not intersecting each other thus, angles do not qualify to be vertical angles

Supplementary angles are two angles whose sum is 180 degrees.

since we do not the value of angle we cannot say with certainty that the angles are Supplementary.

Hence correct option is Congruent angles

Answer:

congruent angles

Step-by-step explanation:

Answer:

Look at the underlined numbers

So we have 16 = 16*1

then 64 = 16*4

the difference would be 3

then 144 = 16*9

the difference would be 5

256 = 16*16

the difference would be 7

400 = 16*25

the difference would be 9

so the next one would be 11+25=

3, 5, 7, 9, 11

ANSWER: 16*(11+25) = 36*16 = 576

Step-by-step explanation:

I explained before this

Answer: Look at the number of points where the graphs intersect each other...the points where the graphs of the functions cross each other are the solutions to the system. 

Upon looking, you should see 4 points where the graphs intersect, so there are 4 solutions to the non-linear system of equations. 

Step-by-step explanation:

Answer:

You Should see 4 Points

Step-by-step explanation:

Answer:

the length is 98 meters and the width 98 meterss

Step-by-step explanation:

We have that the length is l and the width is w, we know that:

P = 2 * w + 2 * l

if we solve for it, we have:

l = P / 2 - w

Now, we know that the area is:

A = l * w

if we replace l, we are left with:

A = (P / 2 - w) * w

A = P * w / 2 - w ^ 2

we derive to know the maximum area and we equal 0 and we have:

A '= P / 2 - 2 * w

0 = P / 2 - 2 * w

w = P / 4

now for him:

l = P / 2 - P / 4

l = P / 4

Therefore, if we replace:

l = 392/4 = 98

w = 392/4 = 98

For the maximum area the length is 98 meters and the width 98 meterss

Answer:

Option (1)

Step-by-step explanation:

Characteristics of the graph attached,

1). Heart rates of the teenagers (0 to 20 years) varies from 112 beats per minute to 72 beats per minute.

2). Heart rates of the adults (20 years to 50 years) remains constant (72 beats per minute)

Option 1). Since average resting heart rate of the teenagers decreases from 0 to 10 years, so at the 20 years of age heart rate will be less than a teenager of 20 years.

Therefore, statement is not supported by the graph.

Option (2). A 20-year-old has the same average resting heart as at 30-year-old. [True]

Therefore, this option is supported by the graph.

Option (3). A 40-year-old may have the same average resting heart rate for 10 years.

[True]

Therefore, this statement is supported by the graph.

Option (4). The average resting heart rate for teenagers steadily decreases.

[True]. There is a linear decrease in the teenagers heart rate shown in the graph.

Therefore, the given statement is true and supported by the graph.

Option (1) will be the answer.

Answer:

6x^2

Step-by-step explanation:

What goes in the box is

2x* 3x

6 x*x

6x^2

Answer:

2x+7 = 6

x = -1/2

Step-by-step explanation:

Answer:

2x+7=6

Step-by-step explanation:

The gradient of the blue line which shown in the graph and passes from the point (3,0) and (-1,2) is -1/2.

The gradient of a line is the difference in the height of the y coordinates and the difference in the width of the coordinates. It can be calculated with the following formula.

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Here, (x1,y1) and (x2,y2) are the coordinates of two points lies on the line.

In the given graph, the blue line passes through the point (3,0) and the form the point (-1,2). Thus, the gradient of the line is,

[tex]m=\dfrac{2-0}{-1-3}\\m=\dfrac{2}{-4}\\m=-\dfrac{1}{2}[/tex]

Thus, the gradient of the blue line which shown in the graph and passes from the point (3,0) and (-1,2) is -1/2.

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Answer: 8 miles per hour

Step-by-step explanation:

Speed = distance / time

When diatance is 60 miles

Speed = 60 / 1.5 = 40 miles per hour

When distance is 20% more (72 miles)

Speed = 72 / 1.5 = 48 mph

Answer:

A. Domain : (-∞, ∞)

B. Function is increasing in the interval (-2, 0) and (2, ∞)

   Decreasing in the interval of (-∞, -2) and (0, 2).

Step-by-step explanation:

A. Given function is, y = |2x - 1|

This function is the transformed form of the parent function, y = |x|

Domain of the parent function is { x | x is a set of real numbers}

Therefore, domain of the transformed function will be the same as the domain of the parent function.

Domain of the function = {x | x is a real number}

B. Given function is f(x) = [tex](x^2-4) ^{\frac{2}{3} }[/tex]

Domain of the function : (-∞, ∞)

Critical points of the function are,

⇒ x = 0, ±2

Now we find the three intervals where we have to check the function to be increasing or decreasing.

(-∞ -2), (-2, 0), (0, 2), (2, ∞)

Derivative of the function f(x),

f'(x) = [tex]\frac{4x}{3(x^2-4)^{\frac{1}{3} } }[/tex]

Here, f'(x) < 0 for (-∞, -2)

f'(x) > 0 for (-2, 0)

f'(x) < 0 for (0, 2)

f'(x) > 0 for (2, ∞)

Therefore, given function is increasing in the interval (-2, 0) and (2, ∞)

And it's decreasing in the interval of (-∞, -2), and (0, 2).

Answer:

tens place

Step-by-step explanation:

tens  ones . tenths hundredths

2        3     .     4       5

Answer:

[tex]x = 14\\y = 20 \\[/tex]

Step-by-step explanation:

Finding x:

8x + 3x + 26 = 180 (Angle on a straight line add up to 180°)

11x = 180-26

11x = 154

Dividing both sides by 11

x = 14

Finding y:

3x + 5y + 38 = 180 (Angle on a straight line add up to 180°)

3(14) + 5y + 38 = 180

42 + 38 + 5y = 180

80 + 5y = 180

5y = 180-80

5y = 100

Dividing both sides by 5

y = 20

Answer:

x = 14, y = 20

Step-by-step explanation:

[tex](8x + 26) \degree + 3x \degree = 180 \degree..(straight \: line \: \angle s) \\ (11x + 26) \degree = 180 \degree \\ 11x + 26 = 180 \\ 11x = 180 - 26 \\ 11x = 154 \\ \\ x = \frac{154}{11} \\ \\ \huge \red { \boxed{x = 14}} \\ \\ (5y + 38) \degree = (8x + 26) \degree..(vertical \: \angle s) \\ 5y + 38 = 8 \times 14 + 26 \\ 5y + 38 = 112 + 26 \\ 5y + 38 = 138 \\ 5y = 138 - 38 \\ 5y = 100 \\ \\ y = \frac{100}{5} \\ \\ \huge \purple{ \boxed{ y = 20}}[/tex]

Answer:

6 days

Step-by-step explanation:

Answer:

Step-by-step explanation:

a number greater than 5 - 1/6

a prime number - 1/2

a number greater than 4 - 1/3

a number less than 6 - 5/6

Answer:

A cicle centered in the origin has equation.

[tex]x^2+y^2=r^2\\4^2+1^2=r^2\\r=\sqrt{17}\\ \\\sqrt{5}^2+\sqrt{2}^2\neq \sqrt{17}^2\\ 7\neq 17[/tex]

The point does not lies on the circle

Answer:

17-(- 2 / 5j)

Step-by-step explanation:

16 + (- 5 ) - 2/5j - 4/5 j + 6

    \/                  \/            \/

    11-         ( -2/5j )       + 6

From here you over  the 6 over to the 11

11+6-(-2/5j)

 \/

17-(-2/5j)

It can not be simplified farther I believe

Answer:

62

Step-by-step explanation:

Because 775 divided by 12 1/2= 62

Answer:

The answer would be A. 1 1/5

48/40 = 1 8/40

1 8/40 Simplify to 1 1/5

Hope this helps!

Step-by-step explanation: