Which is the recursive formula for the explicitly defined sequence?
an = 8n-3

The correct answer is 17: 30

Explanation:

The purpose of a ratio is to express the relationship between two elements in terms of quantities. For example, if there are 5 oranges and 4 lemons the ratio is 5 to 4. Additionally, this relationship between the quantities of two different things can be expressed as a fraction, by using a colon (:) or by using the word "to." In the last two cases, the colon or word "to" separate the two amounts compared.

In the case presented, the total of days observed was 30 days (17 days with rain + 13 days with no rain) and the ratio of rainy days to the total of days can be expressed as 17:30, [tex]\frac{17}{30}[/tex] or as 17 to 30, considering there were 17 rainy days out of a total of 30 days.

Answer:

9, 8, 7

Step-by-step explanation:

This is the rank of the cards from highest to lowest and the terms are:

So the next 3 terms are 9, 8, 7

Answer:

A. 3x^2+7x^2+2×3x ×7-84x = 3x^2+7x^2-2×3x×7

9x^2+49x^2+42x-84 x= 9x^2+49x^2-42x

9x^2+49x^2-42 = 9x^2+49 x^2-42x

verified

B.

Answer:

Give him or her brainlist

Step-by-step explanation:

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Answer:

Area of the rectangular pen is: [tex]18 \,x-x^2[/tex]

Step-by-step explanation:

We need to specify that the perimeter of the rectangular area of side x adds to the amount of fence Pablo has (36 feet). Recall as well that the opposite sides of a rectangle are equal, so if there is a side of length x, there must be another one of this size as well (a total of 2 x in the perimeter),let's assume that the perpendicular sides to x are of length y, then:

Perimeter= 2 x + 2 y = 36

so, 2 (x+y)  = 36   then  (x+y) = 18

and therefore the side y should be:

y = 18 - x

Now we can write the formula for representing the area of the rectangle (product of both quantities: x * y

[tex]Area=x\,*\,y = x\,(18-x) =18 \,x-x^2[/tex]

Answer:

A) Mean cost per game= $202.8

B). Range= $104

C). Variance= 1182.96

D).Standard deviation=34.39

E). $1014 per person

Step-by-step explanation:

The data of the cost

= $266, $201, $197, $188, $162

A). Mean cost per game

Mean = (266+201+197+188+162)/5

Mean = 1014/5

Mean = 202.8

Mean cost per game= $202.8

B) range = highest value- Lowest value

Range= 266-162

Range= $104

C) variance= ((266-202.8)²+(201-202.8)²+(197-202.8)²+(188-202.8)²+(162-202.8)²)/5

Variance=(3994.24+3.24+33.64+219.04+1664.64)/5

Variance= 5194.8/5

Variance= 1182.96

D). Standard deviation= √variance

Standard deviation= √1182.96

Standard deviation=34.39

E).Mean cost per person

= Mean *5

= 202.8 *5

= $1014 per person

Answer: the three positive numbers are; 70, 70, 70

Step-by-step explanation:

Given that sum is equal = 210

Lets ( x, y, z ) be the three positive numbers

such that

x + y + z = 210

what is the maximum of xyz

take f(x,y,z) = xyz

Q(x,y,z) = 0

x + y + z -210 = 0

consider the function

F(x,y,z) = f(x,y,z) + λQ(x,y,z)

F = xyz + λ(x+y+z-210)

dF/dx = 0 ⇒ yz + λ(1) = 0 ⇒ λ = -yz   ..............equ(1)

dF/dy = 0 ⇒ xz + λ(1) = 0 ⇒ λ = -xz.................equ(2)

dF/dz = 0 ⇒ xy + λ(1) = 0 ⇒ λ = -xy...............equ(3)

Now

equ(1)/equ(2) ⇒ λ/λ = -yz/-xz ⇒ x = +y

equ(1)/equ(3) ⇒ λ/λ = - yz/-xy ⇒ x = +z

⇒ y = z = x

by substitution

x + y + z = 210

x + x + x = 210

3x = 210

x = 210/3 = 70

∴ x, y, z = 70, 70 ,70

MAXIMUM

∛xyz = 70  { when x = y = z = 70}

Answer:

P' (2, -4)

Q' (3, -1)

R' (4, -4)

Step-by-step explanation:

Reflection in the y axis

(x, y) → (-x, y)

P(⁻²₋₄ ) → P'(²₋₄ ) ∴ P'(2, -4)

Q(⁻³₋₁ ) → Q'(³₋₁ ) ∴ Q'(3, -1)

R(⁻⁴₋₄ ) → R'(⁴₋₄ ) ∴ R'(4, -4)

Answer:

D . 9 .1/13

Step-by-step explanation:

[tex]9\div 13 = \frac{9}{13} \\\\9\cdot \frac{1}{13}\\\\=\frac{9}{1}\cdot \frac{1}{13}\\\\=\frac{9\cdot \:1}{1\cdot \:13}\\\\=\frac{9}{13}[/tex]

Answer:

It has a negative slope = -2

Step-by-step explanation:

Let y be the price and x be the quantity purchased . Then putting the value of x in the equation we can find the price= y

where  y = −2x+8

x      0       1         2         3         4         5         6        7

y      8       6        4         2         0        -2         -4       -6

So we can plot the demand curve which has a negative slope.

We see from the values above that the slope is negative having a value equal to -2. This means that for every increase in the number of quantities there is a decrease in the price.

Each interior angle of a rectangle measures 90°

A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles (90°). The opposite sides of a rectangle are equal and parallel.

According to the property of a rectangle, we have,

Hence, Each interior angle of a rectangle measures 90°

For more references on rectangle, click;

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Answer:

f(7)=10-14=-4

Answer=-4

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

f(x)=10-2x

Let x = 7

f(7) = 10 -2(7)

     = 10 -14

     = -4

Answer: 24 m

Step-by-step explanation:

Given: area of the circle is 144 π m² .

Area of a circle = [tex]\pi r^2[/tex], where r= radius of the circle.

Then, [tex]144\pi = \pi r^2[/tex]

Cancelling π from both sides , we get

[tex]144 = r^2[/tex]

Taking square root on both sides , we get'

[tex]12= r[/tex]

i.e. radius = 12 m

Then diameter = 2 (radius ) = 2 (12)= 24 m

Hence, the diameter of the circle is 24 m.

The diameter of the circle is 13.54cm

The formula for calculating the area of the circle is expressed as:

A = πd²/4

d is the diameter of the circle

GIven the following

A = 144m²

Substitute the area into the circle

144 = πd²/4

πd² = 144 * 4

πd² = 576

d² = 576/3.14

d² =183.44

d = 13.54cm

Hence the diameter of the circle is 13.54cm

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Greetings from Brasil....

Remember that F(X) = Y

Looking at the graph we can conclude that:

Y > 0 when X < - 4 (up until -∞)

Y = 0 when X = - 4

Y < 0 when X > - 4 (up until +∞)

So choose:

[F(X) = Y]  > 0 over the interval ]-∞; -4[

(last option)

Answer:

Only B

Step-by-step explanation:

Did this in Khan Academy.

=> Also, there are 2 '-' symbols in the question.

In Option A, there is only 1 "-' symbol.

In Option B, there are 2 '-' symbols.

Option C says none of the above.

Since, Option B has 2 '-' symbols, it is the correct.

Answer:

[tex] \frac{3}{5} [/tex]

Step-by-step explanation:

Let the side length for the octagon having 9m² as area = x

Side length for the octagon having area of 25m² = y.

Thus:

[tex] \frac{9}{25} = (\frac{x}{y})^2 [/tex] (area of similar polygons theorem)

The scale factor of their sides would be [tex] \frac{x}{y} [/tex]. Which is:

[tex] \sqrt{\frac{9}{25}} = \frac{x}{y} [/tex]

[tex] \frac{\sqrt{9}}{\sqrt{25}} = \frac{x}{y} [/tex]

[tex] \frac{3}{5} = \frac{x}{y} [/tex]

Scale factor of their sides = [tex] \frac{3}{5} [/tex]

Answer:

3:5

Step-by-step explanation:

Answer:

[tex]\Huge \boxed{y=-1}[/tex]

[tex]\rule[250]{250}{3}[/tex]

Step-by-step explanation:

[tex]y=14-0.5x[/tex]

The input x is 30. Switching x with 30.

[tex]y=14-0.5(30)[/tex]

Solving for y.

[tex]y=14-15[/tex]

[tex]y=-1[/tex]

[tex]\rule[250]{250}{3}[/tex]

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{y = - 1}}}}}[/tex]

Step-by-step explanation:

Given, Value of x is 30

To find : Value of y

[tex] \sf{y = 14 - 0.5x}[/tex]

Plug the value of x

⇒[tex] \sf{y = 14 - 0.5 \times 30}[/tex]

Multiply the numbers : 0.5 and 30

⇒[tex] \sf{y = 14 - 15}[/tex]

Subtract 15 from 14

⇒[tex] \sf{y = - 1}[/tex]

Hope I helped!

Best regards!!

===============================================

Work Shown:

Part I

[tex]\displaystyle \lim_{x \to 2}\frac{x-2}{x+2} = \frac{2-2}{2+2}\\\\\\\displaystyle \lim_{x \to 2}\frac{x-2}{x+2} = \frac{0}{4}\\\\\\\displaystyle \lim_{x \to 2}\frac{x-2}{x+2} = 0\\\\\\[/tex]

----------

Part II

[tex]\displaystyle \lim_{x \to 0}\frac{\sin(x)}{x+2} = \frac{\sin(0)}{0+2}\\\\\\\displaystyle \lim_{x \to 0}\frac{\sin(x)}{x+2} = \frac{0}{2}\\\\\\\displaystyle \lim_{x \to 0}\frac{\sin(x)}{x+2} = 0\\\\\\[/tex]

----------

Part III

[tex]\displaystyle \lim_{x \to 5}\frac{x}{x} = \lim_{x \to 5}1\\\\\\\displaystyle \lim_{x \to 5}\frac{x}{x} = 1\\\\\\[/tex]

Answer:

The Confidence Interval = (66.1476, 68.8524)

Step-by-step explanation:

The formula for confidence interval of a normal distribution is given as:

Confidence Interval = μ ± z × σ/√n

Where:

μ is the mean height = 67.5

σ is the standard deviation = 2.1 inches

n is the number of samples = 16 bookcases

z = 99% confidence interval = 2.576

Confidence Interval = 67.5 ± 2.576 ×2.1√16

= 67.5 ± 2.576 × 2.1/4

Confidence Interval = 67.5 ± 1.3524

67.5 - 1.3524 = 68.8524

67.5 + 1.3524 = 66.1476

Therefore, the Confidence Interval = (66.1476, 68.8524)

Answer:  see below

Step-by-step explanation:

The coordinates on the Unit Circle are (cos, sin). Since we are focused on cosine, we only need to focus on the left side of the coordinate. The cosine value (left side) will be the y-value of the function y = cos x

Use the quadrangles (angles on the axes) to represent the x-values of the function y = cos x.

Quadrangles are: 0°, 90°, 180°, 270°, 360°  (360° = 0°)

Together, the coordinates will be as follow:

[tex]\boxed{\begin{array}{c||c|c||c}\underline{(cos,sin)}&\underline{x=angle}&\underline{y=cosx}&\underline{\quad (x,y)\quad}\\(1,0)&0^o&1&(0^o,1)\\(0,1)&90^o&0&(90^o,0)\\(-1,0)&180^o&-1&(180^o,-1)\\(0,-1)&270^o&0&(270^o,0)\\(1,0)&360^o&1&(360^o,1)\end{array}}[/tex]

Answer: Mass of Lamina is (K/3)

Centre of mass is (3/8, 3pi/16)

Step-by-step explanation:

Find explanation in the attachments

Answer:

[tex]2.5[/tex]    [tex]-1.25[/tex]      [tex]\sqrt{16}[/tex]        [tex]0.6[/tex]

Step-by-step explanation:

Required

Which of the given parameters can be represented as fraction of integers

Taking them one at a time;

1.  2.5

This can be rewritten as

[tex]2.5 = \frac{2.5}{1}[/tex]

Multiply numerator and denominator by 2

[tex]2.5 = \frac{2.5 * 2}{1 * 2}[/tex]

[tex]2.5 = \frac{5}{2}[/tex]

Hence, 2.5 can be represented as fraction of integers

2.  √14

This can be rewritten as

[tex]\sqrt{14} = 3.74165738677...[/tex]

The ... implies that the decimal continues and this cannot be represented as a fraction

3.  -1.25

This can be rewritten as

[tex]-1.25 = \frac{-1.25}{1}[/tex]

Multiply numerator and denominator by 4

[tex]-1.25 = \frac{-1.25 * 4}{1 * 4}[/tex]

[tex]-1.25 = \frac{-5}{4}[/tex]

Hence, -1.25 can be represented as fraction of integers

4.  5.33333.....

The ... implies that the decimal continues and this cannot be represented as a fraction

5.  √16

[tex]\sqrt{16} = \±4[/tex]

This can be rewritten as

[tex]\sqrt{16} = \±\frac{4}{1}[/tex]

Multiply numerator and denominator by 2

[tex]\sqrt{16} = \±\frac{4 * 2}{1 * 2}[/tex]

[tex]\sqrt{16} = \±\frac{8}{2}[/tex]

Hence, √16 can be represented as fraction of integers

6.  0.6

This can be rewritten as

[tex]0.6 = \frac{0.6}{1}[/tex]

Multiply numerator and denominator by 10

[tex]0.6 = \frac{0.6 * 10}{1 * 10}[/tex]

[tex]0.6 = \frac{6}{10}[/tex]

Hence, 0.6 can be represented as fraction of integers

Answer/Step-by-step explanation:

We are told that:

Area of the given square = 1 square units

2 of the small triangles will make up the square when joined together.

Since area of the square is 1 square units, area of the 2 small triangles = 1 square units.

We are also told that 2 of the small triangle will also make up the medium triangle when joined together.

Therefore, since area of 2 small triangles = area of the square = 1 square units, the medium triangle would also have an area of 1 square units.

1. Area of the small triangle is ½ square units. I know this because 2 small triangles = area of the square = 1 square units.

2. The area of the medium triangle is 1 square units. I know this because 2 small triangles make up the medium triangle, and 1 small triangle has an area of ½ square units.

3. The area of the large triangle is 2 square units. I know this because if the medium triangle is made up of 2 small triangles, then 4 small triangles will make up the big triangle, or 2 medium triangle will make up the big triangle.

Answer:

I tried to answer but I still would like to know what doesn't make sense.

Considering the identity:

[tex]\sec^2\theta-\tan^2\theta=1 \implies |\sec\theta|\geq1[/tex]

[tex]$\forall\;\theta\in\mathbb{R}-\{(2n+1)\frac{\pi}{2}, n\in\mathbb{Z} \}$[/tex]

The identity is true whenever both sides are defined. It is not supposed to hold the values when we have division by zero, because it is undefined.

If the value doesn't make sense, it is probably not a function, or it is undefined by the given value of [tex]x[/tex].

Let's go back to the definition of function again:

A function relates a set of inputs and a set of allowable outputs where each input is related to only one output. It basically defines the relation of ordered pairs.

Hope it helped you a bit.

Answer:

$12 up to $15

Step-by-step explanation:

Given

Hourly Earning: $6 - $9 || $9 - $12 || $12 - $15

Frequency:          16        ||         4      ||   10

Required

Determine the limits of the least frequency;

First, we have to determine the lowest frequency;

From the table. the lowest frequency is:

[tex]Lowest = 10[/tex]

Next is to determine the corresponding class limits

The corresponding class limit is $12 up to $15

Answer:

sinx = perpendicular/hypotenuse

sinx = 12/16

sinx = 3/4

x = arcsin 3/4

x = 48.6 degrees (using calculator)

Answer: 16/77

Step-by-step explanation: Here we're asked to evaluate ab

given that a = 4/7 and b = 4/11.

So we start by plugging in our given

values for a and b into the problem.

If we do this, ab would then be (4/7)(4/11).

When multiplying two fractions together, we multiply across

the numerator and we also multiply across the denominators.

So (4/7)(4/11) is 16/77 which is our final answer.

Answer:

16/77

Step-by-step explanation:

When two numbers are close togtether, you want to multiply them.  Since it is ab, you multiply a and b.  

a= 4/7

b= 4/11

so, 4/7 times 4/11

When you multiply fractions, you multiply the numerators (the top number of a fraction) of the fractions together.  You also multiply the denominators(the bottom number) of the fractions together.

So, let's multiply the numerators first.

4 times 4 equals 16, so that is the new numerator

7 times 11 is 77, so that is the new denominator

Let's combine it into a fraction.  Numerator/denominator= 16/77

Sometimes, you will need to reduce.  Reducing meaning that you divide the fraction by a number so it can't be reduced/divided anymore.  Until a fraction is at it's simplest form.  

Example: 2/4 reduces to 1/2 because both the numerator, 2, and the denominator, 4, can be reduced by 2.  As you can see, 1/2 is at it's simplest form and cannot be reduced any further.

Answer:

(a) Approximately 68 % of women in this group have platelet counts within 1 standard deviation of the mean, or between 195.5 and 319.7.

(b) Approximately 99.7% of women in this group have platelet counts between 71.3 and 443.9.

Step-by-step explanation:

We are given that the blood platelet counts of a group of women have a bell-shaped distribution with a mean of 257.62 and a standard deviation of 62.1

Let X = the blood platelet counts of a group of women

So, X ~ Normal([tex]\mu=257.62, \sigma^{2} =62.1^{2}[/tex])

Now, the empirical rule states that;

(a) The approximate percentage of women with platelet counts within 1 standard deviation of the mean, or between 195.5 and 319.7 is 68% according to the empirical rule.

(b) The approximate percentage of women with platelet counts between 71.3 and 443.9 is given by;

       z-score of 443.9 =  [tex]\frac{X-\mu}{\sigma}[/tex]

                                   =  [tex]\frac{443.9-257.62}{62.1}[/tex]  = 3

       z-score of 71.3 =  [tex]\frac{X-\mu}{\sigma}[/tex]

                                =  [tex]\frac{71.3-257.62}{62.1}[/tex]  = -3

So, approximately 99.7% of women in this group have platelet counts between 71.3 and 443.9.