what is the range of the data set?

69

49

40

19

Answer:

d

Step-by-step explanation:

Given

f(n + 1) = f(n) - 2 with f(1) = 10

To generate the sequence substitute values for n into the recursive formula.

f(1) = 10

f(2) = f(1) - 2 = 10 - 2 = 8

f(3) = f(2) - 2 = 8 - 2 = 6

f(4) = f(3) - 2 = 6 - 2 = 4

f(5) = f(4) - 2 = 4 - 2 = 2

The first 5 terms are 10, 8, 6, 4, 2

Answer:

D,10,8,6,4,2

Step-by-step explanation:

Answer: D: 1/16

Step-by-step explanation:

Answer:

the answer is 1/16

Step-by-step explanation:

For this case we must solve the following equations:

[tex]5x + 7 = 3x + 21[/tex]

We subtract 3x on both sides of the equation:

[tex]5x-3x + 7 = 21[/tex]

We subtract 7 on both sides of the equation:

[tex]5x-3x + 21-72x = 14[/tex]

We divide between 2 on both sides of the equation:

[tex]x = \frac {14} {2}\\x = 7[/tex]

The second equation is:

[tex]3x-2 (5-x) = - 3 (x-10) + 3x[/tex]

We apply distributive property to the terms of parentheses:

[tex]3x-10 + 2x = -3x + 30 + 3x[/tex]

We add common terms:

[tex]5x-10 = 30[/tex]

We add 10 to both sides of the equation:

[tex]5x = 30 + 10\\5x = 40[/tex]

We divide between 5 on both sides of the equation:

[tex]x = \frac {40} {5}\\x = 8[/tex]

Third equation:

[tex]5 (x + 1) = 3 (2x + 3) +5[/tex]

We apply distributive property to the terms within parentheses:

[tex]5x + 5 = 6x + 9 + 5[/tex]

We add similar terms:

[tex]5x + 5 = 6x + 14[/tex]

We subtract 6x on both sides of the equation:

[tex]5x-6x + 5 = 14[/tex]

We subtract 5 on both sides of the equation:

[tex]-x = 14-5\\-x = 9\\x = -9[/tex]

Answer:

[tex]x = 7\\x = 8\\x = -9[/tex]

Answer:

No, the ladder will not be save at the height 16.5 feet from the ground

She must to buy 9 rolls to have enough crepe papers to decorate her ceiling

Step-by-step explanation:

* Lets change the story problem to mathematics information

- The ladder , the wall and the ground formed together a right

  angle triangle

- The wall and the ground are perpendicular to each other

- The length of the ladder is the hypotenuse of the triangle

- The vertical height of the ladder is the vertical leg of the triangle

- The horizontal distance between the ladder and the vertical wall

 on the ground is the horizontal leg of the triangle

* Lets revise the trigonometry functions

- In any right angle triangle:

# The side opposite to the right angle is called the hypotenuse

# The other two sides are called the legs of the right angle

* If the name of the triangle is ABC, where B is the right angle

∴ The hypotenuse is AC

∴ AB and BC are the legs of the right angle

- ∠A and ∠C are two acute angles

- For angle A

# sin(A) = opposite/hypotenuse

∵ The opposite to ∠A is BC

∵ The hypotenuse is AC

∴ sin(A) = BC/AC

# cos(A) = adjacent/hypotenuse

∵ The adjacent to ∠A is AB

∵ The hypotenuse is AC

∴ cos(A) = AB/AC  

# tan(A) = opposite/adjacent

∵ The opposite to ∠A is BC

∵ The adjacent to ∠A is AB

∴ tan(A) = BC/AB

* Lets solve the problem

- We need to calculate the measure of the angle between the

  ladder and the ground, let it called Ф

- The vertical height is the opposite to this angle Ф

- The hypotenuse is the length of the ladder

∵ We have the opposite and the hypotenuse, we can use

  the sin function

∵ sin(Ф) = opposite/hypotenuse

∵ The opposite is the vertical height = 16.5 feet

∵ The hypotenuse is the length of the ladder = 17 feet

∴ sin(Ф) = 16.5/17

∴ Ф = [tex]sin^{-1}\frac{16.5}{17}=76.1[/tex] dgree

- The ladder will be save if the angle between the ladder and

 the ground is no more than 70°

∵ The angle between the ladder and the ground is 76.1°

∴ Its measure is greater than 70°

* The ladder will not be save at the height 16.5 feet from the ground

* Lets study the information in the problem

- Katie wants to put the crepe paper around the perimeter of the

 ceiling which shaped a square of side length 12 feet

- And also from each corner to the opposite corner

- She needs the length of the 4 sides of the square and the length

 of its 2 diagonals

* Lets find the length of the diagonal of the square

∵ The two adjacent sides of the square formed two legs of a right

   angle triangle and the diagonal joining the endpoints of the legs

  is the hypotenuse of the triangle

- Use Pythagoras theorem to find the length of the diagonal

∴ The length of the diagonal = √(s² + s²) √(2s²) = s√2

∵ The length of the side of the square = 12 feet

∴ The length of the diagonal = 12√2

* Now lets find the length of the crepe papers she needs

∵ She needs the length of the 4 sides of the square and the length

  of its 2 diagonals

∴ The length of crepe papers = 12 + 12 + 12 + 12 + 12√2 + 12√2 = 81.94 feet

∵ Each roll of the crepe papers contain 10 feet

- To find the number of rolls divide the length of the crepe papers by 10

∴ The number of rolls = 81.94 ÷ 10 = 8.194

* She must to buy 9 rolls to have enough crepe papers to decorate

 her ceiling

* V.I.N:

- If she decide to buy 8 rolls, some part of ceiling will not decorate

 because the 8 rolls have 80 feet only and she needs 81.94 feet

Answer;

NO!!!!!!!!!!

Step-by-step explanation:

a^2 + b^2 =c^2

17^2 + b^2=16.5^2

289 + b = 272.25

-289          -289

b=[16.75

b=4.09

Answer:

  -2

Step-by-step explanation:

The midpoint is the average of the end point coordinates, so ...

  4 = (y +10)/2 . . . . the y-coordinate is the average of the y-coordinates

  8 = y +10 . . . . . . . multiply by 2

  -2 = y . . . . . . . . . . subtract 10

Answer:

Step-by-step explanation:

We have

two right triangle with legs 6ft and 8ft

one rectangle 8ft × 12ft

one rectangle 6ft × 12ft

one rectangle 10ft × 12ft

The formula of an area of a right triangle:

[tex]A=\dfrac{ab}{2}[/tex]

a,b - legs

Substitute:

[tex]A_1=\dfrac{(6)(8)}{2}=(3)(8)=24\ ft^2[/tex]

The formula of an area of a rectangle:

[tex]A=lw[/tex]

l,w - length, width (dimensions of rectangle)

Substitute:

[tex]A_2=(6)(12)=72\ ft^2\\\\A_3=(8)(12)=96\ ft^2\\\\A_4=(10)(12)=120\ ft^2[/tex]

The Surface Area:

[tex]S.A.=2A_1+A_2+A_3+A_4\\\\S.A.=(2)(24)+72+96+120=336\ ft^2[/tex]

Answer:

Step-by-step explanation:

True

7 X 9 X 6 = 378

Answer:

First option: True.

Step-by-step explanation:

To know if the volume of this rectangular prism is 378 m³, you need to use the formula for calculate the volume of a rectangular prism:

[tex]V=lwh[/tex]

Where "l" is the lenght, "w" is the width and "h" is the height.

You know that that this rectangular prism measures 7 meters long, 9 meters wide, and 6 meters high, then you can substitute these values into the formula.

Therefore, the volume of the rectangular prism is:

[tex]V=(7m)(9m)(6m)\\V=378m^3[/tex]

Then the answer is: True.

Answer: 28%

Step-by-step explanation:

Add all the numbers in the table = 593

Divide 165/593 = .278

Move decimal 2 places to the right = 27.8

Rounds up to 28%

Answer:

B. Range - 5

Mode - 6

Median - 7

Mean - 8

step by step explaination:

if it's actually around 7, that's mean 7 is equal to median. And then, specifically, the mode & the mean number will side-to-side number of 7..which means number 6 and number 8.

The group of measures which would lead to the provided conclusion is range is 6, mean of the data is 8, median is 7 and mode is 6.

The mean of the data is the average value of the given data. The mean of the data is the ratio of sum of all the values of data to the total number of values of data.

The median of the data is the middle value of the data set when it arrange in ascending or descending order. The data is around 7 which suggest that the median is 7.

Median=7

Mode of a data set is the the value, which occurs most times for that data set. The value which has the highest frequency in the given set of data is known as the mode of that data set.

Mean and mode is around the median. For this case the mean of the data is 8 and mode is 6.

Mode=6

Mean=8

Thus, the group of measures which would lead to the provided conclusion is range is 6, mean of the data is 8, median is 7 and mode is 6.

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Answer: 1008 revolutions

Step-by-step explanation:

1 revolution is equal to [tex]2\pi r[/tex]

To find how many revolutions the wheel makes, you must divide the distance traveled in the race between the circumference of the wheel

You must first convert 62.8318 in to meters.

We know that 1 inch is 0.0254 meters

Then

[tex]62.8318\ in*\frac{0.0254\ m}{1\ in}= 1.5959\ m[/tex]

[tex]revolutions = \frac{1609}{1.5959}\\\\revolutions=1008.21\\[/tex]

Finally The wheel made 1008.21 revolutions

The height of the triangle is 22 centimeters. When The area of a triangular flag is 330 square centimeters

To find the height of the triangle, we can use the formula for the area of a triangle, which is given by:

Area = (1/2) * base * height

where "base" is the length of the base of the triangle, and "height" is the height of the triangle.

Given that the area of the triangular flag is 330 square centimeters and the base is 30 centimeters, we can plug these values into the formula and solve for the height:

330 = (1/2) * 30 * height

To find the height, first, multiply 30 by (1/2):

330 = 15 * height

Now, divide both sides of the equation by 15 to solve for the height:

height = 330 / 15

height = 22

So, the height of the triangle is 22 centimeters.

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Answer:

The standard deviation is 22.6 to the nearest tenth

Step-by-step explanation:

* Lets study how to find the standard deviation (σ) for data set

- First step find the mean of the data

∵ The mean = the sum of the data ÷ the number of the data

# The sum of the data is

  359 + 320 + 365 + 310 + 349 + 351 + 310 + 314 + 364 = 3042

# The number of the data is 9

∴ The mean = 3042 ÷ 9 = 338

- Second step find the difference between each data and the mean

 and square the difference

# 359 - 338 = 21 ⇒ (21)² = 441

# 320 - 338 = -18 ⇒ (-18)² = 324

# 365 - 338 = 27 ⇒ (27)² = 729

# 310 - 338 = -28 ⇒ (-28)² = 784

# 349 - 338 = 11 ⇒ (11)² = 121

# 351 - 338 = 13 ⇒ (13)² = 169

# 310 - 338 = -28 ⇒ (-28)² = 784

# 314 - 338 = -24 ⇒ (-24)² = 576

# 364 - 338 = 26 ⇒ (26)² = 676

- Third step find the variance (σ²)

# Add all the square difference and divide the sum by the

  number of data

∴ σ² = (441 + 324 + 729 + 784 + 121 + 169 + 784 + 576 + 676) ÷ 9

∴ σ² = 4604 ÷ 9 = 511.5555556

- Fourth step find the standard deviation σ  it is the square root of

 the variance

∴ σ = 22.6 to the nearest tenth

* The standard deviation is 22.6 to the nearest tenth

Answer:

24.0

Step-by-step explanation:

i took the test on k12

Answer:

The third equation down is the one you want

Step-by-step explanation:

What you need for this is the point-slope form of a line:

[tex]y-y_{1} =m(x-x_{1} )[/tex]

where y1 is the y coordinate from our point and x1 is the x coordinate from our point.  m is the slope.  That m has to be positive, according to the instructions.  So the first equation and the last one are out, since those are both negative.

If we fit our point into the point-slope form, it looks like this:

[tex]y-(-8)=4(x-(4))[/tex]

which simplifies to

[tex]y+8=4(x-4)[/tex]

and that matches the third equation down.

Answer:

The total area of the prism is [tex]SA=(\frac{9\sqrt{3}}{2}+54)\ in^{2}[/tex]

Step-by-step explanation:

we know that

The surface area of the triangular prism of the figure is equal to

[tex]SA=2B+PL[/tex]

where

B is the area of the triangular face

P is the perimeter of the triangular face

L is the length of the prism

Find the area of the base B

The base is an equilateral triangle

so

Applying the law of sines the area is equal to

[tex]B=\frac{1}{2}(3)^{2}sin(60\°)[/tex]

[tex]B=\frac{9\sqrt{3}}{4}\ in^{2}[/tex]

Find the perimeter P of the triangular face

[tex]P=(3+3+3)=9\ in[/tex]

we have

[tex]L=6\ in[/tex]

substitute

[tex]SA=2(\frac{9\sqrt{3}}{4})+(9)(6)[/tex]

[tex]SA=(\frac{9\sqrt{3}}{2}+54)\ in^{2}[/tex]

Answer:

89.0°

Step-by-step explanation:

The segment from the centre of the circle to the chord is a perpendicular bisector, hence

third side of right triangle = 12.7 ÷ 2 = 6.35

The angle subtended at the centre by arc CD is twice the angle subtended by the right triangle at the centre

The triangle from the centre to C is congruent to the triangle from the centre to D

Calculate the angle (Θ ) in the right triangle using the sine ratio

sinΘ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{6.35}{9.06}[/tex]

Θ = [tex]sin^{-1}[/tex] ( [tex]\frac{6.35}{9.06}[/tex] ) ≈ 44.5°

Hence

measure of CD = 2 × Θ = 2 × 44.5 = 89.0°

Answer:

the answer is C

Step-by-step explanation:

I THOUGHT IT WAS B BUT I WAS WRONG

1 green and 3 blue are in the bag at the beginning.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given

The sum has been solved using a tree diagram.

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Answer:

try the second one because it is the smallest and close togehet so maybe that means that the mean is closer to the number and it nots some outlier.

Step-by-step explanation:

If the box plot or the distribution is spread out then the mean absolute deviations i.e. MAD is high.

and if the box plot is clustered that is the distribution is less spread out that is all the data values are close to the center value then the mean absolute deviation i.e. MAD is small.

From the given four box plot we see that  the second box plot is less spread and the data values are close to the mean of the data.

Hence, it will lead to the least Mean absolute deviation.

Answer:

tan(B)

Step-by-step explanation:

we know that

The tangent of an angle is equal to divide the opposite side to the angle by the adjacent side to the angle

In this problem

tan(B)=AC/AB

substitute

tan(B)=8/15

Answer:

tan(B)

Step-by-step explanation:

Correct

Answer:

D. 3

Step-by-step explanation:

If the prisms are said to the similar, that means that the ratio/relation between their corresponding sides have to equal, so

[tex]\frac{x}{1} = \frac{9}{3} = \frac{30}{10}[/tex]

We can easily use the part x/1 = 9/3 to make a cross-multiplication that would give us:

x = (1 * 9) / 3 = 9/3 = 3

So, the green prism is a dilated version of the blue one by a dilation/scale factor of 3.

As a math teacher, I would guide you through solving the problem of finding the value of \( x \) for two similar prisms. However, without specific information about the measurements of the prisms, we can't calculate this value. Similarity in prisms implies that corresponding lengths are proportional, but without knowing these lengths or their ratios, we can't determine \( x \).
However, let's assume you have provided the dimensions for both prisms. For similar prisms, the ratio of any two corresponding linear measurements (such as the height, width, or depth) is the same. If we were given that the ratio of a pair of corresponding dimensions is 1:3, for example, then all other pairs of corresponding dimensions would also have a 1:3 ratio.
Here's a typical process to follow if you had the dimenions:
1. Determine the ratio of corresponding lengths:
Suppose for the smaller prism, a certain length is given as 'a', and for the corresponding length on the larger prism, the length is given as '3a' (implying a 1:3 ratio for the sides).
2. Apply the ratio to unknown lengths:
If 'x' is an unknown length on the larger prism and its corresponding length on the smaller prism is given as some value 'b', then we set up the proportion \( \frac{b}{x} = \frac{1}{3} \).
3. Solve for 'x':
To find 'x', you would solve the proportion by cross-multiplying and dividing as necessary, \( x = 3b \).
However, since we don't have actual numbers here, we can't follow these steps. To answer this question, I would need specific lengths for the corresponding sides of the prisms. Once provided, I can demonstrate the mathematical process to find \( x \). For now, there is not enough information to solve for \( x \), and none of the options A, B, C, or D can be verified as correct.

[tex]63 \times \frac{2}{3} = \frac{63 \times 2}{3} = \frac{126}{3} = 42 \\ [/tex]

The area of the smaller circle is

[tex]42\pi \: square \: meters[/tex]

Answer:

30°

Step-by-step explanation:

In m KÔL, the angle is Ô and angle Ô is actually 30 degrees ;)

Answer:

m∠KOL = 30°

Step-by-step explanation:

It is given that mKL = 90and mMN = 30∘.

If two secants intersect in the exterior of a circle, then the measure of the angle formed is half the difference of the measures of its intercepted arcs. So,  

m∠KOL= 1/2(mKL− mMN)

Substitute the given values and simplify.

m∠KOL= 1/2 (90∘−30∘)

= 1/2(60∘)

= 30∘

Therefor, m∠KOL=30∘.

Step-by-step explanation:

From the total revenue, we know that:

8t + 12s + 10h = 406

We're also told:

t = 3h

s = 2h

If we substitute these for t and s:

8 (3h) + 12 (2h) + 10h = 406

24h + 24h + 10h = 406

58h = 406

h = 7

Now we can find t and s:

t = 3h = 21

s = 2h = 14

The store sold 21 T-shirts, 14 shorts, and 7 hats.

The clothing store has sold a total of 21 t-shirts, 7 hats, and 14 shorts.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Given,

T-shirts, t, for $8 a shirt; shorts, s, for $12; and hats, h, for $10 each and stored earn $406

So,

8t + 12s + 10h = 406

And

the store sold three times as many T-shirts than hats

So,

t = 3h

And

twice as many shorts as hats.

s = 2h

By substituting t and s into the equation first

8(3h) + 12(2h) + 10h = 406

h = 7

Now

t = 21 and s = 14.

Hence, The clothing store has sold a total of 21 t-shirts, 7 hats, and 14 shorts.

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Answer:

a) 13, b) (-5, 2)

Step-by-step explanation:

Point slope form of a line is:

y − y₁ = m (x − x₁)

where m is the slope and (x₁, y₁) is a point on the line.

In this case, m = 13 and (x₁, y₁) = (-5, 2).

Here's a graph:

desmos.com/calculator/pknwab84xs

Answer:

y=-2x+3

Step-by-step explanation:

Slope intercept form is y = mx + b where m is the slope, b is the y-intercept, and y and x are their respective coordinates.

The questions gives us a coordinate pair and a slope so all we need to find is the y-intercept to find the equation.

Begin by plugging in what we know.

(3) = (-2)(0) + b

3 = 0 + b

3 = b

Plug in the y-intercept (b) and slope (m)

y=-2x+3

For this case we must write algebraically the following statement:

"The sum of p and q is equal to 24"

The sum of p and q is represented as:

[tex]p + q[/tex]

If the sum is equal to 24 we have:

[tex]p + q = 24[/tex]

If they tell us that [tex]q = 3[/tex], then the expression is:

[tex]p + 3 = 24[/tex]

Answer:

[tex]p + 3 = 24[/tex]

Answer:

C) very likely

Step-by-step explanation:

Out of the 20 balls inside of the bag, 18 of them are green.

That means you have a 18/20 or 90% chance of getting a green ball.

Therefore, the probability of drawing a green ball is [tex]90[/tex] % then the option (C) is correct i.e., very likely.

What is the probability?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Probability has been introduced in Maths to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen.

Here given that,

A bag contains [tex]2[/tex] red balls and [tex]18[/tex] green balls. A ball is chosen at random from the bag.

So,the total balls are [tex]18+2=20[/tex]

Green balls are [tex]18[/tex].

So the probability is

[tex]\frac{18}{20}[/tex] ×[tex]100=90[/tex] %

Hence, the probability of drawing a green ball is [tex]90[/tex] % then the option (C) is correct i.e., very likely.

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Answer:

Both expressions are equivalent to 78 when t = 6 ⇒ answer A

Step-by-step explanation:

* To solve this problem substitute the value of t and then check

  the answer

∵ The first expression is 2(7t - 3) ⇒ simplify it

# 2(7t) = 14t

# 2(3) = 6

∴ 2(7t - 3) = 14t - 6

- Substitute t by 4

∴ 14t - 6 = 14(4) - 6 = 56 - 6 = 50

- Substitute t by 6

∴ 14t - 6 = 14(6) - 6 = 84 - 6 = 78

∵ The second expression is 15t - 12

- Substitute t by 4

∴ 15t - 12 = 15(4) - 12 = 60 - 12 = 48

- Substitute t by 6

∴ 15t - 12 = 15(6) - 12 = 90 - 12 = 78

- The first expression has two values

# 50 when t = 4

# 78 when t = 6

- The second expression has two values

# 48 when t = 4

# 78 when t = 6

- From these information

# The two expressions have the same value 78 when t = 6

∴ Both expressions are equivalent to 78 when t = 6

Answer: 60 mph.

(486+316+638)/24

The distances given by the table. The time driven is 24 (given by the problem). So the average speed is simply the total distance divided by the time driven.

Step-by-step explanation:

Answer:

On Graph B, at 0 minutes, the height of the graph will be at 12 miles

Then, the graph will decrease until 15 minutes, when Adalyn reaches the school. At 15 minutes, the height of Graph B will be at 0 miles.

Step-by-step explanation:

Since she is coming back from school the numbers are decreasing.

Answer:

A es la respuesta a tu pregunta ue acabas de preguntar para que alguien la respondiera.