help me with my math please
(2 -1/2 * 7 1/3)^6

Answers

Answer 1

Answer:

21 316/729

Key rules to solve:

[tex]\left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}[/tex][tex]\frac{1}{\frac{b}{c}}=\frac{c}{b}[/tex]Convert mixed numbers to improper fractions

Step-by-step explanation:

[tex]\left(\frac{2-1}{2\cdot \:7\frac{1}{3}}\right)^6[/tex]

[tex]=\left(\frac{2-1}{2\cdot \frac{22}{3}}\right)^6[/tex]

[tex]=\frac{\left(2-1\right)^6}{\left(2\cdot \frac{22}{3}\right)^6}[/tex]

[tex]=\frac{1}{\left(2\cdot \frac{22}{3}\right)^6}[/tex]

[tex]=\frac{1}{\frac{7256313856}{729}}[/tex]

[tex]\rightarrow 21 \frac{316}{729}[/tex]


Related Questions

3x+5y = 15 find the slope of a line perpendicular to each given line

Answers

Answer:

Slope = 5/3

Step-by-step explanation:

See attached image

this question confuses me any help​

Answers

Answer:

42.25π m²

Step-by-step explanation:

Let's solve!

⇒ Take the radius of the lawn to be 'r'

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

Then, area of the path equals :

⇒ Area of (lawn + path) - Area of lawn

⇒ π (r + 2)² - πr² = 30π

⇒ πr² - πr² + 4πr + 4π = 30π

⇒ 4πr = 26π

r = 6.5 m

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

Area of the lawn :

⇒ Area = πr²

⇒ Area = π × (6.5)²

⇒ Area = 42.25π m²

5.) The price of gas last year was $1.75 per gallon. The price went up by 5%,
what is the new price for a gallon of gas?

Answers

Answer: 1.75•5%=0.0875

1.75+0.0875=$1.84

I’m pretty sure this is correct

Answer:

5% of 1.75 is 0.085.

So 1.75 + 0.085 is 1.8375.

Help me please given ABcd is a parallelogram

Answers

AC is congruent to AC (reflexive property)Triangle CDA is congruent to triangle ABC (SAS)AB is congruent to CD, BC is congruent to DA (CPCTC)

A circle has an area of 144pie square feet what is the diameter of the circle

Answers

Answer:

13

Step-by-step explanation:

144 = pie radio square

144 divided by pie = 45.83662361

45.83662361 square root = 6.770275003

6.770275003 multiply by 2 =  13.54055001

13.54055001 = diameter

1 Pound brown sugar is equivalent to _____ cups

Answers

Answer:

3 1/2 or said as 3.5 cups is equal to 1 pound

Step-by-step explanation:

1 Pound brown sugar is equivalent to ___3 1/2 or 3.5 __ cups

Hope This Helped

A certain television is advertised as a 95-inch tv (the diagonal length). if the width of the tv is 77 inches, how tall is the tv? round to the nearest tenth of an inch.

Answers

The height of the television given the length of its diagonal and its width is 55.6 inches

What the height of the tv?

The  height of the television can be determined using Pythagoras Theorem.

The Pythagoras theorem: a² + b² = c²

where a = length

b = base

c = hypotenuse

√95² - 77² = 55.6 inches

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Answer: 55.6

Step-by-step explanation: 55.6 that's what I put in and got it right

Calcula el valor de la expresion
m + (m – 3), si m = –5

Answers

Answer: -13

Step-by-step explanation:

m = -5

-5 + (-5-3)

-5 -8

-13

Answer:

-13

Step-by-step explanation:

dado m= -5

m+(m-3) = -5+(-5-3) = -5 + (-8) = -5-8 = -13

Help plsss i dont get it

Answers

Part A

The pattern of squares is 1, 4, 9, ... which is the set of perfect squares

1 = 1^24 = 2^29 = 3^2

and so on

The 7th figure will have 49 squares because 7^2 = 49

Answer: 49

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

Part B

Each pattern has one circle per corner (4 circles so far). In addition, there's one circle per unit side to form the perimeter.

Pattern 1 has 4+4(1) = 8 circlesPattern 2 has 4+4(2) = 12 circlesPattern 3 has 4+4(3) = 16 circles

The nth term will have 4+4n circles. The first '4' is the number of circles at the corners. The 4n is the circles along the perimeter. If you wanted, 4+4n factors to 4(1+n).

Plug in n = 20 to find the 20th figure has 4+4n = 4+4(20) = 84 circles

Answer: 84

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

Part C

Pattern 1 has 1 square + 8 circles = 9 items totalPattern 2 has 4 squares + 12 circles = 16 items totalPattern 3 has 9 squares + 16 circles = 25 items total

This seems to suggest if the pattern number is odd, then we need an odd number of tiles (square + circular).

Let n be the pattern number. Pattern n needs n^2 square tiles and 4+4n = 4n+4 circular tiles. Overall, n^2+4n+4 tiles are needed.

It turns out that if n is odd, then n^2+4n+4 is always odd. The proof is shown below.

Side note: n^2+4n+4 factors to (n+2)^2

Answer: B) will always be odd

how to simplify 8x-6x

Answers

You simplify 8x-6x by:

subtracting 6x from 8x. It's quite simple to deal with small two-part numbers like these. After subtracting 6x from 8x, you will get the answer 2x.

Quick Answer:

You simply 8x-6x by subtracting 6x from 8x, and then you will get the answer 2x

HAVE A NICE DAY

Which triangles are similar please help lol

Answers

Answer:

triangles A and B are similar

Step-by-step explanation:

Write the equation of the trigonometric graph

Answers

The equation for the trigonometric graph given above is:

y = 4sin(2x + (π/2))

y = 4 cos 2x

What is a trigonometric graph?

It is to be noted that the domain value of θ  is displayed on the horizontal x-axis and the range value is depicted on the vertical y-axis in the graphs of trigonometric functions.

What is the step-by-step solution to the question?

Note that

y = A Sin (Bx - C) + D

The vertical shift → D

Horizontal [Phase] shift → C/B

Wavelength [Period] →  (2/B) π

Amplitude → | A |

Vertical Shift → 0
Horizontal | Phase | Shift → C/B → [- (π/4)] → (-π/2/2)

Wavelength | Period | → (2/B)π → π → (2/2)π

Amplitude → 4

Hence, working the above further we get:

y = 4sin(2x + (π/2))

y = 4 cos 2x

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Answer(s):

[tex]\displaystyle y = 4sin\:(2x + \frac{\pi}{2}) \\ y = -4cos\:(2x \pm \pi) \\ y = 4cos\:2x[/tex]

Step-by-step explanation:

[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{4}} \hookrightarrow \frac{-\frac{\pi}{2}}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4[/tex]

OR

[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4[/tex]

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 4sin\:2x,[/tex]in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{4}\:unit[/tex]to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle \frac{\pi}{4}\:unit,[/tex]which means the C-term will be negative, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{\pi}{4}} = \frac{-\frac{\pi}{2}}{2}.[/tex]So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 4sin\:(2x + \frac{\pi}{2}).[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit [tex]\displaystyle [-1\frac{1}{4}\pi, 0],[/tex]from there to [tex]\displaystyle [-\frac{\pi}{4}, 0],[/tex]they are obviously [tex]\displaystyle \pi\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle \pi.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex]in which each crest is extended four units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

What is the period of f(x) = sin (8x)?
X/8
X/4
4
8

Answers

Answer: B- x/4

Step-by-step explanation:

The period is the horizontal distance needed for the values to repeat themselves.

What are the values of x and y?

A- x=56, y=68
B- x=68, y=56
C- x=57, y=66
D- x=66, y=57

Answers

Answer :-

Option c,

x = 57° and y=66°

Explanation ;-
Kindly check the attachment below
Given:Exterior angle= 123°To find:

The value of "x" and "y".

Solution:

Let's solve "x" first.

Given is a supplementary angle so it should add up to 180°

[tex]x=180-123[/tex]

[tex]\large\boxed{x=57°}[/tex]

Now, we can solve "y"

Given is an isosceles triangle so the opposite sides will be equal.

[tex]57+57[/tex]

[tex]114°[/tex]

Angle sum of triangle is 180° so, it should add up to 180°

[tex]y=180-114[/tex]

[tex]\large\boxed{y=66°}[/tex]

Therefore, the correct answer is option C

Use the listing method to represent the following set. {x | x I, x ≤ 3}

....,0,1,2,3
4,5,6,7...
3,4,5,6....

Answers

Here the set given is

{x|x,x≤3}

So the set should be

(-oo,3]

The set elements are

{..,1,2,3}

Answer:

{ ..., 0, 1, 2, 3}

Step-by-step explanation:

Set notation is used in math to list numbers, objects or outcomes.

It uses curly brackets called "braces". Objects placed within the braces are the elements of the set.

Given set notation:   { x | x ∈ I, x ≤ 3 }

The ∈ symbol means "is an element of".

Therefore, x ∈ I means that x is an element of the set of integers. (Integers are whole numbers that can be positive, negative, or zero).

The ≤ symbol means "less than or equal to".

Therefore, x ≤ 3 means that x is less than or equal to 3.

Therefore, the given set notation means:

x is an element of the set of integers less than or equal to 3

The listing method of set notation simply lists the numbers in the set.

The three dots "..." means it is infinite (goes on forever).

Therefore:

{ x | x ∈ I, x ≤ 3 } = { ..., 0, 1, 2, 3}

One number is 4 times another. Their difference is 27. How to get the other two numbers?​

Answers

Answer:

x = 36; y = 9

Step-by-step explanation:

To solve this problem you need to set up two equations. The first equation comes from the first sentence "One number is 4 times another." This equation can be written as x = 4*y where x and y are the two numbers. The second equation comes from the second sentence "Their difference is 27." This equation can be written as x-y = 27. To find the numbers you need to rearrange one equation and plug it into the other.

Step 1: write equations

x = 4*y

x-y = 27

Step 2: rearrange

Not necessary here

Step 3: substitute in

x - y = 27

4y -y = 27

3y = 27

y = 9

Step 4: solve for x

x = 4*y

x = 4*9

x = 36

[tex]x[/tex] - one number

[tex]4x[/tex] - the other number

[tex]4x-x=27\\3x=27\\x=9\\\\4x=4\cdot9=36[/tex]

These numbers are 9 and 36.

An 8in x 11in photo is enlatged by 200% what are the Dimensions of the enlargement?

Answers

Answer:

16in x 22in

Step-by-step explanation:
8in = 100%
x = 200%
(200*8) / 100 = 16

11in = 100%
X = 200%
(200*11) / 200 = 22

The trick is to cross multiply (without multiplying the X) and then divide by the number that was not multiplied :)

Answer:

  16 in by 22 in

Step-by-step explanation:

Each dimension is multiplied by the scale factor when a photo is enlarged or reduced.

__

The enlarged photo will have dimensions ...

  (200% × 8 in) by (200% × 11 in) = 16 in by 22 in

_____

Additional comment

The factor 200% is equal to 200/100 = 2. (% and /100 are interchangeable)

What is the standard form of y=2x-2

Answers

Answer:

A standard form of a linear equation would look like this Ax+ By = C A x + B y = C

Step-by-step explanation:

Y= ax + b. is the standard form

Can you guys help me with this math questions

Answers

Answer:

2)  $40 per shirt

3)  80/9 m = 8.9 m (nearest tenth)

Step-by-step explanation:

The first question has been answered here: https://brainly.com/question/27846862

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Question 2

Given information:

Previous sales = 300 shirts at $20 eachFor every $1 increase in price, the number of sales diminishes by 5

Let [tex]x[/tex] = number of $1 increases

Let [tex]y[/tex] = total revenue (in dollars)

From the given information:

Price change of shirt:  [tex](20 + x)[/tex]Number of sales change:  [tex](300 - 5x)[/tex]

Therefore, we can create a quadratic equation with the given information:

[tex]\implies y = (20+x)(300-5x)[/tex]

As we need to find the maximum amount of revenue, we need to find the vertex of [tex]y[/tex].  As the equation is already factored, the quickest way to do this is to the find the mid-point of the zeros (since a quadratic curve is symmetrical).

[tex]\begin{aligned}y & =0\\\implies (20+x)(300-5x) & =0\\\implies (20+x) & =0 \implies x=-20\\\implies (300-5x) & = 0 \implies x=60\end{aligned}[/tex]

[tex]\textsf{Midpoint}=\dfrac{-20+60}{2}=20[/tex]

Therefore, Sammy should have 20 $1 increases to maximize the revenue, so the new price will be:

[tex]\implies \$20 + 20 \times \$1 = \$40\: \sf per\:shirt[/tex]

------------------------------------------------------------------------------------------------------

Question 3

Given information:

Bridge is modeled as a parabolaWidth of bridge = 30 mMax height of bridge = 10 m high (in the middle)

As the bridge is modeled as a parabola, and we have been given the width and height, we can create a quadratic equation using the vertex form.

Vertex form:  [tex]y=a(x-h)^2+k[/tex]

where:

x is the horizontal distance of the bridgey is the height of the bridge(h, k) is the vertexa is some constant

Middle of the bridge = 30 m ÷ 2 = 15 m

Max height of the bridge = 10 m

Therefore, the vertex of the parabola is (15, 10)

[tex]\implies y=a(x-15)^2+10[/tex]

We know that when [tex]x = 0, y = 0[/tex].  Therefore, substitute these values into the equation and solve for a:

[tex]\implies 0=a(0-15)^2+10[/tex]

[tex]\implies 0=225a+10[/tex]

[tex]\implies 225a=-10[/tex]

[tex]\implies a=-\dfrac{10}{225}[/tex]

[tex]\implies a=-\dfrac{2}{45}[/tex]

Therefore, the equation of the parabola is:

[tex]\implies y=-\dfrac{2}{45}(x-15)^2+10 \quad \quad \textsf{for }0\leq x\leq 30[/tex]

The horizontal distance at 5 m right of the middle is:

[tex]\implies \dfrac{30}{2}+5=20\:\sf m[/tex]

Therefore, to find the height at this point, input [tex]x=20[/tex] into the equation and solve for y:

[tex]\implies -\dfrac{2}{45}(20-15)^2+10=\dfrac{80}{9}\:\sf m[/tex]

Therefore, the height of the bridge at 5 m to the right of the middle is:

[tex]\dfrac{80}{9}\:=8.9\: \sf m\:(nearest\:tenth)[/tex]

Mr. Franco's class wants to raise at least $750 for a fundraiser. Let r be the amount of money, in dollars, the class raised.help ASAP..

Answers

Answer:

>

Step-by-step explanation:

Cause 750 was the least they could raise

Answer:

>=

Step-by-step explanation:

>= because the teacher wants AT LEAST 750. at least meaning you can raise 750 or MORE

HELP
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real world and mathematical problems in two and three dimensions

Answers

You did not provide any question. I will give general advice.

Pythagorean Theorem: a² + b² = c²

If you know two sides, you know ll three sides.

A house sits in the shade.

The house is 18 feet tall. The shadow is 24 feet long. What is the hypotenuse of this triangle?

We know a and b here! a=18, b=24.

18 * 18 = 324.

24 * 24 = 576.
324+576 = 900

The square root of 900 is what will be your answer:

18*18 + 24*24 = 30*30.

I hope this helps!

Describe how to determine the average rate of change between x = 3 and x = 5 for the function f(x) = 3x3 + 2. include the average rate of change in your answer.

Answers

Answer:

147

Step-by-step explanation:

[tex]\displaystyle \frac{f(b)-f(a)}{b-a}\\ \\\frac{f(5)-f(3)}{5-3}\\ \\\frac{(3(5)^3+2)-(3(3)^3+2)}{2}\\ \\\frac{(3(125)+2)-(3(27)+2)}{2}\\ \\\frac{(375+2)-(81+2)}{2}\\ \\\frac{377-83}{2}\\ \\\frac{294}{2}\\ \\147[/tex]

Recall that if a function [tex]f[/tex] is continuous over the interval [tex][a,b][/tex], then its average rate of change is [tex]\frac{f(b)-f(a)}{b-a}[/tex].

Which table represents a linear function?

Answers

The last table because each value goes up proportionally. The equation is actually y= 5x -10.

Have a great day.

40% of the students in a class are girls and the number of boys is 24 find the total number of students and the number of girls​

Answers

Answer:

Girls = 16

Total students = 40

Step-by-step explanation:

40% of the students are girls, this means 60% of the students are boys.

To find the number of girls, setup a proportion using the percentages and actual number of students in the class. I am going to make the numerator the numbers that go with the girls and the denominator will be the numbers that go with the boys.

Also let's convert the percentages to decimals by moving the decimal two places left.

40% = 0.4 and 60% = 0.6

[tex]\frac{.4}{.6} =\frac{g}{24} \\.6g=9.6\\\frac{.6g}{.6} =\frac{9.6}{.6} \\g=16[/tex]

Now let's find the total number of students by adding the number of girls to the number of boys.

16 + 24 = 40

i need help grades are do today sorry for the trouble

Answers

Answer:

13

Step-by-step explanation:

[tex]Sin = \frac{opp}{hyp} \\cos= \frac{adj}{hyp} \\tan = \frac{opp}{adj}[/tex]

=> get the length of the diag on bottom

[tex]tan x = \frac{3}{4} x = 36.87[/tex] degree

[tex]sin(36.87)=\frac{3}{y}[/tex]

y is about 5

=> calculate max length of stick

[tex]tan\left(x\right)\:=\frac{5}{12}, x= 22.62degree[/tex]

[tex]sin\left(22.62\right)\:=\:\frac{5}{x}[/tex]

which is 13

The measure of an angle is 44.8°. What is the measure of its supplementary angle?

Answers

Answer:

Step-by-step explanation:

Please help me with this

Answers

Answer:

1 and 4

Step-by-step explanation:

(x²+1)(x²-4)  = x^4 -3x²-4

The green blank is 1 and the blue/purple is 4.

Hope this helped and brainliest please

i NEED HELP ASAP
A(n) sampling method is one that is representative of the population, selected at random, and large enough to provide accurate data.

Answers

A sample is one that is representative of the population, selected at random, and large enough to provide accurate data.

What is a sample?

A sample is a smaller group that is representative of the population. A sample is sometimes necessary because it might not be feasible or cost effective to access the whole population.

For example, if a researcher is studying the impact of inflation on US families. It is not feasible to reach the whole of the families in the US. So, the researcher would use a representative group of US families. This is known as a sample.

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pls pls pls pls pls help me assap.

Answers

The quadrilaterals and their corresponding properties as shown in the given table are explained below.

How to Identify properties of Quadrilaterals?

Property 1; All sides are Congruent means all sides are equal and only Square and Rhombus have this property.

Property 2; All angles are congruent means all angles are equal. Only Rectangle and Square have this property.

Property 3; Diagonals are perpendicular to each other. Only Square and rhombus have this property.

Property 4; Diagonals are congruent. This means the diagonals are equal and only Square and Rectangle have this property.

Property 5; Exactly One pair of parallel sides is given by Only Trapezoid.

Property 6; Two pairs of opposite sides are congruent. Only Parallelogram, Rectangle, Rhombus and Square have this property.

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The quadratic function
d=-9x² + 40 models a
skateboarder's distance, in
feet, from the bottom of a hill
x seconds after the skateboarder
starts moving down the hill.
After how many seconds is the
skateboarder 4 ft from the
bottom of the hill?

A) 3s B) 4s C) 2s D) 3.5s

Please help!! Also if you could explain that would be great! Tysm!

Answers

Answer:

C

Step-by-step explanation:

equate d to 4 and solve for t , that is

- 9x² + 40 = 4 ( subtract 40 from both sides )

- 9x² = - 36 ( divide both sides by - 9 )

x² = 4 ( take square root of both sides )

x = [tex]\sqrt{4}[/tex] = 2

It takes 2 seconds for the skateboarder to be 4m from bottom of hill

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SO CONFUSED PLEASE SOMEONE EXPLAIN! DUE SOON AND NEED HELP!!!!!!!! QUESTION IN PICTURE BELOW What is the maximum probability of committing a Type I error that the researcher is willing to commit? a. Critical values b. p-value c. Level of Significance d. Confidence level In a(n) ________ strategy, managers try to gain a competitive advantage by focusing the energy of all the organization's departments or functions on driving the company's expenses down below the expenses of its industry rivals. Read the article, and create an outline by selecting subtopics from the text. Two "bears" have been duplicated for children's toys, the panda bear and the koala bear. Panda bears live in the mountains of China. These large, black and white bears are hard to find, so no one knows how many there are. Panda bears eat bamboo. Koala bears are not really bears, even though they resemble bears. They live in Australia in eucalyptus trees. They feed on the tree leaves. They are smaller in size, about two feet long. Since the panda and koala are endangered species, they are now protected by the governments in the countries in which they live. No one is allowed to take pandas out of China or koalas out of Australia. similarities between chromosphere and corona State And define the types of essay writing and give two examples each please help... The triangle represents a cross section from a 3D prism. Draw or describe the 3D prism that produced this cross section. What is the importance of factors of production? Can somebody help me find the surface area Through ____ managers get to know employees and their work ethics, and they can determine which employees will help the business achieve its goals and meet its objectives. answer choices: -planning -leading -organizing -controlling Which statements are true about the dollhouses? Select three options.The space inside dollhouse 1 can be found using the equation V = 6 (6) (5) + one-half (6) (6) (4).The space inside dollhouse 1 can be found using the equation V = 6 (6) (5) + one-third (6) (6) (4).The space inside dollhouse 2 can be found using the equation V = 6 (6) (5) + one-half (6) (6) (4).The space inside dollhouse 2 can be found using the equation V = 6 (6) (5) + one-third (6) (6) (4).The space inside dollhouse 1 is 24 inches cubed greater than the space inside dollhouse 2. Which statements describe how traits are inherited Arianna invests $5600 in a new savings account which earns 5.4% annual interest, compounded quarterly. What will be the value of her investment after 8 years? Round to the nearest cent. A forces of 5 N accelerates an object. The objects mass is 50 g. What is the acceleration of the object? (Formula: F=ma) A timer is started and a few moments later a swimmer dives into the water and then comes back up. The swimmer's depth (in feet) as a function of time (in seconds after the timer was started) is given by the equation h(t)=t212t+27 Rewrite the formula in factored form and select each true statement below. The swimmer is underwater for 12 seconds. The swimmer dives into the water 3 seconds after the timer was started. The swimmer comes back up 9 seconds after the timer was started. The swimmer dives to a maximum depth of 27 feet. The swimmer dives into the water 12 seconds after the timer was started. 29)Select the correct answer.Which details should the writer add before sentence 6 to best help readers imagine how the author physically feels when she opens the attic door?A) As I stepped into the room, a cold breeze brought me chills and a cloud of dust burst into the air as I coughed and gasped for fresh air; I wasconvinced no one had been in this room for ages and I was the first explorer.B) As I walked into the room, I realized most people would be scared of going up to the attic alone, but I proved to myself how brave I was toventure up here all by myself-I felt a sense of accomplishment I never felt before!C) When I peered into the dark room, I noticed that there were shelves upon shelves full of old boxes sealed with tape that has not been tamperedwith; it was evident that no one had opened any of the boxes for a very long time.D) When I tiptoed into the room, I imagined all the interesting things I would find when I uncovered what was in the old boxes that filled everycorner and wall of the attic room-there was so much to look through and so little time! What challenges did the two-front war present to the allied effort Baseballs pitched by a machine have a horizontal velocity of 30 meters/second. The machine accelerates the baseball from 0 meters/second to 30 meters/second in 0.5 seconds. If a baseball has a mass of 0.15 kilograms, the force the machine exerts is______ newtons. The diagram shows a system in which a collision occurs between two toy cars.What is the decrease in kinetic energy during the collision?(A) -63 J(B) -1.4 J(C) -1.1 J(D) -0.17 J Find the volume.Area = 16.4 cm8.1 cmcm