A right square pyramid has a volume of 12 cubic centimeters. If the height remains fixed but the sides of the base are multiplied by 3, what is the volume of the new pyramid?
A. 36 cm³
B. 48 cm³
C. 108 cm³
D. 72 cm³

Answer:

D, [tex]\frac{7(x-4)}{6}[/tex]

Step-by-step explanation:

Basically you have to simplify the (x² - 16). Since it is the difference of 2 squares, it's simplified as (x + 4)(x - 4). Now that everything is simplified, you can start doing the multiplication.

[tex]\frac{(x+4)(x-4)}{6x} *\frac{7x}{(x+4)}[/tex], You can cancel out the (x+4)'s

[tex]\frac{(x-4)}{6x} *{7x}[/tex], There is a common factor between 7x and 6x. The common factor is x. So cancel out both "x".

You end up with this, [tex]\frac{7(x-4)}{6}[/tex]

Answer:

The skeletal system has many functions. Besides giving us our human shape and features, it:

Allows movement: Your skeleton supports your body weight to help you stand and move. Joints, connective tissue and muscles work together to make your body parts mobile.

Produces blood cells: Bones contain bone marrow. Red and white blood cells are produced in the bone marrow.

Protects and supports organs: Your skull shields your brain, your ribs protect your heart and lungs, and your backbone protects your spine.

Stores minerals: Bones hold your body’s supply of minerals like calcium and vitamin D.

Using proportions, it is found that the error was treating the 100% value as a percent(100) instead of a decimal 1, hence the correct value is of 96.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, we have that 100% = 1 of the number is w, while 6 is equals to 6.25% = 0.0625. Hence the rule of three is given by:

1 - w

0.0625 - 6

Applying cross multiplication:

0.0625w = 6.

w = 6/0.0625

w = 96.

The error was treating the 100% value as a percent(100) instead of a decimal 1, hence the correct value is of 96.

More can be learned about proportions at https://brainly.com/question/24372153

Answer:

I will help you.

but first what is the problem

give brainliest

Answer:

Help you with what??

whats the question????

Step 1 :

Find the mean of the data :

(2+4+6+8) / 4 = 20/4 = 5

Step 2 :

Find the distance between each data and mean.

Distance between 2 and 5 is 3

Distance between 4 and 5 is 1

Distance between 6 and 5 is 1

Distance between 8 and 5 is 3

Step 3 :

Add all the distances :

3+1+1+3 = 8

Step 4 :

Divide it by the number of data :

8 / 4 = 2

2 is the average absolute deviation.

"The beautiful thing about learning is that no one can take it away from YOU"

B.B.King

We will see that for Stuart the maximum height is 30ft, and for Francisco it is 46.0625 ft

In the case of Stuart it is simple, as we have a graph, we just need to see the largest y-value on the graph. We can see that it is y = 30, then for Stuart, the largest distance from the ground is 30ft.

In the case of Francisco, we need to find the maximum of:

g(x)= -16x^2 + 50x +7

Notice that this is a quadratic of negative leading coefficient, so the maximum is at the vertex.

x = -50/(2*-16) = 25/16

Evaluating the function in 25/16 we get:

g(25/16) = -16*(25/16)^2 + 50*(25/16) +7 = 46.0625 ft

If you want to learn more about quadratic functions, you can read:

https://brainly.com/question/1214333

Answer:

5x+1=7

Step-by-step explanation:

Answer:

The graph is stretched horizontally by a factor of 4 and shifted up 1 unit

Step-by-step explanation:

The effect of transforming the function is (b) The graph is stretched horizontally by a factor of 4 and shifted up 1 unit

The functions are given as:

f(x) = 3sin(x)+1

g(x) = 3sin(x/4)+2

Start by stretching the function f(x) horizontally by a scale factor of 4.

So, we have:

f'(x) = 3sin(x/4) + 1

Next, shift the function f'(x) upward by 1 unit.

So, we have:

f'(x) = 3sin(x/4) + 1 + 1

Evaluate the sum

f'(x) = 3sin(x/4) + 2

Rewrite as:

g(x) = 3sin(x/4) + 2

Hence, the effect of transforming the function is (b) The graph is stretched horizontally by a factor of 4 and shifted up 1 unit

Read more about function transformation at:

https://brainly.com/question/17586310

Step-by-step explanation:

(−3/4b^2)(−6a^2b^5)

= 9 a²b³

Answer:

3/4 ratio

Step-by-step explanation:

This is the answer

a function is odd if f(-x) = - f(x)

f(x) = x³ + 2x

and

f(-x) = (-x)³ + 2 * (-x) = - x³ - 2x = - (x³+2x) = - f(x)

Answer:

Step-by-step explanation:

tlk here

Answer: 134. 89 $

Step-by-step explanation: Dina wishes to 1000$ deposit  into an investment account and then withdraw the total in the account in five years. She has the choice of two different accounts. Blue Star account: interest is earned at an annual interest rate of 6.13%  compounded weekly (52 weeks in a year). Red Star account: interest is earned at an annual interest rate of 5.95%  compounded continuously. Which investment account - Blue Star or Red Star - will result in the greatest total at the end of five years? What is the total after five years for this account? How much more is it than the total for the other account?

In a parallelogram, angles that are opposite each other (as in, in opposite corners) are congruent. Angles that are next to each other (as in, on the same side) are supplementary.

It is very easy to solve for the value of y first because the expression is across from a known angle. Because these angles are opposite each other, they are congruent.

83 = 5y - 7

90 = 5y

y = 18

We can also use the same 83 degree angle to solve for the other two variables. 83 is on the same side as both of the remaining expressions, separately. As such 83 and another angle on the same side will add up to 180.

83 + -5x - 3 = 180

80 - 5x = 180

-5x = 100

x = -20

83 + z - 7 = 180

90 + z = 180

z = 90

Hope this helps!

Answer:

The Inch To Feet Calculator is available online here for free at BYJU'S. One inch is equal to 0.083333 feet. One foot is equal to 12 inches.

Step-by-step explanation:

Answer:

Part 1: -10, -5, 0, 8 Part 2: -3/2, -15%, 0.80, 143%, 2 1/4

Step-by-step explanation:

Part 1: The lower the number, the lower the temperature
Part 2: Convert the fractions into decimals

2 1/4 = 2.25
-15% = -0.15
143% = 1.43
-3/2 = -1.5
0.80 = 0.80
The order from least to greatest is -3/2, -15%, 0.80, 143%, 2 1/4
Hope this helps :)

Using the unit circle, it is found that the approximate decimal value of tan(α) is given by -3.274.

For an angle [tex]\alpha[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\alpha}, \sin{\alpha})[/tex].

In this problem, we have point (-0.292, 0.956), hence [tex]\cos{\alpha} = -0.292, \sin{\alpha} = 0.956[/tex].

Applying the definition of the tangent, we have that:

[tex]\tan{\alpha} = \frac{\sin{\alpha}}{\cos{\alpha}} = \frac{0.956}{-0.292} = -3.274[/tex].

Hence the second option is correct.

More can be learned about the unit circle at https://brainly.com/question/16852127

The answer: -3.274.
Hope you got it right! :)

Answer:

20,442,240 account numbers are possible.

Step-by-step explanation:

The first character has 10 possible values.

The next 2 has 26 * 26 = 676 possible combinations.

The last 4 has 9*8*7*6 = 3024 possible combinations.

So the answer is 10 * 676 * 3024

= 20,442,240.

There exist 20,442,240 possible combinations if no digit appears more than once.

The first character contains 10 possible values.

The next 2 contains 26 [tex]*[/tex] 26 = 676 possible combinations.

The last 4 have 9 [tex]*[/tex] 8 [tex]*[/tex] 7 [tex]*[/tex] 6 = 3024 possible combinations.

The has 10 [tex]*[/tex] 676 [tex]*[/tex] 3024 = 20,442,240 possible combinations.

Therefore, there are 20,442,240 possible combinations if no digit appears more than once.

To learn more about combinations

https://brainly.com/question/4658834

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Answer:

5/5 out of the 7/5 make ONE whole while 2/5 is left over.

The ONE whole is added to nine to make 10 and the remaining 2/5 is also added to the 10 hence 9 7/5 = 10 2/5

Step-by-step explanation:

5/5 out of the 7/5 make ONE whole while 2/5 is left over.

The ONE whole is added to nine to make 10 and the remaining 2/5 is also added to the 10 hence 9 7/5 = 10 2/5

Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1

Rewrite and add each vector:

[tex]p=\langle40cos70^\circ,40sin70^\circ\rangle\\q=\langle50cos270^\circ,50sin270^\circ\rangle\\r=\langle60cos235^\circ,60sin235^\circ\rangle\\p+q+r=\langle40cos70^\circ+50cos270^\circ+60cos235^\circ,40sin70^\circ+50sin270^\circ+60sin235^\circ\rangle\\p+q+r\approx\langle-20.73,-61.56\rangle[/tex]

Find the magnitude of the resulting vector:

[tex]||p+q+r||=\sqrt{x^2+y^2}\\||p+q+r||=\sqrt{(-20.73)^2+(-61.56)^2}\\||p+q+r||\approx64.96[/tex]

Therefore, the best answer is D) 64.959

Problem 2

Think of the vectors like this:

[tex]t=\langle7cos240^\circ,7sin240^\circ\rangle\\u=\langle10cos30^\circ,10sin30^\circ\rangle\\v=\langle15cos310^\circ,15sin310^\circ\rangle[/tex]

By adding the vectors, we have:

[tex]t+u+v=\langle7cos240^\circ+10cos30^\circ+15cos310^\circ,7sin240^\circ+10sin30^\circ+15sin310^\circ\rangle\\t+u+v\approx\langle14.8,-12.55\rangle[/tex]

Since the direction of a vector is [tex]\theta=tan^{-1}(\frac{y}{x})[/tex], we have:

[tex]\theta=tan^{-1}(\frac{y}{x})\\\theta=tan^{-1}(\frac{-12.55}{14.8})\\\theta\approx-40.3^\circ[/tex]

Don't forget to take into account that the resulting vector is in Quadrant IV since the horizontal component is positive and the vertical component is negative, so we will add 360° to our angle to get the result:

[tex]\theta=360^\circ+(-40.3)^\circ\\\theta=319.7^\circ[/tex]

Therefore, the best answer is D) 320°

Problem 3

Again, rewrite the vectors and add them:

[tex]u=\langle30cos70^\circ,30sin70^\circ\rangle\\v=\langle40cos220^\circ,40sin220^\circ\rangle\\u+v=\langle30cos70^\circ+40cos220^\circ,30sin70^\circ+40sin220^\circ\rangle\\u+v\approx\langle-20.38,2.48\rangle[/tex]

Using the direction formula:

[tex]\theta=tan^{-1}(\frac{y}{x})\\\theta=tan^{-1}(\frac{2.48}{-20.38})\\\theta\approx-6.94^\circ[/tex]

As the vector is located in Quadrant II, we need to add 180° to our angle:

[tex]\theta=180^\circ+(-6.94)^\circ\\\theta=173.06^\circ[/tex]

Therefore, the best answer is D) 173°

Problem 4

Using scalar multiplication:

[tex]-3u=-3\langle35,-12\rangle=\langle-105,36\rangle[/tex]

Find the magnitude of the resulting vector:

[tex]||-3u||=\sqrt{x^2+y^2}\\||-3u||=\sqrt{(-105)^2+(36)^2}\\||-3u||=111[/tex]

Find the direction of the resulting vector:

[tex]\theta=tan^{-1}(\frac{y}{x})\\\theta=tan^{-1}(\frac{36}{-105})\\\theta\approx-18.92^\circ[/tex]

As the vector is located in Quadrant II, we need to add 180° to our angle:

[tex]\theta=180^\circ+(-18.92)^\circ\\\theta=161.08^\circ[/tex]

Therefore, the best answer is C) 111; 161°

Problem 5

Using scalar multiplication:

[tex]5v=5\langle25cos40^\circ,25sin40^\circ\rangle=\langle125cos40^\circ,125sin40^\circ\rangle[/tex]

Since the direction of the angle doesn't change in scalar multiplication, it only affects the magnitude, so the magnitude of the resulting vector would be [tex]||5v||=125[/tex], making the correct answer C) 125; 200°

Answer:

A = -18.

Step-by-step explanation:

We are given that y = 3x +9.

From this, we gather 3x - y = -9.

We then multiply both sides by 2 to get 6x – 2y = -18. Therefore, A = -18.

Answer:

-9 3/4a+10 2/5

Step-by-step explanation:

-12 * 5/6a = -10a

-12 * -7/8 =  10 1/2

1/14 * 3 1/2a = 1/4 a

1/14 * -1 2/5 = -1/10

Put it together: -10a + 10 1/2 + 1/4a - 1/10

-10a+1/4a = -9 3/4a

10 1/2-1/10= 10 2/5

-9 3/4a + 10 2/5

Answer:

  (b)  0.3 microns or larger

Step-by-step explanation:

A particle of size 0.3 microns is judged to be the most penetrating particle size. So, a rating for the filtering of those particles will be a worst-case rating. For particles of any other size, the filter will perform better than for 0.3 micron particles. HEPA filters are rated based on their performance with particles ...

  0.3 microns or larger

Step-by-step explanation:

formula

an = a1 + (n - 1) d

10 = a1

15 = a2

20 = a3

n = unknown number

d = difference between each sequence

a10 = 10 + (10 - 1) 5

a10 = 10 + (9)5

a10 = 10 + 45

a10 = 55

Answer:

given ,

two points A ( -1 , 2 ) and B ( 0 , -14 )

______________________________________

[tex]\fbox\pink{Solution -}[/tex]

let the midpoint be P ( x , y )

using midpoint formula ,

[tex]P(x,y) = ( \frac{ x_{1} + x_{2} }{2} , \frac{ y_{1} + y_{2} }{2} ) \\ \\ P(x,y) = ( \frac{ - 1 + 0}{2} , \frac{2 + ( - 14)}{2} ) \\ \\ (x,y) = ( \frac{ - 1}{2} , \frac{ - 12}{2} ) \\ \\ x = \frac{ - 1}{2} \\ \\ y = \frac{ - 12}{2} => - 6[/tex]

thus ,

the coordinates of the midpoint are

[tex]\red{P( \frac{ - 1}{2} , - 6)} \\ \\ or \\ \\ \red{P( -0.5 , - 6 )} [/tex]

hope helpful :D

Answer:

Step-by-step explanation:

A(-1,2)  x₁ = -1  &  y₁ = 2

B(0 ,-14)   x₂ = 0  & y₂ = -14

[tex]\text{ \sf Midpoint = $\left(\dfrac{x_{1}+x_{2}}{2} ,\dfrac{y_{1}+y_{2}}{2}\right)$ }[/tex]

              [tex]= \left (\dfrac{-1+0}{2} ,\dfrac{2+[-14]}{2} \right) \\\\\\=\left(\dfrac{-1}{2}, \dfrac{-12}{2}\right)\\\\\\=\left( -0.5 , -6 \right)[/tex]

Answer:

8

Step-by-step explanation:

Now consider an experiment of tossing three coins simultaneously. The possible outcomes will be HHH, TTT, HTT, THT, TTH, THH, HTH, HHT. So the total number of outcomes is 23 = 8.

Answer:

8

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

Volume to fill =  1 x 2 x 3/2 = 3  cm^3

Volume of cube to fill this volume  1/2 * 1/2 * 1/2 = 1/8 cm^3

3/ (1/8) = 24

well, hmmm to check for polar symmetry, hmmm say we simply replace the value for either "r" or "θ" or both in the original equation, if the equation rendered is the same as the original, there you have it, symmetry, so let's do that.

[tex]\underline{\textit{testing for symmetry to the }\frac{\pi }{2}~line\qquad \qquad r=-r~~,~~\theta =-\theta } \\\\\\ r=-7+2cos(3\theta )\implies (-r)=-7+2cos[3(-\theta )]\implies -r=-7+2cos(-3\theta ) \\\\\\ \stackrel{symmetry~identity}{-r=-7+2\stackrel{\downarrow }{cos(3\theta )}}\implies r=7-2cos(3\theta )\impliedby \textit{woopsie, no dice} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\underline{\textit{testing for symmetry to the polar axis}\qquad \qquad \theta =-\theta} \\\\\\ r=-7+2cos(3\theta )\implies r=-7+2cos[3(-\theta )]\implies r=-7+2cos(-3\theta ) \\\\\\ \stackrel{symmetry~identity}{r=-7+2\stackrel{\downarrow }{cos(3\theta )}}\impliedby \textit{low and behold\qquad \Large \checkmark}[/tex]

now, we could run a test for "the pole" or namely the origin by simply changin r = -r, however we already know where the symmetry is, so no need.

Check the picture below.

Answer:

1. The length is longer.

2. The length is longer.

Step-by-step explanation:

1. 7/10 = 0.70 > 0.67. Here, the length is greater than the width.

2. 9/10 of a yard is .9 * 36, or 32.4 inches. Here, the length is greater than the width.

Check the picture below, so the lines look more or less like so, so the shape that we'll be getting will be the shape of a bowl with a hole in it, thus we'll use the washer method.

the way I use to get the larger Radius is simply using the "area under the curve" method, namely f(x) - g(x), where g(x) in this case is the axis of rotation.

so to get "R" and "r" we can get it by

[tex]\stackrel{y = 1}{(1)}~~ - ~~\stackrel{\stackrel{\textit{axis of rotation}}{y = -3}}{(-3)}\implies 1+3\implies \stackrel{R}{4} \\\\\\ \stackrel{y = \ln(x)}{\ln(x)}~~ - ~~\stackrel{\stackrel{\textit{axis of rotation}}{y = -3}}{(-3)}\implies \stackrel{r}{ln(x)+3} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{R^2}{(4)^2}~~ - ~~\stackrel{r^2}{[\ln(x)+3]^2}\implies 16~~ - ~~[\ln^2(x)+6\ln(x)+9] \\\\\\ \ln^2(x)+6\ln(x)+7~\hfill \boxed{\displaystyle\int~[\ln^2(x)+6\ln(x)+7]dx}[/tex]

Answer:

Pi times radius to the power of two times the height  

Step-by-step explanation

i gave you the formula now solve