Mathematics High School

What is the volume of the pyramid?
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3192 cm3 12,768 cm3 19,152 cm3 6384 cm3

Answers

Answer 1
6384 is the correct answer.
Answer 2

The correct answer is 3192 cm3. I just did the test.

Related Questions

Can someone show me how to do this?

16! / 4! 12!

Answers

what do you mean lol, there is no such thing as that in math. if your question is 16/412 then let me know

Which of the following is not an example of like terms? A. 2 and –6 B. 2b and –6b C. 2b and 2 D. 2b^2 and 6b^2

Answers

C. 2b and 2

This is because in order have like terms, they have to have the same properties. One of them (2b) has a variable next to it, while the other does not. This makes them not alike.

Hope this helps! :)

A 3-lb force acting in the direction of the vector (3,-1) moves an object just over 9 ft from point (0,5) to (6,-2). Find the work done to move the object to the nearest foot-pound

Answers

Answer: The Work done to move the object is  [tex]=23.15 \text { foot pounds }[/tex]

Step-by-step explanation:

Given;

Force F=3 [tex]l b s[/tex]

Vectors of F= (3,-1)

Moves object to a distance=9 [tex]f t s[/tex]

Let A and B be the displacements Vectors

A= (0,-5)

B= (6,-2)

To Find:

Work done in foot-pounds

Solution:

Work done [tex]W=F \times D[/tex]

Direction of force vector= (3,-1)  (i, j)  

                                        =3i-j

Unit of force vector [tex]=\sqrt{3^{2}+\left(-1^{2}\right)}[/tex]

                                 [tex]=\sqrt{9+1}[/tex]

Force vector=(Force/Unit Vector)Direction of  force vectors

                   F=[tex]3 / \sqrt{10} \times(3 i-j)[/tex]

Direction of motion vector= (B-A)  

                                          = (6,-2)-(0,-5) x i,j)

                                          =(6-0),(-2-5) x (i, j)

                                          =(6,-7) x (i, j)

                                          =6i-7j

Unit of motion vector [tex]=\sqrt{6^{2}+\left(-7^{2}\right)}[/tex]

                                   [tex]=\sqrt{36+49}[/tex]

                                   [tex]=\sqrt{85}[/tex]

Motion Vector= (Distance moved by the object/Unit motion vector) × (Direction of motion vectors)

                        [tex]D=9 / \sqrt{85} \times(6 i-7 j)[/tex]

Workdone [tex]W=F \times D[/tex]

                  [tex]= [3/ \sqrt{10} \times (3i-j)] \times [9/ \sqrt{85} \times (6i-7j)][/tex]

                  [tex]= [3/ \sqrt{10} \times 9/ \sqrt{85}] \times [(3i-j)  \times(6i-7j)][/tex]

                  [tex]= [3/3.1623 \times 9/9.2195] \times [(3\times6) + ((-1) \times (-7))][/tex]

                  [tex]= [0.94867 \times 0.97619] \times [18+7][/tex]

                  [tex]=23.15 \text { foot pounds }[/tex]

Result:

   Work done to move an object [tex]=23.15 \text { foot pounds }[/tex]

Answer:

[tex]W = 25.617\,lbf\cdot ft[/tex]

Step-by-step explanation:

The work done to move the object is:

[tex]W = F \cdot s \cdot \cos \alpha[/tex]

The angle of the force with respect to change in the position vector is:

[tex]\alpha = \tan^{-1}\left(-\frac{7}{6} \right) - \tan^{-1}\left(-\frac{1}{3} \right)[/tex]

[tex]\alpha \approx 18.415^{\textdegree}[/tex]

The magnitude of the work done is:

[tex]W = (3\,lbf)\cdot (9\,ft)\cdot \cos 18.415^{\textdegree}[/tex]

[tex]W = 25.617\,lbf\cdot ft[/tex]

The length of a rectangle is 5 yd less than three times the width, and the area of the rectangle is 28 yd2 . find the dimensions of the rectangle.

Answers

The answer is 4.

The formula for the area of a rectangle is A = lw. Substitute, so then it's 28 = (3x-5) * x, and you evaluate.

Hope this helps you! And rate so I can see if I did well!

The dimensions of the rectangle are width = 4 yds and length = 7 yds.

What is the area of the rectangle?

The area of a rectangle is defined as the product of the length and width.

The area of a rectangle = L × W

Where W is the width of the rectangle  and L is the length of the rectangle

We have been given that the length of a rectangle is 5 yds less than three times the width,

The area of the rectangle is 28 yds square.

Let the width of the rectangle is x

So the length of the rectangle = 3x - 5

The area of a rectangle = x × (3x - 5)

28 = 3x² - 5x

3x² - 5x - 28 = 0

(3x + 7)(x - 4) = 0

3x + 7 = 0 and and x - 4 = 0

x = -7/3 and x = 4

Take x = 4 as the width

So the length of the rectangle = 3(4) - 5 = 12 - 5 = 7

Therefore, the dimensions of the rectangle are width = 4 yds and length = 7 yds.

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ind the equation of a line perpendicular to y - 3x = – 8 that passes through the point (3, 2). (answer in slope-intercept form)

Answers

we have that
Find the equation of a line perpendicular to y - 3x = – 8 that passes through the point (3, 2)
y - 3x = – 8-----> y=3x-8------> the slope m=3

we know that
if two lines are perpendicular 
then
m1*m2=-1
m1=3
so
m2=-1/3

with m=-1/3 and point (3, 2) find the equation of the line
y=mx+b
2=(-1/3)*3+b------> 2=-1+b-----> b=3

the equation of the line is
y=(-1/3)x+3

the answer is
y=(-1/3)x+3

see the attached figure

He altitude of a triangle is increasing at a rate of 3000 centimeters/minute while the area of the triangle is increasing at a rate of 3500 square centimeters/minute. at what rate is the base of the triangle changing when the altitude is 10000 centimeters and the area is 89000 square centimeters?

Answers

By definition, the area of a triangle is given by:
 A = (1/2) * (b) * (h)
 Where,
 b: base of the triangle
 h: height of the triangle
 Deriving the area we have:
 A '= (1/2) * ((b') * (h) + (b) * (h '))
 Clearing b' we have:
 b '= (2A' - (b) * (h ')) / (h)
 We must look for the value of the base:
 A = (1/2) * (b) * (h)
 Substituting values:
 89000 = (1/2) * (b) * (10000)
 b = (89000) / (5000)
 b = 17.8 cm
 Then, the speed at which the base changes is:
 b '= (2 * (3500) - (17.8) * (3000)) / (10000)
 b '= -4.64 cm / min
 Answer:
 The base of the triangle is decreasing at:
 4.64 cm / min

Help please??????????

Answers

[tex](13x-13)+(7x-9)=18x+14\\\\13x-13+7x-9=18x+14\\\\20x-22=18x+14\ \ \ |+22\\\\20x=18x+36\ \ \ \ |-18x\\\\2x=36\ \ \ |:2\\\\x=18\\\\|PR|=18x+14[/tex]

substitute the value of x:

[tex]|PR|=18\cdot18+14=324+14=338[/tex]

please help no will mark brainlyst


Explain how you would find 90% of 120.

Answers

Our trick here is to think that a fraction in %

land is the same as the correspondent in "number" land; so we can write:
100%
90%
= 120x
Where X is the correspondent of 90% in numbers.
Rearranging: x = 120⋅
90% 100% =108
If 120 = 100% then how much of it is 90%?

To find out you will have to multiply 90 with 120 and then divide what you get with 100.

90 x 120 = 10800

10800/100 = 108

so 90% of 120 is 108.

Hope this helped :)


Jesse earns $420 a week, and he works 5 days a week. What is his daily wage?

A. $84
B. $415
C. $60
D. $425

Answers

420 divided by 5= $84
$84 is his daily wage

Kali invests $3516 in a savings account with a fixed annual interest rate of 7% compounded 3 times per year. What will the account balance be after 7 years

Answers

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$3516\\ r=rate\to 7\%\to \frac{7}{100}\to &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{well, is just three} \end{array}\to &3\\ t=years\to &7 \end{cases} \\\\\\ A=3516\left(1+\frac{0.07}{3}\right)^{3\cdot 7}\implies A=3516\left( \frac{307}{300} \right)^{21}\implies A\approx 5707.0070[/tex]

Silvia wants to retire at 65 and live on $40,000 a year. How much does she need to save to ensure that her retirement funds last until she is 85?


Select the best answer from the choices provided.
$800,000 because she will need to save for 20 years times $40,000
more than $800,000 because taxes and inflation will increase the value of her savings
less than $800,000 because returns will continue to increase the amount in her savings even after retirement
more than $800,000 because compound return will reduce her savings

Answers

She must save 800,000 because that's how much she'll need in those 20 years of retirement. The first choice is correct.

Answer:

$800,000 because she will need to save for 20 years times $40,000

Step-by-step explanation:

Silvia wants to retire at 65 and live on $40,000 a year.

She wants to live till 85 and retire at 65 years.

So, number of years to save = [tex]85 -65= 20[/tex]

And she needs to save [tex]40000\times20=800000[/tex]

Hence, she must save 800,000.

Find the equation of the line that passes through (-2,5) and is parallel toy= -1/3x+2

Answers

We need to find an equation of the line in form y = mx+b,
If lines are parallel, then their slopes are equal, so m=-1/3.
So we can write 
y=(-1/3)x+b
To find be, we need substitute value's of x and y using point (-2,5).
5=(-1/3)*(-2)+b
5=2/3+b
b= 5-2/3=15/3-2/3=13/3

The equation of the line is
y=(-1/3)x+13/3



Lines that are not in the same plane are called _____ lines. A.perpendicular B.transversal C.skew D.parallel

Answers

C is correct answer.

Skew is a line that does not have a same plane.

Hope it helped you.

-Charlie

Thanks!

Lines that are not in the same plane are called skew lines.

What is a line?

"A line is a one-dimensional figure, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely."

Given, two lines are not in the same plane.

Here, perpendicular lines, transversal lines, and parallel lines should be in the same plane.

Two lines are called skew lines are two lines if they do not intersect and are not parallel.

Therefore, skew lines are not in the same plane.

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Which path is a Hamiltonian circuit?

Answers

the second one s h o w p t a p s

Solve for x in the image below

Answers

[tex] \dfrac{7}{8} - \dfrac{1}{x} = \dfrac{3}{4} \\\\ \dfrac{7x - 8}{8x} = \dfrac{6x}{8x} \\\\ 7x - 8 = 6x \\\\ x = 8[/tex]

Answer : x = 8

Hope this helps. - M

The value of x in the equation given is 8

Using the equations given for our Calculation;

7/8 - 1/x = 3/4

Take the L.C.M of 8 and x ; which is 8x

(7x - 8) / 8x = 3/4

Now we cross multiply;

4(7x - 8) = 3 * 8x

open the bracket

28x - 32 = 24x

28x - 24x = 32

4x = 32

x = 8

Hence, the value of x = 8

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Anyone know?
A. 99
B. 100
C. 121
D. Cannot be determined

Answers

Since, it is given that the pentagon ABCDE is congruent to pentagon FGHIJ.

By being congruent, the corresponding angles and sides are equal.

Therefore, [tex]\angle A = \angle F[/tex], [tex]\angle B = \angle G[/tex], [tex]\angle C = \angle H[/tex], [tex]\angle D= \angle I[/tex], [tex]\angle E = \angle J[/tex].

By using [tex]\angle A = \angle F[/tex]

So, [tex]100^\circ = \angle 1[/tex]

Therefore, the measure of angle 1 is 100 degrees.

So, Option B is the correct answer.

please help with this??

Answers

48, 50, 51, 56, 62, 62, 64, 73, 75
The mode is the number that is repeated more often than any other, so 62 is the mode.


At a high school 7 student volunteer for a committtee how many different 5 person committees can be chosen

Answers

Total number of volunteer students for a committee = 7
Number of committee = 5

Number of ways of selecting the committee from the 7 volunteers = 7C5 = 7!/(5!*2!) = 21 ways.

There are 21 ways in which the 5-committee member can be selected from the 7 volunteers.

Using the combination formula, 21 different 5-person committees can be chosen from a group of 7 students.

To determine how many different 5-person committees can be chosen from a group of 7 students, we use the concept of combinations, specifically the combination formula which is defined as:

C(n, k) = n! / [k! * (n - k)!]

where n is the total number of items to choose from, k is the number of items to choose, and the exclamation point represents a factorial, which is the product of all positive integers up to that number.

Applying this to the given problem, we have:

C(7, 5) = 7! / [5! * (7 - 5)!]

This simplifies to:

C(7, 5) = (7 * 6) / (2 * 1)

Therefore, C(7, 5) = 21.

There are 21 different 5-person committees that can be formed from 7 students.

Use the method of completing the square to transform the quadratic equation into the equation form (x + p)2 = q. 3 + x - 3x2 = 9 A) (x - 1 6 )2 = 71 36 B) (x - 1 3 )2 = 71 36 C) (x - 1 6 )2 = - 71 36 Eliminate D) (x - 1 3 )2 = - 71 36

Answers

To transform the quadratic equation into the equation form (x + p)2 = q we shall proceed as follows:
3+x-3x^2=9
putting like terms together we have:
-3x^2+x=6
dividing through by -3 we get:
x^2-x/3=-2
but
c=(b/2a)^2
c=(-1/6)^2=1/36
thus the expression will be:
x^2-x/3+1/36=-2+1/36
1/36(6x-1)²=-71/36

the answer is:
1/36(6x-1)²=-71/36

On a highway, Nick's car uses 12.5 gallons of gas to travel 240 miles. The gas tank in Nick's car holds 20 gallons of gas. How far can Nick's car travel on a highway using a full tank of gas?

Answers

12.5 : 240
20 : x

[tex]12.5x = 4800 \\ x = 384[/tex]

Answer : Nick's car can travel 384 miles using a full tank of gas.

Hope this helps. - M

Answer:

Nick's car can travel 384 miles using a full tank of gas.

Step-by-step explanation:

The antarctic peninsula is less than 700 miles from what continent

Answers

the answer would be south america is is a total of 1.130 kilometers away or 700 miles sorry if i got to you to late
 

A spherical ball of wax with a radius of 4 inches is melted and poured into a container shaped like a rectangular prism with a 6 inch x 6 inch base. What is the height of the melted wax in the new shape?

Answers

Volume of a sphere = 4/3 π r³ 

Volume of the spherical ball = 4/3 π (4)³ = 267.95 in³

Area of a rectangular prism = Length x Width x Height

267.95 = 6 x 6 x Height

Height = 267.95 ÷ 36 = 7.44 in

Answer: 7.44 inch


**MARKING BRAINLIEST IF RIGHT AND IF YOU SHOW WORK**
3. Use the Fermi process to estimate the number of bricks needed to fill an empty bathtub. Show your work.

My teacher said you can use approximate dimensions of the bricks and bathtub. He said use the easiest ones so that it will be easy to solve.

Answers

bath tub: 60 x 30 x 18

brick: 8 x 4 x 2

fermi process:
(60 x 30 x 18) /  (8 x 4x 2)
             
 =  32,400 / 64

 = 506.25

 estimated as 500 bricks


A die is thrown twice. What is the probability that:
1. Neither a doublet ordered pair nor a total of 10 will appear?
2. Neither a multiple of 2 on the first throw nor a total of 6 will appear?
A. 7/9
B. 5/12

Answers

1.) 1/2
2.) B would be your answer.

Answer:

1.)- B. 5/12

2)- A. 7/9

Step-by-step explanation:


In how many different ways can the letters of the word china be arranged

Answers

There are 5 letters total.

5!= 5*4*3*2*1
5!=120 different options 

Evaluate the expression
A. arctan ( - \sqrt{3} )
B. Arctan ( - \sqrt{3} )

Pls help i need this asap!

Answers

Based on the link I shared above, the value of [tex]\arctan(-\sqrt3)[/tex] is that number [tex]x[/tex] that satisfies

[tex]\tan x=-\sqrt3[/tex]

where [tex]x[/tex] lies in what you might call the "principal branch". That is, [tex]\arctan x[/tex] is bounded below by [tex]-\dfrac\pi2[/tex] and above by [tex]\dfrac\pi2[/tex], so it's only a valid inverse of [tex]\tan x[/tex] if we restrict the domain of [tex]\tan x[/tex] to [tex]-\dfrac\pi2<x<\dfrac\pi2[/tex].

In other words, [tex]x[/tex] is some angle whose terminus lies in either the first or fourth quadrant (I'm assuming you're at least a little familiar with the typical unit circle diagrams used in trig). The only value of [tex]x[/tex] in this domain that satisfies the equation above is [tex]x=-\dfrac\pi3[/tex].

On the other hand, [tex]\mathrm{Arctan}(-\sqrt 3)[/tex] captures all possible values of [tex]x[/tex] that satisfy

[tex]\tan x=-\sqrt3[/tex]

First, we know that [tex]\tan(x+\pi)=\tan x[/tex] (in other words, [tex]\tan[/tex] has a period of [tex]\pi[/tex]), so in fact [tex]\tan(x+2\pi)=\tan(x-2\pi)=\cdots=\tan x[/tex] as well. In general, then, we know that [tex]x+n\pi[/tex] will be a valid solution to the equation above, where [tex]n[/tex] is any integer.

Earlier we found that [tex]\arctan(-\sqrt3)=-\dfrac\pi3[/tex], so in this case, [tex]\mathrm{Arctan}(-\sqrt3)=-\dfrac\pi3+n\pi[/tex] for [tex]n\in\mathbb Z[/tex].

The requried both A and B refer to the same calculation, which is finding the inverse tangent of -√3. The result is -60 degrees or -π/3 radians.

A. The expression "arctan(-√3)" represents the inverse tangent function of the value -√3. The inverse tangent function returns an angle whose tangent is equal to the given value.

To evaluate arctan(-√3), we can use a calculator or reference table that provides trigonometric function values. In this case, the value is approximately -60 degrees or -π/3 radians.

B. The expression "Arctan(-√3)" is the same as "arctan(-√3)" and represents the inverse tangent function of -√3. The uppercase "Arctan" notation is commonly used in mathematical literature and calculators to represent the inverse tangent function.

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What is the answer to the jones family plans a trip to the amusement park...

Answers

The answer would be C: 128+8.50x+9.50y+10z.

This is because all of the costs of the different items will add up depending on how much of them the family buys. This is why they all have the corresponding variables next to the prices. The prices of those items will be added on to the initial cost of the 128$ family package, so all of the prices would be added up together to get the total.

Please help me idk this

Answers

Answer:

  1 13/20

Step-by-step explanation:

You want the total of distances walked to be the length of the hike:

  2 1/10 + 1 1/4 + (left to walk) = 5

Then the amount left to walk is the difference ...

  left to walk = 5 - 2 1/10 - 1 1/4

___

You are expected to know how to do arithmetic with mixed numbers, and/or to be able to use a calculator for the purpose.

  5 - 2 1/10 - 1 1/4

  = (5 -2 -1/10) - 1 1/4

  = 2 9/10 - 1 1/4

  = (2 -1) + (9/10 -1/4)

  = 1 + (9/10 -1/4)

  = 1 + (18/20 - 5/20)

  = 1 13/20 . . . miles left to walk

___

Using a calculator:

  5 -2.1 -1.25 = 1.65 = 1 65/100 = 1 13/20

Your job pays 6$ per hour write a variable expression for your pay in dollars for working h hours what is your Pay if you work 32 hours

Answers

6h

Fill in 32 for h

6x32

For 32 hours, you would earn $192

PLEASE HELP!!! ASAP!!!!!!!!!!!!!!! 10 POINTS

Expand the number 1800 into its corresponding exponential form.


2^3 · 3^2 · 5^2


9^2 · 100


8 · 9 · 25


2^2 · 3^3 · 5^2



Select expression equal to ^3√320


4

4^3√5

5^3√4

5^3√5

Answers

[tex]1800|2\\.\ 900|2\\.\ 450|2\\.\ 225|5\\.\ \ 45|5\\.\ \ \ 9|3\\.\ \ \ 3|3\\.\ \ \ 1|\\\\1880=2\cdot2\cdot2\cdot5\cdot5\cdot3\cdot3=2^3\cdot5^2\cdot3^2\\\\Answer:\ \boxed{2^3\cdot3^2\cdot5^2} [/tex]

[tex]\sqrt[3]{320}\\\\320|2\\160|2\\.\ 80|2\\.\ 40|2\\.\ 20|2\\.\ 10|2\\.\ \ 5|5\\.\ \ 1|\\\\320=2\cdot2\cdot2\cdot2\cdot2\cdo2\cdot5=2^3\cdot2^3\cdot5=2^3\cdot2^3\cdot\\\\\sqrt[3]{320}=\sqrt[3]{2^3\cdot2^3\cdot5}=\sqrt[3]{2^3}\cdot\sqrt[3]{2^3}\cdot\sqrt[3]{5}=2\cdot2\sqrt[3]{5}=4\sqrt[3]5\\\\Answer:\ \boxed{\sqrt[3]{320}=4\sqrt[3]{5}}[/tex]
1. 8 x9x25=1800 but
They all have factors that can be smaller so
8= 2^3
3=3^2
25= 5^2
So they answer is 2^3 x 3^2 x 5^5
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