Mathematics High School

A prism with a volume of 3125 ft³ is scaled down to a volume of 200 ft³.

What is the scale factor?
Enter your answer, as a decimal or a fraction in simplest form, in the box.

I think it's 2/5 or 0.4

Answers

Answer 1
the right answer is 2/5

Answer 2

Answer:

The scale factor is equal to [tex]0.4[/tex]  or [tex]\frac{2}{5}[/tex]

Step-by-step explanation:

we know that

If two figures are similar. then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z------> the scale factor

x------> the volume of the dilated prism

y------> the volume of the original prism

so

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

we have

[tex]x=200\ ft^{3}[/tex]

[tex]y=3,125\ ft^{3}[/tex]

substitute

[tex]z^{3}=\frac{200}{3,125}[/tex]

[tex]z=\sqrt[3]{\frac{200}{3,125}}[/tex]

[tex]z=0.4[/tex]  or [tex]z=\frac{2}{5}[/tex]

             

Related Questions

can anyone find an irrational number between 7.7 and 7.9??



Answers

[tex] \sqrt{62} [/tex] is an irrational number; then, [tex] \sqrt{62} [/tex]≈ 7,8 and 7,7 < 7,8 < 7,8.

Jay took out a small-business loan for 210,000. The terms of the loan are 5% annual interest for four years.

Jay will pay back $_____ by the end of the four years.

Show your work.

A. 420,000
B.252,000
C. 168,000
D. 42,000

Answers

5% of 210000=
(210000/100)5= $10500 anually

so 4 years will be $42000

he'll pay 42000 + 210000
$252000
answer is B

I will assume that this is a simple interest. In this problem, you are asked to find the future value of the loan at the end of four years.

The formula in finding the future value of the loan is:

F = P (1 + rt)

Where F = future value of the loan

             P = principal amount of the loan

             r = simple interest rate

             t = time in years

Substituting the amounts given in the problem:

F = 210,000 (1 + 5%x4)

   = 210,000 (1.2)

   = 252,000

Therefore, Jay will pay back $252,000 by the end of four years.

Which of the following describes the transformations of g(x)=-(2)x+4-2 from the parent function f(x)=2x

Answers

This graph has a few changes. It is reflected across the axis, then shifted left 4 units. it is also shifted down two units. 

Answer:

function f(x) first reflect across x axis and then shifted 4 unit up and then 2 unit down.

Step-by-step explanation:

Given  : Transformations of g(x)=-(2)x+4-2 from the parent function f(x)=2x.

To find : Which of the following describes the transformations.

Solution : We have given

Parent function f(x) = 2x.

Transformed function  g(x) = -(2)x+4-2.

By the transformation rule : (1) reflection across x - axis f(x) →→ -f(x) .

(2) f(x)  →→ f(x) + k  it mean function shifted up by k unit.

(3) f(x)  →→ f(x) - k  it mean function shifted down by k unit.

Then

f(x) = 2x →→→→-(2)x+4-2.

It mean function f(x) first reflect across x axis and then shifted 4 unit up and then 2 unit down.

Therefore,  function f(x) first reflect across x axis and then shifted 4 unit up and then 2 unit down.

Perform the following calculations.

To calculate the number of pounds of meat required to feed diners do the following: for poultry or meat with bones, divide the number to be served by 2.5; for meat with little or no bone, divide the number to be served by 3.5; and for fish fillets divide the number to be served by 3.5.

Guests = 100

Meat served = boneless chicken
How many pounds of chicken required?



30
40
250
350,

Answers

30 lbs. The question itself tells you how to solve it. Since you're serving boneless chicken, that would be "meat with little or no bone, divide the number to be served by 3.5". And you've been given 100 guests. So: 100 / 3.5 = 28.57142857 And of the 4 options given 30 lbs is the closest, so that's the correct answer.

To feed 100 guests with boneless chicken, divide the number of guests by 3.5 to get 28.57 pounds, and round up to the closest whole number or choose the closest option given. Therefore, you would need 30 pounds of chicken.

The question involves a calculation related to catering and food preparation. To find out how many pounds of boneless chicken are needed to serve 100 guests, use the provided guideline: 'for meat with little or no bone, divide the number to be served by 3.5.' Therefore, we perform the calculation:

Number of guests ÷ Serving ratio = Required meat in pounds

100 ÷ 3.5 = 28.57 pounds

Since you cannot have a fraction of a pound of chicken when buying, you would need to round up to the closest whole number. Therefore, you would need 29 pounds of boneless chicken to serve 100 guests. However, to answer the multiple choice question provided, the closest option given is 30 pounds, which should be sufficient to feed 100 guests with slight leftovers.

Seven pounds of birdseed is used to fill 4 identical bird feeders.

A.How many pounds of birdseed are used to fill each bird feeder?

Answers

to find that out you would do 7 divided by 4 and you get 1.75. 1.75 is how many pounds are used to fill each bird feeder

I'm having a problem with probability. Please someone help ASAP.

A first grade class of nine girls and seven boys walks into a class in alphabetical order (by last name). What is the probability that three girls are the first to enter the room? Show your calculation.

(A) 0.15
(B) 0.20
(C) 0.35
(D) 0.45,

Answers

The total number of students in the class is 9 + 7 = 16 The probability first person is a girl is 9/16 The probability second person is a girl is 8/15 The probability third person is a girl is 7/14 The probability that three girls are the first to enter is 9/16 * 8/15 * 7/14 = 504/3360 = 0.15. Option A.

Please helplpppp solve each equation 9.4k + 3.5 + 4.8k =46.2

Answers

9.4k+4.8k+3.5=46.2
we subtract 3.5 from both sides
14.20 k=42.70 divide both sides by 14.20
k=3.007

Which of these following debts could possibly be forgiven under chapter 7 bankruptcy?
A. A mortgage
B. A student loan
C. Alimony
D. Child support

Answers

A. A mortgage 

Hope it helps

Answer:

A. A mortgage

Step-by-step explanation:

The chapter 7 of bankrupcy states that the person that owes the money should have his/her posessions taken away and by selling them repay the creditors, even if the sum of the belongings does not cover up for the whole amount that the person owes, this means that a mortgage is forgiven, but the house or the property is taken away and sold in an auction in order for the creditor to recover some of the money lost.

Miriam ahorró durante toda la semana $14.00.El sabado se gasto 1/7 de esa cantidad y el domingo 5/8, ¿Que cantidad gastó en total durante esos dos días?

Answers

1/7 de catorce es dos, ahora Miriam tiene doce dólares restantes. 5/8 de 12 es 7.5, luego todos juntos, Miriam gastó nueve dólares.

helpppppppppppppppppppppppppp

Answers

For this case we evaluate the function when x = 0
 We then have to evaluate:
 y = -2sinx - 1
 y = -2sin (0) - 1
 y = -1
 Then, the intersection with the y-axis is -1 and the amplitude is 2.
 Answer:
 y = -2sinx - 1
 option 2

help, please simplify.. thank you

Answers

[tex]\bf \cfrac{3.7\times 10^{-12}(42)}{(.000000025)(4.0\times 10^{-15})}\implies \cfrac{37\times 10^{-13}(42)}{(25\times 10^9)(4\times 10^{-15})}[/tex]

[tex]\bf \cfrac{37(42)\times 10^{-13}}{25(4)\times 10^910^{-15}}\implies \cfrac{1554\times 10^{-13}}{100\times 10^{9-15}}\implies \cfrac{1554\times 10^{-13}}{1\times 10^2\times 10^{9-15}} \\\\\\ \cfrac{1554\times 10^{-13}}{10^{2+9-15}}\implies \cfrac{1554\times 10^{-13}}{10^{-4}}\implies 1554\times 10^{-13}\times 10^4 \\\\\\ 1554\times 10^{-13+4}\implies 1554\times 10^{-9}\implies \cfrac{1554}{10^9}\implies 0.000001554[/tex]

which choice is equivalent to the expression below?
√- 20
A. -20i
B. 2i √5
C. -2 √5
D. 2 √5i
E. 20i,

Answers

D) since
[tex] \sqrt{ - 20} = \sqrt{ 4 \times - 5} = 2 \sqrt{ - 5} = 2 \sqrt{5 \times ( - 1)} = 2 \ \sqrt{5} i[/tex]
B. 2i √5. To simplify √- 20 , it becomes √(-2)*(-2)*5, then √(-2)^5*5, which then becomes 2i because you cannot find the square root of a negative number. i means √-1, so √-20 is the same as 2i√5.

Dimitri is helping to plan the school talent show. Each performer for the talent show has 6 66 minutes for his or her performance, which includes transition time between performances. If the introduction for the talent show is 24 minutes long and the entire show, including the introduction, will last 1 5 0 150150 minutes, how many different performances can the talent show accommodate? Choose 1 answer: (Choice A) A 2 1 2121 (Choice B) B 2 4 2424 (Choice C) C 2 5 2525 (Choice D) D 2 9 29

Answers

Correct Answer:
Choice A) 21 performances

Solution:
Total time available for the show = 150 minutes
Time required for the introduction = 24 minutes
Time available for the performances = 150 - 24 = 126 minutes

Time of each performance = 6 minutes
So,

Number of performance = Total time available for the performance / Time of each performance 

Number of performance = 126/6 = 21

Therefore, 21 performances can be performed in the available time. 

Which of the following are continuous functions of time?
The quantity of gas in the tank of a car on a journey between New York and Boston (continuous or discontinuous)
The number of students enrolled in a class during a semester (continuous or discontinuous)

I want to verify my answers:
Discontinuous for the car
Continuous for the students,

Answers

Continuous functions of time are a function if small changes are made to the source then the result will have those small changes in them. The quantity of gas is a continuous function of time because small variations can be made to the quantity of the gas in use to the extent of molecules and atoms whereas same cannot be done to the student as we cannot half them.
Final answer:

The quantity of gas in a car's tank during a journey is continuous, whereas the number of students enrolled in a class is discontinuous due to discrete changes.

Explanation:

Continuous functions of time imply that values can change smoothly without jumps or breaks. For the quantity of gas in the tank of a car on a journey between New York and Boston, this would be a continuous function because the gas level decreases gradually as the car is driven. However, for the number of students enrolled in a class during a semester, this is a discontinuous function, because the enrollment can only change through discrete additions or subtractions when students enroll or drop out of the class.

You must be at least 48 inches tall to ride a certain roller coaster.iIan is 3 ft, 11 in. tall. Is ian tall enough to ride the roller coaster?

Answers

1 foot= 12 inches
STEP 1
Multiply 3 feet by 12 inches per foot

= 3 feet * 12 inches per foot
= 36 inches


STEP 2
Add inches in 3 feet with the additional 11 inches

= 36 inches + 11 inches
= 47 inches


ANSWER: Ian is 47 inches tall so he is not tall enough to ride.

Hope this helps! :)

PLEASE HELP! ^^
A 300-page book is 10 inches long, 8 inches wide, and 3/4 inches tall. What is the volume of 100 pages of the book?

A. 20 in^3
B. 60 in^3
C. 188 in^3
D. 6,000 in^3

I think it's 600 and I think they made a typo but, help please.,

Answers

The volume of 100 pages of the book is 20 in³.

Explanation:
Since the book is rectangular, we use the formula for the volume of a rectangular prism: V = l*w*h.

Using the measurements of the book we have
V = 10*8*(3/4) = 80*(3/4) = 240/4 = 60 in³.

However, 100 out of 300 pages means we want 100/300 = 1/3 of the book: 60(1/3) = 60/3 = 20 in³.

Answer:

A. [tex]20\text{ in}^3[/tex]

Step-by-step explanation:

We have been given that a 300-page book is 10 inches long, 8 inches wide, and 3/4 inches tall. We are asked to find the volume of 100 pages of the book.

First of all, we will find the volume of whole book using volume of cuboid formula.

[tex]\text{Volume of cuboid}=l\cdot w\cdot h[/tex], where,

l = Length of cuboid,

w = Width of cuboid,

h = Height of cuboid.

Upon substituting our given values in volume formula we will get,

[tex]\text{Volume of entire book}=10\text{ in}\times 8\text{ in}\times \frac{3}{4}\text{ in}[/tex]

[tex]\text{Volume of entire book}=10\text{ in}\times 2\text{ in}\times 3\text{ in}[/tex]

[tex]\text{Volume of entire book}=60\text{ in}^3[/tex]

Since there are 300 pages in entire book and 100 is 1/3 of 300, so the volume of 100 pages will be the 1/3 of the volume of entire book.

[tex]\text{Volume of 100 pages}=\frac{60\text{ in}^3}{3}[/tex]

[tex]\text{Volume of 100 pages}=20\text{ in}^3[/tex]

Therefore, the volume of 100 pages will be 20 cubic inches and option A is the correct choice.

Medals and Fan!

Given a segment with endpoints A and B, what figure can you construct using the steps below?
Step 1: Draw a ray with endpoint C.
Step 2. Open the compass to the length of AB
Step 3: With the same compass setting, put the compass point on point C. Draw and arc that intersects the ray. Label the point of intersection D.

A. A perpendicular Bisector
B. A congruent segment
C. an angle bisector
D. a congruent angle,

Answers

The answer here is B , congruent segment. Because by opening the compass to the length of AB you are setting the radius of the circle the compass could create to the same length of AB then by intersecting with the ray C, you have copied the length of AB to ray C. For that reason, CD and AB will be congruent.

How many of the first 200 positive integers are multiples of neither 6 nor 15

Answers

There are
.. floor(200/6) = 33 multiples of 6
in the range 1 .. 200.

There are
.. floor(200/15) = 13 multiples of 15
in the range 1 .. 200, half of which are also multiples of 6.

So, there are 33 +13 -6 = 40 numbers in the range 1 .. 200 that are multiples of either 6 or 15 or both.

The remaining 200 -40 = 160 numbers are not multiples of either.

A blueprint for a house has a scale of 1:10. A wall in the blueprint is 8in. What is the length of the actual wall?
A) 6.67 inches
B) 80 feet
C) 960 feet
D) 6.67 feet

Answers

B 80 Feet, 8 x 10 would be 80, therefore 80 feet . 

Answer:

the length of the actual wall= 80 feet

Step-by-step explanation:

A blueprint for a house has a scale of 1:10. A wall in the blueprint is 8in.

Blueprint has a scale ratio of [tex]\frac{1}{10}[/tex]

As per the scale, the wall in the blue print is 1 in then the length of the actual wall is 10 feet

A wall in the blueprint is 8 inches, the length of the actual wall is [tex]10*8= 80[/tex] feet

the length of the actual wall= 80 feet

Troy’s canoe is 18 feet long. Ariel’s canoe is 5/6 the length of Troy’s canoe.

What is the length of Ariel’s canoe?
Express your answer in simplest form

Answers

18 * 5 = 90
90/6 = 15
 it is 15 feet

Last question thanks guys!! (only 1!)

Answers

The correct answer is:  [C]:  " x² = √32 " .
_________________________________________________
Explanation:
_________________________________________________
Note:  Working backward,   "(± 4√2)" , squared, equals what value(s)?
_________________________________________________
Note:  We are actually given 2 (TWO) solutions:

  " +4√2" and "–4√2" ; 
_______________________________________
√32 = √8 √4 = √4 √2 √4 = 4√2 ;

- √32 = -1 * √32  =   - 4√2
_______________________________
or:  

√32 = √16 √2  = 4√2 ; 

-1 * √32  =   - 4√2
______________________________________________________
However, BOTH these values, when "squared" (i.e. raised to the exponential power of "two"; will result in the same value— which is:  "32" ; 
_______________________________________________________

 is equal to:  "(4√2)²  = (4)² *(√2)²  =  (4*4) (√2*√2) = 16*2 = " 32 " .

______________________________________________________
√32 = √8 √4 = √4 √2 √4 = 4√2 ;

- √32 = -1 * √32  =   - 4√2
_______________________________
or:  

√32 = √16 √2  = 4√2 ; 

-1 * √32  =   - 4√2
_________________________________________________
          " (4√2)²  =  (4)²  * (√2)²  =  (4 * 4) (√2*√2)  =  16 * 2 = " 32 " .  

         " (-4√2)²  = (-4)²  * (√2)²  = (-4 *-4) (2) = 16 * 2 = " 32 " .
_________________________________________________
The correct answer is:  " 32 " ; which is:  Answer choice:  [D]:  " x² = 32 " .

We know that the answer is: " " {" ± 8 "}; since we are dealing with equations that contain "x SQUARED"; that is, " x²"; and when we solve for the 'square root of all values of a [variable raised to an even positive integer] ;

we take the "plus or minus" square root values ;  since the value, "x" could be plus or minus;  since a "negative value" multiplied by a "negative value" is a "positive value" ; 
______________________________________________
So, the correct answer is:  Answer choice:  [B]:  " x² = ± 8 " .
______________________________________________
Let us check our answer:  

√32 = √16*√2 = 4√2 ;

– √32  =  – 4√2 ;
________________________________________________
Also, note:
________________________________________________

   x²  =  32 ;  Solve for "x" ; 

→ Take the square root of "each side" of the equation ; 
     to isolate "x" on one side of the equation; & to solve for "x" ;

→  √(x²)  =  √32 ; 

→  | x |   = √32 ;

→  x = ±   √32 . Yes!
____________________________________________________
[tex]x=\pm4 \sqrt{2} \\ x^2=(4 \sqrt{2} )^2 \\ x^2=4^2\cdot(\sqrt{2} )^2 \\ x^2=16\cdot (2) \\ x^2=32[/tex]

You deposit $2200 Into three separate bank accounts for each pay 3% annual interest. How much interest does each account earn after 6 years?

Answers

Final answer:

Each of the three separate bank accounts with $2200 deposited at an annual interest rate of 3% will earn $396 in interest after 6 years.

Explanation:

The question asks about the amount of interest earned after 6 years on three separate bank accounts that each have a deposit of $2200 and an annual interest rate of 3%. To calculate the interest for each account, we can use the formula for simple interest, which is I = PRT, where I is the interest, P is the principal amount ($2200), R is the annual interest rate (0.03), and T is the time in years (6).

The interest for each account is calculated as follows:

I = PRT = $2200 × 0.03 × 6 = $396.

Therefore, each account earns $396 in interest after 6 years.

Each account earns [tex]\( \$396 \)[/tex] in interest after 6 years.

To calculate the interest earned on each account after 6 years, we'll use the formula for simple interest:

[tex]\[ \text{Simple Interest} = P \times r \times t \][/tex]

Where:

- P is the principal amount (the initial deposit)

- r is the annual interest rate (as a decimal)

- t is the time the money is invested or borrowed for, in years

Given:

- [tex]\( P = \$2200 \)[/tex] (the deposit into each account)

- [tex]\( r = 0.03 \)[/tex] (3% annual interest rate as a decimal)

- [tex]\( t = 6 \)[/tex] years (the time period)

Let's calculate the interest earned on each account using the formula.

[tex]\[ \text{Interest} = \$2200 \times 0.03 \times 6 \][/tex]

[tex]\[ \text{Interest} = \$2200 \times 0.18 \][/tex]

[tex]\[ \text{Interest} = \$396 \][/tex]

What is the answer plz help

Answers

Use each number from the tiles in the equation, and find y.
Then y is given, and you have to write the x-value from the tile you used.

2 ---> -3
14 ---> 3
7 ----> 2
-1 ---> -2

Three fourths of the students in class said they like word problems . If fewer than 30 students said they like word problems , how many students are there ?

Answers

To compute for the total number of students in the class, you have to divide the fraction of the students who said they like word problems with the number of students who said they like word problems.

30 students / ¾ of the students said they like word problems = 40 students are there in the class

I need help with this as well

Answers

19. 4/6 or 2/3 (lowest term) or 2:3 in ratio
20. 2/3 or 2:3 in ratio
21. 5/12 or 5:12 in ratio
22. 14
    To get geometric mean, multiply the numbers then get the square root of the product (if there are two numbers), cube root (if there are three numbers), and so on. In this case, 7*28 = 196; √196 = 14
23. 10 ft : 2.5 ft.
    Convert the values so that it will be similar. In this case, 30 inches is converted to ft.
24. 24 is the Perimeter of ABCDE.
    ABCDE and FGHJK are similar shapes. Similar shapes have proportional measurements.

Now compute for the sides of ABCDE.
AB = 4; BC = ?; CD = ?; DE = ?; EA = ?
AB + BC + CD + DE + EA
4 + 4 + 5 + 6 + 5 = 24

Find BC:
AB/BC = FG/GH
   4/BC = 8/8 
    8BC = 32
      BC = 4

Find CD:
BC/CD = GH/HJ
   4/CD = 8/10
    8CD = 40
      CD = 5

Find DE:
CD/DE = HJ/JK
   5/DE = 10/12
  10DE = 60
       DE = 6

Find EA
DE/EA = JK/KF
   6/EA = 12/10
  12EA = 60
      EA = 5

what's the numerator for the following rational expression?
2/f + 5/f = ?/f

Answers

We have 2/f + 5/f = (2+5)/f = 7/f;

Which of the following is the solution to the equation x + 8.6 = 36.2?

10.4
17.2
27.6
44.8

Answers

we have that
x + 8.6 = 36.2
step 1

Subtract 8.6 both members
x+8.6-8.6=36.2-8.6
x=27.6

the answer is
the solution is x=27.6

The answer is 27.6 because 36.2-8.6 is 27.6

complete the equation of the line whose y-intercept is (0,5) and slope is -9

Answers

y= x(-9) + 5
to check--
when you create a line using the y-intercept and the slope. if you put the (x,y) coordinates that are on your line in your function/equation. both sides should equal each other
ex- 14=14✓

it is actually y=-9x+5 because you have to follow y=mx+b

Choose the BEST answer.
1. What is a Web page? (1 point)
A single page of a Web site that consists of an HTML document
The entry page of the Web site
Web page that is located in the same group of Web pages or Web Site as th
document
2. What is a home page? (1 point)
A single page of a Web site that consists of an HTML document
The entry page of the Web site
Web page that is located in the same group of Web pages or Web Site as th
document
3. What is the object of storyboarding? (1 point)
To help you visualize your Web site before writing any pages in HTML. To help prevent duplicati

Answers

1. A web page is a single page of a Web site that consists of an HTML document
 2. A home page is the entry page of the Web site
 3.The object of storyboarding is to help you visualize your Web site before writing any pages in HTML.

Answer:

1)

A single page of a Web site that consists of an HTML document.

2)

The entry page of the Web site.

3)

The object of storyboarding is to help you visualize your Web site before writing any pages in HTML.

Step-by-step explanation:

Web page:

A web page or webpage is a document commonly written in HTML (Hypertext Markup Language) that is accessible through the Internet or other networks using an Internet browser.

Hence, option: A is true.

Home page:

A home page also refers to the first page that appears upon opening a web browser, sometimes called the start page.

Hence, option: B is correct.

( The entry page of the Web site )

object of storyboarding:

The object of storyboarding is to help you visualize your Web site before writing any pages in HTML

The park ranger stocks the children fishing pond keeping a ratio of 4 sunfish to 3 perch if he puts 300 sunfish into the pond how many perch should be put into the pond

Answers

400 sunfish in the pond. :)
225 perch. 4x75=300 then you could just take that 75 multiply it by 3, which is how you get 225.
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