A regular pentagonal prism has 9-cm base edges. A larger, similar prism of the same material has 36-cm case edges. How does each indicated measurement for the larger prism compare to the same measurement for the smaller prism? A)volume B) weight

Answers

Answer 1

To compare the volumes of the prism we used the scale factor:
volume scale factor=(linear scale factor)³
the linear scale factor of the prism is:
(length of larger prism)/(length of smaller prism)
=36/9
=4
thus the volume scale factor will be:
4³=64
hence the volume of the larger prism is 4 times that of the smaller prism.

Answer 2

Do you have the answers to this quiz?

Related Questions

Write an equation of a line containing (2, 1) and (3, 4) in point-slope form.

Answers

Note that points are: (x₁,y₁), (x₂,y₂)

Your equation is:

(y₂ - y₁)/(x₂ - x₁) = Slope

Let:
(2,1) = (x₁,y₁)
(3,4) = (x₂,y₂)

Plug into corresponding numbers

(4 - 1)/(3 - 2) = 3/1

3/1 is your slope

hope this helps

If a single die is rolled twice there are how many possible outcomes

Answers

Total number of possible outcomes = 36

WZ and XR are diameters of circle C. The diagram is not drawn to scale.
What is the measure of convex arc upper ZWX?

Answers

The measure of the convex arc is given by the following relationship:
WZ + 41 = ZWX
From here, we must clear We must replace the value of WZ.
The value of WZ is given by
WZ=180
We have then:
ZWX = 180 + 41
ZWX = 221 degrees
Answer:
the measure of convex arc upper ZWX is:
ZWX = 221 degrees

Final answer:

The measure of convex arc upper ZWX is 180 degrees.

Explanation:

The measure of convex arc upper ZWX can be found by considering the angles formed by the diameters WZ and XR. Since WZ and XR are diameters of the circle, they intersect at the center of the circle. The angle formed by the diameters at the center is a right angle, which means that arc upper ZWX is a semicircle. A semicircle has a measure of 180 degrees. Therefore, the measure of convex arc upper ZWX is 180 degrees.

Find the volume of a sphere with a great circle area of 201.06 square inches

Answers

assuming you meant a "circular cross-section" of 201.06 in².

so, we know if we cut the sphere like a cantaloupe, in half, the circular inner-part of the cantaloupe will have an area of 201.6 in².

keeping in mind that, the radius of that circular section, is the same radius of the sphere, what is it anyway?

[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\ -----\\ A=201.06 \end{cases}\implies 201.06=\pi r^2 \\\\\\ \cfrac{201.06}{\pi }=r^2\implies \sqrt{\cfrac{201.06}{\pi }}=r\\\\ -------------------------------[/tex]

[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}\qquad \qquad \implies V=\cfrac{4\pi \left( \sqrt{\frac{201.06}{\pi }} \right)^3}{3}\implies V=\cfrac{4\pi \left( \frac{\sqrt{201.06^3}}{\sqrt{\pi ^3}} \right)}{3} \\\\\\ V=\cfrac{4\pi \cdot \frac{\sqrt{201.06^3}}{\pi \sqrt{\pi }}}{3}\implies V=\cfrac{\frac{4\sqrt{201.06^3}}{\sqrt{\pi }}}{3}\implies V=\cfrac{4\sqrt{201.06^3}}{3\sqrt{\pi }}[/tex]

Final answer:

To find the volume of a sphere with a given great circle area, solve the equation 4πr² = 201.06 to find the radius, then use the formula V = (4/3)πr³ to calculate the volume. The volume is approximately 267.97 cubic inches.

Explanation:

To find the volume of a sphere with a given great circle area, we first need to find the radius of the sphere. The great circle area is equal to the surface area of the sphere, which is 4πr², where r is the radius of the sphere. In this case, the great circle area is 201.06 square inches, so we can solve the equation 4πr² = 201.06 to find the radius. Once we have the radius, we can use the formula for the volume of a sphere, V = (4/3)πr³, to calculate the volume.

First, let's solve the equation 4πr² = 201.06 for r:

4πr² = 201.06

r² = 201.06 / (4π)

r² ≈ 16.06

r ≈ √16.06 ≈ 4.01

Now that we have the radius, we can calculate the volume using the formula V = (4/3)πr³:

V ≈ (4/3)π(4.01)³ ≈ 267.97 cubic inches

Look at the figure rectangle PQRS, find m angel P

Answers

144 degrees, q=s, so 3a=4a-12. a=12, and 12*12= 144

Answer: [tex]144^{\circ}[/tex]

Step-by-step explanation:

In the given figure , we have given a parallelogram .

We know that the opposite sides and angles of a parallelogram are equal.

Thus from the given parallelogram PORS we have

[tex]\angle {Q}=\angle {S}\\\\\Rightarrow\ (4\alpha-12)^{\circ}=3\alpha^{\circ}\\\\\Rightarrow\ 4\alpha-12=3\alpha\\\\\Rightarrow 4\alpha-3\alpha=12\\\\\Rightarrow\ \alpha=12[/tex]

Also, the value of angle p is given by :-

[tex]\angle {P}=12\alpha^{\circ}\\\\\Riightarrow\ \angle {P}=12(12)^{\circ}\\\\\Riightarrow\ \angle {P}=144^{\circ}[/tex]

Mr. and Mrs. Yeager want to buy a home valued at $320,000. If they have 15% of this amount saved for a down payment, how much have they saved? a. $480 b. $4,080 c. $4,800 d. $48,000

Answers

Answer:

The correct answer is D

Step-by-step explanation:

I got it right on Edge.2020. Have a great day!

If they have 15% of this amount saved for a down payment, then they saved 48000 dollar.

So option D) $48,000 is correct.

What is the fundamental principle of multiplication?

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We are given that Mr. and Mrs. Yeager want to buy a home valued at $320,000.

If they have 15% of this amount saved for a down payment, then

15% =15/100=0.15

Therefore, we get;

0.15 (320000)=48000

If they have 15% of this amount saved for a down payment, then they saved 48000 dollar.

So option D) $48,000 is correct.

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A 20-ounce candle is expected to burn for 60 hours. A 12-ounce candle is expected to burn for 36 hours. Assuming the variables are directly related, how many hours would a 9-ounce candle be expected to burn?

18
27
33
45

Answers

divide size of candle by number of hours
to find the rate it burns:

20 ounce / 60 hours = 1/3 ounce per hour

divide 9 ounces by 1/3 ounce per hour to find total time:

9 / 1/3 = 27 hours

Answer:

B. 27.

Step-by-step explanation:

We have been given that a 20-ounce candle is expected to burn for 60 hours. A 12-ounce candle is expected to burn for 36 hours.

We know that a direct proportional equation is in form [tex]y=kx[/tex], where k represents constant of proportionality.

Let is find value of k by substituting [tex]x=20[/tex] and [tex]y=60[/tex] in above equation as:

[tex]60=k*20[/tex]

[tex]\frac{60}{20}=\frac{k*20}{20}[/tex]

[tex]3=k[/tex]

The equation [tex]y=3x[/tex] represents our given direct proportional relation.

Now, we will substitute [tex]x=9[/tex] to solve for y as:

[tex]y=3*9[/tex]

[tex]y=27[/tex]

Therefore, a 9-ounce candle would be expected to burn for 27 hours and option B is the correct choice.

Center c of the circle above has coordinates of (4, 3). what is the circumference of the circle?

Answers

Well if it is touching the x-axis, the radius is 3 units.
C = 2 * pi * r = (2)(3.14)(3) = 18.8 or so

An integer greater than 1 that is not prime is called composite. if the two-digit integer n is greater than 20, is n composite?

Answers

It might be composite or prime
eg 21 is composite and 23 is prime.

The square root of the sum of a number and 7 is 8. find the number

Answers

There are two possibilities of the formulas since I'm not exactly sure what this question is asking:

Possibility 1: 8 = sqrt(x+7) in which the answer is 57.

Possibility 2: 8 = sqrt(x) + 7, in which the answer is 1.

Hope this helps! I'm sorry if I get it wrong.

Subtract. (4x^2+8x−2)−(2x^2−4x+3) Enter answer, in standard form

Answers

[tex](4x^2+8x-2)-(2x^2-4x+3)\\\\=4x^2+8x-2-2x^2+4x-3\\\\=(4x^2-2x^2)+(8x+4x)+(-2-3)\\\\=\boxed{2x^2+12x-5}[/tex]

what are solutions to the equation sinx cosx = square root 3 over4

Answers

[tex]\sin(x)\cos(x)=\dfrac{\sqrt{3}}{4}\\\\2\sin(x)\cos(x)=\dfrac{\sqrt{3}}{2}\\\\\sin(2x)=\dfrac{\sqrt{3}}{2}\\\\2x=\arcsin\left( \dfrac{\sqrt{3}}{2} \right)\\\\2x=\left\{ \dfrac{\pi}{3},\dfrac{2\pi}{3}\right\}+2n\pi\\\\\boxed{x=\left\{ \dfrac{\pi}{6},\dfrac{\pi}{3}\right\}+n\pi}[/tex]

For each example below, determine whether a positive, negative, or no cause and effect relationship exists.

1) Smoking and cases of lung cancer.
2) Amount of time spent at school each day and number of text sent per day
3) The number of licks taken and the size of the Tootsie Pop

Answers

#1 - Positive,
#2 - No relationship.
#3 - Negative

Answer:

A positive relation between two things means that they are proportional to each other. One affects the other thing.

1) Smoking and cases of lung cancer. This is positive. As smoking affects lungs and can cause lung cancer. So, with increased smoking comes the increased risk of lung cancer thus increasing cases of lung cancer.

2) Amount of time spent at school each day and number of text sent per day - These two events are independent of each other. They are not based on each other. Hence, no relationship here.

A negative relation implies that if one thing increases, the other decreases.

3) The number of licks taken and the size of the Tootsie Pop. This is negative. As the number of licks increases, the size of the pop decreases.

How would you find the width of a golden rectangle if your givin the length?

Answers

A golden rectangle is a rectangle whose length and width follow the golden ratio (about 1:1.618).

Given the length, you would divide by 1.618 to find the width.

Edit: The exact value is [tex] \frac{ 1+\sqrt{5} }{2} [/tex], but 1.618 should suffice.

What is the value of y in the equation 2(3y + 6 + 3) = 196 âˆ’ 16?

Answers

2(3y + 6 + 3) = 196
2(3y + 9) = 196
6y + 18 = 196
6y + 18 - 18 = 196 - 18
6y = 178

Divide both sides by 6

y = 178 / 6

y ≈ 29.667

You plan on financing a new road bike for $2,500. The bike shop offers a 13.5% APR for a 24 month loan. Use this information, and the table above, to determine the monthly payments. Round your answer to the nearest cent.

Answers

This question can be approached using the present value of annuity formula. The present value of annuity is given by [tex]PV=P\left( \frac{1-\left(1+ \frac{r}{t} \right)^{-nt}}{ \frac{r}{t} } \right)[/tex], where: PV is the present value/amount of the loan, P is the periodic (monthly in this case) payment, r is the APR, t is the number of payments in one year and n is the number of years.

Given that the financing is for a new road bike of $2,500 and that the bike shop offers a 13.5% APR for a 24 month loan.

Thus, PV = $2,500; r = 13.5% = 0.135; t = 12 payments (since payment is made monthly); n = 2 years (i.e. 24 months)

Thus,

[tex]2500=P\left( \frac{1-\left(1+ \frac{0.135}{12} \right)^{-2\times12}}{ \frac{0.135}{12} } \right) \\ \\ =P\left( \frac{1-\left(1+ 0.01125 \right)^{-24}}{ 0.01125 } \right)=P\left( \frac{1-\left(1.01125 \right)^{-24}}{ 0.01125 } \right) \\ \\ =P\left( \frac{1-0.764531}{ 0.01125 } \right)=P\left( \frac{0.235469}{ 0.01125 } \right)=20.9306P \\ \\ \Rightarrow P= \frac{2500}{20.9306} =119.44[/tex]

Therefore, his monthly payment is $119.44

Please help i'm really confused.

0! = 0

True
False

Answers

That is False . 0! = 1

This is false.

0! is defined to be 1

Two trains leave towns 1250 km apart at the same time and travel toward each other. one train travels 10 km/hr slower than the other. if they meet in 5 hours, what is the rate of each train?

Answers

Here are the rates of the trains:
(n represents train A's speed)
A: n
B: n + 10
We know it is 5 hours, and total distance, so:
5(n) + 5(n + 10) = 1250
5n + 5n + 50 = 1250
10n = 1200
Divide:
n = 120
One train goes 120, the other goes 130

Anyone know this geometry question?

Answers

Given:
∠JEK + ∠DFH = 90°

Find:
relationship, if any, of ∠JEK to angles CFL, HFG, LFE

Solution:
We note that ∠DFG = 90° = ∠DFH + ∠HFG, so ∠JEK ≅∠HFG.
We also note that ∠HFG and ∠CFL are vertical angles, so ∠JEK ≅∠CFL.
And ∠LFE and ∠DFH are vertical angles, so ∠JEK + ∠LFE = 90°.

Evaluating the choices, we find
A) false. The angles are not complementary, they are equal.
B) false. The angles are not equal, they are complementary.
C) false. The angles are not supplementary, they are equal.
D) TRUE. The angles are equal.

The appropriate choice is ...
D) ∠JEK ≅∠CFL

What does y=mx+b mean

Answers

Y = mx + b is the equation for a straight line. "B" is the point value of where the line intercepts the y axis, called the y intercept. "M" is the value of the slope of the line.

The answer to this question is that y=mx+b is the slope-intercept form of an equation of a line that is graphed in the xy-plane. m is the quantity defined as
m = rise/run = Δy/Δx = (y2-y1)/(x2-x1)
with (x1,y1) and (x2,y2) as points on the line. b is the quantity defined as the y-intercept, that is, the y-value of where the line crosses the vertical y-axis.

please help...
The radius of the planet is 4100 miles. Find the distance d to the horizon that a person can see on a clear day from a height of 1298 feet above the planet. (hint: use the conversion 1 mile = 5280 ft) Round your answer to the nearest 10th, and don't forget to convert feet to miles.

Answers

First, we are going to convert 1298 feet to miles. Since we know that 1 mile = 5280 ft, we are going to multiply 1298 ft by [tex] \frac{1mi}{5280ft} [/tex] to do that:
[tex]1298ft*\frac{1mi}{5280ft}= \frac{59}{240} mi[/tex]

Next, we are going to set up a right triangle using the radius of the Earth and the distance above the planet.
The hypotenuse of our triangle will be the radius of the Earth + the distance above the planet. One of the legs of our triangle will be the radius of the Earth, and the other leg, [tex]d[/tex], will be the distance that a person will see on a clear day.
Using the Pythagorean theorem:
[tex]d^2= (\frac{984059}{240} )^2-4100^2[/tex]
[tex]d= \sqrt{(\frac{984059}{240} )^2-4100^2} [/tex]
[tex]d=44.9[/tex] miles

We can conclude that the distance, [tex]d[/tex], to the horizon that a person can see on a clear day from a height of 1298 feet above the planet is 44.9 miles.

A multiple choice test has 9 questions each of which has 5 possible answers

Answers

The total number of possible answer will be 9×5= 45 if that was the question.

Cancelling a dance class after several students hurt themselves is an example of which risk management strategy?

Answers

Answer:
Avoid strategy as the threat/risk is directly related to identified threats and these sources of threats are cancelled

Explanation:
Risk management is defined as:
The identification , analysis, control and possibly elimination of any undesired hazards or risks arising from a certain situation or activity

There are four risk management strategies which are:
1- Avoid: To eliminate the risk by totally avoiding the situation/activity
2- Mitigate: To try to reduce the expected hazards of the situation/activity
3- Accept: To accept the hazards and take your chances
4- Transfer: To outsource the risk (as in case of insurance)

In case of cancelling the dance class, we can note that the risks are directly related to identified threats and the threats are totally cancelled in order to avoid those risks. Therefore, the best strategy describing this situation is "avoid strategy"

Hope this helps :)

Final answer:

The scenario of cancelling a dance class due to student injuries is an example of the 'risk avoidance' strategy in risk management, which aims to avoid potential harm.

Explanation:

Canceling a dance class due to multiple students getting injured is a risk management strategy known as risk avoidance. This strategy eliminates the risk by not participating in the activity that could lead to the risk. In this context, the dance class risks injury to the students. In such a scenario, the dance instructor or school chooses to avoid the risk (moral hazard) by cancelling the activity (i.e., the dance class), thereby protecting the students from further harm. This is a common approach employed in situations where the potential adverse outcomes of risk outweigh any potential benefits of the activity.

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Slips of paper numbered 1 through 14 are placed in a hat. in how many ways can two numbers be drawn so that the sum of numbers is 12

Answers

the possibilities are to draw
1 and 11
2-10
3-9
4-8
5-6
6-6
so there are 6 ways

What did the prince do whenever he found a girl who might be cinderella

Answers

Final answer:

When a prince in fairy tales finds a potential Cinderella, he typically engages in a quest to determine if she is the one, reflecting the theme of male heroism and romantic pursuit found in traditional literature and films.

Explanation:

The passage raises the theme of romantic endeavors and the traditional role of women in classical literature and film, typically anchored within the context of royalty and fairy tales. When the prince in such stories finds a girl that could potentially be Cinderella, typically he would engage in a quest to discover if she truly is the one - often symbolized by a glass slipper fitting or other identifying item. This quest underscores the narrative of countless romantic tales where the male lead seeks to find and often rescue his female counterpart, a concept reflected in various Disney princess movies.

In the greater realm of literature and films, the prince often represents the chivalrous savior. This tradition is evident in the series of princess-centric stories produced by Disney, where a common girl becomes royalty by marriage or starts as a princess whose ultimate happiness is achieved through romance. Although contemporary stories may showcase more agency in their female protagonists, the motif of the male hero remains prevalent.

able below shows the relative frequencies of the color of cars bought last month by males and females. Which percentage represents the car bought most often? Male Female Total Blue Car 0.04 0.12 0.17 Black Car 0.08 0.06 0.13 White Car 0.11 0.20 0.31 Gray Car 0.02 0.09 0.11 Red Car 0.17 0.10 0.27 Total 0.43 0.57 1.00

Answers

Answer:

31%

Step-by-step explanation:

Answer:

31%

Step-by-step explanation:

A distribution reasonably well described by the normal curve has a mean of 60.00 with a standard deviation of 10.00 points. basing your prediction on the normal (z) curve, approximately what percent of the population would you predict will score within 10.00 points of the mean (between 50.00 and 70.00)?

Answers

68% will be within 10 points of the mean.

The empirical rule states that 68% of data will fall within 1 standard deviation of the mean. 10 is the standard deviation, so anything within 10 points of the mean is within 1 standard deviation.

Answer:

68%

Step-by-step explanation:

When the temperature is 68 F, the speed of the sound in air is approximately 343 meters per second. Approximately how many kilometers dose sound travel in five seconds?

Show all your work

Answers

We have our initial unit of speed: 343 m/s.
We want to find how many kilometers sound will travel when the air is at 68 degrees in five seconds.
Step 1: Multiply 343 by five. (1 sec. to 5 secs.)343 * 5 = 1715
Step 2: Divide 1715 by 1000. (1 m. to 0.001 km)1715/1000 = 1.715 km/5 secs.
At a temperature of 68°, sound will travel 1.715 km in 5 seconds.

What is the height of the trapezoid?

Answers

Area = 1/2 (sum of bases ) *h

40 *2 = (10+6)*h

80/16 = h

5 unit = h

I really need help with this!!

Answers

sine (x) = opp/hyp definition

= wx/xy substitute

= 12/13 plug in wx

12 and xy= 13

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