Surface Area: Change in Dimensions
Draw your own original rectangular prism and give it your own length, width and height values. (Use different numbers for each dimension but make them as small as you
want to make calculations easier).
a) What is the Surface Area (S1) of the prism?
b) Now triple times 3) the length of the prism and keep the other two dimensions the same. Find the new Surface Area (S2) of the prism. Next divide $2/81. How many
times bigger did the new surface area get?
c) Now triple all three dimensions of your orginal prism. Find the new Surface Area (S3) of the prism. Next divide S3/S1. How many times bigger did the new surface
area get? What happens to the surface area when you double all of the dimensions of a 3-Dimensional figure?
Click "Create Journal Entry" to enter your answer.

Answer:

6m

Step-by-step explanation:

h=3(/V πr^2)=3(226/ π·6^2)≈5.99484

round to 6

No because 5^2 +10^2 is not equavalent to 13^2

by using the pythagoras' theorem

Answer:

downwards

Step-by-step explanation:

Given the quadratic function in standard form

y = ax² + bx + c ( a ≠ 0 )

• If a > 0 then the graph opens upwards

• If a < 0 then the graph opens downwards

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Answer:

  33.3%

Step-by-step explanation:

The selling price of £42 is (1 +40%) times the total purchase price.

  1.40 × purchase price = £42

  purchase price = £42/1.40 = £30

The total profit is 40% of this, so is ...

  £30 × 40% = £12

The purchase price of the skirt is ...

  total cost - glove cost = skirt cost = £30 -3 = £27

The profit on the skirt is ...

  total profit - glove profit = skirt profit = £12 -100% × £3 = £9

Then the percentage profit on the skirt is ...

  skirt profit % = skirt profit / skirt cost × 100% = £9/£27 × 100% = 33.3%

The percentage profit on the cost of the skirt was 33.3%.

Answer:

(a) 129600 J

(b) 81000 J

Step-by-step explanation:

The work done is given by the product of force and the displacement in the direction of force.

Force, F = 500 N

distance, d = 324 m

(a) friction force, f = 100 N

The work done is

W = (F - f) x d

W = (500 - 100) x 324

W = 129600 J

(b) Friction, f = 250 N

The work done is

W = (F - f) d

W = (500 - 250) x 324

W = 81000 J

Answer:

? what is this question asking

Step-by-step explanation:

Answer:

0.00084

Step-by-step explanation:

We are given that

Mean,[tex]\mu=2400[/tex] square feet

Standard deviation, [tex]\sigma=450[/tex]square feet

n=50

We have to find the probability that a random sample of 50 homes in Anytown, USA has mean square footage less than 2200 square feet.

[tex]P(x<2200)=P(\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}<P(\frac{2200-2400}{\frac{450}{\sqrt{50}}})[/tex]

[tex]P(x<2200)=P(Z<\frac{-200}{\frac{450}{\sqrt{50}}})[/tex]

Using the formula

[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]P(x<2200)=P(Z<-3.14)[/tex]

[tex]P(X<2200)=0.00084[/tex]

Hence, the probability that a random sample of 50 homes in Anytown, USA has mean square footage less than 2200 square feet=0.00084

Answer:

x = 105/16

Step-by-step explanation:

2/3x - 1 = 27/8

Add 1 to each side

2/3x - 1+1 = 27/8+1

2/3x = 27/8 + 8/8

2/3x = 35/8

Multiply each side by 3/2

3/2 * 2/3x = 35/8 *3/2

x = 105/16

Answer:

3000

growth

3.4

Step-by-step explanation:

Answer:

k bestie here we go again...

Initial price:  $3200

Function represents growth

Price increases by 4.1% every year

yo so ill give you a trick

the very first number in the equation is ALWAYS the initial price for exponential functions

if the decimal in the parantheses has a 1 in front of it (e.g. 1.041) it's ALWAYS going to be growth

To find how much it increases move the decimal forward by 2 places

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Answer:

  3

Step-by-step explanation:

AB is 1 unit long.

A'B' is 3 units long.

The scale factor is the ratio of these lengths:

  scale factor = A'B'/AB = 3/1 = 3

ABC is dilated by a factor of 3 to get A'B'C'.

Answer:

The car will depreciate at a rate of 21.14% per year.

Step-by-step explanation:

Given that the value of a car will “depreciate” over time, and, for example, a car that was worth $ 24,000 when it was new, is being sold for $ 13,500 three years later, to determine the annual depreciation rate on this car the following calculation must be performed:

13,500 x (1 + X) ^ 1x3 = 24,000

13,500 x (1 + 0.2114) ^ 3 = 24,000

X = 21.14%

Therefore, the car will depreciate at a rate of 21.14% per year.

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Answer:

  A)  (2, ∞) . . . . or C) (-∞, 0) ∪ (2, ∞) if you don't think about it

Step-by-step explanation:

We want ...

  C(x)/x < 100

  (20x +160)/x < 100

  20 +160/x < 100 . . . . . separate the terms on the left

  160/x < 80 . . . . . . . subtract 20

  160/80 < x . . . . . multiply by x/80 . . . . . assumes x > 0

  x > 2 . . . . . . simplify

In interval notation this is (2, ∞).   matches choice A

__

Technically (mathematically), we also have ...

  160/80 > x . . . . and x < 0

which simplifies to x < 0, or the interval (-∞, 0).

If we include this solution, then choice C is the correct one.

_____

Comment on the solution

Since we are using x to count physical items, we want to assume that the practical domain of C(x) is whole numbers, where x ≥ 0, so this second interval is not in the domain of C(x). That is, the average cost of a negative number of items is meaningless.

Answer:

d=10.45t

Step-by-step explanation:

The last one is the answer.

Hope this helps!

--Applepi101

Answer:

D) d=10.45t

Step-by-step explanation:

His distance(d) was 100. And his time(t) was 9.58 seconds.

So 100=9.58x

x≈10.44

The answer is D, because 10.45 is greater than 10.44.

I hope this helps!

Answer:

Following are the solution to the given question:

Step-by-step explanation:

In this the hypothesis is:

[tex]H_{0}:\mu=10\\\\H_{1}:\mu\neq10[/tex]

The bankers assert that their bank's average maturity was distinct from that of ten years, that's why the hypothesis of the alternative.

Answer:

36

Step-by-step explanation:

Total students un the contest = 84

Number of students who gave their speech yesterday:-

[tex] \frac{1}{4} \: of \: total \\ = \frac{1}{4} \times 84 \\ = 21[/tex]

so 21 students gave their speech yesterday

= 63

Number of students who gave their speech today:-

[tex] \frac{3}{7} \: of \: remaining \\ = \frac{3}{7} \times 63 \\ = 27[/tex]

Number of students who have given their speech:-

= 21 + 27

= 48

Number of students who still haven't given their speech :-

= total - 48

= 84 - 48

= 36

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Answer:

  linear

Step-by-step explanation:

The points all lie on a straight line. The relationship is linear.

Answer:

= 1296x √ xy

Step-by-step explanation:

Apply exponent rule: a^b . a^c = a^b + c    3 . 3 = 3^ 1 + 1

= x . 3^1+1 √648x . 4y . 8

Add the numbers: 1 + 1 = 2

= x . 3^2 √648x . 4y . 8

= 3^2 . 144x √ xy

Refine

= 1296x √ xy

Answer:

strength of the relationship between two variables.

Step-by-step explanation:

The Pearson r correlation Coefficient used to measure the relationship or association between two variables. The correlation Coefficient, R ranges between - 1 and 1. As it provides information on both the strength and type of the relationship. The type of relationship could be positive or negative.

The absolute size of r measures Tha strength of the relationship as it ignores the sign. As the Pearson r value moves closer to 1, the higher the strength of the relationship.

Answer:

x = one number

y = second number

Where,

x = y - 3

2y = 4x - 16

Multiply the first equation by 2 and substitute the second equation into it.

2(x=y-3) : 2x = 2y - 6

2x = (4x - 16) - 6

Combine like terms

2x = 4x - 22

2x - 2x + 22 = 4x - 2x -22 + 22

22 = 2x

22/2 = 2x/2

11 = x

Step-by-step explanation:

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Answer:

  D.

Step-by-step explanation:

The linear portion of the curve is in the region x ≥ 2. The only function defined that way is the one in choice D.

Answer:

[tex]\displaystyle \frac{d}{dx}[x^2] = 2x[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Basic Power Rule:

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = x^2[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

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Answer:

  $562,500 per hour

Step-by-step explanation:

The cost will be a minimum where C'(x) = 0.

 C'(x) = 0.56x -0.7 = 0

  x = 0.7/0.56 = 1.25

The cost at that production point is ...

  C(1.25) = (0.28×1.25 -0.7)1.25 +1 = -0.35×1.25 +1 = 0.5625

The minimum production cost is $562,500 per hour for production of 1250 items per hour.

_____

Additional comment

This is different than the minimum cost per item. This level of production gives a per-item cost of $450. The minimum cost per item is $358.30 at a production level of 1890 per hour.

The identity property of 1 says that any number multiplied by 1 keeps its identity. In other words, any number multiplied by 1 stays the same. The reason the number stays the same is because multiplying by 1 means we have 1 copy of the number. For example, 32x1=32.

Answer:

4*12*2

Step-by-step explanation:

it will be the right answer

Answer:

There are 6 boys in group.

Step-by-step explanation:

Since we have given that

Number of arrangement of 4 boys = 12 times the number of arrangement of 2 boys.

So, Let the number of boys in the group be 'x'.

So, Number of boys in the group will be

\begin{gathered}x=\frac{12\times 2}{4}\\\\x=\frac{24}{4}\\\\x=6\end{gathered}

x=

4

12×2

x=

4

24

x=6

Hence, there are 6 boys in the group.

hope it helps you a follow would be appreciated

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Answer:

  [tex](S)\cdot(H)\cdot(E)\cdot(e)\cdot(\theta)\cdot(\epsilon+1+1)\cdot(\xi)\cdot(s)\cdot(h)[/tex]

Step-by-step explanation:

The inverse function of fun(x) is indicated using a -1 exponent. That is ...

  [tex]\text{fun}(\text{fun}^{-1}(x)) = x\\\text{fun}^{-1}(\text{fun}(x)) = x[/tex]

The usual trig identities apply:

  sin²(x) +cos²(x) = 1

  sec²(x) -tan²(x) = 1

  sin(x) = 1/csc(x)

__

So, the expression simplifies to ...

  [tex](S)\cdot(H)\cdot(E)\cdot(e)\cdot(\theta)\cdot(\epsilon+1+1)\cdot(\xi)\cdot(s)\cdot(h)[/tex]

Answer:

Hence, we reject H_0 as There  is sufficient evidence to show that population variance is not 23

Step-by-step explanation:

From the question we are told that:

Sample size [tex]n=30[/tex]

Variance [tex]\sigma= 16.8[/tex]

Significance Level [tex]\alpha=0.05[/tex]

[tex]\sigma = 23[/tex]

Genet=rally the Hypothesis are as follows

Null [tex]H_0=\sigma^2=23[/tex]

Alternative [tex]H_a=\sigma^2 \neq 23[/tex]

Generally the equation for Chi distribution t is mathematically given by

t test statistics

[tex]X^2=\frac{(n-1)\sigma}{\sigma^2}[/tex]

[tex]X^2=\frac{(30-1)16.8^2}{23}[/tex]

[tex]X^2=355.86[/tex]

Therefore

Critical Value

[tex]P_{\alpha,df}[/tex]

Where

[tex]df=29[/tex]

[tex]P_{\alpha,df}=16.0471 and 45.7223[/tex]

[tex]X^2=45.7223[/tex]

Hence, we reject H_0 as There  is sufficient evidence to show that population variance is not 23